question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
sequencelengths 1.02k
1.02k
|
|---|---|---|
<p>Had physics for 2 years now on highschool, but there is a thing I am wondering about.</p>
<p>You know the in the height above the earth surface around where the satellites are (Or the ISS), I've calculated that there actually is a big amount of gravity-forces, even up there. (9.1 - 9.2 <code>m/s^2</code>) - How come that things aren't dragged down to earth, and why are you even weightless?</p>
<p>Why doesn't satellites fall down more frequently, and does it have something to do with their orbit-speed?</p>
<p>Okay, many questions here, but just a curious guy.</p> | 33 | [
-0.014779399149119854,
-0.026665618643164635,
-0.007313819136470556,
-0.025873802602291107,
-0.005651410203427076,
0.005403673276305199,
0.001087464508600533,
-0.021408330649137497,
0.016719017177820206,
-0.051918160170316696,
0.005994896404445171,
0.0546545572578907,
0.033419717103242874,
-0.0021820897236466408,
0.010294980369508266,
0.008587254211306572,
-0.03617650270462036,
0.0007113289320841432,
0.010618291795253754,
-0.00393226183950901,
-0.014469366520643234,
0.019763564690947533,
0.022154439240694046,
0.012154285795986652,
-0.03964419290423393,
-0.035888947546482086,
0.04815765842795372,
0.007242344319820404,
0.04003395512700081,
0.05107336863875389,
0.009138748049736023,
0.00022213287593331188,
-0.016591735184192657,
0.011887448839843273,
0.029774677008390427,
-0.008656734600663185,
-0.05419087037444115,
0.02571154199540615,
-0.0015664970269426703,
0.03713345527648926,
-0.03907046094536781,
-0.06065170466899872,
-0.05522238090634346,
0.04178643599152565,
-0.011366965249180794,
0.01605716533958912,
0.010668187402188778,
0.0031993226148188114,
0.07719950377941132,
-0.07966376841068268,
0.03702081739902496,
-0.013426998630166054,
0.055319879204034805,
0.048830438405275345,
0.00740843778476119,
-0.03832819685339928,
0.08441949635744095,
0.05950881540775299,
-0.03196733072400093,
-0.03703964129090309,
0.002993880771100521,
-0.011567248031497002,
-0.029684336856007576,
-0.009587137959897518,
-0.0008350571151822805,
0.033248621970415115,
-0.06369031220674515,
-0.02112778089940548,
0.024136675521731377,
0.02722456119954586,
0.009146581403911114,
0.003051514970138669,
-0.00677163852378726,
-0.02549205906689167,
-0.016953961923718452,
-0.02454044483602047,
0.052411507815122604,
-0.005009305663406849,
0.06108621880412102,
0.01440361887216568,
-0.022382313385605812,
0.008449507877230644,
0.041584257036447525,
0.029486551880836487,
0.023398712277412415,
-0.02629532665014267,
0.062169093638658524,
-0.0046974290162324905,
-0.0035344555508345366,
0.0537092350423336,
-0.01671450212597847,
0.02091316133737564,
-0.007845005951821804,
0.0009668560232967138,
-0.019192976877093315,
0.029287511482834816,
-0.001942116185091436,
0.06901968270540237,
0.005881772376596928,
0.005419097375124693,
-0.009755479171872139,
-0.015940755605697632,
0.0023169696796685457,
0.08932361751794815,
-0.022079266607761383,
0.005384625401347876,
-0.040137458592653275,
0.019973276183009148,
-0.021257223561406136,
-0.013021733611822128,
-0.022418633103370667,
0.000685631821397692,
-0.005904722027480602,
-0.06909458339214325,
0.022083504125475883,
-0.019858114421367645,
0.028002822771668434,
-0.0223175548017025,
0.008810807950794697,
0.03213581442832947,
0.04540814459323883,
0.008788220584392548,
0.039590250700712204,
-0.03229937702417374,
-0.04718022421002388,
0.04119328781962395,
0.030284171923995018,
0.00035355048021301627,
-0.011194420047104359,
0.01280307024717331,
0.0014366339892148972,
0.011516732163727283,
0.002799189416691661,
-0.02892107330262661,
0.08010850846767426,
0.02239374630153179,
-0.09684284776449203,
-0.04006211832165718,
0.037696730345487595,
0.014400961808860302,
0.0017560124397277832,
-0.0469522699713707,
0.008976442739367485,
-0.012919068336486816,
0.05945699289441109,
0.009195142425596714,
0.02936306968331337,
0.010220151394605637,
0.01984391361474991,
0.031329505145549774,
-0.011849668808281422,
-0.002322650048881769,
-0.018201669678092003,
-0.08931557834148407,
0.022675955668091774,
-0.10804269462823868,
0.019414620473980904,
0.02750730700790882,
0.00909118726849556,
-0.025665173307061195,
0.02236069366335869,
-0.03227028623223305,
0.013233529403805733,
-0.028495358303189278,
-0.01891804300248623,
-0.025098972022533417,
0.053416311740875244,
0.03395983949303627,
0.0022807358764111996,
0.0657777264714241,
0.02595524676144123,
0.03138752281665802,
-0.0013046461390331388,
0.021523363888263702,
0.0006298297084867954,
-0.036503616720438004,
-0.041001126170158386,
-0.045860081911087036,
-0.00013367467909120023,
-0.0023291567340493202,
-0.030031537637114525,
-0.04444767162203789,
0.020917315036058426,
0.005257159937173128,
-0.015505773946642876,
0.04621867835521698,
0.01973695494234562,
-0.016267085447907448,
-0.0008787117549218237,
-0.02674858644604683,
-0.008086868561804295,
-0.06494788825511932,
0.038609642535448074,
-0.044009312987327576,
-0.0015531386015936732,
-0.013428779318928719,
0.02414492703974247,
-0.01633530482649803,
-0.04547860100865364,
-0.00622149184346199,
-0.024498851969838142,
0.032335057854652405,
-0.0012640052009373903,
-0.009196282364428043,
0.0013180545065551996,
0.04299618676304817,
0.012155471369624138,
0.0039444793947041035,
0.01158268190920353,
-0.006891057826578617,
-0.021419508382678032,
-0.022630255669355392,
-0.031633321195840836,
-0.026625819504261017,
0.011008339002728462,
-0.018496867269277573,
0.05602380260825157,
-0.023694638162851334,
-0.014140400104224682,
0.028112923726439476,
-0.0408487394452095,
0.10402043908834457,
0.040038835257291794,
0.01199280098080635,
0.014150863513350487,
0.03916659578680992,
0.0057544712908566,
-0.003930289763957262,
0.00955957267433405,
0.009892153553664684,
-0.06893377006053925,
-0.003247640561312437,
0.01804683916270733,
0.0024210475385189056,
-0.03350013867020607,
0.019364720210433006,
0.042937021702528,
0.05271577090024948,
0.007186161354184151,
0.031246423721313477,
-0.007133156061172485,
-0.017877968028187752,
0.01920274831354618,
-0.0028644257690757513,
0.004001288674771786,
0.034214358776807785,
0.024856746196746826,
0.05577632039785385,
-0.015172192826867104,
-0.017190556973218918,
-0.02797471173107624,
0.023501720279455185,
-0.010569190606474876,
0.032582834362983704,
0.025618670508265495,
-0.0074274251237511635,
0.040707990527153015,
-0.043322086334228516,
0.0033291983418166637,
-0.006828625220805407,
-0.02051234059035778,
-0.007327644620090723,
-0.05287574231624603,
-0.007078362163156271,
0.05386120826005936,
0.002043809276074171,
-0.03652050346136093,
-0.014141065068542957,
0.040721096098423004,
-0.03644116222858429,
-0.005426500458270311,
-0.023560846224427223,
-0.009391283616423607,
-0.05574019253253937,
0.03636196255683899,
0.028578033670783043,
0.003161404747515917,
0.05875479057431221,
-0.010434983298182487,
-0.01855296641588211,
0.0010678431717678905,
-0.034110285341739655,
-0.010335318744182587,
0.013655906543135643,
-0.04469361901283264,
0.02988014928996563,
-0.027249770238995552,
-0.019483041018247604,
0.06242677569389343,
0.014662535861134529,
0.02187223732471466,
0.006585915572941303,
-0.013295617885887623,
-0.0028619563672691584,
-0.023923886939883232,
-0.012340687215328217,
-0.0011908685555681586,
-0.005738124717026949,
0.01972333714365959,
0.05555851757526398,
-0.017907211557030678,
-0.0025759199634194374,
0.04524526372551918,
-0.07933181524276733,
-0.04403243213891983,
-0.001155437552370131,
0.03731833025813103,
-0.015224723145365715,
-0.053497616201639175,
-0.02577589638531208,
-0.00931340828537941,
-0.055346015840768814,
-0.0047247703187167645,
-0.02597641386091709,
-0.038891665637493134,
0.0020188165362924337,
-0.0047887093387544155,
0.056276172399520874,
-0.017442580312490463,
-0.027623744681477547,
0.09423621743917465,
0.01553153432905674,
-0.02174678072333336,
-0.016749918460845947,
-0.017323963344097137,
-0.041847169399261475,
0.012166256085038185,
0.05252630636096001,
0.025230638682842255,
-0.04591406136751175,
-0.023754337802529335,
0.05466820299625397,
0.027590012177824974,
0.0005388291901908815,
-0.002144484082236886,
-0.006997698452323675,
-0.028901780024170876,
0.024364419281482697,
-0.013358740136027336,
0.052388034760951996,
0.020346827805042267,
-0.043120741844177246,
0.013154060579836369,
0.0058089750818908215,
0.02392052672803402,
-0.01381854247301817,
-0.07299376279115677,
0.05426998808979988,
-0.037318985909223557,
-0.005790454801172018,
0.024714171886444092,
-0.008034249767661095,
-0.00017535693768877536,
-0.009555865079164505,
0.009039665572345257,
-0.00990871898829937,
0.042601149529218674,
0.016241228207945824,
-0.040922507643699646,
0.01763978786766529,
0.09535599499940872,
-0.032496530562639236,
-0.048472605645656586,
0.003445192240178585,
0.010024712421000004,
-0.006830404046922922,
-0.019259106367826462,
-0.01159067451953888,
0.04999186471104622,
0.017979618161916733,
0.050771504640579224,
0.019788485020399094,
-0.03813421353697777,
0.017028938978910446,
-0.08169122785329819,
0.00015385592996608466,
-0.016836971044540405,
0.05328221619129181,
-0.02559894137084484,
0.055352598428726196,
0.008193078450858593,
0.04441433772444725,
0.020411502569913864,
0.006733024958521128,
-0.0760815218091011,
0.007235834840685129,
-0.03495197743177414,
-0.03576945886015892,
0.023907357826828957,
0.024599799886345863,
-0.033059313893318176,
-0.03231704607605934,
-0.012632123194634914,
-0.015080546028912067,
0.021590035408735275,
-0.041339654475450516,
0.005159085616469383,
-0.034878071397542953,
0.0038781396578997374,
-0.022162796929478645,
0.014641992747783661,
0.015402937307953835,
-0.0379270538687706,
0.04342300072312355,
0.023350464180111885,
-0.019316280260682106,
-0.034808170050382614,
0.007154086139053106,
-0.0036667545791715384,
0.01552544068545103,
0.006395332049578428,
0.005915602669119835,
0.029296863824129105,
-0.015234577469527721,
-0.01194168534129858,
-0.0016929731937125325,
0.03174784779548645,
0.018501965329051018,
0.0034941418562084436,
-0.0263486560434103,
-0.042832545936107635,
-0.04726317897439003,
0.008769804611802101,
0.029735980555415154,
-0.0013758179266005754,
-0.02982255443930626,
0.018603043630719185,
0.014418521896004677,
-0.0003801072889473289,
0.04119810089468956,
0.029101019725203514,
-0.008104290813207626,
0.0057539548724889755,
-0.0572565458714962,
-0.027031531557440758,
-0.0465698316693306,
0.012657216750085354,
0.04364582523703575,
-0.006804082076996565,
-0.055737029761075974,
-0.0040474641136825085,
0.020382845774292946,
0.00016991188749670982,
0.0029071064200252295,
-0.009192326106131077,
0.029804375022649765,
0.04408044368028641,
-0.011494425125420094,
0.006040419917553663,
0.008680559694766998,
0.016239391639828682,
0.03629602491855621,
-0.004987969994544983,
0.01570323295891285,
-0.09948867559432983,
-0.036257531493902206,
0.02624211087822914,
0.03237314894795418,
0.002337939105927944,
-0.009808521717786789,
-0.054566606879234314,
-0.015593253076076508,
0.03833775222301483,
-0.01841895654797554,
0.023105943575501442,
-0.016491252928972244,
0.028276287019252777,
-0.019238244742155075,
-0.026985235512256622,
0.013419028371572495,
-0.012671496719121933,
-0.011645466089248657,
0.02347565069794655,
-0.008844751864671707,
-0.0020220924634486437,
0.0021050781942903996,
0.0490998737514019,
0.04140158370137215,
0.05736220255494118,
0.028935156762599945,
0.012473102658987045,
-0.01527485903352499,
-0.006052741315215826,
-0.03820892050862312,
-0.06064087897539139,
-0.02021046169102192,
-0.004845866002142429,
0.01362217590212822,
0.04906521737575531,
-0.03483560308814049,
-0.05675967037677765,
0.003831826616078615,
0.0009646927937865257,
0.005736552178859711,
-0.0038980229292064905,
-0.028954235836863518,
0.028227221220731735,
0.07337628304958344,
0.00004348440052126534,
0.0007237067329697311,
0.030921606346964836,
-0.0024005738086998463,
-0.02722533605992794,
-0.03581356629729271,
0.017691245302557945,
-0.021611781790852547,
-0.009534699842333794,
-0.0049414015375077724,
-0.01434930507093668,
-0.021540435031056404,
0.03227025270462036,
0.0050466484390199184,
0.018389051780104637,
-0.015048595145344734,
-0.02966674603521824,
-0.021960947662591934,
0.046546585857868195,
0.018649611622095108,
-0.0023411165457218885,
0.031403135508298874,
0.01524714007973671,
-0.040402140468358994,
-0.04804859310388565,
0.001963578863069415,
0.029529128223657608,
-0.04471490904688835,
0.0018812405178323388,
-0.012006111443042755,
-0.02670610323548317,
-0.023572299629449844,
-0.013734636828303337,
0.002635966520756483,
-0.05220583826303482,
0.06702900677919388,
-0.022319024428725243,
-0.01764732599258423,
0.034058742225170135,
-0.06247960403561592,
-0.01415184885263443,
-0.026761597022414207,
-0.005496598314493895,
0.0500878170132637,
-0.01836314983665943,
0.004569234326481819,
0.013089543208479881,
0.024374302476644516,
-0.06412902474403381,
-0.040585242211818695,
0.0521928109228611,
0.03968228027224541,
0.003486885456368327,
-0.032441332936286926,
-0.010847042314708233,
-0.03565869480371475,
-0.02130173146724701,
-0.009768414311110973,
0.032152965664863586,
-0.04205504059791565,
0.0011762685608118773,
0.049995098263025284,
0.011509277857840061,
0.05094658210873604,
-0.0076023731380701065,
-0.042156241834163666,
0.010723339393734932,
0.002080637728795409,
0.006686364766210318,
-0.022974083200097084,
0.09141746163368225,
-0.0250464528799057,
-0.03973691910505295,
-0.012732908129692078,
-0.051772553473711014,
0.02553129941225052,
-0.02511586621403694,
0.021929455921053886,
0.03817668557167053,
0.004771078936755657,
0.03950604423880577,
0.01665622368454933,
0.044452566653490067,
-0.021492864936590195,
0.02386944554746151,
0.005402770824730396,
0.0009583247592672706,
-0.028999367728829384,
-0.03322741389274597,
0.00791907124221325,
-0.00923524983227253,
0.06675206124782562,
0.01174770575016737,
0.04607938975095749,
-0.01793842390179634,
-0.04855214059352875,
0.0176834799349308,
0.010237129405140877,
0.013520941138267517,
0.0005041350377723575,
-0.002599132712930441,
0.0195922814309597,
0.006352139171212912,
-0.0034887923393398523,
-0.009932427667081356,
-0.024783918634057045,
-0.011097717098891735,
0.07401333004236221,
-0.047149378806352615,
0.01790742389857769,
-0.0058684758841991425,
-0.025365745648741722,
0.01623867079615593,
-0.022472742944955826,
-0.015777170658111572,
-0.007494181860238314,
0.009904664941132069,
-0.005921206437051296,
-0.012538633309304714,
-0.0030827242881059647,
0.020413842052221298,
0.04896558076143265,
-0.041364897042512894,
0.006420114543288946,
0.038035955280065536,
-0.018785787746310234,
0.021605022251605988,
-0.007683364674448967,
-0.011860316619277,
0.041395142674446106,
-0.025097055360674858,
0.056952472776174545,
0.029733765870332718,
-0.019622499123215675,
0.045376669615507126,
0.01218681875616312,
0.014450429007411003,
-0.03092978335916996,
-0.02114911377429962,
-0.058898262679576874,
0.013904987834393978,
0.013705819845199585,
-0.008734681643545628,
-0.020609652623534203,
0.01386965624988079,
0.027044102549552917,
0.05449110269546509,
0.014725208282470703,
0.0055692074820399284,
-0.05574946478009224,
-0.017105814069509506,
-0.011590709909796715,
-0.05154964700341225,
0.039410870522260666,
0.012280695140361786,
-0.00262457225471735,
0.010760636068880558,
-0.029337812215089798,
0.007925346493721008,
0.028138935565948486,
0.029724059626460075,
-0.02818657085299492,
0.06975078582763672,
-0.011873317882418633,
-0.0041315434500575066,
-0.01873593032360077,
-0.00549599714577198,
0.0943913385272026,
0.01589524745941162,
-0.00018281812663190067,
-0.023831011727452278,
0.015657147392630577,
-0.03019465133547783,
0.023618461564183235,
-0.038797635585069656,
-0.016770362854003906,
0.009933923371136189,
0.013630484230816364,
0.0057031456381082535,
0.033711954951286316,
-0.03704700991511345,
-0.02180751971900463,
0.06035669893026352,
-0.027083322405815125,
-0.04648321121931076,
-0.03299416974186897,
0.03163765370845795,
-0.018495507538318634,
0.006915918551385403,
-0.02931293286383152,
0.047698065638542175,
-0.024145564064383507,
0.0028744081500917673,
-0.044829897582530975,
-0.039232805371284485,
0.0056475489400327206,
-0.012137757614254951,
-0.08536387979984283,
0.01087778527289629,
0.0075840940698981285,
-0.033682744950056076,
-0.06460851430892944,
0.05177830532193184,
0.019658416509628296,
-0.019151218235492706,
0.014882992021739483,
0.004967434331774712,
-0.020158153027296066,
0.011202951893210411,
0.013391620479524136,
-0.00869245920330286,
-0.04475957155227661,
0.025786198675632477,
-0.0427069365978241,
0.03541460633277893,
-0.025467243045568466,
-0.02401876263320446,
0.010492472909390926,
0.011975818313658237,
-0.01793633960187435,
-0.042824506759643555,
-0.0017379383789375424,
-0.007487999740988016,
0.01740230992436409,
-0.01100810058414936,
-0.023196794092655182,
0.013009966351091862,
0.002652108669281006,
-0.0123465396463871,
0.01360365841537714,
0.017591262236237526,
0.029997846111655235,
0.026236416772007942,
-0.038702793419361115,
0.042510438710451126,
-0.029434992000460625,
0.026333613321185112,
-0.011625547893345356,
0.0000019145707028656034,
-0.03796457499265671,
0.001034330460242927,
0.012417490594089031,
0.026614341884851456,
0.027390334755182266,
0.018726874142885208,
-0.01974712312221527,
-0.030005833134055138,
0.010873513296246529,
0.06387477368116379,
-0.013257515616714954,
0.009337175637483597,
-0.04149787127971649,
-0.007228709291666746,
0.0035605242010205984,
0.009921053424477577,
0.031232107430696487,
0.013354485854506493,
-0.03598318248987198,
0.008402617648243904,
-0.00430291285738349,
-0.03700237721204758,
-0.026318907737731934,
0.010379059240221977,
0.005732298828661442,
0.005408086348325014,
0.007605285383760929,
0.03089219145476818,
0.031187787652015686,
0.002402558224275708,
-0.015430792234838009,
0.011993602849543095,
-0.037715934216976166,
0.02086450345814228,
-0.0029528613667935133,
-0.01630442775785923,
-0.010858317837119102,
0.017785916104912758,
-0.009232250042259693,
-0.013586712069809437,
-0.0169267226010561,
-0.007034675218164921,
0.005041475407779217,
0.0032695692498236895,
0.07166503369808197,
-0.007038723677396774,
0.04813343286514282,
-0.027033070102334023,
0.03717173635959625,
-0.03586025536060333,
0.007589221931993961,
-0.06229975447058678,
0.01566624827682972,
-0.012557903304696083,
0.00023486763529945165,
-0.03452623635530472,
0.00021751924941781908,
-0.06731778383255005,
-0.010882128030061722,
0.0061200764030218124,
0.0001810737157939002,
-0.013004994951188564,
-0.023000046610832214,
0.03151814639568329,
-0.03841755539178848,
0.040782731026411057,
-0.025520553812384605,
-0.025607086718082428,
0.029416635632514954,
-0.025244243443012238,
-0.07401743531227112,
0.027974458411335945,
-0.02686339244246483,
0.02182036265730858,
0.01929364539682865,
-0.06056886538863182,
-0.03602851927280426,
0.06655078381299973,
-0.03015931509435177,
0.019042862579226494,
-0.004859349690377712,
0.010059374384582043,
0.0020728118252009153,
0.02279607579112053,
0.010744133964180946,
-0.055445101112127304,
0.024445075541734695,
0.032220080494880676,
0.024199770763516426,
0.000607352121733129,
0.01594550348818302,
-0.0388958714902401,
-0.010751004330813885,
0.005858547054231167,
0.04044588655233383,
0.005018235184252262,
0.011492732912302017,
0.03942509740591049,
-0.049136821180582047,
0.025359194725751877,
0.015100793913006783,
0.01725047640502453,
-0.05041630566120148,
-0.004915124271064997,
-0.0002285454684169963,
-0.0015495683765038848,
0.03672872856259346,
-0.04591624438762665,
-0.016291694715619087,
0.02733040228486061,
-0.05705553665757179,
0.03242422640323639,
-0.04324089363217354,
-0.024936946108937263,
-0.02454455755650997,
-0.009783326648175716,
0.005808809772133827,
0.05024287477135658,
0.029702968895435333,
0.03111538290977478,
-0.025855666026473045,
-0.010615837760269642,
-0.004420414101332426,
-0.01591261476278305,
-0.02052311971783638,
0.02881184034049511,
-0.02830190397799015,
0.0068410164676606655,
0.03610002622008324,
-0.010380235500633717,
-0.003918022383004427,
0.019922122359275818,
0.038451045751571655,
0.005138075910508633,
0.015760818496346474,
-0.009623780846595764,
-0.007741526234894991,
0.013233079575002193,
0.00027390997274778783,
0.002362734405323863,
-0.03005167469382286,
0.039802808314561844,
0.015290865674614906,
0.03761378675699234,
-0.007223826367408037,
0.023305265232920647,
0.016980240121483803,
-0.028996223583817482,
-0.01338118501007557,
0.0055318595841526985,
-0.022572249174118042,
0.03779767453670502,
-0.0002752714208327234,
0.0066837226040661335,
0.045145679265260696,
-0.0402945801615715,
-0.013698240742087364,
-0.08273592591285706,
-0.003559018950909376,
0.028600355610251427,
-0.020259328186511993,
-0.0054083107970654964,
0.03912568837404251,
0.026416895911097527,
-0.0038837026804685593,
-0.011886951513588428,
0.01055124681442976,
-0.010878614149987698,
-0.02538292668759823,
-0.004169389605522156,
0.012538688257336617,
-0.011921977624297142,
0.0002502491988707334,
-0.027538003399968147,
-0.03352862223982811,
0.043376628309488297,
0.03902187570929527,
0.01187538355588913,
0.009303806349635124,
-0.04766733571887016,
0.010121145285665989,
-0.05694285035133362,
0.031198708340525627,
-0.027313970029354095,
0.030103012919425964,
-0.03843636438250542,
-0.04561217501759529,
-0.003827524371445179,
0.015056719072163105,
0.03834765776991844,
-0.0035470102448016405,
0.0452067106962204,
0.03076072223484516,
-0.0004088138521183282,
-0.002823157934471965,
-0.04524354264140129,
0.024903830140829086,
0.03917127847671509,
-0.058441974222660065,
0.016979878768324852,
-0.00688865827396512,
0.011570717208087444,
-0.008453377522528172,
0.029693251475691795,
-0.014646301977336407,
0.04399115592241287,
-0.0132215591147542,
-0.0029625496827065945,
0.04331010580062866,
0.02907206304371357,
-0.015188416466116905,
0.07208950817584991,
0.0030285969842225313,
0.009807423688471317,
0.06532930582761765,
-0.028848780319094658,
0.004823885392397642,
0.06965664774179459,
-0.01176442764699459,
0.011591054499149323,
-0.05643868073821068,
-0.020575271919369698,
0.01318829320371151,
-0.03121098503470421,
-0.0012027916964143515,
0.052150458097457886,
-0.035205669701099396,
0.00043316837400197983,
0.0830707848072052,
0.02826710045337677,
0.03437087684869766,
-0.010608475655317307,
0.01172454934567213,
0.056386798620224,
-0.03516902029514313,
0.021023912355303764,
0.056650128215551376,
0.04603969678282738,
-0.022383760660886765,
0.013213058933615685,
0.05185722932219505,
0.04845188558101654,
0.01648895815014839,
0.02227022498846054,
0.0322701595723629,
-0.039974503219127655,
-0.036870285868644714,
-0.008949212729930878,
0.005930469371378422,
0.010207189247012138,
0.03851493075489998,
-0.029744209721684456,
0.07753872871398926,
-0.019384756684303284,
-0.005107562057673931,
0.017744608223438263,
-0.006528861820697784,
0.026901446282863617,
0.00001128572694142349,
-0.0249642226845026,
0.024833928793668747,
-0.0018859811825677752,
-0.03201828524470329,
-0.007015565875917673,
0.007752662058919668,
0.054017435759305954,
0.01835797354578972,
0.053169455379247665,
-0.02086011879146099,
0.0021869176998734474,
0.0033745449036359787,
-0.030217021703720093,
-0.043083563446998596,
-0.016210170462727547,
0.06645356118679047,
0.027623433619737625,
0.0027171410620212555,
-0.012004651129245758,
-0.0061385296285152435,
-0.050310008227825165,
0.04502628743648529,
-0.04836714640259743,
-0.03003462590277195,
-0.033493321388959885,
0.032771095633506775,
-0.014475544914603233,
-0.0013296164106577635
] |
<p>My book about quantum mechanics states that the hamiltonian, defined as $H=i\hbar\frac{\partial}{\partial t}$ is a hermitian operator. But i don't really see how I have to interpret this. First of all: from which to which space is this operator working? They are defining a vectorspace called the "wavefunctionspace $F$" which contains all square-integrable functions that are continious and infinite differentiable (and everywhere defined). But it looks to me, that if the hamiltonian acts on this space, it's not necessary true that the image of a random vector of $F$ is again in $F$. </p>
<p>I think in fact, that there are some vectors of $F$ so that the hamiltonian of those vectors is not an element of $F$ (so that it's not an endomorphism on $F$). And if the hamiltonian has to be hermitian, it has to be an endomorphism on some space. </p>
<p>If we define instead the vectorspace $V$, which is the same space as $F$ but where functions don't have to be square-integrable, the hamiltonian will be an endomorphism (so at first I thought this was the solution). But now the inner product on functions $<f,g> = \int_{-\infty}^\infty{f^*g}$ which was defined well on $F$ because the integral will always exist if $f$ and $g$ are function of $F$, is no longer properly defined. </p>
<p>I hope someone can clarify how I have to interpet this operator (the same question holds in fact for some other operators). </p> | 1,975 | [
0.023822279646992683,
-0.02174692042171955,
0.030364062637090683,
-0.03365679085254669,
0.02865920029580593,
0.01474575512111187,
-0.01371162012219429,
-0.029575275257229805,
0.016096943989396095,
-0.03825146332383156,
0.017443442717194557,
0.029737578704953194,
0.07758673280477524,
-0.016691016033291817,
0.03824090212583542,
0.005480507854372263,
-0.036721181124448776,
-0.030252667143940926,
-0.04206529259681702,
0.012051494792103767,
-0.0004951460286974907,
0.0655997022986412,
0.02737290970981121,
-0.013264359906315804,
-0.0014696430880576372,
0.000055937780416570604,
-0.0061636115424335,
0.017611050978302956,
0.040690384805202484,
0.07328709959983826,
-0.021375836804509163,
-0.02126835472881794,
0.0033408256713300943,
0.03354191035032272,
-0.0148210683837533,
0.010446982458233833,
-0.025754733011126518,
-0.02234378643333912,
0.007613149471580982,
-0.023452164605259895,
-0.04437030106782913,
0.003951197490096092,
-0.03749438375234604,
0.06598535180091858,
-0.0042419154196977615,
0.04551068693399429,
0.013022534549236298,
-0.021732773631811142,
0.008372941985726357,
-0.03627924621105194,
0.07757176458835602,
0.013382777571678162,
0.048512835055589676,
0.03878186643123627,
-0.005996568128466606,
0.013972913846373558,
0.061543289572000504,
0.078285351395607,
0.0014378802152350545,
-0.03229917213320732,
-0.023966047912836075,
-0.03398177772760391,
-0.021692216396331787,
-0.024417219683527946,
-0.029147928580641747,
-0.0034529517870396376,
0.004126149229705334,
-0.023108424618840218,
0.006125659216195345,
0.0015603967476636171,
-0.007694831117987633,
0.010077853687107563,
0.028484031558036804,
-0.06741952151060104,
0.02890200726687908,
-0.014562851749360561,
0.0368504524230957,
0.029176954180002213,
0.02893543429672718,
-0.022028272971510887,
0.0018665301613509655,
0.025189287960529327,
0.007802101317793131,
0.01728973537683487,
0.011277317069470882,
0.02208949811756611,
0.06730543822050095,
0.002755817724391818,
0.021037641912698746,
0.03369554132223129,
-0.04020922631025314,
0.015189765021204948,
0.040625207126140594,
0.006730509456247091,
-0.046246856451034546,
0.012541418895125389,
0.0012727899011224508,
0.02831251360476017,
-0.034560900181531906,
-0.01932629756629467,
0.023329662159085274,
-0.036431510001420975,
0.006651515606790781,
0.06574548780918121,
-0.021567795425653458,
-0.009920128621160984,
-0.045137543231248856,
0.007906543090939522,
0.02137373387813568,
-0.011617656797170639,
-0.030754605308175087,
0.044847141951322556,
-0.003893624059855938,
-0.013354946859180927,
0.010628810152411461,
-0.005199938081204891,
-0.010196414776146412,
0.005621613468974829,
0.04726537689566612,
0.08452539145946503,
0.054681722074747086,
-0.031206639483571053,
0.045699190348386765,
-0.047481242567300797,
-0.07172732055187225,
0.03654928505420685,
0.021575339138507843,
0.016098596155643463,
-0.06805046647787094,
0.023060278967022896,
0.04468400031328201,
-0.029514197260141373,
0.010197601281106472,
0.005778050981462002,
0.04830307140946388,
-0.022529853507876396,
-0.0936790257692337,
-0.08040265738964081,
0.031718939542770386,
-0.016369912773370743,
-0.0016657194355502725,
-0.09104360640048981,
0.026011865586042404,
0.021564600989222527,
0.07452675700187683,
-0.015567653812468052,
0.02946707420051098,
0.004808032885193825,
0.005037026014178991,
0.0011865532724186778,
-0.005081282462924719,
-0.02477930299937725,
-0.021456662565469742,
-0.017973849549889565,
0.021778620779514313,
-0.05144049972295761,
0.025575464591383934,
0.0229890625923872,
0.00731523334980011,
-0.040361158549785614,
0.08159911632537842,
-0.027271538972854614,
0.011357929557561874,
-0.012856731191277504,
0.023278674110770226,
-0.03379996865987778,
0.051081012934446335,
0.03441472351551056,
0.028784768655896187,
0.028432022780179977,
0.03345496952533722,
0.018974212929606438,
0.011761394329369068,
0.038610950112342834,
0.01061831321567297,
-0.03961572051048279,
-0.014157246798276901,
-0.00832066684961319,
0.006353445816785097,
0.022099412977695465,
0.003294782480224967,
-0.005193861201405525,
-0.012022880837321281,
0.02468084543943405,
0.0014473891351372004,
0.03674935922026634,
0.00037673069164156914,
0.019560595974326134,
-0.011991907842457294,
-0.05201144143939018,
-0.009382214397192001,
-0.04649611562490463,
0.030852649360895157,
0.03543664887547493,
-0.014083817601203918,
0.045222241431474686,
0.023812174797058105,
0.01785886287689209,
-0.014506910927593708,
-0.046559888869524,
-0.010375105775892735,
0.007878650911152363,
0.004514063708484173,
-0.00916402880102396,
0.03897247463464737,
0.058339957147836685,
0.03393407166004181,
0.0063840895891189575,
0.03687682002782822,
-0.01159820519387722,
-0.02901163510978222,
0.03205198422074318,
-0.022622626274824142,
0.026220306754112244,
-0.011484573595225811,
-0.013040764257311821,
-0.014165248721837997,
-0.009706743061542511,
0.004740338772535324,
0.014261975884437561,
-0.03448110818862915,
0.026958536356687546,
0.0022013166453689337,
0.03998127579689026,
0.014232267625629902,
0.061066895723342896,
0.007556939963251352,
0.00557048711925745,
-0.013267319649457932,
-0.012985697016119957,
-0.022302011027932167,
0.027128728106617928,
0.025028841570019722,
0.025187909603118896,
-0.025403883308172226,
0.0024431876372545958,
0.03670835867524147,
0.019642509520053864,
0.037150461226701736,
0.03172670304775238,
-0.012966881506145,
-0.02428019978106022,
0.004631747025996447,
-0.0116749731823802,
0.03809283301234245,
0.01359793171286583,
-0.02349533513188362,
0.0012245937250554562,
0.0005351504660211504,
0.02456311695277691,
-0.02229464426636696,
0.06675365567207336,
-0.02244406007230282,
0.028470467776060104,
0.009508960880339146,
0.007978901267051697,
0.016672441735863686,
-0.015571690164506435,
-0.016542384400963783,
0.011687930673360825,
-0.0004753345565404743,
-0.01873278245329857,
-0.02884095534682274,
-0.028640761971473694,
0.010491389781236649,
0.0011640378506854177,
-0.033670637756586075,
-0.013470612466335297,
0.017668116837739944,
-0.021263785660266876,
0.00945440772920847,
-0.0022447481751441956,
0.007558558136224747,
-0.021852368488907814,
0.010483545251190662,
0.024134354665875435,
0.014501245692372322,
0.01288010086864233,
-0.03444148600101471,
-0.016396258026361465,
-0.018683942034840584,
-0.052540652453899384,
0.0416044220328331,
-0.003405645489692688,
-0.051920924335718155,
0.032941270619630814,
-0.08601914346218109,
-0.03792925924062729,
0.03779609501361847,
0.005822408013045788,
0.02272476814687252,
-0.036498092114925385,
-0.02382737584412098,
-0.06337545812129974,
-0.00031117169419303536,
-0.054065439850091934,
-0.003451901488006115,
-0.04523979499936104,
-0.014153295196592808,
0.0536685511469841,
-0.005273572634905577,
-0.017477696761488914,
-0.007178919855505228,
0.0008844431722536683,
-0.06550990790128708,
-0.008625688031315804,
-0.02759198658168316,
0.03358934819698334,
-0.03931426256895065,
0.014032592996954918,
0.0475454144179821,
-0.031195586547255516,
-0.029300164431333542,
-0.06573861092329025,
-0.07199244201183319,
-0.022377418354153633,
0.024488801136612892,
-0.009959297254681587,
0.01583392173051834,
-0.04230840131640434,
0.10415007919073105,
0.017062891274690628,
-0.03231760859489441,
-0.012790258973836899,
-0.004367240238934755,
-0.006077338941395283,
-0.032632503658533096,
-0.012198632583022118,
0.017568163573741913,
-0.009889858774840832,
0.07870377600193024,
0.02224811352789402,
0.003894336288794875,
0.03292655572295189,
-0.010918661952018738,
-0.036375436931848526,
0.04065650701522827,
0.006890218239277601,
0.03573719784617424,
0.051410265266895294,
-0.010548006743192673,
-0.00427460391074419,
0.015777280554175377,
-0.015737419947981834,
-0.0018439923878759146,
0.0033506532199680805,
-0.027225153520703316,
0.052342671900987625,
0.0019961155485361814,
0.012236393988132477,
-0.04702062904834747,
0.04492154344916344,
0.00864431168884039,
-0.02210833691060543,
0.021558521315455437,
0.02308144047856331,
0.0535246878862381,
-0.03257877752184868,
0.04970501363277435,
-0.0022920328192412853,
0.007037892937660217,
-0.022809932008385658,
-0.02075772173702717,
-0.008146128617227077,
-0.006081677041947842,
0.010212743654847145,
-0.0027822835836559534,
-0.05994658172130585,
0.027800003066658974,
0.04256318509578705,
0.023029016330838203,
-0.03297140449285507,
-0.025511519983410835,
-0.0008411175804212689,
-0.007507679983973503,
-0.0021753881592303514,
0.02037401869893074,
0.020711509510874748,
0.019496975466609,
0.029147684574127197,
0.01839105784893036,
0.017879027873277664,
0.02483401633799076,
0.025621652603149414,
-0.06952184438705444,
0.011374659836292267,
0.0004710417124442756,
-0.022350704297423363,
-0.023285146802663803,
-0.0005767757538706064,
0.003673211205750704,
-0.010176490992307663,
-0.039948008954524994,
-0.0018493165262043476,
-0.0336163304746151,
-0.06403665244579315,
-0.0024952576495707035,
-0.039092984050512314,
-0.027460820972919464,
-0.024952564388513565,
0.011163579300045967,
0.04014065861701965,
-0.01696217991411686,
-0.0060677677392959595,
0.03530997782945633,
-0.03787853941321373,
0.005207464564591646,
-0.014652257785201073,
-0.020776376128196716,
0.050457343459129333,
0.0065175811760127544,
0.04536405950784683,
0.040552474558353424,
-0.003145549912005663,
0.001415723585523665,
0.004212032537907362,
0.06818990409374237,
0.003955824300646782,
-0.025736773386597633,
0.04076270014047623,
-0.06251183152198792,
0.016407528892159462,
-0.01564982905983925,
0.04138406366109848,
0.027276957407593727,
0.008015003055334091,
0.03979962691664696,
0.0124172018840909,
-0.02949143387377262,
0.011715451255440712,
0.01058669202029705,
0.02289613150060177,
-0.0018056812696158886,
-0.032409850507974625,
-0.02005869895219803,
-0.029278505593538284,
-0.028334522619843483,
0.016684165224432945,
-0.039028242230415344,
-0.017495328560471535,
0.004069228190928698,
0.00797043927013874,
-0.006586425006389618,
-0.022598445415496826,
-0.008431591093540192,
-0.027422279119491577,
-0.024951357394456863,
-0.004772714339196682,
-0.01190582849085331,
0.01309122797101736,
0.03715450316667557,
0.04000192880630493,
0.038432490080595016,
-0.009265901520848274,
-0.038989536464214325,
-0.014581368304789066,
0.047092825174331665,
0.012374214828014374,
-0.00376911461353302,
-0.01861504651606083,
-0.02976459637284279,
-0.058270640671253204,
0.057044100016355515,
-0.010649378411471844,
0.04501129686832428,
-0.007453997153788805,
-0.03373317793011665,
-0.0044943224638700485,
-0.05933854356408119,
-0.005298356991261244,
-0.018705932423472404,
0.0024203453212976456,
-0.00021256878972053528,
-0.03574017807841301,
0.0073737334460020065,
-0.05046593397855759,
0.008611634373664856,
-0.00001644845360715408,
0.05692113935947418,
0.001686831354163587,
0.0004918552585877478,
-0.006449921987950802,
0.05996491387486458,
-0.02421807125210762,
-0.05086887255311012,
0.008763543330132961,
-0.019230637699365616,
0.00810207799077034,
0.042323626577854156,
-0.03882585093379021,
-0.06306662410497665,
0.02915577031672001,
-0.0021290024742484093,
-0.015258438885211945,
0.03052867017686367,
-0.016518406569957733,
0.06683745980262756,
0.020641179755330086,
0.020344002172350883,
0.04968321695923805,
0.04077671840786934,
0.026137152686715126,
-0.00009805407898966223,
-0.04833041876554489,
0.020485058426856995,
-0.07364339381456375,
-0.007686421275138855,
-0.06606099754571915,
-0.05247030779719353,
-0.024423953145742416,
0.030587857589125633,
0.0030788155272603035,
-0.006043229717761278,
-0.017782507464289665,
-0.03417328745126724,
-0.0010946867987513542,
0.03146295249462128,
-0.018108606338500977,
-0.01575550250709057,
-0.007210932672023773,
0.022598320618271828,
-0.0028118484187871218,
-0.03125999867916107,
-0.04518977925181389,
-0.0184872318059206,
-0.004552013706415892,
0.02961905486881733,
0.010776225477457047,
0.04151591286063194,
-0.029931331053376198,
-0.022667262703180313,
-0.007501482032239437,
-0.042398225516080856,
0.002941515762358904,
-0.008496222086250782,
-0.01998753845691681,
0.013130725361406803,
-0.03942141681909561,
-0.04417991265654564,
-0.029457271099090576,
-0.014981734566390514,
-0.003329053521156311,
-0.00406021298840642,
0.012868053279817104,
0.04007836431264877,
0.01922426000237465,
-0.08232732117176056,
-0.05253206193447113,
-0.003091016784310341,
0.007852775976061821,
-0.03489458188414574,
-0.01291949488222599,
0.03301997855305672,
-0.02662564255297184,
0.011573060415685177,
-0.011801829561591148,
0.03959428519010544,
-0.03561153635382652,
-0.0034361016005277634,
0.0324845127761364,
0.009277702309191227,
0.05124703794717789,
-0.007185495458543301,
0.003531311871483922,
0.025002995505928993,
-0.013116613030433655,
-0.009930615313351154,
0.015487173572182655,
0.05561833456158638,
-0.02704530395567417,
-0.010361496359109879,
-0.0008616566192358732,
0.023243380710482597,
0.033361852169036865,
0.004804648924618959,
-0.0017226400086656213,
0.02939729578793049,
0.037569958716630936,
0.007890520617365837,
-0.010167078115046024,
-0.004032597411423922,
0.02199765481054783,
0.023386947810649872,
0.04559704661369324,
0.01275051198899746,
-0.012814655900001526,
-0.04242635890841484,
0.020623495802283287,
-0.041688092052936554,
0.00866665504872799,
0.008989590220153332,
0.07431143522262573,
-0.0019133706809952855,
0.02392539381980896,
0.021217864006757736,
-0.01741665042936802,
-0.014110147021710873,
-0.027266850695014,
-0.025704272091388702,
-0.01949024572968483,
0.0116210812702775,
-0.04524029418826103,
-0.034347984939813614,
-0.06625950336456299,
0.04092266410589218,
0.054519347846508026,
-0.014137113466858864,
0.03144727274775505,
0.01272618304938078,
0.005720321089029312,
-0.0027753172907978296,
0.001058235764503479,
-0.03194073215126991,
-0.007523542735725641,
0.0019474070286378264,
0.010969452559947968,
-0.008935913443565369,
0.0005344487144611776,
0.05074995383620262,
0.017317574471235275,
-0.0383964478969574,
0.033216722309589386,
0.018419910222291946,
0.04212527349591255,
0.014479145407676697,
0.020702490583062172,
-0.046355124562978745,
0.014345617033541203,
-0.021902479231357574,
0.06102748587727547,
0.013666119426488876,
-0.009528949856758118,
0.033328764140605927,
0.023539036512374878,
-0.01511872373521328,
-0.01718669757246971,
-0.021498113870620728,
-0.03742189705371857,
0.00898805446922779,
0.022114630788564682,
0.010280189104378223,
-0.0034579013008624315,
0.0027541699819266796,
0.006474959664046764,
-0.0015575004508718848,
-0.015077858231961727,
-0.015229579992592335,
-0.052579693496227264,
-0.0051795076578855515,
-0.058186423033475876,
-0.05508468672633171,
0.021579453721642494,
-0.01553867943584919,
-0.05155458673834801,
0.014650224708020687,
-0.014826086349785328,
0.008741279132664204,
-0.002102404134348035,
0.05710052326321602,
-0.035351965576410294,
0.08207916468381882,
0.037981320172548294,
0.052696507424116135,
-0.013146472163498402,
0.0317242331802845,
0.1144455298781395,
0.04260342940688133,
0.003083005314692855,
-0.03835735470056534,
-0.0008230751845985651,
-0.014686337672173977,
0.0007275655516423285,
-0.015703614801168442,
0.03710838779807091,
0.0016319933347404003,
0.00007003951031947508,
-0.023157713934779167,
0.038172073662281036,
-0.0021279004868119955,
0.0052620116621255875,
0.06667715311050415,
-0.0444246307015419,
-0.06981127709150314,
0.001512777293100953,
0.023951387032866478,
0.003900775918737054,
-0.040628381073474884,
-0.03619004040956497,
-0.010936930775642395,
0.0034347730688750744,
0.02840001881122589,
-0.010642939247190952,
-0.016222266480326653,
0.01992867700755596,
0.015768906101584435,
-0.03477340564131737,
-0.02828843705356121,
0.017667697742581367,
0.000484562391648069,
-0.05362025275826454,
0.025993524119257927,
0.030896443873643875,
0.00022097816690802574,
0.03258400410413742,
0.047077540308237076,
0.037024758756160736,
0.01452239602804184,
0.01607678085565567,
-0.008032973855733871,
-0.020004652440547943,
-0.023447688668966293,
-0.004188471473753452,
0.06741480529308319,
-0.021788086742162704,
0.009897064417600632,
-0.018662316724658012,
0.0031961805652827024,
-0.001920534297823906,
-0.07782536000013351,
0.020018253475427628,
-0.020190192386507988,
0.040659669786691666,
0.007990175858139992,
0.006089739967137575,
-0.008323457092046738,
0.012857452034950256,
-0.005201091058552265,
0.0229263287037611,
-0.019067883491516113,
-0.027126600965857506,
0.013756412081420422,
-0.0020141357090324163,
0.023251403123140335,
-0.014924800023436546,
-0.02092934213578701,
-0.036858994513750076,
-0.013808024115860462,
-0.024020738899707794,
-0.04314187914133072,
0.04087890684604645,
0.03817081078886986,
0.08195319771766663,
-0.02267918735742569,
-0.003973199985921383,
0.014923601411283016,
-0.06291870027780533,
0.012882719747722149,
-0.020575234666466713,
-0.03417392820119858,
0.01152955461293459,
-0.0036083878949284554,
0.004532264545559883,
0.051458947360515594,
-0.009268973022699356,
-0.00919579528272152,
-0.011467655189335346,
-0.005892029032111168,
0.020893773064017296,
-0.004856635816395283,
-0.0021048258058726788,
0.014489071443676949,
-0.013754728250205517,
0.025781454518437386,
0.009139526635408401,
-0.01712726429104805,
0.02268730103969574,
0.005270954687148333,
-0.02623008005321026,
0.04978342354297638,
0.004164746962487698,
-0.016784314066171646,
0.012114366516470909,
-0.03025703877210617,
0.018508970737457275,
0.02396698109805584,
0.03468233346939087,
-0.0376812182366848,
-0.04679996892809868,
-0.012002134695649147,
0.015213637612760067,
0.015700792893767357,
0.057243939489126205,
-0.03776133805513382,
-0.032357100397348404,
-0.03531932830810547,
0.0441984124481678,
-0.007608502171933651,
0.012504140846431255,
-0.07291262596845627,
0.023331403732299805,
0.047910213470458984,
-0.021856466308236122,
-0.037573933601379395,
0.01970795914530754,
0.013554500415921211,
-0.035684987902641296,
0.023650046437978745,
0.021588191390037537,
-0.03930528461933136,
-0.008645128458738327,
-0.020271191373467445,
-0.0399404801428318,
0.037558186799287796,
0.012213917449116707,
-0.019183320924639702,
0.03914250433444977,
-0.008818156085908413,
-0.06700015813112259,
0.002212428255006671,
-0.004670700989663601,
0.045437779277563095,
0.0469038188457489,
-0.021348504349589348,
-0.0076807537116110325,
0.026058830320835114,
-0.008826457895338535,
-0.0015003433218225837,
0.0032755115535110235,
-0.0429009273648262,
-0.015366215258836746,
-0.022375542670488358,
0.032232895493507385,
0.003521221922710538,
0.0416923426091671,
0.006250550039112568,
0.0073767839930951595,
0.015273080207407475,
-0.022944282740354538,
0.04063841328024864,
0.012143845669925213,
0.02845565415918827,
0.005245465785264969,
-0.002266902942210436,
0.0012618713080883026,
0.035659343004226685,
-0.03581773862242699,
0.011721501126885414,
0.030209945514798164,
0.019043361768126488,
-0.09218526631593704,
-0.02075411193072796,
0.009554998017847538,
-0.034664422273635864,
0.04675973579287529,
-0.028362255543470383,
-0.022257113829255104,
0.0384143590927124,
-0.07922346144914627,
0.02945828251540661,
-0.032028649002313614,
-0.017219925299286842,
-0.009222515858709812,
-0.003864441765472293,
-0.05790862813591957,
0.034890174865722656,
0.01325179636478424,
0.034078534692525864,
0.03234061598777771,
0.0038639402482658625,
0.003792797215282917,
-0.0040353694930672646,
-0.01450282521545887,
0.0389828085899353,
-0.004172020126134157,
0.010924682952463627,
0.0864245742559433,
-0.004822379909455776,
-0.024389542639255524,
0.01078016497194767,
-0.03205164521932602,
-0.008284050039947033,
-0.022491510957479477,
-0.03143619745969772,
0.010674728080630302,
0.024724068120121956,
0.047961074858903885,
-0.03301722928881645,
-0.010888930410146713,
-0.00821006577461958,
0.04877074435353279,
0.0162438303232193,
0.00970507226884365,
0.007653017528355122,
0.013729402795433998,
-0.049962494522333145,
-0.01828436367213726,
0.042990684509277344,
0.020341409370303154,
-0.006940688472241163,
0.0009509752853773534,
-0.018176326528191566,
0.009453960694372654,
-0.04385775327682495,
0.02711760438978672,
-0.02209741622209549,
-0.014460564590990543,
0.02458728291094303,
-0.0030023842118680477,
-0.03135368600487709,
0.01161563117057085,
-0.00996532291173935,
-0.05376402661204338,
0.023202264681458473,
0.04294683784246445,
-0.019900156185030937,
-0.07418207079172134,
-0.028089698404073715,
0.0026797186583280563,
-0.023335928097367287,
-0.004885710310190916,
-0.023317601531744003,
-0.08242632448673248,
0.004827028140425682,
-0.0005644263583235443,
0.020378494635224342,
-0.06289665400981903,
-0.03587745502591133,
-0.02920784428715706,
-0.05528975650668144,
0.04194309934973717,
0.039457693696022034,
-0.025711245834827423,
-0.019993968307971954,
-0.005351642146706581,
-0.0024693780578672886,
0.012945893220603466,
0.05152402073144913,
0.007751366123557091,
-0.04484821483492851,
-0.0011136530665680766,
0.031472865492105484,
0.023290487006306648,
-0.061211783438920975,
0.011325874365866184,
-0.00617900351062417,
0.023813987150788307,
0.0014064727583900094,
-0.0010523375822231174,
-0.0031765499152243137,
0.0034844556357711554,
-0.012168980203568935,
-0.006349471397697926,
0.0008060084073804319,
0.0038271439261734486,
-0.05938294157385826,
0.03815910220146179,
0.02427215501666069,
-0.030099665746092796,
0.07649415731430054,
-0.013070745393633842,
0.007190745323896408,
0.018158644437789917,
-0.04180539771914482,
-0.013107198290526867,
0.00975660141557455,
-0.038459617644548416,
-0.051712144166231155,
-0.00379609945230186,
0.016264639794826508,
0.025734907016158104,
-0.01305362768471241,
-0.05711110308766365,
0.04996751993894577,
-0.055915508419275284,
-0.03279972821474075,
0.04152137413620949,
0.014658506028354168,
0.021090460941195488,
0.0270778089761734,
0.00847571063786745,
0.029906414449214935,
0.017693670466542244,
0.011578536592423916,
0.039866697043180466,
0.014778285287320614,
-0.015648631379008293,
0.013272950425744057,
0.039369769394397736,
-0.050441641360521317,
0.021474158391356468,
0.039120133966207504,
0.05203237757086754,
-0.05945847928524017,
0.005935198627412319,
0.008319216780364513,
0.003413346828892827,
0.001527539105154574,
0.021686818450689316,
-0.021411677822470665,
0.07855752855539322,
0.025153152644634247,
0.010084521025419235,
-0.025145813822746277,
0.0169166661798954,
-0.0022356496192514896,
0.02336016856133938,
0.056265898048877716,
0.03684278577566147,
-0.06261399388313293,
0.018727973103523254,
-0.042043402791023254,
0.03542615473270416,
0.01121501624584198,
-0.03869087994098663,
-0.01335033681243658,
0.02088216133415699,
-0.03129752352833748,
-0.031731780618429184,
-0.02323104254901409,
-0.01418826263397932,
-0.024479323998093605,
0.031645797193050385,
0.06328573077917099,
0.039488837122917175,
-0.002336467383429408,
-0.010461239144206047,
-0.03486698493361473,
0.054236091673374176,
-0.04251904413104057,
0.03773633763194084,
-0.012748566456139088,
0.002476026304066181,
0.01436284463852644,
0.022208642214536667
] |
<p>Imagine two charges A and B separated by some distance.</p>
<p>Charge A emits a photon which is absorbed by charge B.</p>
<p>Is the recoil momentum received by charge A always equal and opposite to the momentum gained by charge B?</p>
<p>Is this true both for static Coulomb fields and radiation fields from accelerating charges?</p>
<p>I suppose there is no momentum "left over" in the EM field after the interaction so that all the momentum lost by A is absorbed by B. Is this how it works?</p> | 1,976 | [
-0.013698178343474865,
-0.03713379427790642,
-0.012476099655032158,
-0.03527932986617088,
0.0006501725874841213,
0.025773854926228523,
-0.03940887004137039,
0.006811410654336214,
0.015531419776380062,
-0.013494987972080708,
0.03741276264190674,
0.04750773310661316,
0.054365791380405426,
0.019770070910453796,
0.019313262775540352,
0.01720154471695423,
0.01766914315521717,
-0.000634577008895576,
0.00047514575999230146,
-0.03972496837377548,
-0.0191301591694355,
0.02827504277229309,
0.008233997970819473,
0.017445677891373634,
-0.032079342752695084,
0.017006726935505867,
0.019085723906755447,
-0.019235750660300255,
-0.0007966565317474306,
0.06009446829557419,
-0.022904079407453537,
-0.02500961162149906,
-0.0422605499625206,
-0.0017786853713914752,
0.03592414781451225,
-0.011187512427568436,
-0.0033336684573441744,
-0.06536964327096939,
-0.005740538705140352,
0.02328614704310894,
-0.034311000257730484,
0.010712009854614735,
-0.00012654491001740098,
0.05336552858352661,
-0.022331293672323227,
-0.0031644897535443306,
-0.03534720838069916,
-0.0012285357806831598,
0.05187394469976425,
-0.05621841177344322,
0.07242708653211594,
-0.016276758164167404,
0.05866831913590431,
0.008174427784979343,
-0.022541139274835587,
-0.017903506755828857,
0.06749750673770905,
0.07885683327913284,
0.030835840851068497,
-0.0151003273203969,
0.012574692256748676,
-0.011614447459578514,
-0.03503352403640747,
-0.006184091791510582,
-0.01634814776480198,
0.040009934455156326,
-0.005522144492715597,
-0.03082166239619255,
0.05347747355699539,
0.008441952988505363,
0.03594985231757164,
0.004294104408472776,
0.022910747677087784,
-0.03194167837500572,
0.033547718077898026,
-0.022118061780929565,
0.023219574242830276,
0.022505389526486397,
0.04588383063673973,
0.04450952634215355,
-0.0024657666217535734,
-0.0066653103567659855,
0.021573616191744804,
0.04888534918427467,
0.032980192452669144,
-0.025150194764137268,
0.04703741520643234,
0.004816162399947643,
0.0006601701024919748,
0.041584186255931854,
0.002549081342294812,
0.039599690586328506,
0.0012854884844273329,
-0.011242007836699486,
-0.024127695709466934,
0.05619393661618233,
0.018037395551800728,
0.07451891154050827,
-0.009480339474976063,
-0.021185919642448425,
-0.017464149743318558,
0.016026180237531662,
0.02207953855395317,
0.08454273641109467,
0.009878117591142654,
-0.01448118593543768,
-0.02184280753135681,
0.02656102180480957,
-0.048660580068826675,
-0.010825124569237232,
-0.03240882232785225,
0.012545759789645672,
0.0063342745415866375,
-0.012182239443063736,
0.03590710088610649,
-0.0495552197098732,
0.018399208784103394,
-0.014543031342327595,
0.07302728295326233,
0.058049026876688004,
0.03905775025486946,
-0.013891412876546383,
0.005819257348775864,
-0.021356772631406784,
-0.059258267283439636,
-0.032962631434202194,
0.05499379336833954,
0.014841499738395214,
-0.05635412037372589,
0.009888838045299053,
-0.005703664384782314,
-0.030128903687000275,
0.016884801909327507,
-0.016542773693799973,
0.013552140444517136,
-0.04317359998822212,
-0.06402001529932022,
-0.05572426691651344,
-0.008618851192295551,
-0.014371431432664394,
-0.004786990582942963,
-0.0811791718006134,
-0.01986328884959221,
0.01903851330280304,
0.07171343266963959,
-0.004503571894019842,
-0.006241646129637957,
0.0025863507762551308,
0.05436050519347191,
-0.006636953912675381,
0.02144439145922661,
-0.00964448507875204,
0.008998580276966095,
0.0014657627325505018,
-0.037412844598293304,
-0.07303515821695328,
0.011004689149558544,
0.04886730760335922,
0.002989785745739937,
0.033058036118745804,
0.04195372760295868,
-0.015344546176493168,
0.018891211599111557,
0.006158903241157532,
0.01569506898522377,
-0.0165229681879282,
0.06859073787927628,
0.05510657653212547,
-0.023437874391674995,
0.033405423164367676,
0.02966259978711605,
0.029177870601415634,
0.004797506611794233,
-0.029003752395510674,
0.04260159656405449,
-0.05791749060153961,
-0.023806536570191383,
-0.022189214825630188,
0.011788039468228817,
-0.019469641149044037,
-0.04135791212320328,
-0.074293352663517,
-0.03040715493261814,
0.013934536837041378,
-0.0035106700379401445,
0.002278614789247513,
0.03548331558704376,
0.014379912987351418,
-0.03118257410824299,
-0.015696976333856583,
-0.025235943496227264,
-0.06502261757850647,
0.039501339197158813,
0.002167360158637166,
-0.00628557987511158,
0.00576761132106185,
0.01579778641462326,
-0.012690533883869648,
-0.014970730058848858,
-0.053470171988010406,
0.004785290453583002,
0.029313398525118828,
-0.04150790348649025,
0.000375455419998616,
0.002497912384569645,
0.05127392336726189,
0.032088883221149445,
0.013501415960490704,
0.015511109493672848,
-0.0014320863410830498,
-0.039916619658470154,
0.001426176750101149,
-0.03137329965829849,
0.007170193828642368,
0.02650580182671547,
0.015238272026181221,
0.012919431552290916,
-0.016741344705224037,
0.019591933116316795,
0.01753189042210579,
-0.02240132726728916,
0.06731565296649933,
0.05328226462006569,
0.011138313449919224,
-0.016789846122264862,
0.05013959854841232,
0.003437519073486328,
0.020557697862386703,
0.01895175501704216,
-0.04716213420033455,
-0.026550134643912315,
-0.009604307822883129,
0.015863941982388496,
-0.017735276371240616,
-0.04777461662888527,
0.04577597603201866,
0.036960944533348083,
0.005652300082147121,
0.015816640108823776,
0.022997785359621048,
-0.01466913241893053,
-0.07822857797145844,
0.03676130250096321,
0.011735979467630386,
-0.035387635231018066,
0.0016009443206712604,
0.023616008460521698,
-0.021282833069562912,
0.006439980585128069,
0.011687151156365871,
0.00550079345703125,
-0.0010792033281177282,
0.010578509420156479,
0.006235937122255564,
-0.03195939585566521,
-0.08186131715774536,
0.02841484360396862,
0.007232329808175564,
0.0444621741771698,
-0.011540038511157036,
-0.02271980419754982,
-0.0015185116790235043,
-0.032725851982831955,
-0.011372777633368969,
-0.012075749225914478,
-0.03299364075064659,
0.02595970593392849,
-0.02075495943427086,
0.0252539049834013,
-0.05786237120628357,
0.007024877704679966,
-0.0007405168144032359,
-0.01942524127662182,
-0.018467595800757408,
-0.03266850486397743,
0.013912622816860676,
0.0026362380012869835,
0.035717662423849106,
-0.031832754611968994,
-0.04716695100069046,
-0.02692694030702114,
-0.0345660038292408,
-0.015535910613834858,
0.0048095774836838245,
-0.031746163964271545,
0.019988691434264183,
-0.05413513630628586,
-0.03753840923309326,
0.04494767263531685,
-0.000870661111548543,
0.04278557375073433,
0.0792636051774025,
-0.01110018976032734,
-0.0762958973646164,
-0.022767972201108932,
0.0007742665475234389,
-0.0069091180339455605,
-0.03572129085659981,
0.017949357628822327,
0.06621267646551132,
0.006025475915521383,
-0.04962670058012009,
0.0108398562297225,
-0.010525697842240334,
-0.05145348981022835,
-0.012525326572358608,
-0.005512986332178116,
0.0027919423300772905,
-0.013561731204390526,
-0.005114258266985416,
0.0062847924418747425,
-0.04238847270607948,
-0.005312198773026466,
-0.052114810794591904,
-0.03449539095163345,
0.03266138955950737,
0.003942409995943308,
0.029876118525862694,
-0.0019309489289298654,
-0.030505061149597168,
0.09941116720438004,
0.029460906982421875,
0.027538489550352097,
-0.011455297470092773,
-0.01974131166934967,
-0.01665508933365345,
0.01726183108985424,
-0.01971382461488247,
-0.010070479474961758,
-0.005464131012558937,
0.0025927729438990355,
-0.0030115554109215736,
0.029142465442419052,
0.005061131902039051,
0.002350053982809186,
0.0015677270712330937,
0.007832396775484085,
0.03893550857901573,
0.009688112884759903,
0.05170094966888428,
-0.007061013486236334,
-0.03840655833482742,
-0.0008456279756501317,
0.017800411209464073,
0.0378568060696125,
-0.014673813246190548,
-0.03389196842908859,
0.05252692103385925,
0.006749358028173447,
0.025129705667495728,
-0.0211629755795002,
0.052613645792007446,
-0.03962773084640503,
-0.004796749446541071,
0.007737338542938232,
0.006024614442139864,
0.047998953610658646,
-0.006229996681213379,
0.012243881821632385,
0.03947931155562401,
0.07035014778375626,
-0.004740722943097353,
-0.04445478320121765,
0.020103948190808296,
-0.0102350153028965,
0.005485295783728361,
-0.03677740320563316,
-0.018979914486408234,
0.021408021450042725,
0.01221342384815216,
0.013396775349974632,
0.015728788450360298,
-0.025951052084565163,
-0.01373511552810669,
-0.07173646986484528,
0.007640406023710966,
0.003864843165501952,
0.04642948508262634,
0.01886991411447525,
0.06827758997678757,
0.04662179574370384,
0.016980044543743134,
0.024077679961919785,
0.009482254274189472,
-0.0736137181520462,
0.04070216789841652,
-0.0275897104293108,
-0.010008842684328556,
-0.034595247358083725,
-0.012345610186457634,
-0.03338724374771118,
-0.006911044474691153,
-0.031284987926483154,
-0.0333334244787693,
-0.005272114649415016,
-0.05646178498864174,
0.009401392191648483,
-0.052190929651260376,
-0.07538492977619171,
-0.052927255630493164,
0.04113734886050224,
0.04138398915529251,
-0.04234987869858742,
0.03669031709432602,
0.025486605241894722,
-0.030756531283259392,
-0.04171469435095787,
-0.03283780813217163,
0.03845423460006714,
-0.0069843437522649765,
0.021193018183112144,
0.06811100244522095,
0.0032238715793937445,
-0.035321056842803955,
0.023268504068255424,
0.012389629147946835,
0.05167004466056824,
0.034141767770051956,
-0.0432506799697876,
-0.011127723380923271,
-0.03771250694990158,
-0.026737652719020844,
-0.0009300076053477824,
0.03458234295248985,
0.01093916967511177,
-0.013309773057699203,
-0.0005189630319364369,
0.041122086346149445,
0.022217893972992897,
0.032913461327552795,
0.03563776984810829,
0.01937619224190712,
0.010004080832004547,
-0.04416019096970558,
0.060833174735307693,
-0.011300389654934406,
0.025527603924274445,
-0.010731452144682407,
-0.029932351782917976,
-0.015535672195255756,
0.0005847378633916378,
0.023694638162851334,
0.035253170877695084,
-0.006662663072347641,
-0.003175043035298586,
-0.013043977320194244,
-0.015086247585713863,
0.002413180423900485,
0.009668136946856976,
0.02216108702123165,
0.046127114444971085,
0.041230201721191406,
0.04875354468822479,
0.020968608558177948,
-0.04247641563415527,
-0.02321055717766285,
0.03933495283126831,
0.047415684908628464,
-0.009054874069988728,
-0.024409320205450058,
-0.010912704281508923,
0.01771112158894539,
0.05023014917969704,
0.016414230689406395,
0.025125669315457344,
-0.005327590741217136,
0.011770068667829037,
-0.0013176375068724155,
-0.035051845014095306,
-0.05360622704029083,
0.05672696977853775,
-0.024049624800682068,
-0.019282463937997818,
-0.02166428603231907,
-0.02281969040632248,
0.02330794557929039,
0.02893170900642872,
0.029542533680796623,
0.04781465232372284,
0.00605692807585001,
-0.00974563043564558,
0.0007331589586101472,
-0.00017807249969337136,
-0.010947437956929207,
-0.10371725261211395,
0.004138486459851265,
-0.01389718521386385,
-0.03746308758854866,
0.04754010587930679,
-0.03518088907003403,
-0.02760998345911503,
0.01186906173825264,
-0.003743786597624421,
0.007558256387710571,
-0.003967644181102514,
-0.06524233520030975,
0.012149489484727383,
0.02028135396540165,
-0.02608249895274639,
0.0789191797375679,
0.039009131491184235,
-0.015657255426049232,
-0.026280341669917107,
0.0029483039397746325,
0.036477480083703995,
-0.015420341864228249,
0.021990099921822548,
-0.036618366837501526,
0.0023739472962915897,
-0.022991428151726723,
0.05375757813453674,
-0.02107817493379116,
0.0017894915072247386,
0.026600327342748642,
-0.03031725063920021,
-0.011548795737326145,
0.016525808721780777,
-0.030501166358590126,
0.008662578649818897,
-0.027296101674437523,
0.002758200978860259,
-0.045124951750040054,
-0.024657543748617172,
0.0008449749439023435,
0.025037843734025955,
0.014281378127634525,
0.013945926912128925,
-0.031545642763376236,
0.011647328734397888,
-0.01929538883268833,
-0.011521311476826668,
0.005348125007003546,
-0.0041125863790512085,
0.04555220156908035,
-0.018680106848478317,
0.005614997819066048,
0.017463453114032745,
-0.03578679636120796,
-0.03222547471523285,
0.027908239513635635,
-0.007821020670235157,
0.01554410345852375,
-0.08724208176136017,
0.015655092895030975,
0.04213698208332062,
-0.01186287309974432,
-0.06044646352529526,
-0.02142154797911644,
0.017935099080204964,
0.014422531239688396,
-0.003843646263703704,
-0.01759209670126438,
-0.005972070153802633,
-0.03155044466257095,
-0.06022723764181137,
0.005842877551913261,
0.03910703957080841,
-0.04336101561784744,
0.00003444006870267913,
0.01898188330233097,
-0.027605794370174408,
0.004250955767929554,
0.017288869246840477,
-0.019236542284488678,
-0.025071274489164352,
0.003436479950323701,
-0.009777188301086426,
-0.0034393572714179754,
0.07552850991487503,
0.009948978200554848,
-0.023921355605125427,
-0.006859567482024431,
-0.021744979545474052,
0.035405904054641724,
-0.025031084194779396,
-0.03799784556031227,
0.03937631472945213,
0.016500404104590416,
0.010891979560256004,
-0.0037204325199127197,
0.01962408423423767,
0.026095308363437653,
0.03860284015536308,
-0.0017445735866203904,
0.027261987328529358,
-0.03184772655367851,
-0.041976626962423325,
0.022456983104348183,
0.021209510043263435,
0.03653472289443016,
-0.006446299143135548,
0.025058064609766006,
-0.009189436212182045,
0.015614720061421394,
0.016193203628063202,
0.03488980978727341,
0.02133517526090145,
-0.06168939545750618,
0.017428750172257423,
0.015600285492837429,
-0.0004430241242516786,
-0.005094477906823158,
-0.0182435791939497,
-0.025951413437724113,
-0.03593749925494194,
0.05439671874046326,
-0.012321647256612778,
0.051343027502298355,
0.016917511820793152,
0.03467052802443504,
-0.020847443491220474,
-0.025083372369408607,
-0.01721077598631382,
-0.00904358085244894,
0.0013630033936351538,
0.014465609565377235,
-0.03028864599764347,
0.017599085345864296,
0.019952066242694855,
0.06517591327428818,
-0.020742977038025856,
0.008696457371115685,
0.011389262974262238,
0.01039762794971466,
0.025994108989834785,
-0.005136231891810894,
-0.03745783865451813,
0.03480961173772812,
-0.029649753123521805,
0.009825596585869789,
0.008733009919524193,
-0.02585730515420437,
0.05087079852819443,
0.021710844710469246,
0.014653910882771015,
-0.02798338048160076,
-0.022420091554522514,
-0.029436524957418442,
0.015241873450577259,
-0.00924177747219801,
0.039274152368307114,
-0.019709443673491478,
0.005509598646312952,
0.02176741324365139,
0.014411664567887783,
0.022755376994609833,
0.01080887857824564,
-0.03735623508691788,
-0.036514852195978165,
-0.06637494266033173,
-0.016902044415473938,
0.034602969884872437,
-0.03092906065285206,
-0.004114694893360138,
0.02149968221783638,
-0.029212281107902527,
0.03592400252819061,
0.034478891640901566,
-0.007544838357716799,
0.010050282813608646,
0.021505316719412804,
-0.012860748916864395,
0.0007288941415026784,
-0.04963461682200432,
-0.0026585788000375032,
0.11058834195137024,
0.017742043361067772,
0.04814596101641655,
-0.05013633519411087,
-0.026799775660037994,
-0.025869037955999374,
0.029738426208496094,
-0.03206351399421692,
0.017833231016993523,
-0.031123094260692596,
0.0017550862394273281,
0.015313214622437954,
0.024074170738458633,
0.005199415609240532,
-0.006520530208945274,
0.007189108058810234,
-0.022311819717288017,
-0.04208212345838547,
0.007677027489989996,
0.0060688466764986515,
0.01025795005261898,
0.03859511762857437,
-0.051277995109558105,
0.0023170814383774996,
-0.023883452638983727,
-0.005427813623100519,
-0.033312708139419556,
-0.017252180725336075,
-0.02930471859872341,
-0.025615688413381577,
-0.029998892918229103,
0.01882312074303627,
-0.002243355382233858,
-0.0016488699475303292,
-0.04609745368361473,
0.03938514366745949,
0.050148963928222656,
-0.007646965328603983,
-0.018062693998217583,
0.0036953408271074295,
0.030415426939725876,
0.008314290083944798,
0.031019603833556175,
0.015821201726794243,
-0.05978945642709732,
0.024627426639199257,
0.000017018115613609552,
0.07485932856798172,
-0.016292691230773926,
0.024965427815914154,
0.006233748514205217,
-0.011606846004724503,
0.049385979771614075,
-0.03667241707444191,
-0.00917806290090084,
0.012622423470020294,
0.008945675566792488,
-0.0206326674669981,
-0.010326585732400417,
-0.026688413694500923,
0.04058723896741867,
-0.0069755311124026775,
-0.006096506491303444,
-0.016743479296565056,
-0.0008299716282635927,
0.004157621879130602,
-0.00917393621057272,
0.043124500662088394,
-0.011361978948116302,
-0.030692879110574722,
-0.00991534348577261,
-0.025167569518089294,
-0.03711387887597084,
-0.034176867455244064,
-0.01299235224723816,
0.01937500759959221,
0.03136560320854187,
-0.003019255120307207,
-0.001458450686186552,
-0.032848041504621506,
-0.09298522770404816,
0.0810437873005867,
-0.044759780168533325,
-0.004036582075059414,
-0.016180185601115227,
0.023982444778084755,
0.02294178307056427,
0.04008415713906288,
-0.04013621062040329,
-0.007933474145829678,
-0.00599700678139925,
0.0546342171728611,
0.012252045795321465,
-0.01673964411020279,
-0.011290784925222397,
0.014214511960744858,
-0.0309373177587986,
-0.02217952348291874,
-0.004864726215600967,
-0.0038309902884066105,
-0.002858838764950633,
0.019770313054323196,
0.017566585913300514,
0.007302944082766771,
-0.03013729304075241,
0.01057792454957962,
0.026574280112981796,
0.01988782361149788,
-0.007217290345579386,
0.034999486058950424,
0.0035855001769959927,
-0.01344202272593975,
0.005683599971234798,
-0.007355017121881247,
0.017380455508828163,
0.011993655003607273,
0.02971385419368744,
-0.03248245269060135,
-0.013024059124290943,
-0.009606105275452137,
0.019479867070913315,
-0.04785911366343498,
-0.02359294332563877,
-0.054142627865076065,
-0.006368407513946295,
0.017616286873817444,
-0.017566369846463203,
-0.03298420459032059,
0.051257580518722534,
-0.01946534588932991,
-0.005188911687582731,
0.026096390560269356,
0.013269844464957714,
-0.026482602581381798,
0.01193091832101345,
0.024961242452263832,
-0.004175585228949785,
0.0513555109500885,
0.020085690543055534,
0.0027278054039925337,
0.06367027014493942,
-0.02716047875583172,
-0.048078346997499466,
0.011651858687400818,
-0.019088609144091606,
0.012752188369631767,
0.05290495231747627,
-0.021825335919857025,
-0.024366607889533043,
0.07349878549575806,
0.0248712208122015,
-0.021514030173420906,
-0.027957191690802574,
-0.08904702216386795,
0.01694558933377266,
-0.007630500942468643,
0.017655955627560616,
0.004626712296158075,
-0.019410787150263786,
0.049845803529024124,
-0.0041923741810023785,
-0.016230806708335876,
0.001753368298523128,
-0.03972778469324112,
0.0036692838184535503,
0.005904557649046183,
0.012470504269003868,
-0.005153747275471687,
0.012379350140690804,
0.04051850736141205,
-0.009633077308535576,
0.007613908965140581,
0.021108942106366158,
0.00265899789519608,
-0.08993541449308395,
-0.02648564800620079,
-0.00997450202703476,
0.021264003589749336,
0.011341705918312073,
-0.03893694654107094,
-0.008946157991886139,
0.010582376271486282,
-0.09298175573348999,
0.006937064230442047,
0.00921439379453659,
-0.037827685475349426,
-0.02724195271730423,
0.03267815709114075,
0.0007578315562568605,
0.03951903432607651,
0.004508309066295624,
0.06514956057071686,
-0.011354191228747368,
0.016380665823817253,
-0.011393916793167591,
-0.044298090040683746,
-0.06745890527963638,
-0.004843815229833126,
-0.01673988066613674,
0.02593572810292244,
0.0740104541182518,
-0.001684281975030899,
0.00923422072082758,
0.04061959683895111,
-0.016324469819664955,
0.00520616490393877,
-0.02746480144560337,
0.03663234785199165,
0.02293364144861698,
0.016726559028029442,
-0.021761702373623848,
-0.011215309612452984,
0.006326544098556042,
0.0017499520909041166,
0.038198404014110565,
0.017881395295262337,
-0.03411949798464775,
0.012980838306248188,
0.027528861537575722,
-0.03872809186577797,
-0.02950827032327652,
0.02155577577650547,
-0.007735865190625191,
-0.03673328086733818,
-0.001040623988956213,
0.036505140364170074,
-0.013131845742464066,
-0.0020760761108249426,
0.002312498167157173,
-0.04812692850828171,
-0.015583675354719162,
0.046499598771333694,
-0.0028065494261682034,
-0.009103192947804928,
0.0438813678920269,
0.013963228091597557,
-0.005775014404207468,
0.01122896559536457,
0.0014422913081943989,
0.026097850874066353,
-0.03491558879613876,
0.014366786926984787,
0.020723501220345497,
0.02003365010023117,
0.0002159514551749453,
-0.0623287633061409,
-0.05388136953115463,
0.009172008372843266,
-0.0006965407519601285,
0.02909216657280922,
0.00917387381196022,
-0.011076318100094795,
-0.02242254838347435,
-0.09404458105564117,
0.018606919795274734,
-0.026400523260235786,
-0.008541283197700977,
-0.06424916535615921,
-0.030397389084100723,
0.012871173210442066,
0.015766944736242294,
0.06170831620693207,
-0.009402655996382236,
-0.030211081728339195,
0.06110789626836777,
-0.03213353082537651,
0.00203151092864573,
-0.05627477914094925,
0.006376833189278841,
-0.016264012083411217,
-0.0057609290815889835,
0.0005793190211988986,
0.02382872812449932,
-0.04788091778755188,
0.0410768948495388,
0.02448546700179577,
-0.02445227839052677,
0.0022695939987897873,
-0.03712257742881775,
-0.04604272544384003,
0.06059427931904793,
0.012573751620948315,
-0.01909537799656391,
0.03593946620821953,
0.019418735057115555,
0.04605468735098839,
0.02458813413977623,
-0.012419947423040867,
-0.026657093316316605,
0.02000591903924942,
-0.05228715389966965,
-0.017530525103211403,
-0.03764647990465164,
-0.003587929531931877,
0.037760600447654724,
-0.036979228258132935,
0.014902863651514053,
0.035723574459552765,
-0.06118319183588028,
0.0012325904099270701,
0.07597614079713821,
0.0011419984512031078,
0.0581105537712574,
0.03692278638482094,
0.05346263572573662,
0.02201886475086212,
-0.028537949547171593,
-0.013876122422516346,
0.026440134271979332,
0.014177784323692322,
0.014372306875884533,
0.025658348575234413,
0.05217266082763672,
0.0077856117859482765,
-0.0009130311664193869,
-0.006992593873292208,
0.006570075172930956,
-0.0029111108742654324,
-0.008374590426683426,
0.018041474744677544,
0.014352576807141304,
0.001889244420453906,
0.012417381629347801,
-0.02896483801305294,
0.06694791465997696,
-0.0667206197977066,
0.030515041202306747,
-0.0056046368554234505,
0.010850194841623306,
0.022670147940516472,
0.02927318587899208,
0.009825414046645164,
0.028130965307354927,
0.023036975413560867,
-0.021932078525424004,
-0.021475739777088165,
-0.02080237679183483,
0.0025286965537816286,
-0.019673801958560944,
0.03981975466012955,
0.0013694231165573,
0.0029733642004430294,
-0.03363196179270744,
-0.002081760670989752,
-0.012689969502389431,
-0.03415121138095856,
0.0075725349597632885,
0.044791821390390396,
0.0026719789020717144,
0.004525443073362112,
0.02683459036052227,
-0.03702348843216896,
0.053039658814668655,
-0.039797283709049225,
-0.021257318556308746,
-0.01729404181241989,
0.029552431777119637,
0.019509343430399895,
-0.023819871246814728
] |
<p>Is the force which acts perpendicular to a wire due to another current wire in its vicinity consistent or it is just for a brief time? I thought it should be for a brief time because only for a moment all electrons will drift in the direction of force but after that the force will change its direction (it has to be perpendicular to velocity always, right?)
Further, does this force do work on the wire? (Caveat: Kindly keep in mind while answering that I'm just a 12th grader and I know nothing of quantum mechanics)</p> | 1,977 | [
-0.02315397746860981,
0.004795069806277752,
0.0187242329120636,
-0.0657082349061966,
0.024910157546401024,
0.004259765613824129,
-0.014296967536211014,
-0.0000739624083507806,
0.005121737718582153,
-0.028778262436389923,
0.042451728135347366,
0.040879447013139725,
0.06560956686735153,
-0.018466001376509666,
0.014027559198439121,
0.009472288191318512,
0.008877080865204334,
-0.005233381409198046,
0.0033722606021910906,
-0.013554037548601627,
-0.017569314688444138,
0.02450769953429699,
0.022809524089097977,
0.0022743409499526024,
-0.02856367826461792,
-0.0070984638296067715,
0.008960781618952751,
-0.013215241953730583,
0.018586497753858566,
0.06384032964706421,
-0.040973059833049774,
-0.026546617969870567,
0.011394028551876545,
-0.025265216827392578,
0.01844817027449608,
-0.005861676763743162,
-0.02398102544248104,
-0.06735964864492416,
-0.002770813414826989,
0.038015201687812805,
-0.02022419311106205,
0.02066640555858612,
-0.0026156443636864424,
0.03770932927727699,
-0.0259171761572361,
-0.0019922894425690174,
0.002011494943872094,
-0.025967488065361977,
0.054811086505651474,
-0.07530571520328522,
0.05783327668905258,
-0.02560974657535553,
0.06289032101631165,
-0.0036761367227882147,
-0.019251758232712746,
-0.017859652638435364,
0.07644505798816681,
0.05044985190033913,
-0.04380242899060249,
-0.014712551608681679,
-0.02383292466402054,
-0.017733125016093254,
-0.005758786108344793,
-0.024059176445007324,
-0.04114217683672905,
0.03936637565493584,
-0.0019600698724389076,
-0.04337963089346886,
0.043175455182790756,
0.005929943639785051,
0.0073726302944123745,
0.0022216744255274534,
0.03563974052667618,
0.023299457505345345,
-0.014632116071879864,
-0.031261686235666275,
0.015226493589580059,
0.03367021307349205,
0.016941126435995102,
0.041633933782577515,
-0.047606419771909714,
-0.0116570508107543,
0.03494103625416756,
0.0531369149684906,
0.02223651297390461,
-0.048826899379491806,
0.047404754906892776,
-0.027617260813713074,
-0.013367910869419575,
0.02173532545566559,
-0.007909569889307022,
0.03202179819345474,
-0.009156309999525547,
-0.01993592455983162,
-0.018374435603618622,
0.03148869425058365,
0.013218970969319344,
0.03316253796219826,
-0.0036552229430526495,
-0.018245143815875053,
0.04395731911063194,
-0.023988332599401474,
0.0024036187678575516,
0.05930823087692261,
-0.026004251092672348,
-0.030023375526070595,
0.01543110329657793,
0.0169957485049963,
-0.04420861974358559,
-0.012766286730766296,
-0.04236459359526634,
0.021213972941040993,
-0.01667512021958828,
0.013427004218101501,
0.0355028472840786,
-0.00048697408055886626,
0.00952966883778572,
0.018184570595622063,
0.05782163888216019,
0.053460799157619476,
0.011154106818139553,
-0.0507696196436882,
0.024247953668236732,
-0.017912788316607475,
0.00008053569035837427,
0.01952398754656315,
0.02417086623609066,
0.004957198165357113,
0.007194203790277243,
0.04529815539717674,
-0.0052417884580791,
-0.04627251625061035,
-0.00421453220769763,
-0.013289401307702065,
0.08347202092409134,
-0.0020216715056449175,
-0.11381769925355911,
-0.05965205654501915,
0.05345539003610611,
-0.02876647748053074,
0.007082982920110226,
-0.08529181033372879,
-0.010972458869218826,
0.0021298290230333805,
0.06773814558982849,
-0.01264953799545765,
-0.013891656883060932,
-0.025340329855680466,
0.02101505734026432,
-0.00830418523401022,
-0.010626164264976978,
-0.02420397289097309,
0.04028482362627983,
-0.0386599637567997,
-0.016302596777677536,
-0.025591444224119186,
0.05034259706735611,
0.03528573364019394,
0.02841385453939438,
-0.04399177432060242,
0.04173067584633827,
-0.0028319868724793196,
0.019234102219343185,
0.019994359463453293,
-0.021061072126030922,
-0.004154353868216276,
0.07160242646932602,
0.010183276608586311,
-0.015646688640117645,
0.01858142763376236,
0.021211395040154457,
0.009425454773008823,
0.00862137321382761,
0.008866683579981327,
0.0272653941065073,
-0.049680523574352264,
-0.0026686799246817827,
-0.010337457992136478,
0.0325530506670475,
-0.008256874978542328,
-0.042487964034080505,
-0.02724888175725937,
-0.014695439487695694,
0.003527405671775341,
-0.01975906640291214,
0.06332721561193466,
-0.019423833116889,
0.0017310531111434102,
-0.052656129002571106,
-0.027004482224583626,
-0.011728135868906975,
-0.03496742621064186,
0.046261630952358246,
-0.02015470527112484,
-0.04828956350684166,
0.03536851331591606,
-0.017556577920913696,
0.007163528352975845,
-0.03384348005056381,
-0.0234612375497818,
-0.024045269936323166,
0.03909396752715111,
-0.03439777344465256,
-0.007254329044371843,
0.0230562686920166,
0.04519834741950035,
0.029238687828183174,
0.04578752443194389,
0.05450015515089035,
-0.006396510172635317,
-0.007817687466740608,
0.008374786004424095,
-0.02465796284377575,
0.010938643477857113,
0.048222482204437256,
0.008086256682872772,
0.02022896334528923,
-0.03594830632209778,
0.00851661991328001,
0.045239757746458054,
-0.02158849686384201,
0.08028234541416168,
0.03416742384433746,
0.016823332756757736,
-0.0018667265539988875,
0.057712528854608536,
0.017093852162361145,
-0.012757637538015842,
-0.00628213444724679,
-0.0726742073893547,
-0.04329168051481247,
0.02071794867515564,
0.03908006101846695,
0.0012653593439608812,
-0.03406664729118347,
0.005731586366891861,
0.025933779776096344,
0.0261934082955122,
0.04798225685954094,
0.04167857766151428,
-0.021015606820583344,
-0.04148014634847641,
0.02012527361512184,
0.016696250066161156,
-0.0168205164372921,
-0.0035626303870230913,
0.011464516632258892,
0.03571801632642746,
0.02409062162041664,
0.03294781222939491,
-0.0038382033817470074,
0.033159445971250534,
-0.004626930225640535,
0.0177365280687809,
0.003413358936086297,
-0.04800863564014435,
0.050811413675546646,
-0.01393111888319254,
0.05772754177451134,
-0.000957850890699774,
0.01684594713151455,
0.03071465902030468,
-0.012973754666745663,
-0.018167534843087196,
0.03421325981616974,
-0.024074770510196686,
-0.0016955024329945445,
-0.03337334468960762,
0.021838421002030373,
-0.021736344322562218,
-0.0015661129727959633,
-0.015480034053325653,
0.027186499908566475,
-0.002965515712276101,
-0.022154144942760468,
0.026691779494285583,
0.016052428632974625,
0.060925159603357315,
-0.047079965472221375,
-0.029409969225525856,
-0.04309922829270363,
-0.055791936814785004,
0.020057275891304016,
0.021500367671251297,
-0.003993515390902758,
0.015248999930918217,
-0.006548664532601833,
-0.020523346960544586,
0.0471104271709919,
-0.006657401565462351,
0.021149426698684692,
0.02881104126572609,
-0.00955982320010662,
-0.06078249216079712,
0.013006492517888546,
-0.049696411937475204,
0.006366303190588951,
-0.05001628026366234,
-0.0007598450756631792,
0.03536494821310043,
-0.04020995274186134,
-0.00435688067227602,
0.03589491918683052,
-0.03125336393713951,
-0.08181323856115341,
-0.0015352844493463635,
-0.0020430725999176502,
0.021631741896271706,
-0.003872547298669815,
0.03846941888332367,
0.033482011407613754,
-0.062452953308820724,
-0.04255707189440727,
-0.036139510571956635,
-0.016198748722672462,
0.03121018595993519,
-0.028546378016471863,
0.017279179766774178,
-0.015569894574582577,
-0.07285577058792114,
0.06432950496673584,
0.015494326129555702,
-0.038243796676397324,
-0.01069240178912878,
-0.014358687214553356,
-0.09781422466039658,
-0.03397329896688461,
0.01768827624619007,
0.05170666053891182,
-0.007548418827354908,
0.0008780062198638916,
0.028405865654349327,
0.0418640561401844,
0.003642226802185178,
0.012802480719983578,
-0.014399794861674309,
0.011176387779414654,
0.027880948036909103,
0.014246193692088127,
0.05536798760294914,
0.009538484737277031,
-0.04310915991663933,
-0.02000761404633522,
0.015881827101111412,
0.021870199590921402,
0.01689941994845867,
-0.023789329454302788,
0.026336515322327614,
0.0035844258964061737,
0.006711279507726431,
-0.017975304275751114,
0.05766890570521355,
-0.007563162595033646,
0.010165317915380001,
0.029492497444152832,
-0.003926877398043871,
0.03643122315406799,
-0.007648205850273371,
0.007089083548635244,
0.05351589247584343,
-0.004084491636604071,
-0.03917659446597099,
-0.029406121000647545,
0.016917256638407707,
0.016515830531716347,
0.02126201242208481,
-0.03458767756819725,
-0.07433785498142242,
0.019845830276608467,
0.03142453730106354,
0.03297394514083862,
0.03504094108939171,
-0.039467647671699524,
-0.001517289667390287,
-0.04993676394224167,
0.00769528653472662,
0.024873437359929085,
0.027963517233729362,
0.009479103609919548,
0.06524112075567245,
0.03259650617837906,
0.0353788323700428,
-0.018007539212703705,
0.009956569410860538,
-0.07379774749279022,
0.03097686544060707,
-0.03569819778203964,
-0.03359738364815712,
-0.026490865275263786,
-0.014837509021162987,
-0.05836447328329086,
-0.021786566823720932,
0.008986682631075382,
-0.022374458611011505,
-0.023064041510224342,
-0.0390046089887619,
0.002189302584156394,
-0.028412114828824997,
-0.007253601681441069,
-0.04698927327990532,
0.016217293217778206,
0.029997898265719414,
-0.05392839387059212,
0.05766987428069115,
0.02502925880253315,
-0.027909813448786736,
-0.002283864188939333,
-0.010525445453822613,
-0.026997629553079605,
0.020577607676386833,
0.01369271706789732,
0.019474700093269348,
-0.009501347318291664,
-0.039269737899303436,
0.013306163251399994,
0.020244115963578224,
0.06295792758464813,
0.020858366042375565,
-0.006467457395046949,
-0.025939539074897766,
-0.06533566117286682,
-0.028722597286105156,
-0.015736214816570282,
0.055915430188179016,
0.014146716333925724,
-0.007790334522724152,
0.037753473967313766,
0.02589920535683632,
-0.00964585691690445,
0.048668116331100464,
0.028302373364567757,
0.010133527219295502,
-0.01583307422697544,
-0.06239921972155571,
0.023070400580763817,
-0.0373167023062706,
0.008670112118124962,
0.01278893556445837,
-0.051573581993579865,
-0.03313865140080452,
-0.02874644659459591,
-0.003571409499272704,
0.0323263444006443,
0.004876744467765093,
0.006140224635601044,
-0.0014711403055116534,
0.042615655809640884,
0.0012008885387331247,
0.0027377086225897074,
0.043678950518369675,
0.008119096979498863,
-0.007236161734908819,
0.01650945283472538,
-0.005136639811098576,
-0.06585057824850082,
0.013214691542088985,
0.03208763524889946,
0.03950691595673561,
-0.018013836815953255,
-0.006457057315856218,
-0.054894059896469116,
-0.028376249596476555,
0.04367959499359131,
-0.0019266933668404818,
0.018996182829141617,
-0.011656321585178375,
-0.000132478991872631,
-0.026110941544175148,
-0.04933660104870796,
-0.010477308183908463,
0.0334896594285965,
-0.004686129279434681,
0.022422660142183304,
-0.022191565483808517,
-0.04581162706017494,
0.015097063966095448,
-0.005890193860977888,
0.05138188973069191,
0.032059576362371445,
0.021946430206298828,
-0.0018253945745527744,
-0.018446635454893112,
0.026113808155059814,
-0.023483751341700554,
-0.08638153225183487,
-0.0070498972199857235,
0.02527843602001667,
0.00595832010731101,
0.052347224205732346,
-0.012841029092669487,
-0.02151579223573208,
0.0033985089976340532,
-0.04669464752078056,
0.026921775192022324,
0.024662839248776436,
0.011152137070894241,
0.054016172885894775,
0.031684357672929764,
-0.03817027434706688,
0.04476756602525711,
0.023607270792126656,
-0.02195841632783413,
-0.025218551978468895,
0.017057016491889954,
0.07032596319913864,
-0.014423733577132225,
0.01053653471171856,
-0.036298684775829315,
0.01385877002030611,
-0.037630099803209305,
0.04448927193880081,
-0.047308824956417084,
0.02610822394490242,
-0.022612685337662697,
0.004343373700976372,
-0.0020794535521417856,
0.03226494789123535,
0.008393386378884315,
0.016520099714398384,
-0.014006133191287518,
-0.008869561366736889,
-0.021669965237379074,
-0.04248743876814842,
-0.016595149412751198,
-0.00817843060940504,
0.005862387362867594,
0.011993873864412308,
-0.004965085070580244,
-0.008872630074620247,
-0.02712249383330345,
-0.02498955838382244,
0.0014440490631386638,
-0.06904220581054688,
0.04924657195806503,
-0.00861000083386898,
-0.011631881818175316,
0.008540776558220387,
-0.07033376395702362,
-0.03496452048420906,
0.03186291456222534,
-0.01901421695947647,
0.04006561264395714,
-0.03528312221169472,
0.029501093551516533,
0.012238101102411747,
0.0009262434323318303,
-0.06057437136769295,
-0.06589799374341965,
0.005940565373748541,
0.017948325723409653,
-0.003270806046202779,
-0.01138787716627121,
-0.001828801934607327,
-0.021185336634516716,
-0.021462129428982735,
0.008504427038133144,
0.03382039815187454,
-0.01238863356411457,
0.005953314248472452,
0.010253244079649448,
-0.0191939827054739,
0.036797020584344864,
-0.008091378957033157,
-0.03050943650305271,
-0.028297415003180504,
-0.03903302922844887,
-0.004526426550000906,
0.00788081157952547,
0.04850398749113083,
-0.02477256767451763,
-0.014638817869126797,
0.0013185498537495732,
0.008495948277413845,
0.05055657774209976,
-0.023096289485692978,
0.016132652759552002,
0.05745568498969078,
0.011443305760622025,
0.006564289331436157,
-0.0021827155724167824,
0.022002603858709335,
0.024376103654503822,
0.033390067517757416,
0.01874922588467598,
0.016848865896463394,
-0.06921767443418503,
-0.0657099261879921,
0.0024797713849693537,
0.04237334057688713,
0.01790815033018589,
-0.018616393208503723,
0.050297968089580536,
-0.016565388068556786,
-0.015416760928928852,
0.03194493055343628,
0.010385078378021717,
0.0161222405731678,
-0.05842610448598862,
-0.002254227874800563,
0.0023004377726465464,
-0.003726792987436056,
-0.02661200240254402,
-0.019967716187238693,
-0.007597674150019884,
0.006349342409521341,
0.060505080968141556,
-0.05293206125497818,
0.051268644630908966,
0.015093537978827953,
0.008755308575928211,
-0.02839077264070511,
-0.029572326689958572,
-0.00582405598834157,
-0.013192888349294662,
0.01482299342751503,
-0.014086033217608929,
-0.03535202145576477,
0.021866360679268837,
0.03576517477631569,
0.04638548567891121,
-0.012365066446363926,
-0.0012059765867888927,
0.04641547054052353,
0.04704129323363304,
0.049328338354825974,
0.031660206615924835,
-0.021682579070329666,
0.01602192223072052,
-0.012955401092767715,
0.04329270124435425,
-0.011313298717141151,
-0.024116691201925278,
0.04232480376958847,
0.00385222677141428,
0.01084489282220602,
-0.04161043465137482,
-0.02720172517001629,
-0.010904313065111637,
0.0015380176482722163,
-0.01138518750667572,
0.011814714409410954,
-0.013988850638270378,
0.0316803902387619,
0.04825147986412048,
0.029842467978596687,
0.024412378668785095,
-0.020057642832398415,
-0.05230118706822395,
-0.018705036491155624,
0.0018856023671105504,
-0.002913995645940304,
0.046224527060985565,
-0.005974598228931427,
-0.029804464429616928,
0.007297903764992952,
-0.026984959840774536,
0.023879779502749443,
0.0578523613512516,
0.017983419820666313,
-0.011438935063779354,
0.0815189778804779,
-0.002162364311516285,
0.028471335768699646,
-0.030155261978507042,
-0.005640275310724974,
0.09105053544044495,
0.011777840554714203,
0.002072877250611782,
-0.05685489997267723,
-0.004098917823284864,
-0.033593546599149704,
-0.011360971257090569,
-0.03739945963025093,
0.017644697800278664,
-0.007922048680484295,
0.005602688528597355,
0.016833340749144554,
0.04297574236989021,
0.006637383718043566,
-0.016482651233673096,
0.045953117311000824,
-0.013727881945669651,
-0.06414642184972763,
-0.000548706273548305,
0.028410648927092552,
0.01117554772645235,
0.030180232599377632,
-0.035606369376182556,
0.0044835335575044155,
-0.06411069631576538,
-0.009894638322293758,
-0.011303626000881195,
-0.012678388506174088,
0.06100013852119446,
-0.00769174424931407,
-0.020892547443509102,
0.007931523025035858,
0.0035948322620242834,
-0.02536076307296753,
-0.06453271210193634,
0.002060494851320982,
0.03593927249312401,
0.02117060497403145,
0.05198551341891289,
0.005047233309596777,
0.021003222092986107,
0.025919005274772644,
0.04142605885863304,
0.011186198331415653,
-0.0386991873383522,
0.0009633357403799891,
-0.02671101689338684,
0.04298862814903259,
0.014585995115339756,
0.02800561860203743,
0.03907928615808487,
0.004534359090030193,
-0.01008705422282219,
-0.0413936972618103,
-0.050202321261167526,
-0.013656076975166798,
0.008099446073174477,
0.002127758227288723,
0.007344657555222511,
-0.042801592499017715,
0.053905293345451355,
-0.007474751211702824,
-0.019157536327838898,
-0.007044904865324497,
-0.023446790874004364,
0.016343455761671066,
0.006788360420614481,
0.06090545281767845,
-0.026095690205693245,
-0.02512550540268421,
-0.02860727719962597,
-0.033327531069517136,
-0.03820466622710228,
0.006862215232104063,
0.02593938820064068,
0.02168058417737484,
0.029056670144200325,
-0.04025299474596977,
-0.007568013854324818,
-0.011507341638207436,
-0.09029214084148407,
0.04726960510015488,
0.02167229913175106,
-0.020892232656478882,
0.0026179736014455557,
0.006787743419408798,
0.04732964187860489,
0.044673554599285126,
-0.03509952872991562,
0.027686886489391327,
-0.019930193200707436,
0.000590415031183511,
0.018436526879668236,
-0.029957305639982224,
-0.03821002319455147,
-0.01264292560517788,
-0.02041398361325264,
0.011044732294976711,
-0.004792468156665564,
0.01952356845140457,
0.03202345594763756,
-0.02026137337088585,
-0.01438754703849554,
0.02486034668982029,
-0.0032952320761978626,
0.025306856259703636,
0.03408381715416908,
-0.018666012212634087,
0.0031419245060533285,
0.01446353830397129,
-0.014288462698459625,
-0.035282522439956665,
-0.018635790795087814,
-0.0445830300450325,
0.023149965330958366,
0.02259237691760063,
0.03173096850514412,
-0.049637481570243835,
0.0006962706102058291,
0.001731796539388597,
0.028556490316987038,
-0.045457083731889725,
-0.016955869272351265,
-0.04465137794613838,
-0.000854242593050003,
0.022653143852949142,
0.008231510408222675,
-0.002706739120185375,
0.028735844418406487,
-0.016583256423473358,
-0.004766819998621941,
0.03692684695124626,
0.009012985974550247,
0.01636037416756153,
0.008047258481383324,
0.005072188097983599,
0.0009187801042571664,
0.060554973781108856,
-0.025960905477404594,
-0.038647908717393875,
0.04411466419696808,
-0.04392652586102486,
-0.03696281090378761,
0.08046182245016098,
-0.0007903713267296553,
0.029120879247784615,
0.03527477756142616,
0.000486137781990692,
0.017814787104725838,
0.04249785840511322,
-0.01986806094646454,
0.021518947556614876,
0.0199042409658432,
-0.037482842803001404,
-0.0002551560755819082,
-0.035575732588768005,
-0.010429449379444122,
-0.0010611177422106266,
0.01047481968998909,
0.020512733608484268,
0.0396236814558506,
0.014848439022898674,
-0.009087086655199528,
-0.011135558597743511,
-0.0008177318377420306,
0.009951836429536343,
0.07082251459360123,
-0.01443025004118681,
0.005047131795436144,
0.07061892002820969,
-0.03778354823589325,
0.019334856420755386,
0.004244636744260788,
-0.007255253382027149,
-0.08966846764087677,
-0.0285173412412405,
0.005609446205198765,
0.005566659849137068,
0.021014034748077393,
-0.04219847172498703,
0.005283505190163851,
0.05966448783874512,
-0.07262907922267914,
0.0021409103646874428,
-0.02209729142487049,
-0.03364025428891182,
-0.02577654831111431,
-0.0023128152824938297,
0.018877413123846054,
0.05297287553548813,
0.006278779823333025,
0.06294900923967361,
-0.004261345602571964,
-0.0007054448360577226,
0.003925785422325134,
-0.04486621916294098,
0.006470901891589165,
0.054425131529569626,
-0.0063737244345247746,
0.010159832425415516,
0.022150252014398575,
-0.05085400119423866,
-0.015397362411022186,
0.047530483454465866,
-0.012739017605781555,
0.0003730161115527153,
-0.04240977764129639,
0.025053493678569794,
-0.005077796056866646,
0.03370179235935211,
-0.003328614868223667,
-0.04663839563727379,
0.009332270361483097,
0.027260230854153633,
0.018534069880843163,
0.020390426740050316,
-0.0076848287135362625,
-0.011905215680599213,
0.02017379179596901,
-0.05049261450767517,
-0.032703761011362076,
0.04086162894964218,
-0.004935478791594505,
-0.004977118689566851,
0.019313842058181763,
-0.00716728251427412,
0.022005770355463028,
-0.020946871489286423,
-0.01995827816426754,
-0.052108313888311386,
-0.053168103098869324,
0.011973829939961433,
0.008981249295175076,
0.005994366481900215,
0.030593281611800194,
0.004384450148791075,
-0.003476264886558056,
0.03346767649054527,
-0.007476047147065401,
0.001234680414199829,
-0.06801334023475647,
-0.01993250474333763,
0.009056041948497295,
0.00027316404157318175,
0.03245237469673157,
-0.06015283986926079,
0.01596902310848236,
0.031121576204895973,
0.01791335456073284,
-0.0029962905682623386,
-0.002861669287085533,
-0.0663943886756897,
-0.03416437283158302,
-0.016397884115576744,
0.043606098741292953,
-0.010523170232772827,
-0.011708236299455166,
-0.048818279057741165,
-0.050971079617738724,
-0.03044641576707363,
0.03018210269510746,
0.030213037505745888,
-0.0037928009405732155,
0.0033308041747659445,
0.03198724612593651,
-0.024623176082968712,
0.012757586315274239,
-0.06369420140981674,
-0.011883022263646126,
-0.03503282740712166,
-0.015022638253867626,
0.0033897061366587877,
0.005329878535121679,
-0.03102559968829155,
-0.003388448851183057,
-0.021381985396146774,
0.0008054926875047386,
0.026587333530187607,
-0.030624208971858025,
-0.020844923332333565,
0.046530093997716904,
0.03531550243496895,
0.017279786989092827,
0.042174968868494034,
-0.006745375692844391,
0.005153842736035585,
0.00956371333450079,
-0.01892271265387535,
-0.034061089158058167,
0.012451697140932083,
-0.03583185747265816,
0.03030656836926937,
-0.013224366120994091,
0.011523228138685226,
0.04762258008122444,
-0.0406956747174263,
-0.01701386086642742,
-0.0006887356285005808,
-0.02505050227046013,
0.013313628733158112,
0.048067159950733185,
0.005365172401070595,
0.012609858997166157,
-0.04277488961815834,
0.01932101882994175,
0.031059982255101204,
0.024090658873319626,
-0.02341190166771412,
0.04333717003464699,
0.0024157948791980743,
-0.023151030763983727,
0.016465231776237488,
0.022508680820465088,
-0.011389545165002346,
0.014804321341216564,
0.014733945950865746,
0.024490756914019585,
-0.007207931485027075,
-0.004249884281307459,
0.013640675693750381,
-0.026751790195703506,
0.010677004233002663,
0.023220529779791832,
-0.035912394523620605,
0.05966572463512421,
-0.03686978295445442,
0.008239769376814365,
0.01740293577313423,
0.022586029022932053,
0.004108482971787453,
0.026818962767720222,
0.010586094111204147,
0.0312994159758091,
-0.03906374052166939,
-0.04663317650556564,
-0.007057370617985725,
0.013770411722362041,
0.006343685556203127,
-0.0597701296210289,
0.03056664578616619,
-0.025332508608698845,
-0.005402161739766598,
-0.05376976728439331,
0.012437843717634678,
-0.04346764087677002,
0.0023886559065431356,
0.022698432207107544,
0.044247906655073166,
0.01814807578921318,
-0.02986864186823368,
0.02056669257581234,
-0.016283920034766197,
0.06147482991218567,
-0.058460574597120285,
0.0016653042985126376,
-0.02066291868686676,
0.03270431235432625,
0.004498150199651718,
0.03163152560591698
] |
<p>In Chapter II of Dirac's <em>Principles of Quantum Mechanics</em>, Dirac explains that in general it is very difficult to know whether, for a given real linear operator, that any eigenvalues/eigenvectors exist and (if they do) how to find them.</p>
<p>He then goes on to state that a special tractable case can be found in the event that a real linear operator, $\xi$ can be expressed as the algebraic expression:</p>
<p>$\phi$($\xi$) $\equiv$ $\xi$<sup>n</sup> + a<sub>1</sub> $\xi$<sup>n-1</sup> + a<sub>2</sub> $\xi$<sup>n-2</sup> + ... + a<sub>n</sub> = 0</p>
<p>Where the a<sub>i</sub> are all numbers. He then factorises this as:</p>
<p>$\phi$($\xi$) $\equiv$ ($\xi$- c<sub>1</sub>)($\xi$- c<sub>2</sub>)($\xi$- c<sub>3</sub>)...($\xi$- c<sub>n</sub>).</p>
<p>Where the c<sub>i</sub> are also numbers.</p>
<p>I'm unsure how this factorisation has been achieved. Since Dirac didn't explicitly state the difference between $\phi$($\xi$) and plain $\xi$, then I imagine that $\xi$ represents a given dynamical variable and $\phi$($\xi$) the corresponding operator. This may be incorrect however. This is the only step in the logic that I can't work out, I understand his subsequent arguments but this step is eluding me.</p> | 1,978 | [
0.005933741107583046,
-0.008603732101619244,
-0.002474746201187372,
-0.03865645080804825,
0.05301643908023834,
-0.0038612852804362774,
-0.06300939619541168,
-0.012366585433483124,
0.006802484393119812,
-0.04337717220187187,
-0.006971559952944517,
-0.0025141530204564333,
0.0702148824930191,
0.010664483532309532,
0.02860626019537449,
0.045349329710006714,
-0.045967668294906616,
0.001388849108479917,
-0.01881241239607334,
0.0037363143637776375,
0.045019637793302536,
0.009563748724758625,
0.012287859804928303,
-0.010250112041831017,
0.007981399074196815,
0.03851863369345665,
-0.0035778565797954798,
0.00471185427159071,
0.0064611658453941345,
0.04334089159965515,
-0.006836030166596174,
-0.036478959023952484,
0.03330531716346741,
0.04481925442814827,
0.022059552371501923,
-0.007456991821527481,
-0.012943263165652752,
-0.03835714980959892,
-0.0032143867574632168,
0.02460446022450924,
-0.013586505316197872,
-0.034348685294389725,
-0.007668070960789919,
0.052273575216531754,
-0.025950055569410324,
0.03385567665100098,
-0.00008244612399721518,
-0.018694469705224037,
0.033215947449207306,
-0.05674491822719574,
0.08713573962450027,
0.011914685368537903,
0.022909119725227356,
-0.023602887988090515,
-0.013868127018213272,
-0.037308063358068466,
0.0442076101899147,
0.07267427444458008,
-0.0017152060754597187,
-0.027619920670986176,
-0.05145206302404404,
-0.04288855567574501,
-0.022548874840140343,
-0.025846388190984726,
-0.0074482872150838375,
0.0026686692144721746,
-0.0013769213110208511,
-0.031555477529764175,
0.018615324050188065,
-0.024110708385705948,
0.004373785108327866,
0.001782360952347517,
0.027896612882614136,
-0.03355245664715767,
0.007159146945923567,
-0.02419271133840084,
0.035845860838890076,
0.005911290179938078,
0.044850461184978485,
0.021023791283369064,
-0.019867029041051865,
0.042852699756622314,
-0.004951437469571829,
0.03290518745779991,
0.021556278690695763,
-0.044932521879673004,
0.057095568627119064,
0.013182147406041622,
0.007178011350333691,
0.01600642502307892,
-0.011166711337864399,
-0.0019282943103462458,
0.02019627019762993,
0.011270161718130112,
-0.030239848420023918,
0.010199518874287605,
-0.001222262973897159,
0.02289561554789543,
0.020586250349879265,
-0.00609668018296361,
-0.020662199705839157,
-0.012223592959344387,
0.030466608703136444,
0.04873700439929962,
-0.004619269631803036,
0.026348572224378586,
-0.04214048013091087,
0.02235957235097885,
0.01572263427078724,
-0.036958757787942886,
-0.03578370437026024,
0.03375944122672081,
-0.020225489512085915,
0.021298527717590332,
-0.004855849780142307,
-0.07257544994354248,
-0.029973063617944717,
-0.018345899879932404,
0.058501359075307846,
0.05005388706922531,
0.031723614782094955,
-0.00978488102555275,
0.01880481280386448,
-0.023091182112693787,
-0.04880419746041298,
0.004939132370054722,
0.06526314467191696,
-0.0013418359449133277,
-0.06187225133180618,
0.014891930855810642,
0.016446607187390327,
0.0378899909555912,
0.00266224704682827,
0.03697817027568817,
0.0007012432906776667,
-0.023716114461421967,
-0.12930220365524292,
-0.047708574682474136,
0.023216936737298965,
-0.04349188879132271,
-0.02890864759683609,
-0.07155683636665344,
0.019781699404120445,
0.05823613330721855,
0.10108312219381332,
-0.0005079566617496312,
0.03621573746204376,
0.030066097155213356,
-0.030602911487221718,
0.04495915398001671,
0.008326547220349312,
-0.030079687014222145,
0.005079776979982853,
-0.06882557272911072,
-0.018979378044605255,
-0.01045423373579979,
0.030658945441246033,
0.01184972282499075,
0.008064396679401398,
-0.02478191629052162,
0.09297319501638412,
-0.03520980849862099,
-0.03427688032388687,
0.04361957684159279,
-0.002790032187476754,
-0.03263495862483978,
0.06964476406574249,
0.025674719363451004,
0.018876224756240845,
0.06576739251613617,
-0.0025176105555146933,
0.02866913005709648,
0.02977454476058483,
0.05030182749032974,
0.06137315183877945,
-0.010399396531283855,
-0.04709125682711601,
-0.04779735207557678,
0.0029358393512666225,
-0.013712829910218716,
-0.01811135746538639,
-0.059209294617176056,
-0.03340236470103264,
0.04337014630436897,
0.016675129532814026,
0.024405749514698982,
0.006638140417635441,
0.03138435631990433,
0.025684665888547897,
-0.0314050167798996,
-0.013904438354074955,
-0.06395536661148071,
0.03921176493167877,
0.03608890250325203,
-0.005495102144777775,
0.039356496185064316,
0.005885609891265631,
-0.0036516347900032997,
0.014318407513201237,
-0.04061863198876381,
-0.012833372689783573,
0.04846062511205673,
0.015659498050808907,
-0.04628436639904976,
0.031113695353269577,
0.03782818093895912,
0.048878014087677,
-0.005344702862203121,
0.06150849536061287,
-0.008158429525792599,
-0.02777448482811451,
0.012613254599273205,
-0.019258182495832443,
0.04074658080935478,
0.008814653381705284,
0.007790362928062677,
-0.010197928175330162,
-0.026589959859848022,
-0.024686312302947044,
0.023165477439761162,
-0.04435979574918747,
0.05662409961223602,
0.02706049010157585,
0.016543082892894745,
-0.006955616641789675,
0.03371858969330788,
0.00418836111202836,
-0.03319976106286049,
0.023881318047642708,
-0.01934957504272461,
-0.04095609113574028,
-0.007743399124592543,
0.03852708265185356,
0.039269767701625824,
-0.021455172449350357,
0.03550541773438454,
0.02890196070075035,
0.022699102759361267,
0.043376315385103226,
0.03764588385820389,
-0.041797906160354614,
-0.024722805246710777,
0.03517819568514824,
0.02543845772743225,
0.0034059134777635336,
0.02750042825937271,
0.014836359769105911,
0.009282676503062248,
0.018315304070711136,
-0.008280222304165363,
-0.01936732977628708,
0.045486852526664734,
-0.053004562854766846,
-0.0037528048269450665,
-0.02305479533970356,
-0.028123730793595314,
0.07275573164224625,
-0.031206294894218445,
-0.00642902497202158,
0.0029274802654981613,
-0.0303905438631773,
-0.026812182739377022,
-0.023180006071925163,
-0.0019316367106512189,
0.04646239057183266,
-0.013753028586506844,
-0.05682949349284172,
0.0007538865902461112,
0.004161319229751825,
-0.013024314306676388,
0.026119006797671318,
-0.06252266466617584,
-0.010702176950871944,
-0.0013539812061935663,
-0.0017645106418058276,
0.034807801246643066,
0.005774082150310278,
0.013918207958340645,
-0.010257337242364883,
-0.015994621440768242,
-0.010094122029840946,
-0.05846044048666954,
0.014750068075954914,
0.036107487976551056,
-0.03336713835597038,
0.002599417930468917,
-0.06119485944509506,
-0.03512740880250931,
0.02116822823882103,
0.00002346764631511178,
0.052746355533599854,
0.004020703956484795,
-0.03488197177648544,
-0.03787419572472572,
-0.026096943765878677,
-0.041364144533872604,
-0.0005687876837328076,
-0.04108673334121704,
0.0054593514651060104,
0.05469812825322151,
-0.03044299967586994,
0.01393800787627697,
-0.024411683902144432,
0.008920339867472649,
-0.043427933007478714,
-0.01964753307402134,
-0.023563306778669357,
0.01717306487262249,
-0.04518841952085495,
0.05032479017972946,
0.03527350723743439,
-0.00704307621344924,
0.03548735752701759,
-0.06744114309549332,
-0.03735054284334183,
-0.01410904061049223,
0.015892840921878815,
0.007377764210104942,
0.012398846447467804,
0.016087517142295837,
0.09233087301254272,
-0.004521187860518694,
-0.02517038956284523,
-0.009599710814654827,
-0.013038119301199913,
0.0004606804286595434,
-0.01985379122197628,
-0.0044369869865477085,
0.04187319427728653,
-0.0025995809119194746,
0.02029622532427311,
-0.008184491656720638,
-0.007574643474072218,
0.04023394361138344,
0.003085176460444927,
-0.011062238365411758,
0.04180024936795235,
0.010075484402477741,
-0.001616787863895297,
0.04590791091322899,
-0.003674708539620042,
-0.004454498644918203,
-0.011312060058116913,
0.02710041031241417,
0.013467861339449883,
0.00020170527568552643,
-0.03333314508199692,
0.041404981166124344,
0.010653327219188213,
0.04081768915057182,
-0.012428938411176205,
0.033846255391836166,
-0.004773744381964207,
-0.005679131019860506,
-0.007765891496092081,
0.010581503622233868,
0.05105204880237579,
-0.05409535765647888,
0.0073869479820132256,
0.02751990407705307,
0.03881463408470154,
-0.01332277525216341,
-0.019224349409341812,
0.003039086703211069,
-0.021826500073075294,
0.033769331872463226,
-0.04359443113207817,
-0.02764580026268959,
0.03722992539405823,
0.037860944867134094,
0.029703693464398384,
-0.020941730588674545,
-0.013829736970365047,
-0.010681826621294022,
-0.012053467333316803,
-0.013407330960035324,
-0.025127369910478592,
0.04213641956448555,
0.009956242516636848,
0.021525545045733452,
0.019677579402923584,
-0.012209798209369183,
0.026648366823792458,
-0.02496935799717903,
-0.07108183950185776,
-0.04240478202700615,
-0.004322359804064035,
-0.010544398799538612,
0.005890961736440659,
0.01990537717938423,
0.036132942885160446,
0.0004015332378912717,
-0.06786125898361206,
-0.014893039129674435,
-0.015382361598312855,
-0.027668211609125137,
0.03388547524809837,
-0.050837066024541855,
-0.05801110714673996,
-0.02236124314367771,
0.01034843921661377,
0.03070821240544319,
-0.01596902124583721,
-0.0016832149121910334,
0.014302599243819714,
-0.029399126768112183,
0.01906881481409073,
-0.015732385218143463,
-0.007298256736248732,
0.047260478138923645,
0.010061094537377357,
0.014960981905460358,
0.0336034782230854,
0.0007699014968238771,
-0.001796359196305275,
0.009205671027302742,
0.052960943430662155,
0.015999507158994675,
-0.0026510648895055056,
0.00820129830390215,
-0.013733676634728909,
-0.025483418256044388,
0.002051023533567786,
0.07704567164182663,
-0.012030098587274551,
0.05145886912941933,
0.03371407464146614,
0.03572006896138191,
-0.010613970458507538,
0.0632745549082756,
0.06455739587545395,
0.002489833626896143,
-0.037028130143880844,
-0.040745142847299576,
0.020850621163845062,
-0.0290116798132658,
-0.0028445469215512276,
-0.01206397358328104,
0.0006052970420569181,
0.01885332353413105,
0.0008339912164956331,
0.038549572229385376,
0.015655459836125374,
-0.007813685573637486,
0.02438400126993656,
-0.008718708530068398,
0.00833088904619217,
0.021089494228363037,
-0.019903084263205528,
0.003980595618486404,
0.0320696160197258,
0.022767575457692146,
-0.002013125689700246,
0.00970179121941328,
-0.05886591598391533,
-0.03480013087391853,
0.03006824105978012,
0.03164318948984146,
-0.014367078430950642,
-0.014901312999427319,
-0.02809945121407509,
-0.022555595263838768,
0.04537136107683182,
-0.03422004356980324,
0.04906082525849342,
-0.04554010182619095,
-0.03384551778435707,
-0.010360026732087135,
-0.04149451479315758,
0.0032016695477068424,
0.03717610612511635,
0.01963287591934204,
0.03759463503956795,
-0.03155031055212021,
0.006714291404932737,
-0.06400048732757568,
-0.008617449551820755,
0.03521526977419853,
0.0621127225458622,
-0.004005801398307085,
0.01108008436858654,
0.003757701488211751,
0.03149816393852234,
0.00015694207104388624,
-0.057427987456321716,
0.01683645509183407,
0.03083856962621212,
-0.014348425902426243,
0.02746807225048542,
-0.027176065370440483,
-0.036424100399017334,
0.016291238367557526,
0.0049761198461055756,
-0.005277174059301615,
-0.00044455655734054744,
-0.02208329737186432,
0.05548093467950821,
0.020790988579392433,
-0.004663472529500723,
0.04284480959177017,
0.007930546067655087,
-0.01136811263859272,
-0.013477680273354053,
-0.0134185291826725,
-0.01842125877737999,
0.006261775270104408,
0.015262057073414326,
-0.024386757984757423,
0.0323648639023304,
0.021355193108320236,
0.03908662497997284,
0.03810166195034981,
0.006447539199143648,
0.010765744373202324,
-0.01886102929711342,
-0.05959306284785271,
0.026512915268540382,
-0.046244386583566666,
-0.015170598402619362,
-0.027039553970098495,
0.0420442558825016,
0.004130900837481022,
-0.02881375141441822,
0.0004358587902970612,
-0.010734797455370426,
0.005040814634412527,
0.05579211562871933,
-0.014648293145000935,
0.04540126770734787,
-0.015019170008599758,
0.009329618886113167,
0.008660404942929745,
-0.07165836542844772,
0.04062140733003616,
-0.022181645035743713,
-0.00015758842346258461,
0.009248603135347366,
-0.028595348820090294,
-0.04181627556681633,
0.012226800434291363,
-0.017082512378692627,
0.003884047968313098,
-0.033790603280067444,
-0.0007403009221889079,
0.029315130785107613,
-0.03538484871387482,
-0.06155039370059967,
-0.020756810903549194,
0.0008700608159415424,
0.0169338621199131,
-0.0031399924773722887,
-0.012142268009483814,
0.01584490016102791,
-0.010791177861392498,
0.0078218849375844,
0.015331930480897427,
0.019899513572454453,
-0.03948215767741203,
0.0036055208183825016,
0.01781187765300274,
0.04946267232298851,
0.045549698173999786,
-0.029054729267954826,
-0.01905520260334015,
-0.015064789913594723,
-0.017738284543156624,
0.007155851926654577,
0.002481896663084626,
0.06430552154779434,
-0.0367751382291317,
-0.03411054611206055,
0.0022216017823666334,
-0.006991271860897541,
0.04290164262056351,
-0.028977926820516586,
-0.014705222100019455,
0.003609624458476901,
0.03456851467490196,
0.029470834881067276,
-0.01769672892987728,
0.002164339879527688,
0.012372799217700958,
0.049882907420396805,
0.014362779445946217,
0.011134613305330276,
-0.04088892787694931,
-0.0325096994638443,
0.04175342619419098,
-0.03958320617675781,
0.011978811584413052,
0.007222712505608797,
0.048873528838157654,
0.0035155517980456352,
0.018765151500701904,
0.00906927790492773,
0.0024466239847242832,
0.004274831619113684,
0.02705707773566246,
0.04451470822095871,
-0.004826121963560581,
-0.05189570039510727,
-0.012187609449028969,
-0.04159894958138466,
-0.04690055549144745,
0.05445447564125061,
0.03043271414935589,
0.015789305791258812,
0.03405686840415001,
0.040653638541698456,
0.014188621193170547,
-0.016275478526949883,
0.006936165504157543,
-0.02201327122747898,
-0.011515894904732704,
0.047057848423719406,
0.059422776103019714,
-0.04558217152953148,
0.0003650700964499265,
0.025252921506762505,
0.03912264108657837,
-0.009102603420615196,
-0.03997140750288963,
0.025043953210115433,
0.014200468547642231,
0.005337074398994446,
-0.02199452556669712,
-0.0051250276155769825,
0.048501063138246536,
-0.013179751113057137,
0.02603161707520485,
0.029738493263721466,
-0.03565853834152222,
0.017618950456380844,
0.029066290706396103,
0.019993454217910767,
-0.04344858601689339,
-0.04145236685872078,
-0.03754420578479767,
0.007434734143316746,
0.007851103320717812,
0.020661735907197,
0.021116822957992554,
0.017827484756708145,
-0.010980055667459965,
0.039455510675907135,
0.031376928091049194,
0.021130964159965515,
-0.051273804157972336,
-0.028753161430358887,
-0.0578547902405262,
-0.05709433555603027,
0.036377839744091034,
0.002943893428891897,
-0.021182088181376457,
0.005316772498190403,
-0.03867609426379204,
0.016656113788485527,
0.036021847277879715,
0.03419514745473862,
-0.04145418480038643,
0.045636240392923355,
0.004446938168257475,
-0.028521735221147537,
0.0018428543116897345,
0.009727468714118004,
0.1127762719988823,
0.05522662773728371,
0.02833464741706848,
-0.04190542548894882,
-0.01117838267236948,
-0.003081669332459569,
0.008962776511907578,
-0.01922394521534443,
0.010138105601072311,
0.019876912236213684,
-0.0004703588492702693,
-0.030799390748143196,
0.05678056925535202,
0.015813717618584633,
0.009116039611399174,
0.04881651699542999,
-0.03176158294081688,
-0.04037097468972206,
0.006948947440832853,
0.0329011008143425,
0.021506410092115402,
0.008580894209444523,
-0.025331012904644012,
0.024745892733335495,
-0.017053278163075447,
-0.003794219344854355,
0.012161338701844215,
-0.037536609917879105,
0.010376707650721073,
0.0032314909622073174,
-0.06831821799278259,
0.01758759841322899,
0.003792226780205965,
-0.027910860255360603,
-0.020215624943375587,
0.031981777399778366,
0.007894673384726048,
0.009151341393589973,
0.04035384953022003,
0.006908951792865992,
0.008001109585165977,
0.016525229439139366,
0.0019010696560144424,
0.010818150825798512,
-0.06655418127775192,
-0.030571071431040764,
-0.03486993536353111,
0.03556792810559273,
-0.01453522127121687,
-0.05869977921247482,
-0.005752016324549913,
-0.04064152017235756,
-0.00812204834073782,
-0.03620145097374916,
-0.004547796677798033,
-0.022658919915556908,
0.03223060071468353,
-0.024763982743024826,
-0.011760127730667591,
-0.01826789788901806,
-0.02442268468439579,
-0.0130961574614048,
0.004499758128076792,
-0.011624136008322239,
-0.037673529237508774,
0.020017342641949654,
-0.004510519560426474,
-0.01123210322111845,
-0.005624085199087858,
0.0007749904179945588,
-0.008253357373178005,
-0.0302854273468256,
-0.03656148165464401,
-0.023043053224682808,
0.0050872089341282845,
0.0019550621509552,
0.040046922862529755,
-0.002460058080032468,
0.00896025262773037,
-0.009678684175014496,
-0.07594513148069382,
-0.013199998997151852,
-0.02806423418223858,
-0.017735254019498825,
0.009118104353547096,
-0.03784056752920151,
0.020981118083000183,
0.03375053033232689,
-0.052806004881858826,
-0.02530866488814354,
0.013198408298194408,
0.013500871136784554,
0.04957273602485657,
-0.04083581268787384,
0.01324466336518526,
0.00210771057754755,
-0.012794316746294498,
0.01579202339053154,
-0.034071508795022964,
-0.004177183378487825,
0.04683413729071617,
0.016938433051109314,
-0.01964280940592289,
0.066716268658638,
-0.03148800879716873,
-0.007532318588346243,
0.01264978852123022,
-0.07135168462991714,
0.022418631240725517,
0.0360405407845974,
0.04063509404659271,
-0.04075193032622337,
-0.06474408507347107,
-0.04247227683663368,
0.01508260052651167,
0.004562200978398323,
-0.006629282142966986,
-0.050549641251564026,
-0.03131597116589546,
-0.008241250179708004,
0.02184142731130123,
-0.04649581015110016,
-0.0028119608759880066,
-0.03397265076637268,
0.05613844096660614,
0.016665304079651833,
-0.008699503727257252,
-0.04333465173840523,
0.04061150923371315,
0.003113935235887766,
-0.04803803563117981,
0.017209235578775406,
0.027383169159293175,
-0.016918763518333435,
-0.015485882759094238,
0.019124198704957962,
0.003384421346709132,
0.023332281038165092,
-0.023498427122831345,
-0.039089903235435486,
0.005397615022957325,
-0.04151938483119011,
-0.018644830211997032,
0.03134692832827568,
-0.024649741128087044,
0.0034569485578686,
0.07212909311056137,
-0.02515513077378273,
0.006385117303580046,
0.028968706727027893,
-0.042838919907808304,
0.014034336432814598,
-0.00014313202700577676,
-0.007838429883122444,
-0.026813603937625885,
-0.007272258400917053,
-0.028477013111114502,
-0.004938695579767227,
-0.0337454192340374,
0.014591994695365429,
0.030659927055239677,
-0.012025956995785236,
0.00467640208080411,
-0.0037990983109921217,
0.02536969631910324,
0.031855784356594086,
0.042433008551597595,
-0.007958604954183102,
-0.012937435880303383,
0.04499978572130203,
-0.06443431973457336,
0.004015127196907997,
0.028611907735466957,
0.03700090944766998,
-0.10134512186050415,
0.005393441300839186,
-0.02787160314619541,
0.005981164518743753,
0.04536048322916031,
-0.03023352287709713,
0.027539214119315147,
0.016710111871361732,
-0.06084749102592468,
0.02674240991473198,
-0.0552295558154583,
-0.018221529200673103,
-0.0013763619353994727,
-0.01760934852063656,
-0.020153146237134933,
0.04811049997806549,
0.012808290310204029,
-0.007126472424715757,
0.025444800034165382,
-0.0024640136398375034,
-0.017310498282313347,
-0.0672874003648758,
0.01880498230457306,
0.015611384063959122,
-0.014321875758469105,
-0.02592039294540882,
0.051788728684186935,
-0.012467583641409874,
-0.048493336886167526,
0.02300524152815342,
-0.020053328946232796,
-0.016707653179764748,
-0.0200071781873703,
0.03222077339887619,
0.02950182557106018,
0.024825502187013626,
0.025891277939081192,
0.006542867515236139,
-0.01909002847969532,
-0.010475668124854565,
0.012131118215620518,
0.00041011840221472085,
0.024959664791822433,
-0.007879555225372314,
0.05293016508221626,
-0.013975570909678936,
-0.03483985736966133,
-0.0035939677618443966,
-0.019006874412298203,
0.019896702840924263,
-0.022655339911580086,
-0.008586913347244263,
0.014566188678145409,
0.0034594759345054626,
0.04217788577079773,
-0.010919066146016121,
-0.028241099789738655,
0.010631900280714035,
0.015218690037727356,
0.007967062294483185,
0.019642401486635208,
-0.022069131955504417,
-0.04103239253163338,
0.029376987367868423,
0.04292288050055504,
-0.0006203330121934414,
-0.1098392978310585,
-0.010754337534308434,
0.043021563440561295,
-0.004267473705112934,
0.006483226083219051,
-0.03985967859625816,
-0.0682067945599556,
0.004004490561783314,
0.004938287194818258,
0.012043806724250317,
-0.04533115029335022,
-0.026141930371522903,
0.009905852377414703,
-0.06897875666618347,
0.04097076877951622,
0.031888097524642944,
0.029682153835892677,
-0.002895886078476906,
0.004794515203684568,
-0.022005442529916763,
-0.009841278195381165,
0.05733458697795868,
-0.016953706741333008,
-0.032866474241018295,
0.0070487759076058865,
0.0005266621592454612,
0.012136782519519329,
-0.0028362146113067865,
-0.024958666414022446,
-0.03463062644004822,
-0.008909196592867374,
-0.04827350378036499,
0.011638645082712173,
-0.030246678739786148,
0.025600936263799667,
0.03285449743270874,
0.00774178234860301,
-0.019868968054652214,
-0.01532307080924511,
-0.036057230085134506,
0.046378474682569504,
-0.0017375205643475056,
0.0048471055924892426,
0.041987333446741104,
-0.004135215654969215,
0.015329952351748943,
0.01872313767671585,
-0.01576506346464157,
-0.028827227652072906,
0.03880665823817253,
-0.03901103511452675,
0.004290375858545303,
-0.01762077398598194,
-0.00993460975587368,
0.03946496173739433,
-0.023349324241280556,
-0.004516409710049629,
0.02835463546216488,
0.0019242205889895558,
-0.035099782049655914,
0.049849797040224075,
0.02098369598388672,
0.03708627447485924,
0.06251950562000275,
-0.009083508513867855,
0.06526786088943481,
0.02721165306866169,
0.013311317190527916,
0.0471913106739521,
0.011432107537984848,
-0.0021080428268760443,
0.028128501027822495,
0.02129240147769451,
-0.01797795295715332,
0.04083295911550522,
0.02177847921848297,
0.04347328841686249,
-0.0318780280649662,
0.011084085330367088,
0.047282874584198,
-0.017727719619870186,
-0.010781304910779,
-0.017006583511829376,
-0.047013770788908005,
0.10043052583932877,
-0.004667052533477545,
0.035682015120983124,
-0.0405779704451561,
0.020232368260622025,
0.01085224561393261,
-0.01488160528242588,
0.014605560339987278,
0.038033343851566315,
-0.04104946181178093,
0.014312759041786194,
-0.03711859881877899,
0.005241861566901207,
0.003872545436024666,
-0.050351597368717194,
-0.032889850437641144,
0.02599199116230011,
-0.011224944144487381,
-0.020798377692699432,
-0.03549987077713013,
-0.0275066327303648,
-0.02285758964717388,
-0.0029521300457417965,
0.042628057301044464,
0.007103960495442152,
-0.018151063472032547,
-0.019309036433696747,
-0.012315874919295311,
0.04167379066348076,
-0.02816956117749214,
-0.034667596220970154,
-0.004519777372479439,
0.0170336551964283,
-0.03502164036035538,
0.015384010970592499
] |
<p>I first heard about the Tokamak in highschool 10 years ago and was wondering how far the technology has come since then. Can it sustain a reaction for more than a few seconds? Are these devices still huge or have they been made on a smaller scale?</p> | 1,979 | [
-0.013026680797338486,
-0.07762183994054794,
0.009262810461223125,
-0.03703869506716728,
0.08986999839544296,
-0.02050979994237423,
-0.028138762339949608,
-0.022676803171634674,
-0.00580683583393693,
-0.04670373722910881,
0.0007435701554641128,
0.03905671462416649,
0.014289054088294506,
-0.0002761582436505705,
-0.020667467266321182,
-0.0010335195111110806,
-0.0032710107043385506,
-0.014182482846081257,
0.016654683277010918,
-0.014917953871190548,
-0.02081703208386898,
-0.015144353732466698,
0.0014314600266516209,
0.008877785876393318,
-0.016823479905724525,
-0.001966616604477167,
0.009781726635992527,
0.00993972085416317,
0.06302142888307571,
0.06375035643577576,
0.006461042910814285,
-0.0318160206079483,
0.007174512837082148,
-0.006428978871554136,
0.03461463749408722,
0.0014992969809100032,
-0.01618453674018383,
-0.07691464573144913,
0.020094547420740128,
-0.010817533358931541,
-0.028408434242010117,
-0.04144371673464775,
-0.00878736563026905,
0.03153329715132713,
-0.018615346401929855,
-0.003743419423699379,
-0.016674527898430824,
-0.05585810914635658,
0.04731224104762077,
-0.07650667428970337,
0.018629688769578934,
-0.004135132767260075,
0.06453748047351837,
-0.018167857080698013,
0.013154658488929272,
0.005758966319262981,
0.06931249052286148,
0.023728368803858757,
0.0009270724258385599,
-0.023985082283616066,
-0.02160828560590744,
0.009449766017496586,
-0.0016380312154069543,
0.012499663978815079,
-0.025658277794718742,
0.01951017417013645,
-0.03579965978860855,
-0.053965214639902115,
0.013907290995121002,
-0.012747389264404774,
-0.001603354001417756,
0.022441500797867775,
0.017604712396860123,
0.04579062759876251,
-0.009456918574869633,
-0.0022208639420568943,
0.015993468463420868,
-0.019604280591011047,
0.05615000054240227,
0.057829421013593674,
-0.03579238802194595,
0.010323104448616505,
0.03674245998263359,
0.025475023314356804,
0.030507011339068413,
-0.005306962877511978,
0.08789759129285812,
-0.014098330400884151,
0.010072126053273678,
0.013496393337845802,
-0.03284857049584389,
0.026052866131067276,
0.036963608115911484,
0.014843557961285114,
-0.008993910625576973,
0.0073763532564044,
0.028043784201145172,
0.07957377284765244,
0.014684833586215973,
-0.01969919167459011,
0.08121778070926666,
0.0012957490980625153,
0.027154818177223206,
0.03406127169728279,
0.04414921626448631,
-0.028587084263563156,
-0.016511162742972374,
-0.008786190301179886,
-0.038980595767498016,
0.005917545408010483,
-0.06115865707397461,
0.024746229872107506,
0.02235964871942997,
-0.00005161093213246204,
0.0016717934049665928,
-0.01389989908784628,
0.014940322376787663,
-0.001872729160822928,
0.06361941993236542,
0.06444215774536133,
0.024705303832888603,
0.016882574185729027,
0.026656262576580048,
-0.026687176898121834,
-0.06158348545432091,
0.04765154793858528,
0.03015388362109661,
0.00041666353354230523,
0.0015640981728211045,
0.033791616559028625,
-0.008095086552202702,
-0.019598886370658875,
0.001327280537225306,
-0.0077551547437906265,
0.07789833098649979,
-0.016439169645309448,
-0.05798288807272911,
-0.05572827532887459,
0.05019205063581467,
-0.00809167418628931,
-0.02515723928809166,
-0.0919308289885521,
0.01068310346454382,
0.011255750432610512,
0.03774498030543327,
0.009359097108244896,
-0.029610052704811096,
0.0032054812181741,
0.044043608009815216,
-0.014258842915296555,
-0.05180015414953232,
0.006681469734758139,
0.033133022487163544,
-0.006550490390509367,
-0.0024374756030738354,
-0.08102347701787949,
0.04011889174580574,
0.035591211169958115,
0.016408231109380722,
-0.04026477783918381,
0.08156294375658035,
0.009246873669326305,
-0.022763993591070175,
0.0009267056011594832,
-0.007646242156624794,
-0.02683066762983799,
0.1191420704126358,
0.00483087170869112,
0.009303603321313858,
0.01995571330189705,
0.017479361966252327,
0.00663060462102294,
0.04559751972556114,
0.01008548866957426,
0.02940659411251545,
-0.04954681172966957,
0.010576766915619373,
-0.006090265698730946,
-0.01541862916201353,
0.006977471522986889,
-0.02131596952676773,
-0.0021525337360799313,
0.001508259098045528,
0.020860541611909866,
0.011272838339209557,
0.08082844316959381,
-0.04382815212011337,
-0.015796992927789688,
-0.0230275746434927,
-0.051281943917274475,
-0.02534860372543335,
-0.021537872031331062,
0.016673127189278603,
-0.010639934800565243,
-0.027582276612520218,
0.003439263440668583,
0.005688710603863001,
0.01919429376721382,
-0.03619943559169769,
-0.07032288610935211,
-0.010588129051029682,
0.04876147583127022,
0.010372145101428032,
0.02205699495971203,
0.004576147999614477,
0.06885360926389694,
0.01769430935382843,
-0.005285235587507486,
0.01764199696481228,
-0.013943789526820183,
-0.02960215136408806,
-0.032997988164424896,
-0.00996687076985836,
0.017670996487140656,
0.05359532684087753,
-0.02809770405292511,
0.023109562695026398,
-0.04642651230096817,
-0.03685936704277992,
0.035816490650177,
0.01686178147792816,
0.08054894953966141,
0.007986476644873619,
0.02819438837468624,
-0.019321206957101822,
0.02293390966951847,
-0.0019382302416488528,
-0.0052933101542294025,
0.028403256088495255,
-0.018997885286808014,
-0.08331657946109772,
0.020355381071567535,
0.028752392157912254,
0.028980687260627747,
-0.03492499515414238,
0.0361572802066803,
-0.0006061399471946061,
0.01451724860817194,
0.03665446117520332,
-0.003863369347527623,
-0.041604578495025635,
-0.01402516569942236,
0.009778416715562344,
0.007635718677192926,
-0.03761487454175949,
-0.028143351897597313,
0.015000133775174618,
0.02412528358399868,
0.0034724336583167315,
0.025675944983959198,
0.007044983096420765,
0.024014869704842567,
0.0024261735379695892,
-0.023356853052973747,
0.02792312577366829,
-0.013971774838864803,
0.05027400329709053,
-0.03431368246674538,
0.0009829729096964002,
-0.030448751524090767,
0.010305107571184635,
0.04660838097333908,
0.0190107598900795,
0.007500939071178436,
0.006252985913306475,
-0.051332857459783554,
0.0029241801239550114,
-0.015003039501607418,
0.04655218496918678,
-0.009407488629221916,
0.03572140261530876,
-0.025061367079615593,
0.014195702038705349,
-0.0023565872106701136,
-0.007044206839054823,
0.019013844430446625,
-0.011603554710745811,
0.02913086675107479,
-0.025209691375494003,
-0.039082616567611694,
0.0023704597260802984,
-0.07222596555948257,
0.02621798776090145,
0.016374612227082253,
-0.05368504300713539,
0.042482640594244,
-0.015703711658716202,
-0.012619067914783955,
0.04151773825287819,
-0.008461268618702888,
-0.006242405157536268,
0.006209827493876219,
-0.022831646725535393,
-0.08814428001642227,
0.00830893125385046,
0.014416060410439968,
-0.004917831160128117,
-0.014895165339112282,
-0.006705027539283037,
0.03689006716012955,
0.004470441024750471,
0.009762506932020187,
0.0288919135928154,
-0.022023946046829224,
-0.005785311572253704,
-0.022810498252511024,
0.008158731274306774,
0.014100650325417519,
-0.03592836856842041,
0.024254845455288887,
0.023716581985354424,
-0.06253475695848465,
0.021731268614530563,
-0.018647219985723495,
-0.0049898927100002766,
0.029088281095027924,
-0.029737209901213646,
0.06405562162399292,
-0.04315527528524399,
-0.04161638766527176,
0.02816094271838665,
0.02699032612144947,
-0.040043558925390244,
0.002641748869791627,
0.00307268975302577,
-0.007106786128133535,
0.0023818116169422865,
0.014091700315475464,
0.011973214335739613,
0.003753454890102148,
-0.012842469848692417,
-0.012553300708532333,
0.0013716593384742737,
0.0027143273036926985,
0.022789379581809044,
-0.029963288456201553,
-0.0034274596255272627,
-0.005551891401410103,
0.03200635686516762,
0.04895308241248131,
0.04628220573067665,
-0.047924041748046875,
0.019698312506079674,
-0.002929446054622531,
0.04429342597723007,
0.012328708544373512,
-0.03729037940502167,
0.04417082294821739,
-0.014357519336044788,
-0.03673771023750305,
-0.004767080768942833,
0.00931632425636053,
-0.020785875618457794,
-0.013513483107089996,
0.02729451283812523,
0.03971203789114952,
0.03634021803736687,
-0.010114636272192001,
-0.020334582775831223,
0.0020612217485904694,
0.02895856276154518,
-0.015190159901976585,
-0.01733865961432457,
0.00953220296651125,
-0.020655691623687744,
0.001722114160656929,
0.007310141809284687,
-0.020971348509192467,
0.027809713035821915,
0.0026198874693363905,
0.020930776372551918,
0.0023426469415426254,
0.011495377868413925,
0.012805256061255932,
-0.08721628040075302,
-0.015433724969625473,
0.017443539574742317,
0.06827652454376221,
0.007279363926500082,
0.017823178321123123,
-0.014402292668819427,
0.0007899427437223494,
0.013314332813024521,
-0.05306641012430191,
-0.0818825289607048,
0.00696221087127924,
-0.06788213551044464,
0.00678254896774888,
-0.03012249246239662,
0.006626565009355545,
-0.032559942454099655,
0.03510677069425583,
-0.0061996569857001305,
-0.05111906677484512,
-0.008120180107653141,
-0.053132545202970505,
0.008812411688268185,
-0.02129383198916912,
-0.02627004124224186,
-0.016904721036553383,
0.005993874277919531,
0.03345099464058876,
0.014596594497561455,
0.032673291862010956,
0.014411602169275284,
-0.033955056220293045,
-0.00026464241091161966,
0.0061550443060696125,
0.03567127510905266,
0.013458777219057083,
0.04233085736632347,
0.007806115783751011,
0.010269992053508759,
-0.04246104881167412,
0.006781379692256451,
0.0344141386449337,
0.03515717387199402,
0.01253958698362112,
-0.001333702588453889,
-0.033879268914461136,
-0.053183671087026596,
-0.027606824412941933,
0.025231489911675453,
0.04465137794613838,
0.017564354464411736,
0.007896661758422852,
0.00988167803734541,
0.010374519042670727,
-0.031087445095181465,
0.029245691373944283,
0.009442106820642948,
-0.01692061685025692,
-0.004341769032180309,
-0.06307093054056168,
-0.01350327953696251,
-0.033434756100177765,
0.012781204655766487,
-0.007833709940314293,
-0.021031536161899567,
-0.024470455944538116,
0.0199587345123291,
0.033314719796180725,
0.01115420088171959,
-0.023203033953905106,
0.017618166282773018,
-0.007522123865783215,
-0.010845835320651531,
0.02049678936600685,
0.003357619745656848,
0.007180072367191315,
0.023803358897566795,
0.0709584653377533,
-0.0011057782685384154,
0.00893194880336523,
-0.08010004460811615,
-0.0016207111766561866,
0.0486944317817688,
0.011955694295465946,
0.005484660621732473,
0.007192237768322229,
-0.0746123194694519,
0.0005906909354962409,
0.05417586490511894,
-0.012389720417559147,
0.009441022761166096,
-0.04071702063083649,
-0.018813151866197586,
-0.03884422779083252,
-0.022672202438116074,
0.04129524156451225,
0.008082223124802113,
0.011481464840471745,
-0.014515078626573086,
-0.029802678152918816,
-0.017956433817744255,
0.008594552055001259,
0.013295931741595268,
0.02229989506304264,
0.03130723908543587,
0.023562926799058914,
-0.005035243928432465,
0.004293603822588921,
0.026706550270318985,
-0.023715829476714134,
-0.06287909299135208,
-0.015813713893294334,
-0.006452142260968685,
-0.006367652676999569,
0.027540937066078186,
-0.04538010060787201,
-0.044547948986291885,
0.003874965710565448,
0.003258375683799386,
-0.0000552566307305824,
-0.04406065121293068,
-0.024543358013033867,
0.013280883431434631,
0.002774815773591399,
-0.022385699674487114,
0.03788299486041069,
0.016251124441623688,
0.0011492114281281829,
0.03380383178591728,
0.014554663561284542,
0.021681001409888268,
-0.0037534579169005156,
0.021001534536480904,
0.023225655779242516,
0.01376822404563427,
-0.03652581945061684,
0.053167276084423065,
-0.035786084830760956,
0.0047064246609807014,
0.005635763518512249,
0.010541223920881748,
0.020844651386141777,
0.048538997769355774,
0.0018176137236878276,
-0.04560403525829315,
0.02201436087489128,
0.024176526814699173,
-0.005626536440104246,
-0.026032282039523125,
0.006019278895109892,
-0.03050878643989563,
0.011218596249818802,
-0.021793242543935776,
-0.038222964853048325,
-0.011443856172263622,
-0.04515623301267624,
-0.020178847014904022,
0.021604014560580254,
-0.026229431852698326,
0.08181624114513397,
-0.03883863985538483,
-0.006781785283237696,
0.052065249532461166,
-0.0845988318324089,
-0.02269561029970646,
-0.01922074519097805,
-0.0055540199391543865,
0.03783555328845978,
-0.03311055526137352,
0.047901738435029984,
0.0006334391073323786,
0.007431477773934603,
-0.05132681131362915,
-0.04608608037233353,
0.041091952472925186,
-0.005174248944967985,
-0.021352620795369148,
-0.026299135759472847,
-0.02465754561126232,
-0.015185022726655006,
-0.04033181071281433,
-0.0016119458014145494,
0.03425280749797821,
-0.010396283119916916,
0.007814855314791203,
0.01384633220732212,
-0.00969277136027813,
0.07169567048549652,
-0.006893890909850597,
-0.019477419555187225,
-0.0015374592039734125,
-0.04120336472988129,
-0.004471467342227697,
-0.044919464737176895,
0.02100861631333828,
-0.02414330467581749,
0.020003505051136017,
-0.005188856739550829,
-0.012370718643069267,
0.02214478701353073,
-0.041392192244529724,
0.02974221669137478,
0.07960058003664017,
-0.017052795737981796,
0.012209564447402954,
-0.00925392284989357,
0.005165833048522472,
-0.04256695881485939,
0.011779196560382843,
-0.02140207216143608,
-0.02934485860168934,
-0.029442165046930313,
-0.004903754219412804,
0.023185452446341515,
0.014850378036499023,
0.014368798583745956,
-0.03931742161512375,
0.01313009113073349,
0.01743336394429207,
-0.016141319647431374,
0.002378928940743208,
-0.02947608381509781,
0.024635357782244682,
-0.045116107910871506,
-0.011656740680336952,
-0.0031783771701157093,
-0.021248649805784225,
-0.008065369911491871,
-0.04290160909295082,
-0.01641860045492649,
-0.003723784349858761,
0.020187588408589363,
-0.04870571196079254,
0.032611094415187836,
-0.010729433968663216,
-0.009329129941761494,
-0.003064938820898533,
-0.020833207294344902,
-0.03973865509033203,
0.005673955660313368,
-0.006408165208995342,
-0.010860205627977848,
-0.012442577630281448,
0.024903643876314163,
0.03193352371454239,
0.0347217433154583,
0.005586713552474976,
-0.006511004641652107,
0.016228364780545235,
0.00516404677182436,
0.01772010512650013,
0.007828334346413612,
-0.05677789822220802,
0.02664109505712986,
-0.050873834639787674,
0.04290137439966202,
-0.009591810405254364,
-0.01165953278541565,
0.02096463553607464,
-0.03632707893848419,
0.015103880316019058,
0.000972981855738908,
0.019908357411623,
-0.016805090010166168,
0.020420409739017487,
0.03250635415315628,
0.017543025314807892,
-0.022475503385066986,
-0.007151484023779631,
0.03341057151556015,
0.021433275192975998,
0.0025209870655089617,
0.0005234421114437282,
-0.05788398161530495,
-0.05101602151989937,
-0.006148089189082384,
-0.053585704416036606,
0.015998445451259613,
0.016166504472494125,
-0.04360703006386757,
-0.0017751299310475588,
-0.014847137965261936,
0.02415529638528824,
0.00479649193584919,
0.06175278127193451,
-0.009495824575424194,
0.04242156818509102,
-0.016346098855137825,
0.03631146252155304,
-0.028367681428790092,
0.03531888499855995,
0.11940263211727142,
0.01143769919872284,
-0.010567105375230312,
-0.048795435577631,
0.026435304433107376,
-0.048359259963035583,
0.0051609817892313,
-0.04257844015955925,
0.03345479071140289,
0.013042706996202469,
-0.02979203499853611,
0.036779697984457016,
0.03055722638964653,
0.01097083743661642,
0.05256880074739456,
0.05624593421816826,
-0.004702695179730654,
-0.04533003270626068,
0.033837560564279556,
0.04824204370379448,
-0.0108713423833251,
-0.005790231749415398,
-0.033139824867248535,
0.015045116655528545,
-0.020395709201693535,
-0.017273567616939545,
-0.005884912330657244,
-0.029619162902235985,
0.04721574857831001,
0.01942538656294346,
-0.061517711728811264,
-0.010106904432177544,
0.005133007653057575,
0.004692306276410818,
-0.04528850317001343,
0.009314342401921749,
0.016412369906902313,
0.022807031869888306,
-0.018103227019309998,
0.029485682025551796,
0.01841772347688675,
0.007528339978307486,
0.003148657502606511,
0.008497140370309353,
-0.013052864000201225,
-0.010950403288006783,
-0.024398064240813255,
-0.024272801354527473,
-0.015397518873214722,
0.06820345669984818,
-0.0020332587882876396,
0.014536158181726933,
-0.00859523843973875,
-0.011749436147511005,
-0.06129942089319229,
0.019952954724431038,
0.006973665207624435,
-0.014190541580319405,
-0.007705110125243664,
-0.04308347404003143,
0.02226947993040085,
-0.06206449866294861,
0.016588876023888588,
-0.010980230756103992,
-0.004280115012079477,
0.0343979150056839,
-0.019303731620311737,
0.0028735571540892124,
0.01301491353660822,
-0.007329975720494986,
-0.04745792970061302,
-0.004169348627328873,
-0.04421279579401016,
-0.0008748971158638597,
0.020682182163000107,
0.013370949774980545,
0.03204396739602089,
0.006277482956647873,
-0.04190978407859802,
-0.029995135962963104,
-0.03526413068175316,
0.048623353242874146,
-0.0038384569343179464,
-0.025478476658463478,
-0.016333676874637604,
-0.008112536743283272,
0.008883385919034481,
0.038257159292697906,
-0.06860369443893433,
0.053749486804008484,
-0.04953068867325783,
-0.012071818113327026,
0.011997872963547707,
-0.014704229310154915,
-0.0047857691533863544,
0.028097597882151604,
-0.049916308373212814,
-0.00974338036030531,
-0.04350535571575165,
0.07367312908172607,
0.05665729567408562,
-0.025524333119392395,
0.040492646396160126,
0.029881279915571213,
-0.015435227192938328,
-0.00021977674623485655,
0.027757512405514717,
-0.03171490877866745,
-0.003392949001863599,
-0.04101282358169556,
0.036581747233867645,
-0.006520015187561512,
-0.04194914922118187,
-0.032609742134809494,
0.005816950462758541,
-0.011620152741670609,
0.020617222413420677,
0.013956194743514061,
0.01351407915353775,
-0.02326960675418377,
0.04563925787806511,
-0.017585819587111473,
0.007980608381330967,
-0.029554903507232666,
0.006421138532459736,
0.019269846379756927,
-0.00005478003731695935,
0.007549383211880922,
0.025031033903360367,
-0.013160956092178822,
0.02381225861608982,
0.027963444590568542,
0.019346006214618683,
-0.017028067260980606,
0.014408075250685215,
0.0002465924480929971,
0.03487168997526169,
0.06344933807849884,
-0.03672655299305916,
-0.012968367896974087,
0.05011046305298805,
-0.042449865490198135,
-0.07417211681604385,
0.04169264808297157,
-0.007404692936688662,
0.0006143588689155877,
0.0561956949532032,
-0.009541395120322704,
0.007595796138048172,
0.06980030238628387,
-0.0048649911768734455,
-0.016075382009148598,
0.02970665879547596,
-0.006566047202795744,
0.01761210896074772,
0.03548869118094444,
0.028578665107488632,
-0.03928682580590248,
-0.005153140053153038,
0.024325847625732422,
0.01973104476928711,
0.021695397794246674,
0.006806899793446064,
-0.043013691902160645,
0.014174633659422398,
0.045855335891246796,
0.02472342737019062,
0.0013822984183207154,
0.03723785653710365,
0.06277301162481308,
-0.053895287215709686,
-0.002336976584047079,
0.01109403744339943,
-0.007059102412313223,
-0.0716056302189827,
0.011354349553585052,
-0.027900181710720062,
-0.03710874542593956,
0.04184802994132042,
-0.030770909041166306,
0.004571980331093073,
0.055375274270772934,
-0.06186310201883316,
0.006680672522634268,
-0.052218127995729446,
-0.04477272927761078,
-0.03207670897245407,
-0.028554372489452362,
0.012199511751532555,
0.06746697425842285,
0.028922593221068382,
0.05552690476179123,
0.019052395597100258,
0.035395827144384384,
-0.006751497276127338,
-0.006413453258574009,
-0.03253541514277458,
-0.011861256323754787,
-0.008176632225513458,
-0.014983943663537502,
0.046943068504333496,
-0.02930692583322525,
-0.019094200804829597,
0.033862315118312836,
-0.0084894560277462,
-0.00024453719379380345,
-0.014841902069747448,
0.029978372156620026,
0.041612282395362854,
0.017473043873906136,
0.02336038276553154,
-0.05054403468966484,
0.011462727561593056,
0.05682811513543129,
-0.008993164636194706,
0.0033495670650154352,
-0.02342303656041622,
0.027523690834641457,
0.05396830290555954,
-0.017440196126699448,
0.028945643454790115,
0.0381343699991703,
-0.020243939012289047,
-0.03371765464544296,
0.013389174826443195,
0.01997181586921215,
0.025206666439771652,
-0.02517886832356453,
-0.017558420076966286,
-0.015216847881674767,
-0.0194860827177763,
-0.016211504116654396,
0.038986556231975555,
0.013557752594351768,
0.03965200483798981,
-0.0026346214581280947,
0.002130314940586686,
0.018222440034151077,
-0.002868618816137314,
-0.005725116468966007,
-0.029597118496894836,
0.014139891602098942,
0.04056698828935623,
0.013496077619493008,
-0.0019788530189543962,
-0.024639800190925598,
-0.0322888158261776,
0.049772538244724274,
0.011104702018201351,
0.03684069216251373,
0.06636165082454681,
-0.05729217827320099,
-0.013795958831906319,
-0.015512221492826939,
0.026126138865947723,
-0.02084488794207573,
0.006431329529732466,
-0.029924960806965828,
-0.06275579333305359,
-0.01598801277577877,
-0.0051667396910488605,
0.044822730123996735,
-0.00840874295681715,
0.0107591412961483,
0.012142813764512539,
-0.017377544194459915,
0.02412012778222561,
-0.06224702298641205,
0.009780020453035831,
0.0028539560735225677,
-0.024535255506634712,
-0.017101936042308807,
-0.02339778281748295,
-0.01549885980784893,
0.012395340017974377,
0.0651899129152298,
0.017026234418153763,
0.027979785576462746,
-0.016952306032180786,
-0.03970690444111824,
0.047353047877550125,
0.04396666958928108,
-0.0245776679366827,
0.0529804565012455,
-0.031167905777692795,
0.016142824664711952,
-0.02622121199965477,
0.009795287624001503,
-0.014574074186384678,
0.0017768844263628125,
-0.024531511589884758,
0.04722408950328827,
-0.04107905924320221,
-0.04953351616859436,
0.005995223298668861,
-0.056483540683984756,
-0.006969227455556393,
0.04375693202018738,
-0.014670958742499352,
-0.0074051073752343655,
0.08701666444540024,
0.011855022981762886,
0.0002956383104901761,
-0.02612006664276123,
-0.010301714763045311,
0.015255387872457504,
0.04026756435632706,
-0.04543479532003403,
0.05831087380647659,
0.029433714225888252,
-0.002137002069503069,
0.051306672394275665,
-0.00842871330678463,
-0.02153361216187477,
0.004017690196633339,
-0.0055648270063102245,
0.03633807599544525,
-0.011739895679056644,
-0.04662035405635834,
0.01647595688700676,
-0.02491714246571064,
-0.01385999284684658,
0.05640741437673569,
-0.041496917605400085,
0.07976365834474564,
-0.02676503174006939,
0.011650022119283676,
0.023569829761981964,
-0.010363240726292133,
-0.008995146490633488,
0.008539949543774128,
-0.00802211556583643,
0.037541113793849945,
-0.04397980496287346,
0.011095063760876656,
-0.006684173364192247,
0.02187897264957428,
0.05023632198572159,
-0.040915973484516144,
0.047837767750024796,
-0.01949695684015751,
0.01709108240902424,
-0.0371418334543705,
-0.008265700191259384,
-0.016420036554336548,
-0.023239949718117714,
-0.006325095426291227,
0.01345088705420494,
0.008631839416921139,
0.0034006654750555754,
-0.01572924293577671,
-0.006650243885815144,
0.041536614298820496,
-0.04630904272198677,
0.004993286449462175,
-0.03858305141329765,
-0.006478034425526857,
-0.026085177436470985,
0.03652408719062805
] |
<p>Does anyone know the refractive index suppliers? I've found Cargille Labs (which customer service is terrible so far but the liquids may actually be OK), but nothing else comparable. I'd like to have a set of liquids with the refractive index in the range of 1.3...1.4. Are they so hard to produce that almost nobody does it or am I missing something?</p> | 1,980 | [
0.029420070350170135,
0.004392620176076889,
-0.003961813636124134,
0.0022720179986208677,
0.020268959924578667,
0.02169106900691986,
-0.0436873584985733,
-0.004275113344192505,
-0.021241219714283943,
-0.010886565782129765,
0.03727538883686066,
0.061686065047979355,
0.04456288740038872,
0.028931213542819023,
-0.014289570041000843,
-0.000036190183891449124,
0.0014701267937198281,
0.01043012086302042,
-0.02668108604848385,
-0.03686375543475151,
0.00018210243433713913,
0.003910787403583527,
0.013239292427897453,
-0.020294127985835075,
-0.03234434872865677,
0.009257358498871326,
-0.027411172166466713,
-0.012366242706775665,
0.024838676676154137,
-0.001068249810487032,
-0.04786550626158714,
-0.03866792470216751,
-0.018525373190641403,
-0.01599712297320366,
0.01516375970095396,
0.020803144201636314,
-0.03374166041612625,
-0.045934129506349564,
-0.05506400763988495,
0.04083751514554024,
-0.04146568849682808,
-0.013178705237805843,
-0.01906767673790455,
0.012475387193262577,
0.003563895123079419,
-0.025002725422382355,
0.007509551476687193,
-0.057160329073667526,
0.07290057837963104,
-0.1123863160610199,
0.04523879289627075,
0.03589313477277756,
0.024804193526506424,
0.05989093706011772,
-0.01728960871696472,
-0.025833437219262123,
0.059380024671554565,
0.04928802326321602,
0.012795611284673214,
-0.026650868356227875,
0.01677979715168476,
0.028093911707401276,
0.011633242480456829,
-0.0074835121631622314,
-0.025274917483329773,
-0.006453373469412327,
-0.0034863236360251904,
-0.010310080833733082,
0.03236619383096695,
-0.05150855705142021,
0.004423833452165127,
-0.012310843914747238,
0.03273735195398331,
0.007018555421382189,
-0.01854897476732731,
-0.025257496163249016,
-0.042003802955150604,
-0.0004816968576051295,
0.034912776201963425,
0.0628424733877182,
-0.0685439482331276,
-0.005641108378767967,
-0.008371571078896523,
0.009577247314155102,
-0.06729169189929962,
-0.01158891711384058,
0.052385520190000534,
-0.032190416008234024,
0.018542172387242317,
0.06529983878135681,
-0.0380559004843235,
0.000041056726331589743,
0.06335309147834778,
0.022172333672642708,
0.012677481397986412,
-0.022782422602176666,
-0.0338006317615509,
0.0499260388314724,
-0.011202172376215458,
-0.02197759598493576,
0.00942840427160263,
0.01660042442381382,
-0.038702867925167084,
0.10218088328838348,
-0.01651066541671753,
-0.07297415286302567,
-0.038683801889419556,
0.014102763496339321,
-0.02126663736999035,
0.008645320311188698,
0.0194728821516037,
0.0045206728391349316,
-0.015810498967766762,
-0.020373141393065453,
-0.014195059426128864,
-0.04031679034233093,
0.00864952802658081,
-0.02561231702566147,
0.045263152569532394,
0.10418341308832169,
0.03360731527209282,
0.010682560503482819,
0.04034112021327019,
-0.014924882911145687,
-0.06642157584428787,
0.03654041141271591,
-0.005858215969055891,
-0.0031541979406028986,
-0.0183884184807539,
0.0010486579267308116,
0.005594861228018999,
0.0037990508135408163,
0.04139401391148567,
-0.017733227461576462,
0.028037365525960922,
-0.037839069962501526,
-0.058663349598646164,
-0.0785028487443924,
0.044494934380054474,
-0.034882012754678726,
-0.05025347322225571,
-0.06601276248693466,
0.03327742591500282,
0.05396188423037529,
0.05915987864136696,
0.0035912005696445704,
0.03452405706048012,
-0.017457634210586548,
0.027653995901346207,
0.01560270506888628,
-0.06803108751773834,
-0.022400828078389168,
0.009669759310781956,
-0.047785576432943344,
0.013422706164419651,
-0.03868810832500458,
0.008452469483017921,
0.0309041328728199,
0.0012119975872337818,
-0.04141901805996895,
0.05041913688182831,
-0.011671232990920544,
0.02185283973813057,
0.04288816452026367,
0.016464799642562866,
-0.05611922964453697,
0.06113053113222122,
-0.012525168247520924,
0.04140496999025345,
0.007806902751326561,
-0.01280144602060318,
0.0062524559907615185,
0.06707245856523514,
-0.00614153640344739,
0.061957746744155884,
0.019601920619606972,
0.0024964993353933096,
-0.005384338553994894,
0.031522464007139206,
0.04013199731707573,
-0.013117506168782711,
-0.00955032929778099,
0.011163790710270405,
-0.00252051861025393,
-0.02418714202940464,
0.02127610519528389,
-0.02093096822500229,
-0.03603386506438255,
0.06461923569440842,
-0.07693227380514145,
0.008372682146728039,
-0.022050747647881508,
-0.023264536634087563,
0.03529273346066475,
-0.0055081807076931,
0.04240167513489723,
0.03476377949118614,
-0.01856941729784012,
0.0036579391453415155,
-0.06538361310958862,
-0.016881702467799187,
-0.010386927053332329,
0.033028557896614075,
-0.003866021055728197,
0.014431892894208431,
0.06140584871172905,
0.03693525865674019,
-0.045333102345466614,
-0.0032449746504426003,
-0.02922072634100914,
-0.03693987801671028,
-0.017043938860297203,
-0.012626530602574348,
0.020065492019057274,
-0.04548647627234459,
-0.015141269192099571,
0.007484405767172575,
0.01701427809894085,
-0.0017773712752386928,
0.03294065594673157,
-0.0481964610517025,
0.02473040111362934,
0.04961877316236496,
0.033992256969213486,
-0.011851421557366848,
0.016612453386187553,
-0.001120215398259461,
0.013590398244559765,
0.012850189581513405,
0.021613147109746933,
-0.018281957134604454,
-0.011893298476934433,
0.05095097795128822,
0.03325275331735611,
-0.0026174900121986866,
0.022439874708652496,
0.04244004562497139,
0.03212498500943184,
0.06736315786838531,
0.013091336004436016,
-0.0017988982144743204,
-0.056105393916368484,
0.004706342704594135,
-0.012753518298268318,
0.009305436164140701,
0.024983394891023636,
0.011645616963505745,
0.019199039787054062,
0.01237073726952076,
-0.004842337220907211,
0.016162708401679993,
-0.04243267700076103,
0.009669526480138302,
-0.013735638931393623,
0.009727261029183865,
0.011534360237419605,
0.012635746970772743,
-0.03223482519388199,
-0.03069302998483181,
0.025395523756742477,
0.04241349920630455,
0.0013539965730160475,
-0.03820251300930977,
-0.012886324897408485,
0.008655579760670662,
0.02200646512210369,
-0.05574286729097366,
-0.020100638270378113,
0.03456905856728554,
-0.03724468871951103,
-0.0047585731372237206,
-0.031847450882196426,
0.04320988059043884,
-0.03395121917128563,
0.009761588647961617,
-0.0129309743642807,
0.010585249401628971,
0.04763602092862129,
-0.002079767407849431,
-0.015038276091217995,
0.04946927726268768,
-0.023002607747912407,
0.008562772534787655,
-0.01863289624452591,
-0.048041924834251404,
-0.016056187450885773,
0.025274507701396942,
-0.03965388610959053,
0.0594751350581646,
0.006660014390945435,
-0.05254974216222763,
0.01332922838628292,
-0.028774229809641838,
-0.01961212046444416,
-0.024088077247142792,
-0.027709122747182846,
0.0012490026419982314,
-0.002764628268778324,
0.04125649482011795,
-0.01390323881059885,
-0.010240796953439713,
-0.02464340813457966,
-0.025871891528367996,
-0.0583721362054348,
-0.005339328199625015,
0.0028105739038437605,
0.037775494158267975,
-0.002858079271391034,
-0.048586346209049225,
-0.009502670727670193,
0.014643804170191288,
0.002727629616856575,
0.030911237001419067,
-0.057816218584775925,
-0.03559675067663193,
0.02154303714632988,
0.02645491436123848,
0.035069238394498825,
0.020757809281349182,
-0.000016007736121537164,
0.04025871306657791,
0.025358175858855247,
-0.06622621417045593,
-0.015218921937048435,
-0.010659762658178806,
0.021347587928175926,
-0.04213796183466911,
0.03160139545798302,
0.019691236317157745,
-0.013294345699250698,
0.02581348456442356,
0.019126152619719505,
0.014963552355766296,
0.06500522047281265,
0.036827970296144485,
0.043496325612068176,
0.044317614287137985,
0.03299715742468834,
-0.018073245882987976,
0.021303512156009674,
0.0670514851808548,
-0.012992762960493565,
0.024200458079576492,
0.02572363242506981,
0.01949901133775711,
0.038882363587617874,
-0.04922899976372719,
-0.005843816790729761,
0.008937167003750801,
0.022577110677957535,
0.021752120926976204,
0.010720455087721348,
-0.009990554302930832,
0.011693833395838737,
0.0032591233029961586,
0.03805789723992348,
0.040685757994651794,
0.01231390330940485,
0.023518133908510208,
0.06333811581134796,
0.034355487674474716,
0.013127329759299755,
-0.00826528575271368,
0.019204553216695786,
-0.026183610782027245,
0.003794445190578699,
-0.019345741719007492,
0.006651377305388451,
0.05937446653842926,
-0.015011711977422237,
0.026650359854102135,
-0.03964671865105629,
-0.01005309633910656,
0.00436523649841547,
-0.04238762706518173,
0.0025678661186248064,
-0.06829430907964706,
0.0506795272231102,
-0.0010646447772160172,
0.048978786915540695,
-0.0059456112794578075,
0.031422920525074005,
0.010400432161986828,
0.01528942584991455,
-0.055403564125299454,
0.02268759347498417,
-0.04507801681756973,
0.011959230527281761,
-0.03199198842048645,
0.012569640763103962,
-0.026213182136416435,
-0.006848460528999567,
-0.02956949733197689,
-0.007673831190913916,
0.04700222238898277,
-0.02789456956088543,
0.018790150061249733,
-0.01719442568719387,
0.0010302311275154352,
-0.026793409138917923,
0.027065228670835495,
-0.04229837656021118,
0.0087060471996665,
0.016329143196344376,
-0.017778316512703896,
-0.039599549025297165,
0.023691032081842422,
-0.02732432447373867,
0.0199437215924263,
0.0024250696878880262,
0.0629601925611496,
0.028467264026403427,
0.0030639723408967257,
-0.021600577980279922,
-0.009780105203390121,
-0.013099533505737782,
0.011801301501691341,
-0.005154639016836882,
0.034532833844423294,
-0.048997703939676285,
-0.030333107337355614,
-0.044329605996608734,
0.020823445171117783,
0.04551760479807854,
0.009436046704649925,
0.0104379802942276,
-0.029514824971556664,
-0.04604527726769447,
-0.03723367303609848,
-0.005690641701221466,
0.057498980313539505,
0.000045426208089338616,
-0.02243317849934101,
0.013800831511616707,
-0.03427119925618172,
-0.00701132882386446,
0.002896346850320697,
0.04584686830639839,
0.041555777192115784,
0.015797290951013565,
-0.016000665724277496,
0.03783273324370384,
-0.008198102936148643,
-0.015515089966356754,
0.018929986283183098,
-0.010897334665060043,
0.011253711767494678,
-0.01829623430967331,
-0.0028082828503102064,
0.00035012286389246583,
0.03798333555459976,
0.02359476499259472,
0.01704292744398117,
0.007258368656039238,
-0.08507964760065079,
0.03594941273331642,
0.03032861091196537,
0.03819317743182182,
-0.04086654633283615,
-0.010234326124191284,
-0.08111537992954254,
-0.05061745271086693,
0.048742376267910004,
-0.037759337574243546,
0.0028044097125530243,
-0.022537365555763245,
-0.0021184475626796484,
-0.021861715242266655,
-0.03770948946475983,
0.019130785018205643,
0.004665732849389315,
0.01991310343146324,
0.017326558008790016,
0.011042672209441662,
0.04505894333124161,
-0.005269187502563,
0.04442175105214119,
0.027839913964271545,
0.0632932186126709,
-0.010848435573279858,
-0.04768167436122894,
0.024458078667521477,
-0.018029076978564262,
-0.018179263919591904,
-0.03776877373456955,
0.002622759435325861,
0.014760253950953484,
0.02136826328933239,
0.057139262557029724,
-0.04705273360013962,
-0.05678194761276245,
0.05343715474009514,
0.02457035519182682,
-0.02047724835574627,
-0.007243323139846325,
-0.0060796067118644714,
-0.012691105715930462,
0.012689773924648762,
0.009280525147914886,
0.024827880784869194,
0.060722410678863525,
-0.0015187823446467519,
-0.005045211873948574,
-0.05797003582119942,
0.04056747630238533,
-0.02676127851009369,
-0.004706134088337421,
0.019126830622553825,
-0.01901797577738762,
-0.040553394705057144,
0.018450552597641945,
0.015139210969209671,
0.041003670543432236,
-0.010720755904912949,
0.0035002368967980146,
-0.009474202990531921,
0.010647089220583439,
0.014402427710592747,
-0.0294403787702322,
0.023382479324936867,
0.011425791308283806,
-0.02915020100772381,
-0.0018290061270818114,
0.03972475230693817,
-0.0011253206757828593,
0.012614082545042038,
0.04094482585787773,
-0.025562582537531853,
0.0015095093986019492,
-0.05788736790418625,
0.011201247572898865,
-0.00610604602843523,
0.007317108102142811,
0.058778125792741776,
-0.022662146016955376,
0.04841206595301628,
0.0197367575019598,
-0.02660411223769188,
-0.02814069576561451,
0.0035022173542529345,
-0.02197500877082348,
0.05944456160068512,
-0.04289156571030617,
0.021593905985355377,
-0.013740398921072483,
0.005990485195070505,
-0.04041125625371933,
-0.014274957589805126,
0.006412884686142206,
0.026675844565033913,
-0.02838081307709217,
-0.04690435156226158,
-0.015242303721606731,
0.01979593001306057,
-0.02236461266875267,
0.03598819300532341,
0.05320644751191139,
-0.007349963299930096,
-0.02785680629312992,
-0.014334510080516338,
0.02335035242140293,
0.03233181685209274,
-0.021193983033299446,
-0.034888703376054764,
0.02702057547867298,
-0.0018493501702323556,
-0.00873185321688652,
-0.0012724820990115404,
-0.0028726502787321806,
-0.020410673692822456,
-0.024113524705171585,
-0.03445325419306755,
-0.019955024123191833,
0.04786849394440651,
-0.008420399390161037,
0.055189650505781174,
0.009497115388512611,
0.003665250027552247,
-0.04002990573644638,
-0.025572165846824646,
0.025369981303811073,
-0.019392507150769234,
0.012571501545608044,
-0.0323585569858551,
-0.0014596040127798915,
-0.017770349979400635,
0.021570486947894096,
0.008528155274689198,
-0.022152895107865334,
0.04609830677509308,
-0.01953282579779625,
0.06482024490833282,
0.013179312460124493,
0.0038799033500254154,
0.029957491904497147,
-0.016399012878537178,
-0.006139076314866543,
0.017300423234701157,
-0.01878717914223671,
0.01269340980798006,
0.018844036385416985,
-0.009687226265668869,
-0.08824726194143295,
-0.006127228960394859,
0.03114422783255577,
0.03996489569544792,
-0.012110958807170391,
0.031065935268998146,
0.023969177156686783,
-0.013577120378613472,
-0.020556362345814705,
-0.007311444263905287,
-0.01801295392215252,
0.03043106570839882,
-0.05888955295085907,
0.03961765021085739,
-0.0015868950868025422,
-0.0060771312564611435,
-0.015068409033119678,
0.07213634252548218,
0.00035562284756451845,
0.004193228203803301,
0.03393084928393364,
0.033969175070524216,
0.017056087031960487,
-0.045896898955106735,
-0.06622813642024994,
0.011077607981860638,
-0.02703184261918068,
0.048489369451999664,
0.027290761470794678,
-0.014825443737208843,
0.04600003361701965,
-0.008855735883116722,
0.009786801412701607,
-0.0485658198595047,
-0.039792921394109726,
-0.01067478209733963,
0.03490838408470154,
0.044659633189439774,
-0.027521977201104164,
0.0011266982182860374,
0.01353300828486681,
-0.01723356731235981,
0.00907478854060173,
0.003347753081470728,
-0.0085613327100873,
-0.06795267760753632,
-0.032019779086112976,
-0.009864838793873787,
-0.03849684074521065,
0.00862890761345625,
0.019192639738321304,
-0.018112167716026306,
0.029671834781765938,
-0.00014080919208936393,
0.016619019210338593,
0.011957958340644836,
0.008334570564329624,
0.006911226082593203,
0.025424860417842865,
-0.00013046096137259156,
0.04723341017961502,
0.0025139329954981804,
-0.019300349056720734,
0.12822970747947693,
0.05489444360136986,
-0.012115752324461937,
-0.08166529983282089,
-0.012499934062361717,
-0.031037712469697,
0.01770170032978058,
-0.06718353927135468,
0.03736640885472298,
-0.025250103324651718,
0.01818726770579815,
0.026819979771971703,
0.0626823827624321,
-0.003577230265364051,
0.053799767047166824,
0.026793377473950386,
-0.011713307350873947,
0.011821852065622807,
0.02497502602636814,
0.010784856975078583,
-0.009608805179595947,
0.020884372293949127,
-0.027163352817296982,
0.021768582984805107,
-0.010741963982582092,
-0.009784843772649765,
-0.02268264815211296,
-0.04095802083611488,
0.0488317608833313,
-0.01722409948706627,
-0.021808018907904625,
0.00597700709477067,
-0.00004721770892501809,
0.010599995963275433,
-0.02226937748491764,
0.042011331766843796,
0.0004887472605332732,
-0.02586188353598118,
-0.024815872311592102,
0.00814768671989441,
0.014457444660365582,
-0.008972471579909325,
0.009704370982944965,
0.017454110085964203,
-0.01626414805650711,
0.0035324341151863337,
-0.014071114361286163,
-0.024917099624872208,
-0.013544127345085144,
-0.013675808906555176,
-0.017274940386414528,
-0.022149067372083664,
-0.0029218699783086777,
-0.060723114758729935,
-0.02424030378460884,
-0.023966969922184944,
0.02947283536195755,
-0.0226120725274086,
0.017351696267724037,
-0.0022320779971778393,
0.012264392338693142,
-0.03531968966126442,
0.022698938846588135,
-0.043147649616003036,
-0.00008548897312721238,
-0.014386417344212532,
-0.024496909230947495,
0.033009473234415054,
-0.004632034804672003,
-0.05561019852757454,
-0.03706823289394379,
0.009380649775266647,
-0.03144659474492073,
-0.014864737167954445,
-0.01844283565878868,
-0.013220381923019886,
0.03696329891681671,
-0.026069724932312965,
0.013677943497896194,
-0.004820037167519331,
-0.05087823420763016,
0.0035620909184217453,
-0.04122502729296684,
-0.008370354771614075,
-0.02401658333837986,
0.003987856209278107,
0.0024399710819125175,
0.052050646394491196,
-0.009863330982625484,
-0.0058342344127595425,
-0.008528826758265495,
-0.00045237186714075506,
0.034084469079971313,
-0.0114673413336277,
-0.038297418504953384,
0.013097619637846947,
-0.037725891917943954,
0.002807733602821827,
0.0056972564198076725,
0.05276886746287346,
0.01800660230219364,
-0.021893693134188652,
0.03445795550942421,
-0.043794721364974976,
-0.04033327102661133,
0.03184038773179054,
-0.0006522268522530794,
-0.058543041348457336,
0.016317924484610558,
-0.02311449684202671,
-0.0002489363250788301,
-0.01975044049322605,
-0.07112827152013779,
-0.0334063321352005,
-0.022791249677538872,
-0.0040413797833025455,
0.024698561057448387,
-0.011324706487357616,
-0.02417774684727192,
0.031694963574409485,
0.008710489608347416,
-0.011404801160097122,
-0.0051927207969129086,
-0.04806450009346008,
0.013481613248586655,
-0.02542686276137829,
0.05487184599041939,
-0.013808783143758774,
0.01657670922577381,
0.017725929617881775,
-0.011631404981017113,
0.031952910125255585,
0.03581348806619644,
0.031028084456920624,
-0.0062592956237494946,
0.00959419272840023,
0.009708981029689312,
0.03144366666674614,
-0.0489482656121254,
-0.037663377821445465,
0.027565203607082367,
-0.016948992386460304,
-0.06278862059116364,
0.012253159657120705,
0.0014332185965031385,
-0.0071758851408958435,
0.019167739897966385,
-0.015140116214752197,
-0.013976900838315487,
0.11344018578529358,
0.015630729496479034,
0.021749131381511688,
-0.010620860382914543,
0.016298256814479828,
0.062443848699331284,
-0.025591949000954628,
-0.0023725046776235104,
-0.005800796207040548,
0.011195466853678226,
0.06633774191141129,
0.02141161821782589,
0.015547588467597961,
0.026346666738390923,
-0.017972368746995926,
0.018746232613921165,
0.012373887933790684,
0.002822997746989131,
-0.012950345873832703,
0.01679150015115738,
0.0025709851179271936,
-0.056259628385305405,
0.03913866728544235,
0.05768107622861862,
0.04260866343975067,
-0.06330747902393341,
0.012495514936745167,
-0.021134424954652786,
0.02681160718202591,
-0.001778127858415246,
-0.051535699516534805,
0.02648964896798134,
0.037507593631744385,
-0.08768784999847412,
0.0029124708380550146,
-0.010010012425482273,
-0.016097741201519966,
-0.05870703235268593,
0.006722623948007822,
-0.0032042935490608215,
-0.0010882205097004771,
0.008644025772809982,
0.009347911924123764,
0.03367668017745018,
0.024244261905550957,
-0.047776758670806885,
0.026263680309057236,
0.02812410518527031,
0.013665524311363697,
-0.009195837192237377,
-0.04361048340797424,
0.043827079236507416,
-0.012798779644072056,
-0.004938401747494936,
0.015411751344799995,
0.017102299258112907,
0.0027899150736629963,
0.0156294796615839,
0.004503194242715836,
-0.03390949219465256,
0.03374292328953743,
0.005362736061215401,
0.020827073603868484,
-0.018340975046157837,
-0.0006581131601706147,
0.02356709912419319,
0.012584099546074867,
-0.00941639207303524,
0.014609331265091896,
0.0385025218129158,
-0.02509445883333683,
-0.01562584564089775,
0.0291433148086071,
-0.03867973014712334,
0.02722778730094433,
-0.003144332207739353,
0.0272959154099226,
0.039645515382289886,
-0.016354944556951523,
0.03903990238904953,
-0.06404926627874374,
0.008388949558138847,
0.043097175657749176,
0.0032558876555413008,
0.011878849007189274,
0.027415182441473007,
-0.03196442499756813,
-0.012122705578804016,
-0.029649244621396065,
0.008622577413916588,
-0.012753644026815891,
-0.024664776399731636,
0.01937265321612358,
-0.005670097190886736,
-0.018843619152903557,
-0.002173604676499963,
-0.02573598176240921,
-0.037070244550704956,
0.06190946698188782,
-0.01002913061529398,
0.02765509858727455,
0.03902895748615265,
0.050965748727321625,
-0.011869354173541069,
-0.06661736965179443,
0.030463136732578278,
0.0020031838212162256,
0.0037991139106452465,
0.006114191375672817,
-0.017248278483748436,
-0.005243019200861454,
0.01890513114631176,
0.009311350993812084,
-0.022895902395248413,
0.013024034909904003,
-0.026329930871725082,
0.02583875134587288,
-0.02074972353875637,
0.005337972193956375,
0.014812073670327663,
0.02774905413389206,
-0.04059367999434471,
-0.01637142524123192,
0.02004740945994854,
0.010784285143017769,
-0.014752604067325592,
0.006369363982230425,
-0.011581489816308022,
0.018115906044840813,
0.0025915480218827724,
-0.008519484661519527,
-0.021263811737298965,
-0.008708947338163853,
-0.011019866913557053,
0.07986021041870117,
-0.025418614968657494,
-0.002383687300607562,
0.0024749734438955784,
0.01993199624121189,
-0.04867566004395485,
0.07926682382822037,
-0.030178146436810493,
0.030991503968834877,
-0.017266130074858665,
-0.015036359429359436,
0.010269886814057827,
-0.03951406106352806,
0.04044860973954201,
-0.03131275996565819,
-0.023285526782274246,
-0.013032456859946251,
0.05577285587787628,
-0.025896523147821426,
0.00196564057841897,
-0.012205835431814194,
0.03299439325928688,
-0.005820423364639282,
0.026935582980513573,
-0.014473655261099339,
0.05541333183646202,
0.06315610557794571,
0.007325522135943174,
-0.011287503875792027,
0.03265640512108803,
-0.047112513333559036,
0.009618290700018406,
0.003940947353839874,
0.013025443069636822,
-0.017141826450824738,
-0.053749930113554,
-0.00020616287656594068,
-0.07663415372371674,
-0.01258425135165453,
0.04143413528800011,
0.0028139916248619556,
0.05675327032804489,
0.006990409456193447,
0.012941645458340645,
-0.05568322539329529,
-0.0002804859832394868,
0.0065891193225979805,
0.016839226707816124,
-0.02401137351989746,
0.022211993113160133,
-0.005133551079779863,
0.03018692135810852,
-0.03397286310791969,
-0.007016433402895927,
0.02391965314745903,
-0.0456717424094677,
0.004123887047171593,
0.007487328723073006,
0.030312392860651016,
-0.012756327167153358,
-0.03491228073835373,
-0.018460897728800774,
-0.03676614537835121,
-0.07090131938457489,
0.003981342539191246,
-0.027021903544664383,
0.02325757034122944,
-0.012387719005346298,
0.01333275344222784,
0.03324572369456291,
-0.03252566605806351,
-0.009260962717235088,
-0.0007934495806694031,
-0.025518178939819336,
0.003425444010645151,
-0.007030955050140619
] |
<p>As the title says, is it possible to have a Riemannian Ricci flat compact manifold with $U(1)\times{}SU(2)\times{}SU(3) $ <a href="http://en.wikipedia.org/wiki/Isometry_group" rel="nofollow">isometry group</a>?</p> | 1,981 | [
-0.00989297591149807,
-0.004497935064136982,
-0.009407149627804756,
-0.04936811327934265,
0.034200359135866165,
0.00618189200758934,
-0.04538390412926674,
-0.05376061797142029,
-0.008005133830010891,
-0.08746691793203354,
-0.003557556075975299,
-0.020247992128133774,
0.07371275871992111,
0.02677851729094982,
0.003247760934755206,
-0.009219837374985218,
-0.01668504998087883,
-0.003676460823044181,
-0.023660100996494293,
-0.04768830165266991,
0.05235318839550018,
0.022779280319809914,
0.025791365653276443,
-0.015456503257155418,
0.023341428488492966,
0.016664963215589523,
0.0016380851157009602,
0.004477077163755894,
0.004779304843395948,
0.05841538682579994,
-0.034742508083581924,
0.027639111503958702,
0.029107818379998207,
0.015142661519348621,
0.022609993815422058,
-0.007924788631498814,
-0.03694726526737213,
-0.028605911880731583,
-0.013616863638162613,
0.022310949862003326,
-0.0234749186784029,
-0.012288548052310944,
0.012030063197016716,
0.06630668044090271,
-0.033033568412065506,
0.024283625185489655,
0.006633097771555185,
-0.03610827401280403,
0.03897674009203911,
-0.04941738024353981,
0.09089314937591553,
0.0227190051227808,
-0.0011909749591723084,
0.01745404303073883,
-0.008113102987408638,
0.0007833534036763012,
0.041786257177591324,
0.09644635021686554,
0.00776182534173131,
0.01954003982245922,
-0.01681315153837204,
0.013887782581150532,
0.022490667179226875,
0.004589342046529055,
-0.0414828397333622,
0.03555338457226753,
-0.04068804159760475,
0.02198338694870472,
-0.00035072604077868164,
-0.012850078754127026,
-0.0017797211185097694,
-0.0037355348467826843,
0.029365383088588715,
-0.010022914968430996,
0.022561602294445038,
-0.026732005178928375,
-0.003159136278554797,
0.007886944338679314,
0.05641144514083862,
0.0065267872996628284,
-0.010255655273795128,
0.005795435048639774,
0.01114080660045147,
0.020598718896508217,
0.004140355624258518,
0.017702698707580566,
0.05737008526921272,
0.0019014182034879923,
-0.014338147826492786,
0.04685391113162041,
0.02882297895848751,
-0.015429237857460976,
0.05240568891167641,
0.01293683610856533,
-0.010691847652196884,
0.028772078454494476,
-0.004004724323749542,
0.04693823307752609,
0.008642002008855343,
-0.02983330748975277,
0.024929525330662727,
0.014475603587925434,
0.0020289476960897446,
0.07823094725608826,
0.06753052026033401,
-0.008064514957368374,
-0.036444660276174545,
0.011639007367193699,
-0.045056428760290146,
0.01646222360432148,
-0.04832690954208374,
0.003702475456520915,
-0.02751731127500534,
-0.04157077148556709,
0.010755072347819805,
-0.013531433418393135,
0.02649541385471821,
-0.00838174857199192,
0.0021642090287059546,
0.10334908962249756,
0.04157586023211479,
0.007361392956227064,
-0.010725453495979309,
-0.022086990997195244,
-0.06964373588562012,
0.021471204236149788,
0.01889801025390625,
0.016769014298915863,
-0.043669264763593674,
0.021568702533841133,
-0.010006516240537167,
-0.006827604491263628,
0.011487342417240143,
-0.02125810831785202,
0.04097020626068115,
-0.039416659623384476,
-0.10962077230215073,
-0.03195316717028618,
0.019884929060935974,
-0.00453361077234149,
-0.003544352948665619,
-0.0747637078166008,
0.03804650902748108,
0.037843670696020126,
0.05822937563061714,
-0.005257262848317623,
-0.0009609776898287237,
0.038725171238183975,
0.05959261953830719,
-0.004805633332580328,
-0.0016224703285843134,
-0.02779753878712654,
-0.023839522153139114,
-0.044940605759620667,
0.018137691542506218,
-0.04342184588313103,
-0.015888381749391556,
-0.0012698507634922862,
0.03338313475251198,
-0.019444730132818222,
0.048203397542238235,
0.006488950923085213,
0.04418034106492996,
0.01573232188820839,
-0.027026211842894554,
0.008727935142815113,
0.04335211217403412,
0.016773736104369164,
-0.02151975966989994,
0.0030512455850839615,
0.0010382774053141475,
0.014881942421197891,
0.011832185089588165,
0.053841691464185715,
0.014339635148644447,
-0.05810866132378578,
-0.016988208517432213,
-0.02277028001844883,
0.012836676090955734,
0.020712535828351974,
-0.039633914828300476,
-0.01582369953393936,
-0.0283616092056036,
0.002775798784568906,
-0.009744756855070591,
0.0011446905555203557,
-0.016671476885676384,
-0.009984176605939865,
0.022063076496124268,
-0.048150233924388885,
-0.005785556510090828,
-0.048095230013132095,
-0.003915675450116396,
0.04339010268449783,
-0.05982084572315216,
0.026699986308813095,
0.04401974380016327,
0.039771903306245804,
-0.016628239303827286,
-0.041076116263866425,
-0.034061092883348465,
0.022651486098766327,
0.012164064683020115,
0.021077105775475502,
0.0018603162607178092,
0.008406751789152622,
0.05367608740925789,
-0.03898882493376732,
0.03234034404158592,
0.016219930723309517,
-0.024557705968618393,
0.008956176228821278,
-0.017283698543906212,
0.0073638129979372025,
-0.0007209928007796407,
0.0252834502607584,
0.03381723538041115,
0.03362306207418442,
-0.023692382499575615,
0.027849115431308746,
-0.04125359281897545,
0.04125691205263138,
0.0020305824000388384,
-0.015281114727258682,
0.008628545328974724,
0.025429995730519295,
0.043767184019088745,
0.03389919549226761,
-0.02594957873225212,
-0.021853256970643997,
-0.03167061135172844,
-0.0023690974339842796,
0.03693092614412308,
0.03852173686027527,
-0.03913791850209236,
0.030172141268849373,
0.046952929347753525,
0.04424396902322769,
-0.049298375844955444,
0.023004166781902313,
-0.0033812690526247025,
-0.028178973123431206,
0.05049404129385948,
-0.01506491657346487,
0.009566213004291058,
-0.021562112495303154,
-0.020056914538145065,
0.011288242414593697,
0.007931848987936974,
-0.037639081478118896,
0.006372518837451935,
0.053758975118398666,
-0.026658369228243828,
-0.04531733691692352,
0.02438448555767536,
-0.0020076672080904245,
0.013521566055715084,
-0.010032236576080322,
0.02585822157561779,
0.01770608127117157,
0.03130367398262024,
-0.022857893258333206,
-0.015865160152316093,
-0.038281649351119995,
-0.01643950678408146,
0.014474627561867237,
-0.011737416498363018,
-0.02115742862224579,
0.013288977555930614,
-0.05527662858366966,
-0.03149091824889183,
0.0027827147860080004,
-0.005107851233333349,
-0.007026491686701775,
-0.0017322847852483392,
0.044146403670310974,
-0.027242988348007202,
-0.00705524580553174,
-0.027125021442770958,
-0.035099856555461884,
0.051102619618177414,
0.00021204882068559527,
0.024983679875731468,
-0.02934105321764946,
-0.05924209952354431,
0.06034407019615173,
-0.022089758887887,
-0.021320050582289696,
-0.001697580679319799,
0.017048563808202744,
0.020212100818753242,
0.03174871951341629,
-0.02352973073720932,
-0.03795916214585304,
-0.04068784415721893,
-0.06923158466815948,
0.04188314080238342,
-0.010170920751988888,
0.025694768875837326,
0.04075245186686516,
0.029084734618663788,
-0.015726961195468903,
-0.03156057745218277,
-0.03571731224656105,
-0.02780059538781643,
0.006387646310031414,
-0.009135783649981022,
0.04319171980023384,
-0.044894199818372726,
0.033108558505773544,
0.034254055470228195,
-0.043793708086013794,
-0.008968889713287354,
-0.052301712334156036,
-0.027385864406824112,
0.03786245733499527,
0.024585174396634102,
0.038795702159404755,
0.03734930232167244,
-0.025266870856285095,
0.08708512783050537,
0.021264756098389626,
-0.05215521156787872,
-0.03618800267577171,
0.016433948650956154,
-0.0029433276504278183,
-0.03298565745353699,
0.0037180506624281406,
-0.00861472450196743,
-0.014729833230376244,
0.02444527857005596,
0.04420722275972366,
0.02039225958287716,
0.01447051391005516,
-0.001441356842406094,
-0.04965608939528465,
0.0009178380132652819,
0.02345678210258484,
0.042385756969451904,
0.017054039984941483,
0.011465881019830704,
-0.01863093115389347,
0.0023444935213774443,
0.01334055233746767,
0.029085548594594002,
0.00804162584245205,
-0.050819434225559235,
0.04023006558418274,
0.0165401641279459,
0.050323422998189926,
-0.009736316278576851,
0.040771469473838806,
0.023670578375458717,
-0.02368629164993763,
0.002121115103363991,
0.032469265162944794,
0.02589070424437523,
0.0037740408442914486,
0.006142281927168369,
0.014369412325322628,
0.02484220080077648,
0.003499092534184456,
-0.02944672480225563,
-0.019980933517217636,
-0.013061326928436756,
0.00990344863384962,
0.00941475946456194,
-0.028166214004158974,
0.016868188977241516,
0.01447751373052597,
0.009994782507419586,
0.03932299464941025,
-0.017268719151616096,
0.025521695613861084,
-0.05801127105951309,
-0.01079381164163351,
0.01128642912954092,
-0.004253447987139225,
0.019771616905927658,
-0.016884852200746536,
-0.012785632163286209,
-0.0052781905978918076,
-0.01220750529319048,
-0.006184307858347893,
-0.03722137585282326,
0.023037035018205643,
-0.03139100596308708,
0.0034323178697377443,
0.026417402550578117,
-0.015414251014590263,
-0.009603130631148815,
-0.0007154004415497184,
-0.03753213584423065,
0.009992965497076511,
0.021782347932457924,
-0.0387677364051342,
0.006157298572361469,
-0.03428475558757782,
-0.024243555963039398,
0.008333131670951843,
0.06828771531581879,
0.06227419525384903,
-0.01562623307108879,
0.020448315888643265,
-0.0023573676589876413,
-0.05045994371175766,
0.007483364548534155,
-0.014734694734215736,
0.03358669579029083,
-0.0291647519916296,
0.022679388523101807,
-0.0013360141310840845,
0.019124941900372505,
0.06440620869398117,
0.011436138302087784,
-0.022261768579483032,
0.009141839109361172,
0.0016801371239125729,
-0.026458723470568657,
0.00342754740267992,
-0.034974563866853714,
-0.006123129744082689,
0.009012778289616108,
0.05069392919540405,
-0.04584817588329315,
-0.003466117661446333,
0.004282117821276188,
0.0030056519899517298,
-0.007666578982025385,
0.0023279311135411263,
0.05476846545934677,
-0.011195407249033451,
-0.019734689965844154,
-0.057924214750528336,
-0.04723097011446953,
-0.025672292336821556,
-0.015243487432599068,
0.017864732071757317,
0.011819146573543549,
-0.06275441497564316,
0.0614241287112236,
0.0029369713738560677,
0.038018032908439636,
-0.03581468388438225,
-0.01126420870423317,
0.002587169175967574,
0.008662300184369087,
0.0217438954859972,
-0.018271205946803093,
-0.003392830491065979,
0.0447772741317749,
0.04991386458277702,
-0.0044615608640015125,
-0.019768444821238518,
-0.07620035856962204,
-0.014300062321126461,
0.038943372666835785,
0.002171220490708947,
0.007862923666834831,
-0.014220784418284893,
-0.049877334386110306,
0.03174952417612076,
0.06544262170791626,
-0.010582229122519493,
0.009373772889375687,
-0.01494177058339119,
-0.046895597130060196,
0.016891727223992348,
-0.011267274618148804,
-0.003042252967134118,
-0.004075963050127029,
-0.03730428218841553,
-0.033918596804142,
-0.010941066779196262,
0.016330691054463387,
-0.009501926600933075,
0.05704628303647041,
0.024174733087420464,
0.045947521924972534,
0.040687572211027145,
0.04373719170689583,
0.017576180398464203,
0.04522630572319031,
-0.015700893476605415,
-0.06454304605722427,
0.022604143247008324,
0.017869239673018456,
-0.02616187185049057,
0.028635600581765175,
-0.03204929456114769,
-0.017212344333529472,
0.009573464281857014,
-0.007103919982910156,
0.02506914734840393,
0.02473466470837593,
-0.05700376257300377,
0.02281356044113636,
0.061658527702093124,
0.011400673538446426,
0.0047931671142578125,
0.03297325596213341,
0.036115389317274094,
0.0024811592884361744,
-0.04309451952576637,
0.020648298785090446,
-0.033699192106723785,
-0.007588419131934643,
-0.02873433753848076,
-0.0032564804423600435,
-0.01651933416724205,
0.021696941927075386,
-0.03660338371992111,
-0.007499558385461569,
0.05146913602948189,
-0.0017112470231950283,
0.016589239239692688,
0.01589152030646801,
-0.01814384199678898,
-0.00885382667183876,
-0.02283346839249134,
0.028498128056526184,
-0.003186160698533058,
-0.023293975740671158,
-0.01994047500193119,
0.0015151450643315911,
0.002465431112796068,
0.021885138005018234,
-0.0035490517038851976,
0.009325973689556122,
-0.01715664379298687,
-0.008684597909450531,
0.0037504907231777906,
-0.09159758687019348,
0.06473914533853531,
-0.022529365494847298,
0.007858574390411377,
0.0018656025640666485,
-0.012670958414673805,
0.0067701335065066814,
-0.017688259482383728,
-0.03742028400301933,
0.03351617604494095,
-0.03250227868556976,
0.042012572288513184,
0.00447767972946167,
-0.035655759274959564,
-0.0746927261352539,
-0.015266395173966885,
0.057130370289087296,
0.011964811943471432,
-0.0035488521680235863,
-0.04715320095419884,
-0.007945836521685123,
-0.0351991206407547,
-0.020858461037278175,
0.005007268860936165,
0.03168993070721626,
-0.011279108002781868,
-0.008069466799497604,
-0.027575185522437096,
0.04022199660539627,
0.03856835514307022,
-0.021912068128585815,
-0.021652575582265854,
0.005737770348787308,
0.011670191772282124,
-0.02936634048819542,
-0.008585812523961067,
0.020631998777389526,
-0.0010933104204013944,
-0.013589602895081043,
-0.03788701072335243,
-0.03034384548664093,
0.005009990651160479,
-0.04374543949961662,
0.001614503562450409,
0.06412647664546967,
0.020689582452178,
0.04059962183237076,
-0.04956318438053131,
0.019410626962780952,
-0.025487594306468964,
0.004285651724785566,
-0.05222133547067642,
-0.026402218267321587,
-0.019352072849869728,
-0.03962874040007591,
0.07027328014373779,
-0.04080533608794212,
0.0006990041583776474,
-0.004188663326203823,
0.062221162021160126,
0.007519943173974752,
-0.027586592361330986,
-0.037721261382102966,
-0.0347675122320652,
-0.03644247353076935,
-0.026953425258398056,
0.012219230644404888,
0.001813166425563395,
-0.007613489869982004,
-0.02843068726360798,
-0.02133563533425331,
-0.01786871999502182,
0.020339567214250565,
0.05432839319109917,
-0.023040495812892914,
0.05978541448712349,
0.025611747056245804,
-0.018778754398226738,
0.003426885697990656,
-0.002552532823756337,
-0.015577960759401321,
-0.0025294844526797533,
0.028287233784794807,
0.06004342809319496,
-0.029755212366580963,
0.004149806685745716,
0.041129548102617264,
0.06245953217148781,
0.004702460952103138,
0.04675057902932167,
0.0005307172541506588,
0.009484746493399143,
0.02677551470696926,
0.00938196387141943,
-0.0738898441195488,
0.039273589849472046,
-0.04560639336705208,
0.026995863765478134,
0.005346962716430426,
-0.03330710157752037,
0.011525585316121578,
0.027696751058101654,
0.025526558980345726,
0.0008871236350387335,
-0.04758499935269356,
-0.030105844140052795,
0.06635856628417969,
0.0348682776093483,
0.03896204009652138,
0.004580856300890446,
0.0234060175716877,
0.007370743900537491,
0.012318641878664494,
0.009515389800071716,
0.006845550611615181,
-0.06911059468984604,
-0.031780507415533066,
-0.05980346351861954,
-0.005425762385129929,
0.03499949350953102,
0.018286151811480522,
-0.008498248644173145,
0.005906944163143635,
-0.014271353371441364,
0.01936911791563034,
0.013211139477789402,
0.05512494593858719,
-0.003127995878458023,
0.0629681795835495,
0.0002731993154156953,
0.04905484616756439,
0.014963474124670029,
0.02768184244632721,
0.1264439821243286,
0.013104763813316822,
0.0021239598281681538,
-0.04858413711190224,
-0.01315387710928917,
-0.009151739999651909,
-0.024732651188969612,
-0.027961507439613342,
0.05747789517045021,
-0.004049795214086771,
-0.009505211375653744,
-0.01177033968269825,
0.08254726976156235,
-0.02558853104710579,
-0.028799403458833694,
0.053363438695669174,
0.005907163023948669,
0.000842563807964325,
-0.008759729564189911,
-0.004617564380168915,
-0.023141201585531235,
-0.0152904586866498,
0.0030135484412312508,
0.042641568928956985,
-0.017863420769572258,
0.00906627532094717,
-0.0478382483124733,
-0.022633330896496773,
-0.0037935986183583736,
0.028821244835853577,
-0.01686868444085121,
0.004250404890626669,
-0.047889672219753265,
-0.03665492683649063,
-0.04863842576742172,
-0.0328281968832016,
-0.02325349859893322,
-0.012876174412667751,
0.031883422285318375,
0.025124913081526756,
0.02799714356660843,
0.02225983515381813,
-0.00014328416727948934,
0.0024296403862535954,
-0.0530855692923069,
0.006631478667259216,
-0.026669787243008614,
0.02052786387503147,
-0.02072511427104473,
-0.010232275351881981,
-0.03415416553616524,
0.02000221237540245,
0.014000975526869297,
-0.05190099775791168,
-0.0266561359167099,
-0.02710585482418537,
0.015995923429727554,
-0.035214733332395554,
-0.009625229053199291,
-0.0030237387400120497,
0.02549879439175129,
0.015900729224085808,
0.04824112355709076,
-0.0210284274071455,
-0.03625687584280968,
0.021062739193439484,
-0.01536762434989214,
0.06605624407529831,
0.01846737414598465,
-0.01951960101723671,
0.003124764421954751,
0.001073752879165113,
0.00018431524222251028,
-0.032988760620355606,
0.028912201523780823,
0.03619140759110451,
0.048583678901195526,
0.018010500818490982,
-0.02215752564370632,
-0.02056325227022171,
-0.03794756904244423,
0.027311982586979866,
-0.018784044310450554,
-0.0010126548586413264,
-0.0226150993257761,
-0.011075670830905437,
0.030690154060721397,
0.048401765525341034,
-0.03560824692249298,
-0.04085544869303703,
-0.003078246721997857,
0.0003700705128721893,
-0.008372535929083824,
-0.019893867895007133,
-0.009752344340085983,
0.024713218212127686,
-0.045183006674051285,
0.05873384326696396,
-0.007131659891456366,
0.015218551270663738,
0.05203639343380928,
-0.002992392983287573,
-0.0027131359092891216,
0.019503913819789886,
-0.03221968561410904,
-0.028757745400071144,
-0.00430513359606266,
-0.048375893384218216,
0.026204735040664673,
-0.01259440928697586,
0.016759240999817848,
-0.02045760303735733,
-0.06318758428096771,
-0.00899637583643198,
-0.023686494678258896,
-0.025840885937213898,
0.027623536065220833,
-0.033011406660079956,
0.00610837247222662,
-0.011594437062740326,
0.017860736697912216,
-0.04069359600543976,
0.010641475208103657,
-0.036276429891586304,
0.0021540310699492693,
-0.003538591554388404,
0.0063993907533586025,
-0.02723180502653122,
0.02375645749270916,
-0.013206185773015022,
-0.010768274776637554,
0.0038138306699693203,
0.003146989271044731,
-0.06566016376018524,
0.03392791748046875,
0.023400943726301193,
0.02835671976208687,
0.029623037204146385,
-0.022915491834282875,
-0.018464116379618645,
0.029448309913277626,
-0.05968340113759041,
-0.07679054886102676,
0.022495033219456673,
-0.020878084003925323,
0.019028110429644585,
0.01611528918147087,
-0.02206408604979515,
-0.02015114389359951,
0.04734582081437111,
0.001022792188450694,
0.006598930340260267,
0.0280219167470932,
-0.01923779770731926,
-0.007354014553129673,
0.012830708175897598,
0.026539649814367294,
0.006450003013014793,
-0.0340467244386673,
0.02231593430042267,
0.0097603565081954,
-0.040146421641111374,
-0.01953130215406418,
-0.0036094156093895435,
-0.04558952525258064,
0.015539987944066525,
0.009188834577798843,
0.023473583161830902,
0.06719182431697845,
0.02452867478132248,
-0.06395053118467331,
0.029116060584783554,
0.025925036519765854,
0.004768026061356068,
-0.10955121368169785,
-0.006272659637033939,
0.008572112768888474,
-0.0008542428840883076,
0.044637344777584076,
-0.055995307862758636,
0.024615617468953133,
0.03604041412472725,
-0.02652858756482601,
0.01963411085307598,
-0.06996774673461914,
-0.030276713892817497,
-0.05480624735355377,
0.010491264052689075,
-0.041871532797813416,
0.008982417173683643,
0.03851528465747833,
0.01722443290054798,
0.010779643431305885,
0.020356692373752594,
0.011137263849377632,
-0.007799661718308926,
-0.03784988448023796,
-0.024137195199728012,
-0.026976371183991432,
-0.02511931024491787,
0.08076213300228119,
-0.020834041759371758,
-0.0503113828599453,
-0.004041988868266344,
0.01889020949602127,
0.0023980243131518364,
-0.01400389801710844,
-0.018098998814821243,
0.004172020126134157,
-0.014920154586434364,
0.05411997437477112,
0.015250487253069878,
0.005187339149415493,
-0.019618401303887367,
-0.0004004446091130376,
-0.006589192431420088,
-0.008556093089282513,
0.0016642845002934337,
0.018891457468271255,
-0.030428370460867882,
-0.004963332787156105,
0.04579508304595947,
-0.027755530551075935,
-0.04792370647192001,
-0.03606788441538811,
-0.05191972851753235,
0.007112520281225443,
-0.034293148666620255,
-0.00027523288736119866,
-0.02329467050731182,
-0.010557313449680805,
0.018949033692479134,
0.011269597336649895,
-0.0057844966650009155,
0.04879649728536606,
-0.028805475682020187,
-0.024363618344068527,
0.0031798984855413437,
0.014809838496148586,
-0.006026834715157747,
-0.034825000911951065,
-0.01092192716896534,
0.018752606585621834,
0.0031827737111598253,
-0.0011698724702000618,
-0.038464050740003586,
0.02715989388525486,
0.04228741675615311,
0.021708833053708076,
0.015030348673462868,
0.00859717559069395,
-0.02277379296720028,
-0.04245814308524132,
-0.030224597081542015,
0.023456256836652756,
0.016296811401844025,
0.01667597144842148,
0.012697822414338589,
-0.0023399819619953632,
-0.017880186438560486,
0.01041895430535078,
0.05211267247796059,
0.0011515624355524778,
0.011777992360293865,
0.042692407965660095,
0.0002470139297656715,
0.03247235342860222,
-0.039570070803165436,
0.014816698618233204,
-0.005884446669369936,
-0.0183351319283247,
0.008766727522015572,
0.006605444476008415,
-0.01627587527036667,
-0.0006423578015528619,
0.01676003262400627,
-0.031046532094478607,
-0.0008642064640298486,
-0.0059074293822050095,
-0.04159769415855408,
0.03847311809659004,
0.025108832865953445,
0.004675571341067553,
0.04733483865857124,
0.013451170176267624,
0.003839440643787384,
0.015687236562371254,
-0.003221403807401657,
-0.049043457955121994,
0.0043813735246658325,
0.0023889082949608564,
-0.036183275282382965,
-0.030825546011328697,
-0.025097986683249474,
-0.01474655233323574,
-0.027040451765060425,
0.00041854058508761227,
0.06305273622274399,
-0.04587977007031441,
0.0007194217178039253,
0.03856566548347473,
-0.005613378714770079,
0.04461284726858139,
0.006986814551055431,
0.0074720000848174095,
0.037222590297460556,
0.00867412704974413,
0.08413379639387131,
0.06646281480789185,
0.0332612618803978,
-0.03668612241744995,
-0.04013003036379814,
-0.0035953535698354244,
-0.04016654193401337,
-0.004725761245936155,
0.015962675213813782,
0.09380199760198593,
-0.02220744825899601,
0.011569310910999775,
0.006311433855444193,
-0.008725055493414402,
0.025892389938235283,
0.014990346506237984,
-0.04205360263586044,
0.07987715303897858,
-0.016142291948199272,
0.01420313585549593,
-0.05583743005990982,
0.0025888504460453987,
-0.025959214195609093,
0.07582412660121918,
0.04221884161233902,
0.06059723719954491,
-0.013624755665659904,
0.00633662473410368,
-0.023500850424170494,
0.00202693953178823,
0.03835267201066017,
-0.019866235554218292,
0.005308058112859726,
0.009752092882990837,
0.03619806841015816,
-0.005971192382276058,
-0.037861261516809464,
0.025097932666540146,
-0.024050820618867874,
0.012115953490138054,
0.002813147148117423,
0.04599984362721443,
-0.042281221598386765,
-0.0072542354464530945,
-0.0033891310449689627,
0.041398514062166214,
-0.0471574068069458,
-0.035591501742601395,
-0.027915066108107567,
0.0075424667447805405,
0.01723124459385872,
0.031208261847496033
] |
<p>I've read <a href="http://en.wikipedia.org/wiki/Quantum_computer">Wikipedia</a>, I've read <a href="http://www.howstuffworks.com/quantum-computer.htm">How Stuff Works</a>, I've read <a href="http://www.singularity.com/">The Singularity is Near</a>, but I still just don't get it. How does a Quantum Computer work? It sounds very intriguing, but I just can't wrap my mind around it. I would greatly appreciate it if someone could explain it to me as they would explain the basics of it to their 7 year old nephew (who apparently is probably about equal to me in their ability to understand this concept!) </p>
<p>Typically analogies work best when explaining concepts to the unenlightened, but this is quantum theory, so I'm not sure any analogy could exist that can explain such a bizarre concept ;)</p> | 1,982 | [
-0.009529216215014458,
-0.039513882249593735,
-0.01586182601749897,
-0.03641877323389053,
0.021436749026179314,
0.006752450484782457,
0.015240024775266647,
-0.0040939683094620705,
0.009602093137800694,
-0.014003819786012173,
0.025522170588374138,
0.0639021098613739,
0.03354315087199211,
0.011945660226047039,
0.027935026213526726,
0.024690300226211548,
-0.012790339067578316,
-0.036025404930114746,
0.0032562478445470333,
-0.012395584024488926,
0.03473229333758354,
0.029901133850216866,
-0.00018098745204042643,
0.027946842834353447,
-0.004485466051846743,
0.018666934221982956,
0.017059363424777985,
-0.007707739714533091,
0.051000673323869705,
0.06751669943332672,
-0.0144827701151371,
-0.030489131808280945,
0.014589661732316017,
0.03839895874261856,
0.03178014978766441,
0.0013141084928065538,
-0.0124217439442873,
-0.008256620727479458,
0.014717631042003632,
-0.0019221230177208781,
0.014071761630475521,
-0.034630246460437775,
-0.017853762954473495,
0.06368482857942581,
-0.03705207630991936,
-0.017331184819340706,
-0.011641615070402622,
-0.018047327175736427,
0.014592034742236137,
-0.06059651076793671,
0.05150895565748215,
0.011690297164022923,
0.025914939120411873,
0.024082764983177185,
0.011309780180454254,
0.005204745102673769,
0.07943189889192581,
0.07744253426790237,
-0.03608505427837372,
-0.08554979413747787,
-0.005116111598908901,
-0.007058535236865282,
-0.018843645229935646,
-0.016812022775411606,
-0.029433317482471466,
0.03403361514210701,
-0.008972479961812496,
-0.02977151982486248,
0.026623865589499474,
-0.0053718299604952335,
0.018636461347341537,
0.020749690011143684,
0.03020532615482807,
-0.0076052164658904076,
0.008842341601848602,
-0.03962843865156174,
0.012964756228029728,
0.016293147578835487,
0.019169267266988754,
0.025866657495498657,
0.0029000951908528805,
0.012843728996813297,
0.01526098232716322,
0.012668398208916187,
-0.00678842980414629,
-0.002833997132256627,
0.08793283253908157,
-0.02905295230448246,
-0.015130550600588322,
0.01803056336939335,
-0.04018862918019295,
0.02406633459031582,
0.013210325501859188,
-0.015221601352095604,
-0.028491929173469543,
0.021543772891163826,
0.025301747024059296,
0.04103221371769905,
0.030685747042298317,
-0.03037123754620552,
0.03662518411874771,
-0.016561640426516533,
0.004656918812543154,
0.0571676567196846,
0.005059471819549799,
0.007224716246128082,
-0.025178829208016396,
0.06698022782802582,
-0.003385707503184676,
-0.0069802203215658665,
-0.02135920710861683,
0.016709942370653152,
0.026364130899310112,
0.004994948394596577,
-0.007242074701935053,
-0.03467023745179176,
-0.008188286796212196,
-0.028391972184181213,
0.028685133904218674,
0.015955578535795212,
0.027014639228582382,
-0.0556534081697464,
0.0225240346044302,
-0.05706228315830231,
-0.04419362545013428,
0.03421592712402344,
0.022325590252876282,
-0.025466203689575195,
-0.05867127329111099,
0.02182777039706707,
-0.01515783742070198,
-0.04514681547880173,
0.02238783985376358,
-0.0005373155581764877,
0.04900725185871124,
-0.0227990560233593,
-0.12380815297365189,
-0.031280580908060074,
0.06580893695354462,
0.006524593103677034,
-0.02681376412510872,
-0.07985891401767731,
0.03815607354044914,
0.04593391716480255,
0.07285009324550629,
0.004326756577938795,
-0.0009705252596177161,
0.012281357310712337,
0.0071937027387320995,
0.03378365561366081,
-0.012553827837109566,
0.016807571053504944,
-0.009199323132634163,
-0.028200305998325348,
0.04388953372836113,
-0.05850046128034592,
0.00787417870014906,
0.054709888994693756,
-0.01614629477262497,
-0.04480115324258804,
0.04714014008641243,
-0.006345068104565144,
-0.02214794047176838,
0.010862598195672035,
-0.04753520339727402,
-0.02653440833091736,
0.09566878527402878,
0.01137487031519413,
-0.027910854667425156,
0.07294002920389175,
-0.017760174348950386,
0.027535317465662956,
-0.008907774463295937,
0.032154474407434464,
0.029121972620487213,
-0.020555872470140457,
-0.018878431990742683,
-0.016170024871826172,
0.010327187366783619,
-0.018626712262630463,
-0.06670714914798737,
-0.041132304817438126,
0.002695854287594557,
0.026895830407738686,
0.0016719757113605738,
0.016398128122091293,
-0.02032906748354435,
-0.02561827376484871,
-0.0195353664457798,
-0.035973675549030304,
-0.038301385939121246,
-0.0739404708147049,
0.005748986732214689,
-0.02833692356944084,
0.011338266544044018,
0.016554510220885277,
0.03559853509068489,
0.033145803958177567,
-0.031146952882409096,
-0.0309312641620636,
-0.04896742105484009,
-0.005093603394925594,
-0.011305944994091988,
-0.004412940237671137,
0.02430848777294159,
0.07238642871379852,
0.012074454687535763,
0.006384025793522596,
0.022186269983649254,
-0.004255371168255806,
-0.013932262547314167,
0.012535085901618004,
0.03865843266248703,
0.02528209425508976,
-0.005766208749264479,
0.009374585933983326,
0.006105385255068541,
-0.009232730604708195,
0.014923631213605404,
0.005735638551414013,
-0.02580246515572071,
0.06722120195627213,
0.007657761685550213,
0.004852932877838612,
-0.012729918584227562,
0.013280793093144894,
0.004930024966597557,
0.00878562405705452,
0.0026635671965777874,
-0.021508820354938507,
-0.03249049559235573,
0.007917911745607853,
0.027481835335493088,
0.02684480883181095,
-0.029112081974744797,
0.022916194051504135,
0.007769669406116009,
0.07091544568538666,
0.0012105247005820274,
0.0025116039905697107,
-0.04952323064208031,
0.028596049174666405,
0.0011569936759769917,
-0.012850363738834858,
-0.013576540164649487,
0.026510970667004585,
0.03068607486784458,
0.015133599750697613,
-0.021074987947940826,
0.004452844616025686,
-0.03432789072394371,
0.0591464526951313,
-0.032945334911346436,
0.034337978810071945,
0.0004004130023531616,
-0.04842878505587578,
0.027615537866950035,
-0.024373073130846024,
-0.013327564112842083,
-0.01427189540117979,
-0.011964033357799053,
-0.009267122484743595,
-0.04997154325246811,
-0.03896600380539894,
-0.01412242092192173,
0.0460660345852375,
-0.027815645560622215,
0.00204817159101367,
0.015260731801390648,
-0.009415757842361927,
0.05489359796047211,
-0.015132695436477661,
0.017997166141867638,
-0.03286542370915413,
0.015800723806023598,
-0.0021999015007168055,
0.015818042680621147,
0.02990301325917244,
-0.037024885416030884,
-0.05341469496488571,
0.012774826027452946,
-0.044382866472005844,
0.005338872782886028,
0.010385946370661259,
-0.06677044928073883,
0.024982713162899017,
-0.02728806994855404,
-0.026252506300807,
0.05757494643330574,
-0.014471014030277729,
0.0023471980821341276,
-0.02603999525308609,
-0.0370233952999115,
-0.03078344091773033,
0.014421124011278152,
-0.061685312539339066,
0.00857642013579607,
-0.028699392452836037,
0.018803542479872704,
0.03747808188199997,
-0.02688506431877613,
-0.022029893472790718,
-0.004465047735720873,
-0.05017849802970886,
-0.02035161480307579,
0.0009237040067091584,
-0.01744445599615574,
-0.004671286791563034,
-0.03753092885017395,
0.00933179259300232,
0.0004684210289269686,
-0.07401341944932938,
-0.00943774078041315,
-0.023649107664823532,
-0.05489742383360863,
0.04530005156993866,
0.007295308634638786,
0.02889251336455345,
-0.006453325506299734,
-0.022527290508151054,
0.062807597219944,
-0.0337170772254467,
-0.0524245910346508,
-0.027257801964879036,
-0.010537074878811836,
-0.004505047108978033,
-0.007839292287826538,
0.026561010628938675,
0.05028967559337616,
-0.03823258355259895,
-0.003406362608075142,
0.03505830466747284,
0.038463983684778214,
0.022549785673618317,
-0.00017427596321795136,
-0.0309890266507864,
0.00958610326051712,
0.003604873549193144,
-0.0109856640920043,
0.03603958711028099,
-0.01162685826420784,
-0.062403321266174316,
0.024293111637234688,
0.0008957539685070515,
-0.009242364205420017,
0.008457571268081665,
-0.0004207390593364835,
0.04875091835856438,
0.018535446375608444,
0.003270658664405346,
-0.03588048741221428,
0.051684942096471786,
-0.03624272346496582,
0.008015562780201435,
0.018205393105745316,
0.023497480899095535,
0.04197271540760994,
0.001749334391206503,
0.013870726339519024,
0.030985549092292786,
0.02407635748386383,
-0.05576392263174057,
-0.02227485366165638,
-0.007931394502520561,
-0.03936833143234253,
-0.003927133046090603,
-0.018901783972978592,
-0.030617278069257736,
0.04042069613933563,
0.01926371455192566,
0.052717696875333786,
-0.000569845549762249,
-0.013094083406031132,
-0.01811765693128109,
-0.057585541158914566,
0.011216345243155956,
0.010593491606414318,
0.04657108336687088,
0.012819797731935978,
0.07439391314983368,
0.029464172199368477,
0.03201880678534508,
0.01909627392888069,
-0.010996196419000626,
-0.08555781841278076,
0.01407703198492527,
-0.05115026980638504,
-0.0067202141508460045,
0.009738645516335964,
-0.01270647905766964,
0.020403817296028137,
-0.02483500726521015,
-0.060045938938856125,
-0.0015017663827165961,
-0.00607250165194273,
-0.054439645260572433,
0.005722330883145332,
0.005028009880334139,
0.009787213057279587,
-0.0031116120517253876,
-0.0009115614811889827,
0.026409519836306572,
0.0006525436765514314,
-0.023049358278512955,
0.02513054385781288,
-0.0425105020403862,
-0.006329155061393976,
0.016579845920205116,
-0.002817162312567234,
0.04504162818193436,
-0.012706766836345196,
0.03605983778834343,
0.01721777766942978,
-0.00896521471440792,
-0.012570802122354507,
-0.005282439757138491,
0.06866271048784256,
0.006594365928322077,
-0.011420199647545815,
-0.0011130000930279493,
-0.03369714692234993,
-0.00960895698517561,
-0.01797959767282009,
0.06687525659799576,
-0.0043759471736848354,
0.04998883605003357,
0.01658022217452526,
0.02498290129005909,
-0.030019011348485947,
0.023418258875608444,
0.04869900271296501,
-0.0029765423387289047,
-0.02274540439248085,
-0.005605481099337339,
-0.012821989133954048,
-0.061044760048389435,
0.002651595277711749,
0.015401508659124374,
-0.026616692543029785,
-0.038029804825782776,
0.024833502247929573,
0.005429197568446398,
-0.019727131351828575,
-0.006891707424074411,
-0.014701778069138527,
0.0026172229554504156,
0.01201053149998188,
-0.02228778600692749,
0.013427226804196835,
-0.006644674576818943,
0.029864957556128502,
0.012190006673336029,
0.004487293306738138,
0.0014696696307510138,
-0.09251447767019272,
-0.01236684899777174,
0.0671558752655983,
0.020688598975539207,
-0.006580641493201256,
-0.0035279057919979095,
-0.06419695913791656,
-0.02772035449743271,
0.03319071605801582,
-0.03143146634101868,
0.07606283575296402,
-0.0015849758638069034,
0.005377126391977072,
-0.009848830290138721,
0.0018622693605720997,
0.06475220620632172,
0.0045143673196434975,
0.004562284331768751,
0.03244674950838089,
0.0071021015755832195,
0.01170166116207838,
-0.06162093207240105,
-0.04397179186344147,
0.021607505157589912,
0.06431712955236435,
-0.02061321772634983,
0.011786229908466339,
-0.002785665215924382,
0.011539356783032417,
-0.030658595263957977,
-0.10086260735988617,
0.015633653849363327,
-0.002420616801828146,
-0.02797933667898178,
0.05176674947142601,
-0.03962540253996849,
-0.03579462692141533,
0.007034516427665949,
-0.00007794470002409071,
-0.010979974642395973,
-0.01467294991016388,
-0.0363270565867424,
0.041088033467531204,
0.03497251495718956,
0.0055209193378686905,
0.044028256088495255,
0.013065249659121037,
-0.05869094654917717,
-0.0009462046436965466,
-0.026162253692746162,
0.010425296612083912,
-0.019816823303699493,
0.01815398409962654,
-0.01496451161801815,
0.011318247765302658,
-0.045144323259592056,
0.05369282513856888,
-0.033236194401979446,
0.002087469445541501,
-0.01878713257610798,
-0.014049810357391834,
-0.04429887980222702,
0.023870697245001793,
-0.023349693045020103,
0.0003630629798863083,
-0.0354435108602047,
0.015734318643808365,
-0.006984673906117678,
-0.04789644479751587,
0.024091260507702827,
0.002766073914244771,
0.013049003668129444,
0.017002351582050323,
-0.00319602619856596,
0.03253847733139992,
-0.020046699792146683,
-0.023053793236613274,
0.043625228106975555,
-0.06848632544279099,
0.06718166917562485,
-0.013517160899937153,
-0.018610399216413498,
0.027865001931786537,
-0.04543016478419304,
-0.033862948417663574,
-0.003961225040256977,
-0.005568680353462696,
0.0033055278472602367,
-0.009192959405481815,
0.027101414278149605,
-0.004568895790725946,
0.0011743290815502405,
-0.05961450934410095,
-0.05112983658909798,
0.04892228543758392,
0.0014013693435117602,
-0.019073544070124626,
-0.011012200266122818,
0.028600331395864487,
-0.009544923901557922,
-0.0463867224752903,
-0.006987001746892929,
0.004552708938717842,
-0.02025662362575531,
0.01740068756043911,
0.05023155361413956,
0.0015077941352501512,
0.05109638720750809,
0.004436241928488016,
-0.019186608493328094,
-0.012052478268742561,
-0.030701132491230965,
-0.008682701736688614,
-0.011942313052713871,
0.030535325407981873,
-0.031663648784160614,
-0.04912296310067177,
-0.006539344321936369,
0.03468932583928108,
0.03774750232696533,
-0.013867364265024662,
0.019925612956285477,
-0.013687888160347939,
0.047103047370910645,
-0.008080384694039822,
-0.03627537190914154,
-0.013318025507032871,
0.019190829247236252,
0.05777968838810921,
-0.010584081523120403,
-0.027767658233642578,
-0.02806961163878441,
-0.044355083256959915,
0.013308952562510967,
0.0008669544477015734,
0.009241456165909767,
0.024514449760317802,
0.06134334206581116,
-0.03321893513202667,
-0.008298391476273537,
-0.008247745223343372,
-0.05002995952963829,
0.006106966640800238,
0.005719107110053301,
0.020699620246887207,
0.00008958143735071644,
-0.0009123202762566507,
-0.016333362087607384,
-0.013787370175123215,
-0.04287291318178177,
0.0007763918838463724,
0.046631354838609695,
0.000980135751888156,
0.030258266255259514,
0.02681230753660202,
0.0037432394456118345,
-0.008634933270514011,
-0.006182941608130932,
-0.023978495970368385,
0.01763967238366604,
0.024654142558574677,
0.01662205532193184,
-0.012723675929009914,
0.019499249756336212,
0.017112020403146744,
0.0627753883600235,
-0.003935659769922495,
0.024992099031805992,
0.04152735695242882,
0.03687593713402748,
0.020995987579226494,
0.0008133893716149032,
-0.02414541132748127,
0.030025197193026543,
-0.0193736981600523,
0.0436941459774971,
0.013885987922549248,
-0.012085473164916039,
0.04859941080212593,
-0.009716211818158627,
0.00489520700648427,
-0.056018512696027756,
-0.009158548898994923,
-0.038985807448625565,
0.02633681893348694,
-0.00009762500849319622,
0.006585233379155397,
0.03501538932323456,
0.01057159062474966,
-0.012218083254992962,
0.01443856954574585,
0.014381292276084423,
-0.006321369670331478,
-0.06176208704710007,
-0.04701520875096321,
0.0021998819429427385,
-0.07657751441001892,
0.03112986497581005,
0.025138983502984047,
-0.03395378217101097,
0.021471349522471428,
-0.038827598094940186,
0.05406469106674194,
0.01281666662544012,
0.04296158626675606,
-0.023463144898414612,
0.05723654106259346,
0.002648530760779977,
0.03589316084980965,
-0.01974204182624817,
-0.0032854676246643066,
0.08202017098665237,
0.02682550996541977,
-0.02873491309583187,
-0.11240682750940323,
0.004122293554246426,
-0.03320244699716568,
0.040100522339344025,
-0.03894704580307007,
0.01808534376323223,
0.019210215657949448,
0.027612147852778435,
0.003150895470753312,
0.039309658110141754,
-0.009879185818135738,
0.034688662737607956,
0.028920955955982208,
-0.04692346602678299,
-0.0551934652030468,
-0.005092567764222622,
0.04031681641936302,
0.00032388142426498234,
0.003299991600215435,
-0.046338509768247604,
-0.015584474429488182,
-0.047024067491292953,
-0.015271157026290894,
-0.04197651147842407,
-0.015725480392575264,
0.03891516104340553,
0.003874054877087474,
-0.03293979912996292,
0.00718145864084363,
-0.020463934168219566,
-0.04648913815617561,
-0.014369138516485691,
0.022471655160188675,
0.025670064613223076,
-0.02122974768280983,
0.009073655121028423,
0.039151184260845184,
0.018872039392590523,
-0.006040815729647875,
0.021556222811341286,
-0.006518431007862091,
-0.015039648860692978,
0.0037966917734593153,
-0.01978313736617565,
0.035453710705041885,
-0.02761261910200119,
0.0033779218792915344,
-0.03154478222131729,
0.01463343296200037,
0.005560342688113451,
-0.04999907687306404,
0.014091355726122856,
0.015240488573908806,
0.002166011603549123,
-0.01836269348859787,
-0.023463288322091103,
0.007677452173084021,
0.01382741704583168,
-0.030699219554662704,
0.039042867720127106,
-0.029572419822216034,
0.011120069772005081,
0.025358347222208977,
-0.0545484833419323,
-0.0065372479148209095,
-0.035540204495191574,
0.007212743628770113,
-0.01338800135999918,
0.015229664742946625,
-0.05507630109786987,
-0.018835091963410378,
0.034708455204963684,
0.02774864435195923,
0.031108789145946503,
0.012524469755589962,
-0.020555807277560234,
0.01805076003074646,
-0.03522650897502899,
0.02774958312511444,
-0.010799402371048927,
-0.021904483437538147,
-0.005333990789949894,
-0.015049283392727375,
0.0645388588309288,
0.05125568434596062,
-0.019467825070023537,
0.05223517492413521,
-0.021599451079964638,
-0.018692372366786003,
0.022235048934817314,
-0.013265306130051613,
0.009179423563182354,
0.026735274121165276,
-0.04946424067020416,
0.014034533873200417,
-0.016535351052880287,
0.03552062809467316,
0.023100435733795166,
0.002084125066176057,
-0.005446296185255051,
0.03610163927078247,
-0.030138153582811356,
-0.007094843313097954,
0.006484414916485548,
-0.008164770901203156,
-0.02067132107913494,
0.010168641805648804,
0.03206993639469147,
-0.0502329096198082,
-0.05260605365037918,
-0.015032060444355011,
-0.010892882943153381,
-0.0027386818546801805,
0.0581517331302166,
-0.016766002401709557,
0.018714945763349533,
0.00024085886252578348,
0.05046681687235832,
-0.0184648297727108,
-0.009007427841424942,
-0.035852186381816864,
0.019945679232478142,
0.01289241574704647,
0.016213152557611465,
-0.024023454636335373,
0.0170472152531147,
0.019807517528533936,
-0.01839589700102806,
0.02314751222729683,
0.04423683136701584,
-0.0039293053559958935,
0.011284662410616875,
0.013295146636664867,
0.015352960675954819,
0.04384062439203262,
-0.018394479528069496,
-0.012400323525071144,
0.04441996291279793,
-0.047309741377830505,
-0.039778657257556915,
0.037472572177648544,
-0.014522673562169075,
0.027766307815909386,
0.054035257548093796,
-0.02141452766954899,
-0.014723686501383781,
0.03202269971370697,
-0.0022936391178518534,
-0.0044149551540613174,
-0.006358159705996513,
-0.02070750668644905,
-0.014369040727615356,
0.004872751422226429,
-0.002269173739477992,
-0.014117916114628315,
-0.03499085083603859,
-0.0005544735467992723,
0.06676063686609268,
0.002698655705899,
-0.012012194842100143,
0.015569567680358887,
0.03168129175901413,
0.04563209414482117,
0.008587613701820374,
-0.0034093069843947887,
0.03765734285116196,
0.050190702080726624,
-0.033204466104507446,
0.05517125502228737,
-0.007699590176343918,
-0.0249879639595747,
-0.09734442830085754,
0.02123652584850788,
-0.009090251289308071,
-0.003712306497618556,
0.0282229483127594,
-0.03746890649199486,
0.023197226226329803,
0.04642278328537941,
-0.06798791885375977,
0.01772734709084034,
0.002517967950552702,
-0.009917542338371277,
-0.0012233726447448134,
0.027176547795534134,
-0.012378601357340813,
0.042057689279317856,
0.015202387236058712,
0.027284370735287666,
0.017051929607987404,
-0.0028642192482948303,
-0.02858974225819111,
-0.02798372693359852,
-0.015069753862917423,
0.058390263468027115,
-0.03301114961504936,
0.013640915043652058,
0.03485356643795967,
-0.0567469522356987,
-0.018650706857442856,
0.048695553094148636,
-0.01565416343510151,
0.03514692559838295,
-0.016225675120949745,
0.025019565597176552,
0.005397866480052471,
0.014539317227900028,
0.011249290779232979,
-0.001288962666876614,
-0.005809972062706947,
0.029283903539180756,
0.025859734043478966,
0.04922211170196533,
0.028408216312527657,
-0.006484534591436386,
0.03768256679177284,
-0.006678216625005007,
-0.03114418312907219,
0.05265088751912117,
0.006991907022893429,
0.027304593473672867,
-0.008022569119930267,
0.004263314418494701,
0.034026142209768295,
-0.03394104912877083,
0.004213094711303711,
-0.032569658011198044,
0.006327352486550808,
0.013386118225753307,
0.008940290659666061,
0.014197204262018204,
0.017084388062357903,
-0.029957592487335205,
-0.011471674777567387,
0.04235874488949776,
0.006536786910146475,
-0.014189688488841057,
-0.053212035447359085,
-0.00764714740216732,
0.004652390722185373,
0.008041328750550747,
0.04124896600842476,
-0.05168263986706734,
-0.02368639037013054,
0.008240312337875366,
0.0038450888823717833,
0.014956746250391006,
-0.020264526829123497,
-0.01587003655731678,
-0.03915201500058174,
-0.04054299369454384,
0.042874231934547424,
0.001409068237990141,
-0.005476855207234621,
-0.06411424279212952,
-0.026903251186013222,
0.010460320860147476,
0.04895441234111786,
0.08110330253839493,
-0.032602231949567795,
-0.018268294632434845,
0.013173667713999748,
0.017178773880004883,
0.034308627247810364,
-0.028482133522629738,
-0.007514127995818853,
-0.0007011219277046621,
-0.04099207744002342,
-0.010670811869204044,
-0.030470779165625572,
-0.03153882548213005,
0.032159850001335144,
0.01798141375184059,
0.011245327070355415,
-0.004421211779117584,
-0.02375040203332901,
-0.025859354063868523,
0.04964233934879303,
0.011086968705058098,
0.019989872351288795,
0.03883299604058266,
-0.010808450169861317,
0.011351291090250015,
0.04324748367071152,
-0.030094526708126068,
-0.035405483096838,
0.01132951769977808,
-0.012054655700922012,
0.008785516023635864,
-0.013041319325566292,
-0.04232659563422203,
0.04691312089562416,
-0.0755014568567276,
-0.01713516190648079,
0.01499080378562212,
-0.05261797830462456,
0.0024797585792839527,
0.0791589543223381,
0.007905078120529652,
0.03193943575024605,
-0.017688635736703873,
0.02740226313471794,
-0.0197132620960474,
-0.006536978296935558,
0.0294894278049469,
0.06888125091791153,
0.04116986319422722,
-0.0005851887399330735,
0.05222409963607788,
0.05173824355006218,
0.005012924782931805,
0.03868968412280083,
-0.0026387705001980066,
0.0284525528550148,
-0.02027915231883526,
-0.03200456127524376,
0.0034951188135892153,
-0.016038114205002785,
-0.009290438145399094,
0.041086453944444656,
-0.05247988551855087,
0.10276462137699127,
-0.02240409515798092,
0.014084196649491787,
-0.0007794757257215679,
0.01996106281876564,
-0.01616750657558441,
-0.018724940717220306,
0.008190877735614777,
0.03445560112595558,
-0.03874123468995094,
-0.02430923655629158,
-0.02365502156317234,
0.009564190171658993,
0.024075733497738838,
-0.03344586491584778,
0.030148105695843697,
-0.01922737807035446,
-0.004038156941533089,
0.006676229648292065,
-0.011388018727302551,
-0.02869538404047489,
-0.025459539145231247,
0.03642749413847923,
0.03827603533864021,
0.012392775155603886,
0.023997168987989426,
-0.015075094997882843,
0.006025068461894989,
0.05613652244210243,
-0.07463310658931732,
0.0046483660116791725,
-0.0262053981423378,
0.023782769218087196,
-0.06039128452539444,
0.0019148277351632714
] |
<p>I want to outline a solid argument (or bulletpoints) to show how weak is the idea of diff(M) being the gauge group of general relativity.</p>
<p>basically i have these points that in my view are very solid but i want to understand if there are misconceptions on my part that i'm simply not getting and if its so, i ask for help to make the case more solid, or understanding why it doesn't apply (to gravity):</p>
<ul>
<li><p><a href="http://www.mth.kcl.ac.uk/~streater/lostcauses.html#XXII">gauge groups are not the same as a symmetry group</a> (thanks to Raymond Streater for making that point completely clear)</p></li>
<li><p>gauge invariance in electrodynamics is an observation that physical observables are unchanged after a gauge transformation <strong>without changing coordinate frame</strong> ( we are ask to believe that in gravity someone did the same? that is, someone made the observation that physical observables are unchanged after a diffeomorphism-gauge-transformation, only to later argue that because of this, that there are no physical observables to begin with, that doesn't make a lot of sense, to not say that its just plain stupid circular argument )</p></li>
<li><p><a href="http://en.wikipedia.org/wiki/Maxwell%27s_equations_in_curved_spacetime">classic electrodynamics is also invariant (as in symmetry invariant, not as gauge-invariant) under Diff(M)</a>. The invariance is of course broken when the theory is quantized and $\hbar$ makes an appearance, because it assumes a preferred scale for certain energies. The key point here is: <strong>classical gravity is not special regarding having diff(M) as a symmetry group</strong></p></li>
<li><p>from bulletpoints 2 and 3, if i cannot infer that Diff(M) is a gauge-invariance of electrodynamics, the same should apply to gravity</p></li>
</ul>
<p>For this question, i would say that a valid answer would either disprove any of the arguments as fallacies themselves (hence showing a solid argument why gravity is special and diff(M) is without a doubt its gauge group), or improve the argument for making it bullet-proof (sorry for the pun)</p> | 1,983 | [
-0.04969525337219238,
0.0165326539427042,
0.018494807183742523,
-0.05249488353729248,
0.023878123611211777,
0.020318131893873215,
-0.005650760605931282,
-0.007559394463896751,
0.01569957844913006,
-0.02635982818901539,
0.023237604647874832,
-0.02794603817164898,
0.0666753500699997,
0.013116046786308289,
0.0181101206690073,
-0.005084788892418146,
0.025544628500938416,
-0.018544131889939308,
-0.028450604528188705,
-0.023010114207863808,
-0.0406908318400383,
0.047179125249385834,
-0.007451837416738272,
0.008848309516906738,
-0.032564740628004074,
0.007610745262354612,
-0.016185017302632332,
0.003031245432794094,
-0.015329300425946712,
0.08587580174207687,
-0.03565105423331261,
-0.017436595633625984,
0.013187496922910213,
0.00527082709595561,
-0.011325865052640438,
0.0076314727775752544,
-0.008550599217414856,
-0.02937125973403454,
0.0030531121883541346,
-0.010163430124521255,
-0.042777419090270996,
0.00040023133624345064,
-0.027820102870464325,
0.060580212622880936,
-0.030100788921117783,
0.041895993053913116,
-0.013827170245349407,
0.009539168328046799,
0.0745089128613472,
-0.039045047014951706,
0.07920529693365097,
0.004272837191820145,
0.01351279579102993,
0.04539649561047554,
-0.0363437794148922,
-0.04574696719646454,
0.06655646115541458,
0.04361162707209587,
0.0014151710784062743,
-0.05259466543793678,
-0.02944014221429825,
-0.024973899126052856,
0.0037860011216253042,
-0.03453779220581055,
-0.022640546783804893,
0.046577077358961105,
0.004005231894552708,
0.002772894222289324,
0.021596260368824005,
0.003079922404140234,
0.001878331764601171,
-0.0015696496702730656,
0.01971866562962532,
-0.03292284160852432,
0.01959003508090973,
-0.023140212520956993,
0.01132500171661377,
0.005869063548743725,
0.011832754127681255,
0.03826316073536873,
-0.006846517790108919,
0.02960372157394886,
0.03956061974167824,
0.03198285400867462,
0.014090526849031448,
-0.008478604257106781,
0.06548356264829636,
0.0016472995048388839,
-0.010254249908030033,
0.060895439237356186,
-0.02407515048980713,
-0.03533431142568588,
0.0215289443731308,
0.0007854661089368165,
-0.02613784186542034,
0.0280257910490036,
0.006798766553401947,
0.011820128187537193,
-0.020331041887402534,
0.006264503579586744,
-0.026010768488049507,
-0.012087981216609478,
0.02797599881887436,
0.06716419011354446,
0.022066578269004822,
0.0037650621961802244,
-0.02807864546775818,
0.007238082122057676,
-0.028310976922512054,
-0.007661113515496254,
-0.012466887943446636,
-0.007847614586353302,
-0.017959918826818466,
-0.024384358897805214,
-0.004504634067416191,
-0.033599819988012314,
-0.008176125586032867,
-0.02818446420133114,
0.0661274716258049,
0.056254565715789795,
0.02640371210873127,
-0.009055100381374359,
-0.002665579551830888,
-0.029604321345686913,
-0.04737101122736931,
-0.0011839125072583556,
0.04836626350879669,
0.02960112877190113,
-0.033109016716480255,
-0.0037337110843509436,
-0.00008101033017737791,
-0.001832581707276404,
0.009676788002252579,
-0.0017953058704733849,
0.019116979092359543,
-0.041128549724817276,
-0.1061498150229454,
-0.06159456446766853,
0.05578099936246872,
0.032191939651966095,
-0.005831994581967592,
-0.05942661687731743,
0.014491156674921513,
0.004301260691136122,
0.07075075805187225,
-0.0020159143023192883,
0.03203360363841057,
-0.004118775483220816,
0.028596695512533188,
0.018073664978146553,
-0.003759701969102025,
-0.024310942739248276,
0.03043154999613762,
-0.04561786726117134,
0.00042473862413316965,
-0.07094193994998932,
0.010570060461759567,
0.01174979005008936,
0.01708570495247841,
0.012250719591975212,
0.07462110370397568,
-0.02572157420217991,
0.01420445367693901,
0.006889001000672579,
0.009568600915372372,
0.0159461610019207,
0.044791799038648605,
0.0027030494529753923,
-0.0021881619468331337,
0.020115572959184647,
0.0010620325338095427,
0.023782866075634956,
-0.026639649644494057,
0.014042433351278305,
0.02803620509803295,
-0.05115894600749016,
-0.013545452617108822,
0.010325261391699314,
-0.03677617013454437,
-0.019376587122678757,
-0.026291577145457268,
-0.04507086053490639,
0.0008290649275295436,
-0.015797248110175133,
-0.02666589431464672,
0.0218501016497612,
0.007761399261653423,
0.004894969519227743,
-0.0008807132835499942,
-0.017059961333870888,
-0.019386978819966316,
-0.05814780667424202,
0.015797588974237442,
0.008514028042554855,
-0.009244327433407307,
0.027112871408462524,
0.012788413092494011,
-0.01261720061302185,
-0.03336809575557709,
-0.020575810223817825,
0.020241422578692436,
0.03447654843330383,
-0.033840619027614594,
0.00031644641421735287,
0.022954346612095833,
0.024398600682616234,
0.03558162599802017,
0.005660682916641235,
0.00427643395960331,
0.0028859232552349567,
-0.02638687938451767,
0.03237507492303848,
-0.02747216448187828,
0.012700935825705528,
-0.007541634142398834,
0.022033752873539925,
0.03805984929203987,
0.013033691793680191,
-0.010497301816940308,
0.060410600155591965,
-0.04138544574379921,
0.08205541223287582,
-0.009658699855208397,
-0.04850573092699051,
-0.02674921788275242,
0.06119941174983978,
-0.01057043019682169,
0.04420626536011696,
-0.01194021850824356,
-0.0180249884724617,
-0.04019744694232941,
-0.029239332303404808,
0.026903554797172546,
0.04648534581065178,
-0.012254022993147373,
0.020988954231142998,
0.011485880240797997,
0.05127124860882759,
0.013926224783062935,
-0.0014833728782832623,
-0.016865553334355354,
-0.05188978463411331,
0.0505211241543293,
-0.007394883781671524,
0.014579069800674915,
-0.011510670185089111,
0.01650659367442131,
0.0017464045668020844,
0.01986420713365078,
-0.015245764516294003,
0.0032755928114056587,
0.030812526121735573,
-0.014726512134075165,
-0.002025409834459424,
0.0009455815888941288,
-0.01492264959961176,
0.050642747431993484,
-0.007078314665704966,
0.07432100176811218,
0.01937926560640335,
-0.029270268976688385,
0.030365604907274246,
-0.06802226603031158,
-0.02784229815006256,
0.007016834802925587,
0.0013516885228455067,
0.01022900640964508,
-0.012740716338157654,
0.0014133340446278453,
-0.053128499537706375,
-0.0037425090558826923,
-0.016348902136087418,
-0.04414381459355354,
-0.008088228292763233,
0.001515235984697938,
-0.008714858442544937,
0.021788593381643295,
-0.003575835144147277,
-0.03271199017763138,
-0.0113417012616992,
-0.00434759259223938,
-0.01091719139367342,
0.0306695643812418,
0.038627155125141144,
-0.000695649185217917,
0.011944049969315529,
-0.047276146709918976,
0.008998150937259197,
0.05955188721418381,
0.01667495258152485,
0.028102857992053032,
0.020955361425876617,
0.007509482093155384,
-0.05472787097096443,
-0.0002315718593308702,
-0.029910512268543243,
0.011482159607112408,
-0.02734682708978653,
-0.024029996246099472,
0.05469020828604698,
-0.018344871699810028,
-0.04317283630371094,
0.01896917261183262,
-0.015267709270119667,
-0.026200808584690094,
0.00859768781810999,
-0.007375148590654135,
-0.03071233443915844,
-0.03486563637852669,
0.0203924048691988,
0.03371225297451019,
-0.047624316066503525,
-0.03367513045668602,
-0.04817701876163483,
-0.03831212595105171,
0.025885028764605522,
0.009179920889437199,
0.03732098639011383,
0.006596055813133717,
-0.03281469643115997,
0.08500228077173233,
0.06987150758504868,
-0.010934089310467243,
-0.035799164324998856,
0.0264060590416193,
-0.013774856925010681,
-0.033252570778131485,
0.00869862549006939,
0.01569269970059395,
0.026090985164046288,
0.017565283924341202,
0.022722257301211357,
0.022486526519060135,
-0.0104819992557168,
0.0002532794896978885,
-0.018313033506274223,
0.02075106091797352,
-0.007188024930655956,
0.031131256371736526,
0.07407420128583908,
0.04421031475067139,
-0.020976167172193527,
-0.019523270428180695,
-0.0055531165562570095,
0.03185952827334404,
0.021364685148000717,
-0.06740091741085052,
0.0632295310497284,
0.004822691436856985,
0.018118498846888542,
-0.02920740284025669,
0.012037948705255985,
-0.001149353920482099,
-0.02877296507358551,
0.011344341561198235,
-0.023254500702023506,
0.00631942180916667,
-0.02183995582163334,
-0.010418356396257877,
0.03784896805882454,
0.0431479811668396,
-0.014584102667868137,
-0.018793102353811264,
-0.01387198269367218,
0.01672176457941532,
0.041958000510931015,
-0.01260887086391449,
0.004366948734968901,
0.03423849120736122,
0.05337604507803917,
0.000051364011596888304,
-0.02139199897646904,
-0.04147765412926674,
-0.01756313070654869,
-0.04144536331295967,
0.009617066942155361,
0.01233943272382021,
0.05561971664428711,
0.028250044211745262,
0.06256145983934402,
0.014724519103765488,
0.016078995540738106,
-0.024375420063734055,
0.006465068552643061,
-0.09197282791137695,
0.04970691725611687,
-0.01976701058447361,
-0.03912562504410744,
-0.006700063589960337,
-0.013873297721147537,
-0.02971941977739334,
-0.023132596164941788,
-0.04007228463888168,
-0.0321652889251709,
0.03475932776927948,
-0.021471042186021805,
-0.0006975805154070258,
-0.026084598153829575,
-0.05369066447019577,
-0.014612670056521893,
0.04710470139980316,
0.05393625795841217,
-0.031766779720783234,
0.013695456087589264,
0.03139472380280495,
-0.03290226310491562,
-0.012255992740392685,
-0.0014863620745018125,
0.02656605839729309,
0.0289764404296875,
0.024077964946627617,
0.013719135895371437,
-0.005713933147490025,
0.01363606657832861,
-0.026395654305815697,
0.04935823008418083,
0.06427236646413803,
0.0004607359296642244,
0.012136862613260746,
-0.02882736548781395,
-0.04045168682932854,
-0.022758174687623978,
0.021199366077780724,
0.07909196615219116,
0.0014245708007365465,
-0.012198224663734436,
0.033424992114305496,
0.014223038218915462,
-0.008248696103692055,
0.04507425054907799,
0.03181464225053787,
-0.009515020996332169,
-0.03900304064154625,
-0.04457469657063484,
-0.03562666475772858,
-0.018180621787905693,
-0.003264881204813719,
0.002051201183348894,
-0.00807901844382286,
-0.00028974295128136873,
-0.004338535014539957,
0.008613921701908112,
0.04636062681674957,
-0.04991517215967178,
-0.0201858039945364,
-0.03141653910279274,
-0.013411685824394226,
0.01195283979177475,
0.02729334868490696,
0.004126281011849642,
0.06835471093654633,
0.06360314041376114,
0.0007355182315222919,
0.006328917108476162,
-0.0884811207652092,
0.007530908565968275,
0.02251477912068367,
0.01591908186674118,
0.012026136741042137,
-0.013858918100595474,
-0.04474717006087303,
-0.013393609784543514,
0.019132738932967186,
-0.04044114053249359,
0.027920518070459366,
0.015084708109498024,
0.01881249062716961,
-0.03943725302815437,
-0.03920702263712883,
-0.02539915218949318,
0.00411930400878191,
0.000060631773521890864,
0.0032910590525716543,
-0.018115900456905365,
-0.0018730057636275887,
-0.02175726182758808,
-0.003811325179412961,
0.0059196557849645615,
0.03186760097742081,
0.02535976655781269,
0.012173465453088284,
-0.005251601338386536,
-0.002344768261536956,
-0.03951084241271019,
-0.10931568592786789,
-0.004290150944143534,
0.007329171057790518,
-0.0059746489860117435,
0.0589236281812191,
-0.037382837384939194,
-0.022898176684975624,
0.03710635378956795,
-0.006725245621055365,
0.036746323108673096,
0.04515831172466278,
-0.060675475746393204,
0.026356376707553864,
0.013956686481833458,
0.010307020507752895,
0.00810261256992817,
0.0518217459321022,
-0.03609117865562439,
0.006054109428077936,
-0.039199814200401306,
0.009798074141144753,
-0.06185964122414589,
-0.032576918601989746,
-0.018119938671588898,
0.010192299261689186,
-0.08148550987243652,
0.04190964251756668,
-0.014775189571082592,
0.013216673396527767,
-0.0030212157871574163,
-0.03686143457889557,
0.016246186569333076,
-0.01106227096170187,
-0.000037420770240714774,
0.0031302887946367264,
0.005539642181247473,
0.0284220390021801,
0.0024437392130494118,
-0.03856668993830681,
0.03340645134449005,
0.020122285932302475,
-0.029766235500574112,
0.016591129824519157,
-0.024282308295369148,
-0.023114347830414772,
-0.02143099531531334,
-0.014357018284499645,
0.013297094032168388,
-0.0027194134891033173,
0.030159834772348404,
-0.025949904695153236,
0.013075573369860649,
0.0241684690117836,
-0.008027106523513794,
-0.028848495334386826,
0.04226347431540489,
-0.01704428903758526,
0.005632478278130293,
-0.02428135648369789,
-0.006660731974989176,
0.04751359298825264,
0.0016542341327294707,
-0.06543654203414917,
-0.03591287136077881,
0.03635111451148987,
0.0045677595771849155,
-0.06124481186270714,
0.0019238253589719534,
-0.00603411253541708,
-0.0483858622610569,
-0.005168091505765915,
-0.016235794872045517,
0.01909477636218071,
-0.01780981384217739,
0.015112056396901608,
0.010027950629591942,
0.016528349369764328,
0.04325047507882118,
-0.04533008858561516,
-0.012190442532300949,
-0.0023714741691946983,
-0.004513171501457691,
-0.00044797349255532026,
0.021379273384809494,
0.03757576271891594,
-0.009647637605667114,
-0.034368038177490234,
-0.010233291424810886,
-0.010789480060338974,
-0.039114005863666534,
-0.03275231271982193,
-0.023792875930666924,
0.06732981652021408,
-0.02109410986304283,
-0.019499966874718666,
-0.039299506694078445,
0.006619731895625591,
-0.028949061408638954,
0.013164494186639786,
-0.048828836530447006,
0.008494015783071518,
-0.004972573835402727,
-0.03993109241127968,
0.05441935360431671,
-0.000791528495028615,
-0.019635332748293877,
0.009823808446526527,
0.03596681356430054,
0.0047805882059037685,
-0.011475495994091034,
0.03720986098051071,
-0.04631742835044861,
0.013922709971666336,
-0.046355001628398895,
0.01622217893600464,
-0.010282843373715878,
-0.0062888506799936295,
-0.03179994225502014,
-0.05447448417544365,
-0.023069189861416817,
0.001014998648315668,
0.0457298718392849,
0.04894806817173958,
0.03991604596376419,
0.024412212893366814,
-0.02481849677860737,
0.007064905483275652,
-0.005263995844870806,
0.004133899696171284,
0.02190568670630455,
-0.00021193719294387847,
0.02339744381606579,
-0.010412543080747128,
0.021120110526680946,
0.04206588864326477,
0.028989950194954872,
-0.03562655299901962,
-0.01602192595601082,
0.026233242824673653,
-0.013482515700161457,
0.029363613575696945,
0.009517878293991089,
-0.035911738872528076,
0.04355425015091896,
-0.028034647926688194,
0.03079988993704319,
0.012803996913135052,
0.01859593577682972,
0.01764378696680069,
0.034948743879795074,
0.029153095558285713,
0.016040712594985962,
-0.02864057384431362,
-0.07220525294542313,
0.030048035085201263,
-0.005240935366600752,
0.004873006604611874,
0.004779680632054806,
-0.0018677981570363045,
0.0343005545437336,
-0.03748760372400284,
-0.003400644985958934,
-0.019591031596064568,
-0.05351513624191284,
0.011946549639105797,
-0.04596072807908058,
-0.008406969718635082,
0.0717659518122673,
0.00584391038864851,
-0.02036692015826702,
-0.034389037638902664,
-0.024564523249864578,
0.050403956323862076,
0.04212772101163864,
0.022330638021230698,
-0.03128578141331673,
0.04451969638466835,
-0.029489075765013695,
-0.0024582918267697096,
-0.016435343772172928,
-0.03212343156337738,
0.15330548584461212,
0.033635370433330536,
0.011199766770005226,
-0.037480276077985764,
0.03558376431465149,
0.021398328244686127,
0.016020797193050385,
-0.014066812582314014,
0.0048702554777264595,
-0.016521969810128212,
0.012657509185373783,
-0.00785832293331623,
0.04060802608728409,
0.03158180043101311,
-0.03390144929289818,
0.054632410407066345,
-0.04109513759613037,
-0.01535018254071474,
0.0076807825826108456,
0.02516239695250988,
0.004079560283571482,
0.008603917434811592,
-0.0302045289427042,
0.021347101777791977,
-0.03077366203069687,
0.012427879497408867,
-0.031416554003953934,
-0.03901582956314087,
0.01553204096853733,
0.012973332777619362,
-0.05184770002961159,
0.037676796317100525,
-0.023765387013554573,
-0.05185633525252342,
-0.028868962079286575,
0.007946880534291267,
0.023877929896116257,
-0.011482590809464455,
0.0599343404173851,
0.042780328541994095,
-0.0007928808336146176,
-0.01279908511787653,
0.03868269547820091,
0.003029261017218232,
-0.035584066063165665,
0.003639846108853817,
-0.029546717181801796,
0.09861576557159424,
-0.020776858553290367,
-0.02193833328783512,
0.017255203798413277,
-0.021350370720028877,
0.022699590772390366,
-0.0604986697435379,
0.025323843583464622,
-0.014611426740884781,
0.017653748393058777,
-0.015612049028277397,
-0.025492021813988686,
-0.013400433585047722,
0.024257389828562737,
0.010684926994144917,
-0.00429305387660861,
-0.02854863367974758,
-0.012173594906926155,
-0.026867961511015892,
0.0029564329888671637,
0.029708903282880783,
0.006627769209444523,
-0.03111402504146099,
-0.0015194511506706476,
-0.02318587154150009,
-0.006984735373407602,
-0.02664206549525261,
-0.004667062312364578,
0.039131198078393936,
0.07583886384963989,
-0.002992894034832716,
0.023740487173199654,
-0.03247678279876709,
-0.06852410733699799,
0.03926587477326393,
0.00041843531653285027,
-0.023234987631440163,
-0.03510602191090584,
0.028679748997092247,
0.01627000980079174,
0.06293383985757828,
0.014263604767620564,
0.005103627219796181,
0.01633063703775406,
0.011339779943227768,
0.020071156322956085,
-0.00899047963321209,
0.007841144688427448,
0.01697486825287342,
-0.021742401644587517,
-0.016629420220851898,
-0.01421542838215828,
0.009449178352952003,
0.024021783843636513,
0.01427589450031519,
-0.002097807824611664,
0.007905297912657261,
0.009647044353187084,
-0.01549955178052187,
0.06318444013595581,
-0.03367955982685089,
0.024613864719867706,
0.007802242413163185,
0.015205658040940762,
-0.03726724535226822,
-0.004279411397874355,
-0.024631543084979057,
0.015450222417712212,
-0.023849772289395332,
0.005553011316806078,
-0.012726619839668274,
0.022932836785912514,
-0.040611062198877335,
0.032783642411231995,
-0.027418991550803185,
-0.03971182182431221,
-0.03189284726977348,
-0.015963945537805557,
-0.006446551531553268,
-0.015578506514430046,
-0.008713622577488422,
0.02883228287100792,
-0.010824797675013542,
-0.05863413214683533,
0.023916849866509438,
0.02692609280347824,
-0.041392065584659576,
0.003630950814113021,
0.01964668184518814,
0.015747234225273132,
0.00977825466543436,
0.01928821951150894,
-0.05983252450823784,
0.010041749104857445,
-0.012381183914840221,
-0.026434166356921196,
0.06862568110227585,
-0.017503835260868073,
0.0011124436277896166,
0.03095458447933197,
-0.04132150113582611,
0.0009239407372660935,
0.033637527376413345,
0.010649309493601322,
-0.0052918726578354836,
0.001973784528672695,
-0.06879815459251404,
0.01455841027200222,
-0.006882636807858944,
0.043878667056560516,
-0.01893392950296402,
0.009210760705173016,
0.027631739154458046,
0.0027944203466176987,
0.014699932187795639,
0.007760997861623764,
-0.009246110916137695,
-0.0048184702172875404,
0.003462719963863492,
0.002952397568151355,
0.008686326444149017,
0.018027108162641525,
0.08777685463428497,
-0.06148810312151909,
-0.014085356146097183,
0.022416969761252403,
0.016915831714868546,
-0.11074326187372208,
0.022149953991174698,
0.02467428334057331,
0.037446942180395126,
0.06910576671361923,
-0.0594545416533947,
0.03261827304959297,
0.0408770777285099,
-0.06574340909719467,
0.009080436080694199,
-0.021910089999437332,
-0.016398372128605843,
-0.01779979094862938,
-0.026433801278471947,
-0.04165835306048393,
0.04708811640739441,
0.019602464511990547,
0.04180733487010002,
0.02343568205833435,
0.03920264542102814,
-0.005292912479490042,
-0.002141110133379698,
-0.04519534856081009,
-0.0016686643939465284,
0.02783278375864029,
-0.009885280393064022,
0.052044447511434555,
-0.009904712438583374,
-0.016824016347527504,
0.016896476969122887,
-0.022317472845315933,
-0.01079396903514862,
0.005895282607525587,
0.011461364105343819,
0.04398451745510101,
0.03359277546405792,
0.024227600544691086,
0.0014911717735230923,
-0.01265872921794653,
-0.020433280616998672,
0.02935803309082985,
0.033937301486730576,
0.00484761968255043,
-0.007752680219709873,
0.012795359827578068,
-0.0852351039648056,
-0.024280773475766182,
0.021912960335612297,
-0.03829214349389076,
-0.03304380178451538,
-0.002815555315464735,
-0.000718242023140192,
-0.006502540782094002,
-0.012204322032630444,
-0.003808507928624749,
-0.04037618637084961,
-0.023066069930791855,
0.03095860779285431,
-0.001012394088320434,
-0.0013150403974577785,
0.026066359132528305,
-0.01814374513924122,
-0.003277749754488468,
0.02341547980904579,
-0.010768625885248184,
0.019223742187023163,
-0.0573156364262104,
0.02290019765496254,
-0.026797732338309288,
0.018622536212205887,
-0.008859056979417801,
-0.02313576079905033,
-0.02387569099664688,
0.05081239715218544,
0.008319650776684284,
-0.008605272509157658,
-0.05685102567076683,
-0.04586179181933403,
0.009709788486361504,
-0.04875337705016136,
0.022245030850172043,
0.039701126515865326,
-0.013185515068471432,
-0.0201723575592041,
-0.008869617246091366,
-0.007326553575694561,
0.02209777757525444,
0.04836922511458397,
-0.005263907369226217,
-0.015734877437353134,
0.06930485367774963,
0.012918186374008656,
0.014070440083742142,
-0.06431286036968231,
-0.002057737438008189,
-0.022898836061358452,
0.016910798847675323,
0.01191431563347578,
0.015205148607492447,
-0.06894507259130478,
0.015142755582928658,
0.013646763749420643,
-0.023558832705020905,
0.04774222522974014,
0.01765984483063221,
-0.05697762221097946,
0.06804715096950531,
-0.013393205590546131,
-0.03803934156894684,
0.04713757336139679,
0.0033884881995618343,
-0.006997327785938978,
0.05343211069703102,
-0.04310452938079834,
-0.030816713348031044,
0.013570823706686497,
-0.005129732191562653,
-0.020726962015032768,
-0.006190254352986813,
0.007941992953419685,
0.03561602160334587,
-0.02425765059888363,
0.012178313918411732,
0.03992254659533501,
0.0036063429433852434,
-0.04321131110191345,
0.07870931923389435,
0.013653185218572617,
0.017932768911123276,
0.039017923176288605,
0.02148933708667755,
0.01846129074692726,
-0.011849688366055489,
0.05185438320040703,
0.04319477453827858,
0.03862863406538963,
0.031226763501763344,
-0.012871813029050827,
0.00890159048140049,
-0.01946425810456276,
-0.022027259692549706,
-0.0011737965978682041,
0.049425553530454636,
-0.011548250913619995,
0.023916389793157578,
0.02352265827357769,
-0.03731027990579605,
0.024257240816950798,
0.05316750705242157,
-0.015682056546211243,
0.054873544722795486,
-0.031352635473012924,
-0.00764724425971508,
0.010311687365174294,
0.007829531095921993,
-0.019110027700662613,
0.04492573440074921,
-0.0047263032756745815,
0.0661492869257927,
-0.009423889219760895,
0.033050503581762314,
-0.03344612196087837,
-0.026869546622037888,
-0.000826980103738606,
-0.02890991047024727,
0.014340578578412533,
0.04622960090637207,
-0.015272106043994427,
-0.0057640220038592815,
-0.030358992516994476,
-0.0009617062169127166,
-0.019030120223760605,
0.02039027027785778,
-0.0008248776430264115,
0.031150398775935173,
-0.05251258611679077,
0.0016722895670682192,
-0.06211460009217262,
0.031886398792266846,
-0.041626617312431335,
-0.002974924398586154,
-0.025904493406414986,
-0.014441494829952717,
-0.020496157929301262,
-0.019429057836532593
] |
<p>In astrophysics, I often come across the speed of sound. I understand that, broadly, it represents the speed at which perturbations travel through a medium. But there's more than one speed of sound. The most common seem to be <em>isothermal</em> and <em>adiabatic</em>, which are defined as $c_s^2=(dp/d\rho)_T$ and $c_s^2=(dp/d\rho)_S$, respectively.</p>
<p>My question is, when do these different speeds apply? When do perturbations travel at the adiabatic sound speed, and when the isothermal? Are there any other useful sound speeds?</p> | 1,984 | [
0.0064262826927006245,
-0.020607173442840576,
-0.015103694051504135,
-0.03758769854903221,
0.042746126651763916,
0.009038414806127548,
-0.037656720727682114,
-0.023990711197257042,
0.003202226012945175,
-0.010806770995259285,
0.016720006242394447,
0.02282191626727581,
0.07180557399988174,
0.01259617693722248,
0.06448560953140259,
0.006770763546228409,
-0.02559715509414673,
-0.011564110405743122,
0.0000221538375626551,
-0.003930309787392616,
0.01515866443514824,
-0.0006374284857884049,
0.0307118222117424,
0.00032598510733805597,
0.01789340190589428,
0.05055219307541847,
-0.004470934625715017,
0.03780559077858925,
0.020880045369267464,
0.013547006994485855,
0.028926264494657516,
-0.01943320408463478,
-0.020285742357373238,
0.03746519982814789,
0.014038766734302044,
-0.014405760914087296,
-0.01220629084855318,
-0.037665821611881256,
-0.012727434746921062,
0.026525957509875298,
-0.07291905581951141,
-0.037646081298589706,
0.0024721738882362843,
0.003989086486399174,
-0.01456316839903593,
-0.006662390660494566,
0.04344162717461586,
-0.028701994568109512,
0.013267295435070992,
-0.07726666331291199,
0.04747553914785385,
0.009618151001632214,
0.032020311802625656,
0.048484284430742264,
-0.03332885354757309,
0.025390133261680603,
0.08155566453933716,
0.05105423182249069,
-0.03447188064455986,
-0.04566507413983345,
-0.015141294337809086,
0.03669048100709915,
0.013457371853291988,
-0.014847105368971825,
-0.02739185467362404,
0.06383951753377914,
-0.028625160455703735,
0.0037173505406826735,
0.013297605328261852,
0.014829333871603012,
-0.0038943092804402113,
-0.000038488760765176266,
0.01523293275386095,
-0.007010833825916052,
0.0020039088558405638,
-0.0311806071549654,
0.006398716941475868,
0.01513731200248003,
0.030443686991930008,
0.05774950981140137,
-0.009556406177580357,
0.0003973191778641194,
0.003142343135550618,
0.023510398343205452,
-0.006290670949965715,
0.027606677263975143,
0.08157754689455032,
-0.02859388291835785,
0.007160259876400232,
0.0489228330552578,
-0.01459241472184658,
-0.0066701737232506275,
0.003841811092570424,
-0.006930656265467405,
0.020508604124188423,
-0.005581163801252842,
-0.011431857012212276,
0.03615029156208038,
-0.0036108377389609814,
-0.04853416234254837,
-0.002560095628723502,
0.0034670827444642782,
0.05651620775461197,
0.09611906111240387,
-0.01632886938750744,
-0.03968974947929382,
-0.07365602254867554,
0.0148698128759861,
-0.032657723873853683,
-0.019507085904479027,
-0.03004496358335018,
0.0053134486079216,
-0.01707802340388298,
0.02155926264822483,
0.0010805063648149371,
-0.0006791919586248696,
-0.017908910289406776,
-0.01820795051753521,
0.053419169038534164,
0.04612107202410698,
0.07062172889709473,
-0.013322612270712852,
0.027603091672062874,
-0.011409726925194263,
-0.02948654443025589,
0.0331769734621048,
0.004912401549518108,
-0.0058120666071772575,
-0.022424792870879173,
-0.011038445867598057,
-0.014525877311825752,
-0.030066289007663727,
-0.03148973733186722,
-0.04174569621682167,
0.02671584114432335,
-0.016243696212768555,
-0.08597050607204437,
-0.06767188012599945,
0.040267448872327805,
-0.011999486945569515,
-0.02685544081032276,
-0.05915631726384163,
-0.003387918695807457,
0.013674707151949406,
0.05996870622038841,
-0.001962040551006794,
-0.0033505004830658436,
-0.04438365623354912,
0.05802900344133377,
0.006683905143290758,
-0.04613247141242027,
-0.03230370208621025,
-0.006525871343910694,
-0.029384030029177666,
0.019221283495426178,
-0.07443486899137497,
0.0016816511051729321,
0.0309063158929348,
0.008611008524894714,
-0.00474809342995286,
0.08092698454856873,
-0.060054223984479904,
-0.026072759181261063,
0.034166332334280014,
0.015513072721660137,
-0.03862827271223068,
0.09606228023767471,
0.034656718373298645,
0.0017914490308612585,
0.03163983300328255,
0.03962219879031181,
0.004166861064732075,
0.015978621318936348,
-0.001418531988747418,
0.02231917344033718,
-0.015561127103865147,
-0.0001515363692305982,
-0.0029665811453014612,
-0.034335408359766006,
0.01979989744722843,
-0.021165601909160614,
-0.046124786138534546,
0.02245461754500866,
-0.023191001266241074,
-0.029234513640403748,
0.04229209944605827,
-0.010649719275534153,
-0.0002761654614005238,
0.01841878332197666,
-0.0539773553609848,
0.022027263417840004,
-0.056797247380018234,
0.040937770158052444,
0.0034058471210300922,
0.019472254440188408,
0.047201093286275864,
0.04448147490620613,
0.038225047290325165,
-0.000785058131441474,
-0.040095843374729156,
0.0029990740586072206,
0.04131976142525673,
0.02698409929871559,
-0.02325163595378399,
0.03314566612243652,
0.04560694843530655,
0.0031953167635947466,
-0.014043260365724564,
-0.013484571129083633,
0.010543623939156532,
-0.045652907341718674,
-0.017359571531414986,
-0.03161204233765602,
0.040375981479883194,
-0.02999577671289444,
-0.02163953334093094,
0.004537944681942463,
-0.03289596363902092,
-0.010684281587600708,
0.01706606149673462,
-0.020304445177316666,
0.07452291995286942,
0.04842762649059296,
0.018808497115969658,
-0.011992158368229866,
0.05578162521123886,
-0.0010690265335142612,
0.013769022189080715,
-0.016100013628602028,
-0.047956064343452454,
-0.04653528332710266,
0.007792919408529997,
0.05425402149558067,
0.03232957422733307,
-0.055589549243450165,
0.01991349272429943,
0.03421560302376747,
0.002125069499015808,
0.048826973885297775,
0.010306045413017273,
-0.017700985074043274,
-0.047525085508823395,
0.003630642080679536,
-0.00026037386851385236,
0.007453636731952429,
0.017045482993125916,
0.04521989822387695,
-0.014824530109763145,
0.025573216378688812,
-0.02072727307677269,
-0.01875448413193226,
0.03781900182366371,
-0.015077652409672737,
-0.024714114144444466,
-0.021733907982707024,
-0.03169162571430206,
0.002251871395856142,
-0.014860980212688446,
0.032899193465709686,
0.01706896349787712,
0.010261728428304195,
0.04799586161971092,
0.020487306639552116,
0.015834957361221313,
0.017853159457445145,
0.00257951021194458,
0.011851399205625057,
-0.011876018717885017,
0.023746799677610397,
-0.03224465250968933,
0.02422362193465233,
-0.028744379058480263,
0.002398551208898425,
-0.024395892396569252,
-0.012764411978423595,
0.04325230047106743,
-0.002381970640271902,
0.026016099378466606,
-0.03776662424206734,
-0.0629815086722374,
0.007419697940349579,
-0.0575341172516346,
-0.011176255531609058,
0.023642007261514664,
-0.02133331634104252,
0.012811400927603245,
-0.04916754737496376,
-0.03028133139014244,
0.01406592782586813,
-0.038797616958618164,
-0.006460102740675211,
0.019847407937049866,
-0.02384105883538723,
-0.06481535732746124,
-0.03439291566610336,
-0.034169815480709076,
0.00094731425633654,
-0.04119298607110977,
0.029772454872727394,
0.061781689524650574,
-0.03945285826921463,
-0.0001088232675101608,
0.012212108820676804,
-0.027379510924220085,
-0.022575166076421738,
-0.016155192628502846,
-0.023503299802541733,
0.05040563642978668,
-0.04031779244542122,
0.02010742388665676,
0.05773579329252243,
-0.07195387780666351,
-0.010856511071324348,
-0.03526308014988899,
-0.05802735686302185,
0.0554099902510643,
-0.004883843939751387,
0.0560857318341732,
-0.004789411555975676,
-0.057489559054374695,
0.04605644941329956,
0.07127648591995239,
0.0036774214822798967,
0.008019686676561832,
-0.007136572152376175,
-0.00926671177148819,
-0.010525737889111042,
-0.009667843580245972,
0.04511753469705582,
-0.03737568482756615,
0.012529910542070866,
0.0075041609816253185,
0.033753469586372375,
0.03233760595321655,
0.003513684030622244,
-0.01097843423485756,
-0.019839869812130928,
0.016219384968280792,
0.01059575006365776,
0.04360361397266388,
0.0197705440223217,
-0.028581835329532623,
0.026831278577446938,
-0.020375343039631844,
0.04663588106632233,
0.017695914953947067,
-0.051526039838790894,
0.046874336898326874,
0.003633169922977686,
-0.0182768814265728,
-0.04081618785858154,
0.018764348700642586,
0.009395166300237179,
0.017719386145472527,
-0.010533909313380718,
0.02505483664572239,
-0.008853459730744362,
-0.024313637986779213,
-0.010369290597736835,
0.02531319297850132,
0.02882394939661026,
-0.003685509320348501,
-0.017774896696209908,
0.0025760175194591284,
-0.04592902213335037,
0.02931022085249424,
0.0027000249829143286,
-0.02289077453315258,
0.04873363673686981,
0.015760580077767372,
-0.006981911137700081,
-0.03527284041047096,
-0.03618568927049637,
0.02569401077926159,
-0.08807635307312012,
0.0075572640635073185,
-0.0112485121935606,
0.019476665183901787,
-0.005263325292617083,
0.0645163282752037,
0.026633862406015396,
-0.0010989049915224314,
0.02923702262341976,
-0.012293717823922634,
-0.0836576521396637,
0.03323902189731598,
-0.02025340311229229,
-0.04640350863337517,
-0.01354324258863926,
0.005339513532817364,
0.008644668385386467,
-0.03190215304493904,
-0.0029230217915028334,
0.003896566340699792,
0.006151892710477114,
-0.045007288455963135,
0.028550073504447937,
-0.039865218102931976,
-0.06074932590126991,
-0.01158968172967434,
0.05432577803730965,
0.03247841075062752,
-0.008857005275785923,
0.00046372177894227207,
0.04415854066610336,
-0.008133760653436184,
0.002024831948801875,
-0.006191405933350325,
-0.02183576114475727,
-0.04216915741562843,
-0.0023372704163193703,
0.050028666853904724,
-0.0034136248286813498,
-0.04264229163527489,
0.04384235665202141,
0.010917053557932377,
0.04906114935874939,
-0.007448203396052122,
-0.03310078755021095,
-0.0322207473218441,
-0.06584633886814117,
0.020439786836504936,
0.0035595600493252277,
0.05558169260621071,
0.006456291303038597,
0.006425386294722557,
0.022273525595664978,
-0.019947625696659088,
-0.02240268513560295,
0.04212624952197075,
0.018514202907681465,
-0.015201380476355553,
-0.02172682248055935,
-0.05508079007267952,
-0.023384934291243553,
0.000385938270483166,
-0.001026795245707035,
0.029869932681322098,
0.0021755320485681295,
-0.02244722656905651,
0.033622752875089645,
-0.02283075824379921,
-0.009394774213433266,
0.007421708665788174,
-0.010504759848117828,
0.031200259923934937,
0.023930875584483147,
0.013298805803060532,
-0.010768133215606213,
0.011365975253283978,
0.020405709743499756,
0.030924685299396515,
-0.024131132289767265,
-0.014142255298793316,
-0.05961040407419205,
0.011023425497114658,
0.003266263986006379,
0.03729365020990372,
0.0006735658971592784,
-0.004414573311805725,
-0.056180838495492935,
-0.0012477930868044496,
0.026926357299089432,
0.00738212326541543,
0.038339342921972275,
0.01293469499796629,
-0.026309294626116753,
0.00500427046790719,
-0.009995280764997005,
0.0026382156647741795,
0.04559936746954918,
0.0635228306055069,
-0.05121494457125664,
-0.01726851426064968,
-0.002394194947555661,
-0.011134103871881962,
-0.013484559021890163,
-0.0011465656571090221,
0.04229070618748665,
-0.02429414540529251,
-0.014917868189513683,
0.023552536964416504,
0.013512125238776207,
0.015126918442547321,
-0.0636659786105156,
-0.02130364254117012,
0.01539661455899477,
-0.015119786374270916,
0.0330229327082634,
-0.022326119244098663,
-0.04516002908349037,
0.031007787212729454,
0.012078476138412952,
-0.026384156197309494,
0.022801633924245834,
-0.011290094815194607,
0.05321894586086273,
0.020450016483664513,
0.011780664324760437,
0.034429632127285004,
0.02778426930308342,
-0.005310933105647564,
-0.033769816160202026,
-0.00142593530472368,
0.05131750926375389,
-0.022884856909513474,
0.005912225693464279,
-0.020335417240858078,
-0.009455480612814426,
-0.027185779064893723,
0.04980999231338501,
0.013767518103122711,
0.017420781776309013,
-0.01607900857925415,
-0.026566466316580772,
-0.01927758939564228,
0.0660698190331459,
0.019364934414625168,
-0.010152382776141167,
0.014070797711610794,
0.04398472607135773,
-0.027958624064922333,
-0.0004436293093021959,
0.026729494333267212,
0.008936204016208649,
-0.0011728736571967602,
0.040653668344020844,
-0.015394946560263634,
0.03202686831355095,
-0.008818451315164566,
0.008726468309760094,
0.029123948886990547,
-0.020303845405578613,
0.048914585262537,
0.005926846526563168,
0.0008940203115344048,
-0.00590811762958765,
-0.06429072469472885,
-0.005799460224807262,
0.00343634863384068,
-0.011465606279671192,
0.025611737743020058,
-0.06445449590682983,
0.0491524338722229,
-0.018952880054712296,
0.032897043973207474,
-0.07646588981151581,
-0.016060005873441696,
0.02825290523469448,
0.03421921283006668,
-0.022258367389440536,
-0.016216570511460304,
0.02176389843225479,
-0.05149251967668533,
-0.0418194904923439,
0.011231212876737118,
0.06787519156932831,
0.014067535288631916,
-0.018886180594563484,
0.0033527291379868984,
0.03514039143919945,
0.042106084525585175,
-0.03033578023314476,
-0.018119456246495247,
0.05282895267009735,
0.0018190786940976977,
0.001113120117224753,
-0.008802502416074276,
0.07956240326166153,
-0.01757253333926201,
-0.024026760831475258,
-0.03905443847179413,
-0.034333471208810806,
-0.003230208531022072,
-0.02854846604168415,
-0.005416420288383961,
0.03728224337100983,
0.009525501169264317,
-0.009516594931483269,
0.000992298242636025,
0.029215702787041664,
-0.012752929702401161,
0.033047713339328766,
0.001069810357876122,
-0.02258310094475746,
-0.014975011348724365,
-0.04507574439048767,
0.015730857849121094,
0.015877995640039444,
0.027551351115107536,
0.002341125626116991,
0.042769771069288254,
-0.002460832241922617,
-0.0162185151129961,
-0.0010975586483255029,
-0.012008621357381344,
0.04715775325894356,
-0.0045113577507436275,
-0.00730849290266633,
-0.008912780322134495,
-0.01413736306130886,
-0.03545738011598587,
-0.04891607165336609,
-0.02879437804222107,
-0.01473693735897541,
0.099001944065094,
-0.038391128182411194,
0.05266303941607475,
0.022220008075237274,
-0.028309695422649384,
0.02184242382645607,
-0.043766893446445465,
-0.04388497397303581,
-0.0077666593715548515,
-0.004998462740331888,
0.018245317041873932,
0.0024356297217309475,
-0.03789784759283066,
0.02230304293334484,
0.03471897542476654,
-0.028111401945352554,
0.02311413362622261,
0.03246704861521721,
0.04278075322508812,
-0.021410826593637466,
-0.028354957699775696,
-0.0033193996641784906,
0.052528515458106995,
-0.04206639900803566,
0.04602806642651558,
-0.006438274867832661,
0.004853453952819109,
0.04496973007917404,
0.021987855434417725,
0.027562841773033142,
-0.059070032089948654,
0.0016868064412847161,
-0.0468381866812706,
0.009204084984958172,
0.015504103153944016,
-0.004261701833456755,
0.015706755220890045,
-0.02747938223183155,
0.04268404096364975,
0.008214617148041725,
0.031634196639060974,
-0.006550509948283434,
-0.04630085825920105,
-0.032038379460573196,
-0.0022316540125757456,
-0.029621871188282967,
0.025825269520282745,
0.00977056473493576,
-0.06833527237176895,
0.010334473103284836,
-0.025139732286334038,
0.0344083234667778,
-0.007582576014101505,
-0.0097382552921772,
-0.01704922318458557,
0.061658717691898346,
0.01764027774333954,
-0.00846017524600029,
-0.006906035356223583,
0.016477784141898155,
0.13041363656520844,
0.07232385128736496,
0.032314397394657135,
-0.054687753319740295,
0.036241721361875534,
-0.019162414595484734,
0.02205083519220352,
-0.03477349504828453,
0.01240837387740612,
0.00592821603640914,
0.018864914774894714,
0.011796443723142147,
0.0842759758234024,
-0.0032073266338557005,
0.007313523441553116,
0.03542543947696686,
-0.03839757293462753,
-0.0142047805711627,
0.02046438306570053,
0.033339641988277435,
-0.017721764743328094,
0.04631005600094795,
-0.005829712375998497,
-0.022122925147414207,
-0.018960686400532722,
0.00226116762496531,
0.000900590792298317,
-0.055389728397130966,
0.021116670221090317,
-0.013444875366985798,
-0.0303750392049551,
0.012157389894127846,
0.0063154068775475025,
-0.03809685632586479,
-0.029153352603316307,
0.036096442490816116,
0.02236468531191349,
-0.028179096058011055,
-0.01236783992499113,
0.009274134412407875,
-0.018898949027061462,
0.008816363289952278,
-0.00008451373287243769,
0.007229598704725504,
-0.006992097478359938,
0.010005726478993893,
-0.00031146101537160575,
0.029414251446723938,
0.000457051646662876,
-0.012941478751599789,
-0.03687463700771332,
0.03211633116006851,
0.0066499593667685986,
-0.004237528424710035,
-0.015189633704721928,
0.007057253737002611,
0.05875779315829277,
-0.0008454040507785976,
0.0024805220309644938,
-0.037741295993328094,
0.007960021495819092,
-0.005305439233779907,
0.04091111198067665,
-0.010252810083329678,
0.0016544016543775797,
0.01653403788805008,
-0.013603728264570236,
0.024723440408706665,
-0.02775539830327034,
-0.015526368282735348,
-0.02120438776910305,
0.019226016476750374,
-0.05976158007979393,
0.001893211854621768,
0.020649496465921402,
-0.005550628527998924,
0.03132278844714165,
0.03620754927396774,
-0.013877459801733494,
-0.023763218894600868,
-0.08262718468904495,
0.040269043296575546,
0.00981721468269825,
-0.020308619365096092,
-0.043188054114580154,
-0.025485139340162277,
0.04155915230512619,
-0.0060231322422623634,
-0.014407657086849213,
-0.014715645462274551,
-0.019820215180516243,
0.03094595856964588,
0.020190943032503128,
-0.008519979193806648,
-0.016154352575540543,
0.010525795631110668,
-0.004161354154348373,
-0.014473581686615944,
-0.025507133454084396,
0.02351960726082325,
0.009510098025202751,
0.0012785698054358363,
-0.011840496212244034,
0.019563795998692513,
-0.018789326772093773,
0.01162770763039589,
0.012037165462970734,
-0.019940894097089767,
-0.00679257046431303,
0.00948264729231596,
-0.007482406683266163,
-0.015597933903336525,
-0.04615572839975357,
-0.04880375787615776,
0.031163975596427917,
-0.02229044772684574,
-0.006635687313973904,
-0.052778955549001694,
0.05075071007013321,
-0.030112581327557564,
-0.02652876451611519,
-0.08388485759496689,
-0.005109873600304127,
-0.03659716248512268,
0.02630150318145752,
0.008064614608883858,
-0.0023235450498759747,
0.03140542656183243,
0.02508184127509594,
-0.0658259391784668,
-0.03439230099320412,
0.014292935840785503,
0.010736650787293911,
0.02438575029373169,
-0.010908522643148899,
0.016314052045345306,
-0.01118165161460638,
0.041797857731580734,
-0.021225061267614365,
-0.041432786732912064,
-0.006112397648394108,
-0.04654725268483162,
-0.07102611660957336,
0.026652438566088676,
0.007685882970690727,
0.010265273042023182,
0.03542240709066391,
0.043842826038599014,
-0.004541788250207901,
0.07279716432094574,
-0.022385500371456146,
-0.015585513785481453,
0.0100057702511549,
-0.02560749277472496,
-0.018889809027314186,
-0.01029099989682436,
0.062399692833423615,
-0.015330201014876366,
0.009224030189216137,
0.014516393654048443,
-0.003382184077054262,
-0.021774960681796074,
0.04663870856165886,
-0.020292293280363083,
-0.04411083459854126,
0.028727106750011444,
0.021460724994540215,
0.008688188157975674,
0.04485451430082321,
0.053655415773391724,
-0.01783629320561886,
0.028371445834636688,
0.07401664555072784,
0.014615080319344997,
-0.10170940309762955,
0.017315899953246117,
-0.014783726073801517,
0.005648742895573378,
0.0028525195084512234,
-0.048079993575811386,
0.06941261142492294,
0.013618308119475842,
-0.03990022465586662,
0.023618582636117935,
-0.05010019987821579,
-0.0031674394849687815,
-0.03880009800195694,
0.006459410302340984,
-0.004781094845384359,
0.07068105787038803,
0.05613921582698822,
-0.00470907986164093,
-0.008762181736528873,
0.008549162186682224,
-0.015807220712304115,
-0.00660883542150259,
0.03506989777088165,
0.025729907676577568,
0.009428906254470348,
-0.0067320168018341064,
0.062293827533721924,
-0.002316754311323166,
-0.002356463111937046,
0.033156752586364746,
-0.02172606624662876,
0.015777233988046646,
0.02522091381251812,
0.008286573924124241,
-0.006095316261053085,
0.0033148827496916056,
0.046668652445077896,
-0.03048611246049404,
-0.021316921338438988,
0.048198916018009186,
-0.015389536507427692,
0.010239868424832821,
-0.03766811639070511,
-0.01308454480022192,
0.013844041153788567,
-0.02977711334824562,
-0.0333048440515995,
0.023490820080041885,
-0.03072947822511196,
-0.006630274932831526,
0.019191721454262733,
-0.0032827286049723625,
0.02736305631697178,
0.008190266788005829,
0.0112253213301301,
-0.03909967467188835,
-0.029227277263998985,
0.02395973913371563,
0.0009571541449986398,
-0.02209048718214035,
0.012333549559116364,
0.0034979660995304585,
-0.014126109890639782,
0.008262360468506813,
-0.00368696846999228,
0.007015455048531294,
-0.03552281856536865,
-0.022562330588698387,
-0.012569193728268147,
-0.005602400749921799,
-0.04866507276892662,
0.005005290266126394,
0.014464973472058773,
0.0837991014122963,
0.007473823148757219,
0.03950781375169754,
-0.037615153938531876,
-0.02522282861173153,
-0.02747042290866375,
-0.0345291793346405,
-0.013553365133702755,
-0.033764563500881195,
0.022558316588401794,
-0.05099446699023247,
-0.003987128846347332,
-0.01842254400253296,
0.0012976465513929725,
0.0671447291970253,
0.03406943753361702,
0.02753552608191967,
0.032715052366256714,
-0.009277025237679482,
-0.01933816447854042,
-0.038687340915203094,
-0.014606109820306301,
-0.005452116020023823,
-0.010493667796254158,
-0.025501862168312073,
0.00018495692347642034,
-0.00772084528580308,
0.0035952229518443346,
0.01577931083738804,
-0.00889718160033226,
0.04585634171962738,
0.016515489667654037,
-0.008709657937288284,
0.06485070288181305,
0.030799485743045807,
-0.019256029278039932,
0.0672207772731781,
-0.03989234194159508,
-0.0015697994967922568,
0.038423340767621994,
-0.021140554919838905,
-0.026771441102027893,
0.04084024950861931,
0.010698630474507809,
-0.04315794259309769,
0.0036173088010400534,
-0.01574493572115898,
-0.0237292293459177,
-0.03239545598626137,
0.0004080455983057618,
0.03947245702147484,
-0.06188318505883217,
-0.003369036130607128,
0.02000996097922325,
0.022207263857126236,
0.03420211747288704,
-0.0030962356831878424,
-0.0007040997734293342,
0.005591910798102617,
0.017285870388150215,
-0.035690560936927795,
0.017633646726608276,
0.005229720380157232,
0.052847474813461304,
0.0037246260326355696,
-0.011270062066614628,
-0.020732641220092773,
0.01507360115647316,
0.018137777224183083,
-0.003917808178812265,
-0.01924092508852482,
-0.048700060695409775,
0.005106242373585701,
-0.032499443739652634,
-0.005291834007948637,
0.009096721187233925,
-0.01404156256467104,
0.06503666192293167,
-0.03707154467701912,
0.013175799511373043,
-0.02479718253016472,
-0.006970255635678768,
-0.025403674691915512,
-0.02625301107764244,
-0.0216219499707222,
0.026000473648309708,
-0.02664913609623909,
0.02150413766503334,
0.015852641314268112,
-0.0036610125098377466,
0.032025404274463654,
-0.06376399099826813,
0.003715449944138527,
0.016515828669071198,
-0.03147728368639946,
-0.004294170532375574,
0.0005758728366345167,
-0.018049834296107292,
0.012911719270050526,
0.00940132886171341,
0.043067023158073425,
-0.0013839155435562134,
0.007615567184984684,
-0.0020966422744095325,
-0.007785394787788391,
0.040399108082056046,
-0.07672504335641861,
-0.0009958170121535659,
0.0021245500538498163,
0.02643190138041973,
-0.03242480382323265,
0.012544190511107445
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/12435/einsteins-postulates-minkowski-space-in-laymans-terms">Einstein's postulates <==> Minkowski space. (In layman's terms)</a> </p>
</blockquote>
<p>In the spirit of Einstein's arguments using flashes of light, moving trains and mirrors;
what is the best way to go between Einstein's postulates [<a href="http://en.wikisource.org/wiki/On_the_Electrodynamics_of_Moving_Bodies" rel="nofollow">1</a>] of</p>
<ol>
<li>Relativity: Physical laws are the same in all inertial reference frames.</li>
<li>Constant speed of light: "... light is always propagated in empty space with a definite speed $c$ which is independent of the state of motion of the emitting body."</li>
</ol>
<p>to Minkowski's idea [<a href="http://en.wikisource.org/wiki/Space_and_Time" rel="nofollow">2</a>] that space and time are united into a 4D spacetime with the Lorentzian signature.</p>
<p>The argument can only use simple mathematics (algebra, geometry, a little calculus). I want an argument that a smart high school graduate would be able to understand.
None of the group theory and coset/homogeneous spaces of <a href="http://physics.stackexchange.com/questions/12435/einsteins-postulates-minkowski-space/12438#12438">Marek's answer</a> to <a href="http://physics.stackexchange.com/q/12435/429">my previous question</a>. (Although, if you do have a little knowledge of Lie algebras, you should go read Marek's answer and references now!).</p> | 34 | [
-0.03144614398479462,
-0.03725334256887436,
0.0052466257475316525,
-0.03910863399505615,
0.06399145722389221,
-0.0019434199202805758,
-0.024410368874669075,
-0.03735852986574173,
-0.016843251883983612,
-0.030293874442577362,
0.0524219386279583,
-0.0014107186580076814,
0.050449494272470474,
0.05931266397237778,
-0.00029421501676552,
-0.003850847715511918,
0.03708985820412636,
-0.03722173720598221,
-0.03432600200176239,
-0.048829786479473114,
0.01622554287314415,
0.006606868468225002,
0.01938871666789055,
0.007087860256433487,
-0.03865865245461464,
0.019184617325663567,
0.038890279829502106,
-0.0017180885188281536,
0.005228881258517504,
0.04258960857987404,
-0.0393550731241703,
-0.002794158412143588,
0.008701907470822334,
0.02602268010377884,
-0.014862078242003918,
0.002408310305327177,
0.013769560493528843,
0.016439849510788918,
0.03540852293372154,
-0.004752288572490215,
-0.023640207946300507,
0.027554694563150406,
-0.03359117731451988,
0.06062253564596176,
-0.038741353899240494,
0.044744592159986496,
0.006779389455914497,
0.03361593559384346,
0.021931057795882225,
-0.041855137795209885,
0.06650864332914352,
-0.0010969560826197267,
0.021706972271203995,
-0.00016944379603955895,
-0.01918860338628292,
-0.0008320040069520473,
0.06496031582355499,
0.07484664022922516,
-0.010389065369963646,
-0.04227827861905098,
-0.02498347871005535,
-0.008544120006263256,
0.012079043313860893,
0.007622289005666971,
0.006557973567396402,
0.03890348970890045,
0.007677750196307898,
0.04658252000808716,
0.014832639135420322,
-0.007286994252353907,
-0.007176877930760384,
0.002266498049721122,
0.04646331071853638,
-0.011942005716264248,
0.007669287268072367,
-0.032561030238866806,
0.0022834239061921835,
0.01549607329070568,
0.04575579985976219,
0.0333101749420166,
-0.03599363937973976,
0.020441537722945213,
0.021649610251188278,
0.02280675806105137,
0.001857445458881557,
-0.021018121391534805,
0.0883004292845726,
0.02921157144010067,
-0.02645661123096943,
0.041279327124357224,
0.01322206575423479,
0.003653403837233782,
0.051416411995887756,
0.029598325490951538,
-0.016152868047356606,
0.04714241251349449,
-0.009469231590628624,
0.05517188832163811,
-0.003481869352981448,
-0.011440797708928585,
-0.007133400999009609,
-0.011534027755260468,
0.008591056801378727,
0.07446803152561188,
0.016128886491060257,
-0.02664691023528576,
-0.01752014458179474,
0.027366487309336662,
-0.030158402398228645,
-0.036590348929166794,
-0.02358184941112995,
0.052767932415008545,
-0.007197814993560314,
-0.026124214753508568,
-0.010598137974739075,
-0.03623151034116745,
0.03704189136624336,
-0.018466711044311523,
0.019986918196082115,
0.06040559336543083,
0.04160449281334877,
-0.0441623292863369,
-0.017476754263043404,
-0.027879562228918076,
-0.07941823452711105,
-0.02296319790184498,
0.012414506636559963,
0.010109481401741505,
-0.005344649776816368,
0.025633085519075394,
0.017012285068631172,
0.012243714183568954,
-0.025518527254462242,
0.012701764702796936,
0.04560540243983269,
-0.01000607293099165,
-0.11269944161176682,
-0.03120158612728119,
0.03795291855931282,
0.033176735043525696,
-0.028700483962893486,
-0.09206739068031311,
0.037490151822566986,
-0.02727915160357952,
0.06923218071460724,
-0.007784928195178509,
0.022966040298342705,
-0.005496201105415821,
0.06253042817115784,
-0.003411459969356656,
-0.03133378550410271,
-0.0028690253384411335,
-0.004681847989559174,
-0.06064668297767639,
0.014001866802573204,
-0.04207603260874748,
-0.0030284912791103125,
0.018885977566242218,
-0.006863780319690704,
-0.008247618563473225,
0.08064639568328857,
-0.00371766509488225,
0.01737036369740963,
-0.012171169742941856,
0.029238920658826828,
-0.008706634864211082,
0.03617959842085838,
0.01397698000073433,
-0.009202497079968452,
0.013793110847473145,
-0.010299061425030231,
0.014590470120310783,
-0.04356004670262337,
-0.008573193103075027,
0.03287893161177635,
-0.045888595283031464,
0.0014464021660387516,
0.022788971662521362,
-0.012997884303331375,
0.005555883049964905,
-0.03900585323572159,
-0.013721011579036713,
-0.04276039078831673,
-0.009478598833084106,
0.014411860145628452,
0.05239570513367653,
0.031123390421271324,
0.03659827262163162,
0.006775320041924715,
-0.018504077568650246,
-0.0016718035330995917,
-0.07929495722055435,
-0.001072274288162589,
-0.0003120158798992634,
-0.02133062481880188,
0.022734856233000755,
-0.010522720403969288,
0.0021201062481850386,
-0.05591004341840744,
-0.028355536982417107,
-0.019306179136037827,
0.059314414858818054,
0.0220461618155241,
-0.00947179738432169,
0.03302241116762161,
0.022061603143811226,
0.06442736834287643,
-0.014251474291086197,
-0.018595848232507706,
0.01362514402717352,
0.011111658066511154,
0.02847273461520672,
0.0069704861380159855,
0.04326051101088524,
0.03195811063051224,
0.03597436100244522,
0.007443154230713844,
0.005322957877069712,
-0.02985672652721405,
0.03453778848052025,
-0.04120401293039322,
0.029471229761838913,
0.018168264999985695,
0.0012211428256705403,
0.01215624064207077,
0.07364095747470856,
0.0005173221579752862,
0.032697893679142,
0.033724673092365265,
-0.022427411749958992,
-0.021991195157170296,
0.009986632503569126,
0.045920077711343765,
0.025043267756700516,
-0.06810615956783295,
0.03643540292978287,
0.0058473944664001465,
0.06736721843481064,
-0.015738781541585922,
0.018707765266299248,
-0.020703773945569992,
-0.0743783712387085,
0.013011190108954906,
-0.023146547377109528,
0.0035504691768437624,
0.026545895263552666,
0.012871142476797104,
0.011615816503763199,
0.019716346636414528,
0.02139999344944954,
-0.009315353818237782,
0.026567457243800163,
-0.019719259813427925,
-0.01636679470539093,
0.001666538417339325,
-0.027052078396081924,
0.0357227548956871,
0.026186103001236916,
0.029041914269328117,
0.021700510755181313,
-0.01843334175646305,
0.02451177127659321,
-0.03083508089184761,
-0.03231647610664368,
-0.04683071747422218,
0.007730346173048019,
-0.010977680794894695,
0.008676917292177677,
0.01898088864982128,
-0.05332973226904869,
-0.0016919148620218039,
-0.006120025180280209,
-0.04572917893528938,
-0.017949847504496574,
-0.00006319701060419902,
-0.019300304353237152,
0.02942025288939476,
0.017073052003979683,
-0.05091384798288345,
0.007176766637712717,
0.016735021024942398,
0.01434234157204628,
0.0008984541054815054,
-0.018585171550512314,
-0.04204229637980461,
0.03132868558168411,
-0.040328286588191986,
-0.039846356958150864,
0.03219243884086609,
0.0029587342869490385,
0.0055688549764454365,
0.028742780908942223,
-0.007542307488620281,
-0.06306708604097366,
-0.03350400552153587,
-0.0375523641705513,
0.01765253208577633,
-0.0347544364631176,
-0.017087450250983238,
0.05287047103047371,
-0.05011463910341263,
-0.08842143416404724,
-0.00203677243553102,
-0.02855633571743965,
-0.06300158053636551,
-0.020694060251116753,
-0.018531395122408867,
0.007559704594314098,
-0.018864404410123825,
0.024079397320747375,
0.006848837714642286,
-0.015283691696822643,
-0.02003861404955387,
-0.04629957675933838,
-0.06041017174720764,
0.037576768547296524,
0.0015545767964795232,
0.060643915086984634,
0.007089534308761358,
-0.022929171100258827,
0.027883604168891907,
0.0372922383248806,
-0.041294269263744354,
-0.053065620362758636,
0.00888211838901043,
-0.019303621724247932,
-0.019047453999519348,
-0.013967298902571201,
0.01701354794204235,
0.003039961215108633,
0.000015617561075487174,
0.044664736837148666,
0.005793314427137375,
0.01191862765699625,
0.01562998816370964,
0.010504032485187054,
-0.010610545054078102,
0.010567252524197102,
-0.008034791797399521,
0.05807647109031677,
0.02987830340862274,
-0.02449953556060791,
0.005464916583150625,
-0.000574585166759789,
0.016996189951896667,
0.02418549358844757,
-0.07536476105451584,
0.06411232054233551,
0.02321689948439598,
0.014516143128275871,
-0.04473116621375084,
0.03627486526966095,
0.00711891008540988,
-0.050350092351436615,
0.04555728659033775,
-0.005971146281808615,
0.007403746712952852,
0.016909873113036156,
0.010626714676618576,
0.03890974074602127,
0.05504757910966873,
-0.022949829697608948,
-0.010881062597036362,
-0.0014543167781084776,
0.02036111429333687,
0.004036805126816034,
-0.008451612666249275,
0.015313949435949326,
0.0490531288087368,
0.056681759655475616,
-0.020870987325906754,
0.0341641940176487,
-0.020789433270692825,
-0.030796967446804047,
-0.09820133447647095,
-0.004944853018969297,
0.01807423122227192,
0.0383073128759861,
0.00494465883821249,
0.03919901326298714,
-0.0039045128505676985,
-0.014964836649596691,
-0.007804179564118385,
-0.015275354497134686,
-0.09968523681163788,
0.02707183174788952,
-0.044241007417440414,
-0.018507886677980423,
0.011767403222620487,
-0.017746316269040108,
-0.008570453152060509,
-0.005115234758704901,
-0.039530783891677856,
-0.033423908054828644,
0.00012666241673287004,
-0.05842605605721474,
0.022193849086761475,
-0.015683447942137718,
-0.05183258652687073,
-0.011008134111762047,
0.029475800693035126,
0.08208169043064117,
-0.022095244377851486,
0.005244242958724499,
0.01990629732608795,
-0.046023719012737274,
0.0017825844697654247,
0.020355509594082832,
0.005502272862941027,
0.04122712463140488,
0.006569752003997564,
0.000022354133761837147,
-0.008654262870550156,
0.009728665463626385,
-0.012599999085068703,
0.027299441397190094,
0.024050742387771606,
0.007599301636219025,
-0.029284963384270668,
-0.051401544362306595,
-0.020960383117198944,
-0.017308352515101433,
-0.008468056097626686,
0.07173971831798553,
-0.04036981612443924,
0.005195739679038525,
0.014022314921021461,
-0.008287182077765465,
0.01337587833404541,
0.045356784015893936,
0.025886621326208115,
-0.008422201499342918,
0.0005353271262720227,
-0.011487796902656555,
-0.043238408863544464,
-0.02848832681775093,
0.007155864965170622,
0.04510075971484184,
0.026628656312823296,
-0.010676839388906956,
-0.01306251809000969,
0.003125299932435155,
-0.0024776309728622437,
-0.033642638474702835,
0.01947726495563984,
-0.013273919001221657,
0.0033075958490371704,
0.01605348102748394,
0.0033036619424819946,
-0.031967807561159134,
0.03758804872632027,
0.0628594160079956,
0.0048388284631073475,
0.0028323724400252104,
-0.0630832388997078,
-0.03181922435760498,
0.01930714212357998,
0.04446578398346901,
-0.00971959624439478,
-0.001820237492211163,
-0.0537070594727993,
-0.00560761196538806,
-0.011868146248161793,
-0.028935758396983147,
0.031715597957372665,
-0.013333030976355076,
-0.0203693974763155,
-0.038522131741046906,
-0.03393122926354408,
-0.00599938677623868,
-0.021844200789928436,
-0.022925054654479027,
0.00930824689567089,
-0.018844792619347572,
0.026643335819244385,
-0.002829381264746189,
0.011349017731845379,
0.028477558866143227,
0.016677003353834152,
0.014254051260650158,
0.026858868077397346,
0.0009945452911779284,
0.010570204816758633,
-0.06278982758522034,
-0.047403134405612946,
-0.03053451143205166,
0.009758290834724903,
-0.04224495217204094,
0.0347638875246048,
-0.014393476769328117,
-0.03816908225417137,
0.03519168868660927,
-0.02353314496576786,
-0.027953553944826126,
0.00981880258768797,
-0.04414893314242363,
0.014025422744452953,
0.0028005687054246664,
0.029933888465166092,
-0.009000718593597412,
0.04817353934049606,
-0.04149723798036575,
0.020018205046653748,
-0.041612133383750916,
0.021602455526590347,
-0.031438328325748444,
0.010095024481415749,
-0.024636665359139442,
-0.026355836540460587,
-0.03957975655794144,
0.049629710614681244,
-0.06748650968074799,
-0.038314227014780045,
-0.01635945774614811,
-0.01330786757171154,
0.0021513591054826975,
0.026298414915800095,
-0.009458678774535656,
0.024839293211698532,
-0.042678896337747574,
-0.0004506279365159571,
0.0025371804367750883,
-0.020414024591445923,
0.05554758384823799,
0.0005988759803585708,
-0.0009196343016810715,
0.02121814899146557,
0.007218372076749802,
0.020035386085510254,
-0.03812674805521965,
0.022193357348442078,
-0.017695322632789612,
-0.036435600370168686,
0.030656440183520317,
-0.00557558611035347,
-0.003952115774154663,
0.03773381561040878,
-0.03349270671606064,
-0.0522945262491703,
-0.0039925361052155495,
0.01136019267141819,
0.008066732436418533,
-0.005548659712076187,
0.0012852634536102414,
0.011514218524098396,
-0.013159766793251038,
-0.06574056297540665,
-0.024317914620041847,
0.03702940791845322,
0.004924599081277847,
-0.018542464822530746,
-0.06551561504602432,
-0.011310255154967308,
-0.036704856902360916,
-0.010461305268108845,
-0.031009607017040253,
0.0353546142578125,
-0.03702564537525177,
0.006879415363073349,
-0.0010802355827763677,
-0.011375539936125278,
0.06888653337955475,
-0.012702340260148048,
0.0048577082343399525,
0.0028788174968212843,
-0.0171403456479311,
-0.0002988818159792572,
0.011138588190078735,
0.03646422550082207,
-0.015362816862761974,
-0.05076785758137703,
-0.02558194473385811,
0.02403170056641102,
-0.02197999320924282,
-0.030768517404794693,
-0.0076584103517234325,
0.042066480964422226,
-0.017253996804356575,
-0.057773567736148834,
-0.044578779488801956,
0.008930194191634655,
-0.015338205732405186,
0.056823816150426865,
-0.026521580293774605,
0.02992716245353222,
0.004961774684488773,
-0.036345865577459335,
0.01000457163900137,
0.00011807943519670516,
0.022971391677856445,
-0.022567564621567726,
0.04142984747886658,
0.0012764597777277231,
0.006593305617570877,
0.017211584374308586,
-0.03613818436861038,
0.00853116437792778,
-0.02648291550576687,
0.018350636586546898,
0.006520726718008518,
0.0011450005695223808,
-0.004250323865562677,
-0.03770654648542404,
-0.04137437418103218,
0.006379248108714819,
0.042184170335531235,
-0.011175704188644886,
0.02815399132668972,
0.07953989505767822,
-0.0331343412399292,
-0.0028422712348401546,
-0.004362770821899176,
0.029706209897994995,
-0.01094065885990858,
0.02327810786664486,
0.046825770288705826,
-0.026205770671367645,
-0.02063256874680519,
0.06570542603731155,
0.0492822527885437,
-0.018054548650979996,
-0.01635078154504299,
0.053345415741205215,
0.011934739537537098,
0.001132677192799747,
-0.004022936336696148,
-0.036101069301366806,
0.025645850226283073,
-0.002961216727271676,
0.013740911148488522,
0.011744696646928787,
0.006064758636057377,
0.013003850355744362,
0.01416914351284504,
0.020925387740135193,
-0.017362812533974648,
-0.01298621017485857,
-0.04026559367775917,
0.01146459300071001,
0.03985201567411423,
0.03258061036467552,
-0.035503122955560684,
0.02995341457426548,
0.02204785868525505,
0.0008571434300392866,
0.04465313255786896,
-0.029482968151569366,
-0.05672742426395416,
-0.03151070326566696,
-0.023096095770597458,
-0.04987827688455582,
0.056266527622938156,
0.027923133224248886,
-0.04265068098902702,
-0.015072016045451164,
-0.05049937963485718,
0.018494635820388794,
0.031801920384168625,
0.05000550299882889,
-0.054758936166763306,
0.04394075274467468,
-0.03636813163757324,
-0.0018887239275500178,
-0.01603558287024498,
-0.0013835829449817538,
0.1484420895576477,
0.028473760932683945,
-0.014012722298502922,
-0.03853556141257286,
0.044100113213062286,
0.00607543857768178,
-0.014827617444097996,
-0.0420641228556633,
0.021631086245179176,
-0.03906155377626419,
0.0039489613845944405,
0.0448688268661499,
0.05243086442351341,
-0.012870820239186287,
-0.043460916727781296,
0.026817919686436653,
-0.04773583635687828,
-0.012479143217206001,
-0.029796643182635307,
0.04839777573943138,
0.009670105762779713,
0.01772391051054001,
-0.011670698411762714,
0.03406532108783722,
-0.04642578586935997,
0.027191318571567535,
-0.04217658191919327,
-0.040319569408893585,
0.033722177147865295,
0.010524879209697247,
-0.04514463618397713,
0.010695982724428177,
0.02628406509757042,
-0.059449631720781326,
-0.04593488201498985,
0.030973022803664207,
0.04914838448166847,
-0.004775394219905138,
0.03665321320295334,
0.04110858216881752,
-0.01041225902736187,
0.019861062988638878,
0.03371160849928856,
0.025387540459632874,
-0.05470816418528557,
0.03713793307542801,
-0.034855060279369354,
0.057982154190540314,
-0.01359789352864027,
-0.008833110332489014,
0.03452535346150398,
-0.020177703350782394,
0.021105492487549782,
-0.056854233145713806,
0.008674776181578636,
-0.0174925085157156,
0.029034201055765152,
-0.009093789383769035,
-0.012571416795253754,
-0.007777050137519836,
0.043276894837617874,
-0.0025868292432278395,
0.01188112236559391,
-0.03658173605799675,
0.008760425262153149,
-0.02097238413989544,
-0.02799929678440094,
0.007430191617459059,
0.010174633003771305,
-0.016422951593995094,
-0.042707592248916626,
-0.008668704889714718,
0.00015894211537670344,
-0.0031697817612439394,
0.0041960300877690315,
0.03142911568284035,
0.021203873679041862,
-0.005330847110599279,
-0.0034649986773729324,
-0.0009596457821317017,
-0.058280833065509796,
-0.004349915310740471,
-0.0034431261010468006,
-0.009332600980997086,
-0.01628519594669342,
0.02426718920469284,
0.016264285892248154,
0.024187147617340088,
0.0021162773482501507,
0.009035579860210419,
-0.0007779444567859173,
0.03839742764830589,
-0.01619865372776985,
-0.016519978642463684,
0.0330115370452404,
0.002392890164628625,
0.01153112668544054,
-0.012575821951031685,
-0.003818017430603504,
0.01260178443044424,
0.06432104855775833,
0.012428917922079563,
0.011827116832137108,
0.04190843924880028,
-0.014082095585763454,
-0.030878789722919464,
0.006121120881289244,
-0.023775739595294,
-0.002849075710400939,
0.012035507708787918,
0.06779628992080688,
-0.029941095039248466,
-0.006863836664706469,
0.010097399353981018,
-0.00023952379706315696,
0.008591599762439728,
-0.005106448195874691,
-0.031412046402692795,
0.014812614768743515,
-0.013591229915618896,
0.026257403194904327,
-0.03045429289340973,
0.020913241431117058,
-0.01870957762002945,
0.006903026252985001,
-0.029319563880562782,
-0.0005700892070308328,
-0.014875291846692562,
0.010446456260979176,
0.006228259298950434,
-0.023342179134488106,
0.047028668224811554,
0.033812880516052246,
-0.07599502056837082,
0.0035522859543561935,
0.03851556405425072,
0.0034809208009392023,
0.03272499889135361,
0.012683176435530186,
-0.016497492790222168,
0.014044641517102718,
-0.0353202223777771,
-0.03634656220674515,
0.016792837530374527,
-0.03354361280798912,
0.014839579351246357,
0.022775473073124886,
-0.02349180169403553,
0.011751898564398289,
0.06641710549592972,
0.00023013603640720248,
0.021294645965099335,
0.0034813922829926014,
-0.040906231850385666,
0.030765298753976822,
0.009507033042609692,
0.026126787066459656,
0.007645776029676199,
-0.0085037462413311,
-0.015089385211467743,
0.006805300246924162,
-0.024757223203778267,
-0.014074215665459633,
0.006439431570470333,
-0.04000811278820038,
-0.07175871729850769,
0.010064725764095783,
-0.001364641124382615,
0.032584238797426224,
0.03783881664276123,
-0.019961893558502197,
0.020104797556996346,
0.016547786071896553,
0.02295966073870659,
-0.10590250045061111,
0.01510155200958252,
0.003206053748726845,
0.029053742066025734,
0.051147907972335815,
-0.04176206886768341,
0.023733805865049362,
0.043694280087947845,
-0.06394170224666595,
0.0227966345846653,
0.004685265477746725,
-0.004321313928812742,
-0.05980239808559418,
-0.012305711396038532,
-0.013655644841492176,
0.07711441814899445,
0.01937389001250267,
0.0703238919377327,
0.028053591027855873,
0.052716147154569626,
-0.015016172081232071,
-0.024469928815960884,
0.0058610751293599606,
0.0281748715788126,
-0.005291171371936798,
0.022729068994522095,
0.0720483809709549,
0.029645167291164398,
-0.02616277150809765,
0.036991748958826065,
0.011526420712471008,
0.020206287503242493,
-0.00041022794903256,
-0.026540571823716164,
0.0053413002751767635,
-0.010156161151826382,
0.003248224500566721,
0.030277958139777184,
-0.006686926353722811,
0.026537608355283737,
0.009316571988165379,
-0.0032658178824931383,
0.02569289691746235,
-0.025535913184285164,
0.020433301106095314,
-0.06945513933897018,
-0.023742131888866425,
0.044510629028081894,
-0.023407552391290665,
-0.01245874259620905,
-0.00438103498890996,
0.00893901102244854,
-0.019474174827337265,
-0.03314249590039253,
-0.022206250578165054,
-0.049809422343969345,
0.01015469990670681,
0.033524587750434875,
-0.015647759661078453,
-0.017223451286554337,
0.014287707395851612,
-0.04246680065989494,
-0.009409278631210327,
0.011735298670828342,
-0.031706396490335464,
0.006509406492114067,
-0.028938207775354385,
-0.021822478622198105,
0.01002662442624569,
0.015272642485797405,
-0.00024798285448923707,
-0.026819555088877678,
-0.02407495677471161,
0.014626245014369488,
0.03750231862068176,
0.003395617939531803,
-0.037375859916210175,
0.0007838906603865325,
-0.025239242240786552,
-0.03535406291484833,
-0.00795121118426323,
0.022742656990885735,
-0.0017090510809794068,
-0.08461921662092209,
-0.0005101310671307147,
-0.005119553301483393,
0.05031334608793259,
0.04878408461809158,
-0.01197423879057169,
-0.007657922338694334,
0.010420447215437889,
-0.010173623450100422,
0.024061348289251328,
-0.03822436183691025,
-0.015871690586209297,
0.02032916620373726,
-0.017398588359355927,
0.007190965116024017,
0.011669036000967026,
-0.029684055596590042,
0.006082871463149786,
0.03592906519770622,
-0.015974264591932297,
0.0478513203561306,
0.03137260302901268,
-0.040220957249403,
0.025313833728432655,
0.011443577706813812,
-0.03381261229515076,
0.033172037452459335,
-0.014681155793368816,
-0.011327430605888367,
0.03751590475440025,
-0.03670730069279671,
-0.027306685224175453,
0.014614873565733433,
-0.03746474161744118,
-0.016556279733777046,
-0.005261668469756842,
-0.02550247311592102,
0.03834740072488785,
-0.05045322701334953,
0.01765386201441288,
0.04127231240272522,
-0.005880091339349747,
-0.01954708620905876,
0.05401408672332764,
0.0028242403641343117,
0.026973003521561623,
0.021023189648985863,
0.024046000093221664,
-0.0035550598986446857,
-0.026722995564341545,
0.02464647777378559,
0.019822314381599426,
0.028731336817145348,
-0.01731238141655922,
-0.006787393242120743,
0.04244484379887581,
0.03133318945765495,
0.0055848220363259315,
0.005620310548692942,
0.05341816693544388,
-0.013736210763454437,
0.026104342192411423,
0.014022601768374443,
-0.029468100517988205,
-0.00805455818772316,
0.052381858229637146,
0.011879614554345608,
0.08053330332040787,
-0.03418603539466858,
0.016121365129947662,
-0.00196139351464808,
0.010966517962515354,
-0.03469207137823105,
0.020988289266824722,
0.027486693114042282,
0.034270454198122025,
0.0008620610460639,
0.009860415011644363,
-0.05668148398399353,
-0.027270475402474403,
0.03106469288468361,
-0.022161051630973816,
0.015540428459644318,
0.04078524559736252,
-0.01104890275746584,
0.01413681823760271,
0.013651523739099503,
-0.007193002849817276,
-0.015313949435949326,
0.022097555920481682,
-0.008293861523270607,
0.040641963481903076,
-0.058472540229558945,
0.002517183544114232,
-0.04198743402957916,
0.06415818631649017,
-0.04860543832182884,
0.00169164699036628,
-0.017902787774801254,
-0.0024198037572205067,
-0.012819193303585052,
0.004729427397251129
] |
<p>This is not a question pertaining to interpretations, after the last one I realized I should not open Pandora's Box ;) </p>
<p>For theories to be consistent, they must reduced to known laws in the classical domains. The classical domain can be summed up as: </p>
<p>$$\hbar=0 ; c=\infty$$</p>
<p>Which is OK. I need to know, however, is that if QM is an independent and fundamental <em>theory</em>, why does it rely so heavily on the classical formalism. Is it necessary for a classical formalism to exist in order to have a quantum formalism? From as far as I have read, it does not seem so, and I find this puzzling. Suppose you have a dissipative system, or an open system when you cannot write an autonomous Hamiltonian in the classical case, how then do we approach these quantum mechanically, when we cannot even write down the corresponding Hamiltonian. </p> | 1,985 | [
-0.005466862581670284,
0.005082316696643829,
0.017992498353123665,
-0.019526535645127296,
0.013655499555170536,
-0.003934080712497234,
-0.011655816808342934,
-0.006135914009064436,
0.01701480895280838,
0.005784146022051573,
0.015175477601587772,
0.007929272018373013,
0.03282937407493591,
-0.006627373863011599,
0.017433175817131996,
0.0017640066798776388,
0.013678960502147675,
-0.06892216205596924,
-0.0070524984039366245,
-0.012798184528946877,
0.001792884198948741,
0.04113973677158356,
0.019130736589431763,
-0.010562627576291561,
-0.02353178896009922,
0.0100662587210536,
-0.0034382008016109467,
0.021406732499599457,
0.03126782551407814,
0.05308990925550461,
-0.005199155770242214,
-0.017137596383690834,
0.0025062481872737408,
0.015077977441251278,
0.019157616421580315,
-0.002596782287582755,
-0.028604848310351372,
-0.01762467995285988,
-0.005317884963005781,
-0.005217741709202528,
-0.043428193777799606,
-0.03667992353439331,
-0.0002001166285481304,
0.04603970795869827,
-0.006280920933932066,
0.015555625781416893,
0.002033951925113797,
-0.000819242384750396,
0.0466960147023201,
-0.06595019996166229,
0.04395027458667755,
-0.00013195523933973163,
0.03804871812462807,
0.0442153736948967,
0.002252893755212426,
-0.012626254931092262,
0.09724032878875732,
0.05591866374015808,
-0.010411503724753857,
-0.05393900349736214,
-0.05473523586988449,
-0.012631429359316826,
0.000905527442228049,
-0.029713250696659088,
-0.037082210183143616,
0.06234835088253021,
0.029980620369315147,
-0.032196883112192154,
0.03583917394280434,
0.004847255535423756,
-0.02174898236989975,
0.024441074579954147,
0.05407338961958885,
-0.019703427329659462,
0.019594384357333183,
-0.033395588397979736,
0.011986073106527328,
0.018399285152554512,
-0.003752610180526972,
0.027789749205112457,
0.013767869211733341,
0.003641607705503702,
0.026550278067588806,
0.021845396608114243,
-0.00505826435983181,
-0.025828847661614418,
0.07759709656238556,
0.009517282247543335,
-0.01951652020215988,
0.016584739089012146,
-0.009354779496788979,
0.01868932880461216,
0.03754199296236038,
0.0022544548846781254,
-0.03623637929558754,
0.01614289917051792,
0.015889303758740425,
0.052948080003261566,
-0.004147338680922985,
-0.024421483278274536,
0.007164577022194862,
-0.027533017098903656,
0.033989254385232925,
0.03677606210112572,
-0.03183402121067047,
-0.0104601439088583,
-0.03609220311045647,
0.04515039175748825,
-0.010821574367582798,
0.00017381524958182126,
-0.02530297450721264,
0.0653434470295906,
-0.0067713153548538685,
0.01553897000849247,
-0.015929270535707474,
-0.026865458115935326,
0.006508357357233763,
-0.04538809135556221,
0.04385390132665634,
0.03144850209355354,
0.039361126720905304,
-0.03960580378770828,
0.035700902342796326,
-0.0069096386432647705,
-0.05653347447514534,
-0.020628852769732475,
0.026490889489650726,
-0.008839773014187813,
-0.019716540351510048,
0.0023114485666155815,
0.009743867442011833,
0.007437562569975853,
0.0012889549834653735,
0.03217633441090584,
0.025538086891174316,
-0.08479086309671402,
-0.08146774023771286,
-0.06620172411203384,
0.042489878833293915,
0.010746408253908157,
-0.013547182083129883,
-0.097621388733387,
0.011400856077671051,
0.03163834288716316,
0.08116541802883148,
-0.024471759796142578,
-0.027676496654748917,
0.017988108098506927,
-0.00883103534579277,
0.00932801328599453,
-0.019010338932275772,
-0.04717942699790001,
0.024261238053441048,
-0.02736758068203926,
-0.015116257593035698,
-0.07169311493635178,
0.016141017898917198,
0.03088138997554779,
0.04067930206656456,
-0.016827747225761414,
0.05247015133500099,
-0.05470636487007141,
-0.008074240759015083,
0.02463795430958271,
0.007766721770167351,
-0.012582053430378437,
0.07259611040353775,
0.013680842705070972,
0.03196640685200691,
0.038626693189144135,
0.024983437731862068,
0.007513957563787699,
0.013312000781297684,
0.02712302841246128,
0.024326510727405548,
-0.05322358012199402,
-0.013427734375,
0.006630496587604284,
0.0019803803879767656,
-0.0005619350122287869,
-0.036326512694358826,
-0.025423990562558174,
-0.0024861108977347612,
0.013471943326294422,
-0.01944076456129551,
0.0344746895134449,
-0.019292963668704033,
0.03965235874056816,
-0.017350273206830025,
-0.008076673373579979,
0.012723973020911217,
-0.06714507192373276,
0.019227564334869385,
-0.001214901334606111,
-0.002775815548375249,
0.05135131627321243,
0.03299419581890106,
0.012478001415729523,
-0.03303343802690506,
-0.054826728999614716,
-0.0013022361090406775,
0.011510750278830528,
-0.0024754467885941267,
-0.0120646758005023,
0.05614431947469711,
0.022573763504624367,
0.04050925001502037,
-0.008504483848810196,
0.03112410567700863,
-0.0030987721402198076,
-0.04824572429060936,
0.008498605340719223,
0.0031812754459679127,
0.026066889986395836,
-0.008713417686522007,
0.010116071440279484,
0.00418415293097496,
-0.044216182082891464,
-0.006392304785549641,
0.044877953827381134,
-0.0432649701833725,
0.06070711836218834,
0.00615348108112812,
0.0010209433967247605,
-0.00039361437666229904,
0.07890211045742035,
-0.03650528937578201,
0.0015983607154339552,
-0.022646119818091393,
-0.020489849150180817,
-0.04333227872848511,
-0.001152852433733642,
0.03525622561573982,
0.07422839850187302,
-0.04050548002123833,
0.019558371976017952,
0.010899190790951252,
0.04596586525440216,
0.028675036504864693,
0.006156261079013348,
-0.05705375596880913,
-0.023357374593615532,
0.04226618632674217,
-0.005659021902829409,
0.031228141859173775,
0.010261932387948036,
0.014871645718812943,
0.020059069618582726,
-0.016384731978178024,
-0.025471732020378113,
-0.018472662195563316,
0.08242939412593842,
-0.018786000087857246,
0.031104503199458122,
0.005456901621073484,
-0.01658592000603676,
0.028016095981001854,
-0.022593645378947258,
0.029345983639359474,
0.018474506214261055,
-0.02017960324883461,
0.010771494358778,
-0.04923472926020622,
-0.010889187455177307,
0.013544276356697083,
-0.01299459021538496,
-0.045345108956098557,
-0.024348001927137375,
0.013817756436765194,
-0.013164800591766834,
-0.026442915201187134,
-0.02807946503162384,
-0.04333188012242317,
-0.0010173184564337134,
0.02280169166624546,
0.028477836400270462,
-0.0062925079837441444,
0.0348372682929039,
-0.056053560227155685,
-0.04219711944460869,
0.003253621980547905,
-0.05563284084200859,
0.032487981021404266,
0.016053728759288788,
-0.015676338225603104,
0.027941260486841202,
-0.06434769928455353,
-0.00810039322823286,
0.04682955890893936,
-0.03893936797976494,
0.036591537296772,
-0.027134055271744728,
-0.0008436719654127955,
-0.04321485012769699,
-0.029094630852341652,
-0.026096675544977188,
0.012379487045109272,
-0.030534902587532997,
-0.005826389417052269,
0.03662622720003128,
-0.02757083997130394,
-0.022622156888246536,
-0.0019166803685948253,
-0.030872780829668045,
-0.07697612047195435,
-0.007074444554746151,
-0.015822740271687508,
0.03794926404953003,
-0.051726460456848145,
0.025274792686104774,
0.03349771723151207,
-0.0855327770113945,
-0.03425883501768112,
-0.03450639545917511,
-0.07300493866205215,
0.03799347206950188,
0.006072256248444319,
0.003235798329114914,
0.014031291007995605,
0.010482950136065483,
0.06398395448923111,
0.02593032270669937,
-0.05193009972572327,
-0.01031823642551899,
-0.022850340232253075,
0.001954098930582404,
-0.019227271899580956,
-0.029750527814030647,
0.01925571821630001,
-0.019221549853682518,
0.014652115292847157,
0.027881508693099022,
-0.011531520634889603,
-0.005666058044880629,
0.003756002290174365,
-0.02335680089890957,
0.03331109881401062,
0.02652120403945446,
0.008390805684030056,
0.020019013434648514,
0.01444480661302805,
-0.026715241372585297,
-0.014034760184586048,
-0.016617318615317345,
0.017406301572918892,
0.01660742051899433,
-0.07205354422330856,
0.06639616191387177,
0.027519473806023598,
0.028167491778731346,
-0.02390449121594429,
0.024325110018253326,
-0.02609168365597725,
0.0010408377274870872,
0.014000196941196918,
0.00857393816113472,
0.008459523320198059,
-0.028598211705684662,
0.02442207746207714,
0.03042781911790371,
0.011606703512370586,
-0.05064942687749863,
-0.027362864464521408,
0.011298377066850662,
0.018193716183304787,
0.013700542971491814,
0.006767550017684698,
-0.013174215331673622,
0.032310910522937775,
0.02546573244035244,
0.04844299703836441,
-0.001930407714098692,
-0.045195065438747406,
0.009194307960569859,
-0.04850858449935913,
-0.024302905425429344,
0.006557277869433165,
0.05602956935763359,
0.032007329165935516,
0.06790869683027267,
0.010328114964067936,
0.006468108855187893,
0.011198178865015507,
0.001459890860132873,
-0.07669539749622345,
0.0337328240275383,
-0.01762443222105503,
-0.017336996272206306,
0.0010275108506903052,
-0.01146716345101595,
0.053316064178943634,
-0.02905270829796791,
-0.06848166882991791,
-0.016728533431887627,
0.01119233388453722,
-0.07524792104959488,
-0.002981701400130987,
-0.025975970551371574,
-0.060423318296670914,
-0.022113420069217682,
0.020297588780522346,
0.025697369128465652,
-0.004775188863277435,
0.005715470295399427,
0.04106827452778816,
-0.020412787795066833,
-0.010557513684034348,
-0.014660178683698177,
0.008866771124303341,
0.016509374603629112,
0.02453961782157421,
0.04381795972585678,
0.016053171828389168,
-0.0210543442517519,
0.004568994045257568,
0.040370963513851166,
0.08814997225999832,
0.0010498365154489875,
-0.007414297666400671,
0.011350234970450401,
-0.050250157713890076,
0.032198112457990646,
0.021578505635261536,
0.05344224348664284,
0.013712341897189617,
-0.005311728920787573,
0.026350105181336403,
-0.01729462668299675,
-0.010681468062102795,
0.01802673749625683,
0.027044489979743958,
0.005158260930329561,
-0.03737255185842514,
-0.04416874423623085,
-0.008984572254121304,
-0.06117207556962967,
0.032477907836437225,
0.0018270013388246298,
0.006013101898133755,
0.024180162698030472,
0.011976124718785286,
0.01751226931810379,
0.01627536490559578,
-0.01942359283566475,
-0.031421959400177,
0.01642562448978424,
0.04052544757723808,
0.002401909790933132,
0.01869380846619606,
0.02780701406300068,
0.0327245332300663,
0.04187992587685585,
-0.009219478815793991,
-0.030141308903694153,
-0.0672592967748642,
0.0061787087470293045,
0.009616157039999962,
0.014946668408811092,
0.00986943207681179,
-0.00954219326376915,
-0.03491131588816643,
-0.04662749171257019,
0.06354482471942902,
-0.01087720226496458,
0.019483529031276703,
-0.012028225697577,
0.011796597391366959,
-0.013603638857603073,
-0.022809961810708046,
0.02116941101849079,
-0.00492866849526763,
0.027353648096323013,
0.03078501671552658,
-0.027172958478331566,
0.009275996126234531,
-0.04348818585276604,
-0.0014268443919718266,
0.014387673698365688,
0.05639545992016792,
-0.004874655976891518,
0.0001878420589491725,
-0.006659071426838636,
0.01051465142518282,
-0.0177175160497427,
-0.06300316751003265,
0.002249245997518301,
-0.0038984245620667934,
0.015736721456050873,
0.02423243783414364,
-0.0260502640157938,
-0.07424358278512955,
-0.01545665692538023,
-0.0023844570387154818,
-0.012968169525265694,
0.050482310354709625,
-0.016290005296468735,
0.04900198429822922,
-0.03434676304459572,
0.014159969054162502,
0.02188335917890072,
0.0655752569437027,
-0.028130747377872467,
-0.01687234453856945,
-0.03719257190823555,
0.008845088072121143,
-0.032584160566329956,
0.0076958173885941505,
-0.05815736949443817,
0.0063184271566569805,
-0.038410745561122894,
0.04069509357213974,
-0.012751833535730839,
-0.00559184979647398,
-0.0044626835733652115,
-0.036115407943725586,
-0.02615039236843586,
-0.00803726352751255,
-0.011707832105457783,
-0.01733992248773575,
-0.050789974629879,
0.04836989939212799,
-0.007582846563309431,
-0.03441759571433067,
0.014180023223161697,
0.002432160545140505,
-0.027288127690553665,
0.03457501530647278,
-0.011147960089147091,
0.045147329568862915,
-0.008287979289889336,
-0.027835138142108917,
0.02434040978550911,
-0.05286489054560661,
0.01994214579463005,
-0.014102810062468052,
0.020702846348285675,
0.019629253074526787,
-0.07472009211778641,
-0.029734335839748383,
-0.007597672753036022,
-0.028834309428930283,
0.01767687313258648,
-0.03371642157435417,
-0.002579576801508665,
0.027446571737527847,
0.01977400854229927,
-0.05770990252494812,
-0.05137262120842934,
0.009827541187405586,
0.016339335590600967,
-0.025933200493454933,
-0.012291805818676949,
0.041210148483514786,
-0.028422418981790543,
-0.005369328428059816,
0.012564051896333694,
0.04209177941083908,
0.009280359372496605,
0.0033269659616053104,
0.010080232284963131,
0.021625997498631477,
0.02241531014442444,
-0.02448883466422558,
0.0056734848767519,
0.024892207235097885,
-0.0062121180817484856,
-0.03259136155247688,
0.01777803525328636,
0.05044332146644592,
-0.0008974894299171865,
0.010244566015899181,
-0.024000592529773712,
0.01927451230585575,
0.027739040553569794,
0.0059008304961025715,
-0.013697169721126556,
0.009012747555971146,
0.007042685989290476,
-0.019053645431995392,
-0.03384869918227196,
-0.019330047070980072,
0.011238479055464268,
0.050209078937768936,
0.0034791454672813416,
-0.003397917142137885,
-0.010442761704325676,
-0.05367274954915047,
0.03893700987100601,
-0.03335488215088844,
-0.009053150191903114,
0.02064588852226734,
0.038825713098049164,
0.004041166976094246,
-0.022736908867955208,
0.018200334161520004,
-0.024695664644241333,
-0.014698859304189682,
-0.017043858766555786,
0.013004074804484844,
-0.006714663002640009,
-0.003685064148157835,
-0.013246904127299786,
-0.06702050566673279,
-0.04478657618165016,
0.022909697145223618,
0.04446665942668915,
-0.013803571462631226,
0.07364967465400696,
0.015839997678995132,
-0.00566107127815485,
0.007807702291756868,
-0.00763894384726882,
-0.008071079850196838,
0.02760719507932663,
0.03871772065758705,
0.054202668368816376,
-0.05033170059323311,
0.001431280979886651,
0.06442433595657349,
0.029069622978568077,
-0.010574056766927242,
-0.003491640090942383,
0.015348200686275959,
0.026965057477355003,
0.004078554455190897,
0.001761830528266728,
-0.03879895433783531,
0.027913369238376617,
-0.03235795348882675,
0.04614946246147156,
0.019640186801552773,
-0.022598011419177055,
0.01693285070359707,
0.014238539151847363,
-0.028392847627401352,
-0.007872851565480232,
0.0074397968128323555,
-0.003985289018601179,
0.030251184478402138,
-0.03912089392542839,
0.06412647664546967,
-0.0178292915225029,
0.004401094745844603,
0.006564840208739042,
0.002378465374931693,
0.011651523411273956,
0.02959560975432396,
-0.07733935862779617,
-0.0204607006162405,
-0.05259794369339943,
-0.024158893153071404,
0.07848009467124939,
0.01607411913573742,
-0.02114732377231121,
0.004772028885781765,
-0.02562469057738781,
0.05644061416387558,
-0.0019151722081005573,
-0.003632067469879985,
-0.03332684934139252,
0.031607840210199356,
0.02593466453254223,
-0.0020812470465898514,
-0.019541146233677864,
0.029156269505620003,
0.11679253727197647,
0.04550420865416527,
0.016040014103055,
-0.0662079006433487,
-0.005158221814781427,
-0.0032489467412233353,
0.019748127087950706,
-0.01794092170894146,
0.035630155354738235,
0.010270579718053341,
0.011420246213674545,
-0.019586853682994843,
0.0627419576048851,
0.025980016216635704,
0.0025956768076866865,
0.06851575523614883,
-0.03378019854426384,
-0.035813331604003906,
0.003651208942756057,
0.016501523554325104,
-0.02803785540163517,
0.015406948514282703,
-0.019411753863096237,
-0.020663414150476456,
-0.03341430798172951,
0.008315129205584526,
-0.0061477855779230595,
-0.020928679034113884,
0.019893843680620193,
0.038107991218566895,
-0.033371105790138245,
-0.003220778191462159,
0.016417957842350006,
-0.027214407920837402,
-0.0546281673014164,
0.01629103533923626,
0.01649373583495617,
-0.0042875343933701515,
0.014215481467545033,
0.02538985013961792,
0.011450668796896935,
0.006400837562978268,
-0.011069444939494133,
0.010839592665433884,
-0.0055579496547579765,
-0.006476162001490593,
-0.03170081600546837,
0.057171352207660675,
-0.030253104865550995,
0.013182045891880989,
-0.005020782817155123,
-0.02632034197449684,
0.001855153008364141,
-0.03706210479140282,
0.021719515323638916,
0.00768710533156991,
0.028322219848632812,
-0.02068331092596054,
-0.021146774291992188,
-0.0334625318646431,
0.009442908689379692,
-0.007571998052299023,
-0.0074365995824337006,
-0.01690916158258915,
-0.01748136803507805,
-0.002391017274931073,
-0.006087883375585079,
0.02012086659669876,
-0.015049390494823456,
-0.01974327489733696,
-0.03291311487555504,
-0.03793102502822876,
-0.06716939061880112,
-0.02879994735121727,
0.0034525881055742502,
0.005867187399417162,
0.08410600572824478,
-0.0033102792222052813,
0.007168140262365341,
-0.02158401533961296,
-0.06933582574129105,
0.029810728505253792,
-0.01700759120285511,
-0.011635743081569672,
-0.0163937509059906,
-0.016798773780465126,
0.027423212304711342,
0.06479383260011673,
-0.016716884449124336,
0.0024964031763374805,
0.013960733078420162,
-0.03748703747987747,
0.040590327233076096,
-0.007795209065079689,
-0.008198866620659828,
-0.005438802298158407,
-0.046451520174741745,
0.01828015223145485,
-0.0036093599628657103,
-0.0007835396099835634,
0.01677638851106167,
0.018660791218280792,
-0.004354430828243494,
0.05135441944003105,
0.01655680499970913,
0.0048034521751105785,
0.009944668971002102,
-0.009903175756335258,
0.007136265281587839,
0.0033155125565826893,
0.056485600769519806,
-0.041533906012773514,
-0.050216786563396454,
-0.048655733466148376,
0.027508223429322243,
-0.004705417901277542,
0.0157057773321867,
-0.0502503402531147,
0.01599024049937725,
-0.03423919901251793,
0.04217210412025452,
-0.03255355730652809,
-0.01995088718831539,
-0.050614356994628906,
0.03999747708439827,
0.03073940798640251,
-0.04040304198861122,
0.002450008410960436,
0.04098115116357803,
-0.002526507480069995,
-0.07847969979047775,
0.04234405234456062,
0.0571456179022789,
-0.017170701175928116,
0.024459516629576683,
0.001447860267944634,
0.006220648065209389,
0.019553298130631447,
-0.005276883952319622,
-0.03776613995432854,
0.013976654969155788,
-0.023226696997880936,
-0.040799736976623535,
0.011104009114205837,
-0.003459557192400098,
0.02062244713306427,
0.055726852267980576,
-0.0040512396954,
-0.0332612581551075,
-0.0017191726947203279,
-0.007056287489831448,
0.024153880774974823,
0.03181660920381546,
-0.04071606323122978,
-0.017931092530488968,
-0.017938803881406784,
0.036267347633838654,
-0.002517376560717821,
-0.013583117164671421,
0.03297869488596916,
0.03979039564728737,
0.02720162272453308,
-0.022758103907108307,
0.029438329860568047,
-0.01089761033654213,
0.024679062888026237,
0.046340182423591614,
-0.005375891923904419,
0.029979296028614044,
0.05868346989154816,
-0.06151799112558365,
0.01758432388305664,
0.018903998658061028,
0.009350283071398735,
-0.09524649381637573,
-0.00030950072687119246,
-0.004331149626523256,
-0.009227230213582516,
0.03178932145237923,
-0.01800130493938923,
0.010536839254200459,
0.005801938474178314,
-0.08451728522777557,
0.026397839188575745,
-0.019493015483021736,
-0.04602785408496857,
0.011859789490699768,
0.0007786767673678696,
-0.026138663291931152,
0.04993724822998047,
0.02318214811384678,
0.0029437814373522997,
0.024154074490070343,
-0.001916080480441451,
0.026201719418168068,
0.02114298939704895,
-0.028829185292124748,
0.007874254137277603,
-0.0046758390963077545,
0.0014543948927894235,
0.041611768305301666,
-0.043342795222997665,
-0.047941744327545166,
0.025881508365273476,
-0.005654423031955957,
-0.004481758922338486,
-0.005454802419990301,
0.005886581260710955,
0.002630674745887518,
0.04800667241215706,
0.02505628950893879,
-0.04422115534543991,
-0.02199190855026245,
0.00559961749240756,
0.02441757172346115,
0.04617522656917572,
0.010606322437524796,
0.0220935121178627,
0.00808351207524538,
-0.06205242499709129,
-0.042529914528131485,
0.03502023220062256,
-0.006083107553422451,
0.017822684720158577,
0.008921717293560505,
0.02017722837626934,
-0.008721700869500637,
-0.003849044442176819,
0.007724798750132322,
-0.032002128660678864,
0.00772826699540019,
0.007729431614279747,
0.03304056450724602,
0.018290553241968155,
-0.019070906564593315,
-0.0045156837441027164,
-0.01812589354813099,
0.016706859692931175,
0.017321638762950897,
-0.010097300633788109,
-0.07901475578546524,
-0.005232297815382481,
-0.011616812087595463,
-0.0124882273375988,
-0.002685901476070285,
-0.06566202640533447,
-0.029046064242720604,
0.04255440831184387,
-0.0025630758609622717,
0.021719394251704216,
-0.0455503985285759,
-0.047338198870420456,
-0.015516262501478195,
-0.04120694473385811,
0.029665956273674965,
-0.0019863403867930174,
0.015804145485162735,
-0.03626198694109917,
-0.016378596425056458,
0.004645124543458223,
-0.013913140632212162,
0.08812808990478516,
-0.02816622145473957,
-0.017414545640349388,
-0.006648628506809473,
-0.005806687753647566,
0.017964884638786316,
-0.011845635250210762,
-0.0005586376646533608,
-0.010674161836504936,
0.020698415115475655,
-0.0008650094969198108,
-0.019581491127610207,
-0.029433341696858406,
0.02962721511721611,
0.053179457783699036,
-0.044902198016643524,
0.029092472046613693,
-0.0015042707091197371,
-0.05013028159737587,
0.07509001344442368,
0.005723312962800264,
-0.005727655254304409,
0.08284474164247513,
-0.005343529395759106,
0.037638623267412186,
0.07903450727462769,
-0.02723720669746399,
-0.02348083257675171,
0.016907554119825363,
-0.02668958343565464,
-0.022068552672863007,
0.013366644270718098,
0.006782060023397207,
0.03520142287015915,
-0.02461542747914791,
0.0006892587407492101,
0.03747566044330597,
-0.025069329887628555,
-0.024040021002292633,
0.047950368374586105,
0.002901762258261442,
0.016116904094815254,
0.01610160432755947,
0.01683267392218113,
0.03579358011484146,
0.008856181986629963,
0.007335010915994644,
0.030245395377278328,
0.06360964477062225,
-0.0053442539647221565,
0.0411255918443203,
0.029844006523489952,
-0.02457249164581299,
0.017382219433784485,
0.020215041935443878,
0.036905437707901,
-0.031141286715865135,
-0.013985422439873219,
0.01924292743206024,
-0.021722298115491867,
0.018120530992746353,
0.0072232880629599094,
-0.04222670942544937,
0.08647419512271881,
-0.025851039215922356,
0.017280766740441322,
-0.009573281742632389,
0.006607784889638424,
-0.019071239978075027,
0.014684485271573067,
-0.0016925078816711903,
0.04022476077079773,
-0.0454898402094841,
0.007183386478573084,
-0.009585278108716011,
0.013885612599551678,
0.01264225970953703,
-0.0277828648686409,
-0.003139668144285679,
0.025574345141649246,
-0.03145458921790123,
-0.012638270854949951,
-0.02980179525911808,
-0.024643512442708015,
-0.012783952057361603,
0.024921437725424767,
0.07365600019693375,
0.047558415681123734,
-0.02593526616692543,
0.0019661621190607548,
-0.05626058951020241,
0.0420914851129055,
-0.05502117797732353,
0.03345891088247299,
-0.015859557315707207,
0.012515934184193611,
0.010454194620251656,
-0.0073891980573534966
] |
<p>When the shaft of the helicopter rotates, it creates a low pressure. Because of the low pressure, the helicopter lifts. Is my understanding that this is just an application of Bernoulli's theorem?</p> | 17 | [
-0.03933141753077507,
-0.02883477881550789,
-0.04126160591840744,
0.011392701417207718,
0.046398408710956573,
-0.02832893840968609,
-0.022831115871667862,
0.012962578795850277,
-0.0014365820679813623,
-0.06138058006763458,
0.014604335650801659,
0.049831438809633255,
0.04769085720181465,
0.00813268218189478,
0.03889764845371246,
-0.0023396594915539026,
-0.052971627563238144,
-0.0282526146620512,
0.0033946551848202944,
-0.00566720450296998,
-0.016229499131441116,
0.03386813774704933,
0.048163387924432755,
0.00871422328054905,
-0.01211316417902708,
0.014875340275466442,
0.04675791785120964,
-0.02687407098710537,
0.015410992316901684,
0.039219219237565994,
-0.032198820263147354,
0.0075899516232311726,
0.016245746985077858,
0.0646970272064209,
0.044345129281282425,
0.008700694888830185,
-0.05774262174963951,
0.002845342503860593,
-0.009131688624620438,
0.027874412015080452,
-0.00221548811532557,
-0.0065287393517792225,
-0.00221981480717659,
0.03851080685853958,
-0.025861406698822975,
0.0384669192135334,
0.004634153563529253,
-0.024924859404563904,
0.051673710346221924,
-0.0622594952583313,
0.05264267697930336,
0.021570352837443352,
0.02425994724035263,
0.029078038409352303,
0.030838044360280037,
-0.008785748854279518,
0.07646218687295914,
0.05667641758918762,
-0.0338260754942894,
-0.044437844306230545,
-0.000678389158565551,
-0.012086257338523865,
-0.017114901915192604,
-0.030884763225913048,
-0.02772991918027401,
-0.006411013659089804,
0.004946214612573385,
-0.04722357541322708,
0.03265247121453285,
-0.005444466136395931,
-0.0076962062157690525,
0.03783760219812393,
0.04371393471956253,
-0.031615741550922394,
0.01074000634253025,
-0.040871310979127884,
0.00987678300589323,
0.025667518377304077,
-0.0007808260852470994,
0.017083540558815002,
-0.025217048823833466,
0.01935865916311741,
0.025133797898888588,
0.05080042779445648,
0.015454010106623173,
-0.01259828731417656,
0.08913860470056534,
-0.00011706684017553926,
0.030927546322345734,
-0.002319851890206337,
0.004485103767365217,
-0.000641627935692668,
-0.018467295914888382,
-0.013766339980065823,
-0.018194302916526794,
0.009929459542036057,
-0.013082623481750488,
0.0380488857626915,
0.023990444839000702,
-0.049143046140670776,
0.0053507196716964245,
-0.017280980944633484,
0.030217958614230156,
0.04614792764186859,
-0.023262981325387955,
-0.0142109589651227,
-0.018323654308915138,
0.033433880656957626,
-0.019987359642982483,
-0.009205341339111328,
-0.0757080465555191,
0.009100564755499363,
-0.01873103156685829,
-0.0503963828086853,
-0.01769034005701542,
-0.0030604738276451826,
-0.022410597652196884,
0.012683547101914883,
0.02943403087556362,
0.06290289014577866,
0.06990175694227219,
-0.01483974140137434,
0.008204610086977482,
-0.021344659850001335,
-0.049779221415519714,
0.05283862352371216,
-0.006297655403614044,
-0.0704142153263092,
-0.05569332465529442,
0.0199727863073349,
0.01497729867696762,
-0.007744326256215572,
-0.0047700060531497,
0.03239060193300247,
0.025848103687167168,
-0.011129661463201046,
-0.08391357213258743,
-0.027605028823018074,
0.05316820368170738,
-0.010836274363100529,
-0.0031173641327768564,
-0.06424883008003235,
0.03768886625766754,
0.03666354715824127,
0.07379196584224701,
-0.02413000352680683,
0.020466173067688942,
-0.028833579272031784,
0.017729436978697777,
-0.013071918860077858,
-0.018488308414816856,
-0.04339712858200073,
-0.00021580675092991441,
-0.043675005435943604,
-0.021294545382261276,
-0.07178914546966553,
0.02344072423875332,
-0.0011026413412764668,
-0.017754117026925087,
-0.053194575011730194,
0.034655533730983734,
-0.012670256197452545,
0.007669215556234121,
-0.017756668850779533,
0.011096970178186893,
-0.01773592084646225,
0.03670904412865639,
-0.00018524548795539886,
-0.018592312932014465,
0.03884917497634888,
-0.005558198317885399,
0.03257208690047264,
-0.0063047464936971664,
0.0445437878370285,
0.057455819100141525,
-0.042524877935647964,
0.017483292147517204,
-0.0238572396337986,
0.0355868823826313,
-0.002731236396357417,
-0.035542480647563934,
-0.01699766516685486,
-0.01487430464476347,
0.019529756158590317,
-0.02836606092751026,
0.027117855846881866,
0.014167196117341518,
-0.014947191812098026,
0.02122858725488186,
-0.06713968515396118,
-0.0023921621032059193,
-0.08428710699081421,
0.006910020485520363,
-0.008235226385295391,
-0.017283426597714424,
0.012554824352264404,
0.038890715688467026,
0.05330135300755501,
-0.0796210914850235,
0.020428599789738655,
-0.020029159262776375,
-0.03457719832658768,
0.02262483350932598,
-0.018688824027776718,
0.01375774759799242,
0.048951055854558945,
0.040069833397865295,
0.04307258501648903,
0.052842509001493454,
-0.0060324473306536674,
-0.01755417510867119,
0.0030348305590450764,
-0.007306283339858055,
-0.008817841298878193,
0.014994637109339237,
0.007794248405843973,
0.011057344265282154,
0.0076781511306762695,
0.009835375472903252,
0.03641233965754509,
-0.04390357434749603,
0.050071123987436295,
0.0805140882730484,
0.019041841849684715,
0.03189367428421974,
0.014321302063763142,
0.01904436945915222,
-0.025019200518727303,
-0.01395290158689022,
-0.016370318830013275,
-0.04060477763414383,
0.010264446958899498,
0.007436500396579504,
0.07279417663812637,
-0.043680332601070404,
-0.00028812079108320177,
0.04185190796852112,
0.051731500774621964,
0.0040676589123904705,
0.030555767938494682,
-0.007929499261081219,
0.007059319876134396,
0.005253148265182972,
0.02768653631210327,
0.0033245012164115906,
0.02870352193713188,
0.013946530409157276,
0.03185943886637688,
0.043669018894433975,
0.005874298047274351,
-0.04818897321820259,
0.026762310415506363,
0.0007195904036052525,
0.02937561646103859,
0.0015185944503173232,
0.0025373059324920177,
0.02539815381169319,
-0.0003638975613284856,
0.013355332426726818,
0.0017291922122240067,
0.0079409284517169,
0.0004229992628097534,
-0.012843393720686436,
0.0038337651640176773,
0.05482243001461029,
-0.01249211560934782,
-0.025295834988355637,
-0.015628980472683907,
0.05084418132901192,
-0.04831526055932045,
0.00499644223600626,
-0.034406278282403946,
-0.00013959531497675925,
-0.02528754062950611,
0.015924105420708656,
0.0016524152597412467,
0.0013388280058279634,
0.05476786196231842,
-0.015170540660619736,
-0.054123155772686005,
-0.005297794006764889,
-0.015342453494668007,
-0.02035795897245407,
0.03439312428236008,
-0.05024657025933266,
0.008196587674319744,
-0.010878023691475391,
-0.006843387149274349,
0.06499633938074112,
-0.00651950528845191,
0.00459655374288559,
0.03780905902385712,
0.000424943893449381,
-0.03086903691291809,
0.007071359548717737,
-0.0534478984773159,
0.0033919818233698606,
-0.024950506165623665,
-0.004729931242763996,
0.04113871231675148,
0.006231972482055426,
0.010432357899844646,
0.024878989905118942,
-0.07361431419849396,
-0.040221016854047775,
-0.018112029880285263,
-0.028243301436305046,
0.001883312943391502,
-0.02025306597352028,
0.018297268077731133,
-0.02076106145977974,
-0.05841347575187683,
-0.01420035120099783,
-0.03274455666542053,
-0.04100490361452103,
-0.0022459488827735186,
-0.0033106300979852676,
0.03490574657917023,
0.009125026874244213,
-0.06018592044711113,
0.07473428547382355,
-0.010673381388187408,
-0.03262194246053696,
-0.03376271575689316,
-0.04095098003745079,
-0.014494189992547035,
0.0013201222755014896,
0.03299751877784729,
0.051981862634420395,
-0.02412191964685917,
0.036320045590400696,
0.033486343920230865,
0.00871963519603014,
0.028818810358643532,
0.042444076389074326,
-0.016797741875052452,
0.0047051915898919106,
0.007887979038059711,
0.037566039711236954,
0.04097169265151024,
-0.012157403863966465,
-0.025265052914619446,
0.012368233874440193,
-0.012257672846317291,
0.05328734591603279,
-0.0030979779548943043,
-0.02011614851653576,
0.04617539048194885,
0.026396695524454117,
0.030220430344343185,
-0.015294594690203667,
0.053883183747529984,
0.011324618943035603,
-0.017569545656442642,
0.029971260577440262,
0.045501913875341415,
0.04401262849569321,
-0.020503859966993332,
-0.01791849173605442,
0.03348353132605553,
0.028585193678736687,
-0.03102266974747181,
-0.036238450556993484,
0.01564963534474373,
-0.020110007375478745,
0.02951677516102791,
-0.020044829696416855,
-0.02689482644200325,
0.07209014892578125,
0.022074749693274498,
0.003869932610541582,
0.02149816043674946,
-0.032968971878290176,
0.06278478354215622,
-0.056520622223615646,
-0.009491992183029652,
0.01148528978228569,
0.01655777543783188,
-0.029464304447174072,
0.06864522397518158,
-0.010651998221874237,
0.0518694706261158,
0.06038878113031387,
0.0065660434775054455,
-0.0712817907333374,
0.005998007021844387,
-0.014276891946792603,
-0.0074089290574193,
0.002678961493074894,
-0.02515493333339691,
0.014415144920349121,
-0.04289770871400833,
-0.019321683794260025,
-0.04841742664575577,
-0.007644254714250565,
-0.04059287905693054,
0.013587400317192078,
-0.022854723036289215,
-0.04232565313577652,
0.0013944682432338595,
-0.008963998407125473,
0.04626571387052536,
-0.0014843372628092766,
0.05560304969549179,
0.055433403700590134,
-0.03976800665259361,
0.018137075006961823,
-0.006712897680699825,
0.017918111756443977,
-0.01293062511831522,
-0.004368363413959742,
-0.00683291582390666,
0.031937550753355026,
-0.01717924140393734,
0.019001031294465065,
0.010703954845666885,
0.022695695981383324,
-0.004147814586758614,
0.022877031937241554,
-0.008282224647700787,
-0.0165285374969244,
-0.0268831979483366,
0.009094590321183205,
0.02194441482424736,
0.025960879400372505,
0.03899981826543808,
0.015218555927276611,
-0.002870447700843215,
0.0026788641698658466,
0.0361761748790741,
0.04546666145324707,
0.04237633943557739,
0.005519176367670298,
-0.03215691074728966,
-0.011097975075244904,
-0.019162870943546295,
-0.002113207709044218,
0.01914607547223568,
-0.004551203455775976,
-0.05756102874875069,
-0.003708119271323085,
0.033744171261787415,
-0.006485592573881149,
0.0031283083371818066,
0.039098069071769714,
0.000864556641317904,
0.01974186860024929,
-0.014894933439791203,
0.006947771646082401,
0.05612416937947273,
0.025255300104618073,
0.031000560149550438,
0.04457481577992439,
-0.02523416094481945,
-0.09258811175823212,
-0.06710185110569,
0.03367536887526512,
-0.01855010911822319,
-0.0017208385979756713,
0.023893101140856743,
-0.04118218645453453,
-0.03335154801607132,
0.03841429203748703,
-0.020931372418999672,
0.013101175427436829,
-0.022646980360150337,
0.001002360018901527,
0.01013729628175497,
-0.026484563946723938,
-0.035504620522260666,
0.027717364951968193,
-0.04294096305966377,
0.009258504025638103,
0.00797549169510603,
-0.0011286799563094974,
-0.004981046076864004,
0.010758051648736,
0.058611705899238586,
0.04439328983426094,
0.02808171510696411,
0.0016681613633409142,
-0.04823853820562363,
0.027709584683179855,
-0.03808112069964409,
-0.06814561784267426,
-0.008990799076855183,
0.013360944576561451,
-0.00012099710147595033,
0.02855019085109234,
-0.04183446243405342,
-0.03450896590948105,
0.005846402607858181,
-0.008809001184999943,
-0.01862175762653351,
0.01779131405055523,
-0.041061270982027054,
-0.0203551072627306,
0.057183731347322464,
0.01939540170133114,
0.038900226354599,
0.07575307041406631,
-0.026037871837615967,
0.001902913791127503,
0.006368235219269991,
0.046298641711473465,
-0.014058992266654968,
-0.03188179433345795,
-0.022148165851831436,
0.0363151952624321,
-0.007899895310401917,
0.018920550122857094,
-0.00476527214050293,
0.04186360165476799,
-0.016281813383102417,
-0.009072571061551571,
0.011656703427433968,
0.048177409917116165,
0.004265173338353634,
-0.009496274404227734,
-0.0035807143431156874,
0.040097545832395554,
0.03199309855699539,
-0.027007412165403366,
0.006884397938847542,
0.018613219261169434,
-0.008040842600166798,
0.014349418692290783,
-0.01538833137601614,
0.010753706097602844,
-0.02110295183956623,
-0.014631478115916252,
0.018334804102778435,
-0.053380344063043594,
0.04472015053033829,
-0.033386923372745514,
-0.021352997049689293,
-0.008479633368551731,
-0.06055489927530289,
-0.029873177409172058,
-0.008810626342892647,
0.03006722964346409,
0.01168860960751772,
-0.015341931022703648,
0.007425583433359861,
0.0018640587804839015,
-0.005327342078089714,
-0.01319312583655119,
-0.07501220703125,
0.019458167254924774,
0.0038921567611396313,
0.02872239425778389,
-0.0545414499938488,
-0.02832520194351673,
-0.01673092134296894,
-0.04177682101726532,
0.015131905674934387,
0.035664334893226624,
-0.0271130483597517,
0.013941886834800243,
0.03970877453684807,
-0.03454069420695305,
0.05332236364483833,
-0.011214430443942547,
-0.010843734256923199,
-0.003240520367398858,
-0.016839200630784035,
0.002918100217357278,
-0.025948308408260345,
0.03805021196603775,
-0.022629575803875923,
-0.0052824607118964195,
0.013366004452109337,
-0.00626757787540555,
0.01011787448078394,
-0.0258113294839859,
0.032710179686546326,
0.015057669021189213,
0.020944073796272278,
0.002935759024694562,
-0.02535223588347435,
-0.019139181822538376,
0.005072255153208971,
0.03131282329559326,
-0.0008409122820012271,
-0.028409039601683617,
-0.01820668950676918,
-0.06177792698144913,
0.02170773409307003,
0.05166569724678993,
-0.004209220875054598,
0.01241429802030325,
0.04366238787770271,
0.0002362110244575888,
-0.00897278543561697,
0.014300299808382988,
0.0038392350543290377,
0.002023814246058464,
0.020852791145443916,
0.008503451012074947,
0.012792078778147697,
0.0318932868540287,
0.011935540474951267,
-0.021957585588097572,
-0.03130856901407242,
0.029491448774933815,
0.08419255912303925,
-0.008104774169623852,
0.047384221106767654,
0.0019945609383285046,
-0.014944232068955898,
0.00019162747776135802,
-0.021524228155612946,
-0.01373743824660778,
-0.028367044404149055,
-0.014638436958193779,
0.026080576702952385,
-0.027413679286837578,
0.014360866509377956,
0.04601940140128136,
0.03227699175477028,
0.008670095354318619,
-0.009587499313056469,
0.05425424873828888,
0.02481670118868351,
0.016600679606199265,
-0.0016915843589231372,
-0.042029671370983124,
0.03014077991247177,
-0.02495843544602394,
0.06547864526510239,
-0.03159594535827637,
-0.010850457474589348,
0.016017084941267967,
0.02371634915471077,
0.034382984042167664,
-0.08034577965736389,
0.0008317955071106553,
-0.030713127925992012,
0.0062700496055185795,
-0.0059188371524214745,
-0.008990924805402756,
0.017985064536333084,
0.008682196959853172,
0.02343776635825634,
0.015872236341238022,
0.009406122379004955,
-0.020485708490014076,
-0.0015073934337124228,
-0.03946089372038841,
-0.018366467207670212,
-0.02768200822174549,
0.009981370531022549,
0.007656155154109001,
-0.028109638020396233,
0.03891619294881821,
-0.002574089216068387,
-0.003409721190109849,
0.02865947224199772,
0.025587720796465874,
-0.013330947607755661,
0.06739701330661774,
0.008806748315691948,
0.013005356304347515,
-0.002535064471885562,
0.02176133170723915,
0.11368729919195175,
0.01568559743463993,
0.0054119727574288845,
-0.06833487004041672,
-0.008261213079094887,
-0.008175844326615334,
-0.006824706681072712,
-0.04999750852584839,
0.023935329169034958,
0.011664057150483131,
-0.00021561897301580757,
0.008432669565081596,
0.03500077500939369,
0.00043807088513858616,
-0.018121829256415367,
0.05159447342157364,
-0.03929610922932625,
-0.006642202381044626,
-0.020239410921931267,
0.03783157467842102,
-0.03321199119091034,
0.0020299239549785852,
-0.028398988768458366,
0.0046508535742759705,
-0.06329529732465744,
-0.03545965254306793,
0.007773284800350666,
-0.04548406973481178,
0.01452968642115593,
-0.005931850057095289,
-0.06549634784460068,
0.0025795591063797474,
0.014268321916460991,
-0.048914834856987,
-0.0200263112783432,
0.04855354130268097,
-0.01091159787029028,
-0.004581937566399574,
0.0030357479117810726,
-0.0026854134630411863,
0.010420377366244793,
-0.0014888399746268988,
-0.008935250341892242,
-0.0067872037179768085,
-0.058416955173015594,
0.0069664702750742435,
-0.04223203286528587,
0.02719811536371708,
-0.03815104067325592,
0.023226529359817505,
-0.029567550867795944,
-0.011821896769106388,
0.01950879953801632,
-0.07738502323627472,
-0.05643419548869133,
-0.028553839772939682,
-0.007218076381832361,
-0.0044087632559239864,
-0.05805407837033272,
0.0013448897516354918,
0.009572994895279408,
0.00216404115781188,
-0.004557745531201363,
-0.011896106414496899,
-0.004505898337811232,
0.027147427201271057,
0.011905764229595661,
0.04653504490852356,
-0.03530571237206459,
-0.020959021523594856,
-0.0023184185847640038,
0.0022781644947826862,
-0.05904577299952507,
-0.013762987218797207,
0.0026356943417340517,
0.0027155480347573757,
-0.007978541776537895,
0.0035771322436630726,
-0.0386025570333004,
0.007705045863986015,
-0.08207082748413086,
0.014375986531376839,
0.018409311771392822,
-0.02379198558628559,
-0.02115423046052456,
-0.04191502556204796,
0.0052256397902965546,
0.07651311159133911,
-0.023547271266579628,
-0.02753582037985325,
-0.029544219374656677,
0.052625007927417755,
-0.0026071674656122923,
-0.050417713820934296,
-0.0565059520304203,
0.034942738711833954,
-0.056675542145967484,
-0.012053954415023327,
-0.014204070903360844,
0.03570980951189995,
0.056007713079452515,
0.02475767582654953,
-0.026446636766195297,
0.02601918764412403,
-0.03506132587790489,
0.028356675058603287,
0.00787490513175726,
-0.02237444557249546,
-0.015107542276382446,
0.03334946557879448,
0.01783790998160839,
-0.07441622763872147,
-0.018219107761979103,
-0.008576647378504276,
0.0006980620673857629,
-0.029221346601843834,
0.0021737301722168922,
-0.025131413713097572,
-0.012024002149701118,
0.0012589674443006516,
0.02099807746708393,
-0.02851492166519165,
0.035585541278123856,
-0.06299340724945068,
0.03408028185367584,
0.02393311820924282,
0.01905285194516182,
-0.015957586467266083,
-0.011836585588753223,
-0.02890252321958542,
0.011521085165441036,
0.03545438125729561,
-0.026637859642505646,
0.019388806074857712,
0.0009737539803609252,
0.04915802925825119,
-0.031212441623210907,
0.04280770942568779,
-0.010496939532458782,
-0.011935423128306866,
0.04518044367432594,
-0.04294285550713539,
-0.037130337208509445,
0.009365478530526161,
0.009595824405550957,
-0.002925184788182378,
0.0004275212995707989,
-0.02024001255631447,
-0.014787360094487667,
0.03289351239800453,
-0.02117440477013588,
-0.008760989643633366,
-0.013156152330338955,
0.018976055085659027,
0.012960284017026424,
0.0016688619507476687,
0.026214372366666794,
-0.028730720281600952,
0.0020985291339457035,
0.0172914806753397,
0.062362730503082275,
-0.008405492641031742,
-0.020841171965003014,
0.02974037081003189,
0.022111132740974426,
-0.018297890201210976,
0.011259322986006737,
-0.0026939548552036285,
0.02459513023495674,
0.038057856261730194,
-0.048077743500471115,
0.03167526796460152,
0.00911810714751482,
0.017128461971879005,
-0.11790622025728226,
-0.009329739026725292,
-0.008149923756718636,
-0.031226104125380516,
0.040810585021972656,
-0.048867471516132355,
-0.0028149804566055536,
0.006611129269003868,
-0.04062420502305031,
-0.016191421076655388,
-0.03256004676222801,
0.03090292029082775,
-0.047287534922361374,
0.021334879100322723,
0.037229154258966446,
0.07493427395820618,
0.016562247648835182,
0.018850039690732956,
0.03847803547978401,
-0.006638944614678621,
-0.004172566346824169,
0.00434963358566165,
0.042989395558834076,
0.03601386398077011,
-0.011288395151495934,
-0.039838287979364395,
0.042090728878974915,
-0.001015853020362556,
-0.04343989118933678,
0.019057191908359528,
-0.011926183477044106,
0.018190789967775345,
-0.017165763303637505,
0.0014275693101808429,
-0.006182952784001827,
0.015550890937447548,
0.007680950220674276,
0.0006197647890076041,
-0.005667382851243019,
0.04518347233533859,
0.007234001066535711,
0.02047659642994404,
-0.017324132844805717,
0.004857965745031834,
0.015607575885951519,
-0.027779225260019302,
-0.009093640372157097,
0.05028252303600311,
-0.03443429619073868,
0.003401914145797491,
-0.017012638971209526,
-0.005120917223393917,
-0.027750756591558456,
-0.007616003975272179,
0.036321595311164856,
-0.035378556698560715,
0.00017527090676594526,
0.04166833683848381,
-0.013565532863140106,
-0.023341350257396698,
0.013944070786237717,
0.026764104142785072,
-0.03815333917737007,
-0.00510693434625864,
0.013894472271203995,
-0.017857875674962997,
-0.03782826289534569,
0.022892208769917488,
-0.0035761974286288023,
-0.025455089285969734,
0.0007471585995517671,
-0.0485905222594738,
-0.018623031675815582,
0.02910924144089222,
0.06602910161018372,
0.044700924307107925,
0.030607085675001144,
-0.03852710872888565,
-0.013852512463927269,
-0.04931603744626045,
0.07631322741508484,
0.0025660311803221703,
0.011812177486717701,
-0.05399908125400543,
-0.04805879294872284,
-0.006035512313246727,
-0.011019526980817318,
0.0246067363768816,
0.0023276444990187883,
0.0023770371917635202,
-0.007792471908032894,
0.007792861666530371,
0.0072930664755403996,
0.005505438894033432,
0.04234107956290245,
-0.0018946802010759711,
-0.042600829154253006,
0.002989456057548523,
-0.01813015155494213,
-0.015823785215616226,
-0.01126551628112793,
0.008899923413991928,
-0.001241732737980783,
0.06918768584728241,
0.0026408734265714884,
-0.03532303869724274,
0.013220255263149738,
0.07223856449127197,
0.01446529384702444,
0.07150080054998398,
-0.05156727135181427,
0.014106097631156445,
-0.021821489557623863,
-0.020731749013066292,
-0.047977760434150696,
0.066612608730793,
-0.05179797485470772,
-0.0005777335027232766,
-0.0074098920449614525,
-0.04817204177379608,
0.0018997797742486,
-0.038760703057050705,
-0.0005989662604406476,
0.019801821559667587,
-0.019892603158950806,
-0.0157605092972517,
0.013185849413275719,
0.03076457977294922,
0.04389447718858719,
-0.043603114783763885,
-0.005013727582991123,
0.017182286828756332,
-0.008356583304703236,
0.028351034969091415,
0.02850639447569847,
0.0022182916291058064,
-0.024976668879389763,
-0.015550513751804829,
0.02315894328057766,
0.009315983392298222,
0.023263636976480484,
0.027288217097520828,
0.027478009462356567,
-0.025853818282485008,
-0.04517307132482529,
-0.028093142434954643,
-0.044291719794273376,
0.005533149931579828,
-0.0004197178059257567,
0.0009779687970876694,
0.08969257026910782,
-0.008922900073230267,
0.01568617671728134,
-0.020623279735445976,
0.022745776921510696,
0.01157862227410078,
-0.021203206852078438,
0.008312712423503399,
0.043749477714300156,
-0.01506981160491705,
-0.02790924534201622,
0.005358670372515917,
0.014584616757929325,
-0.0005747114773839712,
-0.0055349902249872684,
0.03219117969274521,
0.02787020616233349,
0.026549285277724266,
-0.0110592907294631,
-0.03188314288854599,
0.0009586885571479797,
-0.02587621472775936,
0.02323039434850216,
0.05651262402534485,
0.02391931600868702,
0.008456260897219181,
-0.05411941185593605,
-0.038607072085142136,
0.029546650126576424,
-0.07965677976608276,
0.004321785178035498,
-0.012443541549146175,
0.04535311460494995,
-0.01930897869169712,
0.0035717319697141647
] |
<p>I am speaking about GR with classical fields and energy. One question, spread over three increasingly strict situations:</p>
<p>Is there an energy density limit in GR? (literally, can the energy density have an arbitrarily large value at some point in space at some point in time)</p>
<p>Is there an energy density limit beyond which a blackhole will always form?</p>
<p>Let's choose a small volume, for here I'll just choose the Planck volume. Is there an average energy density limit over this volume beyond which a blackhole will always form?</p>
<p><strong>Clarification:</strong></p>
<p>In light of <a href="http://en.wikipedia.org/wiki/Mass_in_general_relativity">http://en.wikipedia.org/wiki/Mass_in_general_relativity</a> , can those that are answering that the energy density is limited and referring to a mass $M$ in some equations please specifically state how you are defining the $M$ in terms of the energy density, or defining $M$ in terms of $T^{\mu\nu}$ the stress-energy tensor. Does your $M$ depend on coordinate system choice?</p>
<p>Also, reading some comments, it sounds like there is confusion on what energy density means. Based on wikipedia <a href="http://en.wikipedia.org/wiki/File:StressEnergyTensor.svg">http://en.wikipedia.org/wiki/File:StressEnergyTensor.svg</a> , it sounds like we can consider energy density = $T^{00}$ of the stress-energy tensor. If you feel this is not correct terminology, please explain and I'll edit the question if necessary.</p> | 1,986 | [
-0.054980818182229996,
-0.020667128264904022,
0.010114083997905254,
-0.03527459129691124,
0.05333390831947327,
0.01883937232196331,
-0.045895498245954514,
-0.056361183524131775,
-0.011209504678845406,
-0.04488280788064003,
0.008937240578234196,
0.01764446683228016,
0.06935741752386093,
0.028402768075466156,
0.017519429326057434,
-0.022655831649899483,
0.003059126902371645,
-0.03765759617090225,
-0.01822032406926155,
-0.04378415644168854,
0.011187918484210968,
0.02637384459376335,
-0.000479752168757841,
0.0009993452113121748,
-0.023673849180340767,
0.027170201763510704,
0.01078091375529766,
0.004251450300216675,
0.0010770047083497047,
0.07170300930738449,
-0.01843499206006527,
-0.01769098825752735,
-0.008977653458714485,
0.03576561063528061,
0.023141110315918922,
-0.012296224012970924,
-0.032855112105607986,
-0.01993519812822342,
0.0021314620971679688,
-0.0007246778113767505,
-0.06456809490919113,
-0.040923431515693665,
-0.013423550873994827,
0.026883427053689957,
-0.01884307898581028,
0.011339237913489342,
0.034388087689876556,
-0.05225002020597458,
0.04240357503294945,
-0.04346257075667381,
0.0634344220161438,
0.029585469514131546,
0.0489877313375473,
0.027283336967229843,
-0.01340889185667038,
-0.023456105962395668,
0.07522942125797272,
0.08106312900781631,
-0.013652092777192593,
-0.03142344951629639,
-0.027417978271842003,
0.008618992753326893,
0.002382384380325675,
-0.0394340381026268,
0.011769954115152359,
0.05266265943646431,
-0.024314869195222855,
-0.010802214033901691,
0.0423850454390049,
-0.03929731249809265,
-0.006877468898892403,
0.009924914687871933,
0.0057806349359452724,
-0.005021858494728804,
-0.0031569937709718943,
-0.024638298898935318,
0.04525246098637581,
-0.01928483322262764,
0.03329307958483696,
0.04864509776234627,
-0.023368002846837044,
0.012619582004845142,
0.051799431443214417,
0.022993354126811028,
0.02520693466067314,
0.020647142082452774,
0.08327428251504898,
0.0021848443429917097,
0.02891412004828453,
0.03144558146595955,
-0.01003864873200655,
-0.004947114735841751,
-0.0009990963153541088,
-0.017370477318763733,
-0.04638972133398056,
0.018447842448949814,
-0.020949507132172585,
0.054258596152067184,
-0.01579676754772663,
0.015330225229263306,
0.016691962257027626,
-0.01238957978785038,
0.018032256513834,
0.03005748614668846,
0.014934927225112915,
-0.03026628866791725,
-0.09359938651323318,
0.0018389297183603048,
-0.011778979562222958,
-0.007048538886010647,
-0.024824615567922592,
-0.0024847325403243303,
-0.03140462562441826,
-0.03497111424803734,
0.020505115389823914,
-0.051170360296964645,
0.018626809120178223,
-0.022939568385481834,
0.039688706398010254,
0.08112527430057526,
0.05755128711462021,
-0.020782580599188805,
0.030081814154982567,
-0.03152963146567345,
-0.07382209599018097,
0.019981935620307922,
0.06407228112220764,
-0.010417447425425053,
-0.041212014853954315,
-0.00011632242240011692,
-0.004877028521150351,
0.02265024185180664,
0.01234112586826086,
0.000602198124397546,
0.04673673212528229,
-0.02545894868671894,
-0.08744444698095322,
-0.0750238448381424,
0.04468006640672684,
0.003914072178304195,
-0.023930618539452553,
-0.06167924404144287,
0.014477201737463474,
0.016118939965963364,
0.06807493418455124,
0.01023911964148283,
0.006537886802107096,
0.012767354026436806,
0.05340493842959404,
-0.0069063398987054825,
-0.03347828611731529,
-0.009044443257153034,
-0.008576720021665096,
-0.02739143930375576,
0.04334777593612671,
-0.08236190676689148,
0.01354773249477148,
0.009641296230256557,
0.01951253041625023,
-0.03474355489015579,
0.08236635476350784,
-0.019698332995176315,
0.00858145672827959,
0.034217171370983124,
-0.0050170402973890305,
-0.010828712955117226,
0.07876365631818771,
0.03352590650320053,
0.033532436937093735,
0.04576927050948143,
0.05183657258749008,
-0.004252353683114052,
0.010490091517567635,
0.007325270678848028,
0.031015662476420403,
-0.05907125025987625,
-0.0053260731510818005,
-0.010404557920992374,
0.006246919743716717,
0.0252004973590374,
-0.02867097221314907,
-0.03043990023434162,
0.009890706278383732,
-0.028087222948670387,
0.011689979583024979,
0.019479883834719658,
-0.017164213582873344,
0.010541182942688465,
-0.04220152273774147,
-0.024875421077013016,
0.006610801909118891,
-0.05336352810263634,
0.03486800566315651,
-0.011940766125917435,
0.028243156149983406,
0.02362675592303276,
-0.013185407035052776,
0.015389861539006233,
-0.06437879055738449,
-0.022175094112753868,
0.015893593430519104,
0.045722976326942444,
-0.018704039976000786,
-0.03614536672830582,
0.011708356440067291,
0.048783689737319946,
0.01511174812912941,
-0.00023985649750102311,
-0.00006397128163371235,
0.00667562847957015,
-0.03188170865178108,
0.020399779081344604,
-0.017401600256562233,
0.0322599895298481,
-0.007041980512440205,
-0.013159777969121933,
-0.005890312604606152,
0.005129255820065737,
0.007959956303238869,
0.019667334854602814,
-0.03185856342315674,
0.06524330377578735,
0.021476387977600098,
0.014205371029675007,
-0.01641969010233879,
0.0631072074174881,
-0.02118776924908161,
0.028401954099535942,
-0.024353360757231712,
-0.006622637622058392,
-0.03623074293136597,
0.00666341558098793,
0.03973441198468208,
0.02663343772292137,
-0.06311897188425064,
0.05192916840314865,
0.06266026198863983,
-0.0033373390324413776,
-0.0011884073028340936,
0.004015064332634211,
-0.01915576495230198,
-0.04442518949508667,
0.015703419223427773,
0.03298052400350571,
0.011405360884964466,
0.020111216232180595,
0.0017540082335472107,
0.026628250256180763,
-0.01219868566840887,
-0.013091647066175938,
0.005381184630095959,
0.037903692573308945,
-0.03780457004904747,
0.017262764275074005,
0.012923509813845158,
-0.003283975413069129,
0.0315798856317997,
-0.03626337647438049,
0.012626511044800282,
0.059847746044397354,
-0.011800291948020458,
-0.018830735236406326,
-0.05577367544174194,
-0.031420107930898666,
-0.004764632321894169,
0.03198624774813652,
0.001615390763618052,
-0.011703609488904476,
-0.0049136122688651085,
-0.03743346780538559,
-0.01847812533378601,
-0.011674847453832626,
-0.0135448407381773,
-0.019853876903653145,
0.025239793583750725,
0.015458264388144016,
-0.007456216961145401,
0.017526760697364807,
-0.010981778614223003,
-0.031928353011608124,
-0.0002667864318937063,
-0.036571066826581955,
-0.0026775195728987455,
-0.006821114104241133,
-0.04293675348162651,
0.012304733507335186,
-0.03228086233139038,
-0.029871443286538124,
0.05654541775584221,
0.0010025595547631383,
0.023530634120106697,
0.009536175057291985,
0.0099662896245718,
-0.040912531316280365,
-0.01876629702746868,
-0.019460473209619522,
-0.0038299905136227608,
0.01241406612098217,
-0.016235414892435074,
0.07267270237207413,
-0.031433071941137314,
-0.04541369527578354,
0.010769532062113285,
-0.015927398577332497,
-0.04054019972681999,
-0.030224788933992386,
-0.007719648070633411,
0.01843174919486046,
-0.020929161459207535,
0.039375562220811844,
0.04663281515240669,
-0.0526239313185215,
-0.000017395472241332754,
-0.05010219290852547,
-0.012874138541519642,
0.04176326096057892,
-0.03515050560235977,
0.054615214467048645,
0.005815322510898113,
-0.04884342849254608,
0.07639188319444656,
0.044012948870658875,
-0.02032950147986412,
-0.029003949835896492,
-0.01999053917825222,
0.025727925822138786,
-0.010851869359612465,
-0.027384186163544655,
-0.004744203295558691,
-0.006893941201269627,
0.008532620035111904,
0.03324398398399353,
0.051998551934957504,
-0.0018652928993105888,
0.02136610448360443,
-0.02154136449098587,
-0.011553565040230751,
0.006496955640614033,
0.02206466533243656,
0.05222296342253685,
0.021392151713371277,
-0.024092035368084908,
0.010215533897280693,
-0.040638260543346405,
0.038564421236515045,
-0.009878954850137234,
-0.05588802322745323,
0.0417926125228405,
-0.0036291072610765696,
0.00538738165050745,
-0.0548410601913929,
0.02187984064221382,
0.00506167346611619,
-0.037240169942379,
0.03315179795026779,
0.012962454929947853,
0.04296456277370453,
-0.018167654052376747,
-0.03425758704543114,
-0.005809313617646694,
0.04540614038705826,
-0.022110680118203163,
-0.025378592312335968,
0.019013183191418648,
-0.005520906299352646,
0.024019040167331696,
-0.01025557704269886,
-0.003164660418406129,
0.030896179378032684,
0.021900758147239685,
0.044402893632650375,
-0.021789690479636192,
-0.029276855289936066,
0.011402931995689869,
-0.09689623862504959,
-0.02016374282538891,
-0.007850369438529015,
0.048951759934425354,
0.02132437936961651,
0.038898199796676636,
0.04274040088057518,
-0.005661606322973967,
0.055938925594091415,
0.02021242119371891,
-0.07241276651620865,
0.016609568148851395,
-0.029112689197063446,
-0.0008100800332613289,
0.02837485633790493,
-0.015814919024705887,
-0.016650352627038956,
-0.03359181061387062,
-0.0057430509477853775,
-0.0038572996854782104,
0.012337646447122097,
-0.07581495493650436,
0.014384363777935505,
-0.05714767426252365,
-0.044498510658741,
-0.014033160172402859,
0.032055266201496124,
0.03596734255552292,
-0.013263379223644733,
0.023532258346676826,
0.048417672514915466,
-0.02209477685391903,
-0.017070265486836433,
0.011591418646275997,
0.03451615199446678,
0.0022630514577031136,
0.03083093836903572,
0.02602333202958107,
0.008317429572343826,
-0.007755494210869074,
0.002902438398450613,
0.0421602688729763,
0.044204432517290115,
0.006195982918143272,
-0.008206047117710114,
-0.027769703418016434,
-0.03726085275411606,
-0.011669423431158066,
-0.005828038323670626,
0.03717517852783203,
-0.0034889469388872385,
-0.015701519325375557,
-0.001685323310084641,
0.0004692176007665694,
-0.012772408314049244,
0.04926677793264389,
0.06667187809944153,
-0.008638639934360981,
-0.04314460977911949,
-0.05820423364639282,
-0.012927955947816372,
-0.013973573222756386,
0.010001527145504951,
0.014581840485334396,
-0.007261948194354773,
-0.024193452671170235,
0.014990027993917465,
-0.011020337231457233,
-0.000683608406689018,
-0.05066661909222603,
-0.020814254879951477,
0.045296810567379,
0.01833922788500786,
-0.003274932038038969,
0.010005337186157703,
-0.004682839382439852,
0.011762614361941814,
0.05999854579567909,
-0.006344830151647329,
-0.004308255389332771,
-0.08093073964118958,
-0.015274778939783573,
0.03684277459979057,
0.036480143666267395,
0.02173999324440956,
-0.002491448540240526,
-0.054200418293476105,
-0.015019712038338184,
0.03372177109122276,
-0.037524498999118805,
0.016109861433506012,
-0.010130500420928001,
0.018112385645508766,
0.00264546531252563,
-0.02532094530761242,
-0.004249331541359425,
0.031512439250946045,
0.009131100960075855,
0.014662882313132286,
0.00644843652844429,
0.0271363016217947,
-0.020536202937364578,
0.008424332365393639,
0.008787349797785282,
0.051350731402635574,
0.028845839202404022,
-0.027511848136782646,
-0.012211652472615242,
0.0007556332857348025,
-0.010307393968105316,
-0.10561275482177734,
-0.017530962824821472,
-0.004632322583347559,
-0.04152504354715347,
0.02734718844294548,
-0.04131089150905609,
-0.017892079427838326,
0.035675860941410065,
0.015629829838871956,
-0.031143102794885635,
0.005427306517958641,
-0.0363960787653923,
0.057403840124607086,
0.01332075148820877,
-0.0013348233187571168,
0.0334504134953022,
0.010170167312026024,
0.003452507546171546,
0.018885966390371323,
-0.057955753058195114,
0.036696046590805054,
-0.04262768104672432,
0.015265640802681446,
-0.03988231346011162,
-0.005317788105458021,
-0.050999775528907776,
0.045875806361436844,
-0.02261350117623806,
-0.009965931065380573,
-0.003246686654165387,
-0.05389806628227234,
0.0064052436500787735,
0.024375293403863907,
0.02690177969634533,
0.01206117868423462,
0.03363562375307083,
0.011027773842215538,
-0.0176976528018713,
0.004562204238027334,
0.017013749107718468,
0.011021616868674755,
-0.022086868062615395,
0.03690140321850777,
-0.0028383771423250437,
0.03777141496539116,
0.009694479405879974,
-0.00323517806828022,
0.03244800493121147,
-0.014409910887479782,
0.08259035646915436,
-0.009578220546245575,
0.002899119397625327,
0.029201587662100792,
-0.03093590959906578,
-0.016353664919734,
-0.024262096732854843,
-0.008448062464594841,
0.034648578613996506,
-0.024263212457299232,
0.020334478467702866,
0.045688215643167496,
0.04943829029798508,
-0.08821075409650803,
-0.01588120497763157,
0.04071255400776863,
0.02220975235104561,
-0.016985662281513214,
0.0019719128031283617,
0.031427010893821716,
-0.08324296027421951,
-0.013281683437526226,
-0.025292402133345604,
0.04446890205144882,
-0.01677706465125084,
-0.029505154117941856,
-0.010843896307051182,
0.07069414854049683,
0.025491273030638695,
-0.010428724810481071,
0.0005125206662341952,
0.029097678139805794,
0.021812232211232185,
0.009592395275831223,
-0.0011506497394293547,
0.0492696538567543,
-0.036302875727415085,
-0.017689231783151627,
-0.00634641433134675,
-0.01213295478373766,
0.02859879843890667,
0.012850874103605747,
-0.004076051060110331,
0.044063303619623184,
0.006134129129350185,
-0.012038212269544601,
-0.011632067151367664,
0.03467492759227753,
-0.02304682321846485,
0.014519943855702877,
-0.03398929908871651,
-0.023607874289155006,
-0.01390191912651062,
-0.032643962651491165,
0.03594619780778885,
0.003014646004885435,
0.018458468839526176,
-0.009100894443690777,
0.06435428559780121,
0.006185442674905062,
-0.01612222008407116,
0.0032741513568907976,
-0.03538914769887924,
0.008975690230727196,
0.00956662092357874,
-0.017571687698364258,
0.04770680516958237,
-0.01839294284582138,
-0.017022745683789253,
-0.03354024887084961,
-0.02744053117930889,
0.009347192011773586,
0.06253157556056976,
-0.014330115169286728,
0.025910433381795883,
-0.005548243410885334,
-0.002107227686792612,
0.023637430742383003,
-0.030646532773971558,
-0.017797918990254402,
0.010996091179549694,
0.012756895273923874,
0.03295041620731354,
-0.018171120434999466,
-0.046220894902944565,
0.05178913474082947,
0.03291358798742294,
-0.026179291307926178,
0.03706756606698036,
0.0008043088018894196,
0.04046458750963211,
0.004694116767495871,
-0.024431651458144188,
-0.048154883086681366,
0.05325942113995552,
-0.02211819961667061,
0.012318383902311325,
0.005758578889071941,
-0.007917377166450024,
0.015258469618856907,
0.025658993050456047,
0.01739630103111267,
-0.012538694776594639,
-0.01749514974653721,
-0.05736088380217552,
0.00148999213706702,
0.019904091954231262,
-0.003564406419172883,
-0.01283822488039732,
0.0001779907033778727,
-0.006269229110330343,
-0.0014123603468760848,
-0.026911955326795578,
-0.001994924619793892,
-0.06692668050527573,
-0.022803232073783875,
-0.058259330689907074,
-0.09141939133405685,
0.04709594324231148,
0.0051649161614477634,
-0.03138240426778793,
0.03335465490818024,
-0.03845439478754997,
0.007066329009830952,
0.009122076444327831,
0.02207675203680992,
0.006673223339021206,
0.07396654039621353,
-0.00338064506649971,
0.027110781520605087,
-0.026445891708135605,
-0.0036048516631126404,
0.10558495670557022,
0.0926894024014473,
0.02907625213265419,
-0.03697536885738373,
0.0024568524677306414,
-0.002548797521740198,
-0.007618376519531012,
-0.05592815950512886,
0.03579462692141533,
-0.030009372159838676,
-0.006659063510596752,
0.011035619303584099,
0.05478786304593086,
-0.0003346038283780217,
-0.018507661297917366,
0.08207659423351288,
-0.013322291895747185,
-0.01960747316479683,
0.006237036548554897,
0.0410318560898304,
-0.0003317045920994133,
0.01572609506547451,
0.01155725959688425,
0.013701281510293484,
-0.0024692746810615063,
0.01873941905796528,
-0.02540796995162964,
-0.024488357827067375,
0.014036505483090878,
-0.021991390734910965,
-0.04218725115060806,
0.006699145305901766,
-0.011429132893681526,
-0.009389324113726616,
-0.04688689857721329,
-0.011896508745849133,
0.038219016045331955,
0.007909182459115982,
-0.00659975316375494,
0.04864998906850815,
-0.03448983281850815,
0.012932305224239826,
0.023159079253673553,
0.01567831076681614,
-0.02899712510406971,
-0.031052902340888977,
-0.026533696800470352,
0.05388467013835907,
-0.025929033756256104,
0.017093392089009285,
-0.0074864039197564125,
-0.00397461699321866,
0.014416277408599854,
-0.02915671467781067,
0.0009262717794626951,
-0.010900174267590046,
0.03363041952252388,
0.014200831763446331,
-0.03386240452528,
-0.02914271503686905,
0.03010527603328228,
0.020618844777345657,
0.01822788454592228,
-0.019751189276576042,
-0.005319399759173393,
0.0037918579764664173,
-0.03521629795432091,
0.04061600938439369,
-0.02165795862674713,
-0.00231137964874506,
-0.02312156930565834,
-0.018624406307935715,
-0.06219923123717308,
-0.031075136736035347,
0.0036215821746736765,
0.01774587109684944,
0.03921511769294739,
0.013566657900810242,
0.018914930522441864,
0.0034554393496364355,
-0.043159011751413345,
0.008549162186682224,
-0.014327607117593288,
-0.03131546825170517,
-0.03667662665247917,
0.0485401377081871,
-0.015542750246822834,
0.0445050410926342,
-0.015408952720463276,
-0.002843380905687809,
-0.01111125759780407,
-0.008614877238869667,
0.010121660307049751,
-0.014182811602950096,
-0.016910938546061516,
0.0008847352000884712,
-0.028115445747971535,
-0.0023201140575110912,
-0.014372899197041988,
-0.02074684575200081,
0.00999059621244669,
0.03149315342307091,
0.033349622040987015,
0.038364335894584656,
0.020924730226397514,
-0.004665546119213104,
0.022109752520918846,
-0.014818546362221241,
-0.01349234115332365,
0.010698145255446434,
0.025586530566215515,
-0.015143269672989845,
-0.04096604511141777,
-0.004054041113704443,
-0.01591937430202961,
-0.0006784776924178004,
0.03812592849135399,
-0.031245796009898186,
0.033845677971839905,
-0.028447851538658142,
-0.012167897075414658,
-0.03949114307761192,
-0.019143356010317802,
-0.02201165445148945,
0.03638315945863724,
0.03771848604083061,
-0.029274610802531242,
0.0005716694286093116,
0.017151987180113792,
-0.016786299645900726,
-0.0388091616332531,
-0.00046119012404233217,
0.030159825459122658,
-0.03050641156733036,
0.009907949715852737,
0.022532863542437553,
0.006770948879420757,
0.06186036393046379,
0.016957346349954605,
-0.03062230534851551,
0.02502576634287834,
-0.028164351359009743,
-0.041196826845407486,
0.031352415680885315,
-0.019893310964107513,
0.03193947300314903,
0.04934686794877052,
-0.0125412093475461,
-0.010534070432186127,
0.06124415621161461,
0.014934900216758251,
-0.000580997671931982,
0.011089523322880268,
-0.04442862421274185,
-0.01832425408065319,
-0.0144733265042305,
0.0409911647439003,
-0.00770485308021307,
0.006566227879375219,
0.012302190996706486,
0.018159929662942886,
0.00759185990318656,
-0.010229488834738731,
0.030480673536658287,
0.004083269275724888,
-0.01594087854027748,
-0.005311537999659777,
0.008725284598767757,
0.002217309782281518,
0.06151045486330986,
-0.0391634963452816,
0.00012014098319923505,
0.05455620959401131,
0.009359505027532578,
-0.08238162100315094,
-0.008795573376119137,
0.008502068929374218,
0.007837560027837753,
0.0505811981856823,
-0.024139422923326492,
0.024904916062951088,
0.024399995803833008,
-0.06793326139450073,
0.02074749767780304,
-0.008274070918560028,
-0.01245897077023983,
-0.008559206500649452,
-0.009087362326681614,
-0.013879809528589249,
0.028123358264565468,
0.04522522911429405,
0.06819052994251251,
0.004742978140711784,
0.006663708947598934,
-0.004158572759479284,
-0.011588833294808865,
-0.00046534978901036084,
0.03231087327003479,
-0.029547790065407753,
-0.015493755228817463,
0.08999413996934891,
0.012797614559531212,
-0.05332089960575104,
0.03350216522812843,
0.005675524473190308,
-0.013960969634354115,
0.022161882370710373,
-0.008378295227885246,
-0.017474208027124405,
0.024336358532309532,
0.050407953560352325,
-0.028778444975614548,
-0.00236909999512136,
0.03742532804608345,
-0.005057504400610924,
0.009848901070654392,
-0.02296670712530613,
0.013193902559578419,
0.01148458942770958,
-0.04158691689372063,
-0.016052329912781715,
0.07041763514280319,
-0.04133975878357887,
-0.023910146206617355,
-0.00043798156548291445,
0.012066362425684929,
0.016238994896411896,
-0.025638090446591377,
0.005572924390435219,
-0.035385873168706894,
-0.026116445660591125,
0.017970995977520943,
-0.00024457628023810685,
0.004194525070488453,
0.037099502980709076,
0.019330406561493874,
-0.012118253856897354,
0.015268812887370586,
-0.031220758333802223,
-0.013389695435762405,
-0.05328380689024925,
0.02933044545352459,
-0.03654118627309799,
0.01096910797059536,
0.0060592880472540855,
-0.040887877345085144,
-0.05095518380403519,
0.06691428273916245,
0.02055343985557556,
0.009007648564875126,
-0.0034185657277703285,
-0.030882006511092186,
-0.030738510191440582,
-0.09850776940584183,
-0.01206537988036871,
-0.022806018590927124,
0.008133874274790287,
-0.01995331421494484,
-0.03716396540403366,
-0.011291689239442348,
-0.010180043056607246,
0.056853774935007095,
-0.0001383726194035262,
-0.02410377748310566,
0.040569454431533813,
0.0075062839314341545,
0.016020476818084717,
-0.060447148978710175,
-0.0036748049315065145,
0.0006752052577212453,
-0.019987300038337708,
-0.008397428318858147,
-0.002531852340325713,
0.00012602773495018482,
-0.0006747067673131824,
0.04190567880868912,
-0.002523573813959956,
0.0318189337849617,
0.013145811855793,
0.006044724490493536,
0.05565592274069786,
0.018426258116960526,
-0.01591283641755581,
0.05956876650452614,
-0.01929185353219509,
0.021360421553254128,
0.04103964567184448,
-0.02792792022228241,
-0.018348976969718933,
-0.006388511508703232,
-0.023183932527899742,
-0.0452573224902153,
-0.024408387020230293,
-0.01426978874951601,
0.031720321625471115,
-0.048027969896793365,
0.0016799242002889514,
0.07416381686925888,
-0.04631860926747322,
-0.028327660635113716,
0.041004639118909836,
0.023681379854679108,
0.05193326622247696,
-0.005520661827176809,
0.01132167037576437,
0.0107266241684556,
-0.006208430044353008,
-0.03559679538011551,
0.02380385994911194,
0.03544050455093384,
-0.013777241110801697,
-0.008226927369832993,
-0.0009009583154693246,
-0.009085501544177532,
-0.01724986732006073,
-0.007165204733610153,
0.031210273504257202,
-0.03703691437840462,
-0.05841781944036484,
0.02114642783999443,
0.018859442323446274,
0.010104000568389893,
-0.0026814150623977184,
-0.03226887434720993,
0.04475792497396469,
0.020568011328577995,
-0.0040750144980847836,
-0.02643967792391777,
-0.0071519301272928715,
-0.053554050624370575,
0.017116177827119827,
-0.009835527278482914,
0.06632399559020996,
0.024905528873205185,
0.006407818291336298,
-0.021077709272503853,
-0.0027814535424113274,
0.02942751720547676,
-0.03973725065588951,
-0.0037148050032556057,
0.015814881771802902,
-0.012212665751576424,
-0.0052810912020504475,
-0.010109886527061462,
-0.021256202831864357,
-0.031596455723047256,
0.04200566187500954,
0.009511785581707954,
0.04668300226330757,
-0.027752915397286415,
-0.026205895468592644,
-0.011740644462406635,
0.04385661706328392,
-0.05013719201087952,
-0.0032110693864524364,
-0.03644790127873421,
-0.01154607068747282,
0.003067371202632785,
-0.02241925522685051
] |
<p>In 2006 the IAU deemed that Pluto was no longer a planet because it fails to "clear" the neighborhood around its Kuiper Belt orbit. Presumably, this is because Pluto (1.305E22 kg) has insufficient mass to do the job. How massive must a body in Pluto's orbit (semi-major axis 39.5 AU) be to "clear" its orbit? Would Mars (6.24E23 kg) or Earth (5.97E24 kg) be declared planets if they were in Pluto's orbit?</p> | 1,987 | [
-0.004519731737673283,
-0.02935793437063694,
-0.017359182238578796,
0.02058517001569271,
0.04536706581711769,
0.006521859671920538,
-0.04798860475420952,
-0.025799958035349846,
-0.006768706254661083,
-0.02206997759640217,
0.003790895687416196,
0.029499351978302002,
0.021349219605326653,
0.009896302595734596,
-0.009397502988576889,
0.029047144576907158,
-0.0038060133811086416,
-0.034798428416252136,
-0.00788972806185484,
-0.028302909806370735,
0.015613527968525887,
-0.028830692172050476,
0.043419249355793,
0.03178274631500244,
-0.021095391362905502,
0.008301574736833572,
0.01773941144347191,
-0.022842923179268837,
0.03300865739583969,
0.049518123269081116,
0.005129465367645025,
-0.015498429536819458,
0.037214938551187515,
-0.007231237832456827,
-0.013343782164156437,
0.01481575332581997,
-0.0202380008995533,
-0.017489280551671982,
-0.004367235582321882,
0.03558749705553055,
-0.06855319440364838,
-0.01565699465572834,
-0.0015542460605502129,
0.024486437439918518,
-0.005871988367289305,
0.0031348103657364845,
0.015656432136893272,
-0.031784046441316605,
0.05326363816857338,
-0.06372570991516113,
0.09822801500558853,
0.02908535860478878,
0.04262777790427208,
0.014667516574263573,
0.010188419371843338,
0.006687198765575886,
0.08429433405399323,
0.08443962782621384,
-0.03023233264684677,
-0.02274705283343792,
-0.046188533306121826,
-0.0023657975252717733,
-0.0020202109590172768,
-0.001328968326561153,
-0.03208119049668312,
0.04748179391026497,
-0.04734499752521515,
0.0005605531623587012,
0.008233592845499516,
0.07419752329587936,
0.020964806899428368,
0.014696159400045872,
0.0017185602337121964,
-0.012277405709028244,
0.02560768648982048,
-0.05425155162811279,
0.02223372645676136,
0.0015166231896728277,
0.045659877359867096,
0.03902197629213333,
-0.02326473966240883,
0.03476688638329506,
0.0410391204059124,
0.003167256712913513,
0.0071230619214475155,
0.04136141762137413,
0.07169511914253235,
-0.02328534983098507,
-0.027475500479340553,
0.01289738342165947,
-0.014504844322800636,
-0.02369862236082554,
0.051775697618722916,
-0.057520121335983276,
0.020685188472270966,
0.028153477236628532,
0.005000355653464794,
0.05543286353349686,
-0.010019565001130104,
0.008858432061970234,
0.04014536738395691,
-0.008771293796598911,
0.027742501348257065,
0.07331299781799316,
0.032740943133831024,
0.002294069854542613,
-0.02414422482252121,
0.031395625323057175,
0.022379077970981598,
-0.015642179176211357,
-0.033486269414424896,
0.0006275108898989856,
0.012362872250378132,
-0.02631406858563423,
0.033973731100559235,
-0.007885586470365524,
-0.011570360511541367,
-0.04059133306145668,
0.02142813242971897,
0.05123557150363922,
0.02930091880261898,
-0.0012785098515450954,
0.004004961345344782,
-0.054657600820064545,
-0.0423501618206501,
0.047008901834487915,
0.018233027309179306,
0.0030817301012575626,
-0.008728609420359135,
-0.009520016610622406,
-0.04440552368760109,
-0.013362854719161987,
-0.005533467046916485,
-0.05331317335367203,
0.042453598231077194,
0.008841701783239841,
-0.06046316400170326,
-0.0366535410284996,
0.004439234267920256,
0.0001531523885205388,
-0.04363831505179405,
-0.08226992934942245,
0.014322497881948948,
0.015287077985703945,
0.07877683639526367,
0.0043478431180119514,
0.005609574262052774,
0.004737109877169132,
0.03779410570859909,
-0.01048347819596529,
-0.03540236875414848,
-0.013355754315853119,
-0.002514770720154047,
-0.062114499509334564,
0.018302232027053833,
-0.06394410133361816,
0.01778416521847248,
0.02364320307970047,
0.05069759115576744,
-0.046966757625341415,
0.05007029324769974,
-0.05912021920084953,
-0.02196511998772621,
-0.015693318098783493,
0.022413473576307297,
-0.002948841778561473,
0.06466695666313171,
0.03177651762962341,
-0.002730273175984621,
0.03179725632071495,
0.05577334389090538,
0.03805647790431976,
0.06645803898572922,
0.032275568693876266,
0.0733194574713707,
-0.011557032354176044,
-0.05706306919455528,
-0.060729194432497025,
0.03334527835249901,
0.008810890838503838,
-0.04022359475493431,
-0.0009877510601654649,
0.01584099605679512,
0.0068754167295992374,
0.02492857724428177,
0.04728357866406441,
-0.02079026959836483,
-0.019830303266644478,
0.008734679780900478,
-0.03715130686759949,
-0.024023819714784622,
-0.025648364797234535,
0.0274350568652153,
-0.01898919977247715,
0.009952256456017494,
-0.002937519922852516,
0.031665779650211334,
0.0020833152811974287,
-0.01225887332111597,
-0.031039154157042503,
-0.0038112965412437916,
0.03176013380289078,
0.0005309333791956306,
-0.02337392419576645,
-0.009247229434549809,
0.05640608072280884,
0.04745831713080406,
-0.005620866548269987,
0.010534456931054592,
-0.012505716644227505,
-0.05511821061372757,
-0.014356259256601334,
0.03121270425617695,
0.001563055207952857,
-0.028860118240118027,
-0.026022551581263542,
0.00202053040266037,
-0.005458453204482794,
-0.02494225837290287,
0.01677796244621277,
-0.020672747865319252,
0.12293047457933426,
0.021574802696704865,
0.04343940317630768,
0.03305623680353165,
0.014996076934039593,
0.03573371097445488,
-0.01090887002646923,
-0.01659814827144146,
-0.016212860122323036,
-0.03792181611061096,
-0.041989296674728394,
-0.022505320608615875,
0.02681618370115757,
-0.03324955701828003,
0.027403084561228752,
0.017297038808465004,
0.04129892215132713,
0.017265694215893745,
0.0034229073207825422,
-0.016138479113578796,
-0.0307909082621336,
0.03909781575202942,
-0.006557113956660032,
0.024895338341593742,
-0.0066708168014883995,
0.01512642577290535,
0.03647817298769951,
-0.018606990575790405,
-0.011407357640564442,
-0.03330795094370842,
0.023947056382894516,
0.00029950245516374707,
0.0054640816524624825,
0.008330724202096462,
-0.053708069026470184,
0.056739188730716705,
-0.06756129860877991,
-0.005742072127759457,
0.04333953559398651,
-0.014113787561655045,
-0.016498073935508728,
-0.03604460135102272,
0.049740709364414215,
0.011341213248670101,
0.008144772611558437,
0.01560134906321764,
-0.010619556531310081,
0.023439954966306686,
-0.05065855011343956,
0.017238114029169083,
-0.03692442178726196,
-0.017878402024507523,
-0.01605408638715744,
0.020519472658634186,
0.03061811998486519,
-0.001653183251619339,
0.05364758148789406,
-0.003841508412733674,
0.012685428373515606,
-0.044389814138412476,
-0.035248640924692154,
-0.03438189998269081,
0.057233694940805435,
-0.06912127137184143,
0.03575791046023369,
-0.0069417404010891914,
-0.015915367752313614,
0.05012375861406326,
-0.02215786837041378,
0.0016797363059595227,
-0.014049738645553589,
0.006197731476277113,
-0.01999122090637684,
0.012342401780188084,
-0.028026381507515907,
-0.013616474345326424,
-0.009593748487532139,
0.026156170293688774,
0.0057395403273403645,
0.01204790361225605,
-0.02442762441933155,
0.0158891212195158,
-0.0517486035823822,
-0.030120909214019775,
-0.005909795872867107,
0.0033811191096901894,
-0.005819888319820166,
-0.04188230633735657,
0.006330555770546198,
0.024935968220233917,
0.003215543460100889,
0.020715173333883286,
-0.0005639243172481656,
-0.06480257213115692,
0.03377645090222359,
-0.04635633900761604,
0.030013028532266617,
0.005996874533593655,
-0.043003350496292114,
0.04788520932197571,
-0.00426115607842803,
-0.010277402587234974,
-0.006202413700520992,
0.008420581929385662,
0.003957523964345455,
0.01716914400458336,
0.008100886829197407,
0.01382008008658886,
0.0011882863473147154,
-0.005156075116246939,
0.05719369277358055,
-0.015520907007157803,
-0.007559443358331919,
0.012127733789384365,
-0.018671119585633278,
-0.0058584148064255714,
0.01867939718067646,
-0.016942448914051056,
0.03098692186176777,
0.004551479127258062,
-0.003009748412296176,
0.028063323348760605,
-0.01907842606306076,
0.06866812705993652,
0.02468709461390972,
-0.03556155785918236,
0.03820887207984924,
-0.012978048995137215,
0.010790866799652576,
0.018789149820804596,
0.01697472482919693,
-0.02089674212038517,
-0.00968350749462843,
0.005243551917374134,
0.00042817334178835154,
0.07648886740207672,
-0.005080369301140308,
-0.017329389229416847,
0.03147485852241516,
0.045366860926151276,
-0.011536127887666225,
-0.01727944053709507,
-0.0007788263610564172,
-0.01770726963877678,
0.029018495231866837,
-0.017308689653873444,
-0.016818510368466377,
0.07651732861995697,
-0.014625247567892075,
0.016064684838056564,
-0.0006279667722992599,
0.01124116126447916,
-0.00636279908940196,
-0.06730913370847702,
-0.009292363189160824,
0.016252098605036736,
0.03902989625930786,
-0.007359717041254044,
0.012369772419333458,
0.014248219318687916,
-0.011884565465152264,
-0.005627423990517855,
0.009328372776508331,
-0.04564774036407471,
0.022003931924700737,
-0.04503100737929344,
-0.05171142891049385,
0.04148019850254059,
-0.01446024514734745,
-0.013511755503714085,
-0.023148616775870323,
0.0015311582246795297,
-0.0502435602247715,
-0.009391702711582184,
-0.0414041131734848,
-0.0014797833282500505,
-0.006255518179386854,
-0.055893298238515854,
0.015965163707733154,
0.035690005868673325,
0.05231344327330589,
-0.019524216651916504,
0.016556624323129654,
0.017469529062509537,
-0.03451169282197952,
-0.03460900858044624,
-0.013865793123841286,
0.006309723015874624,
-0.03718694671988487,
0.047514285892248154,
0.009151612408459187,
-0.0020100127439945936,
-0.01825438253581524,
-0.03032856062054634,
0.023407207801938057,
0.03900250419974327,
0.0019106450490653515,
-0.01476573571562767,
-0.02855549566447735,
-0.05217443034052849,
-0.005683482624590397,
-0.011292070150375366,
0.03606332093477249,
-0.03894374519586563,
0.011576631106436253,
0.025200292468070984,
-0.0011254976270720363,
0.00003157091487082653,
0.05977592617273331,
0.05922236293554306,
0.03246135264635086,
0.007169458549469709,
-0.036882344633340836,
-0.020594123750925064,
-0.018345972523093224,
-0.00505108805373311,
0.029601598158478737,
0.030102070420980453,
-0.023148126900196075,
-0.015658728778362274,
0.03702419251203537,
-0.008026642724871635,
-0.06110271066427231,
-0.050954096019268036,
-0.02141285315155983,
0.012614287436008453,
-0.06420847773551941,
-0.014294233173131943,
-0.01308358646929264,
0.004238285589963198,
0.0728101134300232,
-0.02249588817358017,
0.01294810138642788,
-0.09093672782182693,
-0.008973566815257072,
0.03547396883368492,
0.03585054725408554,
-0.0045777130872011185,
-0.027906233444809914,
-0.06614512950181961,
0.008043223060667515,
0.05411633476614952,
-0.033550556749105453,
0.027016911655664444,
-0.018412500619888306,
0.024092907086014748,
0.013285359367728233,
-0.020840907469391823,
0.015870701521635056,
-0.013969889841973782,
0.010088816285133362,
0.025550583377480507,
0.010040956549346447,
0.006004944909363985,
-0.02888105809688568,
0.02335694432258606,
0.07176878303289413,
0.06001395359635353,
0.052687618881464005,
-0.008971131406724453,
0.004452654626220465,
-0.015611373819410801,
-0.04814125970005989,
-0.030548499897122383,
-0.013772387988865376,
-0.02000240795314312,
-0.039261218160390854,
0.02807999961078167,
-0.03933589532971382,
-0.05943860858678818,
0.027280636131763458,
0.008876470848917961,
-0.04350781813263893,
-0.002812847727909684,
-0.03580218553543091,
0.023706816136837006,
0.00849827192723751,
0.00017691683024168015,
0.01927109993994236,
0.0010066695977002382,
-0.009339510463178158,
-0.01770731247961521,
-0.0382176972925663,
0.037353117018938065,
-0.04210156202316284,
-0.03726598620414734,
0.01931154355406761,
-0.023334842175245285,
-0.03572789579629898,
0.01856323890388012,
0.00523025868460536,
0.03365611657500267,
0.011960726231336594,
-0.039011433720588684,
-0.005903938785195351,
0.0063393996097147465,
0.009595170617103577,
0.03199941664934158,
0.011691168881952763,
0.053247641772031784,
-0.007552653085440397,
-0.01873978041112423,
0.029002923518419266,
0.0050269123166799545,
0.019540563225746155,
-0.02274232730269432,
-0.004719058983027935,
0.039781033992767334,
-0.009802993386983871,
-0.001088844146579504,
-0.006257150787860155,
-0.040743302553892136,
0.059672944247722626,
-0.009027623571455479,
-0.022680409252643585,
0.035372138023376465,
-0.09006712585687637,
-0.004879348445683718,
-0.015604102052748203,
0.005454169120639563,
0.021430442109704018,
-0.04283249378204346,
0.035069551318883896,
0.02391650900244713,
0.018437830731272697,
-0.07074242830276489,
-0.021083854138851166,
0.022874347865581512,
0.022560087963938713,
0.008500606752932072,
0.0022592847235500813,
0.00883442535996437,
-0.0274325180798769,
-0.007148630917072296,
-0.002205997472628951,
0.05408458784222603,
-0.016303688287734985,
-0.0342346727848053,
0.008503097109496593,
-0.006162642035633326,
0.07383621484041214,
-0.016663864254951477,
-0.028359852731227875,
0.019408032298088074,
-0.01665370911359787,
0.021097874268889427,
-0.017164841294288635,
0.06275054812431335,
-0.03392874076962471,
-0.029802894219756126,
-0.04316301643848419,
-0.0582762211561203,
0.03148690611124039,
0.0021599421743303537,
-0.027955954894423485,
0.0620540976524353,
-0.01406401302665472,
-0.026979783549904823,
0.020606525242328644,
0.01640232838690281,
-0.03373495116829872,
0.041485659778118134,
-0.00822893064469099,
-0.00883455853909254,
0.005266924388706684,
-0.01435261033475399,
0.03997785970568657,
-0.030186880379915237,
-0.0039039188995957375,
0.02236384153366089,
0.03805437311530113,
-0.004367929883301258,
0.01614590361714363,
0.02691655233502388,
-0.01948067545890808,
0.009473588317632675,
-0.006696257274597883,
-0.021783357486128807,
-0.005777915008366108,
0.011900165118277073,
-0.019410522654652596,
-0.014948103576898575,
-0.03709132969379425,
0.0018021722789853811,
0.040091630071401596,
-0.03828853741288185,
0.008167507126927376,
0.004139139782637358,
0.0011659455485641956,
0.008275944739580154,
-0.037616390734910965,
0.0059272306971251965,
-0.010598178952932358,
0.0170476995408535,
0.003811134956777096,
-0.014623020775616169,
-0.008822623640298843,
0.04187072813510895,
0.05088780075311661,
-0.030161216855049133,
0.03618088737130165,
0.03528069704771042,
0.002147679915651679,
0.023202260956168175,
-0.03308020159602165,
-0.010836604051291943,
-0.0021235838066786528,
-0.01241734717041254,
-0.012527604587376118,
0.009244530461728573,
-0.018323928117752075,
0.02673916704952717,
-0.014189199544489384,
0.03283127024769783,
-0.0008448460139334202,
-0.05656673014163971,
-0.037678830325603485,
0.02976611629128456,
0.03576648607850075,
0.00204709661193192,
0.009052606299519539,
-0.03668983653187752,
-0.006978142540901899,
0.03175625577569008,
0.027804607525467873,
-0.01644361950457096,
-0.0711456835269928,
-0.04555478319525719,
-0.03494013473391533,
-0.07914687693119049,
0.032495249062776566,
0.010507820174098015,
-0.02048361301422119,
0.02285180427134037,
-0.003018649760633707,
0.005268462933599949,
-0.01146783772855997,
0.060022179037332535,
-0.010895972140133381,
0.0640583410859108,
-0.03733814135193825,
-0.010856603272259235,
-0.021959766745567322,
0.03909594938158989,
0.11169753223657608,
0.06401956081390381,
0.021914593875408173,
-0.0441165417432785,
0.030514664947986603,
-0.02116689644753933,
-0.02383544109761715,
-0.013495407998561859,
0.006523256655782461,
-0.008756338618695736,
-0.001427368028089404,
-0.002898162929341197,
0.036625247448682785,
-0.0315873809158802,
-0.04468676447868347,
0.05906818434596062,
0.01416252925992012,
-0.04987321048974991,
0.006825826596468687,
0.06724760681390762,
-0.03187916800379753,
-0.025652127340435982,
-0.04142092913389206,
-0.004527550656348467,
-0.004737443756312132,
-0.020855624228715897,
-0.019847996532917023,
0.02638145349919796,
0.030590323731303215,
0.01937907375395298,
-0.043267879635095596,
0.016705473884940147,
-0.004770106635987759,
-0.00432463688775897,
-0.014065932482481003,
0.05578917637467384,
-0.0017936740769073367,
-0.017009476199746132,
-0.016103249043226242,
0.048902727663517,
-0.004079918842762709,
-0.009852138347923756,
-0.010909379459917545,
0.011701932176947594,
-0.047878656536340714,
-0.006889694835990667,
-0.010731961578130722,
0.04317161813378334,
-0.003954961430281401,
0.03775476664304733,
0.010495762340724468,
0.012957129627466202,
-0.028786037117242813,
-0.05152978003025055,
-0.007720817346125841,
-0.010716821998357773,
0.014169749803841114,
0.012747899629175663,
-0.04032852500677109,
0.014271372929215431,
0.016729360446333885,
0.014619325287640095,
0.036679450422525406,
0.020233385264873505,
0.01899692788720131,
0.0021916485857218504,
-0.025166787207126617,
0.03222570940852165,
-0.008750584907829762,
-0.0013769810320809484,
-0.024781880900263786,
0.02111572027206421,
-0.044288720935583115,
-0.030696094036102295,
0.03486458957195282,
0.057085536420345306,
0.011798858642578125,
0.0035232368391007185,
-0.004255408886820078,
-0.035596586763858795,
-0.02590745873749256,
0.02396589331328869,
-0.030294470489025116,
-0.031801626086235046,
-0.04066881164908409,
-0.031214023008942604,
0.020564887672662735,
-0.009945432655513287,
-0.022425305098295212,
0.017238104715943336,
-0.0332551933825016,
0.014217028394341469,
-0.02950657717883587,
-0.009072271175682545,
0.01626359298825264,
0.02792464755475521,
-0.008363311178982258,
0.012973420321941376,
0.005010758060961962,
0.04381030797958374,
0.05334734916687012,
-0.044239722192287445,
-0.0015341999242082238,
0.028926027938723564,
-0.026537414640188217,
0.0028021708130836487,
0.05584251880645752,
-0.022337613627314568,
-0.04280351102352142,
-0.006992373149842024,
0.011609609238803387,
-0.03405943140387535,
-0.02061610296368599,
-0.06800927966833115,
-0.01759815774857998,
-0.01341436617076397,
0.043599024415016174,
-0.03594313934445381,
0.05477451905608177,
-0.030071858316659927,
0.0011149471392855048,
-0.036246709525585175,
0.011970528401434422,
-0.062230825424194336,
0.008298028260469437,
0.020963849499821663,
-0.009947243146598339,
-0.013468318618834019,
0.03846542537212372,
-0.026156337931752205,
-0.021581364795565605,
0.033406276255846024,
-0.024079455062747,
-0.010540622286498547,
-0.007058719173073769,
0.005430413875728846,
-0.02007308602333069,
0.06639561057090759,
-0.012673566117882729,
0.014062806032598019,
0.06573521345853806,
-0.03330003097653389,
-0.05871499702334404,
0.034199319779872894,
-0.030433591455221176,
0.0512922964990139,
0.02140532247722149,
-0.014440269209444523,
-0.05443977937102318,
0.0715535581111908,
-0.05636359006166458,
-0.003929385915398598,
-0.0017451121238991618,
0.03485390171408653,
-0.04517883062362671,
0.04444639012217522,
-0.0023859981447458267,
-0.0122325224801898,
-0.020399099215865135,
0.04444265738129616,
0.015404518693685532,
-0.0042747315019369125,
0.009120311588048935,
-0.00496761966496706,
-0.02214161679148674,
0.0015171440318226814,
0.008017044514417648,
0.025462636724114418,
0.017695993185043335,
0.041631538420915604,
-0.03167325258255005,
0.051863256841897964,
0.03005320020020008,
-0.0016484818188473582,
-0.06342533230781555,
0.009410446509718895,
0.017084360122680664,
0.012384209781885147,
0.037348341196775436,
-0.0496814139187336,
-0.01958303339779377,
0.028866609558463097,
-0.0603567399084568,
-0.026121143251657486,
-0.05911744758486748,
-0.008930837735533714,
-0.008315764367580414,
-0.008529174141585827,
0.0021736917551606894,
0.05423707887530327,
0.009741229005157948,
0.010233291424810886,
0.01697443425655365,
0.021133096888661385,
-0.01868661306798458,
-0.04892916604876518,
-0.0007145318668335676,
0.015169867314398289,
-0.03635605424642563,
-0.0159933902323246,
0.0531686507165432,
-0.019470984116196632,
-0.027888884767889977,
0.06494730710983276,
-0.022050153464078903,
0.06513893604278564,
0.000708404928445816,
-0.01689867116510868,
0.008408600464463234,
-0.010005992837250233,
0.04685422033071518,
-0.00993586890399456,
-0.019863121211528778,
0.012007649056613445,
-0.042362991720438004,
0.05523182451725006,
0.008387519977986813,
0.0006811326020397246,
0.026189420372247696,
-0.032055698335170746,
0.012423774227499962,
-0.02411884069442749,
-0.005546025466173887,
-0.0017078769160434604,
-0.021041743457317352,
0.011625116690993309,
-0.0019181889947503805,
-0.023408139124512672,
0.014819097705185413,
-0.05621413514018059,
-0.02859478071331978,
0.010889113880693913,
-0.00311667681671679,
0.00917111523449421,
0.0329953134059906,
0.0032457069028168917,
-0.05352417007088661,
0.005757076665759087,
-0.02238432876765728,
-0.01681801863014698,
-0.052315883338451385,
0.008528908714652061,
-0.016043851152062416,
-0.011443250812590122,
-0.0003229308349546045,
-0.049649424850940704,
-0.07285623997449875,
0.06444555521011353,
-0.016093125566840172,
0.012348009273409843,
0.0025681210681796074,
-0.051887333393096924,
-0.005263200961053371,
-0.04400515928864479,
0.02191941998898983,
0.0036294886376708746,
0.000132579225464724,
-0.013454098254442215,
-0.00265017943456769,
0.01393940020352602,
-0.009340803138911724,
0.017024315893650055,
0.019999438896775246,
0.00752947898581624,
0.010673734359443188,
-0.036113496869802475,
-0.009691877290606499,
-0.0517398975789547,
-0.0280383862555027,
0.013513730838894844,
-0.02972620725631714,
0.005664259660989046,
-0.029425622895359993,
0.015924718230962753,
0.022953517735004425,
0.032957740128040314,
0.01735137216746807,
0.029139086604118347,
0.025130363181233406,
-0.0010701111750677228,
0.061165254563093185,
0.01714528352022171,
0.036583736538887024,
0.07354613393545151,
0.006277842912822962,
0.030866730958223343,
0.042998261749744415,
-0.011533287353813648,
-0.03369392454624176,
0.029714565724134445,
-0.03176092728972435,
-0.01446587685495615,
-0.0024073002859950066,
-0.004434169270098209,
-0.0050620343536138535,
-0.04353257268667221,
0.027519449591636658,
0.037573087960481644,
0.017111780121922493,
-0.009608893655240536,
0.0015638050390407443,
0.011422986164689064,
0.02092067338526249,
-0.011411662213504314,
0.014448994770646095,
0.046068839728832245,
-0.05039607360959053,
0.0006367067107930779,
0.025242308154702187,
0.05663001164793968,
0.04364946112036705,
0.03481929749250412,
0.03291535750031471,
-0.005774419289082289,
-0.002618655562400818,
0.02867511287331581,
0.04801004379987717,
-0.018151147291064262,
-0.045399632304906845,
-0.014845548197627068,
0.01586960069835186,
0.05452689528465271,
0.03343037888407707,
-0.026151267811655998,
0.06760519742965698,
-0.005412723403424025,
-0.00824530515819788,
-0.0033944190945476294,
-0.024878280237317085,
-0.005315648391842842,
0.007379498332738876,
0.0000835954342619516,
0.0004436933377292007,
0.0023168232291936874,
0.005069780629128218,
-0.025100573897361755,
0.009989800862967968,
0.020664850249886513,
-0.021987978368997574,
0.01454070396721363,
-0.0020249627996236086,
0.02207638882100582,
-0.042489826679229736,
0.0208083875477314,
-0.011264858767390251,
-0.0044808052480220795,
0.022546200081706047,
0.044055867940187454,
0.03699537366628647,
-0.008165712468326092,
0.018783362582325935,
-0.029981588944792747,
0.019057022407650948,
-0.07424776256084442,
-0.020469821989536285,
-0.04392010718584061,
0.03428008779883385,
-0.006245077587664127,
-0.013205773197114468
] |
<p><a href="http://en.wikipedia.org/wiki/Hydrogen_ion" rel="nofollow">Hydrogen ion</a> doesn't have one electron which clearly mean that it has only one proton..So hydrogen ion is only a proton. Am I right, please make it clear. If hydrogen ion and proton are same that how to explain the reactivity with electron?</p> | 1,988 | [
-0.05437057092785835,
-0.001984459813684225,
0.01948687806725502,
0.008757216855883598,
0.007132596801966429,
0.00007958326750667766,
-0.038428716361522675,
-0.008317277766764164,
0.012353426776826382,
-0.05008317530155182,
0.06424366682767868,
-0.007836606353521347,
0.04032108187675476,
0.0071871173568069935,
-0.012904460541903973,
0.03507901355624199,
0.006649407558143139,
-0.03752373531460762,
0.013686181046068668,
0.025912480428814888,
0.01361035369336605,
-0.006450696848332882,
0.005313083529472351,
0.04401600733399391,
0.007109886035323143,
0.03732571750879288,
0.02175169624388218,
0.01199475210160017,
0.06509704142808914,
0.06632710248231888,
0.005496738478541374,
-0.020472461357712746,
0.039327412843704224,
0.003528722794726491,
0.03362080454826355,
-0.009951208718121052,
-0.003066264558583498,
0.0017771486891433597,
-0.04059919714927673,
0.01889822632074356,
0.02264285646378994,
-0.04246820881962776,
0.007061024662107229,
0.06400607526302338,
-0.029564300552010536,
0.007820453494787216,
-0.028109995648264885,
0.0017237354768440127,
0.05246114358305931,
-0.06622746586799622,
0.04669632762670517,
-0.001857022405602038,
0.03970375657081604,
-0.0005529004265554249,
-0.009137524291872978,
0.03102918341755867,
0.07357420772314072,
0.07575903832912445,
-0.03803976625204086,
-0.043361153453588486,
-0.018103083595633507,
-0.05537399649620056,
0.01289859414100647,
-0.005338382441550493,
-0.040424346923828125,
0.029325226321816444,
-0.02650407701730728,
-0.06995312869548798,
0.00611749105155468,
0.013845954090356827,
0.035165444016456604,
0.006135453935712576,
-0.0033731732983142138,
-0.047561049461364746,
0.01741841807961464,
-0.047152213752269745,
0.03382926061749458,
0.02195661887526512,
0.04323975741863251,
0.06230330467224121,
-0.025628967210650444,
0.0060411253944039345,
0.025844328105449677,
0.02065102383494377,
0.02667296677827835,
-0.020169435068964958,
0.06114090234041214,
-0.03027253970503807,
0.0028533935546875,
0.02627527341246605,
-0.018503202125430107,
0.015392160974442959,
0.02522571012377739,
0.03642450273036957,
0.005503344349563122,
0.03869126737117767,
-0.012100093066692352,
0.06925089657306671,
0.006520116701722145,
0.002545410068705678,
0.009272322058677673,
-0.017522139474749565,
0.04384791478514671,
0.04546288028359413,
-0.004672876559197903,
-0.025869598612189293,
-0.061663560569286346,
0.00850845966488123,
0.0006891762022860348,
-0.01595289818942547,
-0.015262864530086517,
0.038265425711870193,
0.004070976749062538,
-0.015025155618786812,
-0.015658531337976456,
-0.03445005789399147,
0.0013252835487946868,
0.009605410508811474,
0.06197836995124817,
0.05375990644097328,
0.030241986736655235,
-0.034885287284851074,
0.025189697742462158,
-0.011608862318098545,
-0.031985845416784286,
-0.012534892186522484,
0.026260657235980034,
0.04781854897737503,
-0.0031565458048135042,
0.029283929616212845,
-0.0005545258754864335,
-0.016272230073809624,
0.016318336129188538,
0.019589964300394058,
0.0644284188747406,
-0.051235850900411606,
-0.12018271535634995,
-0.03995964303612709,
0.012308049947023392,
-0.023303132504224777,
-0.03361610695719719,
-0.07831132411956787,
0.029580755159258842,
0.00825037993490696,
0.05074954777956009,
-0.01100902073085308,
-0.009827914647758007,
0.01753627136349678,
0.03591770678758621,
0.03315643593668938,
-0.010707437060773373,
-0.011365466751158237,
0.01169451791793108,
-0.03912334516644478,
0.0020768470130860806,
-0.055715881288051605,
-0.013408555649220943,
0.00605023605749011,
0.015953216701745987,
0.004479825031012297,
0.059530552476644516,
-0.01767830178141594,
0.023832539096474648,
0.033677492290735245,
0.014561669901013374,
-0.03175484761595726,
0.08561874181032181,
0.016419166699051857,
0.00367391062900424,
0.057704512029886246,
0.010017039254307747,
0.02312454953789711,
-0.020657777786254883,
0.05608309432864189,
0.04264426603913307,
-0.05310691148042679,
-0.05455020070075989,
-0.039996638894081116,
0.044181812554597855,
-0.006583014503121376,
-0.06760747730731964,
-0.034934185445308685,
-0.002001606859266758,
0.01758457161486149,
-0.012618115171790123,
0.04538705572485924,
0.0011202164459973574,
-0.022924449294805527,
-0.009795906953513622,
-0.049324244260787964,
-0.033563144505023956,
-0.07775145024061203,
0.011011422611773014,
0.0096107954159379,
-0.015073115937411785,
0.030267460271716118,
0.027813874185085297,
0.010627614334225655,
-0.042484305799007416,
-0.011424289084970951,
-0.06133545935153961,
0.04535090550780296,
-0.017977207899093628,
-0.022304276004433632,
0.03542608022689819,
0.04076100513339043,
0.02156573161482811,
-0.035730283707380295,
0.027993198484182358,
-0.013682624325156212,
0.008678081445395947,
0.03064812161028385,
-0.02150251343846321,
-0.00496683968231082,
0.036251407116651535,
-0.023259973153471947,
0.012149936519563198,
-0.043587494641542435,
-0.014219854958355427,
0.08095155656337738,
-0.042205631732940674,
0.08619830757379532,
-0.005813778843730688,
-0.008162107318639755,
0.031820423901081085,
0.010297578759491444,
0.028038639575242996,
0.008727342821657658,
-0.007175941485911608,
0.0021307761780917645,
-0.023054732009768486,
0.019693676382303238,
0.0543847531080246,
0.024672457948327065,
-0.04235278069972992,
-0.007644210942089558,
-0.0058152442798018456,
0.021178975701332092,
0.022077109664678574,
0.03689121827483177,
-0.030423259362578392,
-0.028855755925178528,
-0.004286677110940218,
0.02131846360862255,
-0.019367722794413567,
0.03088032267987728,
0.024750610813498497,
0.0007248648907989264,
0.04713789001107216,
-0.016248812898993492,
0.015110981650650501,
0.05923538655042648,
-0.029674753546714783,
0.010323900729417801,
0.028193360194563866,
-0.022874269634485245,
0.03849316015839577,
-0.0289235170930624,
0.011633914895355701,
-0.013706350699067116,
-0.01477126870304346,
-0.012575052678585052,
-0.010708488523960114,
0.00034684373531490564,
-0.002980500925332308,
0.001281284843571484,
-0.05735788121819496,
0.000565096503123641,
0.024298125877976418,
-0.041792817413806915,
-0.004056820645928383,
-0.018186967819929123,
0.01332192774862051,
0.006494797766208649,
0.014392068609595299,
0.02716114930808544,
-0.0007620361284352839,
0.041729483753442764,
-0.026344062760472298,
-0.00905841588973999,
-0.0067221480421721935,
-0.05177155137062073,
0.0017052920302376151,
-0.02010742761194706,
-0.009836782701313496,
0.006609456613659859,
-0.05179232358932495,
-0.014563714154064655,
0.04721524193882942,
0.0058451564982533455,
-0.0005925560253672302,
-0.015005923807621002,
-0.016126474365592003,
-0.03701755031943321,
-0.015796447172760963,
-0.03402615711092949,
0.033513832837343216,
-0.012509560212492943,
-0.013996227644383907,
0.02832985855638981,
-0.02010536566376686,
0.006982916500419378,
0.032367508858442307,
-0.01377051416784525,
-0.029134241864085197,
-0.0027980299200862646,
-0.011379186995327473,
0.030024930834770203,
-0.01799846440553665,
0.015052084811031818,
0.050598789006471634,
-0.056299932301044464,
-0.00598863186314702,
-0.0403590127825737,
-0.030297715216875076,
0.023214643821120262,
0.02414667047560215,
0.018862275406718254,
-0.004600765183568001,
-0.0556546151638031,
0.04451673850417137,
-0.011463942006230354,
-0.04049612209200859,
-0.012735538184642792,
-0.01263603288680315,
-0.03772001340985298,
-0.05153601989150047,
0.0038834726437926292,
0.03320781886577606,
0.0005262496997602284,
0.01265561394393444,
0.008419753983616829,
0.02479696087539196,
-0.008306344039738178,
0.027838775888085365,
-0.019983217120170593,
-0.021107932552695274,
0.03315713629126549,
-0.012587333098053932,
0.0386849008500576,
0.02890603430569172,
-0.030938876792788506,
0.033045995980501175,
0.0061318399384617805,
0.04225800186395645,
0.0021903039887547493,
-0.009728655219078064,
0.04095452278852463,
0.016402721405029297,
0.009837930090725422,
-0.022364355623722076,
0.016608817502856255,
-0.007708302233368158,
0.0023436760529875755,
0.0355125293135643,
-0.011594029143452644,
0.026653077453374863,
0.01002359576523304,
-0.008904590271413326,
0.039916545152664185,
0.02277526631951332,
-0.03653188422322273,
-0.03427067771553993,
0.010281370021402836,
-0.010914282873272896,
0.03462225943803787,
-0.010290922597050667,
-0.0110284723341465,
0.050509169697761536,
0.0169211532920599,
0.03308664634823799,
0.0002757518086582422,
-0.0442679338157177,
0.02477862685918808,
-0.10112446546554565,
-0.00016484552179463208,
0.001782360952347517,
0.04321820288896561,
-0.022379053756594658,
0.07750062644481659,
0.03137722983956337,
0.006749002728611231,
0.0019756066612899303,
-0.005048138089478016,
-0.06548444926738739,
0.029773401096463203,
-0.03155392408370972,
-0.013732598163187504,
-0.020730342715978622,
-0.02890746481716633,
-0.024965358898043633,
-0.011094776913523674,
-0.008252664469182491,
-0.013072947040200233,
-0.03144165128469467,
-0.029122648760676384,
0.028753075748682022,
-0.027897370979189873,
-0.0107243238016963,
-0.032790280878543854,
0.042039401829242706,
0.022557053714990616,
-0.0056572044268250465,
0.00969315692782402,
0.04507646709680557,
-0.033691875636577606,
0.011233475990593433,
-0.022618398070335388,
0.014930510893464088,
0.017708249390125275,
0.018929224461317062,
0.03531038016080856,
0.010885896161198616,
0.005283381324261427,
-0.008597377687692642,
0.006284338887780905,
0.04639703780412674,
0.016634447500109673,
-0.014799671247601509,
-0.013000917620956898,
-0.06577382981777191,
-0.005026976112276316,
-0.011502614244818687,
0.06280457973480225,
-0.012509199790656567,
0.02810203842818737,
-0.004639647901058197,
-0.016295352950692177,
-0.0010409230599179864,
0.048029445111751556,
0.06862494349479675,
0.012708871625363827,
-0.04419943690299988,
-0.06137508526444435,
-0.0037834958638995886,
-0.05365924537181854,
-0.025842448696494102,
0.036943867802619934,
-0.0022900551557540894,
-0.03629168123006821,
-0.017164429649710655,
0.010781900025904179,
0.020283784717321396,
-0.023954210802912712,
-0.000416964030591771,
-0.02464766800403595,
0.015784285962581635,
-0.02541317231953144,
-0.0118777547031641,
0.01904135011136532,
0.03371562063694,
0.008405167609453201,
-0.015517896972596645,
-0.027697961777448654,
-0.08656954765319824,
0.037556007504463196,
0.02462114207446575,
0.0623825341463089,
-0.029749762266874313,
-0.030999379232525826,
-0.044157471507787704,
0.022608261555433273,
0.05032138153910637,
-0.05478179082274437,
0.010805130004882812,
-0.012131728231906891,
0.03943834826350212,
0.020131278783082962,
0.006885977927595377,
-0.006685273256152868,
0.02230057679116726,
0.029705176129937172,
-0.010126412846148014,
-0.04927361011505127,
0.005713063292205334,
-0.030163737013936043,
-0.0008891217294149101,
0.01519980002194643,
0.05670619755983353,
-0.009190952405333519,
0.02045067772269249,
0.009523366577923298,
0.018419822677969933,
-0.011614244431257248,
-0.10817261040210724,
0.03939342126250267,
0.0033156489953398705,
0.014533789828419685,
0.030970042571425438,
-0.04669403284788132,
-0.040510375052690506,
0.04137088358402252,
0.0006866818876005709,
-0.016368228942155838,
-0.023590167984366417,
-0.06552768498659134,
-0.009109359234571457,
0.03957129269838333,
-0.014024010859429836,
0.027583900839090347,
0.020772268995642662,
-0.012104395776987076,
-0.015153639018535614,
-0.03877121955156326,
-0.002923088613897562,
-0.033108461648225784,
-0.008751803077757359,
-0.017696335911750793,
0.030221780762076378,
-0.025986740365624428,
0.05444759130477905,
0.011919467709958553,
0.001390916178934276,
0.0010139044607058167,
-0.017990197986364365,
-0.012622583657503128,
-0.01075692754238844,
-0.024632437154650688,
0.005179970059543848,
-0.003292997367680073,
-0.00153384730219841,
-0.011252320371568203,
-0.024908732622861862,
-0.004883068613708019,
-0.008679580874741077,
-0.02809586003422737,
0.019429482519626617,
0.0008960595587268472,
0.019193440675735474,
0.02473883330821991,
-0.03655824810266495,
0.01810590922832489,
-0.08548570424318314,
0.0038056012708693743,
-0.03620734438300133,
-0.014993281103670597,
0.02079879306256771,
-0.08369642496109009,
-0.02582312561571598,
0.050178080797195435,
-0.0008329438860528171,
0.010975872166454792,
-0.02256341651082039,
0.055601876229047775,
0.020753709599375725,
0.002383606508374214,
-0.0502854585647583,
-0.03958111256361008,
0.009184513241052628,
-0.015272283926606178,
-0.037324536591768265,
-0.012814473360776901,
-0.008373496122658253,
-0.017865125089883804,
-0.023372603580355644,
-0.008332844823598862,
0.03066432848572731,
-0.05710485577583313,
-0.0166695024818182,
0.028168823570013046,
0.009316259995102882,
0.0537709966301918,
0.008673906326293945,
-0.041156623512506485,
-0.028287414461374283,
-0.020746799185872078,
-0.014288839884102345,
-0.010287894867360592,
0.057831648737192154,
-0.016702091321349144,
-0.037231311202049255,
-0.023504657670855522,
-0.02794969640672207,
0.019579723477363586,
-0.018442410975694656,
0.0022960114292800426,
0.018553586676716805,
0.03883647173643112,
-0.025690466165542603,
-0.0422695130109787,
0.030953560024499893,
-0.003008851781487465,
0.031062837690114975,
0.022680336609482765,
0.03422396257519722,
-0.04481007531285286,
-0.03517314791679382,
0.011163636110723019,
0.008886964060366154,
-0.0002825131523422897,
0.011789155192673206,
0.02488994412124157,
-0.00796870980411768,
0.036709193140268326,
0.015734178945422173,
-0.049829188734292984,
0.025515157729387283,
-0.01110864244401455,
-0.007567426189780235,
0.003931437619030476,
0.013488016091287136,
-0.024285145103931427,
0.000024183322238968685,
-0.024026667699217796,
0.02014758065342903,
0.0354386568069458,
0.004775431007146835,
0.033881012350320816,
0.005364445503801107,
0.01977190375328064,
0.0014893792103976011,
0.005275139585137367,
-0.004186208359897137,
-0.013378310017287731,
0.02267448604106903,
0.03443269804120064,
-0.007785346359014511,
0.029427433386445045,
0.03483704850077629,
0.04796985536813736,
-0.0031407633796334267,
-0.01911667361855507,
0.04464566335082054,
0.006614085286855698,
0.0026954440400004387,
0.0057136546820402145,
-0.08317789435386658,
0.03748740628361702,
-0.012881338596343994,
0.05118660628795624,
-0.009729222394526005,
-0.028752615675330162,
0.05331052467226982,
-0.027158861979842186,
0.0322653092443943,
-0.04296587035059929,
-0.03803336247801781,
-0.010782210156321526,
0.04118428751826286,
0.009605355560779572,
0.0056512546725571156,
-0.041675906628370285,
0.039174046367406845,
0.05320754647254944,
0.02069368213415146,
0.03618840128183365,
0.01394171454012394,
-0.049682263284921646,
-0.012400245293974876,
-0.03160613775253296,
-0.012016265653073788,
0.03986407071352005,
-0.019622990861535072,
-0.05975101515650749,
0.007103838492184877,
-0.001773091615177691,
0.014467223547399044,
0.010280380956828594,
0.029556147754192352,
-0.0005000612000003457,
0.04846708104014397,
-0.0048267473466694355,
0.0164033230394125,
0.015199619345366955,
0.0029758899472653866,
0.10706532001495361,
0.059118058532476425,
-0.027976125478744507,
-0.06140001863241196,
-0.0018970760283991694,
-0.01811063475906849,
0.029878973960876465,
0.008553593419492245,
0.023808056488633156,
-0.02285410463809967,
0.02267100289463997,
-0.001804190338589251,
0.04241550713777542,
0.00460111815482378,
0.026302088052034378,
0.0687033087015152,
-0.024811729788780212,
-0.039669983088970184,
-0.01905396394431591,
0.013165012001991272,
-0.0038104529958218336,
0.03045498952269554,
-0.03371154144406319,
0.0310635045170784,
-0.02501186542212963,
0.024966495111584663,
-0.04825489595532417,
-0.018775416538119316,
0.022459901869297028,
0.036144450306892395,
-0.054241523146629333,
-0.0049983542412519455,
0.01646393910050392,
-0.0212557353079319,
-0.022508079186081886,
0.02311614900827408,
0.03962097316980362,
-0.014080379158258438,
-0.012242455035448074,
0.008920883759856224,
0.04074116796255112,
0.005994773469865322,
0.025729190558195114,
0.044925011694431305,
-0.03741138428449631,
0.021852701902389526,
-0.014714534394443035,
0.02916869707405567,
0.006552546285092831,
-0.01775483414530754,
-0.02419154904782772,
0.004915101919323206,
-0.03175481781363487,
-0.06704212725162506,
-0.040049437433481216,
-0.006058961618691683,
0.023651836439967155,
-0.0018734271870926023,
-0.02542368322610855,
-0.07194952666759491,
0.0326329730451107,
-0.05866271257400513,
0.03964864835143089,
0.0015828845789656043,
-0.012606584466993809,
0.014150616712868214,
-0.019983308389782906,
0.007972015999257565,
-0.022215373814105988,
0.0005154337850399315,
-0.003267048392444849,
-0.012918547727167606,
-0.03474978730082512,
-0.04836326465010643,
0.010762656107544899,
0.047102659940719604,
0.08298183232545853,
0.00008148155029630288,
0.021852241829037666,
-0.002624735701829195,
-0.06734027713537216,
0.06151307001709938,
0.029771318659186363,
-0.02342698723077774,
-0.014406661503016949,
-0.007412492763251066,
0.02280009351670742,
0.036611005663871765,
-0.03769504651427269,
0.008652439340949059,
-0.006794886197894812,
-0.015657471492886543,
0.0296569112688303,
-0.051483407616615295,
-0.015011001378297806,
0.06791951507329941,
-0.024879641830921173,
-0.003094287123531103,
-0.012972082942724228,
0.0088042002171278,
0.027318015694618225,
-0.0019435810390859842,
-0.006785877048969269,
0.00762012368068099,
-0.025031594559550285,
0.0016557855997234583,
0.005857349839061499,
0.006972182542085648,
-0.0054917349480092525,
0.010705298744142056,
0.0005632875836454332,
-0.04508340358734131,
-0.01201784797012806,
-0.03531605750322342,
0.006475393194705248,
0.027415966615080833,
0.013710795901715755,
-0.030291348695755005,
0.005018903873860836,
-0.025402361527085304,
0.03513788804411888,
-0.046365849673748016,
-0.023529060184955597,
-0.07633106410503387,
0.008515666238963604,
0.01974739134311676,
-0.007439207751303911,
0.0009193828445859253,
0.022875286638736725,
-0.013718914240598679,
-0.005552953574806452,
0.0659884437918663,
0.018045080825686455,
-0.04751061648130417,
0.02348916418850422,
0.020032264292240143,
-0.04451589658856392,
0.04815760999917984,
-0.03841465339064598,
-0.020484058186411858,
0.03513983637094498,
-0.06401845067739487,
0.0009196579339914024,
-0.005421742796897888,
-0.013822888024151325,
0.006697659846395254,
0.05461597442626953,
-0.002300363266840577,
0.015523252077400684,
0.09101974219083786,
-0.021103907376527786,
0.0036851991899311543,
0.04123295098543167,
-0.03917765989899635,
-0.02557709440588951,
-0.012278330512344837,
-0.03111313469707966,
0.010728051885962486,
-0.008635299280285835,
0.04967716336250305,
0.00713913282379508,
-0.011281942948698997,
0.012058595195412636,
-0.009822594933211803,
0.026004524901509285,
0.05189724266529083,
0.031342439353466034,
-0.005412630271166563,
-0.028351351618766785,
0.017645569518208504,
-0.027689479291439056,
0.036782123148441315,
-0.0004169753228779882,
0.0009149235556833446,
-0.06707530468702316,
-0.0010678564431145787,
-0.025733081623911858,
-0.007924367673695087,
0.006614489946514368,
-0.008839147165417671,
0.024519868195056915,
0.02839265577495098,
-0.0919388011097908,
0.0054958658292889595,
-0.015712132677435875,
-0.021656008437275887,
-0.002277941443026066,
-0.03697215020656586,
-0.006819951813668013,
0.05820421501994133,
0.010469276458024979,
0.06460560113191605,
0.03401477262377739,
0.0025161262601614,
0.010754873044788837,
-0.0020905358251184225,
-0.019186917692422867,
0.036304157227277756,
-0.006823165342211723,
-0.046076491475105286,
0.052050068974494934,
-0.03159305825829506,
-0.013413307256996632,
0.025278881192207336,
0.004369385540485382,
0.007050021085888147,
0.010078387334942818,
-0.006569633726030588,
-0.0008172715897671878,
0.02174990437924862,
-0.041826941072940826,
-0.022576013579964638,
-0.04582367464900017,
0.05102686583995819,
0.02312377654016018,
0.034091509878635406,
0.008158110082149506,
-0.00991776678711176,
0.04399261251091957,
-0.03942374512553215,
-0.032675597816705704,
0.013695908710360527,
-0.006526572164148092,
0.02115347422659397,
-0.028823155909776688,
-0.000057279856264358386,
0.022834448143839836,
-0.030000731348991394,
-0.036578964442014694,
-0.03158529847860336,
0.02834913320839405,
0.048953186720609665,
-0.023821230977773666,
0.019613638520240784,
0.0024592180270701647,
-0.004077090881764889,
0.008754265494644642,
0.05895441770553589,
0.008182636462152004,
-0.011103679426014423,
-0.03706992045044899,
0.005462340544909239,
0.04336845129728317,
0.01553435530513525,
-0.009738335385918617,
-0.05699701979756355,
-0.04676080495119095,
0.048628903925418854,
0.0004517897905316204,
0.0050643268041312695,
-0.012361899949610233,
-0.03478332981467247,
-0.017658300697803497,
-0.034022945910692215,
0.016385724768042564,
0.0026831584982573986,
-0.006011494901031256,
-0.044438425451517105,
-0.03982086107134819,
-0.014174887910485268,
0.01201214175671339,
0.07159523665904999,
-0.007199161220341921,
-0.020242847502231598,
-0.002547620330005884,
0.0031034392304718494,
-0.005300086457282305,
-0.04800146073102951,
-0.023442231118679047,
-0.0011752090649679303,
-0.03251352533698082,
0.03312920778989792,
-0.02509140968322754,
-0.043073903769254684,
0.037718385457992554,
0.012416379526257515,
-0.004195937421172857,
0.009284120053052902,
-0.022775355726480484,
-0.0380992665886879,
0.04088732227683067,
0.0072941044345498085,
-0.008729711174964905,
0.08868502080440521,
-0.0020172877702862024,
0.00005966159005765803,
0.034351129084825516,
-0.0009104468626901507,
-0.019956283271312714,
0.017393629997968674,
-0.02825472690165043,
0.017232196405529976,
0.0010191187029704452,
-0.020485220476984978,
0.014371796511113644,
-0.056992582976818085,
0.00042385951383039355,
0.022420505061745644,
-0.033108048141002655,
-0.04165541008114815,
0.051996223628520966,
0.010707441717386246,
0.026899069547653198,
-0.02073313482105732,
0.004419825971126556,
0.01142057217657566,
0.010772349312901497,
0.02878681942820549,
0.06097584217786789,
0.0002692186099011451,
-0.00021300108346622437,
0.021023474633693695,
0.009428434073925018,
0.03479481115937233,
-0.008220364339649677,
0.03323827683925629,
0.05738406628370285,
-0.013508966192603111,
-0.006182354409247637,
0.013833588920533657,
-0.043144822120666504,
0.021519804373383522,
0.02278827130794525,
-0.0039056020323187113,
0.061688877642154694,
-0.056260719895362854,
0.007436112500727177,
0.012954791076481342,
0.016114793717861176,
-0.01961367018520832,
0.012555037625133991,
0.008970126509666443,
0.03541714325547218,
0.002519772155210376,
-0.04590794816613197,
-0.009004518389701843,
-0.0071707190945744514,
0.045560602098703384,
-0.021501054987311363,
0.015851551666855812,
0.01148652657866478,
-0.01853732392191887,
-0.054699815809726715,
0.020430147647857666,
-0.00010939460480585694,
0.001475704601034522,
0.013142985291779041,
0.022763608023524284,
0.012622075155377388,
-0.018120363354682922,
-0.01160335075110197,
-0.039787910878658295,
0.04470004513859749,
-0.05073762685060501,
-0.020345697179436684,
-0.0030369001906365156,
-0.00044744464685209095,
-0.03243260458111763,
-0.03484617546200752
] |
<p>Here's a question inspired by <a href="http://physics.stackexchange.com/questions/7771/is-there-an-energy-density-limit-in-gr/7773#7773">Edward's answer</a> to <a href="http://physics.stackexchange.com/questions/7771/is-there-an-energy-density-limit-in-gr">this question</a>. </p>
<p>It's my understanding that the average energy density of a black hole in its rest frame is $\rho_\text{BH}(A)$, a function of surface area. I calculated $3c^2/2GA$ for a Schwarzschild black hole, but that's presumably not applicable here since I'm talking about an extended energy distribution. Anyway, suppose you are in a space filled with some sort of energy, matter, or whatever, which produces a potentially time-dependent stress-energy tensor. And further suppose that there is some finite, spherical region of surface area $A$ in this space, over which you measure the average energy density to be $\rho_\text{BH}(A)$, the net charge to be zero, and the total angular momentum of the matter within the region to be zero. (I'm assuming there is a measurement procedure available which can be carried out without entering the region, if it matters.) </p>
<p>Now, Edward's argument in the other question shows that there are at least two ways to produce that (average) energy density:</p>
<ol>
<li>The energy density arises from a fluid or other material at rest, such that the region is a black hole and there are no timelike geodesics exiting it</li>
<li>The energy density has been "augmented" by a Lorentz boost from some other frame, implying that there are timelike geodesics exiting the region</li>
</ol>
<p>Is it possible, in general, to distinguish between case 1 and case 2 by only looking at the other components of the stress energy tensor, without actually calculating the geodesics? If so, how? What would be the "signature" of a black hole in the components of $T^{\mu\nu}$ (or rather, their averages over the region in question)?</p> | 1,989 | [
-0.04901180416345596,
-0.014417438767850399,
0.02250046283006668,
-0.050751812756061554,
0.034602683037519455,
0.017910053953528404,
-0.06476348638534546,
-0.06188228353857994,
-0.012691984884440899,
-0.032333970069885254,
0.041614431887865067,
0.017762186005711555,
0.04428517818450928,
0.06323780864477158,
0.004090578760951757,
-0.008788887411355972,
0.0067342291586101055,
0.02016458660364151,
-0.03015986829996109,
-0.05048513412475586,
0.040102969855070114,
0.017554733902215958,
0.001616443507373333,
-0.031164303421974182,
0.0069120777770876884,
-0.01204086933284998,
0.03271438553929329,
-0.04929324984550476,
-0.0017376518808305264,
0.07297837734222412,
-0.05488567799329758,
-0.019585877656936646,
0.008475298061966896,
0.010497430339455605,
0.04058155044913292,
-0.008994894102215767,
-0.03243737667798996,
-0.007285324390977621,
0.0015932294772937894,
0.04422140493988991,
-0.03440791741013527,
-0.01512509398162365,
0.006191141903400421,
0.06465055048465729,
-0.02947538159787655,
0.0037132150027900934,
0.001688995398581028,
-0.020545510575175285,
0.030035875737667084,
-0.060485728085041046,
0.04616351053118706,
-0.003187623806297779,
0.023976391181349754,
0.02346024289727211,
0.014736630022525787,
-0.03190135583281517,
0.07140789926052094,
0.06617596745491028,
-0.006584288086742163,
-0.023580612614750862,
-0.04446544125676155,
0.012800103984773159,
-0.024807758629322052,
-0.0039243437349796295,
0.02742852456867695,
0.014899381436407566,
-0.01308880653232336,
-0.01113231759518385,
0.026910673826932907,
-0.04744444414973259,
-0.001751529285684228,
0.007712800521403551,
-0.033255867660045624,
-0.0002829597797244787,
-0.017507662996649742,
0.00031576730543747544,
0.021293222904205322,
-0.002709168940782547,
0.019416827708482742,
0.04140424355864525,
-0.029058873653411865,
-0.01788667030632496,
0.0465540885925293,
0.050019338726997375,
0.03538265824317932,
0.03397610783576965,
0.0659121721982956,
-0.024082256481051445,
-0.023056065663695335,
0.040872618556022644,
-0.0007974100299179554,
-0.016618555411696434,
-0.028350412845611572,
-0.008206660859286785,
-0.014915594831109047,
0.03183905407786369,
-0.017142007127404213,
0.05864722281694412,
-0.02069382555782795,
-0.0038181119598448277,
-0.024984996765851974,
-0.028767401352524757,
-0.004989438224583864,
0.06934038549661636,
0.008971424773335457,
-0.031041404232382774,
-0.06419465690851212,
0.01769091747701168,
-0.026566779240965843,
0.000003284897502453532,
-0.03119887039065361,
0.01966509036719799,
-0.034005217254161835,
-0.038189105689525604,
-0.011258820071816444,
-0.0323353111743927,
-0.0039114560931921005,
0.008792259730398655,
0.03868384286761284,
0.06148941442370415,
0.07746712863445282,
0.019128475338220596,
-0.038757942616939545,
-0.023735366761684418,
-0.050219982862472534,
-0.00596059812232852,
0.042786527425050735,
-0.015077142044901848,
-0.031566254794597626,
-0.0012130612740293145,
-0.012813526205718517,
-0.007663465570658445,
0.0306573286652565,
0.012752682901918888,
0.03591351956129074,
-0.01836177334189415,
-0.09058881551027298,
-0.03349553421139717,
0.06888332962989807,
0.006733523216098547,
-0.019424958154559135,
-0.052050333470106125,
-0.023081904277205467,
0.03827902674674988,
0.07332420349121094,
0.010311822406947613,
-0.0052216206677258015,
0.0008557026158086956,
0.05265318229794502,
0.019578807055950165,
-0.026085205376148224,
0.00970205757766962,
-0.00912451557815075,
-0.02568887732923031,
0.022533826529979706,
-0.06478498131036758,
0.015298082493245602,
0.013360220938920975,
-0.0003084982163272798,
0.0033893350046128035,
0.05839618295431137,
0.01634535752236843,
0.008678039535880089,
0.01741754822432995,
-0.026876108720898628,
0.0012829452753067017,
0.076700858771801,
0.01839018426835537,
-0.024916209280490875,
0.04980184882879257,
-0.003909920807927847,
-0.0009601904894225299,
0.0012912456877529621,
-0.0030548900831490755,
0.04799925908446312,
-0.04596075415611267,
0.008988604880869389,
-0.010450588539242744,
-0.001743891043588519,
-0.008307519368827343,
-0.0329258106648922,
0.0005426855641417205,
-0.011813669465482235,
-0.03241056948900223,
0.0348699688911438,
0.03727816417813301,
0.021944185718894005,
-0.024950707331299782,
-0.0256666112691164,
-0.025637971237301826,
0.019913718104362488,
-0.02520982176065445,
-0.006614166311919689,
-0.0026036566123366356,
0.01144294161349535,
0.02118220366537571,
-0.011221139691770077,
0.00825042650103569,
-0.06433657556772232,
-0.013770929537713528,
0.008686024695634842,
0.06322843581438065,
0.009472712874412537,
-0.029027065262198448,
0.021424908190965652,
0.010133540257811546,
0.045573849231004715,
0.0027040676213800907,
-0.026739349588751793,
0.024536361917853355,
-0.0390218086540699,
0.00035676523111760616,
-0.0016141922678798437,
0.05158206820487976,
0.001282159355469048,
0.0010474344016984105,
-0.006066161207854748,
0.051895514130592346,
0.0013877294259145856,
0.0074404263868927956,
-0.023532796651124954,
0.04007244110107422,
0.035456329584121704,
-0.014865889213979244,
-0.0035896897315979004,
0.03981795534491539,
0.02206403762102127,
0.020086942240595818,
-0.027239324524998665,
-0.0120732756331563,
-0.03711709380149841,
-0.017869554460048676,
0.03701772913336754,
0.03960814327001572,
-0.04559991881251335,
0.014036979526281357,
0.04764937609434128,
0.017390606924891472,
-0.01606745831668377,
0.012761089019477367,
-0.002242559101432562,
-0.03770027309656143,
0.023130519315600395,
0.010352562181651592,
0.009066428989171982,
0.0037872130051255226,
0.014149396680295467,
-0.005539850797504187,
-0.01953878253698349,
-0.005324785131961107,
0.012653758749365807,
0.015801729634404182,
-0.023892415687441826,
0.01509582344442606,
-0.0029144117143005133,
0.006884046830236912,
0.042536742985248566,
0.0015554834390059114,
0.037502046674489975,
0.04136456176638603,
-0.01893361285328865,
-0.0226227268576622,
-0.056897327303886414,
-0.026706868782639503,
0.00827581062912941,
0.02029157057404518,
0.03219238668680191,
0.003702688729390502,
0.011444426141679287,
-0.04972006753087044,
-0.01707082986831665,
-0.02075224369764328,
0.00791163556277752,
-0.019286006689071655,
-0.005122532602399588,
0.0343623012304306,
0.02426416426897049,
-0.005311437416821718,
-0.031772006303071976,
-0.012900503352284431,
0.02664397470653057,
0.00036975060356780887,
-0.0045119281858205795,
0.023251790553331375,
-0.07063715904951096,
0.0043796063400805,
-0.04082462191581726,
-0.012801982462406158,
0.04234755039215088,
-0.00294040166772902,
-0.0005601972807198763,
0.060042720288038254,
0.02651655115187168,
-0.03238385170698166,
0.0038589646574109793,
-0.014775218442082405,
-0.032375268638134,
-0.0554831437766552,
-0.0028087273240089417,
0.08187146484851837,
0.00827825628221035,
-0.07101697474718094,
0.008703581988811493,
-0.011865788139402866,
-0.042405787855386734,
0.0019846754148602486,
-0.00535914720967412,
0.02229306660592556,
-0.03526369109749794,
0.04453829303383827,
0.024634456261992455,
-0.024078665301203728,
0.007894694805145264,
-0.043538425117731094,
-0.032368723303079605,
0.02348189614713192,
-0.0072467392310500145,
0.029111700132489204,
-0.002174321562051773,
-0.05052231624722481,
0.0723712369799614,
0.0014291033148765564,
-0.02049163728952408,
-0.011153333820402622,
-0.017032083123922348,
0.028530417010188103,
-0.012950258329510689,
-0.01978978142142296,
0.016471896320581436,
0.0018611395498737693,
-0.008926957845687866,
0.033304713666439056,
0.06100301817059517,
0.00725235790014267,
0.04694546014070511,
0.003075413405895233,
0.009903794154524803,
0.014694783836603165,
0.012836327776312828,
0.047245923429727554,
0.010934585705399513,
-0.01801753230392933,
-0.026746505871415138,
-0.02081356570124626,
0.039199668914079666,
0.05035366863012314,
-0.05808604508638382,
0.05199931934475899,
0.012964574620127678,
0.022583385929465294,
-0.014993838965892792,
0.010505640879273415,
-0.0048865508288145065,
-0.04943682998418808,
0.025461411103606224,
-0.009623952209949493,
0.04878709465265274,
0.008993626572191715,
-0.005011735018342733,
0.030261756852269173,
0.033821653574705124,
-0.019206678494811058,
-0.033719077706336975,
-0.005044830031692982,
-0.01682952232658863,
0.036837175488471985,
-0.01871490851044655,
-0.014452743344008923,
0.037674885243177414,
0.04836190119385719,
0.009793251752853394,
-0.011555752716958523,
-0.010608157142996788,
-0.012295229360461235,
-0.08237345516681671,
-0.024221159517765045,
0.0016250633634626865,
0.04600963369011879,
0.01059369184076786,
0.046127524226903915,
0.02533229999244213,
-0.0041498043574392796,
0.03840186819434166,
-0.01464272290468216,
-0.098922960460186,
0.007313206326216459,
-0.03893410414457321,
0.004795891232788563,
0.00832977145910263,
-0.022921569645404816,
-0.002651746617630124,
-0.01774848997592926,
-0.02924438752233982,
-0.004874829668551683,
0.013337967917323112,
-0.07322335988283157,
0.02755003795027733,
-0.0423649400472641,
-0.0391763299703598,
-0.043621331453323364,
0.07602657377719879,
0.05602061375975609,
-0.010927842929959297,
-0.0013921675272285938,
0.003832143498584628,
-0.036280278116464615,
-0.016009150072932243,
-0.0009288085275329649,
0.043015193194150925,
-0.014293954707682133,
0.04487721249461174,
0.010607898235321045,
0.012360429391264915,
-0.0037795996759086847,
-0.0024463613517582417,
0.03166305273771286,
0.019598467275500298,
-0.035500988364219666,
-0.013838588260114193,
-0.03623742610216141,
-0.020098384469747543,
-0.01883985474705696,
0.008289066143333912,
0.07151126116514206,
-0.026712562888860703,
-0.014268304221332073,
-0.015839632600545883,
0.0006753256311640143,
0.0009270221926271915,
0.04909498617053032,
0.03668081387877464,
-0.019896602258086205,
-0.026666773483157158,
-0.07404621690511703,
-0.023329125717282295,
-0.012012766674160957,
0.028113292530179024,
0.008766609244048595,
-0.0004226295277476311,
-0.023309096693992615,
0.018680443987250328,
-0.0012136859586462379,
0.009970041923224926,
-0.021037986502051353,
-0.030144240707159042,
0.04390745982527733,
0.015890156850218773,
0.010708367452025414,
0.013028472661972046,
0.010224584490060806,
0.00586782768368721,
0.05982170253992081,
0.0028422847390174866,
0.030200809240341187,
-0.0703883245587349,
-0.053952883929014206,
0.03072499670088291,
0.02840949222445488,
0.0052351318299770355,
-0.03532455116510391,
-0.06616055965423584,
-0.0010791230015456676,
0.046699631959199905,
-0.020600469782948494,
0.018697168678045273,
0.006056136451661587,
0.03305599093437195,
-0.02596195600926876,
-0.05106576532125473,
-0.017173053696751595,
0.05533672124147415,
0.007054936606436968,
-0.03060689941048622,
-0.018981119617819786,
0.031904444098472595,
-0.010769709013402462,
0.0035485532134771347,
0.015684982761740685,
0.043902769684791565,
0.009376046247780323,
0.006194146350026131,
-0.006879621185362339,
0.0014468253357335925,
-0.016050901263952255,
-0.08648142218589783,
-0.012464845553040504,
0.027819614857435226,
-0.04469664767384529,
0.036386072635650635,
-0.053706634789705276,
-0.03576624020934105,
0.027600392699241638,
-0.011576338671147823,
-0.02912277542054653,
0.05746908113360405,
-0.06319979578256607,
0.06329401582479477,
0.010676278732717037,
-0.017342792823910713,
0.0289717148989439,
0.009788913652300835,
0.014336561784148216,
-0.0008661669562570751,
-0.07078894972801208,
0.025413960218429565,
-0.055137019604444504,
-0.009545955806970596,
-0.009159949608147144,
0.03183417022228241,
-0.028195468708872795,
0.022501185536384583,
-0.028223302215337753,
0.005600173491984606,
0.019961141049861908,
-0.0528017021715641,
0.009323013946413994,
0.019447609782218933,
-0.0022780082654207945,
0.011871496215462685,
0.011106625199317932,
-0.010736236348748207,
0.008335927501320839,
-0.002150921616703272,
0.01946016028523445,
0.0064604864455759525,
0.009511834010481834,
0.06786790490150452,
0.009412803687155247,
0.011512585915625095,
-0.01996746100485325,
0.005708129145205021,
0.019443469122052193,
-0.020289767533540726,
0.06815510243177414,
-0.006974778138101101,
0.01134218368679285,
0.014773808419704437,
0.0021403830032795668,
-0.009338155388832092,
-0.018030785024166107,
-0.005610953085124493,
0.036823906004428864,
-0.021618753671646118,
0.004031587392091751,
0.05304492264986038,
0.014620378613471985,
-0.08096684515476227,
0.010165601037442684,
0.04435454681515694,
0.026841098442673683,
0.005420877132564783,
-0.028882525861263275,
0.017349032685160637,
-0.06494928151369095,
-0.008377790451049805,
-0.02588924579322338,
0.021326668560504913,
-0.03621451556682587,
0.0028904287610203028,
-0.000607827678322792,
0.04992248862981796,
0.03082679957151413,
-0.03760033845901489,
-0.030110234394669533,
0.04128481447696686,
0.022408291697502136,
0.02207905426621437,
-0.03622325509786606,
0.007009569089859724,
-0.03471142053604126,
-0.013602428138256073,
-0.004999844823032618,
-0.016816385090351105,
0.0032432633452117443,
-0.008797693997621536,
0.007244505453854799,
0.03150331228971481,
-0.024353589862585068,
-0.021028835326433182,
-0.025730378925800323,
0.0031550780404359102,
-0.027973352000117302,
0.012374088168144226,
-0.02692122384905815,
-0.02337421290576458,
-0.025142936035990715,
-0.02424701862037182,
0.012495002709329128,
-0.013053091242909431,
-0.007876766845583916,
-0.030260825529694557,
0.044911015778779984,
0.03244582191109657,
-0.036593250930309296,
-0.008835949003696442,
-0.02881253883242607,
-0.007678510155528784,
0.01594107784330845,
0.025336677208542824,
0.04123605787754059,
-0.0020054164342582226,
-0.0316476933658123,
-0.03992011025547981,
-0.07200895249843597,
0.005562377627938986,
0.09017413854598999,
-0.00621431041508913,
0.015013175085186958,
0.02701674774289131,
-0.02743515372276306,
0.003969206940382719,
-0.0424191951751709,
-0.015069037675857544,
-0.016250070184469223,
0.007003970444202423,
0.03369535505771637,
-0.007883450947701931,
-0.07765863090753555,
0.05539233982563019,
0.011315441690385342,
-0.0335167832672596,
0.048460397869348526,
-0.013020508922636509,
0.017010927200317383,
0.014646857045590878,
-0.02392834797501564,
-0.05369141325354576,
0.035684145987033844,
-0.02339293248951435,
0.01124116312712431,
0.019258340820670128,
0.00046441153972409666,
0.01335492916405201,
0.05029077082872391,
0.013766966760158539,
-0.03088698908686638,
0.0018439540872350335,
-0.055309418588876724,
-0.0018459102138876915,
0.016015738248825073,
-0.004661825485527515,
-0.01009528711438179,
-0.00963998306542635,
0.007953338325023651,
-0.02853046916425228,
0.01179988868534565,
0.010240635834634304,
-0.03391723334789276,
0.000039053131331456825,
-0.04087448492646217,
-0.07073067873716354,
0.03486061096191406,
0.003596117254346609,
-0.002621359657496214,
0.02444123849272728,
-0.044161006808280945,
0.02922630123794079,
0.05002234876155853,
0.05892813578248024,
-0.005836016498506069,
0.06975013762712479,
-0.035632215440273285,
0.04866187274456024,
-0.04132692515850067,
-0.0005208963411860168,
0.12498766928911209,
0.066835917532444,
0.020240111276507378,
-0.038544557988643646,
0.006938749924302101,
0.023429768159985542,
0.024154972285032272,
-0.06794331222772598,
0.018342232331633568,
-0.03414278104901314,
-0.013180533424019814,
-0.004658071789890528,
0.0401991605758667,
-0.022272255271673203,
-0.04158827289938927,
0.035419680178165436,
-0.01971600577235222,
-0.010391220450401306,
-0.005259470548480749,
0.04254348948597908,
-0.020215775817632675,
0.010935697704553604,
-0.019863972440361977,
0.02408577874302864,
-0.006286822725087404,
0.0053454069420695305,
-0.020853407680988312,
-0.027662308886647224,
-0.034356046468019485,
-0.04235736280679703,
-0.0681588277220726,
0.013483717106282711,
0.004889616742730141,
-0.010545032098889351,
-0.017070628702640533,
-0.005118531174957752,
0.029455607756972313,
-0.008055352605879307,
0.01696767471730709,
0.03197229281067848,
-0.025707926601171494,
0.02428499609231949,
0.018927792087197304,
0.031139489263296127,
-0.035612985491752625,
-0.009614365175366402,
-0.01051455456763506,
0.04287795349955559,
-0.03375000134110451,
-0.014965872280299664,
-0.003991150762885809,
-0.025881431996822357,
0.00594646530225873,
-0.01675693690776825,
-0.010607633739709854,
-0.06763169914484024,
0.005023737903684378,
0.042280424386262894,
-0.05118428170681,
0.006912609562277794,
0.02701433002948761,
0.027894647791981697,
0.02665591426193714,
-0.026651086285710335,
0.0216547641903162,
0.01977589540183544,
-0.010437782853841782,
0.0444551557302475,
0.013169396668672562,
-0.002468136604875326,
-0.00839087925851345,
-0.009814362041652203,
-0.04815798997879028,
-0.000014459715202974621,
-0.00412222184240818,
0.013818814419209957,
0.03467279300093651,
0.039373017847537994,
0.014110025018453598,
-0.012690777890384197,
-0.050814609974622726,
0.014240545220673084,
-0.017881806939840317,
-0.03194531425833702,
-0.0023124744184315205,
0.03105800785124302,
-0.021654097363352776,
0.030074741691350937,
0.0026682361494749784,
-0.01642138697206974,
0.01517115905880928,
0.04617965221405029,
-0.0055729118175804615,
-0.003235582262277603,
-0.02541685849428177,
0.0044130608439445496,
0.005395309533923864,
0.014183027669787407,
-0.035122644156217575,
-0.032726168632507324,
0.025493847206234932,
0.008309627883136272,
0.03450074791908264,
0.006028273608535528,
-0.03149937465786934,
-0.004398642107844353,
0.029535066336393356,
-0.024460047483444214,
-0.02035924419760704,
0.01626725308597088,
0.009614828042685986,
-0.055585719645023346,
-0.026002265512943268,
0.010347449220716953,
-0.019217099994421005,
-0.024880753830075264,
0.008830051869153976,
-0.00694635696709156,
0.0009524697088636458,
-0.0194589551538229,
-0.0360233336687088,
-0.03168686851859093,
0.01028650812804699,
-0.0025123427622020245,
0.047167904675006866,
-0.020730283111333847,
-0.017938464879989624,
0.013491667807102203,
0.03568453714251518,
0.013776387088000774,
-0.027654176577925682,
0.018056044355034828,
0.015232749283313751,
-0.025870148092508316,
-0.01225672010332346,
0.03777284547686577,
0.0003658499917946756,
0.026913370937108994,
0.046456921845674515,
-0.025940390303730965,
0.0152316614985466,
-0.024793459102511406,
-0.02489430457353592,
0.03512527421116829,
0.01576473005115986,
0.005197457037866116,
0.03627009689807892,
-0.04076974093914032,
0.007808128371834755,
0.07984297722578049,
0.020028144121170044,
-0.01968347653746605,
0.008609318174421787,
-0.025909576565027237,
0.0111998887732625,
0.005004674196243286,
0.07075859606266022,
-0.018977005034685135,
-0.004457009024918079,
0.023863671347498894,
-0.029973508790135384,
-0.032128021121025085,
-0.008518903516232967,
0.024627236649394035,
-0.03272540494799614,
-0.00995419267565012,
-0.027021799236536026,
-0.01318280678242445,
0.03204111382365227,
0.05005258321762085,
-0.02708289586007595,
0.023026665672659874,
0.03725392371416092,
-0.01702289469540119,
-0.08701085299253464,
-0.01160011813044548,
-0.01490891445428133,
0.029946625232696533,
0.056948695331811905,
-0.029191117733716965,
0.026962433010339737,
0.031026247888803482,
-0.07360547035932541,
0.016976503655314445,
0.00924632977694273,
0.01693734899163246,
-0.031689245253801346,
0.012117828242480755,
-0.040106151252985,
0.009127368219196796,
0.04778356850147247,
0.06534109264612198,
-0.012088718824088573,
0.04479346424341202,
-0.03976030275225639,
-0.02601143904030323,
-0.004450748208910227,
0.03806949406862259,
-0.014649912714958191,
-0.006967255845665932,
0.09062258154153824,
0.00911042932420969,
-0.02539614774286747,
0.019782492890954018,
0.051572903990745544,
-0.015345797874033451,
-0.013012944720685482,
-0.001978891436010599,
-0.028318580240011215,
-0.008846769109368324,
0.010525932535529137,
-0.02247769758105278,
0.03654932975769043,
0.02909046597778797,
0.010311099700629711,
0.022970110177993774,
-0.02612839639186859,
-0.02342342771589756,
0.0007004168001003563,
-0.04647541046142578,
-0.03665194660425186,
0.07132828235626221,
-0.024334879592061043,
-0.015026262030005455,
0.0458863265812397,
0.0049055288545787334,
0.02070396952331066,
-0.01584223099052906,
-0.02152658812701702,
-0.019580835476517677,
0.01145423948764801,
0.031783659011125565,
-0.02435568906366825,
0.0003300691023468971,
0.04346457123756409,
-0.008261284790933132,
-0.014140424318611622,
0.015156395733356476,
-0.026139331981539726,
-0.007940610870718956,
-0.03073917143046856,
0.02805592119693756,
-0.04611140489578247,
0.0025886420626193285,
0.0071878149174153805,
-0.03011219948530197,
-0.02735164389014244,
0.011172572150826454,
0.03288739547133446,
0.004624704364687204,
-0.022729959338903427,
-0.021152935922145844,
-0.02766273356974125,
-0.10988745093345642,
-0.006136511452496052,
0.01815979555249214,
0.002197140594944358,
-0.020966146141290665,
0.002716340124607086,
0.006961756851524115,
0.01249792892485857,
0.07157272100448608,
0.005071309860795736,
-0.006092602852731943,
0.03158304840326309,
-0.015535585582256317,
0.017878880724310875,
-0.028331199660897255,
0.043282583355903625,
0.008070752955973148,
-0.018188605085015297,
0.015562454238533974,
0.014029504731297493,
-0.006005447823554277,
-0.005646813195198774,
0.03745605796575546,
-0.011135418899357319,
0.02853415720164776,
-0.013065547682344913,
-0.0054606543853878975,
0.07722053676843643,
0.013796420767903328,
0.007150112651288509,
0.05187670886516571,
0.002527686534449458,
0.03339824825525284,
0.0400773324072361,
-0.04214072227478027,
-0.0017302751075476408,
0.014137671329081059,
-0.022397151216864586,
-0.03290475159883499,
-0.034305449575185776,
-0.016512306407094002,
0.029156701639294624,
-0.01852632313966751,
-0.012539747171103954,
0.07911691814661026,
-0.02306685596704483,
-0.03651343286037445,
0.044775694608688354,
0.007123937364667654,
0.050525955855846405,
0.011616081930696964,
0.029748134315013885,
-0.009527062997221947,
0.013262837193906307,
-0.008252245374023914,
-0.013209992088377476,
0.06636200100183487,
-0.01972927898168564,
-0.03979790583252907,
0.047794926911592484,
-0.009944099932909012,
0.008449932560324669,
-0.012475556693971157,
0.02107788249850273,
-0.03747938573360443,
-0.01896739937365055,
0.01869056560099125,
-0.005879121366888285,
0.014284602366387844,
0.025158289819955826,
-0.0207966398447752,
0.06719282269477844,
0.006230608560144901,
-0.01079853530973196,
-0.04914434254169464,
-0.021522974595427513,
-0.005475711543112993,
0.05284741520881653,
0.025125859305262566,
0.05805279687047005,
0.018959471955895424,
-0.009674149565398693,
-0.036067407578229904,
-0.01044180803000927,
0.00844410341233015,
-0.012612700462341309,
0.011045482009649277,
0.0562700480222702,
0.011488060466945171,
0.00495446752756834,
-0.028386805206537247,
-0.026277858763933182,
-0.051863886415958405,
-0.0007156521314755082,
-0.010925277136266232,
0.060941021889448166,
-0.030291125178337097,
-0.0002291154523845762,
-0.05204508826136589,
0.04570932686328888,
-0.031915612518787384,
-0.002154777990654111,
-0.012172700837254524,
0.04165346920490265,
-0.007084409240633249,
0.002473849570378661
] |
<p>When an object enters water with high velocity, (like in <a href="http://physics.stackexchange.com/questions/106808/why-jumping-from-high-altitude-into-water-is-fatal">Why is jumping into water from high altitude fatal?</a>), most of it's kinetic energy will be converted, eg to accelerate water, deform the object etc. -<br>
What is the relevance of the surface tension to this? </p>
<p>Are the effects related to surface tension just a small part, or even the dominant part regarding the forces.</p> | 1,990 | [
-0.041043058037757874,
-0.015907788649201393,
-0.042397573590278625,
0.0022359751164913177,
0.00935764703899622,
0.018707331269979477,
-0.023875214159488678,
-0.05061635375022888,
0.03593834117054939,
-0.03653198480606079,
0.024007631465792656,
0.05738948658108711,
0.02939450927078724,
0.03130471706390381,
0.023837409913539886,
-0.004301348701119423,
0.008822525851428509,
-0.045591920614242554,
0.017395561560988426,
0.0021003547590225935,
-0.03199069947004318,
0.006221289746463299,
0.027799641713500023,
0.0071393814869225025,
-0.032436955720186234,
0.0002847839496098459,
0.028749985620379448,
-0.03318101912736893,
0.04796348512172699,
0.022197633981704712,
-0.006283450871706009,
-0.017719559371471405,
0.003030839841812849,
0.008363541215658188,
-0.023984795436263084,
0.0273059643805027,
-0.032054603099823,
-0.03704366087913513,
-0.041259195655584335,
0.030379055067896843,
0.007183449808508158,
-0.025538794696331024,
-0.008342433720827103,
0.06367788463830948,
-0.0355791337788105,
0.028094103559851646,
-0.012708061374723911,
-0.04946884140372276,
0.028711069375276566,
-0.0661686435341835,
0.04465320706367493,
0.0007536537013947964,
0.04536906257271767,
0.035008709877729416,
0.011662120930850506,
-0.0022825042251497507,
0.052012231200933456,
0.08475261181592941,
-0.05928337946534157,
-0.04071878641843796,
-0.01035697665065527,
-0.02231665886938572,
-0.015700314193964005,
-0.00007431117410305887,
-0.016751358285546303,
0.03415285795927048,
-0.027711018919944763,
-0.039472661912441254,
0.050399813801050186,
0.012266765348613262,
-0.01731916330754757,
-0.007715008687227964,
0.024012798443436623,
-0.004203316289931536,
0.016892239451408386,
-0.004686381202191114,
0.03322945907711983,
0.028287198394536972,
0.03381926566362381,
0.08873561769723892,
-0.018633201718330383,
-0.00032156455563381314,
0.03345945104956627,
0.0397818386554718,
0.029947549104690552,
-0.0005662065814249218,
0.07599906623363495,
0.006773189641535282,
0.030516117811203003,
0.032173946499824524,
-0.012521212920546532,
-0.00038785560172982514,
-0.03063778765499592,
-0.00022195983910933137,
-0.026367800310254097,
-0.010080771520733833,
-0.0003470874216873199,
0.07068715989589691,
0.04379117116332054,
-0.019730014726519585,
-0.01212313398718834,
-0.012673242017626762,
0.006062428466975689,
0.061405349522829056,
0.017467956990003586,
-0.02857494167983532,
-0.07607267051935196,
0.0030459538102149963,
-0.028038566932082176,
-0.012793435715138912,
-0.01420295238494873,
-0.023016877472400665,
-0.05164244771003723,
-0.02826712466776371,
-0.0061949146911501884,
-0.019404860213398933,
0.03336535021662712,
0.0012484167236834764,
0.029582588002085686,
0.029704464599490166,
0.05217995494604111,
-0.02954793907701969,
0.008575720712542534,
0.03348306939005852,
-0.04181881248950958,
0.038590870797634125,
0.01849321275949478,
-0.035716600716114044,
-0.01647772267460823,
0.012961316853761673,
-0.0586274228990078,
0.0007036724709905684,
-0.00108229776378721,
0.0011662878096103668,
0.0441843718290329,
-0.020259883254766464,
-0.08876404911279678,
-0.07289734482765198,
0.06826170533895493,
0.008782577700912952,
-0.05033935233950615,
-0.08543933182954788,
0.0036025873851031065,
0.030036699026823044,
0.0670391172170639,
-0.021101966500282288,
0.010817945934832096,
-0.004141293931752443,
0.007330401334911585,
-0.02771672047674656,
-0.01885647512972355,
-0.016689518466591835,
0.03510254994034767,
-0.023795338347554207,
-0.02205107919871807,
-0.05555559694766998,
-0.022284409031271935,
0.05662700906395912,
0.015194418840110302,
-0.0026932174805551767,
0.009641390293836594,
-0.03337078168988228,
0.011509369127452374,
0.011571419425308704,
0.010651716962456703,
-0.029934890568256378,
0.04932946711778641,
0.005212130956351757,
0.03523745387792587,
0.03016609512269497,
0.022546004503965378,
0.034771740436553955,
-0.05402414873242378,
0.018836453557014465,
0.025853123515844345,
-0.004605458118021488,
-0.02497902326285839,
-0.016627706587314606,
0.004972243215888739,
-0.028369957581162453,
-0.02678302489221096,
-0.046223800629377365,
-0.012958558276295662,
0.009351233020424843,
0.00916305836290121,
0.0500679686665535,
0.012484096921980381,
-0.039245735853910446,
-0.030708178877830505,
-0.026621246710419655,
-0.0403083935379982,
-0.06460697948932648,
0.06467119604349136,
-0.03498655557632446,
0.0055632200092077255,
0.0330238863825798,
-0.00982594396919012,
0.006193283945322037,
-0.05569177120923996,
0.013966808095574379,
-0.015094224363565445,
0.027615569531917572,
-0.00420800456777215,
0.0062899659387767315,
0.013831375166773796,
0.02886330336332321,
0.016362300142645836,
-0.018847858533263206,
-0.00859739724546671,
-0.011880757287144661,
-0.0440598800778389,
-0.02038518525660038,
-0.023509522899985313,
0.007491819094866514,
0.0003443346358835697,
-0.0265831109136343,
0.022258872166275978,
0.002162704011425376,
0.003332786727696657,
0.03102412447333336,
-0.040601056069135666,
0.10189682990312576,
0.037699855864048004,
0.0070352256298065186,
-0.002121135126799345,
0.04946403577923775,
0.022251518443226814,
0.000675073591992259,
0.017197230830788612,
-0.005478456150740385,
-0.04386677220463753,
0.001395760802552104,
0.016118261963129044,
0.03860729932785034,
-0.06027988716959953,
-0.0036450561601668596,
0.018219953402876854,
0.02524656057357788,
0.05748062953352928,
0.0021577118895947933,
-0.005896172020584345,
-0.037832699716091156,
0.047854527831077576,
0.021661419421434402,
0.010925387032330036,
0.008971234783530235,
0.00559807475656271,
0.05600748956203461,
0.024348029866814613,
-0.02650389075279236,
0.012872458435595036,
0.02278643473982811,
0.006673235911875963,
0.03179182484745979,
-0.03572464361786842,
-0.016890132799744606,
0.01726769097149372,
-0.038978446274995804,
0.02330741100013256,
0.001214176882058382,
0.032328251749277115,
0.0037768916226923466,
-0.05211431905627251,
-0.03285612165927887,
0.020183827728033066,
0.017370862886309624,
0.00024350594321731478,
0.001111184828914702,
0.024482373148202896,
-0.031687818467617035,
-0.0018691348377615213,
-0.005177145823836327,
-0.029135050252079964,
-0.018287228420376778,
0.020343374460935593,
0.027120081707835197,
-0.01409144327044487,
0.06352218240499496,
-0.024712026119232178,
-0.016049707308411598,
0.017817379906773567,
-0.040334686636924744,
-0.055042680352926254,
-0.004175861831754446,
-0.0585695244371891,
0.00018175174773205072,
-0.03712038695812225,
-0.0364864282310009,
0.05664889141917229,
-0.021761389449238777,
0.00338627933524549,
0.005828181281685829,
0.0002790947910398245,
-0.025498436763882637,
-0.011626414023339748,
-0.028957679867744446,
0.0010381375905126333,
-0.006631392519921064,
-0.009610572829842567,
0.05446757376194,
-0.023495342582464218,
-0.006011949852108955,
0.03360024094581604,
-0.018220342695713043,
-0.05127958953380585,
-0.013516970910131931,
0.005003001075237989,
0.021323461085557938,
-0.021521253511309624,
-0.013568849302828312,
0.040249984711408615,
-0.0676945373415947,
-0.004264833405613899,
-0.06559319794178009,
-0.04463093355298042,
0.020124955102801323,
-0.018464451655745506,
0.024369539692997932,
-0.014587458223104477,
-0.04912412539124489,
0.06270390003919601,
-0.015383325517177582,
-0.049882207065820694,
-0.013060640543699265,
-0.036976709961891174,
-0.005825825035572052,
-0.031135080382227898,
0.0027231117710471153,
0.023135298863053322,
-0.029341569170355797,
0.009143373928964138,
0.023553354665637016,
0.02347497083246708,
0.017601223662495613,
-0.010619642212986946,
-0.005161617882549763,
0.006133855786174536,
0.037599559873342514,
0.0217230636626482,
0.020776383578777313,
0.015448721125721931,
-0.02036658115684986,
0.01971209980547428,
-0.004000938963145018,
0.012751530855894089,
0.04171079397201538,
-0.03666489198803902,
0.08204003423452377,
0.002196928719058633,
-0.013071867637336254,
-0.03493786230683327,
0.02581866830587387,
-0.01610897108912468,
-0.014364433474838734,
0.047677330672740936,
0.01588008552789688,
0.06903007626533508,
-0.021902773529291153,
-0.0008765393286012113,
0.024427929893136024,
0.08126487582921982,
-0.021946795284748077,
-0.04947691783308983,
-0.004550374578684568,
-0.0042145769111812115,
0.02665809914469719,
-0.020599018782377243,
0.017528187483549118,
0.03982451930642128,
0.0005342831136658788,
0.016921892762184143,
-0.015108245424926281,
-0.04301426187157631,
0.0033427823800593615,
-0.06702261418104172,
-0.0033453986980021,
0.003641407936811447,
0.05950295180082321,
-0.01446606032550335,
0.07798091322183609,
0.025510339066386223,
0.0382097028195858,
0.017905380576848984,
0.042124200612306595,
-0.0710740014910698,
0.008203751407563686,
-0.03767848387360573,
-0.017479706555604935,
-0.0019474400905892253,
-0.01701410487294197,
0.006129443179816008,
-0.0537579171359539,
-0.04449077695608139,
-0.011982128024101257,
0.023104574531316757,
-0.049649301916360855,
0.03202399984002113,
-0.019775189459323883,
-0.016147589311003685,
-0.03126369044184685,
0.02788263000547886,
0.025306686758995056,
-0.006061187945306301,
0.022874724119901657,
0.04747382923960686,
-0.03985214978456497,
0.0029203605372458696,
0.01321951299905777,
0.014087350107729435,
0.004792190156877041,
0.032337646931409836,
-0.0008161186124198139,
-0.007794860750436783,
0.022932225838303566,
0.024807656183838844,
0.005503438878804445,
0.03472854197025299,
-0.03284885734319687,
0.020524093881249428,
-0.030299725010991096,
-0.08322960883378983,
-0.010296864435076714,
-0.016057634726166725,
0.03814370185136795,
0.009100648574531078,
-0.0309844221919775,
-0.010115671902894974,
-0.0033424561843276024,
-0.022724755108356476,
0.09704795479774475,
0.06200753152370453,
0.026016084477305412,
-0.021300604566931725,
-0.038225214928388596,
0.004524133168160915,
-0.035133130848407745,
-0.02095995470881462,
0.0144283352419734,
0.022747177630662918,
-0.042049963027238846,
0.024552103132009506,
0.028178244829177856,
-0.004402798600494862,
-0.016134291887283325,
-0.020013784989714622,
0.017790410667657852,
0.03709988296031952,
-0.029051775112748146,
0.015050696209073067,
0.005207496229559183,
0.008316821418702602,
0.04933784529566765,
-0.0036417238879948854,
0.012728196568787098,
-0.06705903261899948,
-0.035722050815820694,
0.03642961382865906,
0.0300307534635067,
-0.021684223785996437,
-0.005925368517637253,
-0.05033178627490997,
-0.005290630739182234,
0.03249836340546608,
-0.03391961008310318,
0.0071314661763608456,
-0.02734088897705078,
0.025398243218660355,
-0.017852842807769775,
-0.0032025768887251616,
-0.010325204581022263,
0.0069150738418102264,
0.006013643927872181,
0.05042789503931999,
-0.04763782024383545,
-0.0010132682509720325,
0.01612631417810917,
0.018910538405179977,
0.013130828738212585,
0.06212697550654411,
0.003318238537758589,
-0.020802924409508705,
-0.012921265326440334,
-0.013294655829668045,
-0.06025487929582596,
-0.050343483686447144,
0.02574239857494831,
-0.020815536379814148,
0.015549601055681705,
0.03192789480090141,
-0.022010311484336853,
-0.04525758698582649,
0.039687108248472214,
0.027911879122257233,
-0.01955009251832962,
0.01287094783037901,
-0.025934983044862747,
0.034824568778276443,
0.057688117027282715,
-0.009818223305046558,
0.010646128095686436,
0.03380274400115013,
-0.05615764856338501,
-0.03419433906674385,
-0.009234778583049774,
0.036746710538864136,
-0.030655398964881897,
-0.03227565065026283,
-0.023880610242486,
-0.00019989356223959476,
-0.03832468390464783,
0.02125660702586174,
-0.028640875592827797,
0.011955111287534237,
-0.007360473275184631,
-0.02385150082409382,
-0.030997682362794876,
-0.0014272236730903387,
0.03588198125362396,
-0.028462672606110573,
0.03266782686114311,
0.016181455925107002,
0.0065291812643408775,
0.017769986763596535,
0.020242031663656235,
0.018951835110783577,
-0.004135969094932079,
0.031555574387311935,
0.0014554939698427916,
0.0028980725910514593,
-0.0013047786196693778,
-0.020524607971310616,
0.03514964506030083,
-0.06045227870345116,
0.045724693685770035,
-0.014063116163015366,
-0.012461104430258274,
0.03360283374786377,
-0.029146114364266396,
0.003990402910858393,
0.020470958203077316,
-0.017347929999232292,
0.04358389228582382,
-0.01616617664694786,
0.07364521920681,
0.014971916563808918,
0.02824360877275467,
-0.04407039284706116,
-0.04708385095000267,
0.0688810795545578,
0.03571878373622894,
0.003829301567748189,
-0.016115987673401833,
0.014375172555446625,
-0.04474911838769913,
-0.019023729488253593,
0.0014848666032776237,
0.02104318141937256,
-0.05606155842542648,
0.002104003680869937,
0.03467359393835068,
0.015231708064675331,
0.048337168991565704,
0.00890229269862175,
-0.006548801902681589,
0.020460879430174828,
-0.0241615679115057,
-0.029794149100780487,
-0.03551415726542473,
0.060270048677921295,
-0.007605738006532192,
-0.006359600927680731,
0.02703278511762619,
-0.01575981266796589,
0.0403595045208931,
0.008771763183176517,
0.011593645438551903,
0.01856284961104393,
0.04108942672610283,
0.00490629393607378,
-0.011227309703826904,
0.016464712098240852,
0.022032251581549644,
0.06560161709785461,
0.019193029031157494,
0.006187195889651775,
-0.03867735341191292,
-0.017943378537893295,
0.01691622845828533,
-0.012848356738686562,
0.012565337121486664,
-0.012819821015000343,
0.06911837309598923,
-0.05013757199048996,
0.003991335164755583,
-0.007433876860886812,
-0.018027184531092644,
0.05870647728443146,
0.010816587135195732,
-0.01882229931652546,
0.043573517352342606,
0.022811319679021835,
-0.012785269878804684,
-0.05623969808220863,
-0.03119697980582714,
0.023969141766428947,
0.07108093798160553,
-0.04236733168363571,
0.04104841127991676,
0.01045981515198946,
-0.01723581925034523,
0.01914873719215393,
-0.026631247252225876,
-0.014631443656980991,
-0.0028422395698726177,
-0.00977878924459219,
0.007975622080266476,
-0.02134675718843937,
0.008500821888446808,
0.017424460500478745,
0.033974211663007736,
-0.020261293277144432,
0.04226573184132576,
0.04061916470527649,
0.017953891307115555,
0.024987418204545975,
-0.022352799773216248,
-0.03613130748271942,
0.033203668892383575,
-0.03252611681818962,
0.04963487759232521,
-0.011963392607867718,
-0.014200232923030853,
0.04478289932012558,
0.021122515201568604,
0.031054945662617683,
-0.05873990058898926,
0.006886988878250122,
0.012990232557058334,
0.015315472148358822,
-0.01777675189077854,
-0.0022406750358641148,
-0.011549429967999458,
0.009145010262727737,
0.029724039137363434,
-0.00952405110001564,
0.0034257585648447275,
-0.03079046681523323,
-0.0677589401602745,
-0.023961901664733887,
-0.03820062801241875,
-0.034710757434368134,
0.007227086927741766,
0.006853195372968912,
-0.04309936240315437,
0.024949289858341217,
-0.029431719332933426,
0.0433107428252697,
-0.011054262518882751,
0.027044272050261497,
-0.03223609924316406,
0.05798766762018204,
-0.01043535117059946,
0.02939324826002121,
-0.00022016552975401282,
0.026646340265870094,
0.10884658992290497,
0.06467704474925995,
0.008783986791968346,
-0.02388540655374527,
-0.005090081132948399,
0.007425200194120407,
0.01965450309216976,
-0.02230685204267502,
-0.025137344375252724,
0.009824510663747787,
0.010899685323238373,
0.006165101192891598,
0.04875190183520317,
-0.002748460741713643,
0.010337970219552517,
0.011364942416548729,
-0.0772700384259224,
-0.026399334892630577,
-0.017873134464025497,
0.011668624356389046,
-0.032959945499897,
0.03715326637029648,
-0.03541559725999832,
0.02142244763672352,
-0.016894761472940445,
0.006251796148717403,
-0.03341794013977051,
-0.03553014248609543,
0.015270783565938473,
0.019062496721744537,
-0.04195446893572807,
-0.010603169910609722,
-0.004164784215390682,
-0.0019254663493484259,
-0.06014818698167801,
0.034375958144664764,
0.03309660404920578,
-0.008014841936528683,
-0.014990267343819141,
0.022120481356978416,
0.023245904594659805,
0.005971727427095175,
0.0016507669351994991,
0.036154605448246,
-0.06336236000061035,
-0.004919610917568207,
-0.03451145067811012,
0.04937222599983215,
-0.025337258353829384,
0.0008768546395003796,
-0.04996350407600403,
-0.04025375470519066,
0.00941312126815319,
-0.03476543352007866,
-0.02540915459394455,
-0.023736780509352684,
0.03409631922841072,
0.0040162005461752415,
-0.03517650067806244,
-0.026457177475094795,
0.030402204021811485,
-0.024496180936694145,
0.01736563630402088,
-0.007604449987411499,
-0.0043581388890743256,
-0.029751267284154892,
-0.00875566340982914,
0.01772625930607319,
-0.03842373192310333,
-0.00485820509493351,
-0.00993366725742817,
-0.02114095352590084,
-0.0713135376572609,
-0.034767478704452515,
0.002475671237334609,
0.038406938314437866,
0.0416889414191246,
0.0052362908609211445,
0.008577539585530758,
-0.02603035420179367,
-0.04386458173394203,
0.06456200033426285,
-0.03370416536927223,
-0.021565014496445656,
-0.05523668974637985,
0.012940905056893826,
0.009659860283136368,
0.028493380174040794,
-0.015384145081043243,
0.010366253554821014,
-0.018828272819519043,
0.018279945477843285,
-0.0014888294972479343,
-0.009846208617091179,
-0.048090238124132156,
-0.01744708977639675,
-0.006420906167477369,
0.016221746802330017,
0.010849591344594955,
0.024161988869309425,
0.016466068103909492,
0.0004240149282850325,
0.0293597225099802,
0.015132605098187923,
-0.017001600936055183,
0.01695987395942211,
0.01266244426369667,
-0.011223141103982925,
-0.03556979447603226,
0.014911222271621227,
0.008237934671342373,
0.014143413864076138,
0.011061570607125759,
-0.03173679858446121,
0.0014576178509742022,
0.008577651344239712,
0.03668318688869476,
-0.00534126115962863,
0.033487264066934586,
-0.03339950740337372,
0.05420347675681114,
-0.04091271385550499,
-0.031087521463632584,
-0.07425606995820999,
0.010473393835127354,
0.021723048761487007,
-0.0007621421245858073,
-0.015610569156706333,
0.009238218888640404,
-0.06219757720828056,
0.0025196897331625223,
-0.02444007806479931,
0.001351047889329493,
-0.017560843378305435,
-0.010582857765257359,
0.043761979788541794,
-0.017494777217507362,
0.03609851747751236,
-0.019863849505782127,
-0.055865488946437836,
0.04190149903297424,
-0.033934641629457474,
-0.024664252996444702,
0.016868824139237404,
-0.028495458886027336,
0.04432467371225357,
0.04307669401168823,
-0.008308454416692257,
-0.03384503349661827,
0.08053457736968994,
-0.002538274507969618,
0.026731522753834724,
0.01395783107727766,
-0.04372532665729523,
-0.021297335624694824,
-0.013819510117173195,
0.017502665519714355,
-0.0010876170126721263,
0.015469243749976158,
0.03786122053861618,
0.01030786894261837,
0.008749561384320259,
0.0024349254090338945,
0.03538531810045242,
-0.016063254326581955,
0.0038258680142462254,
0.028798198327422142,
-0.0021885307505726814,
0.05453740060329437,
0.03586551547050476,
-0.033157043159008026,
0.01247615646570921,
-0.0030448674224317074,
-0.0004596270155161619,
-0.09148455411195755,
-0.00895818043500185,
-0.021449008956551552,
0.038281191140413284,
0.038457296788692474,
-0.05363259091973305,
0.004846084397286177,
0.041607338935136795,
-0.088498555123806,
0.004490996245294809,
-0.016219694167375565,
0.01973409205675125,
-0.012674122117459774,
-0.007624889258295298,
-0.0073960949666798115,
0.06489625573158264,
-0.006012837868183851,
0.030568212270736694,
0.010636378079652786,
0.014369234442710876,
0.014283973723649979,
0.004240626003593206,
-0.021671149879693985,
0.027717309072613716,
-0.01717359572649002,
-0.01510366890579462,
0.09192987531423569,
-0.0028257793746888638,
-0.016570836305618286,
-0.01669570617377758,
-0.018928417935967445,
0.02595530077815056,
0.03740568831562996,
-0.009765745140612125,
0.009937030263245106,
0.015640094876289368,
0.0072542945854365826,
-0.024849513545632362,
-0.012514687143266201,
0.03419753909111023,
0.011185570620000362,
0.023318462073802948,
0.029011106118559837,
0.00007893862493801862,
0.011791608296334743,
-0.0440918430685997,
-0.03499726206064224,
0.030712183564901352,
-0.037874821573495865,
-0.016636617481708527,
0.008537148125469685,
-0.0220477394759655,
0.0580722838640213,
-0.010715234093368053,
-0.025008706375956535,
-0.028306765481829643,
-0.011006467044353485,
0.03373025357723236,
-0.004224651493132114,
-0.002789753954857588,
0.04968562722206116,
-0.0037376529071480036,
0.005034528207033873,
-0.025597603991627693,
-0.01809946820139885,
-0.010023851878941059,
-0.046714480966329575,
0.004755368921905756,
0.008601352572441101,
-0.03815305233001709,
-0.022929152473807335,
-0.019061293452978134,
-0.033073291182518005,
0.033787257969379425,
0.03773878887295723,
0.015018794685602188,
0.010734779760241508,
-0.05958482623100281,
-0.037141088396310806,
-0.08651553094387054,
0.023046141490340233,
0.0042403326369822025,
-0.02982553094625473,
-0.03442676365375519,
0.003736877581104636,
0.036824196577072144,
0.03330406919121742,
0.049713656306266785,
-0.013237102888524532,
-0.007236698176711798,
0.040867552161216736,
-0.01032962091267109,
0.0001708152994979173,
-0.009542061015963554,
-0.021585237234830856,
-0.0032850108109414577,
-0.04417852684855461,
0.03142677620053291,
0.022601447999477386,
0.015724744647741318,
-0.00017054524505510926,
0.009090917184948921,
-0.011441275477409363,
0.015140796080231667,
-0.0018960281740874052,
-0.0007745940238237381,
0.03144179284572601,
0.016715819016098976,
-0.016192946583032608,
0.0826856717467308,
0.004294310696423054,
0.03109203651547432,
0.006729691755026579,
-0.04013940691947937,
-0.025137919932603836,
0.031006162986159325,
-0.018534699454903603,
0.005493115168064833,
0.014311941340565681,
-0.044526100158691406,
-0.003424467286095023,
-0.047871626913547516,
0.04518648609519005,
0.01794440858066082,
-0.032322730869054794,
-0.01678398624062538,
0.07342428714036942,
0.06338818371295929,
0.010683954693377018,
0.00544771458953619,
0.01227246131747961,
0.03195831552147865,
-0.008845852687954903,
-0.009658858180046082,
0.04773334786295891,
0.06962916254997253,
0.008194000460207462,
-0.009515081532299519,
0.009690504521131516,
0.00409937696531415,
0.007627061102539301,
0.04784226790070534,
-0.016623862087726593,
-0.002505715936422348,
-0.05194908380508423,
0.004758941475301981,
0.004186895675957203,
0.014173860661685467,
0.01764035038650036,
-0.01262211799621582,
0.06443241238594055,
-0.005106992553919554,
0.012196620926260948,
-0.014460834674537182,
-0.007869738154113293,
0.0004095237818546593,
0.02248961664736271,
0.018193526193499565,
0.048538561910390854,
0.005976125132292509,
-0.03972605988383293,
-0.021950678899884224,
0.014250091277062893,
-0.015331043861806393,
0.0073225912638008595,
0.03316820040345192,
-0.009883888997137547,
0.013373449444770813,
-0.009020854718983173,
-0.027331121265888214,
-0.00785829871892929,
-0.02076737768948078,
0.027348827570676804,
0.03379742428660393,
0.02594231627881527,
0.020584385842084885,
-0.030875269323587418,
-0.03430131822824478,
0.044772807508707047,
-0.06443974375724792,
-0.013422106392681599,
0.013492206111550331,
0.028740517795085907,
-0.006816727574914694,
-0.012142360210418701
] |
<p>This post relates to <a href="http://physics.stackexchange.com/questions/71526/problems-with-putting-mass-on-yang-mills-theory-by-hand">this previous one</a>. My question is, what is the actual meaning of a theory being renormalizable?</p>
<p>There might be at-least two possibilities (correct me if I am wrong)</p>
<p><strong>1.Power-counting renormalizable</strong></p>
<p>If I understood correctly, the BHPZ theorem guarantees that all superficial divergences for a power-counting-renormalizable theory can be absorbed by counter terms. Formally, it might be possible that a counter term is outside the form of the Lagrangian.</p>
<p><strong>2.Stronger than power-counting renormalizable</strong></p>
<p>The counter term be produced from the original Lagrangian, such as QED. We need to look at all possible divergence explicitly and show how to regularize and renormalize them.</p>
<p><strong>(3. Any further possibility from non-perturbative aspect (I don't know))</strong></p>
<p>This problem also relates to 't Hooft and Veltman's achievement of proving Yang-Mills theory with Higgs mechanism is renormalizable. It cannot simply be power counting.</p>
<p>When people say a theory is renormalizable, what does it mean? Meaning 1 or 2? Is this distinction important? </p> | 1,991 | [
-0.006603395100682974,
0.009842123836278915,
0.02598879300057888,
-0.028642185032367706,
0.0054104868322610855,
0.015919459983706474,
-0.0162984486669302,
-0.013141830451786518,
0.01652183197438717,
-0.05324329808354378,
0.029354672878980637,
-0.004635654389858246,
0.07909782975912094,
0.01633988320827484,
0.013165134936571121,
-0.0055413623340427876,
0.008948219008743763,
-0.0018613922875374556,
-0.0128781758248806,
-0.02143963612616062,
-0.018008330836892128,
0.03880181163549423,
-0.023634998127818108,
0.020751668140292168,
-0.02482348307967186,
-0.01658080704510212,
-0.0035810391418635845,
0.05539044365286827,
-0.031094878911972046,
0.06092846393585205,
-0.00875370018184185,
-0.020228996872901917,
0.04935188218951225,
0.012898602522909641,
0.011079561896622181,
0.0324714258313179,
-0.025541415438055992,
-0.04055454209446907,
-0.005269607529044151,
-0.013901781290769577,
-0.04187273606657982,
-0.014548742212355137,
0.002868414158001542,
0.03853261098265648,
-0.031115932390093803,
0.009467750787734985,
-0.02602137252688408,
-0.030915632843971252,
0.078362837433815,
-0.06560568511486053,
0.03431887552142143,
0.05408266559243202,
0.03213893249630928,
0.027304217219352722,
-0.006706285756081343,
-0.034208253026008606,
0.05167993903160095,
0.08084331452846527,
0.007327317725867033,
-0.03358442336320877,
-0.040552977472543716,
-0.01620454527437687,
0.015403987839818,
-0.009150185622274876,
-0.04216642677783966,
0.06734565645456314,
0.009464597329497337,
0.008237659931182861,
0.03800129517912865,
-0.027355888858437538,
0.023975064978003502,
-0.010146712884306908,
0.0568673200905323,
-0.014289365150034428,
0.03323441743850708,
0.013899927958846092,
-0.008538768626749516,
-0.013967500068247318,
0.0008407107670791447,
0.06671059131622314,
-0.015289230272173882,
0.019585929811000824,
0.023740319535136223,
0.040489476174116135,
-0.02734159305691719,
-0.012475036084651947,
0.06587658822536469,
0.022777916863560677,
-0.004298676736652851,
0.046990904957056046,
-0.0031662608962506056,
-0.004407939501106739,
0.04603048786520958,
-0.023011591285467148,
-0.02014739252626896,
0.03353465721011162,
0.004512713756412268,
0.058202993124723434,
-0.007261602208018303,
0.02174224518239498,
-0.024340400472283363,
-0.02918456867337227,
0.03459805250167847,
0.053768232464790344,
-0.016380345448851585,
0.005756259895861149,
-0.01710178330540657,
-0.02259325608611107,
-0.03914700075984001,
-0.03852922096848488,
-0.041623249650001526,
0.011301877908408642,
-0.04219203442335129,
-0.057492513209581375,
-0.010400515981018543,
-0.04319768399000168,
-0.018409034237265587,
-0.012383799999952316,
0.08738049119710922,
0.07714039087295532,
0.007617495954036713,
0.004179839976131916,
0.02517249435186386,
-0.04999397695064545,
-0.045797597616910934,
0.018188608810305595,
0.05038181692361832,
-0.028001105412840843,
-0.03699110820889473,
0.016341760754585266,
0.02975369244813919,
-0.016459982842206955,
0.008538154885172844,
-0.0010393219999969006,
0.03793568164110184,
-0.06031195446848869,
-0.11129588633775711,
-0.05654660239815712,
0.042780131101608276,
-0.0015289480797946453,
-0.028691183775663376,
-0.05898148566484451,
0.016020100563764572,
0.021247299388051033,
0.09315501153469086,
-0.015572501346468925,
0.018514711409807205,
0.0038578943349421024,
0.031957320868968964,
0.0024697312619537115,
-0.014906455762684345,
0.00016775995027273893,
0.006151048466563225,
-0.020574092864990234,
-0.03779371455311775,
-0.07755375653505325,
0.01959322951734066,
0.03154634311795235,
-0.023170216009020805,
-0.01772797480225563,
0.07397861778736115,
-0.013727877289056778,
0.02004190720617771,
0.00794186256825924,
0.005516084376722574,
0.004162210039794445,
0.04923059046268463,
0.00652542058378458,
0.037331290543079376,
0.058541957288980484,
0.029447020962834358,
0.025424087420105934,
-0.022547518834471703,
0.01748792640864849,
0.04738976061344147,
-0.04001179710030556,
-0.01568138226866722,
-0.035365451127290726,
0.00035954988561570644,
0.004725539591163397,
-0.010930457152426243,
-0.017128784209489822,
-0.025899643078446388,
0.020128527656197548,
-0.0042653921991586685,
-0.007013374008238316,
0.005874438676983118,
0.005468540359288454,
0.047835614532232285,
-0.020807890221476555,
-0.02563493140041828,
-0.06574857234954834,
0.011340011842548847,
0.003816284006461501,
-0.010374796576797962,
0.03441179171204567,
-0.034639064222574234,
-0.006038469262421131,
-0.04493347182869911,
-0.021490084007382393,
0.009571574628353119,
0.048599086701869965,
0.028806546702980995,
0.03524534031748772,
0.007133664563298225,
0.011460988782346249,
0.034154731780290604,
-0.007981820032000542,
0.08815263956785202,
-0.002879456151276827,
-0.0403064601123333,
-0.008640375919640064,
-0.0134994862601161,
-0.00035846917307935655,
-0.020564913749694824,
0.001468713628128171,
0.0019236106891185045,
0.0010926335817202926,
-0.006368250120431185,
0.050295911729335785,
-0.016146276146173477,
0.056643761694431305,
0.030620770528912544,
0.0011148062767460942,
-0.008854134008288383,
0.021152885630726814,
-0.027714373543858528,
0.01712776906788349,
-0.03094824030995369,
-0.0035296594724059105,
-0.04274367541074753,
0.0025845493655651808,
0.03297501057386398,
0.030061297118663788,
-0.027991585433483124,
0.031696565449237823,
0.03707995265722275,
0.009365023113787174,
0.03281857818365097,
0.027462348341941833,
-0.022402672097086906,
-0.011300722137093544,
0.02935617044568062,
0.016652043908834457,
0.005918077193200588,
0.013370012864470482,
0.005830004345625639,
0.008809074759483337,
0.004484820645302534,
0.0015525933122262359,
-0.03456158936023712,
0.03904919698834419,
-0.013438740745186806,
-0.016826055943965912,
-0.019612736999988556,
-0.021359829232096672,
0.025826066732406616,
0.004282376263290644,
0.08277612179517746,
0.01694394089281559,
-0.018506471067667007,
-0.0003324946155771613,
-0.029739273712038994,
-0.02916441485285759,
0.01321554183959961,
0.010095681063830853,
-0.03456616774201393,
-0.024585196748375893,
0.010709628462791443,
-0.03949655592441559,
0.003472554497420788,
-0.03784555941820145,
0.0005227994406595826,
-0.02567235939204693,
0.021294068545103073,
0.022700877860188484,
-0.014615263789892197,
0.058089759200811386,
-0.047263260930776596,
-0.01615346036851406,
0.03059772402048111,
-0.005118971690535545,
-0.0028278084937483072,
0.026583248749375343,
-0.02775738574564457,
-0.024853095412254333,
-0.07866964489221573,
-0.01774289272725582,
0.027548974379897118,
0.0017204518662765622,
0.039019037038087845,
-0.007764981593936682,
0.00949232280254364,
-0.039395805448293686,
-0.0020594666711986065,
-0.03539435565471649,
0.027304716408252716,
0.0020096455700695515,
-0.018666038289666176,
0.05905991792678833,
0.031701844185590744,
-0.04906341806054115,
0.024449113756418228,
0.01288137212395668,
-0.049206074327230453,
-0.01454242318868637,
0.02069847099483013,
0.01192221324890852,
-0.02255764789879322,
0.05790381506085396,
0.02126297727227211,
-0.047626957297325134,
0.022056732326745987,
-0.04396977648139,
-0.03960111737251282,
0.013411181047558784,
0.016958022490143776,
0.03062940202653408,
0.007230762857943773,
-0.07426478713750839,
0.07816097885370255,
0.046373020857572556,
-0.048114143311977386,
-0.011325627565383911,
0.021990764886140823,
-0.006773764733225107,
-0.012095419690012932,
-0.015655390918254852,
0.01113792322576046,
-0.001588132930919528,
0.017042947933077812,
0.014460740610957146,
0.03508973866701126,
0.019395960494875908,
0.008591634221374989,
-0.01320408284664154,
0.02320864610373974,
0.03453381732106209,
0.004411282483488321,
0.04749833792448044,
0.003015401540324092,
-0.01289312168955803,
0.014049642719328403,
-0.005554096773266792,
0.020274952054023743,
0.0005870808381587267,
-0.05555429309606552,
0.05539848282933235,
0.018476158380508423,
0.016040289774537086,
-0.014812479726970196,
0.06061394512653351,
0.018693523481488228,
-0.06363458186388016,
0.018502525985240936,
0.015061615966260433,
0.009474401362240314,
-0.037918951362371445,
-0.011752216145396233,
0.010846703313291073,
0.08268232643604279,
-0.03449157625436783,
-0.029980678111314774,
-0.05498450994491577,
-0.0005321794888004661,
0.018645567819476128,
-0.02152462862432003,
-0.016733506694436073,
0.022502901032567024,
0.031028911471366882,
0.0074101705104112625,
-0.00398781755939126,
-0.030347926542162895,
-0.012879688292741776,
-0.0941244512796402,
0.024386797100305557,
-0.028836658224463463,
0.05268753692507744,
-0.027408799156546593,
0.03703576326370239,
0.008843899704515934,
0.0009377120877616107,
0.006920264568179846,
0.00002029779898293782,
-0.06637127697467804,
0.04133804142475128,
-0.03206125274300575,
-0.0422356091439724,
0.014693991281092167,
0.003693909151479602,
0.02530614472925663,
-0.00411539850756526,
-0.04494162276387215,
-0.029251236468553543,
0.004671978298574686,
-0.06166769936680794,
0.01615809090435505,
-0.04914836212992668,
-0.0281066931784153,
0.006825583986938,
-0.013266501948237419,
0.06731028854846954,
-0.035980820655822754,
0.018743444234132767,
0.029415549710392952,
-0.06320564448833466,
-0.0256713405251503,
-0.01194934081286192,
0.019734695553779602,
-0.009672130458056927,
0.025802619755268097,
0.03820699825882912,
0.05996739864349365,
-0.021252378821372986,
-0.020309574902057648,
0.0620897077023983,
0.05102108046412468,
0.018086768686771393,
0.012259174138307571,
-0.006360998842865229,
-0.054286256432533264,
-0.028446566313505173,
0.021244578063488007,
0.06859884411096573,
0.012959799729287624,
0.008298775181174278,
0.033269356936216354,
0.020481370389461517,
-0.007577316835522652,
0.009117268025875092,
0.037263691425323486,
0.00439504673704505,
-0.020836345851421356,
-0.08384156972169876,
0.01308329589664936,
0.011150219477713108,
-0.005442843772470951,
0.0038485799450427294,
0.01518019288778305,
0.005140496883541346,
-0.006710236892104149,
0.012976917438209057,
0.014885385520756245,
-0.01626509800553322,
0.023505955934524536,
0.00019252902711741626,
0.02007397823035717,
0.0022360056173056364,
0.0032816887833178043,
-0.01876460388302803,
0.029916411265730858,
0.05460597947239876,
0.013324027881026268,
-0.00717162387445569,
-0.04184604808688164,
-0.012297958135604858,
0.05538732185959816,
0.06538857519626617,
0.0005624797195196152,
0.015424506738781929,
-0.01216136198490858,
-0.02529224008321762,
0.021314546465873718,
-0.022056235000491142,
0.04017958045005798,
-0.035922009497880936,
-0.020811710506677628,
0.004333161283284426,
-0.01721087284386158,
-0.014625562354922295,
0.02621709182858467,
-0.016472868621349335,
0.0008046041475608945,
-0.02008197270333767,
0.008894735015928745,
-0.03865087777376175,
-0.011819620616734028,
0.0032994630746543407,
0.0436023585498333,
0.0027532665990293026,
0.03589776158332825,
-0.009958363138139248,
0.01508458610624075,
-0.028691358864307404,
-0.0945003479719162,
-0.0035642613656818867,
0.02171100303530693,
-0.07126672565937042,
0.021999450400471687,
-0.07511327415704727,
-0.047560449689626694,
0.019699577242136,
-0.005581336561590433,
-0.038128986954689026,
0.006734082475304604,
-0.07741466909646988,
0.03465352952480316,
0.06353005021810532,
0.0038432737346738577,
0.06336803734302521,
0.05085508152842522,
0.015901852399110794,
0.01864396221935749,
0.013818740844726562,
-0.018803246319293976,
-0.003761571366339922,
0.0046054827980697155,
-0.05123234540224075,
-0.0019325847970321774,
-0.05729174241423607,
0.056636061519384384,
0.009121790528297424,
-0.003678011940792203,
-0.011979194357991219,
-0.021660348400473595,
0.0027857415843755007,
0.029611941426992416,
0.010147787630558014,
-0.017796948552131653,
-0.010246925055980682,
0.043530650436878204,
0.01015776302665472,
-0.004645098932087421,
0.043912243098020554,
0.016864709556102753,
0.003914272412657738,
0.04721757397055626,
0.005240068770945072,
-0.004661968909204006,
0.005030529107898474,
0.01846894808113575,
0.0004919841303490102,
-0.02103203721344471,
0.028735268861055374,
-0.004144643433392048,
-0.0021853316575288773,
-0.019550859928131104,
-0.04201732948422432,
-0.0565253421664238,
-0.01560756005346775,
-0.013237636536359787,
0.008323612622916698,
-0.02777586504817009,
0.03258253261446953,
0.007874546572566032,
-0.011857721023261547,
-0.07480047643184662,
-0.047282904386520386,
-0.004928630776703358,
0.03786768019199371,
-0.02083268202841282,
0.011205058544874191,
-0.024922184646129608,
-0.026218118146061897,
-0.04428229480981827,
-0.05050801858305931,
0.04821988195180893,
-0.05790921673178673,
0.009785889647901058,
0.027702271938323975,
0.0576179139316082,
0.001833409070968628,
-0.03184279054403305,
-0.022000471130013466,
0.015645144507288933,
-0.024100475013256073,
-0.000906109344214201,
0.000521710142493248,
0.028657639399170876,
-0.03798586502671242,
-0.03488117456436157,
-0.014075875282287598,
-0.006351820658892393,
0.032375697046518326,
-0.013340143486857414,
-0.020891498774290085,
0.03060656413435936,
-0.02230924740433693,
-0.006805889308452606,
-0.04256856441497803,
-0.010492006316781044,
0.015244612470269203,
0.056104883551597595,
-0.002846700372174382,
0.022060180082917213,
0.008156733587384224,
-0.019487867131829262,
0.04990783706307411,
0.0005905804573558271,
-0.005025808699429035,
-0.009487511590123177,
0.018341530114412308,
-0.0025783211458474398,
0.013715192675590515,
0.023622777312994003,
-0.015913503244519234,
0.029915083199739456,
0.010856128297746181,
0.0589166022837162,
-0.01125891599804163,
0.004532057326287031,
-0.05112726613879204,
-0.01927105523645878,
-0.029393969103693962,
0.026236774399876595,
0.06291773915290833,
0.010890918783843517,
0.040254078805446625,
-0.006251474376767874,
-0.035463299602270126,
0.01693732477724552,
-0.014614715240895748,
-0.00640829186886549,
0.009253311902284622,
0.007838168181478977,
0.055265266448259354,
-0.03443596512079239,
-0.010990045964717865,
0.03839811310172081,
0.05256213992834091,
0.007406536024063826,
0.027100825682282448,
0.06501640379428864,
0.013196513056755066,
0.01533652376383543,
0.01782180555164814,
-0.02954033948481083,
0.053120166063308716,
-0.017410369589924812,
0.01902824640274048,
-0.0031130188144743443,
-0.012622233480215073,
0.057541050016880035,
0.0016211775364354253,
0.011999838054180145,
-0.014319048263132572,
-0.041903164237737656,
-0.06049497798085213,
0.004344923421740532,
-0.02644670195877552,
0.027923045679926872,
0.00927753932774067,
-0.025496922433376312,
0.0050781527534127235,
-0.0014454235788434744,
0.021616628393530846,
0.0005680673057213426,
-0.06298705190420151,
-0.009700492955744267,
-0.03967296704649925,
-0.050869327038526535,
0.03688054904341698,
-0.013743880204856396,
-0.03050977550446987,
-0.002352851675823331,
-0.03312477841973305,
0.004778753034770489,
-0.015331254340708256,
0.05688435956835747,
-0.035184748470783234,
0.034619420766830444,
-0.008282791823148727,
0.026581501588225365,
-0.016818080097436905,
0.010984715074300766,
0.10980691015720367,
0.08016930520534515,
0.014973028562963009,
-0.05980728566646576,
0.00705418037250638,
-0.02156859263777733,
0.02238953299820423,
-0.06240270659327507,
0.039001960307359695,
-0.024305453523993492,
0.0060996729880571365,
0.013101927004754543,
0.10050205141305923,
0.0132481399923563,
-0.022548353299498558,
0.06668821722269058,
-0.03523164615035057,
-0.0400562658905983,
0.02866920828819275,
0.005064844619482756,
-0.030051453039050102,
-0.012473884969949722,
-0.04259981960058212,
0.04312072694301605,
0.01247459463775158,
-0.0030167042277753353,
0.005901433061808348,
-0.021125348284840584,
0.005306238774210215,
0.015072287991642952,
-0.014184216037392616,
-0.0008907419978640974,
-0.019075073301792145,
-0.003430041251704097,
-0.02220846898853779,
-0.004689608700573444,
0.0036811926402151585,
-0.01682642661035061,
0.00517254788428545,
0.053390875458717346,
0.017997968941926956,
-0.0009568086825311184,
-0.0132333068177104,
0.008822238072752953,
-0.052216049283742905,
-0.009162086993455887,
0.015605485066771507,
0.053078681230545044,
-0.013192654587328434,
-0.00036905810702592134,
0.021875130012631416,
-0.0015747908037155867,
-0.006135099101811647,
-0.032814983278512955,
-0.01669016107916832,
0.01008460484445095,
0.01978924497961998,
-0.013683265075087547,
-0.012013240717351437,
-0.02004263922572136,
0.04273112118244171,
-0.017009437084197998,
-0.0003992427373304963,
-0.0033163465559482574,
-0.048148564994335175,
-0.038007527589797974,
0.00747127877548337,
0.011441614478826523,
0.015474134124815464,
-0.04167100042104721,
-0.06001818925142288,
0.03585973009467125,
-0.046607133001089096,
-0.005324902478605509,
-0.010650279931724072,
0.016020867973566055,
0.0179454255849123,
0.009563881903886795,
0.024436667561531067,
-0.04492536187171936,
-0.031852882355451584,
0.02236308343708515,
-0.022578898817300797,
0.019468292593955994,
0.003790554590523243,
-0.00536607438698411,
-0.006734771654009819,
0.06354369223117828,
0.003662165952846408,
-0.032949116080999374,
-0.011841222643852234,
0.03251537308096886,
0.008976181037724018,
-0.04136097803711891,
-0.021192101761698723,
0.0012668096460402012,
-0.05264386534690857,
-0.047600287944078445,
-0.009961998090147972,
-0.0034038193989545107,
0.00010099318024003878,
0.018803725019097328,
0.026515930891036987,
-0.0007201216649264097,
-0.008744931779801846,
0.0023635104298591614,
0.012451824732124805,
-0.0198508370667696,
0.019128188490867615,
0.020554082468152046,
-0.00023239364963956177,
-0.0071426802314817905,
-0.03713209927082062,
-0.008836492896080017,
0.005949833896011114,
-0.0016656240914016962,
0.01700475811958313,
-0.05027000233530998,
-0.009478292427957058,
0.0001991102035390213,
0.0364261157810688,
-0.0075911181047558784,
-0.015383199788630009,
-0.03486104682087898,
0.021636705845594406,
0.0011877816868945956,
-0.004114843904972076,
0.0285137128084898,
0.013498829677700996,
-0.007137935142964125,
-0.032238367944955826,
-0.018646063283085823,
0.02412877231836319,
-0.03852446377277374,
-0.005555666051805019,
-0.0033523242454975843,
0.01893039606511593,
0.027982408180832863,
0.015785440802574158,
-0.03403189778327942,
0.05074463412165642,
-0.049431100487709045,
-0.0709419995546341,
0.053786907345056534,
-0.039496101438999176,
0.02304701693356037,
0.026249060407280922,
-0.00865680631250143,
-0.04240370914340019,
0.005772966425865889,
-0.0033434098586440086,
-0.027152031660079956,
0.0005188520299270749,
-0.0030522600281983614,
-0.028945038095116615,
0.006423072423785925,
0.03397013619542122,
0.00020939696696586907,
0.040186479687690735,
0.020225275307893753,
0.020230568945407867,
0.002550761681050062,
-0.020245710387825966,
-0.017706995829939842,
-0.021819867193698883,
0.04263582453131676,
0.00013200697139836848,
0.012487144209444523,
-0.007100152783095837,
0.0668925940990448,
-0.04329748824238777,
0.005994075443595648,
-0.03746524453163147,
0.005880243144929409,
-0.09735651314258575,
-0.031353626400232315,
-0.006732303183525801,
0.007140377536416054,
0.011549635790288448,
-0.0757930651307106,
0.008946085348725319,
-0.001338366186246276,
-0.0587020069360733,
0.03691292926669121,
-0.028868403285741806,
-0.004082278814166784,
0.011129108257591724,
0.026774097234010696,
0.005944977514445782,
0.03789995238184929,
0.04132329672574997,
0.03402462229132652,
-0.033585529774427414,
0.024222256615757942,
0.017286378890275955,
-0.013696616515517235,
-0.006938857492059469,
0.014697777107357979,
-0.019905338063836098,
-0.052284449338912964,
0.06712982803583145,
-0.018309975042939186,
-0.029359430074691772,
0.003956422675400972,
-0.012245520949363708,
-0.004531239625066519,
-0.01873679645359516,
-0.003294368041679263,
-0.006143083795905113,
-0.00644654780626297,
0.022071579471230507,
-0.028868796303868294,
-0.007217768579721451,
0.01124415174126625,
0.01582411676645279,
0.05462999641895294,
-0.03412628173828125,
0.004789099562913179,
0.035860855132341385,
-0.04637505114078522,
-0.012091780081391335,
0.04834019020199776,
-0.03384125232696533,
-0.03702380880713463,
-0.012259699404239655,
0.006284620147198439,
0.00722420634701848,
-0.0018697016639634967,
0.010774007998406887,
-0.04911178722977638,
0.005025251302868128,
0.01954558864235878,
0.005740829277783632,
-0.00418039970099926,
0.031381696462631226,
-0.006183010060340166,
-0.02782101184129715,
0.02023187465965748,
-0.03299448639154434,
0.004283258691430092,
-0.04072007164359093,
-0.0033180268947035074,
-0.004034482873976231,
0.029998240992426872,
0.014740663580596447,
-0.04165058210492134,
-0.04686233401298523,
0.0055578937754035,
-0.013423937372863293,
0.005637562833726406,
-0.03778298571705818,
-0.004866438452154398,
-0.00621030991896987,
-0.08077950030565262,
0.025789909064769745,
0.04290557652711868,
0.031108085066080093,
-0.019004499539732933,
0.0019949711859226227,
-0.00037781393621116877,
0.01630423218011856,
0.055129945278167725,
0.0033852194901555777,
-0.02037965878844261,
0.034355372190475464,
0.016597043722867966,
0.02892082743346691,
-0.029180485755205154,
0.005583342630416155,
0.02646339125931263,
0.009681234136223793,
-0.02483227476477623,
-0.011682024225592613,
0.007869354449212551,
0.045626573264598846,
0.056356221437454224,
0.013091892935335636,
0.005650860257446766,
0.04756028950214386,
-0.049216486513614655,
0.06443534046411514,
-0.023114902898669243,
-0.001029927283525467,
0.05261746793985367,
0.004320382606238127,
0.0077096810564398766,
0.002485110191628337,
-0.0160333514213562,
-0.03469611331820488,
0.026313137263059616,
-0.03694712743163109,
-0.0005346242687664926,
0.006083656568080187,
0.009426299482584,
0.016731465235352516,
-0.0394187830388546,
-0.008776004426181316,
0.05820317938923836,
-0.01995076984167099,
-0.02356422320008278,
0.040006060153245926,
0.020790113136172295,
0.04917224124073982,
-0.01615520566701889,
-0.01680520735681057,
0.019918251782655716,
-0.0024248945992439985,
0.015406996943056583,
0.04216204211115837,
0.02337060309946537,
-0.016546593979001045,
0.00505202729254961,
0.004449703264981508,
-0.013763006776571274,
0.031663257628679276,
0.01788015104830265,
0.046376947313547134,
-0.008132022805511951,
-0.05080996826291084,
0.008814794942736626,
-0.015905506908893585,
0.0012701982632279396,
-0.005320916883647442,
-0.011530869640409946,
0.07963556051254272,
-0.023256396874785423,
0.017014188691973686,
-0.0012489687651395798,
-0.004407825414091349,
-0.019191483035683632,
-0.006101313978433609,
-0.013597514480352402,
0.07377496361732483,
-0.006070263218134642,
0.001792524941265583,
-0.0037737409584224224,
0.00528247095644474,
0.005365478806197643,
-0.034185659140348434,
0.024029649794101715,
-0.013604161329567432,
0.0049380469135940075,
-0.019289707764983177,
-0.03926052525639534,
-0.030902450904250145,
0.0008629914955236018,
0.012391061522066593,
0.014943993650376797,
0.049302972853183746,
0.003257437376305461,
-0.039949215948581696,
-0.013505837880074978,
0.042675990611314774,
-0.02956361323595047,
-0.011201389133930206,
-0.03732502833008766,
-0.0010186124127358198,
-0.004458507057279348,
-0.0430372878909111
] |
<p>I'm not a physicist and just making some research by the way of creating simple physics simulator, because of that, sorry if this is very dumb question, but I really need help with it.</p>
<p>Let's assume that some body (rectangle, square, N-polygon, etc.), exists in 2D world in rest (no friction, gravity, etc.) and can be freely moved in any direction.</p>
<p>If some pushing / pulling force will be applied to center of mass, then only translational force will exist, this case is very clear to me. But what if force will be applied on the edge of body? What will be if force will be applied at some angle to edge? I understand that this will involve a rotational forces. But how can I calculate the resulting translational vector in this case?</p>
<p>Here is image, demonstrating the problem. Force F2 will not involve any rotational forces, I can calculate net force (= F2) and get acceleration vector. All this question is about F and finding resulting translational vector after apply of F.</p>
<p><img src="http://i.stack.imgur.com/v8UwH.png" alt="example of forces-related question"></p> | 1,992 | [
-0.023460300639271736,
0.006709652487188578,
-0.03351527079939842,
0.028981002047657967,
0.053283557295799255,
-0.002825673669576645,
-0.006544213276356459,
-0.007962075993418694,
0.011778182350099087,
-0.05221039801836014,
0.00565078342333436,
0.03366365283727646,
0.04333487153053284,
0.02157379500567913,
0.005974970292299986,
-0.002845378592610359,
-0.07633055746555328,
-0.02268485352396965,
0.015690041705965996,
-0.02643485739827156,
0.0077148019336164,
-0.0005209161317907274,
0.019213521853089333,
-0.00686532910913229,
-0.01207281555980444,
0.038258448243141174,
0.01808325946331024,
-0.0485435426235199,
0.02736806683242321,
0.0391373485326767,
-0.027136147022247314,
-0.02421843633055687,
0.01720435544848442,
-0.009032376110553741,
-0.0019581806845963,
0.014969834126532078,
-0.057707641273736954,
-0.015764763578772545,
0.020922400057315826,
0.010745463892817497,
-0.03926660493016243,
-0.015483139082789421,
-0.023548642173409462,
0.08681845664978027,
-0.03455108031630516,
0.03207331895828247,
-0.008208371698856354,
0.008335595950484276,
0.07710719108581543,
-0.06889903545379639,
0.09131563454866409,
0.008422174490988255,
0.05581148713827133,
-0.018910210579633713,
0.02242928184568882,
-0.016433222219347954,
0.05978645011782646,
0.0274579469114542,
0.003588458988815546,
-0.021067099645733833,
-0.005249631591141224,
-0.0404726080596447,
-0.04584747552871704,
-0.08186940848827362,
-0.001589810592122376,
0.040745798498392105,
-0.018394729122519493,
-0.006996960379183292,
0.026547422632575035,
0.021473372355103493,
0.007197703700512648,
0.010717630386352539,
0.028572943061590195,
-0.023672975599765778,
0.004296094179153442,
-0.015765564516186714,
0.039010610431432724,
0.008638376370072365,
0.008510117419064045,
0.026541922241449356,
-0.03889632225036621,
0.013372648507356644,
0.05316006764769554,
0.06987839937210083,
0.022009557113051414,
-0.05508897081017494,
0.022128477692604065,
-0.023395691066980362,
0.003311607986688614,
0.004078027792274952,
-0.0001615733781363815,
-0.03593529760837555,
0.03060397319495678,
-0.016718897968530655,
-0.0360981747508049,
-0.0006825188756920397,
0.0061370618641376495,
0.03139829263091087,
0.017921295017004013,
-0.022697601467370987,
0.004749543499201536,
-0.016814446076750755,
-0.027966290712356567,
0.07386200875043869,
-0.015765724703669548,
0.028371267020702362,
-0.0466751903295517,
0.013535336591303349,
-0.05245216563344002,
-0.027624206617474556,
-0.022207660600543022,
0.00558321550488472,
-0.0165933258831501,
0.0027532102540135384,
0.013597125187516212,
-0.013893612660467625,
-0.038510508835315704,
0.0015260697109624743,
0.038456760346889496,
0.0509486086666584,
0.032120026648044586,
-0.036330293864011765,
-0.0040170494467020035,
-0.035804860293865204,
-0.03740695118904114,
-0.007158193737268448,
0.02147216536104679,
-0.014205233193933964,
-0.016967082396149635,
0.03358614444732666,
0.02814427763223648,
-0.06124626472592354,
0.0017001075902953744,
-0.006914377212524414,
0.030384354293346405,
-0.011466712690889835,
-0.07540441304445267,
-0.08189613372087479,
0.05619174614548683,
-0.0018958681030198932,
0.012352433986961842,
-0.08581725507974625,
-0.0016009480459615588,
0.038534898310899734,
0.07802438735961914,
0.018758287653326988,
-0.014775730669498444,
0.022115536034107208,
0.035349372774362564,
-0.018770886585116386,
0.01500644814223051,
-0.006923700217157602,
-0.021080337464809418,
-0.03013737127184868,
-0.019270552322268486,
-0.05582381784915924,
0.05075174570083618,
0.00209816824644804,
-0.00006079896047594957,
-0.0335238091647625,
0.03594017028808594,
-0.016968201845884323,
0.010646894574165344,
0.023671995848417282,
-0.003697500564157963,
-0.018332619220018387,
0.07068219780921936,
-0.0017379180062562227,
-0.007228364236652851,
0.03518444299697876,
0.012024468742311,
0.018019957467913628,
-0.0077626146376132965,
0.022122271358966827,
0.06314823031425476,
-0.013492727652192116,
-0.03168376907706261,
-0.02879742719233036,
0.0030996447894722223,
0.0017741756746545434,
-0.040209583938121796,
-0.04596185311675072,
-0.015340420417487621,
0.000034937154850922525,
0.023105183616280556,
0.04675948992371559,
-0.003469700925052166,
-0.00986795499920845,
0.009805499576032162,
-0.048143867403268814,
0.00017003041284624487,
-0.08808363974094391,
0.07183308899402618,
-0.009769218042492867,
-0.018419472500681877,
-0.004636941943317652,
0.026736048981547356,
0.016999898478388786,
-0.00912181194871664,
-0.0026193768717348576,
-0.036103423684835434,
0.038575172424316406,
0.024445442482829094,
-0.020447278395295143,
0.029872868210077286,
0.04163484647870064,
0.03901331499218941,
0.014671853743493557,
0.0050659808330237865,
-0.03502993658185005,
-0.03641437739133835,
0.012104207649827003,
-0.05213932693004608,
0.008797729387879372,
0.009015069343149662,
0.018233323469758034,
0.028932658955454826,
0.014110228978097439,
-0.05425769090652466,
-0.00024812674382701516,
-0.020758740603923798,
0.0851016715168953,
0.0534292533993721,
0.03277769684791565,
0.03009691834449768,
0.04000414162874222,
0.009000127203762531,
-0.01288947556167841,
0.010927371680736542,
-0.015508911572396755,
-0.07642234861850739,
-0.01689535565674305,
0.009745856747031212,
0.0010637380182743073,
-0.04162522032856941,
-0.00878762174397707,
0.05208461359143257,
0.003569399705156684,
0.03832526504993439,
0.010389359667897224,
-0.0024974835105240345,
-0.008040145970880985,
0.04173107445240021,
0.0492795892059803,
0.012880813330411911,
0.013852499425411224,
0.04687071964144707,
0.05122097581624985,
0.02898040972650051,
0.038382261991500854,
-0.02951914072036743,
0.03367729112505913,
0.017594167962670326,
0.015520716086030006,
0.012865282595157623,
-0.014793242327868938,
0.035493988543748856,
0.0141805000603199,
0.0076606241054832935,
0.030356016010046005,
-0.0025529288686811924,
-0.0291624516248703,
-0.04458704963326454,
0.00027360895182937384,
0.03143516182899475,
-0.0059034740552306175,
-0.012114662677049637,
-0.027019215747714043,
0.03481090068817139,
-0.022761443629860878,
0.012575263157486916,
-0.000867856724653393,
0.0070861526764929295,
-0.030827011913061142,
0.008568481542170048,
0.020889941602945328,
0.031490158289670944,
0.03569028154015541,
-0.012911544181406498,
0.016368722543120384,
-0.009101981297135353,
-0.045661814510822296,
-0.00975230522453785,
0.031629059463739395,
-0.04594940319657326,
0.02919824793934822,
-0.05595150217413902,
-0.026902703568339348,
0.04796505719423294,
0.013366155326366425,
-0.008951135911047459,
0.05073468014597893,
0.01532504241913557,
-0.07225760072469711,
-0.01597287319600582,
-0.0466010607779026,
0.014259528368711472,
-0.032532524317502975,
0.012303747236728668,
0.04064546152949333,
-0.004772440530359745,
-0.03457483649253845,
0.024459928274154663,
-0.05118357762694359,
-0.03801698610186577,
-0.03332442045211792,
0.0004234205698594451,
0.03840727359056473,
-0.023962566629052162,
0.004604991525411606,
0.01284250058233738,
-0.017827674746513367,
0.009997240267693996,
-0.053487930446863174,
-0.0270374808460474,
-0.00551827484741807,
-0.0006455049151554704,
0.05668289586901665,
-0.0174395851790905,
-0.018891263753175735,
0.07999202609062195,
-0.0036578024737536907,
-0.05029826611280441,
-0.015250739641487598,
-0.006510445848107338,
-0.003043483244255185,
-0.04405517876148224,
0.001687479205429554,
0.021726472303271294,
-0.020343920215964317,
-0.02270837500691414,
-0.006690210662782192,
-0.0022700380068272352,
0.04593789204955101,
0.010453828610479832,
0.013388724997639656,
-0.013800236396491528,
0.05492585152387619,
0.006209289655089378,
0.07219106703996658,
-0.0013942844234406948,
-0.02702801302075386,
0.02942136861383915,
0.021406710147857666,
0.035915907472372055,
0.018248597159981728,
-0.04862629249691963,
0.017712051048874855,
0.00013649063475895673,
-0.015032513067126274,
-0.00126207887660712,
0.028668047860264778,
0.0062128761783242226,
-0.0012324944837018847,
0.013988010585308075,
0.04855458065867424,
0.06486968696117401,
-0.021418210119009018,
-0.005109958816319704,
0.07804550975561142,
0.011042033322155476,
-0.011779198423027992,
-0.041548311710357666,
-0.0030461116693913937,
0.00911102257668972,
0.023363551124930382,
-0.012038180604577065,
-0.0012431436916813254,
0.02622145786881447,
0.05099248141050339,
0.04568544030189514,
0.04840227589011192,
-0.0026322794146835804,
0.024160411208868027,
-0.012285779230296612,
0.009348456747829914,
-0.02152210660278797,
0.054493509232997894,
-0.013144486583769321,
0.05159132927656174,
0.03679050877690315,
0.029756484553217888,
-0.001097604283131659,
0.020792467519640923,
-0.10124190151691437,
0.027226444333791733,
-0.017974482849240303,
-0.028700795024633408,
-0.014276971109211445,
-0.02883525937795639,
-0.03909481316804886,
-0.013036870397627354,
-0.017374644055962563,
-0.023633934557437897,
0.007750323507934809,
-0.030955223366618156,
0.0010434715077280998,
-0.0240922961384058,
-0.042102064937353134,
0.0003883068566210568,
0.01684742607176304,
0.02648632973432541,
-0.05211848393082619,
0.011228938587009907,
0.015151320025324821,
-0.026744134724140167,
-0.003992517478764057,
0.0008184132748283446,
-0.005055188201367855,
-0.004417105112224817,
0.0337369367480278,
0.00365893030539155,
0.06824629753828049,
-0.004107743967324495,
0.012022734619677067,
-0.027602985501289368,
0.04509814456105232,
0.012673853896558285,
0.006943574175238609,
-0.02570321410894394,
-0.08691854029893875,
-0.0018230169080197811,
-0.01822647452354431,
0.053174395114183426,
-0.014499089680612087,
-0.02157966047525406,
0.03335985168814659,
0.010407128371298313,
-0.013457020744681358,
0.011309522204101086,
0.06780975311994553,
0.03653305768966675,
-0.03668233007192612,
-0.07844088971614838,
-0.015791527926921844,
-0.010816538706421852,
-0.02103903703391552,
0.041548267006874084,
-0.042045824229717255,
-0.024427643045783043,
0.009226767346262932,
0.03482722491025925,
0.0017847866984084249,
-0.0179817546159029,
0.0036346446722745895,
-0.013620027340948582,
0.03934739530086517,
-0.024403531104326248,
0.012251087464392185,
-0.0009131195838563144,
0.01262136921286583,
0.01817680522799492,
-0.0307688619941473,
-0.023097647354006767,
-0.059589933604002,
0.015570409595966339,
0.024041110649704933,
0.021789664402604103,
-0.0023700206074863672,
0.00969160906970501,
-0.029695287346839905,
-0.038810696452856064,
0.01404520682990551,
-0.023949792608618736,
0.03966061770915985,
-0.024942677468061447,
-0.012676436454057693,
0.0026755989529192448,
-0.013859011232852936,
-0.048999425023794174,
-0.0029803391080349684,
-0.05770383030176163,
0.010122498497366905,
-0.04783323407173157,
0.001340768882073462,
-0.0015754293417558074,
0.020585184916853905,
0.029496923089027405,
0.028922181576490402,
0.01354826521128416,
0.005049678962677717,
0.014928805641829967,
0.03246896713972092,
-0.027131138369441032,
-0.052461571991443634,
-0.005268728360533714,
0.025601597502827644,
0.00787079706788063,
0.01779985800385475,
-0.03471535071730614,
-0.03401575982570648,
-0.003396105719730258,
-0.031949736177921295,
0.012703622691333294,
0.005451914854347706,
-0.010294473730027676,
0.042390819638967514,
0.032343845814466476,
-0.023675469681620598,
0.062490809708833694,
0.04686971753835678,
-0.008361474610865116,
-0.025541523471474648,
0.009671704843640327,
0.03166772797703743,
0.012942580506205559,
-0.024294381961226463,
-0.04721292853355408,
0.016676492989063263,
-0.018642503768205643,
0.009530022740364075,
-0.029936019331216812,
0.051806848496198654,
-0.02701178751885891,
-0.013751516118645668,
-0.022829782217741013,
0.04554373770952225,
0.006327097769826651,
0.006028797943145037,
-0.026967212557792664,
0.013011724688112736,
-0.0006550985854119062,
-0.06993217766284943,
-0.022257786244153976,
0.010523646138608456,
0.010209702886641026,
0.018043240532279015,
-0.005472252145409584,
0.006659833714365959,
-0.006271278951317072,
-0.01781589165329933,
-0.008965815417468548,
-0.08293259888887405,
0.048608630895614624,
-0.005975482519716024,
0.01454686839133501,
0.029719142243266106,
-0.05573020875453949,
-0.03159249573945999,
0.03860083594918251,
0.02330210991203785,
0.00486293900758028,
-0.013148965314030647,
-0.0005644003394991159,
0.037150733172893524,
0.025162868201732635,
-0.024550708010792732,
-0.07154592126607895,
0.011901219375431538,
0.0009747197036631405,
-0.009219651110470295,
-0.04537295922636986,
-0.015235829167068005,
-0.03125041350722313,
-0.004500333685427904,
0.00784364715218544,
0.06323754042387009,
-0.014458734542131424,
-0.01201959140598774,
0.07096991688013077,
-0.04038127511739731,
0.021660950034856796,
-0.014036732725799084,
-0.02591797336935997,
-0.000358447025064379,
0.003505961736664176,
-0.017680510878562927,
0.010418906807899475,
0.06004555523395538,
-0.043024007230997086,
0.020161878317594528,
-0.015476454980671406,
0.014895477332174778,
0.04413803294301033,
0.021678652614355087,
0.02729402855038643,
0.0043991380371153355,
0.01347574032843113,
-0.03281020373106003,
-0.02392951026558876,
0.025460412725806236,
0.011412197723984718,
0.008874554187059402,
0.015034551732242107,
0.006929990369826555,
-0.04288759082555771,
-0.0313846617937088,
-0.004953144118189812,
0.001731179771013558,
0.043591368943452835,
-0.0057980092242360115,
0.05551838129758835,
-0.01857106387615204,
0.014483503997325897,
0.0015790853649377823,
-0.013283422216773033,
0.03752916678786278,
-0.001385645940899849,
-0.02732240781188011,
0.00044274277752265334,
0.022228337824344635,
-0.017723102122545242,
0.0008039215463213623,
-0.03909837827086449,
0.03487497195601463,
0.10733940452337265,
-0.037651024758815765,
0.0599781796336174,
0.03500795364379883,
0.030625004321336746,
-0.013559090904891491,
0.033117640763521194,
0.016571499407291412,
-0.013975202105939388,
-0.0013506296090781689,
0.03401760756969452,
-0.005046321079134941,
-0.014483163133263588,
0.02817954681813717,
-0.004300704225897789,
-0.01533630769699812,
-0.002116454765200615,
0.0138771403580904,
0.023945264518260956,
0.024166787043213844,
-0.023498259484767914,
-0.003907037433236837,
0.017457900568842888,
-0.0226711705327034,
0.052454814314842224,
0.0029215749818831682,
-0.04336364567279816,
0.05023582652211189,
0.02315503917634487,
-0.01639244146645069,
-0.07517241686582565,
0.007961702533066273,
-0.01622728630900383,
0.011517554521560669,
-0.020293626934289932,
-0.009739850647747517,
-0.020590374246239662,
0.01302824541926384,
0.040972381830215454,
-0.01190328598022461,
0.015175946056842804,
-0.032612331211566925,
-0.06199207901954651,
-0.022836510092020035,
-0.04960506409406662,
-0.03821922838687897,
0.04035155847668648,
0.05675113573670387,
-0.0036594613920897245,
0.040194910019636154,
-0.018727537244558334,
0.0146262152120471,
0.017494259402155876,
0.03601076826453209,
-0.01796780712902546,
0.08319902420043945,
-0.033881742507219315,
0.03348414599895477,
-0.027125919237732887,
0.005994184873998165,
0.09347280859947205,
0.019392311573028564,
0.0018648504046723247,
-0.0532245971262455,
0.0007522554369643331,
-0.032802484929561615,
-0.027068521827459335,
-0.005235186778008938,
0.014993926510214806,
0.032604869455099106,
-0.003154488280415535,
0.0038537720683962107,
0.03660706430673599,
0.011862613260746002,
-0.026053903624415398,
0.03674944117665291,
-0.034508995711803436,
-0.05575109273195267,
-0.015348860993981361,
-0.008765257894992828,
0.0020357549656182528,
-0.013051134534180164,
-0.030495131388306618,
0.031984928995370865,
-0.02510763332247734,
0.011325222440063953,
-0.03236263245344162,
-0.01557969767600298,
0.019456377252936363,
-0.0002400545054115355,
-0.08030353486537933,
0.0027451668865978718,
0.0003569040272850543,
-0.058400992304086685,
-0.044937264174222946,
0.017975661903619766,
-0.007681068032979965,
0.0012625836534425616,
0.02475370094180107,
0.02339193969964981,
0.023471200838685036,
0.030060401186347008,
0.026583271101117134,
-0.028455529361963272,
-0.017666149884462357,
0.020224787294864655,
-0.04434202238917351,
0.08206059038639069,
-0.009688879363238811,
0.01009133830666542,
0.023459579795598984,
0.010188001208007336,
0.011932861059904099,
-0.048068609088659286,
0.028158938512206078,
-0.002470411593094468,
0.043324023485183716,
0.016149412840604782,
0.009256548248231411,
-0.015027369372546673,
0.043528810143470764,
0.01852802373468876,
-0.023861808702349663,
0.017380813136696815,
0.006544078700244427,
-0.007301227655261755,
0.022271838039159775,
0.0864144116640091,
-0.029141472652554512,
-0.013517755083739758,
-0.0033461065031588078,
-0.0348447747528553,
-0.02622031792998314,
0.032737426459789276,
0.019069043919444084,
0.03266959264874458,
-0.00651110615581274,
-0.027163008227944374,
-0.03191789239645004,
-0.04022612422704697,
-0.01694381609559059,
0.0061501371674239635,
-0.037494461983442307,
-0.02493167109787464,
-0.015529071912169456,
-0.004963464103639126,
0.05097423121333122,
0.018518952652812004,
-0.01677118055522442,
-0.00500243715941906,
-0.0039538973942399025,
-0.016431789845228195,
0.032160595059394836,
-0.021946633234620094,
-0.04186343029141426,
0.02142823487520218,
-0.00037937427987344563,
0.011025410145521164,
-0.03733397647738457,
0.03941810131072998,
0.042289622128009796,
-0.03406134247779846,
-0.00828677136451006,
0.003739924170076847,
-0.024532655254006386,
0.01051366701722145,
0.03658723831176758,
-0.019931379705667496,
-0.012021415866911411,
0.001446280861273408,
-0.028724780306220055,
-0.056534428149461746,
0.008974594995379448,
-0.010762817226350307,
-0.03464783728122711,
-0.009269220754504204,
0.044067006558179855,
-0.03260055184364319,
0.0007400474860332906,
-0.04175999388098717,
0.04949143901467323,
-0.007725930772721767,
0.001501770573668182,
-0.04698643833398819,
-0.013241341337561607,
0.018832644447684288,
-0.0188822653144598,
-0.027465038001537323,
0.03774286434054375,
-0.0041072857566177845,
0.010050100274384022,
-0.009665164165198803,
0.04214007407426834,
0.0058617619797587395,
0.026847023516893387,
0.006278741639107466,
-0.03157015144824982,
0.05917251855134964,
-0.0009654283639974892,
0.015157178044319153,
0.03127264603972435,
-0.028447067365050316,
-0.02178112417459488,
0.02109476737678051,
0.0031343104783445597,
0.03221284970641136,
-0.024748630821704865,
-0.01779063418507576,
0.0027030142955482006,
0.07928303629159927,
-0.024147341027855873,
-0.008514183573424816,
-0.0022896798327565193,
-0.03658705949783325,
-0.042970288544893265,
-0.03410223126411438,
0.02504783682525158,
-0.0345039889216423,
0.007229903247207403,
0.022828618064522743,
0.0029424449894577265,
-0.02069750986993313,
-0.04056727886199951,
0.03314888849854469,
-0.003310087136924267,
-0.00643577054142952,
0.05317659676074982,
0.00008166144107235596,
0.005050935782492161,
0.06917215138673782,
-0.024572499096393585,
0.009921914897859097,
0.004789271391928196,
0.007408503443002701,
-0.09874086827039719,
-0.008200791664421558,
0.04343577101826668,
-0.030856439843773842,
0.052462801337242126,
-0.07917917519807816,
-0.03250831738114357,
0.02376733347773552,
-0.07799171656370163,
0.01415323931723833,
-0.027487510815262794,
-0.006772478111088276,
-0.006242229137569666,
-0.016703324392437935,
0.04591086879372597,
0.02663753554224968,
0.003730482654646039,
0.03742782771587372,
0.032341502606868744,
0.002645006636157632,
-0.036577772349119186,
-0.03456156700849533,
0.04067271202802658,
0.034391600638628006,
0.011265574023127556,
-0.0024347123689949512,
0.021473046392202377,
0.02319297380745411,
-0.037867624312639236,
0.011271706782281399,
-0.01115337386727333,
0.014257825911045074,
-0.02558114007115364,
0.019542109221220016,
-0.02276661992073059,
0.03644328564405441,
-0.02351384423673153,
-0.01849403791129589,
0.01831655763089657,
0.015676379203796387,
-0.008584976196289062,
0.0338730588555336,
-0.025511903688311577,
-0.005810295231640339,
0.0012822943972423673,
-0.010546207427978516,
0.015854094177484512,
0.04564915969967842,
-0.011537925340235233,
-0.01778430864214897,
0.01084873080253601,
-0.01592324860394001,
0.0066903927363455296,
-0.025099599733948708,
0.008963056840002537,
-0.030435651540756226,
0.012133893556892872,
0.002965710125863552,
-0.00993412546813488,
-0.008951348252594471,
0.03560353443026543,
-0.01240056473761797,
-0.002821889938786626,
0.025204945355653763,
-0.017397474497556686,
-0.0282415971159935,
-0.07584132999181747,
-0.020000170916318893,
0.015725241973996162,
-0.042523015290498734,
-0.005224092397838831,
-0.05080658197402954,
-0.02754540741443634,
0.007018230855464935,
0.05098133534193039,
0.0162816159427166,
0.008206939324736595,
-0.0019593406468629837,
-0.01478640828281641,
-0.08834005892276764,
0.05140547454357147,
0.013447877950966358,
-0.025004152208566666,
-0.023451432585716248,
-0.0017285384237766266,
0.00574524886906147,
0.011571355164051056,
0.04075760394334793,
-0.009920075535774231,
-0.0017243927577510476,
-0.014890288934111595,
-0.012207153253257275,
-0.008025635033845901,
-0.033959101885557175,
-0.0037032715044915676,
-0.030721597373485565,
-0.013582851737737656,
-0.02133580483496189,
-0.0019008765229955316,
-0.01574563793838024,
-0.01835588365793228,
0.014358353801071644,
0.0018447638722136617,
0.03175302967429161,
-0.008686300367116928,
-0.03627244755625725,
0.008313490077853203,
0.016172228381037712,
0.010445383377373219,
0.07695158571004868,
-0.005859933793544769,
0.005471563432365656,
0.01746109500527382,
-0.025618620216846466,
0.012422830797731876,
0.01753738336265087,
-0.04334782809019089,
0.0003514152194838971,
-0.05460936948657036,
-0.005561055615544319,
0.0440857820212841,
-0.06541839241981506,
0.006074072793126106,
0.04010583460330963,
-0.04788842052221298,
0.049429118633270264,
0.00835530087351799,
0.02534099668264389,
0.0028912590350955725,
-0.012991688214242458,
0.046779122203588486,
0.022295799106359482,
-0.040612947195768356,
0.004213121719658375,
0.016740117222070694,
-0.005608022212982178,
-0.009194253012537956,
0.008554496802389622,
0.08663440495729446,
-0.007697471883147955,
0.039218634366989136,
-0.02946842648088932,
0.01521384995430708,
-0.029069270938634872,
0.01011705119162798,
0.002232658676803112,
0.0073216622695326805,
0.022139349952340126,
0.0028474903665483,
-0.007691941224038601,
0.04628262296319008,
-0.035999640822410583,
0.039021700620651245,
-0.001765709719620645,
-0.007613675203174353,
-0.003120783483609557,
0.005977295339107513,
-0.0030879578553140163,
0.022057028487324715,
-0.0035937228240072727,
0.0070371865294873714,
-0.006466543767601252,
-0.0020008361898362637,
0.03682221472263336,
0.022558540105819702,
0.035207681357860565,
0.018070099875330925,
-0.02756137028336525,
0.0013632145710289478,
-0.024811474606394768,
-0.007505712565034628,
-0.018362224102020264,
0.04521782323718071,
0.04675216227769852,
0.009044109843671322,
-0.014944407157599926,
0.020870056003332138,
-0.019212760031223297,
0.07743139564990997,
-0.08726038038730621,
-0.03733569383621216,
-0.014638126827776432,
0.03518209606409073,
0.005001908168196678,
0.020403537899255753
] |
<p>The average kinetic energy (KE) per molecule of a gas is $\frac{3}{2}kT$. While finding this we do </p>
<p>$$ \text{ Average KE} =\frac{1}{2} M \frac{1}{N}\sum v^2=\frac{3}{2}kT$$
But why do we not add rotational kinetic energy here?</p> | 1,993 | [
-0.0564415343105793,
0.0015237494371831417,
-0.04056619852781296,
0.0042226482182741165,
0.04025525972247124,
-0.013715247623622417,
-0.04230612516403198,
-0.030808471143245697,
0.007431517820805311,
-0.020708706229925156,
0.03866404667496681,
0.05870862305164337,
0.05762568116188049,
0.0032130074687302113,
-0.001982565503567457,
0.022437818348407745,
-0.043344177305698395,
-0.005791292991489172,
0.009903009049594402,
0.0031444679480046034,
-0.03378886729478836,
0.006677521858364344,
0.029262971132993698,
-0.0297047421336174,
-0.029652845114469528,
0.04680592194199562,
0.051821738481521606,
-0.02856926992535591,
0.060577392578125,
0.003825070336461067,
-0.028516650199890137,
-0.006720736622810364,
0.07700415700674057,
0.010307539254426956,
-0.012996724806725979,
0.015693912282586098,
-0.014415702782571316,
-0.006085611879825592,
-0.00938725471496582,
0.04055170342326164,
-0.03869255632162094,
-0.0030835301149636507,
-0.022701557725667953,
0.013646755367517471,
-0.04081074520945549,
0.024183882400393486,
-0.01672692596912384,
-0.016232801601290703,
0.031180022284388542,
-0.07072954624891281,
0.034476496279239655,
0.015249358490109444,
0.04378439486026764,
0.015223527327179909,
-0.007715644780546427,
0.03173515200614929,
0.06222747638821602,
0.08081810921430588,
-0.006510189268738031,
-0.02712375298142433,
0.021096358075737953,
-0.0469854436814785,
0.00891436729580164,
0.023828499019145966,
0.010085830464959145,
0.019900351762771606,
-0.008203921839594841,
-0.01963096670806408,
0.03823326155543327,
0.03510346636176109,
0.0609331876039505,
0.0073857661336660385,
0.009947463870048523,
-0.006747623905539513,
-0.013650123961269855,
0.031649574637413025,
0.015361453406512737,
-0.009465847164392471,
0.0498448871076107,
0.031025879085063934,
0.020054318010807037,
-0.014942486770451069,
0.09291715174913406,
0.023735612630844116,
0.012453468516469002,
0.012628552503883839,
0.06299348920583725,
0.019912736490368843,
0.014333883300423622,
0.027160799130797386,
0.02495429292321205,
0.015513460151851177,
0.023495517671108246,
-0.000748376187402755,
-0.007059292867779732,
0.050836071372032166,
-0.02350872941315174,
0.031455494463443756,
0.018637727946043015,
0.0011830254225060344,
-0.0009624513913877308,
-0.004125075414776802,
0.03281880542635918,
0.06001336872577667,
0.0009533358970656991,
-0.04210316017270088,
-0.07391892373561859,
0.028988203033804893,
-0.000367969274520874,
-0.026671074330806732,
-0.038844164460897446,
-0.00008957396494224668,
-0.039851076900959015,
0.006245792377740145,
-0.030144179239869118,
0.01061868853867054,
-0.007197823375463486,
-0.0207024235278368,
0.030388548970222473,
0.05732522904872894,
0.04244364798069,
-0.028191130608320236,
-0.02831413596868515,
-0.005005375016480684,
-0.031052930280566216,
0.02013503760099411,
0.03245649114251137,
-0.017066771164536476,
-0.04313558340072632,
-0.008958901278674603,
-0.0040815528482198715,
-0.022796358913183212,
0.015467507764697075,
0.006161945406347513,
0.03521548956632614,
-0.027964208275079727,
-0.06866570562124252,
-0.032593194395303726,
0.025090208277106285,
-0.04141123220324516,
-0.01461835391819477,
-0.08094661682844162,
-0.01454374473541975,
0.01636195369064808,
0.0691908746957779,
0.010366750881075859,
-0.006312834098935127,
-0.00957365334033966,
0.018184831365942955,
-0.008095292374491692,
-0.03257530927658081,
-0.034900564700365067,
-0.007502811495214701,
-0.04493231698870659,
-0.02775169536471367,
-0.05400261655449867,
0.028509488329291344,
0.03956633433699608,
0.03614635020494461,
0.009633134119212627,
0.01795387454330921,
-0.016479285433888435,
-0.00008716147567611188,
0.0008035033824853599,
0.006666922476142645,
-0.014574898406863213,
0.032093264162540436,
0.03477606549859047,
0.03571789711713791,
0.003858079668134451,
0.011466857977211475,
0.008611615747213364,
-0.009842897765338421,
0.03371749073266983,
0.07733185589313507,
-0.01209919061511755,
-0.0259819645434618,
0.00018576988077256829,
0.02273089438676834,
-0.029812145978212357,
-0.0374365970492363,
-0.028483403846621513,
0.015203974209725857,
0.021874189376831055,
0.011160271242260933,
0.05478479713201523,
-0.00937089417129755,
0.006869724951684475,
-0.031918130815029144,
-0.05216749384999275,
-0.01182206254452467,
-0.049610089510679245,
0.007755108643323183,
-0.009800509549677372,
-0.041457753628492355,
0.008725129067897797,
0.024499693885445595,
0.050513505935668945,
-0.000626810418907553,
-0.024073626846075058,
-0.03477878496050835,
0.022256486117839813,
0.016979044303297997,
-0.010784437879920006,
0.015065520070493221,
0.030521104112267494,
0.056959282606840134,
-0.0036866802256554365,
-0.00977856945246458,
0.014253342524170876,
-0.03475864231586456,
0.0004946418339386582,
-0.03770037740468979,
-0.031110020354390144,
0.008064154535531998,
-0.02124975249171257,
0.023235294967889786,
0.023113876581192017,
-0.021164357662200928,
0.03589625284075737,
-0.03590232506394386,
0.0582573339343071,
0.05807443708181381,
0.015623676590621471,
0.007980131544172764,
0.07625726610422134,
-0.0037011499516665936,
-0.014317198656499386,
0.01631881669163704,
-0.047632042318582535,
-0.03321342542767525,
0.012415309436619282,
0.06324071437120438,
0.036502640694379807,
-0.07486174255609512,
-0.019665919244289398,
0.07525064796209335,
0.01079696137458086,
0.014596323482692242,
-0.006731737870723009,
0.022515174001455307,
-0.035513781011104584,
0.03096920996904373,
0.016069578006863594,
-0.006943788379430771,
-0.01962488703429699,
0.03931744024157524,
0.024066278710961342,
0.002530758734792471,
0.04041711986064911,
-0.04762473329901695,
0.019220784306526184,
0.002065913286060095,
0.015238424763083458,
0.019230417907238007,
0.00020660027803387493,
0.03215740621089935,
-0.021197296679019928,
0.021755902096629143,
0.02516154944896698,
0.013458451256155968,
0.017810417339205742,
-0.0179836917668581,
-0.0353049598634243,
0.010166185908019543,
0.02033698372542858,
-0.020834000781178474,
-0.014500021934509277,
0.01238762866705656,
-0.033894553780555725,
0.014989419840276241,
-0.03483738750219345,
0.01822567731142044,
0.00878471601754427,
0.012317616492509842,
0.03169656917452812,
-0.006975528784096241,
0.03923638537526131,
-0.014728846959769726,
-0.02539614774286747,
-0.0004170202591922134,
-0.03699618577957153,
-0.02988330088555813,
0.024701815098524094,
-0.019805854186415672,
-0.014070884324610233,
-0.0007348008803091943,
-0.03021104447543621,
0.033563073724508286,
-0.028038443997502327,
-0.03992123156785965,
0.01827872544527054,
0.006549024488776922,
-0.060367878526449203,
0.007396632339805365,
-0.0007058597402647138,
0.005402558483183384,
-0.04322972521185875,
-0.009678334929049015,
0.018343312665820122,
-0.03009670227766037,
-0.01811712235212326,
0.06238475814461708,
-0.05974659323692322,
-0.04754768684506416,
-0.00909104011952877,
-0.04047717526555061,
0.04766026511788368,
-0.026997298002243042,
0.0016559673240408301,
0.019489537924528122,
-0.05638869106769562,
-0.01760869286954403,
-0.06627286225557327,
0.008539716713130474,
-0.0027685118839144707,
-0.005284483544528484,
0.07363005727529526,
0.009426970966160297,
-0.019965890794992447,
0.06154763326048851,
0.006941149942576885,
-0.026611490175127983,
0.008367535658180714,
-0.01853056252002716,
-0.008430800400674343,
-0.04836256802082062,
0.00032111210748553276,
0.011703843250870705,
-0.003354338463395834,
0.027079448103904724,
0.01117345318198204,
0.020925097167491913,
0.058601148426532745,
-0.018638355657458305,
-0.014326232485473156,
0.012396549805998802,
-0.0006986400694586337,
0.015952393412590027,
0.0641220435500145,
-0.0004954361938871443,
-0.0395389124751091,
0.02688300423324108,
0.01821727119386196,
0.01442824024707079,
0.03307918459177017,
-0.08786658197641373,
0.08493290841579437,
-0.009508943185210228,
0.022411318495869637,
-0.036817338317632675,
0.03718135878443718,
0.03669024631381035,
-0.02149880677461624,
0.029390577226877213,
0.05112934857606888,
0.04678954556584358,
-0.017761440947651863,
0.021042780950665474,
0.02726072445511818,
0.03723231703042984,
0.00612814724445343,
-0.03648477420210838,
-0.006813626270741224,
-0.009651657193899155,
-0.00017196829139720649,
0.024440458044409752,
-0.01596812531352043,
0.024325687438249588,
0.05939757823944092,
0.02997821383178234,
-0.015615264885127544,
-0.057171933352947235,
0.009673387743532658,
-0.07155701518058777,
-0.02876797877252102,
-0.050317347049713135,
0.02457580715417862,
-0.020953256636857986,
0.0582536943256855,
0.013921140693128109,
0.001287192339077592,
0.029358122497797012,
-0.00692537147551775,
-0.07049981504678726,
0.021936634555459023,
-0.008478689007461071,
-0.03582748770713806,
-0.006935771554708481,
-0.024782642722129822,
-0.032506946474313736,
-0.05543981492519379,
-0.0025454184506088495,
-0.014523005113005638,
-0.017755845561623573,
-0.022423934191465378,
-0.0046495855785906315,
-0.005770151969045401,
-0.005548388231545687,
-0.009099996648728848,
0.03337453678250313,
0.057191573083400726,
-0.027110248804092407,
0.005402791779488325,
0.07846762984991074,
-0.011303011327981949,
0.005345520563423634,
-0.040105562657117844,
0.012413516640663147,
-0.021471234038472176,
0.016642440110445023,
0.038774795830249786,
0.00209731119684875,
0.013595359399914742,
-0.019596794620156288,
0.016373127698898315,
0.020182548090815544,
0.026351677253842354,
-0.006940125022083521,
-0.02474004402756691,
-0.034807391464710236,
0.0032265575136989355,
0.008600273169577122,
0.02954559586942196,
0.024071430787444115,
0.02849861979484558,
-0.004538840148597956,
-0.0012602132046595216,
0.005823384039103985,
0.011543558910489082,
0.048137228935956955,
-0.006019785068929195,
-0.03250569477677345,
-0.0787404477596283,
-0.0007476144237443805,
-0.014375085942447186,
-0.03689960762858391,
0.04699016734957695,
-0.007438259199261665,
-0.02206006646156311,
0.013599894009530544,
0.004220989998430014,
0.006039628759026527,
0.006167873740196228,
0.004683112725615501,
0.0004914741148240864,
0.04080625995993614,
-0.006473621819168329,
-0.026798853650689125,
-0.0008016896317712963,
0.021647466346621513,
0.008598551154136658,
-0.00639133108779788,
-0.022658346220850945,
-0.08185883611440659,
-0.006002824287861586,
0.01841338910162449,
0.004407810512930155,
-0.03891558200120926,
-0.005016890820115805,
-0.030890818685293198,
0.01835549995303154,
0.038023337721824646,
-0.05612858012318611,
0.004838780965656042,
-0.028619341552257538,
0.021358169615268707,
-0.009244104847311974,
-0.05858101323246956,
-0.0043862685561180115,
0.01841532066464424,
0.03592679277062416,
0.015147742815315723,
-0.024385571479797363,
0.0014546755701303482,
-0.004415510222315788,
0.010336627252399921,
0.04396187141537666,
0.028690427541732788,
-0.021484995260834694,
-0.015615398995578289,
0.01574784889817238,
0.03170286864042282,
-0.02757442370057106,
-0.0796392560005188,
-0.025740981101989746,
0.00005093358413432725,
0.027719317004084587,
-0.0013552432646974921,
-0.0615839809179306,
-0.05555865541100502,
0.014434946700930595,
0.0030841040425002575,
-0.03277287632226944,
-0.015361330471932888,
-0.020345108583569527,
0.05567742884159088,
0.04697296395897865,
0.010892271995544434,
0.07945818454027176,
0.03968939185142517,
-0.018115084618330002,
0.03527472913265228,
-0.05949997901916504,
0.03063555434346199,
-0.005759325344115496,
-0.029977641999721527,
-0.04398901388049126,
-0.013028479181230068,
0.021037645637989044,
0.00449428241699934,
-0.02495322935283184,
0.03443945199251175,
-0.01008003018796444,
-0.023360345512628555,
-0.014606853015720844,
0.017333082854747772,
0.020510874688625336,
0.02507591061294079,
-0.0011828163405880332,
0.023202210664749146,
-0.012854738160967827,
-0.013626793399453163,
0.033448122441768646,
0.024708451703190804,
-0.048173654824495316,
0.023789934813976288,
0.006900879554450512,
0.00016605522250756621,
-0.031286995857954025,
-0.018426571041345596,
0.02016076259315014,
-0.031937114894390106,
0.024185817688703537,
-0.029222970828413963,
0.0199612807482481,
0.004026186186820269,
-0.054763004183769226,
-0.030500391498208046,
-0.010376732796430588,
-0.01618095487356186,
0.00964504387229681,
-0.02403419278562069,
0.0400371216237545,
-0.008783217519521713,
0.022799136117100716,
-0.05437884479761124,
-0.004412134177982807,
0.018978482112288475,
0.008601830340921879,
-0.031099239364266396,
-0.05359805375337601,
-0.01342592854052782,
-0.04087080806493759,
-0.026965145021677017,
0.02016778290271759,
0.06181224808096886,
-0.008596621453762054,
-0.03545168414711952,
0.019091332331299782,
0.04688718169927597,
0.03055175021290779,
-0.047928620129823685,
-0.018170790746808052,
0.02685031294822693,
-0.02886609174311161,
-0.04111570864915848,
-0.0032137632369995117,
0.05282364413142204,
-0.017682386562228203,
-0.013932442292571068,
0.012243974022567272,
-0.02679782174527645,
0.0312441848218441,
-0.013759743422269821,
0.0012960170861333609,
0.038645680993795395,
-0.011764856986701488,
-0.009018681943416595,
-0.03237821161746979,
0.02934671752154827,
-0.0122910151258111,
0.05644179880619049,
-0.0010021304478868842,
0.009940438903868198,
-0.038021236658096313,
-0.005981865804642439,
0.031377412378787994,
0.032177723944187164,
0.014887552708387375,
-0.016595924273133278,
0.0597594678401947,
-0.01582852005958557,
0.01903242990374565,
-0.002986028790473938,
0.0003558924945537001,
0.024838551878929138,
0.005674010142683983,
-0.013428223319351673,
0.028862841427326202,
-0.005041247233748436,
-0.0071675777435302734,
-0.044800933450460434,
-0.03824228048324585,
0.012364024296402931,
0.078785240650177,
-0.040635693818330765,
0.05687051638960838,
-0.03625833988189697,
-0.010058269836008549,
0.012380296364426613,
-0.06067507714033127,
-0.010598617605865002,
-0.008686603978276253,
0.01641441509127617,
0.03633784502744675,
-0.00798688642680645,
0.03791183605790138,
0.028718307614326477,
0.04653036594390869,
-0.004429263528436422,
0.024491192772984505,
0.0210956409573555,
-0.006571394391357899,
-0.024004383012652397,
0.023380601778626442,
-0.04518434777855873,
0.03330354392528534,
-0.010012063197791576,
0.06931047141551971,
-0.030523192137479782,
-0.014286650344729424,
0.03447730839252472,
0.005124679766595364,
-0.01689784973859787,
-0.08317719399929047,
0.03117130883038044,
-0.01103358343243599,
0.01716739311814308,
0.012467743828892708,
-0.02360599674284458,
0.018502943217754364,
-0.00885741040110588,
0.04693681001663208,
0.019784295931458473,
-0.01509347278624773,
-0.011985630728304386,
-0.05243801698088646,
-0.006544545758515596,
-0.012957465834915638,
-0.05757828429341316,
0.01619441993534565,
0.0001645846205065027,
-0.04862421005964279,
0.016755016520619392,
-0.0034147179685533047,
0.03421199694275856,
-0.0028376567643135786,
0.0011365492828190327,
0.02315198816359043,
0.09258463978767395,
0.023812659084796906,
0.04624410718679428,
-0.028751561418175697,
0.04607875645160675,
0.11302731931209564,
0.026437973603606224,
0.026152465492486954,
-0.029745766893029213,
0.00841403566300869,
0.004714823793619871,
0.003878482850268483,
-0.037151649594306946,
0.027974169701337814,
-0.01173995342105627,
0.03620855510234833,
-0.027986841276288033,
0.05805562809109688,
-0.02824375033378601,
0.003029260551556945,
0.00959148071706295,
-0.03983069583773613,
-0.04320808872580528,
0.011324607767164707,
-0.00031020992901176214,
0.022257734090089798,
0.03271326422691345,
-0.03256558999419212,
0.0157435592263937,
-0.02345002442598343,
-0.008313977159559727,
-0.03469405323266983,
-0.03904804214835167,
0.008308442309498787,
0.0006136934389360249,
-0.0659695416688919,
0.035179536789655685,
0.03241795301437378,
-0.02434409223496914,
-0.023824770003557205,
-0.0062079355120658875,
0.01938367635011673,
-0.03643792122602463,
0.01664460264146328,
0.0012091071112081409,
0.0006212189327925444,
0.024912793189287186,
0.017376739531755447,
0.018819909542798996,
-0.06683693826198578,
-0.004373545758426189,
-0.029552791267633438,
0.0464794747531414,
-0.03060363605618477,
0.02536172792315483,
-0.027337748557329178,
-0.006982876919209957,
-0.014734827913343906,
-0.05538990721106529,
-0.002795603359118104,
-0.02476627193391323,
0.04251793399453163,
-0.007255381904542446,
-0.025878047570586205,
-0.06086299940943718,
0.004809005185961723,
0.009650849737226963,
0.036732207983732224,
-0.002208945108577609,
0.01120723970234394,
0.02802305296063423,
0.018246987834572792,
0.031107895076274872,
-0.0622534453868866,
-0.0034103645011782646,
-0.005748073570430279,
-0.0021823877468705177,
-0.04411989077925682,
-0.030291784554719925,
0.018502943217754364,
0.024400241672992706,
0.07459986209869385,
-0.023302439600229263,
0.010386260226368904,
-0.019476160407066345,
-0.0912788137793541,
0.018721800297498703,
0.008727366104722023,
-0.035455651581287384,
0.0054880776442587376,
0.00047845407971180975,
0.019235802814364433,
0.022233521565794945,
-0.054837290197610855,
0.016409587115049362,
-0.0036103634629398584,
0.029070621356368065,
0.0270745437592268,
0.006958894897252321,
-0.047148771584033966,
0.006062829401344061,
-0.044624097645282745,
0.01655016653239727,
-0.014115569181740284,
0.006133371964097023,
0.03174574673175812,
0.016684740781784058,
0.009070205502212048,
0.030427411198616028,
-0.021578295156359673,
0.012320385314524174,
0.008454487659037113,
-0.002775781322270632,
-0.014013778418302536,
0.021415920928120613,
0.0009009510977193713,
-0.009060985408723354,
-0.02066701464354992,
-0.005966897122561932,
-0.008272814564406872,
0.003505910513922572,
0.007632690481841564,
-0.02465840056538582,
0.02086079865694046,
-0.05826568230986595,
0.044143110513687134,
-0.0303618386387825,
-0.03225058689713478,
-0.04851866513490677,
0.03461766988039017,
-0.015556639060378075,
0.0026626852340996265,
-0.02115643210709095,
0.012426868081092834,
-0.012880153954029083,
0.026738367974758148,
0.03654950112104416,
0.048213593661785126,
0.01232592947781086,
-0.025510860607028008,
-0.004439861048012972,
-0.03995104506611824,
0.04693111032247543,
-0.03908711299300194,
-0.0315345823764801,
0.05567868426442146,
-0.019593002274632454,
-0.056489236652851105,
-0.016000481322407722,
-0.003345883684232831,
0.012870554812252522,
0.026519736275076866,
-0.02027941308915615,
-0.0416945219039917,
0.04222732409834862,
-0.06855432689189911,
-0.010569687001407146,
-0.0036666570231318474,
-0.03273819014430046,
-0.006699192337691784,
-0.03980182483792305,
0.01108360756188631,
-0.029775282368063927,
0.009094234555959702,
0.05109584331512451,
0.047995999455451965,
-0.04578239470720291,
-0.0011080895783379674,
0.01340204942971468,
-0.015651557594537735,
0.027159789577126503,
0.050511423498392105,
0.03240695595741272,
0.016635706648230553,
0.023200998082756996,
-0.05940736457705498,
0.021248793229460716,
0.01288572046905756,
-0.00721136387437582,
-0.09642253071069717,
-0.012030500918626785,
-0.006704953033477068,
-0.007668967358767986,
0.023596148937940598,
-0.030714580789208412,
-0.0024048988707363605,
0.03372795134782791,
-0.09277055412530899,
-0.009851635433733463,
-0.040627509355545044,
-0.003936377353966236,
-0.04193619266152382,
-0.018130965530872345,
-0.002860085107386112,
0.013506160117685795,
0.014857466332614422,
0.02518727257847786,
0.03615536540746689,
-0.006782919634133577,
-0.0067712655290961266,
-0.03243613988161087,
-0.007172208745032549,
0.03310296684503555,
-0.03140677511692047,
-0.014374829828739166,
0.05748040974140167,
0.009283889085054398,
-0.024648427963256836,
0.010739493183791637,
-0.026894714683294296,
0.012126215733587742,
-0.004472387954592705,
0.0009793475037440658,
-0.022544225677847862,
0.013785636983811855,
0.02961362525820732,
-0.014499961398541927,
0.0036009098403155804,
0.010305684991180897,
0.053682681173086166,
0.011603056453168392,
-0.026240162551403046,
-0.0073639401234686375,
0.025503842160105705,
-0.0258682481944561,
-0.03159216046333313,
0.03053775243461132,
-0.0013714689994230866,
-0.03724530339241028,
0.017436133697628975,
0.02733675390481949,
0.018726274371147156,
-0.02271428517997265,
-0.007967443205416203,
-0.01894662156701088,
0.008531083352863789,
0.02436831034719944,
-0.020912904292345047,
0.02222096361219883,
-0.0026751935947686434,
0.024975767359137535,
-0.003264632076025009,
0.0062305014580488205,
0.01162534486502409,
-0.028346065431833267,
-0.06268993765115738,
-0.005734392907470465,
0.023427361622452736,
-0.007595069240778685,
-0.02230554074048996,
-0.032030049711465836,
-0.017078887671232224,
0.047902025282382965,
0.02504221349954605,
0.02561076730489731,
0.002892052289098501,
-0.03883671760559082,
-0.025383437052369118,
-0.07051608711481094,
0.02482585236430168,
0.0015706460690125823,
-0.021373266354203224,
-0.040743280202150345,
-0.040037039667367935,
0.008431732654571533,
-0.009991376660764217,
0.09896432608366013,
0.03152776509523392,
-0.009588774293661118,
0.004604249726980925,
0.00979363452643156,
0.027995936572551727,
-0.039141181856393814,
0.01806802861392498,
-0.025700394064188004,
-0.04609629884362221,
0.020077088847756386,
-0.03189066797494888,
-0.014231215231120586,
0.016468441113829613,
0.01969774067401886,
-0.029232032597064972,
0.03305123373866081,
-0.026175960898399353,
0.019175179302692413,
0.022623416036367416,
0.018159037455916405,
-0.02497182786464691,
0.047108542174100876,
-0.011530639603734016,
0.04374933987855911,
0.03553808107972145,
0.007915288209915161,
-0.020230695605278015,
0.018388720229268074,
-0.02859693579375744,
-0.029603732749819756,
-0.052346087992191315,
0.001415471313521266,
0.038161247968673706,
-0.041262347251176834,
0.009743278846144676,
0.06516111642122269,
-0.06409557908773422,
0.014349382370710373,
0.04084295034408569,
0.003099642228335142,
0.04653364419937134,
0.026186225935816765,
0.02575298398733139,
0.03386184200644493,
0.012138868682086468,
0.01481482945382595,
0.05285903811454773,
0.044463708996772766,
0.0168997161090374,
-0.0044484250247478485,
0.010174724273383617,
-0.031841203570365906,
-0.004164218902587891,
0.008142814971506596,
0.0201653391122818,
-0.03468071296811104,
-0.024974456056952477,
0.009618675336241722,
-0.025738244876265526,
0.03351240232586861,
0.013247302733361721,
0.009638944640755653,
0.08792777359485626,
0.002710482571274042,
0.013488845899701118,
-0.027873670682311058,
-0.032695334404706955,
0.0011879795929417014,
-0.0012748842127621174,
-0.01098902802914381,
0.037901706993579865,
-0.010493787936866283,
-0.00025531338178552687,
-0.021108683198690414,
0.031078996136784554,
0.018927644938230515,
-0.016530754044651985,
0.013113959692418575,
0.006695665419101715,
-0.0011110922787338495,
-0.040853630751371384,
-0.008106674067676067,
0.01677236519753933,
-0.025444498285651207,
0.008195851929485798,
0.04396757110953331,
0.030331522226333618,
0.03189104050397873,
-0.04649832472205162,
0.0027670590206980705,
0.08267876505851746,
-0.05365126207470894,
-0.010382192209362984,
-0.023463085293769836,
0.025110391899943352,
-0.004285047296434641,
-0.00753100635483861
] |
<p>Which is more appropriate regarding Bernoulli's principle</p>
<ul>
<li>fast moving air causes low pressure or</li>
<li>lower pressure causes fast moving air.</li>
</ul> | 1,994 | [
-0.04986195266246796,
-0.029225461184978485,
-0.02430441975593567,
-0.019383711740374565,
0.010756631381809711,
-0.033366139978170395,
-0.0126096336171031,
0.005474578123539686,
0.00627503776922822,
0.005326097831130028,
0.032436553388834,
0.03862428665161133,
0.032520223408937454,
0.0013253830838948488,
0.011395856738090515,
0.030969807878136635,
-0.013106968253850937,
-0.0034579881466925144,
-0.021026771515607834,
-0.029257917776703835,
-0.03582754731178284,
-0.011874367482960224,
0.02277541533112526,
0.01725476235151291,
-0.03830431029200554,
0.024987654760479927,
0.054411083459854126,
0.0015258926432579756,
-0.014234141446650028,
0.019975746050477028,
-0.035013504326343536,
0.0015636085299775004,
-0.00644589401781559,
0.018405238166451454,
0.013192756101489067,
0.020114868879318237,
-0.017263304442167282,
-0.015706200152635574,
-0.014991986565291882,
0.03212727606296539,
-0.014573533087968826,
0.00740867480635643,
0.021412484347820282,
-0.0031989840790629387,
-0.037811435759067535,
0.05356584116816521,
0.030098963528871536,
-0.02360331080853939,
0.02768591232597828,
-0.08457499742507935,
0.006271072663366795,
0.01776673085987568,
0.029260218143463135,
0.05508695915341377,
-0.030516164377331734,
-0.046956829726696014,
0.06325102597475052,
0.08710943907499313,
-0.03989976644515991,
-0.0566866360604763,
0.033403970301151276,
0.000619043770711869,
-0.009501799009740353,
-0.04148250073194504,
-0.004925721790641546,
0.03752664104104042,
-0.0022955345921218395,
0.004422483965754509,
0.003546939231455326,
0.014258312061429024,
0.016426654532551765,
-0.012792041525244713,
0.045542504638433456,
-0.013537964783608913,
0.04035729542374611,
-0.016480743885040283,
0.006225095130503178,
0.0410144180059433,
0.045191776007413864,
0.04244492948055267,
-0.019490422680974007,
0.02398216724395752,
0.0513094924390316,
0.023846004158258438,
-0.023075086995959282,
-0.033153001219034195,
0.11009229719638824,
0.004310042131692171,
0.008953415788710117,
0.022059578448534012,
-0.0030735156033188105,
0.013365660794079304,
0.016620676964521408,
0.0066867368295788765,
0.023898089304566383,
0.017469745129346848,
-0.017611073330044746,
0.026919884607195854,
0.03254549205303192,
-0.03505131974816322,
-0.0093999607488513,
-0.024397095665335655,
0.039549022912979126,
0.08501189202070236,
0.0031680893152952194,
-0.04985184594988823,
-0.05155571177601814,
0.018572278320789337,
-0.05124650523066521,
0.00795987993478775,
-0.04406101256608963,
0.03273028880357742,
-0.03301919624209404,
-0.006688000168651342,
-0.02936416119337082,
-0.0015996056608855724,
0.014816539362072945,
-0.0029506846331059933,
0.054404523223638535,
0.030814791098237038,
0.06450634449720383,
-0.04075927287340164,
0.014827374368906021,
0.0122611653059721,
-0.056737758219242096,
0.02994658052921295,
-0.02140064164996147,
-0.04816407337784767,
-0.03324086591601372,
0.01768411137163639,
-0.00395790534093976,
-0.005578316282480955,
-0.0128862913697958,
0.010962086729705334,
0.024165313690900803,
0.03086235374212265,
-0.08783652633428574,
-0.029218632727861404,
0.062274277210235596,
0.0004926914698444307,
-0.007250504102557898,
-0.06727669388055801,
0.016297219321131706,
0.016032112762331963,
0.06159767508506775,
-0.016803698614239693,
0.03395751491189003,
-0.011010236106812954,
0.02870933525264263,
-0.02751152403652668,
0.0034123645164072514,
0.010752839967608452,
0.014502831734716892,
-0.022359803318977356,
0.0031948175746947527,
-0.03571305796504021,
0.003086917335167527,
0.035881172865629196,
-0.022679343819618225,
-0.004703579004853964,
0.04520772397518158,
-0.026348866522312164,
-0.017156066372990608,
-0.037574805319309235,
0.061063993722200394,
-0.009822360239923,
0.03433888778090477,
0.0016546943224966526,
0.013035500422120094,
0.032883815467357635,
0.02058124542236328,
0.03554742783308029,
-0.028502829372882843,
-0.03338713198900223,
0.08546967804431915,
-0.0122878672555089,
0.008801275864243507,
-0.004384707659482956,
0.01520927157253027,
0.021060314029455185,
-0.055998146533966064,
-0.0078861890360713,
-0.019732896238565445,
0.0027560126036405563,
-0.03435580059885979,
0.03808234632015228,
0.0008196887210942805,
0.031081916764378548,
0.033010225743055344,
-0.039122574031353,
-0.05613021180033684,
-0.08686956763267517,
0.010431846603751183,
-0.017657777294516563,
-0.009893005713820457,
0.03644146770238876,
-0.017399242147803307,
0.0382339172065258,
-0.043876878917217255,
0.037670403718948364,
0.00843305978924036,
0.00022664949938189238,
0.01962447352707386,
-0.013128216378390789,
-0.016786959022283554,
0.06242581456899643,
0.02048746682703495,
0.005098765250295401,
0.011842486448585987,
-0.00891419593244791,
-0.027648167684674263,
0.0008135537500493228,
-0.015940343961119652,
0.035325732082128525,
0.020715199410915375,
-0.020097898319363594,
0.004754917696118355,
0.00756026478484273,
0.008678803220391273,
0.0073640006594359875,
-0.04321473091840744,
0.07924623787403107,
0.0682789757847786,
0.00047846802044659853,
0.04237976670265198,
0.0369051918387413,
0.010362669825553894,
-0.018162252381443977,
0.032314836978912354,
-0.024269817396998405,
-0.06575401872396469,
-0.010529542341828346,
0.02007026970386505,
0.03343743458390236,
-0.0409221388399601,
0.010790553875267506,
0.013954932801425457,
0.015358206816017628,
0.0019859829917550087,
0.03998501971364021,
0.012930680997669697,
-0.06512819230556488,
0.012869123369455338,
0.032443467527627945,
-0.015519438311457634,
0.030065098777413368,
0.028825845569372177,
0.02465902455151081,
0.048104800283908844,
-0.024210380390286446,
-0.052732422947883606,
0.012453899718821049,
0.04442374035716057,
0.022197185084223747,
-0.00020509143359959126,
-0.004254499450325966,
0.003485224675387144,
-0.0177129078656435,
0.010346721857786179,
-0.007529900409281254,
-0.0014231207314878702,
0.02589966356754303,
-0.008574902079999447,
-0.015870437026023865,
0.007812602445483208,
0.007345303427428007,
-0.02062818966805935,
-0.018501851707696915,
0.05149252712726593,
-0.039057713001966476,
0.007591929752379656,
-0.048720523715019226,
-0.010068390518426895,
-0.027715282514691353,
-0.0025121725630015135,
-0.00947490893304348,
0.017331071197986603,
0.011044050566852093,
-0.056631866842508316,
-0.041511647403240204,
-0.026338307186961174,
-0.005893746856600046,
-0.025248385965824127,
0.033144865185022354,
-0.030918564647436142,
0.012884380295872688,
-0.053881775587797165,
-0.03922038525342941,
0.04937410727143288,
-0.007948717102408409,
0.007185442838817835,
0.038541603833436966,
0.0012462023878470063,
-0.048031482845544815,
-0.0030073628295212984,
-0.059199005365371704,
0.023216476663947105,
0.013087304309010506,
-0.0483386293053627,
0.09210880100727081,
-0.009070118889212608,
-0.027678625658154488,
0.007137067150324583,
-0.05337870866060257,
-0.04230784624814987,
-0.03321468085050583,
0.0040388330817222595,
0.022207465022802353,
0.006558299530297518,
-0.0004885670496150851,
0.027390995994210243,
-0.060760702937841415,
-0.026712531223893166,
-0.03310991823673248,
-0.07396683096885681,
0.027729518711566925,
-0.004019887652248144,
0.05800117924809456,
-0.022896187379956245,
-0.03472493216395378,
0.06363485753536224,
0.02521076239645481,
-0.010473032481968403,
-0.015878504142165184,
-0.053997304290533066,
-0.013976335525512695,
-0.020229067653417587,
0.0011471419129520655,
0.0640358254313469,
-0.00023256234999280423,
0.0008906882139854133,
0.019769133999943733,
0.06698116660118103,
0.03683614730834961,
0.029179144650697708,
-0.019549217075109482,
-0.025972986593842506,
0.026067914441227913,
0.003073405474424362,
0.041500747203826904,
-0.016514096409082413,
-0.010088718496263027,
0.020741857588291168,
-0.03435596823692322,
0.05067872628569603,
0.03376570716500282,
-0.04444233700633049,
0.04075382649898529,
-0.0015716548077762127,
-0.011916900984942913,
-0.0400870107114315,
0.030097780749201775,
0.023174183443188667,
-0.031112108379602432,
0.008434992283582687,
0.011066078208386898,
0.06196952611207962,
0.004377211444079876,
-0.033111702650785446,
0.051575493067502975,
0.054152533411979675,
-0.019286340102553368,
-0.02186332829296589,
0.01933230832219124,
-0.03367557004094124,
0.04377347603440285,
-0.0010697372490540147,
0.0014158438425511122,
0.03170754015445709,
0.010430772788822651,
-0.007213775999844074,
0.02188844047486782,
-0.052126411348581314,
0.019846560433506966,
-0.0548165962100029,
0.013101381249725819,
-0.02877483144402504,
0.01950216479599476,
-0.03469647094607353,
0.04794839397072792,
-0.008604049682617188,
0.024125466123223305,
0.0501798577606678,
0.0020893148612231016,
-0.0772380381822586,
0.02849251590669155,
-0.009206430986523628,
-0.008867278695106506,
0.010581213980913162,
-0.021185846999287605,
0.00209051207639277,
-0.05142248049378395,
-0.009547348134219646,
-0.04299791902303696,
0.04373103380203247,
-0.02696620486676693,
0.03207215294241905,
-0.04054957628250122,
-0.04088931903243065,
0.006229066755622625,
0.001810361398383975,
0.02333015948534012,
-0.02223224565386772,
0.053875863552093506,
0.046250905841588974,
-0.0006330528412945569,
-0.008835687302052975,
-0.013823253102600574,
0.011753442697227001,
0.0013234874932095408,
-0.023244189098477364,
-0.021940961480140686,
0.01536475121974945,
-0.02087266929447651,
0.02297939546406269,
0.047729603946208954,
-0.0012623711954802275,
-0.022744065150618553,
-0.013284833170473576,
-0.048352014273405075,
-0.03472422808408737,
-0.016425536945462227,
-0.009149905294179916,
0.030833488330245018,
0.019777856767177582,
0.014018271118402481,
0.004627860616892576,
-0.01528129167854786,
0.04126722738146782,
0.06586074084043503,
0.008236798457801342,
0.010675137862563133,
-0.00937445554882288,
-0.05104035884141922,
0.0015809637261554599,
-0.011312052607536316,
-0.008674581535160542,
0.057189520448446274,
0.027973415330052376,
-0.03022805042564869,
0.00009454720566282049,
0.017634907737374306,
0.025423677638173103,
-0.029585938900709152,
0.0423751138150692,
-0.010396650061011314,
-0.00633108988404274,
0.02279084548354149,
-0.041148364543914795,
0.022126270458102226,
0.015077593736350536,
0.009333557449281216,
0.044529423117637634,
-0.006732242181897163,
-0.07214828580617905,
-0.04579738900065422,
0.032877907156944275,
0.0008487589075230062,
-0.032162897288799286,
0.03883083537220955,
-0.058465417474508286,
-0.03680562227964401,
0.021385367959737778,
-0.00885096751153469,
0.010708088986575603,
-0.044948890805244446,
-0.003056278917938471,
-0.009672388434410095,
-0.06623250246047974,
-0.019742878153920174,
0.016703004017472267,
-0.021468255668878555,
0.015069971792399883,
-0.006781758274883032,
-0.01072634756565094,
-0.018930424004793167,
0.01027604378759861,
0.037762392312288284,
0.030101239681243896,
-0.007910795509815216,
0.021097593009471893,
-0.03605717420578003,
-0.012114668264985085,
-0.054187923669815063,
-0.044930387288331985,
-0.01218697801232338,
-0.018664244562387466,
0.01485736295580864,
0.0015986057696864009,
-0.025377443060278893,
-0.0291327852755785,
0.03778938949108124,
-0.036018699407577515,
-0.04632261022925377,
-0.009427887387573719,
-0.05174403637647629,
0.024505913257598877,
0.028027860447764397,
0.026689456775784492,
0.0038423684891313314,
0.03851501643657684,
-0.03298690542578697,
-0.005169610492885113,
-0.012835774570703506,
0.015394187532365322,
-0.04604800045490265,
-0.017586184665560722,
-0.03086564503610134,
-0.0006656509358435869,
-0.020495377480983734,
0.028293238952755928,
0.005053826607763767,
0.020049460232257843,
-0.0287189781665802,
-0.08194154500961304,
0.01469192560762167,
0.024336157366633415,
0.03025118075311184,
0.006866368465125561,
-0.024958539754152298,
0.03580334782600403,
0.0023934203200042248,
-0.015934936702251434,
0.023196641355752945,
-0.00016535328177269548,
0.04068439453840256,
0.04960760101675987,
-0.028469935059547424,
0.01562062744051218,
-0.03477933257818222,
-0.0160154290497303,
0.003991037141531706,
-0.058307863771915436,
0.04987949877977371,
0.010786221362650394,
-0.008442126214504242,
0.0087575763463974,
-0.03786267340183258,
-0.03317010775208473,
0.023616278544068336,
0.02007908746600151,
0.009702220559120178,
-0.0548127107322216,
0.05844337120652199,
-0.002638367936015129,
0.003958133049309254,
-0.030246568843722343,
-0.06283164024353027,
-0.006063740700483322,
-0.001680344925262034,
0.017826572060585022,
-0.03878554701805115,
-0.009559828788042068,
-0.03979023918509483,
-0.03796965256333351,
0.0299306008964777,
0.04491620138287544,
-0.009798306040465832,
-0.023706557229161263,
0.029067818075418472,
-0.0280812606215477,
0.05794636532664299,
0.006209016311913729,
0.0074508595280349255,
-0.008226322010159492,
0.0005029513849876821,
-0.014921491965651512,
-0.04862258583307266,
0.06375130265951157,
-0.01626276597380638,
0.0026180970016866922,
0.027700966224074364,
-0.010001289658248425,
0.03726966679096222,
-0.011461256071925163,
0.027809007093310356,
0.04003073275089264,
0.034466300159692764,
-0.028849171474575996,
-0.03207851201295853,
0.005071479361504316,
0.012307845056056976,
0.014831453561782837,
0.02594800852239132,
-0.020756248384714127,
-0.0209469236433506,
-0.024837225675582886,
-0.00018676207400858402,
0.028332697227597237,
-0.03422939032316208,
0.00809243693947792,
0.059417154639959335,
-0.006549207493662834,
-0.009721972048282623,
0.015201705507934093,
-0.018111711367964745,
0.04823813587427139,
0.014510778710246086,
0.003752222051844001,
-0.004976494703441858,
0.02158207818865776,
0.02962835133075714,
-0.033613596111536026,
-0.031393349170684814,
0.01222925167530775,
0.06732162833213806,
0.0005580928409472108,
0.0729767382144928,
0.009991015307605267,
-0.011245915666222572,
0.027805255725979805,
-0.035793475806713104,
0.0100684380158782,
-0.02410694770514965,
0.00235879048705101,
0.005662484560161829,
-0.01767704449594021,
-0.0007161806570366025,
0.04747582599520683,
0.0039981575682759285,
0.012514508329331875,
-0.015827815979719162,
0.03847089409828186,
0.030038276687264442,
0.01949499361217022,
-0.02698691561818123,
-0.011516289785504341,
0.044573672115802765,
-0.051736652851104736,
0.05256307125091553,
-0.03773297742009163,
-0.0021417380776256323,
0.03564563766121864,
0.0198839008808136,
-0.019069232046604156,
-0.06088763475418091,
0.042007699608802795,
-0.025075137615203857,
0.009850812144577503,
0.013184103183448315,
0.005550133064389229,
0.009889396838843822,
0.006230065133422613,
0.03579992055892944,
0.0013238393003121018,
0.00499318540096283,
-0.005030298605561256,
-0.01853279024362564,
-0.024763748049736023,
-0.012453095987439156,
-0.02156979963183403,
0.020661741495132446,
-0.00822354294359684,
-0.051521185785532,
-0.006594492122530937,
-0.002639797981828451,
0.009389866143465042,
0.02606264129281044,
-0.005104920361191034,
-0.012269550003111362,
0.04251481220126152,
0.018602512776851654,
-0.01998627372086048,
0.0016414651181548834,
0.02903919108211994,
0.14160864055156708,
0.04343719407916069,
0.016539104282855988,
-0.05160309374332428,
0.03070048987865448,
0.008592951111495495,
0.007504697889089584,
-0.008685328997671604,
-0.004686081316322088,
-0.008114026859402657,
0.02989475056529045,
0.04752064123749733,
0.042717497795820236,
0.0051580858416855335,
0.0029950153548270464,
0.0445985309779644,
-0.06798487156629562,
0.004267244599759579,
0.007618991658091545,
0.010018975473940372,
-0.012462097220122814,
0.04689895361661911,
0.012997596524655819,
0.012738349847495556,
-0.04080219566822052,
-0.033368486911058426,
0.01015916746109724,
-0.04423996061086655,
0.008497893810272217,
-0.016835706308484077,
-0.05161789804697037,
0.024702608585357666,
0.03880877047777176,
-0.0349690243601799,
-0.04451552405953407,
0.03306550532579422,
-0.013187388889491558,
-0.01850244402885437,
0.019244546070694923,
0.02261078543961048,
-0.000962601276114583,
0.0027753945905715227,
0.010148653760552406,
0.024703631177544594,
-0.060650963336229324,
0.03486119583249092,
-0.02489662915468216,
-0.0047533102333545685,
0.004357004072517157,
0.008849168196320534,
0.00994745921343565,
-0.0036752368323504925,
-0.006250694394111633,
-0.043336085975170135,
-0.04899809882044792,
0.010384444147348404,
0.028941165655851364,
-0.0033591031096875668,
-0.057493310421705246,
-0.034343525767326355,
0.016690831631422043,
-0.023520510643720627,
0.00886047724634409,
-0.014931670390069485,
0.0034613588359206915,
-0.01806771010160446,
0.04140804708003998,
0.049927666783332825,
-0.030709804967045784,
0.002721392782405019,
-0.02990891970694065,
0.004483067896217108,
-0.07445337623357773,
0.0033545061014592648,
0.03278905898332596,
0.007732888218015432,
0.007596729323267937,
0.018525518476963043,
0.0028781183063983917,
-0.023500608280301094,
-0.09008356928825378,
0.06135819852352142,
0.04145778343081474,
0.019205080345273018,
-0.003133597783744335,
-0.01242070272564888,
0.0004527442797552794,
0.03572935238480568,
-0.016026608645915985,
-0.006543074268847704,
0.0009739653905853629,
0.05225886404514313,
0.0005625440971925855,
-0.03536398336291313,
-0.05376240238547325,
0.007990304380655289,
-0.01694299839437008,
0.020662082359194756,
0.020164618268609047,
0.028266828507184982,
0.030502526089549065,
0.002662061480805278,
-0.0011331787100061774,
0.020326722413301468,
-0.03203040361404419,
0.020608432590961456,
-0.001407466595992446,
-0.025004027411341667,
-0.03506641089916229,
0.05363697558641434,
0.014799671247601509,
-0.04710344225168228,
0.011189162731170654,
-0.030963851138949394,
0.017841750755906105,
0.007133081089705229,
-0.0024115624837577343,
0.005142228212207556,
0.05328885838389397,
-0.016243912279605865,
0.02728964015841484,
-0.039884209632873535,
0.005325698759406805,
-0.08571431040763855,
-0.006705452688038349,
0.0046821050345897675,
0.0029690121300518513,
-0.03343741223216057,
0.022270187735557556,
-0.023996960371732712,
0.015899479389190674,
0.008396168239414692,
-0.015039730817079544,
0.005590541288256645,
0.008549250662326813,
0.05302254483103752,
-0.03759600222110748,
0.028579531237483025,
-0.024881698191165924,
-0.027470918372273445,
-0.0015511522069573402,
0.009064169600605965,
-0.05909530445933342,
0.010003132745623589,
0.010400609113276005,
-0.03122982755303383,
0.009183903224766254,
0.009042978286743164,
0.010712587274610996,
0.08074688166379929,
-0.02748691476881504,
-0.000509587989654392,
0.004230611026287079,
-0.020070992410182953,
-0.010373154655098915,
-0.01666303165256977,
0.0104589331895113,
-0.01206297054886818,
-0.009756802581250668,
0.003938395995646715,
0.04125845804810524,
-0.004289621487259865,
-0.0023552661295980215,
-0.00008186366903828457,
-0.01744820363819599,
-0.00023989139299374074,
-0.004868939518928528,
0.0009679195936769247,
0.05307752639055252,
-0.003511160844936967,
-0.038340773433446884,
-0.01584528014063835,
-0.017620157450437546,
0.00032018133788369596,
-0.12729118764400482,
0.0033638884779065847,
0.029797839000821114,
-0.028393138200044632,
0.04480674862861633,
-0.028805892914533615,
-0.0007182036060839891,
0.02137700654566288,
-0.003907551523298025,
-0.006304049398750067,
-0.02321179397404194,
0.04924454540014267,
-0.052890509366989136,
0.021649600937962532,
0.01605740189552307,
0.09139590710401535,
-0.0033588178921490908,
0.04865240305662155,
0.017179297283291817,
0.024039145559072495,
0.002332055941224098,
-0.01068138238042593,
0.0055941371247172356,
0.009712543338537216,
0.02400794066488743,
-0.04614612087607384,
0.059524666517972946,
-0.0012343114940449595,
-0.021778706461191177,
0.04920501261949539,
0.0030896777752786875,
0.038071319460868835,
-0.036478813737630844,
-0.013059938326478004,
-0.009069614112377167,
0.021152380853891373,
0.002893247874453664,
-0.002484443597495556,
0.008915814571082592,
0.011716499924659729,
-0.0109859062358737,
0.024082282558083534,
-0.013132086955010891,
-0.018445618450641632,
0.007366175763309002,
-0.019541358575224876,
-0.026914287358522415,
0.010655873455107212,
-0.009818058460950851,
-0.02290235087275505,
-0.009104662574827671,
0.006715541239827871,
-0.0021794172935187817,
-0.0015991150867193937,
-0.0017046541906893253,
-0.01587796024978161,
-0.010897286236286163,
0.050462137907743454,
-0.01346916239708662,
-0.053123779594898224,
0.02517305314540863,
0.026106130331754684,
-0.033232081681489944,
-0.02425380051136017,
-0.015400494448840618,
0.009616986848413944,
-0.039674825966358185,
-0.018255695700645447,
0.002164966892451048,
-0.0068040043115615845,
-0.037206899374723434,
-0.055928442627191544,
-0.019669240340590477,
0.024078454822301865,
0.04262491688132286,
0.017110375687479973,
-0.008328290656208992,
-0.03323421627283096,
0.0006006762851029634,
-0.04830994829535484,
0.04093709588050842,
-0.02261814847588539,
0.006025415379554033,
-0.054032742977142334,
-0.022928165271878242,
0.0156507957726717,
0.005710411351174116,
0.06515397876501083,
0.028827229514718056,
-0.010621953755617142,
0.0026553154457360506,
-0.008443768136203289,
0.03963066637516022,
0.0018204840598627925,
0.018235916271805763,
0.011612403206527233,
-0.016450539231300354,
-0.007576111704111099,
-0.02267957292497158,
-0.005252200644463301,
0.01921967789530754,
0.015660908073186874,
0.028087465092539787,
0.0509808249771595,
-0.008913831785321236,
-0.020475048571825027,
0.028403334319591522,
0.06894802302122116,
-0.007122659590095282,
0.04878635331988335,
-0.041290126740932465,
0.033473968505859375,
0.011968528851866722,
-0.02168477140367031,
-0.08953892439603806,
0.028005799278616905,
-0.045949265360832214,
-0.016365431249141693,
0.014857628382742405,
-0.047861889004707336,
0.0038151219487190247,
-0.06263981759548187,
-0.011442827060818672,
0.010563199408352375,
-0.04087868332862854,
-0.010073116980493069,
0.01872808299958706,
0.003990076016634703,
0.049355991184711456,
-0.026658102869987488,
0.016104653477668762,
0.03698672354221344,
0.00045290443813428283,
-0.009122445248067379,
0.04498371109366417,
0.008408833295106888,
-0.02298085018992424,
0.009705361910164356,
0.036732375621795654,
0.02488221786916256,
0.027117997407913208,
0.05643068253993988,
0.0017416112823411822,
-0.015625283122062683,
-0.041298918426036835,
0.032546378672122955,
0.0020128278993070126,
-0.032298482954502106,
0.051932450383901596,
0.028356842696666718,
0.07652004808187485,
-0.02133779413998127,
0.02123023383319378,
-0.03252851963043213,
0.004640935454517603,
-0.040983278304338455,
-0.02036081813275814,
0.00258272304199636,
0.028008680790662766,
0.007414605468511581,
-0.005230878014117479,
0.008696528151631355,
-0.011761164292693138,
-0.024453142657876015,
-0.003061317140236497,
-0.0038602983113378286,
-0.0011714601423591375,
0.022820448502898216,
-0.01725359819829464,
-0.0016662609996274114,
-0.05227261781692505,
-0.010074017569422722,
0.0509861595928669,
0.04778424650430679,
0.012110392563045025,
0.01840996742248535,
-0.008399919606745243,
-0.030373288318514824,
0.037755515426397324,
-0.06359129399061203,
-0.010048173367977142,
-0.008608830161392689,
0.015956684947013855,
-0.01606113836169243,
-0.03115951269865036
] |
<p>The "<a href="http://www.vacuvin.com/270/Vacuum_Wine_Saver.html" rel="nofollow">Vacuum Wine Saver</a>" comes with the following "warning":</p>
<blockquote>
<p>Not for sparkling wines</p>
</blockquote>
<p>Intuitively and naively, I imagine that the <a href="http://en.wikipedia.org/wiki/Sparkling_wine#Bubbles" rel="nofollow">bubbles</a> (or the "bubble-potential"—my made-up terminology) will be sucked out of the wine by the pump and that this is also the reason for the "warning".</p>
<p>What is the better-formulated physical/chemical description and explanation? In other words: What happens and why?</p>
<hr>
<p>Extra: Is this (your answer) also a reason for not semi-compressing half-full flexible plastic cola bottles before closing them?</p> | 1,995 | [
-0.03442748263478279,
-0.02405882067978382,
0.0021389296744018793,
-0.01399561483412981,
-0.027709899470210075,
-0.03194614499807358,
0.014940413646399975,
0.013053450733423233,
0.021392816677689552,
0.007376528345048428,
0.017156722024083138,
0.02688847854733467,
0.045153867453336716,
-0.004938145633786917,
-0.023755040019750595,
0.004519852343946695,
0.02060038596391678,
-0.036353472620248795,
0.012384003959596157,
0.0021388521417975426,
-0.0043131341226398945,
0.004049360286444426,
-0.04263295233249664,
0.004436072893440723,
0.003402663627639413,
0.0020072325132787228,
0.03387318179011345,
-0.01890522986650467,
0.01146017387509346,
0.02594514936208725,
-0.018519219011068344,
-0.0005539209814742208,
-0.01604282110929489,
0.006382359657436609,
0.01632743887603283,
-0.004236974753439426,
-0.012455631978809834,
-0.02087010070681572,
0.00010856790322577581,
0.00272858957760036,
-0.03351198881864548,
0.010863634757697582,
0.010522807016968727,
0.05883468687534332,
-0.003633101237937808,
-0.011200625449419022,
-0.03280806913971901,
-0.005442956928163767,
0.033188361674547195,
-0.09255914390087128,
0.013075830414891243,
0.03358413279056549,
0.0377228818833828,
0.033985625952482224,
0.01799306645989418,
0.023478882387280464,
0.050218600779771805,
0.06482468545436859,
-0.056763142347335815,
-0.06360501796007156,
-0.01064438745379448,
0.021058563143014908,
-0.04941873252391815,
-0.04034847393631935,
-0.0290121678262949,
0.03606061637401581,
0.0004996945499442518,
-0.022240133956074715,
0.05580247566103935,
0.04596893861889839,
0.03895361348986626,
-0.03623734414577484,
0.010229203850030899,
-0.015761300921440125,
0.025321783497929573,
-0.03094102256000042,
-0.009167663753032684,
0.0234881192445755,
0.04438565671443939,
0.046421706676483154,
-0.012846599332988262,
-0.00916371215134859,
0.023099437355995178,
0.037405192852020264,
0.015481588430702686,
-0.03334617614746094,
0.08837016671895981,
-0.004686621483415365,
-0.0081818588078022,
0.04361260309815407,
0.007637729402631521,
0.01546468771994114,
0.006712364964187145,
-0.00547824427485466,
-0.021789006888866425,
0.00722896121442318,
0.0005115332896821201,
0.06425642222166061,
0.01125368569046259,
-0.021714715287089348,
-0.01466437615454197,
0.056880876421928406,
0.019841060042381287,
0.07690909504890442,
-0.017059188336133957,
-0.030444465577602386,
-0.027020258828997612,
0.016499701887369156,
0.0002284366637468338,
-0.007250392343848944,
-0.06558921933174133,
-0.015181201510131359,
0.01161422859877348,
0.014875771477818489,
0.02364901453256607,
-0.019116805866360664,
-0.02514512836933136,
0.00213348469696939,
0.06437724828720093,
0.012230521067976952,
0.07114312797784805,
-0.02786189503967762,
0.01827642321586609,
-0.045899469405412674,
-0.034309886395931244,
0.05384485796093941,
0.020590320229530334,
0.013202748261392117,
-0.0329752154648304,
0.014407588168978691,
0.042418383061885834,
0.008004031144082546,
-0.02923022396862507,
0.006666916888207197,
0.025878984481096268,
0.0009450126672163606,
-0.09722965210676193,
-0.021132642403244972,
0.029604472219944,
0.029486244544386864,
-0.003066321834921837,
-0.06675471365451813,
-0.01775973103940487,
-0.0008403738029301167,
0.05898410454392433,
-0.0075637223199009895,
-0.012774551287293434,
0.013287355192005634,
0.060187745839357376,
0.0054241688922047615,
-0.028645487502217293,
0.03371164947748184,
-0.01696016825735569,
-0.020772133022546768,
-0.01533704623579979,
-0.028959278017282486,
0.009738551452755928,
0.0472467802464962,
0.025620227679610252,
-0.025266282260417938,
0.017612818628549576,
-0.03645684942603111,
-0.026830270886421204,
-0.009794442914426327,
0.016199778765439987,
-0.03851873055100441,
0.05112014338374138,
0.020611625164747238,
0.0016135930782184005,
0.052303653210401535,
-0.025614053010940552,
0.02733227238059044,
-0.0243107620626688,
-0.009822456166148186,
0.06755381077528,
0.0011266503715887666,
0.0035427138209342957,
-0.013387608341872692,
0.05399357154965401,
0.008684429340064526,
-0.0037140247877687216,
-0.04644347354769707,
-0.031052792444825172,
0.006559455767273903,
0.026271959766745567,
0.022073931992053986,
-0.0025436116848140955,
0.0024150426033884287,
-0.011598469689488411,
-0.04490996524691582,
-0.060391101986169815,
-0.05542445927858353,
0.015591463074088097,
-0.009648621082305908,
-0.028926903381943703,
0.02167060784995556,
0.0015686802798882127,
0.038257088512182236,
-0.03879007324576378,
0.01930532231926918,
0.000025570350771886297,
0.013375735841691494,
0.012515048496425152,
-0.012516055256128311,
-0.0067528486251831055,
0.017088480293750763,
0.023717205971479416,
-0.02845858596265316,
0.028253525495529175,
0.010777567513287067,
0.03277311846613884,
0.011055437847971916,
-0.010469173081219196,
-0.00622473144903779,
-0.02064373902976513,
-0.03850242495536804,
0.0505191944539547,
-0.01248546689748764,
0.04425562545657158,
0.014347326941788197,
-0.0019038235768675804,
0.05586274713277817,
0.06290184706449509,
-0.004151755012571812,
0.06876493990421295,
-0.00998492818325758,
-0.0015284877736121416,
0.031094569712877274,
0.03621695563197136,
-0.0523453950881958,
0.01381068117916584,
-0.026070771738886833,
0.021427279338240623,
0.0456068255007267,
0.007160962093621492,
0.010712727904319763,
0.011074082925915718,
-0.0023123163264244795,
0.015460235066711903,
0.016282007098197937,
0.009318241849541664,
-0.01867576502263546,
0.03265121951699257,
0.027639102190732956,
-0.02124490961432457,
0.01892833039164543,
0.0012490925146266818,
0.012094918638467789,
0.06967311352491379,
-0.034622300416231155,
0.008164266124367714,
0.027377763763070107,
0.02527765929698944,
0.015032383613288403,
-0.014781944453716278,
0.025511685758829117,
0.03830406814813614,
-0.018693501129746437,
0.0174866933375597,
-0.017285829409956932,
-0.011515168473124504,
-0.0050041391514241695,
-0.03354712948203087,
-0.03150390088558197,
-0.0398239865899086,
0.06462905555963516,
-0.03251279518008232,
-0.007150812540203333,
0.03181806206703186,
-0.05744187906384468,
0.017140774056315422,
-0.0236839447170496,
-0.01884572021663189,
0.003819610457867384,
-0.00663842773064971,
-0.004913355689495802,
-0.014718062244355679,
0.022081421688199043,
-0.04795233905315399,
-0.021698854863643646,
-0.0408838614821434,
0.001128673437051475,
-0.005820510908961296,
0.009264199994504452,
0.008611384779214859,
0.04828740283846855,
0.002970254747197032,
0.014395163394510746,
0.04133882746100426,
-0.006774305831640959,
-0.01797468215227127,
0.0017593299271538854,
0.007371988147497177,
-0.0430620051920414,
-0.02112548239529133,
-0.019058290868997574,
0.044988323003053665,
0.003712139092385769,
-0.027585791423916817,
0.002398792654275894,
-0.0007950248545967042,
-0.07599520683288574,
0.030697526410222054,
-0.04847250133752823,
-0.04818951338529587,
-0.01220072153955698,
-0.003260016907006502,
0.01403594110161066,
-0.04140303656458855,
-0.023252153769135475,
0.016811886802315712,
-0.01886235736310482,
-0.009921260178089142,
-0.057363949716091156,
-0.0764128789305687,
0.006773435976356268,
0.007292136549949646,
0.04779543727636337,
-0.022888442501425743,
-0.03695088252425194,
0.06394822895526886,
-0.016892168670892715,
-0.042454902082681656,
-0.003805727232247591,
-0.023464081808924675,
-0.028373371809720993,
-0.03695725277066231,
-0.03367616608738899,
0.027010930702090263,
-0.033511873334646225,
0.04219120740890503,
-0.00714512262493372,
0.09498268365859985,
0.026194965466856956,
0.011832794174551964,
-0.02742702141404152,
-0.005216700490564108,
0.00490934681147337,
-0.02945866994559765,
0.039899781346321106,
0.041501522064208984,
0.006819495931267738,
0.013409513048827648,
-0.016598928719758987,
0.02976050414144993,
0.037240903824567795,
-0.041573069989681244,
0.047911208122968674,
0.0052155619487166405,
-0.014775210060179234,
-0.01856924034655094,
-0.0024972856044769287,
-0.03056861087679863,
-0.06188366934657097,
0.013019153848290443,
0.021716343238949776,
0.05363566428422928,
-0.028659189119935036,
-0.02373882383108139,
0.027761034667491913,
0.0909593254327774,
-0.06781433522701263,
-0.040071696043014526,
0.008054979145526886,
-0.018736479803919792,
0.03263327106833458,
-0.006658239755779505,
0.022288478910923004,
0.072959303855896,
0.024694792926311493,
0.03128248453140259,
-0.0019060972845181823,
-0.034959208220243454,
0.000719454197678715,
-0.06002258509397507,
-0.007158746477216482,
-0.014740841463208199,
0.023327050730586052,
0.02065170928835869,
0.04724548012018204,
0.01639910414814949,
0.025894323363900185,
-0.009452547878026962,
0.027786454185843468,
-0.044729553163051605,
0.027089951559901237,
0.00804330687969923,
-0.0051132673397660255,
-0.045786287635564804,
-0.00713739637285471,
0.03139293193817139,
0.001432955265045166,
-0.037259023636579514,
-0.029284868389368057,
0.04432392120361328,
-0.05506953224539757,
0.009897211566567421,
-0.019913705065846443,
-0.012614600360393524,
-0.032077860087156296,
-0.007840078324079514,
0.0320308543741703,
-0.016465244814753532,
0.05719306692481041,
-0.0022010914981365204,
-0.02617797814309597,
0.012192638590931892,
0.003018279792740941,
-0.014515700750052929,
0.013236967846751213,
0.006396144162863493,
-0.008172997273504734,
0.025957560166716576,
-0.021504560485482216,
-0.01579740084707737,
0.02657325752079487,
0.024458657950162888,
-0.02298486791551113,
0.027410347014665604,
-0.03451211005449295,
-0.04198220744729042,
-0.017693879082798958,
0.02675928920507431,
0.035369873046875,
-0.007854456081986427,
0.08479298651218414,
0.01509089395403862,
-0.02684120461344719,
-0.005068263504654169,
0.0454958975315094,
0.03934059664607048,
0.008827196434140205,
-0.011997072026133537,
-0.021592915058135986,
-0.007155161816626787,
-0.0020177150145173073,
-0.008558405563235283,
-0.00009449259232496843,
0.06488024443387985,
-0.04391699284315109,
-0.018230531364679337,
-0.014037075452506542,
-0.015902604907751083,
-0.04146602749824524,
0.0031571791041642427,
-0.015216493979096413,
0.011170715093612671,
-0.025801897048950195,
-0.00029098294908180833,
-0.0022289915941655636,
0.025764716789126396,
0.056695062667131424,
0.03073446825146675,
-0.014415507204830647,
-0.08634089678525925,
-0.03870595619082451,
0.04309363290667534,
0.05036816745996475,
-0.0038638445548713207,
0.003298379946500063,
-0.06898058950901031,
-0.034590329974889755,
0.030479300767183304,
-0.09090456366539001,
0.020224131643772125,
-0.02592381462454796,
0.03353272005915642,
-0.029852544888854027,
-0.013881921768188477,
-0.001694460865110159,
-0.02285701222717762,
-0.014658505097031593,
0.018334101885557175,
0.028440536931157112,
-0.017571160569787025,
-0.009923337027430534,
0.03613869100809097,
0.005286899395287037,
0.04545466974377632,
-0.018101193010807037,
-0.02589648775756359,
-0.02481948956847191,
-0.0020808822009712458,
-0.0461781807243824,
-0.046247996389865875,
0.021114910021424294,
-0.023344723507761955,
-0.005432107951492071,
0.04478342458605766,
0.0004990147426724434,
-0.06490359455347061,
0.019186345860362053,
-0.0052556670270860195,
-0.02228413335978985,
0.006953827105462551,
-0.015596257522702217,
0.00018274062313139439,
0.05376842990517616,
0.025219593197107315,
0.03090851567685604,
0.04159491881728172,
-0.040313683450222015,
-0.0024627665989100933,
-0.05009619519114494,
0.016322162002325058,
-0.04669003188610077,
-0.009743088856339455,
-0.06806422024965286,
-0.0007054160232655704,
-0.021377617493271828,
0.05858151614665985,
0.0012626536190509796,
-0.01146695762872696,
-0.022837962955236435,
-0.03384933993220329,
-0.016137726604938507,
0.00027758421492762864,
0.014755554497241974,
-0.012539535760879517,
-0.026825502514839172,
0.0038555494975298643,
0.008953023701906204,
0.01973993144929409,
0.046691589057445526,
0.017214305698871613,
-0.0008720954065211117,
0.012396699748933315,
-0.013009120710194111,
0.006604798138141632,
0.001146550290286541,
0.023055514320731163,
0.00656853849068284,
-0.0552586205303669,
0.07503027468919754,
0.004281986504793167,
-0.006822576746344566,
0.0247096698731184,
-0.026218418031930923,
0.011510459706187248,
0.0038793960120528936,
-0.04065883159637451,
0.044812265783548355,
-0.05857216566801071,
0.06645435094833374,
-0.022311517968773842,
0.005579566117376089,
-0.05142144113779068,
-0.03614354506134987,
0.054018884897232056,
-0.010659902356564999,
-0.02915339544415474,
-0.02916967123746872,
0.001739431987516582,
-0.006089029833674431,
-0.026386182755231857,
0.020985988900065422,
-0.005083453841507435,
-0.057320378720760345,
-0.0037153714802116156,
0.034223876893520355,
-0.012220163829624653,
0.04959502071142197,
0.026369541883468628,
0.015484070405364037,
0.012210797518491745,
-0.008778070099651814,
-0.04347532242536545,
0.0262563806027174,
0.0005722310161218047,
-0.05094899609684944,
-0.02276257798075676,
-0.02050243318080902,
0.00009119604510487989,
0.0505688413977623,
-0.04619738832116127,
0.01666131243109703,
-0.016411734744906425,
0.016456903889775276,
-0.012668753042817116,
-0.030762355774641037,
0.024231649935245514,
-0.0015343164559453726,
0.043494366109371185,
0.02564498968422413,
-0.007217041216790676,
-0.017731402069330215,
-0.02576444111764431,
-0.0005578304408118129,
-0.0052408818155527115,
-0.023812908679246902,
0.021117737516760826,
0.0398981049656868,
-0.0433029867708683,
0.0041168611496686935,
0.0067556812427937984,
-0.021349160000681877,
0.043600380420684814,
0.03170555830001831,
-0.028971213847398758,
0.01613728515803814,
-0.0019497430184856057,
-0.025026103481650352,
-0.03092024475336075,
-0.02637469209730625,
0.02812787890434265,
0.04745626822113991,
-0.013633565977215767,
0.02530762180685997,
-0.006660528481006622,
-0.040309514850378036,
-0.021475037559866905,
-0.0590205192565918,
0.02320650964975357,
0.020579710602760315,
0.01294033695012331,
0.021715981885790825,
-0.02433289773762226,
0.00016804262122604996,
0.023699600249528885,
0.03836255148053169,
-0.01270893681794405,
0.011028232984244823,
0.06380311399698257,
0.02923542633652687,
0.01199442707002163,
-0.056225575506687164,
-0.03553648665547371,
0.043225791305303574,
-0.06395603716373444,
0.03895150125026703,
0.020728841423988342,
-0.015179217793047428,
0.0229670237749815,
-0.009977276436984539,
-0.009402052499353886,
-0.06420936435461044,
-0.0147749288007617,
-0.01729893498122692,
0.034969959408044815,
-0.0025780308060348034,
-0.03442047908902168,
-0.00876590982079506,
-0.011913828551769257,
0.015953276306390762,
0.020768340677022934,
0.014187836088240147,
-0.0038889318238943815,
-0.03976082056760788,
0.002703980077058077,
-0.03477508947253227,
0.026807047426700592,
0.026965713128447533,
0.01320237573236227,
-0.0469195619225502,
0.005529605783522129,
-0.017589930444955826,
0.02063800022006035,
-0.01663910411298275,
0.003875051625072956,
0.0016088110860437155,
0.05565831437706947,
-0.017658259719610214,
-0.004875045269727707,
-0.006072672549635172,
0.014852299354970455,
0.14805500209331512,
0.014890426769852638,
-0.0033501777797937393,
-0.018614642322063446,
0.011329296045005322,
0.026840822771191597,
0.04178142920136452,
0.0018299963558092713,
-0.018499070778489113,
-0.020573701709508896,
0.04191454127430916,
0.008377261459827423,
0.08661148697137833,
-0.022514887154102325,
0.03980650752782822,
0.02402716875076294,
-0.05231783539056778,
-0.0008869647863321006,
0.025462212041020393,
0.042989712208509445,
-0.021443365141749382,
0.009537484496831894,
-0.014423343352973461,
0.02432142198085785,
-0.021991733461618423,
0.013788008131086826,
-0.04571239650249481,
-0.025191795080900192,
0.03653506934642792,
0.0059786089695990086,
-0.04071315377950668,
-0.010585271753370762,
0.02700592391192913,
-0.009159714914858341,
-0.030220340937376022,
0.0033635857980698347,
0.04397350177168846,
-0.024189680814743042,
0.009889737702906132,
-0.01036800630390644,
0.03003639541566372,
0.00557083822786808,
0.042014140635728836,
0.029566066339612007,
-0.06303037703037262,
0.0077911000698804855,
0.00036918441765010357,
0.008382711559534073,
0.02035871520638466,
-0.016444982960820198,
-0.023670323193073273,
-0.02927960269153118,
-0.008741610683500767,
-0.061610545963048935,
-0.0579926073551178,
-0.0005947666359134018,
-0.0003574419242795557,
0.030855277553200722,
-0.04300839826464653,
-0.02404569461941719,
-0.027864567935466766,
-0.005859312601387501,
0.028478475287556648,
-0.04316425696015358,
-0.006422506645321846,
-0.019259948283433914,
-0.02249610610306263,
0.008301103487610817,
-0.007105594035238028,
-0.026413407176733017,
-0.04258212074637413,
0.011922666803002357,
-0.05801979824900627,
0.005481743719428778,
-0.02214156836271286,
0.036887869238853455,
0.059846628457307816,
0.0014205820625647902,
0.0012994748540222645,
0.007803431246429682,
-0.08621016144752502,
0.04602399840950966,
-0.021732158958911896,
-0.007906807586550713,
-0.0339035727083683,
0.009261260740458965,
-0.00035022941301576793,
0.011662363074719906,
-0.03435751423239708,
-0.007620694115757942,
-0.006710830610245466,
0.07378309220075607,
0.012099659070372581,
0.006139767821878195,
-0.030700070783495903,
0.01212085410952568,
-0.024979157373309135,
-0.03962840139865875,
0.0030087651684880257,
0.04656912013888359,
0.0024383270647376776,
0.020738016813993454,
0.01982324756681919,
-0.016378989443182945,
-0.03771760314702988,
0.021720392629504204,
0.034706149250268936,
0.0037648745346814394,
-0.03689388558268547,
0.015448508784174919,
0.01154420431703329,
-0.031976889818906784,
-0.005842604674398899,
0.0041935378685593605,
-0.01651185378432274,
0.012570394203066826,
0.02770620957016945,
-0.0012365226866677403,
0.005518810357898474,
-0.05254313722252846,
0.06603391468524933,
-0.05555562674999237,
-0.02546682022511959,
-0.07102375477552414,
0.025110509246587753,
-0.009941442869603634,
0.01252050045877695,
-0.018093032762408257,
0.007244815584272146,
-0.050632279366254807,
-0.005420459434390068,
-0.01573999971151352,
0.024103637784719467,
-0.01721717044711113,
-0.02830827422440052,
0.018089575693011284,
0.005566023290157318,
0.034057967364788055,
-0.02902739867568016,
-0.04323629289865494,
0.04474031925201416,
-0.0237784031778574,
-0.05862593650817871,
-0.026332471519708633,
0.0024680818896740675,
0.00769471563398838,
0.029049478471279144,
0.030185580253601074,
-0.021245064213871956,
0.058190714567899704,
-0.017688477411866188,
0.012176696211099625,
-0.0089042903855443,
-0.012153244577348232,
0.014326083473861217,
0.004297837149351835,
0.00018892406660597771,
0.02225298061966896,
0.0012695657787844539,
0.017537234351038933,
0.052557963877916336,
0.004937175661325455,
0.0013368456857278943,
-0.0030082545708864927,
-0.004013500642031431,
-0.011495066806674004,
-0.017418628558516502,
0.01459781639277935,
0.0020085691940039396,
0.046810682862997055,
-0.01165777537971735,
0.001123842434026301,
0.009946807287633419,
-0.029074016958475113,
-0.12156209349632263,
-0.011239885352551937,
0.0067865727469325066,
0.014892744831740856,
0.000007316359187825583,
-0.01510398369282484,
0.05586814135313034,
0.009813491255044937,
-0.07904647290706635,
-0.02137092873454094,
-0.031578321009874344,
-0.0006734521593898535,
-0.03378814458847046,
0.028528600931167603,
-0.023777784779667854,
0.0742993876338005,
0.010768283158540726,
-0.009559152647852898,
0.011817713268101215,
-0.024805771186947823,
-0.016125774011015892,
-0.016490748152136803,
0.02035762183368206,
0.047711268067359924,
-0.022336216643452644,
0.004128885455429554,
0.07840700447559357,
-0.019315434619784355,
-0.010358297266066074,
0.005207302048802376,
0.0011583265149965882,
0.05748099833726883,
0.02828894928097725,
-0.022507809102535248,
-0.02966921776533127,
0.008797995746135712,
0.01760927587747574,
0.04369555041193962,
-0.023579755797982216,
0.05341476947069168,
0.044021639972925186,
0.025876378640532494,
0.0004060025094076991,
0.047131866216659546,
0.011391939595341682,
-0.026380518451333046,
-0.03261714056134224,
0.0030185857322067022,
-0.01723744347691536,
0.009934947825968266,
-0.016397133469581604,
0.017248928546905518,
0.02750050649046898,
-0.03009023331105709,
0.03923586383461952,
-0.06966419517993927,
0.019313663244247437,
0.027888720855116844,
0.004683239851146936,
0.013734150677919388,
0.024615930393338203,
0.011047931388020515,
0.00919781718403101,
-0.02267571911215782,
0.022249335423111916,
-0.006718285847455263,
-0.014295563101768494,
-0.023420140147209167,
0.006017804611474276,
0.0293426513671875,
-0.012370739132165909,
-0.025506094098091125,
-0.0409700982272625,
0.07106220722198486,
0.06924445927143097,
0.03338330239057541,
0.04462219402194023,
-0.021191591396927834,
0.01958049088716507,
-0.06632035225629807,
-0.009121616370975971,
-0.005189414136111736,
-0.040372513234615326,
-0.03209982067346573,
-0.06855835765600204,
0.029871800914406776,
0.026451636105775833,
0.034627411514520645,
-0.010159807279706001,
-0.02943957969546318,
0.03689972683787346,
0.019526461139321327,
0.0014440834056586027,
-0.02009125053882599,
0.005333776585757732,
0.020374730229377747,
0.003257882548496127,
0.029010629281401634,
0.02018367312848568,
-0.00945490226149559,
-0.01756669580936432,
0.07001332193613052,
0.010690011084079742,
0.01830185391008854,
-0.0007887865067459643,
0.01111022848635912,
0.030698439106345177,
0.01975579746067524,
0.017015088349580765,
0.06919845193624496,
-0.018022891134023666,
0.02112226001918316,
-0.0006743290578015149,
0.011680063791573048,
-0.02944561466574669,
0.04468109831213951,
-0.03534894809126854,
-0.018433431163430214,
0.008092804811894894,
-0.06925469636917114,
0.014912993647158146,
-0.03444257006049156,
-0.022711990401148796,
0.03560580685734749,
-0.03154733404517174,
-0.014810595661401749,
0.006612890399992466,
0.007063364144414663,
0.07087553292512894,
-0.0007682476425543427,
-0.002439881907775998,
0.026200328022241592,
0.0055505046620965,
-0.04225754737854004,
0.04705179110169411,
0.04840834438800812,
0.03157037869095802,
-0.02900329977273941,
0.032316192984580994,
-0.002518070861697197,
0.01338889729231596,
0.034637417644262314,
0.010559728369116783,
-0.0024395808577537537,
-0.028478406369686127,
-0.00947133731096983,
0.009192418307065964,
-0.0024493348319083452,
0.024783466011285782,
0.02751312032341957,
0.06129302456974983,
-0.005956279579550028,
0.024124249815940857,
-0.03543555364012718,
0.03704351931810379,
-0.01969068869948387,
0.009927176870405674,
-0.026328450068831444,
0.02044101431965828,
-0.02800924889743328,
-0.00413745641708374,
-0.036964051425457,
-0.01056886650621891,
0.002007019007578492,
-0.010741181671619415,
0.015703432261943817,
-0.0002085020678350702,
-0.0042961095459759235,
0.0021789916791021824,
-0.030564995482563972,
-0.018024813383817673,
-0.007399884518235922,
0.03916063904762268,
0.028551634401082993,
-0.004198306705802679,
-0.0057490188628435135,
0.005187195725739002,
-0.005544780753552914,
0.08480687439441681,
-0.036336179822683334,
-0.011661600321531296,
0.012304496020078659,
-0.017075560986995697,
-0.03863378241658211,
-0.013492688536643982
] |
<p>Not sure if this is the right place to ask this but here goes.</p>
<p>If the north pole ice sheets melt, everyone agrees this would be a bad thing, however one of the reasons they state for this being a bad thing is the rise in sea level.</p>
<p>Given that the north pole is essentially a massive ice sheet floating on water, how can the melting of this ice raise the sea levels?</p>
<p>In my understanding the amount of water displaced by the ice, is equal to the amount of water that would be added to the ocean.</p>
<p>I tried an experiment where i marked the water level in a glass of water with ice, then waited for the ice to melt. the water level was identical.</p>
<p>Am I missing something here?</p> | 35 | [
0.0105982581153512,
-0.03702490031719208,
-0.0031537513714283705,
0.00009458288695896044,
0.027433892711997032,
0.015226270072162151,
-0.025198083370923996,
-0.04040266200900078,
0.012207900173962116,
-0.03983258455991745,
-0.0019660652615129948,
0.04924093186855316,
0.041809987276792526,
-0.0043985070660710335,
0.006705717649310827,
0.03987876698374748,
0.0016763441963121295,
-0.020851371809840202,
0.01425517350435257,
-0.018006274476647377,
-0.02623230591416359,
0.033027730882167816,
-0.002694827737286687,
0.005317034665495157,
-0.018595028668642044,
0.02481691725552082,
0.06185126304626465,
0.00488172797486186,
0.014869706705212593,
0.04812631383538246,
0.014847079291939735,
-0.042692653834819794,
0.03172801807522774,
0.04829861596226692,
0.010374998673796654,
0.0032291084062308073,
-0.028868675231933594,
0.0002512706851121038,
-0.013404402881860733,
0.05079638212919235,
-0.005219621118158102,
-0.03207826986908913,
-0.020613480359315872,
0.052102748304605484,
-0.026702838018536568,
0.01233640220016241,
0.01884022168815136,
-0.019543997943401337,
0.007615245878696442,
-0.05352361872792244,
0.04280955344438553,
0.016347946599125862,
0.04423627257347107,
0.06330188363790512,
0.0126905906945467,
-0.00045604119077324867,
0.09540801495313644,
0.05431535840034485,
-0.01808122731745243,
-0.03886296972632408,
-0.022607574239373207,
-0.011885452084243298,
-0.011248975060880184,
-0.005504809785634279,
-0.0027448656037449837,
0.036133475601673126,
-0.03741918504238129,
0.02422664687037468,
0.01917709782719612,
0.012663683854043484,
0.012042154558002949,
0.008235453628003597,
0.016056997701525688,
-0.0019446362275630236,
0.027552837505936623,
-0.022554459050297737,
0.011231131851673126,
0.07366980612277985,
0.00037955748848617077,
0.06452679634094238,
-0.000002397639491391601,
0.01332108210772276,
0.0578082911670208,
0.05362604185938835,
0.021067727357149124,
0.019989371299743652,
0.05736815929412842,
-0.011269107460975647,
0.02671106345951557,
0.01625824347138405,
-0.0005422968533821404,
-0.026598529890179634,
-0.016436876729130745,
-0.02576804906129837,
0.000188187143066898,
0.009706929326057434,
-0.00861858669668436,
0.08711693435907364,
0.04475812986493111,
0.0017113788053393364,
0.025713959708809853,
-0.01748812198638916,
0.0017083740094676614,
0.033946067094802856,
0.001788654481060803,
-0.014233889058232307,
-0.03838236257433891,
0.03960072621703148,
-0.0034892696421593428,
-0.03820664808154106,
-0.018681293353438377,
0.01286403089761734,
-0.011360254138708115,
-0.055143311619758606,
-0.0005831274902448058,
-0.022455699741840363,
0.005588431376963854,
-0.02868328057229519,
0.05346537381410599,
0.03208605945110321,
0.04190054535865784,
-0.03249780833721161,
0.019692186266183853,
-0.009069693274796009,
-0.0968141257762909,
0.012200959026813507,
-0.003991484176367521,
-0.009813264012336731,
-0.028843093663454056,
0.03132925555109978,
-0.006370511371642351,
0.024860579520463943,
0.034258950501680374,
-0.020062504336237907,
0.07459193468093872,
0.0035622736904770136,
-0.07469378411769867,
-0.07272598892450333,
0.0817943587899208,
0.0076879654079675674,
-0.01237404253333807,
-0.0625806450843811,
-0.0036055531818419695,
0.0005728212418034673,
0.051850516349077225,
-0.013038544915616512,
0.02117800898849964,
0.019338225945830345,
0.0014570819912478328,
-0.008899305947124958,
-0.005225533619523048,
-0.014912500977516174,
0.023839034140110016,
-0.03579508513212204,
-0.029302453622221947,
-0.07375535368919373,
0.023571623489260674,
0.03882071003317833,
-0.007146528922021389,
-0.017471961677074432,
0.03441697359085083,
-0.02436072938144207,
0.01431237068027258,
-0.007869559340178967,
-0.00464616809040308,
-0.01725245825946331,
0.0445210337638855,
0.0029331210535019636,
-0.029263678938150406,
0.03959792107343674,
0.011904856190085411,
0.047274406999349594,
0.0015594852156937122,
0.03201845660805702,
0.04784425348043442,
-0.04789840802550316,
0.006314931903034449,
-0.04220875725150108,
0.0005666170036420226,
0.04092973470687866,
-0.03660350292921066,
-0.0053619020618498325,
-0.015104825608432293,
0.0064128125086426735,
0.020642120391130447,
0.04529351741075516,
-0.003999059554189444,
-0.006308427546173334,
0.021653292700648308,
-0.0837116539478302,
-0.008546228520572186,
-0.08052168041467667,
0.016317222267389297,
-0.04456130042672157,
0.04860963299870491,
0.011760661378502846,
0.02282770164310932,
0.010776760056614876,
-0.04525000974535942,
-0.028376493602991104,
-0.02116076461970806,
0.03925672546029091,
0.009929083287715912,
-0.017062857747077942,
0.044322289526462555,
0.06145893409848213,
0.0280093215405941,
-0.012858670204877853,
-0.007345234043896198,
-0.03843563422560692,
-0.014820334501564503,
0.012829856015741825,
-0.02465236186981201,
-0.01249855849891901,
-0.013722190633416176,
-0.012598760426044464,
-0.018926238641142845,
0.02232876420021057,
-0.0028758912812918425,
0.03614095225930214,
-0.010138030163943768,
0.12312664836645126,
0.030843619257211685,
0.016300225630402565,
-0.000240269087953493,
0.00852192472666502,
0.04089618846774101,
-0.015020028688013554,
-0.01240969356149435,
-0.0187186598777771,
-0.035236600786447525,
0.0342392660677433,
0.019260937348008156,
0.015614419244229794,
-0.03613128513097763,
0.0030548933427780867,
0.02458060346543789,
0.06504446268081665,
0.0314081646502018,
0.017645642161369324,
0.012084851041436195,
0.015449035912752151,
0.0143092330545187,
0.010975656099617481,
0.011515938676893711,
0.024795884266495705,
0.0302274189889431,
0.03805866092443466,
0.0000612852891208604,
-0.0053499056957662106,
-0.024521488696336746,
-0.00040314902435056865,
0.010410615243017673,
0.044988688081502914,
-0.004640538245439529,
0.0015715110348537564,
0.015132250264286995,
-0.04935329034924507,
0.012016365304589272,
0.007608620449900627,
0.015127927996218204,
-0.034077238291502,
-0.0499921552836895,
0.0016601320821791887,
0.019360573962330818,
0.01145061757415533,
-0.00430231774225831,
-0.008256567642092705,
0.0295279361307621,
-0.01848277449607849,
0.0225616917014122,
-0.01373129989951849,
-0.033350903540849686,
-0.016443351283669472,
0.02603563666343689,
0.030659787356853485,
-0.010537789203226566,
0.06517619639635086,
-0.046500708907842636,
-0.012929821386933327,
-0.010461484082043171,
-0.03023778460919857,
-0.04151753708720207,
0.030103202909231186,
-0.05488152056932449,
0.015359380282461643,
-0.015351262874901295,
-0.021322615444660187,
0.04638555273413658,
0.008271032012999058,
0.011521941982209682,
0.026307109743356705,
-0.029117872938513756,
-0.014976405538618565,
-0.047471579164266586,
-0.06681926548480988,
0.012601610273122787,
-0.0018233447335660458,
-0.00275429361499846,
0.056872181594371796,
-0.02422044612467289,
-0.028764335438609123,
0.02758866176009178,
-0.06200848147273064,
-0.026292873546481133,
0.010548986494541168,
-0.003354917047545314,
0.0016525699757039547,
-0.05144393816590309,
-0.017067227512598038,
0.0028677070513367653,
-0.07933388650417328,
-0.0038550058379769325,
-0.0272133257240057,
-0.093287393450737,
0.04665461927652359,
0.010114474222064018,
0.030093329027295113,
-0.027635162696242332,
-0.023906182497739792,
0.05532441660761833,
0.019910702481865883,
-0.022878361865878105,
-0.02952556125819683,
-0.009486629627645016,
-0.01691494509577751,
-0.021723000332713127,
0.005196853075176477,
0.04001115635037422,
-0.014787144027650356,
0.03360994905233383,
0.029901430010795593,
0.012974813580513,
-0.005659645888954401,
0.029980413615703583,
0.0024714642204344273,
-0.012963249348104,
0.027883172035217285,
0.03695196285843849,
0.01971566118299961,
-0.004653155338019133,
-0.03800920397043228,
-0.019999653100967407,
-0.008211851119995117,
0.07843203842639923,
0.03427870571613312,
-0.012744436971843243,
0.035022299736738205,
-0.016599522903561592,
-0.012971892952919006,
-0.06008423864841461,
0.028109807521104813,
0.00698101194575429,
0.02539392188191414,
0.030071072280406952,
-0.032861847430467606,
0.05290580913424492,
0.022425582632422447,
-0.007149399258196354,
0.026940064504742622,
0.04333702102303505,
-0.03986062854528427,
-0.030789492651820183,
-0.02815890498459339,
0.017686333507299423,
0.031089114025235176,
-0.006062755361199379,
0.024439789354801178,
0.04560711979866028,
-0.0053070951253175735,
0.01673804596066475,
-0.00689009390771389,
-0.05129488930106163,
-0.0035945833660662174,
-0.07706405967473984,
-0.006148444022983313,
0.0006896874983794987,
0.03920937702059746,
0.023176811635494232,
0.036567576229572296,
0.036626216024160385,
-0.0034803657326847315,
0.06286672502756119,
-0.004879673942923546,
-0.052285872399806976,
0.0017351503483951092,
-0.06424645334482193,
-0.0017361120553687215,
0.005743120331317186,
-0.02434217743575573,
0.021132921800017357,
-0.047274213284254074,
-0.009522803127765656,
-0.030015533789992332,
-0.012012037448585033,
-0.033868882805109024,
0.012908294796943665,
0.0162223931401968,
-0.006535770837217569,
-0.011512547731399536,
0.014265752397477627,
0.04079362377524376,
-0.03511242941021919,
0.0042028361931443214,
0.04867047443985939,
-0.007593480404466391,
-0.006268236320465803,
-0.026614947244524956,
0.008531847968697548,
0.041247013956308365,
0.030019409954547882,
0.007774300407618284,
0.01681223139166832,
-0.023006973788142204,
0.013318942859768867,
0.0041846949607133865,
-0.006441215053200722,
-0.007325941231101751,
0.023356787860393524,
-0.04716508463025093,
-0.03878791257739067,
-0.005783111788332462,
0.014433972537517548,
0.022058071568608284,
-0.0006140280165709555,
0.0009526248322799802,
0.018347585573792458,
0.01393755804747343,
0.002971704350784421,
0.06141354516148567,
0.06745631992816925,
-0.0013637291267514229,
0.04019689932465553,
-0.03667442873120308,
-0.04592747986316681,
-0.03415847197175026,
0.000054140899010235444,
0.0387871190905571,
-0.00878407433629036,
-0.013668776489794254,
0.0009828958427533507,
0.05694873258471489,
-0.01930798590183258,
-0.019541211426258087,
-0.02928927168250084,
0.006107653956860304,
0.01127201784402132,
-0.015062653459608555,
0.02338576316833496,
0.021392829716205597,
-0.00956269446760416,
0.028350595384836197,
-0.03982439264655113,
-0.012532306835055351,
-0.10378582775592804,
-0.008159777149558067,
0.02854057401418686,
0.015701336786150932,
-0.01751113496720791,
-0.003953170496970415,
-0.07360722124576569,
0.009752126410603523,
0.023379327729344368,
-0.043211329728364944,
-0.004382811952382326,
0.00016526672698091716,
0.007215880788862705,
-0.011975381523370743,
0.001198295853100717,
0.005777469836175442,
-0.012892679311335087,
-0.021408244967460632,
0.02796139195561409,
0.0014109078329056501,
0.004138578660786152,
-0.004245026968419552,
0.03908761963248253,
0.049126412719488144,
0.05719788372516632,
0.02825797162950039,
-0.013117044232785702,
-0.011567746289074421,
0.006717171519994736,
-0.04705846309661865,
-0.050704941153526306,
0.02994334138929844,
0.0016922330250963569,
-0.016977783292531967,
0.014270774088799953,
-0.013692614622414112,
-0.07569949328899384,
0.0240874532610178,
0.030841972678899765,
-0.001986702671274543,
-0.010275616310536861,
-0.04521872475743294,
0.033561449497938156,
0.039461761713027954,
0.008246022276580334,
0.06651628017425537,
0.046147290617227554,
-0.027821749448776245,
-0.002428203821182251,
-0.030358830466866493,
0.03272667154669762,
-0.07366545498371124,
-0.020849494263529778,
0.0028941843193024397,
0.004055140074342489,
-0.019606266170740128,
0.031784553080797195,
-0.012174407951533794,
-0.0170912966132164,
-0.025663474574685097,
-0.0348944254219532,
-0.0054464759305119514,
0.010482607409358025,
0.023449724540114403,
-0.01159466989338398,
-0.015408793464303017,
0.0012981852050870657,
0.010796899907290936,
-0.05584929138422012,
0.0275280699133873,
0.005727841984480619,
-0.003350778017193079,
-0.01725972443819046,
-0.013130676932632923,
0.014082683250308037,
0.012081911787390709,
-0.013973993249237537,
0.0189837496727705,
-0.00042787808342836797,
0.013815624639391899,
-0.019662506878376007,
-0.010148386470973492,
-0.013290101662278175,
-0.05789094790816307,
-0.0050392355769872665,
0.01511786226183176,
0.003931779880076647,
0.015585015527904034,
-0.03869938105344772,
-0.0020258454605937004,
0.04643614590167999,
0.056476350873708725,
-0.06116941571235657,
-0.07336369156837463,
0.04324093461036682,
0.01833263784646988,
0.01452791877090931,
-0.018625568598508835,
-0.03545507788658142,
-0.02642964944243431,
0.006326090078800917,
-0.04109513759613037,
0.05260087922215462,
-0.03600463271141052,
-0.01608988270163536,
0.025141991674900055,
0.007209315430372953,
0.07942208647727966,
-0.04482042044401169,
-0.018567422404885292,
0.005170592572540045,
-0.053005948662757874,
-0.03492937982082367,
-0.01671263575553894,
0.06327355653047562,
-0.037784427404403687,
-0.025245195254683495,
-0.0067580631002783775,
-0.02164195291697979,
0.036811280995607376,
-0.003576772753149271,
-0.019432520493865013,
0.02794911153614521,
0.05037272721529007,
-0.01838669925928116,
-0.04784732684493065,
0.00614275922998786,
-0.02184978313744068,
0.00005475798388943076,
-0.001408916199579835,
0.022115876898169518,
-0.008864824660122395,
-0.038407742977142334,
0.016636155545711517,
-0.010029313154518604,
-0.0036116279661655426,
0.001649903366342187,
0.07109613716602325,
-0.04550889879465103,
-0.02331804484128952,
0.0049419826827943325,
-0.04373959079384804,
0.03410336375236511,
0.031078564003109932,
0.023100471124053,
0.02382499910891056,
0.031448282301425934,
-0.05125970393419266,
-0.047348830848932266,
-0.029009822756052017,
-0.002281314693391323,
0.05720214545726776,
-0.03373551741242409,
0.017879579216241837,
0.009608362801373005,
0.003766298061236739,
0.01023680530488491,
-0.008649235591292381,
-0.0082219447940588,
0.029154740273952484,
-0.0030930463690310717,
0.015151829458773136,
-0.029406333342194557,
-0.002881674561649561,
-0.015892192721366882,
0.0657142773270607,
0.01577444188296795,
0.02465001493692398,
0.05133805051445961,
-0.0023731973487883806,
0.0007756591076031327,
-0.008404744789004326,
-0.06484606862068176,
0.05619434267282486,
-0.015496544539928436,
0.010467668995261192,
-0.03043956682085991,
-0.007657673209905624,
0.04204382747411728,
0.009532099589705467,
0.030989304184913635,
-0.06448104977607727,
-0.03396059572696686,
-0.03247758746147156,
0.0033403339330106974,
-0.025484509766101837,
0.044088225811719894,
0.007954629138112068,
0.00606023333966732,
0.007819156162440777,
-0.0023750518448650837,
0.0007327043567784131,
-0.049070682376623154,
-0.10025481134653091,
-0.03454120084643364,
-0.03552722558379173,
-0.01435621827840805,
0.022293556481599808,
0.013376040384173393,
-0.02154705300927162,
0.022899866104125977,
-0.021420059725642204,
-0.006573102902621031,
0.022829856723546982,
0.011962421238422394,
-0.04924839362502098,
0.06604020297527313,
0.009246147237718105,
0.034605979919433594,
-0.007053494919091463,
0.003921671770513058,
0.09327421337366104,
0.03916998952627182,
0.00660431943833828,
-0.07347851246595383,
0.03152639418840408,
0.0012169551337137818,
-0.006749643012881279,
-0.03396597132086754,
-0.018721403554081917,
-0.011048559099435806,
0.014797029085457325,
-0.0006910801748745143,
0.03527289628982544,
-0.013733592815697193,
0.0410260446369648,
0.05089458078145981,
-0.05756451562047005,
-0.013457431457936764,
-0.01382459420710802,
-0.010301537811756134,
-0.021934479475021362,
0.00028826785273849964,
-0.02378358319401741,
0.027705702930688858,
-0.029756074771285057,
-0.0376160591840744,
-0.025059960782527924,
0.0012310950551182032,
0.009007954970002174,
0.05417855456471443,
-0.10197103023529053,
-0.0035144879948347807,
-0.011326736770570278,
0.013186277821660042,
-0.06897172331809998,
0.04843837022781372,
-0.0022705362644046545,
-0.018062520772218704,
-0.0008648777729831636,
0.016829701140522957,
0.009607610292732716,
0.0016963471425697207,
0.007773367688059807,
0.022974394261837006,
-0.019181452691555023,
0.0006615120801143348,
-0.025306567549705505,
0.046919085085392,
-0.018337123095989227,
-0.040193405002355576,
-0.004557546228170395,
0.031626712530851364,
-0.02396572381258011,
-0.01492550689727068,
-0.008801992051303387,
0.005849031265825033,
0.04252856224775314,
-0.000794542720541358,
-0.004718900192528963,
-0.003227628068998456,
0.009252388961613178,
-0.03708465397357941,
0.010995874181389809,
0.05104342848062515,
-0.012952116318047047,
-0.02621712163090706,
-0.012828045524656773,
0.05303337424993515,
-0.017333781346678734,
0.009819822385907173,
-0.020415810868144035,
0.010776865296065807,
-0.023911811411380768,
-0.01863947883248329,
-0.010850498452782631,
0.03824256733059883,
0.036514103412628174,
-0.014071572571992874,
-0.01330750435590744,
0.013359344564378262,
-0.05097321420907974,
0.05001142993569374,
-0.028663627803325653,
-0.02095751464366913,
-0.05802860110998154,
0.0023590740747749805,
0.028410857543349266,
0.03308872878551483,
0.005660002585500479,
0.04419668763875961,
0.007894602604210377,
0.02471626177430153,
0.009796216152608395,
-0.0587989017367363,
-0.012191764079034328,
0.02200116589665413,
-0.03716856986284256,
-0.021002216264605522,
0.025619277730584145,
0.049419332295656204,
0.03371865674853325,
-0.010188505053520203,
0.014433201402425766,
-0.003419251414015889,
-0.05116528272628784,
-0.007315254770219326,
-0.009167838841676712,
-0.018058106303215027,
-0.03136251121759415,
-0.00838427897542715,
-0.007351983338594437,
-0.01783914677798748,
-0.01074972003698349,
0.0076359473168849945,
0.023029854521155357,
0.00799468345940113,
0.013733090832829475,
-0.03679097816348076,
0.03356547653675079,
-0.02313537895679474,
0.023221498355269432,
-0.01717388816177845,
-0.029626626521348953,
-0.0839293897151947,
-0.022484684363007545,
0.011689629405736923,
-0.027827417477965355,
-0.039390578866004944,
0.0034761005081236362,
-0.038760505616664886,
-0.0022975686006247997,
0.032272450625896454,
0.002021590480580926,
-0.011984235607087612,
-0.005411854479461908,
0.03831038996577263,
-0.0057854498736560345,
0.052568692713975906,
-0.047087784856557846,
-0.0631459429860115,
0.061729926615953445,
-0.01667761243879795,
-0.045871809124946594,
0.009167001582682133,
-0.005440321750938892,
0.020032202824950218,
0.002431650646030903,
0.006696921773254871,
-0.035258010029792786,
0.08174124360084534,
-0.024813812226057053,
0.00519555201753974,
-0.03697435185313225,
-0.0028352888766676188,
-0.005858182907104492,
0.009683642536401749,
0.02674143575131893,
-0.025193562731146812,
0.020790891721844673,
0.06814176589250565,
0.07153987884521484,
-0.013150371611118317,
0.005760667379945517,
-0.022172708064317703,
-0.035413336008787155,
0.000751844490878284,
-0.0030115810222923756,
-0.007989522069692612,
-0.006155680399388075,
0.0379488542675972,
-0.022103995084762573,
0.03409452363848686,
0.009823208674788475,
-0.014820517972111702,
-0.06715968251228333,
0.007845391519367695,
-0.019835948944091797,
-0.008057184517383575,
0.011370445601642132,
-0.026728322729468346,
0.01704654097557068,
0.0559220127761364,
-0.04715406894683838,
-0.003027279395610094,
-0.02511894330382347,
-0.017977889627218246,
-0.043768733739852905,
-0.008999062702059746,
0.013235870748758316,
0.04148871824145317,
0.015281314961612225,
0.04682154580950737,
0.01987079717218876,
-0.007123804651200771,
0.006720702163875103,
-0.03115885891020298,
-0.010697598569095135,
0.021827781572937965,
0.028313638642430305,
-0.009229432791471481,
0.029602915048599243,
-0.009469226002693176,
-0.028726443648338318,
0.02486691065132618,
-0.018596550449728966,
0.05081617087125778,
0.02070116065442562,
0.022851688787341118,
0.010923748835921288,
0.00995699129998684,
-0.022732296958565712,
0.02253877744078636,
-0.024613963440060616,
0.048291973769664764,
0.014907690696418285,
0.03734181821346283,
0.023964175954461098,
0.005080322735011578,
-0.007173619233071804,
-0.0662151649594307,
0.013554162345826626,
0.001578887109644711,
-0.014116894453763962,
0.033728841692209244,
0.002412745263427496,
0.02182968147099018,
0.040105536580085754,
-0.029450953006744385,
-0.024787088856101036,
-0.005645166151225567,
-0.0252643134444952,
0.024607820436358452,
-0.034029632806777954,
-0.044582549482584,
-0.029474694281816483,
-0.0061660162173211575,
0.011245707981288433,
-0.004400315228849649,
0.010419846512377262,
-0.007384869735687971,
-0.036233365535736084,
-0.010810209438204765,
0.00854573305696249,
-0.016864335164427757,
0.0012311531463637948,
-0.011626389808952808,
-0.06063521280884743,
0.04535837098956108,
0.0059597548097372055,
0.02961183898150921,
-0.0005874489434063435,
-0.026077207177877426,
-0.008389364928007126,
-0.05039630085229874,
0.0708133801817894,
0.0076410286128520966,
0.01943023130297661,
-0.02895728312432766,
-0.01432890072464943,
0.0034497929736971855,
0.02769932709634304,
0.05755642428994179,
-0.037533003836870193,
0.03220512717962265,
0.003999181557446718,
-0.03808017820119858,
0.030596863478422165,
-0.023637723177671432,
0.01722136326134205,
0.029200362041592598,
-0.02536061778664589,
0.01998109370470047,
-0.018433120101690292,
0.010710067115724087,
-0.009711649268865585,
0.004707172978669405,
-0.009328905493021011,
0.06864263862371445,
0.0076974667608737946,
0.008977122604846954,
0.033988434821367264,
-0.014520145952701569,
-0.054779328405857086,
0.06731729954481125,
-0.023749876767396927,
0.01018615998327732,
0.02722993865609169,
-0.004248373676091433,
-0.054214250296354294,
0.026956748217344284,
-0.03930065035820007,
0.020938685163855553,
-0.018320752307772636,
-0.029170610010623932,
0.03763803094625473,
-0.034930068999528885,
0.0014110775664448738,
0.018447672948241234,
-0.05289763584733009,
0.01626657508313656,
0.03974708914756775,
0.0009390840423293412,
0.007523270323872566,
-0.025160949677228928,
0.00466995919123292,
-0.02202168107032776,
0.016759339720010757,
0.027866454795002937,
0.05156153813004494,
0.04499177634716034,
0.009344345889985561,
0.04178134351968765,
0.020963622257113457,
0.056362397968769073,
0.03493213281035423,
0.025593021884560585,
0.03606549650430679,
0.003989551216363907,
-0.05066758021712303,
0.020979654043912888,
-0.02449307031929493,
0.0027302501257508993,
0.015689410269260406,
0.013012313283979893,
0.03495866432785988,
0.0015308717265725136,
-0.00941224955022335,
-0.014337573200464249,
-0.006998977158218622,
-0.010684008710086346,
-0.002970281755551696,
-0.01135715190321207,
0.01244115736335516,
0.024163663387298584,
0.002301617059856653,
0.004237182904034853,
0.008137287572026253,
0.012550163082778454,
-0.020239192992448807,
0.041301511228084564,
-0.030423762276768684,
0.0052546230144798756,
-0.012070910073816776,
-0.004755986854434013,
-0.014766158536076546,
0.0015510173980146646,
0.05110497400164604,
0.02031186781823635,
0.0074647157453000546,
0.012967822141945362,
-0.02468670718371868,
-0.01532639842480421,
0.044353555887937546,
-0.09251673519611359,
-0.033236533403396606,
-0.0283045694231987,
0.022543517872691154,
-0.023818112909793854,
-0.029128536581993103
] |
<p>I'm really interested in quantum physics and would like to learn more. However, I don't know where to start and in what order I should learn things. So, ideally I'm looking for some sort of roadmap of what to learn. What physics topics do I need to know to start learning about quantum mechanics? (In addition to the mathematical topics mentioned at <a href="http://physics.stackexchange.com/questions/16814/what-is-the-math-knowledge-necessary-for-starting-quantum-mechanics">What is the math knowledge necessary for starting Quantum Mechanics?</a>)</p>
<p>My current knowledge is mostly popular science stuff, like tv shows on Discovery Science and National Geographic Channel. So I have a basic understanding of some basic principals. There's also a recent lecture from Brian Cox that I have watched which gave a bit more in-depth information.</p> | 223 | [
0.013098964467644691,
-0.07119174301624298,
-0.00773942144587636,
-0.029180049896240234,
0.009736795909702778,
0.00786647293716669,
-0.009292537346482277,
-0.03895217180252075,
0.004408509004861116,
-0.05249308422207832,
0.0299005638808012,
0.058627933263778687,
0.012458971701562405,
-0.010946717113256454,
0.0408799909055233,
0.012833674438297749,
0.0021929158829152584,
-0.061222709715366364,
-0.0163558516651392,
0.011046282947063446,
0.014367139898240566,
-0.005353196524083614,
0.040900975465774536,
0.03137851879000664,
-0.0069198221899569035,
0.06242294982075691,
0.02748585119843483,
0.04269450157880783,
0.03179717808961868,
0.05610525980591774,
0.026994550600647926,
-0.034393832087516785,
0.009196142666041851,
0.03585657849907875,
0.001180653227493167,
0.0013731792569160461,
-0.007834242656826973,
0.002701016841456294,
-0.008040189743041992,
-0.010968953371047974,
-0.052593521773815155,
-0.030669357627630234,
-0.01769394241273403,
0.04819741100072861,
-0.048039812594652176,
0.015048493631184101,
0.013509551994502544,
-0.040052466094493866,
0.043633222579956055,
-0.06276797503232956,
0.07667038589715958,
0.02774733491241932,
0.04779794067144394,
0.039566416293382645,
-0.0022222576662898064,
-0.021963756531476974,
0.08787856251001358,
0.08126004040241241,
-0.0014704742934554815,
-0.053687307983636856,
-0.00984495785087347,
-0.05138882249593735,
-0.0007325933547690511,
-0.0476236529648304,
-0.04455651342868805,
0.07093954086303711,
-0.009789855219423771,
-0.0031018471345305443,
0.012706940993666649,
-0.010813032276928425,
-0.005253393668681383,
0.037220146507024765,
0.05781194195151329,
-0.012582510709762573,
0.003661311697214842,
-0.037279631942510605,
0.00926083605736494,
0.02217974327504635,
0.033399101346731186,
0.018813934177160263,
0.008885225281119347,
0.005169217940419912,
-0.00599097041413188,
0.04714420437812805,
-0.0012956444406881928,
-0.02314971573650837,
0.10439131408929825,
-0.009720913134515285,
-0.0320601724088192,
0.015695728361606598,
-0.02505512908101082,
0.021862423047423363,
0.01892220415174961,
-0.005289371125400066,
-0.03373243287205696,
0.028648192062973976,
0.0055602798238396645,
0.047786418348550797,
0.02524702437222004,
-0.038705043494701385,
0.017874250188469887,
-0.014048491604626179,
0.02919829450547695,
0.08151198923587799,
-0.005511865485459566,
0.004489400424063206,
-0.03662926331162453,
0.04841507226228714,
-0.0003894974652212113,
-0.03261556848883629,
-0.006706545129418373,
0.04448467493057251,
-0.026652880012989044,
-0.0021062572486698627,
-0.013129799626767635,
-0.028039149940013885,
-0.0006197052425704896,
-0.04360930621623993,
0.06155342981219292,
0.05671660229563713,
0.05446871370077133,
-0.04104478284716606,
0.02334759011864662,
-0.03897319361567497,
-0.07533922046422958,
-0.02899964712560177,
0.04115494713187218,
-0.015181475318968296,
-0.039413899183273315,
0.049856312572956085,
0.005553987808525562,
-0.02130018174648285,
0.004578807856887579,
0.006450900342315435,
0.036572426557540894,
0.009652690961956978,
-0.1107725128531456,
-0.051599081605672836,
0.05649779736995697,
-0.018729083240032196,
-0.04045668989419937,
-0.07827826589345932,
0.05000085383653641,
0.018081558868288994,
0.06888523697853088,
-0.010423179715871811,
0.01227288506925106,
-0.02027491107583046,
0.00925504881888628,
-0.006107129622250795,
-0.04013542830944061,
-0.013060341589152813,
-0.0009504352929070592,
-0.006534729152917862,
0.0374826118350029,
-0.04507521167397499,
0.03105778619647026,
0.037409599870443344,
-0.002014918951317668,
-0.028029397130012512,
0.07058586925268173,
-0.017003817483782768,
-0.007753625046461821,
0.016192421317100525,
-0.028109457343816757,
-0.006974873598664999,
0.0681058019399643,
0.0038432336878031492,
0.0149063216522336,
0.043001603335142136,
-0.0026450108271092176,
0.024306481704115868,
0.011490912176668644,
0.027995815500617027,
0.05367574095726013,
-0.03069995902478695,
-0.012820292264223099,
0.008203912526369095,
0.0003494828415568918,
-0.004782999865710735,
-0.04652444273233414,
-0.015468495897948742,
-0.008593600243330002,
0.027350768446922302,
-0.002530633006244898,
0.024187380447983742,
-0.002767405938357115,
0.0034302968997508287,
0.009466486983001232,
-0.03278511017560959,
-0.011872840113937855,
-0.060285527259111404,
0.02651306241750717,
-0.019595768302679062,
-0.019775154069066048,
0.033061858266592026,
0.013276152312755585,
0.02504231408238411,
-0.03273507207632065,
-0.03816273808479309,
-0.01659182645380497,
0.015993570908904076,
0.01961652748286724,
-0.008147330954670906,
0.013933646492660046,
0.06904499977827072,
0.04949316382408142,
-0.030355624854564667,
0.015361694619059563,
-0.040529053658246994,
-0.01923404633998871,
-0.020529014989733696,
-0.011575707234442234,
0.02804882638156414,
0.011908911168575287,
0.0038709070067852736,
-0.01152532733976841,
-0.018971074372529984,
-0.027619177475571632,
0.019935300573706627,
-0.01594429835677147,
0.0687391608953476,
0.011645755730569363,
0.016079435124993324,
-0.02038762718439102,
0.04547043517231941,
0.027569890022277832,
-0.006421026308089495,
0.022972503677010536,
0.0009390601771883667,
-0.04885643348097801,
0.03084803745150566,
0.03911294415593147,
0.007746553979814053,
-0.048300087451934814,
0.027467617765069008,
0.0007567620486952364,
0.04986794292926788,
0.026873713359236717,
0.0006330577889457345,
-0.04562707990407944,
-0.031094254925847054,
-0.015407819300889969,
0.005532562732696533,
-0.025155555456876755,
0.024545658379793167,
0.01678847335278988,
0.030367551371455193,
-0.021656891331076622,
0.015907784923911095,
-0.06257335096597672,
0.04678240418434143,
-0.031644124537706375,
-0.0009821663843467832,
-0.0043877726420760155,
-0.03889979049563408,
0.03919556736946106,
-0.03261460363864899,
-0.007100800517946482,
-0.003801879473030567,
-0.020976219326257706,
-0.01931295171380043,
-0.015741750597953796,
-0.04602919518947601,
-0.008509742096066475,
0.015277368016541004,
-0.04425406828522682,
0.023313891142606735,
0.0261139664798975,
-0.035181041806936264,
0.0017447610152885318,
-0.0055930474773049355,
-0.014680189080536366,
-0.058021411299705505,
-0.011375215835869312,
0.01838056556880474,
0.0016393407713621855,
0.02702176757156849,
-0.06276838481426239,
-0.049150027334690094,
0.012710626237094402,
-0.05060321092605591,
0.020791633054614067,
0.017048310488462448,
-0.044249773025512695,
0.02140367031097412,
-0.057157114148139954,
-0.03802676126360893,
0.03640103340148926,
-0.018692409619688988,
0.02128852903842926,
0.009548291563987732,
-0.008819843642413616,
-0.018368130549788475,
-0.01844937913119793,
-0.009218246676027775,
0.022035948932170868,
-0.026707524433732033,
-0.010383627377450466,
0.027765804901719093,
-0.04363834112882614,
-0.012389031238853931,
0.010594937950372696,
-0.045408379286527634,
-0.04430864378809929,
-0.031447138637304306,
0.024967938661575317,
0.02150570973753929,
-0.034021250903606415,
-0.010819762945175171,
0.024657651782035828,
-0.07077883183956146,
0.022703856229782104,
-0.039026595652103424,
-0.0580030120909214,
0.026536479592323303,
0.03482577204704285,
0.018909666687250137,
0.020424868911504745,
-0.013317044824361801,
0.08488599210977554,
0.02605419233441353,
-0.04214954748749733,
-0.019404336810112,
-0.001841553021222353,
0.003105888841673732,
-0.03378121927380562,
0.027400517836213112,
0.04315672442317009,
-0.026784764602780342,
0.023769201710820198,
0.024249283596873283,
0.01915646716952324,
0.031427111476659775,
0.023474888876080513,
0.004613394383341074,
0.004820819012820721,
-0.007170827127993107,
0.02988060936331749,
0.05006637051701546,
0.008681658655405045,
-0.06289012730121613,
0.006691990420222282,
-0.014558246359229088,
0.01968974433839321,
0.001119794324040413,
-0.021576443687081337,
0.07154566049575806,
-0.010312879458069801,
-0.017149822786450386,
-0.023975970223546028,
0.049721959978342056,
-0.021615520119667053,
-0.015499705448746681,
0.03153048828244209,
0.013282177969813347,
0.008876935578882694,
-0.008005546405911446,
0.02077655680477619,
0.03427566960453987,
0.01923407055437565,
-0.03792424872517586,
-0.002202339470386505,
-0.013461094349622726,
-0.01942763850092888,
0.02265053056180477,
-0.04257773980498314,
-0.006368331145495176,
0.032741107046604156,
0.04055030271410942,
0.03331734240055084,
-0.01997450739145279,
-0.03272746130824089,
-0.003671756712719798,
-0.06490938365459442,
-0.006769197061657906,
-0.01452011801302433,
0.047720104455947876,
-0.015843644738197327,
0.06613506376743317,
0.02286386303603649,
-0.019593549892306328,
0.02784525230526924,
0.01105789840221405,
-0.05656949803233147,
0.04130316153168678,
-0.04527515545487404,
-0.008889418095350266,
0.0023656035773456097,
0.012042303569614887,
0.0076904334127902985,
-0.016944684088230133,
-0.06834385544061661,
-0.03169513866305351,
0.005299299024045467,
-0.026247067376971245,
0.02232479490339756,
-0.033257633447647095,
-0.03514071926474571,
-0.010347118601202965,
0.016930218786001205,
0.03411775082349777,
0.004273025318980217,
0.008941352367401123,
0.04815499112010002,
-0.0299711711704731,
-0.0025992244482040405,
0.03147472068667412,
0.029715560376644135,
0.005966137163341045,
0.005102857947349548,
0.03144785761833191,
0.015088483691215515,
-0.015200787223875523,
0.017994195222854614,
-0.02281682938337326,
0.07965870946645737,
-0.010889293625950813,
-0.030871855095028877,
0.023105891421437263,
-0.04874511808156967,
0.0013155728811398149,
-0.01548629067838192,
0.05896032974123955,
0.015168074518442154,
0.006455543916672468,
0.057275768369436264,
-0.022769207134842873,
-0.06126050651073456,
0.04088962823152542,
0.05653214827179909,
-0.008369036950170994,
-0.01280965656042099,
-0.03195791691541672,
-0.02039741724729538,
-0.06844548135995865,
0.002461642725393176,
0.013026903383433819,
0.0011036877986043692,
-0.024030130356550217,
0.015645405277609825,
0.027703143656253815,
-0.003920726012438536,
-0.023324228823184967,
-0.018717870116233826,
0.0002816800551954657,
0.033024754375219345,
0.007665326818823814,
-0.005523258354514837,
-0.0010000895708799362,
0.008355082012712955,
0.02889964170753956,
-0.028647691011428833,
0.0005635183770209551,
-0.07475265860557556,
-0.003880309173837304,
0.039295993745326996,
0.040515657514333725,
-0.0036567728966474533,
0.0022863009944558144,
-0.06355705857276917,
-0.035604413598775864,
0.05059700086712837,
-0.007017614785581827,
0.04076189175248146,
-0.0315803699195385,
-0.03355832025408745,
-0.03412333503365517,
-0.01537945494055748,
0.01961662992835045,
0.029489019885659218,
0.018712133169174194,
0.04210328683257103,
-0.016401702538132668,
0.004845167510211468,
-0.05206621438264847,
0.029291056096553802,
0.03107164427638054,
0.06617619842290878,
0.018435489386320114,
-0.009778857231140137,
0.00016331799270119518,
0.023151610046625137,
0.004300589673221111,
-0.07020911574363708,
-0.0014735532458871603,
-0.01284860074520111,
-0.04014616087079048,
0.027421222999691963,
-0.023957474157214165,
-0.04543960094451904,
-0.009112841449677944,
0.009051738306879997,
-0.017660727724432945,
0.013684160076081753,
-0.03192242607474327,
0.04115040600299835,
-0.0016446190420538187,
0.0065594264306128025,
0.033717039972543716,
0.03161388635635376,
-0.018295692279934883,
0.014073451980948448,
-0.011657589115202427,
0.04455380141735077,
-0.023950379341840744,
0.02248869463801384,
-0.02055269293487072,
-0.03303543105721474,
-0.028215762227773666,
0.05326814949512482,
-0.05105989798903465,
-0.001995364436879754,
-0.020533397793769836,
-0.02652965858578682,
-0.03789850324392319,
0.029320327565073967,
-0.006145849358290434,
-0.01674184948205948,
0.014037448912858963,
0.03251657634973526,
-0.011681368574500084,
-0.009398192167282104,
0.022126024588942528,
0.019754350185394287,
0.008042532950639725,
-0.006498799659311771,
-0.012898847460746765,
0.036913372576236725,
-0.02514813095331192,
-0.018157532438635826,
-0.0031612333841621876,
-0.057641949504613876,
0.06165704131126404,
0.003393006045371294,
-0.0246732234954834,
0.026481127366423607,
-0.06242711842060089,
-0.033874791115522385,
-0.008474076166749,
-0.007793913595378399,
0.033112555742263794,
-0.04225759208202362,
0.0242459699511528,
-0.024463383480906487,
0.028389068320393562,
-0.04444022476673126,
-0.07259080559015274,
0.0024604483041912317,
0.025181762874126434,
-0.02830965258181095,
-0.018497750163078308,
0.05514269694685936,
-0.02228829823434353,
-0.00832244660705328,
-0.013030732981860638,
0.03243762627243996,
-0.030219778418540955,
-0.005276349373161793,
0.02898608334362507,
0.02528296783566475,
0.03410884737968445,
-0.008879510685801506,
-0.002934715710580349,
0.02199295535683632,
0.011724465526640415,
0.002981676487252116,
0.0035539157688617706,
0.04999064281582832,
-0.017345843836665154,
-0.018155129626393318,
-0.022746363654732704,
0.029579434543848038,
0.026154156774282455,
-0.05268051102757454,
0.03180714696645737,
0.017365874722599983,
0.03167097270488739,
-0.012670752592384815,
-0.012635914608836174,
0.00573723716661334,
-0.011609280481934547,
0.026980221271514893,
-0.0012464000610634685,
0.004598591942340136,
0.0016786507330834866,
-0.05337803065776825,
0.04404570162296295,
-0.01955297216773033,
0.038585640490055084,
0.011895253323018551,
0.04531889408826828,
0.011730284430086613,
-0.0016138209030032158,
0.017523977905511856,
-0.039759837090969086,
-0.029326392337679863,
0.0000518892084073741,
0.01534607820212841,
0.007368003483861685,
-0.007831776514649391,
-0.0228595994412899,
-0.06483791023492813,
-0.0447193942964077,
-0.015936696901917458,
0.07261903584003448,
0.00594263756647706,
0.04852701351046562,
0.02844787761569023,
-0.012595459818840027,
0.0025993725284934044,
-0.002421088982373476,
-0.019946975633502007,
-0.015199333429336548,
0.040513940155506134,
0.02040642686188221,
-0.034969575703144073,
-0.0019980953074991703,
0.008762102574110031,
0.059794213622808456,
-0.032519057393074036,
0.012560198083519936,
0.02602694369852543,
0.017115892842411995,
0.03018302284181118,
-0.004576391540467739,
-0.019652964547276497,
0.019308939576148987,
-0.021631935611367226,
0.05586681142449379,
0.004111831076443195,
-0.0301236379891634,
0.02326212264597416,
0.00793702993541956,
-0.010972712188959122,
-0.002452002838253975,
-0.01944444328546524,
-0.037476520985364914,
0.020951643586158752,
0.016430797055363655,
0.029343724250793457,
-0.010973231866955757,
0.02548217959702015,
0.02903004363179207,
0.012816431000828743,
0.0032219376880675554,
-0.011658316478133202,
-0.05597659945487976,
-0.04579654708504677,
-0.02290886454284191,
-0.07262018322944641,
0.026064174249768257,
0.0026900162920355797,
-0.030004577711224556,
-0.006972295232117176,
-0.01692897081375122,
0.05083999037742615,
-0.015407336875796318,
0.04307396709918976,
-0.055621638894081116,
0.035593431442976,
0.0016175112687051296,
0.009662846103310585,
-0.006119647063314915,
0.016229862347245216,
0.09669418632984161,
0.053173501044511795,
0.004961110185831785,
-0.07771679013967514,
0.007955348119139671,
-0.002902424894273281,
0.03592902049422264,
-0.028279097750782967,
0.02148757502436638,
-0.005278178956359625,
0.029319537803530693,
-0.010893100872635841,
0.06286204606294632,
0.01252273190766573,
0.010129201225936413,
0.07080994546413422,
-0.04418794438242912,
-0.05534256994724274,
-0.012967261485755444,
0.009584955871105194,
-0.0003241811355110258,
0.03700258210301399,
-0.030373649671673775,
0.020547371357679367,
-0.044265590608119965,
-0.008397760801017284,
-0.0216659028083086,
-0.02290128543972969,
0.03924935311079025,
-0.016836287453770638,
0.010138548910617828,
0.010504767298698425,
-0.008249886333942413,
0.00017127041064668447,
-0.033634670078754425,
0.037680111825466156,
0.05014760419726372,
-0.017415151000022888,
0.017485663294792175,
0.01540003065019846,
0.006006462965160608,
0.001042376272380352,
-0.006590273231267929,
-0.005202774424105883,
-0.03593328967690468,
0.004833308979868889,
-0.008733883500099182,
0.05980237200856209,
-0.03940945863723755,
0.015036912634968758,
-0.007891926914453506,
-0.01319033745676279,
-0.0076539176516234875,
-0.03515900298953056,
-0.002144069876521826,
0.03592685982584953,
0.035666294395923615,
-0.04461236670613289,
0.01453410554677248,
-0.02044006623327732,
0.018336238339543343,
-0.024347085505723953,
0.035351864993572235,
-0.018006836995482445,
-0.007947685196995735,
-0.012183562852442265,
-0.011118248105049133,
-0.0013144619297236204,
-0.040514759719371796,
-0.013137740083038807,
-0.031340230256319046,
-0.00033901186543516815,
-0.04112673178315163,
-0.03643188998103142,
0.07097826898097992,
0.03389602527022362,
0.04825728014111519,
0.0017581736901775002,
-0.027765734121203423,
0.015360571444034576,
-0.05436940863728523,
0.025845350697636604,
-0.020826280117034912,
-0.021111352369189262,
-0.03555969521403313,
-0.0030236251186579466,
0.030329151079058647,
0.03976445645093918,
-0.018781611695885658,
0.027511930093169212,
0.016949137672781944,
-0.020845316350460052,
0.05121263489127159,
0.0034040077589452267,
0.034232839941978455,
0.003518922021612525,
-0.014274057000875473,
0.002915217773988843,
-0.03346456587314606,
0.019305694848299026,
0.025276903063058853,
-0.01166184525936842,
-0.006679606158286333,
0.02354021742939949,
-0.023416180163621902,
-0.004542149603366852,
-0.0002736154419835657,
-0.044964831322431564,
-0.01398427877575159,
0.011328105814754963,
0.051802076399326324,
-0.04222042113542557,
-0.055751025676727295,
-0.008377683348953724,
0.014822231605648994,
0.004514208063483238,
0.03203274682164192,
-0.027566710487008095,
0.03309160843491554,
-0.007368973921984434,
0.0534513033926487,
-0.026552140712738037,
-0.01560266688466072,
-0.04545673355460167,
0.030812958255410194,
0.007911664433777332,
-0.01725246012210846,
-0.010946064256131649,
0.000784539442975074,
0.014014371670782566,
-0.025077495723962784,
0.04026441648602486,
0.03290581703186035,
-0.00636873347684741,
-0.025230836123228073,
0.007358266972005367,
-0.03191772475838661,
0.03652577102184296,
-0.0008224494522437453,
-0.018268292769789696,
0.028914088383316994,
-0.04425709322094917,
-0.041944775730371475,
0.023768795654177666,
-0.019928419962525368,
0.013590462505817413,
0.06806882470846176,
-0.027713801711797714,
-0.009457581676542759,
0.021825259551405907,
0.009386410005390644,
0.007955402135848999,
0.005747842602431774,
-0.019685659557580948,
-0.029239650815725327,
0.012526234611868858,
0.025616617873311043,
-0.041853103786706924,
-0.00953492522239685,
0.013600362464785576,
0.07209663838148117,
0.008030131459236145,
0.01058271061629057,
0.008897935971617699,
-0.004200777970254421,
0.04184518754482269,
0.03921686112880707,
-0.0227024145424366,
0.03330400213599205,
0.019992858171463013,
-0.05007048696279526,
0.05427403002977371,
0.016032958403229713,
0.015888111665844917,
-0.08800952881574631,
-0.0038001229986548424,
-0.0022604442201554775,
-0.021526288241147995,
0.030337335541844368,
-0.04989316686987877,
0.0069957394152879715,
0.05851481854915619,
-0.05203578248620033,
0.06912114471197128,
-0.01490734051913023,
-0.016937468200922012,
0.02979583851993084,
0.013742491602897644,
0.018080957233905792,
0.05323265492916107,
-0.009216425009071827,
0.043490197509527206,
0.014713193289935589,
-0.0155071085318923,
-0.004009743686765432,
-0.00960063561797142,
0.014271443709731102,
0.011785781942307949,
-0.015036235563457012,
-0.009061982855200768,
0.03280980885028839,
-0.011340190656483173,
-0.026106979697942734,
0.02394445613026619,
-0.0166484285145998,
0.019193943589925766,
0.01236498262733221,
-0.001771078910678625,
-0.013590160757303238,
0.030120009556412697,
0.031666360795497894,
-0.011671916581690311,
0.008041994646191597,
0.02047918550670147,
0.047667279839515686,
0.026997262611985207,
0.003839620156213641,
-0.0057083480060100555,
0.012929621152579784,
-0.03187602013349533,
-0.057737842202186584,
0.032103098928928375,
0.021406088024377823,
0.016935881227254868,
0.004010654054582119,
-0.011744590476155281,
-0.00513068214058876,
-0.014566061086952686,
0.01785290613770485,
-0.062114931643009186,
-0.03269410878419876,
0.013487461023032665,
-0.001612344873137772,
0.0031256191432476044,
0.02661963924765587,
-0.014596778899431229,
-0.03830605372786522,
0.0338364914059639,
0.0004645588342100382,
-0.0060320645570755005,
-0.06331296265125275,
-0.0006080301245674491,
0.04208800196647644,
0.003351460909470916,
0.026865927502512932,
-0.05370611697435379,
-0.03255460038781166,
0.04024505615234375,
-0.01614123396575451,
0.013891260139644146,
-0.008098028600215912,
-0.02207842655479908,
-0.02188963070511818,
-0.0674528181552887,
0.04417549446225166,
0.018733158707618713,
0.024322109296917915,
-0.04447763040661812,
0.01899951510131359,
0.026501035317778587,
-0.010965779423713684,
0.04393159598112106,
-0.01428130827844143,
-0.0005959945265203714,
-0.007846866734325886,
-0.012049023993313313,
0.02969716116786003,
-0.009184306487441063,
0.009814235381782055,
-0.02313053049147129,
-0.03073900379240513,
-0.03702808916568756,
-0.0023368096444755793,
-0.008603369817137718,
0.007298103533685207,
0.012286381796002388,
0.007900486700236797,
0.0008869447628967464,
-0.03478007763624191,
-0.032540567219257355,
0.046691570430994034,
0.023136595264077187,
0.0037172860465943813,
0.03777587413787842,
-0.036576125770807266,
0.01418373268097639,
0.06349827349185944,
-0.039499614387750626,
-0.013468380086123943,
0.03267911821603775,
-0.034146230667829514,
-0.035128626972436905,
0.01272262167185545,
-0.022700008004903793,
0.012387195602059364,
-0.07395908236503601,
-0.009228311479091644,
0.02942727692425251,
-0.026720745489001274,
0.0011052987538278103,
0.04804639518260956,
-0.007263231091201305,
0.01763060688972473,
-0.005874461494386196,
0.012658209539949894,
0.04639000445604324,
-0.0006351424963213503,
-0.0006984787760302424,
0.02448216639459133,
0.05572126805782318,
-0.01109317597001791,
0.041309479624032974,
0.03628093749284744,
0.003455287078395486,
0.019879324361681938,
-0.00010829472739715129,
0.03924886882305145,
-0.027838412672281265,
0.005545525811612606,
0.005445620510727167,
-0.007425653748214245,
-0.03407483547925949,
0.008035863749682903,
-0.054871778935194016,
0.05244588106870651,
-0.018406836315989494,
0.0157920029014349,
-0.001723036402836442,
0.008993151597678661,
-0.023747045546770096,
-0.014112015254795551,
-0.005760525818914175,
0.045137304812669754,
-0.04508248344063759,
-0.0032881745137274265,
-0.04452955350279808,
0.01357993483543396,
0.01472775824368,
-0.0382772795855999,
0.043468911200761795,
0.003538917750120163,
-0.009119688533246517,
-0.0009357850649394095,
-0.03185150772333145,
-0.004462056793272495,
-0.03367239609360695,
0.010511540807783604,
0.04701096564531326,
-0.0036218019668012857,
-0.03170628845691681,
-0.012825251556932926,
-0.024501871317625046,
0.049497753381729126,
-0.05679391324520111,
0.005021912977099419,
-0.05610785633325577,
-0.001359639223664999,
-0.03886996954679489,
0.025212736800312996
] |
<p>I'm working on a physics problem in preparation for the MCAT and there's this particular problem that's troubling me. I don't know if it's a bad question or if I'm not understanding some sort of concept. I was hoping someone here can clarify. Here's the problem verbatim:</p>
<blockquote>
<p>A 1kg cart travels down an inclined plane at 5 m/s and strikes two billiard balls, which start moving in opposite directions perpendicular to the initial direction of the cart. Ball A has a mass of 2kg and moves away at 2m/s and ball B has a mass of 1kg and moves away at 4m/s. Which of the following statements is true?</p>
<p>a) the cart will come to a halt in order to conserve momentum</p>
<p>b) the cart will slow down</p>
<p>c) the cart will continue moving as before, while balls A and B will convert the gravitational potential energy of the cart into their own kinetic energies</p>
<p>d) these conditions are impossible because they violate either the law of conservation of momentum or conservation of energy</p>
</blockquote>
<p>At first glance, it appears to me that the answer is (D) because the system seemingly has more total momentum after the collision than before the collision. However, the answer explanation insists the correct answer to be (C) since it claims that "kinetic energy is not conserved; the system gains energy in this inelastic collision".</p>
<p>I can understand that this gain in energy can come from gravitational potential energy from the incline the cart is on; however, it is ambiguous if the cart is <em>accelerating</em> down the incline. In order for the scenario to be consistent with choice (C), does the cart have to be accelerating down the incline? Or do you take the problem to mean that the cart is leaving the incline at 5m/s? Or am I missing or not understanding something?</p>
<p>How would you interpret this problem and which explanation do you think is most consistent with the scenario? What assumptions do you have to make to arrive at your answer?</p>
<p>The answer key's explanation, verbatim is as follows:</p>
<blockquote>
<p>The law of conservation of momentum states that both the vertical and horizontal components of momentum for a system must stay constant. If you take the initial movement of the cart as horizontal and the two balls move in perpendicular directions to the horizontal, it means that the cart must maintain its horizontal component of velocity. Therefore, (A) and (B) are wrong. If the billiard balls move as described, then kinetic energy is not conserved; the system gains energy in this inelastic collision. (C) correctly describes how this scenario is possible.</p>
</blockquote> | 1,996 | [
-0.08497314900159836,
-0.030249983072280884,
-0.03942534327507019,
0.002498396672308445,
0.019788937643170357,
0.017875254154205322,
-0.021800169721245766,
0.0037765128072351217,
-0.01250868197530508,
0.02802206017076969,
-0.017447320744395256,
0.02534746751189232,
0.015823744237422943,
0.05032240226864815,
0.02041899971663952,
0.01836002618074417,
0.007021102122962475,
-0.02028927393257618,
0.03412047401070595,
-0.0038324177730828524,
-0.027363697066903114,
-0.01571880839765072,
0.017748011276125908,
-0.018303798511624336,
-0.010530728846788406,
0.0353301577270031,
0.05456205829977989,
-0.03834943473339081,
-0.011589035391807556,
0.05043608322739601,
-0.009632221423089504,
0.015237783081829548,
-0.007851698435842991,
-0.008702567778527737,
0.013404483906924725,
0.018214814364910126,
-0.034290846437215805,
-0.009830382652580738,
-0.013525763526558876,
0.021919459104537964,
-0.008193254470825195,
0.004397336859256029,
-0.012902150861918926,
0.05554742366075516,
-0.030722441151738167,
0.01992231421172619,
0.02328616939485073,
0.012563429772853851,
0.01814565248787403,
-0.08247267454862595,
0.07774177193641663,
0.008298955857753754,
-0.015504187904298306,
0.007787719834595919,
0.004027397371828556,
-0.002746125916019082,
0.052938077598810196,
0.09280285239219666,
-0.005970780272036791,
-0.05964895710349083,
-0.025648249313235283,
-0.037819188088178635,
-0.043524645268917084,
-0.027543719857931137,
-0.0016921705100685358,
0.007641694508492947,
0.020421722903847694,
-0.018249671906232834,
0.04027996584773064,
0.003951155114918947,
0.03643910214304924,
0.03186098486185074,
0.005044116172939539,
-0.044220346957445145,
0.028424901887774467,
-0.008416018448770046,
0.023335132747888565,
0.027270488440990448,
0.014038799330592155,
0.04065516218543053,
-0.012401482090353966,
-0.027418507263064384,
0.06937658786773682,
0.0679793581366539,
0.020934034138917923,
0.0027122837491333485,
0.06307605654001236,
0.02652449905872345,
0.04719065874814987,
0.05336951091885567,
0.008345520123839378,
-0.01184083241969347,
0.004674220457673073,
-0.002574490150436759,
-0.008533666841685772,
0.04076049104332924,
-0.03279540687799454,
0.07604987174272537,
0.006456433329731226,
-0.016986094415187836,
-0.04292706772685051,
-0.02739873342216015,
0.01811419054865837,
0.05500362813472748,
0.011610697023570538,
0.006397059187293053,
-0.03266529738903046,
-0.004759164061397314,
-0.010890303179621696,
0.007361589930951595,
-0.04843512177467346,
0.020228011533617973,
-0.03222116455435753,
0.01215326227247715,
-0.015228137373924255,
-0.012424864806234837,
-0.005345025099813938,
0.0062369368970394135,
0.04970286414027214,
0.020466575399041176,
0.03821922466158867,
-0.03070531226694584,
-0.01951681077480316,
-0.017888939008116722,
-0.05855736881494522,
0.005685847252607346,
-0.0022755395621061325,
-0.006195553578436375,
-0.026503339409828186,
0.008977413177490234,
0.01777968928217888,
0.01342678815126419,
-0.02704717591404915,
0.01490816567093134,
0.011491118930280209,
-0.020097244530916214,
-0.10804364830255508,
-0.0707753598690033,
0.06887327879667282,
0.0182680394500494,
-0.027560999616980553,
-0.07790197432041168,
-0.015709148719906807,
0.04268786683678627,
0.07407712936401367,
-0.015683073550462723,
0.011152214370667934,
0.00342799280770123,
0.033204786479473114,
-0.01362633891403675,
0.01473210845142603,
-0.03368349000811577,
-0.00006611664139200002,
-0.006016023922711611,
0.01745530031621456,
-0.08242560178041458,
0.014676857739686966,
0.04727640002965927,
0.0018487087218090892,
-0.012809681706130505,
0.034511204808950424,
-0.03085210546851158,
0.010928048752248287,
-0.0034485035575926304,
0.00955027062445879,
0.028926284983754158,
0.06512600928544998,
0.01925591193139553,
0.015873299911618233,
0.015407142229378223,
0.04918479174375534,
0.021872494369745255,
-0.04679723456501961,
0.02092900313436985,
0.07154391705989838,
0.003781910054385662,
-0.021514391526579857,
-0.027756838127970695,
0.0018054883694276214,
-0.03604743257164955,
-0.003204616019502282,
-0.04759975150227547,
-0.004849513527005911,
-0.026216555386781693,
-0.01449598278850317,
0.01952042244374752,
0.013410734012722969,
-0.004025778267532587,
-0.027461815625429153,
0.00007393879059236497,
-0.04634367302060127,
-0.055521778762340546,
0.027939531952142715,
-0.009299839846789837,
0.00764933368191123,
0.021126333624124527,
0.005199565552175045,
0.03614038974046707,
-0.04295950010418892,
0.029448745772242546,
0.0015703504905104637,
0.024613728746771812,
-0.030265318229794502,
0.002840664004907012,
-0.006296316161751747,
0.039194393903017044,
0.05962130054831505,
0.019642682746052742,
-0.030170639976859093,
0.027835585176944733,
-0.004026478622108698,
-0.006836968008428812,
0.004677065182477236,
0.019336266443133354,
-0.002527387347072363,
0.049150969833135605,
-0.00994307640939951,
0.009335875511169434,
-0.013701710850000381,
0.019196756184101105,
-0.035385508090257645,
0.10853008180856705,
0.048633575439453125,
-0.008581297472119331,
-0.0008210215601138771,
0.03259221091866493,
-0.01317521370947361,
0.013140073977410793,
-0.004461474251002073,
-0.04537754878401756,
-0.034053072333335876,
-0.0018576238071545959,
-0.020660707727074623,
0.028858639299869537,
-0.03019574098289013,
0.02278292551636696,
0.03851195052266121,
0.0065069361589848995,
0.014985918067395687,
0.02776920050382614,
0.00036920758429914713,
-0.04781002923846245,
0.059369344264268875,
0.022468578070402145,
-0.015662791207432747,
0.022530321031808853,
0.018033651635050774,
-0.00039546668995171785,
0.010443746112287045,
-0.005965616088360548,
0.007608514744788408,
-0.011813518591225147,
0.02501409314572811,
0.056679077446460724,
-0.013394654728472233,
-0.013407425954937935,
0.035708703100681305,
-0.010183753445744514,
0.04370863735675812,
0.057336218655109406,
0.02317386120557785,
-0.015430637635290623,
-0.045104287564754486,
-0.028766458854079247,
-0.029426906257867813,
0.035563912242650986,
0.0042220549657940865,
-0.02170662209391594,
0.007551244460046291,
-0.0346938781440258,
0.020135995000600815,
0.003168267896398902,
-0.05222993716597557,
0.015580415725708008,
-0.005413423292338848,
0.01608183979988098,
0.014678001403808594,
0.011389138177037239,
-0.04602291062474251,
0.006656496319919825,
-0.02288065478205681,
-0.038709856569767,
-0.029647793620824814,
-0.020267950370907784,
-0.08592264354228973,
0.02028898149728775,
-0.0494341142475605,
-0.010868553072214127,
0.04402700439095497,
-0.01038662064820528,
0.004499608650803566,
0.06408074498176575,
0.016797835007309914,
-0.051015980541706085,
-0.012226101011037827,
0.005458280444145203,
-0.0033573328983038664,
-0.03502247855067253,
-0.0019532055594027042,
0.08608916401863098,
0.02690335363149643,
-0.01517565082758665,
0.019331537187099457,
-0.031916294246912,
-0.035319507122039795,
-0.02139710821211338,
0.005998218897730112,
0.0074025290086865425,
0.013165643438696861,
-0.0002693092974368483,
-0.019491659477353096,
0.0010350480442866683,
-0.004715701099485159,
-0.04684382677078247,
-0.06896688044071198,
0.024249475449323654,
-0.019473431631922722,
0.015565520152449608,
-0.028766881674528122,
-0.017399733886122704,
0.08463455736637115,
0.05702880397439003,
-0.011973267421126366,
-0.011660797521471977,
-0.015569147653877735,
0.017039064317941666,
-0.033232059329748154,
-0.006520968396216631,
0.031182680279016495,
-0.02484607696533203,
-0.007926412858068943,
-0.001032698550261557,
0.041193921118974686,
0.02179482951760292,
-0.02450110949575901,
0.012313554994761944,
0.0012045305920764804,
0.019731374457478523,
0.011321338824927807,
0.005470511503517628,
0.0215664803981781,
-0.026876211166381836,
-0.002832636469975114,
-0.04522961750626564,
0.046355728060007095,
-0.018802549690008163,
-0.06935182213783264,
0.06360948830842972,
-0.014729194343090057,
0.0022436659783124924,
-0.03414911404252052,
0.03367488086223602,
0.005920617841184139,
-0.03342314437031746,
0.017157940194010735,
0.019928516820073128,
0.05392077937722206,
-0.01588778756558895,
0.03424321487545967,
0.05849194526672363,
0.028132149949669838,
-0.029623929411172867,
-0.025628168135881424,
0.019984394311904907,
0.006266189273446798,
0.02079830877482891,
-0.01757240481674671,
0.008951577357947826,
0.01720968261361122,
0.008833599276840687,
0.025191498920321465,
0.0051373448222875595,
-0.06643087416887283,
-0.020007507875561714,
-0.056254129856824875,
0.016660157591104507,
-0.017155395820736885,
0.04756748676300049,
-0.003941272385418415,
0.060017868876457214,
0.005307156126946211,
-0.00430131983011961,
0.018501853570342064,
0.011015092022716999,
-0.11226534098386765,
0.05062653869390488,
-0.004537856671959162,
-0.019205886870622635,
0.008969459682703018,
-0.02499905601143837,
0.002338635502383113,
-0.0379495732486248,
-0.01960223913192749,
-0.003512631868943572,
0.015808269381523132,
-0.04170742630958557,
0.020066870376467705,
-0.05274497717618942,
-0.04744824022054672,
0.014804220758378506,
0.014838307164609432,
0.01235934253782034,
-0.03481864556670189,
0.0372798778116703,
0.05810222029685974,
-0.02148975431919098,
0.00813382863998413,
-0.007560401223599911,
0.02574535459280014,
0.013578111305832863,
0.03317726030945778,
-0.0011074611684307456,
0.016631700098514557,
0.02275845780968666,
0.008461324498057365,
0.024270903319120407,
0.03115670196712017,
0.007399763911962509,
-0.015597623772919178,
-0.05931910127401352,
-0.05798698589205742,
-0.0019659148529171944,
-0.010878000408411026,
0.030584510415792465,
-0.02037758193910122,
-0.004875084385275841,
0.01816621609032154,
0.04353411868214607,
0.014586345292627811,
0.04282599315047264,
0.045852165669202805,
0.02280346490442753,
-0.0043640462681651115,
-0.04740548133850098,
-0.03533919155597687,
-0.00782571081072092,
-0.005961931310594082,
0.04258967563509941,
-0.021136850118637085,
-0.02979029342532158,
0.008640616200864315,
0.0035307544749230146,
0.05982488393783569,
-0.0213156770914793,
0.04237751290202141,
-0.03955541178584099,
0.011475554667413235,
-0.0054390267468988895,
-0.006571552250534296,
0.0074841901659965515,
0.03849022462964058,
0.04216808080673218,
-0.005144497845321894,
-0.0053660254925489426,
-0.05314797908067703,
-0.031146714463829994,
0.012526693753898144,
0.07109786570072174,
-0.0425492562353611,
0.0028310043271631002,
-0.011406919918954372,
-0.006053471006453037,
0.027659175917506218,
-0.04371769353747368,
0.04958866909146309,
-0.04438163712620735,
0.036438509821891785,
-0.009801102802157402,
-0.0386526994407177,
-0.05344611033797264,
0.004182453267276287,
-0.009052146226167679,
0.01693449541926384,
0.011124134063720703,
-0.025360682979226112,
0.01021482702344656,
-0.021848002448678017,
0.03136461228132248,
0.04472113028168678,
0.011278378777205944,
0.001853486057370901,
-0.00009358644456369802,
-0.0019407120998948812,
-0.03299515321850777,
-0.07138468325138092,
-0.013541382737457752,
-0.043704111129045486,
-0.02940519154071808,
0.004201655276119709,
-0.047381166368722916,
-0.05417631193995476,
0.03091767057776451,
-0.00012676778715103865,
0.022291069850325584,
0.0005094774533063173,
-0.04817812889814377,
0.06908435374498367,
0.044317156076431274,
-0.03310209512710571,
-0.0067158848978579044,
-0.002674426883459091,
-0.038074810057878494,
0.0037548672407865524,
-0.028373196721076965,
0.006746999453753233,
-0.03577440604567528,
-0.002014691010117531,
-0.0363750234246254,
0.019480613991618156,
-0.04210693761706352,
0.034561771899461746,
0.021233640611171722,
0.03143719956278801,
-0.048830147832632065,
-0.05085023492574692,
-0.02736068330705166,
0.0488801971077919,
0.013282808475196362,
0.0024875192902982235,
-0.027624301612377167,
-0.00947137176990509,
0.013734189793467522,
0.005874390713870525,
0.043770432472229004,
-0.00659736804664135,
-0.012790772132575512,
0.0184856615960598,
-0.003975201863795519,
0.014909586869180202,
-0.01335647888481617,
-0.025195954367518425,
-0.005567628424614668,
-0.03766856715083122,
0.05076545476913452,
0.007378122303634882,
-0.009905878454446793,
0.027636893093585968,
-0.03733260929584503,
-0.0614682100713253,
0.04519880935549736,
-0.013919302262365818,
0.010863423347473145,
-0.044381070882081985,
0.038406357169151306,
-0.00027174828574061394,
0.04576427862048149,
-0.04302290081977844,
-0.033044300973415375,
0.028068717569112778,
0.0045485966838896275,
-0.014983182772994041,
0.006160972639918327,
-0.03948788344860077,
-0.02275783009827137,
-0.031124740839004517,
0.00920594111084938,
0.02450478821992874,
-0.05108848959207535,
0.021557215601205826,
0.02990681305527687,
0.027825582772493362,
0.04820163547992706,
0.04180416837334633,
-0.0017896206118166447,
0.0011560784187167883,
-0.008565890602767467,
-0.008284821175038815,
-0.001862048520706594,
0.05212407931685448,
-0.019762465730309486,
-0.028338007628917694,
0.0005815453478135169,
0.0185736995190382,
0.04980754107236862,
-0.023154178634285927,
0.022891143336892128,
0.00604309793561697,
-0.01670747436583042,
-0.011735382489860058,
0.00677177868783474,
0.05135249346494675,
-0.02081427164375782,
0.023524699732661247,
0.02645709365606308,
-0.035567592829465866,
-0.00004183330383966677,
-0.05322772264480591,
0.007546973880380392,
0.002252786885946989,
-0.006524262018501759,
0.007654210086911917,
0.08660735934972763,
-0.03687497228384018,
-0.0002612621756270528,
0.004366795998066664,
-0.02799273282289505,
0.04341118410229683,
-0.044957101345062256,
0.0046150051057338715,
-0.0006802600692026317,
-0.019167937338352203,
-0.031967341899871826,
-0.03080121986567974,
-0.04476844519376755,
0.03338721767067909,
0.06844224035739899,
0.010435566306114197,
0.07471884042024612,
-0.0037207796704024076,
-0.0016082958318293095,
0.007098356261849403,
-0.010973121039569378,
0.017725665122270584,
0.005245630629360676,
0.016424616798758507,
0.021038919687271118,
-0.028964797034859657,
0.01087652612477541,
0.01799391582608223,
0.005433212500065565,
-0.0007249836344271898,
0.0025109027046710253,
0.07319416850805283,
-0.005681645590811968,
0.014897912740707397,
-0.01427149586379528,
-0.05707942321896553,
0.002153421752154827,
-0.0014878115616738796,
0.062199197709560394,
-0.00671954732388258,
-0.05680900067090988,
0.04748564958572388,
0.04104599729180336,
-0.0022377432323992252,
-0.05017475411295891,
0.03559654951095581,
-0.06496352702379227,
0.012586727738380432,
-0.0010526416590437293,
-0.010104862973093987,
0.017822301015257835,
-0.010375501587986946,
0.01603848673403263,
-0.001810586778447032,
0.009730998426675797,
-0.02174999564886093,
-0.058015596121549606,
-0.020084181800484657,
-0.02186482772231102,
-0.037588316947221756,
0.008491240441799164,
-0.009504834190011024,
0.03242712467908859,
0.00811053067445755,
-0.05794185400009155,
-0.02840755693614483,
0.0003391988284420222,
0.010919042862951756,
0.009690745733678341,
0.0629878044128418,
-0.007659668568521738,
0.02789417654275894,
-0.061547182500362396,
0.005624997429549694,
0.12214871495962143,
0.02573453076183796,
-0.008557031862437725,
-0.010858921334147453,
0.023201769217848778,
0.016492201015353203,
0.004033087752759457,
-0.020821943879127502,
-0.010807574726641178,
0.014616289176046848,
-0.02415993995964527,
-0.005003436468541622,
0.019673211500048637,
-0.01768137514591217,
-0.016810117289423943,
0.03886330500245094,
-0.055038850754499435,
-0.0435151532292366,
0.0012888923520222306,
0.028983209282159805,
-0.024355711415410042,
0.02057105489075184,
-0.006043930072337389,
0.021413370966911316,
-0.02740916982293129,
-0.03227052837610245,
-0.004055754281580448,
-0.025830455124378204,
-0.019571829587221146,
0.028651392087340355,
-0.04204273968935013,
0.009873408824205399,
-0.006928402930498123,
-0.01950082927942276,
-0.061226941645145416,
0.023976007476449013,
0.03547699749469757,
0.0031455615535378456,
0.01607748121023178,
0.04944103583693504,
-0.0018508994253352284,
-0.01108029205352068,
0.02933056838810444,
-0.01045345701277256,
-0.031805604696273804,
0.006471395492553711,
-0.04527820274233818,
0.05054734647274017,
-0.0012361223343759775,
0.03698687627911568,
-0.004270794801414013,
-0.03408224135637283,
0.00010900039342232049,
-0.05195900797843933,
0.0035795625299215317,
-0.007715852465480566,
0.023322079330682755,
-0.003335252171382308,
-0.018839845433831215,
-0.03797540441155434,
-0.010704992339015007,
0.0413668192923069,
0.008390361443161964,
0.00491497153416276,
-0.01369897834956646,
-0.016163963824510574,
-0.017140498384833336,
0.00518546998500824,
-0.006064676214009523,
-0.011623231694102287,
-0.023138070479035378,
0.0015519673470407724,
-0.06345679610967636,
-0.013387748971581459,
0.0019205734133720398,
0.02320363186299801,
0.00221742014400661,
0.02811611071228981,
0.02202831208705902,
-0.01749785616993904,
-0.04440171644091606,
0.043770331889390945,
-0.004822635557502508,
-0.024438653141260147,
-0.05747780203819275,
0.0011862494284287095,
-0.02774261124432087,
0.0370049886405468,
-0.024617737159132957,
0.027348196133971214,
-0.0034781182184815407,
0.025002431124448776,
0.003088463330641389,
0.012551998719573021,
-0.00706693297252059,
0.00752556836232543,
-0.05713614448904991,
-0.0003821417049039155,
-0.02080594003200531,
0.03572932258248329,
-0.009115025401115417,
0.01612810418009758,
-0.0010068219853565097,
-0.005824054591357708,
-0.0019830260425806046,
0.045602183789014816,
0.02554408274590969,
-0.017223645001649857,
-0.010324637405574322,
0.05609160661697388,
0.012496905401349068,
-0.019050700590014458,
-0.022335069254040718,
-0.01620284840464592,
0.0003426052862778306,
-0.020209576934576035,
0.007889930158853531,
-0.008340811356902122,
0.03758610412478447,
-0.02955756150186062,
0.05468565598130226,
-0.04421557858586311,
0.0069009410217404366,
-0.01741936430335045,
-0.001088602701202035,
0.04203670471906662,
-0.025495661422610283,
-0.0025563370436429977,
0.054567452520132065,
-0.02439657784998417,
-0.019375907257199287,
0.008518542163074017,
0.023905325680971146,
-0.00644271494820714,
-0.07168307155370712,
0.010841557756066322,
-0.024352258071303368,
0.04550480842590332,
-0.009346785955131054,
-0.0545651912689209,
0.05461718887090683,
-0.010926153510808945,
-0.028732391074299812,
0.012351728044450283,
-0.006404991261661053,
0.0005919533432461321,
0.02526555210351944,
-0.03735603764653206,
-0.004275015089660883,
0.08071864396333694,
-0.032277531921863556,
-0.00978296622633934,
-0.017075516283512115,
-0.07500429451465607,
-0.03776264190673828,
-0.026089390739798546,
-0.0021432118955999613,
-0.005235845223069191,
-0.012892113998532295,
0.0553552508354187,
0.004444445017725229,
0.001865189871750772,
-0.005107196979224682,
0.004378834273666143,
-0.00909589882940054,
-0.006764543242752552,
0.02362285554409027,
0.008738314732909203,
0.029762500897049904,
0.03259908780455589,
-0.012455771677196026,
0.007660849951207638,
0.03762223199009895,
0.0036658102180808783,
-0.07512590289115906,
-0.028774118050932884,
0.017376530915498734,
0.033213503658771515,
0.04752746596932411,
-0.08023275434970856,
-0.003783897031098604,
0.04654591903090477,
-0.0807570368051529,
0.007033111527562141,
-0.025708718225359917,
0.009056485258042812,
-0.011290101334452629,
-0.004044173751026392,
0.02200782299041748,
0.006825197488069534,
0.03397970274090767,
0.0364145003259182,
0.03497680649161339,
0.001629277947358787,
-0.000538534892257303,
-0.017704058438539505,
0.017816098406910896,
0.03351530805230141,
-0.01943170092999935,
0.009880832396447659,
0.09622623771429062,
0.0022907713428139687,
-0.02382662333548069,
0.013220397755503654,
-0.04877954348921776,
0.0283266119658947,
-0.009227131493389606,
-0.012641342356801033,
0.002522221300750971,
0.04428470507264137,
-0.004025810863822699,
-0.021869132295250893,
0.03261708840727806,
-0.007597753778100014,
0.049206722527742386,
0.0280919149518013,
-0.002044153865426779,
0.009037395007908344,
-0.003605692181736231,
-0.04110943526029587,
-0.028384702280163765,
0.041081126779317856,
-0.035574719309806824,
-0.02462581917643547,
0.006009811535477638,
0.026785852387547493,
0.0024134728591889143,
-0.0030218034517019987,
-0.035044364631175995,
-0.015531293116509914,
-0.0036204627249389887,
0.03130311518907547,
-0.02227741852402687,
0.0036323736421763897,
0.0024167774245142937,
-0.0021112437825649977,
0.0210532508790493,
0.008564438670873642,
-0.013212006539106369,
-0.024463769048452377,
-0.05109533295035362,
0.0038859753403812647,
-0.007727338466793299,
0.006158242467790842,
0.008626465685665607,
-0.057036932557821274,
-0.027576759457588196,
0.02868218906223774,
0.012959206476807594,
0.007149785757064819,
0.008370024152100086,
-0.030907699838280678,
-0.03863414749503136,
-0.08312535285949707,
0.020598936825990677,
-0.011538231745362282,
-0.07078143954277039,
0.0016345696058124304,
-0.019124068319797516,
0.0065621319226920605,
-0.0029680198058485985,
0.07132161408662796,
-0.007810445502400398,
-0.043016765266656876,
0.04283387213945389,
-0.02788681536912918,
0.01460963487625122,
-0.028992213308811188,
0.009645950049161911,
-0.016892196610569954,
0.011213880963623524,
0.045556459575891495,
0.03301846608519554,
-0.016468944028019905,
0.026081010699272156,
0.023405879735946655,
-0.014853471890091896,
0.03602755814790726,
0.009885559789836407,
-0.02641957253217697,
0.04634803533554077,
0.01923433318734169,
-0.00643262080848217,
0.06830327957868576,
0.008861640468239784,
0.021654870361089706,
0.0207841657102108,
-0.03129538521170616,
-0.04681337624788284,
0.035693395882844925,
-0.038559991866350174,
-0.013380007818341255,
-0.014069237746298313,
-0.03244711831212044,
0.0202901940792799,
-0.04915643110871315,
0.015522453002631664,
0.05497005581855774,
-0.0035246587358415127,
-0.03660139441490173,
0.005760874133557081,
0.01414094865322113,
0.05442064628005028,
0.005462296772748232,
0.05524362623691559,
-0.020133206620812416,
0.006394445430487394,
-0.004374748095870018,
0.038742586970329285,
0.05341970920562744,
-0.017269810661673546,
-0.017353607341647148,
0.04497222229838371,
-0.04283217713236809,
0.01717507652938366,
-0.02448517642915249,
0.02563021145761013,
-0.028562039136886597,
-0.04144858568906784,
0.006807243917137384,
-0.010898835025727749,
-0.001305478741414845,
0.0276754479855299,
-0.003468085313215852,
0.029677189886569977,
-0.005005310755223036,
-0.020477330312132835,
-0.0342225506901741,
0.03163221478462219,
-0.03540360927581787,
0.003124644048511982,
0.016144374385476112,
-0.008510354906320572,
0.04358522966504097,
-0.016199646517634392,
-0.01734193228185177,
0.01039911713451147,
0.002129620173946023,
0.01654144935309887,
0.009078720584511757,
0.04107252508401871,
0.0053564682602882385,
-0.014557097107172012,
-0.02137795090675354,
-0.018121812492609024,
-0.0024675526656210423,
0.04634298384189606,
0.051066555082798004,
0.007557444274425507,
-0.03709813952445984,
0.009637481532990932,
-0.020941058173775673,
0.06522676348686218,
0.009157595224678516,
-0.011537454091012478,
0.030212193727493286,
0.010246794670820236,
0.025665204972028732,
-0.014627120457589626
] |
<p>If we roll a normal egg and a boiled egg at the same time on a floor </p>
<p>1) with friction </p>
<p>2) without friction</p>
<p>which one will come to stop first (if they will stop at all) and why?</p>
<p>Can anyone tell me reason for this?</p> | 1,997 | [
-0.050383783876895905,
-0.05392143502831459,
-0.002770974999293685,
0.005880268290638924,
-0.006696823984384537,
-0.013531663455069065,
-0.05769761651754379,
-0.018224969506263733,
-0.020990552380681038,
0.02204097807407379,
0.02769729495048523,
0.024502897635102272,
0.01282182801514864,
0.038694366812705994,
0.030314607545733452,
-0.008568525314331055,
-0.0145445317029953,
-0.02721746638417244,
0.005918904207646847,
-0.015804976224899292,
-0.009510121308267117,
-0.03471924737095833,
0.02925116755068302,
-0.004679672885686159,
-0.025994397699832916,
0.012113600969314575,
0.05765601992607117,
-0.02776101976633072,
-0.002939860336482525,
0.027677571401000023,
-0.01791345700621605,
-0.00838018860667944,
0.007856315933167934,
0.031777117401361465,
0.01585421897470951,
0.015168453566730022,
-0.026928219944238663,
-0.0026942056138068438,
-0.035333797335624695,
0.021946756169199944,
-0.03384694457054138,
-0.027073560282588005,
-0.03715306892991066,
0.027830250561237335,
-0.02901705913245678,
0.0218033529818058,
0.009920225478708744,
-0.029643328860402107,
0.020212069153785706,
-0.07793159037828445,
0.04008664935827255,
0.016998903825879097,
0.01399468258023262,
-0.012981490232050419,
0.019483687356114388,
-0.01015239767730236,
0.050599388778209686,
0.05579376965761185,
-0.006723023485392332,
-0.06633993238210678,
-0.0038107396103441715,
-0.007951377891004086,
-0.04466007649898529,
-0.03830050304532051,
-0.04537340998649597,
0.06526249647140503,
-0.037314027547836304,
-0.01597910188138485,
0.018201470375061035,
-0.009356485679745674,
0.034016113728284836,
0.018581165000796318,
0.0847463458776474,
-0.0017248011427000165,
0.028341980651021004,
-0.016740722581744194,
0.021701162680983543,
0.019858377054333687,
0.012367387302219868,
0.04561004415154457,
-0.004966097418218851,
0.004963827785104513,
0.053752630949020386,
0.07242769002914429,
0.024264108389616013,
-0.05280972644686699,
0.04519962519407272,
0.03505435585975647,
0.019459014758467674,
0.06360337138175964,
0.0303348395973444,
-0.03300681710243225,
0.04356346279382706,
0.012753774411976337,
0.02067405730485916,
0.021349644288420677,
0.005666427779942751,
0.06244006007909775,
0.013621058315038681,
-0.02139919064939022,
-0.0233369879424572,
-0.011561146005988121,
0.06445417553186417,
0.08726086467504501,
0.023416630923748016,
-0.02502679079771042,
-0.04582460969686508,
0.009712070226669312,
-0.009486095979809761,
0.012630367651581764,
0.011300899088382721,
0.0018387844320386648,
-0.01010268833488226,
-0.006556752137839794,
0.023021649569272995,
0.005692324601113796,
0.01136544719338417,
0.013054450042545795,
0.01670433022081852,
0.059664878994226456,
0.02447071112692356,
-0.02979709953069687,
-0.011694125831127167,
-0.029955334961414337,
-0.03835274651646614,
0.014273304492235184,
0.03750205039978027,
-0.04843910038471222,
-0.011701449751853943,
0.029496483504772186,
-0.02480621449649334,
0.011340031400322914,
-0.02165103890001774,
-0.0028860410675406456,
0.04154594987630844,
-0.013877223245799541,
-0.09385804831981659,
-0.007905934005975723,
0.07884243875741959,
-0.05760945752263069,
-0.029600191861391068,
-0.08664649724960327,
-0.0013536063488572836,
0.02102545090019703,
0.07783599197864532,
-0.023808687925338745,
0.01653975620865822,
-0.008562702685594559,
0.016303353011608124,
0.009317460469901562,
-0.012378441169857979,
-0.004097617696970701,
0.01852281577885151,
-0.03529176115989685,
0.007389866281300783,
-0.031206702813506126,
0.005902427714318037,
0.029313238337635994,
-0.013166219927370548,
-0.04758744314312935,
0.02213888242840767,
-0.03830670192837715,
0.0072471750900149345,
0.0008015907951630652,
0.0257333442568779,
-0.05383499711751938,
0.10712137818336487,
-0.019038300961256027,
0.012198137119412422,
0.015549179166555405,
0.02918248437345028,
0.0438678041100502,
-0.026946214959025383,
0.04222407564520836,
0.021093370392918587,
-0.01356118731200695,
0.009270362555980682,
-0.012960062362253666,
0.014751208014786243,
-0.03438826650381088,
-0.016514474526047707,
-0.01471362542361021,
-0.007962539792060852,
0.010640828870236874,
-0.007656613830476999,
0.05426377058029175,
0.014863669872283936,
0.03345775231719017,
-0.0057839821092784405,
0.0033186469227075577,
-0.03543824329972267,
-0.11231525987386703,
0.006956796627491713,
0.015678055584430695,
-0.019355732947587967,
0.056676093488931656,
-0.0025968861300498247,
0.01356895174831152,
-0.024734526872634888,
-0.008826839737594128,
-0.04565257206559181,
0.04046120122075081,
0.007137930486351252,
-0.026301220059394836,
-0.0027569462545216084,
0.0805724561214447,
0.017322564497590065,
-0.012241928838193417,
-0.013803334906697273,
-0.031693123281002045,
0.007136341650038958,
0.0011786989634856582,
0.010170506313443184,
0.017306752502918243,
-0.020241370424628258,
-0.0051763784140348434,
0.0274850744754076,
0.020062953233718872,
-0.013882254250347614,
0.029534947127103806,
-0.042113471776247025,
0.07096211612224579,
0.008300047367811203,
-0.031004084274172783,
0.010246161371469498,
-0.004446977283805609,
0.002431311411783099,
0.01023773942142725,
0.031109733507037163,
-0.02391774393618107,
-0.023383302614092827,
-0.004716232419013977,
0.005990937817841768,
0.022585779428482056,
-0.03607534244656563,
0.009187942370772362,
0.007031282410025597,
0.03275446221232414,
0.010761247016489506,
0.022162415087223053,
0.037513282150030136,
-0.009905933402478695,
0.020446140319108963,
-0.013662196695804596,
0.03355816751718521,
0.035310082137584686,
0.0245065800845623,
0.013948395848274231,
0.029881516471505165,
-0.02385132387280464,
-0.042921826243400574,
0.0315699502825737,
0.003817584365606308,
0.010289042256772518,
-0.009428026154637337,
-0.03209512680768967,
0.011390907689929008,
-0.016871565952897072,
-0.001118845189921558,
0.04205708205699921,
0.010295416228473186,
-0.017386380583047867,
-0.02118190936744213,
-0.028095601126551628,
0.013109815306961536,
0.0070840902626514435,
-0.027339309453964233,
-0.016132881864905357,
0.03624386340379715,
-0.032847512513399124,
-0.010232323780655861,
0.007130847312510014,
-0.01854323036968708,
0.0004210895567666739,
0.014897621236741543,
0.046208009123802185,
-0.035332340747117996,
0.027307232841849327,
-0.010699800215661526,
-0.03096046671271324,
0.017482196912169456,
-0.08592489361763,
-0.006050845608115196,
-0.045407019555568695,
-0.0749187171459198,
0.04315514490008354,
-0.04195640608668327,
-0.035919349640607834,
0.05726344510912895,
0.016387170180678368,
0.03305874764919281,
0.07820592820644379,
0.002631250536069274,
-0.05250248312950134,
-0.044321004301309586,
-0.008092447184026241,
-0.00672883540391922,
-0.030693206936120987,
0.013472109101712704,
0.07219257950782776,
-0.014306217432022095,
-0.004463983234018087,
0.00859141442924738,
-0.03785449266433716,
-0.07296402752399445,
-0.01737898588180542,
-0.024887297302484512,
0.04349130019545555,
-0.001196311553940177,
-0.023379798978567123,
0.024251217022538185,
-0.03590697422623634,
-0.020483514294028282,
-0.052327144891023636,
-0.06243518367409706,
0.01233593001961708,
-0.024460148066282272,
0.05128256604075432,
-0.005855313036590815,
-0.018325306475162506,
0.03490327671170235,
0.03283371776342392,
-0.014991865493357182,
-0.03808489441871643,
-0.023988105356693268,
-0.006439449265599251,
-0.06174479424953461,
0.029774362221360207,
0.015992291271686554,
-0.02454780414700508,
0.016608983278274536,
-0.00008584159513702616,
0.052671149373054504,
0.04606053605675697,
-0.00460701622068882,
0.011562418192625046,
-0.024543657898902893,
0.013816789723932743,
-0.011020227335393429,
0.0034557487815618515,
0.020983202382922173,
0.0026019951328635216,
-0.0007586691644974053,
0.0016937712207436562,
0.02677707001566887,
-0.015950435772538185,
-0.037998929619789124,
0.05009179189801216,
0.00021944890613667667,
0.011313479393720627,
0.00047152352635748684,
0.023700600489974022,
0.035794977098703384,
-0.019489644095301628,
0.011990946717560291,
0.02035919763147831,
0.044921811670064926,
-0.025377076119184494,
0.009585389867424965,
0.03880610316991806,
0.02453451044857502,
-0.013825882226228714,
-0.0019077311735600233,
0.003148886142298579,
-0.00379537814296782,
0.06518575549125671,
-0.04835917055606842,
-0.018809102475643158,
0.031170161440968513,
0.009309928864240646,
0.024737615138292313,
-0.005729332100600004,
-0.03985343128442764,
-0.028615474700927734,
-0.09863054752349854,
-0.005632100626826286,
0.0057764495722949505,
0.07892140746116638,
-0.010741000063717365,
0.06400591135025024,
0.012423770502209663,
0.04257719963788986,
-0.008373863995075226,
0.010734678246080875,
-0.09302224963903427,
0.033779505640268326,
-0.02478598989546299,
-0.022694678977131844,
-0.006015816703438759,
-0.02249477617442608,
0.01950560137629509,
-0.006553370039910078,
0.01084695104509592,
-0.014047130942344666,
-0.006799773778766394,
-0.04676220938563347,
0.0295205470174551,
-0.04893307760357857,
-0.020981281995773315,
0.003927717916667461,
-0.004750899504870176,
-0.023144733160734177,
0.006899138912558556,
0.05077414587140083,
0.041816599667072296,
-0.04468992352485657,
0.036984365433454514,
0.005903143435716629,
0.028566379100084305,
-0.0031003858894109726,
0.013683309778571129,
0.008303850889205933,
0.033157188445329666,
-0.010243488475680351,
0.026006074622273445,
0.00240045553073287,
0.04036135971546173,
0.0072458963841199875,
-0.022602228447794914,
-0.035148266702890396,
-0.02103552408516407,
-0.01037037093192339,
-0.003972688689827919,
0.0625186413526535,
-0.021178338676691055,
0.006689541507512331,
0.00834557693451643,
0.0005500111728906631,
0.03607076406478882,
0.0405934639275074,
0.06416694819927216,
0.019029920920729637,
-0.025729788467288017,
-0.057356372475624084,
-0.03804367780685425,
-0.034288521856069565,
-0.006050716154277325,
0.01422804780304432,
-0.0037874181289225817,
0.004478320479393005,
0.005178397987037897,
0.005289097782224417,
0.03612227737903595,
0.028358718380331993,
0.011530301533639431,
-0.030310872942209244,
0.008251074701547623,
0.007400014903396368,
-0.03479943796992302,
-0.023552346974611282,
0.054646287113428116,
0.03605419024825096,
-0.0012495580594986677,
-0.008021854795515537,
-0.052745431661605835,
0.011504405178129673,
0.0381169393658638,
0.043962594121694565,
-0.05056052654981613,
0.011799774132668972,
-0.02111881598830223,
-0.03822287172079086,
0.06136723607778549,
-0.022112097591161728,
0.040630120784044266,
-0.03824242576956749,
-0.006447968538850546,
-0.04060535132884979,
-0.002838015090674162,
-0.04467776045203209,
0.021008040755987167,
0.011950057931244373,
0.009644201956689358,
0.015068032778799534,
0.02201911062002182,
-0.017928646877408028,
0.011929146945476532,
0.0216884296387434,
0.03476282209157944,
-0.014761212281882763,
0.0234364066272974,
0.02060575783252716,
0.027345478534698486,
-0.04601890221238136,
-0.062439315021038055,
0.020258063450455666,
-0.019628722220659256,
-0.018949810415506363,
0.018216092139482498,
-0.012782320380210876,
-0.06034546718001366,
0.04052610322833061,
0.015038703568279743,
0.006568488664925098,
0.00871368683874607,
-0.012029903940856457,
0.030103106051683426,
0.05254281684756279,
-0.012740235775709152,
-0.0026866409461945295,
0.024506859481334686,
-0.0183767918497324,
-0.04145980626344681,
-0.0017910496098920703,
0.0020847551058977842,
-0.048992663621902466,
0.005703187547624111,
-0.03466549515724182,
0.01739971898496151,
-0.036537591367959976,
0.031660668551921844,
-0.015799369663000107,
0.04171992465853691,
-0.03292429819703102,
-0.06331688165664673,
-0.01790538989007473,
0.013718544505536556,
0.010504264384508133,
-0.03580700233578682,
-0.028700949624180794,
0.00003721535540535115,
-0.006554591003805399,
-0.008344210684299469,
0.021090498194098473,
0.006208321545273066,
0.035642072558403015,
0.033893369138240814,
-0.04384925216436386,
0.03767896443605423,
-0.03071189858019352,
-0.020593801513314247,
0.015580487437546253,
-0.06972351670265198,
0.025203097611665726,
-0.005773182027041912,
0.024960046634078026,
0.05513438209891319,
-0.02667643502354622,
-0.006146623753011227,
0.014978221617639065,
-0.016718648374080658,
0.0016960259526968002,
-0.04505440965294838,
0.0766393169760704,
0.02175864204764366,
-0.039147116243839264,
-0.05127672851085663,
-0.04857402667403221,
0.06678876280784607,
0.022983869537711143,
-0.013661500066518784,
-0.028058137744665146,
0.021465271711349487,
-0.044426459819078445,
-0.03709352761507034,
-0.006834483705461025,
0.0428868904709816,
-0.020589839667081833,
0.024763034656643867,
0.057584863156080246,
-0.007564553525298834,
0.06728681921958923,
0.019543180242180824,
-0.027688244357705116,
-0.0034941970370709896,
-0.037327591329813004,
-0.052725426852703094,
-0.042216893285512924,
0.088625468313694,
-0.018232397735118866,
-0.01016372349113226,
0.01542442012578249,
-0.037126827985048294,
0.0647418275475502,
-0.020808424800634384,
0.018326951190829277,
0.024034814909100533,
0.03814120218157768,
0.001311641768552363,
-0.036682482808828354,
0.005212205462157726,
0.04214358702301979,
0.038112204521894455,
0.034741174429655075,
0.008877614513039589,
0.006801263429224491,
-0.05964767187833786,
0.028182266280055046,
0.020396150648593903,
-0.006962815765291452,
0.010995380580425262,
0.053285788744688034,
-0.031644389033317566,
0.005015581846237183,
-0.021795915439724922,
0.001621611532755196,
0.04303416609764099,
-0.022983547300100327,
-0.015216526575386524,
-0.0011795449536293745,
-0.02099663019180298,
-0.022108815610408783,
-0.006865815259516239,
-0.01703922636806965,
-0.007429575547575951,
0.05162249132990837,
-0.038821153342723846,
0.05558453127741814,
0.011695572175085545,
0.004951216280460358,
-0.026851285248994827,
0.037357114255428314,
0.007157048676162958,
0.0030145361088216305,
0.05517188087105751,
0.010191208682954311,
-0.03909754753112793,
-0.017215367406606674,
0.05279509723186493,
0.015457252971827984,
0.004555454012006521,
0.029988180845975876,
0.0477936714887619,
-0.010901322588324547,
0.03944077342748642,
-0.023926690220832825,
-0.03242335841059685,
0.020211111754179,
-0.028310537338256836,
0.026200201362371445,
-0.0387723371386528,
0.0017507208976894617,
0.05376819521188736,
0.037515804171562195,
0.014114877209067345,
-0.027311354875564575,
0.00043946981895715,
-0.042970772832632065,
0.012416251003742218,
0.01791679859161377,
0.009537586942315102,
0.010375363752245903,
0.007987921126186848,
0.0401618666946888,
0.015971947461366653,
0.010357222519814968,
-0.052323825657367706,
-0.06196906045079231,
0.004620353225618601,
-0.03168031945824623,
-0.03893514722585678,
0.04202700033783913,
0.011297144927084446,
-0.02180740237236023,
-0.016196854412555695,
-0.018552381545305252,
-0.00936718937009573,
0.02048168145120144,
0.0265196580439806,
-0.019414331763982773,
0.041655898094177246,
0.037344079464673996,
0.015524894930422306,
0.005584719590842724,
0.0028754789382219315,
0.1246306449174881,
0.04378426447510719,
0.018181905150413513,
-0.07593455165624619,
0.01594110019505024,
0.028945328667759895,
0.0030432490166276693,
-0.007301072124391794,
-0.016492610797286034,
0.017807254567742348,
0.0317901149392128,
0.02740609459578991,
0.06906708329916,
-0.012260316871106625,
0.007561917882412672,
0.0027450912166386843,
-0.0484510138630867,
-0.029700307175517082,
-0.027260366827249527,
0.02643861621618271,
-0.02403131127357483,
0.013371904380619526,
-0.019081100821495056,
0.017743535339832306,
-0.024452514946460724,
0.004176642745733261,
-0.023215672001242638,
-0.06329641491174698,
-0.011105828918516636,
0.01807362399995327,
-0.0681706890463829,
-0.006929516792297363,
0.03965548053383827,
-0.011819107457995415,
-0.05610468611121178,
0.03535414859652519,
0.015013349242508411,
-0.07577023655176163,
0.019175469875335693,
0.02262989804148674,
0.021096523851156235,
0.0030076911207288504,
0.020679084584116936,
0.006986632477492094,
-0.04649931564927101,
-0.001021145610138774,
-0.03638319671154022,
-0.005771603435277939,
-0.020397169515490532,
0.021889397874474525,
0.0006324990536086261,
-0.0299628097563982,
0.01401237677782774,
-0.02806299924850464,
-0.029489895328879356,
-0.021683597937226295,
0.009808352217078209,
-0.0008831701125018299,
-0.028124555945396423,
-0.039543237537145615,
0.024715857580304146,
0.0018463819287717342,
0.017093267291784286,
0.018045179545879364,
-0.018848519772291183,
0.006411639507859945,
0.0017875496996566653,
0.063291035592556,
-0.01897336170077324,
0.03334863483905792,
-0.024144364520907402,
-0.024375509470701218,
-0.04768851399421692,
0.013487027958035469,
0.020399918779730797,
0.027821635827422142,
0.02502816915512085,
-0.02453548088669777,
-0.026600098237395287,
-0.019097842276096344,
-0.00543660344555974,
0.06455229967832565,
-0.0027373533230274916,
0.0013036261079832911,
-0.03320138156414032,
-0.01535908691585064,
0.00798667874187231,
0.033632081001996994,
-0.02475113980472088,
0.0016155258053913713,
0.0312795527279377,
0.005046196281909943,
0.0028638625517487526,
-0.008142232894897461,
-0.03487855941057205,
0.01683647558093071,
-0.019854243844747543,
-0.019106868654489517,
-0.027830379083752632,
0.035495880991220474,
0.0013946150429546833,
-0.0429375022649765,
-0.003848947351798415,
0.012225625105202198,
-0.0013115380425006151,
0.016028359532356262,
-0.004222807474434376,
-0.03346017375588417,
-0.02785039320588112,
0.046957582235336304,
0.001711949473246932,
-0.03657851740717888,
-0.039157260209321976,
-0.024980925023555756,
0.0003585128579288721,
-0.045309603214263916,
0.028516089543700218,
0.007064132951200008,
0.01839102804660797,
-0.03602999821305275,
0.07871267944574356,
-0.026873363181948662,
-0.013502341695129871,
-0.054529812186956406,
0.004147063475102186,
0.06473793089389801,
0.006115614902228117,
-0.04748278856277466,
0.033257707953453064,
0.0076134041883051395,
-0.0017079217359423637,
-0.03713671490550041,
0.020273607224225998,
0.02943289652466774,
0.006892357021570206,
0.018493331968784332,
-0.018530551344156265,
0.035987142473459244,
-0.015603575855493546,
-0.03351077064871788,
-0.0006245040567591786,
-0.04685264825820923,
-0.06157584488391876,
0.027547625824809074,
0.0010789273073896766,
0.0025611664168536663,
0.018227754160761833,
0.012382806278765202,
0.00649816170334816,
0.05453738197684288,
-0.02480662427842617,
0.0010915764141827822,
-0.009011336602270603,
-0.023845668882131577,
-0.046362362802028656,
0.01359737478196621,
-0.0021725953556597233,
-0.031045211479067802,
-0.012831104919314384,
0.03359508886933327,
0.012187346816062927,
-0.02423885092139244,
-0.003699693363159895,
-0.026843247935175896,
-0.01916654221713543,
0.007682128809392452,
0.017965879291296005,
0.012284437194466591,
0.016485394909977913,
0.04259364679455757,
-0.03834684193134308,
0.04609161615371704,
-0.008399496786296368,
-0.03911217302083969,
-0.07321847975254059,
-0.026906752958893776,
0.001246266532689333,
-0.003758032573387027,
0.021352414041757584,
-0.00007401306356769055,
-0.020209046080708504,
0.037062130868434906,
-0.0706697329878807,
0.0371306873857975,
-0.006686781998723745,
0.010096030309796333,
-0.02409449778497219,
0.014669651165604591,
-0.00005127067197463475,
0.05597900226712227,
0.009174617938697338,
0.014967726543545723,
0.030582791194319725,
0.0239165760576725,
-0.019658947363495827,
-0.007515132427215576,
-0.002307473449036479,
0.016090115532279015,
-0.03663790971040726,
-0.01597975194454193,
0.055642951279878616,
-0.016026759520173073,
-0.01631269045174122,
0.008893058635294437,
-0.042867615818977356,
0.03708367422223091,
-0.03325242921710014,
-0.009815038181841373,
-0.010235752910375595,
0.005705661606043577,
0.006724885664880276,
0.02423551306128502,
-0.0007485243258997798,
0.055743973702192307,
0.01840989664196968,
0.016142649576067924,
-0.02024935558438301,
0.004275091458112001,
0.03292478248476982,
-0.008165762759745121,
-0.0359741635620594,
0.005868760868906975,
-0.02519768476486206,
-0.026927655562758446,
-0.01954459771513939,
0.02024642378091812,
0.018503330647945404,
0.017267273738980293,
-0.025614062324166298,
-0.035271093249320984,
-0.008409684523940086,
-0.021686188876628876,
0.003589649684727192,
-0.01744743436574936,
0.06798799335956573,
0.004300856031477451,
0.011043687351047993,
-0.05120393633842468,
-0.008636631071567535,
-0.005430979188531637,
-0.04748236760497093,
0.023280082270503044,
0.010645509697496891,
-0.025514038279652596,
-0.009711447171866894,
-0.040463563054800034,
-0.008170166984200478,
0.008774418383836746,
0.007751740049570799,
-0.008095826953649521,
0.016454793512821198,
-0.021517569199204445,
-0.028739972040057182,
-0.05045069754123688,
-0.009088593535125256,
-0.023379437625408173,
-0.02959495782852173,
0.004488782957196236,
-0.012111254036426544,
-0.0005581592558883131,
0.023901082575321198,
0.04327242821455002,
0.009101549163460732,
0.004410410299897194,
0.0028762263245880604,
-0.018533620983362198,
0.06369064748287201,
-0.02372361533343792,
0.0031633502803742886,
-0.053169772028923035,
-0.015012805350124836,
0.0030621213372796774,
0.02223248966038227,
-0.014516829513013363,
0.023327184841036797,
0.012123813852667809,
-0.019219577312469482,
0.02789289504289627,
-0.002597739454358816,
-0.0007044861558824778,
0.03222675248980522,
0.02934245392680168,
0.0365571565926075,
0.08459921181201935,
-0.028326939791440964,
0.0049188463017344475,
0.006082154344767332,
-0.01910790428519249,
-0.03897057846188545,
0.07098476588726044,
-0.012864138931035995,
0.0237733144313097,
-0.031208205968141556,
-0.027205366641283035,
0.016831833869218826,
-0.05494854971766472,
0.011176086962223053,
-0.002962893107905984,
-0.006104390602558851,
-0.007211747579276562,
0.00011343605729052797,
0.020832590758800507,
-0.00016617798246443272,
-0.017987141385674477,
-0.0037445328198373318,
-0.01806528866291046,
0.0073425741866230965,
0.005368894897401333,
0.040812745690345764,
0.009148577228188515,
-0.013430903665721416,
-0.016340333968400955,
0.02548360265791416,
-0.01570277102291584,
0.04563162848353386,
-0.006982952821999788,
0.04614180326461792,
0.011336775496602058,
-0.03295210748910904,
0.02623794600367546,
-0.008618713356554508,
-0.015189307741820812,
0.008779076859354973,
0.0031408267095685005,
0.045743536204099655,
-0.02155412547290325,
0.04272537678480148,
-0.016582103446125984,
0.012997632846236229,
-0.054357901215553284,
-0.05315087363123894,
0.0398118831217289,
0.02179691754281521,
-0.01645810157060623,
-0.03804830461740494,
0.016321539878845215,
0.0021182619966566563,
0.02004883624613285,
-0.001975066028535366,
0.04677881672978401,
0.000060059159295633435,
-0.024625437334179878,
0.016194511204957962,
-0.025803498923778534,
-0.02883043698966503,
0.02791604772210121,
0.04923390969634056,
0.03280774876475334,
0.013739493675529957,
0.0009871394140645862,
0.014159491285681725,
-0.02936951071023941,
0.05555109679698944,
-0.028086738660931587,
-0.04916001111268997,
-0.029378974810242653,
0.06083807721734047,
-0.004520704969763756,
0.02878333441913128
] |
<p>My research has led me to look into the idea of bubble universes which I don't know very much about. The first thing that I am looking for is understanding or visualising how could many bubbles co-exist geometrically, assuming each bubble universe is like ours (that is, a flat euclidean geometry). Are we talking about an n-manifold that has multiple bubbles embedded in it? Submanifolds? Or can we extend the idea of branes to the notion of bubbles? Is it perhaps a 3-sphere that houses multiple 2-spheres? Put simply, what is the theoretical geometry that engulfs all the bubbles and how would they be connected?</p> | 1,998 | [
-0.02174767665565014,
-0.0031375533435493708,
0.013114653527736664,
-0.05159410089254379,
0.030593838542699814,
0.0016384143382310867,
-0.03635292872786522,
-0.03946910798549652,
0.013985792174935341,
-0.04704074189066887,
0.012153230607509613,
0.013937216252088547,
0.024248750880360603,
-0.011767025105655193,
0.014279051683843136,
-0.019065650179982185,
-0.023905478417873383,
-0.03254606947302818,
-0.0013008989626541734,
-0.034317124634981155,
0.06023290753364563,
0.003571407636627555,
-0.001475735567510128,
-0.001046342309564352,
-0.00370159768499434,
0.048743218183517456,
0.0026046354323625565,
-0.028932593762874603,
0.030296050012111664,
0.03791622072458267,
0.005883972160518169,
-0.01264273189008236,
0.020783301442861557,
0.03441819176077843,
-0.017220545560121536,
-0.04327008128166199,
-0.03693201392889023,
-0.02670007385313511,
0.009451196528971195,
0.015230586752295494,
-0.06605324894189835,
-0.04644220322370529,
-0.03268994018435478,
0.050906188786029816,
-0.03298773616552353,
-0.03042297251522541,
-0.0046562799252569675,
-0.03807742893695831,
0.02346879057586193,
-0.07868962734937668,
0.07591968029737473,
0.03116725943982601,
0.06372495740652084,
0.04324468597769737,
-0.009104904718697071,
0.02869686856865883,
0.06664213538169861,
0.07107838988304138,
0.007368110585957766,
-0.034393977373838425,
-0.04193612560629845,
0.034977614879608154,
-0.0094094667583704,
-0.06315364688634872,
-0.03742213174700737,
0.035174448043107986,
-0.034290146082639694,
0.012995061464607716,
-0.01066250167787075,
-0.004826015792787075,
-0.004372029565274715,
0.0051097869873046875,
0.0710102990269661,
-0.008379162289202213,
0.018062498420476913,
-0.019735030829906464,
0.02172759920358658,
-0.016374943777918816,
0.06136217340826988,
0.028133384883403778,
-0.01680373214185238,
-0.011007004417479038,
0.007023032754659653,
0.014420839957892895,
-0.0046736798249185085,
0.005203559063374996,
0.07880343496799469,
-0.02521391399204731,
0.020411530509591103,
0.02430136688053608,
0.00033362992689944804,
-0.03246840834617615,
0.06379927694797516,
0.002882526023313403,
-0.0486132986843586,
0.033362437039613724,
0.0052092596888542175,
0.03607654199004173,
0.005055984947830439,
-0.04132895916700363,
-0.012408148497343063,
0.003933256026357412,
0.016724683344364166,
0.09282911568880081,
0.029435137286782265,
-0.03457161784172058,
-0.06931257247924805,
0.026826435700058937,
-0.01826416328549385,
-0.024011611938476562,
-0.035544198006391525,
0.02503024786710739,
-0.002809875411912799,
-0.021341649815440178,
0.019738398492336273,
-0.021687407046556473,
0.0030064829625189304,
-0.060674235224723816,
0.026966657489538193,
0.06561239063739777,
0.05727213993668556,
-0.009680485352873802,
0.03385680541396141,
0.008287378586828709,
-0.10332883149385452,
0.020764894783496857,
0.04739176854491234,
0.015385066159069538,
-0.02719895727932453,
0.035879407078027725,
-0.0018344607669860125,
-0.004879312589764595,
0.009816468693315983,
0.014805970713496208,
0.07817832380533218,
-0.030686482787132263,
-0.09376450628042221,
-0.06583074480295181,
0.05398837476968765,
0.010873406194150448,
0.00351928872987628,
-0.02033132314682007,
0.015030828304588795,
0.036158040165901184,
0.07685959339141846,
-0.016092544421553612,
-0.0372067354619503,
0.014329214580357075,
0.05983418971300125,
0.0144423209130764,
-0.0272403322160244,
0.002709719119593501,
-0.017054323107004166,
-0.03718675300478935,
0.01585523784160614,
-0.03916914016008377,
0.03275882825255394,
0.03413765877485275,
0.017029354348778725,
-0.06018644571304321,
0.07489760220050812,
0.011860918253660202,
0.010309992358088493,
0.018628980964422226,
-0.017205553129315376,
-0.025097740814089775,
0.06816957890987396,
-0.010007842443883419,
-0.0026203771121799946,
0.03584953397512436,
-0.054483070969581604,
0.014295820146799088,
0.029167132452130318,
0.06675522029399872,
0.009176596067845821,
-0.010720398277044296,
0.001691564917564392,
-0.007594013120979071,
0.01345978956669569,
0.01998758874833584,
-0.0015330653404816985,
-0.01673821546137333,
-0.03164346143603325,
0.0025043762288987637,
0.007003431674093008,
0.026285573840141296,
-0.010421708226203918,
-0.04910976067185402,
-0.011729296296834946,
-0.07502952963113785,
0.0031685419380664825,
-0.08776617050170898,
0.007368207443505526,
-0.011893438175320625,
-0.027841757982969284,
0.00319907465018332,
-0.00649242801591754,
0.005715235602110624,
-0.044013235718011856,
-0.036027248948812485,
-0.03446734696626663,
0.061312105506658554,
0.02413284406065941,
0.010074264369904995,
0.0008468231535516679,
0.02089451625943184,
0.00039999085129238665,
-0.014199402183294296,
0.015779942274093628,
0.018981290981173515,
0.017101911827921867,
-0.00959975179284811,
-0.020216401666402817,
0.00986718200147152,
-0.02482185699045658,
-0.004579233471304178,
0.037196408957242966,
0.007989741861820221,
-0.012297417968511581,
0.02020353451371193,
-0.057605892419815063,
0.057161595672369,
0.022631550207734108,
0.0007853600545786321,
-0.02759096398949623,
0.03416385501623154,
0.019612953066825867,
0.014602079056203365,
-0.0056671868078410625,
-0.03376920148730278,
-0.03991139307618141,
-0.006433635484427214,
0.05826409161090851,
0.05628862604498863,
-0.016088848933577538,
0.012560693547129631,
0.0005018258234485984,
0.029748346656560898,
-0.012968677096068859,
-0.005150249693542719,
-0.025212084874510765,
-0.007903304882347584,
0.0014189216308295727,
0.005855042487382889,
0.0203163530677557,
0.02616157755255699,
0.016968905925750732,
0.03783702105283737,
-0.0032477262429893017,
-0.036436792463064194,
-0.0402105338871479,
0.042913101613521576,
-0.02476043440401554,
-0.018546780571341515,
-0.029023632407188416,
0.016716117039322853,
0.03018692135810852,
-0.03958616033196449,
0.021294541656970978,
0.021232537925243378,
0.02824993245303631,
-0.01969987340271473,
-0.019025452435016632,
-0.025161048397421837,
0.015421772375702858,
0.051867589354515076,
-0.005815189331769943,
-0.007491043768823147,
-0.003008643863722682,
-0.04536660760641098,
0.02615888975560665,
0.006295772269368172,
0.0033129099756479263,
0.00023967541346792132,
0.02319278195500374,
0.0032794116996228695,
0.003626224584877491,
0.019327176734805107,
-0.026347573846578598,
-0.06915252655744553,
0.02071959525346756,
-0.02065032161772251,
0.011870769783854485,
-0.0032326048240065575,
-0.07314351946115494,
0.02571006491780281,
-0.027254829183220863,
0.003978413995355368,
0.012472438625991344,
-0.01933102123439312,
0.0132394814863801,
0.015045330859720707,
-0.019948096945881844,
-0.00018714343605097383,
-0.01759265549480915,
-0.010630411095917225,
0.051627520471811295,
-0.017628654837608337,
0.03135696426033974,
0.03792700171470642,
-0.008006531745195389,
-0.05881441384553909,
0.009219855070114136,
-0.03198258578777313,
-0.06726988404989243,
-0.034670211374759674,
0.004280524794012308,
0.04157707467675209,
-0.03967834636569023,
0.01708667166531086,
0.041602473706007004,
-0.04241011291742325,
0.0008326410898007452,
-0.054288432002067566,
-0.06287816166877747,
-0.0019366376800462604,
-0.010174383409321308,
0.03062131442129612,
-0.012920144014060497,
-0.040779959410429,
0.0944143608212471,
-0.02144676260650158,
-0.03395203500986099,
-0.0016805690247565508,
-0.01139992568641901,
-0.0033504520542919636,
-0.033611249178647995,
0.029249146580696106,
0.03290664032101631,
-0.015784919261932373,
0.0066235060803592205,
0.05422408506274223,
0.044316135346889496,
0.037215717136859894,
-0.006207833532243967,
-0.030374011024832726,
-0.005972268059849739,
0.00871969573199749,
0.033584389835596085,
0.03428451344370842,
0.014956924133002758,
-0.02366577461361885,
0.013578481040894985,
0.01325696986168623,
-0.004866092000156641,
0.027231426909565926,
-0.04030212387442589,
0.03792351111769676,
0.010431624948978424,
-0.012545250356197357,
0.00301596918143332,
-0.03625214099884033,
0.0038688182830810547,
-0.023915864527225494,
0.026326270774006844,
0.04090132564306259,
0.04362546280026436,
-0.02059941180050373,
-0.020378105342388153,
0.03875552862882614,
0.04051599279046059,
-0.049859244376420975,
-0.02332824282348156,
-0.016461476683616638,
0.0029237649869173765,
0.016953421756625175,
0.007080433890223503,
-0.021693479269742966,
0.05141303315758705,
0.0023841208312660456,
0.02002144046127796,
0.012129110284149647,
-0.02617846243083477,
0.009065660648047924,
-0.08100737631320953,
-0.022795308381319046,
0.0038255667313933372,
0.022756805643439293,
-0.011053098365664482,
0.010746096260845661,
-0.01940036378800869,
-0.010657125152647495,
-0.013971371576189995,
-0.018583225086331367,
-0.03405458852648735,
-0.013745187781751156,
-0.04288878291845322,
0.0400189645588398,
0.004677594639360905,
0.0025432186666876078,
0.012462940998375416,
0.003257600823417306,
-0.012329591438174248,
-0.019921159371733665,
0.009224272333085537,
-0.07220879197120667,
0.015390679240226746,
-0.04178502410650253,
-0.024962684139609337,
-0.004263058304786682,
0.0330808162689209,
0.050251130014657974,
0.009691513143479824,
0.03182179480791092,
0.003176695667207241,
-0.03787676617503166,
0.025381922721862793,
0.010774165391921997,
0.010215487331151962,
0.011409877799451351,
0.005054713226854801,
0.005611740052700043,
0.02797088585793972,
0.02767065539956093,
0.0018775804201141,
-0.003179030492901802,
0.031474608927965164,
-0.008711015805602074,
-0.0016264821169897914,
0.013039982877671719,
-0.03644022345542908,
0.008620521053671837,
-0.021631181240081787,
0.05247795209288597,
-0.0192157793790102,
0.016036788001656532,
0.039241790771484375,
0.011289612390100956,
-0.00333410850726068,
0.04371391236782074,
0.0817800760269165,
-0.001455486286431551,
-0.034135572612285614,
-0.02419259212911129,
-0.05973518639802933,
-0.0198411475867033,
0.0249186884611845,
0.002817146247252822,
0.011224526911973953,
-0.052486252039670944,
0.030447861179709435,
0.032452408224344254,
-0.01082061417400837,
-0.01491100899875164,
-0.04340502992272377,
0.0030181638430804014,
0.03946883603930473,
-0.02396533638238907,
0.0008176923147402704,
-0.03485836833715439,
0.029988249763846397,
0.04153972119092941,
-0.0006361033883877099,
-0.025715969502925873,
-0.08383204787969589,
-0.005452959332615137,
0.010886001400649548,
-0.007201923057436943,
0.051126301288604736,
-0.013707095757126808,
-0.07736553251743317,
-0.006522058509290218,
0.05343548208475113,
-0.04825602471828461,
-0.0025110444985330105,
-0.008546705357730389,
-0.006478084251284599,
0.0009339425014331937,
0.016802234575152397,
0.024303056299686432,
0.023947205394506454,
0.0012048583012074232,
0.006253661122173071,
0.001741842832416296,
0.0299494918435812,
-0.012971044518053532,
0.06054484099149704,
0.0012297459179535508,
0.021948887035250664,
0.022642862051725388,
-0.0023389586713165045,
0.0006371644558385015,
0.048500847071409225,
-0.014409183524549007,
-0.06635743379592896,
0.03769643232226372,
0.008032162673771381,
-0.0534331277012825,
0.05268384516239166,
-0.011479697190225124,
-0.028166623786091805,
-0.002081808866932988,
-0.004212190397083759,
0.005580257158726454,
0.027808191254734993,
-0.02929309755563736,
0.033243704587221146,
0.03612334281206131,
0.023271003738045692,
0.008619883097708225,
0.030214693397283554,
-0.01465392205864191,
-0.01942051760852337,
-0.03826623782515526,
0.027528218924999237,
-0.019722625613212585,
-0.006412305403500795,
-0.02095215395092964,
-0.04306543245911598,
-0.025189334526658058,
0.025546250864863396,
-0.024298444390296936,
-0.010361973196268082,
0.019961245357990265,
-0.06362070143222809,
-0.010848796926438808,
0.04160182550549507,
0.019988952204585075,
0.0014890055172145367,
-0.003425460308790207,
0.003816713346168399,
0.03982684016227722,
-0.01605040207505226,
0.026977797970175743,
-0.014264942146837711,
0.0016167728463187814,
0.01494358666241169,
-0.008596619591116905,
0.013317452743649483,
-0.005879079923033714,
0.010559041053056717,
0.014498348347842693,
-0.049873385578393936,
0.06392090022563934,
-0.004157001152634621,
0.014830468222498894,
0.0436130091547966,
-0.05920703709125519,
0.0031875213608145714,
-0.010837700217962265,
-0.016437768936157227,
0.01309819333255291,
-0.04476786032319069,
0.009495717473328114,
0.01974426954984665,
-0.0013582292012870312,
-0.09236540645360947,
-0.04828919842839241,
0.07314665615558624,
0.012627573683857918,
-0.020407849922776222,
-0.06682559102773666,
0.040258005261421204,
-0.025831876322627068,
-0.004662895575165749,
0.0066854339092969894,
0.03732099384069443,
-0.05028936639428139,
-0.010786205530166626,
-0.0025468424428254366,
0.046967100352048874,
0.020761867985129356,
-0.01981160044670105,
-0.006353757344186306,
0.008273893967270851,
0.036011599004268646,
-0.009895428083837032,
-0.016401799395680428,
0.01999390497803688,
-0.0037840164732187986,
-0.0156758651137352,
-0.03865785524249077,
0.004564743954688311,
0.029026096686720848,
-0.0838879942893982,
0.01008671149611473,
0.027739960700273514,
0.01658065803349018,
0.00804554857313633,
-0.0236614178866148,
0.006283637136220932,
0.0053559560328722,
0.025064559653401375,
-0.04170958697795868,
0.002658568089827895,
0.007107687648385763,
-0.06508684903383255,
0.055978234857320786,
-0.026527661830186844,
-0.010076018050312996,
0.006699820049107075,
0.05032801628112793,
0.017624465748667717,
-0.03371596336364746,
0.0042762611992657185,
-0.02672559581696987,
0.01488634292036295,
-0.00330700003542006,
-0.01588696800172329,
0.025774678215384483,
0.02557654306292534,
-0.03390296921133995,
-0.06331907957792282,
-0.017866529524326324,
0.017744265496730804,
0.05656040832400322,
-0.05518675222992897,
0.025626275688409805,
0.03562721982598305,
-0.04251248762011528,
-0.002203261246904731,
-0.03335558995604515,
-0.009847543202340603,
0.029186081141233444,
-0.008207322098314762,
0.05622902140021324,
-0.0319015309214592,
-0.01509549468755722,
0.04316824674606323,
0.05133659020066261,
0.007095710374414921,
0.040207333862781525,
0.008562915958464146,
0.028151381760835648,
0.019060907885432243,
0.003834477858617902,
-0.04320470243692398,
0.07767381519079208,
-0.03894852101802826,
0.02737620659172535,
0.008868514560163021,
-0.022275539115071297,
0.043776679784059525,
0.005402674432843924,
0.03569633886218071,
0.0038457729388028383,
-0.0227962676435709,
-0.003040504176169634,
0.030856139957904816,
0.03668281435966492,
0.03451274707913399,
-0.00805794820189476,
0.0012864158488810062,
0.03276385739445686,
0.0024895884562283754,
0.028353389352560043,
-0.013338427990674973,
-0.06704778224229813,
-0.029118528589606285,
-0.045877981930971146,
-0.007807434070855379,
0.04325098916888237,
0.03091289848089218,
-0.03546883165836334,
-0.004647394642233849,
-0.0201190784573555,
0.013420024886727333,
-0.024733709171414375,
0.034082792699337006,
-0.03277357295155525,
0.07395120710134506,
-0.006625470705330372,
0.031523726880550385,
-0.013907515443861485,
-0.012191135436296463,
0.10459225624799728,
0.04247700050473213,
-0.009641995653510094,
-0.0667482540011406,
-0.012200836092233658,
-0.024466466158628464,
0.0018128344090655446,
-0.05171472579240799,
0.026465384289622307,
0.019677793607115746,
0.02721419185400009,
0.005480436608195305,
0.07520131766796112,
-0.012444700114428997,
-0.009196323342621326,
0.05990360677242279,
-0.04314178600907326,
-0.05295495688915253,
0.0027190563268959522,
0.02124549075961113,
-0.012223497033119202,
0.03208373486995697,
-0.04948790743947029,
0.05667433515191078,
-0.013695317320525646,
0.000503521179780364,
-0.031707681715488434,
-0.005375639069825411,
0.0345977321267128,
0.0012233264278620481,
-0.02015729434788227,
0.00035747166839428246,
-0.00251954048871994,
-0.06531964987516403,
-0.014226805418729782,
-0.029128942638635635,
0.012056013569235802,
0.006846175063401461,
0.03067850135266781,
-0.023052746430039406,
0.0033561931923031807,
0.009259872138500214,
-0.005094014573842287,
0.030603844672441483,
-0.04709536209702492,
-0.021306553855538368,
-0.0028176018968224525,
0.04459355026483536,
-0.018138239160180092,
0.00634714076295495,
-0.021686004474759102,
0.008256546221673489,
0.021194474771618843,
-0.01802726276218891,
-0.009296953678131104,
-0.006999035831540823,
0.02397821843624115,
-0.016408715397119522,
-0.02625954896211624,
0.008070196956396103,
0.02957448922097683,
0.013438361696898937,
0.04618454352021217,
-0.04088892042636871,
-0.015632085502147675,
0.009437046945095062,
-0.05067213997244835,
0.032214585691690445,
-0.011302338913083076,
0.00396545697003603,
-0.046248145401477814,
0.024953532963991165,
-0.017972024157643318,
-0.0011651671957224607,
0.030863115563988686,
0.028158610686659813,
0.03056366927921772,
0.025248970836400986,
-0.012200016528367996,
0.03418504074215889,
-0.0021428782492876053,
0.0075227040797472,
-0.03178555518388748,
-0.020688924938440323,
-0.03560347855091095,
0.019171983003616333,
0.052518077194690704,
0.0244654081761837,
-0.015340572223067284,
0.0015527661889791489,
-0.012489981018006802,
-0.011517425999045372,
0.013126743026077747,
-0.013124560937285423,
0.011937424540519714,
-0.008157183416187763,
-0.04442339017987251,
-0.03537701070308685,
-0.024815352633595467,
0.023861754685640335,
0.017896952107548714,
-0.00018056451517622918,
0.029230456799268723,
0.07268922030925751,
-0.0016156176570802927,
-0.020733647048473358,
0.00809074379503727,
-0.031106607988476753,
-0.0064528449438512325,
-0.011677335016429424,
0.033391986042261124,
-0.025235692039132118,
-0.030547330155968666,
0.007536706980317831,
-0.010586063377559185,
-0.023465240374207497,
0.01833644136786461,
-0.01879001222550869,
0.007821748033165932,
-0.0011266996152698994,
0.0008354903548024595,
-0.035129714757204056,
-0.008166041225194931,
-0.035546015948057175,
0.007157137151807547,
0.015356960706412792,
0.007965028285980225,
0.027835147455334663,
-0.008824974298477173,
-0.0352841392159462,
-0.03022688813507557,
0.0017586381873115897,
0.04141392558813095,
-0.03737446665763855,
-0.005654553417116404,
0.04622650146484375,
0.011561209335923195,
0.016843179240822792,
-0.025147436186671257,
-0.048032622784376144,
0.0034271003678441048,
-0.022584814578294754,
-0.06766707450151443,
-0.00596751319244504,
-0.00822792574763298,
0.010612992569804192,
0.025837399065494537,
-0.028759384527802467,
-0.08039579540491104,
0.03602926805615425,
-0.017186081036925316,
-0.019391050562262535,
0.020817037671804428,
0.0073882644064724445,
-0.03347103297710419,
-0.021280691027641296,
0.04925575479865074,
-0.013731027022004128,
-0.009820702485740185,
0.015388230793178082,
0.01883898675441742,
-0.007158331573009491,
-0.02159860171377659,
-0.016814595088362694,
-0.026875289157032967,
0.034500978887081146,
-0.03415217995643616,
0.02593035064637661,
0.06052267551422119,
0.04167860373854637,
-0.04483603686094284,
0.030345601961016655,
0.05067810043692589,
-0.010764330625534058,
-0.09401796758174896,
0.00209235236980021,
0.044037554413080215,
0.0075235627591609955,
0.054314617067575455,
-0.0317198671400547,
0.03586504980921745,
0.03039296343922615,
-0.07624591141939163,
0.037633612751960754,
-0.0650624930858612,
-0.01456470601260662,
-0.03885892033576965,
0.007156513165682554,
-0.020094696432352066,
0.06519348919391632,
0.03807323798537254,
0.04279192164540291,
0.013253158889710903,
-0.0017379621276631951,
-0.020098427310585976,
-0.02870507724583149,
-0.021455587819218636,
0.0026445554103702307,
-0.036622561514377594,
-0.01343277283012867,
0.06341052055358887,
-0.01767568662762642,
-0.029748648405075073,
0.021372253075242043,
-0.010097779333591461,
-0.011930767446756363,
0.01330508477985859,
-0.010968359187245369,
0.005088673438876867,
-0.011084296740591526,
0.04771289974451065,
0.015110131353139877,
-0.011072373017668724,
0.03800821304321289,
0.054607536643743515,
0.013340617530047894,
0.0034870861563831568,
0.004971654154360294,
-0.0012224351521581411,
-0.03003326803445816,
0.005719176027923822,
0.023393671959638596,
-0.00923146028071642,
-0.005357787013053894,
-0.02682669088244438,
-0.00008172685193130746,
0.04052609205245972,
-0.0035206463653594255,
0.00040906257345341146,
-0.05467929691076279,
0.011283465661108494,
0.03136296942830086,
-0.004755082540214062,
-0.0038487440906465054,
0.06252887845039368,
-0.01105703879147768,
-0.022862114012241364,
0.009458793327212334,
-0.013409695588052273,
0.013324779458343983,
-0.010192318819463253,
-0.019428279250860214,
0.018623970448970795,
-0.014325084164738655,
0.022818146273493767,
-0.03021835722029209,
0.009570940397679806,
0.05757235363125801,
0.03661158308386803,
0.03834050893783569,
0.01883726380765438,
-0.05909770354628563,
-0.01354959700256586,
-0.05042129009962082,
0.014822871424257755,
-0.019964493811130524,
0.026636091992259026,
-0.0047746459022164345,
0.004446621984243393,
0.022614173591136932,
0.006938355043530464,
0.04006180167198181,
-0.025385508313775063,
0.0349682979285717,
0.016415538266301155,
0.026148075237870216,
0.032015006989240646,
-0.016849379986524582,
-0.005832864437252283,
0.0017182186711579561,
-0.04707519710063934,
-0.02042393386363983,
0.028199678286910057,
-0.006311643868684769,
-0.008342822082340717,
0.027492789551615715,
-0.01156610157340765,
0.03854166716337204,
-0.001491048256866634,
-0.022275177761912346,
0.021939851343631744,
-0.0002892476040869951,
-0.038076404482126236,
0.06397166103124619,
-0.003987859934568405,
-0.006506776437163353,
0.028636040166020393,
-0.010679305531084538,
-0.008811870589852333,
-0.0016234178328886628,
0.026338066905736923,
-0.016932079568505287,
-0.02700427547097206,
-0.030127424746751785,
0.016245706006884575,
-0.0354483500123024,
-0.0146968187764287,
0.017563391476869583,
-0.03644845262169838,
0.015363815240561962,
0.056382860988378525,
-0.008042274974286556,
-0.006813453044742346,
-0.031717538833618164,
-0.0008831549785099924,
0.019664794206619263,
0.013940426521003246,
-0.00025405792985111475,
0.03653295710682869,
0.0370015874505043,
-0.004473263397812843,
-0.01717999577522278,
0.003992660436779261,
-0.0027509008068591356,
0.027522673830389977,
-0.017648939043283463,
0.04726634547114372,
-0.04262201488018036,
0.009448760189116001,
0.01014157384634018,
0.008739969693124294,
0.018702654168009758,
-0.00028711193590424955,
-0.01201153825968504,
0.0871981829404831,
-0.02230203151702881,
0.010094696655869484,
-0.010246815159916878,
-0.020022744312882423,
-0.0124132065102458,
0.036681126803159714,
-0.009989326819777489,
0.06837274134159088,
0.003714423393830657,
-0.010552736930549145,
-0.03257521614432335,
0.016657629981637,
0.03411265090107918,
-0.0005082564312033355,
0.034130703657865524,
-0.010787209495902061,
-0.0023127892054617405,
0.0022846711799502373,
-0.01084273960441351,
-0.019706903025507927,
-0.040363211184740067,
0.019876722246408463,
-0.005093409679830074,
0.019983915612101555,
-0.01880139298737049,
-0.011560874059796333,
-0.03492489457130432,
0.055126674473285675,
-0.04583464190363884,
-0.027089033275842667,
-0.010358240455389023,
0.0075760167092084885,
0.005341514945030212,
0.005744760390371084
] |
<p>I've seen some discussions regarding the movement of a spinning object, say a curveball. However, all have been largely qualitative. I was wondering if anyone has seen or worked through a calculation of how far a curveball moves laterally on its way from the mound to homeplate - even in an order-of-magnitude sense.</p> | 1,999 | [
-0.0383412167429924,
-0.040192678570747375,
-0.001669291639700532,
0.00013373489491641521,
0.044797904789447784,
-0.02061590924859047,
-0.003667093114927411,
0.022977031767368317,
0.004575947765260935,
0.02292991243302822,
-0.0323634073138237,
0.03202182799577713,
0.02486107312142849,
0.016737600788474083,
0.035569000989198685,
0.01297722477465868,
-0.013072101399302483,
0.01173273753374815,
0.020535355433821678,
-0.032207462936639786,
0.004664865788072348,
0.0007720354478806257,
-0.0010354362893849611,
-0.002024151384830475,
0.030254820361733437,
-0.015156533569097519,
0.017319809645414352,
-0.0051588863134384155,
0.006407575216144323,
0.0332176499068737,
0.0021193078719079494,
0.006677001714706421,
0.019880466163158417,
0.044367991387844086,
0.029861660674214363,
-0.003949927166104317,
-0.03628161549568176,
-0.0339382030069828,
-0.04001793637871742,
0.03425968065857887,
-0.025741420686244965,
-0.025979645550251007,
-0.01254624966531992,
0.032224684953689575,
-0.029879195615649223,
0.03204994648694992,
-0.03102947026491165,
0.008875491097569466,
0.081252321600914,
-0.05450526252388954,
0.055728182196617126,
-0.017110249027609825,
0.007743466645479202,
0.015754830092191696,
-0.004691291134804487,
0.028043029829859734,
0.08738388121128082,
0.024278247728943825,
-0.03037378564476967,
-0.0767299234867096,
-0.050452444702386856,
-0.028939561918377876,
-0.015971001237630844,
-0.05161257088184357,
0.001415745005942881,
0.018894536420702934,
0.017733458429574966,
-0.03105132281780243,
0.008345348760485649,
-0.010760849341750145,
0.012723216786980629,
0.018983902409672737,
0.07003811746835709,
0.011291644535958767,
0.0055070179514586926,
-0.02107701264321804,
0.018627198413014412,
-0.002840110333636403,
-0.0010904151713475585,
0.002529529854655266,
-0.0438278503715992,
0.015058194287121296,
0.058623455464839935,
0.029836473986506462,
0.016500554978847504,
0.012776056304574013,
0.062090788036584854,
-0.02046232856810093,
0.03716859221458435,
0.04257167875766754,
0.02201893925666809,
-0.03846626728773117,
0.03071480058133602,
-0.018732547760009766,
-0.03902026265859604,
0.0339975506067276,
-0.005588464438915253,
0.04574158042669296,
0.007952195592224598,
-0.0310602355748415,
0.021434705704450607,
-0.03227756917476654,
-0.000254588172538206,
0.060542281717061996,
0.039621587842702866,
-0.0033785379491746426,
-0.011779251508414745,
-0.0026727530639618635,
0.004398006945848465,
-0.018419299274683,
-0.057018179446458817,
0.017986873164772987,
0.008623195812106133,
0.02948300912976265,
-0.012443948537111282,
0.011826119385659695,
-0.02075427584350109,
-0.034010354429483414,
0.033268850296735764,
0.03681834414601326,
0.0577387735247612,
-0.05362177640199661,
0.00046928785741329193,
-0.0405629426240921,
-0.03393726795911789,
0.022456316277384758,
0.024778204038739204,
-0.00323601346462965,
-0.05321062356233597,
0.03192833438515663,
0.0390876904129982,
-0.005092490930110216,
0.017544062808156013,
-0.0118210194632411,
0.010993128642439842,
-0.017432987689971924,
-0.055679354816675186,
-0.0684603825211525,
0.06090230494737625,
0.025903217494487762,
-0.00737876258790493,
-0.048734504729509354,
-0.0029751837719231844,
0.03540143370628357,
0.0782252848148346,
0.026808593422174454,
0.01829267106950283,
-0.04436204209923744,
0.05755934491753578,
-0.0024304050020873547,
-0.009428245946764946,
0.006374988704919815,
0.023653902113437653,
-0.030426619574427605,
0.013622727245092392,
-0.0506557859480381,
0.015985138714313507,
0.04083957150578499,
-0.014821979217231274,
-0.05083824694156647,
0.032947927713394165,
0.016647767275571823,
0.02012525498867035,
-0.024542327970266342,
-0.01626555621623993,
-0.033997245132923126,
0.06838341802358627,
0.007353532128036022,
-0.03667069971561432,
0.007184682879596949,
-0.0012849613558501005,
0.022250447422266006,
0.03560623899102211,
-0.014561643823981285,
0.03579585254192352,
-0.024443278089165688,
0.002611093921586871,
-0.015592848882079124,
-0.00197303993627429,
-0.028434982523322105,
-0.014811172150075436,
0.003376958193257451,
0.00641345139592886,
0.01022137701511383,
0.017482871189713478,
0.04798220098018646,
-0.022759683430194855,
-0.002609874587506056,
0.007159094791859388,
-0.06571287661790848,
0.000001101418092730455,
-0.030038855969905853,
0.021847059950232506,
-0.020078416913747787,
0.018854370340704918,
0.01146097294986248,
0.02348552830517292,
0.0483272522687912,
-0.03073115646839142,
-0.010383165441453457,
-0.0025144745595753193,
0.055259767919778824,
0.011625422164797783,
0.007304554805159569,
-0.006038321647793055,
0.07632352411746979,
0.00898616574704647,
-0.009222608990967274,
0.01907499134540558,
-0.03349536657333374,
-0.01012533437460661,
-0.005522457882761955,
0.007734974846243858,
0.020001862198114395,
0.04517260566353798,
0.019998174160718918,
-0.004977336153388023,
-0.021863672882318497,
-0.006389704067260027,
0.024464542046189308,
-0.019607482478022575,
0.05502857640385628,
0.0390690341591835,
0.03163411095738411,
0.0024456654209643602,
0.04828979820013046,
-0.0027550917584449053,
-0.015661150217056274,
0.027665486559271812,
-0.010098750703036785,
-0.05044121667742729,
-0.014781303703784943,
0.06253529340028763,
0.04133754223585129,
-0.016403386369347572,
-0.01711202785372734,
0.03930572047829628,
0.016972487792372704,
0.012047391384840012,
0.009484547190368176,
-0.04919520020484924,
-0.06367930769920349,
-0.04349639266729355,
0.0005966509925201535,
0.01647770032286644,
-0.01982050947844982,
0.028816895559430122,
0.0017368056578561664,
-0.002914290176704526,
0.037549618631601334,
-0.03431791812181473,
0.023702925071120262,
0.04421760141849518,
0.006981051526963711,
0.0005573049420490861,
-0.024631768465042114,
0.0652477964758873,
-0.029466861858963966,
0.009124623611569405,
0.01395446341484785,
0.024864615872502327,
0.03421036899089813,
-0.0012608981924131513,
-0.005857406184077263,
0.0384235642850399,
0.020325446501374245,
0.0010933584999293089,
0.03131803125143051,
0.03698370233178139,
-0.023836834356188774,
0.024209344759583473,
-0.02022983320057392,
0.0023725370410829782,
-0.007294584531337023,
-0.02692587487399578,
0.010781721211969852,
0.05637233704328537,
0.033583782613277435,
-0.003939881455153227,
-0.04484444484114647,
-0.018386732786893845,
-0.008583582006394863,
-0.013705535791814327,
-0.012218530289828777,
-0.04626275971531868,
0.046207673847675323,
-0.010138440877199173,
-0.021159900352358818,
0.005100247450172901,
-0.0236518494784832,
0.011503363959491253,
0.03780170530080795,
-0.009576004929840565,
-0.06499103456735611,
-0.006666804198175669,
-0.009758936241269112,
-0.016599668189883232,
-0.056432101875543594,
0.03139754384756088,
0.024396954104304314,
0.0016574084293097258,
-0.03323621675372124,
0.02794862724840641,
-0.022403914481401443,
-0.014557383954524994,
-0.02978307381272316,
0.023415755480527878,
0.030341073870658875,
-0.023191995918750763,
0.0029367634560912848,
-0.02424265630543232,
-0.004726625978946686,
-0.010240355506539345,
-0.04039070010185242,
-0.02493554912507534,
0.039589639753103256,
-0.03680497407913208,
0.024169018492102623,
-0.008125539869070053,
0.00685662217438221,
0.06135685369372368,
0.020028725266456604,
-0.07219994813203812,
-0.027859540656208992,
0.007747551891952753,
0.04041862487792969,
0.005369993858039379,
0.008707765489816666,
0.03983457386493683,
0.006586931645870209,
0.04089926928281784,
0.0077773695811629295,
-0.008485214784741402,
0.013032127171754837,
-0.01413273997604847,
0.023083854466676712,
-0.016043981537222862,
-0.012496192939579487,
0.006836296059191227,
0.003205273998901248,
0.008817172609269619,
-0.015010764822363853,
0.04332058131694794,
-0.02072896622121334,
0.03179395943880081,
0.015344067476689816,
-0.0278740543872118,
0.04216831922531128,
0.004618789069354534,
-0.02679518610239029,
0.014874090440571308,
0.030092164874076843,
-0.000910904083866626,
0.026138165965676308,
-0.005420420318841934,
0.02696951851248741,
0.044222861528396606,
0.018382597714662552,
-0.013027993030846119,
0.043786000460386276,
-0.004390031564980745,
-0.036660436540842056,
-0.024911731481552124,
-0.05960570648312569,
0.014864601194858551,
0.03492297977209091,
-0.02267933264374733,
-0.054032888263463974,
-0.011403443291783333,
-0.012624895200133324,
-0.0032541684340685606,
0.018590806052088737,
-0.01609811559319496,
-0.0011381683871150017,
-0.060073647648096085,
0.010059277527034283,
-0.01046974677592516,
0.004057928454130888,
0.0014662541216239333,
0.020981106907129288,
-0.015621945261955261,
0.00919279083609581,
0.022839756682515144,
-0.0001953640894498676,
-0.09475919604301453,
0.012271529994904995,
-0.06995144486427307,
-0.0051279193721711636,
-0.03632601350545883,
-0.00594424270093441,
0.005647477228194475,
-0.013695981353521347,
0.01516894530504942,
-0.05026114732027054,
-0.021055757999420166,
-0.03858599811792374,
-0.006606720853596926,
0.024503007531166077,
-0.027914203703403473,
-0.006585422437638044,
0.03851759061217308,
0.00864258874207735,
-0.010156109929084778,
0.024639202281832695,
-0.005109441000968218,
-0.03653506934642792,
-0.019504839554429054,
-0.019825737923383713,
0.03276201710104942,
-0.033086538314819336,
0.01687236689031124,
0.010484184138476849,
-0.009741605259478092,
-0.01378425769507885,
0.04154377058148384,
0.004303674679249525,
0.02399579808115959,
0.0221150740981102,
-0.014184857718646526,
-0.04193422943353653,
-0.08313494920730591,
-0.013956960290670395,
0.0040954467840492725,
0.047743022441864014,
0.012691376730799675,
0.021710332483053207,
0.06458736956119537,
-0.018949102610349655,
-0.0065617342479527,
-0.009908719919621944,
0.04925844818353653,
0.01678130403161049,
-0.0017083546845242381,
-0.06110304594039917,
-0.04136500507593155,
0.010031481273472309,
0.006211591884493828,
0.03956872597336769,
-0.038987379521131516,
0.010765064507722855,
0.014098632149398327,
0.0389164574444294,
-0.004470007959753275,
-0.025661947205662727,
0.018166955560445786,
-0.02148636057972908,
0.03303312882781029,
-0.03200768679380417,
0.027646033093333244,
0.029273951426148415,
0.04871309548616409,
0.068299300968647,
0.005364844109863043,
-0.03402560576796532,
-0.05742517486214638,
-0.02345973812043667,
0.04817607253789902,
0.013734695501625538,
-0.02755046635866165,
0.015412057749927044,
-0.03722510486841202,
-0.03161980211734772,
0.08346670866012573,
-0.0035422530490905046,
0.03778181970119476,
-0.06076955050230026,
0.0007036722963675857,
-0.02779407612979412,
-0.020343203097581863,
-0.04596200957894325,
0.01206141710281372,
-0.005936549045145512,
-0.0013267064932733774,
-0.03758172318339348,
0.022205276414752007,
-0.03058410808444023,
-0.015647558495402336,
0.03622788190841675,
0.024281179532408714,
0.03249523788690567,
0.0201580710709095,
-0.0179532989859581,
0.013352234847843647,
-0.016034483909606934,
-0.04323793202638626,
-0.00006552888225996867,
-0.005012209061533213,
0.006243498530238867,
0.02755781263113022,
-0.015203273855149746,
-0.03177117183804512,
0.012748503126204014,
0.022173013538122177,
0.02893243357539177,
0.005100402515381575,
-0.039955414831638336,
0.039859872311353683,
0.008840171620249748,
-0.007688457611948252,
0.050705134868621826,
-0.017535371705889702,
-0.007254975847899914,
0.013462871313095093,
0.03413556143641472,
0.03818665072321892,
0.03297088295221329,
-0.02298375591635704,
-0.029102826490998268,
0.0002724415680859238,
-0.051090799272060394,
0.018450818955898285,
-0.01815422996878624,
0.033985234797000885,
-0.04630327224731445,
-0.03134094923734665,
-0.03130558505654335,
0.028030700981616974,
0.025645315647125244,
0.00106804259121418,
-0.00789280328899622,
0.011382711119949818,
-0.008358304388821125,
-0.0214471947401762,
-0.001120170229114592,
-0.00966711062937975,
0.01079705823212862,
0.06033066287636757,
-0.010830672457814217,
0.002115159761160612,
-0.02491658367216587,
-0.013051646761596203,
0.0005636265850625932,
-0.04231546074151993,
0.06028839200735092,
-0.015320169739425182,
-0.010649462230503559,
0.040826935321092606,
-0.07785830646753311,
-0.0198090560734272,
0.0033725874964147806,
-0.007373589091002941,
0.02517206221818924,
-0.04911011829972267,
-0.04483199119567871,
-0.0058457921259105206,
0.006782690528780222,
-0.03557192161679268,
-0.04553724080324173,
0.03180930018424988,
0.040677592158317566,
-0.025066962465643883,
-0.021830232813954353,
0.014040691778063774,
-0.019959766417741776,
-0.047466155141592026,
0.0009233638411387801,
0.03123023919761181,
-0.033699456602334976,
-0.004927510395646095,
0.04512198641896248,
-0.04171232134103775,
0.08515415340662003,
0.014611351303756237,
-0.017461534589529037,
-0.0006942630279809237,
-0.0022342579904943705,
-0.021491996943950653,
-0.0028005035128444433,
0.05048670992255211,
-0.039581600576639175,
-0.02864920347929001,
0.00855205301195383,
-0.00579163059592247,
0.03495165705680847,
-0.02442065253853798,
-0.0286603681743145,
0.017930611968040466,
-0.01642599143087864,
-0.0010447311215102673,
-0.024158503860235214,
0.030171044170856476,
-0.0068917288444936275,
0.02381623350083828,
-0.01883791573345661,
-0.020408689975738525,
-0.04224065691232681,
-0.046111851930618286,
0.013359271921217442,
0.04193488508462906,
0.023758715018630028,
-0.008559737354516983,
0.038181282579898834,
-0.0032673475798219442,
-0.051766395568847656,
0.01887913979589939,
0.0009801796404644847,
0.04029245674610138,
-0.014383027330040932,
0.0027854552026838064,
0.01378552708774805,
0.035555798560380936,
-0.024584617465734482,
-0.03134036064147949,
-0.012742484919726849,
-0.0059984903782606125,
0.07433508336544037,
-0.022973475977778435,
0.0439816452562809,
0.0021069571375846863,
0.004675884265452623,
-0.04569485783576965,
0.011697454378008842,
0.010822356678545475,
0.027071237564086914,
0.011884386651217937,
0.02894529141485691,
-0.017810795456171036,
0.0469265952706337,
-0.002612709067761898,
0.016921058297157288,
-0.03430381417274475,
0.008843835443258286,
-0.0006760812248103321,
0.01135965995490551,
0.05182897299528122,
-0.0053870901465415955,
-0.04473818838596344,
0.009400337003171444,
-0.010248380713164806,
0.07056082040071487,
-0.03522877022624016,
-0.03871532157063484,
0.05346892029047012,
0.002257320797070861,
-0.0002958520199172199,
-0.021076826378703117,
-0.01349080353975296,
-0.02213716134428978,
-0.017631055787205696,
0.011569510214030743,
0.0016816358547657728,
-0.01798332668840885,
-0.0022402952890843153,
0.020293904468417168,
0.008310450240969658,
0.042898282408714294,
-0.018107978627085686,
-0.037732742726802826,
-0.029821008443832397,
-0.030114393681287766,
-0.0865454152226448,
0.021618330851197243,
0.06601636111736298,
0.00721500301733613,
0.0014244884951040149,
-0.011673437431454659,
0.01870495267212391,
0.005833087023347616,
0.008307051844894886,
-0.002806642558425665,
0.12433717399835587,
-0.029509352520108223,
-0.0034138616174459457,
-0.03410022705793381,
0.004207948222756386,
0.12325345724821091,
0.03336114063858986,
-0.0019516939064487815,
-0.05057484284043312,
0.008757445961236954,
-0.04802735149860382,
0.013279891572892666,
-0.04840672388672829,
0.01975778490304947,
0.00782894715666771,
-0.0037468355149030685,
0.023840438574552536,
0.08073226362466812,
-0.00664186105132103,
-0.013533457182347775,
0.05514026805758476,
-0.012939197942614555,
-0.0007165463757701218,
0.01176314428448677,
0.019284993410110474,
-0.02082296460866928,
-0.013934187591075897,
-0.02554083615541458,
0.010454103350639343,
-0.02049465849995613,
-0.018253283575177193,
0.008860643953084946,
-0.04439157247543335,
0.014811508357524872,
-0.009416625835001469,
-0.08313266187906265,
-0.00443475553765893,
0.020472776144742966,
-0.038189828395843506,
-0.055905237793922424,
0.014760994352400303,
0.018255140632390976,
-0.01958751678466797,
0.029178468510508537,
0.02234611101448536,
0.029247920960187912,
0.02635556273162365,
0.021252967417240143,
0.01812843233346939,
-0.028562992811203003,
-0.018510909751057625,
-0.052498526871204376,
-0.0023240952286869287,
0.005092327948659658,
0.04321582242846489,
0.00684648472815752,
-0.028797833248972893,
0.03594766557216644,
-0.03758767992258072,
0.010880558751523495,
-0.002595077035948634,
0.03486104682087898,
0.000693446141667664,
0.009953939355909824,
-0.02642815373837948,
0.031329408288002014,
0.017084861174225807,
0.005503347143530846,
-0.0017923922277987003,
-0.011326311156153679,
-0.011841250583529472,
-0.016362156718969345,
0.05476923659443855,
-0.05708334967494011,
-0.0700736939907074,
-0.0361504890024662,
0.006769014988094568,
-0.04211210086941719,
0.04881424456834793,
0.02315937727689743,
-0.013704671524465084,
-0.010754144750535488,
0.004681423772126436,
-0.027546178549528122,
-0.008564822375774384,
-0.017060905694961548,
0.003557484829798341,
-0.020946666598320007,
-0.003037908812984824,
-0.019573722034692764,
-0.03316449746489525,
0.07214111089706421,
0.017079869285225868,
-0.04323795810341835,
0.027373056858778,
-0.049339164048433304,
0.03288087248802185,
0.017237653955817223,
-0.03939172253012657,
0.002903569955378771,
0.044432010501623154,
-0.062375809997320175,
-0.004566344898194075,
-0.02915954403579235,
0.06780925393104553,
0.03261341154575348,
0.01874382793903351,
0.009235654026269913,
-0.0041248612105846405,
-0.005218804813921452,
0.0528983473777771,
0.0385904535651207,
-0.04352009668946266,
-0.03839898481965065,
-0.014489040710031986,
-0.04021996632218361,
-0.031060144305229187,
-0.03677087649703026,
-0.07678180932998657,
-0.0010236991802230477,
-0.023889772593975067,
0.0034421030431985855,
-0.06232675909996033,
0.02464142255485058,
-0.015531777404248714,
0.006355027202516794,
-0.024043353274464607,
0.02886464260518551,
-0.020305415615439415,
-0.01156790740787983,
0.028061358258128166,
0.008832130581140518,
0.010449432767927647,
0.04272279888391495,
-0.014612852595746517,
-0.0031263402197510004,
-0.015996340662240982,
0.013458291068673134,
0.03270631656050682,
-0.006968302186578512,
0.017776714637875557,
-0.023439401760697365,
0.03263543173670769,
-0.02746380865573883,
-0.0024522142484784126,
0.04425664246082306,
-0.028467653319239616,
-0.04864989221096039,
0.03949986770749092,
-0.05061612278223038,
0.007643057964742184,
0.006297308020293713,
-0.0328608937561512,
-0.023341448977589607,
0.0459909662604332,
0.006461434066295624,
-0.01824932172894478,
0.006024707108736038,
0.0004508538986556232,
0.00017877919890452176,
-0.029524171724915504,
0.030726687982678413,
-0.049561262130737305,
-0.0074983141385018826,
0.020500948652625084,
0.01168782263994217,
0.016495423391461372,
-0.002526858588680625,
0.00421137735247612,
-0.029747281223535538,
-0.0021628495305776596,
-0.008778969757258892,
-0.020050831139087677,
0.0643940344452858,
0.049126554280519485,
-0.044414326548576355,
0.04812239110469818,
0.030617792159318924,
0.018261251971125603,
-0.07041184604167938,
0.01958719827234745,
0.00009943452459992841,
-0.008207391016185284,
0.04221222922205925,
-0.10743493586778641,
0.009438217617571354,
0.008736899122595787,
-0.08917037397623062,
0.012918083928525448,
-0.0711938887834549,
0.024038009345531464,
-0.03244705870747566,
-0.03276745602488518,
0.05038261041045189,
0.03478623554110527,
0.031816937029361725,
0.032925162464380264,
0.003405446419492364,
-0.0053881085477769375,
-0.039821598678827286,
-0.018107999116182327,
0.019448652863502502,
0.03125574067234993,
0.0017892821924760938,
-0.003705778392031789,
0.07636595517396927,
-0.028979716822504997,
-0.04529937356710434,
0.030622312799096107,
-0.05178409069776535,
0.031236760318279266,
-0.007522284053266048,
0.02443193644285202,
-0.012921636924147606,
0.030207369476556778,
0.0001472853182349354,
-0.018570689484477043,
-0.01219695620238781,
0.0037326961755752563,
0.01791614294052124,
0.03302337974309921,
-0.05425623804330826,
-0.02708517387509346,
0.0031600065995007753,
-0.013977010734379292,
-0.006839233450591564,
0.03173394128680229,
-0.03104938007891178,
0.000786092656198889,
-0.030016092583537102,
0.0063400608487427235,
0.06191403418779373,
-0.011684193275868893,
0.0591801218688488,
0.0020584252197295427,
0.01650165766477585,
0.022746825590729713,
0.0023435954935848713,
-0.048067376017570496,
0.034274399280548096,
0.036468297243118286,
-0.04101362079381943,
-0.027214856818318367,
-0.021394729614257812,
-0.006183493882417679,
-0.04655203968286514,
-0.01768830232322216,
0.011594941839575768,
-0.018755033612251282,
-0.011876893229782581,
-0.013224606402218342,
-0.01960490457713604,
0.008343038149178028,
-0.0038110644090920687,
0.04010317847132683,
0.05682562291622162,
-0.01399462390691042,
0.01702270098030567,
-0.06846940517425537,
0.03513043373823166,
0.02070441283285618,
-0.004913313779979944,
0.006393872667104006,
-0.029421662911772728,
0.01732952520251274,
-0.040487851947546005,
0.06488481163978577,
-0.0660710409283638,
-0.02883043885231018,
-0.017727164551615715,
-0.000016952870282693766,
-0.0005728388205170631,
-0.056926824152469635,
-0.04510173946619034,
-0.029240760952234268,
-0.04444415494799614,
0.01063754502683878,
-0.026777012273669243,
0.013951142318546772,
-0.02576414868235588,
0.011045225895941257,
0.022377008572220802,
0.03476693853735924,
0.0008057638769969344,
-0.0392305813729763,
0.032661307603120804,
0.06325899064540863,
-0.0009384412551298738,
0.06053183600306511,
0.04248756542801857,
-0.007473020348697901,
0.014275732450187206,
-0.023331496864557266,
-0.02456444688141346,
0.05916071683168411,
-0.0417017862200737,
-0.009395018219947815,
-0.0478171706199646,
-0.004013772122561932,
0.0057480898685753345,
-0.021986471489071846,
-0.01422148384153843,
0.03398147225379944,
-0.004560418426990509,
0.0034462343901395798,
0.02118443138897419,
0.009903914295136929,
0.03274475038051605,
-0.02345094084739685,
0.004519786220043898,
0.026914823800325394,
0.00794971827417612,
0.009060624986886978,
0.020848341286182404,
0.017726436257362366,
0.010640281252563,
-0.013584435917437077,
0.038091760128736496,
-0.011873963288962841,
0.03340940549969673,
0.05426838994026184,
0.027023306116461754,
0.021852947771549225,
-0.02980477549135685,
-0.009788368828594685,
-0.01645074225962162,
-0.00440888199955225,
0.03969139605760574,
-0.049454089254140854,
0.06912743300199509,
0.01664705201983452,
0.0016842271434143186,
-0.004145666025578976,
0.011616474948823452,
0.023115234449505806,
-0.026184139773249626,
0.017071597278118134,
0.005847180262207985,
0.02617678977549076,
0.0035836100578308105,
0.025550497695803642,
0.032890673726797104,
0.03386203572154045,
-0.01735960692167282,
-0.007361534051597118,
-0.02574092335999012,
0.02992706000804901,
-0.01177374180406332,
-0.022656401619315147,
-0.01668861135840416,
-0.0040379418060183525,
0.03946487605571747,
0.042081642895936966,
0.02051086537539959,
0.01852639764547348,
0.027512874454259872,
-0.01185580249875784,
0.05907531827688217,
-0.09119823575019836,
-0.004696554038673639,
-0.02509307861328125,
0.040666479617357254,
0.0003490853705443442,
0.0012619392946362495
] |
<p>Trying to determine the speed of a falling body with respect to traveled distance and initial speed. I've been provided with the following equation for acceleration as a function of distance and the grav. parameter(constant) of the attracting body :</p>
<p>$a=GM/r^2$ </p>
<p>Where:</p>
<p>$a$ - acceleration.<br>
$GM$ - gravitational parameter(constant).<br>
$r$ - distance to the attracting body.</p>
<p>I have entered inputs for $GM$ and $r$ and integrated this equation with respect to $r$. This obviously yielded total acceleration per traveled distance, in other words $m^2/s^2$ at the given altitude.</p>
<p>How do I proceed to determine speed at this altitude?</p> | 1,000 | [
-0.009106340818107128,
-0.03177713230252266,
-0.03526077792048454,
0.016990426927804947,
0.008536078035831451,
-0.016264602541923523,
-0.024305207654833794,
-0.04220437631011009,
0.0089234234765172,
0.0033048070035874844,
0.017008231952786446,
0.06326888501644135,
0.07575561851263046,
0.017156733199954033,
0.03985960781574249,
0.0002917052188422531,
-0.06148308143019676,
0.016187168657779694,
0.04188450053334236,
-0.04175334796309471,
0.00281921518035233,
0.000985184102319181,
0.05064743384718895,
-0.038428984582424164,
-0.0011718620080500841,
0.011179548688232899,
0.020170781761407852,
-0.03453085571527481,
0.002755365101620555,
0.03634435683488846,
-0.020468533039093018,
-0.013334929011762142,
0.009462515823543072,
0.026574961841106415,
0.015214110724627972,
0.02180819772183895,
-0.04554913565516472,
-0.009229627437889576,
-0.038767650723457336,
0.041828274726867676,
-0.01079375296831131,
-0.02544550597667694,
-0.004848985001444817,
0.03974685072898865,
-0.0007300954894162714,
0.018183650448918343,
0.03705454617738724,
0.0019094862509518862,
0.027618883177638054,
-0.05923351272940636,
0.07663499563932419,
-0.00864776037633419,
0.039730802178382874,
0.0307175163179636,
0.00627805246040225,
-0.0145519208163023,
0.06619518995285034,
0.0709402859210968,
-0.03106149658560753,
-0.04659496992826462,
-0.002192480256780982,
-0.07102489471435547,
-0.003910268656909466,
-0.019711924716830254,
-0.011965321376919746,
0.04212094098329544,
-0.012472442351281643,
0.019272135570645332,
0.025053752586245537,
-0.015383437275886536,
0.018846753984689713,
0.014581955038011074,
0.003337531117722392,
-0.02412257343530655,
0.01153871975839138,
-0.024164993315935135,
0.021239545196294785,
0.03910116106271744,
0.003963160794228315,
0.033162571489810944,
-0.012553097680211067,
0.03085450828075409,
0.05630546435713768,
0.03159046173095703,
0.009279699996113777,
0.01703585311770439,
0.05240529775619507,
0.023096991702914238,
-0.010799855925142765,
-0.002516802866011858,
-0.036240383982658386,
0.0016445404617115855,
0.0024536841083317995,
-0.0006988217937760055,
-0.0007150855381041765,
0.025278355926275253,
-0.02823406271636486,
0.07944837212562561,
-0.01306131575256586,
-0.04681968688964844,
-0.012252794578671455,
-0.03425631672143936,
0.008692742325365543,
0.07578857988119125,
0.006145985331386328,
-0.0004957946366630495,
-0.026559431105852127,
-0.010663783177733421,
-0.024494819343090057,
-0.021449260413646698,
-0.04548798128962517,
0.021065257489681244,
-0.019161250442266464,
-0.028374172747135162,
0.006150542292743921,
0.004276548977941275,
-0.027461154386401176,
-0.01669728383421898,
0.022886963561177254,
0.02497788891196251,
0.06588242202997208,
-0.012997915968298912,
0.01697821356356144,
0.0010831994004547596,
-0.03281094878911972,
0.016519121825695038,
0.005970474798232317,
-0.0316518172621727,
-0.027872826904058456,
0.02552870474755764,
-0.010167112573981285,
-0.021126387640833855,
0.0004343115142546594,
-0.013601982034742832,
0.045013297349214554,
0.010427325032651424,
-0.09424150735139847,
-0.06735692173242569,
0.01972261443734169,
0.0241833608597517,
0.007862756960093975,
-0.07532700151205063,
0.01591637171804905,
0.0254448801279068,
0.06393775343894958,
0.04233980551362038,
0.008855558931827545,
0.013017935678362846,
0.018428465351462364,
0.014103629626333714,
-0.009456106461584568,
-0.03374830260872841,
-0.0252543892711401,
-0.03567967191338539,
0.004738826770335436,
-0.05030436813831329,
-0.016834715381264687,
0.023366356268525124,
0.000018707787603489123,
-0.02474152483046055,
0.07214175164699554,
-0.019538942724466324,
0.020066389814019203,
0.021348915994167328,
0.012020725756883621,
0.0006961995386518538,
0.06466400623321533,
0.04159272834658623,
-0.030059821903705597,
0.041477400809526443,
0.04933542385697365,
0.06031341105699539,
0.008491197600960732,
-0.015862876549363136,
0.0587056502699852,
-0.013033822178840637,
-0.049977850168943405,
-0.0008677099831402302,
-0.01942051202058792,
0.008950148709118366,
-0.015376990661025047,
-0.07402928918600082,
0.03888404369354248,
-0.02202129177749157,
0.010229961946606636,
0.04311834275722504,
0.019654780626296997,
0.017308153212070465,
-0.0168001689016819,
-0.0022342512384057045,
0.006328920368105173,
-0.07900888472795486,
0.015874577686190605,
-0.00956050492823124,
0.014983046799898148,
0.01572236977517605,
0.0029820988420397043,
0.005134462844580412,
-0.008236424997448921,
-0.01374258566647768,
-0.00784281175583601,
-0.008406146429479122,
-0.010811639949679375,
-0.016739696264266968,
0.00044180318946018815,
0.034854549914598465,
0.029605500400066376,
-0.0017788136610761285,
-0.004071900621056557,
-0.010470482520759106,
0.00737951323390007,
-0.02880559116601944,
-0.013971138745546341,
0.00812677200883627,
-0.027482373639941216,
-0.0045505608431994915,
0.016088131815195084,
0.0038178241811692715,
0.0035304888151586056,
0.042587760835886,
-0.04657508060336113,
0.07519817352294922,
0.07301940023899078,
0.049262430518865585,
0.029707014560699463,
0.01436589565128088,
0.026552891358733177,
0.00184438971336931,
-0.033876314759254456,
-0.016282688826322556,
-0.03972521424293518,
-0.05376899242401123,
0.03588564693927765,
0.004994289483875036,
-0.07002885639667511,
0.013780774548649788,
0.06821724772453308,
0.030977731570601463,
0.03338051959872246,
0.03974998742341995,
-0.005372651387006044,
-0.04602012038230896,
0.020630596205592155,
-0.003962952643632889,
-0.033098407089710236,
-0.005107277538627386,
0.020634468644857407,
0.04251333698630333,
0.0005550152854993939,
-0.0005982931470498443,
-0.01215625274926424,
0.03377954289317131,
0.0021725804544985294,
0.03606830909848213,
-0.002025519497692585,
-0.032883420586586,
0.04667752981185913,
0.0030568677466362715,
0.02925628051161766,
0.06549592316150665,
0.026269255205988884,
0.002240557223558426,
-0.0491076223552227,
-0.009162049740552902,
0.029609056189656258,
0.007930176332592964,
-0.019457940012216568,
0.0011284545762464404,
0.021107017993927002,
-0.016076691448688507,
0.009177681989967823,
-0.025451142340898514,
0.0018802358536049724,
-0.03894767910242081,
0.027983006089925766,
-0.0007434015860781074,
0.05204314738512039,
0.027292538434267044,
-0.009844684042036533,
-0.021315593272447586,
-0.0007939350325614214,
-0.051117561757564545,
-0.006573937367647886,
0.036002267152071,
-0.047320280224084854,
0.008532446809113026,
-0.03356103599071503,
-0.018424082547426224,
0.06253720074892044,
0.016577504575252533,
-0.03744363784790039,
0.006220002193003893,
-0.022587832063436508,
-0.034068867564201355,
-0.015021393075585365,
-0.005560902412980795,
-0.007511813193559647,
-0.061808593571186066,
0.012661539018154144,
0.028502466157078743,
-0.0014486681902781129,
0.0036189870443195105,
0.02132406085729599,
-0.07484203577041626,
-0.037136469036340714,
0.005109648685902357,
0.00489375414326787,
0.014195216819643974,
-0.032462071627378464,
-0.0016777828568592668,
-0.002220866736024618,
-0.01706661656498909,
-0.004107892047613859,
-0.04927227273583412,
-0.043760571628808975,
0.018413323909044266,
-0.0001713726669549942,
0.03549632057547569,
0.011942032724618912,
-0.04478840529918671,
0.06759755313396454,
0.02468620240688324,
-0.008005951531231403,
-0.04632258787751198,
0.000670743640512228,
-0.004256484564393759,
-0.029056860134005547,
-0.0324600487947464,
0.0017138858092948794,
-0.021172288805246353,
-0.01890147291123867,
0.016309430822730064,
0.024818025529384613,
0.05970350652933121,
-0.0004283685702830553,
-0.017607057467103004,
0.007040396332740784,
0.030338848009705544,
0.012386854737997055,
0.04718002304434776,
0.01810036227107048,
-0.002179770264774561,
0.030941853299736977,
-0.04201561212539673,
0.03812374174594879,
-0.005226730834692717,
-0.05067389830946922,
0.032866910099983215,
-0.04174960032105446,
-0.01868290640413761,
0.01278462540358305,
0.029647385701537132,
0.021097000688314438,
0.020733509212732315,
-0.012354030273854733,
0.0279067475348711,
0.057918813079595566,
-0.009485467337071896,
0.011792348697781563,
0.025628482922911644,
0.010530686005949974,
-0.024749940261244774,
-0.04894574359059334,
0.009342570789158344,
-0.04406517744064331,
0.03459277004003525,
0.011243849992752075,
-0.002823692047968507,
0.035248659551143646,
0.0077813975512981415,
0.024095961824059486,
0.013418314047157764,
-0.036064568907022476,
0.0033504508901387453,
-0.08422570675611496,
-0.01572190225124359,
-0.01412578858435154,
0.048964470624923706,
-0.008653308264911175,
0.05295077711343765,
0.050799887627363205,
0.0051072025671601295,
0.043807417154312134,
0.01771770603954792,
-0.10559460520744324,
0.055207718163728714,
-0.06711672246456146,
-0.049472663551568985,
0.015348631888628006,
-0.003707155352458358,
-0.02794826589524746,
-0.053692806512117386,
-0.003866799408569932,
0.01813836582005024,
-0.00003960890899179503,
-0.04448779672384262,
0.008790293708443642,
-0.03755892813205719,
-0.021139075979590416,
-0.030491743236780167,
0.02085447683930397,
0.008807427249848843,
-0.02198597975075245,
0.011851324699819088,
0.05354411527514458,
-0.01744631491601467,
-0.009779831394553185,
-0.04527769610285759,
-0.038186073303222656,
-0.001505696796812117,
0.011202356778085232,
0.04545607790350914,
0.04456581175327301,
-0.02216741070151329,
0.021487241610884666,
0.006570883560925722,
0.03693034127354622,
-0.008073888719081879,
-0.017070835456252098,
-0.05396241694688797,
-0.06654656678438187,
-0.016129346564412117,
-0.011027276515960693,
0.013544229790568352,
-0.006737984251230955,
-0.023782895877957344,
0.03842979669570923,
0.01708557829260826,
0.0033508746419101954,
0.03938465192914009,
0.06072523444890976,
-0.0177447572350502,
0.003626481629908085,
-0.022082410752773285,
-0.027597157284617424,
-0.03274130821228027,
-0.02582447975873947,
0.052440959960222244,
-0.006407732609659433,
-0.028518395498394966,
-0.0019162875832989812,
0.022574417293071747,
0.02699524722993374,
0.014461039565503597,
-0.006440404336899519,
0.019739609211683273,
0.030426932498812675,
0.018084699288010597,
-0.05152405798435211,
-0.025420820340514183,
0.05198000743985176,
0.010521741583943367,
-0.030917132273316383,
-0.0035314965061843395,
-0.06175105273723602,
-0.007242053281515837,
0.03771977126598358,
0.01759318634867668,
-0.023644959554076195,
0.010171376168727875,
-0.04176361858844757,
-0.03312169760465622,
0.012982700951397419,
-0.0008526943274773657,
0.03538096323609352,
-0.003230295842513442,
0.02273508906364441,
0.011433032341301441,
-0.02020232193171978,
-0.0015359019162133336,
0.023702571168541908,
-0.00714285671710968,
-0.005563919898122549,
-0.04624198004603386,
0.010758396238088608,
-0.0014563126023858786,
-0.001135643688030541,
0.003513708943501115,
0.06964713335037231,
0.03697311505675316,
-0.01906953565776348,
-0.0008065104484558105,
-0.024660516530275345,
-0.04838842153549194,
-0.04577481746673584,
-0.02584347315132618,
-0.00546585489064455,
-0.00422596326097846,
0.005121448542922735,
-0.02780795469880104,
-0.036528266966342926,
0.07300075888633728,
-0.009798794984817505,
0.0038898056373000145,
-0.014224540442228317,
-0.04754345118999481,
0.02755044214427471,
0.03458959981799126,
0.011044589802622795,
0.042392753064632416,
0.0021488761994987726,
-0.011955496855080128,
-0.017570236697793007,
0.00019475801673252136,
0.030134005472064018,
-0.011651093140244484,
-0.03538406640291214,
0.0005947810132056475,
0.00020539213437587023,
-0.03674249351024628,
0.05844243988394737,
0.022617073729634285,
0.03896425664424896,
-0.022866597399115562,
-0.02122122421860695,
-0.008915490470826626,
0.04986750707030296,
0.009820923209190369,
0.025070292875170708,
0.04010453820228577,
0.017408769577741623,
-0.026765890419483185,
-0.01627747341990471,
0.0028060488402843475,
-0.023352863267064095,
0.009117675945162773,
0.0168591495603323,
-0.02265268936753273,
0.01657152734696865,
-0.02186989225447178,
-0.03704297915101051,
0.004189592320472002,
-0.05045245960354805,
0.06816986948251724,
-0.02195151150226593,
-0.023526079952716827,
0.04192885756492615,
-0.07537508010864258,
-0.049101173877716064,
0.02632175199687481,
0.025157468393445015,
0.00896143727004528,
-0.07494291663169861,
0.005961674265563488,
0.029127439484000206,
0.07064257562160492,
-0.048007670789957047,
-0.004338572267442942,
0.02436484955251217,
0.011450719088315964,
-0.03572961688041687,
-0.02820047177374363,
0.001155688427388668,
-0.04215491563081741,
-0.0007585977436974645,
-0.020430533215403557,
0.0494130440056324,
0.0025108568370342255,
-0.0013849021634086967,
0.017441842705011368,
0.02816583961248398,
0.04379332438111305,
0.001893996144644916,
0.004831317346543074,
0.013530420139431953,
0.005324602592736483,
0.017827270552515984,
0.020395733416080475,
0.0804799348115921,
-0.03360225260257721,
-0.027644652873277664,
-0.02445908449590206,
-0.04922328144311905,
0.025730744004249573,
0.006380592472851276,
0.00216006045229733,
0.0030295460019260645,
0.015492822043597698,
-0.010343663394451141,
0.0009704754338599741,
0.035858020186424255,
0.01732662506401539,
-0.011716928333044052,
-0.013754760846495628,
0.0015955076087266207,
-0.0038042913656681776,
0.0038776283618062735,
0.03126748278737068,
-0.01734127104282379,
0.03878672793507576,
-0.025522593408823013,
0.08279886841773987,
-0.009515655227005482,
-0.030303146690130234,
0.019214794039726257,
0.009589359164237976,
0.039356984198093414,
-0.018885208293795586,
-0.011030653491616249,
0.06170077621936798,
0.0021687839180231094,
-0.007024130318313837,
0.001604104065336287,
-0.03233577683568001,
-0.024790549650788307,
0.10089586675167084,
-0.04969990253448486,
0.05982687324285507,
0.003643911797553301,
0.045954447239637375,
0.005842387676239014,
-0.03306903690099716,
-0.023127593100070953,
-0.023257095366716385,
0.018078764900565147,
0.025956332683563232,
0.008896371349692345,
-0.012059240601956844,
-0.022112270817160606,
0.018203824758529663,
-0.005425602197647095,
0.004401061218231916,
0.0037654396146535873,
0.026805518195033073,
0.021671297028660774,
0.005498453509062529,
-0.009435039013624191,
0.030249368399381638,
0.0037339285481721163,
0.04695238173007965,
-0.03743031248450279,
-0.021017983555793762,
0.05682004243135452,
0.04726431518793106,
0.016712017357349396,
-0.044053494930267334,
0.013386216945946217,
-0.036411531269550323,
-0.00414609257131815,
0.044335804879665375,
-0.007690191734582186,
-0.0027975516859441996,
0.04117678105831146,
0.020261669531464577,
-0.00014655257109552622,
0.01722692884504795,
-0.018107041716575623,
-0.03984937071800232,
0.011083812452852726,
-0.0499560683965683,
-0.037813346832990646,
0.003929925616830587,
0.015197760425508022,
-0.007369323633611202,
0.0073267146944999695,
0.01655847392976284,
-0.004332347307354212,
0.027229951694607735,
0.0030919464770704508,
-0.023138822987675667,
0.1199178546667099,
-0.021286791190505028,
-0.011175138875842094,
0.0167323537170887,
0.011808618903160095,
0.09439032524824142,
0.059100355952978134,
0.012916733510792255,
-0.0460425540804863,
-0.004894733428955078,
-0.006458467338234186,
0.037648122757673264,
-0.050998661667108536,
0.007057804614305496,
0.004957627970725298,
-0.02663077600300312,
0.03227043151855469,
0.04071231186389923,
-0.029414642602205276,
-0.0345570370554924,
0.06792599707841873,
-0.011627606116235256,
-0.025565197691321373,
-0.02203628234565258,
0.009813016280531883,
-0.016189858317375183,
0.02364935167133808,
0.02029259316623211,
0.024355029687285423,
-0.008825879544019699,
-0.012012436985969543,
-0.03964720666408539,
-0.02538212388753891,
0.011614670045673847,
-0.015401010401546955,
-0.059438835829496384,
0.046703118830919266,
-0.016615236178040504,
0.00021253337035886943,
-0.0341152548789978,
0.022846410050988197,
0.02212844230234623,
-0.0236972663551569,
0.016047924757003784,
0.041891831904649734,
-0.00612996518611908,
0.038978639990091324,
-0.0026098808739334345,
-0.006453321315348148,
-0.03819077089428902,
-0.004347627051174641,
-0.03258359059691429,
0.057022448629140854,
-0.042674824595451355,
0.010641755536198616,
0.0007074082968756557,
0.0005213578115217388,
-0.013955548405647278,
-0.05947182700037956,
0.028068924322724342,
-0.0006525657954625785,
0.016887111589312553,
-0.015352718532085419,
-0.01612919196486473,
-0.03580153360962868,
0.004559068474918604,
0.0058007375337183475,
-0.014723693951964378,
-0.0037124198861420155,
0.007154678925871849,
0.010119739919900894,
-0.022188333794474602,
0.03130428120493889,
-0.007684354670345783,
-0.02381374128162861,
-0.027752142399549484,
-0.014985860325396061,
-0.012839452363550663,
0.00067704584216699,
0.028073903173208237,
0.031324103474617004,
-0.005280739162117243,
0.010311183519661427,
-0.0061019412241876125,
-0.0114030996337533,
-0.0611354298889637,
0.05370378866791725,
-0.0028923593927174807,
-0.012027963064610958,
-0.05344786494970322,
-0.04874036833643913,
0.025796759873628616,
0.018551746383309364,
-0.0046807327307760715,
0.034726209938526154,
-0.008954716846346855,
0.019160214811563492,
0.007448514923453331,
-0.04542842507362366,
0.005055160261690617,
0.008756285533308983,
-0.02628997713327408,
0.047125380486249924,
-0.002302289241924882,
0.024176016449928284,
0.017135046422481537,
0.029579102993011475,
-0.025074878707528114,
0.010021370835602283,
-0.0198996439576149,
0.05779348686337471,
0.011045749299228191,
-0.01940344087779522,
0.017528964206576347,
0.0019846633076667786,
0.002528736600652337,
-0.016028204932808876,
0.0026214488316327333,
-0.0028273274656385183,
-0.026879694312810898,
0.00360271823592484,
0.010583003982901573,
-0.008834452368319035,
0.07903306931257248,
-0.027871649712324142,
-0.010993605479598045,
-0.04184995964169502,
0.05270746350288391,
-0.03694739565253258,
0.00865733902901411,
-0.024373400956392288,
-0.03360702842473984,
-0.031102461740374565,
0.00142965919803828,
-0.03492243215441704,
0.01535242609679699,
-0.002270628698170185,
0.02127346396446228,
0.023844901472330093,
-0.01564362272620201,
0.03536868467926979,
-0.02272949181497097,
0.07410764694213867,
-0.011096276342868805,
-0.0046085468493402,
0.012025744654238224,
-0.0362384058535099,
-0.015122447162866592,
0.03690166771411896,
0.024862738326191902,
0.056699179112911224,
0.008721883408725262,
-0.04143354296684265,
-0.017351549118757248,
0.09064991027116776,
-0.0016584360273554921,
0.013817328959703445,
-0.029479442164301872,
-0.04449104517698288,
-0.026985056698322296,
-0.026901403442025185,
-0.008722110651433468,
-0.02238401025533676,
0.02700481191277504,
0.016356514766812325,
0.00833855476230383,
-0.054362136870622635,
0.05382729321718216,
-0.0030679439660161734,
-0.013987310230731964,
-0.027488643303513527,
0.032899949699640274,
-0.005511390045285225,
0.06186407059431076,
0.038559239357709885,
0.0011763274669647217,
0.014135776087641716,
-0.002072475850582123,
0.019715197384357452,
-0.0972963497042656,
0.032349999994039536,
-0.017118342220783234,
0.020608561113476753,
0.04603246599435806,
-0.06056607887148857,
0.009116105735301971,
0.0482146255671978,
-0.043856874108314514,
0.007792159449309111,
-0.05625701695680618,
-0.0033190171234309673,
-0.003444529604166746,
-0.05473445728421211,
0.03626497462391853,
-0.0005245793727226555,
0.008375989273190498,
0.03804391995072365,
0.014590874314308167,
-0.00673318188637495,
-0.018237948417663574,
-0.043518222868442535,
0.03321896493434906,
0.04282985255122185,
-0.018801432102918625,
-0.02800632081925869,
0.037653300911188126,
-0.003742872504517436,
-0.021337540820240974,
0.03617024049162865,
-0.01998637057840824,
0.03372715786099434,
-0.015379677526652813,
0.029309285804629326,
-0.0036093657836318016,
0.036445483565330505,
0.004109082743525505,
0.011048528365790844,
-0.0445091612637043,
0.005050755105912685,
0.003346079960465431,
0.042462896555662155,
-0.06511931866407394,
-0.014924895018339157,
-0.006190676707774401,
-0.00843544490635395,
-0.07899410277605057,
0.020341530442237854,
-0.05502636730670929,
0.0005066693411208689,
0.018985651433467865,
-0.017598379403352737,
-0.009129027836024761,
-0.05206851288676262,
-0.009021968580782413,
-0.0231168270111084,
0.037971772253513336,
0.037768393754959106,
-0.048378217965364456,
-0.01993139460682869,
0.010664663277566433,
-0.017313042655587196,
-0.003828388871625066,
-0.007076718378812075,
-0.01809406280517578,
-0.013815079815685749,
-0.05105731636285782,
0.005315983202308416,
-0.019526246935129166,
-0.015103516168892384,
-0.0010248181642964482,
-0.036795832216739655,
-0.0016075886087492108,
0.021458271890878677,
0.01016926858574152,
0.00048597727436572313,
-0.0020225264597684145,
0.0019055993761867285,
0.004415714647620916,
-0.06430649012327194,
0.03007400594651699,
0.019867531955242157,
-0.058193501085042953,
-0.03571471571922302,
-0.016997994855046272,
0.00021736466442234814,
-0.0068135797046124935,
0.06153309345245361,
-0.02270938828587532,
-0.00039426147122867405,
0.013480155728757381,
0.006380442995578051,
-0.006242378614842892,
-0.010645521804690361,
0.015923837199807167,
0.00656226696446538,
-0.02059253677725792,
-0.0000037923362015135353,
-0.015376465395092964,
0.014286471530795097,
0.020921768620610237,
-0.011243090033531189,
-0.0010818041628226638,
0.02537987381219864,
0.002965265652164817,
-0.042431946843862534,
0.007544617634266615,
0.0312533937394619,
0.009785834699869156,
0.0607060045003891,
-0.0030736075714230537,
-0.01578254997730255,
0.03008194826543331,
-0.02169260010123253,
-0.028522327542304993,
0.04587753862142563,
-0.0030865133740007877,
-0.047451477497816086,
0.010350135155022144,
-0.010423933155834675,
-0.005211128853261471,
-0.06283657997846603,
-0.01939305290579796,
0.0008336288738064468,
-0.04145808145403862,
-0.02311200089752674,
0.042821742594242096,
0.03414245694875717,
0.04751009866595268,
0.022297274321317673,
0.01808999292552471,
0.01813802681863308,
-0.035808395594358444,
-0.0024701824877411127,
0.02249836176633835,
0.028640231117606163,
0.01705271005630493,
-0.0027888629119843245,
0.07502558827400208,
0.016751540824770927,
0.00463922880589962,
0.023614292964339256,
-0.0051792277954518795,
-0.03624068200588226,
-0.017044980078935623,
-0.011195228435099125,
-0.035653483122587204,
0.025843115523457527,
0.0017130294581875205,
-0.03155169636011124,
0.04853545129299164,
-0.026740683242678642,
-0.0018632084829732776,
-0.0008457349031232297,
-0.022485170513391495,
-0.03524976223707199,
0.030436284840106964,
-0.008394400589168072,
-0.002747558755800128,
-0.0014127274043858051,
-0.016013512387871742,
0.0021806058939546347,
-0.014846191741526127,
0.022925710305571556,
0.022522414103150368,
0.02614143118262291,
0.02343122474849224,
-0.016970986500382423,
-0.006909235380589962,
-0.03915076702833176,
-0.03409690409898758,
-0.028520001098513603,
0.05484391376376152,
0.050641629844903946,
0.010204793885350227,
-0.04104715213179588,
-0.01843860186636448,
-0.019951820373535156,
0.058716628700494766,
-0.10416316986083984,
-0.029071621596813202,
-0.011536440812051296,
0.020370278507471085,
0.003058511996641755,
-0.023838497698307037
] |
<p>I was re-studying university physics last week, I'm now in the chapter about kinematics in 2 dimensions and specifically the one treating projectile motion. In page 86 of his book (Serway - Physics for scientists and engineers) he derives the equation of the range of the projectile motion to be: $$R=\frac{{v_i}^2\sin2\theta_i}{g}$$
But I don't know why he used one of his assumptions</p>
<p><img src="http://i.stack.imgur.com/9O7fi.png" alt="book"></p>
<p>$\color{red}{\bf Question1:}$ Why $v_{xi}=x_{x\rlap\bigcirc B}$? Where $\rlap\bigcirc {\,\sf B}$ is the time when the projectile stops.</p>
<p>$\color{darkorange}{\bf Question2:}$ Why did he use the particle under constant velocity model to derive that formula, whereas here we deal with a projectile under constant acceleration?</p>
<p>Any responses are welcome, I'm disappointed a lot about those matters!</p> | 2,000 | [
-0.014076832681894302,
-0.005536792799830437,
-0.02198868617415428,
-0.018716542050242424,
0.03749464079737663,
0.021887296810746193,
-0.026087133213877678,
0.00920887105166912,
0.011147093959152699,
-0.020379595458507538,
0.018699392676353455,
0.02485497109591961,
0.07290071249008179,
0.024784419685602188,
0.055465586483478546,
-0.003938419744372368,
0.011420000344514847,
-0.03530270978808403,
-0.02316015027463436,
-0.009662644937634468,
0.015757901594042778,
0.0027044585440307856,
-0.006254400592297316,
-0.03148634731769562,
-0.003783609252423048,
0.01156423520296812,
0.02044375240802765,
0.007476459722965956,
-0.0008768305997364223,
0.04675683751702309,
0.0009859723504632711,
0.005053793545812368,
0.008095622062683105,
-0.007376423105597496,
-0.007552771363407373,
0.0014032615581527352,
-0.03617801517248154,
-0.04845762997865677,
0.0021397494710981846,
0.03506888076663017,
-0.05501418188214302,
0.02817479334771633,
0.008904690854251385,
0.06844435632228851,
-0.020657075569033623,
0.043166305869817734,
-0.012735472992062569,
-0.030584020540118217,
0.04128933325409889,
-0.04147770628333092,
0.07542825490236282,
0.0007680663838982582,
0.027867132797837257,
-0.010500216856598854,
0.008465716615319252,
-0.008890469558537006,
0.05360866338014603,
0.05752766877412796,
-0.026826584711670876,
-0.04631426930427551,
-0.008726147934794426,
-0.04119907319545746,
-0.038005974143743515,
0.012365567497909069,
0.0013142367824912071,
0.021662363782525063,
-0.004891754128038883,
-0.03785941004753113,
0.031710755079984665,
-0.005970490165054798,
-0.008860311470925808,
-0.00368753750808537,
-0.01830706186592579,
-0.020592782646417618,
0.030459696426987648,
-0.017551306635141373,
0.03191137686371803,
0.008559935726225376,
-0.002343192230910063,
0.03514261543750763,
-0.05083378776907921,
-0.0030196052975952625,
0.08805309981107712,
0.0515684112906456,
-0.018448518589138985,
-0.006971361115574837,
0.04882892221212387,
0.035152021795511246,
0.0010210622567683458,
0.05317319184541702,
-0.00041081273229792714,
0.06606631726026535,
0.021116727963089943,
0.004819465801119804,
-0.026498589664697647,
0.06220705062150955,
0.014284717850387096,
0.05751661956310272,
0.030537793412804604,
-0.03735385462641716,
-0.008084788918495178,
-0.043803296983242035,
0.01837727800011635,
0.06425748020410538,
0.004996648523956537,
-0.012178490869700909,
-0.00701887346804142,
-0.009871683083474636,
-0.06803401559591293,
-0.03045409917831421,
-0.06443896144628525,
0.03774174302816391,
-0.014434524811804295,
0.04788942635059357,
-0.01842462457716465,
-0.008534243330359459,
0.03429145738482475,
0.010252372361719608,
0.06883479654788971,
0.04188155010342598,
0.027039596810936928,
0.019796598702669144,
0.043571945279836655,
0.0033081311266869307,
-0.051127441227436066,
0.001300271600484848,
0.039577994495630264,
-0.015785494819283485,
-0.044991809874773026,
0.004278413951396942,
0.04133300855755806,
0.011622903868556023,
0.002561398083344102,
0.027786459773778915,
0.045804671943187714,
-0.00322342268191278,
-0.09757247567176819,
-0.07114891707897186,
0.0429619662463665,
0.03895031288266182,
-0.035417553037405014,
-0.07488278299570084,
-0.012381371110677719,
0.04390333965420723,
0.07511813938617706,
-0.021915709599852562,
0.008664574474096298,
-0.019796686246991158,
0.025344830006361008,
-0.03248006850481033,
-0.044860728085041046,
-0.024437230080366135,
0.0019619592931121588,
-0.04510987550020218,
-0.0038238936103880405,
-0.08631724864244461,
0.05401978641748428,
-0.01033844891935587,
0.030200062319636345,
-0.0000727003498468548,
0.06732570379972458,
-0.013887528330087662,
-0.01656700111925602,
0.021345024928450584,
-0.006045602727681398,
0.0003368793404661119,
0.07356373965740204,
0.01690305769443512,
0.004278889391571283,
0.012636852450668812,
-0.0023827555123716593,
0.028854193165898323,
-0.0073674567975103855,
0.00508427107706666,
0.06297534704208374,
-0.04180452600121498,
-0.016568243503570557,
-0.018648415803909302,
-0.030808309093117714,
0.018493041396141052,
-0.027401018887758255,
-0.05577167496085167,
0.01866852678358555,
0.0027801066171377897,
-0.011873365379869938,
0.05591632425785065,
0.002690295223146677,
0.012894900515675545,
-0.009707019664347172,
-0.022519880905747414,
-0.0018307005520910025,
-0.05986475571990013,
0.06065373122692108,
0.039625320583581924,
0.003679809160530567,
0.06442820280790329,
0.0004449289699550718,
-0.03638577461242676,
0.04121575132012367,
0.0009544466156512499,
-0.03572969511151314,
0.03249211609363556,
-0.012125068344175816,
-0.009851736947894096,
0.004496936686336994,
0.05450959876179695,
0.019478505477309227,
0.04512569308280945,
0.015393951907753944,
-0.005301199853420258,
-0.016925709322094917,
-0.00314153335057199,
-0.008040259592235088,
0.05280817672610283,
0.005154908634722233,
0.0022120680660009384,
-0.01026515755802393,
-0.0018952586688101292,
-0.03382905200123787,
0.0331418514251709,
-0.0665319487452507,
0.0625602975487709,
0.06866533309221268,
-0.024079013615846634,
0.004373331554234028,
0.06264383345842361,
0.00880182720720768,
-0.011594696901738644,
0.0365595668554306,
-0.03430506959557533,
-0.023847434669733047,
0.0278360303491354,
0.013239102438092232,
-0.006317593157291412,
-0.003232120769098401,
0.020192278549075127,
0.022249480709433556,
0.021655939519405365,
0.011826126836240292,
0.02838599681854248,
-0.01733776181936264,
-0.0687943771481514,
0.006945087108761072,
0.009254329837858677,
-0.01711752451956272,
0.012296793982386589,
0.011775795370340347,
-0.006722320336848497,
-0.025551946833729744,
-0.019138164818286896,
-0.025440216064453125,
0.00739970663562417,
0.02945587784051895,
0.004551936872303486,
0.023710401728749275,
-0.0017563420115038753,
0.041095051914453506,
0.0031722593121230602,
0.029535993933677673,
0.06252077221870422,
0.027855027467012405,
-0.019374830648303032,
-0.04295061528682709,
-0.0015921380836516619,
0.013497693464159966,
0.012056132778525352,
-0.022601418197155,
-0.046719230711460114,
0.02947358228266239,
-0.052813660353422165,
-0.033995579928159714,
-0.06367935240268707,
-0.03682081028819084,
-0.0304009597748518,
0.00784968864172697,
0.026466578245162964,
0.05297808349132538,
0.007288645952939987,
-0.0020015232730656862,
-0.01509768981486559,
0.017364194616675377,
-0.04812218248844147,
-0.00421774061396718,
0.010132212191820145,
-0.017298264428973198,
0.02844693697988987,
-0.04143218696117401,
-0.02778429538011551,
0.06007067486643791,
-0.0049976324662566185,
0.017456455156207085,
0.022514192387461662,
-0.022789930924773216,
-0.05700363218784332,
-0.02487960271537304,
-0.033292002975940704,
0.0003383547009434551,
-0.047658517956733704,
-0.008626935072243214,
0.06454626470804214,
-0.004498380236327648,
-0.021703321486711502,
0.020740371197462082,
-0.04882040247321129,
-0.021422410383820534,
-0.016595447435975075,
-0.01377876941114664,
0.01554170437157154,
0.009604904800653458,
0.02008546143770218,
0.020094046369194984,
0.008851268328726292,
-0.030043689534068108,
-0.05310807004570961,
-0.028668375685811043,
-0.000967414234764874,
-0.011630408465862274,
0.04539469629526138,
-0.014195038937032223,
-0.019858775660395622,
0.08506615459918976,
0.021609680727124214,
-0.0044197202660143375,
-0.007561557926237583,
-0.01009442936629057,
-0.008792589418590069,
-0.0224983561784029,
-0.006869615986943245,
0.026518145576119423,
-0.028096770867705345,
0.009070192463696003,
-0.041636839509010315,
0.03203882277011871,
0.03997430577874184,
0.019522424787282944,
0.03521634638309479,
0.0013261018320918083,
0.02407902665436268,
-0.0006716155330650508,
0.02364252507686615,
-0.004579275380820036,
-0.035620540380477905,
-0.003087335731834173,
-0.010551797226071358,
0.04477986693382263,
0.028285855427384377,
-0.06877300888299942,
0.01566668227314949,
-0.03158825263381004,
-0.011457633227109909,
0.014719828963279724,
0.02223859168589115,
-0.017432380467653275,
-0.013446524739265442,
-0.0005000288365408778,
0.03446944057941437,
0.03526507690548897,
-0.025959495455026627,
-0.010563267394900322,
-0.016129128634929657,
0.03445573151111603,
-0.04028391093015671,
-0.005018892232328653,
-0.0006857776897959411,
0.03440554812550545,
0.05804848670959473,
-0.040405645966529846,
-0.04130665212869644,
0.02091340534389019,
0.017708787694573402,
0.017406493425369263,
-0.016482269391417503,
-0.04235770180821419,
-0.013434370048344135,
-0.05747879296541214,
0.009313748218119144,
-0.0685948058962822,
0.04116775467991829,
0.030765242874622345,
0.04370930790901184,
-0.0004869314725510776,
0.0088524604216218,
0.02872180938720703,
-0.01936543919146061,
-0.1010177955031395,
0.006526402663439512,
-0.028017213568091393,
-0.04195844382047653,
-0.009182951413094997,
-0.012054040096700191,
0.016325796023011208,
-0.013413709588348866,
-0.0047444552183151245,
-0.0369611456990242,
-0.013333740644156933,
-0.04748734459280968,
0.028625214472413063,
-0.035711620002985,
-0.048201870173215866,
-0.01944347843527794,
0.030785297974944115,
0.011173210106790066,
-0.04991622269153595,
0.027222782373428345,
0.023733539506793022,
-0.04519110545516014,
0.007094813510775566,
-0.01518936362117529,
-0.016051068902015686,
0.017294324934482574,
0.010597153566777706,
-0.028530985116958618,
0.03764069080352783,
0.009632439352571964,
0.010396821424365044,
-0.0034834053367376328,
0.06837153434753418,
0.015675310045480728,
0.006664799526333809,
-0.01967824436724186,
-0.0653425082564354,
0.007585762534290552,
0.021220751106739044,
0.074330173432827,
-0.00024465328897349536,
-0.01843910664319992,
0.018531229346990585,
0.03765159845352173,
0.014022866263985634,
-0.011314386501908302,
0.03564686328172684,
-0.004850372206419706,
0.02859504148364067,
-0.038627032190561295,
0.03230312466621399,
0.007620241027325392,
-0.021408500149846077,
0.0012828772887587547,
-0.01864418387413025,
-0.02269185148179531,
-0.015559692867100239,
0.01345265656709671,
0.005068658851087093,
-0.01366383209824562,
0.016356604173779488,
-0.019492637366056442,
-0.005822817794978619,
0.009225527755916119,
-0.008604318834841251,
0.029470093548297882,
0.02605656161904335,
0.0701974481344223,
0.006380509585142136,
0.007237494457513094,
-0.06030118837952614,
-0.037883657962083817,
0.025791505351662636,
0.013966766186058521,
-0.024472564458847046,
-0.018787551671266556,
-0.028292018920183182,
-0.05709027498960495,
0.04955524578690529,
0.0025566513650119305,
0.04830276966094971,
-0.021869972348213196,
0.008976619690656662,
-0.03343724086880684,
-0.030992211773991585,
-0.04721424728631973,
-0.004688461776822805,
-0.02467854879796505,
0.05597890168428421,
-0.005383175797760487,
-0.01327558420598507,
0.0018539153970777988,
-0.009679993614554405,
0.034322965890169144,
0.030464572831988335,
0.03150085359811783,
0.0033418722450733185,
0.017172634601593018,
-0.0014474816853180528,
-0.04828384146094322,
-0.0648442879319191,
0.01360245794057846,
0.0018576864385977387,
0.01111898198723793,
0.026322156190872192,
-0.01097091380506754,
-0.058668363839387894,
0.02712191268801689,
-0.0029292760882526636,
0.018016884103417397,
-0.0250737052410841,
-0.04174485430121422,
0.03498978912830353,
0.07218911498785019,
-0.05805673450231552,
0.02710796520113945,
0.023036113008856773,
-0.009263346903026104,
-0.028603684157133102,
-0.014576415531337261,
0.009890377521514893,
-0.014433713629841805,
-0.008917370811104774,
-0.0668891966342926,
0.00544284051284194,
-0.025530295446515083,
0.05494357645511627,
0.037822142243385315,
0.019463257864117622,
-0.04545291140675545,
-0.037921421229839325,
0.004599627573043108,
0.002580203115940094,
0.0015756229404360056,
0.01110000628978014,
-0.02184421196579933,
0.037332694977521896,
-0.008929586037993431,
-0.02354590781033039,
0.0199769027531147,
-0.00030507927294820547,
0.016496064141392708,
0.051766619086265564,
0.02459767274558544,
-0.00038509766454808414,
-0.039566975086927414,
-0.023524466902017593,
0.004078637342900038,
-0.07358285039663315,
0.06518196314573288,
-0.004482480231672525,
-0.041574228554964066,
0.02376575954258442,
-0.02968679368495941,
-0.06657207012176514,
-0.0017326120287179947,
-0.000327201938489452,
0.011682084761559963,
-0.051070015877485275,
-0.003364237956702709,
0.013112192042171955,
0.035099126398563385,
-0.07882992923259735,
-0.03911120072007179,
0.038123179227113724,
-0.017852216958999634,
-0.020620690658688545,
0.0015391093911603093,
0.01898263208568096,
-0.01980208232998848,
-0.019669322296977043,
0.016542011871933937,
0.03892148286104202,
-0.001839413191191852,
-0.021705033257603645,
-0.01948513276875019,
0.06096161529421806,
0.03942011669278145,
0.0024910648353397846,
-0.04106828197836876,
0.029520584270358086,
-0.005643964745104313,
0.0032567090820521116,
-0.016012782230973244,
0.07693400233983994,
-0.025024643167853355,
-0.017535775899887085,
0.005069351755082607,
0.004166653845459223,
0.03476407006382942,
-0.003985199145972729,
0.014978347346186638,
0.056677207350730896,
0.014780938625335693,
0.00171405088622123,
0.0016410804819315672,
-0.007505073677748442,
-0.005470238160341978,
0.029006710276007652,
-0.012131474912166595,
-0.012324105016887188,
-0.008718816563487053,
-0.005352594889700413,
0.04257170855998993,
0.008380930870771408,
0.017250817269086838,
0.007952002808451653,
0.035661887377500534,
-0.03477991744875908,
-0.009655877947807312,
0.05772969871759415,
0.025019051507115364,
0.013201767578721046,
0.014592654071748257,
-0.02623745985329151,
0.0613163523375988,
0.019147267565131187,
-0.008008572272956371,
-0.03575872257351875,
-0.04007594659924507,
0.06757830828428268,
0.0644916445016861,
-0.06490009278059006,
0.055689457803964615,
-0.030030876398086548,
-0.0011025737039744854,
-0.009387766942381859,
-0.01497526466846466,
-0.008945535868406296,
-0.05433417484164238,
0.016223119571805,
0.027341220527887344,
-0.039005380123853683,
-0.022785814478993416,
0.011609618552029133,
0.04216901585459709,
-0.016596779227256775,
-0.021755389869213104,
0.02843330428004265,
-0.016609545797109604,
0.01421597134321928,
0.016422610729932785,
-0.030783474445343018,
0.04003415256738663,
0.015986129641532898,
0.02334475889801979,
0.00516161136329174,
0.006178559269756079,
0.020103299990296364,
0.0025129623245447874,
-0.026134483516216278,
-0.06798046082258224,
0.004388498608022928,
-0.04773546755313873,
-0.007934259250760078,
0.014405445195734501,
0.00370257836766541,
0.013675485737621784,
0.001253081951290369,
0.0435759536921978,
0.012039056047797203,
-0.0056029572151601315,
-0.030382895842194557,
-0.043492719531059265,
0.009552798233926296,
-0.03182661160826683,
-0.03580978512763977,
0.04502765089273453,
-0.011154677718877792,
-0.0021484459284693003,
-0.005452826153486967,
-0.017479462549090385,
0.02805701084434986,
0.0008552748477086425,
0.046859875321388245,
-0.020349690690636635,
0.07069525122642517,
-0.011218520812690258,
-0.033128004521131516,
-0.035627614706754684,
-0.01294381357729435,
0.11346692591905594,
0.018130766227841377,
0.009409792721271515,
0.0001899112539831549,
0.017491357401013374,
-0.006631794385612011,
-0.016334017738699913,
-0.01613934151828289,
-0.008854459971189499,
0.004295467399060726,
-0.004515935201197863,
0.01822020672261715,
0.037164971232414246,
-0.025405623018741608,
-0.007792784366756678,
0.027040570974349976,
-0.030156686902046204,
-0.045155879110097885,
-0.04438517242670059,
-0.001032221713103354,
-0.03136318549513817,
0.010656418278813362,
-0.012206529267132282,
0.06073044240474701,
-0.021595485508441925,
0.018624844029545784,
-0.030476564541459084,
-0.03583522513508797,
-0.003966168034821749,
0.006076408084481955,
-0.04834999889135361,
0.018890734761953354,
0.024412207305431366,
-0.016301069408655167,
-0.025757145136594772,
0.0181292537599802,
0.03174981847405434,
0.004239498171955347,
0.02555062063038349,
0.04939195141196251,
0.017215337604284286,
0.008869023993611336,
0.0010304218158125877,
-0.002512686885893345,
-0.04177609086036682,
-0.015045723877847195,
-0.02240544557571411,
0.043813105672597885,
-0.0020278976298868656,
-0.01291261613368988,
-0.007388181518763304,
0.024093255400657654,
-0.017682256177067757,
-0.0692773312330246,
-0.014865261502563953,
0.007872377522289753,
0.0227026529610157,
-0.027174217626452446,
0.04201247915625572,
-0.0037733169738203287,
0.013199396431446075,
0.02227770909667015,
-0.020607665181159973,
0.02032720297574997,
-0.01902671903371811,
0.012271030806005001,
-0.004975400865077972,
0.05922394245862961,
-0.025041209533810616,
-0.010724363848567009,
0.004526194650679827,
0.01597377099096775,
-0.03764624521136284,
-0.021871667355298996,
0.020033355802297592,
0.03806312382221222,
0.028165871277451515,
0.0033036188688129187,
0.006335684563964605,
-0.026604216545820236,
-0.0587705597281456,
0.006157393101602793,
0.014532276429235935,
0.003141652327030897,
-0.04709230735898018,
-0.017257239669561386,
-0.051351845264434814,
0.016985148191452026,
-0.030017713084816933,
0.0008011351455934346,
-0.021080071106553078,
0.060559362173080444,
0.027516482397913933,
-0.025744741782546043,
-0.0575917549431324,
0.002410594606772065,
-0.035351723432540894,
0.037973109632730484,
-0.014825026504695415,
0.010033968836069107,
0.034737709909677505,
0.03127475082874298,
0.006091624032706022,
0.020299620926380157,
0.010938762687146664,
-0.006661157589405775,
0.03534708172082901,
-0.048942264169454575,
0.018638523295521736,
0.04120807722210884,
0.03002486377954483,
-0.03230132907629013,
-0.005358763039112091,
-0.004386545158922672,
-0.01637548767030239,
0.002625359920784831,
-0.022198036313056946,
-0.012616705149412155,
0.014703279361128807,
-0.06702759861946106,
-0.0017305935034528375,
-0.02087070420384407,
0.005361570511013269,
0.01860852725803852,
0.022446593269705772,
-0.01678350381553173,
-0.016364431008696556,
-0.019829289987683296,
0.030554523691534996,
-0.0503411628305912,
-0.01851450279355049,
-0.0037569336127489805,
-0.008110820315778255,
-0.020089613273739815,
-0.033021531999111176,
-0.010114561766386032,
0.005118107423186302,
0.0501299649477005,
-0.020769471302628517,
-0.016965948045253754,
0.02294338122010231,
0.00803006999194622,
-0.05501275509595871,
0.029476726427674294,
-0.01595078967511654,
0.01467564981430769,
-0.006577174179255962,
-0.027962632477283478,
0.022398969158530235,
0.0654941201210022,
-0.01712077483534813,
0.0010870612459257245,
-0.006975067313760519,
-0.02583989128470421,
0.016028089448809624,
-0.02558138780295849,
-0.010062148794531822,
-0.02423800900578499,
0.012267880141735077,
0.04825684055685997,
0.013527139090001583,
-0.036397162824869156,
0.004887144081294537,
-0.0016305801691487432,
-0.044979143887758255,
0.013545310124754906,
0.01737901382148266,
0.011840499006211758,
0.019710754975676537,
0.03805387392640114,
0.005889865104109049,
0.018426405265927315,
0.002705521881580353,
-0.0043727802112698555,
-0.08179690688848495,
0.008799560368061066,
0.01437450759112835,
0.007282203994691372,
0.0219403263181448,
-0.05965482443571091,
-0.03482446447014809,
0.020801395177841187,
-0.08883819729089737,
-0.016584105789661407,
-0.023955071344971657,
-0.02838892862200737,
-0.024507099762558937,
-0.05805036053061485,
-0.009187939576804638,
0.0036033925134688616,
0.032632291316986084,
0.02393653802573681,
0.012144714593887329,
-0.006205896846950054,
0.0044929333962500095,
-0.09522217512130737,
0.012794551439583302,
0.03658846765756607,
-0.011110024526715279,
0.01721695438027382,
0.059533167630434036,
-0.011441895738244057,
0.022369731217622757,
0.010363672859966755,
-0.0052462113089859486,
0.03577044606208801,
-0.012879721820354462,
0.031836606562137604,
0.005092444363981485,
0.02555682323873043,
0.056323692202568054,
0.0001631528721190989,
0.0031676602084189653,
-0.014895166270434856,
-0.005519106052815914,
0.00242162449285388,
-0.011732126586139202,
-0.010272577404975891,
-0.008447105996310711,
-0.027798011898994446,
-0.035507116466760635,
0.03326128423213959,
-0.009025788865983486,
-0.029036764055490494,
0.03931460529565811,
0.010876527056097984,
-0.008198951371014118,
-0.02552228607237339,
-0.005254657007753849,
-0.04440941661596298,
-0.016189463436603546,
0.01607051119208336,
-0.0006583218346349895,
0.01011944841593504,
0.019386274740099907,
-0.012274115346372128,
-0.032575152814388275,
0.015848325565457344,
0.0093282675370574,
-0.018256202340126038,
-0.04475531354546547,
-0.019228225573897362,
0.001126328599639237,
0.00926707498729229,
-0.01691513881087303,
-0.016468115150928497,
-0.04243776202201843,
0.010857737623155117,
-0.0009041705634444952,
0.01622709445655346,
0.003644787473604083,
-0.00803151074796915,
-0.02520572766661644,
-0.08962173014879227,
0.06969695538282394,
0.033928968012332916,
-0.017265914008021355,
-0.01564783975481987,
-0.03872457891702652,
0.013029377907514572,
0.01773936115205288,
0.06065426394343376,
0.002738442737609148,
-0.010926775634288788,
0.027117859572172165,
0.006682229228317738,
0.014584705233573914,
-0.07430824637413025,
0.0034054797142744064,
-0.00259829661808908,
0.0036840313114225864,
-0.004315689671784639,
0.016546322032809258,
-0.04305301234126091,
0.010420311242341995,
0.002874223981052637,
0.03257031738758087,
0.027312375605106354,
0.014908522367477417,
-0.010445411317050457,
0.03481446951627731,
0.010327431373298168,
0.0147679653018713,
0.07337896525859833,
0.02718021161854267,
0.0018919759895652533,
0.021553151309490204,
-0.021783992648124695,
-0.043970994651317596,
0.0484514981508255,
-0.026291636750102043,
-0.03592551499605179,
0.011755941435694695,
-0.02503308840095997,
0.010087690316140652,
-0.06834525614976883,
-0.0006817731191404164,
0.05074030160903931,
0.004375067073851824,
-0.03302541375160217,
0.031049279496073723,
0.011343232356011868,
0.03839704766869545,
-0.017323780804872513,
0.0349995493888855,
0.05760658532381058,
-0.015582590363919735,
-0.006140807177871466,
0.02840345911681652,
0.04839670658111572,
0.01632482372224331,
0.004704086109995842,
0.03863478824496269,
-0.016182556748390198,
0.038573816418647766,
0.018891075626015663,
0.04034716263413429,
-0.02225608006119728,
-0.015477554872632027,
-0.01697593741118908,
-0.033490054309368134,
-0.03287149965763092,
0.03550644591450691,
-0.02041877619922161,
0.07680481672286987,
-0.005266254767775536,
0.028864415362477303,
-0.018223559483885765,
0.007128523197025061,
-0.035748355090618134,
0.01041241642087698,
0.035339269787073135,
0.014880959875881672,
0.02830267883837223,
-0.025414690375328064,
-0.012693986296653748,
0.009891140274703503,
0.021747535094618797,
0.02060556970536709,
0.006563977804034948,
0.0663268119096756,
0.022998934611678123,
-0.008050083182752132,
-0.022701747715473175,
0.008387458510696888,
-0.0032061683014035225,
0.06722667813301086,
0.03413083776831627,
0.01737860217690468,
-0.010017499327659607,
0.022626526653766632,
0.007845568470656872,
0.019986197352409363,
-0.07058603316545486,
-0.04552602767944336,
-0.0068968795239925385,
0.0052223242819309235,
-0.025215834379196167,
0.011133559048175812
] |
<p>I can't understand the concept of the curl of an electromagnetic wave. </p>
<p>$$
\nabla \times E = -\frac{\partial \textbf{B}}{\partial t}
$$</p>
<p>All of the examples I find show a current through a conductor, or that paddle wheel in water which I fail to see the distinction of that with an E-M wave. What I am trying to understand is the curl of say a laser beam light. </p>
<p>So lets say I have this sin wave which I plot in MATLAB which represents a section of a laser beam propagating through free space (We shall say it is the net product of $E_x$ and $E_y$):</p>
<p><img src="http://i.stack.imgur.com/yMbjt.png" alt="laser radiation"></p>
<p>How do you take the curl of it?
Where do you take the curl of it. eg the whole beam, a certain section? Can I do this in MATLAB to see visualization of the concept of curl?</p>
<p>I mainly seek descriptive or pictorial answers.</p>
<p>Thank you for your time.</p> | 2,001 | [
-0.01985403150320053,
0.024236081168055534,
0.00028719211695715785,
-0.048266466706991196,
0.05872587487101555,
0.04228539019823074,
-0.04789377748966217,
0.004548963159322739,
0.01004205271601677,
-0.04374358430504799,
0.05992395058274269,
0.06540791690349579,
0.03803340718150139,
0.03280215337872505,
0.04385386407375336,
0.010705346241593361,
-0.009822096675634384,
-0.004505786579102278,
0.0033446243032813072,
-0.008200226351618767,
-0.0025008507072925568,
-0.004702902864664793,
-0.033091261982917786,
0.013910461217164993,
-0.025589754804968834,
0.03584945574402809,
0.02413042075932026,
-0.010910307988524437,
0.0324716791510582,
0.05710588023066521,
0.0022042037453502417,
-0.04119408503174782,
-0.010792949236929417,
-0.0020656983833760023,
0.009162177331745625,
-0.007703487295657396,
-0.03045315109193325,
-0.01465588342398405,
0.003719270695000887,
0.016276106238365173,
-0.012642391957342625,
-0.021637722849845886,
-0.00527010764926672,
0.05093991756439209,
-0.056419119238853455,
-0.0005789562128484249,
0.0000952727350522764,
-0.01704922877252102,
0.05222902074456215,
-0.05495792627334595,
0.07896891981363297,
-0.019667096436023712,
0.041329436004161835,
-0.014810995198786259,
-0.020463041961193085,
0.018639104440808296,
0.07755889743566513,
0.03739095479249954,
0.0010876915184780955,
-0.044205762445926666,
0.020395545288920403,
-0.025713298469781876,
-0.03636825084686279,
-0.03643765673041344,
-0.02319466695189476,
0.027240274474024773,
-0.012141311541199684,
-0.002878054277971387,
0.03321600705385208,
0.017230242490768433,
-0.038609497249126434,
-0.0007614235510118306,
0.008253597654402256,
-0.045512016862630844,
0.002499563153833151,
-0.04804946482181549,
0.01604115217924118,
0.04234825074672699,
0.03877905383706093,
0.017288928851485252,
-0.017394572496414185,
0.005193759221583605,
0.011936348862946033,
0.0550585575401783,
0.009696566499769688,
-0.024685826152563095,
0.07072696089744568,
0.0033581405878067017,
0.045004624873399734,
0.003043417353183031,
-0.0107189966365695,
0.04610617831349373,
-0.0021484848111867905,
0.022169698029756546,
-0.014593926258385181,
0.04058615863323212,
0.002173496875911951,
0.026830395683646202,
0.03765714913606644,
-0.045512259006500244,
0.028441540896892548,
-0.013912664726376534,
0.021505165845155716,
0.06141513213515282,
0.00729937432333827,
0.006205894518643618,
-0.016927368938922882,
0.00697469525039196,
-0.0299718976020813,
-0.04240923374891281,
-0.029759058728814125,
0.04425583407282829,
0.006293208803981543,
0.014974551275372505,
0.014191157184541225,
-0.05685381963849068,
0.006961992476135492,
-0.012927509844303131,
0.0505627766251564,
0.08387187868356705,
0.024553176015615463,
-0.0663493275642395,
0.029805418103933334,
0.013885213062167168,
-0.11284475028514862,
0.006091912742704153,
0.0330977626144886,
0.018850205466151237,
-0.036347825080156326,
0.02183650992810726,
-0.0029957990627735853,
-0.00536197517067194,
0.044090449810028076,
-0.011279813945293427,
0.019205590710043907,
-0.049837708473205566,
-0.09743095934391022,
-0.053048282861709595,
0.01486868504434824,
0.009419431909918785,
-0.02760903537273407,
-0.08460720628499985,
0.002128953579813242,
0.028886893764138222,
0.09270225465297699,
0.015733197331428528,
0.03082137368619442,
-0.008298899047076702,
0.057881034910678864,
-0.01091382559388876,
-0.014951284043490887,
0.015239463187754154,
-0.006292941514402628,
-0.021124906837940216,
0.001467005000449717,
-0.04731518775224686,
-0.021762391552329063,
0.04566953331232071,
-0.023174993693828583,
-0.008981361985206604,
0.04186690226197243,
-0.00726289302110672,
0.023676428943872452,
0.0301741324365139,
-0.038338638842105865,
-0.021955784410238266,
0.10610992461442947,
0.021213991567492485,
-0.0013576067285612226,
0.03756442666053772,
-0.014821457676589489,
-0.030175158753991127,
-0.029735296964645386,
0.018406586721539497,
0.042742565274238586,
-0.03401124104857445,
0.0031257530208677053,
-0.0068418001756072044,
0.01819504052400589,
0.02796315960586071,
-0.032110217958688736,
-0.04654846712946892,
-0.003839308163151145,
0.011863753199577332,
0.005015370436012745,
0.054868392646312714,
0.024285253137350082,
-0.0065158368088305,
0.04201514646410942,
-0.04895356297492981,
-0.015572408214211464,
-0.04632202163338661,
0.04502396658062935,
-0.0016266829334199429,
-0.051028426736593246,
0.0032260206062346697,
-0.014155696146190166,
0.009718666784465313,
-0.013726074248552322,
-0.034103065729141235,
0.0024278198834508657,
0.038033414632081985,
0.007104179356247187,
-0.02448059804737568,
0.016789637506008148,
0.025082021951675415,
0.012801463715732098,
0.017656004056334496,
0.007240183185786009,
-0.03290487080812454,
-0.01541055552661419,
-0.01599407196044922,
-0.04971476271748543,
0.03420596942305565,
0.03958703204989433,
-0.032134003937244415,
-0.03373897075653076,
-0.0029505810234695673,
-0.019158607348799706,
0.004001188091933727,
-0.018492653965950012,
0.039932191371917725,
0.07888448238372803,
0.02636638842523098,
0.015329089015722275,
0.023850053548812866,
0.01885414309799671,
0.016667941585183144,
-0.0064621418714523315,
-0.026332471519708633,
-0.01938837394118309,
0.008562318980693817,
0.037692587822675705,
0.022421114146709442,
-0.06238320469856262,
0.00503247557207942,
0.019026167690753937,
0.039224427193403244,
0.05117153003811836,
0.05170300975441933,
-0.052414000034332275,
-0.04383544623851776,
-0.013503311201930046,
0.052480220794677734,
-0.009366787038743496,
0.006536714732646942,
0.015182734467089176,
0.029948219656944275,
0.054728828370571136,
0.0068193054758012295,
-0.04039502516388893,
0.03423962742090225,
-0.0616445317864418,
-0.0009173983125947416,
0.012057662010192871,
0.004237757530063391,
0.06449876725673676,
-0.01784670166671276,
-0.02376534603536129,
0.0020942327100783587,
-0.02401532046496868,
0.011044028215110302,
0.006016598083078861,
-0.015850866213440895,
0.016711877658963203,
-0.0035956762731075287,
-0.020157894119620323,
-0.04164428263902664,
0.010079880245029926,
-0.02215704508125782,
0.025823861360549927,
-0.005435602273792028,
-0.007360533345490694,
-0.04400816932320595,
0.008985163643956184,
0.025842193514108658,
0.02282809279859066,
0.021711407229304314,
-0.04202735796570778,
-0.07766775041818619,
0.01408277079463005,
-0.00938156433403492,
-0.006446373648941517,
-0.023380141705274582,
-0.06763239204883575,
-0.00008709052781341597,
-0.026642749086022377,
-0.013368776068091393,
0.05830787867307663,
0.014172974042594433,
-0.02668430283665657,
0.008568819612264633,
-0.0200286153703928,
-0.053296491503715515,
-0.05159958079457283,
-0.022108260542154312,
0.016382470726966858,
-0.007805860601365566,
0.003599815769121051,
0.022297756746411324,
-0.011053787544369698,
-0.018224485218524933,
0.02016049437224865,
-0.04294198751449585,
-0.028653591871261597,
-0.01329423300921917,
-0.028500553220510483,
0.00825263001024723,
-0.004928558599203825,
0.009504393674433231,
0.0008272284176200628,
-0.0558343380689621,
-0.00594464223831892,
-0.06101950258016586,
-0.030817264690995216,
0.02685847319662571,
0.008867491967976093,
0.00986134447157383,
0.01888602413237095,
-0.048426609486341476,
0.07336059957742691,
0.031184010207653046,
-0.03784614056348801,
-0.02733485773205757,
0.0028383152093738317,
-0.009163538925349712,
-0.012784566730260849,
-0.008936533704400063,
0.031474970281124115,
-0.028609609231352806,
0.04116707295179367,
-0.018722418695688248,
0.029831474646925926,
0.044955842196941376,
0.026132382452487946,
0.0007882601348683238,
-0.003693077014759183,
-0.02801641821861267,
0.028250500559806824,
0.05563521012663841,
0.038981843739748,
-0.008155550807714462,
0.04989732429385185,
-0.003289654618129134,
0.02471037022769451,
0.023036181926727295,
-0.024919552728533745,
0.025336449965834618,
-0.025222469121217728,
0.0007715511601418257,
-0.04982680454850197,
0.019724387675523758,
-0.020468082278966904,
0.014230371452867985,
0.007990826852619648,
0.03362422436475754,
0.011956892907619476,
0.0025511300191283226,
0.007123191375285387,
0.028165321797132492,
0.002863192930817604,
-0.014471066184341908,
-0.010889433324337006,
-0.025702396407723427,
-0.002111070789396763,
0.04005658999085426,
-0.034294627606868744,
0.003934272099286318,
0.040983397513628006,
0.026121890172362328,
0.0049558160826563835,
-0.03149785101413727,
-0.006890912540256977,
0.015134288929402828,
-0.032338496297597885,
-0.046275217086076736,
0.011604546569287777,
0.0510847233235836,
0.013587411493062973,
0.062175169587135315,
0.014975335448980331,
0.04406921938061714,
0.04199576377868652,
-0.013893497176468372,
-0.08222141861915588,
0.01793992519378662,
-0.032379262149333954,
-0.0015077011194080114,
-0.022784434258937836,
0.008131557144224644,
0.009842422790825367,
-0.03114369697868824,
-0.008965257555246353,
0.00305826379917562,
-0.012088301591575146,
-0.05173741281032562,
0.009375401772558689,
0.0022988116834312677,
-0.012560209259390831,
-0.030909622088074684,
0.018323145806789398,
0.016301756724715233,
-0.031305357813835144,
-0.0005986896576359868,
0.028129413723945618,
-0.03482314571738243,
-0.014635779894888401,
0.0029831749852746725,
-0.003055437235161662,
0.0314323753118515,
0.01968533918261528,
0.03708256408572197,
0.020703541114926338,
-0.04283268004655838,
0.033691223710775375,
0.0064291818998754025,
0.06626719981431961,
0.023422276601195335,
-0.005570912268012762,
-0.022250892594456673,
-0.0560709685087204,
0.005217442754656076,
-0.035907793790102005,
0.06864288449287415,
0.006836254149675369,
0.0007283786544576287,
0.03708568215370178,
-0.002398513723164797,
-0.011215515434741974,
0.01030550617724657,
0.017835749313235283,
0.02640005387365818,
0.010456347838044167,
-0.05027873441576958,
0.011388682760298252,
-0.035547103732824326,
-0.0031678960658609867,
0.03618782386183739,
0.0026969793252646923,
-0.014689099043607712,
-0.003422941081225872,
0.07709431648254395,
0.005243869498372078,
0.03862018510699272,
0.02812626212835312,
0.0270067248493433,
0.007810951676219702,
0.013384722173213959,
-0.02903391234576702,
0.015860214829444885,
0.06664358824491501,
0.04920683801174164,
-0.016927888616919518,
-0.03693234547972679,
-0.08030848950147629,
-0.02419557236135006,
0.02648039348423481,
0.020921558141708374,
-0.02262064814567566,
-0.018604496493935585,
-0.011292479932308197,
-0.057382915169000626,
0.030880603939294815,
-0.033970508724451065,
0.03571760654449463,
-0.0442507229745388,
0.02394350804388523,
-0.03132433071732521,
-0.00034374769893474877,
-0.0045829350128769875,
0.028593480587005615,
-0.024059530347585678,
0.0038201012648642063,
-0.05376430228352547,
-0.02298540621995926,
0.019962074235081673,
0.011256293393671513,
0.01717124693095684,
0.05019541457295418,
-0.0015452837105840445,
-0.05342120677232742,
0.013904308900237083,
0.008219779469072819,
-0.019952328875660896,
-0.04915611073374748,
-0.0035057507921010256,
0.026942003518342972,
-0.033065345138311386,
0.0847558081150055,
-0.006095311604440212,
-0.031110605224967003,
0.04125913977622986,
0.04001728072762489,
0.028842443600296974,
0.01996399275958538,
-0.01883731223642826,
0.02883366122841835,
0.002209089696407318,
-0.008438214659690857,
0.01637229323387146,
0.05084032192826271,
-0.008636965416371822,
-0.028500180691480637,
0.0008902681292966008,
0.06640131026506424,
-0.023120248690247536,
-0.02928115427494049,
-0.023199280723929405,
0.009618308395147324,
-0.016852451488375664,
0.05817311629652977,
-0.04401937127113342,
-0.019974298775196075,
-0.02362949028611183,
-0.033649224787950516,
-0.005050099454820156,
0.031647246330976486,
-0.011952218599617481,
-0.03345896676182747,
0.0036014693323522806,
0.045060425996780396,
-0.0070775882340967655,
-0.01730208843946457,
0.0014685108326375484,
-0.006095638498663902,
0.019824951887130737,
0.02466999739408493,
-0.011955833062529564,
-0.0014732840936630964,
-0.02576597034931183,
-0.004674582742154598,
0.01715148240327835,
-0.04576203227043152,
0.033441148698329926,
-0.016807876527309418,
0.009688272140920162,
0.006963806692510843,
-0.06787918508052826,
-0.008432507514953613,
0.003826525527983904,
0.005701478570699692,
0.04760468751192093,
-0.039439231157302856,
0.001612053019925952,
0.036187052726745605,
-0.007533850613981485,
-0.03293024003505707,
-0.09089530259370804,
-0.003926095552742481,
-0.005397800821810961,
-0.005309250671416521,
-0.015347564592957497,
-0.005001107230782509,
-0.03512800484895706,
-0.03014804795384407,
0.01691761054098606,
0.029852818697690964,
-0.0401003360748291,
-0.001315634697675705,
0.011800924316048622,
-0.00820425059646368,
0.05081012472510338,
0.01281591784209013,
-0.027227135375142097,
0.029206737875938416,
-0.009782915003597736,
-0.02276799827814102,
0.015752553939819336,
0.017810547724366188,
-0.002455705078318715,
-0.019083241000771523,
-0.016105743125081062,
0.039282433688640594,
0.05693327635526657,
0.012294653803110123,
-0.018788570538163185,
0.010187254287302494,
0.01214037835597992,
-0.009307065047323704,
-0.009214798919856548,
-0.0014151491923257709,
0.002158750081434846,
0.02098827250301838,
-0.04139675572514534,
-0.04910839721560478,
-0.038017310202121735,
-0.07163915038108826,
0.014067936688661575,
0.026419755071401596,
0.017599547281861305,
0.010954856872558594,
0.03729119524359703,
-0.01497604325413704,
-0.001992658246308565,
0.0028322641737759113,
0.01769106090068817,
-0.0032544774003326893,
0.019536521285772324,
0.03740685433149338,
0.019358279183506966,
0.014894162304699421,
-0.0055586351081728935,
-0.015214210376143456,
-0.038590531796216965,
0.0060776653699576855,
0.09580815583467484,
-0.021149497479200363,
0.05600939318537712,
0.029832646250724792,
0.010310839861631393,
0.009031850844621658,
-0.00626152940094471,
-0.0018174860160797834,
0.01894480735063553,
-0.01529636513441801,
0.026728525757789612,
-0.01133215706795454,
-0.020175324752926826,
0.02429836243391037,
0.04798117280006409,
-0.03603840246796608,
0.023628339171409607,
0.014903947710990906,
0.02606218121945858,
0.003168954513967037,
0.023400837555527687,
-0.04259196296334267,
0.0324462428689003,
-0.016933569684624672,
0.05708765983581543,
0.0013413750566542149,
-0.014392407611012459,
0.03560157120227814,
0.011226966045796871,
0.010114304721355438,
-0.045261360704898834,
0.006139553617686033,
-0.021597038954496384,
0.00124534429050982,
0.009552317671477795,
-0.008806589059531689,
-0.000310264527797699,
0.01765991747379303,
0.041419290006160736,
-0.003216426819562912,
0.05102664232254028,
0.01979506015777588,
-0.04083964228630066,
-0.012037994340062141,
-0.048968639224767685,
-0.032237134873867035,
0.07169878482818604,
0.015874642878770828,
0.002657011616975069,
0.007380264811217785,
-0.0293843112885952,
0.00220381747931242,
0.03172440081834793,
0.01879790984094143,
0.01384164672344923,
0.05189204588532448,
-0.016339581459760666,
-0.001230247551575303,
0.012061035260558128,
-0.006189664360135794,
0.11963190138339996,
0.02387336455285549,
0.03014117293059826,
-0.06753052771091461,
0.014546114951372147,
-0.016755852848291397,
-0.008973052725195885,
-0.05622943490743637,
0.00303261773660779,
-0.040136631578207016,
0.01459241658449173,
0.03802350535988808,
0.02200947143137455,
0.02132064290344715,
0.007991974242031574,
0.023275131359696388,
-0.04746443033218384,
-0.035946931689977646,
0.03244839608669281,
0.024955643340945244,
-0.024531690403819084,
0.02658218890428543,
-0.0907752513885498,
0.030955880880355835,
-0.024799806997179985,
-0.007121473550796509,
-0.04091987386345863,
-0.025853322818875313,
0.038876984268426895,
-0.01937207765877247,
-0.04748539254069328,
-0.03164364770054817,
-0.006456026807427406,
-0.032880328595638275,
-0.03430916741490364,
0.009745978750288486,
0.04459453001618385,
0.0027594114653766155,
0.008234167471528053,
0.001355092623271048,
0.013257576152682304,
-0.012279078364372253,
0.0031804218888282776,
0.004542343784123659,
-0.03401761129498482,
0.0029098642989993095,
-0.04413653537631035,
0.05017087236046791,
0.006823164410889149,
0.011446066200733185,
-0.017480775713920593,
0.055651359260082245,
0.02978454902768135,
-0.06482628732919693,
-0.006334247533231974,
-0.003584229154512286,
0.036492813378572464,
-0.023404035717248917,
-0.023831816390156746,
-0.005215732846409082,
0.014498919248580933,
0.003460096661001444,
0.006044374778866768,
0.008127550594508648,
-0.01780347153544426,
0.019545597955584526,
-0.02726566791534424,
0.026575615629553795,
-0.005232023075222969,
-0.059139639139175415,
-0.0252875704318285,
-0.008180055767297745,
-0.010717692784965038,
-0.008686622604727745,
0.03246970847249031,
0.018331071361899376,
-0.01321748923510313,
0.0005993844824843109,
-0.040479809045791626,
0.00002355191645619925,
-0.07022175192832947,
0.029607422649860382,
-0.011093059554696083,
-0.026628607884049416,
-0.01921505108475685,
0.021966688334941864,
0.05491139739751816,
0.03133758530020714,
0.004491807892918587,
0.0023017795756459236,
0.016902286559343338,
0.008391137234866619,
0.04054448381066322,
-0.036193396896123886,
-0.044355425983667374,
0.006054648198187351,
0.027342932298779488,
-0.0015827716561034322,
0.014734315685927868,
0.010051143355667591,
0.04086558520793915,
0.032682113349437714,
-0.020961875095963478,
0.03868042677640915,
-0.032496191561222076,
-0.04422072321176529,
0.020318936556577682,
-0.013514332473278046,
-0.001856707502156496,
-0.010547218844294548,
-0.02168983779847622,
-0.06252644211053848,
0.01871950551867485,
0.004073446616530418,
-0.015063611790537834,
0.015441006049513817,
0.005235531833022833,
0.024154087528586388,
0.004217742010951042,
-0.008833745494484901,
-0.0006823260919190943,
-0.05849389359354973,
-0.017764246091246605,
-0.050127509981393814,
0.014172403141856194,
-0.014385557733476162,
-0.008563910610973835,
-0.05775657668709755,
0.02332981489598751,
-0.03480004146695137,
-0.013098452240228653,
0.012914792634546757,
0.049949344247579575,
0.014867382124066353,
0.009481692686676979,
0.032879993319511414,
-0.02455100603401661,
0.0359739251434803,
-0.018242042511701584,
-0.012005784548819065,
0.06506415456533432,
-0.038341812789440155,
-0.0006625580717809498,
0.005664377938956022,
-0.019439073279500008,
0.0027354713529348373,
0.031609222292900085,
-0.00730358250439167,
-0.005668194964528084,
0.013497449457645416,
0.03406834974884987,
0.0073698158375918865,
-0.019232772290706635,
-0.02309892326593399,
0.004983145743608475,
-0.017801953479647636,
0.02441992238163948,
-0.015784109011292458,
0.004636553581804037,
0.04583510383963585,
0.02667873166501522,
0.0006735867355018854,
-0.002265063812956214,
0.02599336765706539,
-0.027590421959757805,
0.0020429673604667187,
0.040629804134368896,
-0.010665252804756165,
0.05373776704072952,
0.06928874552249908,
-0.005357655696570873,
0.025739656761288643,
0.004163532983511686,
0.011024164967238903,
-0.0986693948507309,
-0.005388649646192789,
-0.0014390485594049096,
-0.0005297273746691644,
0.0331999771296978,
-0.05853171646595001,
0.017544200643897057,
0.027098072692751884,
-0.08526323735713959,
-0.0119753647595644,
-0.029684938490390778,
-0.0028173262253403664,
-0.043339602649211884,
-0.0039228457026183605,
-0.014734748750925064,
0.046382855623960495,
0.030471518635749817,
0.05440934747457504,
0.059060268104076385,
0.02228912152349949,
-0.03599858283996582,
-0.009331101551651955,
-0.010272327810525894,
0.038445837795734406,
0.02797449752688408,
-0.037642937153577805,
0.04662037268280983,
0.011621041223406792,
-0.044280946254730225,
0.011852428317070007,
-0.009687012061476707,
0.031351182609796524,
0.01321109663695097,
0.001160892192274332,
0.01059481967240572,
0.019406139850616455,
-0.007556874305009842,
-0.02174948900938034,
0.010988832451403141,
0.021891500800848007,
0.04222557693719864,
0.009423699229955673,
0.012988809496164322,
0.028128167614340782,
0.018978096544742584,
-0.06301520764827728,
-0.03367191553115845,
0.03329364210367203,
-0.02449774742126465,
-0.02729230932891369,
-0.0035337419249117374,
-0.054736968129873276,
0.04026540741324425,
-0.04835275560617447,
0.036589641124010086,
-0.06886958330869675,
-0.03232580050826073,
0.006055991165339947,
-0.018456144258379936,
-0.0016159708611667156,
-0.010732697322964668,
0.014923756010830402,
-0.0670936107635498,
0.04124225676059723,
0.011396397836506367,
-0.008893699385225773,
-0.06024688482284546,
0.023524107411503792,
-0.004220577888190746,
-0.018388235941529274,
0.016094321385025978,
-0.020263444632291794,
-0.017803523689508438,
0.02804870530962944,
0.023635266348719597,
-0.004581413697451353,
0.009230230003595352,
-0.01899171620607376,
-0.032746538519859314,
-0.04863489046692848,
0.02495105378329754,
-0.0024505252949893475,
-0.03744552284479141,
-0.03915693238377571,
-0.00046287616714835167,
-0.007779250852763653,
0.052052658051252365,
0.023428460583090782,
0.0025059226900339127,
0.01610649935901165,
0.022717490792274475,
-0.0036673129070550203,
-0.014448655769228935,
-0.06482341885566711,
0.0011560305720195174,
-0.013072185218334198,
-0.03473922237753868,
-0.005733897909522057,
0.010980839841067791,
-0.030497120693325996,
0.05496686324477196,
0.03301280364394188,
0.030591651797294617,
0.007563846185803413,
-0.03246745467185974,
-0.029641270637512207,
0.013240236788988113,
0.0009748145821504295,
-0.07567743211984634,
0.03806599602103233,
0.0024542217142879963,
-0.025366749614477158,
0.0007728281780146062,
-0.03911738842725754,
-0.039385836571455,
0.0041691637597978115,
-0.006220769137144089,
0.019608408212661743,
-0.041652750223875046,
0.02081446163356304,
0.05419101193547249,
-0.06145187094807625,
-0.023430943489074707,
-0.0010161205427721143,
-0.02378765121102333,
-0.0039925603196024895,
0.03361762687563896,
0.002153957961127162,
0.001205607084557414,
-0.010622574016451836,
0.03128183260560036,
-0.005926549434661865,
-0.01591644249856472,
-0.002304204972460866,
0.03552445396780968,
0.009213780052959919,
0.007415983360260725,
-0.00169504398945719,
0.02308632619678974,
-0.022917015478014946,
0.01828494854271412,
-0.025757890194654465,
0.019474133849143982,
-0.014925851486623287,
-0.009767767041921616,
0.029557913541793823,
-0.009725517593324184,
-0.01835857331752777,
0.01184226106852293,
-0.007647199090570211,
0.04915596544742584,
-0.03928788751363754,
0.03454006090760231,
0.0006096684373915195,
0.007721557281911373,
0.013109506107866764,
0.014482864178717136,
0.04383200779557228,
0.044448453933000565,
0.01930469088256359,
-0.03339090943336487,
-0.0216953344643116,
-0.06337102502584457,
0.05276334285736084,
-0.014848322607576847,
0.03071497566998005,
-0.02422909066081047,
-0.02593284659087658,
-0.004273280501365662,
-0.04682540148496628,
-0.03939623013138771,
-0.022228393703699112,
0.010101808235049248,
0.018377434462308884,
0.016596298664808273,
-0.011646921746432781,
-0.016739539802074432,
-0.010671555064618587,
0.0458604097366333,
-0.07131505757570267,
-0.0005504941800609231,
-0.001979066524654627,
0.018589584156870842,
0.02641475200653076,
0.034850526601076126
] |
<p>There is a few questions that need to be answered in detail but in an easy way...</p>
<ol>
<li><p>What does it mean to describe the 'plane of polarisation' of electromagnetic waves?</p></li>
<li><p>Why will some antenna have rods which are horizontal and some which are vertical? What does this have to do with polarization of electromagnetic waves?</p></li>
</ol> | 2,002 | [
-0.06083162501454353,
-0.007521273568272591,
-0.004046556074172258,
-0.022269856184720993,
0.04249703511595726,
0.0372738391160965,
-0.034051116555929184,
-0.027894319966435432,
0.019882000982761383,
-0.06311418861150742,
0.029364265501499176,
0.04795275628566742,
0.02375619113445282,
0.012168290093541145,
0.01869419403374195,
-0.0000774794680182822,
-0.013457901775836945,
-0.00858279224485159,
-0.007805243134498596,
-0.02273392304778099,
-0.006846382282674313,
0.0039304993115365505,
-0.024033505469560623,
0.041356101632118225,
-0.035241201519966125,
0.019603271037340164,
0.05565057322382927,
0.0032290376257151365,
0.04083457961678505,
0.05933617055416107,
-0.007852255366742611,
-0.000020450612282729708,
0.02022356353700161,
0.005220151040703058,
0.02561752311885357,
-0.05596942454576492,
-0.026698796078562737,
-0.030496962368488312,
-0.014724856242537498,
0.008937381207942963,
0.01431270781904459,
0.00979379191994667,
-0.03143049031496048,
0.029355891048908234,
-0.0367453470826149,
0.021747909486293793,
0.010845816694200039,
-0.022688383236527443,
0.02255867049098015,
-0.06846935302019119,
0.04240468144416809,
-0.02164319157600403,
0.008560039103031158,
0.031334295868873596,
0.0020273723639547825,
0.015098988078534603,
0.07551208883523941,
0.04550003260374069,
-0.010737324133515358,
-0.054104242473840714,
0.009441153146326542,
0.002917327918112278,
-0.019729051738977432,
-0.0291494932025671,
-0.031890809535980225,
0.017123516649007797,
-0.006336315535008907,
-0.01243249885737896,
0.010346632450819016,
0.024326447397470474,
-0.006737431976944208,
0.036898721009492874,
0.007936821319162846,
-0.012604990974068642,
0.002227649325504899,
-0.04810072481632233,
-0.0017008736031129956,
0.018093835562467575,
0.03131254017353058,
-0.004688673187047243,
0.026860373094677925,
0.031102780252695084,
0.010582867078483105,
0.008842423558235168,
0.020168516784906387,
-0.020661085844039917,
0.0873713567852974,
0.007860724814236164,
0.030862636864185333,
0.0005786062683910131,
0.0151216434314847,
0.03418312966823578,
0.028204819187521935,
0.024577723816037178,
-0.028216280043125153,
0.01671774871647358,
-0.00846102088689804,
0.03588736429810524,
0.010334541089832783,
-0.023834409192204475,
0.05062119662761688,
-0.010674570687115192,
0.013641749508678913,
0.06023702397942543,
0.007650251965969801,
-0.030246585607528687,
-0.02808401547372341,
0.031500134617090225,
-0.02190188318490982,
-0.030735144391655922,
-0.022803498432040215,
0.06628181785345078,
-0.023454222828149796,
0.007850093767046928,
-0.01594029925763607,
-0.029788127169013023,
0.04435868188738823,
-0.03061196766793728,
0.06047439202666283,
0.08299117535352707,
0.009653627872467041,
-0.033627089112997055,
0.022333519533276558,
-0.029840560629963875,
-0.11180564761161804,
-0.014497504569590092,
0.013844690285623074,
0.010437710210680962,
-0.054589055478572845,
0.030678866431117058,
-0.009521217085421085,
0.010898205451667309,
0.04017331078648567,
-0.014758188277482986,
0.001267114537768066,
0.009261466562747955,
-0.1300741583108902,
-0.04719514027237892,
0.012298951856791973,
-0.01020824071019888,
0.00467862281948328,
-0.06515055149793625,
0.00742380740121007,
0.051574792712926865,
0.07001929730176926,
-0.03039422444999218,
0.015262064523994923,
-0.0085800401866436,
0.019107351079583168,
-0.015165144577622414,
-0.005080683622509241,
-0.004033864941447973,
-0.018873687833547592,
-0.03731415420770645,
0.0030089442152529955,
-0.05880378186702728,
-0.0029635687824338675,
0.04071927070617676,
-0.01467313151806593,
-0.029863115400075912,
0.03685472533106804,
-0.012146003544330597,
-0.0077375853434205055,
0.01819264516234398,
-0.061800580471754074,
-0.02326786518096924,
0.08871874958276749,
-0.0018451231298968196,
0.01946442387998104,
0.025889091193675995,
-0.03025832027196884,
0.04553857073187828,
-0.024047518149018288,
0.014260729774832726,
0.023128066211938858,
-0.034444645047187805,
-0.011819282546639442,
0.0005102154100313783,
0.03089507296681404,
0.0027266887482255697,
-0.05945620313286781,
-0.038586925715208054,
0.020779402926564217,
0.04917699843645096,
0.007893969304859638,
0.07162550836801529,
-0.001967035699635744,
-0.015288161113858223,
-0.010123006999492645,
-0.03518738970160484,
-0.01893123798072338,
-0.02488732524216175,
0.04908130690455437,
-0.01010213978588581,
-0.022709693759679794,
-0.015287441201508045,
0.020394880324602127,
-0.011893675662577152,
-0.052151501178741455,
-0.03452989086508751,
-0.00933514628559351,
0.03959198296070099,
0.015429829247295856,
0.00462389038875699,
0.012242533266544342,
0.06201813742518425,
0.023586103692650795,
-0.00032687612110748887,
0.005443572532385588,
-0.03407628461718559,
-0.022703252732753754,
-0.01292316522449255,
-0.0042635719291865826,
0.0201431717723608,
0.026312436908483505,
-0.0002444933634251356,
-0.0011453176848590374,
0.04846840724349022,
-0.011318754404783249,
0.039118435233831406,
-0.04827152565121651,
0.0685243308544159,
0.07014194875955582,
0.003930576611310244,
0.04170810803771019,
0.07371208071708679,
0.004096353892236948,
0.01955999992787838,
-0.01569196954369545,
0.004484792705625296,
-0.07091750204563141,
0.00040916705620475113,
0.06081200763583183,
0.008521872572600842,
-0.031816620379686356,
-0.019931791350245476,
-0.002035098848864436,
0.04393191263079643,
0.016830818727612495,
0.03666350990533829,
-0.03421942889690399,
-0.022378938272595406,
-0.00704837404191494,
-0.009626100771129131,
-0.013418526388704777,
0.03453599661588669,
0.00806579552590847,
-0.011930534616112709,
0.006798137910664082,
-0.016534365713596344,
-0.024392414838075638,
0.07940331101417542,
-0.010050434619188309,
0.010928647592663765,
0.030771108344197273,
-0.02365446463227272,
0.03840717673301697,
-0.028909042477607727,
0.004513215273618698,
-0.004957157652825117,
0.002594425342977047,
-0.011242327280342579,
-0.036493491381406784,
0.013471793383359909,
0.006081216037273407,
0.014719962142407894,
-0.03090277686715126,
-0.011883050203323364,
0.044876813888549805,
-0.03756021335721016,
0.007953226566314697,
-0.039589617401361465,
-0.025424879044294357,
-0.004666535649448633,
-0.051241353154182434,
0.04567060247063637,
-0.0027104986365884542,
0.04533957690000534,
-0.00643145851790905,
-0.00923667661845684,
0.011723235249519348,
-0.0480327345430851,
0.004499503877013922,
-0.010484232567250729,
-0.016342638060450554,
-0.008538664318621159,
-0.05076158791780472,
0.010073143057525158,
0.024476533755660057,
-0.011913030408322811,
-0.003960276022553444,
-0.006644099019467831,
-0.02043798193335533,
-0.06976369023323059,
-0.02906491607427597,
-0.015751320868730545,
0.04603965952992439,
-0.01020883210003376,
-0.033780794590711594,
0.02720245160162449,
-0.02841249480843544,
0.02608577162027359,
0.004581246059387922,
-0.026841284707188606,
-0.021293580532073975,
-0.00304310186766088,
-0.018500398844480515,
0.02529270201921463,
-0.002954379189759493,
-0.010263337753713131,
0.029152490198612213,
-0.043065667152404785,
0.0034890114329755306,
-0.03511091321706772,
-0.020972128957509995,
0.022932186722755432,
-0.0283913966268301,
0.031219620257616043,
-0.0072762127965688705,
-0.013162926770746708,
0.056356772780418396,
0.020242806524038315,
-0.030043626204133034,
-0.016596924513578415,
-0.015194973908364773,
-0.04454786702990532,
-0.01671670563519001,
0.009196310304105282,
0.0398973748087883,
-0.014869503676891327,
0.013867698609828949,
0.022519828751683235,
-0.011092441156506538,
0.036087263375520706,
0.027687709778547287,
-0.020245416089892387,
-0.011362199671566486,
0.003525523701682687,
0.003332827240228653,
0.056144408881664276,
0.04765325039625168,
-0.017898891121149063,
0.02180469036102295,
-0.0005917007802054286,
0.024952132254838943,
0.03148926794528961,
-0.02398291602730751,
0.013369851745665073,
0.0026209645438939333,
0.01889963634312153,
-0.04811858385801315,
0.06759196519851685,
0.012888667173683643,
-0.0018481235019862652,
0.008045272901654243,
0.010287121869623661,
0.053014952689409256,
-0.029558826237916946,
-0.03043205849826336,
0.04371308162808418,
0.021563412621617317,
-0.03936426341533661,
-0.002919499296694994,
0.00679390411823988,
-0.006466408260166645,
-0.0063116056844592094,
-0.044966328889131546,
-0.03603093698620796,
0.058339301496744156,
0.029523463919758797,
0.02340659126639366,
0.023983189836144447,
-0.0568012036383152,
0.004358131904155016,
-0.06050444766879082,
0.027711931616067886,
-0.01496437843888998,
0.04732028394937515,
0.00009101949399337173,
0.06283782422542572,
-0.007105694618076086,
0.02107451856136322,
0.0006127366796135902,
0.010144125670194626,
-0.057337403297424316,
-0.01160039659589529,
-0.04613901302218437,
0.017749125137925148,
-0.017773063853383064,
-0.011922890320420265,
-0.027343178167939186,
-0.03716054558753967,
-0.035596638917922974,
-0.026837019249796867,
-0.026293940842151642,
-0.03295654430985451,
0.023588083684444427,
-0.027722420170903206,
-0.02034742757678032,
-0.01071837916970253,
0.04059654101729393,
0.015725871548056602,
-0.0064069125801324844,
0.02478688396513462,
0.05887902155518532,
-0.021976690739393234,
-0.016708986833691597,
0.008441474288702011,
0.0061438726261258125,
0.0028212026227265596,
0.028270764276385307,
0.0009455084218643606,
-0.019860992208123207,
-0.010167887434363365,
-0.008823943324387074,
0.0013013071147724986,
0.06373254209756851,
0.03250637650489807,
-0.018983669579029083,
-0.016042528674006462,
-0.04754287749528885,
-0.009799569845199585,
-0.057982154190540314,
0.054203297942876816,
-0.0017745225923135877,
-0.00020571850473061204,
0.0033698170445859432,
-0.027539707720279694,
-0.031130503863096237,
0.022766854614019394,
0.014124107547104359,
0.02292933687567711,
0.009232157841324806,
-0.036781053990125656,
-0.031123658642172813,
-0.05066541209816933,
0.0019415925489738584,
0.010639210231602192,
-0.027355751022696495,
-0.02369622141122818,
-0.004438922740519047,
0.023721177130937576,
-0.017767753452062607,
0.003318137489259243,
0.05624488368630409,
-0.0061467490158975124,
-0.012334601022303104,
-0.0185195654630661,
-0.01782330684363842,
-0.00429010484367609,
0.046374429017305374,
0.05088355764746666,
0.015360118821263313,
-0.05696113035082817,
-0.07341233640909195,
-0.006830049678683281,
-0.009749197401106358,
0.05913621187210083,
0.008307537995278835,
0.009740320034325123,
-0.03549511730670929,
-0.037848714739084244,
0.04004208371043205,
-0.044337645173072815,
0.012002924457192421,
-0.04086906462907791,
-0.01700497604906559,
-0.05384400859475136,
0.008025340735912323,
-0.03256113827228546,
-0.003523648716509342,
-0.008062888868153095,
0.0457773432135582,
-0.011052670888602734,
-0.007021444849669933,
-0.017864665016531944,
0.019340792670845985,
0.03459901362657547,
0.03151147812604904,
0.03315995633602142,
0.028254857286810875,
-0.0073021757416427135,
0.02538534626364708,
-0.010325059294700623,
-0.05682014673948288,
-0.010974183678627014,
0.03787034749984741,
-0.027379129081964493,
0.05964689329266548,
-0.022382933646440506,
-0.04709753394126892,
0.03213011845946312,
0.0021464682649821043,
0.0052627865225076675,
-0.0018185973167419434,
-0.05028064176440239,
0.012749316170811653,
0.022304097190499306,
-0.03308667615056038,
0.06590332835912704,
0.014352904632687569,
-0.04089190438389778,
-0.009425746276974678,
-0.028410939499735832,
0.03443390503525734,
0.015182428993284702,
-0.01063118688762188,
-0.02935594506561756,
-0.0007300535799004138,
-0.0025783926248550415,
0.07006925344467163,
0.014834372326731682,
-0.013831264339387417,
-0.02430131658911705,
-0.055202383548021317,
-0.03786170855164528,
0.019956108182668686,
-0.0027292908634990454,
-0.01419169269502163,
-0.01668723300099373,
0.0019575529731810093,
0.011162910610437393,
-0.03918658569455147,
-0.009153949096798897,
-0.0063605718314647675,
0.013519166968762875,
0.010865133255720139,
0.031040392816066742,
-0.007301453500986099,
-0.046309661120176315,
0.001490811468102038,
-0.016537735238671303,
-0.05478130280971527,
0.05441039800643921,
-0.00045416184002533555,
-0.007163173984736204,
0.041697755455970764,
-0.07273368537425995,
-0.027157077565789223,
0.02457776479423046,
-0.011096365749835968,
0.016124004498124123,
-0.027147887274622917,
0.004707007668912411,
0.002292341087013483,
-0.004787225276231766,
-0.010398305021226406,
-0.04682012274861336,
0.014527416788041592,
0.029244692996144295,
-0.03032483160495758,
-0.020426228642463684,
0.023980215191841125,
0.008108805865049362,
-0.04752318188548088,
0.005811900366097689,
0.024452516809105873,
-0.0523630790412426,
-0.00007919384370325133,
0.0006739102536812425,
-0.021052459254860878,
0.08875705301761627,
-0.02190350368618965,
-0.03347184509038925,
0.02141423337161541,
-0.028398629277944565,
0.008755660615861416,
-0.04452557861804962,
0.043589845299720764,
0.00031479523750022054,
-0.06992848962545395,
-0.01136966422200203,
0.0096407076343894,
0.03207947313785553,
-0.0015937595162540674,
0.002013378543779254,
-0.004435231909155846,
0.002781872870400548,
-0.032247550785541534,
-0.006508451420813799,
0.012471849098801613,
0.020723825320601463,
0.03475102037191391,
-0.010229351930320263,
0.021593065932393074,
-0.043262284249067307,
-0.03571224585175514,
0.036820411682128906,
0.012603135779500008,
0.015322309918701649,
-0.0030679048504680395,
0.07092297822237015,
-0.030544769018888474,
0.008943779394030571,
0.020530709996819496,
-0.04034950211644173,
0.005209110211580992,
0.018337441608309746,
-0.007564444560557604,
0.014747506938874722,
0.014219982549548149,
0.009339241310954094,
-0.04959133267402649,
-0.013588638044893742,
0.005862072110176086,
0.05633031576871872,
0.006716909818351269,
0.07283160835504532,
0.042399123311042786,
0.0072770267724990845,
-0.042159441858530045,
-0.02207220159471035,
-0.015125934965908527,
-0.029951388016343117,
-0.004168336279690266,
0.007167471572756767,
-0.024139491841197014,
0.007910694926977158,
0.0319879986345768,
0.07995240390300751,
-0.004202067852020264,
-0.009677553549408913,
0.026555515825748444,
0.025861499831080437,
0.014491142705082893,
-0.003637478454038501,
-0.06290058046579361,
0.041425157338380814,
-0.03986630216240883,
0.01731736771762371,
0.003581780008971691,
-0.01834910921752453,
0.05304061993956566,
-0.004696756601333618,
0.017166797071695328,
-0.024575719609856606,
0.028521638363599777,
-0.03501805290579796,
0.020234201103448868,
0.0011703527998179197,
0.020630592480301857,
-0.013081400655210018,
0.021121809259057045,
0.04908138886094093,
-0.03404740244150162,
0.015248408541083336,
0.01827077567577362,
-0.03792011737823486,
-0.040415242314338684,
-0.004149858374148607,
-0.041085291653871536,
0.09179852157831192,
0.014314397238194942,
-0.0013873823918402195,
-0.004190315026789904,
-0.040663328021764755,
0.021930653601884842,
0.0029202764853835106,
0.052641455084085464,
-0.02792339213192463,
0.0635853111743927,
-0.014973686076700687,
0.010683372616767883,
0.0038777864538133144,
-0.031545303761959076,
0.1195208728313446,
0.04742354899644852,
-0.004168460611253977,
-0.065650075674057,
0.002333681099116802,
-0.03308240324258804,
0.0072366055101156235,
-0.0185249000787735,
-0.005682377610355616,
-0.03918285295367241,
0.06369008123874664,
0.01885007694363594,
-0.023008214309811592,
-0.018579790368676186,
-0.02067635953426361,
0.02799108438193798,
-0.04029880091547966,
-0.02985846810042858,
-0.0008938780520111322,
0.011969517916440964,
-0.02614964172244072,
0.04818688705563545,
-0.06937475502490997,
0.03228333219885826,
-0.02538798376917839,
-0.005630492698401213,
-0.021566588431596756,
-0.029046013951301575,
0.050290726125240326,
-0.035773828625679016,
-0.030625978484749794,
0.006030722986906767,
0.0034913376439362764,
-0.04189557954668999,
-0.04709424823522568,
0.05616036430001259,
0.004581874702125788,
-0.005623070988804102,
0.0021436605602502823,
0.0004015546874143183,
0.012691752053797245,
-0.02177104912698269,
0.03260734677314758,
0.0472409687936306,
-0.040527477860450745,
-0.002093630377203226,
-0.012901464477181435,
0.03273686766624451,
-0.014768610708415508,
0.0050167515873909,
-0.00782045442610979,
0.046436697244644165,
-0.005718362983316183,
-0.06528543680906296,
0.000996316084638238,
0.017282556742429733,
0.02894611284136772,
-0.006107774563133717,
-0.016727305948734283,
-0.028289638459682465,
-0.0014524678699672222,
-0.007358597591519356,
0.017263539135456085,
0.011195876635611057,
-0.005283953156322241,
0.010005072690546513,
-0.0017435477348044515,
0.05347633734345436,
0.019385432824492455,
0.0012742903782054782,
-0.04666874557733536,
-0.020554888993501663,
-0.03294871747493744,
-0.0021255584433674812,
0.03203362971544266,
0.04001199081540108,
0.02202966809272766,
0.006603572983294725,
-0.008199878968298435,
0.0002722789067775011,
-0.0356711819767952,
0.03368932381272316,
-0.008680781349539757,
-0.023667320609092712,
0.002812650054693222,
0.017883459106087685,
0.029050137847661972,
0.04936397075653076,
0.011920676566660404,
0.04779282212257385,
-0.017201386392116547,
-0.00709465192630887,
0.007343947421759367,
-0.02631860226392746,
-0.06724834442138672,
0.01214682124555111,
-0.02082149311900139,
0.008899025619029999,
0.02713305689394474,
0.02462545409798622,
0.045296307653188705,
0.02591850236058235,
-0.017168832942843437,
0.010351781733334064,
-0.01358260028064251,
-0.04060238599777222,
0.0032584574073553085,
-0.02533489651978016,
0.026704540476202965,
0.025899888947606087,
-0.00156214099843055,
-0.027831515297293663,
-0.011159206740558147,
-0.003279071534052491,
-0.02731463685631752,
0.01111094281077385,
0.014856135472655296,
0.012410006485879421,
-0.014107897877693176,
-0.04253244400024414,
0.005830065347254276,
-0.017969727516174316,
0.009979676455259323,
-0.03244888037443161,
0.021845070645213127,
0.0038587539456784725,
0.005030365660786629,
-0.02256636880338192,
0.017258619889616966,
-0.03521781414747238,
-0.005419169086962938,
0.028594205155968666,
0.03578674793243408,
0.007456864695996046,
0.030339490622282028,
0.0265622790902853,
0.013084028847515583,
0.05446714907884598,
0.00034807829069904983,
-0.035973601043224335,
0.02200407162308693,
-0.014651276171207428,
-0.04130904749035835,
0.024915877729654312,
0.001346608973108232,
0.04881511256098747,
0.01703503727912903,
-0.020141296088695526,
0.003971681464463472,
0.019820887595415115,
0.013183432631194592,
-0.012320468202233315,
0.00678538903594017,
-0.003572203917428851,
0.03283106908202171,
-0.027833109721541405,
-0.004251900129020214,
-0.01978554204106331,
-0.03746328502893448,
0.03483472019433975,
-0.009983831085264683,
-0.005378695670515299,
-0.0038487259298563004,
0.020427126437425613,
0.0139897046610713,
-0.00024517130805179477,
0.030537670478224754,
0.019975366070866585,
0.04044577479362488,
0.041345953941345215,
-0.018711809068918228,
0.05260210484266281,
0.0020380718633532524,
0.01328129693865776,
-0.10495472699403763,
-0.025996331125497818,
0.041459642350673676,
0.03264075517654419,
0.04114094749093056,
-0.02961401268839836,
0.010283458046615124,
0.054486438632011414,
-0.08683252334594727,
0.030020879581570625,
0.02214909717440605,
-0.023731732740998268,
-0.02837102860212326,
0.0001287564664380625,
-0.008346532471477985,
0.05649382993578911,
0.004278724081814289,
0.06154068559408188,
0.02479453943669796,
0.02497793361544609,
-0.027060702443122864,
-0.05133683606982231,
-0.022644974291324615,
0.05543196573853493,
-0.027963444590568542,
-0.028569107875227928,
0.056914325803518295,
-0.004132898990064859,
-0.006327431183308363,
0.01740179769694805,
-0.02422787807881832,
-0.005225293338298798,
0.032867636531591415,
-0.00847173947840929,
0.004537288099527359,
0.036588914692401886,
-0.006121398881077766,
-0.03229743614792824,
-0.05782487988471985,
0.005343963857740164,
0.010327879339456558,
0.015697447583079338,
0.01869751326739788,
-0.014096179977059364,
0.010234328918159008,
-0.02249768003821373,
0.0020564221777021885,
0.02545796148478985,
-0.04888638108968735,
-0.01577044278383255,
-0.00573810376226902,
0.003473875345662236,
0.0008956949459388852,
-0.028595028445124626,
0.03743975982069969,
-0.06224770471453667,
-0.014812723733484745,
0.001176869380287826,
-0.023952143266797066,
0.01414062175899744,
0.01679696887731552,
0.04752323776483536,
-0.010366681031882763,
0.032163918018341064,
-0.01254140306264162,
-0.005244167055934668,
-0.04150420054793358,
0.03786104917526245,
0.0250985287129879,
-0.017097514122724533,
0.040634818375110626,
-0.011111960746347904,
-0.03186310827732086,
0.008014609105885029,
0.006014230661094189,
-0.00516798160970211,
0.014329572208225727,
-0.05037969350814819,
-0.03268308565020561,
-0.046328213065862656,
0.06797480583190918,
-0.004388040862977505,
-0.05325859785079956,
-0.04090605676174164,
-0.04133399575948715,
-0.03996831923723221,
0.0695355087518692,
0.0773431584239006,
-0.004593675956130028,
-0.006379519589245319,
-0.013112302869558334,
0.014250597916543484,
0.04752028360962868,
-0.049092985689640045,
0.007686894852668047,
0.04177410900592804,
-0.02827165089547634,
0.02229088731110096,
-0.019057685509324074,
-0.01897595077753067,
-0.0009422338916920125,
-0.004245804622769356,
0.0023721305187791586,
0.05780196189880371,
-0.019562816247344017,
-0.05385721102356911,
0.015718156471848488,
0.025468891486525536,
-0.029029425233602524,
0.04820537194609642,
-0.0033788662403821945,
-0.0006463109166361392,
0.019676804542541504,
-0.04620480164885521,
-0.02736135758459568,
-0.008766807615756989,
-0.034391846507787704,
0.011338316835463047,
-0.032198913395404816,
0.04696432128548622,
0.05981262028217316,
-0.053737279027700424,
0.0018473141826689243,
0.03068174049258232,
-0.0683470070362091,
-0.009489496238529682,
0.03921471908688545,
-0.005271109286695719,
0.011774295940995216,
-0.026516780257225037,
0.03529796749353409,
0.01799788884818554,
-0.04878821223974228,
0.004059316590428352,
0.036506231874227524,
0.0350152850151062,
0.026940753683447838,
0.01029529795050621,
0.049802567809820175,
0.013267336413264275,
0.033146053552627563,
0.0030899178236722946,
0.026242997497320175,
-0.03988094627857208,
0.00021235638996586204,
0.01787433587014675,
-0.005403965711593628,
-0.029673952609300613,
0.04466697946190834,
-0.003388291923329234,
0.05443798005580902,
-0.018654854968190193,
-0.000036703007936012,
-0.0188700370490551,
0.003649243386462331,
0.0006337836384773254,
0.009082981385290623,
0.044328723102808,
0.01771959476172924,
0.000545161310583353,
-0.007958674803376198,
-0.019380465149879456,
-0.01055190246552229,
0.08195927739143372,
-0.011552534066140652,
0.03726517781615257,
-0.025660397484898567,
-0.016027797013521194,
-0.013295198790729046,
-0.02645738050341606,
-0.0011353787267580628,
0.027312304824590683,
0.05098511278629303,
0.0134572209790349,
0.014361171051859856,
0.014754201285541058,
0.022315792739391327,
-0.038043905049562454,
0.0013499383348971605,
-0.053870804607868195,
-0.005971470382064581,
-0.027966413646936417,
0.03972160071134567,
-0.0026606242172420025,
-0.006949236616492271
] |
<p>I have to calculate the total number of electric field lines through a proton. I tried using Gauss' Law, i.e, $$\phi = \oint\boldsymbol E.d\boldsymbol s = {\frac{q}{\epsilon_0}} $$ $$So, \phi = {\frac{q}{\epsilon_0}} $$</p>
<p>$$ \textrm{Therefore}, \phi = \frac{1.6\times10^{-19}}{8.854\times10^{-12}}$$, as $q=1.6\times10^{-19}C$ and
$\epsilon_0 = 8.854\times10^{-12}C^2N^{-1}m^{-2}$.</p>
<p>But the answer is $0.18\times10^{-7}$ or something like that. How can that be the number of field lines? How can that be the number of anything? I mean it's a fractional number. Any help is appreciated. Thanks.</p> | 2,003 | [
0.005335282068699598,
-0.03646156191825867,
-0.005406578071415424,
-0.009742646478116512,
0.045667726546525955,
0.020426243543624878,
-0.04638456180691719,
-0.01203601248562336,
-0.002909355331212282,
-0.0049684601835906506,
0.07835663110017776,
0.022211020812392235,
0.06237728148698807,
-0.003709460375830531,
-0.01597970724105835,
0.015208189375698566,
-0.030338821932673454,
0.025810452178120613,
0.039155956357717514,
-0.04026203230023384,
0.001283082296140492,
0.04207476228475571,
0.005764284636825323,
0.005455648992210627,
-0.03621184825897217,
0.05956340953707695,
0.02072984166443348,
-0.02308463491499424,
0.03750861436128616,
0.033344198018312454,
0.010771406814455986,
-0.06128692254424095,
0.07100465893745422,
0.020919809117913246,
0.04210526496171951,
-0.005089729558676481,
0.0066886539570987225,
-0.022244535386562347,
-0.02250426821410656,
0.01981171779334545,
-0.0528789684176445,
-0.043511416763067245,
-0.009694532491266727,
0.03393755108118057,
-0.03789878636598587,
0.00512391934171319,
0.005180120933800936,
-0.011053869500756264,
0.05705700442194939,
-0.05825509876012802,
0.0737113431096077,
0.00984677579253912,
0.050998955965042114,
0.010263078846037388,
0.03530922904610634,
-0.008512268774211407,
0.07586976885795593,
0.028439253568649292,
0.0025259782560169697,
-0.06527490168809891,
-0.025834187865257263,
-0.02288726530969143,
-0.026027217507362366,
-0.015501461923122406,
-0.009325367398560047,
0.026173897087574005,
-0.01604713499546051,
-0.027331288903951645,
0.03313136845827103,
0.0037460101302713156,
0.030146487057209015,
0.027295386418700218,
0.03812142089009285,
-0.02957075834274292,
0.01363682933151722,
-0.009248471818864346,
0.04937721788883209,
0.04580274596810341,
0.006819904316216707,
0.0350072979927063,
-0.018652070313692093,
0.01154593750834465,
-0.025746487081050873,
0.009942599572241306,
0.03940477594733238,
-0.012922065332531929,
0.036193981766700745,
-0.037155166268348694,
0.030272163450717926,
0.01569700799882412,
-0.009559307247400284,
0.031204398721456528,
0.02284340374171734,
0.04075286164879799,
-0.03333967179059982,
0.03728419542312622,
0.0010236300295218825,
0.019889729097485542,
-0.013371406123042107,
-0.009412199258804321,
-0.004508203361183405,
-0.00039391283644363284,
0.012093642726540565,
0.09218423813581467,
-0.03262489289045334,
0.023616360500454903,
-0.013818216510117054,
-0.014033403247594833,
-0.056235432624816895,
-0.0051974146626889706,
-0.024522248655557632,
0.023610107600688934,
0.030467916280031204,
-0.012102311477065086,
-0.011818048544228077,
-0.03568483144044876,
-0.018796149641275406,
-0.01780337281525135,
0.04779656231403351,
0.07423635572195053,
0.01642450876533985,
-0.028005613014101982,
0.021725071594119072,
-0.03624923154711723,
-0.05779002234339714,
0.001675214502029121,
0.011542227119207382,
-0.007689261808991432,
-0.03130749240517616,
0.0067527322098612785,
-0.017435934394598007,
0.015264242887496948,
-0.006778815761208534,
0.004475659225136042,
0.014598689042031765,
-0.024355590343475342,
-0.0836314931511879,
-0.055033691227436066,
0.016273031011223793,
-0.029275305569171906,
0.015084882266819477,
-0.06470993161201477,
0.016085613518953323,
0.017489485442638397,
0.0618288479745388,
0.00894178170710802,
0.006458588410168886,
-0.005243318155407906,
0.04374923184514046,
0.019253727048635483,
0.01582367531955242,
0.03163319453597069,
-0.04243326187133789,
-0.03182808309793472,
-0.01793200895190239,
-0.0378112718462944,
0.0663287416100502,
0.03331458568572998,
-0.009867033921182156,
-0.002336200326681137,
0.03830496966838837,
0.011620678007602692,
0.021341940388083458,
0.017963455989956856,
-0.029073363170027733,
-0.06513064354658127,
0.04434686526656151,
0.04408320039510727,
0.03383630886673927,
0.05618414282798767,
-0.0038976084906607866,
-0.010051382705569267,
0.00579989654943347,
0.005066901445388794,
0.06705888360738754,
-0.029103821143507957,
-0.009957931004464626,
-0.029551513493061066,
-0.0172771904617548,
0.030955424532294273,
-0.04809408262372017,
-0.056085288524627686,
-0.0029647275805473328,
0.06917071342468262,
0.006601703818887472,
0.028497258201241493,
0.00786809716373682,
-0.0014010051963850856,
0.004944998770952225,
-0.020830953493714333,
-0.026025665923953056,
-0.04116104915738106,
0.04992284998297691,
0.03654373064637184,
-0.025132490321993828,
-0.007046237122267485,
0.005137606989592314,
0.013895661570131779,
-0.02502334676682949,
-0.05233972892165184,
0.01570599153637886,
0.02069355733692646,
-0.005288055632263422,
-0.05073324963450432,
0.013228921219706535,
0.02185840718448162,
0.010640324093401432,
-0.010105958208441734,
0.05744525417685509,
-0.0351480208337307,
0.021234974265098572,
-0.021046070381999016,
-0.038842786103487015,
0.030341360718011856,
-0.01639905758202076,
-0.03174225613474846,
0.024233780801296234,
0.006071506068110466,
-0.0012696156045421958,
0.06181880459189415,
-0.03443177044391632,
0.0810481458902359,
0.06927929073572159,
0.0083002345636487,
0.0020391291473060846,
-0.012440268881618977,
-0.02883335016667843,
0.00543855968862772,
-0.00795427430421114,
-0.044442757964134216,
-0.031464584171772,
0.010492237284779549,
0.04242066293954849,
-0.018147824332118034,
-0.015370558016002178,
-0.0263217780739069,
0.036944251507520676,
0.04016709700226784,
0.03951907157897949,
0.029919560998678207,
-0.05980992689728737,
-0.02396019548177719,
-0.0037190858274698257,
0.02967759035527706,
-0.03686954453587532,
-0.025451896712183952,
0.03180159628391266,
0.006525058299303055,
0.015292318537831306,
0.024142364040017128,
-0.0018131507094949484,
0.02851697988808155,
-0.03909033536911011,
0.037522125989198685,
0.01196119375526905,
-0.0221810732036829,
0.041307613253593445,
-0.02025546506047249,
0.03637346625328064,
0.02146415039896965,
-0.02418592758476734,
0.018376052379608154,
-0.02474028989672661,
-0.008937140926718712,
0.019128069281578064,
-0.00365325971506536,
-0.038224682211875916,
-0.029783256351947784,
0.024999288842082024,
-0.05516985058784485,
0.016102591529488564,
-0.021082565188407898,
0.013748571276664734,
-0.011415790766477585,
0.01107752788811922,
0.06845999509096146,
0.03680897504091263,
0.04151828587055206,
-0.03012533113360405,
-0.028286071494221687,
0.039243973791599274,
-0.016938408836722374,
0.05826825276017189,
0.027915606275200844,
-0.048538751900196075,
-0.013233545236289501,
-0.023639574646949768,
0.006486617028713226,
0.01965857669711113,
-0.023986442014575005,
-0.026457732543349266,
-0.010035362094640732,
-0.028992539271712303,
-0.03828466311097145,
-0.009295948781073093,
-0.050744544714689255,
0.021466122940182686,
-0.020469699054956436,
0.00904411543160677,
0.03925171494483948,
-0.0026861545629799366,
-0.03983042389154434,
0.020011913031339645,
-0.044560421258211136,
-0.02102886326611042,
-0.03198632970452309,
-0.006505183409899473,
-0.0035724209155887365,
-0.019771309569478035,
0.014615760184824467,
-0.012857252731919289,
-0.013745009899139404,
-0.011576944030821323,
-0.03635680302977562,
-0.05653633549809456,
0.006062955129891634,
0.009956257417798042,
0.033046234399080276,
-0.01755446568131447,
-0.01876905746757984,
0.06345853209495544,
0.032217495143413544,
-0.06156778335571289,
-0.009138011373579502,
0.0225662924349308,
-0.005852750036865473,
-0.045194804668426514,
-0.015796178951859474,
0.022018300369381905,
-0.049278032034635544,
-0.0041770003736019135,
-0.003241774858906865,
0.06767897307872772,
0.020291456952691078,
-0.004948090296238661,
-0.010868093930184841,
0.011865050531923771,
-0.025916798040270805,
-0.004035918042063713,
0.05797788128256798,
0.028534550219774246,
0.017338234931230545,
0.021260177716612816,
0.017366718500852585,
0.020862648263573647,
0.014050773344933987,
-0.044268347322940826,
0.040150005370378494,
0.00293597299605608,
0.0427715890109539,
-0.02571195922791958,
-0.01139217708259821,
-0.002277899067848921,
-0.03311538323760033,
0.026566537097096443,
0.02139480970799923,
0.02813020348548889,
-0.0597454234957695,
0.0022165041882544756,
0.00790643785148859,
0.050769366323947906,
-0.009227458387613297,
-0.019842801615595818,
-0.013830234296619892,
-0.014911973848938942,
0.006211931351572275,
-0.0037994005251675844,
-0.031131017953157425,
0.0014724606880918145,
0.06036331132054329,
0.05240336060523987,
-0.008579679764807224,
-0.021012483164668083,
0.01935715600848198,
-0.031076733022928238,
-0.03233535587787628,
-0.008936457335948944,
0.04311123490333557,
0.01271936483681202,
0.042723655700683594,
0.0022319818381220102,
-0.026945356279611588,
-0.0008753937436267734,
-0.010856973938643932,
-0.05816200375556946,
0.02287018485367298,
-0.01163544598966837,
-0.009107065387070179,
-0.027112970128655434,
-0.030568895861506462,
-0.011257958598434925,
-0.00021890780772082508,
-0.007718533743172884,
0.000044793341658078134,
0.02562950737774372,
-0.03827432915568352,
0.015681080520153046,
-0.07174992561340332,
-0.04100140556693077,
-0.01547213178128004,
0.04017915949225426,
-0.010079307481646538,
-0.047183968126773834,
-0.038365788757801056,
0.014042225666344166,
-0.01697029359638691,
-0.049665600061416626,
-0.0053887744434177876,
0.024197043851017952,
-0.003943431656807661,
0.049108847975730896,
0.018200969323515892,
0.01545995008200407,
-0.011343741789460182,
-0.01986030675470829,
-0.01293815765529871,
0.05919947102665901,
0.03093820810317993,
-0.009915960021317005,
-0.004952909890562296,
-0.035003405064344406,
0.029987882822752,
0.005854042246937752,
0.04422278329730034,
-0.0040277522057294846,
0.010784701444208622,
0.03769131749868393,
-0.027150126174092293,
0.004733799956738949,
0.0327213779091835,
0.042418137192726135,
-0.02742290124297142,
-0.022134026512503624,
-0.07207341492176056,
0.04117661342024803,
-0.032960034906864166,
0.008341426029801369,
0.0014517158269882202,
0.015411666594445705,
-0.009452126920223236,
-0.017399394884705544,
0.01443654764443636,
-0.004336141515523195,
-0.004488919861614704,
0.019027940928936005,
-0.017567025497555733,
0.0059900530613958836,
-0.005798489321023226,
-0.02520981803536415,
0.00936808716505766,
0.03931542858481407,
0.04243563115596771,
-0.0037069586105644703,
-0.04230577498674393,
-0.07571513950824738,
0.012604635208845139,
0.04391086474061012,
0.036376018077135086,
0.015303026884794235,
0.016936112195253372,
-0.020118361338973045,
0.018929455429315567,
0.06589110195636749,
-0.046447254717350006,
0.0010388154769316316,
0.009346343576908112,
0.02186163328588009,
-0.007480521686375141,
-0.03544371947646141,
-0.030906694009900093,
0.034039877355098724,
0.0062209246680140495,
0.020888635888695717,
-0.03605928272008896,
0.01747530698776245,
0.008866818621754646,
0.030630914494395256,
0.00967369694262743,
0.04036939516663551,
-0.006123576778918505,
-0.010437711142003536,
0.010201639495790005,
0.020014122128486633,
0.005990682169795036,
-0.04793809354305267,
0.025390153750777245,
-0.0020616641268134117,
0.0213175006210804,
0.04635436087846756,
-0.012179821729660034,
-0.05270859971642494,
0.04948469623923302,
0.02764643169939518,
0.012777145020663738,
-0.025523794814944267,
-0.06264369189739227,
0.020369479432702065,
0.031003227457404137,
0.05451511964201927,
0.0742088258266449,
0.032887157052755356,
-0.013990609906613827,
0.010511942207813263,
-0.031494513154029846,
0.0368620902299881,
-0.021558810025453568,
-0.02354341186583042,
-0.025949627161026,
0.04150935634970665,
-0.028868451714515686,
0.07074691355228424,
-0.038427017629146576,
0.015698431059718132,
-0.013945438899099827,
-0.03232274204492569,
-0.008341416716575623,
-0.011732815764844418,
-0.02639947086572647,
0.001029264647513628,
-0.0020388890989124775,
0.04105217382311821,
0.038147393614053726,
-0.04398655891418457,
0.006367132067680359,
0.005399240180850029,
-0.027734927833080292,
-0.027497930452227592,
-0.01415308192372322,
-0.01532528642565012,
0.012772505171597004,
-0.0073834811337292194,
0.013823646120727062,
-0.056299563497304916,
0.01924825832247734,
-0.05846858397126198,
-0.023539721965789795,
-0.0026123030111193657,
-0.04440680518746376,
-0.03991897031664848,
-0.012730235233902931,
0.02463775873184204,
0.01898256689310074,
-0.038171086460351944,
-0.03949081152677536,
-0.011673043482005596,
0.04653576761484146,
-0.06634286791086197,
-0.026143161579966545,
0.030574774369597435,
0.0010270295897498727,
-0.022133834660053253,
-0.007392860483378172,
-0.023818364366889,
0.03596195578575134,
-0.05567854642868042,
0.011585129424929619,
0.01591298170387745,
-0.03323785960674286,
-0.007659522816538811,
0.019442088901996613,
0.031617797911167145,
0.037200428545475006,
0.005008386913686991,
-0.04403156414628029,
0.03543543070554733,
-0.028470542281866074,
-0.024834897369146347,
-0.02118452824652195,
0.01765025407075882,
-0.028928620740771294,
-0.035061679780483246,
-0.027476288378238678,
-0.020365500822663307,
0.0029172867070883512,
-0.028063837438821793,
-0.001211503753438592,
0.01040763221681118,
0.04061911627650261,
0.0099527882412076,
0.02848423458635807,
0.0020296478178352118,
0.00044759418233297765,
0.02555135264992714,
-0.01196315512061119,
0.01874813251197338,
-0.014959238469600677,
-0.004728090483695269,
0.0059096054174005985,
0.021877193823456764,
0.03212672844529152,
-0.00290051125921309,
0.03445487096905708,
-0.020318670198321342,
-0.04538922384381294,
0.02585435099899769,
-0.0199714507907629,
-0.0015542656183242798,
0.02615407481789589,
-0.010452811606228352,
0.007693073246628046,
0.00851371232420206,
-0.0012225561076775193,
-0.0008297514286823571,
-0.046221356838941574,
0.015613241121172905,
0.06647887080907822,
-0.008996822871267796,
0.02012109011411667,
-0.027852164581418037,
0.0140663031488657,
0.007744280621409416,
0.02288655750453472,
-0.053689759224653244,
-0.001658639870584011,
0.045980121940374374,
0.025251705199480057,
-0.02516459859907627,
-0.024315953254699707,
0.01735220104455948,
0.03703981637954712,
0.01752770133316517,
-0.005644738674163818,
0.018685074523091316,
0.04492191597819328,
-0.011864189989864826,
-0.021321378648281097,
-0.043049007654190063,
0.0511532723903656,
-0.021891798824071884,
0.04326089471578598,
0.017508020624518394,
0.029829807579517365,
0.06846298277378082,
-0.010988311842083931,
-0.010972483083605766,
-0.024633342400193214,
-0.020580777898430824,
-0.004137137904763222,
-0.0002569541975390166,
0.03345148265361786,
-0.04971664398908615,
-0.040943171828985214,
0.023475587368011475,
0.012461314909160137,
0.03154933825135231,
0.02710307389497757,
0.007742204703390598,
-0.040178511291742325,
-0.03386881202459335,
-0.029927397146821022,
-0.06464919447898865,
0.06873606145381927,
-0.012423913925886154,
-0.03451971337199211,
-0.006262692157179117,
0.02503110282123089,
0.053570959717035294,
0.0030826341826468706,
0.00679829902946949,
-0.025310521945357323,
0.02995917946100235,
0.00044174480717629194,
0.013379217125475407,
0.013445026241242886,
-0.007190358359366655,
0.11069844663143158,
0.05098602548241615,
0.029934439808130264,
-0.016232149675488472,
-0.003351945662871003,
-0.0379609689116478,
0.003227083943784237,
-0.01604139246046543,
0.016855349764227867,
-0.03952282667160034,
-0.00007487786933779716,
0.02030661702156067,
0.0474003329873085,
-0.0058952514082193375,
0.012017321772873402,
0.08016398549079895,
-0.008057170547544956,
-0.01862408220767975,
-0.02102924883365631,
0.05022652819752693,
-0.019970331341028214,
0.018392283469438553,
-0.015429825522005558,
0.04394515976309776,
-0.03977752849459648,
0.014277728274464607,
-0.04162096232175827,
-0.01218345109373331,
-0.015215490944683552,
0.02486254833638668,
-0.04272708669304848,
-0.0078001609072089195,
0.019747985526919365,
-0.009422115981578827,
-0.023854874074459076,
0.01778712496161461,
0.045875005424022675,
0.005895962473005056,
-0.021333415061235428,
0.036681197583675385,
0.00010665587615221739,
0.053168363869190216,
-0.00037987870746292174,
0.04076530039310455,
-0.04445183649659157,
-0.0030384412966668606,
-0.022343186661601067,
0.05559102073311806,
-0.019375093281269073,
-0.012435213662683964,
-0.01422187127172947,
0.04283745586872101,
0.023725349456071854,
-0.04963359981775284,
-0.053630296140909195,
-0.022294390946626663,
-0.004205640871077776,
-0.03406118229031563,
0.0035406218376010656,
-0.005645693279802799,
0.029743816703557968,
0.006766044069081545,
0.01699197292327881,
0.03912017494440079,
0.03746689483523369,
0.014773717150092125,
0.027997760102152824,
0.027455229312181473,
0.003613515058532357,
-0.0060586570762097836,
-0.013588792644441128,
-0.02407955564558506,
-0.0031681377440690994,
-0.014176540076732635,
-0.007373190019279718,
0.025967970490455627,
0.022790228947997093,
-0.0003512463590595871,
-0.04529625177383423,
-0.01727631688117981,
-0.05122046917676926,
0.05690397694706917,
0.0019001238979399204,
0.015344415791332722,
-0.0028997967019677162,
-0.026498131453990936,
-0.013290672563016415,
0.045408815145492554,
-0.03327948600053787,
0.01889641396701336,
0.02056179940700531,
0.006555837579071522,
0.028846411034464836,
-0.028277406468987465,
-0.044367026537656784,
-0.011574589647352695,
-0.021231334656476974,
-0.018010077998042107,
-0.0020279197487980127,
0.02396426536142826,
-0.005454220809042454,
0.045190323144197464,
0.01032510306686163,
0.05759195610880852,
-0.052596673369407654,
-0.0022359236609190702,
0.002188617130741477,
-0.025300098583102226,
0.014841378666460514,
-0.024141889065504074,
0.003644123673439026,
-0.07430367171764374,
-0.014028074219822884,
0.002587703987956047,
0.01214616373181343,
0.039986468851566315,
0.03359198197722435,
-0.023017726838588715,
-0.02987067960202694,
-0.006111331284046173,
-0.018406126648187637,
0.0027849599719047546,
0.005909822881221771,
-0.061982885003089905,
0.014731988310813904,
-0.009173877537250519,
-0.021986227482557297,
-0.027620365843176842,
0.01896752044558525,
-0.00034064732608385384,
-0.041892047971487045,
0.018132269382476807,
0.028522765263915062,
0.0037654475308954716,
-0.028521524742245674,
0.05436517670750618,
0.020795002579689026,
0.02721652202308178,
-0.04793824255466461,
0.0013780462322756648,
0.018915148451924324,
-0.06435094028711319,
-0.06387417018413544,
0.03747521713376045,
-0.02579144760966301,
0.039025064557790756,
0.029557669535279274,
0.03335026279091835,
-0.024233417585492134,
0.038832541555166245,
-0.020497700199484825,
0.013601802289485931,
-0.04210793599486351,
-0.013531153090298176,
0.04533759504556656,
-0.046430960297584534,
-0.013289791531860828,
-0.0036425674334168434,
0.02349211275577545,
0.028966346755623817,
0.011586575768887997,
-0.030877001583576202,
0.012707438319921494,
-0.022084085270762444,
0.008501102216541767,
0.01599849760532379,
0.03798818588256836,
0.03702118992805481,
0.0013205977156758308,
0.0029502154793590307,
0.0032656039111316204,
0.008551794104278088,
0.01978055015206337,
0.040872231125831604,
-0.04145260900259018,
-0.03306956589221954,
-0.012518642470240593,
0.028835417702794075,
0.00941518135368824,
-0.027150150388479233,
-0.0085500068962574,
0.03204764425754547,
-0.06938088685274124,
0.013947835192084312,
-0.03340587392449379,
-0.029894601553678513,
-0.034984342753887177,
-0.03650682419538498,
-0.004088187124580145,
0.05336179956793785,
0.03205987066030502,
0.03764251247048378,
0.027664780616760254,
0.01596066728234291,
-0.008418642915785313,
-0.06953441351652145,
-0.0253591388463974,
0.03523937985301018,
0.010126289911568165,
-0.037716612219810486,
0.047616127878427505,
-0.019246673211455345,
-0.006973675452172756,
0.04276625066995621,
0.0032388358376920223,
0.03782001510262489,
-0.016603941097855568,
0.03271210193634033,
0.020205708220601082,
0.05626920238137245,
-0.0026544982101768255,
0.029127854853868484,
-0.020765528082847595,
-0.0018500868463888764,
0.04682547226548195,
0.003865049220621586,
0.004567132797092199,
0.024780064821243286,
0.06959138810634613,
-0.01033612061291933,
-0.052056923508644104,
-0.009765255264937878,
-0.01490976195782423,
0.01964528299868107,
0.006183220073580742,
0.006976036820560694,
-0.0010665347799658775,
-0.04282229393720627,
0.010159921832382679,
-0.06127617135643959,
0.03971882909536362,
0.038182489573955536,
-0.004506244324147701,
0.002020658692345023,
-0.0038413689471781254,
-0.029101431369781494,
-0.03463100641965866,
0.026014156639575958,
0.008592866361141205,
0.030565686523914337,
-0.060969892889261246,
-0.005269880406558514,
0.008730757050216198,
0.03407466411590576,
0.06272345036268234,
-0.039622388780117035,
-0.10386493057012558,
0.029696565121412277,
0.022558702155947685,
0.03765691816806793,
-0.014683938585221767,
-0.048098158091306686,
0.01627201773226261,
-0.055162157863378525,
0.004673324059695005,
-0.014707252383232117,
-0.022050628438591957,
-0.034812383353710175,
-0.055106427520513535,
-0.0192630123347044,
0.006558961700648069,
0.0501079224050045,
-0.0008989808848127723,
0.006834367755800486,
-0.00377520895563066,
0.02388954348862171,
0.0005229159723967314,
-0.09816809743642807,
-0.04789803549647331,
0.020375164225697517,
-0.018579784780740738,
0.0020863856188952923,
-0.00818598736077547,
-0.0359790101647377,
-0.011278257705271244,
0.01881237141788006,
0.02569509856402874,
-0.003604855388402939,
-0.008745286613702774,
-0.05222233012318611,
0.03624758496880531,
-0.003286378225311637,
-0.017418086528778076,
0.06080411747097969,
-0.007605729158967733,
0.028820093721151352,
0.01665966585278511,
-0.020010951906442642,
-0.0001250795612577349,
-0.006862661801278591,
-0.04357600212097168,
0.0062934765592217445,
-0.03985009342432022,
-0.01620752178132534,
0.07618700712919235,
-0.028279444202780724,
0.002120145596563816,
0.06297945976257324,
-0.047833312302827835,
0.0017656630370765924,
0.05964428186416626,
0.00834672525525093,
0.025897182524204254,
0.007792184595018625,
0.020529069006443024,
0.010436766780912876,
-0.04222382605075836,
-0.014440120197832584,
0.04093693196773529,
0.036924757063388824,
0.012091132812201977,
0.00821735244244337,
0.056831348687410355,
0.00321928015910089,
0.013054566457867622,
0.00910628866404295,
0.018933363258838654,
-0.015097791329026222,
-0.024802615866065025,
-0.0026151190977543592,
-0.032561011612415314,
-0.007289585191756487,
-0.003754087258130312,
-0.01890559121966362,
0.08289288729429245,
-0.051898691803216934,
0.0316820964217186,
0.00575809134170413,
-0.010618737898766994,
-0.019176172092556953,
0.025945207104086876,
-0.010022321715950966,
0.03198087960481644,
-0.010843698866665363,
0.001980574568733573,
-0.019455786794424057,
0.008083069697022438,
0.008439288474619389,
-0.06764382869005203,
-0.017649168148636818,
0.03337903693318367,
-0.020134223625063896,
0.009347451850771904,
-0.03635618835687637,
-0.022974131628870964,
-0.028358636423945427,
0.019617464393377304,
-0.004548972938209772,
-0.017148688435554504,
0.00028075213776901364,
-0.02526603639125824,
-0.03810827434062958,
0.05909726768732071,
-0.02952413819730282,
-0.009319854900240898,
-0.020211897790431976,
0.01618601754307747,
-0.0376337468624115,
-0.049772053956985474
] |
<p>I wish to find an everyday situation that illustrates the following:</p>
<p>A rod is moving in a direction perpendicular to its axis. One end "gets caught" and the rod starts rotating around this end. THE SPEED OF THE OTHER END OF THE ROD WILL THEN INCREASE BY A FACTOR SQRT(3).</p>
<p>Here is an <a href="https://www.dropbox.com/s/71wk7k6y79wvekz/DSC_0154.JPG" rel="nofollow">illustration</a>.</p>
<p>Can someone please think of a simple situation in everyday life that illustrates this transition from translation to rotation. Of course it is not needed to see the increase in speed, but just a situation where you could ask a student what speed the rotating object will have. (Just rods flying through the air is not what you see every day.)</p>
<p>If the situation is free of gravity (moving horizontally), it would be a better illustration, I believe.</p>
<p>(A related situation, but too complex and different is if you sit on the top of a telegraph pole. If the pole breaks at the bottom you will suffer less injury (theoretically) if you jump off the pole immediately rather than going down with it. (Speed less by a factor sqrt(1.5) I believe.))</p>
<p>A pair of ice skaters meeting with speed and taking each others hands and starting to rotate together would resemble the situation a little. But the mass of the skaters is concentrated to their bodies and the only thing accelerating would be their hands if they held them out.</p>
<p>(The classical illustration of a skater making a pirouette by pulling in the arms will not help here, of course.)</p>
<p>Thanks</p> | 2,004 | [
-0.04038146510720253,
-0.030125871300697327,
-0.02695617824792862,
-0.0035844645462930202,
0.016626713797450066,
-0.021358991041779518,
-0.011736098676919937,
-0.015381697565317154,
0.015138457529246807,
0.021097056567668915,
0.02693035639822483,
0.06238299980759621,
0.0449213869869709,
0.046963851898908615,
-0.0023384287487715483,
0.042402975261211395,
-0.000002405606210231781,
-0.03201394900679588,
-0.022735629230737686,
-0.030063427984714508,
0.004787365440279245,
-0.00001073439034371404,
0.0013005627552047372,
0.01967189833521843,
-0.020819200202822685,
0.009780916385352612,
0.017660049721598625,
-0.02176435850560665,
-0.013917671516537666,
0.023520980030298233,
-0.02257773093879223,
0.01331985741853714,
0.02192775346338749,
-0.0013389665400609374,
0.018657227978110313,
0.05708304047584534,
-0.030134808272123337,
0.017987484112381935,
0.004652953706681728,
0.0230623297393322,
-0.028656071051955223,
0.015166436322033405,
-0.04181245341897011,
0.03362710773944855,
-0.020709974691271782,
0.055879171937704086,
-0.00011880842066602781,
-0.032256659120321274,
0.0674700140953064,
-0.026221726089715958,
0.06739680469036102,
-0.004754476714879274,
-0.008402695879340172,
-0.03528355062007904,
-0.006085377186536789,
-0.016023630276322365,
0.0638265311717987,
0.03346797823905945,
-0.02715032361447811,
-0.04763779416680336,
-0.05121634155511856,
-0.040853045880794525,
-0.03818662837147713,
-0.04211702570319176,
0.006575983017683029,
0.027892258018255234,
-0.027184508740901947,
-0.009347769431769848,
0.01100004743784666,
0.0037107288371771574,
-0.015630969777703285,
0.03020627796649933,
0.05349360778927803,
0.019509147852659225,
-0.014509140513837337,
-0.002757817506790161,
0.013635851442813873,
-0.011419267393648624,
0.04918023943901062,
0.05389195308089256,
-0.044994138181209564,
-0.00450173718854785,
0.0648287683725357,
0.023798367008566856,
0.018348153680562973,
-0.01591900736093521,
0.07282077521085739,
0.022158898413181305,
-0.003557621967047453,
0.07342275232076645,
-0.00767097482457757,
-0.030128933489322662,
0.004152840003371239,
-0.02033298835158348,
-0.00968021061271429,
-0.0015478315763175488,
-0.004699530079960823,
0.044672876596450806,
0.02352578192949295,
0.010225140489637852,
-0.01481108833104372,
-0.0187178123742342,
0.009330511093139648,
0.05381940305233002,
0.010661935433745384,
-0.025861814618110657,
-0.026126164942979813,
-0.001266508479602635,
-0.0320725254714489,
-0.019807890057563782,
-0.02106938324868679,
0.016208073124289513,
-0.020200274884700775,
0.005123696755617857,
-0.04448099061846733,
-0.02183864824473858,
0.0005513128126040101,
0.00723141198977828,
0.08684365451335907,
0.04946494847536087,
0.0857064425945282,
-0.03344646096229553,
0.009306193329393864,
-0.027302298694849014,
-0.03202233090996742,
0.06029056757688522,
0.007473149336874485,
-0.026867767795920372,
-0.021794719621539116,
0.024964410811662674,
-0.0006854521343484521,
0.009173124097287655,
0.018383635208010674,
-0.03371923789381981,
0.011863290332257748,
-0.020041214302182198,
-0.059950537979602814,
-0.053919717669487,
0.06095458194613457,
0.04250715300440788,
-0.014635908417403698,
-0.1214161291718483,
0.020222237333655357,
0.017005309462547302,
0.0838145911693573,
0.04250059276819229,
-0.002042704727500677,
-0.026717226952314377,
0.008862419053912163,
-0.0007247590110637248,
-0.009397199377417564,
0.010535823181271553,
0.019780155271291733,
-0.05184516683220863,
-0.009288172237575054,
-0.05631345883011818,
-0.0039262897334992886,
0.05608198046684265,
-0.013514352962374687,
-0.016980139538645744,
-0.012607686221599579,
-0.03958328440785408,
0.01041458174586296,
-0.005162148270756006,
-0.0029268928337842226,
0.009694189764559269,
0.06093424931168556,
-0.0020281916949898005,
-0.059437915682792664,
0.012117412872612476,
0.043780386447906494,
0.05343250185251236,
-0.0033928779885172844,
-0.005932495463639498,
0.06242051720619202,
-0.015350649133324623,
0.0248798169195652,
0.006656089331954718,
-0.026963144540786743,
-0.006506618577986956,
0.003102809889242053,
-0.049640629440546036,
-0.02826489508152008,
0.0004154327907599509,
0.004063201602548361,
0.07532830536365509,
0.006997434888035059,
0.03502589836716652,
0.018699636682868004,
-0.02869323454797268,
-0.023153655230998993,
-0.03183334320783615,
0.03448132798075676,
-0.006465265993028879,
-0.0018903337186202407,
0.0015544961206614971,
0.00442085787653923,
0.04276685789227486,
-0.06180891394615173,
-0.0011735124280676246,
0.020396092906594276,
-0.005126630887389183,
0.017280733212828636,
-0.027579061686992645,
-0.026604769751429558,
0.04224839434027672,
0.010631483048200607,
-0.01865304447710514,
-0.03037814237177372,
-0.01888345181941986,
0.03441132232546806,
-0.013008847832679749,
-0.029728442430496216,
-0.005605282261967659,
0.03331721946597099,
0.03922140598297119,
0.022814322263002396,
-0.017122408375144005,
-0.008559350855648518,
0.03245063126087189,
-0.021877018734812737,
0.06335033476352692,
0.03171377256512642,
-0.01024158950895071,
0.028836054727435112,
0.02628805860877037,
0.025106696411967278,
-0.018826907500624657,
-0.00033864632132463157,
-0.05205751210451126,
-0.03323822841048241,
0.0037972629070281982,
0.03220105171203613,
0.043244536966085434,
-0.0475330725312233,
-0.004395562224090099,
0.06727466732263565,
0.02252369187772274,
0.02407083846628666,
0.019269252195954323,
-0.005486511159688234,
-0.0312240868806839,
0.015276117250323296,
0.012865099124610424,
-0.009522763080894947,
-0.001624765107408166,
0.011332410387694836,
0.00975490640848875,
-0.0031752297654747963,
0.047378312796354294,
-0.0496809221804142,
-0.034830763936042786,
0.018801162019371986,
0.04762498661875725,
0.008077366277575493,
-0.0006527272635139525,
0.04593261331319809,
-0.00799714494496584,
0.021814072504639626,
0.0502888485789299,
-0.016248030588030815,
0.015104909427464008,
-0.01979704014956951,
0.013080102391541004,
0.015466736629605293,
-0.0010633558267727494,
-0.0052488320507109165,
-0.004296306055039167,
0.03625166416168213,
-0.05635401979088783,
-0.044196177273988724,
-0.014047949574887753,
-0.016430368646979332,
-0.016449134796857834,
-0.0026073118206113577,
0.0018897487316280603,
0.032828669995069504,
0.05709823966026306,
-0.048113781958818436,
-0.021349171176552773,
-0.00451862346380949,
-0.010440005920827389,
0.006656918674707413,
0.017484253272414207,
-0.04147456958889961,
0.03875696659088135,
-0.01995282992720604,
-0.04817793518304825,
0.07061276584863663,
-0.009615984745323658,
-0.017447935417294502,
0.037307918071746826,
-0.00864084716886282,
-0.04083804413676262,
0.0027152509428560734,
-0.015894392505288124,
0.0006040536100044847,
-0.01708192378282547,
-0.009571637026965618,
0.05096643045544624,
-0.027564499527215958,
-0.03522677719593048,
0.0059548672288656235,
-0.05571337416768074,
-0.04801647737622261,
-0.04487626254558563,
0.03269294649362564,
0.01899922825396061,
-0.02114458568394184,
-0.010418606922030449,
-0.0061365757137537,
0.02460317313671112,
0.015611591748893261,
-0.05900997668504715,
-0.03659503906965256,
-0.012707021087408066,
0.03175083175301552,
0.04262770339846611,
-0.0041241636499762535,
-0.05581698566675186,
0.08855221420526505,
0.003642193041741848,
-0.047414179891347885,
-0.03888123482465744,
0.007086438592523336,
-0.004911038093268871,
-0.03268267214298248,
0.011572628282010555,
0.042161256074905396,
-0.04037173464894295,
0.011475346982479095,
-0.0046766879968345165,
0.040420591831207275,
0.05192609503865242,
0.026962662115693092,
0.01965978741645813,
0.009409492835402489,
-0.006579037755727768,
0.008719143457710743,
0.03633976727724075,
0.022473091259598732,
-0.036312736570835114,
0.03398501127958298,
-0.019593490287661552,
0.00533292256295681,
0.017508501186966896,
-0.057911865413188934,
0.05527173727750778,
0.008173374459147453,
-0.026037679985165596,
0.012235887348651886,
0.023229116573929787,
0.01842908374965191,
-0.02331053651869297,
-0.002791588893160224,
0.05654838681221008,
0.05412248894572258,
0.0020194819662719965,
0.007566962856799364,
0.03477580472826958,
0.03944000229239464,
-0.0018825021106749773,
-0.024897927418351173,
-0.019133836030960083,
0.019055509939789772,
0.03741699829697609,
-0.04147439822554588,
-0.0016637000953778625,
0.016664855182170868,
0.000698786461725831,
-0.024271786212921143,
-0.021166935563087463,
-0.006619025021791458,
0.03206026554107666,
-0.06565646082162857,
-0.032873380929231644,
-0.016832733526825905,
0.03686532750725746,
0.02488257922232151,
0.047969717532396317,
0.01078362949192524,
0.034828394651412964,
-0.011959743686020374,
0.014307188801467419,
-0.08574408292770386,
0.02106313966214657,
-0.021970193833112717,
-0.01109329704195261,
0.032093215733766556,
0.028019163757562637,
-0.026851868256926537,
-0.016639048233628273,
-0.014474296011030674,
-0.004364083055406809,
0.022912267595529556,
-0.03905205428600311,
-0.006237882189452648,
0.019138921052217484,
-0.039017077535390854,
-0.005050708074122667,
0.026427756994962692,
0.055273354053497314,
-0.0324263758957386,
0.03767455369234085,
0.020486963912844658,
-0.005767085123807192,
-0.0033845833968371153,
-0.01608695276081562,
0.014289801940321922,
-0.0008178738644346595,
0.022632893174886703,
0.020026210695505142,
-0.004403179045766592,
-0.011618736200034618,
0.04522327706217766,
-0.004390943795442581,
0.0011723671341314912,
0.012503627687692642,
0.008327932097017765,
-0.0161875132471323,
-0.039791665971279144,
-0.020658697932958603,
-0.029926124960184097,
0.026242103427648544,
-0.023312147706747055,
0.004838763736188412,
-0.012480411678552628,
0.0013235616497695446,
0.024116531014442444,
0.017589876428246498,
0.06942857801914215,
0.007285538595169783,
-0.016061855480074883,
-0.06324868649244308,
-0.07121146470308304,
-0.018233198672533035,
-0.010174513794481754,
0.029421700164675713,
0.012884961441159248,
0.008898655883967876,
-0.01207250077277422,
0.02267145738005638,
0.03697757050395012,
-0.0062447222881019115,
0.045912206172943115,
-0.014268523082137108,
0.02429685741662979,
-0.017672833055257797,
-0.013963015750050545,
0.005324090365320444,
0.017611432820558548,
0.050667088478803635,
0.0005466666771098971,
0.0016046013915911317,
-0.03832051157951355,
-0.026346033439040184,
0.025728708133101463,
0.03405192494392395,
-0.008661879226565361,
0.0193534716963768,
-0.043799955397844315,
-0.022526655346155167,
0.029479248449206352,
-0.03718062862753868,
0.012315436266362667,
-0.03966004028916359,
0.019536666572093964,
-0.037132155150175095,
-0.050498299300670624,
-0.044335540384054184,
0.010317149572074413,
-0.02089053951203823,
-0.0036439429968595505,
-0.03367472067475319,
-0.02180677279829979,
0.023229587823152542,
0.005075694527477026,
0.056000035256147385,
0.02962607517838478,
0.016737116500735283,
-0.038984328508377075,
-0.009668251499533653,
0.024727899581193924,
-0.06463515013456345,
-0.0723707526922226,
0.04043113812804222,
-0.005323098972439766,
0.0060474141500890255,
0.004128813743591309,
-0.05736742541193962,
-0.053066689521074295,
-0.021946601569652557,
-0.02592993900179863,
-0.001985869137570262,
0.02833990752696991,
-0.035025957971811295,
0.029017167165875435,
0.06455563008785248,
-0.0010885059600695968,
0.011061766184866428,
0.03582852706313133,
-0.01362912543118,
-0.007362881675362587,
0.003917129244655371,
0.03738240525126457,
0.00755369383841753,
-0.008009606972336769,
-0.027503598481416702,
0.015381568111479282,
-0.01995304971933365,
0.06763215363025665,
-0.014865990728139877,
0.03892035409808159,
-0.026865273714065552,
-0.045009128749370575,
-0.01062979456037283,
-0.0024081054143607616,
0.014572212472558022,
-0.04439021274447441,
0.0055325753055512905,
-0.010103021748363972,
0.018694354221224785,
-0.016500266268849373,
0.020308105275034904,
-0.013658255338668823,
0.0050859954208135605,
0.02412651851773262,
-0.005035221576690674,
0.0034971139393746853,
-0.032877661287784576,
-0.02866157330572605,
-0.031114712357521057,
-0.06957568228244781,
0.06234796717762947,
-0.03181910514831543,
0.03278043866157532,
-0.005095203407108784,
-0.016380824148654938,
-0.01250305026769638,
0.01804952509701252,
-0.004863178823143244,
-0.004230164922773838,
-0.04732286557555199,
-0.018534692004323006,
-0.014334450475871563,
0.01612618751823902,
0.0008881569956429303,
-0.04742042347788811,
0.049791283905506134,
0.005638929083943367,
0.004782349336892366,
-0.025257837027311325,
-0.05304770544171333,
-0.027690917253494263,
-0.05743252858519554,
0.006120298523455858,
0.05747847631573677,
-0.03843437507748604,
-0.0032873153686523438,
0.019702846184372902,
0.004426882602274418,
0.0701923593878746,
-0.029870791360735893,
-0.015367025509476662,
0.0035013407468795776,
-0.009958644397556782,
-0.03633827716112137,
0.016464337706565857,
0.07268722355365753,
-0.03782719746232033,
-0.024763379245996475,
-0.013373691588640213,
-0.022197306156158447,
0.021863844245672226,
0.013227967545390129,
0.0012892208760604262,
0.0055948602966964245,
-0.004344967659562826,
0.026900121942162514,
-0.015536626800894737,
0.05556640401482582,
0.04987324774265289,
0.02279847115278244,
0.010305438190698624,
0.03762752190232277,
-0.015463066287338734,
-0.03822382166981697,
-0.0026649744249880314,
0.03907638415694237,
-0.0004945464315824211,
-0.016318172216415405,
0.05562357231974602,
-0.03343433514237404,
-0.020450562238693237,
0.02826940454542637,
-0.012653214856982231,
0.07610660046339035,
0.006249271333217621,
-0.007318681571632624,
0.013563047163188457,
0.01626991294324398,
-0.01754818856716156,
-0.033527832478284836,
-0.025476984679698944,
-0.00599647406488657,
0.03622235730290413,
-0.029182802885770798,
0.07826724648475647,
0.029117640107870102,
-0.0025923592038452625,
0.0021230520214885473,
0.008224970661103725,
-0.008724243380129337,
0.0017076610820367932,
-0.0175793394446373,
0.021883737295866013,
-0.03806320205330849,
0.027400165796279907,
0.062319692224264145,
0.054449692368507385,
0.006990979891270399,
0.012797001749277115,
0.0316675528883934,
0.0031203264370560646,
0.034829892218112946,
-0.045550864189863205,
-0.03774454817175865,
0.009201236069202423,
-0.021179355680942535,
0.07309932261705399,
-0.014842945151031017,
-0.013010596856474876,
0.07356653362512589,
-0.000991030945442617,
-0.0030415623914450407,
-0.04152337461709976,
0.009883123449981213,
-0.02778162993490696,
-0.026409892365336418,
-0.0007834277348592877,
-0.03418693691492081,
-0.024685455486178398,
-0.018859457224607468,
0.06807906180620193,
-0.03399370238184929,
0.050146084278821945,
-0.05310749262571335,
-0.04185003042221069,
-0.019544214010238647,
-0.03633234649896622,
-0.043448466807603836,
0.04772249981760979,
0.00554816285148263,
-0.012405665591359138,
0.01310422271490097,
-0.025298502296209335,
-0.011425617150962353,
0.009544989094138145,
0.028145192191004753,
-0.012004587799310684,
0.10295400768518448,
-0.00542296189814806,
-0.004812084138393402,
-0.013985546305775642,
0.02727927826344967,
0.14842374622821808,
0.033413540571928024,
0.012938526459038258,
0.010874313302338123,
0.008153613656759262,
-0.047195229679346085,
0.012042195536196232,
-0.0013239391846582294,
-0.006445781327784061,
0.008035504259169102,
0.006438765209168196,
0.021882550790905952,
0.06969054043292999,
0.03433210402727127,
-0.021964596584439278,
0.026653049513697624,
-0.04178033024072647,
0.01491631381213665,
-0.03072955273091793,
0.0077768974006175995,
-0.004694776143878698,
0.0035379924811422825,
-0.0044069536961615086,
0.0448225699365139,
-0.008143559098243713,
-0.0036579701118171215,
-0.026770172640681267,
-0.031951822340488434,
0.03902231156826019,
-0.014865746721625328,
-0.06088341772556305,
0.054351262748241425,
0.04868659749627113,
-0.03750567138195038,
-0.03361067548394203,
0.02156568504869938,
0.008811377920210361,
-0.014700187370181084,
0.005692385137081146,
0.05409150943160057,
-0.005027216859161854,
0.015799473971128464,
0.018828844651579857,
0.010861080139875412,
-0.055081579834222794,
-0.004281114786863327,
-0.05681822821497917,
0.024940751492977142,
0.005497507285326719,
0.026718635112047195,
-0.008610530756413937,
0.016525529325008392,
0.005240509752184153,
-0.05850622057914734,
-0.018107101321220398,
-0.0026025932747870684,
0.016072196885943413,
0.012954003177583218,
0.012190711684525013,
-0.019760146737098694,
0.014715737663209438,
0.006821822840720415,
0.011684705503284931,
0.04692455381155014,
-0.011981276795268059,
-0.014469512738287449,
0.009428741410374641,
0.045138631016016006,
-0.01070169173181057,
0.0036403555423021317,
-0.0056096469052135944,
0.011730031110346317,
-0.0314301922917366,
0.025614552199840546,
-0.004675616975873709,
-0.0009019425488077104,
0.02893167920410633,
-0.015377546660602093,
-0.04657477140426636,
-0.02845531515777111,
0.0055345636792480946,
0.02437109313905239,
0.00001609463470231276,
-0.043793436139822006,
-0.020913081243634224,
-0.01391543447971344,
-0.007126305252313614,
0.013971499167382717,
-0.046895526349544525,
-0.03084534965455532,
-0.009532579220831394,
0.06917184591293335,
0.02294960990548134,
-0.0035077459178864956,
-0.024041535332798958,
-0.0006294084596447647,
-0.007520643062889576,
0.00019313758821226656,
0.012745683081448078,
0.06494160741567612,
0.03684230521321297,
-0.02716020867228508,
0.01330251432955265,
-0.021833837032318115,
-0.009128683246672153,
0.017051909118890762,
0.022974688559770584,
-0.0397392213344574,
-0.021194100379943848,
0.017679650336503983,
-0.0017006221460178494,
-0.017631426453590393,
-0.0019497823668643832,
-0.00577158946543932,
-0.007392283529043198,
-0.04975906014442444,
0.0548035092651844,
-0.002876955782994628,
0.0659422054886818,
-0.045150358229875565,
0.028682680800557137,
-0.023603422567248344,
0.00940944068133831,
-0.030064549297094345,
-0.013475652784109116,
0.027723142877221107,
0.003141755936667323,
-0.01875077188014984,
0.04777960106730461,
0.011313267983496189,
0.010821516625583172,
-0.00799142848700285,
-0.0014964075526222587,
-0.006390618160367012,
-0.01821024715900421,
0.006113424431532621,
-0.017275001853704453,
0.020936595275998116,
-0.028732530772686005,
-0.027493178844451904,
0.023800529539585114,
-0.03173712641000748,
-0.009702693670988083,
0.02622336335480213,
-0.028584476560354233,
0.05125261843204498,
-0.03081471100449562,
-0.023389670997858047,
-0.007038125768303871,
0.0638214498758316,
-0.0006999856559559703,
-0.024662433192133904,
0.006589640397578478,
-0.00832056999206543,
-0.025070782750844955,
-0.02984938770532608,
0.0035725198686122894,
-0.03701072931289673,
-0.002465713769197464,
0.034516166895627975,
0.03689165040850639,
-0.047975972294807434,
0.019662868231534958,
0.011423456482589245,
-0.02310139499604702,
-0.028013138100504875,
0.005421714391559362,
0.0095708342269063,
0.03735889494419098,
0.027673248201608658,
-0.03435797989368439,
0.0015992457047104836,
-0.022556250914931297,
-0.0009102873154915869,
-0.09511180967092514,
-0.015000076033174992,
0.002416368806734681,
0.007519164122641087,
0.04934116080403328,
-0.06209886446595192,
0.0021451921202242374,
0.04248384013772011,
-0.08688625693321228,
0.011539204977452755,
-0.04562247171998024,
-0.018633229658007622,
-0.045758530497550964,
-0.055862605571746826,
0.018905969336628914,
0.0468829870223999,
0.0006486866041086614,
0.04563203081488609,
0.024622052907943726,
0.03881584107875824,
-0.02958463877439499,
-0.02143355831503868,
0.036003001034259796,
0.028554627671837807,
-0.020296581089496613,
-0.028236787766218185,
0.05725247040390968,
-0.004730819724500179,
0.0034916342701762915,
0.02918284758925438,
-0.028864184394478798,
0.024440119042992592,
0.005762697197496891,
0.0035712863318622112,
-0.009173496626317501,
0.013189056888222694,
-0.04356493055820465,
-0.025877991691231728,
-0.027713848277926445,
0.02422911487519741,
-0.0068015665747225285,
0.04410567879676819,
-0.023623859509825706,
0.006737540476024151,
0.031210286542773247,
-0.04626009240746498,
-0.03162277117371559,
-0.010754445567727089,
-0.017385199666023254,
-0.022897869348526,
0.028568437322974205,
-0.003697626991197467,
0.004083049017935991,
-0.021399980410933495,
0.011310658417642117,
-0.0017338270554319024,
0.013055787421762943,
0.0034070645924657583,
-0.017984995618462563,
0.0053300997242331505,
0.021621879190206528,
-0.004568301606923342,
0.006671906914561987,
-0.039101991802453995,
-0.024616848677396774,
-0.025891732424497604,
-0.039806585758924484,
-0.008511250838637352,
0.010354061610996723,
-0.02135091833770275,
-0.02006632648408413,
-0.029931021854281425,
0.00849988218396902,
0.018658842891454697,
0.010524814948439598,
0.015042589977383614,
0.05552492290735245,
0.015426360070705414,
-0.033893752843141556,
-0.07929521799087524,
0.01154214795678854,
0.015987446531653404,
-0.0011864827247336507,
-0.03891562297940254,
-0.01930287852883339,
-0.029333356767892838,
0.019611870869994164,
0.05863667279481888,
-0.03077210672199726,
0.0036112007219344378,
0.025744926184415817,
-0.010868169367313385,
-0.0014513633213937283,
-0.03123440220952034,
-0.008911995217204094,
-0.018835779279470444,
-0.009378240443766117,
0.026793338358402252,
0.025161437690258026,
0.03266485035419464,
-0.026190297678112984,
0.0034271408803761005,
0.016658158972859383,
0.028634002432227135,
0.025506142526865005,
-0.02739737741649151,
0.0014684679917991161,
0.03375278413295746,
-0.0047400291077792645,
0.03924422711133957,
-0.011128933168947697,
-0.01844906248152256,
-0.006460716016590595,
-0.049311649054288864,
-0.0743412896990776,
0.08369890600442886,
-0.020242612808942795,
0.010571231134235859,
0.005107578355818987,
-0.04661759361624718,
-0.008914895355701447,
-0.05670003965497017,
0.04174387827515602,
-0.002948863198980689,
-0.0364861935377121,
-0.01670585200190544,
-0.007875798270106316,
0.04369114711880684,
0.06080789864063263,
-0.04740295931696892,
0.007428141310811043,
0.00042863585986196995,
-0.032771456986665726,
-0.018448393791913986,
-0.013126729987561703,
0.017320428043603897,
0.006006741896271706,
0.013698572292923927,
0.022716820240020752,
-0.024399150162935257,
0.018210511654615402,
0.02372109331190586,
0.02473302371799946,
0.010493038222193718,
-0.014363085851073265,
0.01542622409760952,
-0.04096013307571411,
-0.00725227827206254,
0.047874171286821365,
0.0024620795156806707,
0.04279518872499466,
0.00214967830106616,
0.015323597937822342,
0.009820337407290936,
0.020041780546307564,
-0.024051886051893234,
-0.03831583261489868,
0.011475260369479656,
0.023098446428775787,
-0.027819184586405754,
-0.03001178242266178,
-0.018865613266825676,
-0.025123408064246178,
0.011465328745543957,
0.023196764290332794,
0.0483272522687912,
0.018214872106909752,
0.00027362024411559105,
0.00940532423555851,
-0.035518936812877655,
-0.03367751091718674,
-0.009107697755098343,
0.05606944113969803,
0.019859008491039276,
0.03940483182668686,
-0.010277172550559044,
-0.02107551321387291,
-0.0007604022393934429,
0.04679461941123009,
-0.07412151247262955,
-0.020005544647574425,
0.0014527183957397938,
0.06657097488641739,
0.03199049085378647,
0.01208396628499031
] |
<p>I have studied about the two types of doping which result in p and n type semiconductors. I also came to know that they are neutral. But, how can it be? </p>
<p>Is it that the positive charge(holes) in p-type and negative charge in n-type are negligibly small to affect the overall neutrality of the substance? But, in that case with very few holes or negative charges how can semiconductors work the way it actually does? </p>
<p>So, I think there is another possible explanation and I would like to know the correct one. </p> | 2,005 | [
-0.008849428035318851,
-0.017732858657836914,
0.0029956467915326357,
-0.030055837705731392,
0.022167304530739784,
0.01886727660894394,
-0.007896721363067627,
-0.0101905707269907,
-0.02719893492758274,
-0.05255172774195671,
0.031254712492227554,
0.0017660495359450579,
-0.012287185527384281,
0.05112844333052635,
-0.026175566017627716,
0.0030232840217649937,
-0.009716683998703957,
-0.02255362831056118,
-0.051820866763591766,
-0.00004538913708529435,
0.00022224946587812155,
0.03531308472156525,
-0.01888658106327057,
0.013661135919392109,
-0.030329613015055656,
0.008378028869628906,
-0.008874250575900078,
-0.009039721451699734,
0.044404640793800354,
0.05963698402047157,
0.002314480487257242,
-0.016758298501372337,
-0.0015699575887992978,
-0.012907231226563454,
0.013740373775362968,
-0.019356943666934967,
-0.012135446071624756,
-0.05995769053697586,
-0.020868495106697083,
0.029983047395944595,
-0.008737714029848576,
0.023581234738230705,
0.02385600283741951,
-0.0012139384634792805,
-0.021118823438882828,
-0.0035547418519854546,
0.04520529508590698,
-0.020962895825505257,
0.011067288927733898,
-0.10272977501153946,
0.017211133614182472,
-0.025287481024861336,
0.05247250944375992,
0.012660893611609936,
-0.011760983616113663,
-0.015454117208719254,
0.07958215475082397,
0.06992035359144211,
-0.0277188029140234,
-0.03552325814962387,
0.025884069502353668,
-0.019376395270228386,
-0.0003488900838419795,
-0.034372299909591675,
-0.029222486540675163,
-0.011624671518802643,
0.0213931854814291,
-0.0608302503824234,
0.034702036529779434,
-0.008226980455219746,
0.04444093629717827,
0.007292909547686577,
-0.0005463436245918274,
-0.007154899649322033,
0.029286867007613182,
-0.03717502951622009,
0.04787500202655792,
0.022317195311188698,
0.016723189502954483,
0.04263246804475784,
-0.02196091040968895,
0.016217205673456192,
0.02639888785779476,
0.01792101003229618,
0.0011993966763839126,
-0.04701187461614609,
0.07900800555944443,
-0.008024127222597599,
0.01271933875977993,
0.019006460905075073,
-0.0141720250248909,
0.002421720651909709,
0.054821912199258804,
-0.014012801460921764,
-0.05746321380138397,
0.015091328881680965,
-0.00144938041921705,
0.05415669083595276,
0.013200007379055023,
-0.0009525908972136676,
0.016315674409270287,
0.005685401149094105,
0.060344990342855453,
0.053120411932468414,
-0.03165313974022865,
-0.043747544288635254,
-0.030823618173599243,
0.00693969102576375,
-0.02255256474018097,
0.026058809831738472,
-0.02249947190284729,
0.00537009397521615,
-0.008733364753425121,
-0.0009691637824289501,
0.02440847083926201,
-0.027090629562735558,
-0.014678466133773327,
-0.045692652463912964,
0.02614562399685383,
0.04703648015856743,
-0.015512402169406414,
-0.037182778120040894,
0.03598175570368767,
0.013161287643015385,
-0.0634937584400177,
0.031058581545948982,
0.009257407858967781,
0.013112522661685944,
-0.014793423004448414,
-0.012192408554255962,
-0.0004583770933095366,
0.0029844448436051607,
0.0254827830940485,
0.010254334658384323,
0.07301588356494904,
0.029006095603108406,
-0.0798070877790451,
-0.06756383180618286,
0.03912902995944023,
-0.03628193214535713,
-0.0067405239678919315,
-0.07788629084825516,
-0.007884202525019646,
0.02404513768851757,
0.0624137781560421,
-0.02092776447534561,
-0.011780258268117905,
0.0030027981847524643,
0.020247822627425194,
0.04708943888545036,
0.012441282160580158,
-0.02693045511841774,
0.008734411559998989,
-0.013018115423619747,
0.010475597344338894,
-0.08863736689090729,
0.0658845603466034,
0.006318359635770321,
0.019366227090358734,
-0.036514803767204285,
0.037498220801353455,
-0.01370945293456316,
-0.03463933989405632,
0.007002655882388353,
-0.02631876990199089,
-0.02762584201991558,
0.08946878463029861,
0.012345113791525364,
0.03860132396221161,
0.03421524539589882,
-0.025481602177023888,
0.04713675007224083,
0.029486840590834618,
0.043715499341487885,
0.00047183301649056375,
-0.02464265748858452,
-0.0444638691842556,
-0.05173764377832413,
0.051452577114105225,
-0.018084298819303513,
-0.0648665651679039,
-0.006945732515305281,
-0.0039043959695845842,
0.03174201771616936,
0.01126096025109291,
0.025970790535211563,
0.013602709397673607,
0.004118907265365124,
0.035782892256975174,
-0.05151708051562309,
-0.015918366611003876,
-0.0793536901473999,
0.01002910640090704,
0.0008374775061383843,
-0.05394527688622475,
0.05688674747943878,
-0.0009671692969277501,
-0.02005465142428875,
-0.026845352724194527,
-0.005728480406105518,
-0.015057235956192017,
0.020307466387748718,
0.011478886008262634,
-0.020626571029424667,
0.02267083153128624,
0.06161119416356087,
0.01360216923058033,
0.024446895346045494,
0.03584107756614685,
0.021830298006534576,
-0.02351633831858635,
0.03368900343775749,
-0.0364796444773674,
0.016437947750091553,
0.017705639824271202,
-0.0029014574829488993,
0.018474889919161797,
-0.014311984181404114,
0.001162202563136816,
0.029955074191093445,
-0.04765316843986511,
0.06739760935306549,
0.04028208553791046,
-0.02129684016108513,
-0.007290058769285679,
0.02453160285949707,
-0.019614096730947495,
0.018457848578691483,
0.005995596293359995,
-0.015169874764978886,
-0.05751412361860275,
-0.016012566164135933,
0.04347100481390953,
0.040781229734420776,
-0.006458126474171877,
-0.009617126546800137,
-0.0007048081024549901,
0.008175063878297806,
0.022110113874077797,
0.0448765866458416,
-0.019530421122908592,
-0.027370251715183258,
0.04173837974667549,
0.0005137069383636117,
0.0014875144697725773,
0.05489354580640793,
0.021673662588000298,
-0.02813105843961239,
0.027873966842889786,
-0.03542381152510643,
-0.0326557494699955,
0.038695260882377625,
0.059677306562662125,
0.03594105318188667,
0.025604143738746643,
-0.0428018681704998,
0.00559459300711751,
0.000222883332753554,
0.02070380188524723,
-0.0004957247874699533,
-0.00026612976216711104,
-0.0021388025488704443,
-0.011825088411569595,
-0.017895499244332314,
0.03038397990167141,
0.027602756395936012,
0.009106467477977276,
-0.006323644425719976,
0.010238703340291977,
-0.035617951303720474,
-0.004740695934742689,
-0.01858934946358204,
0.012380393221974373,
-0.026504751294851303,
0.004194843117147684,
0.02755996584892273,
0.02729048952460289,
0.04573581740260124,
-0.05385487899184227,
-0.01820194162428379,
-0.026614395901560783,
-0.0455179288983345,
0.03712134808301926,
0.03752599656581879,
-0.020335957407951355,
0.0004588662413880229,
-0.025676222518086433,
-0.04300239682197571,
0.028366226702928543,
-0.0004804508644156158,
0.005054539535194635,
-0.002166908932849765,
-0.007904041558504105,
-0.010433684103190899,
-0.007624296937137842,
-0.03833255544304848,
0.007089703809469938,
-0.03362179920077324,
-0.012061627581715584,
0.029508264735341072,
-0.0014142171712592244,
-0.019070621579885483,
0.05766560509800911,
-0.04165390133857727,
-0.04365234822034836,
-0.00814312044531107,
-0.025150783360004425,
0.01687718741595745,
-0.019786326214671135,
0.008197982795536518,
0.04092329367995262,
-0.02209297940135002,
-0.014007745310664177,
-0.05887448787689209,
-0.04298907145857811,
0.04609419405460358,
-0.049954067915678024,
0.0050316317938268185,
-0.05199785903096199,
-0.02589324675500393,
0.06788898259401321,
0.011332875117659569,
-0.0030057758558541536,
-0.010331771336495876,
-0.03252892941236496,
-0.06586828827857971,
-0.017757367342710495,
0.06118391081690788,
0.09732606261968613,
-0.001642271177843213,
0.010231071151793003,
-0.0016990846488624811,
0.061065923422575,
0.03917958587408066,
-0.01686476171016693,
-0.0008909684256650507,
0.015760773792862892,
-0.0019945099484175444,
0.00397941330447793,
0.049304280430078506,
0.03280304744839668,
-0.021155524998903275,
0.008745660074055195,
-0.01151974592357874,
0.01952187716960907,
0.020160125568509102,
-0.026667127385735512,
0.029513666406273842,
-0.01728431135416031,
0.026914162561297417,
-0.047611020505428314,
0.019300417974591255,
0.012080029584467411,
0.00997764989733696,
0.019455481320619583,
-0.009295409545302391,
0.043165698647499084,
-0.0377357043325901,
0.028589142486453056,
0.015502696856856346,
0.043463341891765594,
-0.054256416857242584,
-0.04088660329580307,
0.06379737704992294,
0.008647977374494076,
0.011805455200374126,
-0.028482388705015182,
-0.001914127729833126,
0.06706371903419495,
0.028158295899629593,
0.05473288148641586,
0.03113347478210926,
-0.022342374548316002,
-0.021101640537381172,
-0.027468007057905197,
-0.0057114502415061,
-0.016087202355265617,
0.049332160502672195,
0.005358507391065359,
0.05194447189569473,
0.00937633216381073,
0.02668096125125885,
-0.032446637749671936,
-0.030267225578427315,
-0.08754003793001175,
-0.003986826166510582,
-0.005062522366642952,
-0.012539871968328953,
-0.04002150520682335,
-0.0017755256267264485,
-0.016581490635871887,
-0.04817448556423187,
-0.019941415637731552,
-0.02031739614903927,
0.0010506234830245376,
-0.03817367926239967,
0.009763347916305065,
-0.0165854524821043,
-0.05506690591573715,
-0.017310643568634987,
0.03216429427266121,
-0.015713084489107132,
-0.003072964958846569,
-0.04658760130405426,
-0.01112356036901474,
-0.025003531947731972,
0.023815128952264786,
-0.024946345016360283,
-0.025240717455744743,
0.03233352303504944,
0.03623880445957184,
0.01770688220858574,
0.02125043235719204,
0.006848201155662537,
-0.008583195507526398,
-0.020350398495793343,
0.06503921002149582,
0.039318643510341644,
0.001695271348580718,
-0.015606241300702095,
-0.06176649406552315,
-0.029298461973667145,
-0.003967227879911661,
0.04816506430506706,
-0.016564030200242996,
0.0034100539050996304,
0.0375351682305336,
0.0014809278072789311,
-0.02990858256816864,
0.013909530825912952,
0.016370221972465515,
0.03308838605880737,
0.0017374660819768906,
-0.05766190215945244,
-0.007325512357056141,
-0.031663328409194946,
0.037547387182712555,
0.03545114025473595,
-0.0005282887723296881,
-0.038057517260313034,
-0.03447278216481209,
0.047971922904253006,
-0.012885130941867828,
-0.012184941209852695,
-0.014942332170903683,
-0.007810944691300392,
0.04517696052789688,
-0.010136635042726994,
0.00907671358436346,
0.04518689587712288,
0.02870599552989006,
-0.006517567206174135,
-0.0053463466465473175,
-0.01878420077264309,
-0.06701509654521942,
0.012703686021268368,
0.033375948667526245,
0.026355119422078133,
-0.011238214559853077,
0.002617405029013753,
-0.04787817224860191,
0.0122959790751338,
0.000015271067240973935,
0.0019049206748604774,
0.03151950612664223,
-0.0035589290782809258,
-0.009097718633711338,
-0.06154188513755798,
0.006679551210254431,
-0.011788438074290752,
0.020871996879577637,
0.018781881779432297,
0.03825309872627258,
-0.027482321485877037,
-0.021016107872128487,
-0.020345235243439674,
0.007019899785518646,
0.029788829386234283,
0.08243976533412933,
-0.025963392108678818,
0.02217751368880272,
0.0445902980864048,
0.011674177832901478,
-0.01747225597500801,
-0.11432203650474548,
0.0019630505703389645,
0.022224321961402893,
0.03290030360221863,
0.044745199382305145,
-0.0189596526324749,
-0.06787848472595215,
-0.012353646568953991,
-0.011208591051399708,
-0.012191644869744778,
-0.00475891400128603,
-0.03722035512328148,
0.040890373289585114,
0.015900759026408195,
-0.015675300732254982,
0.03856183588504791,
-0.003007099963724613,
-0.06943259388208389,
-0.021610261872410774,
-0.030934859067201614,
0.04742272570729256,
-0.02889903075993061,
0.003544875420629978,
-0.03155004233121872,
0.006470219232141972,
0.017932923510670662,
0.07156798988580704,
0.040056318044662476,
0.05127851292490959,
-0.00021098728757351637,
-0.0403062105178833,
-0.006969695910811424,
-0.021650345996022224,
-0.01042471919208765,
-0.008542036637663841,
-0.023532217368483543,
0.013629121705889702,
0.03687398508191109,
-0.020995967090129852,
0.0029011457227170467,
0.017301706597208977,
0.024957984685897827,
0.025325588881969452,
0.00805647112429142,
0.026463598012924194,
-0.041196227073669434,
-0.012201422825455666,
-0.024119194597005844,
-0.025804288685321808,
0.07958851009607315,
0.03284786641597748,
-0.0007896756869740784,
0.03632934018969536,
-0.04478346183896065,
-0.04179108142852783,
0.0536142960190773,
-0.002344851614907384,
-0.009587340988218784,
-0.05041199550032616,
0.05416758731007576,
0.008870174176990986,
0.012597732245922089,
-0.08516570925712585,
-0.04480723664164543,
0.02087581902742386,
-0.0028565763495862484,
-0.028429854661226273,
-0.014295301400125027,
0.014602085575461388,
0.027516106143593788,
-0.04128168150782585,
0.06905250996351242,
0.03816699609160423,
-0.07181375473737717,
-0.003211027244105935,
0.02443312667310238,
0.024188846349716187,
0.0794529840350151,
0.000516370462719351,
-0.04358798265457153,
0.010903694666922092,
-0.04220494627952576,
0.005356949288398027,
0.01191641017794609,
0.020004630088806152,
0.012069798074662685,
-0.05342724546790123,
-0.010912522673606873,
0.010447322390973568,
0.025582866743206978,
-0.011313031427562237,
0.0019089564448222518,
0.012109750881791115,
-0.008269292302429676,
-0.017929688096046448,
-0.003566312836483121,
0.012646074406802654,
0.0005408900324255228,
0.024014785885810852,
0.03186910226941109,
0.00648068031296134,
-0.031091440469026566,
-0.0033232974819839,
0.02946525812149048,
0.013274962082505226,
0.000165287172421813,
0.010314489714801311,
0.05899107828736305,
-0.030095309019088745,
-0.005884472280740738,
0.06235567480325699,
-0.01261148601770401,
0.051785241812467575,
0.01038909237831831,
-0.00939220655709505,
-0.012171206064522266,
0.0013155757915228605,
-0.01615118980407715,
-0.04383787885308266,
-0.03698812797665596,
0.0043618339113891125,
0.026825087144970894,
-0.00844789668917656,
0.05013103410601616,
0.0164957195520401,
-0.0037889466620981693,
-0.024264639243483543,
-0.03507820889353752,
-0.014750683680176735,
0.001949229510501027,
-0.026124106720089912,
0.001504387240856886,
-0.010021806694567204,
0.00035908998688682914,
0.05704621598124504,
0.02403368428349495,
-0.025347918272018433,
0.02232513390481472,
0.05540400370955467,
-0.006742000114172697,
0.022640883922576904,
-0.019002176821231842,
-0.053448233753442764,
0.05911925807595253,
-0.03701234236359596,
0.0464373342692852,
0.022139238193631172,
-0.0222813468426466,
0.04124554246664047,
-0.04834175854921341,
0.007211778312921524,
-0.05930639058351517,
-0.02005527913570404,
-0.015478722751140594,
-0.010730957612395287,
0.026724543422460556,
-0.019919030368328094,
-0.024526258930563927,
-0.016957229003310204,
0.0387645848095417,
-0.003580947872251272,
-0.0015511108795180917,
0.009384490549564362,
-0.028611257672309875,
-0.017259180545806885,
-0.01902410015463829,
-0.013061068020761013,
-0.01721162162721157,
-0.024056829512119293,
-0.008966885507106781,
0.020560840144753456,
-0.029263867065310478,
0.025876546278595924,
0.0011344623053446412,
0.013867376372218132,
-0.024078812450170517,
0.0239776112139225,
0.009991182945668697,
0.049983177334070206,
0.00098611309658736,
-0.009682808071374893,
0.12544550001621246,
0.038328975439071655,
0.0007480693166144192,
-0.06902187317609787,
-0.010937278158962727,
-0.030896253883838654,
0.04596596211194992,
0.000761780480388552,
0.03967827931046486,
-0.013470882549881935,
0.01991259679198265,
-0.01497216708958149,
0.0063640642911195755,
0.005894199945032597,
-0.003337613306939602,
0.031548384577035904,
-0.04532454162836075,
-0.03865256533026695,
0.018825426697731018,
0.017520857974886894,
-0.02811494842171669,
-0.00013669123291037977,
-0.01816573552787304,
0.026779314503073692,
-0.030560873448848724,
-0.0031430667731910944,
-0.04854225739836693,
-0.012405072338879108,
0.04478498920798302,
0.03221997991204262,
-0.041563838720321655,
-0.014684535562992096,
0.0406586155295372,
-0.005956965032964945,
-0.03391347452998161,
-0.005396605469286442,
-0.0032274804543703794,
-0.017165489494800568,
0.008854986168444157,
0.020659856498241425,
0.021415315568447113,
-0.01928851567208767,
0.02450667880475521,
0.011842739768326283,
-0.0723152905702591,
0.010335671715438366,
-0.013003223575651646,
0.014257344417273998,
-0.016747718676924706,
0.009162223897874355,
-0.012376070022583008,
0.023804865777492523,
-0.015772199258208275,
-0.025048311799764633,
-0.05683629587292671,
-0.005056123249232769,
-0.0004975891206413507,
-0.015680965036153793,
-0.006599580403417349,
0.020757850259542465,
0.012035542167723179,
0.02065892145037651,
0.006888393312692642,
-0.025843266397714615,
0.016667718067765236,
0.016803251579403877,
-0.012504265643656254,
0.019039440900087357,
-0.010685564950108528,
-0.0041184816509485245,
-0.04443654417991638,
-0.0073396265506744385,
-0.05791475996375084,
-0.016995377838611603,
-0.009321638382971287,
0.005876702722162008,
0.012260571122169495,
0.03615783900022507,
-0.006226752419024706,
0.0017581668216735125,
-0.024421794340014458,
0.013091698288917542,
-0.011933496221899986,
0.02225768193602562,
-0.018434496596455574,
0.012469192035496235,
0.019092760980129242,
0.027745725587010384,
-0.0396723635494709,
0.039252713322639465,
-0.002100177574902773,
-0.011189342476427555,
0.014323578216135502,
-0.0638958290219307,
-0.03631981462240219,
0.015765955671668053,
-0.03589579090476036,
0.03528663516044617,
-0.005224382039159536,
-0.007095258217304945,
-0.0019905553199350834,
0.027181588113307953,
0.03294619172811508,
0.0005320732016116381,
-0.023699181154370308,
0.014826091006398201,
0.008968117646872997,
-0.02416294999420643,
0.015293019823729992,
0.020105306059122086,
0.02602759748697281,
-0.011937281116843224,
-0.031055334955453873,
0.02194853127002716,
-0.004622230771929026,
0.009816196747124195,
0.012282973155379295,
0.020504740998148918,
-0.00325640756636858,
-0.04033706709742546,
0.005666225682944059,
-0.05581771582365036,
0.005008159205317497,
-0.049074187874794006,
0.014376131817698479,
-0.00419999472796917,
0.0445069894194603,
0.009469562210142612,
0.006330959033221006,
-0.013567515648901463,
0.013955329544842243,
0.058999136090278625,
0.011313209310173988,
0.001421710243448615,
-0.006093338131904602,
0.03632195666432381,
-0.005232592113316059,
0.03370006009936333,
-0.010041828267276287,
-0.016995228826999664,
0.021821849048137665,
-0.043985072523355484,
-0.044434916228055954,
-0.009100423194468021,
0.016852207481861115,
0.026622720062732697,
-0.006705375388264656,
-0.03125429153442383,
-0.03472254052758217,
0.07372656464576721,
-0.030749749392271042,
-0.03031097538769245,
-0.010637717321515083,
-0.020890697836875916,
0.017394309863448143,
0.009026473388075829,
-0.013720402494072914,
-0.014681537635624409,
0.0077688805758953094,
0.08042403310537338,
-0.0040075345896184444,
-0.01518026739358902,
-0.028477521613240242,
-0.017678506672382355,
0.01285481359809637,
0.0029340616893023252,
0.01108086109161377,
0.0023468881845474243,
-0.007798822596669197,
0.009230110794305801,
0.012714289128780365,
0.07352503389120102,
0.020049788057804108,
0.01575317792594433,
-0.05660499259829521,
-0.038815684616565704,
0.008753759786486626,
0.003252826165407896,
0.027037430554628372,
-0.046407923102378845,
-0.008995079435408115,
-0.03427780047059059,
-0.0973203033208847,
0.009020618163049221,
-0.01770463027060032,
-0.04949834197759628,
-0.07220201939344406,
-0.013012281619012356,
-0.03455265983939171,
0.02566804364323616,
0.0016279441770166159,
0.05743560940027237,
-0.019124304875731468,
0.022074947133660316,
-0.0006463958416134119,
0.022801464423537254,
-0.02684045396745205,
0.024617226794362068,
-0.0003847586049232632,
-0.016941826790571213,
0.03076975978910923,
-0.02101927623152733,
0.013106031343340874,
0.044233597815036774,
0.0035431236028671265,
-0.012262487784028053,
0.013337832875549793,
0.03557247668504715,
-0.0018581257900223136,
0.05275483429431915,
-0.015369788743555546,
-0.016263416036963463,
-0.013544941321015358,
-0.009671207517385483,
0.048451732844114304,
0.037308599799871445,
0.027643496170639992,
0.0015818518586456776,
-0.023264791816473007,
-0.03205067664384842,
0.0020206612534821033,
0.03409811854362488,
-0.006248688790947199,
-0.00046324930735863745,
-0.01277985516935587,
0.03209985792636871,
0.0028700390830636024,
-0.015859350562095642,
0.0008469286258332431,
-0.048468347638845444,
-0.018677281215786934,
0.027885502204298973,
0.03906483203172684,
0.017178399488329887,
0.017652997747063637,
0.004322930239140987,
-0.03274088725447655,
0.018617240712046623,
0.01624608412384987,
0.014988432638347149,
-0.014802031219005585,
0.00575359258800745,
0.018536118790507317,
0.009933343157172203,
0.015342069789767265,
-0.0536191388964653,
-0.010231689549982548,
0.02928432635962963,
-0.0044534290209412575,
0.01902848109602928,
-0.03744426742196083,
-0.09290339797735214,
0.015513775870203972,
-0.05429689958691597,
0.023025447502732277,
-0.012279736809432507,
0.026977332308888435,
-0.03695431351661682,
-0.05636776611208916,
-0.03085295483469963,
0.04656929150223732,
0.06788769364356995,
0.00614068191498518,
-0.03600955381989479,
-0.009577526710927486,
-0.027981247752904892,
0.04361392557621002,
-0.018628161400556564,
0.0195643100887537,
0.018015306442975998,
-0.05121418088674545,
0.021390385925769806,
-0.01359260082244873,
-0.009942431002855301,
0.04377704858779907,
0.019951092079281807,
-0.012414037249982357,
-0.001605068682692945,
-0.0018003603909164667,
-0.02877560257911682,
0.05808280035853386,
0.0037701427936553955,
0.01151997409760952,
0.08255049586296082,
-0.00019529649580363184,
0.006924460642039776,
0.015330636873841286,
0.00722748227417469,
-0.05158229172229767,
-0.0018678013002499938,
-0.009342560544610023,
-0.004962312523275614,
0.0014759658370167017,
-0.011256696656346321,
0.06339247524738312,
-0.010019148699939251,
-0.018399689346551895,
0.03135125711560249,
-0.02972331829369068,
-0.003118593944236636,
0.06280608475208282,
0.04244314134120941,
0.026342948898673058,
-0.013543429784476757,
0.007626047357916832,
-0.03010229393839836,
-0.007947967387735844,
-0.02025413326919079,
0.036768149584531784,
0.017040446400642395,
0.014332287944853306,
-0.0008505217265337706,
0.028907410800457,
0.014768768101930618,
0.011609498411417007,
-0.0005475992220453918,
0.02739599160850048,
-0.02396659553050995,
-0.007005722261965275,
0.06322348117828369,
0.00975952111184597,
0.037426866590976715,
0.03310973942279816,
-0.012181094847619534,
0.09639658778905869,
-0.0005481963744387031,
0.002570061245933175,
-0.05635213106870651,
0.006661115679889917,
-0.00457915710285306,
-0.018049364909529686,
0.0007536957855336368,
0.03191328048706055,
0.015556823462247849,
-0.05592568963766098,
-0.018196899443864822,
0.019141938537359238,
0.017090830951929092,
-0.06006692722439766,
0.0362217053771019,
-0.0004818418819922954,
-0.016111698001623154,
-0.009169262833893299,
0.006087240297347307,
-0.030603595077991486,
-0.007087090518325567,
0.0014031074242666364,
0.04297944903373718,
0.02296070195734501,
0.022295953705906868,
0.01169504038989544,
-0.01517871581017971,
0.03554115071892738,
-0.03878895938396454,
-0.030990665778517723,
-0.014681215398013592,
0.006880662869662046,
-0.029094785451889038,
-0.005461836699396372
] |
<p>In case of solar system,we can explain "Why Sun would not revolve around any other planet?",by giving the reason that Sun is heavier than any other planets. </p>
<p><a href="http://physics.stackexchange.com/questions/81648/why-heavier-bodies-produce-greater-gravitational-pull-than-the-lighter-bodies">Heavier the body,greater will be the gravitational strength produced by it</a>.Thus,Sun being heaviest,produces greater gravitational pull,and keeps other planets revolving around it. </p>
<p>In case of atom,we can consider coulomb's law.Here,we can see that both protons and electrons have same charge in magnitude(Don't consider electron to have less charge than proton,because of negative sign.It just implies that electron is resinously charged i.e charge similar to amber). </p>
<p>So,in case of atom we don't have electrons and proton with different charge in magnitude,as like we had Sun to be heavier than other planets,to make other planets to revolve around the sun.Thus,we can also expect protons to revolve around the electron.But,this doesn't happen.So,what is the reason for protons not revolving around the nucleus cotaining electrons and neutrons? </p> | 2,006 | [
-0.0346759594976902,
0.012812808156013489,
-0.004172357730567455,
-0.010505803860723972,
0.0055326251313090324,
0.028136279433965683,
-0.02353939227759838,
-0.03541678935289383,
0.006257836241275072,
-0.03544262424111366,
0.07257314771413803,
0.03154497966170311,
0.07390215247869492,
0.012350544333457947,
0.0015047498745843768,
0.01719728671014309,
-0.01743895187973976,
-0.014263831079006195,
-0.002720964141190052,
-0.01819285750389099,
-0.018004879355430603,
-0.004345578141510487,
0.004795563407242298,
0.03031890094280243,
-0.0174194797873497,
0.045277081429958344,
0.02601250819861889,
-0.004411596339195967,
0.05817311629652977,
0.06809860467910767,
0.016465960070490837,
0.0008062887936830521,
0.043694477528333664,
0.021761415526270866,
0.04205700755119324,
0.009935101494193077,
0.011106287129223347,
-0.01698734052479267,
-0.0254740659147501,
0.028116803616285324,
-0.01050263736397028,
-0.015878239646553993,
-0.009429793804883957,
0.026143798604607582,
-0.01569143310189247,
0.05774438753724098,
0.02077806554734707,
0.003742428030818701,
0.07649382203817368,
-0.06636670976877213,
0.04380248859524727,
0.0215821024030447,
0.021604208275675774,
0.027581268921494484,
0.018855426460504532,
-0.05318225175142288,
0.062303218990564346,
0.04162132367491722,
-0.028463415801525116,
-0.052276600152254105,
-0.017156081274151802,
-0.022395633161067963,
-0.02525990456342697,
-0.00904388539493084,
-0.00729465764015913,
0.01850132644176483,
-0.022836582735180855,
-0.057126887142658234,
0.00035911399754695594,
0.03193948045372963,
0.020740220323204994,
0.017302198335528374,
-0.0205425675958395,
-0.014478875324130058,
0.012626702897250652,
-0.041416071355342865,
0.04111870750784874,
-0.022491829469799995,
0.03423767536878586,
0.05185858905315399,
-0.023479891940951347,
0.007159273140132427,
-0.0007049679988995194,
0.0126872006803751,
0.0222258809953928,
-0.023143840953707695,
0.034630581736564636,
-0.031099146232008934,
-0.006909090094268322,
0.04637954756617546,
-0.01758318394422531,
0.0014039090601727366,
0.024834521114826202,
0.021321015432476997,
-0.0226815864443779,
0.026037883013486862,
-0.0025507768150418997,
0.04059517756104469,
0.014095817692577839,
0.008979559876024723,
-0.016166595742106438,
-0.018124811351299286,
0.02036455273628235,
0.09677743911743164,
0.01776931807398796,
-0.011866144835948944,
-0.03184426203370094,
-0.008798767812550068,
-0.03252227231860161,
0.007334801834076643,
-0.01876717619597912,
0.0068350182846188545,
0.011353377252817154,
-0.026071948930621147,
0.006853150669485331,
-0.03568962588906288,
0.03129861131310463,
-0.023180630058050156,
0.028770633041858673,
0.06595102697610855,
0.03033633716404438,
-0.01042847242206335,
0.015292736701667309,
-0.06534634530544281,
-0.0723511204123497,
-0.010013020597398281,
0.04277331009507179,
0.015593442134559155,
7.951567226882617e-7,
0.03643055632710457,
-0.002702551195397973,
-0.007458257023245096,
-0.023359287530183792,
-0.023348847404122353,
0.060797836631536484,
0.016686037182807922,
-0.1312268227338791,
-0.027919374406337738,
0.028187889605760574,
0.012853882275521755,
-0.025143824517726898,
-0.06649886816740036,
0.02121943049132824,
0.0030790865421295166,
0.07045511156320572,
0.027593720704317093,
-0.031071266159415245,
0.002152405446395278,
0.021695252507925034,
0.012728153727948666,
-0.007173293735831976,
0.01689385436475277,
-0.008162343874573708,
-0.02583537995815277,
-0.017624584957957268,
-0.0711873471736908,
0.025451673194766045,
-0.0006831535138189793,
0.022845791652798653,
-0.006826621945947409,
0.01958571746945381,
-0.05805486440658569,
0.02369718626141548,
-0.02303881011903286,
0.02385557070374489,
-0.0334538035094738,
0.0615026019513607,
0.0378691665828228,
-0.01590910740196705,
0.05522768944501877,
0.011029611341655254,
0.03674892708659172,
-0.0006794513901695609,
0.013472258113324642,
0.025232763960957527,
-0.051291968673467636,
-0.06019578129053116,
-0.026353059336543083,
-0.008851944468915462,
0.007441711612045765,
-0.03337268531322479,
-0.041074879467487335,
-0.006998185068368912,
-0.013310437090694904,
-0.009242462925612926,
0.04189581051468849,
0.012018374167382717,
-0.00008623123721918091,
0.0049601211212575436,
-0.03483837842941284,
0.00405637314543128,
-0.08137214183807373,
0.03362471982836723,
-0.027536025270819664,
-0.045419611036777496,
0.036525800824165344,
0.008985748514533043,
-0.002673762384802103,
-0.009779407642781734,
-0.0077897352166473866,
-0.01627342775464058,
0.058831412345170975,
-0.027962932363152504,
0.014928520657122135,
-0.0025344188325107098,
0.05326902121305466,
-0.000024162956833606586,
-0.0007390027167275548,
0.0011507105082273483,
-0.005374209955334663,
-0.02099277265369892,
-0.0010508759878575802,
-0.03242867439985275,
-0.016534388065338135,
0.030022043734788895,
-0.01112681720405817,
0.014766007661819458,
0.009052598848938942,
-0.01809692569077015,
0.07666032761335373,
-0.009732711128890514,
0.10053002834320068,
0.03502821922302246,
0.010910261422395706,
0.012083136476576328,
0.05552405118942261,
0.014232748188078403,
0.01568533107638359,
-0.012462192215025425,
-0.020504865795373917,
-0.06387042254209518,
-0.0026483996771275997,
0.01170018408447504,
0.020923787727952003,
-0.04926881939172745,
0.03418419882655144,
0.01924077421426773,
0.04512088745832443,
-0.005454959347844124,
0.016732336953282356,
-0.02778352051973343,
-0.04498681053519249,
0.030573073774576187,
-0.01543207187205553,
0.022667549550533295,
0.03542688488960266,
0.026963932439684868,
0.009880504570901394,
0.027735892683267593,
0.009183633141219616,
-0.051481734961271286,
0.04138530418276787,
0.003754312638193369,
0.018782153725624084,
0.022175904363393784,
-0.054642919450998306,
0.013434851542115211,
0.0021766009740531445,
0.017348317429423332,
0.0065597607754170895,
-0.03431140258908272,
-0.02605435624718666,
-0.0563136488199234,
-0.027956122532486916,
-0.008339829742908478,
0.0018800788093358278,
-0.022508125752210617,
-0.024240393191576004,
0.011626125313341618,
-0.061983902007341385,
-0.00787655171006918,
0.014775335788726807,
0.009603702463209629,
-0.0409107431769371,
-0.004328050650656223,
0.058660607784986496,
0.005224679131060839,
0.020781831815838814,
-0.014963425695896149,
0.002054208656772971,
-0.0025272874627262354,
-0.04429631307721138,
-0.04070287197828293,
0.007907923310995102,
-0.02676679752767086,
0.02064615860581398,
-0.015102601610124111,
-0.028516177088022232,
0.03620656207203865,
0.016169290989637375,
0.027756255120038986,
-0.003591327928006649,
-0.013368606567382812,
-0.032522205263376236,
0.0016278671100735664,
-0.015087999403476715,
0.00986768864095211,
-0.03864109516143799,
-0.02254149317741394,
0.07103171944618225,
0.013554385863244534,
-0.001399432891048491,
0.0001887211255962029,
-0.0617557168006897,
-0.040376927703619,
0.015603939071297646,
-0.01585984230041504,
-0.007241215091198683,
-0.024543555453419685,
0.0008162223966792226,
0.02676481381058693,
-0.03744902089238167,
-0.037801533937454224,
-0.035755228251218796,
-0.009816693142056465,
0.03040674328804016,
-0.007907058112323284,
0.03030342049896717,
-0.00211690878495574,
-0.059361089020967484,
0.0643162727355957,
0.004196564666926861,
0.0006504243356175721,
-0.016260210424661636,
-0.005357163026928902,
-0.03900458663702011,
-0.023320499807596207,
-0.007495254743844271,
0.03778853639960289,
0.02094186469912529,
-0.00555055495351553,
0.0375516377389431,
0.025388943031430244,
-0.00963691808283329,
-0.008141056634485722,
0.005148056894540787,
0.007998444139957428,
0.0009978278540074825,
-0.006542128976434469,
0.07145749777555466,
-0.0025345468893647194,
-0.0040625035762786865,
-0.004735513124614954,
0.006465113256126642,
0.03229521960020065,
-0.015509095974266529,
-0.05485212430357933,
0.05089307948946953,
0.004771517124027014,
0.019910138100385666,
-0.0004747518396470696,
0.018653443083167076,
0.004257054068148136,
-0.01940837875008583,
0.00660444051027298,
0.03891878202557564,
0.06780912727117538,
0.0027119179721921682,
-0.02240203320980072,
0.025243962183594704,
0.04089656472206116,
-0.00970500335097313,
-0.034699272364377975,
0.009179966524243355,
-0.0004459691990632564,
0.017036601901054382,
-0.04804886132478714,
0.0009237919002771378,
0.03611903637647629,
-0.005367859732359648,
0.02815023995935917,
0.01474376767873764,
-0.04928302392363548,
0.00385231408290565,
-0.08054628223180771,
0.013531908392906189,
-0.033930208534002304,
0.07376699894666672,
-0.010251387022435665,
0.05759424716234207,
0.031153177842497826,
0.03441518172621727,
-0.029517756775021553,
-0.01844213902950287,
-0.0817863866686821,
0.03353654593229294,
-0.04131017625331879,
-0.03736887499690056,
-0.016672052443027496,
-0.0016719584818929434,
-0.025983016937971115,
-0.0026776816230267286,
0.027323467656970024,
-0.05763712525367737,
-0.0035575663205236197,
-0.018645385280251503,
0.01681903749704361,
-0.05866402015089989,
-0.05558941140770912,
0.006948207505047321,
0.03763555735349655,
0.029595734551548958,
-0.0405813567340374,
0.05660558491945267,
0.018254892900586128,
-0.035989489406347275,
-0.022963562980294228,
-0.03684884309768677,
0.02218431606888771,
0.0005192688549868762,
-0.002521723508834839,
0.04444924741983414,
0.024297397583723068,
-0.009155846200883389,
-0.022120460867881775,
0.01684405282139778,
0.023533860221505165,
0.021316146478056908,
-0.03409193828701973,
-0.01173595804721117,
-0.0361085869371891,
-0.010704736225306988,
-0.014641789719462395,
0.05111929029226303,
-0.01025012694299221,
0.005890734493732452,
-0.00025700373225845397,
-0.025063607841730118,
0.016928767785429955,
0.04864010214805603,
0.05302492529153824,
0.03054816462099552,
-0.04020245745778084,
-0.027196094393730164,
0.0072280545718967915,
-0.026223791763186455,
-0.002355955308303237,
0.04226952791213989,
-0.009209487587213516,
-0.02108021266758442,
-0.032246559858322144,
0.008466330356895924,
-0.00041463127126917243,
-0.0008566423784941435,
0.031711187213659286,
-0.029869910329580307,
0.026798423379659653,
-0.036850035190582275,
0.013254915364086628,
0.03170279040932655,
0.006985795684158802,
0.023506876081228256,
-0.015822457149624825,
-0.017230747267603874,
-0.06023189052939415,
-0.005047396291047335,
0.041655123233795166,
0.06555502116680145,
-0.05225519463419914,
-0.0014007401186972857,
-0.07517855614423752,
-0.015250809490680695,
0.03027069754898548,
-0.0320446752011776,
0.039630815386772156,
-0.03474239259958267,
0.026372410356998444,
0.0005806083790957928,
-0.020942533388733864,
0.015193559229373932,
0.019255468621850014,
-0.04676737263798714,
0.0053249248303473,
-0.023522980511188507,
-0.009183166548609734,
-0.015266659669578075,
-0.00034593266900628805,
0.044168565422296524,
0.010942116379737854,
-0.019266517832875252,
0.025829754769802094,
0.004661689978092909,
0.007018849719315767,
0.0046553779393434525,
-0.0956430584192276,
-0.014350105077028275,
-0.012824933975934982,
-0.03443324938416481,
0.05077594518661499,
-0.03684721887111664,
-0.05694084241986275,
-0.007074116263538599,
-0.00026794630684889853,
-0.011874983087182045,
-0.038521528244018555,
-0.06381385028362274,
0.03477983549237251,
0.021888554096221924,
-0.03845152258872986,
0.006560366600751877,
0.03703741729259491,
-0.03225181996822357,
-0.01809185929596424,
-0.022447189316153526,
0.008464561775326729,
-0.03873914107680321,
-0.017933085560798645,
-0.005204574670642614,
0.015039322897791862,
-0.013029085472226143,
0.041635025292634964,
0.02163589745759964,
0.012836892157793045,
0.0017862448003143072,
-0.04539469629526138,
-0.013171984814107418,
0.006077921483665705,
-0.010557392612099648,
0.006213855929672718,
-0.05292807146906853,
0.0373229905962944,
0.02271994575858116,
-0.020647000521421432,
0.0076653119176626205,
0.013654876500368118,
0.009598962962627411,
0.0374777689576149,
-0.037656012922525406,
0.0015917299315333366,
-0.0203535333275795,
-0.0038510821759700775,
0.005419475957751274,
-0.05114369839429855,
0.03193265572190285,
-0.013909022323787212,
-0.030555035918951035,
0.048914067447185516,
-0.03758146986365318,
-0.033975750207901,
0.03312775865197182,
-0.05358462035655975,
0.002209137426689267,
-0.02075059898197651,
0.032454609870910645,
0.010257645510137081,
-0.0029158852994441986,
-0.06376847624778748,
-0.03542977198958397,
0.004811725579202175,
0.0054116761311888695,
-0.020320460200309753,
0.0007006298983469605,
0.003897470887750387,
-0.004694890696555376,
-0.016222666949033737,
-0.0006040631560608745,
0.01705845445394516,
-0.06658925116062164,
-0.005331982392817736,
0.03581242263317108,
0.005778083577752113,
0.06874626874923706,
-0.016817638650536537,
-0.028468811884522438,
0.00533330487087369,
-0.014850053004920483,
0.01660488173365593,
-0.005714357830584049,
0.04511457681655884,
-0.0032156570814549923,
-0.08352567255496979,
0.015593541786074638,
-0.013351358473300934,
0.024791201576590538,
-0.014282946474850178,
-0.028340432792901993,
0.031231937929987907,
0.012990685179829597,
-0.018918462097644806,
-0.005264177918434143,
0.03203493356704712,
0.000937598932068795,
0.043649397790431976,
0.005728256888687611,
0.033986955881118774,
-0.033139668405056,
-0.06857918202877045,
0.024799251928925514,
0.006975258234888315,
0.010075039230287075,
0.00975787453353405,
0.06982868909835815,
0.009131163358688354,
0.0122903473675251,
0.03395144268870354,
-0.003997629042714834,
0.044117167592048645,
-0.008813980966806412,
-0.010759704746305943,
-0.0049893795512616634,
0.011340394616127014,
-0.011815721169114113,
-0.01054835319519043,
-0.04290950670838356,
0.01712031289935112,
0.08024505525827408,
-0.017517369240522385,
0.03977669030427933,
0.016471225768327713,
0.032293230295181274,
0.009601268917322159,
-0.01527460664510727,
-0.008105771616101265,
-0.02848520688712597,
-0.0038729668594896793,
0.0070124780759215355,
-0.037299126386642456,
0.018257105723023415,
0.07451853901147842,
0.07556252181529999,
-0.0411665104329586,
0.016123225912451744,
0.031658727675676346,
-0.0007060563075356185,
-0.0013414622517302632,
-0.021375393494963646,
-0.032531045377254486,
0.0381246842443943,
-0.0008764344383962452,
0.05135529860854149,
-0.004353509750217199,
-0.025116458535194397,
0.04295387119054794,
-0.008853101171553135,
0.029156917706131935,
-0.021175820380449295,
-0.059266526252031326,
-0.036813899874687195,
0.032788485288619995,
0.04110034927725792,
-0.016394518315792084,
-0.04178180545568466,
0.03417942672967911,
0.042362578213214874,
0.006097876001149416,
-0.011031446047127247,
-0.012796904891729355,
-0.06441324204206467,
-0.017564402893185616,
-0.017665386199951172,
-0.036223314702510834,
0.024417435750365257,
-0.0029499572701752186,
-0.01391877792775631,
0.017382729798555374,
0.016017697751522064,
0.03405150771141052,
0.027607511729002,
0.028196269646286964,
-0.009040405973792076,
0.061020199209451675,
-0.038400448858737946,
-0.027663782238960266,
-0.00821225717663765,
0.02158939093351364,
0.10704068094491959,
0.008266996592283249,
-0.0064279912039637566,
-0.02889711782336235,
-0.0014354184968397021,
0.005480327643454075,
0.012763801962137222,
0.00038471343577839434,
0.027308721095323563,
-0.01592402532696724,
0.04139930009841919,
-0.027709176763892174,
0.009032608941197395,
0.022778354585170746,
0.005716091953217983,
0.03549225255846977,
-0.031907130032777786,
-0.04552019014954567,
-0.018332254141569138,
0.016972342506051064,
0.0015755149070173502,
-0.0005371993174776435,
-0.07236919552087784,
0.022636307403445244,
-0.029997335746884346,
-0.0004421972844284028,
-0.06434270739555359,
-0.00036605537752620876,
-0.002430127700790763,
0.01848718337714672,
-0.044801756739616394,
0.01678764633834362,
-0.009285732172429562,
-0.024619214236736298,
-0.04637381434440613,
0.03420634940266609,
0.04687735438346863,
-0.02228892408311367,
0.00956304557621479,
0.011091780848801136,
0.007883399724960327,
0.02074793353676796,
-0.011768425814807415,
0.03575775399804115,
-0.06137910485267639,
0.023927830159664154,
-0.022967448458075523,
0.04074529930949211,
-0.020955126732587814,
0.009890150278806686,
0.0046011642552912235,
0.010561427101492882,
-0.0014788085827603936,
-0.04114745929837227,
0.009937531314790249,
-0.0041790734976530075,
0.00510564586147666,
-0.00576440617442131,
-0.03848877176642418,
0.011969806626439095,
0.023784257471561432,
-0.019548695534467697,
0.043139077723026276,
-0.006500388495624065,
0.02715306729078293,
-0.0013521324144676328,
0.004038429819047451,
0.021608687937259674,
0.00003603177174227312,
0.040417686104774475,
-0.02266542613506317,
-0.028844201937317848,
-0.031643304973840714,
-0.04135645553469658,
0.04263006150722504,
0.058346450328826904,
0.026757920160889626,
0.02623564936220646,
0.004040325526148081,
-0.02047063782811165,
-0.01071398425847292,
0.0707269087433815,
-0.0029500240925699472,
-0.032614562660455704,
-0.02236386574804783,
0.006135785020887852,
0.019131112843751907,
0.019851813092827797,
-0.0219519454985857,
-0.007421778980642557,
0.03356047719717026,
0.022980911657214165,
-0.003981900401413441,
-0.02343807741999626,
0.000962994818110019,
0.022831248119473457,
0.003835066920146346,
0.01998499408364296,
0.041953250765800476,
-0.00138784886803478,
0.027867889031767845,
-0.013459702953696251,
-0.008041039109230042,
0.05959244444966316,
-0.024690181016921997,
0.008294790051877499,
0.039606932550668716,
0.004972246941179037,
0.01820201985538006,
0.02754664421081543,
-0.01964995078742504,
-0.047638826072216034,
0.005003642290830612,
-0.016934137791395187,
-0.038781628012657166,
0.04406195506453514,
0.028748255223035812,
-0.020233478397130966,
0.014571204781532288,
-0.04228242486715317,
0.021348044276237488,
-0.020945236086845398,
-0.005411370657384396,
-0.08636564016342163,
0.0008761506760492921,
-0.00001948256976902485,
-0.023355400189757347,
-0.03985970467329025,
0.020650742575526237,
-0.015001822263002396,
-0.01900055631995201,
0.04304779693484306,
0.017118098214268684,
-0.023326991125941277,
-0.0012907804921269417,
0.02421971596777439,
-0.033606480807065964,
0.041446685791015625,
-0.028077010065317154,
-0.019335806369781494,
0.03238091617822647,
-0.02287830226123333,
-0.014768307097256184,
0.006382505409419537,
-0.03761410340666771,
0.014651241712272167,
0.006315012462437153,
-0.00008813603926682845,
0.01887674815952778,
0.0800919383764267,
-0.039114583283662796,
0.01617748662829399,
-0.012419185601174831,
-0.0016206959262490273,
0.0037403907626867294,
-0.008188223466277122,
-0.019346382468938828,
-0.01970912329852581,
-0.011767943389713764,
0.052918754518032074,
0.026857350021600723,
-0.018051521852612495,
0.006496741436421871,
-0.019529208540916443,
-0.010617813095450401,
0.02838878706097603,
0.02928224205970764,
0.02428038790822029,
0.004954089410603046,
0.0057289679534733295,
-0.052087120711803436,
0.06460651755332947,
0.03711070865392685,
-0.019296500831842422,
-0.057925835251808167,
-0.004330604337155819,
-0.015749378129839897,
-0.013091678731143475,
0.005329412408173084,
-0.019834769889712334,
-0.010403030551970005,
0.008367526344954967,
-0.11318110674619675,
0.024167707189917564,
-0.022277453914284706,
-0.018700463697314262,
0.011070356704294682,
-0.03786000236868858,
-0.017269251868128777,
0.08016996085643768,
-0.012100265361368656,
0.02970392070710659,
0.007869388908147812,
0.027174493297934532,
-0.007306528277695179,
-0.03834155574440956,
-0.05012918636202812,
0.01504102349281311,
-0.01483069732785225,
-0.0025331045035272837,
0.05590075999498367,
-0.026927536353468895,
0.015505990944802761,
0.02608073689043522,
0.03456353768706322,
0.01976923830807209,
-0.03365623578429222,
0.004619400482624769,
-0.004278643988072872,
0.013938140124082565,
-0.0008786091348156333,
-0.0031075996812433004,
-0.029539750888943672,
0.015794439241290092,
-0.01001667883247137,
0.029303617775440216,
0.017365163192152977,
0.0077166371047496796,
0.024200083687901497,
-0.024061856791377068,
-0.03241581469774246,
0.011249925009906292,
0.005955588072538376,
0.024291250854730606,
-0.021657323464751244,
0.00453707342967391,
0.03523024916648865,
-0.016567183658480644,
-0.0071910410188138485,
-0.03255903348326683,
0.04116996005177498,
0.02861645631492138,
0.009230264462530613,
-0.008862092159688473,
0.06050475314259529,
-0.009465373121201992,
0.0006667484412901103,
0.001387096126563847,
0.01367110013961792,
-0.018383262678980827,
-0.017413664609193802,
0.0306079238653183,
0.010207202285528183,
0.02627156674861908,
-0.02907898649573326,
-0.057935141026973724,
-0.09290491789579391,
0.0448908768594265,
0.025798410177230835,
0.036752182990312576,
0.013360119424760342,
-0.054678190499544144,
0.013964471407234669,
-0.06335844099521637,
0.015896759927272797,
-0.011276200413703918,
-0.006076209247112274,
-0.03276202455163002,
-0.0387403778731823,
-0.02123679406940937,
0.03802099823951721,
0.043646056205034256,
0.04594480246305466,
-0.0022451344411820173,
0.011911368928849697,
-0.029700040817260742,
-0.006127119064331055,
-0.03322834149003029,
0.011037630960345268,
-0.002559524029493332,
-0.020485462620854378,
0.040256600826978683,
-0.010153704322874546,
-0.05728019401431084,
0.020157037302851677,
0.018197640776634216,
-0.001124572823755443,
0.030108274891972542,
-0.004281557165086269,
-0.025532567873597145,
0.06089020147919655,
0.026005243882536888,
0.010779633186757565,
0.09501966089010239,
0.02415623888373375,
0.0019155252957716584,
0.019704371690750122,
-0.017736440524458885,
-0.02044118195772171,
0.029342344030737877,
-0.04530718922615051,
0.019220085814595222,
-0.031964924186468124,
-0.04477935656905174,
0.03007817268371582,
-0.03865000978112221,
0.0064321244135499,
0.05045434460043907,
-0.030442912131547928,
-0.025446537882089615,
0.001735003897920251,
0.016905739903450012,
0.026998260989785194,
0.012918339110910892,
0.008846794255077839,
0.01296590268611908,
-0.024451596662402153,
0.016688717529177666,
0.04372711479663849,
0.02857564389705658,
0.008333845995366573,
0.009917921386659145,
0.06144580990076065,
0.03965777903795242,
0.030613359063863754,
0.01786907948553562,
0.026685500517487526,
-0.023760799318552017,
0.00007279757119249552,
0.014754155650734901,
-0.001303279772400856,
0.04102224484086037,
0.02614908292889595,
-0.016451388597488403,
0.10815566033124924,
-0.04402540996670723,
0.019649485126137733,
0.030994843691587448,
-0.027197478339076042,
0.009335523471236229,
0.010786784812808037,
-0.005793163552880287,
0.015115535818040371,
-0.011440834030508995,
-0.04474145174026489,
-0.021056246012449265,
-0.019076457247138023,
0.02588694728910923,
-0.023571958765387535,
0.0077859750017523766,
-0.009497564285993576,
0.005140650551766157,
-0.029942985624074936,
-0.006248997058719397,
-0.02364376001060009,
0.006970551796257496,
0.03754086047410965,
0.03357486054301262,
0.05789002776145935,
-0.011756382882595062,
0.004177137278020382,
-0.017331084236502647,
0.01919880509376526,
-0.0569148026406765,
-0.05534937232732773,
-0.018477067351341248,
0.017761869356036186,
-0.03337325155735016,
-0.025287028402090073
] |
<p>I have hacked a FitDesk exercise bike to output the RPM of the pedals and the position of the resistance control within its range of travel.</p>
<p>I want to characterize the energy that is required to pedal the bike at different RPMs and resistance settings.</p>
<p>My approach is to determine the torque required to the turn the bike at different settings.</p>
<p>My first idea is to use a variable speed drill to turn the bike while measuring the amperage the drill is pulling. Keeping the drill speed constant, I would change the resistance setting and observe the change in amperage. I would also baseline the amperage pulled with no load on the drill.</p>
<p>I am able to turn the bike using the drill, but I am worried that the measurements will be non-linear because the amount of heat generated by the drill changes quite a bit as resistance is added and I don't know how this relates to the amperage reading.</p>
<p>My second idea is to drop a weight which will turn the bike using a simple pulley arrangement. If I know the weight and can measure the angular acceleration of the bike, I should be able to calculate how much torque the weight is overcoming at different resistance settings.</p>
<p>But I am worried that after setting all that up, the differences in acceleration will be too small for meaningful comparison. (I really have no idea if this would be a problem or not.)</p>
<p>So I ask the experts: what is the easiest way to accomplish my goal?</p> | 2,007 | [
-0.009079941548407078,
-0.008437145501375198,
-0.006042908877134323,
0.0073796664364635944,
0.044646553695201874,
-0.0017058915691450238,
-0.03881780058145523,
-0.03182665631175041,
0.007992282509803772,
-0.015402036719024181,
0.012091857381165028,
0.030636215582489967,
0.024119999259710312,
0.040719252079725266,
0.0019606950227171183,
-0.02043314464390278,
-0.003602394601330161,
-0.01077713817358017,
0.006060543470084667,
-0.01642708294093609,
-0.028047500178217888,
0.00532381609082222,
-0.0069851563312113285,
-0.014704887755215168,
-0.03749261796474457,
-0.0034163324162364006,
0.04681134223937988,
-0.043392114341259,
-0.04666736349463463,
0.04030673950910568,
-0.0337090790271759,
-0.008292609825730324,
-0.011438858695328236,
0.021910972893238068,
0.013246356509625912,
0.037539299577474594,
-0.04772258922457695,
-0.06340953707695007,
0.010796728543937206,
0.04708142578601837,
-0.004828477744013071,
0.013826940208673477,
-0.04315727949142456,
0.0437191016972065,
-0.017278971150517464,
0.053027231246232986,
-0.013835357502102852,
0.019380424171686172,
0.05441378802061081,
-0.03729556128382683,
0.04975157603621483,
0.022206472232937813,
0.03872854262590408,
0.045703984797000885,
0.008913573808968067,
-0.009318423457443714,
0.07908692210912704,
0.03815357759594917,
-0.011038909666240215,
-0.04024956375360489,
-0.03801732137799263,
-0.020709184929728508,
-0.026541702449321747,
-0.03769644349813461,
-0.016960006207227707,
-0.01500079594552517,
-0.011628691107034683,
0.005776318721473217,
0.03811262920498848,
0.00629236176609993,
0.038524046540260315,
0.034430257976055145,
0.01779118739068508,
-0.007276030257344246,
-0.013823416084051132,
-0.05537497624754906,
-0.016482669860124588,
0.010026371106505394,
0.019097838550806046,
0.04702465236186981,
-0.04289935529232025,
-0.007757176179438829,
0.02887309156358242,
0.04384681209921837,
0.015348806045949459,
-0.03364467993378639,
0.02530028484761715,
-0.005366198718547821,
-0.018200457096099854,
0.036163561046123505,
0.025347845628857613,
0.005165380425751209,
-0.020533226430416107,
-0.007778194732964039,
0.003921023104339838,
0.0187387615442276,
-0.031038543209433556,
0.04361237958073616,
-0.032209571450948715,
-0.02236175164580345,
0.011990136466920376,
-0.0075933742336928844,
-0.007290519308298826,
0.061852335929870605,
0.01831197552382946,
-0.007895532995462418,
0.019903235137462616,
-0.0017672415124252439,
0.02029500901699066,
-0.018784036859869957,
-0.03868727385997772,
-0.009709193371236324,
-0.0038366643711924553,
0.0027789927553385496,
0.005237127188593149,
-0.011787250638008118,
-0.035181861370801926,
-0.021951263770461082,
0.06481920182704926,
0.030683249235153198,
0.0019750443752855062,
-0.013780063018202782,
-0.012322630733251572,
-0.06892096251249313,
-0.022435439750552177,
0.02044946514070034,
0.03351200744509697,
-0.049566131085157394,
-0.02156725525856018,
0.043711211532354355,
-0.0073899258859455585,
-0.009015228599309921,
-0.012453604489564896,
-0.030446624383330345,
0.005456275772303343,
-0.027780193835496902,
-0.054753195494413376,
-0.050787005573511124,
0.019431063905358315,
0.011875794269144535,
-0.010978571139276028,
-0.05517653748393059,
-0.006171989720314741,
0.05086046829819679,
0.05450313910841942,
0.00669529102742672,
0.0235107634216547,
-0.001035687979310751,
0.019801262766122818,
0.03289368003606796,
-0.006048634648323059,
-0.020576786249876022,
-0.004958667792379856,
-0.011901834048330784,
0.020301468670368195,
-0.03619210049510002,
0.01222001202404499,
0.015598554164171219,
-0.021752627566456795,
-0.006421853322535753,
0.0204816535115242,
-0.007383483927696943,
-0.02574816532433033,
0.0623965859413147,
0.03607140854001045,
-0.0018013145308941603,
0.08009815961122513,
-0.03430827334523201,
-0.008128254674375057,
0.0031094010919332504,
0.01503723580390215,
0.031503207981586456,
0.03639524057507515,
-0.030569026246666908,
0.06415227055549622,
-0.01755395159125328,
-0.016999222338199615,
-0.0259381253272295,
-0.009826956316828728,
0.004265692085027695,
-0.036056965589523315,
-0.060542866587638855,
-0.006768729072064161,
0.0027314473409205675,
0.024037141352891922,
0.03623727709054947,
0.010486639104783535,
0.007753660436719656,
0.07745198905467987,
-0.03818179666996002,
-0.011257587932050228,
-0.0721110925078392,
0.028735792264342308,
0.006883889436721802,
-0.005444684065878391,
0.012318648397922516,
0.008861514739692211,
0.026086466386914253,
0.010011964477598667,
-0.012834574095904827,
0.048928286880254745,
0.04151433706283569,
0.0028295123483985662,
0.010160242207348347,
-0.02578442357480526,
0.03457053750753403,
0.02647068351507187,
-0.014002312906086445,
-0.00741851981729269,
-0.002643197076395154,
-0.038243234157562256,
0.011393020860850811,
-0.07046119123697281,
-0.018347103148698807,
0.016961321234703064,
0.01104214508086443,
0.008617701008915901,
0.00862354226410389,
-0.00504537858068943,
0.052674636244773865,
0.029544193297624588,
0.07631195336580276,
0.03855885565280914,
-0.003171933116391301,
-0.0027630506083369255,
0.05569123849272728,
-0.00230383756570518,
0.03362983837723732,
-0.030646445229649544,
0.00047370800166390836,
-0.05640912428498268,
0.010213524103164673,
0.020280588418245316,
0.017026802524924278,
-0.061137035489082336,
0.03962773457169533,
0.06495635211467743,
0.0325322151184082,
-0.010355174541473389,
0.02372407168149948,
0.014549925923347473,
0.008648987859487534,
0.0278763584792614,
0.05789843574166298,
0.020108496770262718,
0.030925897881388664,
-0.0010614049388095737,
0.046577904373407364,
-0.002499496331438422,
0.012973720207810402,
0.007712846156209707,
0.0670878067612648,
0.030518323183059692,
0.004329855088144541,
0.02095966599881649,
-0.009393016807734966,
0.02980106882750988,
0.003527898108586669,
0.025558648630976677,
0.04519657790660858,
0.0026085195131599903,
0.03136406093835831,
-0.002614593133330345,
-0.009292538277804852,
0.016918614506721497,
-0.008057204075157642,
0.019702965393662453,
-0.03321649134159088,
0.014386455528438091,
-0.06370596587657928,
0.019039751961827278,
-0.07739542424678802,
0.005430010613054037,
-0.05422941595315933,
-0.021944237872958183,
-0.03142466023564339,
0.01672021485865116,
0.029641343280673027,
-0.03366191312670708,
-0.028136223554611206,
0.004273386672139168,
-0.00854502059519291,
0.019682785496115685,
0.016189850866794586,
-0.04657437652349472,
0.019933978095650673,
-0.008579163812100887,
-0.03485378250479698,
0.0567614883184433,
-0.004359584767371416,
-0.00627675699070096,
0.032723318785429,
0.02079271897673607,
-0.0429338701069355,
0.006431220564991236,
-0.0001439947955077514,
-0.01701340079307556,
-0.007476491387933493,
0.012119836173951626,
0.05768565088510513,
0.01260708924382925,
-0.06242125853896141,
0.01843579299747944,
-0.011051437817513943,
0.012788229621946812,
0.00451810285449028,
-0.023093784227967262,
-0.011728300713002682,
0.0017096863593906164,
0.023223361000418663,
0.0347520112991333,
-0.04052333906292915,
-0.031649406999349594,
-0.07748064398765564,
-0.041452325880527496,
0.0048918998800218105,
0.022558530792593956,
0.034299012273550034,
0.007315074559301138,
-0.0007443813374266028,
0.07427772134542465,
0.02514783851802349,
-0.01322218868881464,
-0.058361221104860306,
-0.00770332757383585,
-0.01464841142296791,
-0.06316626816987991,
-0.02659694105386734,
0.03394590690732002,
0.00972193107008934,
0.020543472841382027,
-0.0004864587099291384,
0.054313745349645615,
0.06626921147108078,
0.01668863743543625,
0.001280150143429637,
0.010754814371466637,
-0.00652683200314641,
-0.016905467957258224,
0.069068543612957,
0.02966715395450592,
-0.031188659369945526,
0.00894994754344225,
-0.02764974720776081,
0.01616343855857849,
-0.006688636261969805,
-0.09174179285764694,
0.003534811781719327,
0.005946238525211811,
0.001956912688910961,
-0.023558475077152252,
0.02553979679942131,
-0.007470994256436825,
-0.0336909182369709,
-0.00029603144503198564,
0.052521880716085434,
0.06245758384466171,
0.007015913259238005,
-0.0057809664867818356,
0.06267455220222473,
0.02401479333639145,
-0.002287413226440549,
-0.05868512764573097,
-0.014510606415569782,
-0.011528531089425087,
-0.019294220954179764,
-0.0040745302103459835,
-0.05751607567071915,
0.025218762457370758,
-0.019544627517461777,
0.054297156631946564,
0.019820561632514,
-0.022552283480763435,
0.024142958223819733,
-0.04210240766406059,
-0.04340803995728493,
0.006109175272285938,
0.07917671650648117,
0.003348196856677532,
0.03167709335684776,
0.03278881683945656,
-0.010811405256390572,
0.004069290589541197,
-0.04374193027615547,
-0.11039284616708755,
0.06682910770177841,
-0.04362200200557709,
-0.041721850633621216,
0.027957545593380928,
0.012145443819463253,
-0.011391625739634037,
-0.04558359459042549,
0.00694000069051981,
-0.01820780336856842,
0.0077897668816149235,
-0.04024649038910866,
0.0010899617336690426,
0.003501645987853408,
-0.03756003826856613,
-0.02454942651093006,
0.024531040340662003,
0.020439576357603073,
-0.04653208702802658,
0.04322926700115204,
-0.017280325293540955,
0.008403811603784561,
-0.019081316888332367,
-0.026897281408309937,
0.017527354881167412,
-0.03912736847996712,
0.03528020158410072,
0.01208560261875391,
0.017247837036848068,
-0.003447490744292736,
-0.008678419515490532,
0.007312448229640722,
0.04212833195924759,
0.03878603130578995,
-0.019948728382587433,
-0.060357023030519485,
-0.02033643238246441,
-0.0156987514346838,
-0.010861236602067947,
0.02588498778641224,
-0.003684306051582098,
0.006802024319767952,
0.021348651498556137,
0.0036877503152936697,
-0.05701948329806328,
0.006318888161331415,
0.01636807806789875,
0.011487984098494053,
-0.03012828528881073,
-0.058529436588287354,
-0.01774400845170021,
-0.01225813664495945,
-0.012565740384161472,
0.00731235696002841,
0.018382057547569275,
0.003950674086809158,
-0.002209410537034273,
0.049133263528347015,
-0.010888096876442432,
-0.033739231526851654,
0.05962822213768959,
-0.009660590440034866,
0.07924968749284744,
0.00027957753627561033,
0.00792299211025238,
0.028875131160020828,
0.037464674562215805,
0.05595484375953674,
-0.008856108412146568,
-0.009626831859350204,
-0.09316857159137726,
-0.048233602195978165,
0.016685297712683678,
0.04672510176897049,
-0.028820529580116272,
-0.009457476437091827,
-0.004706935491412878,
-0.027538912370800972,
0.048903144896030426,
-0.04054481163620949,
0.06308741867542267,
-0.03302464634180069,
-0.003431453602388501,
-0.06176888570189476,
-0.023628462105989456,
-0.03497304022312164,
0.04643953964114189,
-0.02933976985514164,
-0.00665896013379097,
-0.06629356741905212,
0.001457765931263566,
0.011090279556810856,
0.04263410344719887,
0.01718587428331375,
0.061333395540714264,
-0.012170592322945595,
-0.009146197699010372,
0.0127756018191576,
0.03407318890094757,
-0.001036641770042479,
-0.08796849101781845,
-0.0009347680606879294,
0.004765721037983894,
0.00881302822381258,
-0.002303988439962268,
-0.04130778834223747,
-0.053172118961811066,
0.013431811705231667,
-0.03589635714888573,
-0.02178221568465233,
-0.02042851410806179,
-0.05660727620124817,
0.023638268932700157,
0.031741805374622345,
0.010413623414933681,
0.03139821067452431,
0.05203573405742645,
-0.020216718316078186,
-0.0060296072624623775,
0.011109809391200542,
-0.005708901211619377,
-0.039554085582494736,
-0.050515737384557724,
-0.06369704008102417,
0.005379498936235905,
-0.04104567691683769,
0.009960687719285488,
-0.000551137316506356,
0.0575108639895916,
0.004673427902162075,
-0.031438421458005905,
-0.016161160543560982,
-0.00303634419105947,
0.01764572411775589,
-0.024020114913582802,
0.036710094660520554,
0.03048219531774521,
0.0005371381994336843,
-0.018976185470819473,
-0.020713482052087784,
0.0029429246205836535,
0.02436872385442257,
0.037519607692956924,
-0.026679309085011482,
0.044833954423666,
-0.037827569991350174,
-0.0011273989221081138,
-0.013020041398704052,
-0.0010201649274677038,
0.04357106238603592,
0.007694265339523554,
0.012294230982661247,
-0.010121420957148075,
-0.015400562435388565,
-0.013767833821475506,
0.016436124220490456,
-0.012180323712527752,
-0.003066551173105836,
-0.024427440017461777,
0.050250984728336334,
0.005540509708225727,
-0.027746060863137245,
-0.016243545338511467,
-0.04102611169219017,
0.021861007437109947,
0.00012448543566279113,
0.018061574548482895,
-0.007523384876549244,
0.009587871842086315,
-0.02023172378540039,
-0.04295751824975014,
0.002308610826730728,
0.0461595356464386,
-0.038087330758571625,
0.012318606488406658,
-0.01794774830341339,
-0.009678015485405922,
0.05133013799786568,
-0.02552887611091137,
-0.019554942846298218,
0.01816726103425026,
-0.01717394031584263,
-0.023146871477365494,
0.0007195817306637764,
0.0007748361094854772,
-0.03930806741118431,
0.010991064831614494,
-0.002934365998953581,
0.025799524039030075,
0.05793759599328041,
0.0011331860441714525,
-0.009126780554652214,
0.02672720141708851,
0.017821352928876877,
-0.02157564088702202,
0.001706711482256651,
0.03130348399281502,
0.03751235082745552,
0.010914407670497894,
0.007505067158490419,
0.0038322769105434418,
-0.02262187749147415,
-0.0311195757240057,
0.03498436138033867,
0.0176386721432209,
-0.0321306437253952,
-0.0019711453933268785,
0.05667772516608238,
-0.013025556690990925,
0.01821731962263584,
0.004925137385725975,
-0.024054039269685745,
0.00969765055924654,
-0.0037015096750110388,
0.02117437683045864,
0.00044712109956890345,
-0.025650912895798683,
-0.02431904897093773,
-0.05794733762741089,
-0.031870003789663315,
-0.04757023602724075,
0.06636282801628113,
0.004900433123111725,
0.06433754414319992,
0.04218440130352974,
-0.001024350174702704,
0.02311404049396515,
0.02516494132578373,
-0.006861218251287937,
0.00144818180706352,
0.013696178793907166,
0.02210402674973011,
0.03392530605196953,
-0.03744768351316452,
0.07244095951318741,
0.018888434395194054,
-0.03213551640510559,
0.003349963342770934,
0.04467371478676796,
0.024160457774996758,
0.007303218822926283,
-0.007689873222261667,
-0.05640033259987831,
-0.005976569373160601,
-0.027254188433289528,
0.06430128961801529,
-0.027656786143779755,
0.014991395175457,
0.06612574309110641,
0.021288136020302773,
0.003725433489307761,
-0.021300112828612328,
0.020739542320370674,
-0.08199512213468552,
0.033273689448833466,
0.03282972797751427,
0.012126777321100235,
0.0080470135435462,
0.03801250830292702,
0.05715349689126015,
-0.028252504765987396,
0.01015737745910883,
-0.05157512426376343,
-0.044813647866249084,
0.009102114476263523,
-0.018938062712550163,
-0.05374019593000412,
0.050643645226955414,
-0.010333866812288761,
-0.010274279862642288,
0.03402884304523468,
-0.014375472441315651,
0.015873920172452927,
0.03236498683691025,
0.012137488462030888,
-0.020155709236860275,
0.06109881028532982,
-0.016567619517445564,
-0.014878211542963982,
0.005301575176417828,
-0.02214551344513893,
0.11834022402763367,
0.055013470351696014,
0.020490828901529312,
-0.04030075669288635,
-0.006426811218261719,
-0.00003943177580367774,
-0.013814101926982403,
0.013980629853904247,
-0.0044310190714895725,
0.008030453696846962,
-0.0066014500334858894,
0.03554961457848549,
0.002476252382621169,
-0.02667401358485222,
-0.01826634630560875,
0.0588088184595108,
0.006369625683873892,
0.010803723707795143,
0.050867337733507156,
0.04482771083712578,
-0.022136002779006958,
-0.032488707453012466,
-0.014351923018693924,
0.028803905472159386,
-0.021631907671689987,
-0.03385067358613014,
-0.03343259170651436,
-0.0582331120967865,
0.019005684182047844,
-0.010856225155293941,
-0.05602893978357315,
0.011477554216980934,
-0.01026355754584074,
-0.0055370815098285675,
-0.004083260893821716,
0.056392405182123184,
-0.014706115238368511,
0.023714633658528328,
-0.004917592275887728,
0.033245742321014404,
0.010667162016034126,
-0.03408624231815338,
0.003514990909025073,
-0.024686994031071663,
-0.04901529476046562,
-0.01978965289890766,
-0.040885671973228455,
0.008829401805996895,
-0.02481009252369404,
0.028346508741378784,
0.017113998532295227,
0.008721665479242802,
-0.03437279909849167,
-0.08008327335119247,
0.006015520542860031,
0.011200966313481331,
0.019626811146736145,
-0.008181625977158546,
-0.003054953645914793,
-0.02331024780869484,
0.03616228327155113,
-0.01744895428419113,
-0.018312377855181694,
0.033027831465005875,
-0.019784631207585335,
-0.0006962522747926414,
0.030291510745882988,
0.08042525500059128,
-0.018281063064932823,
-0.0329410620033741,
-0.006746902130544186,
-0.014699123799800873,
-0.02066686376929283,
0.042310930788517,
0.015021590515971184,
0.006984318140894175,
0.013321676291525364,
0.01304150465875864,
-0.04861455038189888,
-0.004630689509212971,
-0.06941051781177521,
0.00007068858394632116,
-0.0063455491326749325,
0.00938920397311449,
-0.049050718545913696,
0.008467069827020168,
0.043915219604969025,
0.04408992826938629,
-0.003991090226918459,
-0.005207623355090618,
0.014758910052478313,
0.022225841879844666,
0.01800164394080639,
-0.011189830489456654,
-0.03844130411744118,
0.019043082371354103,
-0.02926434390246868,
0.025318503379821777,
-0.011995247565209866,
0.05458863452076912,
0.01571473479270935,
0.00227850372903049,
-0.01722504384815693,
-0.006890284363180399,
0.008284603245556355,
0.019061964005231857,
0.010938538238406181,
-0.014479692094027996,
-0.02323741465806961,
0.008615327067673206,
-0.0038926091510802507,
-0.061995502561330795,
-0.014995550736784935,
-0.029622705653309822,
-0.04401101544499397,
0.00009607683023205027,
-0.003022188553586602,
0.006866691168397665,
0.03366469964385033,
-0.0622481070458889,
0.015930287539958954,
-0.027382107451558113,
0.02419653907418251,
-0.004614335484802723,
-0.0317755751311779,
0.013536685146391392,
0.023453982546925545,
-0.010426752269268036,
0.03319282457232475,
0.021699126809835434,
-0.008612135425209999,
0.00536976708099246,
-0.009587417356669903,
0.007595350034534931,
0.0002471358166076243,
0.024070553481578827,
-0.009181788191199303,
0.033782053738832474,
-0.047925371676683426,
-0.0478486567735672,
0.06693793833255768,
-0.03339289501309395,
0.007126916665583849,
0.04180258885025978,
-0.0006719460943713784,
0.01951219141483307,
0.005065358709543943,
-0.041609346866607666,
0.003982739523053169,
-0.0016625843709334731,
0.0026429675053805113,
-0.02154795452952385,
0.011396357789635658,
-0.0011745109222829342,
-0.0257685799151659,
0.04720516875386238,
0.03722567856311798,
-0.044952940195798874,
0.008550915867090225,
0.054359935224056244,
0.023434365168213844,
-0.010832425206899643,
-0.018217718228697777,
0.0004228673642501235,
0.01950710266828537,
0.02914697304368019,
0.02922690659761429,
-0.00791139155626297,
0.07056993246078491,
0.013357271440327168,
-0.01799151673913002,
0.027989180758595467,
-0.029374176636338234,
-0.0038982010446488857,
-0.06709715723991394,
0.000985809601843357,
-0.01086340844631195,
-0.006517587695270777,
0.002709315624088049,
-0.052834898233413696,
0.00033499699202366173,
-0.011742235161364079,
-0.054716840386390686,
-0.029717979952692986,
-0.010293939150869846,
0.005289747845381498,
-0.008554312400519848,
0.017847541719675064,
-0.004219392314553261,
-0.03021051362156868,
0.04939006641507149,
0.03993286192417145,
0.013635504990816116,
0.005621960386633873,
-0.02817818522453308,
-0.0031775878742337227,
0.0015045934123918414,
0.0058020236901938915,
0.013208749704062939,
-0.02375984564423561,
0.034611254930496216,
-0.02214627154171467,
-0.048919428139925,
0.03033936396241188,
-0.0224288459867239,
0.04396329075098038,
-0.03367079421877861,
0.022069336846470833,
-0.015161648392677307,
0.03932078927755356,
0.025557011365890503,
-0.0019493274157866836,
-0.04397863149642944,
0.003086354350671172,
0.012914715334773064,
0.05427519977092743,
-0.026326293125748634,
0.017707400023937225,
0.049149006605148315,
-0.01645738258957863,
0.016856564208865166,
0.05622580274939537,
-0.044488634914159775,
-0.05420871078968048,
0.03725573047995567,
-0.004311862867325544,
-0.0023727966472506523,
-0.04231904074549675,
0.009672395884990692,
-0.04275849834084511,
-0.02239776775240898,
0.014232405461370945,
-0.012001561932265759,
-0.011488418094813824,
0.0005406717536970973,
-0.031905144453048706,
-0.010037307627499104,
0.021949725225567818,
-0.014784007333219051,
-0.06452004611492157,
-0.05669490247964859,
-0.01824091374874115,
-0.014175494201481342,
-0.011519565246999264,
-0.010279815644025803,
-0.04078374430537224,
0.008535210974514484,
0.06217312440276146,
0.011068223975598812,
0.007653184700757265,
0.031932421028614044,
0.015996666625142097,
-0.009278685785830021,
-0.07824327051639557,
0.054969482123851776,
0.03039455972611904,
-0.04013819247484207,
-0.03217826411128044,
-0.008686255663633347,
0.003384380368515849,
-0.019393861293792725,
0.03290306031703949,
-0.0035798726603388786,
-0.04763547331094742,
0.03218872472643852,
-0.02269100956618786,
0.017628731206059456,
-0.019617218524217606,
0.057453691959381104,
-0.02497219666838646,
-0.022007785737514496,
0.0036955871619284153,
-0.029827414080500603,
-0.04432103782892227,
-0.005591234657913446,
0.022443650290369987,
-0.005542694590985775,
-0.028593288734555244,
-0.01408650167286396,
0.0294700488448143,
0.04867010936141014,
0.0027135885320603848,
0.007104580756276846,
0.05830001458525658,
0.02968875877559185,
0.023241590708494186,
-0.0015622862847521901,
0.023162173107266426,
-0.02403842844069004,
0.07466661930084229,
-0.03167983517050743,
0.040018364787101746,
0.014894844964146614,
-0.008410410024225712,
0.05765054374933243,
-0.058681853115558624,
-0.0002937510726042092,
0.0404500886797905,
-0.02636253833770752,
0.012965996749699116,
0.006116983946412802,
0.04393180459737778,
-0.027377460151910782,
-0.021955713629722595,
0.0334019809961319,
0.011894917115569115,
-0.018714848905801773,
-0.005527166649699211,
0.02518225833773613,
0.03246502950787544,
-0.009807082824409008,
-0.025452660396695137,
0.07648859173059464,
0.00023042657994665205,
0.028037045150995255,
0.01835762709379196,
0.024440744891762733,
-0.023689959198236465,
-0.02881554886698723,
-0.007818346843123436,
-0.032533932477235794,
-0.002180539770051837,
0.026527147740125656,
-0.009310792200267315,
0.04146311432123184,
-0.0244760662317276,
-0.030428651720285416,
-0.035147227346897125,
-0.0008885296410880983,
0.010676596313714981,
-0.01992938108742237,
0.010595717467367649,
0.03995869308710098,
0.008098176680505276,
-0.008084801957011223,
-0.0024682513903826475,
-0.02187635749578476,
0.029446380212903023,
-0.025386346504092216,
0.04090896248817444,
-0.01191285066306591,
-0.005201352760195732,
-0.010012321174144745,
-0.010507304221391678,
-0.039365556091070175,
-0.04309237003326416,
0.0303728636354208,
0.012291151098906994,
0.04837867617607117,
-0.009395275264978409,
-0.0598578080534935,
0.00155706109944731,
0.023333869874477386,
-0.049166493117809296,
-0.026915712282061577,
0.0025356283877044916,
-0.0036174014676362276,
0.04485045373439789,
-0.012824499979615211
] |
<p><img src="http://i.stack.imgur.com/dBS2M.png" alt="This is the image of the paragraph from the book"></p>
<p>Why should an equation (<a href="http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation" rel="nofollow">TDSE</a>) in which first time derivative is related to second space derivative have a solution that contains $i$?The wave function is supposed to be complex, but I am unable to understand why it can also be assumed to be complex directly from my previous statement as stated in Quantum Physics by <a href="http://www.google.com/#q=Eisberg+Resnick" rel="nofollow">Eisberg & Resnick</a>. Can anyone help me develop an intuition?</p> | 36 | [
-0.015971019864082336,
-0.005360767245292664,
0.0071281008422374725,
0.0001211247144965455,
0.03297335281968117,
-0.0010763591853901744,
-0.06882593780755997,
-0.012948798015713692,
-0.014922557398676872,
-0.05823978781700134,
0.03275169059634209,
0.04490179941058159,
0.04017288237810135,
0.03907357528805733,
0.025334341451525688,
0.018423857167363167,
0.00888548232614994,
-0.016157247126102448,
-0.031138237565755844,
-0.000615125463809818,
0.019921565428376198,
0.0082762585952878,
0.004549246747046709,
0.0042885346338152885,
0.003985237795859575,
0.009043139405548573,
0.017487237229943275,
0.015183099545538425,
0.010498653165996075,
0.05146937444806099,
0.001388482516631484,
-0.034743767231702805,
-0.02042529359459877,
0.03194773569703102,
-0.005912003573030233,
-0.006756988354027271,
-0.022573472931981087,
-0.01577390916645527,
0.02163533866405487,
0.012782598845660686,
0.014696922153234482,
-0.009183282032608986,
-0.03241275995969772,
0.056636929512023926,
-0.031505037099123,
0.027501648291945457,
-0.005481502506881952,
-0.009521319530904293,
0.033216677606105804,
-0.06281667202711105,
0.06068486347794533,
0.00875631533563137,
0.03341616317629814,
-0.0007063404773361981,
-0.020518280565738678,
-0.016079818829894066,
0.06655490398406982,
0.08507347851991653,
0.004965349566191435,
-0.05664828047156334,
-0.036708831787109375,
-0.029376186430454254,
-0.009562868624925613,
-0.019485367462038994,
-0.05036897957324982,
0.004507009871304035,
0.0029004148673266172,
-0.029179783537983894,
0.010889646597206593,
-0.024238789454102516,
0.04606044664978981,
0.016808198764920235,
0.019948583096265793,
-0.023828867822885513,
0.006507350597530603,
-0.02528596669435501,
0.01049925945699215,
-0.004421563353389502,
0.04094155877828598,
-0.00765876704826951,
-0.017506321892142296,
0.014581854455173016,
0.005256284028291702,
0.011640935204923153,
-0.008904242888092995,
-0.02007698453962803,
0.0958036333322525,
0.04163963720202446,
0.01124648004770279,
0.00354421092197299,
0.007027529180049896,
0.03108796663582325,
0.033914901316165924,
-0.020643675699830055,
-0.0026637064293026924,
0.029183415696024895,
-0.0020421575754880905,
0.033956557512283325,
0.002699511358514428,
-0.000621239363681525,
0.005953924264758825,
-0.0672965794801712,
0.007743831258267164,
0.03874655440449715,
-0.006170498672872782,
0.0016529472777619958,
-0.05443964898586273,
0.03555797412991524,
0.037377484142780304,
-0.026220442727208138,
-0.020604411140084267,
0.04821547865867615,
-0.022111965343356133,
0.025207679718732834,
-0.012628147378563881,
-0.041345659643411636,
-0.004659123253077269,
-0.00726668955758214,
0.07038053870201111,
0.0715855062007904,
0.04570641368627548,
-0.042681917548179626,
0.03423168882727623,
-0.02242499217391014,
-0.04569312557578087,
0.013043632730841637,
0.02995295077562332,
-0.005200486164540052,
-0.025427592918276787,
-0.012308440171182156,
0.012653376907110214,
0.010836392641067505,
0.02877884916961193,
0.04635443165898323,
0.034114938229322433,
-0.017908437177538872,
-0.12972281873226166,
-0.09980230033397675,
0.021892238408327103,
-0.02691441774368286,
-0.004506405908614397,
-0.09853527694940567,
0.0047154659405350685,
0.036137260496616364,
0.08981688320636749,
-0.019385244697332382,
0.00667875399813056,
0.00880848802626133,
0.029186459258198738,
0.04738637059926987,
-0.004429477732628584,
-0.04618820548057556,
-0.0018764880951493979,
-0.05334548279643059,
-0.01198242325335741,
-0.0332263819873333,
0.0009000214631669223,
0.012603272683918476,
0.001729278708808124,
-0.02790280058979988,
0.06053073704242706,
-0.023415125906467438,
0.01705331914126873,
0.027241041883826256,
-0.0013620470417663455,
-0.043232887983322144,
0.0751798003911972,
0.02217133529484272,
0.02437012642621994,
0.05113708972930908,
0.012158718891441822,
0.06830410659313202,
0.01466681994497776,
0.026851218193769455,
-0.014314474537968636,
-0.037028491497039795,
-0.005025606136769056,
-0.015891406685113907,
0.0026333394926041365,
-0.011916103772819042,
0.011859891004860401,
-0.04151000455021858,
-0.027843892574310303,
0.020177429541945457,
-0.005971030797809362,
0.0373370498418808,
-0.01086314208805561,
0.010239683091640472,
-0.010954881086945534,
-0.04434112459421158,
0.009954351931810379,
-0.056703224778175354,
0.012227412313222885,
0.012305385433137417,
-0.030521180480718613,
0.01756765879690647,
0.0004204110591672361,
0.03752995282411575,
0.01820633001625538,
-0.01617034710943699,
0.007740349043160677,
0.04606756195425987,
0.03904815390706062,
-0.030250931158661842,
0.04928910359740257,
0.05809450149536133,
0.03549182415008545,
0.04764311760663986,
0.02596607245504856,
-0.018819916993379593,
-0.018926307559013367,
0.03394476696848869,
-0.004967226646840572,
0.030564840883016586,
0.005105520598590374,
0.00015755965432617813,
-0.01200379990041256,
-0.028950953856110573,
-0.005563041195273399,
0.012205410748720169,
-0.049486979842185974,
0.058046676218509674,
0.0461067296564579,
0.026083599776029587,
0.01692703180015087,
0.04978703707456589,
0.02675532177090645,
0.0030889573972672224,
0.030191462486982346,
-0.057119060307741165,
-0.020557381212711334,
0.022389288991689682,
0.018177835270762444,
0.04947786405682564,
-0.04151704162359238,
0.023647014051675797,
0.0018143587512895465,
0.036406151950359344,
0.02402586303651333,
0.034874506294727325,
-0.023400088772177696,
-0.04907942935824394,
0.02841624803841114,
-0.0021116032730787992,
-0.011154316365718842,
0.022591928020119667,
0.029974207282066345,
-0.00019920914201065898,
0.03522615134716034,
-0.0463985912501812,
-0.005922182463109493,
0.03582734242081642,
-0.033037684857845306,
-0.012693031691014767,
0.031161466613411903,
0.006974123418331146,
0.046542197465896606,
-0.030360328033566475,
0.0013718996196985245,
0.020488668233156204,
-0.03910475969314575,
-0.029799852520227432,
-0.007739005144685507,
-0.01472104899585247,
0.03589235991239548,
-0.03523828461766243,
-0.06968805938959122,
-0.03187795728445053,
0.013428505510091782,
-0.04071661829948425,
-0.011832364834845066,
0.016660990193486214,
0.012156222946941853,
-0.004227382596582174,
-0.0122522646561265,
0.01685342565178871,
0.022787006571888924,
0.01635568216443062,
-0.016692332923412323,
-0.05308293178677559,
0.008881771005690098,
-0.04165693372488022,
-0.009380094707012177,
0.0006231267470866442,
-0.05425753444433212,
0.050377387553453445,
-0.07364381849765778,
-0.055656615644693375,
0.01301917526870966,
-0.0010374848498031497,
0.0019144137622788548,
-0.00046378886327147484,
-0.008666367270052433,
-0.06509393453598022,
-0.028513019904494286,
-0.047185130417346954,
0.024014318361878395,
-0.02720499038696289,
-0.014427696354687214,
0.05140526220202446,
-0.019370483234524727,
0.021716700866818428,
0.016103869304060936,
0.0007117909844964743,
-0.04394843056797981,
0.016585705801844597,
-0.0065295943059027195,
0.023849405348300934,
-0.030784139409661293,
0.01729433983564377,
-0.017929472029209137,
-0.028407666832208633,
-0.017848754301667213,
-0.058462850749492645,
-0.06126479431986809,
0.012898758053779602,
0.01886397786438465,
0.011696725152432919,
0.031596530228853226,
-0.05526421219110489,
0.11121571063995361,
0.02358313277363777,
-0.005103438626974821,
-0.009974482469260693,
0.006445731036365032,
-0.01277964748442173,
-0.009987005963921547,
-0.011623183265328407,
0.02074812538921833,
-0.01928740181028843,
0.02384895272552967,
0.015055780299007893,
0.02913154847919941,
0.07275529950857162,
0.00020342932839412242,
-0.007984430529177189,
0.03132788464426994,
-0.0024051007349044085,
0.028707031160593033,
0.04149715229868889,
0.005548001267015934,
-0.028228770941495895,
0.01855063997209072,
0.012451435439288616,
0.023142170161008835,
0.004143604543060064,
-0.030363330617547035,
0.036074649542570114,
0.0016154757468029857,
0.02839876338839531,
-0.01850801706314087,
0.04333261772990227,
-0.015358670614659786,
-0.007524210959672928,
0.005014380440115929,
-0.0008881425019353628,
0.05812077224254608,
-0.051552221179008484,
0.02130238711833954,
0.002846839837729931,
-0.0019509866833686829,
-0.04205944016575813,
0.016979310661554337,
-0.02241218090057373,
-0.026747744530439377,
0.0419418103992939,
-0.009177710860967636,
-0.029623225331306458,
0.035707999020814896,
0.021046461537480354,
0.011575425043702126,
-0.05358089879155159,
-0.048918768763542175,
-0.03436816483736038,
-0.03398173674941063,
0.036917343735694885,
-0.006539386697113514,
0.0315554141998291,
0.006245949771255255,
0.05593511834740639,
0.0359773151576519,
0.014401772990822792,
0.01949555054306984,
0.014849473722279072,
-0.07344482094049454,
0.006817671004682779,
-0.02721000276505947,
0.022362876683473587,
-0.025219017639756203,
-0.004967874381691217,
0.004970093257725239,
-0.04238813370466232,
-0.019356301054358482,
-0.026003116741776466,
-0.03163296356797218,
-0.07202137261629105,
0.0010515227913856506,
-0.007888546213507652,
-0.008795961737632751,
-0.034379344433546066,
0.01858937181532383,
0.022533003240823746,
0.00467707822099328,
-0.004060441628098488,
0.05667661502957344,
-0.05982489138841629,
0.001761078368872404,
-0.02423502504825592,
-0.020901544019579887,
0.03047776222229004,
0.008487827144563198,
0.034420471638441086,
0.010511353611946106,
-0.006917504593729973,
-0.010430741123855114,
-0.0033588996157050133,
0.06732089072465897,
0.014021739363670349,
-0.030428890138864517,
-0.011836925521492958,
-0.03139246627688408,
-0.0035469047725200653,
0.001876909751445055,
0.07933540642261505,
0.02684272639453411,
0.020854365080595016,
0.030862120911478996,
0.005473525263369083,
0.005350037943571806,
0.016179582104086876,
0.04405304417014122,
0.020357543602585793,
-0.016961462795734406,
-0.0019154190085828304,
0.03513871133327484,
-0.048228465020656586,
-0.004781045485287905,
0.004915077704936266,
-0.014877483248710632,
-0.024307750165462494,
-0.024187378585338593,
0.02040506713092327,
0.0058543202467262745,
-0.014634245075285435,
-0.008810244500637054,
-0.02316487394273281,
0.007285592146217823,
-0.00903007946908474,
-0.023085596039891243,
0.007096305023878813,
0.046494197100400925,
0.04691532999277115,
-0.025411661714315414,
-0.004830277990549803,
-0.05672238767147064,
-0.029751837253570557,
0.020273679867386818,
0.03947979211807251,
-0.010882159695029259,
0.012666282244026661,
-0.07371196150779724,
-0.03537409007549286,
0.03549467399716377,
-0.011763961985707283,
0.042104240506887436,
0.00632121367380023,
-0.04046885669231415,
-0.012713351286947727,
-0.06162115931510925,
-0.008619088679552078,
0.018498297780752182,
-0.0008911326294764876,
0.01430495548993349,
-0.006847062613815069,
0.021201390773057938,
-0.04431923106312752,
-0.00238417717628181,
-0.006226949393749237,
0.06479015201330185,
0.019367044791579247,
-0.015476391650736332,
-0.015214434824883938,
0.02243003249168396,
-0.02658945508301258,
-0.05102583393454552,
0.007587192114442587,
-0.026247840374708176,
0.019236203283071518,
0.054234400391578674,
-0.038013849407434464,
-0.07482663542032242,
0.04025093838572502,
0.02532361075282097,
-0.007916390895843506,
-0.0023896389175206423,
-0.01686273142695427,
0.016315706074237823,
0.02453089877963066,
-0.013559184968471527,
0.0332990363240242,
0.026567960157990456,
0.009640078991651535,
-0.014142797328531742,
-0.026179298758506775,
0.037503618746995926,
-0.0401812344789505,
0.003302714554592967,
-0.041537441313266754,
-0.0005981108406558633,
-0.036904580891132355,
0.03049132041633129,
-0.008987713605165482,
-0.02953217551112175,
-0.009294756688177586,
-0.019359450787305832,
-0.0018036200199276209,
0.019047291949391365,
-0.02925773523747921,
0.019028225913643837,
-0.03641432896256447,
0.01221189834177494,
0.004158350173383951,
-0.012794357724487782,
-0.01676577888429165,
-0.022746432572603226,
-0.01850867085158825,
0.04025209695100784,
-0.012470566667616367,
0.049943991005420685,
-0.03156142681837082,
-0.002120880177244544,
0.0013964071404188871,
-0.07880087941884995,
0.022724051028490067,
-0.018868202343583107,
-0.018923619762063026,
0.023304153233766556,
-0.04001464322209358,
-0.04453835263848305,
-0.011311691254377365,
-0.005031311884522438,
0.006992657203227282,
-0.04051429405808449,
-0.0015534742269665003,
0.05216287821531296,
-0.0012757617514580488,
-0.08549875020980835,
-0.049195945262908936,
0.023897012695670128,
-0.009141848422586918,
-0.07040534913539886,
-0.027751414105296135,
0.009647883474826813,
-0.018219219520688057,
-0.005551225505769253,
0.010940865613520145,
0.05671513080596924,
-0.0021725737024098635,
-0.03516507148742676,
0.00974498875439167,
0.03716001659631729,
0.007605980150401592,
-0.02189905010163784,
0.000450656283646822,
0.01628739759325981,
-0.015880564227700233,
0.007104088086634874,
0.020679574459791183,
0.0523575134575367,
-0.02242322266101837,
-0.052576106041669846,
-0.016227323561906815,
0.014179821126163006,
0.026841728016734123,
0.007762317080050707,
-0.026779934763908386,
0.01027657836675644,
0.020655576139688492,
0.0172587800770998,
0.004861512687057257,
0.009743782691657543,
-0.010059483349323273,
0.027383513748645782,
0.03188389167189598,
-0.009091101586818695,
-0.02561643160879612,
-0.04403671622276306,
0.010695898905396461,
-0.004447937943041325,
0.004802145529538393,
0.03746798634529114,
0.08203448355197906,
-0.003366278950124979,
-0.0008563283481635153,
0.011182962916791439,
0.019846538081765175,
-0.00021200613991823047,
0.012058560736477375,
-0.015036516822874546,
0.03454827889800072,
0.00803894829005003,
-0.04226993769407272,
-0.00037748023169115186,
-0.04438876360654831,
0.03884005546569824,
0.05811629071831703,
0.006740849930793047,
0.03004683367908001,
0.022165991365909576,
0.036843620240688324,
0.007000480778515339,
0.013715909793972969,
-0.016803348436951637,
0.012366663664579391,
0.018741147592663765,
0.03447146341204643,
-0.04110736772418022,
-0.001937694614753127,
0.015338263474404812,
0.04947001114487648,
-0.04499932751059532,
0.005117224529385567,
0.03822590783238411,
0.015815919265151024,
-0.001309651299379766,
0.006135240197181702,
-0.03415342792868614,
0.03318973258137703,
-0.005510361865162849,
0.05301787704229355,
0.018489208072423935,
-0.01852380484342575,
0.03271838277578354,
0.005959930829703808,
0.013067805208265781,
-0.03252202644944191,
-0.03974545747041702,
-0.037894561886787415,
0.024815991520881653,
0.03460828587412834,
0.0028267474845051765,
0.029067281633615494,
0.054108425974845886,
0.005579937249422073,
0.021817589178681374,
0.030529441311955452,
0.016148289665579796,
-0.04110665246844292,
0.004202066920697689,
-0.04737238585948944,
-0.02392575331032276,
0.04831983894109726,
0.008537502028048038,
-0.013072121888399124,
0.015561211854219437,
-0.05892110615968704,
0.02815735898911953,
0.0019619627855718136,
0.017209379002451897,
0.0014363107038661838,
0.0649188682436943,
0.017163462936878204,
-0.0000952690388658084,
0.01779758557677269,
-0.002000422915443778,
0.0985928550362587,
0.05776834860444069,
0.012758035212755203,
-0.051279570907354355,
0.03407875448465347,
-0.022715814411640167,
0.00047312062815763056,
-0.002795533509925008,
0.02603045292198658,
-0.0038361316546797752,
0.02061304822564125,
-0.01074225828051567,
0.046842630952596664,
0.019916994497179985,
0.016407528892159462,
0.008706637658178806,
-0.08391354978084564,
-0.06200581043958664,
0.009922018274664879,
0.0008159743156284094,
0.015952186658978462,
-0.009067405946552753,
0.0020921870600432158,
0.012949950993061066,
-0.03230199217796326,
0.005977371241897345,
-0.033270612359046936,
-0.02211053855717182,
0.03629283234477043,
-0.03100867010653019,
-0.04583081603050232,
-0.013331390917301178,
-0.024557648226618767,
-0.012758913449943066,
-0.045808859169483185,
0.060958195477724075,
0.03388608619570732,
0.007723548915237188,
0.017873233184218407,
0.018236087635159492,
0.031728342175483704,
-0.008086179383099079,
0.020769961178302765,
0.025013737380504608,
-0.049751412123441696,
-0.0026089614257216454,
-0.02086877077817917,
0.023685771971940994,
-0.009130376391112804,
-0.03368214890360832,
-0.028469575569033623,
-0.01031787320971489,
0.009171373210847378,
-0.08825351297855377,
-0.0071897380985319614,
0.019830623641610146,
0.039052240550518036,
-0.03365839272737503,
0.005347521975636482,
-0.026712702587246895,
-0.011482542380690575,
0.00606826227158308,
0.017019154503941536,
-0.010480163618922234,
-0.03537154570221901,
-0.024816876277327538,
-0.013172256760299206,
0.036999329924583435,
-0.022516433149576187,
-0.015072567388415337,
-0.03615100309252739,
-0.0019315460231155157,
-0.03998324275016785,
-0.045988790690898895,
0.028401987627148628,
0.03026978299021721,
0.04306226223707199,
-0.019550826400518417,
-0.020680293440818787,
-0.042488399893045425,
-0.04730222374200821,
-0.013045746833086014,
0.020284073427319527,
-0.011564990505576134,
-0.03300955519080162,
0.015121937729418278,
-0.005455228965729475,
0.06334863603115082,
-0.02634742669761181,
0.03775610402226448,
-0.026737650856375694,
-0.01384478434920311,
0.03504401445388794,
-0.020673615857958794,
-0.013873349875211716,
-0.004854966886341572,
-0.021780015900731087,
-0.007177410181611776,
0.0017451359890401363,
-0.008017466403543949,
0.000441254407633096,
0.00969432108104229,
-0.004895486868917942,
0.0425935760140419,
-0.0321686677634716,
0.019198236986994743,
0.015709875151515007,
-0.01981365494430065,
0.0341067835688591,
0.03162690997123718,
0.04850136861205101,
-0.024329019710421562,
-0.01903018355369568,
-0.008665550500154495,
-0.00801088660955429,
0.01607307605445385,
0.02896006591618061,
-0.01613147370517254,
-0.004825327079743147,
0.00172227097209543,
0.04752206802368164,
-0.03994574770331383,
-0.02492157742381096,
-0.07478991895914078,
0.042743146419525146,
0.000792185717727989,
-0.007393618579953909,
-0.02230071648955345,
0.03772164508700371,
-0.031168397516012192,
-0.058903347700834274,
0.03429284319281578,
0.03545258194208145,
-0.05264424905180931,
0.0286555178463459,
0.02804211527109146,
-0.012488669715821743,
0.03571026027202606,
-0.002608534414321184,
-0.028049826622009277,
0.016304202377796173,
-0.024328893050551414,
-0.05343809723854065,
0.016424857079982758,
-0.005703691393136978,
0.027354780584573746,
0.011640004813671112,
-0.021703997626900673,
-0.019946981221437454,
0.023855136707425117,
-0.024448873475193977,
0.0037851682864129543,
0.012114294804632664,
-0.01547611877322197,
0.00781992543488741,
-0.04021148383617401,
-0.027154304087162018,
0.0033925080206245184,
-0.0008013816550374031,
0.017672475427389145,
-0.0026295820716768503,
-0.01418762281537056,
-0.014268247410655022,
0.02063979022204876,
0.00299629382789135,
0.042867034673690796,
0.04190296679735184,
0.010883498005568981,
0.022097120061516762,
0.03533719852566719,
-0.01601051352918148,
0.004297256004065275,
0.014334028586745262,
0.027827104553580284,
-0.10351774096488953,
-0.0026472110766917467,
0.01864265650510788,
0.02584097348153591,
0.028930645436048508,
-0.03696544095873833,
-0.02235427126288414,
0.013173709623515606,
-0.05521940812468529,
0.012075966224074364,
-0.04722696542739868,
-0.004493683110922575,
-0.044999271631240845,
-0.0005277885356917977,
-0.032349057495594025,
0.01834253966808319,
0.041026435792446136,
0.054523393511772156,
0.04442712292075157,
0.015168741345405579,
0.01504677813500166,
-0.031453054398298264,
0.021521233022212982,
0.043872635811567307,
-0.02319524809718132,
-0.00036100155557505786,
0.06308718770742416,
0.009866483509540558,
-0.03446398675441742,
0.015084417536854744,
0.003299352014437318,
0.010730030946433544,
0.001276517054066062,
0.025913788005709648,
0.03463263437151909,
0.021936388686299324,
0.028567010536789894,
-0.036109570413827896,
-0.03602985292673111,
0.002780826995149255,
0.023031538352370262,
0.00921168178319931,
0.005086982622742653,
-0.006631562486290932,
0.01638074778020382,
-0.03191434592008591,
-0.02630780078470707,
0.05040570721030235,
0.006218837108463049,
-0.013547596521675587,
-0.01131920050829649,
-0.013870742172002792,
-0.01608181744813919,
-0.02296368032693863,
0.04230492562055588,
-0.038739144802093506,
-0.020471038296818733,
0.02100379206240177,
0.0042821322567760944,
-0.01607910729944706,
0.030644971877336502,
-0.0274937953799963,
-0.06512336432933807,
0.029971960932016373,
0.028125446289777756,
-0.03469870239496231,
-0.058690235018730164,
0.012910469435155392,
0.021658768877387047,
-0.0029276900459080935,
0.0054208068177104,
-0.02361058071255684,
-0.040112197399139404,
0.01976289413869381,
0.011446330696344376,
-0.005367275793105364,
-0.00016543627134524286,
-0.02808089554309845,
-0.03665230795741081,
-0.08912438154220581,
0.02933524176478386,
0.02777797356247902,
-0.02257198467850685,
-0.04183522239327431,
-0.018601596355438232,
-0.012773118913173676,
0.020362231880426407,
0.06620192527770996,
-0.04787931963801384,
-0.057506587356328964,
0.05077356845140457,
0.015351079404354095,
0.0006826226599514484,
-0.04562489688396454,
0.00586240878328681,
0.009404812008142471,
0.008606326766312122,
-0.004512894432991743,
0.03609461337327957,
-0.003781053237617016,
0.0532715767621994,
0.016158655285835266,
0.017835015431046486,
0.028003407642245293,
-0.021660229191184044,
-0.032966021448373795,
0.051340166479349136,
0.01051462534815073,
-0.0031699524261057377,
0.06726144999265671,
-0.0159731674939394,
0.0042370217852294445,
0.02345925383269787,
-0.04150750860571861,
-0.01625043712556362,
0.0028019046876579523,
0.004234645515680313,
-0.02834627404808998,
-0.01472716685384512,
-0.014682302251458168,
0.02450564131140709,
-0.03185095638036728,
-0.028231173753738403,
0.002494696993380785,
-0.01898675598204136,
-0.030548032373189926,
0.03128482401371002,
-0.002894145902246237,
0.022197285667061806,
0.029783211648464203,
-0.012248385697603226,
0.03941609337925911,
0.024773987010121346,
-0.008322189562022686,
0.03760262951254845,
0.008259146474301815,
0.015321401879191399,
0.019558126106858253,
0.02889282815158367,
0.014604325406253338,
0.006264515221118927,
0.010660556145012379,
0.07174035906791687,
-0.03428889811038971,
-0.023570898920297623,
0.03293340280652046,
-0.011793865822255611,
-0.017554208636283875,
0.01695464923977852,
-0.025600770488381386,
0.08493702113628387,
-0.020860008895397186,
0.04940294846892357,
-0.007683722302317619,
0.03887146711349487,
-0.04305768385529518,
0.032367803156375885,
0.07781129330396652,
0.024626778438687325,
-0.012469780631363392,
-0.016095226630568504,
-0.01466804277151823,
-0.030501805245876312,
0.0034470169339329004,
-0.047767698764801025,
-0.02550612948834896,
0.04654480144381523,
-0.039181314408779144,
-0.012029840610921383,
0.0025281403213739395,
-0.010508696548640728,
-0.014511767774820328,
0.03865610435605049,
0.037347570061683655,
0.008550948463380337,
-0.010315757244825363,
0.0017792516155168414,
-0.018577776849269867,
0.06270968168973923,
-0.05935502424836159,
0.0027749105356633663,
-0.013129848055541515,
0.0042302580550313,
-0.029847517609596252,
-0.014320011250674725
] |
<p>If you have, say, a proton it has gluon field fluctuations around it. Those flux tubes between the quarks suppresses the gluon field fluctuations and create a true vacuum between them(correct me if I'm wrong), but how does that bind the quarks together?</p>
<p>I've read that it costs energy to clear the vacuum out, but I still don't quite get it.</p>
<p>Thank you!</p> | 2,008 | [
0.013133658096194267,
0.002010019263252616,
0.011194529943168163,
-0.03970307856798172,
0.02609427459537983,
0.06917782127857208,
-0.02327432855963707,
-0.005640503019094467,
-0.02076825499534607,
-0.011748004704713821,
0.014622925780713558,
0.025315027683973312,
0.057370372116565704,
-0.022674262523651123,
0.006927789654582739,
0.010921115055680275,
0.03249143809080124,
-0.029487663879990578,
0.007280206773430109,
-0.06973730772733688,
-0.015189802274107933,
0.04189151152968407,
-0.014832067303359509,
0.006249572150409222,
-0.025510273873806,
0.036614999175071716,
0.012568267062306404,
0.021113716065883636,
-0.001329638995230198,
0.05151442810893059,
0.004843741189688444,
-0.04637709632515907,
-0.0008259461028501391,
0.007971145212650299,
0.01460403110831976,
-0.012241008691489697,
-0.04645422101020813,
-0.03426162898540497,
-0.02341172844171524,
0.0006820514099672437,
-0.06666161864995956,
-0.006989120040088892,
-0.01086029876023531,
0.05792964622378349,
-0.019686231389641762,
0.020854510366916656,
0.04535522311925888,
0.023346228525042534,
0.06333817541599274,
-0.0634692907333374,
0.012731261551380157,
0.028542259708046913,
0.04046403616666794,
0.016557898372411728,
-0.0009254315518774092,
-0.00295702344737947,
0.07775826007127762,
0.04966428875923157,
0.0010802170727401972,
-0.0299883633852005,
-0.055717334151268005,
-0.002918386599048972,
-0.021607067435979843,
-0.019202111288905144,
-0.014248023740947247,
0.022329796105623245,
-0.025106802582740784,
-0.017901146784424782,
0.012033429928123951,
-0.030980166047811508,
0.02593027986586094,
0.010708315297961235,
0.026754453778266907,
-0.02360130473971367,
0.01757620833814144,
-0.014035612344741821,
0.044378865510225296,
0.0419372096657753,
0.04308703914284706,
0.05473679304122925,
-0.04608674347400665,
-0.006943828891962767,
0.019711200147867203,
0.028024831786751747,
0.018770501017570496,
-0.012756865471601486,
0.06964866816997528,
-0.0276664849370718,
-0.011046908795833588,
0.050245098769664764,
-0.0034722345881164074,
0.04097974672913551,
0.0290101058781147,
0.031191641464829445,
-0.03676258400082588,
0.0071281129494309425,
0.0031039156019687653,
0.04126928001642227,
0.026681451126933098,
-0.022865135222673416,
-0.010826092213392258,
0.0024735373444855213,
-0.0035211192443966866,
0.08723744750022888,
0.005473129916936159,
-0.025415852665901184,
-0.03657360002398491,
0.01194057334214449,
-0.012434141710400581,
-0.0038986308500170708,
-0.03857320174574852,
-0.06127133592963219,
0.0055720009841024876,
-0.030002279207110405,
0.03854726254940033,
-0.054640211164951324,
-0.029247039929032326,
-0.0016388952499255538,
0.05823143199086189,
0.07244065403938293,
0.06755001097917557,
-0.01147043239325285,
0.02432924509048462,
-0.020474378019571304,
-0.056671466678380966,
0.018786225467920303,
0.029311446473002434,
-0.026013361290097237,
-0.042050328105688095,
0.01661534421145916,
-0.0009188295807689428,
-0.032517995685338974,
-0.005231552291661501,
-0.03365355357527733,
0.04868949204683304,
-0.03389868512749672,
-0.06981783360242844,
-0.03923187032341957,
0.060292474925518036,
-0.04046841710805893,
-0.016673902049660683,
-0.07134241610765457,
-0.01375637762248516,
-0.021524671465158463,
0.08682327717542648,
-0.01419207826256752,
-0.05427190288901329,
-0.005147827789187431,
0.024492859840393066,
-0.005022615659981966,
-0.011203357949852943,
-0.00944695807993412,
-0.030086083337664604,
-0.03220687061548233,
0.0007420736947096884,
-0.04049699753522873,
0.02058676816523075,
0.024669425562024117,
0.004033743869513273,
-0.02612091600894928,
0.07679493725299835,
-0.015361952595412731,
0.00040307617746293545,
0.02527395263314247,
-0.04079214110970497,
-0.039833422750234604,
0.02118084952235222,
0.000646530301310122,
0.02144038863480091,
0.05652325972914696,
-0.002042509615421295,
-0.025342926383018494,
0.04021015018224716,
0.022885847836732864,
0.02244996838271618,
-0.03170667216181755,
-0.03391700237989426,
-0.025626232847571373,
0.0024059221614152193,
-0.004351234529167414,
-0.037453602999448776,
-0.03876165300607681,
-0.017600739374756813,
0.029873017221689224,
0.02147500030696392,
0.031402479857206345,
-0.015236621722579002,
-0.029245024546980858,
-0.047000981867313385,
-0.03277939558029175,
-0.015143278986215591,
-0.0838116779923439,
-0.008603141643106937,
-0.04270287975668907,
-0.020249560475349426,
-0.010837269946932793,
0.026777425780892372,
0.015266373753547668,
-0.02041083574295044,
-0.07891414314508438,
-0.005879840813577175,
0.050719182938337326,
-0.002356559270992875,
0.0036665156949311495,
0.01984313875436783,
0.019063759595155716,
0.057634059339761734,
-0.0029433080926537514,
0.06337325274944305,
-0.012389495968818665,
-0.005793658550828695,
-0.0017986823804676533,
-0.0008389742579311132,
0.01702970638871193,
-0.039573803544044495,
-0.023825855925679207,
0.018991686403751373,
-0.020589403808116913,
0.030616920441389084,
0.030605290085077286,
-0.02897266298532486,
0.07982180267572403,
0.03134637326002121,
0.011398212984204292,
-0.01526455394923687,
0.03348049521446228,
-0.015735626220703125,
0.029439551755785942,
-0.03635070472955704,
-0.048396073281764984,
-0.027636904269456863,
-0.019330766052007675,
0.04420747980475426,
0.017159778624773026,
0.0021458978299051523,
0.022361507639288902,
0.02594747021794319,
0.0297381728887558,
0.01281751785427332,
0.02053472027182579,
-0.0464789941906929,
-0.006737809162586927,
0.016365231946110725,
0.03322494775056839,
0.0029230571817606688,
0.008808286860585213,
0.013643159531056881,
0.013554533943533897,
-0.00858079269528389,
0.0009030753863044083,
-0.025648554787039757,
0.0335928238928318,
0.016281817108392715,
0.009983875788748264,
0.013478265143930912,
-0.04640553519129753,
0.035201545804739,
-0.008248050697147846,
0.03369831293821335,
0.026903631165623665,
-0.0018603808712214231,
0.015488327480852604,
-0.0152934230864048,
0.0041587622836232185,
0.011533714830875397,
0.012917312793433666,
-0.012031419202685356,
0.011334557086229324,
0.014926834031939507,
-0.023780429735779762,
0.020900212228298187,
-0.00034246916766278446,
0.01040009967982769,
0.0103230532258749,
0.024834999814629555,
0.041257478296756744,
0.0037643529940396547,
0.04369168356060982,
-0.0346776582300663,
-0.05096274986863136,
0.02946617640554905,
-0.023420775309205055,
-0.010437902994453907,
0.06053677946329117,
-0.014501383528113365,
0.022861065343022346,
-0.03733740746974945,
-0.020052514970302582,
0.028783921152353287,
-0.04007226601243019,
0.004796216264367104,
-0.0001931398583110422,
-0.02109919674694538,
-0.05514958128333092,
0.00026588875334709883,
-0.03112262487411499,
0.010981821455061436,
-0.0006836471729911864,
0.0568741150200367,
0.04876883327960968,
0.010090818628668785,
-0.03398314490914345,
0.023357484489679337,
-0.04368123039603233,
-0.0205104760825634,
0.011934950947761536,
0.026701822876930237,
0.03328414261341095,
-0.04045889899134636,
0.016662804409861565,
0.01715666800737381,
-0.07770831882953644,
0.007255676202476025,
-0.027314893901348114,
-0.019757432863116264,
0.008732081390917301,
0.02290191501379013,
0.011995410546660423,
-0.001767877722159028,
-0.07011884450912476,
0.08143782615661621,
0.025501135736703873,
-0.04590518772602081,
0.03471565619111061,
-0.031951505690813065,
-0.011793562211096287,
-0.042595308274030685,
0.031982000917196274,
0.028678204864263535,
-0.004428029991686344,
0.007678316906094551,
0.03771863877773285,
0.029990019276738167,
-0.004370437934994698,
0.017568206414580345,
-0.021044814959168434,
-0.0012366928858682513,
0.025749169290065765,
-0.003883346449583769,
0.04607610031962395,
0.02183215320110321,
-0.030960286036133766,
-0.0276519563049078,
0.024511221796274185,
0.00970480963587761,
0.01789381355047226,
-0.03000415861606598,
0.05980491265654564,
0.014567645266652107,
0.0400194376707077,
-0.04140249267220497,
0.03439028561115265,
-0.027350103482604027,
-0.009792680852115154,
0.022320443764328957,
-0.021304016932845116,
0.0343368835747242,
-0.0011862594401463866,
0.0027806537691503763,
-0.015363011509180069,
0.07437517493963242,
-0.05775628238916397,
-0.028212014585733414,
-0.007082140538841486,
-0.0164659321308136,
0.01712508499622345,
-0.018006732687354088,
-0.012515184469521046,
0.017086001113057137,
0.03099430352449417,
0.03177286311984062,
-0.010949049144983292,
-0.04114530235528946,
-0.034662168473005295,
-0.07011079043149948,
0.01149611733853817,
0.0011646253988146782,
0.03513343259692192,
0.02973528578877449,
0.05527651309967041,
-0.004143514204770327,
0.016217468306422234,
0.007174265570938587,
-0.03031189739704132,
-0.053737059235572815,
0.011980852112174034,
0.0013398650335147977,
-0.020246459171175957,
-0.01992514170706272,
-0.021214056760072708,
-0.005880451295524836,
0.005235791206359863,
-0.06129777804017067,
-0.036851219832897186,
0.00916457548737526,
-0.03803376853466034,
0.016346115618944168,
-0.04113684967160225,
0.0006489466177299619,
-0.02985990419983864,
0.02762318029999733,
0.046185873448848724,
-0.02426919713616371,
0.002145542996004224,
0.022908184677362442,
-0.046441350132226944,
-0.014492691494524479,
-0.0007294162642210722,
0.033256929367780685,
0.023107439279556274,
0.010758880525827408,
0.027212806046009064,
0.013141962699592113,
-0.017151694744825363,
-0.03772209957242012,
0.04285130277276039,
0.032285869121551514,
-0.00021161310723982751,
-0.005507401190698147,
0.024063708260655403,
-0.031089331954717636,
-0.02004448138177395,
0.01259125117212534,
0.05840042233467102,
-0.031152138486504555,
0.023087535053491592,
0.012741386890411377,
0.035370834171772,
-0.021081453189253807,
0.051303423941135406,
0.06307739019393921,
0.013583919033408165,
-0.036506108939647675,
-0.03996012732386589,
0.018337352201342583,
-0.01015737559646368,
-0.0014213150134310126,
-0.026430096477270126,
0.017371123656630516,
-0.07065054774284363,
0.001938512665219605,
-0.019411958754062653,
0.0137832872569561,
0.0036075073294341564,
0.019188815727829933,
0.018975701183080673,
0.023847484961152077,
-0.022468507289886475,
0.008039252832531929,
0.02031007781624794,
0.06216290593147278,
0.04844413697719574,
0.012436969205737114,
0.006099003367125988,
-0.06442044675350189,
-0.015929533168673515,
0.019729509949684143,
0.053592849522829056,
0.025951921939849854,
-0.023342551663517952,
-0.03962814435362816,
-0.03703596815466881,
0.047856103628873825,
-0.03752650320529938,
0.017723308876156807,
-0.0009876051917672157,
0.0003036244015675038,
-0.0038907495327293873,
-0.03959725797176361,
-0.007091043051332235,
-0.0011916194343939424,
-0.0488780252635479,
0.018943797796964645,
-0.01719662733376026,
-0.013992730528116226,
-0.03512641042470932,
0.042600613087415695,
-0.0008290728437714279,
0.03560386970639229,
0.029288889840245247,
0.005547882057726383,
0.02376432530581951,
0.02225365675985813,
0.0007201454718597233,
-0.09149571508169174,
0.0037927208468317986,
0.001556249218992889,
0.005582123063504696,
0.06434682011604309,
-0.022472504526376724,
-0.01982465386390686,
-0.028072968125343323,
0.00804966501891613,
0.009416724555194378,
-0.008988477289676666,
-0.05015004053711891,
0.04118648171424866,
0.043036770075559616,
0.02754349447786808,
0.06363138556480408,
0.03969205543398857,
-0.06679347902536392,
-0.0025941089261323214,
-0.015994859859347343,
0.02671925723552704,
-0.0365692675113678,
0.02410588599741459,
-0.002677076030522585,
0.00019085152598563582,
-0.028061581775546074,
0.04653424397110939,
-0.058677807450294495,
0.02433566190302372,
0.02295510098338127,
-0.023146694526076317,
-0.021504180505871773,
0.02728773094713688,
-0.0002859426022041589,
-0.041363708674907684,
0.015507771633565426,
0.019569654017686844,
0.007602060679346323,
-0.042269814759492874,
0.02768671326339245,
-0.002938196761533618,
-0.027585549280047417,
-0.005170551128685474,
0.003729338524863124,
0.009405109100043774,
-0.021471621468663216,
-0.010604657232761383,
0.02238137647509575,
-0.041902799159288406,
0.04259967431426048,
-0.024543264880776405,
0.001780525897629559,
0.001314091496169567,
-0.017193162813782692,
-0.03240978717803955,
0.00024578452575951815,
-0.02900647185742855,
0.02755451202392578,
-0.030370162799954414,
0.030405648052692413,
0.001228576758876443,
0.029311425983905792,
-0.058733221143484116,
-0.02115526609122753,
0.03459782153367996,
0.00444702198728919,
-0.01900920271873474,
-0.022780757397413254,
0.013841348700225353,
-0.02466212958097458,
-0.03502112999558449,
-0.011284799315035343,
0.012529803439974785,
-0.048545148223638535,
-0.002446364611387253,
-0.010356801562011242,
0.06279996782541275,
0.03564829006791115,
0.0364677868783474,
-0.036689165979623795,
0.012714572250843048,
-0.02699502557516098,
-0.03131851181387901,
0.007069975137710571,
0.03755660355091095,
-0.012186878360807896,
-0.032795581966638565,
-0.004515683278441429,
0.011005218140780926,
0.027051005512475967,
-0.021869037300348282,
0.00724551547318697,
0.047503553330898285,
0.06378530710935593,
0.019192295148968697,
-0.022051585838198662,
0.043045151978731155,
0.0058839027769863605,
0.0752219557762146,
0.017290940508246422,
0.004063054919242859,
-0.026494713500142097,
-0.048801250755786896,
0.0323772169649601,
-0.02982816845178604,
0.020039143040776253,
-0.026876898482441902,
0.04814809188246727,
0.003975734580308199,
-0.022260287776589394,
0.005075621884316206,
-0.043332539498806,
0.011081348173320293,
0.0027355817146599293,
0.03499799221754074,
0.04085908457636833,
-0.00457018194720149,
-0.00668597687035799,
-0.014410414732992649,
-0.022176681086421013,
-0.006295961327850819,
0.059112321585416794,
-0.04873338341712952,
0.039536602795124054,
-0.0025674323551356792,
-0.010282100178301334,
0.025660663843154907,
-0.032376982271671295,
-0.010901897214353085,
0.028352025896310806,
-0.002523804781958461,
0.028391024097800255,
-0.0011243638582527637,
-0.03437726944684982,
0.014606691896915436,
0.04551608860492706,
-0.027377162128686905,
0.008364584296941757,
0.039583753794431686,
0.04606889933347702,
0.008195803500711918,
-0.0075147501192986965,
-0.04340466856956482,
0.03474894538521767,
-0.04008705914020538,
0.0475781075656414,
0.014782019890844822,
0.014812751673161983,
0.04303394630551338,
-0.000001439385982848762,
0.016281340271234512,
0.0021811588667333126,
-0.03828408941626549,
-0.03321501612663269,
0.022052615880966187,
0.00879233330488205,
-0.01249903067946434,
-0.016499128192663193,
0.05007004365324974,
0.009836637414991856,
0.014293825253844261,
0.014083449728786945,
0.032346781343221664,
-0.03514600917696953,
-0.02220507711172104,
-0.032870907336473465,
-0.017687637358903885,
0.03513474762439728,
-0.049747735261917114,
-0.04962392896413803,
0.008119878359138966,
-0.029198694974184036,
0.009602751582860947,
-0.03171448037028313,
0.008436819538474083,
-0.03875473886728287,
0.028383100405335426,
0.01846661977469921,
0.03614882752299309,
-0.03383728861808777,
0.02224750816822052,
0.10384047776460648,
0.04057842865586281,
0.02899043820798397,
-0.04999803006649017,
-0.012865336611866951,
-0.03345092013478279,
0.022605177015066147,
-0.0350850448012352,
0.03498489782214165,
-0.00811866857111454,
0.015319889411330223,
0.022245917469263077,
0.07129861414432526,
0.01355583593249321,
-0.0023284710478037596,
0.07612725347280502,
-0.04052277281880379,
-0.0513998381793499,
-0.0009262678795494139,
0.04157493636012077,
-0.02468191832304001,
0.016076209023594856,
-0.04517471790313721,
0.031758248805999756,
-0.016193712130188942,
-0.008227858692407608,
-0.0268455408513546,
-0.03965648636221886,
0.03252323344349861,
-0.00046881934395059943,
-0.033388085663318634,
0.02602931298315525,
-0.007254046853631735,
0.026422416791319847,
-0.042197953909635544,
-0.001556757022626698,
0.03111949935555458,
0.0009467767085880041,
0.0005251599941402674,
0.01646273583173752,
0.016185680404305458,
0.0036097487900406122,
-0.05394934117794037,
0.02080422453582287,
-0.01626761257648468,
-0.037172090262174606,
-0.014853568747639656,
0.055654287338256836,
-0.015704108402132988,
-0.023234030231833458,
0.006081980653107166,
0.02199711836874485,
0.018457770347595215,
-0.024524372071027756,
-0.013590646907687187,
0.0015017841942608356,
-0.012597985565662384,
-0.017107589170336723,
0.02539900317788124,
-0.030954957008361816,
0.03930140659213066,
-0.02532879449427128,
0.005484275985509157,
-0.009665248915553093,
0.02443835139274597,
0.006748002488166094,
-0.012733833864331245,
0.0344933345913887,
-0.041004572063684464,
-0.0023707004729658365,
-0.03854367509484291,
-0.01700691506266594,
-0.02608385682106018,
-0.017716268077492714,
-0.010509170591831207,
0.027393987402319908,
0.037367384880781174,
-0.01344707328826189,
-0.009519141167402267,
0.0073760077357292175,
-0.0874120369553566,
0.06502295285463333,
-0.009514415636658669,
-0.021930985152721405,
-0.04405961185693741,
0.002322225831449032,
-0.023889539763331413,
0.037047531455755234,
-0.0051300860941410065,
-0.0030384983401745558,
-0.0049169170670211315,
0.01063148770481348,
0.008247346617281437,
-0.006713781971484423,
-0.04017084836959839,
-0.012804166413843632,
-0.045361362397670746,
-0.008572550490498543,
-0.0047217425890266895,
0.038818489760160446,
0.018969519063830376,
0.017856786027550697,
0.03073120303452015,
0.007842550985515118,
-0.014806678518652916,
0.017378272488713264,
0.02839519828557968,
-0.038323499262332916,
0.03059440478682518,
0.015545306727290154,
0.004195760935544968,
-0.023923233151435852,
-0.019818875938653946,
-0.014876611530780792,
0.013018806464970112,
0.0013045064406469464,
0.058619432151317596,
-0.024542508646845818,
0.025117522105574608,
-0.024509070441126823,
0.03301035985350609,
-0.04844498634338379,
0.002039484214037657,
-0.098260298371315,
0.04267408698797226,
0.015750765800476074,
0.00025886809453368187,
-0.019415097311139107,
0.009760084562003613,
-0.026248399168252945,
-0.03805776312947273,
0.012277844361960888,
-0.013719271868467331,
-0.031116021797060966,
-0.0131080886349082,
0.038308385759592056,
0.023994065821170807,
0.03160294145345688,
0.030908798798918724,
-0.013609170913696289,
0.03242086246609688,
-0.04832885041832924,
-0.05944176763296127,
-0.011465394869446754,
0.003450564341619611,
0.024170909076929092,
0.034460607916116714,
-0.039799537509679794,
-0.0558643601834774,
0.05233771353960037,
-0.023232750594615936,
-0.02046404778957367,
-0.00769520178437233,
-0.02596908248960972,
0.015773441642522812,
-0.03641858696937561,
-0.0201082956045866,
0.006494419649243355,
-0.0017051430186256766,
0.030781269073486328,
0.01972452737390995,
-0.028336143121123314,
0.0060391295701265335,
-0.023197749629616737,
-0.026733502745628357,
0.032558999955654144,
-0.004222054034471512,
0.0225051362067461,
-0.0291184913367033,
0.02907560020685196,
0.0015843719011172652,
-0.015960467979311943,
0.00866744201630354,
0.009707714430987835,
-0.11836560070514679,
-0.0239440705627203,
-0.022715073078870773,
-0.018686847761273384,
0.028808077797293663,
-0.04178084060549736,
0.037154342979192734,
0.02304193750023842,
-0.046661701053380966,
0.056893497705459595,
-0.0378100760281086,
-0.029798192903399467,
-0.06466934829950333,
-0.015110926702618599,
-0.02329093962907791,
0.05080718174576759,
0.039067428559064865,
0.005096549168229103,
-0.006576184183359146,
0.0020697626750916243,
0.003097988199442625,
-0.003912292420864105,
-0.002195328241214156,
0.01394600048661232,
-0.027363520115613937,
-0.005975666455924511,
0.06910631060600281,
-0.009817343205213547,
0.0006138798780739307,
0.010449976660311222,
-0.027559207752346992,
-0.012905365787446499,
-0.034983083605766296,
0.0023129780311137438,
-0.003321833210065961,
0.018442098051309586,
-0.001558658666908741,
0.04067223146557808,
0.010167652741074562,
-0.0006102468469180167,
0.040265876799821854,
0.027982670813798904,
0.02168557234108448,
0.021721508353948593,
0.018403969705104828,
-0.014574825763702393,
-0.019019287079572678,
0.04565110802650452,
-0.024217505007982254,
0.029617348685860634,
0.002431690227240324,
-0.020406575873494148,
0.02800997532904148,
0.003692379454150796,
-0.03195299953222275,
-0.0338418185710907,
0.023539144545793533,
0.04800810292363167,
0.037797316908836365,
0.011179265566170216,
0.0005450136959552765,
-0.0077359555289149284,
-0.0035099731758236885,
0.011529716663062572,
0.05226653069257736,
0.01032166089862585,
-0.01063566841185093,
-0.016584353521466255,
0.013229022733867168,
0.010531649924814701,
0.05617547035217285,
-0.04809659719467163,
-0.01829332485795021,
0.04581870883703232,
0.019130615517497063,
0.030548827722668648,
-0.02700876258313656,
-0.026524895802140236,
-0.012628521770238876,
-0.05325104296207428,
0.010038424283266068,
-0.02591840922832489,
-0.004242434166371822,
-0.00810823030769825,
-0.013574963435530663,
0.015023726969957352,
0.029266241937875748,
0.0348556786775589,
0.009332950226962566,
-0.023041443899273872,
0.021271806210279465,
-0.00904112122952938,
0.013170839287340641,
-0.011827375739812851,
-0.007326229941099882,
-0.012245554476976395,
0.005589856766164303,
0.006068209186196327,
-0.02183813415467739,
-0.008256976492702961,
0.029775217175483704,
0.04875226691365242,
-0.0028686763253062963,
0.008618123829364777,
-0.013393646106123924,
-0.05577819421887398,
0.04186152666807175,
-0.025589531287550926,
0.0064999498426914215,
0.05968533456325531,
-0.003339568618685007,
0.016046207398176193,
0.04628236964344978,
-0.037782564759254456,
-0.03887219727039337,
0.009413798339664936,
-0.04404062405228615,
0.008848444558680058,
0.00925060547888279,
-0.03201775252819061,
0.019205618649721146,
-0.03088674135506153,
0.008856147527694702,
0.048279162496328354,
-0.055699631571769714,
-0.012357900850474834,
0.06870497763156891,
0.03212541341781616,
0.05328710004687309,
-0.03912339359521866,
0.008024611510336399,
0.000910439935978502,
0.04026058688759804,
0.015051435679197311,
0.08188486844301224,
0.010923204943537712,
0.04503742232918739,
0.012163006700575352,
0.03229609504342079,
0.0008751665009185672,
0.002798644592985511,
0.0019609611481428146,
0.021437961608171463,
-0.038531482219696045,
-0.01583617739379406,
0.003570827189832926,
-0.031497690826654434,
0.026937255635857582,
0.019200721755623817,
-0.0247646477073431,
0.09941337257623672,
-0.06444356590509415,
0.005116909742355347,
-0.004891631193459034,
0.002434341935440898,
-0.0322687067091465,
0.04660509154200554,
0.01321566291153431,
0.058496106415987015,
0.004852376878261566,
-0.026001662015914917,
-0.012232442386448383,
-0.013881622813642025,
-0.014239901676774025,
-0.04034130275249481,
0.03132188320159912,
0.0010127578862011433,
-0.029880354180932045,
-0.03464560955762863,
0.013728613965213299,
-0.02046777494251728,
-0.051982078701257706,
0.01413488108664751,
0.022635435685515404,
-0.03583073243498802,
0.01192399300634861,
-0.023520682007074356,
-0.03265561908483505,
0.038848936557769775,
-0.04637157544493675,
0.016407087445259094,
-0.026745110750198364,
0.024721061810851097,
-0.05826456844806671,
0.009853413328528404
] |
<p>I need an inexpensive instrument to measure cryogenic temperatures (down to -200C).</p>
<p>I can build a thermistor-based thermometer using an Arduino that is accurate to under 1 degree for 0 to 100C.</p>
<p>First of all, can ordinary NTC thermistors be used at cryogenic temperatures?
Second, if I were to try to use this approach, I would need ways to calibrate the device.</p>
<p>I have found a chipset from Analog Devices that would let me use a thermocouple down to that range.</p>
<p>I would take other ideas on how to build one, but then I need some equipment to calibrate whatever I build. Is there anything I can buy for < $100, I don't need huge accuracy, but I need something.</p> | 2,009 | [
0.012687208130955696,
-0.05289291590452194,
-0.050800543278455734,
-0.003909769468009472,
0.05904212221503258,
0.022480657324194908,
-0.031544316560029984,
0.0021685899700969458,
0.021723035722970963,
-0.05791174992918968,
0.038704413920640945,
0.04915914684534073,
-0.007435815874487162,
0.019039705395698547,
-0.008776909671723843,
0.011868380010128021,
-0.025838153436779976,
-0.03188984468579292,
0.004531275015324354,
-0.05049438774585724,
0.006291123107075691,
0.006506283767521381,
-0.006820324342697859,
0.027323653921484947,
-0.04548155516386032,
0.027922917157411575,
0.012565722689032555,
-0.029743315652012825,
-0.018768223002552986,
0.037724949419498444,
-0.06813274323940277,
-0.03645904362201691,
0.016504555940628052,
0.016667339950799942,
0.03383073955774307,
-0.0035834750160574913,
-0.019112536683678627,
-0.03424588218331337,
-0.006957658100873232,
0.03966568782925606,
-0.030098576098680496,
-0.010483880527317524,
0.018102843314409256,
0.003974908031523228,
-0.013863278552889824,
-0.024454832077026367,
0.005172089207917452,
-0.03201192617416382,
0.01328118983656168,
-0.08986549079418182,
0.008148656226694584,
0.014682327397167683,
0.0764053612947464,
0.039492733776569366,
-0.018812965601682663,
0.008989236317574978,
0.07745274901390076,
0.07501060515642166,
-0.013736344873905182,
-0.024716928601264954,
-0.0010438309982419014,
-0.008423731662333012,
0.02746235765516758,
-0.019709201529622078,
-0.012350526638329029,
0.002259220462292433,
-0.03488260507583618,
0.0031619819346815348,
-0.018429487943649292,
-0.028078271076083183,
0.036521997302770615,
0.04003801569342613,
0.009448317810893059,
0.034350816160440445,
-0.011179400607943535,
-0.054160986095666885,
-0.015568493865430355,
0.029890650883316994,
0.052279554307460785,
0.10404817014932632,
-0.006674864329397678,
-0.005159175489097834,
0.014678891748189926,
0.015232455916702747,
0.002585067879408598,
-0.021477103233337402,
0.07351189106702805,
-0.028854943811893463,
0.018186939880251884,
0.013555310666561127,
0.017640547826886177,
0.03704999014735222,
-0.011481287889182568,
0.01631876826286316,
-0.023607242852449417,
-0.001785711501725018,
-0.010400539264082909,
0.020687585696578026,
-0.039757564663887024,
-0.054970882833004,
0.015965545549988747,
0.053544070571660995,
0.002533840946853161,
0.08681590855121613,
-0.00005258077726466581,
-0.02255413681268692,
0.0001988808362511918,
0.0004686327010858804,
-0.006118196994066238,
-0.0014611893566325307,
-0.0223404448479414,
-0.003938468173146248,
-0.027387427166104317,
-0.010944532230496407,
0.0398063138127327,
-0.020619520917534828,
-0.006006836425513029,
-0.03644765540957451,
0.04568122327327728,
-0.009057861752808094,
0.022232014685869217,
0.00934838131070137,
0.03211162984371185,
-0.038286224007606506,
-0.06775438040494919,
0.03130488842725754,
0.008275206200778484,
-0.004800735041499138,
0.0030728736892342567,
0.01583884283900261,
-0.03637712448835373,
0.0040833596140146255,
0.02069886401295662,
-0.0321529321372509,
0.05094918981194496,
-0.007089533377438784,
-0.0672527402639389,
-0.0881279930472374,
0.05094129592180252,
0.006228472106158733,
-0.017587872222065926,
-0.0730026438832283,
0.04684474319219589,
0.02853684313595295,
0.04512995108962059,
0.0136319100856781,
-0.014351426623761654,
-0.044695399701595306,
-0.04858984053134918,
-0.007093848194926977,
-0.03898848593235016,
-0.009034717455506325,
-0.01905675046145916,
-0.03389773517847061,
-0.02760503999888897,
-0.032312944531440735,
0.05947934463620186,
0.02643386647105217,
0.0005863519618287683,
-0.013960584998130798,
0.030643971636891365,
0.00629966938868165,
0.00887870229780674,
0.018225420266389847,
0.004568749573081732,
-0.0376436673104763,
0.08722851425409317,
-0.013199860230088234,
-0.027555033564567566,
0.004973796661943197,
-0.007210191804915667,
0.006007510703057051,
0.0377776212990284,
-0.042260587215423584,
0.07311020791530609,
-0.019216585904359818,
0.020443543791770935,
-0.014244604855775833,
0.0038571287877857685,
0.047815483063459396,
-0.04595426097512245,
-0.005183452274650335,
0.0006772324559278786,
0.0001744134206091985,
0.005704947281628847,
0.022677522152662277,
0.0021096353884786367,
0.002310659736394882,
0.05586825683712959,
-0.022602656856179237,
0.0031744958832859993,
-0.04411609098315239,
-0.012214072979986668,
0.0023193913511931896,
0.0033288453705608845,
0.03862171992659569,
0.00800282508134842,
0.0007583339465782046,
0.0040167467668652534,
-0.03351787477731705,
0.0338040255010128,
0.01932465098798275,
0.03642452880740166,
0.02870926633477211,
0.03365817293524742,
0.060478366911411285,
0.06020142883062363,
-0.025693340227007866,
0.04100438952445984,
-0.006196571979671717,
-0.024474112316966057,
-0.021024176850914955,
-0.036896903067827225,
-0.015306202694773674,
0.006122924387454987,
0.006744050420820713,
0.03107267990708351,
-0.006247583776712418,
-0.004168787505477667,
0.041801296174526215,
-0.000943533843383193,
0.0757412537932396,
-0.023143688216805458,
0.016961535438895226,
0.012386256828904152,
0.012451693415641785,
0.06521071493625641,
0.02231917716562748,
-0.016113627701997757,
0.007888906635344028,
-0.102794349193573,
-0.013487538322806358,
0.030874501913785934,
0.02889891341328621,
-0.05805428698658943,
0.019571680575609207,
0.030660822987556458,
0.006966475863009691,
0.04052023962140083,
-0.02370937168598175,
-0.004728500731289387,
0.015940243378281593,
-0.00006867824413347989,
-0.0020647894125431776,
0.020992634817957878,
0.012929612770676613,
0.02819860354065895,
0.012464622035622597,
0.003551640547811985,
-0.0015808758325874805,
-0.009517485275864601,
0.009006000123918056,
0.045192331075668335,
0.014272002503275871,
-0.0135479886084795,
-0.02207094430923462,
0.010738454759120941,
0.01327893603593111,
0.02912752702832222,
-0.000026409987185616046,
0.021441081538796425,
0.03416905552148819,
0.016694586724042892,
-0.00812194962054491,
0.030522597953677177,
0.014460778795182705,
-0.01256294921040535,
-0.013189814984798431,
0.018520783632993698,
-0.03802933543920517,
0.011312389746308327,
-0.027427708730101585,
0.004515650682151318,
-0.029089799150824547,
0.01065240241587162,
0.031034579500555992,
-0.003697160864248872,
0.019300565123558044,
-0.05384131520986557,
-0.036263320595026016,
0.014341949485242367,
-0.02215997315943241,
0.009854328818619251,
0.04567531496286392,
-0.03887312486767769,
0.023719632998108864,
-0.011187412776052952,
-0.060106147080659866,
0.007709256839007139,
0.022379985079169273,
0.0014068561140447855,
0.016575248911976814,
0.00828015711158514,
-0.05115479603409767,
-0.010985950008034706,
0.016006307676434517,
-0.026251545175909996,
-0.04850417748093605,
0.010131356306374073,
0.04804561659693718,
-0.03610263019800186,
-0.002148312283679843,
0.0508621521294117,
-0.06217947229743004,
-0.017636597156524658,
-0.00687055941671133,
0.012208792380988598,
0.007585003972053528,
-0.036838509142398834,
0.00666096480563283,
0.034477636218070984,
-0.06204446032643318,
-0.0020736646838486195,
-0.044130925089120865,
-0.06188127025961876,
0.02006193995475769,
0.025164974853396416,
0.03662488982081413,
0.03225419297814369,
-0.00007305486360564828,
0.061894491314888,
0.01898169331252575,
-0.010499762371182442,
-0.04049181938171387,
-0.027716360986232758,
-0.028671687468886375,
-0.057163648307323456,
-0.016161054372787476,
-0.005488838534802198,
-0.03095593862235546,
-0.012479845434427261,
0.005510538350790739,
0.0021520149894058704,
0.056710075587034225,
0.04262838885188103,
-0.009214292280375957,
0.005205347202718258,
0.028409318998456,
0.018189866095781326,
0.07797256112098694,
0.018659204244613647,
0.0037469821982085705,
0.0174605343490839,
-0.004086491651833057,
0.020843898877501488,
0.04262300580739975,
-0.05341693386435509,
0.03545388579368591,
-0.008174753747880459,
-0.03784786909818649,
-0.05408535897731781,
-0.028186745941638947,
0.01626761071383953,
0.01560237631201744,
-0.009321928024291992,
0.0445471927523613,
0.03306056186556816,
0.004891863092780113,
-0.011036954820156097,
0.04249579459428787,
0.02852303348481655,
0.01707720197737217,
-0.03544359281659126,
0.011658739298582077,
-0.019060442224144936,
0.006379920057952404,
0.012779587879776955,
0.005960885901004076,
0.014257987961173058,
0.0414041168987751,
0.04413236305117607,
-0.008964908309280872,
-0.005691151600331068,
0.034913577139377594,
-0.0317680686712265,
-0.018651770427823067,
-0.04917532205581665,
0.07894455641508102,
0.018745461478829384,
0.03947959095239639,
0.024449991062283516,
-0.010157850570976734,
0.03823408856987953,
-0.008854063227772713,
-0.1033419743180275,
0.019430264830589294,
-0.032950397580862045,
-0.01974722184240818,
0.0069482396356761456,
0.029210131615400314,
0.0009228111011907458,
-0.02522379159927368,
0.0047906204126775265,
-0.01898667961359024,
0.024945314973592758,
0.017376506701111794,
0.018589770421385765,
0.013103054836392403,
-0.02219863049685955,
-0.016848795115947723,
0.02399889938533306,
0.00826375000178814,
-0.003079838352277875,
-0.0006081204046495259,
-0.008568668738007545,
0.028545645996928215,
-0.01667756587266922,
-0.0020418413914740086,
0.022859590128064156,
-0.0034197326749563217,
0.0334208607673645,
0.0031342091970145702,
0.017292479053139687,
-0.008135581389069557,
-0.013809040188789368,
0.028680115938186646,
0.014735651202499866,
-0.009044643491506577,
-0.016628680750727654,
-0.02421395294368267,
-0.03980032354593277,
-0.04302645102143288,
0.03892354667186737,
0.021426577121019363,
-0.005827734712511301,
0.02890758216381073,
0.019446510821580887,
-0.007860743440687656,
-0.0382857471704483,
0.00944991409778595,
0.04044320061802864,
-0.018167272210121155,
0.007215872406959534,
-0.010124504566192627,
-0.051691994071006775,
-0.012202591635286808,
0.017567522823810577,
-0.014461761340498924,
0.02539108134806156,
-0.028469938784837723,
-0.009981791488826275,
0.04407186061143875,
0.0007679954287596047,
-0.023477934300899506,
0.0009359408868476748,
0.025919945910573006,
0.06929390877485275,
-0.012641248293220997,
0.01619335077702999,
0.03721529617905617,
0.018336636945605278,
-0.0038810716941952705,
-0.03057040087878704,
-0.033989887684583664,
-0.11635588854551315,
-0.024013737216591835,
-0.0014939643442630768,
0.05714741349220276,
0.004981886595487595,
-0.056210074573755264,
-0.06082090735435486,
-0.03699525073170662,
0.03261794149875641,
-0.02912459895014763,
0.02358333393931389,
-0.0006139953620731831,
-0.0033922449219971895,
-0.017414679750800133,
-0.022902941331267357,
0.009240252897143364,
0.03520018607378006,
-0.008728764951229095,
0.0006287642172537744,
-0.045524753630161285,
-0.006606919225305319,
0.008463004603981972,
0.005444953218102455,
0.03110761009156704,
0.08355199545621872,
-0.023208076134324074,
0.0015774620696902275,
0.02826828882098198,
-0.026705292984843254,
-0.02719571441411972,
-0.07101484388113022,
-0.021424677222967148,
0.021111825481057167,
0.008012484759092331,
0.024164803326129913,
0.0062756408005952835,
-0.05808376520872116,
0.057733211666345596,
-0.006768189370632172,
-0.035960640758275986,
-0.009706176817417145,
-0.018521711230278015,
0.05200490355491638,
0.03651691600680351,
0.05365750938653946,
0.0731753408908844,
0.051211584359407425,
-0.0020292189437896013,
0.039960503578186035,
0.009547251276671886,
0.023351935669779778,
-0.05723828077316284,
0.009387264028191566,
-0.025743650272488594,
-0.026856495067477226,
-0.027643555775284767,
0.02081109583377838,
-0.033557578921318054,
0.036496732383966446,
-0.0018787664594128728,
-0.01839430071413517,
0.01309826411306858,
0.02694668434560299,
0.0073426151648163795,
-0.03335864841938019,
0.001175529439933598,
0.0014629989163950086,
-0.018061377108097076,
-0.04995424300432205,
0.005463012959808111,
0.024133993312716484,
0.015262456610798836,
-0.0010733373928815126,
-0.062045544385910034,
0.03477153182029724,
-0.061638813465833664,
-0.005162730347365141,
0.024858277291059494,
-0.028511393815279007,
0.03185122832655907,
-0.014057041145861149,
0.00955358799546957,
0.017974570393562317,
-0.018493765965104103,
0.0020800279453396797,
0.01952303759753704,
-0.0011830040020868182,
-0.01958455890417099,
-0.03189107030630112,
0.026778530329465866,
-0.021905722096562386,
0.03788607195019722,
-0.04940120875835419,
-0.011346656829118729,
-0.002554822713136673,
-0.017070874571800232,
0.015621629543602467,
-0.031163575127720833,
-0.010465703904628754,
0.02373240515589714,
-0.008800477720797062,
0.016417212784290314,
0.05548051372170448,
-0.0036644001957029104,
-0.013322283513844013,
-0.020815791562199593,
0.01830885373055935,
0.03351174667477608,
-0.018289506435394287,
-0.02371969446539879,
0.005875842180103064,
-0.015773538500070572,
-0.05103544145822525,
0.03778592869639397,
0.02714357152581215,
-0.026457905769348145,
-0.02348361164331436,
0.013447852805256844,
0.011125484481453896,
0.025073975324630737,
0.01818169094622135,
0.011022689752280712,
0.028971794992685318,
0.002963841427117586,
-0.04101501405239105,
-0.04731340706348419,
0.032046593725681305,
0.024253807961940765,
0.004304047673940659,
-0.036906059831380844,
-0.038113802671432495,
-0.014122654683887959,
-0.02093149907886982,
0.022098088636994362,
0.008614660240709782,
-0.012806525453925133,
-0.01601245626807213,
0.08516064286231995,
-0.013370650820434093,
-0.007524849381297827,
-0.0008782741497270763,
-0.026489803567528725,
0.02589491568505764,
0.017120083793997765,
0.00400044908747077,
0.014199885539710522,
0.0071152872405946255,
-0.023680761456489563,
-0.04915966838598251,
-0.039789773523807526,
-0.047845710068941116,
0.04700996354222298,
0.02946718968451023,
0.045838501304388046,
0.02470499463379383,
-0.04328666627407074,
0.017877904698252678,
-0.014782642014324665,
-0.044986359775066376,
0.01621284894645214,
0.005687590688467026,
0.013760600239038467,
-0.0377054363489151,
-0.038498587906360626,
0.01394692063331604,
0.030312467366456985,
-0.02134445682168007,
0.028286069631576538,
0.015634678304195404,
0.048239968717098236,
-0.006215953268110752,
-0.03349515050649643,
-0.022887615486979485,
0.032164283096790314,
-0.03016451559960842,
0.05077456310391426,
-0.011388499289751053,
-0.029044687747955322,
0.022518474608659744,
0.006176976021379232,
0.011892592534422874,
-0.04619216546416283,
-0.012650439515709877,
-0.027341853827238083,
0.0015358123928308487,
0.05172254517674446,
-0.030183371156454086,
0.0008347711409442127,
0.00714333588257432,
0.04783181473612785,
0.011958898976445198,
-0.005702257622033358,
-0.025446811690926552,
-0.05122966319322586,
-0.01853008009493351,
0.00040155439637601376,
-0.02370140515267849,
0.05974060669541359,
0.002690874505788088,
-0.022603530436754227,
0.026004379615187645,
-0.003844562219455838,
0.02387228049337864,
-0.002955829259008169,
0.018064329400658607,
-0.040437251329422,
0.026706386357545853,
-0.02177494578063488,
0.011582333594560623,
0.015225537121295929,
0.0031416635029017925,
0.1282113641500473,
0.05937688425183296,
-0.026920177042484283,
-0.06860930472612381,
-0.00048014879575930536,
-0.03647362440824509,
0.025847814977169037,
0.00032210591598413885,
-0.005013568792492151,
-0.008968990296125412,
0.019784793257713318,
0.020512651652097702,
0.02562098763883114,
-0.05467800050973892,
0.02175849676132202,
0.06752242892980576,
-0.0045799813233315945,
-0.009733887389302254,
0.022220054641366005,
-0.001386110670864582,
0.033475298434495926,
-0.0096433125436306,
0.028324341401457787,
0.03413690626621246,
-0.04455288499593735,
-0.034580379724502563,
-0.041456423699855804,
-0.03815371170639992,
0.03545118495821953,
0.033048372715711594,
-0.05217096954584122,
0.005028910934925079,
0.023104185238480568,
-0.01433371752500534,
-0.004147478844970465,
0.008288362063467503,
-0.011608980596065521,
0.039157453924417496,
0.021978849545121193,
-0.0024680630303919315,
0.04088642820715904,
-0.016928205266594887,
0.014775647781789303,
-0.024368304759263992,
-0.05289695784449577,
-0.0021812517661601305,
-0.03960254043340683,
-0.000736322661396116,
-0.003137018997222185,
-0.024170951917767525,
-0.05407285317778587,
0.03178565576672554,
0.00928706955164671,
-0.008975259959697723,
-0.0563543438911438,
0.04277898371219635,
0.007704492192715406,
-0.041176389902830124,
-0.017059506848454475,
-0.025359466671943665,
0.02642986737191677,
0.00577473035082221,
-0.03159135580062866,
-0.003056214889511466,
-0.008441763930022717,
-0.0027937323320657015,
0.023652300238609314,
0.03025626577436924,
-0.009233837015926838,
-0.0021498992573469877,
0.008030732162296772,
0.0009840464917942882,
-0.038976870477199554,
0.0034938452299684286,
0.0032821246422827244,
0.010846950113773346,
0.02983424998819828,
-0.0006734254420734942,
0.00540575198829174,
0.012977664358913898,
-0.05754180997610092,
0.02242283709347248,
-0.034707583487033844,
-0.01543809100985527,
-0.012556592002511024,
-0.008503423072397709,
0.017872441560029984,
0.034852150827646255,
-0.020017456263303757,
-0.007764867041260004,
0.03842994570732117,
0.013438613153994083,
0.07526423037052155,
0.00020974615472368896,
0.0019611376337707043,
0.02074170671403408,
-0.05315199866890907,
0.03108588606119156,
-0.008697599172592163,
0.035169534385204315,
0.04445530101656914,
0.003288082079961896,
0.033189691603183746,
-0.023948077112436295,
-0.09047026187181473,
0.015810366719961166,
-0.009892917238175869,
-0.04518665373325348,
-0.013672501780092716,
-0.012738385237753391,
0.02606152556836605,
-0.026131989434361458,
-0.05638328567147255,
-0.03105224296450615,
-0.013913200236856937,
-0.006022170651704073,
0.026905221864581108,
-0.02307639643549919,
0.020376671105623245,
-0.024606019258499146,
-0.006168865133076906,
-0.06950744986534119,
0.022829027846455574,
-0.01721094362437725,
-0.0046871015802025795,
0.0031310163903981447,
0.001966778887435794,
-0.012787098065018654,
0.009883090853691101,
-0.03348884731531143,
-0.023765550926327705,
0.04308805987238884,
0.014229240827262402,
-0.006079398095607758,
-0.006981895305216312,
0.007949013262987137,
0.012961908243596554,
0.015513502061367035,
-0.08583186566829681,
-0.0469808466732502,
0.04692159965634346,
-0.01313964556902647,
-0.032917849719524384,
0.07303763180971146,
0.0159732885658741,
-0.012212892062962055,
0.011547001078724861,
-0.029515020549297333,
0.012026148848235607,
0.05385257676243782,
-0.01770835928618908,
-0.02714064158499241,
-0.0035317479632794857,
-0.04573492333292961,
0.012256651185452938,
0.010187841951847076,
0.011263662949204445,
-0.04882517084479332,
-0.004291088320314884,
0.07540621608495712,
0.028829654678702354,
0.037116020917892456,
0.009948882274329662,
-0.015537157654762268,
-0.0018428623443469405,
0.010759033262729645,
0.0156309325248003,
-0.01087647769600153,
0.008028693497180939,
0.019930191338062286,
-0.020248908549547195,
0.005581314209848642,
0.00802475493401289,
0.020463868975639343,
-0.06861140578985214,
-0.007061141077429056,
-0.032074958086013794,
0.005424871109426022,
0.01929229125380516,
-0.04642451927065849,
0.041821423918008804,
0.04997605085372925,
-0.028906170278787613,
0.007335537113249302,
-0.041340190917253494,
-0.06670766323804855,
-0.01717839203774929,
-0.008941618725657463,
0.004343405365943909,
0.014688265509903431,
-0.010492895729839802,
0.03287478908896446,
-0.0065654581412673,
0.03493981808423996,
-0.0026690729428082705,
-0.06759648770093918,
0.025421371683478355,
0.016171950846910477,
0.025389311835169792,
-0.012968325056135654,
0.04085937514901161,
-0.021389856934547424,
-0.0005394088802859187,
0.03929019719362259,
-0.014849130064249039,
0.017019975930452347,
0.025052040815353394,
0.04388134181499481,
-0.022172240540385246,
0.06023663654923439,
0.02116641215980053,
-0.00027728156419470906,
-0.01574874296784401,
0.005181593354791403,
0.018767699599266052,
0.05619882419705391,
0.018707316368818283,
0.009265823289752007,
0.03761783242225647,
-0.023368239402770996,
-0.007317776791751385,
0.047740720212459564,
-0.038441892713308334,
-0.0059370421804487705,
0.03647088631987572,
-0.016363641247153282,
0.0045549883507192135,
-0.048434145748615265,
-0.04199182242155075,
-0.047585487365722656,
-0.03429030254483223,
0.0634901225566864,
0.012613038532435894,
0.0019647767767310143,
-0.05183156579732895,
-0.04170168936252594,
-0.00420231930911541,
0.05519504100084305,
0.047419119626283646,
-0.04119092971086502,
-0.02282034046947956,
0.00840411800891161,
-0.004678771831095219,
0.010286533273756504,
0.006424481514841318,
-0.023679332807660103,
-0.03191583976149559,
0.029340604320168495,
-0.020312458276748657,
0.03493574261665344,
-0.007407018914818764,
-0.029503773897886276,
-0.0042641316540539265,
-0.051600877195596695,
0.023834165185689926,
-0.013546369038522243,
0.024616306647658348,
-0.027359170839190483,
-0.031532738357782364,
-0.009739465080201626,
0.006943254731595516,
0.05533258616924286,
0.01177693996578455,
-0.019696522504091263,
0.015718376263976097,
-0.018610697239637375,
0.023657526820898056,
-0.037846796214580536,
0.08210361003875732,
-0.006605507805943489,
-0.029239457100629807,
0.014256101101636887,
-0.016688892617821693,
-0.049706216901540756,
0.00879066251218319,
0.04289640113711357,
0.002457674592733383,
0.014339376240968704,
-0.013088524341583252,
-0.01611381582915783,
0.04054456576704979,
-0.03236423805356026,
-0.022805936634540558,
0.0682343915104866,
-0.0029571056365966797,
0.018783338367938995,
0.0072208428755402565,
0.013859311118721962,
-0.02927190251648426,
0.013766216114163399,
-0.011166797019541264,
0.0209509190171957,
-0.01912684179842472,
0.010453429073095322,
0.015457644127309322,
-0.04038748890161514,
-0.0017708531813696027,
-0.011830130591988564,
-0.04121879115700722,
-0.018220771104097366,
0.04106324166059494,
-0.005991528742015362,
0.018047435209155083,
-0.02767106145620346,
0.041180819272994995,
0.021150240674614906,
0.011977806687355042,
0.017832333222031593,
0.034033454954624176,
0.011820849031209946,
-0.00779398949816823,
0.050773996859788895,
0.020552106201648712,
0.008726583793759346,
0.010664012283086777,
0.02307184413075447,
0.03770850971341133,
-0.006392538081854582,
-0.045593295246362686,
0.05567113310098648,
-0.018841590732336044,
-0.005104334093630314,
0.011540673673152924,
-0.03919363394379616,
0.08273818343877792,
-0.02714279480278492,
-0.005082167685031891,
-0.06887871772050858,
-0.014290046878159046,
0.011426816694438457,
0.01749529130756855,
-0.01731756329536438,
0.03287661820650101,
-0.05620167404413223,
0.037373531609773636,
-0.023444605991244316,
0.03493461757898331,
0.014001521281898022,
-0.08214351534843445,
0.0029687939677387476,
0.0005431800382211804,
0.020519310608506203,
-0.018759343773126602,
-0.0026883725076913834,
-0.030842246487736702,
-0.04133325070142746,
0.012879692949354649,
0.025728734210133553,
0.02333294041454792,
0.013953831978142262,
-0.03227674216032028,
0.002089223125949502,
0.02929515391588211,
-0.04371703788638115,
0.02809169515967369,
-0.008363877423107624,
0.020931433886289597,
0.0068657067604362965,
0.006106366403400898
] |
<p>If we have two parallel charged plates, equal and opposite in charge:</p>
<p>What is the flux felt on a Gaussian surface between them? surely it sum to 0 as each amount of flux will enter and then leave? This must be wrong as it would mean the field between the two plates is also zero?</p>
<p>Let me know what i'm missing, thanks!</p> | 2,010 | [
-0.0007208243478089571,
0.014432509429752827,
-0.021873893216252327,
0.007642433512955904,
0.03523709252476692,
-0.019464032724499702,
-0.01899024099111557,
-0.004319437779486179,
-0.006026682443916798,
0.008312797173857689,
0.029604559764266014,
0.02129971608519554,
0.04819917678833008,
0.030346205458045006,
-0.006402095779776573,
-0.026010051369667053,
-0.00893484614789486,
-0.009104946628212929,
0.01707337237894535,
-0.02664446271955967,
-0.044716231524944305,
0.046703822910785675,
0.014415806159377098,
0.022066477686166763,
-0.03405257686972618,
0.004887184593826532,
0.027453089132905006,
-0.012988392263650894,
0.02655157446861267,
0.05833874270319939,
-0.00942244753241539,
-0.03426889702677727,
-0.0018363591516390443,
0.0007559368968941271,
0.03151671960949898,
0.004257666878402233,
-0.05117156729102135,
-0.04563535749912262,
-0.015434902161359787,
0.0022239694371819496,
0.008857804350554943,
-0.04668312519788742,
0.018434615805745125,
0.041815850883722305,
-0.01542701292783022,
-0.02859993278980255,
0.014458230696618557,
0.017721019685268402,
0.056120600551366806,
-0.06842546910047531,
0.03258083388209343,
0.012296551838517189,
0.06549538671970367,
0.019298989325761795,
0.030179401859641075,
-0.0020830966532230377,
0.06766419857740402,
0.04557512328028679,
-0.013830109499394894,
-0.046709105372428894,
-0.027840225026011467,
-0.006060555577278137,
-0.0046161157079041,
-0.02888820506632328,
-0.030259963124990463,
0.053060635924339294,
-0.020310556516051292,
-0.039342250674963,
0.03423989564180374,
0.024056274443864822,
0.011348502710461617,
0.05411407724022865,
0.0003487593203317374,
-0.02630671113729477,
0.025728562846779823,
-0.021527912467718124,
0.047850728034973145,
0.03908183053135872,
0.030883904546499252,
0.04308478534221649,
-0.01045143511146307,
0.004104445222765207,
0.019640417769551277,
0.08806885778903961,
0.04445758834481239,
0.004949013702571392,
0.030591744929552078,
-0.03215711936354637,
0.018964556977152824,
0.046812836080789566,
0.010762812569737434,
0.019677212461829185,
-0.0007839864119887352,
0.01683908700942993,
-0.03404015675187111,
0.017771055921912193,
0.002358905738219619,
0.04090193659067154,
-0.0069200750440359116,
-0.0010599128436297178,
-0.015966005623340607,
-0.011295945383608341,
-0.00022178282961249352,
0.056044094264507294,
0.004376656841486692,
-0.02411179058253765,
-0.025199830532073975,
0.025011777877807617,
0.0017031049355864525,
-0.02842876873910427,
-0.054918453097343445,
0.015877775847911835,
0.03822438418865204,
-0.010243307799100876,
0.01594761200249195,
-0.025434289127588272,
0.004222914110869169,
-0.022229336202144623,
0.021782517433166504,
0.05510414391756058,
0.043544963002204895,
-0.027918558567762375,
0.0028356215916574,
-0.01574927754700184,
-0.07609403878450394,
0.007709074299782515,
0.02103377878665924,
-0.029448410496115685,
-0.007829993963241577,
0.02608858048915863,
0.007326713763177395,
-0.01837857812643051,
-0.017706483602523804,
-0.0023634859826415777,
0.02190590836107731,
-0.02942289412021637,
-0.06611916422843933,
-0.07088349759578705,
-0.011982766911387444,
-0.014824144542217255,
-0.009861219674348831,
-0.06943749636411667,
-0.05191536247730255,
0.02821207232773304,
0.03145516663789749,
-0.02321753278374672,
-0.020437292754650116,
-0.014034252613782883,
0.05481112748384476,
-0.027824239805340767,
-0.007337870541960001,
0.0068094776943326,
-0.03415614366531372,
-0.045845694839954376,
-0.0174002293497324,
-0.028305569663643837,
0.009923480451107025,
0.03670992702245712,
-0.023072320967912674,
-0.015742065384984016,
0.030718989670276642,
0.0012149298563599586,
0.0150000536814332,
0.0034121873322874308,
-0.017212603241205215,
-0.04157644882798195,
0.08189553022384644,
0.02476455457508564,
0.03182896226644516,
0.030216358602046967,
0.010671619325876236,
0.00242432439699769,
-0.01563425548374653,
0.022324034944176674,
0.04464627429842949,
-0.04018785431981087,
-0.02962629497051239,
-0.022473173215985298,
0.02767319045960903,
0.018758846446871758,
-0.044699836522340775,
-0.04412487521767616,
0.010607479140162468,
0.009859539568424225,
0.003169155213981867,
0.04501321539282799,
-0.000360830599674955,
-0.028702160343527794,
-0.061335984617471695,
-0.04289102181792259,
-0.020466051995754242,
-0.06097003445029259,
0.04025454446673393,
0.01734883338212967,
0.002511576283723116,
0.007356138899922371,
-0.007161100395023823,
0.020101239904761314,
-0.04969083517789841,
-0.04214419052004814,
0.02545975148677826,
0.016539858654141426,
-0.033461276441812515,
-0.01697172038257122,
0.01484730839729309,
0.02944105863571167,
0.04371029511094093,
0.0020484484266489744,
0.04928091913461685,
-0.038930874317884445,
0.0023897532373666763,
0.007887098006904125,
-0.0031722215935587883,
0.03874899446964264,
0.017032772302627563,
-0.02416602522134781,
0.0030889236368238926,
0.013035261072218418,
-0.01406332291662693,
0.0673799067735672,
-0.039971161633729935,
0.06250830739736557,
0.04621535912156105,
0.015073521994054317,
-0.018456587567925453,
0.02261705882847309,
-0.01557867880910635,
0.012147006578743458,
-0.03161562234163284,
-0.04843158274888992,
-0.023339537903666496,
0.017309941351413727,
0.04158154875040054,
0.030088944360613823,
-0.011925204657018185,
0.004424075596034527,
0.04032844305038452,
0.010589124634861946,
-0.004011006094515324,
0.01125221885740757,
-0.0036949096247553825,
-0.05075638368725777,
0.03876372426748276,
0.003295667702332139,
-0.014835100620985031,
0.009744717739522457,
0.05192624405026436,
0.005997673142701387,
0.011514072306454182,
0.04033343866467476,
-0.031193947419524193,
0.03810367360711098,
-0.004506572615355253,
0.04600538685917854,
-0.022429954260587692,
-0.04920630902051926,
0.02509165368974209,
-0.009137272834777832,
0.04866069555282593,
0.00218239170499146,
0.024137435480952263,
-0.005895528476685286,
-0.009037257172167301,
0.02092154137790203,
0.002422724151983857,
-0.04603917896747589,
-0.00046555176959373057,
-0.004445123951882124,
0.03864021226763725,
-0.06313393265008926,
0.02657569944858551,
0.009499519132077694,
0.00642656022682786,
0.0016553511377424002,
-0.030097996816039085,
-0.012000651098787785,
0.015500450506806374,
0.062496960163116455,
-0.025479869917035103,
-0.023999497294425964,
0.008002896793186665,
-0.019786056131124496,
0.022764401510357857,
0.022018399089574814,
-0.03279346600174904,
0.034928660839796066,
-0.04335283860564232,
-0.0029342120978981256,
0.046437010169029236,
-0.01908905617892742,
0.005858215969055891,
0.023229248821735382,
-0.041621558368206024,
-0.04169141873717308,
0.022884713485836983,
-0.007985386066138744,
-0.011376122012734413,
-0.03312167152762413,
0.02858993597328663,
0.036055997014045715,
-0.0005701857153326273,
-0.03711653873324394,
0.01958317495882511,
-0.062435999512672424,
-0.04723627120256424,
-0.008020502515137196,
0.00031293468782678246,
0.014270074665546417,
-0.013433292508125305,
0.021966230124235153,
0.019786765798926353,
-0.07653521746397018,
-0.009370488114655018,
-0.0509663000702858,
-0.04502991586923599,
0.01335375290364027,
-0.0331149660050869,
0.027736613526940346,
-0.025064462795853615,
-0.08477502316236496,
0.06665924191474915,
0.03867921978235245,
-0.006058801431208849,
0.0012901055160909891,
-0.04443720728158951,
0.008507870137691498,
-0.01865644007921219,
0.002872531535103917,
0.029631929472088814,
-0.028814490884542465,
0.026606671512126923,
0.003389510093256831,
0.02903512679040432,
0.0012348421150818467,
0.01864727959036827,
0.022200828418135643,
-0.018355952575802803,
0.002237992826849222,
-0.013078813441097736,
0.04798578843474388,
0.03382274508476257,
-0.006174359004944563,
0.0033509479835629463,
0.021533241495490074,
0.030682172626256943,
0.030186068266630173,
0.0005834783660247922,
0.0506298765540123,
-0.006913619115948677,
0.02604551799595356,
-0.024623241275548935,
0.04665376991033554,
0.017240609973669052,
0.003678226610645652,
-0.006802605930715799,
0.009811658412218094,
0.03314317762851715,
-0.04323703795671463,
-0.021469024941325188,
0.038831304758787155,
0.04567324370145798,
-0.01416170597076416,
-0.05360216647386551,
0.0033876800443977118,
0.004432084504514933,
0.0015173848951235414,
-0.022511031478643417,
-0.029118206351995468,
0.027992982417345047,
0.046086568385362625,
0.004338499158620834,
0.023547876626253128,
-0.016852792352437973,
-0.03323613852262497,
-0.08143778890371323,
-0.008226870559155941,
0.018128134310245514,
0.05082232877612114,
0.013000816106796265,
0.03396228700876236,
0.020235538482666016,
0.024080151692032814,
-0.013318202458322048,
0.022333163768053055,
-0.0733911320567131,
0.012576843611896038,
-0.010805424302816391,
-0.04118733108043671,
-0.01121870893985033,
-0.031093301251530647,
-0.019145965576171875,
-0.017119206488132477,
-0.000891891831997782,
-0.041610173881053925,
-0.003228268586099148,
-0.07085418701171875,
0.003715922823175788,
-0.016978289932012558,
-0.059138473123311996,
-0.016898050904273987,
0.03628764674067497,
0.008825038559734821,
-0.041522253304719925,
0.028477743268013,
0.0484868623316288,
-0.04918947070837021,
-0.038047634065151215,
-0.0054331147111952305,
0.013027971610426903,
0.0020402870140969753,
0.044155847281217575,
0.03803665190935135,
0.01761636696755886,
-0.02877601981163025,
0.03037252090871334,
-0.011693770065903664,
0.0663134977221489,
-0.008092641830444336,
-0.0437932163476944,
-0.015884052962064743,
-0.05067097395658493,
-0.037013303488492966,
-0.01696888543665409,
0.049729906022548676,
0.013379305601119995,
-0.010351828299462795,
0.0004279825952835381,
0.03348361328244209,
0.014662805944681168,
0.02615508623421192,
0.05441039428114891,
0.01395320612937212,
-0.003678314620628953,
-0.06278996914625168,
-0.0037257696967571974,
-0.04287528991699219,
0.01462521217763424,
0.02044379524886608,
-0.009551597759127617,
-0.03084637224674225,
-0.035018038004636765,
-0.010472467169165611,
0.00579700106754899,
0.018907660618424416,
0.017009107396006584,
-0.0035280603915452957,
0.009547197259962559,
0.012631919234991074,
0.004449927248060703,
0.021585678681731224,
0.04835722595453262,
0.041941672563552856,
0.006902324501425028,
-0.03884264826774597,
-0.06352549046278,
0.0007730877259746194,
0.03275148570537567,
0.050081294029951096,
0.005462991073727608,
-0.04108045995235443,
-0.0041977763175964355,
0.0019990047439932823,
0.028910357505083084,
-0.014242064207792282,
0.0012590731494128704,
-0.031367164105176926,
0.01999160647392273,
-0.007283225189894438,
-0.013210847042500973,
-0.03431568667292595,
0.04370569810271263,
0.001234633382409811,
0.029779307544231415,
-0.012711375020444393,
-0.001878265873529017,
0.015704208984971046,
0.007677413988858461,
0.001980635803192854,
0.043298982083797455,
-0.024377575144171715,
0.01807224377989769,
0.01567845419049263,
0.011488314718008041,
-0.032121628522872925,
-0.07217948138713837,
0.025995608419179916,
-0.018615366891026497,
0.0030537855345755816,
0.040693555027246475,
-0.027189061045646667,
-0.04773904010653496,
0.021049682050943375,
0.004572805017232895,
0.025853024795651436,
0.012875841930508614,
-0.04065471515059471,
0.015070189721882343,
0.04726775735616684,
0.006773862987756729,
0.07986283302307129,
0.022319646552205086,
-0.0846351757645607,
-0.02495083026587963,
0.011783795431256294,
0.0323205441236496,
0.006397348362952471,
0.005815288983285427,
-0.021813364699482918,
-0.009327560663223267,
-0.056250087916851044,
0.021820513531565666,
-0.04512658715248108,
0.041427917778491974,
-0.01597425900399685,
-0.05562383309006691,
-0.006862018257379532,
-0.011616122908890247,
0.015046577900648117,
0.02776482328772545,
-0.011411229148507118,
0.011972890235483646,
0.01831081695854664,
-0.0360356867313385,
-0.0013601257232949138,
0.007143096067011356,
0.0263697300106287,
0.015194038860499859,
0.03985707834362984,
0.019900113344192505,
-0.007481262553483248,
-0.02472768910229206,
0.004384580068290234,
-0.06548161804676056,
0.04897676780819893,
-0.04205320030450821,
0.012957227416336536,
0.0032919596415013075,
-0.029478343203663826,
-0.019201217219233513,
0.03145860880613327,
0.011982990428805351,
0.03280840069055557,
-0.03927987068891525,
0.020057901740074158,
0.04135254770517349,
0.011834658682346344,
-0.057194504886865616,
-0.03936860337853432,
0.041982829570770264,
0.024179840460419655,
-0.011721807532012463,
-0.006879848428070545,
-0.01770208030939102,
-0.031907808035612106,
-0.0363936722278595,
-0.0035844033118337393,
0.05493636056780815,
-0.044229984283447266,
-0.001200999366119504,
0.03934895247220993,
-0.01889551430940628,
0.04180683195590973,
0.004345967434346676,
-0.0270619448274374,
0.05243280529975891,
-0.0368632897734642,
-0.05137818679213524,
-0.028128277510404587,
0.053090568631887436,
-0.023541726171970367,
-0.02830064855515957,
0.009194329380989075,
-0.025567032396793365,
0.049728233367204666,
-0.010086502879858017,
-0.018015950918197632,
0.008631783537566662,
0.015353625640273094,
-0.0472136065363884,
-0.02534588612616062,
0.02931416779756546,
0.010497601702809334,
0.0312974639236927,
-0.031186005100607872,
-0.014498076401650906,
-0.05230036377906799,
-0.020780684426426888,
-0.019154174253344536,
0.0020384860690683126,
-0.0004802498151548207,
-0.016996094956994057,
0.06823304295539856,
0.006531902588903904,
-0.026005642488598824,
0.03168584778904915,
0.026310201734304428,
0.035810135304927826,
0.020707614719867706,
0.023042017593979836,
0.003595736576244235,
0.006606403738260269,
-0.048307958990335464,
0.030519351363182068,
-0.0342104509472847,
-0.027626294642686844,
0.08055253326892853,
-0.01773727312684059,
0.065375916659832,
-0.021167295053601265,
-0.017175499349832535,
0.0005577136180363595,
-0.01730448566377163,
-0.029933473095297813,
-0.010114447213709354,
-0.020729832351207733,
-0.0032140975818037987,
-0.026802442967891693,
0.008137036114931107,
0.0006147351232357323,
0.02232234925031662,
0.03670378029346466,
0.0066898781806230545,
0.015563920140266418,
0.035314884036779404,
0.039468664675951004,
-0.0025156259071081877,
-0.05541255697607994,
0.0383777841925621,
-0.03718801587820053,
0.03636696934700012,
-0.023132964968681335,
-0.02353614754974842,
0.05807780474424362,
-0.015292113646864891,
0.011115798726677895,
-0.03247866407036781,
-0.01502627320587635,
-0.001747802016325295,
0.02340424433350563,
0.04499600827693939,
0.021089846268296242,
-0.05108968913555145,
0.0077734654769301414,
0.03266188129782677,
0.013448757119476795,
0.018043015152215958,
0.016052288934588432,
-0.04783806949853897,
-0.02271396666765213,
-0.04825086519122124,
-0.040922656655311584,
0.027562594041228294,
0.001095034647732973,
-0.026726756244897842,
0.0015528224175795913,
-0.019313208758831024,
0.05112671107053757,
0.010321526788175106,
-0.004191855434328318,
-0.027617165818810463,
0.03378327935934067,
-0.009870610199868679,
0.03799712285399437,
-0.07250623404979706,
0.01947873644530773,
0.11766459792852402,
0.04347141087055206,
0.03664238005876541,
-0.04973587393760681,
0.023887300863862038,
-0.052269499748945236,
-0.007008643355220556,
-0.020270701497793198,
0.048927899450063705,
-0.03680499643087387,
-0.001177043654024601,
0.009936410002410412,
0.05577802658081055,
0.005957202985882759,
-0.010479975491762161,
0.020102281123399734,
-0.020560817793011665,
-0.03715452179312706,
0.0017129500629380345,
0.034602854400873184,
-0.013369965367019176,
0.032080937176942825,
-0.04778316989541054,
0.03394685313105583,
-0.050861526280641556,
0.03211869299411774,
-0.03166567534208298,
-0.029745526611804962,
-0.0036660118494182825,
0.025042066350579262,
-0.026777876541018486,
0.030448855832219124,
0.013603974133729935,
-0.01864534802734852,
-0.05784048140048981,
0.014238960109651089,
0.07701309770345688,
0.008706053718924522,
0.002723455661907792,
0.044701073318719864,
0.006398284807801247,
0.024917054921388626,
0.03349284455180168,
0.014503984712064266,
-0.05299029126763344,
-0.00856750551611185,
-0.03641393035650253,
0.06848350912332535,
-0.016393527388572693,
0.02902957610785961,
0.015485680662095547,
0.018398737534880638,
0.010461117140948772,
-0.06266822665929794,
-0.030425097793340683,
-0.02424042671918869,
0.012104315683245659,
0.0007237084791995585,
-0.011610751040279865,
-0.004274486564099789,
0.06404940038919449,
-0.00168170768301934,
-0.004707151558250189,
0.031008129939436913,
0.00029437404009513557,
0.013408707454800606,
0.009887306950986385,
0.06282420456409454,
-0.007181023713201284,
-0.007824658416211605,
0.0032018846832215786,
-0.046473179012537,
-0.053802136331796646,
-0.014110436663031578,
-0.008169091306626797,
0.028465919196605682,
0.02054126188158989,
-0.011101623997092247,
-0.0345006063580513,
-0.02051600255072117,
-0.06969068199396133,
0.06204599887132645,
0.006945851258933544,
0.027609745040535927,
0.007480242755264044,
-0.015634790062904358,
0.0007851123809814453,
0.035210367292165756,
-0.01593243144452572,
0.019939521327614784,
0.04627251997590065,
0.028112417086958885,
0.009272634983062744,
0.020389661192893982,
-0.03206025809049606,
-0.02386164292693138,
-0.027804549783468246,
-0.016360510140657425,
0.021701283752918243,
0.0217885822057724,
0.005401770584285259,
0.0266948901116848,
0.033692654222249985,
0.02949838899075985,
-0.020633911713957787,
-0.007952968589961529,
0.0158398374915123,
-0.0216701440513134,
0.008620177395641804,
0.021602652966976166,
0.005974141880869865,
-0.006924637593328953,
-0.0011723678326234221,
-0.020905494689941406,
0.008686049841344357,
-0.019686035811901093,
0.024992985650897026,
-0.03222202509641647,
-0.04923825338482857,
0.017059052363038063,
0.013810809701681137,
-0.033888254314661026,
-0.030130332335829735,
-0.04454078897833824,
-0.008271119557321072,
0.033353619277477264,
0.04078990966081619,
-0.0017776783788576722,
0.02287161722779274,
-0.049858465790748596,
-0.022503117099404335,
0.03374481201171875,
-0.017438963055610657,
-0.00750519335269928,
0.01272687129676342,
0.03902198001742363,
-0.006168271880596876,
0.03689755126833916,
-0.01865878887474537,
-0.03006373532116413,
0.0261556226760149,
-0.03448127955198288,
-0.06431853771209717,
0.022892706096172333,
0.029252292588353157,
0.03954475745558739,
0.007027179002761841,
0.0010985255939885974,
-0.06044650450348854,
0.04805009067058563,
0.0023529629688709974,
0.0027985437773168087,
-0.04731319099664688,
-0.015468241646885872,
-0.011479931883513927,
-0.028653157874941826,
0.026577666401863098,
0.012093895114958286,
-0.001137008424848318,
0.009233534336090088,
-0.015578384511172771,
-0.013837485574185848,
0.0006168528343550861,
-0.015886874869465828,
-0.027127757668495178,
-0.06787815690040588,
0.02811512164771557,
0.0005578390555456281,
-0.013699584640562534,
0.05480758845806122,
-0.009644361212849617,
0.006780869793146849,
-0.027205802500247955,
0.019561681896448135,
-0.05278869718313217,
-0.03179268166422844,
0.002501988783478737,
0.008618361316621304,
0.012697570957243443,
-0.05787772312760353,
0.0156431645154953,
0.04225863143801689,
-0.10207857936620712,
0.008816773071885109,
0.02856101654469967,
-0.029746877029538155,
-0.0039808489382267,
0.001532049267552793,
0.005695106461644173,
0.04907098785042763,
0.008735350333154202,
0.05599530413746834,
0.02404169738292694,
0.020905522629618645,
-0.005658713169395924,
-0.05502428486943245,
-0.05843294784426689,
0.02264002151787281,
-0.025293558835983276,
-0.019284050911664963,
0.03167160227894783,
0.0031667309813201427,
0.010310669429600239,
0.02922234870493412,
-0.008851678110659122,
-0.014508837834000587,
-0.020676247775554657,
0.04578626528382301,
0.023815633729100227,
0.026764575392007828,
-0.013545496389269829,
-0.009287259541451931,
-0.029376663267612457,
0.02462526224553585,
-0.015502906404435635,
0.006767048500478268,
-0.03593626245856285,
0.0008146911859512329,
0.06795684248209,
0.0033129118382930756,
-0.029750052839517593,
0.011695033870637417,
-0.04491773620247841,
-0.012825865298509598,
0.001058403286151588,
0.045442283153533936,
0.035657837986946106,
-0.024997638538479805,
-0.016466040164232254,
-0.048832450062036514,
0.028356019407510757,
0.0074432361871004105,
-0.0026543601416051388,
-0.015728702768683434,
0.02014637365937233,
0.00334034557454288,
0.004114286508411169,
0.01868007332086563,
0.0020963530987501144,
0.02328442968428135,
-0.023977553471922874,
-0.0189003124833107,
0.008217357099056244,
0.0032423888333141804,
0.05372568964958191,
-0.028379011899232864,
-0.03475790098309517,
0.011465253308415413,
0.006537931505590677,
0.00927013996988535,
-0.020087309181690216,
-0.07685811072587967,
-0.004743339028209448,
-0.05208948254585266,
0.004971139132976532,
-0.006350843235850334,
-0.04411650821566582,
-0.026883428916335106,
-0.0313275121152401,
-0.016281262040138245,
-0.017199108377099037,
0.0678841769695282,
-0.00487910583615303,
-0.008099737577140331,
0.04160614684224129,
0.01525427307933569,
0.05037156492471695,
-0.04861309751868248,
0.010830730199813843,
0.014788889326155186,
-0.032542839646339417,
0.026180068030953407,
-0.01737443543970585,
-0.03805476427078247,
0.030284978449344635,
0.025795701891183853,
-0.024596020579338074,
0.017525216564536095,
-0.045554447919130325,
-0.04184982553124428,
0.04368334636092186,
0.04118482023477554,
0.008256715722382069,
0.0914735347032547,
-0.026023296639323235,
0.061842311173677444,
0.013883507810533047,
-0.03159826248884201,
-0.03441191837191582,
-0.013156126253306866,
-0.04904880374670029,
0.019129309803247452,
-0.04243742302060127,
0.01805763877928257,
0.021584685891866684,
-0.026442131027579308,
-0.014954234473407269,
0.04949859902262688,
-0.03720684349536896,
-0.031284771859645844,
0.07240080833435059,
0.01711791194975376,
0.028128428384661674,
0.001117176259867847,
0.021074801683425903,
-0.005297014955431223,
0.0035196973476558924,
0.028586959466338158,
0.06890040636062622,
0.023462889716029167,
0.030212797224521637,
0.0033104128669947386,
0.06490862369537354,
-0.030881153419613838,
0.008880291134119034,
0.004527430981397629,
-0.003273787209764123,
0.0022719530388712883,
-0.024559175595641136,
-0.006565040908753872,
0.005420670844614506,
-0.00748126907274127,
0.014159910380840302,
-0.013325359672307968,
0.09535738825798035,
-0.0330217108130455,
-0.005711020436137915,
0.0214469525963068,
0.023253370076417923,
-0.004526941105723381,
0.01544261910021305,
0.014381246641278267,
0.03714526444673538,
-0.02760923095047474,
-0.060273658484220505,
-0.023093242198228836,
0.021565042436122894,
0.013287905603647232,
-0.03234812617301941,
0.007636372931301594,
-0.0017048309091478586,
0.014021474868059158,
0.01022858265787363,
0.01877422258257866,
-0.021647073328495026,
0.01084933616220951,
0.02311757765710354,
-0.00559429032728076,
0.0006432980881072581,
0.0002836506173480302,
0.006811144296079874,
-0.031865350902080536,
0.029407843947410583,
-0.06157604604959488,
-0.02046605944633484,
-0.005773718468844891,
0.02926005609333515,
-0.010945160873234272,
-0.008642353117465973
] |
<p>If we imagine a object made up of Hydrogen gas that is optically thick to all radiation, and is in thermal equilibrium, then, microscopically, photons will be emitted and absorbed as emission/absorption lines.</p>
<p>However, the overall object should emit radiation according to <a href="https://en.wikipedia.org/wiki/Planck_function" rel="nofollow">Planck’s Law</a>, which describes intensity as a continuous function of wavelength (and temperature).</p>
<p>How does this occur and where do the photons we detect at wavelengths between spectral lines of hydrogen come from originally?</p> | 2,011 | [
-0.018697354942560196,
-0.029246550053358078,
0.039401765912771225,
-0.020882075652480125,
0.022553734481334686,
0.04605242237448692,
-0.02326739951968193,
0.004725119564682245,
0.02102687954902649,
-0.04395561292767525,
0.035860054194927216,
0.0018808090826496482,
0.0419328399002552,
0.0025788755156099796,
0.012269658967852592,
0.011534657329320908,
-0.004933311603963375,
-0.02656804770231247,
-0.022800374776124954,
-0.027096107602119446,
-0.025676626712083817,
0.019362952560186386,
0.0199135635048151,
0.00403561070561409,
-0.09593086689710617,
0.044095586985349655,
-0.0025216357316821814,
0.03169260174036026,
0.04006366431713104,
0.03465227037668228,
-0.019077107310295105,
0.010276051238179207,
-0.004630433861166239,
0.024457907304167747,
0.0004758922441396862,
0.006444466765969992,
-0.02381841279566288,
-0.036725275218486786,
-0.0006711847963742912,
-0.0015305649721994996,
-0.021234950050711632,
-0.0028689492028206587,
-0.008694877848029137,
0.021055806428194046,
-0.030809501186013222,
-0.03091190755367279,
-0.020689958706498146,
-0.005249663256108761,
0.03973635286092758,
-0.060271255671978,
0.03504277020692825,
-0.0008685869979672134,
0.0631021112203598,
0.025654299184679985,
0.003980643581598997,
-0.0016578977229073644,
0.08019748330116272,
0.09215250611305237,
0.0019189049489796162,
-0.014716648496687412,
-0.017762428149580956,
-0.02485210821032524,
-0.04276805371046066,
-0.030450867488980293,
-0.003822900587692857,
0.04260672628879547,
-0.007634800858795643,
-0.030547497794032097,
0.018714971840381622,
0.03524860739707947,
0.02207764983177185,
0.001060177804902196,
0.07277516275644302,
0.01306937262415886,
0.054386161267757416,
-0.004443502984941006,
0.035021815448999405,
0.03098021261394024,
0.04760335758328438,
0.040195614099502563,
0.00594791304320097,
-0.007839457131922245,
0.010140788741409779,
0.01784736104309559,
0.027341730892658234,
0.013080104254186153,
0.08450915664434433,
-0.003533837152644992,
0.022635411471128464,
0.02162921614944935,
0.011101975105702877,
0.03315567225217819,
0.040361903607845306,
0.03670194000005722,
-0.006198436487466097,
0.027282388880848885,
-0.026745706796646118,
0.04534776136279106,
-0.027863601222634315,
-0.01925051584839821,
0.029619233682751656,
-0.003528964938595891,
0.04485146701335907,
0.04794759303331375,
0.004705552943050861,
-0.004631770309060812,
-0.05549221858382225,
0.013151663355529308,
-0.03940163552761078,
0.033550627529621124,
-0.035644300282001495,
0.039441097527742386,
-0.0021070425864309072,
-0.005874105729162693,
-0.005099560134112835,
-0.002594595542177558,
0.02658376656472683,
-0.05005680024623871,
0.06524243205785751,
0.06539050489664078,
0.004070456139743328,
-0.01840423233807087,
0.022625043988227844,
-0.016190173104405403,
-0.0277115348726511,
-0.0021274741739034653,
-0.0006350293988361955,
-0.0011312277056276798,
-0.04129452630877495,
0.04290880635380745,
-0.028628483414649963,
-0.03907022252678871,
0.034617118537425995,
0.017312578856945038,
-0.009674121625721455,
-0.022590791806578636,
-0.08402808755636215,
-0.07780776917934418,
0.037754982709884644,
0.005686057731509209,
-0.010409943759441376,
-0.04775402694940567,
0.016803281381726265,
0.06826168298721313,
0.06923200190067291,
-0.005401937291026115,
-0.01467853132635355,
-0.01886448822915554,
0.02584872394800186,
-0.01175831537693739,
-0.009639432653784752,
-0.0146167678758502,
-0.021683352068066597,
-0.005118576809763908,
-0.011806872673332691,
-0.04793738201260567,
0.03437730669975281,
0.03776054456830025,
0.007960919290781021,
-0.0217684805393219,
0.05703083053231239,
-0.0058669596910476685,
-0.02373695559799671,
0.004022609442472458,
-0.007607183884829283,
-0.055019576102495193,
0.07243167608976364,
0.041342251002788544,
-0.002582926768809557,
0.02011306956410408,
0.014810948632657528,
0.007601565681397915,
0.024019431322813034,
0.04803020879626274,
-0.03921941667795181,
-0.032556794583797455,
-0.002199646085500717,
-0.03359690308570862,
0.04321752488613129,
0.033887531608343124,
-0.03766052424907684,
-0.05646011605858803,
-0.03062109649181366,
0.020336834713816643,
0.039564941078424454,
0.03819255903363228,
0.019601596519351006,
-0.02114129066467285,
-0.007061353884637356,
-0.05405989661812782,
0.0038605304434895515,
-0.03645713999867439,
0.041225310415029526,
0.03218021243810654,
-0.021554335951805115,
-0.0072998465038836,
0.023181281983852386,
0.003003546269610524,
-0.01836123690009117,
-0.051083896309137344,
0.000602859363425523,
0.032367005944252014,
-0.005716392770409584,
0.00852862000465393,
0.022593650966882706,
0.08207575231790543,
0.05740019306540489,
0.009373264387249947,
-0.017163407057523727,
-0.03444468602538109,
-0.02279147133231163,
-0.00305412826128304,
-0.04073503986001015,
0.0076644266955554485,
-0.0008562364964745939,
0.010943710803985596,
-0.0013769918587058783,
-0.024902621284127235,
-0.010433919727802277,
0.019394036382436752,
-0.024216989055275917,
0.041321903467178345,
0.037982698529958725,
0.022462263703346252,
-0.03299843892455101,
0.021201493218541145,
-0.013000470586121082,
-0.00204499252140522,
-0.021772833541035652,
-0.033890049904584885,
-0.050520554184913635,
0.018405821174383163,
0.04826217517256737,
-0.003383379429578781,
-0.03719903901219368,
-0.021392926573753357,
-0.02411375194787979,
0.023531582206487656,
0.002086155116558075,
0.017727728933095932,
-0.06337017565965652,
-0.01593000441789627,
0.010009360499680042,
0.002597585553303361,
0.015351705253124237,
-0.0097967479377985,
0.015948649495840073,
0.03345673903822899,
0.008920258842408657,
0.0019247784512117505,
0.015144388191401958,
0.038441337645053864,
0.0031284166034311056,
0.034976258873939514,
-0.032282885164022446,
-0.03243109583854675,
0.011347259394824505,
-0.01876562088727951,
0.0118046710267663,
0.001028721104376018,
-0.026436738669872284,
0.007787028327584267,
-0.03657042607665062,
-0.035306259989738464,
0.003302880795672536,
-0.0024911125656217337,
-0.02337172068655491,
-0.00794035941362381,
0.03378647565841675,
-0.036838069558143616,
0.02024601213634014,
-0.03302018716931343,
-0.01928306557238102,
-0.04183584824204445,
-0.008430801331996918,
0.010923667810857296,
0.021818071603775024,
0.04521183297038078,
-0.08983881026506424,
-0.05369307100772858,
-0.0067259096540510654,
-0.04827465862035751,
0.016091959550976753,
-0.004387764725834131,
-0.009724934585392475,
-0.0014329591067507863,
-0.04106440767645836,
-0.04855629801750183,
0.01498808991163969,
0.004184030927717686,
0.005669522099196911,
-0.005797186400741339,
-0.032083526253700256,
-0.04514303803443909,
0.025472378358244896,
0.02412741258740425,
-0.03197270259261131,
0.0021462568547576666,
0.015275971964001656,
0.05492663383483887,
-0.05925920233130455,
-0.041882943361997604,
0.043477632105350494,
-0.04148835316300392,
-0.05673821642994881,
-0.04230112209916115,
-0.020399631932377815,
-0.016139833256602287,
0.01362833846360445,
0.031073298305273056,
0.02661895751953125,
-0.060369327664375305,
-0.024790693074464798,
-0.04645154997706413,
-0.015780547633767128,
0.0315261073410511,
-0.017093414440751076,
0.011021409183740616,
-0.007396935485303402,
-0.01309817936271429,
0.03983628749847412,
0.0294398982077837,
-0.005276362411677837,
-0.030992118641734123,
-0.006050655152648687,
0.018870562314987183,
-0.06828274577856064,
0.03171329200267792,
0.024539858102798462,
0.018335508182644844,
0.016211027279496193,
0.012129715643823147,
0.0033763565588742495,
0.04965163767337799,
-0.0019481913186609745,
-0.01704755239188671,
0.008646809495985508,
-0.009466956369578838,
-0.01795853115618229,
0.061239153146743774,
0.051306888461112976,
-0.005678434390574694,
0.0014895859640091658,
-0.008027677424252033,
0.011289285495877266,
0.03362516686320305,
-0.04484737664461136,
0.04727581515908241,
0.027600999921560287,
0.006650138180702925,
-0.046585813164711,
0.02933618240058422,
0.01267155073583126,
-0.011300374753773212,
-0.0008959395927377045,
0.003781119594350457,
0.05106702074408531,
0.007254022639244795,
-0.025249680504202843,
0.01810290291905403,
0.015452737919986248,
0.004978042095899582,
-0.0243925042450428,
0.0260333064943552,
0.007509280927479267,
0.011009722016751766,
-0.0012227637926116586,
0.003838862292468548,
0.05454471707344055,
0.037073902785778046,
0.015239323489367962,
0.007138073444366455,
-0.045663077384233475,
-0.02359379269182682,
-0.033376459032297134,
-0.029327716678380966,
-0.0035296492278575897,
0.05662539228796959,
0.007951251231133938,
0.07204969972372055,
0.034375254064798355,
0.027366815134882927,
0.028248634189367294,
-0.03597766533493996,
-0.10256513208150864,
0.006141688209027052,
-0.023738566786050797,
-0.0277094766497612,
-0.03363055735826492,
-0.01757107302546501,
-0.029426440596580505,
-0.029431510716676712,
-0.018921440467238426,
-0.004648349713534117,
-0.02888953872025013,
-0.030598299577832222,
-0.002411835826933384,
-0.011911153793334961,
-0.08294103294610977,
-0.03524677827954292,
0.021049652248620987,
0.04352359473705292,
0.00925542414188385,
0.024609612300992012,
0.03076227940618992,
-0.0025680556427687407,
0.02828451246023178,
-0.0027894400991499424,
0.015100689604878426,
0.003237284952774644,
0.03543546423316002,
0.035821761935949326,
0.017426135018467903,
-0.027902403846383095,
0.004365241155028343,
0.024942265823483467,
0.03750619664788246,
-0.003850587410852313,
-0.03466884419322014,
-0.008451382629573345,
-0.006705195177346468,
0.00021994383132550865,
0.00546173844486475,
0.05476925149559975,
-0.020198747515678406,
-0.01158488355576992,
0.000013179133020457812,
-0.008060403168201447,
-0.020909951999783516,
0.023819290101528168,
0.04098524898290634,
-0.025262929499149323,
-0.018992483615875244,
-0.018992066383361816,
-0.005079492926597595,
-0.03140643611550331,
0.0042716218158602715,
0.005263329483568668,
-0.003708470379933715,
0.008926354348659515,
0.003594563575461507,
0.01211710274219513,
0.05096079036593437,
0.018723731860518456,
-0.036123838275671005,
-0.013603060506284237,
0.030349334701895714,
-0.03198913484811783,
-0.006298742722719908,
0.020909590646624565,
0.054502882063388824,
0.05225701257586479,
-0.013375082053244114,
0.0014851740561425686,
-0.09068232774734497,
-0.023153208196163177,
-0.00882081687450409,
-0.0065824794583022594,
0.021737391129136086,
0.0037112084683030844,
-0.06532672792673111,
0.004688572604209185,
0.05287638306617737,
-0.002790333703160286,
0.034689195454120636,
-0.027668386697769165,
-0.012660214677453041,
-0.006171722896397114,
-0.024956321343779564,
-0.01727079227566719,
0.0236222967505455,
0.0018692400772124529,
0.020133167505264282,
-0.0251274686306715,
-0.008800731040537357,
-0.002652255352586508,
0.04782478138804436,
0.020968200638890266,
-0.0018331335159018636,
-0.03653008118271828,
-0.015536666847765446,
0.006410675123333931,
0.007265112828463316,
0.008855379186570644,
-0.09254810214042664,
-0.0018521560123190284,
-0.020108390599489212,
0.005267210304737091,
0.04304349422454834,
-0.037726014852523804,
-0.03641197830438614,
0.006211044732481241,
0.025176027789711952,
-0.013567126356065273,
-0.008471055887639523,
-0.03730012848973274,
0.051660213619470596,
0.028119327500462532,
-0.004057323560118675,
0.05638531222939491,
0.049596842378377914,
0.004357900470495224,
0.0066464738920331,
-0.01930934190750122,
0.045945536345243454,
-0.0306272953748703,
0.001368619268760085,
-0.04630103334784508,
-0.010524463839828968,
-0.016013644635677338,
0.03521057963371277,
0.04610990732908249,
-0.012118099257349968,
0.024537373334169388,
-0.049698859453201294,
0.03056476265192032,
0.028696903958916664,
-0.03943609073758125,
0.007284886669367552,
-0.038761530071496964,
0.05786342918872833,
0.00758308544754982,
-0.0033345057163387537,
0.030508190393447876,
0.01996421627700329,
-0.00025423686020076275,
0.005106007214635611,
-0.00022784255270380527,
0.07784690707921982,
-0.0062493314035236835,
0.0013671198394149542,
0.0053811934776604176,
-0.028933772817254066,
0.0020032732281833887,
-0.017242081463336945,
0.019089996814727783,
0.0398823618888855,
-0.03163613751530647,
-0.015922725200653076,
-0.006402895320206881,
-0.027315733954310417,
0.016337469220161438,
-0.028407858684659004,
0.035151634365320206,
-0.01832744851708412,
0.014295139349997044,
-0.06371588259935379,
0.003567545674741268,
-0.00809639971703291,
0.03446732833981514,
-0.0004802346811629832,
-0.04834699258208275,
0.025109710171818733,
-0.017720220610499382,
-0.029883073642849922,
0.003637065878137946,
-0.004180362913757563,
-0.008311167359352112,
0.003776193130761385,
-0.020501110702753067,
0.017242928966879845,
0.04033881053328514,
-0.030380534008145332,
-0.010126592591404915,
0.005606392864137888,
0.04320142790675163,
-0.03896082937717438,
-0.005366542376577854,
0.021595783531665802,
-0.004472862929105759,
-0.0336034819483757,
-0.0042670308612287045,
-0.011333352886140347,
-0.0012633095029741526,
-0.01202112901955843,
-0.03722340613603592,
0.047703102231025696,
0.04087202623486519,
-0.029911629855632782,
-0.02318759635090828,
0.002626527799293399,
-0.01849777065217495,
0.03693583607673645,
0.019629230722784996,
-0.0160830020904541,
-0.00851613562554121,
-0.009221779182553291,
0.03032923862338066,
-0.006715008988976479,
0.026341699063777924,
-0.00033200313919223845,
0.06944697350263596,
-0.034296389669179916,
0.019405733793973923,
-0.016872849315404892,
-0.009919760748744011,
0.010900726541876793,
-0.014459535479545593,
0.00026933621848002076,
-0.0008377759368158877,
0.006326237693428993,
-0.008791766129434109,
-0.011426218785345554,
-0.07337403297424316,
-0.038644470274448395,
0.04028778523206711,
-0.016923533752560616,
0.05956551432609558,
0.001475428231060505,
-0.010195749811828136,
0.011820201762020588,
-0.06603032350540161,
-0.03506970778107643,
-0.01863674446940422,
0.006138744298368692,
-0.01758321188390255,
-0.008970831520855427,
0.012928650714457035,
0.060673508793115616,
0.05523495003581047,
-0.042138710618019104,
0.015264775604009628,
0.007453224156051874,
0.03540870174765587,
-0.0014101887354627252,
-0.024902576580643654,
-0.03645457699894905,
-0.005712296348065138,
-0.04046093299984932,
0.03357507288455963,
-0.0021710789296776056,
-0.001906564342789352,
0.028885165229439735,
0.024046385660767555,
0.0005291371489875019,
-0.07087340205907822,
-0.0008174963295459747,
-0.03562966734170914,
0.03281151503324509,
0.021443339064717293,
0.03620809316635132,
-0.0180632583796978,
0.030330238863825798,
0.012471252121031284,
-0.0028088497929275036,
0.00883167888969183,
0.01772867701947689,
-0.03471899405121803,
-0.053001582622528076,
-0.05871449410915375,
-0.02547558769583702,
0.06449820101261139,
-0.03827512264251709,
-0.06476718932390213,
0.01992308907210827,
-0.02522682584822178,
0.010317414067685604,
0.03113057278096676,
0.03200346976518631,
0.009154146537184715,
0.016113964840769768,
-0.027157073840498924,
0.004053953569382429,
-0.01582314260303974,
0.03091386705636978,
0.10778661072254181,
0.05891254171729088,
0.024814782664179802,
-0.05592606961727142,
-0.03408781811594963,
-0.009454591199755669,
0.007656764704734087,
-0.007964699529111385,
0.03355221822857857,
-0.04917677491903305,
0.036148156970739365,
0.007793394383043051,
0.0539589487016201,
-0.003910660743713379,
0.03238916024565697,
0.03361019492149353,
-0.03828778862953186,
0.01740577071905136,
0.033037930727005005,
0.02139759063720703,
0.016306670382618904,
0.043882232159376144,
-0.05350741371512413,
0.005491307005286217,
-0.015512504614889622,
-0.02174113132059574,
-0.01797342486679554,
-0.032654959708452225,
0.01235257275402546,
-0.0345892533659935,
-0.08509127795696259,
0.03132142871618271,
-0.005444424692541361,
-0.04021498188376427,
0.005054200068116188,
-0.006099960301071405,
0.03166297450661659,
-0.005172026809304953,
-0.021855536848306656,
-0.006239715963602066,
0.03592054173350334,
0.0110519640147686,
0.009125693701207638,
0.018399883061647415,
-0.012975513935089111,
0.016814550384879112,
-0.0026796304155141115,
0.07148337364196777,
-0.031100362539291382,
-0.00787117425352335,
0.009513160213828087,
-0.02020368166267872,
-0.004025910049676895,
-0.03864217549562454,
0.0074511319398880005,
0.0007338431314565241,
0.0021364304702728987,
0.0034979539923369884,
-0.017163289710879326,
-0.000520908972248435,
0.021592874079942703,
-0.0015456938417628407,
0.025277594104409218,
0.009457414038479328,
0.02999522164463997,
0.015966080129146576,
0.016431942582130432,
0.05645497143268585,
-0.0114408815279603,
0.0018910312792286277,
-0.018924131989479065,
-0.024325981736183167,
-0.032555099576711655,
-0.05410449951887131,
0.034119054675102234,
0.028450999408960342,
0.032535336911678314,
0.005699635948985815,
-0.008324577473104,
-0.03636413812637329,
-0.06322912871837616,
-0.013448060490190983,
-0.0022806255146861076,
-0.023653244599699974,
-0.012275585904717445,
-0.011188449338078499,
0.006657707970589399,
0.04715944826602936,
-0.009535127319395542,
-0.01582135260105133,
0.031089551746845245,
0.018389049917459488,
0.04378814995288849,
-0.026083605363965034,
-0.008365456946194172,
0.021781133487820625,
0.007606804370880127,
-0.013056297786533833,
0.006690767593681812,
0.03888138383626938,
0.025266431272029877,
0.04631330817937851,
0.02039979211986065,
0.029487432911992073,
-0.025748958811163902,
0.02182489074766636,
-0.01781492494046688,
-0.018458373844623566,
0.009402693249285221,
0.028484875336289406,
0.02177591808140278,
-0.06578464806079865,
-0.03173774108290672,
-0.012651924975216389,
0.011168194003403187,
0.025176264345645905,
0.041126057505607605,
-0.017519881948828697,
0.04458913579583168,
-0.03195147588849068,
0.06507370620965958,
-0.0311944168061018,
0.0009628830011934042,
-0.05173417180776596,
-0.02218673937022686,
0.015044729225337505,
-0.005467485636472702,
0.012951710261404514,
0.02922581136226654,
-0.010454842820763588,
-0.0450739711523056,
0.022544071078300476,
0.02334635518491268,
-0.009212634526193142,
0.009502113796770573,
0.03571136295795441,
-0.03761045262217522,
0.008845443837344646,
0.02932913601398468,
-0.02896326594054699,
-0.010921766050159931,
-0.03287026286125183,
-0.020854877308011055,
0.011575046926736832,
-0.00677220243960619,
0.02621089667081833,
0.03491397202014923,
-0.010823824442923069,
0.015318650752305984,
0.035143349319696426,
0.008252355270087719,
-0.030843941494822502,
0.003121795132756233,
-0.04862336069345474,
0.005948413163423538,
0.005604499485343695,
0.03563230484724045,
0.02028794214129448,
-0.003684817347675562,
0.0810215026140213,
-0.01859145425260067,
-0.0061833965592086315,
-0.0023439056240022182,
0.019681567326188087,
-0.012649289332330227,
0.008914198726415634,
0.022643079981207848,
0.013302045874297619,
0.03414562717080116,
0.03645496815443039,
-0.048956774175167084,
0.04599134624004364,
0.04679487273097038,
0.0070579624734818935,
-0.0976024866104126,
-0.011483477428555489,
-0.009873799048364162,
-0.005275732837617397,
0.015281133353710175,
-0.03047189675271511,
0.004300334956496954,
0.06553806364536285,
-0.10022076219320297,
0.03506654128432274,
-0.0010212251218035817,
-0.012402252294123173,
-0.030393680557608604,
0.016507724300026894,
-0.03553894907236099,
0.01197503786534071,
0.0006988252862356603,
0.08112630248069763,
0.03408830240368843,
0.03200475499033928,
-0.009334723465144634,
-0.055611222982406616,
-0.0007426766096614301,
0.009978404268622398,
-0.0021721969824284315,
-0.0006274937768466771,
0.06635572016239166,
0.005399075336754322,
0.022034958004951477,
0.007500752806663513,
-0.02286645397543907,
0.008912744000554085,
-0.013835043646395206,
-0.006702598184347153,
0.020858613774180412,
-0.005894328933209181,
-0.004047547932714224,
-0.005033642984926701,
0.0005525624146685004,
0.022225135937333107,
0.023507796227931976,
0.020791755989193916,
-0.007626120466738939,
0.004941870458424091,
0.03173857182264328,
-0.08651326596736908,
-0.03651977330446243,
0.03227834403514862,
0.03183596208691597,
0.01314226072281599,
0.03729572892189026,
0.016654614359140396,
-0.011086281388998032,
-0.005910608451813459,
-0.005192877259105444,
-0.07245948165655136,
-0.01383128110319376,
0.012288530357182026,
0.04873087257146835,
0.003747225971892476,
-0.03185214847326279,
-0.04292336478829384,
-0.023339547216892242,
0.021407505497336388,
-0.006507974583655596,
-0.01708325743675232,
-0.031072895973920822,
-0.006193267647176981,
0.020438630133867264,
-0.005450334399938583,
0.03148587793111801,
-0.043567758053541183,
-0.08293577283620834,
0.0472184456884861,
-0.028448257595300674,
0.008291469886898994,
-0.02201845869421959,
-0.08322949707508087,
-0.05433639511466026,
-0.06488506495952606,
0.05755331367254257,
-0.017463909462094307,
-0.009607204236090183,
-0.01971924491226673,
-0.02414056472480297,
-0.03422337770462036,
0.01039524283260107,
0.06159665063023567,
0.0026240507140755653,
-0.027060357853770256,
-0.02961503155529499,
-0.008218584582209587,
0.0419674888253212,
-0.05275924131274223,
0.022029584273695946,
-0.003577806754037738,
-0.023473680019378662,
-0.013058202341198921,
0.007216841913759708,
-0.026643799617886543,
0.01900188811123371,
0.020157331600785255,
0.01182172168046236,
0.03237668424844742,
-0.020709116011857986,
-0.035001661628484726,
0.0661579892039299,
0.014769135974347591,
-0.020762216299772263,
0.05390980839729309,
0.0034550721757113934,
0.024780331179499626,
0.04669250175356865,
0.023809144273400307,
-0.06433889269828796,
0.005780449137091637,
-0.00412703026086092,
0.007281805854290724,
0.0013590737944468856,
0.02425367198884487,
0.03276250138878822,
-0.05906769633293152,
0.021498985588550568,
0.02825119160115719,
-0.050510648638010025,
-0.00895257480442524,
0.04551135376095772,
-0.02105785347521305,
0.038384124636650085,
-0.0004939784412272274,
-0.0005876675131730735,
0.0035151152405887842,
-0.008762718178331852,
-0.03924182057380676,
0.07415297627449036,
0.016058264300227165,
-0.036249786615371704,
0.05596693232655525,
0.021145084872841835,
-0.005412626545876265,
-0.022274602204561234,
-0.019465412944555283,
0.010029147379100323,
-0.053417231887578964,
-0.018525490537285805,
0.003786794375628233,
0.0013554891338571906,
-0.022105911746621132,
0.012685363180935383,
0.002272178651764989,
0.08809357136487961,
-0.02940264344215393,
0.028169147670269012,
-0.025525856763124466,
-0.001908017206005752,
-0.0009576199227012694,
0.03130408003926277,
-0.00019743609300348908,
0.015199918299913406,
-0.007347402162849903,
-0.014276145957410336,
-0.02437623403966427,
0.0048477621749043465,
0.034832872450351715,
-0.01571783609688282,
0.020224679261446,
0.025606388226151466,
-0.031113259494304657,
-0.0027921737637370825,
0.0025059334002435207,
0.0189183559268713,
-0.0382399745285511,
0.005341058596968651,
0.04818488284945488,
0.013003182597458363,
0.009493596851825714,
-0.014987196773290634,
-0.035143401473760605,
0.025583161041140556,
-0.06751231849193573,
0.03265303000807762,
0.0012123928172513843,
0.024449801072478294,
-0.023254720494151115,
-0.05682681128382683
] |
<p>Current in wire + moving charge next to wire creates magnetic force in the stationary reference frame OR electric force in the moving reference frame from special relativity due to change in charge density etc.... I think I understand this and I think it's super cool. Now here's the rub...</p>
<p>Current in wire + <strong>stationary</strong> charge next to wire creates no net charge. This is how nature behaves. I get it. My question is why can't I use the same special relativity logic as above, that is, current in wire cause electrons in wire to contract in accordance with special relativity so there has to be a net charge on the wire, which then acts on stationary charge next to wire.</p>
<p>I have been reading and reading and reading and I have come up with the following:</p>
<p>(1) When electrons in wire get accelerated to create current the distance between them actually expands in accordance with special relativity - something to do with bells spaceship paradox - which I am not going to pretend to understand</p>
<p>(2) This expansion from (1) above is exactly opposite and equal in magnitude to the contraction special relativity then causes and the expansion and contraction cancel out to keep the charge density in the wire constant and therefore no net charge on the wire</p>
<p>Here are my questions:</p>
<p>Is the explanation above correct? If so, please elaborate because i dont understand</p>
<p>If not correct, what is going on?</p>
<p>This is driving me absolutely nuts. </p> | 780 | [
-0.01909167319536209,
-0.02579483762383461,
0.016594335436820984,
-0.04458840563893318,
0.000023030135707813315,
0.003020609961822629,
-0.023659007623791695,
-0.022272326052188873,
0.0024422078859061003,
-0.023942096158862114,
0.03949037939310074,
0.014710570685565472,
0.0654570534825325,
0.006017240229994059,
0.010889329947531223,
-0.005132793914526701,
0.02757657691836357,
-0.015834098681807518,
0.011388433165848255,
-0.053545400500297546,
0.02162465825676918,
0.040461450815200806,
0.01521991565823555,
-0.001964591909199953,
-0.04197688028216362,
0.03129957616329193,
0.0013899020850658417,
-0.003444769186899066,
-0.0011773891746997833,
0.06578143686056137,
-0.03582914173603058,
-0.02544194832444191,
-0.015765484422445297,
-0.00644572963938117,
0.025792039930820465,
-0.0008286630618385971,
-0.05006225034594536,
-0.05439026281237602,
0.013449992053210735,
0.009818874299526215,
-0.0069752344861626625,
0.010950528085231781,
-0.005770981777459383,
0.06481631100177765,
-0.030269086360931396,
-0.011994343250989914,
0.009024855680763721,
0.010219001211225986,
0.037867918610572815,
-0.0732918381690979,
0.05416468530893326,
-0.016010666266083717,
0.053911902010440826,
0.012157066725194454,
0.001775696175172925,
-0.00416730809956789,
0.09087913483381271,
0.04886813834309578,
-0.03540155664086342,
-0.01983513869345188,
-0.022050991654396057,
-0.01974635012447834,
-0.012904294766485691,
-0.026126297190785408,
0.0008920300169847906,
0.06298445165157318,
-0.03938376531004906,
-0.009561790153384209,
0.020784467458724976,
-0.015215527266263962,
0.011408023536205292,
0.00665883906185627,
-0.024063851684331894,
-0.009592026472091675,
0.026928357779979706,
-0.0392267145216465,
0.03879626840353012,
-0.0026527591980993748,
0.041196469217538834,
0.06227751076221466,
-0.05042189359664917,
-0.004396481905132532,
0.04008437693119049,
0.04608055204153061,
0.029168011620640755,
-0.0363822877407074,
0.05752929300069809,
-0.009703004732728004,
0.005034430883824825,
0.02599482424557209,
-0.014261367730796337,
0.019900258630514145,
0.0047619943507015705,
-0.001499475329183042,
0.006906750146299601,
0.045492082834243774,
0.007740128319710493,
0.06434454023838043,
0.01122266985476017,
-0.008725425228476524,
0.022667257115244865,
-0.004171773791313171,
0.019905591383576393,
0.06840270012617111,
-0.009677251800894737,
-0.03639395162463188,
-0.02103617414832115,
0.02320028655230999,
-0.023061620071530342,
-0.015113011002540588,
-0.04083510860800743,
0.01037430390715599,
0.0016380141023546457,
-0.015062391757965088,
0.013766084797680378,
-0.042423393577337265,
0.015286915935575962,
-0.0003438569256104529,
0.04520395025610924,
0.056354694068431854,
-0.00038018010673113167,
-0.01909569837152958,
0.024767179042100906,
-0.003691628575325012,
-0.035029683262109756,
0.025192447006702423,
-0.0070917061530053616,
0.010866375640034676,
0.03405337035655975,
0.0565386563539505,
-0.008767527528107166,
-0.024593012407422066,
0.0068987454287707806,
0.020096147432923317,
0.05422502011060715,
-0.018987124785780907,
-0.11821283400058746,
-0.04628130421042442,
0.061115022748708725,
-0.006447124760597944,
-0.000682273821439594,
-0.08738446980714798,
0.015583640895783901,
0.001964293420314789,
0.08933468908071518,
-0.008070014417171478,
-0.03182963654398918,
-0.005622304044663906,
0.05342730134725571,
0.03270738199353218,
-0.015927165746688843,
-0.00478683365508914,
0.011918480508029461,
-0.02621919848024845,
-0.004023351240903139,
-0.041716769337654114,
0.010382622480392456,
0.017658114433288574,
0.010236119851469994,
-0.03223365172743797,
0.06430653482675552,
0.007135641295462847,
0.001885784324258566,
0.011590611189603806,
-0.016533028334379196,
0.0038397586904466152,
0.08799377083778381,
0.005075753666460514,
-0.04171205312013626,
0.05467814952135086,
0.013809135183691978,
0.037986256182193756,
-0.008249678649008274,
0.02589142695069313,
0.021602727472782135,
-0.06190597638487816,
0.005339856259524822,
-0.017569201067090034,
0.01653793640434742,
0.016377011314034462,
-0.02599104307591915,
-0.029232896864414215,
-0.03361410275101662,
-0.04181767255067825,
0.02095264010131359,
0.0581950843334198,
-0.005585270933806896,
0.014400490559637547,
-0.03288969770073891,
-0.03620867431163788,
-0.013633813709020615,
-0.08825186640024185,
0.030406299978494644,
-0.016212891787290573,
-0.03545546159148216,
0.005675588268786669,
-0.01118896622210741,
0.022216981276869774,
-0.028947453945875168,
-0.013743726536631584,
0.00157869269605726,
0.0507240928709507,
-0.0360504649579525,
-0.02439211681485176,
0.01043971348553896,
0.045962993055582047,
0.029798083007335663,
0.03850087523460388,
-0.012241747230291367,
0.00847695954144001,
-0.01586475968360901,
0.02535773627460003,
-0.02168121747672558,
-0.0048637972213327885,
0.027732722461223602,
-0.018592502921819687,
0.021115627139806747,
-0.0107555678114295,
0.0036016199737787247,
0.06932172924280167,
0.00439111003652215,
0.08393239229917526,
0.03873326629400253,
-0.015142439864575863,
0.005652143154293299,
0.059733591973781586,
0.0002701584016904235,
0.005342461168766022,
-0.01575378142297268,
-0.04301084578037262,
-0.052357323467731476,
-0.002451439620926976,
0.030853280797600746,
0.015373158268630505,
-0.05382901057600975,
0.017201077193021774,
0.015960922464728355,
0.03761913254857063,
0.022412586957216263,
0.017227936536073685,
-0.019476663321256638,
-0.05342136323451996,
0.01100139133632183,
0.016198845580220222,
0.006373995449393988,
0.00701935077086091,
0.016674529761075974,
0.035403721034526825,
0.01963261514902115,
-0.011213393881917,
-0.00899557489901781,
0.03789426386356354,
-0.018831156194210052,
-0.00008708944369573146,
0.003416131716221571,
-0.025039006024599075,
0.0340607650578022,
-0.012011545710265636,
0.045121751725673676,
0.012722155079245567,
0.00446454668417573,
0.007157947402447462,
-0.047533370554447174,
-0.004186367616057396,
-0.0033281766809523106,
-0.019049163907766342,
-0.014144226908683777,
-0.017816023901104927,
-0.006824164185672998,
-0.07894103229045868,
-0.01706250198185444,
0.00888680201023817,
0.013657533563673496,
-0.027727169916033745,
0.0024329540319740772,
0.0001002771095954813,
0.03348936885595322,
0.04770699515938759,
-0.03535784035921097,
-0.0231162142008543,
-0.014846081845462322,
-0.008268643170595169,
0.012058740481734276,
0.02538335882127285,
-0.03708495572209358,
0.018140673637390137,
-0.02501155436038971,
-0.04317960515618324,
0.05469343811273575,
0.02749294973909855,
0.03096228837966919,
0.05010074004530907,
-0.009068275801837444,
-0.04909465089440346,
0.005549746565520763,
-0.0549771822988987,
0.025410600006580353,
-0.029287034645676613,
-0.009393340907990932,
0.09764786064624786,
0.002027856884524226,
-0.023057520389556885,
0.0038310771342366934,
-0.04992246627807617,
-0.0485835038125515,
-0.006376584991812706,
0.0302392840385437,
-0.0031047039665281773,
-0.038915954530239105,
0.03553725406527519,
0.027608422562479973,
-0.046112060546875,
-0.02520754002034664,
-0.04729609936475754,
-0.03164026141166687,
0.01823974773287773,
0.01720328815281391,
0.05862606316804886,
-0.009256267920136452,
-0.07690178602933884,
0.07090140879154205,
0.021813515573740005,
-0.02130262553691864,
-0.06061597540974617,
-0.0173428226262331,
-0.04298543930053711,
-0.01805112697184086,
0.013684779405593872,
0.0681379958987236,
-0.02616427280008793,
-0.012268874794244766,
0.05400519818067551,
0.048927344381809235,
0.006417560391128063,
0.02244550921022892,
0.019691647961735725,
-0.0039519970305264,
-0.0011357824550941586,
0.0053825718350708485,
0.06172950938344002,
0.002692646346986294,
-0.024672381579875946,
-0.023550795391201973,
0.008168833330273628,
0.029074179008603096,
0.02021016739308834,
-0.027555378153920174,
0.036528196185827255,
0.013948590494692326,
0.019692493602633476,
-0.026582088321447372,
0.028966428712010384,
-0.012831590138375759,
-0.03211818262934685,
-0.011554540134966373,
0.01628260686993599,
0.013022128492593765,
-0.015316292643547058,
-0.013927598483860493,
0.040013473480939865,
0.01037042960524559,
-0.059800293296575546,
-0.047186799347400665,
-0.0052657946944236755,
-0.009003499522805214,
0.015921400859951973,
-0.031076114624738693,
-0.0244175773113966,
0.028041008859872818,
0.03297717124223709,
0.031991686671972275,
0.029626935720443726,
-0.029085464775562286,
0.020737608894705772,
-0.06714242696762085,
0.0065227085724473,
0.014670138247311115,
0.04607555270195007,
-0.003679705783724785,
0.05597269907593727,
0.013640882447361946,
0.021841350942850113,
0.035805538296699524,
-0.0016851971158757806,
-0.08700276166200638,
0.021776901558041573,
-0.03807811439037323,
-0.04655635729432106,
-0.010628015734255314,
0.003608102910220623,
-0.04502242058515549,
-0.02360793575644493,
0.007417673245072365,
-0.04594125598669052,
-0.012479010969400406,
-0.0526614785194397,
0.006075605750083923,
-0.018370626494288445,
-0.017712382599711418,
-0.03596587851643562,
0.0014640579465776682,
0.055220670998096466,
-0.0494840182363987,
0.028794217854738235,
0.00932385679334402,
-0.034477926790714264,
-0.014937183819711208,
-0.01871238462626934,
-0.003805840155109763,
0.04428892210125923,
0.004533394239842892,
0.026438841596245766,
-0.018901586532592773,
-0.03655949607491493,
0.013105024583637714,
0.029924198985099792,
0.032549962401390076,
0.023494325578212738,
-0.010103991255164146,
-0.05864855274558067,
-0.015056719072163105,
-0.035592835396528244,
-0.01934615522623062,
0.06889265030622482,
0.03649357706308365,
0.0031341149006038904,
0.028209300711750984,
0.013795522972941399,
0.008217215538024902,
0.014820941723883152,
0.05134793743491173,
-0.018105391412973404,
-0.019643578678369522,
-0.03533811494708061,
-0.017255838960409164,
-0.028831113129854202,
-0.013269579969346523,
0.026364143937826157,
-0.024696411564946175,
-0.020302996039390564,
-0.026190560311079025,
0.015697218477725983,
0.005708493757992983,
-0.0021754836197942495,
0.0034741342533379793,
0.004736287984997034,
0.03600491210818291,
0.020081868395209312,
0.017080320045351982,
0.003914904315024614,
0.019506586715579033,
0.04544004797935486,
-0.002188245067372918,
-0.013695256784558296,
-0.10179045796394348,
0.0013544493122026324,
0.0029924435075372458,
0.03940874710679054,
-0.014320531859993935,
-0.008852336555719376,
-0.04799376800656319,
0.004317000973969698,
0.03516240790486336,
-0.03712192922830582,
0.03303617238998413,
0.0001417182938894257,
-0.018421582877635956,
-0.023016754537820816,
-0.020892824977636337,
-0.019064461812376976,
0.015822893008589745,
-0.029240233823657036,
0.026126889511942863,
-0.029672304168343544,
0.012229971587657928,
-0.003273632610216737,
0.000159312883624807,
0.0494406633079052,
0.03782721236348152,
0.0039914194494485855,
0.02458149380981922,
-0.014617969281971455,
0.04306939244270325,
-0.025693679228425026,
-0.06038174778223038,
-0.00629510497674346,
0.013760619796812534,
-0.009304208680987358,
0.05440680310130119,
-0.014406559988856316,
-0.017684336751699448,
-0.003915505483746529,
-0.0181574746966362,
0.008407993242144585,
0.004315387923270464,
-0.03299843892455101,
0.0330597348511219,
0.0353059284389019,
-0.021602587774395943,
0.017367905005812645,
0.014817317016422749,
-0.010966315865516663,
0.025172144174575806,
0.011148562654852867,
0.04580981656908989,
-0.008156832307577133,
0.007700888905674219,
-0.028785167261958122,
0.036342136561870575,
-0.05604449287056923,
0.07489976286888123,
-0.05666469782590866,
-0.007015715818852186,
-0.030966535210609436,
0.0035954832565039396,
0.03413902223110199,
0.040969885885715485,
0.020866651087999344,
0.03886231407523155,
-0.030988143756985664,
0.011737750843167305,
-0.011937345378100872,
-0.04227219894528389,
-0.00027057825354859233,
0.009534357115626335,
0.0012377554085105658,
0.03139077126979828,
-0.019923977553844452,
0.0009635620517656207,
-0.01717647910118103,
-0.008426143787801266,
0.02807857282459736,
-0.054293904453516006,
0.044483840465545654,
-0.010649249888956547,
-0.013198350556194782,
-0.00028067658422514796,
-0.034288275986909866,
-0.04334964603185654,
0.010308614932000637,
-0.008385811001062393,
0.034769829362630844,
-0.05148037150502205,
0.008609956130385399,
0.03572746738791466,
-0.008975178003311157,
-0.06350210309028625,
-0.0895836278796196,
0.02842780575156212,
-0.013703555800020695,
-0.004453195724636316,
-0.03589402511715889,
0.0075113121420145035,
-0.04508557915687561,
-0.03457897529006004,
-0.020680248737335205,
0.02183767966926098,
-0.02536335587501526,
-0.021732071414589882,
0.03731115534901619,
-0.023708637803792953,
0.024628346785902977,
-0.02758171781897545,
-0.010551090352237225,
-0.029056526720523834,
-0.02906138263642788,
-0.011663421988487244,
-0.027121011167764664,
0.03950728476047516,
-0.031216289848089218,
-0.05442691221833229,
-0.001272079418413341,
0.00813080370426178,
0.03297682851552963,
-0.02341424487531185,
-0.01738545671105385,
0.00836255308240652,
0.020141346380114555,
-0.013909388333559036,
-0.0181257501244545,
0.036376193165779114,
0.02538829669356346,
0.03783425688743591,
-0.013958843424916267,
0.018740486353635788,
-0.07070288062095642,
-0.04508368670940399,
0.008618516847491264,
0.014262450858950615,
0.01313686091452837,
-0.002984355902299285,
0.04446367919445038,
-0.00856763031333685,
-0.016379836946725845,
0.02320391871035099,
0.008834434673190117,
0.020931890234351158,
-0.019535571336746216,
0.0026066626887768507,
0.014192596077919006,
-0.017760474234819412,
-0.04169568791985512,
0.013024330139160156,
0.008403251878917217,
0.030319541692733765,
0.05770227685570717,
-0.034956350922584534,
0.06166002154350281,
0.006899846717715263,
-0.02262687124311924,
-0.019509583711624146,
-0.007471525575965643,
-0.004168535582721233,
-0.0031467261724174023,
-0.008074532262980938,
0.012583357281982899,
-0.01831098459661007,
-0.002267858013510704,
0.037942346185445786,
0.04988253116607666,
-0.017908284440636635,
0.008339154534041882,
0.044999271631240845,
0.03724070265889168,
0.0345623642206192,
0.023796875029802322,
-0.023000137880444527,
0.036150868982076645,
-0.005487077869474888,
-0.004199536517262459,
0.026996351778507233,
0.0034131002612411976,
0.06324195861816406,
-0.0016650398029014468,
-0.00622707512229681,
-0.008350886404514313,
-0.0340355783700943,
-0.01631750538945198,
-0.0030267536640167236,
0.002009669551625848,
-0.005436296109110117,
0.006525844801217318,
0.03252329304814339,
0.020887341350317,
0.006506762467324734,
0.03326651453971863,
-0.01670984737575054,
-0.06024853512644768,
-0.004251391626894474,
-0.04890129342675209,
-0.002417536685243249,
0.08367978036403656,
0.005713832098990679,
-0.02044779062271118,
-0.00412286352366209,
-0.03317796066403389,
0.02088450826704502,
0.06448085606098175,
0.011135547421872616,
-0.013548198156058788,
0.09780547022819519,
0.0017013117903843522,
0.017156947404146194,
-0.026024973019957542,
-0.002776545938104391,
0.08688648045063019,
0.011061477474868298,
-0.020893994718790054,
-0.07618248462677002,
-0.011615016497671604,
-0.019927652552723885,
-0.004374819807708263,
-0.02754143625497818,
0.04370743781328201,
-0.04153387248516083,
0.019320126622915268,
0.026803795248270035,
0.03857790306210518,
0.011548293754458427,
-0.008941295556724072,
0.03983497992157936,
-0.030041489750146866,
-0.035017501562833786,
0.00925932452082634,
0.023499689996242523,
0.02167236991226673,
0.006209201645106077,
-0.04910535737872124,
0.04421240836381912,
-0.06672876328229904,
-0.0023319998290389776,
-0.04735622555017471,
-0.02171335741877556,
0.022856974974274635,
-0.015613281168043613,
-0.03796431049704552,
-0.006708699744194746,
0.00658287201076746,
-0.01626034639775753,
-0.05993817001581192,
-0.0004927219706587493,
0.030910061672329903,
0.024134507402777672,
0.03897911310195923,
-0.00955270230770111,
0.020235076546669006,
0.008054033853113651,
0.04933590814471245,
0.05687613785266876,
-0.05719068646430969,
0.013042343780398369,
-0.041015367954969406,
0.04550692066550255,
0.015962757170200348,
-0.006534172687679529,
0.0526929534971714,
0.02813764289021492,
0.016846556216478348,
-0.0332828015089035,
-0.03955618664622307,
-0.0024609367828816175,
0.002293212339282036,
0.05017644912004471,
-0.0282016359269619,
-0.05341868847608566,
0.03270498663187027,
0.014743652194738388,
-0.019003285095095634,
-0.014986864291131496,
0.020839082077145576,
0.01394303422421217,
-0.010690336115658283,
0.03374654799699783,
-0.004350877832621336,
-0.021912824362516403,
-0.03080104850232601,
-0.016072571277618408,
-0.03274626284837723,
-0.0007899082265794277,
0.01846434734761715,
0.016965942457318306,
0.022010305896401405,
-0.01870906539261341,
0.007938620634377003,
0.023868316784501076,
-0.0702793076634407,
0.052463315427303314,
0.007711546961218119,
-0.0037868982180953026,
-0.0369495265185833,
0.020405961200594902,
0.01624307595193386,
0.027447037398815155,
-0.027529442682862282,
0.004424029495567083,
-0.012887466698884964,
0.045393940061330795,
-0.00528052868321538,
-0.025923779234290123,
-0.004930227063596249,
-0.012497530318796635,
0.009383787401020527,
-0.0019127671839669347,
-0.014429816976189613,
0.026201514527201653,
0.016821997240185738,
-0.00967391487210989,
0.0022122985683381557,
0.022432180121541023,
-0.019845254719257355,
-0.008411060087382793,
0.035089846700429916,
-0.011338241398334503,
0.01433233916759491,
0.0215616337954998,
0.008262124843895435,
-0.01782849431037903,
-0.007352239917963743,
-0.00565095990896225,
0.00008900123066268861,
0.003919272683560848,
0.03351771458983421,
-0.043737489730119705,
-0.013187035918235779,
0.0015380345284938812,
-0.0035248214844614267,
-0.050647176802158356,
-0.010861769318580627,
-0.06277107447385788,
0.0353737436234951,
-0.008193123154342175,
-0.023778775706887245,
-0.0175490602850914,
0.042146068066358566,
-0.03583018481731415,
0.0009895296534523368,
0.026468751952052116,
0.005640018731355667,
-0.041871216148138046,
0.008221536874771118,
0.009938923642039299,
0.0019429298117756844,
0.04806919023394585,
-0.03846291825175285,
-0.026903199031949043,
0.02861837111413479,
-0.03820054233074188,
-0.03211324289441109,
0.04114179685711861,
-0.026050446555018425,
0.00609888881444931,
0.017872385680675507,
0.0018939031288027763,
-0.0013496896717697382,
0.06597543507814407,
0.001279375865124166,
0.011252042837440968,
0.005810587201267481,
-0.03883758932352066,
0.014905455522239208,
-0.01366235688328743,
0.013013895601034164,
0.01865164376795292,
-0.004584950860589743,
0.021849552169442177,
0.04983319714665413,
0.019786396995186806,
0.004631874151527882,
-0.016335392370820045,
-0.01118755154311657,
-0.016769664362072945,
0.04752799868583679,
-0.0048976317048072815,
0.009138049557805061,
0.05805362015962601,
-0.024452894926071167,
0.002868061885237694,
-0.021496737375855446,
-0.006943842396140099,
-0.09610622376203537,
0.02426730841398239,
-0.009048975072801113,
-0.006808021105825901,
0.009276840835809708,
-0.05142474174499512,
-0.006888058502227068,
0.025502735748887062,
-0.08873701095581055,
0.0011122223222628236,
-0.014438807033002377,
-0.02945636212825775,
-0.02803577110171318,
-0.019418790936470032,
-0.005373757798224688,
0.06550034880638123,
0.05305170267820358,
0.07456687092781067,
-0.004915809258818626,
-0.0031937339808791876,
-0.011730733327567577,
-0.03860203176736832,
-0.034786686301231384,
0.046604055911302567,
0.0023155019152909517,
-0.004161227494478226,
0.02374071627855301,
-0.010243137367069721,
-0.017581209540367126,
0.038398124277591705,
0.0006934716948308051,
-0.0013731796061620116,
-0.007218198385089636,
0.01649145781993866,
0.002015013713389635,
0.008239440619945526,
-0.0027875308878719807,
-0.009301973506808281,
0.024244965985417366,
0.023871205747127533,
0.02722501941025257,
0.017077788710594177,
-0.01971770077943802,
-0.0326029472053051,
0.03524653613567352,
-0.04560147970914841,
-0.011969057843089104,
0.046379104256629944,
-0.0075379288755357265,
0.008226139470934868,
-0.0003357864625286311,
0.051041312515735626,
0.0321313813328743,
-0.02719721570611,
-0.01338901836425066,
-0.014435973018407822,
-0.04195835068821907,
0.02933330647647381,
0.004206226672977209,
-0.005810226779431105,
0.037841372191905975,
-0.009590443223714828,
-0.007624628487974405,
-0.01038513146340847,
-0.007578712422400713,
0.02559981867671013,
-0.0471697635948658,
-0.004324096720665693,
0.029637649655342102,
0.01798596791923046,
0.03563790023326874,
-0.061200812458992004,
-0.027898842468857765,
0.040582332760095596,
0.021308911964297295,
0.010751700960099697,
0.022186119109392166,
-0.03589740768074989,
-0.02171216532588005,
-0.07534563541412354,
0.02248179167509079,
-0.015059213154017925,
-0.02745973877608776,
-0.04735135659575462,
-0.04776904731988907,
-0.049853816628456116,
0.04580261930823326,
0.06005571410059929,
0.00960174947977066,
-0.00260545639321208,
0.04893100634217262,
-0.027560966089367867,
0.02832876890897751,
-0.05883492901921272,
0.0018442757427692413,
0.016379717737436295,
-0.004033542703837156,
0.03424378111958504,
-0.0010708170011639595,
-0.04352497309446335,
0.01692885160446167,
0.004356549587100744,
-0.01699686236679554,
0.04442334920167923,
-0.002190888160839677,
-0.03757017105817795,
0.03171677887439728,
0.027192911133170128,
-0.0027701635845005512,
0.05794104188680649,
-0.013301711529493332,
-0.011844675987958908,
0.00656897621229291,
0.021703951060771942,
-0.03354155272245407,
0.023581981658935547,
-0.031310126185417175,
0.027166711166501045,
-0.026874857023358345,
0.008801965042948723,
0.042392197996377945,
-0.035195425152778625,
0.005101118702441454,
0.03175006061792374,
-0.04050334170460701,
-0.028886182233691216,
0.037718579173088074,
0.0020767354872077703,
-0.008040378801524639,
-0.015256112441420555,
0.021189959719777107,
-0.0008371260482817888,
0.024251757189631462,
0.007508162409067154,
0.04697391018271446,
0.0096450699493289,
-0.027780238538980484,
0.007399032823741436,
0.07053546607494354,
0.014368860982358456,
0.009759949520230293,
-0.004032921511679888,
0.03733490779995918,
-0.02270512469112873,
-0.011813735589385033,
-0.020451778545975685,
-0.04463732987642288,
0.03965527191758156,
0.032332275062799454,
-0.034034643322229385,
0.07242665439844131,
-0.021967194974422455,
0.025124628096818924,
0.03620278835296631,
0.0021698593627661467,
-0.0034927381202578545,
0.01865796186029911,
-0.01934889703989029,
0.054300457239151,
-0.025992749258875847,
-0.023691629990935326,
0.002551265060901642,
-0.023386215791106224,
0.023516284301877022,
-0.021245431154966354,
0.014982428401708603,
-0.02274092100560665,
-0.019678287208080292,
-0.04154769703745842,
-0.0046613202430307865,
-0.010888161137700081,
0.020403403788805008,
0.04543881490826607,
0.02860967442393303,
0.023085683584213257,
-0.043510884046554565,
-0.014143758453428745,
-0.03460867330431938,
0.045834362506866455,
-0.05813174322247505,
-0.02017282135784626,
-0.023613130673766136,
-0.004486543126404285,
-0.00973617471754551,
0.0027717887423932552
] |
<p>In M. Salmhofer's "Renormalization, An Introduction" Wick ordering is defined as follows:</p>
<blockquote>
<p>Let $C = C_\Gamma$ be a nonnegative symmetric operator on $\mathbb{C}^\Gamma$. For $J: \Gamma \to \mathbb{C}$, let</p>
<p>$$\mathcal{W}_\Gamma (J, \phi) = e^{i(J,\phi)_\Gamma + \frac{1}{2} (J, CJ)_\Gamma},$$</p>
<p>where $\Gamma = \Gamma_{\varepsilon,L} = \varepsilon \mathbb{Z}^d / L \mathbb{Z}^d$. Let $\mathcal{P}_\Gamma$ be the algebra of polynomials in $(\phi(x))_{x \in \Gamma}$. Wick ordering is the $\mathbb{C}$-linear map $\Omega_C: \mathcal{P}_\Gamma \to \mathcal{P}_\Gamma$, that takes the following values on the monomials:</p>
<p>$$\Omega_C(1) = 1,$$</p>
<p>and for $n \geq 1$ and $x_1, \dots, x_n \in \Gamma$ (not necessarily distinct)</p>
<p>$$\Omega_C(\phi(x_1) \dots \phi(x_n)) = \left[ \prod_{k=1}^n \frac{1}{i} \frac{\delta}{\delta J(x_k)} \mathcal{W}_\Gamma (J, \phi) \right]_{J=0},$$</p>
<p>where $\frac{\delta}{\delta \phi(x)} = \varepsilon^{-d} \frac{\partial}{\partial \phi(x)}$.</p>
</blockquote>
<p><strong>Question 1:</strong> What exactly does the $J=0$ part in the last equation do? Also, I don't quite understand the part $\frac{\delta}{\delta J(x_k)}$. We multiply over $k$ and $J$ is a map $\Gamma \to \mathbb{C}$, so $J(x_k) \in \mathbb{C}$ for all $k$. How does it make sense to derive with respect to a constant complex number?</p>
<p>Later, the following theorem is proven (I will only copy the relevant part):</p>
<blockquote>
<p>For all $n \geq 1$:</p>
<p>$$\int \, \mathrm d \mu_C(\phi) \; \Omega_C(\phi(x_1) \dots \phi(x_n)) = 0,$$</p>
<p>where $\mathrm d \mu_C(\phi) = (\det 2 \pi C)^{-1/2} e^{-\frac{1}{2} (\phi, C^{-1} \phi)} \mathrm d^N \phi$.</p>
</blockquote>
<p><strong>Question 2:</strong> Does this imply that the integral of any Wick ordered polynomial vanishes since Wick ordering is $\mathbb{C}$-linear? </p>
<p>Thank you in advance for any help.</p> | 2,012 | [
0.008098282851278782,
-0.005083524156361818,
0.056291818618774414,
-0.03200959041714668,
0.028583364561200142,
-0.01818239688873291,
-0.03922759369015694,
-0.007219952996820211,
-0.007266071625053883,
-0.0454980842769146,
0.04480655491352081,
-0.025851232931017876,
0.07147956639528275,
0.019927386194467545,
0.039226822555065155,
-0.00923430360853672,
0.01982790045440197,
-0.0014612022787332535,
-0.022365372627973557,
-0.004430029541254044,
-0.002825686940923333,
0.07701849192380905,
-0.027571706101298332,
0.005515074357390404,
-0.0036071885842829943,
0.021420437842607498,
-0.044819366186857224,
-0.004225525539368391,
-0.011285061948001385,
0.06125140190124512,
-0.02352079190313816,
-0.03477250784635544,
-0.018158070743083954,
-0.00008437833457719535,
0.007315152790397406,
0.01039956696331501,
-0.023781219497323036,
-0.03317435458302498,
0.023020612075924873,
-0.002417379291728139,
-0.031573452055454254,
-0.03885073959827423,
-0.027681998908519745,
-0.018637368455529213,
-0.02914334461092949,
-0.009678316302597523,
0.02857530303299427,
-0.02956673502922058,
0.060093704611063004,
-0.032836105674505234,
0.040546827018260956,
0.004418891854584217,
-0.008690883405506611,
-0.011006309650838375,
-0.017132675275206566,
-0.000024101922463160008,
0.018808698281645775,
0.0415937565267086,
0.062086474150419235,
-0.03506757691502571,
-0.04854781553149223,
-0.026702359318733215,
0.02803664281964302,
0.011122194118797779,
0.005045546684414148,
0.016997987404465675,
0.023640329018235207,
-0.028432603925466537,
-0.018221711739897728,
-0.006530763115733862,
0.015229573473334312,
-0.026401208713650703,
0.03239398077130318,
-0.03472867235541344,
0.004403545521199703,
0.010813633911311626,
-0.006880139000713825,
0.0012601669877767563,
0.033399008214473724,
0.015871010720729828,
0.019163047894835472,
0.03171629458665848,
-0.040864668786525726,
-0.008584566414356232,
-0.019851895049214363,
0.007876508869230747,
0.0866810530424118,
-0.02356519177556038,
-0.0005475364159792662,
0.009371153078973293,
0.010401375591754913,
-0.0354471318423748,
0.025594651699066162,
-0.044271670281887054,
-0.02525031566619873,
-0.001606890233233571,
-0.03220749646425247,
-0.018420228734612465,
-0.021273145452141762,
0.010493757203221321,
-0.05912347882986069,
-0.05693216249346733,
-0.0361313596367836,
0.05791453272104263,
0.01793842390179634,
-0.007869684137403965,
-0.012321013025939465,
0.020399494096636772,
-0.06478288769721985,
-0.05261310562491417,
-0.056523870676755905,
0.023025454953312874,
-0.007469124160706997,
0.01802642270922661,
-0.0515231229364872,
-0.002034029457718134,
-0.0029823104850947857,
0.013063749298453331,
0.05610981583595276,
0.059731315821409225,
0.08062679320573807,
-0.01579584740102291,
0.012061313726007938,
-0.00842201802879572,
-0.08868459612131119,
0.007618078961968422,
0.031096523627638817,
-0.016551662236452103,
-0.06458667665719986,
-0.020115414634346962,
0.06492059677839279,
0.012784361839294434,
0.04475438594818115,
0.01078486256301403,
0.012739410623908043,
-0.04153529182076454,
-0.09454816579818726,
-0.015565737150609493,
0.038085732609033585,
-0.0013304646126925945,
0.0626394972205162,
-0.047281909734010696,
-0.0005147570627741516,
0.03335452452301979,
0.09707501530647278,
-0.005000435747206211,
0.03257177770137787,
0.034029826521873474,
0.012431913986802101,
0.0004459847405087203,
-0.004362179432064295,
-0.05825863033533096,
0.03385571390390396,
-0.026993388310074806,
-0.025006309151649475,
-0.03843481093645096,
0.041147228330373764,
0.048983387649059296,
-0.008192234672605991,
0.007403836585581303,
0.04573025926947594,
-0.02957247383892536,
-0.005344551522284746,
0.018260832875967026,
0.000299492763588205,
-0.030962752178311348,
0.026411617174744606,
0.0352679081261158,
0.05233893170952797,
-0.002963780891150236,
-0.009361912496387959,
0.009102550335228443,
-0.008717359974980354,
0.030549224466085434,
0.05384684354066849,
-0.04265598952770233,
-0.00030347364372573793,
-0.01535508781671524,
0.03308534622192383,
0.021157804876565933,
-0.0320962555706501,
-0.004156940151005983,
-0.030261453241109848,
0.032305825501680374,
0.023147886618971825,
-0.03439292311668396,
-0.00920162908732891,
0.04007011279463768,
0.01839936338365078,
-0.03873499110341072,
-0.02033403143286705,
-0.028745334595441818,
-0.039015430957078934,
0.0406392440199852,
-0.018078293651342392,
0.06754820048809052,
-0.011135331355035305,
-0.023081408813595772,
0.017312709242105484,
-0.02537819929420948,
0.013597899116575718,
0.01360438670963049,
0.061685141175985336,
-0.01975802332162857,
0.029363730922341347,
0.017711656168103218,
0.060173407196998596,
-0.011560161598026752,
0.028042178601026535,
-0.022083118557929993,
-0.028479427099227905,
-0.005169048439711332,
-0.0027354182675480843,
0.026095807552337646,
0.008999986574053764,
0.007039366289973259,
0.024352652952075005,
-0.0011925611179322004,
-0.01018834114074707,
0.008225536905229092,
-0.029616933315992355,
-0.003925819415599108,
0.0877661183476448,
0.0033410147298127413,
-0.02779519371688366,
0.043753765523433685,
-0.03937351703643799,
0.010920100845396519,
-0.017084836959838867,
-0.06049111858010292,
-0.04229697585105896,
-0.03067024238407612,
0.008893461897969246,
0.05950087681412697,
-0.02429170534014702,
-0.008262421004474163,
0.005391569808125496,
0.02910534292459488,
0.02751392498612404,
0.022705771028995514,
-0.008705477230250835,
-0.014995120465755463,
0.01129086036235094,
-0.009912952780723572,
0.04838864877820015,
-0.01837240345776081,
0.01108841598033905,
-0.024166885763406754,
0.0280372966080904,
-0.02884852886199951,
-0.01589321717619896,
0.022772548720240593,
-0.017800025641918182,
-0.02086116187274456,
0.009791816584765911,
0.006200358271598816,
0.0554695650935173,
-0.010651091113686562,
0.02264515496790409,
0.02923731505870819,
-0.024657290428876877,
0.0030772422906011343,
0.006527315359562635,
0.007777668535709381,
0.016488000750541687,
-0.0221560001373291,
-0.04273383319377899,
-0.019114900380373,
0.015819787979125977,
-0.037470486015081406,
0.008746997453272343,
-0.022071318700909615,
-0.03618265315890312,
-0.01913822628557682,
-0.023599091917276382,
0.04861857742071152,
0.024808257818222046,
0.019407274201512337,
-0.031261760741472244,
-0.010947911068797112,
0.010056808590888977,
-0.003249525325372815,
0.06517785787582397,
0.051343753933906555,
-0.03416704013943672,
-0.011107740923762321,
-0.026402955874800682,
0.008129010908305645,
0.018018970265984535,
-0.022765370085835457,
-0.04945310205221176,
0.007709607481956482,
0.011175887659192085,
-0.01409181859344244,
-0.04910692945122719,
-0.03847050294280052,
0.025911511853337288,
-0.034141916781663895,
-0.02748727798461914,
0.047321710735559464,
0.01964845322072506,
-0.08935888111591339,
-0.00016340463480446488,
-0.0022181731183081865,
-0.017047597095370293,
-0.029129482805728912,
0.02232353761792183,
0.0037618724163621664,
-0.009547747671604156,
0.016427699476480484,
0.0004925205139443278,
0.007575239986181259,
-0.0005036225775256753,
-0.048588305711746216,
-0.028042813763022423,
0.02917388081550598,
-0.008042505010962486,
0.003612126223742962,
-0.014036071486771107,
-0.03797690570354462,
0.06841815263032913,
0.06252952665090561,
-0.0038030182477086782,
-0.038767486810684204,
0.027103601023554802,
-0.0177508182823658,
-0.008792059496045113,
-0.005631937645375729,
0.010241076350212097,
0.008535854518413544,
0.0541197694838047,
0.04052919149398804,
0.055850401520729065,
0.02292214334011078,
-0.019043536856770515,
-0.021197166293859482,
0.053204260766506195,
0.006987754721194506,
-0.025202682241797447,
0.036556780338287354,
0.002740986878052354,
0.024012893438339233,
0.014290516264736652,
0.002737373113632202,
-0.018744168803095818,
0.019166575744748116,
-0.04205649718642235,
0.0365888848900795,
0.0077921124175190926,
0.0072205825708806515,
-0.015602110885083675,
0.05089155212044716,
0.03423583507537842,
-0.05710878595709801,
0.027002248913049698,
-0.004430065862834454,
-0.0009555721189826727,
-0.030672114342451096,
0.02875998429954052,
-0.016477908939123154,
0.031006349250674248,
-0.050118960440158844,
-0.01725074090063572,
-0.022040221840143204,
-0.02298014611005783,
0.025432227179408073,
-0.040172137320041656,
-0.03810065612196922,
0.03300384059548378,
0.027829129248857498,
-0.029870569705963135,
-0.025664981454610825,
-0.04794345796108246,
-0.01245235837996006,
-0.046132154762744904,
0.020354658365249634,
-0.014684447087347507,
0.06138176470994949,
0.015230133198201656,
0.03672097250819206,
0.02319488860666752,
-0.006661269813776016,
0.010248775593936443,
-0.0061000860296189785,
-0.07489130645990372,
0.004003480076789856,
0.009178882464766502,
0.07393833994865417,
-0.015028045512735844,
-0.02378714643418789,
0.03968300670385361,
0.02165130153298378,
-0.06324971467256546,
-0.007783917710185051,
-0.016174575313925743,
-0.0655551478266716,
0.022001923993229866,
-0.06177392229437828,
-0.07043572515249252,
-0.003393232123926282,
0.019517868757247925,
0.053652066737413406,
-0.05351441353559494,
-0.020749038085341454,
0.021343329921364784,
-0.00975312665104866,
0.011965729296207428,
0.0020948261953890324,
0.021333448588848114,
0.04797463119029999,
0.03221135213971138,
0.008691213093698025,
0.03462980315089226,
-0.01883525773882866,
0.025419728830456734,
0.024738483130931854,
0.03497307747602463,
0.021379996091127396,
-0.029042784124612808,
0.02522520162165165,
-0.06944074481725693,
-0.008908324874937534,
0.021720293909311295,
0.06402193754911423,
0.00915847159922123,
0.00461743026971817,
0.05655907839536667,
0.011230751872062683,
-0.0019544383976608515,
0.006910855881869793,
0.05122851952910423,
0.007611327804625034,
-0.015548770315945148,
0.008814790286123753,
0.005432362202554941,
0.015261505730450153,
0.005975054576992989,
-0.019657965749502182,
0.01240979228168726,
-0.007052254397422075,
-0.0032855079043656588,
0.034224238246679306,
0.01592477783560753,
-0.02533888630568981,
0.019930632784962654,
0.05794196203351021,
0.008779075928032398,
0.004490420687943697,
-0.005835636984556913,
0.0008411546004936099,
-0.0057417117059230804,
0.030587824061512947,
0.020548533648252487,
-0.017456620931625366,
-0.047994766384363174,
-0.03154870867729187,
0.04258999228477478,
0.021739134564995766,
0.005813288502395153,
0.030861372128129005,
-0.0252019464969635,
-0.0016740591963753104,
0.015762243419885635,
0.010111476294696331,
0.013963223434984684,
0.022346150130033493,
-0.02084965445101261,
-0.013615536503493786,
-0.03362230211496353,
-0.015962474048137665,
0.06057136505842209,
0.008775390684604645,
-0.016457032412290573,
-0.035227127373218536,
0.024890925735235214,
-0.022195277735590935,
0.038502056151628494,
-0.013546677306294441,
0.043948374688625336,
-0.006925251800566912,
-0.0019521802896633744,
0.00011508582247188315,
0.005594843067228794,
0.013561168685555458,
-0.07251345366239548,
0.03430034965276718,
0.03243882954120636,
-0.04068982973694801,
0.02405284158885479,
-0.009174583479762077,
-0.055998433381319046,
0.005640536081045866,
-0.018066447228193283,
-0.03868664428591728,
0.03447027876973152,
-0.031403783708810806,
0.050651002675294876,
0.02162378467619419,
-0.019447416067123413,
0.05666673928499222,
0.07157307863235474,
-0.043943341821432114,
-0.009412319399416447,
-0.013146906159818172,
0.006133996415883303,
0.013739597983658314,
0.06122219190001488,
-0.03384467959403992,
-0.0069788978435099125,
-0.04564489796757698,
0.0335279181599617,
-0.03177141025662422,
0.00983401108533144,
0.001825785730034113,
-0.006669185124337673,
0.02191028743982315,
0.012498142197728157,
-0.0492265559732914,
-0.027726653963327408,
0.0011406788835301995,
0.01816018857061863,
0.046561744064092636,
-0.041727062314748764,
0.035420652478933334,
-0.00770209077745676,
0.017389973625540733,
0.01920682191848755,
-0.01557720173150301,
-0.020001251250505447,
-0.024967102333903313,
-0.011515280231833458,
-0.020554304122924805,
0.015849284827709198,
0.021335886791348457,
0.02147100865840912,
0.009295069612562656,
0.0011595491087064147,
-0.021025339141488075,
-0.02133876644074917,
-0.001632506144233048,
-0.01973567344248295,
-0.019121911376714706,
-0.03301653265953064,
-0.022068941965699196,
0.019317014142870903,
-0.030230922624468803,
-0.05760937184095383,
-0.010891702026128769,
-0.014220422133803368,
-0.041190605610609055,
-0.0376419834792614,
-0.0006061699241399765,
0.015483463183045387,
0.016699129715561867,
-0.06348609179258347,
0.002523157512769103,
0.02769593708217144,
-0.04496980831027031,
0.05305420234799385,
0.03528599068522453,
0.003113159677013755,
0.021647226065397263,
-0.04104190692305565,
0.004170646425336599,
0.021446146070957184,
-0.032938484102487564,
-0.006974395364522934,
0.002375624841079116,
-0.0010768661741167307,
-0.03261466696858406,
-0.014344441704452038,
-0.013149122707545757,
-0.0036184436175972223,
0.029321853071451187,
0.006241791415959597,
-0.025352636352181435,
0.03741898387670517,
0.018233073875308037,
0.02293471060693264,
0.005024880636483431,
-0.03281594067811966,
-0.02008986473083496,
0.026797983795404434,
0.0037553375586867332,
-0.009016871452331543,
-0.03524382412433624,
-0.018756119534373283,
-0.005505091045051813,
-0.0008523587603121996,
-0.01857301965355873,
0.0011889651650562882,
0.04607760161161423,
-0.003310412634164095,
-0.008001121692359447,
0.018184667453169823,
-0.03117593191564083,
0.014965822920203209,
0.010610714554786682,
0.02379227802157402,
-0.014272167347371578,
0.020418930798768997,
0.0032994654029607773,
-0.02009831927716732,
-0.06515640020370483,
0.025509951636195183,
0.07429082691669464,
0.04198524355888367,
0.005336575210094452,
0.0450398214161396,
-0.05513313412666321,
0.023299215361475945,
0.00025031171389855444,
-0.03473525494337082,
0.002790972124785185,
-0.014631809666752815,
0.038674142211675644,
-0.06457960605621338,
-0.026695871725678444,
0.04574081674218178,
0.0370168536901474,
-0.05104801803827286,
0.022787760943174362,
0.0020817548502236605,
0.006278631743043661,
0.027841530740261078,
-0.02142307721078396,
-0.03551535680890083,
0.05619993805885315,
-0.0211383905261755,
0.0372784249484539,
-0.0023302750196307898,
-0.018230192363262177,
0.0014017598005011678,
0.03581244498491287,
0.004686637315899134,
-0.023194570094347,
-0.016480237245559692,
-0.05981183424592018,
0.042737457901239395,
-0.02445003017783165,
0.004021034110337496,
-0.004286990966647863,
-0.004339057020843029,
0.005191146396100521,
0.015637265518307686,
0.027061106637120247,
0.00972798839211464,
-0.0029079902451485395,
0.010088211856782436,
-0.008138940669596195,
-0.049396906048059464,
0.02014968916773796,
-0.0006520521710626781,
-0.05729330703616142,
0.010936523787677288,
-0.03685416281223297,
0.0517701730132103,
0.030921095982193947,
0.05650673434138298,
0.0365375280380249,
0.014096963219344616,
-0.011660311371088028,
0.012013878673315048,
0.0016175319906324148,
-0.009292658418416977,
0.14417074620723724,
0.07576555758714676,
0.014999727718532085,
-0.0774315744638443,
0.007976364344358444,
0.040491119027137756,
-0.00999538879841566,
-0.012722055427730083,
-0.005354724824428558,
-0.04146108031272888,
-0.028362737968564034,
-0.010878798551857471,
0.04593859985470772,
0.0011947101447731256,
0.017337439581751823,
0.01227346621453762,
-0.05824584886431694,
-0.0269126258790493,
0.027245094999670982,
-0.005752830300480127,
-0.021160384640097618,
-0.007620099000632763,
-0.03351473808288574,
0.009087190963327885,
-0.009219634346663952,
0.00903819315135479,
-0.022734489291906357,
-0.007959354668855667,
0.0151493139564991,
-0.0114993155002594,
-0.02534894086420536,
0.040759094059467316,
-0.00839877501130104,
0.020513756200671196,
-0.012230063788592815,
0.04676198959350586,
0.009818249382078648,
-0.023961421102285385,
0.01748199202120304,
0.05878074839711189,
0.019996510818600655,
0.00014411220035981387,
-0.009615260176360607,
0.00155731663107872,
-0.022719552740454674,
-0.04742215946316719,
-0.008837218396365643,
0.02426292560994625,
0.009773909114301205,
-0.007805258501321077,
0.002418262418359518,
-0.042908310890197754,
0.03382718563079834,
-0.011145568452775478,
-0.011287404224276543,
-0.010868795216083527,
0.02289186231791973,
-0.04769520089030266,
-0.0006967233493924141,
-0.017356662079691887,
0.0006435608374886215,
-0.06163334101438522,
0.03393067792057991,
-0.024409295991063118,
-0.08391072601079941,
-0.028521118685603142,
-0.03380603715777397,
0.06741012632846832,
0.018751870840787888,
0.006076229736208916,
-0.039602357894182205,
-0.018394190818071365,
0.002901405096054077,
-0.06613890826702118,
-0.03871682658791542,
-0.02310643158853054,
0.08128159493207932,
0.00485250074416399,
-0.023767493665218353,
-0.02350340038537979,
-0.034165509045124054,
-0.009168995544314384,
-0.023578230291604996,
0.0018554626731202006,
-0.036641061305999756,
-0.046793125569820404,
0.05311840400099754,
0.020667171105742455,
-0.0024704455863684416,
-0.047095414251089096,
-0.001364362658932805,
0.03838314116001129,
0.0406239815056324,
-0.01105765625834465,
-0.026759473606944084,
0.0155517952516675,
-0.036536093801259995,
-0.012904150411486626,
0.006939270533621311,
0.001664241892285645,
0.034669339656829834,
-0.031015364453196526,
-0.007157119922339916,
0.003380425041541457,
-0.029518485069274902,
-0.03134145960211754,
0.03314245864748955,
-0.05289603769779205,
0.003734398167580366,
0.013069520704448223,
-0.0008345662499777973,
-0.02682064287364483,
-0.01815842092037201,
-0.013090207241475582,
0.022188015282154083,
-0.03782851621508598,
0.0006492626271210611,
-0.046190571039915085,
-0.05418064072728157,
0.015147029422223568,
0.05360173061490059,
0.018929611891508102,
-0.061078377068042755,
0.0016840213211253285,
0.02342517301440239,
0.0036198378074914217,
0.05953052267432213,
0.015319460071623325,
0.020055362954735756,
-0.0026283718179911375,
-0.00924046989530325,
-0.0012302438262850046,
0.013341699726879597,
0.022706767544150352,
0.0027032471261918545,
-0.01247568428516388,
0.03477130085229874,
0.033941905945539474,
0.008096511475741863,
-0.02676325850188732,
0.028934307396411896,
-0.06980675458908081,
-0.018658284097909927,
0.03350412845611572,
-0.01672026328742504,
0.024977728724479675,
0.03708045557141304,
-0.004851316101849079,
-0.04925241693854332,
0.017275182530283928,
-0.0024314362090080976,
-0.0027958566788583994,
-0.018162183463573456,
-0.011584975756704807,
0.03539334610104561,
-0.01740473136305809,
0.028862953186035156,
0.005274021532386541,
0.024121670052409172,
0.009126199409365654,
0.044312186539173126,
-0.024390432983636856,
-0.04584801197052002,
0.014957628212869167,
0.007916663773357868,
-0.004866311326622963,
-0.01285252720117569,
-0.022781670093536377,
0.018646826967597008,
0.04338331148028374,
-0.04584016650915146,
0.05206495150923729,
-0.0007181733381003141,
-0.006083103362470865,
-0.09253691136837006,
-0.027751242741942406,
-0.02544070966541767,
0.03379610925912857,
0.03417534753680229,
-0.02515542320907116,
0.032630763947963715,
0.008685999549925327,
-0.05646100640296936,
0.06768229603767395,
-0.014017934910953045,
0.0220978781580925,
-0.038085177540779114,
0.002173586515709758,
-0.03370831534266472,
0.06939687579870224,
0.026573218405246735,
0.03163253143429756,
0.0048949457705020905,
0.019338706508278847,
-0.04689472168684006,
0.011701835319399834,
-0.06839010864496231,
-0.001499420264735818,
0.015497074462473392,
-0.026857322081923485,
0.035917241126298904,
0.008744901046156883,
0.007799605838954449,
0.03880558907985687,
0.0027769310399889946,
-0.041887734085321426,
0.010101990774273872,
0.05808951333165169,
0.0031938706524670124,
0.02836587093770504,
0.004166887141764164,
0.014016963541507721,
-0.012405780144035816,
-0.037305545061826706,
0.055733129382133484,
0.018546121194958687,
0.0035070974845439196,
0.019166354089975357,
0.03199511021375656,
-0.007063933182507753,
-0.012481915764510632,
0.026969512924551964,
-0.014689096249639988,
-0.029993999749422073,
-0.03473829850554466,
0.0013340135337784886,
-0.007187334820628166,
0.04312627762556076,
0.04085826128721237,
-0.02171499654650688,
-0.002149181440472603,
0.012361914850771427,
0.04595409333705902,
-0.016274593770503998,
-0.0007301445584744215,
-0.0034944131039083004,
-0.04127544164657593,
0.039272554218769073,
-0.00009749930177349597,
-0.017491331323981285,
0.002147528575733304,
-0.04480726271867752,
-0.035206668078899384,
0.049749284982681274,
0.03154774010181427,
-0.012690681964159012,
-0.042820725589990616,
0.024525588378310204,
-0.02394881844520569,
-0.008187751285731792,
-0.04381716251373291,
-0.019544903188943863,
0.03955436870455742,
-0.025126300752162933,
0.053434036672115326,
0.009068886749446392,
0.009172633290290833,
-0.005455734208226204,
-0.006499956827610731,
0.03619303181767464,
0.006420527119189501,
0.04406236112117767,
0.008675782941281796,
-0.04275764152407646,
0.008349775336682796,
0.037740904837846756,
0.016701484099030495,
-0.03224943205714226,
0.028517624363303185,
-0.008803988806903362,
0.025532107800245285,
-0.003683866234496236,
-0.010043824091553688,
0.023004094138741493,
0.032574184238910675,
0.016794534400105476,
-0.012402193620800972,
0.008663242682814598,
-0.028336357325315475,
-0.031191173940896988,
0.036533620208501816,
-0.001712577766738832,
-0.008402538485825062,
0.04912695661187172,
-0.004737036768347025,
0.023838596418499947,
0.007630662992596626,
-0.014582157135009766,
-0.048942841589450836,
0.015485048294067383,
-0.020590512081980705,
-0.016857977956533432,
-0.005918786395341158,
-0.014585494995117188,
0.0024209236726164818,
-0.00007425777585012838,
-0.006957004312425852,
0.024005111306905746,
-0.04066978394985199,
-0.03741999715566635,
0.0651879832148552,
0.016988588497042656,
0.03652992099523544,
0.038656409829854965,
-0.003589984029531479,
0.015478617511689663,
0.016211265698075294,
0.020998923107981682,
0.052892159670591354,
0.008531260304152966,
0.02416885457932949,
0.013561408966779709,
-0.015207363292574883,
-0.032348137348890305,
0.04117199406027794,
-0.007142466958612204,
0.021444600075483322,
0.018897440284490585,
0.01614961214363575,
0.06896411627531052,
-0.012470938265323639,
-0.027788767591118813,
-0.019878461956977844,
-0.009823698550462723,
0.08983777463436127,
-0.01018617209047079,
0.031135229393839836,
-0.01910884492099285,
0.050641488283872604,
-0.04623943194746971,
-0.011779350228607655,
0.014014041051268578,
0.04662557318806648,
-0.034795958548784256,
0.009592224843800068,
-0.02784658595919609,
-0.039829809218645096,
0.004579913802444935,
-0.06137878820300102,
-0.010491265915334225,
0.05728562921285629,
0.0021926097106188536,
0.03448213264346123,
-0.049191176891326904,
-0.011323930695652962,
-0.04653334990143776,
0.0095519432798028,
-0.0030581895262002945,
0.015460553579032421,
0.043515607714653015,
-0.000014954333892092109,
-0.021656790748238564,
0.04795966297388077,
0.014868341386318207,
-0.0210537388920784,
0.004861111752688885,
0.003070077858865261,
-0.014584802091121674,
0.01296683494001627
] |
<p>Usually in texts about Physics that uses tensors defines them as multilinear maps. So if $V$ is a vector space over the field $F$, a tensor is a multilinear mapping:</p>
<p>$$T:V\times\cdots\times V\times V^\ast\times\cdots\times V^\ast\to F.$$</p>
<p>In texts about multilinear algebra, however, a tensor is defined differently. They consider a collection $V_1,\dots,V_k$ of vector spaces over the same field, consider the free vector space $\mathcal{M}=F(V_1\times\cdots\times V_k)$, consider the subspace $\mathcal{M}_0$ genereated by vectors of the form</p>
<p>$$(v_1,\dots,v_i+v_i',\dots,v_k)-(v_1,\dots,v_i,\dots,v_k)-(v_1,\dots,v_i',\dots,v_k)$$</p>
<p>$$(v_1,\dots,kv_i,\dots,v_k)-k(v_1,\dots,v_i,\dots,v_k)$$</p>
<p>And then define the <a href="http://en.wikipedia.org/wiki/Tensor_product" rel="nofollow">tensor product</a> $V_1\otimes\cdots\otimes V_k = \mathcal{M}/\mathcal{M}_0$ and define tensors as elements of such space, which are equivalence classes of functions with finite support in $V_1\times\cdots\times V_k$.</p>
<p>Now, is there some cases in Physics where it's better to think as tensors as such equivalence classes rather than multilinear mappings? If so, how then we get some physical intuition behind those objects?</p> | 2,013 | [
-0.016891201958060265,
0.018075352534651756,
-0.014448451809585094,
-0.035357024520635605,
0.014449567534029484,
0.04451147839426994,
0.004853090271353722,
0.007751251105219126,
0.02314620092511177,
-0.01590702496469021,
-0.002337751444429159,
-0.0069241756573319435,
0.051104556769132614,
-0.025522775948047638,
0.008690593764185905,
0.033208705484867096,
-0.05571581795811653,
-0.028773698955774307,
-0.010199574753642082,
0.0034884768538177013,
0.03533419966697693,
0.05324598029255867,
-0.014334021136164665,
0.006640662904828787,
-0.0005411620950326324,
0.04384429007768631,
-0.01489578653126955,
-0.0009367174352519214,
0.046573836356401443,
0.047014109790325165,
0.008217905648052692,
-0.043896451592445374,
-0.001518928213045001,
0.01427424605935812,
-0.019367851316928864,
-0.004442488308995962,
-0.03541184589266777,
0.010700549930334091,
0.06043264642357826,
-0.011753512546420097,
-0.04949067160487175,
-0.021997179836034775,
-0.014744235202670097,
0.044714197516441345,
-0.013341978192329407,
0.02581174299120903,
0.010804720222949982,
-0.03420587629079819,
0.015019750222563744,
0.0035244824830442667,
0.033846836537122726,
0.04172566905617714,
0.01837576925754547,
0.03483617678284645,
-0.0215303972363472,
0.012593728490173817,
0.07799496501684189,
0.06260223686695099,
0.005063813645392656,
-0.06976629793643951,
-0.053385354578495026,
-0.027265606448054314,
0.009142772294580936,
-0.027604520320892334,
-0.005529613234102726,
0.06673508137464523,
-0.02305767685174942,
0.016847219318151474,
0.027626510709524155,
-0.04300502687692642,
0.0012962007895112038,
0.009194902144372463,
0.02834445796906948,
-0.027589719742536545,
-0.02009464241564274,
0.027791790664196014,
0.01859831064939499,
0.022596625611186028,
0.04961244389414787,
0.019140930846333504,
-0.03145596757531166,
-0.006189846433699131,
0.017286011949181557,
-0.008077961392700672,
0.02885398268699646,
-0.015883104875683784,
0.052408020943403244,
-0.012428204528987408,
0.023821789771318436,
0.050270624458789825,
-0.007615579757839441,
-0.02469334565103054,
-0.013023698702454567,
-0.007870946079492569,
-0.06220978498458862,
0.02078956551849842,
0.015305009670555592,
0.020978301763534546,
0.02541651576757431,
-0.03175252676010132,
-0.0018087592907249928,
-0.012792588211596012,
0.008797220885753632,
0.054891087114810944,
-0.0067734126932919025,
0.022140203043818474,
-0.06795411556959152,
0.009773602709174156,
-0.03235451877117157,
0.009063483215868473,
-0.028205854818224907,
-0.006064862944185734,
0.014150623232126236,
0.026840360835194588,
-0.012039152905344963,
-0.0368441641330719,
0.058129627257585526,
0.013768068514764309,
0.07519713789224625,
0.10620756447315216,
0.04766641929745674,
-0.017559975385665894,
0.039601702243089676,
0.009588361717760563,
-0.09504973143339157,
0.00792674906551838,
0.022591877728700638,
-0.0006270632147789001,
-0.0401846319437027,
-0.003414097474887967,
0.002513078972697258,
-0.022424280643463135,
0.04170463979244232,
-0.012193779461085796,
0.03791387379169464,
-0.06060037761926651,
-0.0925368070602417,
-0.041226133704185486,
0.017454354092478752,
0.013045795261859894,
-0.03935854136943817,
-0.039618734270334244,
0.00710724201053381,
0.02288946509361267,
0.04783150926232338,
-0.01989654451608658,
0.049954626709222794,
0.020624062046408653,
0.033972546458244324,
-0.016518477350473404,
-0.018250247463583946,
-0.015817629173398018,
-0.0072372895665466785,
-0.02121288701891899,
0.004447477869689465,
-0.060296107083559036,
0.026874907314777374,
0.046017471700906754,
-0.027819035574793816,
0.02362126111984253,
0.10215257853269577,
-0.024379093199968338,
0.0009522108593955636,
0.02500760927796364,
-0.013698291033506393,
-0.005301767494529486,
0.03282208368182182,
0.013909806497395039,
0.07191446423530579,
0.057237666100263596,
0.017165325582027435,
0.05230511352419853,
0.018094925209879875,
0.059908054769039154,
0.027343058958649635,
-0.011328673921525478,
-0.021366704255342484,
0.023770473897457123,
0.011124479584395885,
0.0029202192090451717,
-0.04014665260910988,
-0.024779314175248146,
-0.005043918266892433,
-0.0010404292261227965,
-0.0022691674530506134,
0.0385180301964283,
0.007039390504360199,
-0.001814399380236864,
-0.00820158701390028,
-0.05205795541405678,
0.0028378020506352186,
-0.08860981464385986,
0.04826664552092552,
-0.014197587966918945,
-0.027935614809393883,
0.07226225733757019,
-0.00595918670296669,
-0.025554979220032692,
-0.011514000594615936,
-0.05102613940834999,
-0.009226778522133827,
0.035823047161102295,
0.0033349625300616026,
-0.021297011524438858,
0.007839006371796131,
0.008564054034650326,
0.02995356172323227,
0.01931663230061531,
0.00720191327854991,
-0.00560337956994772,
-0.014217660762369633,
0.029220854863524437,
0.005193481687456369,
0.006475483998656273,
-0.008878971450030804,
-0.010325673036277294,
-0.004623092710971832,
-0.0021599920000880957,
-0.028700822964310646,
0.036598771810531616,
-0.014969173818826675,
0.05159204825758934,
0.07399822771549225,
0.014789966866374016,
-0.009614390321075916,
0.04584767296910286,
-0.013515670783817768,
0.012976687401533127,
-0.009322535246610641,
-0.006414337083697319,
-0.04058683663606644,
0.01753605529665947,
0.017848525196313858,
0.07354238629341125,
-0.03205861896276474,
0.028068019077181816,
0.03347836434841156,
0.03317008167505264,
-0.01026278454810381,
-0.005307175684720278,
-0.037082403898239136,
-0.04147572070360184,
0.022647397592663765,
-0.009082330390810966,
0.042691558599472046,
-0.0008700895123183727,
0.0038979612290859222,
-0.02703055739402771,
0.00938468612730503,
0.010295804589986801,
0.006243337877094746,
0.060449615120887756,
-0.01632063463330269,
0.01908990368247032,
0.025017183274030685,
-0.038660574704408646,
0.008375980891287327,
-0.009229188784956932,
0.007967360317707062,
0.04558022320270538,
0.00430321553722024,
0.007132571190595627,
-0.03375767543911934,
-0.009733738377690315,
0.02743375115096569,
-0.010968859307467937,
-0.0018896663095802069,
-0.027595046907663345,
0.025317389518022537,
-0.0756554827094078,
-0.018180184066295624,
-0.0074225072748959064,
-0.03534480556845665,
-0.005889671389013529,
0.0024038853589445353,
0.01944955252110958,
-0.024965837597846985,
0.019517987966537476,
-0.013131258077919483,
0.0037920628674328327,
0.05175287276506424,
-0.01973571628332138,
0.01552122738212347,
-0.00766353216022253,
-0.05055179446935654,
0.0507894791662693,
-0.07838331162929535,
-0.04735440015792847,
0.03789548948407173,
-0.0369439572095871,
-0.00020116781524848193,
-0.009971908293664455,
-0.007408768869936466,
-0.03838580846786499,
-0.04111446440219879,
-0.0533057264983654,
-0.0047632306814193726,
-0.022686246782541275,
0.007340308744460344,
0.04250631108880043,
-0.017785226926207542,
-0.06344222277402878,
-0.0438876636326313,
-0.015549813397228718,
-0.0555565245449543,
-0.0033898872788995504,
-0.03939944878220558,
0.012429381720721722,
-0.04127359390258789,
0.021594654768705368,
0.03984646871685982,
-0.03964893892407417,
-0.010476391762495041,
-0.06302165240049362,
-0.05793437734246254,
0.003263082355260849,
0.024240128695964813,
0.06411654502153397,
0.02857952006161213,
-0.06262195110321045,
0.09272705763578415,
0.029544521123170853,
-0.057133276015520096,
-0.01293302420526743,
0.0187646746635437,
-0.03662862256169319,
-0.04058447107672691,
-0.008701684884727001,
0.010729527100920677,
-0.011547479778528214,
0.0385146401822567,
0.029081249609589577,
0.006798195652663708,
0.05183723196387291,
-0.014591771177947521,
-0.025112653151154518,
-0.02491770125925541,
0.017951669171452522,
0.0008877887157723308,
0.0294113177806139,
0.011505925096571445,
-0.003849406959488988,
0.009689184837043285,
-0.013348350301384926,
0.024117914959788322,
0.008927557617425919,
-0.002688067499548197,
0.04850359261035919,
0.01687813736498356,
-0.0019343277672305703,
-0.02477441355586052,
0.01050612237304449,
0.0037907857913523912,
0.018276024609804153,
0.017748601734638214,
0.048137202858924866,
0.008932091295719147,
-0.08314219117164612,
0.024688394740223885,
-0.000826741277705878,
0.03098686784505844,
-0.06521187722682953,
-0.006764566525816917,
-0.017878413200378418,
0.008750814013183117,
0.006605809088796377,
-0.027060143649578094,
0.012963472865521908,
0.051122840493917465,
0.026857225224375725,
0.036594703793525696,
0.005965519696474075,
-0.028299743309617043,
0.02743416093289852,
-0.005617599003016949,
-0.01594788394868374,
-0.011093512177467346,
0.020786205306649208,
0.003432928817346692,
0.02010319195687771,
0.021280277520418167,
0.013831079937517643,
-0.020149588584899902,
-0.012867013923823833,
-0.07121177017688751,
0.004500787705183029,
-0.007790536154061556,
-0.023685377091169357,
-0.008485217578709126,
-0.011193771846592426,
0.02195739932358265,
-0.007037014700472355,
-0.04041024670004845,
0.00372951733879745,
-0.010746249929070473,
-0.06066185235977173,
0.018368180841207504,
-0.0004215171793475747,
-0.06537274271249771,
-0.00722529785707593,
0.025678755715489388,
0.071611188352108,
-0.011064331978559494,
-0.017370201647281647,
0.04268667474389076,
-0.02366839535534382,
0.023674067109823227,
0.012651937082409859,
0.018210992217063904,
0.055445700883865356,
-0.0029487728606909513,
0.01666794717311859,
0.022407343611121178,
-0.02193777821958065,
0.027057329192757607,
-0.002331225201487541,
0.06841886043548584,
-0.003486183239147067,
-0.04097018018364906,
-0.011552760377526283,
-0.06531807780265808,
-0.04821033030748367,
-0.01091348472982645,
0.05654367804527283,
0.02884240821003914,
-0.044106923043727875,
0.030832720920443535,
0.04366046190261841,
-0.021271442994475365,
0.02200160175561905,
0.032972779124975204,
-0.026912372559309006,
-0.03471666947007179,
-0.024146242067217827,
-0.026015624403953552,
-0.002921472070738673,
-0.007893853820860386,
0.02924777939915657,
-0.012837526388466358,
0.0004372845869511366,
0.0330011360347271,
0.022846980020403862,
0.009378636255860329,
-0.044871795922517776,
0.03562154620885849,
0.004413455259054899,
-0.021299561485648155,
-0.01048516295850277,
-0.0006844183662906289,
0.010850190185010433,
0.0632844939827919,
0.04052730277180672,
-0.0074705928564071655,
-0.01551843248307705,
-0.08224599063396454,
-0.013356603682041168,
0.028730139136314392,
0.04006914049386978,
-0.003057671943679452,
-0.016835736110806465,
-0.02540355734527111,
-0.010709337890148163,
0.05711860582232475,
-0.011051165871322155,
0.03384539857506752,
0.012854889035224915,
-0.013357603922486305,
-0.03418572247028351,
-0.001085082651115954,
0.004516505636274815,
0.03943163901567459,
0.008408749476075172,
0.018567398190498352,
0.011862318031489849,
0.03743045777082443,
0.01889875717461109,
0.01574680767953396,
0.012505888938903809,
0.05580749362707138,
0.007085436023771763,
-0.03993125632405281,
-0.025151269510388374,
0.02663222886621952,
0.0016556002665311098,
-0.09680228680372238,
-0.00261731818318367,
0.017214564606547356,
-0.0359034538269043,
0.00223953346721828,
-0.03078451193869114,
-0.05299732834100723,
0.03810407966375351,
0.002301077824085951,
0.015809202566742897,
0.034758713096380234,
-0.04939309507608414,
0.03515778109431267,
0.00017542284331284463,
0.0171959325671196,
0.03489186242222786,
0.009577714838087559,
-0.018314436078071594,
-0.0038670070935040712,
-0.035309672355651855,
0.044559359550476074,
-0.03557867184281349,
0.022925756871700287,
-0.02873268537223339,
-0.012660948559641838,
-0.031793199479579926,
0.05889276787638664,
-0.018750138580799103,
-0.013999070040881634,
-0.020844824612140656,
-0.047626420855522156,
-0.034448787569999695,
0.02962489426136017,
-0.03813885897397995,
-0.03344668820500374,
0.003289637388661504,
0.017219243571162224,
-0.00096146046416834,
-0.011986549943685532,
-0.014536385424435139,
0.024696219712495804,
0.017342831939458847,
0.03084556944668293,
-0.0014863513642922044,
0.011398742906749249,
-0.015432745218276978,
-0.024266395717859268,
0.034438520669937134,
-0.04787793010473251,
0.023509856313467026,
0.000689323409460485,
-0.03978051617741585,
0.014047310687601566,
-0.04368991777300835,
-0.02324218675494194,
0.015944939106702805,
-0.01033745612949133,
0.017880938947200775,
-0.011607573367655277,
-0.018583916127681732,
0.031173432245850563,
0.027922887355089188,
-0.0734943076968193,
-0.0340336449444294,
-0.0054538436233997345,
-0.023235900327563286,
-0.021214237436652184,
-0.0019501252099871635,
0.030276210978627205,
-0.018111996352672577,
-0.03806735947728157,
0.03088539093732834,
0.06041737273335457,
-0.038999754935503006,
-0.03789198398590088,
0.003540612757205963,
0.015019879676401615,
0.0348762646317482,
-0.015385388396680355,
-0.008202199824154377,
0.008632848970592022,
0.004385898821055889,
0.009739063680171967,
0.025887152180075645,
0.038402725011110306,
-0.036306411027908325,
0.010154476389288902,
-0.017389468848705292,
-0.004105167463421822,
0.032258979976177216,
0.009327984414994717,
0.023659592494368553,
0.03614212945103645,
0.022662503644824028,
-0.018209125846624374,
-0.030161017552018166,
0.020682938396930695,
0.015255521051585674,
0.053624723106622696,
0.007961170747876167,
0.008774151094257832,
-0.014674643985927105,
-0.031025543808937073,
0.024690790101885796,
-0.023698581382632256,
-0.0009652549051679671,
0.020548218861222267,
0.05614544451236725,
-0.018708785995841026,
0.04023824632167816,
0.005498818121850491,
-0.013104691170156002,
0.028053779155015945,
0.012445654720067978,
-0.02124185860157013,
0.010728131979703903,
0.005901897791773081,
-0.018017852678894997,
-0.036587417125701904,
-0.02139093354344368,
0.01582595705986023,
0.08822733163833618,
-0.02463451772928238,
0.055888477712869644,
0.01857142522931099,
-0.046156734228134155,
0.021052613854408264,
-0.005559181794524193,
-0.0315285362303257,
0.018785705789923668,
0.0113733671605587,
0.02765294723212719,
-0.024006472900509834,
0.008064061403274536,
0.012454998679459095,
0.0116951959207654,
-0.029766136780381203,
0.014627587050199509,
0.0046984246000647545,
0.01975717768073082,
0.020716482773423195,
-0.029613999649882317,
-0.07763174921274185,
0.05542083829641342,
-0.037237994372844696,
0.02145002782344818,
0.021231181919574738,
-0.02337217889726162,
0.04963812977075577,
-0.013991224579513073,
0.0019368433859199286,
-0.040230900049209595,
-0.02178015746176243,
-0.07813000679016113,
0.030379848554730415,
0.013815408572554588,
0.045808494091033936,
0.00040349600021727383,
-0.025561010465025902,
0.06274151057004929,
-0.009073454886674881,
0.004484257195144892,
0.018968548625707626,
-0.02503969892859459,
-0.032488979399204254,
-0.058396320790052414,
-0.019541339948773384,
0.006704001221805811,
-0.008393595926463604,
-0.04556487500667572,
-0.022856729105114937,
-0.041772253811359406,
0.043009743094444275,
0.0010913154110312462,
0.04454261437058449,
-0.015463956631720066,
0.05077892914414406,
-0.01772894337773323,
0.027222493663430214,
0.025223281234502792,
-0.02202480286359787,
0.13175556063652039,
0.055431317538022995,
0.023281369358301163,
-0.05178389698266983,
0.03493238613009453,
-0.018514294177293777,
-0.02653445675969124,
-0.043022315949201584,
0.061004266142845154,
-0.011066957376897335,
0.027508873492479324,
-0.029921893030405045,
0.03713621944189072,
-0.0051877740770578384,
-0.008648362942039967,
0.048004280775785446,
-0.04380006715655327,
-0.009688209742307663,
-0.028869271278381348,
0.0024647386744618416,
-0.0012225694954395294,
0.014973730780184269,
-0.052721455693244934,
0.022376080974936485,
-0.0020255735144019127,
0.033099494874477386,
-0.031598757952451706,
-0.0043968744575977325,
0.034507766366004944,
0.051927387714385986,
-0.0017252214020118117,
0.012949437834322453,
0.0019530272111296654,
0.0031170148868113756,
-0.03297381475567818,
0.01959053985774517,
0.04557004198431969,
-0.008731084875762463,
0.03168347477912903,
0.010833119973540306,
0.04308656230568886,
-0.008575334213674068,
0.0162969920784235,
0.004075971897691488,
-0.061381906270980835,
-0.004345277789980173,
-0.04258568212389946,
0.06160790100693703,
-0.012859764508903027,
0.025964751839637756,
-0.003655449952930212,
-0.023637928068637848,
0.01455923542380333,
-0.0508074052631855,
-0.01941714622080326,
0.002257686108350754,
0.03246850520372391,
0.005178238730877638,
0.015268493443727493,
-0.03557310253381729,
0.016441788524389267,
-0.020216288045048714,
0.03949504718184471,
-0.018610890954732895,
-0.009371665306389332,
0.021797392517328262,
-0.009842336177825928,
0.04560999944806099,
-0.016484646126627922,
0.028020335361361504,
-0.01282842829823494,
-0.003341749543324113,
-0.03100026771426201,
-0.04054665192961693,
0.0008040938409976661,
0.029188422486186028,
0.06209658086299896,
-0.006085837259888649,
-0.031205033883452415,
0.012492109090089798,
-0.05118923261761665,
0.02336525171995163,
-0.004697579424828291,
-0.03667561337351799,
-0.03024393878877163,
0.00728742266073823,
0.014925392344594002,
-0.0030183850321918726,
-0.005386833567172289,
-0.005965325515717268,
-0.01602979749441147,
0.01756945066154003,
0.014048824086785316,
-0.02878068946301937,
-0.004796526860445738,
0.008053590543568134,
0.0019622910767793655,
0.001964790979400277,
-0.035299357026815414,
0.023698685690760612,
0.045321300625801086,
-0.0007783827604725957,
-0.015544376336038113,
0.03435753285884857,
0.030242236331105232,
-0.000584947585593909,
0.046994421631097794,
-0.030634833499789238,
0.05540968105196953,
0.015820814296603203,
0.010162356309592724,
-0.05687470734119415,
-0.020696047693490982,
-0.0008804806275293231,
-0.010837062261998653,
0.007974842563271523,
0.028343074023723602,
-0.03137931227684021,
0.004453831817954779,
-0.02744445763528347,
0.047885067760944366,
-0.01638953760266304,
-0.034678008407354355,
-0.02416170760989189,
0.0056265308521687984,
0.026084214448928833,
-0.00827824603766203,
-0.0037236071657389402,
0.022339744493365288,
-0.04591105505824089,
-0.009854186326265335,
0.03887820243835449,
0.016596797853708267,
-0.014444584958255291,
0.0050481148064136505,
0.008265580050647259,
-0.01055135764181614,
0.040939003229141235,
-0.008674783632159233,
-0.034994982182979584,
0.020049825310707092,
-0.023448361083865166,
-0.020498240366578102,
0.02433907799422741,
-0.0010246282909065485,
0.046130746603012085,
0.027623500674962997,
-0.0069654593244194984,
-0.052477773278951645,
0.06380302459001541,
-0.02915794961154461,
0.004708597436547279,
0.005249643232673407,
-0.07460201531648636,
-0.014379635453224182,
-0.0025397478602826595,
0.015808995813131332,
0.0064348927699029446,
-0.007910762913525105,
-0.00616886280477047,
0.025386402383446693,
0.03476674109697342,
-0.053144700825214386,
0.0195158664137125,
-0.005171550903469324,
0.007464825175702572,
0.002358947414904833,
0.013529782183468342,
0.015210771933197975,
0.030952421948313713,
-0.020929789170622826,
0.029775403439998627,
0.018710149452090263,
0.02756989188492298,
-0.07314300537109375,
-0.040507722645998,
-0.00858827494084835,
0.013721435330808163,
0.028666391968727112,
-0.04713962972164154,
0.004912094678729773,
0.01759328506886959,
-0.0672653317451477,
0.035514961928129196,
-0.034003570675849915,
-0.05546056851744652,
-0.04493892565369606,
0.007555119693279266,
-0.028948310762643814,
0.04020150378346443,
0.0175784919410944,
0.039254479110240936,
0.019340552389621735,
0.010022089816629887,
0.0057704858481884,
-0.0035064409021288157,
-0.06387227773666382,
0.013932658359408379,
-0.00048610210069455206,
-0.02437414973974228,
0.08771948516368866,
0.00751426350325346,
-0.050351403653621674,
0.014200477860867977,
0.004807312041521072,
-0.026719428598880768,
0.015535966493189335,
-0.004056795034557581,
0.0221976637840271,
0.006940584164112806,
0.002586177783086896,
-0.008057582192122936,
-0.008949410170316696,
0.027614427730441093,
0.025403475388884544,
-0.00492778979241848,
-0.012711615301668644,
-0.0007470367709174752,
0.035978030413389206,
-0.03876263275742531,
-0.005191438365727663,
0.02240322157740593,
0.006870484445244074,
-0.02581975609064102,
-0.04596346244215965,
-0.016488194465637207,
0.0001228455366799608,
-0.016239838674664497,
-0.00500719528645277,
-0.032219428569078445,
-0.022705528885126114,
0.028533577919006348,
-0.0012078171130269766,
-0.03585679456591606,
0.028893645852804184,
-0.029943015426397324,
-0.025535838678479195,
0.02176962047815323,
0.01441824622452259,
-0.0076344795525074005,
-0.05730628967285156,
-0.023510880768299103,
0.0114214438945055,
-0.01739942654967308,
-0.026116354390978813,
-0.03325266391038895,
-0.027380315586924553,
0.02780461311340332,
-0.025758519768714905,
0.05941833183169365,
-0.01000203937292099,
-0.039946459233760834,
-0.010528299026191235,
-0.057046279311180115,
0.047658246010541916,
-0.008191755041480064,
-0.01655714213848114,
-0.0367036797106266,
-0.03237295150756836,
-0.014459265395998955,
0.02041143923997879,
0.04841000959277153,
0.01851585879921913,
-0.00710892491042614,
-0.009973540902137756,
0.013015085831284523,
0.01537390612065792,
-0.033913448452949524,
-0.02559041604399681,
-0.019170599058270454,
-0.007555840536952019,
0.021330682560801506,
-0.020249493420124054,
-0.024824105203151703,
-0.01776699908077717,
0.04561448097229004,
-0.008464631624519825,
0.02273028902709484,
-0.008647801354527473,
-0.033262770622968674,
0.03838062658905983,
0.03379448875784874,
-0.009340943768620491,
0.05903064087033272,
-0.00787005852907896,
0.0011065570870414376,
0.0219558272510767,
-0.033111341297626495,
-0.006711110472679138,
-0.018304545432329178,
-0.040939465165138245,
-0.006905789021402597,
-0.009835315868258476,
-0.02663467824459076,
0.01445026881992817,
-0.05262647941708565,
-0.001878721988759935,
0.06348031759262085,
-0.03410452604293823,
-0.0003683726827148348,
0.07180525362491608,
0.014410268515348434,
0.008885969407856464,
-0.0107911741361022,
0.024773966521024704,
0.029100896790623665,
-0.03988012298941612,
0.02200358174741268,
0.019819704815745354,
-0.0005542891449294984,
-0.004645218141376972,
-0.018478156998753548,
0.025037318468093872,
-0.02952965721487999,
0.008087357506155968,
0.019097860902547836,
0.047113947570323944,
-0.05374126881361008,
-0.01849409192800522,
-0.0016905770171433687,
0.010074513033032417,
-0.005755309946835041,
-0.005069028586149216,
-0.01978744938969612,
0.06417571753263474,
-0.03230511024594307,
0.008061318658292294,
-0.05139249935746193,
0.0161278173327446,
-0.00868015456944704,
0.013290448114275932,
0.01066031027585268,
0.05782968923449516,
-0.03704028204083443,
0.01711088977754116,
-0.030612438917160034,
-0.05168173089623451,
0.026195691898465157,
-0.03011135198175907,
0.009956185705959797,
0.009250394068658352,
0.0020365442615002394,
0.02853117510676384,
0.0062980689108371735,
-0.005629553925246,
-0.023812636733055115,
0.03530218079686165,
0.023167764768004417,
0.03905937075614929,
-0.024553515017032623,
-0.002658467972651124,
-0.040293049067258835,
0.04462006688117981,
-0.05111200734972954,
0.004074950702488422,
-0.023157158866524696,
-0.0005694105057045817,
0.015456338413059711,
0.043574847280979156
] |
<p>Suppose a particle with mass $m_1$ and speed $v_{1i}$ undergoes an elastic collision with stationary particle of mass $m_2$. After the collision, particle of mass $m_1$ moves with speed $v_{1f}$ in a direction of angle $\theta$ above the line it was moving previously. Particle with mass $m_2$ moves with speed $v_{2f}$ in a direction of angle $\phi$ below the line which particle with mass $m_1$ was moving previously. Using equations for conservation of momentum and kinetic energy, how can we prove these two equations</p>
<p>$\frac{v_{1f}}{v_{1i}}=\frac{m_1}{m_1+m_2}[\cos \theta \pm \sqrt{\cos^2 \theta - \frac{m_1^2-m_2^2}{m_1^2}}]$</p>
<p>and</p>
<p>$\frac{\tan(\theta +\phi)}{\tan(\phi)}=\frac{m_1+m_2}{m_1-m_2}$
?</p>
<p>EDIT. Here is what I've done:</p>
<p>For the first one, set the $xy$ coordinate system so that the positive direction of the $x$ axis points toward the original path of the particle with mass $m_1$. So we have three equations:</p>
<p>$m_1v_{1i}=m_1v_{1f}\cos \theta + m_2v_{2f} \cos \phi$</p>
<p>$0=m_1v_{1f}\sin \theta - m_2v_{2f}\sin \phi$</p>
<p>$m_1v_{1i}^2=m_1v_{1f}^2+m_2v_{2f}^2$.</p>
<p>From the second one, we get:</p>
<p>$v_{2f}=\frac{m_1v_{1f}\sin \theta}{m_2 \sin \phi}$</p>
<p>Plotting this into third equation, we get</p>
<p>$v_{1i}^2=v_{1f}^2(1+\frac{m_1 \sin^2 \theta}{m_2 \sin^2 \phi})$ (1)</p>
<p>From the first equation, we have</p>
<p>$\cos \phi =\frac{m_1(v_{1i}-v_{1f}\cos \theta)}{m_2v_{2f}}$</p>
<p>which after applying the equation we have for $v_2f$ becomes</p>
<p>$\sin^2 \phi = \frac{1}{1+\frac{(v_{1i}-v_{1f}\cos \theta)^2}{\sin^2 \theta \times v_1f^2}}$</p>
<p>Plotting this into equation (1), gives us an equation in terms of $m_1$, $m_2$, $v_{1f}$, $v_{1i}$ and $\theta$, but it is too far from what I expected.</p>
<p>For the second one, assigning the $xy$ coordinate in a way that the positive direction of the $x$ axis points toward the final path of the particle $m_2$, will give us three equations (two for conservation of linear momentum and one for conservation of kinetic energy), but I don't know what to do next.</p> | 429 | [
-0.03563763573765755,
-0.011323006823658943,
-0.04232205078005791,
-0.02243485115468502,
0.028636286035180092,
-0.004739443305879831,
-0.019470712170004845,
-0.026214340701699257,
-0.0036740857176482677,
-0.009128570556640625,
0.03452666103839874,
0.025875838473439217,
0.06762959808111191,
0.042602308094501495,
0.021365728229284286,
-0.019097408279776573,
-0.01125797163695097,
-0.008426675572991371,
-0.008628006093204021,
-0.04775819927453995,
-0.002008837414905429,
-0.013147355057299137,
0.012392458505928516,
-0.02208079770207405,
0.004231773782521486,
0.041258107870817184,
0.04186592251062393,
-0.030215268954634666,
-0.02318441867828369,
0.04789765551686287,
0.007797371130436659,
0.017955206334590912,
-0.028321726247668266,
0.00010654921061359346,
0.00017790317360777408,
0.017533380538225174,
-0.037418194115161896,
-0.029004214331507683,
0.013094513677060604,
0.0022164597176015377,
-0.049119602888822556,
-0.005741807632148266,
-0.018508803099393845,
0.060294751077890396,
-0.013459838926792145,
0.007353614550083876,
0.01544209010899067,
0.012684626504778862,
0.050753816962242126,
-0.04418385773897171,
0.10124380141496658,
-0.03241030499339104,
0.029460985213518143,
-0.007739300839602947,
0.004534295294433832,
-0.03988786041736603,
0.0343082994222641,
0.03866312652826309,
0.022252310067415237,
-0.036378923803567886,
-0.003524825209751725,
-0.01046660915017128,
-0.05948247015476227,
0.008826362900435925,
-0.015853742137551308,
0.018342439085245132,
-0.027348162606358528,
-0.024360431358218193,
0.03550977259874344,
-0.015538121573626995,
0.0016947449184954166,
-0.020677288994193077,
0.028994740918278694,
-0.03803829103708267,
0.005086676683276892,
-0.02298310026526451,
0.035995740443468094,
0.04555779695510864,
-0.012142891995608807,
0.05011655017733574,
-0.0017372280126437545,
0.014987747184932232,
0.08186829835176468,
0.05356958508491516,
-0.020007599145174026,
-0.0026231014635413885,
0.06563764810562134,
0.023612359538674355,
0.005897623486816883,
0.050178710371255875,
0.017109856009483337,
0.0259692445397377,
0.022600648924708366,
0.02933613583445549,
0.018515437841415405,
0.0049151210114359856,
-0.017953529953956604,
0.040855128318071365,
0.0328759141266346,
-0.017514022067189217,
0.003549674293026328,
-0.03194652870297432,
0.04841151461005211,
0.051966045051813126,
0.0010074778692796826,
0.0019421631004661322,
-0.04779544845223427,
0.006526057608425617,
-0.039682891219854355,
-0.016911426559090614,
-0.02830095961689949,
-0.01261948887258768,
-0.015765486285090446,
0.021392857655882835,
0.000650068512186408,
-0.03496440500020981,
0.01142206508666277,
-0.017825216054916382,
0.07761870324611664,
0.04358397424221039,
0.061570554971694946,
-0.02230466715991497,
0.024726176634430885,
-0.026921574026346207,
-0.05596153065562248,
-0.03490140661597252,
0.019196346402168274,
0.010376391932368279,
-0.03222071751952171,
0.010222055949270725,
0.022273974493145943,
-0.01319529116153717,
-0.003796622157096863,
0.0018316172063350677,
0.007835445925593376,
0.004956448916345835,
-0.10441359132528305,
-0.0553031750023365,
0.06924702227115631,
-0.002994450507685542,
0.009191015735268593,
-0.0684739351272583,
0.014914059080183506,
0.024146387353539467,
0.08750400692224503,
-0.017332732677459717,
0.0006243158713914454,
0.01007873471826315,
0.04499031603336334,
-0.021630462259054184,
0.029879599809646606,
-0.019201088696718216,
-0.0137541014701128,
0.006039330270141363,
0.0016483553918078542,
-0.06008889153599739,
0.05117262154817581,
0.02543458715081215,
-0.028087666258215904,
-0.005553867667913437,
0.06375671923160553,
-0.02017027512192726,
0.02439958229660988,
0.0016326679615303874,
-0.022903522476553917,
-0.009154635481536388,
0.06417232006788254,
0.03464948758482933,
-0.02972503937780857,
0.027254780754446983,
0.019089585170149803,
0.005147362127900124,
-0.041074659675359726,
0.009277403354644775,
0.049204520881175995,
-0.032917898148298264,
-0.03681480139493942,
-0.022663699463009834,
-0.0384603887796402,
-0.009061463177204132,
-0.0005109899793751538,
-0.06957152485847473,
-0.019864676520228386,
-0.009405486285686493,
0.013259206898510456,
0.0416315421462059,
0.03945920243859291,
0.02918989583849907,
-0.012903542257845402,
-0.027007943019270897,
0.0028940641786903143,
-0.03641064092516899,
0.04239243268966675,
-0.010080353356897831,
-0.027748074382543564,
0.038074854761362076,
0.007685448974370956,
0.027121931314468384,
-0.015425894409418106,
-0.008016611449420452,
0.008924645371735096,
0.050990212708711624,
-0.010201863944530487,
0.012764315120875835,
0.008503916673362255,
0.04851885512471199,
0.04598589986562729,
0.028403909876942635,
-0.024169839918613434,
0.011479519307613373,
0.04001329466700554,
-0.008717996999621391,
-0.011071864515542984,
0.010826977901160717,
0.001968950964510441,
0.026891030371189117,
0.019008029252290726,
-0.03316355496644974,
-0.03776288405060768,
0.03123871050775051,
-0.04600803554058075,
0.060823820531368256,
0.04561586305499077,
0.0055596292950212955,
-0.003076388267800212,
0.04638371244072914,
-0.021368013694882393,
0.038758233189582825,
0.01915348507463932,
-0.02895614318549633,
-0.015279718674719334,
-0.03892562538385391,
0.022697636857628822,
0.010417899116873741,
-0.06131741404533386,
0.0035784030333161354,
0.041642606258392334,
0.014376716688275337,
0.016967520117759705,
0.015960900112986565,
0.022490927949547768,
-0.07946937531232834,
0.04759937897324562,
0.030057411640882492,
0.001433223020285368,
-0.0030433200299739838,
0.018783332780003548,
-0.01865611970424652,
-0.014513086527585983,
-0.008233820088207722,
-0.04455415904521942,
0.01628146506845951,
0.016501959413290024,
0.013860964216291904,
0.03833746537566185,
0.017591748386621475,
0.029042834416031837,
0.004392577800899744,
0.0534258671104908,
0.03166647627949715,
-0.009289600886404514,
-0.03895959258079529,
-0.039109114557504654,
0.05806107446551323,
-0.005046514794230461,
0.029818350449204445,
0.034925978630781174,
0.020860174670815468,
0.031016064807772636,
-0.06576495617628098,
-0.02176085114479065,
-0.0026788096874952316,
-0.06153038889169693,
0.019309058785438538,
-0.023389387875795364,
0.013320080935955048,
0.046163078397512436,
0.002371697686612606,
-0.006958907935768366,
-0.010436784476041794,
-0.00655356515198946,
-0.017664415761828423,
0.012298266403377056,
0.029022149741649628,
-0.016357582062482834,
0.04915770888328552,
-0.048837218433618546,
-0.011766740120947361,
0.06864073872566223,
0.030229754745960236,
-0.016166161745786667,
0.04584036022424698,
0.009736442938446999,
-0.0857112780213356,
0.0008182047749869525,
-0.03974766284227371,
-0.014530607499182224,
-0.04472361505031586,
0.006556110922247171,
0.021873852238059044,
0.023839576169848442,
-0.05149416625499725,
-0.00005425403287517838,
-0.03758017718791962,
-0.029188502579927444,
-0.03360725939273834,
-0.017497984692454338,
0.018162310123443604,
-0.007318919990211725,
0.017107784748077393,
0.021800849586725235,
-0.0010970761068165302,
-0.0022392768878489733,
-0.05050938203930855,
0.011278877966105938,
-0.004841505084186792,
-0.012759646400809288,
0.056375280022621155,
-0.04183901473879814,
-0.023666758090257645,
0.07247335463762283,
0.02775733545422554,
-0.025578666478395462,
-0.00397856580093503,
0.01592232473194599,
0.01800067164003849,
-0.021562447771430016,
-0.004164392128586769,
0.04015425965189934,
-0.04976164177060127,
0.007436024025082588,
0.016813112422823906,
0.011073279194533825,
0.052375491708517075,
-0.002783683128654957,
0.026159830391407013,
0.017583468928933144,
0.028285512700676918,
-0.008164935745298862,
0.050662811845541,
0.018460776656866074,
-0.007101773750036955,
0.023071760311722755,
0.0038750076200813055,
0.05338520556688309,
0.012182272039353848,
-0.06544653326272964,
0.05471055954694748,
0.028790993615984917,
0.0069696903228759766,
-0.02007376402616501,
0.017918670549988747,
-0.0014217904536053538,
-0.03512810543179512,
-0.0069623845629394054,
0.04401811584830284,
0.03692178428173065,
-0.007432691752910614,
0.0021902769804000854,
0.004935225006192923,
0.044422149658203125,
-0.01358890812844038,
-0.01168074831366539,
-0.046774618327617645,
-0.012871963903307915,
0.04697886109352112,
-0.03720012307167053,
-0.026675714179873466,
0.012404097244143486,
0.01913563162088394,
0.031715214252471924,
-0.03601561859250069,
-0.02404552698135376,
0.004198652692139149,
-0.046809323132038116,
-0.012271818704903126,
-0.005452355369925499,
0.039950478821992874,
0.006676789373159409,
0.06083062291145325,
0.021273918449878693,
0.00019579265790525824,
0.03566215559840202,
-0.020131483674049377,
-0.11765832453966141,
0.04148418828845024,
-0.0060203042812645435,
-0.011296125128865242,
-0.0026165202725678682,
-0.021474048495292664,
0.005604976322501898,
-0.03239763528108597,
0.01901843585073948,
-0.021081769838929176,
-0.0053631095215678215,
-0.04870108142495155,
0.01321396604180336,
-0.05308518558740616,
-0.07148671895265579,
0.01641952618956566,
0.05808485671877861,
0.056844573467969894,
-0.053652796894311905,
0.0324440561234951,
0.06293383240699768,
-0.04725170508027077,
0.007572018541395664,
-0.06535626947879791,
-0.0030795710626989603,
0.012530308216810226,
-0.0008670485112816095,
-0.033630356192588806,
0.022007863968610764,
0.025056570768356323,
-0.002093750750645995,
-0.017222965136170387,
0.042168740183115005,
0.021385585889220238,
-0.006723836995661259,
-0.03159618005156517,
-0.037422388792037964,
-0.01244925893843174,
-0.02541860193014145,
0.09209135174751282,
-0.002451325301080942,
-0.03245016932487488,
-0.010912267491221428,
0.0357084646821022,
0.023323411121964455,
0.04243491217494011,
0.03484194353222847,
0.028050823137164116,
0.02189081534743309,
-0.017355849966406822,
-0.016943227499723434,
-0.005804297048598528,
-0.01880943402647972,
0.02204011380672455,
-0.023544427007436752,
0.00882546603679657,
0.0004149906453676522,
0.005888308864086866,
0.05649040266871452,
-0.0006463361205533147,
0.03460405021905899,
-0.04996338486671448,
-0.012674410827457905,
-0.013140149414539337,
-0.02951914072036743,
-0.0005502199637703598,
0.026829440146684647,
0.03937852382659912,
-0.018405845388770103,
0.02616734430193901,
-0.037592846900224686,
-0.01848638243973255,
0.023197097703814507,
0.03186185285449028,
-0.026972562074661255,
0.02822713926434517,
-0.02719094790518284,
-0.028454236686229706,
0.04087943583726883,
-0.025096898898482323,
0.05177713558077812,
-0.01264252606779337,
-0.00490144407376647,
-0.025570400059223175,
-0.019124329090118408,
-0.05026819556951523,
0.029323019087314606,
-0.02277448959648609,
-0.006786875892430544,
-0.01064732763916254,
0.00047113143955357373,
0.005109044723212719,
-0.005018304567784071,
0.009047734551131725,
0.056898705661296844,
0.013297771103680134,
-0.0287039615213871,
-0.004829473793506622,
0.007344014011323452,
-0.030927496030926704,
-0.04766612872481346,
0.006930316332727671,
-0.019187573343515396,
-0.004193074069917202,
0.0009777479572221637,
-0.015850050374865532,
-0.09401622414588928,
0.04104498773813248,
-0.007086335215717554,
-0.00039569794898852706,
0.016540993005037308,
-0.017216622829437256,
0.05397354066371918,
0.06181978061795235,
-0.015526551753282547,
-0.004989577457308769,
0.008125204592943192,
-0.03211637958884239,
-0.02090202458202839,
-0.017347319051623344,
0.004293996375054121,
0.0006315936334431171,
-0.018208900466561317,
-0.04831064119935036,
0.017389604821801186,
-0.04142485558986664,
0.01623731479048729,
0.008153030648827553,
0.0064403763972222805,
-0.03731577843427658,
-0.02510184235870838,
0.008506732061505318,
0.02385829947888851,
-0.01600135862827301,
-0.015957854688167572,
-0.006651581265032291,
0.011222519911825657,
0.01967494562268257,
-0.01495521329343319,
0.039574239403009415,
-0.017170505598187447,
0.018887169659137726,
0.013370915316045284,
-0.003630551742389798,
-0.0035619318950921297,
-0.07848555594682693,
-0.022591210901737213,
-0.013201550580561161,
-0.04659540206193924,
0.02902638167142868,
-0.02042337879538536,
0.008847677148878574,
0.044453613460063934,
-0.045471083372831345,
-0.04149699956178665,
0.043534040451049805,
-0.008545533753931522,
0.00661892257630825,
-0.04255275800824165,
-0.01376943476498127,
0.03696947544813156,
0.006765233818441629,
-0.04576563462615013,
-0.03380132466554642,
0.0019577634520828724,
-0.023173723369836807,
-0.01215555239468813,
-0.017046215012669563,
-0.0038167003076523542,
-0.003820285899564624,
-0.04469412937760353,
0.015877701342105865,
0.01651197485625744,
-0.013974398374557495,
-0.010647375136613846,
0.029646728187799454,
0.05148937925696373,
0.028596872463822365,
-0.016330592334270477,
-0.008779769763350487,
0.004491534549742937,
-0.03616728261113167,
0.0011327093234285712,
0.009291539900004864,
0.04133091866970062,
-0.019947728142142296,
-0.04917958006262779,
0.010982317849993706,
-0.0014567720936611295,
0.0016956711187958717,
0.028536224737763405,
0.005189559888094664,
-0.0007164356647990644,
-0.003085231874138117,
-0.0009003355517052114,
-0.008914419449865818,
0.02555963210761547,
0.003695775056257844,
0.043889109045267105,
-0.03098873607814312,
0.014758598990738392,
-0.011780527420341969,
-0.038099464029073715,
0.03047122433781624,
-0.02623320370912552,
0.004716747440397739,
-0.019503464922308922,
0.04847637936472893,
-0.04246825352311134,
0.005714512430131435,
0.04020760580897331,
0.016159433871507645,
0.018872464075684547,
-0.0471605584025383,
-0.01164758950471878,
-0.0037581929937005043,
-0.011008367873728275,
-0.021633019670844078,
-0.009051784873008728,
-0.03420375660061836,
0.020102478563785553,
0.0719001442193985,
-0.004401721525937319,
0.06287293136119843,
-0.0016792488750070333,
-0.004604274407029152,
0.0000817129694041796,
-0.02802647091448307,
-0.019809583202004433,
-0.009840274229645729,
-0.020651796832680702,
0.021752292290329933,
-0.05008300021290779,
-0.022158855572342873,
0.03953035548329353,
0.03359496593475342,
-0.04871369153261185,
-0.026723703369498253,
-0.0002884382556658238,
-0.014610866084694862,
-0.00338688213378191,
-0.026348933577537537,
-0.025474993512034416,
0.000037431902455864474,
0.00959838181734085,
0.04891069605946541,
-0.032511599361896515,
-0.0012167225359007716,
0.05991797894239426,
0.05689168721437454,
-0.009295581839978695,
-0.04458347707986832,
0.003449569456279278,
-0.04831607639789581,
0.01733512431383133,
0.011384498327970505,
-0.01241808757185936,
0.0038358517922461033,
0.030997278168797493,
0.027126748114824295,
-0.0013723059091717005,
-0.0018125934293493629,
-0.050213608890771866,
-0.03382508456707001,
-0.015088068321347237,
-0.03315816819667816,
-0.051456160843372345,
0.04072180762887001,
-0.025993039831519127,
0.011357855051755905,
0.0014069352764636278,
-0.019537782296538353,
-0.0009477838175371289,
0.00482183089479804,
0.006331773940473795,
-0.02842869982123375,
0.05685993283987045,
-0.041922129690647125,
0.03695368394255638,
-0.024105608463287354,
0.005011659115552902,
0.12561090290546417,
0.02136460691690445,
0.022130535915493965,
-0.007023950107395649,
0.012932895682752132,
-0.014503030106425285,
0.005611680913716555,
-0.033171311020851135,
0.026984747499227524,
0.005868624895811081,
0.00014889401791151613,
-0.0022133593447506428,
0.040745072066783905,
-0.006120213307440281,
-0.01291868556290865,
0.025271549820899963,
-0.0423576645553112,
-0.03389764204621315,
-0.04837050661444664,
0.005164710804820061,
-0.02704264409840107,
0.029610181227326393,
-0.013680938631296158,
0.04200439900159836,
-0.09008467197418213,
-0.027691634371876717,
-0.04322628676891327,
-0.041980110108852386,
0.008984985761344433,
0.004300163127481937,
-0.03205054998397827,
0.02265964448451996,
0.03416094556450844,
-0.019921980798244476,
0.00035648851189762354,
0.033743005245923996,
0.011030929163098335,
-0.028520146384835243,
0.04921684414148331,
0.059397585690021515,
0.02135239541530609,
0.01586177572607994,
0.014030995778739452,
-0.00801069475710392,
-0.055206287652254105,
0.03661205247044563,
-0.04980058595538139,
0.09576555341482162,
-0.00411750515922904,
-0.02511436492204666,
-0.008745483122766018,
-0.01708507537841797,
0.018625060096383095,
-0.032655708491802216,
-0.0033456964883953333,
0.008274868130683899,
0.024077819660305977,
-0.011194447986781597,
0.053403109312057495,
-0.002802732866257429,
0.03394098952412605,
0.060749128460884094,
-0.0014540004776790738,
0.0007977301138453186,
-0.02638254314661026,
-0.02737313136458397,
0.02694135345518589,
0.047310423105955124,
-0.012449422851204872,
-0.018122609704732895,
-0.007950078696012497,
0.009889216162264347,
-0.029100336134433746,
-0.012666580267250538,
-0.006965354084968567,
0.04642250016331673,
0.03255026042461395,
0.025012753903865814,
-0.027662131935358047,
-0.005573565140366554,
-0.04747243598103523,
0.03321908786892891,
-0.0001769274240359664,
-0.018836507573723793,
-0.052189502865076065,
-0.0028928518295288086,
-0.002503936877474189,
0.04625093936920166,
-0.017764264717698097,
0.01665128953754902,
0.010673634707927704,
0.05031763017177582,
0.03859950974583626,
-0.00991052109748125,
-0.06385163962841034,
0.0019447465892881155,
0.010538145899772644,
0.0002588146599009633,
-0.025831574574112892,
0.018485605716705322,
0.02300083264708519,
0.020036863163113594,
0.0027473443187773228,
0.02594352699816227,
-0.003477861639112234,
-0.005090233404189348,
0.0159438606351614,
-0.02728329598903656,
0.024729877710342407,
0.03349699825048447,
0.06719236820936203,
-0.0035129734314978123,
0.02440403215587139,
0.02026076801121235,
0.0016860958421602845,
0.004008666146546602,
0.004964175634086132,
-0.008140474557876587,
0.04847535118460655,
-0.03089822083711624,
0.028675826266407967,
-0.04642137512564659,
-0.009965752251446247,
0.00497644767165184,
0.02732519991695881,
-0.001735241967253387,
-0.019133735448122025,
-0.043954554945230484,
0.07647247612476349,
-0.019570335745811462,
-0.007029163185507059,
0.019149169325828552,
0.04071824997663498,
-0.013132369145751,
-0.027589812874794006,
0.04081938788294792,
-0.013167204335331917,
0.022914228960871696,
0.0028777942061424255,
-0.021255861967802048,
-0.0005220891907811165,
0.005422599613666534,
-0.025673720985651016,
-0.00515332818031311,
0.004962798673659563,
0.03828525170683861,
-0.010077964514493942,
-0.02693304978311062,
-0.01993074268102646,
0.10138297826051712,
-0.01482610497623682,
-0.020565105602145195,
-0.013072106055915356,
-0.06720007956027985,
-0.04450502246618271,
-0.013005774468183517,
0.011655610054731369,
-0.02325497940182686,
-0.012727669440209866,
0.04772219434380531,
-0.008017059415578842,
-0.020147863775491714,
-0.025233112275600433,
0.011013750918209553,
0.007989221252501011,
0.02532120607793331,
0.03562773019075394,
0.0019548204727470875,
0.04926733672618866,
0.0592193603515625,
0.01810424216091633,
-0.022496134042739868,
0.008631673641502857,
-0.022172637283802032,
-0.060430727899074554,
-0.028943905606865883,
0.029410792514681816,
0.03647185117006302,
0.013922391459345818,
-0.047545529901981354,
0.027063686400651932,
0.006634593941271305,
-0.07851184904575348,
-0.012857237830758095,
-0.020578714087605476,
-0.0002558508131187409,
-0.021057983860373497,
-0.03789949417114258,
-0.03719974681735039,
0.04025603458285332,
0.012249696999788284,
0.054863277822732925,
-0.0021579358726739883,
0.047584742307662964,
-0.018607476726174355,
-0.04572291672229767,
-0.0028011808171868324,
0.0241384394466877,
-0.007187058683484793,
0.0017531603807583451,
0.08896761387586594,
-0.015051714144647121,
0.025965731590986252,
0.008285810239613056,
-0.0004805928037967533,
0.024281634017825127,
-0.013994863256812096,
0.010361293330788612,
0.0018323494587093592,
0.00022192069445736706,
-0.0443415567278862,
0.01496333908289671,
0.024294471368193626,
-0.03331974893808365,
-0.0012888298369944096,
-0.02162984572350979,
-0.004418937489390373,
-0.03220974653959274,
0.03912011906504631,
-0.03577280417084694,
-0.027275104075670242,
0.016124386340379715,
0.0028463886119425297,
-0.01209213025867939,
-0.000870399409905076,
0.009128417819738388,
0.016389120370149612,
-0.007649096194654703,
-0.0106665575876832,
-0.03880559653043747,
-0.01077805645763874,
0.019888292998075485,
-0.013053401373326778,
-0.021639637649059296,
0.007416249718517065,
-0.005986933596432209,
-0.00729338126257062,
0.012873878702521324,
-0.016868101432919502,
-0.004454740788787603,
-0.023267196491360664,
-0.02720814011991024,
-0.012758273631334305,
0.04406918212771416,
-0.016288142651319504,
-0.05501808598637581,
-0.03758372738957405,
0.019267644733190536,
0.024037225171923637,
0.03975272923707962,
-0.013874568045139313,
-0.022864438593387604,
-0.04860362783074379,
-0.05977997928857803,
0.027729488909244537,
0.015294437296688557,
-0.05354779213666916,
-0.012209276668727398,
-0.03362315148115158,
-0.016307499259710312,
0.041270721703767776,
0.07057145237922668,
-0.015009711496531963,
0.003627926576882601,
0.03227626532316208,
-0.024536732584238052,
0.01653105393052101,
-0.06704512238502502,
-0.005675213877111673,
-0.017425229772925377,
0.011320982128381729,
0.02242271602153778,
0.01668471470475197,
-0.020434042438864708,
0.03312521427869797,
0.0019214466447010636,
-0.03905321657657623,
0.016269957646727562,
0.015165106393396854,
-0.03615448251366615,
-0.036403097212314606,
-0.041102491319179535,
0.02485864795744419,
0.08286616951227188,
0.01889897882938385,
0.018026474863290787,
0.007324827369302511,
-0.030111735686659813,
-0.045608919113874435,
0.012565799057483673,
-0.0628807470202446,
-0.04428249970078468,
-0.03864319249987602,
-0.012668708339333534,
0.03748324140906334,
-0.05562547966837883,
0.00853301677852869,
0.0203990675508976,
-0.04062488302588463,
-0.039586424827575684,
0.026480786502361298,
0.017098238691687584,
0.03476356714963913,
0.016888510435819626,
0.05334891751408577,
0.004539211746305227,
-0.022937407717108727,
0.042830925434827805,
0.008495979011058807,
0.014171983115375042,
0.007584610488265753,
-0.02999241091310978,
0.02947300858795643,
-0.012435642071068287,
0.03162146732211113,
-0.028634896501898766,
0.02677852101624012,
0.02311765030026436,
-0.007421855349093676,
0.018956933170557022,
-0.0030713235028088093,
-0.016960784792900085,
0.021606070920825005,
0.0023700089659541845,
0.06039462983608246,
-0.04412182793021202,
0.015610539354383945,
-0.012376546859741211,
0.009021446108818054,
-0.023387469351291656,
-0.0066589913330972195,
-0.0028363701421767473,
0.007998162880539894,
-0.011904017068445683,
-0.01622622460126877,
-0.018151039257645607,
-0.01802857778966427,
0.001115541672334075,
-0.0009211861761286855,
-0.00551183894276619,
0.05334674194455147,
-0.0033924977760761976,
0.044142335653305054,
-0.02273217961192131,
-0.023796463385224342,
-0.01962929405272007,
0.040903981775045395,
0.035918548703193665,
0.007910462096333504,
-0.01729288324713707,
0.02183246985077858,
-0.02968236804008484,
0.03426104784011841,
-0.04774674028158188,
-0.01785498857498169,
0.01875883899629116,
0.014929946511983871,
0.03988039493560791,
-0.02470751665532589
] |
<p>I'm trying to help a child research a science project on refrigeration.
Refreshing my incredibly rusty thermodynamics skills....</p>
<p>The ideal gas law: $PV=nRT$. Let's take air at STP:</p>
<p>$P = 101\,kPa$
$V = 1\,L = 0.001\,m^3$
$R = 8.3\,J/mol\cdot K$
$T = 298\,K$</p>
<p>$n=PV/RT = (101000) (.001) / (8.3 \cdot 298) = 0.04\, moles$?</p>
<p>If we compress the air to ~7atm adiabatically
$P_2 = 7P$</p>
<p>I would think the volume goes to $\frac{1}{7V}$</p>
<p>$V_2 = \frac{V}{7}$</p>
<p>then I would expect the gas to be hotter. But I'm obviously confused because with that pressure and volume, the temperature is obviously the same. I'm assuming that I'm wrong about what the volume would be for an ideal gas if I compress to $7\,atm?$</p>
<p>$T_2 = \frac{P_2V_2}{nR} = ???$</p>
<p>The specific heat of air: $c_p = 1.006\,kJ/kg\cdot K$</p>
<p>Of course air is not quite ideal. I would also appreciate someone explaining what the non-ideal behavior is due to. Is it related to the mixing? Some kind of chemical interaction between the different components? </p>
<p>What I want to know is how to calculate the temperature of a gas given an initial temperature, pressure, heat capacity and final pressure, Adiabatically.</p> | 2,014 | [
-0.032157234847545624,
-0.02090580202639103,
-0.0007731780642643571,
-0.004513178486377001,
0.038299474865198135,
-0.024839216843247414,
-0.042093198746442795,
-0.01995299942791462,
-0.01771378330886364,
-0.002117855940014124,
0.05475138500332832,
0.043508756905794144,
0.03595525026321411,
0.013064158149063587,
0.0165504589676857,
-0.01245314534753561,
-0.0023938296362757683,
-0.03003799542784691,
0.026282411068677902,
0.005932094994932413,
-0.04934031516313553,
-0.001869191532023251,
0.006035820115357637,
-0.007518279831856489,
-0.033056724816560745,
0.06600691378116608,
0.03889310359954834,
-0.032127879559993744,
0.00842619314789772,
0.030119752511382103,
-0.00992741622030735,
-0.038931943476200104,
0.03771542012691498,
-0.016833055764436722,
0.02168862894177437,
0.04392826557159424,
-0.010224312543869019,
0.016837626695632935,
-0.024079466238617897,
0.05006223917007446,
-0.02332145906984806,
-0.009474708698689938,
0.030072534456849098,
-0.028605744242668152,
-0.023784352466464043,
0.03519215062260628,
0.010883458890020847,
-0.01995241641998291,
0.030393270775675774,
-0.0690397173166275,
0.015262985602021217,
0.04262653738260269,
-0.0030107118654996157,
0.06407688558101654,
-0.03019007481634617,
0.007627667859196663,
0.05586368590593338,
0.06839155405759811,
0.018107961863279343,
-0.04055510833859444,
0.0016896981978788972,
-0.018254093825817108,
-0.044297900050878525,
-0.0016121877124533057,
-0.009361395612359047,
-0.001547816675156355,
-0.0010003207717090845,
0.020685501396656036,
0.04792964458465576,
0.010075051337480545,
0.03476574644446373,
0.04057503864169121,
0.06123540177941322,
-0.0025804575998336077,
0.027917908504605293,
-0.006529740057885647,
0.032996587455272675,
0.0034671828616410494,
0.0710204690694809,
0.04876131936907768,
-0.004138048738241196,
0.049595337361097336,
0.015649108216166496,
0.028821760788559914,
-0.022649655118584633,
-0.0325801856815815,
0.07313540577888489,
-0.0021224820520728827,
0.022166864946484566,
0.024273846298456192,
0.02447955310344696,
-0.0032369091641157866,
0.02520928531885147,
0.02010129578411579,
0.020348988473415375,
0.02177377976477146,
-0.01211464311927557,
0.05403221398591995,
-0.005999927408993244,
-0.04245900362730026,
-0.005140272434800863,
0.04639511555433273,
0.05337327718734741,
0.082335464656353,
-0.021307745948433876,
-0.06190268322825432,
-0.032650452107191086,
0.01476020272821188,
-0.0026331478729844093,
-0.0047558085061609745,
-0.031157800927758217,
-0.01122691947966814,
-0.0016722435830160975,
-0.018408767879009247,
0.00701720267534256,
-0.031150510534644127,
0.005750130396336317,
-0.04243088513612747,
0.09155724197626114,
0.0346166156232357,
0.06735371053218842,
-0.015811987221240997,
0.019972147420048714,
-0.005856010597199202,
-0.05781203880906105,
0.006967384833842516,
0.004155740141868591,
-0.018503747880458832,
-0.03760823979973793,
0.004233289044350386,
-0.034739892929792404,
-0.018184149637818336,
-0.00429629348218441,
0.0051025645807385445,
0.03055422753095627,
-0.009646609425544739,
-0.05980042740702629,
-0.07539720833301544,
0.041195280849933624,
-0.004747234750539064,
-0.07571905106306076,
-0.07986080646514893,
0.02957461215555668,
0.028065456077456474,
0.04588661715388298,
-0.01623718813061714,
0.01370279211550951,
-0.005560191348195076,
0.031060583889484406,
0.040454573929309845,
-0.05695691704750061,
-0.027115946635603905,
0.023566775023937225,
-0.04241322726011276,
0.009424719959497452,
-0.047653816640377045,
0.03537183627486229,
0.0529242642223835,
-0.01311563327908516,
-0.03059620037674904,
0.010671216063201427,
-0.04592622071504593,
-0.04783705249428749,
-0.02375277690589428,
0.008111287839710712,
-0.01447536051273346,
0.05764083191752434,
0.01328243687748909,
-0.030607709661126137,
0.02248714119195938,
0.01961183361709118,
0.025826741009950638,
0.00295806466601789,
-0.004242490045726299,
0.06474217772483826,
0.03064473159611225,
0.019187841564416885,
-0.04163246229290962,
0.01987745799124241,
0.027058452367782593,
-0.04422499239444733,
-0.02649248018860817,
0.0058029936626553535,
-0.018580490723252296,
0.009447498247027397,
0.053119320422410965,
0.020549040287733078,
0.01019454188644886,
0.00772439269348979,
-0.054602015763521194,
-0.05485376715660095,
-0.07101649791002274,
0.022905666381120682,
-0.012347733601927757,
0.004154089372605085,
0.009124888107180595,
0.016631778329610825,
0.0408841036260128,
-0.004110847134143114,
-0.011406108736991882,
0.03085389733314514,
0.006924847606569529,
-0.006291268393397331,
-0.0024951251689344645,
0.042363643646240234,
0.056555528193712234,
0.017701072618365288,
-0.023871440440416336,
0.01133672147989273,
-0.020433509722352028,
-0.006144532468169928,
-0.0044718594290316105,
-0.02332056686282158,
-0.006782566662877798,
0.015051428228616714,
-0.0005549336201511323,
0.018443360924720764,
0.021851645782589912,
0.024906478822231293,
0.029053911566734314,
0.015015884302556515,
0.04976310953497887,
0.03367828205227852,
0.010343528352677822,
0.0004621847765520215,
0.02269267663359642,
0.0011914005735889077,
0.008200369775295258,
0.016113940626382828,
-0.018587376922369003,
-0.011410309933125973,
-0.020475205034017563,
0.06770121306180954,
0.0038215876556932926,
-0.06281156092882156,
-0.005856935400515795,
0.02852455899119377,
0.02003730647265911,
0.016112305223941803,
0.0225520096719265,
0.01143324002623558,
-0.009341610595583916,
0.03642772138118744,
0.008813184686005116,
0.004194923210889101,
0.022034231573343277,
-0.004759881645441055,
0.048559390008449554,
0.02411859855055809,
0.00368560291826725,
-0.031624678522348404,
0.02823472209274769,
0.031890396028757095,
-0.018547454848885536,
-0.04057704284787178,
0.0037157810293138027,
0.03679085895419121,
-0.01000518910586834,
0.042739495635032654,
0.04993263632059097,
0.008575967513024807,
0.03834819793701172,
0.003727587405592203,
-0.021944250911474228,
0.012041572481393814,
0.016839994117617607,
0.015987733379006386,
-0.0016887154197320342,
0.019378168508410454,
-0.045161206275224686,
0.02299337647855282,
-0.02530735358595848,
0.041853390634059906,
-0.04629790782928467,
-0.010658834129571915,
0.015788927674293518,
-0.015590231865644455,
0.023377392441034317,
-0.009415578097105026,
-0.026256421580910683,
-0.02586689405143261,
-0.04716009274125099,
0.0041008442640304565,
-0.00779664795845747,
-0.03738444671034813,
-0.003030966967344284,
-0.012027090415358543,
-0.035692185163497925,
-0.0008857424254529178,
0.0029010323341935873,
-0.0335482619702816,
0.031263407319784164,
-0.03827517852187157,
-0.06807604432106018,
-0.0053877513855695724,
-0.05291641876101494,
-0.011446313001215458,
-0.034342825412750244,
-0.008605565875768661,
0.05909281596541405,
-0.058042000979185104,
-0.008012098260223866,
0.030093898996710777,
-0.06048530712723732,
-0.02854841575026512,
-0.03552853688597679,
-0.03568282723426819,
0.008509200066328049,
-0.011227977462112904,
0.029824666678905487,
0.03936907276511192,
-0.0183357372879982,
-0.027052942663431168,
-0.03250817954540253,
-0.021028490737080574,
0.02222333662211895,
0.011694858781993389,
0.0413752943277359,
0.007454785518348217,
-0.02666332572698593,
0.04898947477340698,
-0.0010813975241035223,
-0.01727871596813202,
-0.007607027422636747,
0.015111078508198261,
-0.03339521214365959,
-0.024677177891135216,
0.020136704668402672,
0.05185903236269951,
-0.039362840354442596,
0.014304046519100666,
0.008591587655246258,
0.06724636256694794,
0.009871461428701878,
0.0347832590341568,
-0.016326604411005974,
0.01464919000864029,
-0.018320133909583092,
0.04281235858798027,
0.06418225914239883,
-0.041926365345716476,
-0.03788946568965912,
0.03262978419661522,
-0.05545010790228844,
0.053793955594301224,
0.08246100693941116,
-0.07199154794216156,
0.03382957726716995,
0.007506401743739843,
-0.005416766740381718,
-0.07294522970914841,
0.004961761180311441,
-0.020523417741060257,
-0.024458054453134537,
0.024223394691944122,
0.010252282954752445,
0.02710784040391445,
-0.02365851029753685,
-0.0009208467090502381,
0.036994822323322296,
0.0523390993475914,
-0.019008396193385124,
-0.022801754996180534,
0.042304009199142456,
-0.04805276542901993,
0.006113470997661352,
0.015265563502907753,
0.007581903599202633,
0.028371842578053474,
0.049478475004434586,
0.02272249385714531,
-0.04458916559815407,
-0.04435701668262482,
0.02490668185055256,
-0.05404120311141014,
-0.012812646105885506,
-0.02887636609375477,
0.05558612197637558,
-0.014511803165078163,
0.07365312427282333,
0.00794271007180214,
0.02117438055574894,
0.04133160784840584,
0.025075726211071014,
-0.07393158227205276,
0.024661002680659294,
-0.0046760886907577515,
-0.026900747790932655,
0.0034422443713992834,
0.000027929128918913193,
-0.014070602133870125,
-0.018019990995526314,
-0.01079315971583128,
0.017724977806210518,
-0.023905225098133087,
-0.030995599925518036,
-0.0024381631519645452,
-0.019242536276578903,
0.006381163839250803,
0.00848621129989624,
0.0389244444668293,
0.0452364943921566,
-0.03936358913779259,
0.011199240572750568,
0.05598406493663788,
0.0012417882680892944,
-0.014390516094863415,
-0.05711826682090759,
-0.0004820413887500763,
0.016090257093310356,
0.031570278108119965,
0.020053744316101074,
-0.010422627441585064,
0.0045359134674072266,
-0.011733329854905605,
-0.005423057358711958,
0.03393302857875824,
-0.03000934049487114,
0.025832664221525192,
-0.015158865600824356,
-0.03209204599261284,
-0.015354929491877556,
0.018912652507424355,
0.0010350992670282722,
-0.02681226097047329,
0.03283469378948212,
0.003987741656601429,
-0.0031569707207381725,
-0.003986735828220844,
0.01838458888232708,
0.04199207201600075,
-0.038091763854026794,
-0.01432521641254425,
-0.011856509372591972,
-0.016029227524995804,
-0.02226473018527031,
-0.014665425755083561,
0.00914989784359932,
0.01805565319955349,
-0.04576997458934784,
-0.029611319303512573,
0.0007241801358759403,
0.018266385421156883,
0.011900902725756168,
0.0400843471288681,
0.02315060980618,
0.02126041240990162,
-0.013042382895946503,
-0.03601692616939545,
-0.008283213712275028,
0.0016442742198705673,
0.016992131248116493,
-0.012210928834974766,
-0.00522364117205143,
-0.10503795742988586,
-0.0022952784784138203,
0.018906233832240105,
0.03093850240111351,
-0.01577940583229065,
0.013977576978504658,
-0.07136791199445724,
-0.008292673155665398,
0.026506274938583374,
-0.04815783351659775,
0.03612847626209259,
-0.00805571023374796,
-0.004220571834594011,
0.015252889133989811,
-0.02399691566824913,
-0.03417021036148071,
0.008086174726486206,
0.001438670908100903,
-0.027456581592559814,
-0.02560269832611084,
-0.01844295673072338,
-0.008981653489172459,
-0.01383515726774931,
0.051515959203243256,
0.02320670522749424,
-0.008847598917782307,
-0.04173842817544937,
0.01078743115067482,
-0.012336419895291328,
-0.0328802652657032,
-0.05658676475286484,
-0.02597435936331749,
-0.0013675515074282885,
0.02910653129220009,
0.06136360019445419,
-0.04717091843485832,
-0.04972943663597107,
0.04186532646417618,
0.0074676210060715675,
0.001425334601663053,
-0.010089032351970673,
-0.010675493627786636,
0.08015571534633636,
0.01944449171423912,
0.01863201893866062,
0.040274955332279205,
0.07754994928836823,
-0.010112273506820202,
-0.01741805300116539,
-0.0566989928483963,
0.0325334332883358,
-0.00716171320527792,
-0.002228941535577178,
-0.03770973160862923,
-0.0059052822180092335,
-0.01143118180334568,
0.043664030730724335,
-0.015995213761925697,
0.040308088064193726,
-0.04099015146493912,
-0.031984537839889526,
0.043526019901037216,
0.0395439974963665,
0.039622582495212555,
0.01603516936302185,
-0.005073072388768196,
0.011091138236224651,
-0.01259370893239975,
-0.04097631946206093,
-0.010929223150014877,
0.0012048892676830292,
0.016933832317590714,
0.020394815132021904,
-0.05064801871776581,
0.06418584287166595,
-0.024766476824879646,
0.0043413289822638035,
0.0047462573274970055,
-0.06551231443881989,
0.04248989373445511,
-0.009013152681291103,
0.007186158560216427,
0.0071083237417042255,
-0.03185645118355751,
-0.002791879465803504,
0.012838507071137428,
0.012992610223591328,
0.04597067832946777,
-0.03879568725824356,
0.04133886471390724,
-0.0036688658874481916,
0.012743262574076653,
-0.04951874911785126,
-0.05318547412753105,
0.03526621311903,
-0.0119662806391716,
-0.013953170739114285,
-0.04891446977853775,
0.008114014752209187,
-0.016333580017089844,
-0.04219120740890503,
0.019109409302473068,
0.03874565660953522,
0.00892470870167017,
-0.03218035027384758,
0.009555511176586151,
0.06638862937688828,
0.04478289932012558,
0.0034302682615816593,
-0.029215015470981598,
0.0015937208663672209,
0.024349480867385864,
-0.012493586167693138,
0.023306161165237427,
0.0009242032538168132,
-0.018225496634840965,
-0.042233631014823914,
0.002868874929845333,
0.015177399851381779,
0.05209359899163246,
-0.004122455138713121,
0.02053113281726837,
0.03818893805146217,
0.010074030607938766,
-0.02879156731069088,
-0.010131241753697395,
0.021800899878144264,
0.002342772204428911,
0.009562799707055092,
-0.02321176417171955,
-0.036168184131383896,
-0.010156876407563686,
-0.03344261646270752,
-0.007169882766902447,
-0.0008825048571452498,
0.0029182962607592344,
-0.0025681783445179462,
0.06757152825593948,
-0.01841183379292488,
-0.019345104694366455,
0.00424342742189765,
-0.045615434646606445,
0.034527115523815155,
0.040153272449970245,
-0.041814014315605164,
0.003487455192953348,
0.0378798246383667,
-0.03687717765569687,
-0.010293986648321152,
-0.03352539241313934,
0.003987012431025505,
0.0647192969918251,
-0.03329487144947052,
0.036503273993730545,
-0.01531702745705843,
0.01230448018759489,
0.015462503768503666,
-0.01577708125114441,
-0.010943543165922165,
0.002322586253285408,
0.01938200555741787,
0.02159578911960125,
0.03145616129040718,
-0.015772217884659767,
0.034221895039081573,
0.036508601158857346,
-0.003373355371877551,
0.000950220157392323,
0.015307889319956303,
-0.01931656524538994,
-0.03631139174103737,
-0.053156960755586624,
-0.02251255325973034,
0.06739967316389084,
-0.02722141705453396,
0.02784469909965992,
-0.008357246406376362,
0.02198377251625061,
0.03928449749946594,
-0.033176079392433167,
-0.02206137776374817,
-0.06607954204082489,
-0.015784977003932,
-0.044563744217157364,
-0.005635177716612816,
0.0200321264564991,
-0.023013245314359665,
0.034926824271678925,
-0.0000488922705699224,
0.04314545542001724,
-0.013025910593569279,
0.016787061467766762,
-0.017736144363880157,
-0.023248067125678062,
-0.025444762781262398,
0.004744820296764374,
-0.03154405578970909,
0.02655969373881817,
0.007079670671373606,
-0.05030275881290436,
0.02334192767739296,
-0.010830235667526722,
0.010825569741427898,
0.005792343057692051,
0.01358403917402029,
0.012105446308851242,
0.11064092069864273,
0.010762693360447884,
0.01314117293804884,
-0.03355288878083229,
0.05535615608096123,
0.13096290826797485,
0.013088813051581383,
0.017737824469804764,
-0.03743351995944977,
0.0029331911355257034,
0.0039195166900753975,
-0.026748379692435265,
-0.02118760719895363,
0.011953315697610378,
0.002640994032844901,
0.01973770000040531,
0.04509692266583443,
0.06670733541250229,
-0.008351759053766727,
0.008706185966730118,
0.015558290295302868,
-0.04707193374633789,
-0.021637465804815292,
-0.025330372154712677,
-0.0016190716996788979,
0.005855428986251354,
0.010691030882298946,
-0.011895916424691677,
0.009229808114469051,
-0.02464159019291401,
0.027680814266204834,
-0.044177453964948654,
-0.017297448590397835,
0.04375528171658516,
-0.013550538569688797,
-0.022604918107390404,
0.010711444541811943,
0.0019238810054957867,
0.008036984130740166,
-0.016668541356921196,
-0.01097905170172453,
0.02325167879462242,
-0.00040315045043826103,
0.022275593131780624,
0.04650640860199928,
0.0019450400723144412,
-0.008845898322761059,
0.011823070235550404,
0.021360207349061966,
-0.04163283854722977,
-0.02187614142894745,
0.008065016940236092,
0.03584863990545273,
-0.006314897444099188,
-0.017577407881617546,
-0.015221891924738884,
0.01452257577329874,
0.012356909923255444,
-0.02148730494081974,
-0.02687809430062771,
0.024281712248921394,
0.046355970203876495,
-0.03460918366909027,
-0.014846771955490112,
-0.027005009353160858,
-0.007740320637822151,
-0.01125848013907671,
0.009194941259920597,
-0.03171827271580696,
0.008116583339869976,
0.006981329061090946,
-0.02550552599132061,
0.04053458198904991,
-0.020733969286084175,
-0.016016773879528046,
0.0005952781648375094,
-0.02233467996120453,
-0.01896713301539421,
-0.03061128407716751,
0.01172624621540308,
0.04598908871412277,
0.04332270845770836,
-0.012309618294239044,
-0.01432433258742094,
-0.0049659269861876965,
-0.03407829627394676,
0.03281715139746666,
0.005393375176936388,
-0.04139097034931183,
0.01791594736278057,
-0.00015357705706264824,
-0.028422275558114052,
0.05200830101966858,
-0.02484363690018654,
0.0026344384532421827,
0.03928515687584877,
0.046356454491615295,
0.0404711551964283,
-0.037114277482032776,
-0.053033702075481415,
-0.008355922996997833,
-0.05320027098059654,
0.014872541651129723,
0.03777259960770607,
0.04610464721918106,
-0.0009556426084600389,
-0.009162595495581627,
0.004884329158812761,
-0.007078207563608885,
-0.00885914545506239,
0.03509187698364258,
0.007776215672492981,
-0.0072311400435864925,
0.0016324619064107537,
-0.01636544056236744,
0.012618198990821838,
-0.03196234256029129,
-0.03015451319515705,
-0.021359151229262352,
0.0026245019398629665,
-0.05151145160198212,
-0.020263833925127983,
-0.004980959463864565,
0.04905915632843971,
-0.030288798734545708,
0.0042732818983495235,
-0.030973125249147415,
-0.022816967219114304,
-0.03059590980410576,
0.011664851568639278,
0.012252779677510262,
0.0027110895607620478,
-0.005928320810198784,
0.026699993759393692,
-0.05854259058833122,
-0.009846819564700127,
0.01869281940162182,
0.021065132692456245,
0.011582187376916409,
-0.06775327771902084,
-0.016113149002194405,
-0.005315491463989019,
0.06015004962682724,
-0.04190810024738312,
-0.05480185151100159,
0.04357164353132248,
-0.021582555025815964,
-0.080267034471035,
-0.005364467389881611,
0.03226931020617485,
0.020114677026867867,
0.06223299354314804,
0.017717529088258743,
-0.0006042019231244922,
0.06419306993484497,
-0.04776013642549515,
-0.025164922699332237,
0.01058118510991335,
-0.01791011355817318,
0.018966520205140114,
0.008255488239228725,
0.006013462319970131,
-0.010273470543324947,
-0.00005692638296750374,
0.03621409088373184,
0.026200098916888237,
-0.0459679439663887,
0.014487093314528465,
0.0019197541987523437,
-0.014397282153367996,
0.017149949446320534,
0.036624327301979065,
0.005265903193503618,
0.024149630218744278,
0.04890359938144684,
-0.022475268691778183,
0.00037249494926072657,
0.019916189834475517,
-0.016865437850356102,
-0.11791267991065979,
-0.019812937825918198,
0.00010617006773827597,
-0.01255179475992918,
0.03707030043005943,
-0.00485053937882185,
0.034478191286325455,
0.02393396385014057,
-0.039849571883678436,
-0.027922803536057472,
-0.025479452684521675,
-0.011081088334321976,
-0.040675681084394455,
0.003729995572939515,
-0.02418946847319603,
0.0267068799585104,
0.012815729714930058,
0.02564270794391632,
-0.01168813370168209,
0.019254187121987343,
-0.03321085125207901,
-0.006435192655771971,
0.022167060524225235,
0.011895902454853058,
-0.016823604702949524,
-0.009202714078128338,
0.0010926277609542012,
-0.0013237700331956148,
-0.01594802364706993,
0.04057982191443443,
-0.0347319059073925,
-0.00542307598516345,
-0.028281215578317642,
0.0002592441451270133,
-0.06780673563480377,
0.05443057790398598,
0.037046167999506,
0.013066267594695091,
0.01122225634753704,
0.039377834647893906,
0.047308094799518585,
0.002107691252604127,
-0.0034901974722743034,
-0.0035845404490828514,
0.04372641444206238,
-0.028818145394325256,
-0.027305440977215767,
0.055661264806985855,
-0.008562509901821613,
-0.010991650633513927,
0.03561718016862869,
-0.025524554774165154,
-0.016680646687746048,
-0.05227052420377731,
-0.0008410749724134803,
-0.030063042417168617,
-0.0012628198601305485,
0.020581021904945374,
0.003671724582090974,
-0.022745545953512192,
-0.026366829872131348,
-0.019659560173749924,
0.0319008007645607,
0.026968739926815033,
0.012130599468946457,
-0.005155197344720364,
-0.05306774377822876,
-0.052649710327386856,
-0.014357047155499458,
-0.012277580797672272,
-0.026946764439344406,
-0.037676792591810226,
-0.02034769393503666,
0.036419808864593506,
0.040311072021722794,
0.018569152802228928,
-0.04963560402393341,
-0.016642864793539047,
-0.009652441367506981,
-0.056794021278619766,
-0.006840300280600786,
-0.032764215022325516,
0.0018493670504540205,
-0.039869509637355804,
0.005987444892525673,
0.007498755119740963,
0.02262921817600727,
0.06067749857902527,
0.02862486056983471,
-0.027261244133114815,
0.01305796205997467,
-0.021340517327189445,
0.00743918027728796,
-0.049387142062187195,
0.020610075443983078,
0.016489233821630478,
-0.015233191661536694,
0.036388855427503586,
-0.024831317365169525,
-0.004167196340858936,
0.002301272237673402,
0.024521835148334503,
-0.034053415060043335,
-0.011512004770338535,
-0.038768235594034195,
-0.007195066194981337,
0.04339122027158737,
0.00667450251057744,
-0.014882215298712254,
0.03213595598936081,
-0.030200794339179993,
0.02827121503651142,
0.03968046233057976,
-0.005610148888081312,
-0.055938851088285446,
0.005059343762695789,
-0.030840236693620682,
-0.020011864602565765,
-0.038703981786966324,
-0.03030649945139885,
0.034567561000585556,
-0.043662313371896744,
0.0334109365940094,
0.041709139943122864,
-0.052505020052194595,
-0.013340404257178307,
0.03220770135521889,
0.05733199417591095,
0.053265493363142014,
-0.024508776143193245,
-0.008299161680042744,
0.031935740262269974,
0.010166766121983528,
0.005625263787806034,
0.04262133687734604,
0.02598925679922104,
-0.01694929040968418,
0.027324765920639038,
0.03220667317509651,
0.005567471496760845,
0.016115829348564148,
0.015418263152241707,
0.007693998049944639,
-0.04894230142235756,
-0.015908831730484962,
0.009289604611694813,
0.005237267818301916,
0.019514912739396095,
0.03483690693974495,
-0.009537485428154469,
0.08756037801504135,
-0.002767423167824745,
0.021825220435857773,
-0.05384469032287598,
0.038995880633592606,
-0.010059257969260216,
0.020107924938201904,
0.005933266598731279,
0.01801668480038643,
-0.006195842754095793,
0.021718665957450867,
-0.05090866982936859,
0.0168492179363966,
-0.0027347381692379713,
-0.033418577164411545,
-0.020340271294116974,
-0.02279057167470455,
-0.021678516641259193,
-0.042456064373254776,
-0.028625262901186943,
-0.012252318672835827,
-0.029067475348711014,
0.021806925535202026,
0.011575626209378242,
-0.0035242841113358736,
0.028912561014294624,
-0.02685505524277687,
0.0244673490524292,
0.06674474477767944,
-0.05939348042011261,
-0.03139399364590645,
-0.0010241554118692875,
-0.013351953588426113,
-0.017743026837706566,
-0.004438761156052351
] |
<p>In the following image,three cases have been mentioned. $N$ is the normal force acting on the object inside the lift and $mg$ is the force of attraction due to gravity.<br>
In case 1, $N = mg$.<br>
In case 2, $N = m(g+a)$ and<br>
in case 3, $N = m(g-a)$. Why is it so in 2nd and 3rd case?
<img src="http://i.stack.imgur.com/xdA80.png" alt="enter image description here"></p> | 2,015 | [
-0.01938733085989952,
-0.01182653196156025,
-0.06764732301235199,
0.023714860901236534,
0.03378083184361458,
0.01576875150203705,
-0.026036126539111137,
-0.02184991165995598,
0.011678693816065788,
-0.04071270674467087,
0.027235722169280052,
0.010951031930744648,
0.05033707991242409,
0.03422563523054123,
0.019028130918741226,
0.0011044020066037774,
-0.027370529249310493,
-0.00689113000407815,
0.028499405831098557,
-0.000150225474499166,
-0.02272671088576317,
0.040187325328588486,
0.011653808876872063,
-0.003909031394869089,
0.009315017610788345,
-0.0103464899584651,
0.03385049104690552,
-0.006603539921343327,
0.04442905634641647,
0.044595953077077866,
-0.004420736338943243,
0.0005448833690024912,
0.009159140288829803,
0.0425572395324707,
0.003620296251028776,
0.012443488463759422,
-0.0010978973004966974,
0.017668627202510834,
0.0007392329280264676,
0.01609824225306511,
-0.01564359851181507,
-0.029851548373699188,
-0.0010001860791817307,
0.039591871201992035,
-0.027345141395926476,
0.02279052324593067,
-0.002616024808958173,
-0.012406645342707634,
0.05534565448760986,
-0.0602034330368042,
0.07978932559490204,
-0.0037186683621257544,
0.018684547394514084,
0.019168157130479813,
-0.02097049355506897,
-0.02330828458070755,
0.03098258376121521,
0.04301191121339798,
0.0015240181237459183,
-0.04357065632939339,
-0.008026165887713432,
-0.05410604923963547,
-0.040468085557222366,
-0.019547762349247932,
-0.0066674272529780865,
0.027338998392224312,
-0.0016228309832513332,
-0.013367299921810627,
0.030194159597158432,
0.011529343202710152,
0.006118514575064182,
-0.0014124789740890265,
0.04609676077961922,
-0.05671495571732521,
0.00920476671308279,
-0.008779356256127357,
0.011364947073161602,
0.0018690654542297125,
0.05664793401956558,
0.025530295446515083,
0.0002919931139331311,
0.02688007242977619,
0.041964009404182434,
0.040287118405103683,
0.008786626160144806,
-0.03744146600365639,
0.0840105414390564,
-0.0017343590734526515,
0.012108169496059418,
0.011470475234091282,
-0.01947362720966339,
0.008736974559724331,
0.026931442320346832,
-0.03282144293189049,
-0.007322572637349367,
0.033098865300416946,
-0.008202126249670982,
-0.0006344526191242039,
0.05948169156908989,
-0.0065167914144694805,
-0.025063982233405113,
-0.03723697364330292,
0.013866417109966278,
0.09450780600309372,
-0.0056890686973929405,
0.004768167622387409,
-0.02835504524409771,
0.0331474244594574,
-0.00024583670892752707,
0.008232422173023224,
-0.021711502224206924,
-0.0036686407402157784,
-0.024587076157331467,
-0.0426173210144043,
0.013297069817781448,
-0.014504087157547474,
0.004136861767619848,
0.009174567647278309,
0.049692634493112564,
0.05553214251995087,
0.033514998853206635,
-0.037616580724716187,
0.03383879363536835,
-0.008651464246213436,
-0.040489908307790756,
0.02264329232275486,
0.05854726955294609,
-0.0137323047965765,
-0.002297647064551711,
0.017279550433158875,
0.002231230726465583,
-0.016355182975530624,
-0.018942968919873238,
0.0074227615259587765,
0.010325650684535503,
0.014828200452029705,
-0.09717869013547897,
-0.03919145464897156,
0.045601215213537216,
-0.032284848392009735,
-0.004763774573802948,
-0.07468404620885849,
0.004582344554364681,
0.06884778290987015,
0.0682525634765625,
-0.0038892815355211496,
-0.006527027580887079,
-0.010996435768902302,
0.03277820348739624,
-0.014157787896692753,
0.03340468183159828,
-0.045756131410598755,
-0.003048011101782322,
-0.03868499770760536,
-0.046664316207170486,
-0.07523008435964584,
0.041335925459861755,
0.0248472411185503,
0.016675349324941635,
-0.0651208758354187,
0.07575633376836777,
-0.014949851669371128,
0.025019682943820953,
-0.002588428556919098,
0.04197768121957779,
-0.030510032549500465,
0.049087513238191605,
0.03240774944424629,
0.014518015086650848,
0.07745105028152466,
0.03158899024128914,
0.04976629838347435,
-0.007096751593053341,
0.03323490172624588,
0.02548276260495186,
-0.012439622543752193,
-0.017628256231546402,
-0.04927368834614754,
0.024637065827846527,
-0.0046068225055933,
-0.03693762049078941,
-0.02842753380537033,
-0.024049146100878716,
-0.007565731648355722,
0.015071365050971508,
0.02830037660896778,
-0.0014040173264220357,
-0.012607842683792114,
0.01672438718378544,
-0.030400512740015984,
-0.03365654870867729,
-0.08777366578578949,
0.037559155374765396,
-0.010682686232030392,
-0.0216810405254364,
0.011095990426838398,
0.012155607342720032,
0.017498964443802834,
-0.013782305642962456,
0.0004781879251822829,
-0.0076749734580516815,
-0.015070626512169838,
-0.036408618092536926,
-0.026170434430241585,
0.03923463448882103,
0.029389604926109314,
0.04097752645611763,
0.03215106204152107,
0.04901296645402908,
-0.03633388131856918,
-0.025492457672953606,
0.02566799707710743,
-0.03073909506201744,
0.011673943139612675,
-0.005220918916165829,
0.0283968523144722,
0.011010601185262203,
0.016470080241560936,
-0.032501209527254105,
0.04921838641166687,
-0.04454405605792999,
0.036678414791822433,
0.07579944282770157,
0.01035181526094675,
0.027388477697968483,
-0.007694302126765251,
0.0163589958101511,
0.010337434709072113,
0.012504135258495808,
-0.025204826146364212,
-0.04806479811668396,
-0.06333070248365402,
-0.011666616424918175,
0.05793815478682518,
-0.05175280570983887,
0.02612152136862278,
0.05700463429093361,
0.03428170830011368,
0.027816183865070343,
0.029991822317242622,
-0.007757359649986029,
-0.05870558321475983,
0.013475722633302212,
0.09572133421897888,
-0.015368921682238579,
0.018296707421541214,
0.0036566019989550114,
0.03251457214355469,
0.019159844145178795,
0.019578760489821434,
-0.010408839210867882,
0.01653752662241459,
0.0015268551651388407,
0.0071272593922913074,
-0.024895966053009033,
-0.014014427550137043,
0.06759168952703476,
-0.022496389225125313,
0.024087119847536087,
0.07644212990999222,
0.007022491190582514,
-0.01919601857662201,
-0.030808405950665474,
-0.017155975103378296,
0.03750437870621681,
-0.005680440459400415,
-0.013549817726016045,
0.00344265578314662,
0.015303483232855797,
-0.028846269473433495,
0.02697531133890152,
-0.07257187366485596,
0.0028198601212352514,
-0.017965614795684814,
0.030913783237338066,
-0.010427368804812431,
-0.014363541267812252,
0.06052066758275032,
-0.011392072774469852,
-0.00004763165634358302,
-0.0033467283938080072,
-0.03509063273668289,
0.0075998674146831036,
0.0027380126994103193,
-0.04918712005019188,
0.011938081122934818,
-0.04467945545911789,
-0.007714322302490473,
0.0745827853679657,
0.018112383782863617,
-0.0023302205372601748,
0.02613559551537037,
0.025943174958229065,
0.007910137996077538,
-0.040423404425382614,
-0.007901806384325027,
-0.003545015584677458,
-0.012091094627976418,
-0.03577549010515213,
0.04941987618803978,
0.0028881807811558247,
0.0006733345217071474,
0.034589674323797226,
-0.04505954682826996,
-0.06977920234203339,
-0.03047550842165947,
-0.011942080222070217,
-0.0024250242859125137,
-0.026401713490486145,
-0.004870642442256212,
-0.003864011261612177,
-0.004741720389574766,
0.022595878690481186,
-0.033084601163864136,
-0.04702773317694664,
-0.00028551812283694744,
-0.038499340415000916,
0.03968247398734093,
-0.00956697203218937,
-0.029440587386488914,
0.09137003868818283,
0.02776610292494297,
-0.0015464015305042267,
-0.035459063947200775,
-0.03336011990904808,
-0.04513726755976677,
-0.04134291037917137,
0.0025652742478996515,
0.02264242246747017,
-0.006736958399415016,
0.051107876002788544,
0.02473744936287403,
0.014512692578136921,
0.026368360966444016,
0.021555475890636444,
0.004731921479105949,
0.0361512266099453,
0.03651255741715431,
-0.02606029622256756,
0.08861687034368515,
-0.00004445975355338305,
0.002035193145275116,
0.02639821730554104,
-0.009812676347792149,
0.026942657306790352,
-0.018021414056420326,
-0.05686948820948601,
0.06755784898996353,
-0.02589293383061886,
0.030987141653895378,
-0.029896629974246025,
0.039960719645023346,
0.013442978262901306,
-0.002346976427361369,
0.0008180884760804474,
0.029816973954439163,
0.04812056943774223,
-0.07574938982725143,
0.006849569268524647,
0.031013114377856255,
0.030330190435051918,
-0.024194933474063873,
-0.029329586774110794,
-0.0004619821556843817,
-0.02010098472237587,
0.05729192495346069,
-0.021743085235357285,
-0.011558306403458118,
0.019442686811089516,
0.03300679102540016,
0.027539120987057686,
0.013372233137488365,
-0.01660938188433647,
0.007678323425352573,
-0.0610567070543766,
-0.013522416353225708,
0.018522925674915314,
0.00523609621450305,
-0.016621507704257965,
0.0610620342195034,
0.012893667444586754,
0.05229751393198967,
0.022236116230487823,
-0.0008736299932934344,
-0.10896196216344833,
0.018848134204745293,
-0.029678067192435265,
-0.028705675154924393,
0.009437940083444118,
-0.02783481776714325,
0.007684965617954731,
-0.02473231963813305,
-0.026707617565989494,
0.022902196273207664,
0.01149044744670391,
-0.07216215878725052,
-0.011672132648527622,
-0.03315884992480278,
-0.03308950364589691,
0.00941183976829052,
0.003907852340489626,
0.019193075597286224,
-0.03127504885196686,
-0.002956537064164877,
0.06670716404914856,
-0.03935132920742035,
-0.0013796722050756216,
-0.001405538059771061,
-0.010358231142163277,
-0.012364477850496769,
-0.004864889662712812,
0.022897934541106224,
0.05340325087308884,
-0.0012060379376634955,
-0.013831120915710926,
0.02590658888220787,
0.030219249427318573,
-0.015823710709810257,
0.004497422371059656,
-0.03484315052628517,
-0.04442897439002991,
-0.015278861857950687,
0.024212580174207687,
0.04049871489405632,
0.013096514157950878,
0.020832598209381104,
0.010658680461347103,
-0.009461070410907269,
-0.008099925704300404,
0.038875967264175415,
0.03075019083917141,
0.042741671204566956,
-0.014574388973414898,
-0.04618695750832558,
0.025131143629550934,
-0.026956843212246895,
-0.028777532279491425,
0.042630430310964584,
0.0038035137113183737,
-0.04391834884881973,
0.006695596966892481,
0.05236019194126129,
0.021425636485219002,
0.009895851835608482,
0.0060699814930558205,
0.011424925178289413,
0.023689260706305504,
-0.007986772805452347,
0.011847629211843014,
-0.02148314006626606,
0.05968958139419556,
0.05407147482037544,
-0.04088127985596657,
-0.027871234342455864,
-0.07139322906732559,
-0.04979194328188896,
0.032489337027072906,
0.0008338057668879628,
-0.03357633575797081,
0.005364296492189169,
-0.03636590763926506,
-0.005806992296129465,
0.008770324289798737,
-0.008905074559152126,
0.05375617370009422,
0.005143706686794758,
0.04148927330970764,
0.018278032541275024,
0.015413543209433556,
-0.04187145084142685,
0.0027685214299708605,
0.031065920367836952,
0.016613706946372986,
-0.005983066279441118,
0.00012086946662748232,
0.03114728257060051,
0.011637452058494091,
0.027633607387542725,
0.04588400572538376,
0.008551077917218208,
-0.023877860978245735,
-0.020728711038827896,
-0.023142129182815552,
-0.036742959171533585,
-0.07174801081418991,
0.0005147284246049821,
0.01615186221897602,
-0.006900174543261528,
0.014043387025594711,
-0.02390039898455143,
-0.07806108146905899,
-0.001297699403949082,
-0.0014278227463364601,
0.021666554734110832,
-0.016384288668632507,
-0.03140056133270264,
0.0034814660903066397,
0.051310036331415176,
-0.022583968937397003,
0.03998519480228424,
0.012656801380217075,
-0.02362467534840107,
-0.021549737080931664,
-0.01470202300697565,
0.05158666521310806,
-0.01770094223320484,
-0.043022509664297104,
-0.005517688579857349,
0.001703683054074645,
-0.0007411891128867865,
0.06292449682950974,
0.009775113314390182,
0.036063291132450104,
-0.0150673296302557,
-0.05491224303841591,
0.0012465190375223756,
0.06713977456092834,
0.012029427103698254,
0.00717585813254118,
0.04596205800771713,
-0.013756982050836086,
0.022245202213525772,
0.00041769008385017514,
0.01903655007481575,
-0.0317346528172493,
0.002359572099521756,
0.0353994145989418,
-0.0032299868762493134,
0.006846840027719736,
-0.016103804111480713,
-0.013762949034571648,
0.01742805913090706,
-0.05086192116141319,
0.039257314056158066,
0.0033473761286586523,
0.0006756715592928231,
0.02320142649114132,
-0.04113103449344635,
-0.03237980976700783,
-0.0006398276309482753,
0.025802189484238625,
0.0029064170084893703,
-0.01611330173909664,
0.027775688096880913,
0.022742999717593193,
0.020292839035391808,
-0.03164239227771759,
-0.030042076483368874,
-0.0116021279245615,
0.002688950626179576,
0.011166125535964966,
-0.015727099031209946,
-0.01943655125796795,
-0.006244129501283169,
-0.05690823122859001,
-0.018049661070108414,
0.06877020001411438,
-0.04883241280913353,
-0.021612681448459625,
0.03981262817978859,
0.01952347159385681,
0.05696222931146622,
0.008794452995061874,
-0.022754758596420288,
-0.014269069768488407,
-0.012078323401510715,
0.004038764163851738,
0.02732911705970764,
0.05622333660721779,
-0.014981810003519058,
-0.032303184270858765,
0.022150268778204918,
-0.03146030381321907,
0.03801978379487991,
-0.0295574814081192,
0.00851045735180378,
0.054667647927999496,
0.02411068230867386,
0.004869778174906969,
-0.004740448202937841,
0.00809165183454752,
0.013017605990171432,
0.035047225654125214,
0.019609306007623672,
0.00816077459603548,
0.0038469061255455017,
-0.028498811647295952,
0.04785621538758278,
0.010539551265537739,
0.0015806215815246105,
0.04744337499141693,
0.04339735954999924,
-0.04883134737610817,
-0.014713054522871971,
0.0206484142690897,
-0.00854601338505745,
0.05902540311217308,
0.006612698081880808,
0.005360617768019438,
0.027702780440449715,
0.014773936942219734,
-0.020638033747673035,
-0.025724662467837334,
-0.029495472088456154,
0.05185987427830696,
0.053892020136117935,
-0.012059282511472702,
0.07634776085615158,
-0.00640949048101902,
-0.01085982657968998,
-0.0036763260141015053,
-0.021014895290136337,
-0.004620731808245182,
-0.020507672801613808,
0.011713271960616112,
0.013933653011918068,
-0.015200952999293804,
0.002911744639277458,
0.004051010124385357,
0.013068338856101036,
-0.007331633009016514,
-0.030322715640068054,
0.01388455182313919,
0.00770649453625083,
0.004440502729266882,
-0.01166422851383686,
-0.011527489870786667,
0.05688178539276123,
0.002513765124604106,
0.07172088325023651,
0.003081247676163912,
-0.02744939550757408,
0.019481640309095383,
0.017905790358781815,
-0.015812279656529427,
-0.07353266328573227,
-0.03012215346097946,
-0.022683465853333473,
-0.010720147751271725,
0.03862658888101578,
-0.026044931262731552,
0.03394944593310356,
0.008847947232425213,
0.018048541620373726,
-0.018324820324778557,
0.008768702857196331,
0.005521629471331835,
-0.04325628653168678,
-0.01835457794368267,
-0.026026681065559387,
-0.04854830726981163,
0.011972007341682911,
-0.017152391374111176,
-0.03125882148742676,
0.012772309593856335,
-0.037908345460891724,
0.012020141817629337,
0.027677061036229134,
0.02120497077703476,
-0.027150960639119148,
0.08193030208349228,
-0.02246742695569992,
0.013195201754570007,
-0.004289023578166962,
-0.007404129020869732,
0.10037138313055038,
0.07101984322071075,
0.007909206673502922,
-0.04948027431964874,
-0.017002234235405922,
-0.005024669226258993,
-0.030045589432120323,
-0.009749703109264374,
0.020328927785158157,
0.006271695252507925,
-0.007223441731184721,
-0.0043877228163182735,
0.023501936346292496,
-0.02477228082716465,
0.0046978602185845375,
0.013851379044353962,
-0.027935750782489777,
-0.04821007698774338,
-0.02238396368920803,
0.018035482615232468,
-0.0229386854916811,
-0.003211601870134473,
0.004782488569617271,
0.020092429593205452,
0.006841523107141256,
-0.00558141153305769,
0.008945838548243046,
-0.03159661591053009,
0.03712506592273712,
-0.004131638444960117,
-0.03060293011367321,
0.0170175489038229,
-0.00878931675106287,
-0.02955792285501957,
-0.04086696356534958,
0.032565467059612274,
-0.00808553397655487,
-0.042739491909742355,
0.01974932663142681,
0.010204048827290535,
-0.0027392199262976646,
-0.02068261057138443,
0.01848844438791275,
-0.024346090853214264,
-0.10019776970148087,
0.0062306784093379974,
-0.03239975497126579,
-0.00960496161133051,
-0.020656052976846695,
0.010400129482150078,
0.011138251051306725,
0.0015457785921171308,
0.0013837405713275075,
-0.06199951842427254,
-0.024458298459649086,
-0.0007063078810460865,
0.018316257745027542,
-0.03976725414395332,
-0.036816492676734924,
0.03263700380921364,
0.010179432108998299,
0.02990332618355751,
0.009454868733882904,
-0.008183599449694157,
0.03509143367409706,
0.010258426889777184,
-0.024746205657720566,
0.036843277513980865,
0.010617401450872421,
-0.013062993995845318,
-0.03781929612159729,
-0.030291160568594933,
-0.018924567848443985,
-0.008329153060913086,
-0.0012754735071212053,
0.05043305084109306,
0.008729914203286171,
0.022055834531784058,
0.003238885197788477,
0.012388564646244049,
-0.029085403308272362,
0.006963084917515516,
0.00010649165778886527,
0.004880089312791824,
-0.04153480380773544,
-0.03802945837378502,
-0.019890081137418747,
0.03276829048991203,
0.04085585102438927,
0.026459727436304092,
0.006175982300192118,
0.04891433194279671,
-0.006847500801086426,
-0.060657404363155365,
-0.020266814157366753,
-0.009597493335604668,
-0.05457139387726784,
-0.02694375067949295,
-0.01021171547472477,
0.013478713110089302,
0.013379260897636414,
0.030930181965231895,
0.0058511183597147465,
0.029350653290748596,
-0.012040160596370697,
-0.0029173048678785563,
0.014626369811594486,
-0.005407500080764294,
0.06152305752038956,
0.03647799417376518,
-0.038068871945142746,
-0.060057297348976135,
-0.036831051111221313,
0.022320503368973732,
-0.02972823940217495,
0.014765624888241291,
0.022132709622383118,
-0.025987958535552025,
-0.006174090318381786,
0.022311590611934662,
0.03934895247220993,
-0.022497327998280525,
-0.04482690989971161,
-0.04842540994286537,
0.010199273936450481,
-0.013521256856620312,
-0.006282135844230652,
-0.052044790238142014,
-0.0035830505657941103,
-0.01019614189863205,
-0.001246700994670391,
-0.01686253398656845,
-0.006825075019150972,
0.009203030727803707,
-0.06885291635990143,
-0.014663036912679672,
-0.04177609458565712,
0.03741631656885147,
0.010360945016145706,
-0.011213701218366623,
0.010235040448606014,
-0.03451250120997429,
-0.010981793515384197,
0.009320196695625782,
0.019034400582313538,
0.03261849656701088,
0.020122691988945007,
-0.02373201958835125,
-0.018045373260974884,
0.04845258221030235,
-0.04474468156695366,
-0.006120701786130667,
-0.05130532383918762,
-0.030520981177687645,
-0.03417056053876877,
-0.032543133944272995,
-0.047827403992414474,
-0.03187650069594383,
0.0021999329328536987,
0.010125353932380676,
0.002578700426965952,
-0.023635786026716232,
-0.025655442848801613,
0.037953492254018784,
0.0009978893212974072,
-0.025131719186902046,
0.0400160476565361,
0.0534486286342144,
-0.0044085439294576645,
0.039113402366638184,
-0.0141143174842,
0.021242499351501465,
-0.005622092634439468,
0.005596517119556665,
-0.08954519033432007,
-0.052218422293663025,
0.020614219829440117,
-0.020588872954249382,
0.04104502126574516,
-0.0686245784163475,
0.02020983397960663,
0.006162587087601423,
-0.06245062127709389,
-0.001276466646231711,
-0.054557643830776215,
0.006251867860555649,
-0.015224584378302097,
-0.018088020384311676,
0.05353693664073944,
0.026764869689941406,
-0.008854669518768787,
0.0034462835174053907,
0.04054487496614456,
-0.013070663437247276,
-0.04360732436180115,
-0.010731465183198452,
0.002479932038113475,
0.04579467326402664,
0.0029954572673887014,
-0.03507490083575249,
0.03953738510608673,
0.01504703052341938,
-0.029998790472745895,
0.028946124017238617,
-0.023040376603603363,
-0.004719907883554697,
0.014186098240315914,
0.022821955382823944,
-0.0232416782528162,
0.01061857957392931,
0.045648809522390366,
0.02584008127450943,
-0.022318009287118912,
0.03249354660511017,
0.016412310302257538,
0.03210661932826042,
-0.016106348484754562,
-0.006703588180243969,
0.013128274120390415,
-0.02780802547931671,
-0.049454107880592346,
0.021721774712204933,
-0.03081953525543213,
-0.027572255581617355,
0.0010090807918459177,
0.006635751575231552,
-0.03256171941757202,
-0.02938718907535076,
0.017996041104197502,
-0.04778566583991051,
0.020992279052734375,
0.04395204409956932,
-0.016261590644717216,
-0.01942294090986252,
0.025008277967572212,
0.018246997147798538,
-0.014056880958378315,
-0.02582518197596073,
-0.005309928208589554,
-0.002168485661968589,
-0.025911208242177963,
-0.0015600991901010275,
0.0014966722810640931,
-0.00441792281344533,
-0.0020716902799904346,
-0.04932233691215515,
-0.0421011745929718,
0.030370870605111122,
0.029653487727046013,
0.01486156601458788,
-0.008607353083789349,
-0.06509986519813538,
-0.029299339279532433,
-0.09386974573135376,
0.036264147609472275,
0.04131148010492325,
-0.018767403438687325,
-0.029349956661462784,
0.004948956426233053,
-0.015857132151722908,
-0.0021428242325782776,
0.07009676098823547,
0.0038442614022642374,
-0.02958027645945549,
0.005959515925496817,
0.01721053384244442,
-0.012002653442323208,
0.010972904972732067,
0.029949888586997986,
0.028595395386219025,
-0.010024438612163067,
0.006515362299978733,
-0.0024307365529239178,
0.025701453909277916,
0.026154078543186188,
-0.026489438489079475,
0.0094920564442873,
0.052396345883607864,
0.006726691033691168,
0.009736432693898678,
0.02189473994076252,
0.013394186273217201,
-0.02963678538799286,
0.04857905954122543,
-0.0366179533302784,
0.02048506960272789,
0.0057711354456841946,
-0.03906828165054321,
-0.06932196766138077,
0.052015967667102814,
0.02306048944592476,
0.002977135358378291,
-0.048168476670980453,
-0.008423207327723503,
0.01926279440522194,
-0.05484660342335701,
0.01739218644797802,
0.008094274438917637,
-0.05261325463652611,
-0.00146264408249408,
0.024165865033864975,
0.03928622230887413,
0.011094548739492893,
0.0060224817134439945,
0.0076236603781580925,
0.031572893261909485,
-0.009771163575351238,
0.03257104381918907,
0.0389147624373436,
0.01492245402187109,
-0.0017967460444197059,
-0.03628945350646973,
0.031301192939281464,
-0.006353576201945543,
0.0033641953486949205,
0.031455814838409424,
0.012127330526709557,
-0.030504079535603523,
-0.0447758249938488,
0.017019743099808693,
-0.013932442292571068,
0.03878457099199295,
0.001704846159555018,
-0.02480890043079853,
0.06699638813734055,
-0.019550735130906105,
0.022024737671017647,
-0.004474146291613579,
0.017950518056750298,
0.0032999874092638493,
-0.028575973585247993,
-0.015869826078414917,
0.037172310054302216,
0.009415156207978725,
-0.03190216049551964,
0.00025113014271482825,
-0.03691369295120239,
0.012979911640286446,
0.04037803038954735,
0.019511066377162933,
0.002962420228868723,
0.02959258295595646,
-0.021021263673901558,
-0.02989577129483223,
-0.054113175719976425,
-0.04595991596579552,
0.03266897797584534,
0.032131094485521317,
0.021985236555337906,
-0.01648283563554287,
-0.001198618090711534,
-0.03422195091843605,
0.015622890554368496,
-0.04140080139040947,
-0.05919722095131874,
-0.01871909759938717,
0.03184618055820465,
0.01721036620438099,
-0.0006069250521250069
] |
<p>Let's say I know the size of the container, size of the hole the air leaks through, pressure the air is under and temperature of the air if that helps anything. Is it possible to calculate this only from these variables? What is the formula for how fast air leaks out of a hole?</p> | 2,016 | [
-0.0268891379237175,
-0.015498604625463486,
-0.017931988462805748,
-0.020168567076325417,
0.0249385554343462,
-0.03485666215419769,
0.0006950503448024392,
0.007243673782795668,
0.01667463220655918,
0.026360321789979935,
0.020124811679124832,
0.07180408388376236,
0.024586031213402748,
0.005104332696646452,
-0.013076766394078732,
0.0023751594126224518,
-0.007566231302917004,
0.005976938642561436,
0.004789539612829685,
-0.02441645972430706,
0.01032352726906538,
0.0009161097696051002,
-0.0011908623855561018,
-0.02675313502550125,
-0.02150561474263668,
0.06136089190840721,
0.04396554082632065,
-0.004555465653538704,
0.0012369232717901468,
0.01752113178372383,
0.0002425894927000627,
-0.03029915690422058,
0.027337925508618355,
0.03165442869067192,
0.023864412680268288,
-0.0028756060637533665,
-0.01833975873887539,
-0.025492776185274124,
-0.0437365397810936,
0.04041574150323868,
-0.022634990513324738,
-0.019929250702261925,
0.01519098225980997,
0.019630644470453262,
-0.0006443443126045167,
0.029699746519327164,
-0.012903563678264618,
-0.035017356276512146,
0.029647696763277054,
-0.09220069646835327,
0.059692755341529846,
-0.01580495946109295,
0.07856383919715881,
0.059804193675518036,
-0.04071662202477455,
0.027262670919299126,
0.06596722453832626,
0.08177068829536438,
-0.036464907228946686,
-0.031001757830381393,
0.01710311882197857,
0.013920444063842297,
-0.023344198241829872,
-0.055387943983078,
-0.01821823976933956,
-0.01141617726534605,
-0.05498082563281059,
-0.010305850766599178,
0.026727741584181786,
-0.008151696994900703,
0.01961379311978817,
-0.01451888307929039,
0.08748181909322739,
-0.019065216183662415,
0.018177980557084084,
-0.00048532450455240905,
-0.009604505263268948,
0.028419211506843567,
0.0393233485519886,
0.07112210988998413,
-0.03834105655550957,
0.0039448728784918785,
0.03519528731703758,
0.009128276258707047,
0.013213885948061943,
-0.025159722194075584,
0.07539580017328262,
-0.02171109803020954,
0.0027205562219023705,
0.01956718973815441,
-0.020539650693535805,
0.003154206555336714,
0.03810705989599228,
-0.0012076039565727115,
0.015551554970443249,
0.041103214025497437,
-0.030601296573877335,
0.05389333516359329,
0.024009445682168007,
-0.04320111870765686,
0.03186935558915138,
0.013801565393805504,
0.009362657554447651,
0.0884600505232811,
-0.01632656529545784,
-0.01508271787315607,
-0.004854570142924786,
0.02147549018263817,
0.01922767609357834,
0.01615860126912594,
-0.02989519014954567,
-0.022385478019714355,
-0.0037966303061693907,
-0.020809831097722054,
0.003725846065208316,
-0.018684417009353638,
-0.026147855445742607,
-0.03853638842701912,
0.0040192254818975925,
0.03175726905465126,
0.030141666531562805,
-0.037707626819610596,
0.02280454710125923,
-0.015104463323950768,
-0.05428188294172287,
0.024332381784915924,
0.004204035736620426,
-0.019630970433354378,
-0.050573721528053284,
0.030936256051063538,
-0.0031240105163306,
-0.03677927702665329,
0.02104809507727623,
0.014166807755827904,
0.0396350733935833,
0.00030558861908502877,
-0.06662944704294205,
-0.0902731642127037,
0.012955906800925732,
-0.023565499112010002,
-0.022982781752943993,
-0.04576434940099716,
0.0307700764387846,
0.019114337861537933,
0.035358358174562454,
0.015718799084424973,
0.0036346912384033203,
-0.019133394584059715,
0.026494082063436508,
-0.00042202038457617164,
-0.04293288663029671,
0.015107398852705956,
0.021684667095541954,
-0.02258905954658985,
0.013008926063776016,
-0.03267868235707283,
0.0017472944455221295,
0.035173870623111725,
-0.006673936732113361,
-0.047986339777708054,
0.03512240946292877,
-0.019758345559239388,
-0.0390353761613369,
-0.0025204899720847607,
-0.006480916868895292,
-0.06373392045497894,
0.05604678764939308,
-0.009977667592465878,
-0.006474200636148453,
0.027332887053489685,
0.0290768351405859,
0.022485533729195595,
-0.005937047302722931,
-0.0303661972284317,
0.07071956992149353,
0.014867246150970459,
-0.01430963072925806,
-0.02243015356361866,
0.02544698305428028,
0.03636544942855835,
-0.06110818684101105,
-0.03211625665426254,
0.013829018920660019,
0.00012576495646499097,
0.040480371564626694,
0.0001830221590353176,
-0.002609110437333584,
-0.024649780243635178,
-0.0005267527885735035,
-0.03566674888134003,
-0.015938403084874153,
-0.08627888560295105,
0.04470403119921684,
-0.021058984100818634,
0.03250858560204506,
-0.016502749174833298,
-0.007860244251787663,
0.017301347106695175,
-0.029473619535565376,
-0.026523740962147713,
-0.005686958320438862,
-0.0127556212246418,
0.021625204011797905,
-0.05281403660774231,
0.003533907700330019,
0.04445973038673401,
0.04041224345564842,
-0.02970231883227825,
0.05356588587164879,
-0.024558838456869125,
-0.024920208379626274,
0.005987401120364666,
-0.05799926817417145,
-0.003243944840505719,
-0.011989240534603596,
-0.03364177048206329,
0.0661420226097107,
0.0265840832144022,
0.018481722101569176,
-0.00497825164347887,
-0.017819823697209358,
0.07146329432725906,
0.058763645589351654,
0.04875306040048599,
0.02474188059568405,
-0.022645195946097374,
0.009121906943619251,
0.014110984280705452,
0.05730792135000229,
-0.040482182055711746,
-0.04268606752157211,
-0.03443390503525734,
-0.011660808697342873,
-0.011126266792416573,
-0.02071504108607769,
-0.017078591510653496,
0.04536442831158638,
0.0012698763748630881,
0.04439130797982216,
0.03165534883737564,
-0.005006675608456135,
0.00960555113852024,
-0.03800152242183685,
0.03824411705136299,
-0.024150699377059937,
0.03531751036643982,
0.02154100313782692,
0.06332188844680786,
0.03321352228522301,
-0.007053379435092211,
-0.019992802292108536,
0.010830234736204147,
0.016492486000061035,
-0.0035230088979005814,
-0.0360540933907032,
0.003795677563175559,
0.028831571340560913,
-0.04926321282982826,
0.009403662756085396,
0.010852860286831856,
0.017629537731409073,
0.04884832724928856,
-0.024148210883140564,
-0.0042502195574343204,
0.03749222680926323,
0.029755255207419395,
-0.01161679532378912,
0.013770753517746925,
0.02786313369870186,
-0.007963712327182293,
0.038235943764448166,
-0.031242098659276962,
0.011197160929441452,
-0.028762293979525566,
-0.013047624379396439,
0.014903387986123562,
-0.0010698430705815554,
0.01694345474243164,
-0.00076870690099895,
-0.037842441350221634,
-0.013476752676069736,
-0.013505117036402225,
-0.005091775208711624,
-0.007488014176487923,
-0.00957560259848833,
0.012608679011464119,
0.004622370470315218,
-0.07719292491674423,
0.027610406279563904,
-0.005549839697778225,
-0.013736564666032791,
0.0420137457549572,
-0.02220577374100685,
-0.03898092359304428,
0.013297894969582558,
-0.012406948022544384,
0.04005574807524681,
-0.017070481553673744,
0.013558512553572655,
0.043441127985715866,
-0.03529466688632965,
-0.03100784868001938,
0.03232070803642273,
-0.047969453036785126,
-0.047760456800460815,
-0.061335690319538116,
-0.01194780133664608,
0.019210370257496834,
-0.026298195123672485,
0.01672767661511898,
0.010712790302932262,
-0.02096141129732132,
-0.011204374022781849,
-0.005509120877832174,
-0.04447954148054123,
0.030297251418232918,
0.01956906169652939,
0.02168842777609825,
-0.03203670680522919,
-0.02052784152328968,
0.05855589359998703,
0.00009281942766392604,
-0.04704302176833153,
0.02886335551738739,
-0.0027631225530058146,
-0.0025240303948521614,
-0.042042750865221024,
0.008218889124691486,
0.02114785648882389,
0.013778516091406345,
0.010737800039350986,
0.017125874757766724,
0.028745554387569427,
0.06753045320510864,
0.023382054641842842,
0.0021883794106543064,
-0.019269809126853943,
0.02535317651927471,
-0.00958041287958622,
0.042403340339660645,
0.012352566234767437,
-0.023073291406035423,
0.04816422238945961,
0.00861440785229206,
0.04950261116027832,
0.04188815504312515,
-0.05788417160511017,
0.007935026660561562,
-0.012044352479279041,
-0.00624833581969142,
-0.034900542348623276,
0.009389846585690975,
-0.04157862812280655,
-0.013188954442739487,
0.0228430163115263,
0.019833624362945557,
0.025424210354685783,
0.0029969511087983847,
-0.006863734684884548,
0.05076337605714798,
0.06960238516330719,
-0.04357777535915375,
-0.04654278606176376,
-0.0053554982878267765,
-0.014027795754373074,
0.035894088447093964,
-0.011288362555205822,
-0.015183435752987862,
0.03721145913004875,
0.05586828291416168,
0.022153588011860847,
0.01527873333543539,
0.010387321002781391,
0.0052657718770205975,
-0.10014943033456802,
-0.03486733138561249,
-0.004682464059442282,
0.04895514249801636,
-0.001194091746583581,
0.05341422185301781,
0.02389623410999775,
0.004246699623763561,
0.06235616281628609,
-0.0005886394646950066,
-0.06233563646674156,
0.0417020358145237,
0.007661080919206142,
-0.02620464377105236,
-0.01721964403986931,
-0.013186953030526638,
0.03211630508303642,
-0.03353913873434067,
-0.02476632595062256,
0.017527008429169655,
0.03321046382188797,
-0.06000072881579399,
0.05005623400211334,
-0.011744842864573002,
-0.005689227022230625,
-0.00608797324821353,
0.043622247874736786,
0.02299496904015541,
0.013248620554804802,
0.03033926896750927,
0.0502316877245903,
-0.014079357497394085,
0.008130342699587345,
-0.012409108690917492,
-0.02663707360625267,
-0.006488613318651915,
0.03967517614364624,
0.011106617748737335,
0.005099243018776178,
-0.014985019341111183,
0.001879207557067275,
0.005234254989773035,
0.031445715576410294,
-0.03680245205760002,
0.002145554171875119,
-0.04895256459712982,
-0.05075884237885475,
0.01058400422334671,
0.015546208247542381,
0.01721353270113468,
-0.006467057392001152,
0.05895780026912689,
0.0395674854516983,
-0.015430666506290436,
-0.03818351402878761,
0.009725483134388924,
0.07121017575263977,
0.006514350418001413,
-0.05740083009004593,
-0.04070345684885979,
-0.007333008572459221,
-0.021091336384415627,
-0.016782408580183983,
0.012135756202042103,
0.04635445773601532,
-0.03451375290751457,
0.0002708359097596258,
0.025811992585659027,
-0.006371425464749336,
-0.009703568182885647,
0.014280521310865879,
0.013702874071896076,
0.008900460787117481,
-0.003983371891081333,
-0.004780000075697899,
0.016495276242494583,
0.03751916065812111,
0.010964678600430489,
0.006092734634876251,
-0.011204833164811134,
-0.08779796212911606,
-0.000025692179406178184,
0.03901953250169754,
0.030810249969363213,
-0.022178350016474724,
0.008525262586772442,
-0.05123050883412361,
-0.016797367483377457,
0.07149523496627808,
0.00303458608686924,
0.012632911093533039,
0.003930424340069294,
-0.01072455570101738,
-0.005664409138262272,
-0.01628115214407444,
-0.05215125530958176,
0.020110074430704117,
-0.01152809802442789,
-0.01657741144299507,
-0.011198118329048157,
-0.0055043757893145084,
-0.01597742922604084,
0.014285970479249954,
0.05879659950733185,
0.037121567875146866,
0.01915089227259159,
0.017103759571909904,
-0.01837514340877533,
0.008342250250279903,
-0.026533259078860283,
-0.03648534417152405,
0.005692534148693085,
-0.012316528707742691,
-0.014471552334725857,
0.004033142700791359,
-0.02438468299806118,
-0.04305218532681465,
0.037388432770967484,
-0.008833914995193481,
-0.003786218585446477,
-0.018143344670534134,
-0.060117464512586594,
0.040576983243227005,
0.023302564397454262,
0.019209112972021103,
0.026758087798953056,
0.02737494371831417,
-0.0123915309086442,
0.01958884857594967,
-0.01691886968910694,
0.008460071869194508,
-0.02121116779744625,
-0.019192330539226532,
-0.03001818247139454,
0.027395719662308693,
-0.014113973826169968,
0.03391699120402336,
0.010597271844744682,
0.031079431995749474,
-0.01824467070400715,
-0.01843947544693947,
0.014631384052336216,
0.01370555255562067,
0.010424072854220867,
-0.003290794789791107,
0.02468937821686268,
0.009511146694421768,
0.03597594052553177,
-0.05416226387023926,
-0.01580040343105793,
-0.0012974534183740616,
0.049360547214746475,
0.027915053069591522,
-0.05357383191585541,
0.0040007964707911015,
-0.037464674562215805,
0.006989997811615467,
0.0215349942445755,
-0.0004560892703011632,
0.060523830354213715,
-0.02230478636920452,
-0.025159673765301704,
0.01900188811123371,
-0.03828240558505058,
-0.009088135324418545,
0.017734015360474586,
0.009659217670559883,
0.05237537622451782,
-0.07769438624382019,
0.029847044497728348,
-0.020214280113577843,
-0.028465041890740395,
-0.07302872836589813,
-0.01488584280014038,
0.035551682114601135,
0.007356715388596058,
-0.03548763692378998,
-0.08714073151350021,
-0.012384613044559956,
-0.03126998245716095,
-0.041175298392772675,
0.017013205215334892,
0.04413914307951927,
-0.016531076282262802,
-0.005361569579690695,
0.032166387885808945,
-0.019046129658818245,
0.03480187803506851,
0.04292424023151398,
-0.00350310024805367,
-0.0016045501688495278,
0.005394280888140202,
-0.02271924912929535,
0.03363461792469025,
0.009260931983590126,
-0.026576995849609375,
0.00541188009083271,
0.004077787045389414,
-0.02781926654279232,
0.02578193135559559,
-0.04587699845433235,
0.031430475413799286,
-0.0007407638477161527,
0.04086533188819885,
-0.01139761134982109,
0.007214476820081472,
0.04424219951033592,
0.004759598523378372,
0.029169069603085518,
-0.004508424084633589,
-0.01796947792172432,
-0.03916003182530403,
0.00723646255210042,
-0.01327436976134777,
0.00849107839167118,
0.01747860386967659,
-0.009539024904370308,
0.03856838867068291,
-0.018249593675136566,
-0.016069214791059494,
0.005772886797785759,
-0.0329686738550663,
0.02993312105536461,
0.01909002475440502,
-0.015131828375160694,
0.010625098831951618,
0.007347873877733946,
-0.01745213381946087,
-0.051743220537900925,
-0.04925983399152756,
-0.042342353612184525,
0.05975886434316635,
-0.024174101650714874,
0.035881899297237396,
0.0382467545568943,
0.020155735313892365,
-0.00294328760355711,
-0.008032112382352352,
-0.005072468426078558,
0.045661162585020065,
0.024143384769558907,
0.04367630556225777,
0.02703462354838848,
0.014660232700407505,
0.02529359608888626,
0.006510235369205475,
-0.014931530691683292,
0.012201678939163685,
0.005975146312266588,
0.029429832473397255,
0.003418675623834133,
-0.01965341903269291,
-0.020296018570661545,
0.06126003712415695,
-0.009643550030887127,
0.016855619847774506,
-0.02572767809033394,
0.0021541903261095285,
0.06054168939590454,
0.022199954837560654,
-0.020623905584216118,
-0.02210419811308384,
-0.029515240341424942,
-0.047785621136426926,
0.0014476808719336987,
0.026512594893574715,
0.008071745745837688,
0.024532204493880272,
0.03211177513003349,
0.04692468047142029,
-0.026467617601156235,
0.001224358449690044,
-0.0000071902054514794145,
-0.02177995629608631,
0.004185187630355358,
-0.013417879119515419,
-0.03206738084554672,
0.015519052743911743,
0.01211328525096178,
-0.028485829010605812,
0.0038991165347397327,
0.010625210590660572,
-0.0013685171725228429,
-0.0028436402790248394,
0.03835539519786835,
-0.0021719178184866905,
0.0882708951830864,
-0.006669563241302967,
-0.0239113736897707,
-0.02237754501402378,
0.04557780921459198,
0.08666487038135529,
0.028492724522948265,
0.009507053531706333,
-0.048111338168382645,
-0.020009314641356468,
-0.044871389865875244,
0.001221096608787775,
-0.03918939083814621,
0.036779921501874924,
-0.03784536197781563,
0.017332715913653374,
0.058714695274829865,
0.08450032770633698,
-0.03321944922208786,
-0.0031210591550916433,
0.012730393558740616,
-0.03201248496770859,
-0.00397259509190917,
0.011430395767092705,
0.024398814886808395,
-0.02445969544351101,
0.014004537835717201,
-0.011088441126048565,
0.05638663470745087,
-0.022516857832670212,
-0.015111289918422699,
-0.021547876298427582,
-0.02804422564804554,
0.02498064748942852,
-0.037168655544519424,
-0.07029127329587936,
0.032635584473609924,
0.020663319155573845,
-0.021672600880265236,
-0.040750473737716675,
0.03562323376536369,
0.05702877789735794,
0.0017911723116412759,
-0.03080335631966591,
0.052912306040525436,
0.02684294618666172,
0.002547658048570156,
0.0036614621058106422,
0.01081519853323698,
-0.02852765843272209,
-0.021244268864393234,
-0.024487411603331566,
-0.005298441741615534,
0.002270938130095601,
-0.0030656468588858843,
0.020520435646176338,
-0.028208211064338684,
-0.012224421836435795,
-0.04471573606133461,
-0.02185020036995411,
0.013535378500819206,
0.0360424667596817,
-0.021583646535873413,
-0.00822717510163784,
-0.01811717078089714,
0.02188592217862606,
-0.014417730271816254,
0.010915158316493034,
-0.011627321131527424,
-0.0006116483127698302,
-0.0029601268470287323,
-0.010731368325650692,
0.0687938705086708,
-0.03893012925982475,
-0.03412744402885437,
-0.030475206673145294,
-0.03876104578375816,
-0.016343887895345688,
0.01942206360399723,
0.03127112612128258,
0.022159216925501823,
0.022768527269363403,
-0.0049004633910954,
0.003662067698314786,
0.03111550770699978,
-0.10555589199066162,
0.03913123160600662,
-0.022112486883997917,
0.00708647770807147,
-0.04210657626390457,
-0.000004562789854389848,
0.019360527396202087,
0.07169193774461746,
0.009469259530305862,
0.01301331166177988,
0.0043317899107933044,
0.04375942051410675,
0.017381854355335236,
-0.06755345314741135,
-0.01911812648177147,
-0.021559255197644234,
-0.02581239491701126,
-0.021468501538038254,
-0.012692457996308804,
0.05631435662508011,
0.013314957730472088,
0.02477440983057022,
-0.016125086694955826,
-0.022650867700576782,
-0.03459418565034866,
0.03927909582853317,
-0.001612132415175438,
-0.02206609770655632,
-0.01835249736905098,
-0.005220730323344469,
0.02571641281247139,
-0.033906131982803345,
-0.011984416283667088,
-0.032652925699949265,
0.018271349370479584,
-0.004030316136777401,
-0.004019012674689293,
-0.008286643773317337,
0.040919382125139236,
-0.007045522797852755,
0.00829785130918026,
-0.02037947252392769,
0.03685024753212929,
-0.02894609048962593,
-0.027181116864085197,
0.027907053008675575,
-0.01218746043741703,
-0.013892032206058502,
0.008793972432613373,
-0.04914392903447151,
0.004170230124145746,
0.0012266752310097218,
0.0207484420388937,
0.006586610339581966,
-0.02430809661746025,
0.02377440594136715,
0.009166021831333637,
0.03984509035944939,
-0.026550741866230965,
-0.03431829810142517,
0.01832452043890953,
-0.031741928309202194,
-0.02958623319864273,
0.022648677229881287,
0.018202589824795723,
0.028593162074685097,
0.027197761461138725,
-0.006348367314785719,
-0.0378546379506588,
0.06617105007171631,
-0.05651215463876724,
-0.012216571718454361,
0.009263226762413979,
-0.010906222276389599,
-0.03378502279520035,
-0.0067228469997644424,
0.018260210752487183,
-0.034286171197891235,
-0.009808230213820934,
0.010633938014507294,
-0.004197428934276104,
0.009461775422096252,
0.04421662166714668,
0.035782985389232635,
-0.003452220931649208,
0.03752141818404198,
0.021448751911520958,
-0.005777954589575529,
0.02883218787610531,
0.04927840083837509,
0.0025948502589017153,
0.01889781281352043,
0.02337646298110485,
0.020625151693820953,
-0.1298566311597824,
0.026450781151652336,
0.0027945537585765123,
0.01721297949552536,
0.043279118835926056,
-0.04603511095046997,
0.014497470110654831,
0.03863583877682686,
-0.02969479374587536,
-0.02000489830970764,
-0.04182960093021393,
0.019022170454263687,
-0.03676554933190346,
0.0032347943633794785,
0.019489845260977745,
0.030564062297344208,
0.04556810483336449,
0.015344113111495972,
0.0030195375438779593,
-0.0028473681304603815,
-0.02692546509206295,
-0.030270978808403015,
0.016287680715322495,
0.019437355920672417,
0.005785493645817041,
-0.027054760605096817,
0.025274360552430153,
-0.03243520110845566,
0.031917233020067215,
-0.0018757914658635855,
-0.026476526632905006,
0.018134938552975655,
-0.022674329578876495,
-0.0011840083170682192,
-0.022703053429722786,
0.0257869940251112,
0.021607059985399246,
0.028403159230947495,
0.005636253394186497,
0.026281794533133507,
-0.01053549349308014,
-0.011783278547227383,
-0.039459917694330215,
0.012405688874423504,
0.015877224504947662,
-0.008024030365049839,
-0.025766145437955856,
0.020538415759801865,
-0.01959066465497017,
-0.019956856966018677,
0.04142395034432411,
-0.014349673874676228,
0.023649245500564575,
-0.03890514746308327,
0.0007181403925642371,
-0.040853239595890045,
0.027034208178520203,
0.032810408622026443,
0.021155493333935738,
-0.04527784511446953,
-0.012798434123396873,
-0.003930053673684597,
-0.03736457973718643,
0.010990352369844913,
0.02275642566382885,
-0.012117261067032814,
-0.042464978992938995,
-0.0031380716245621443,
-0.0006115756114013493,
-0.029227837920188904,
-0.012033281847834587,
-0.06264699250459671,
-0.015790004283189774,
0.02672891691327095,
0.022928718477487564,
0.021269239485263824,
0.05788315087556839,
-0.0023732383269816637,
-0.0016488343244418502,
-0.07628712058067322,
0.029993880540132523,
-0.01692596822977066,
-0.0038078499492257833,
-0.0440572053194046,
-0.031764738261699677,
0.002914157696068287,
0.0014817597111687064,
0.08829238265752792,
-0.025760339573025703,
-0.025214092805981636,
-0.0009602340869605541,
0.005352250766009092,
0.01488142553716898,
-0.021722689270973206,
-0.008977898396551609,
-0.024314751848578453,
-0.056649088859558105,
-0.022553082555532455,
-0.00020518798555713147,
0.03239206597208977,
-0.027265246957540512,
0.02758607640862465,
-0.012263025157153606,
0.0018968908116221428,
-0.0022531363647431135,
-0.026607347652316093,
0.01769491843879223,
0.03466179221868515,
-0.035016387701034546,
0.07762642949819565,
-0.018856242299079895,
-0.017328748479485512,
0.03662853688001633,
0.013512682169675827,
-0.05952213332056999,
0.0074703628197312355,
-0.004385320469737053,
0.011715035885572433,
-0.01118462160229683,
-0.048097800463438034,
-0.0046123056672513485,
-0.06277747452259064,
-0.02165234088897705,
0.04992542043328285,
-0.06134779378771782,
-0.004535367246717215,
0.05108874663710594,
0.017842315137386322,
0.03838123753666878,
-0.043678510934114456,
0.004680028650909662,
0.04897448047995567,
0.02505311369895935,
-0.04297289252281189,
0.04998299106955528,
0.03687160089612007,
-0.021793050691485405,
0.018184881657361984,
0.02578497678041458,
-0.0063252924010157585,
-0.005037815775722265,
0.01686842367053032,
0.007870707660913467,
-0.00974270235747099,
-0.04971488565206528,
-0.01978495717048645,
-0.013362756930291653,
-0.005824790336191654,
0.0030697365291416645,
-0.04697436839342117,
0.06289131939411163,
0.0036387015134096146,
-0.010096020996570587,
-0.049519844353199005,
0.048133473843336105,
-0.03389940783381462,
0.00013134843902662396,
-0.007358481176197529,
0.011430028825998306,
0.014647422358393669,
0.03863373026251793,
0.01782717928290367,
-0.006581700406968594,
0.03110775724053383,
-0.05081498995423317,
0.017242183908820152,
-0.014978364109992981,
0.012162499129772186,
-0.06906230747699738,
-0.005815213546156883,
-0.027054142206907272,
-0.03177458047866821,
0.01572110876441002,
0.023707138374447823,
0.009943063370883465,
0.020819077268242836,
-0.008558438159525394,
0.003950496204197407,
0.10154765844345093,
-0.08841198682785034,
-0.018414990976452827,
-0.020050542429089546,
0.011634618043899536,
-0.012744085863232613,
-0.045740339905023575
] |
<p>I read an article which tells power consumption by many devices. It say that a desktop computer (computer and monitor) use 400 to 600 watt.<br>
While when i checked my computer and monitor with meter, it was about 60 + 60 = 120 watt (computer + 17" CRT monitor) after loading windows xp and running an application. The voltage is 220V here.<br>
Which one is correct? How much power does it consume?</p> | 2,017 | [
-0.07146423310041428,
-0.044929053634405136,
-0.0015102650504559278,
-0.05475159361958504,
0.01600738614797592,
0.04826777055859566,
0.0012013786472380161,
-0.006259898189455271,
0.022026658058166504,
-0.01849409006536007,
0.030877694487571716,
0.06186635419726372,
0.0702265053987503,
0.03638589382171631,
0.03996076062321663,
0.008402088657021523,
0.000008706117114343215,
0.012854276224970818,
0.0045419717207551,
-0.0011775132734328508,
-0.024647604674100876,
-0.012441552244126797,
-0.0103609012439847,
0.002216255059465766,
-0.029236571863293648,
0.050575610250234604,
0.030893273651599884,
0.03643510863184929,
-0.0073721520602703094,
0.02220717817544937,
-0.007931149564683437,
-0.03237522765994072,
0.013610687106847763,
0.018349703401327133,
0.03081429749727249,
-0.03819170594215393,
-0.007354687433689833,
-0.04184647649526596,
-0.017216496169567108,
0.020796241238713264,
0.04482506588101387,
0.019101103767752647,
-0.0022616551723331213,
0.03031974285840988,
-0.010161055251955986,
0.01865025795996189,
-0.014011183753609657,
-0.03340381011366844,
0.013318595476448536,
-0.07013076543807983,
0.086797796189785,
-0.04807215556502342,
0.09641653299331665,
0.01635819487273693,
-0.009717480279505253,
0.02110241912305355,
0.06410639733076096,
0.06332940608263016,
-0.003416874445974827,
-0.050415556877851486,
-0.006262912414968014,
0.0049657560884952545,
-0.020330065861344337,
-0.020996419712901115,
-0.025086142122745514,
0.02911355160176754,
-0.021725254133343697,
-0.03525369614362717,
0.0710417702794075,
0.02009979821741581,
0.0365663580596447,
0.017537526786327362,
0.026567567139863968,
-0.02334887720644474,
-0.0021262974478304386,
-0.027662253007292747,
0.062465958297252655,
0.054863341152668,
0.015272833406925201,
0.04826699569821358,
0.00820893794298172,
0.015241190791130066,
0.04666053131222725,
0.03623642772436142,
0.04171735420823097,
-0.001108939410187304,
0.06721439957618713,
0.0002812544407788664,
0.013353141024708748,
-0.017110833898186684,
0.012525558471679688,
0.02090499922633171,
0.014822441153228283,
-0.010010029189288616,
-0.013622061349451542,
0.04634503275156021,
-0.026267534121870995,
0.06947444379329681,
-0.016412990167737007,
-0.02146269753575325,
0.03945358097553253,
0.008583016693592072,
0.030183808878064156,
0.037622224539518356,
-0.020453471690416336,
-0.019944651052355766,
-0.022517288103699684,
0.004143639467656612,
0.05161592364311218,
0.006718836724758148,
-0.03167920559644699,
0.0042246743105351925,
0.0021705981343984604,
0.002572542754933238,
0.01694723777472973,
-0.0028821525629609823,
-0.0012435488170012832,
0.01682738959789276,
0.04177946224808693,
0.006549740210175514,
0.005564679391682148,
-0.02628508023917675,
0.030230507254600525,
-0.03093624673783779,
-0.0357508659362793,
0.0450124554336071,
0.026767166331410408,
-0.009982898831367493,
-0.05949471518397331,
0.03311178460717201,
-0.01423281617462635,
-0.03199825435876846,
0.015054536052048206,
-0.05772453919053078,
0.07101955264806747,
-0.0002445759018883109,
-0.06072555482387543,
-0.038378115743398666,
0.01686078868806362,
-0.015587430447340012,
-0.0016389635857194662,
-0.05056516453623772,
0.009700554423034191,
0.01374903041869402,
0.03375237435102463,
0.0034564901143312454,
0.0007596510695293546,
-0.0010449890978634357,
0.00045584727195091546,
-0.006739420350641012,
-0.026426348835229874,
0.00825471617281437,
0.005568388849496841,
-0.012615698389708996,
0.04958304390311241,
-0.08915872871875763,
-0.0030989893712103367,
0.05248929187655449,
0.00868877675384283,
-0.0267348513007164,
0.031075702980160713,
0.026322292163968086,
-0.032826703041791916,
-0.01509716548025608,
-0.015489816665649414,
-0.03850524500012398,
0.058368220925331116,
-0.03363082557916641,
0.039133407175540924,
0.02730030193924904,
-0.008832063525915146,
0.0053732730448246,
0.018402183428406715,
0.0034111279528588057,
0.06706462055444717,
-0.001390144694596529,
-0.045616015791893005,
-0.04213741794228554,
0.026557806879281998,
0.009033682756125927,
-0.09144125133752823,
-0.06591913849115372,
0.026304293423891068,
0.017353441566228867,
0.035877689719200134,
0.05018089711666107,
-0.011857905425131321,
-0.023156655952334404,
0.03525639697909355,
-0.03854116424918175,
-0.02472163364291191,
-0.04615125060081482,
0.03698015213012695,
-0.053457893431186676,
0.01208304800093174,
-0.009503841400146484,
0.020428359508514404,
0.013610572554171085,
-0.04250390827655792,
-0.009481781162321568,
-0.007505523040890694,
0.006178291980177164,
0.01575801521539688,
-0.02150678262114525,
0.013685079291462898,
0.05843297019600868,
0.040342677384614944,
-0.006824910175055265,
0.016234278678894043,
-0.0003906054771505296,
-0.03775629773736,
-0.029256286099553108,
-0.047535113990306854,
-0.020422793924808502,
-0.0006057217833586037,
-0.007552282884716988,
-0.004322219640016556,
0.016948828473687172,
-0.020837074145674706,
0.03769697621464729,
-0.0007976908818818629,
0.03944199159741402,
0.03811724856495857,
0.005844831466674805,
-0.03042573481798172,
-0.008012371137738228,
0.013400939293205738,
-0.00030810473253950477,
-0.0016588778235018253,
-0.00836059171706438,
-0.0356365442276001,
0.019914185628294945,
0.047646284103393555,
-0.02852191962301731,
-0.031369030475616455,
-0.0007933647721074522,
0.030745254829525948,
0.014552964828908443,
0.006869701202958822,
0.03122483193874359,
-0.03332062438130379,
-0.0052359700202941895,
-0.007282055914402008,
0.02342046983540058,
0.014168743044137955,
0.0542571023106575,
-0.011841957457363605,
0.03126953914761543,
0.00852922536432743,
-0.023321250453591347,
-0.004242041148245335,
0.06575971096754074,
0.009410387836396694,
0.04823799058794975,
0.00805658008903265,
-0.04205112159252167,
0.04363071918487549,
-0.04871336743235588,
-0.018888145685195923,
-0.00869228970259428,
-0.02697988972067833,
0.03979869186878204,
-0.0008199404110200703,
-0.03721947222948074,
-0.013499720953404903,
0.017090901732444763,
-0.01923767477273941,
-0.004641031380742788,
0.03272050991654396,
-0.05128451809287071,
0.023764338344335556,
-0.017688453197479248,
-0.031818415969610214,
-0.032526105642318726,
0.007504280656576157,
0.026813160628080368,
0.02667650207877159,
0.034536007791757584,
-0.046159617602825165,
-0.01544869039207697,
-0.04890159144997597,
-0.09248394519090652,
-0.044902630150318146,
-0.036527667194604874,
0.005164476577192545,
0.00210195011459291,
-0.020130977034568787,
-0.021767865866422653,
0.039964690804481506,
0.014028416015207767,
0.0054179043509066105,
0.032684631645679474,
-0.0006255111657083035,
-0.07653479278087616,
0.0027703691739588976,
0.008521690964698792,
0.020656397566199303,
-0.008768009021878242,
-0.021271003410220146,
0.0326726995408535,
0.004057613667100668,
-0.00930604338645935,
0.03536597266793251,
-0.047764528542757034,
-0.0634307786822319,
-0.00585341127589345,
-0.007371577434241772,
0.037031907588243484,
-0.017291013151407242,
0.010407456196844578,
0.028864547610282898,
-0.07829899340867996,
-0.01170280296355486,
-0.04684529826045036,
-0.05058123543858528,
0.016966575756669044,
-0.017147403210401535,
0.05032651871442795,
-0.02268974483013153,
-0.055921778082847595,
0.0361638218164444,
0.009944941848516464,
-0.03157690539956093,
-0.004350495524704456,
-0.035735875368118286,
-0.005304356571286917,
-0.022544007748365402,
0.012866324745118618,
0.06019964814186096,
0.02179046720266342,
0.001153907971456647,
0.002069045789539814,
-0.008429867215454578,
0.0205391738563776,
0.03294472396373749,
-0.02466047927737236,
-0.005400551948696375,
-0.010310192592442036,
-0.018457159399986267,
0.017727581784129143,
-0.030602257698774338,
-0.0041700624860823154,
0.021113364025950432,
-0.019450854510068893,
0.034427423030138016,
-0.004332280717790127,
-0.011437426321208477,
0.039618246257305145,
-0.01701718010008335,
0.013288806192576885,
-0.056093115359544754,
0.05505385622382164,
0.052911315113306046,
0.02443639189004898,
0.027888575568795204,
0.03388843685388565,
0.009677070192992687,
-0.046921733766794205,
-0.017508933320641518,
0.026401091367006302,
0.004575574770569801,
-0.05295730009675026,
-0.06362380087375641,
-0.008078992366790771,
0.008916552178561687,
-0.022903060540556908,
0.0005795671604573727,
-0.040075138211250305,
0.012365496717393398,
0.016552239656448364,
0.054325297474861145,
0.03524789959192276,
-0.02200710028409958,
-0.019428540021181107,
-0.09211423248052597,
0.01067060511559248,
-0.03390328586101532,
0.043612290173769,
0.0037024246994405985,
0.07407406717538834,
0.015432853251695633,
0.005551403388381004,
0.043367911130189896,
-0.02596612088382244,
-0.03305894136428833,
0.03134554252028465,
-0.013205699622631073,
0.0212937630712986,
0.0033307792618870735,
-0.020467761904001236,
-0.010019013658165932,
-0.0319472961127758,
-0.028744017705321312,
-0.0029675764963030815,
-0.00256644026376307,
-0.02412332408130169,
0.0256922859698534,
-0.013629769906401634,
-0.02847108244895935,
-0.001615284476429224,
0.011125626973807812,
0.030205722898244858,
-0.04410885274410248,
0.0043916767463088036,
0.052018389105796814,
-0.002006379421800375,
-0.05475098267197609,
-0.0398508682847023,
0.022469788789749146,
-0.02621973305940628,
0.04439277946949005,
0.018880320712924004,
0.028656136244535446,
-0.011441795155405998,
-0.0010899266926571727,
0.007718800101429224,
0.03616379201412201,
0.020805301144719124,
-0.04986124485731125,
-0.028012707829475403,
-0.03565703332424164,
-0.02849818579852581,
-0.042694780975580215,
0.008125959895551205,
-0.003487215144559741,
0.02277304045855999,
0.03054513968527317,
0.0009622407960705459,
-0.006603294517844915,
0.02897503785789013,
0.06390613317489624,
0.009274144656956196,
-0.028596259653568268,
-0.042578231543302536,
0.0017621247097849846,
-0.04422899708151817,
-0.01174143236130476,
0.02006891928613186,
-0.02342989854514599,
-0.03683260828256607,
-0.04115677252411842,
0.03459751605987549,
-0.00553399370983243,
-0.031003763899207115,
0.04161538556218147,
0.035157881677150726,
-0.014813093468546867,
0.010663161054253578,
-0.03962549567222595,
0.042299963533878326,
0.0373353585600853,
0.014822610653936863,
0.014454515650868416,
-0.014783043414354324,
-0.09667588025331497,
-0.02478526532649994,
0.032896269112825394,
0.052385780960321426,
-0.03701917827129364,
0.007190453354269266,
-0.008522472344338894,
0.01361656840890646,
0.014882887713611126,
-0.06681298464536667,
0.03692953661084175,
-0.028300361707806587,
0.06077950820326805,
-0.03201115131378174,
0.01048496924340725,
0.0014477260410785675,
-0.006873268634080887,
0.015430002473294735,
0.036850400269031525,
-0.007641726639121771,
-0.012721759267151356,
-0.0012359374668449163,
0.013707363046705723,
0.018448926508426666,
0.07910184562206268,
0.006360108498483896,
0.008464209735393524,
0.020237255841493607,
0.04712345823645592,
-0.024728205054998398,
-0.04682948812842369,
0.012742751277983189,
-0.0036276548635214567,
0.0011973401997238398,
0.05546164512634277,
0.016591394320130348,
-0.0206584669649601,
0.02023901604115963,
-0.0036006798036396503,
-0.018224479630589485,
-0.012593390420079231,
-0.04800722002983093,
0.04859570786356926,
0.013132423162460327,
0.0018384417053312063,
0.029778968542814255,
0.009265073575079441,
-0.021650167182087898,
-0.01718844659626484,
0.025231746956706047,
0.009959995746612549,
-0.0070326067507267,
-0.0007843086495995522,
0.001485754270106554,
-0.04123752936720848,
-0.04351138696074486,
0.05059215798974037,
-0.026134805753827095,
0.0346793457865715,
-0.03076532669365406,
-0.02622807025909424,
-0.0510273240506649,
-0.010143418796360493,
0.014053494669497013,
-0.023848757147789,
-0.011817076243460178,
0.003251132555305958,
-0.036663301289081573,
-0.023302607238292694,
0.014501682482659817,
-0.041298795491456985,
-0.013329870998859406,
0.002471831627190113,
-0.02039278671145439,
0.029869182035326958,
-0.022704623639583588,
0.025280755013227463,
0.00030566626810468733,
-0.011983562260866165,
0.03931736201047897,
0.036877457052469254,
0.02081291563808918,
0.027424145489931107,
-0.10477456450462341,
-0.06145574897527695,
0.02300688996911049,
0.0400531031191349,
0.006897027604281902,
-0.016021404415369034,
0.07040771096944809,
0.0018593030981719494,
0.011057663708925247,
-0.04562235623598099,
-0.03841063007712364,
0.02312787063419819,
0.016576889902353287,
-0.011044016107916832,
0.02704646624624729,
0.003982353024184704,
0.005674074403941631,
-0.01837807707488537,
-0.010607409290969372,
0.0005971327773295343,
0.029202749952673912,
0.020977092906832695,
0.02343139797449112,
0.021932950243353844,
0.0507393516600132,
0.017212314531207085,
-0.016520297154784203,
-0.015010197646915913,
0.01092659030109644,
-0.027140246704220772,
0.004819215275347233,
0.0036615440621972084,
-0.00553909782320261,
0.0014857214409857988,
-0.008097520098090172,
0.0006813798099756241,
0.034115031361579895,
0.006444282364100218,
0.03877612575888634,
0.04420514777302742,
0.016912320628762245,
-0.031007595360279083,
-0.026090651750564575,
0.0629468485713005,
0.002678074175491929,
0.036625102162361145,
0.0077315429225564,
-0.05605185031890869,
-0.03995329514145851,
-0.014443336986005306,
-0.01079926174134016,
0.012764102779328823,
0.025069627910852432,
0.04036648944020271,
0.06625216454267502,
-0.01038559339940548,
0.000042555580876069143,
0.006240140646696091,
-0.02799074910581112,
-0.019214551895856857,
-0.009201274253427982,
-0.00039811304304748774,
-0.0012750744353979826,
-0.015169830992817879,
-0.038485296070575714,
-0.01260746642947197,
-0.04031211510300636,
-0.0007212240598164499,
0.057036012411117554,
0.0030729619320482016,
0.03218619152903557,
0.00990939512848854,
0.006372182164341211,
0.039635490626096725,
-0.029219621792435646,
0.007383742369711399,
-0.020885005593299866,
-0.01328502781689167,
0.021801823750138283,
-0.02573533169925213,
-0.010894494131207466,
0.01602732203900814,
0.016541145741939545,
-0.004221710376441479,
0.027442997321486473,
0.035268884152173996,
-0.015590938739478588,
0.00632771011441946,
0.0066230338998138905,
-0.04083852469921112,
0.002812765771523118,
-0.024582039564847946,
0.020672818645834923,
-0.0033035147935152054,
-0.01579868048429489,
0.0686863586306572,
-0.0196586512029171,
-0.01814284175634384,
-0.020901959389448166,
0.004933840595185757,
-0.025152401998639107,
-0.052074331790208817,
-0.02282334305346012,
0.014156634919345379,
-0.0008240234456025064,
0.022388897836208344,
0.01645500585436821,
0.03351530805230141,
0.03064507246017456,
-0.017232663929462433,
-0.057639963924884796,
-0.035927340388298035,
-0.0013827900402247906,
-0.06390012800693512,
0.06766300648450851,
-0.004332376178354025,
-0.008387531153857708,
0.023212408646941185,
-0.05111400783061981,
-0.017663728445768356,
0.003554711351171136,
0.043247904628515244,
0.0037249173037707806,
0.055078063160181046,
-0.052197180688381195,
0.0242269616574049,
-0.020914655178785324,
0.00505884550511837,
0.11155923455953598,
0.062194518744945526,
-0.017535319551825523,
-0.05526096373796463,
0.031756069511175156,
-0.03306753933429718,
0.029831787571310997,
0.0022059346083551645,
-0.01462449412792921,
-0.03299283981323242,
0.017167001962661743,
0.03696153685450554,
0.018120605498552322,
0.01818303018808365,
0.04807902127504349,
0.02679641731083393,
-0.017489714547991753,
-0.04459637776017189,
0.05426404997706413,
0.01743423193693161,
0.00623644795268774,
-0.0030698326881974936,
-0.020316408947110176,
0.010625761933624744,
0.00356996338814497,
-0.03794945776462555,
0.021395858377218246,
-0.01146784983575344,
0.05679362267255783,
0.004289775621145964,
-0.03617392107844353,
0.013257626444101334,
0.004927323665469885,
0.012026014737784863,
-0.053943779319524765,
-0.026211654767394066,
0.040227219462394714,
0.014012597501277924,
-0.008897978812456131,
0.0546085499227047,
0.004559891764074564,
0.006877650506794453,
-0.0315076969563961,
0.007888581603765488,
-0.05476321280002594,
-0.0093699274584651,
-0.02453659661114216,
-0.018855368718504906,
0.02760344184935093,
0.04011108726263046,
0.02155250869691372,
0.037579163908958435,
-0.024830633774399757,
-0.05489799752831459,
0.008034499362111092,
0.003890399821102619,
0.01391049288213253,
-0.01787039265036583,
-0.026413999497890472,
-0.053305644541978836,
0.02858779951930046,
-0.027151670306921005,
0.04230531305074692,
0.023059383034706116,
0.013338031247258186,
0.008262088522315025,
-0.021047541871666908,
0.01872600056231022,
0.008419562131166458,
-0.0046326881274580956,
-0.011595474556088448,
0.01179192028939724,
-0.010166647844016552,
-0.014691495336592197,
0.030744221061468124,
0.0477091446518898,
0.022281184792518616,
0.011950482614338398,
-0.008170725777745247,
-0.02678304724395275,
-0.07728676497936249,
0.033513393253088,
0.00514801824465394,
-0.019972799345850945,
-0.04368690028786659,
0.008257993496954441,
0.025109877809882164,
0.031368084251880646,
0.012377193197607994,
0.014943468384444714,
-0.012543585151433945,
0.016793804243206978,
0.0322987399995327,
-0.025395188480615616,
-0.0209407489746809,
0.04446893185377121,
-0.04322207346558571,
-0.0008323409711010754,
-0.021967029199004173,
0.03031311184167862,
0.010706326924264431,
-0.003841950325295329,
-0.02575497142970562,
0.013891004025936127,
-0.01181765366345644,
0.008941921405494213,
-0.025477036833763123,
-0.01654885895550251,
-0.024453984573483467,
0.018334710970520973,
-0.02516685612499714,
0.010397720150649548,
-0.006470502354204655,
-0.03613658249378204,
0.020906170830130577,
-0.012336918152868748,
-0.0037634430918842554,
-0.011548273265361786,
0.02654464915394783,
-0.02925381250679493,
0.004853778053075075,
-0.025309761986136436,
-0.014773436821997166,
-0.008715975098311901,
0.01063571684062481,
0.04072941839694977,
0.03003089316189289,
-0.03950759395956993,
0.032697878777980804,
-0.03126433119177818,
-0.0035184556618332863,
0.016949355602264404,
0.02824316918849945,
0.01778145134449005,
-0.020856719464063644,
-0.014876995235681534,
-0.019726132974028587,
0.022330233827233315,
-0.03522763401269913,
-0.036568596959114075,
0.08483652770519257,
-0.05053763836622238,
-0.0008435563649982214,
0.06156313791871071,
0.004397929180413485,
0.024152236059308052,
-0.006302040535956621,
-0.01345056015998125,
0.013531393371522427,
0.04322207719087601,
-0.06090569123625755,
0.05003632232546806,
-0.005633272230625153,
-0.0014259266899898648,
0.0062468149699270725,
0.04153914377093315,
-0.03374002128839493,
-0.005737831816077232,
0.0016210711328312755,
0.03835102170705795,
0.011456736363470554,
-0.029520854353904724,
0.00925046019256115,
-0.018857890740036964,
0.015201488509774208,
0.016100427135825157,
0.03413332626223564,
-0.01744031347334385,
0.010347975417971611,
0.021409062668681145,
-0.04328783601522446,
0.022485828027129173,
0.023758213967084885,
-0.04346609488129616,
-0.06360182166099548,
0.002611637581139803,
-0.02821221388876438,
-0.012512421235442162,
0.017502451315522194,
-0.05574876442551613,
0.017529690638184547,
0.008593118749558926,
-0.08804548531770706,
-0.026601320132613182,
0.005546278785914183,
-0.009253942407667637,
-0.013965701684355736,
0.02003008872270584,
0.012507809326052666,
0.009001246653497219,
0.013567611575126648,
0.05048408731818199,
0.03360547125339508,
-0.000006025702532497235,
0.006808206904679537,
-0.04004449397325516,
0.02548304572701454,
0.06561999022960663,
-0.0003779333783313632,
-0.028380868956446648,
0.010929754003882408,
-0.049439936876297,
-0.038514964282512665,
0.02461853250861168,
-0.0046185399405658245,
0.03788871690630913,
0.014445659704506397,
0.025792280212044716,
-0.00019710289780050516,
0.0647222027182579,
0.0407303161919117,
-0.03569558635354042,
-0.02597392536699772,
0.004812539089471102,
0.04052739590406418,
0.028967780992388725,
-0.008090822026133537,
-0.016601642593741417,
0.02213570475578308,
-0.007067227736115456,
-0.0008052447810769081,
0.015640152618288994,
-0.024164509028196335,
-0.024432897567749023,
0.030449936166405678,
-0.012081902474164963,
0.02257450297474861,
-0.01637830212712288,
-0.014544231817126274,
-0.06365927308797836,
-0.036980148404836655,
0.03727668896317482,
-0.056530557572841644,
0.04392728582024574,
0.028257295489311218,
0.01274548564106226,
-0.008181721903383732,
0.026534687727689743,
-0.001478396006859839,
-0.028339480981230736,
-0.04607672989368439,
0.0008908762247301638,
0.0054070008918643,
0.01897568441927433,
-0.0024804524146020412,
-0.04753023386001587,
-0.0185223538428545,
-0.006166090257465839,
0.0010204805294051766,
-0.015276025980710983,
-0.0011513321660459042,
-0.05947170406579971,
-0.013891270384192467,
-0.021512644365429878,
0.08554186671972275,
0.02410668320953846,
-0.023266447708010674,
-0.04378698021173477,
-0.03386276587843895,
0.009574808180332184,
0.031999681144952774,
0.05328088626265526,
-0.023578230291604996,
-0.0406888946890831,
-0.029520146548748016,
-0.025145720690488815,
0.02449377253651619,
-0.07286403328180313,
-0.009022658690810204,
0.028834199532866478,
-0.04879435524344444,
0.0030837119556963444,
-0.032270729541778564,
-0.023913413286209106,
0.027495067566633224,
0.00968166720122099,
-0.030356233939528465,
-0.016372816637158394,
-0.012361142784357071,
-0.016787074506282806,
0.01802635006606579,
0.04237876459956169,
-0.0034302636049687862,
0.07501774281263351,
-0.022443382069468498,
-0.0004618647799361497,
0.06157990172505379,
-0.0012652777368202806,
-0.05069464445114136,
-0.01924227923154831,
0.012319403700530529,
0.03200933337211609,
0.03958847373723984,
0.01817966252565384,
0.009866796433925629,
-0.05402860417962074,
-0.018974989652633667,
0.02231479436159134,
-0.014990882948040962,
-0.006806518416851759,
0.056973423808813095,
0.02536960132420063,
0.03521677106618881,
0.01349957101047039,
0.020064525306224823,
-0.03511296957731247,
0.02001812681555748,
-0.006198687944561243,
0.023053597658872604,
0.021420856937766075,
-0.004823446739464998,
0.015957240015268326,
0.036031510680913925,
0.023066535592079163,
0.04438243433833122,
0.013683401048183441,
0.03167789801955223,
-0.01027047447860241,
-0.059402789920568466,
-0.014958634041249752,
0.003399077570065856,
-0.015321675688028336,
0.030670395120978355,
-0.065193310379982,
0.04987747594714165,
-0.010787928476929665,
-0.023477014154195786,
-0.011478721164166927,
-0.033536121249198914,
-0.02045382745563984,
-0.00026993107167072594,
0.019450446590781212,
0.0314529687166214,
-0.029328903183341026,
-0.01709883101284504,
-0.018384240567684174,
-0.0063794078305363655,
0.02511608973145485,
-0.05416329577565193,
0.02223760262131691,
-0.017063600942492485,
-0.006702910177409649,
-0.058831602334976196,
0.012026063166558743,
0.005903210025280714,
0.026099001988768578,
0.02491873688995838,
0.055006206035614014,
0.002632987452670932,
-0.009925882332026958,
-0.020763229578733444,
0.03297046571969986,
0.024098102003335953,
-0.05630911514163017,
0.0030798560474067926,
0.00946025736629963,
-0.027627423405647278,
0.02666267566382885,
-0.014679254032671452
] |
<p>In the time-independent Schrödinger's equation:</p>
<p>$$ -\frac{\hbar^2}{2m} \frac{d^2} {dx^2} u + Vu ~= Eu, $$</p>
<p>why there is a minus sign before the first term?</p> | 2,018 | [
0.014528865925967693,
-0.0471971295773983,
0.016845539212226868,
-0.014917358756065369,
0.024312695488333702,
0.005849988199770451,
-0.05078369006514549,
0.0037760157138109207,
0.012519747950136662,
-0.036679040640592575,
0.02589772455394268,
0.02197829633951187,
0.0727454423904419,
-0.01098767202347517,
0.03199998289346695,
0.03501454368233681,
0.015268184244632721,
-0.003024182515218854,
-0.013966325670480728,
-0.019121062010526657,
-0.00838118139654398,
0.011689551174640656,
0.058937519788742065,
0.026602722704410553,
0.00014418718637898564,
0.04144841805100441,
0.022876642644405365,
0.039996273815631866,
0.050701092928647995,
0.052116286009550095,
0.00816081091761589,
-0.026186713948845863,
0.014997145161032677,
0.015605623833835125,
0.04427136853337288,
-0.021415753290057182,
-0.02663128264248371,
-0.041206035763025284,
0.012285751290619373,
0.005426866468042135,
-0.03324415162205696,
-0.02557421661913395,
0.007421460468322039,
0.05633384734392166,
-0.002922075567767024,
-0.020930446684360504,
0.04616200923919678,
-0.033250708132982254,
0.04773467779159546,
-0.044058430939912796,
0.05244024097919464,
-0.0050492603331804276,
0.0516124926507473,
-0.004107868764549494,
-0.01719711907207966,
-0.00707294000312686,
0.042044416069984436,
0.07878880202770233,
0.03175985440611839,
-0.022945446893572807,
0.008078934624791145,
-0.03238512575626373,
0.023705992847681046,
0.0025679180398583412,
-0.008208658546209335,
0.04921550303697586,
0.006084994878619909,
-0.01490042358636856,
0.009240218438208103,
-0.005949693266302347,
0.008518503047525883,
-0.01855429820716381,
0.028010157868266106,
-0.07602512091398239,
0.03673224523663521,
-0.02636663243174553,
0.00953618809580803,
0.0250785443931818,
0.008983330801129341,
0.04695352166891098,
0.028098249807953835,
-0.003443392226472497,
0.038611866533756256,
0.010240442119538784,
-0.018055329099297523,
-0.03023766539990902,
0.07374553382396698,
0.01839064620435238,
0.0036619894672185183,
0.03162453696131706,
0.006640091072767973,
0.07604940980672836,
0.024674924090504646,
-0.020759401842951775,
-0.007243529427796602,
0.0175861157476902,
-0.017066527158021927,
0.042268846184015274,
0.03764421120285988,
-0.027951987460255623,
-0.04304804280400276,
-0.024925725534558296,
0.04042048007249832,
0.05482480674982071,
-0.011665291152894497,
0.017663540318608284,
-0.04116419702768326,
0.040728870779275894,
-0.015063448809087276,
-0.004575028084218502,
-0.03069048933684826,
0.0028064188081771135,
-0.00837686937302351,
0.004876816179603338,
-0.01616261713206768,
-0.02418045699596405,
0.009515482932329178,
-0.014964397996664047,
0.03298015519976616,
0.02783641591668129,
0.050055451691150665,
-0.03043554536998272,
0.026859572157263756,
-0.0011309284018352628,
-0.08090956509113312,
0.0027847131714224815,
0.045137640088796616,
0.020410338416695595,
-0.006557175423949957,
-0.0022808911744505167,
-0.002550469245761633,
-0.02552570402622223,
0.02163911797106266,
0.016577478498220444,
0.023872585967183113,
0.02564917504787445,
-0.13201181590557098,
-0.09171994775533676,
0.013267440721392632,
-0.02118987962603569,
-0.01371717732399702,
-0.045918311923742294,
0.004529413301497698,
0.030046019703149796,
0.11072591692209244,
-0.019742701202630997,
0.006164643447846174,
0.017246397212147713,
0.009847615845501423,
0.00804056879132986,
0.02092926949262619,
-0.054223041981458664,
-0.012734898366034031,
-0.012244385667145252,
0.00891832634806633,
-0.06064722687005997,
-0.01393796969205141,
0.049031954258680344,
-0.010740240104496479,
0.011360465548932552,
0.08484982699155807,
-0.0402674674987793,
0.017566882073879242,
0.014165324158966541,
-0.04935268685221672,
-0.02788737043738365,
0.11101976782083511,
0.03803476318717003,
-0.0007823722553439438,
0.05371890962123871,
0.04860353469848633,
0.06517206132411957,
-0.026001043617725372,
0.022729165852069855,
0.04918871819972992,
-0.01822304166853428,
-0.012472872622311115,
0.0034429871011525393,
0.01189554762095213,
0.003441569395363331,
-0.02143181674182415,
-0.045323096215724945,
-0.01110009104013443,
0.02141306735575199,
0.012893441133201122,
0.0156861525028944,
0.007270089816302061,
0.035626742988824844,
-0.002061647130176425,
-0.08017423748970032,
-0.02113455906510353,
-0.04736215993762016,
0.011830956675112247,
0.018719198182225227,
-0.029407519847154617,
0.026727132499217987,
0.025638720020651817,
0.013493632897734642,
0.01410183310508728,
-0.04551748186349869,
-0.00634909700602293,
0.01062596496194601,
0.0036579477600753307,
-0.019993143156170845,
0.052596546709537506,
0.04109202325344086,
0.055880822241306305,
0.004326290916651487,
0.050130970776081085,
-0.025981133803725243,
-0.005009139887988567,
0.003187756985425949,
0.013386252336204052,
0.02495615743100643,
-0.017342600971460342,
-0.0211932510137558,
-0.00947471335530281,
-0.021628793329000473,
-0.01679946668446064,
0.006929554510861635,
-0.03873386234045029,
0.049802858382463455,
0.08040416240692139,
0.006623916793614626,
0.0008475957438349724,
0.034252017736434937,
0.03609941899776459,
0.058112334460020065,
0.0010634701466187835,
-0.03339284658432007,
-0.018793515861034393,
-0.014921476133167744,
0.024656835943460464,
0.029753467068076134,
-0.03941650688648224,
0.02169891633093357,
0.017404645681381226,
0.027319513261318207,
0.02704712748527527,
0.0004798084555659443,
-0.01596064679324627,
-0.05297320708632469,
0.03033042699098587,
0.020607193931937218,
-0.0337388813495636,
0.015581045299768448,
0.07617136090993881,
0.029211604967713356,
0.005834972485899925,
-0.03927706182003021,
-0.01023402251303196,
0.026747927069664,
-0.07964660227298737,
0.006281931884586811,
-0.008285359479486942,
-0.04106255620718002,
0.03237457945942879,
-0.05275364965200424,
0.02329484559595585,
0.0031660967506468296,
-0.012356974184513092,
0.022043302655220032,
-0.021784501150250435,
-0.037898313254117966,
-0.01633480004966259,
0.00005198194776312448,
-0.00819448847323656,
-0.012152928858995438,
0.0428914949297905,
-0.04549945518374443,
0.01012478582561016,
-0.05735103413462639,
-0.028945622965693474,
-0.03794214501976967,
-0.03910977393388748,
0.057100921869277954,
0.04664940387010574,
0.030595995485782623,
-0.023118523880839348,
-0.04123600944876671,
0.010640242137014866,
-0.053460195660591125,
0.02738179825246334,
0.002467666519805789,
-0.005448601674288511,
0.03401682525873184,
-0.009384820237755775,
-0.004239351488649845,
0.07820460200309753,
0.04228214547038078,
-0.0077819726429879665,
-0.017954237759113312,
-0.017228396609425545,
-0.06361737102270126,
-0.07336874306201935,
-0.01900501176714897,
-0.006495315115898848,
-0.027776356786489487,
0.004621564410626888,
0.06832476705312729,
-0.00725161749869585,
0.018995312973856926,
0.02249399572610855,
-0.03932442516088486,
-0.02734791301190853,
-0.05728572607040405,
-0.01894819736480713,
0.053804636001586914,
-0.02565455064177513,
0.00547349127009511,
-0.006422429345548153,
-0.03782353177666664,
-0.016661448404192924,
-0.047587908804416656,
-0.0455162413418293,
0.01833999902009964,
0.016664819791913033,
0.015992406755685806,
0.000246887473622337,
-0.005011874251067638,
0.08098583668470383,
0.029933735728263855,
0.01803954876959324,
-0.029249019920825958,
0.010175440460443497,
0.006404086947441101,
-0.04302644357085228,
0.0046821460127830505,
0.03284945711493492,
0.005491387099027634,
0.04651152342557907,
-0.009106546640396118,
0.05035914480686188,
0.032114870846271515,
0.005009764339774847,
-0.010826152749359608,
0.007236952893435955,
-0.03160329908132553,
-0.004621375352144241,
0.04883555322885513,
-0.0034448301885277033,
0.006780690047889948,
0.017392804846167564,
0.015907911583781242,
0.04527375102043152,
0.023429760709404945,
-0.021629733964800835,
0.07734411209821701,
-0.004718187730759382,
0.009241744875907898,
0.0010807914659380913,
0.03182555362582207,
-0.03614424914121628,
-0.006647779140621424,
-0.02879105694591999,
-0.019570233300328255,
0.03349921479821205,
-0.04911831393837929,
0.017937254160642624,
0.013955177739262581,
0.015354203060269356,
-0.03190648928284645,
-0.018421141430735588,
-0.007394112646579742,
-0.014379003085196018,
0.06080320477485657,
-0.020023003220558167,
-0.0065360660664737225,
0.0571431890130043,
0.02906610816717148,
-0.006830006372183561,
-0.022841671481728554,
-0.04218117520213127,
-0.036915373057127,
-0.0495273619890213,
-0.020514247938990593,
-0.0044630044139921665,
0.034261222928762436,
-0.018958233296871185,
0.036251239478588104,
0.012925360351800919,
0.027028514072299004,
0.015269855968654156,
0.004955490119755268,
-0.07565547525882721,
0.02350573055446148,
-0.03543483838438988,
-0.014969998970627785,
-0.020205920562148094,
0.017548462375998497,
-0.03338050842285156,
-0.07300568372011185,
-0.04493055120110512,
-0.009339944459497929,
-0.01511998102068901,
-0.04829991236329079,
0.023280005902051926,
-0.011725496500730515,
-0.013287868350744247,
-0.042374756187200546,
0.0074807628989219666,
0.06237725913524628,
0.02570471726357937,
-0.014432624913752079,
0.05136861279606819,
-0.012429625727236271,
-0.012716810218989849,
-0.02359548583626747,
-0.011193284764885902,
0.021805593743920326,
0.009940299205482006,
0.017910292372107506,
0.01669425517320633,
-0.031065475195646286,
-0.005995734129101038,
0.016244899481534958,
0.04579465463757515,
0.0016550332074984908,
-0.013151749968528748,
-0.013788405805826187,
-0.013596967794001102,
-0.0035785078071057796,
0.012965507805347443,
0.06247228756546974,
0.011537464335560799,
0.049343034625053406,
0.011529841460287571,
-0.006640024017542601,
-0.006783371325582266,
0.018231892958283424,
0.048703622072935104,
0.011834908276796341,
0.020867276936769485,
-0.06723103672266006,
0.008628823794424534,
-0.04360765963792801,
-0.013398265466094017,
-0.0376434251666069,
0.010751653462648392,
-0.04091308265924454,
-0.013463614508509636,
0.014646097086369991,
0.03221747279167175,
0.02832871861755848,
-0.021513190120458603,
-0.007989105768501759,
-0.022604595869779587,
0.009477461688220501,
-0.01845727302134037,
0.026818621903657913,
0.025190915912389755,
0.01457300130277872,
-0.027020778506994247,
-0.0034459917806088924,
-0.07817775756120682,
0.002015202073380351,
0.033454056829214096,
0.07772288471460342,
0.007155589759349823,
-0.012994426302611828,
-0.06872937828302383,
-0.009700797498226166,
0.04790499806404114,
-0.013623512350022793,
0.02237623929977417,
-0.007476051338016987,
-0.0010420798789709806,
-0.0028132987208664417,
-0.04726484417915344,
-0.0635766088962555,
0.022433316335082054,
0.02632249891757965,
0.02150806598365307,
-0.0374029241502285,
0.007474589627236128,
-0.022685956209897995,
0.02100268192589283,
-0.00904133077710867,
0.062078721821308136,
0.0007283526356332004,
-0.01702767424285412,
-0.008368232287466526,
0.002231345511972904,
-0.033613912761211395,
-0.073996901512146,
0.02106485515832901,
0.007008962798863649,
0.029100079089403152,
0.02434038557112217,
-0.03597711771726608,
-0.0656857043504715,
0.01827314682304859,
0.025546496734023094,
0.005383452866226435,
-0.0005186530761420727,
-0.02652854472398758,
0.012714872136712074,
0.038963962346315384,
-0.004712632391601801,
0.05797380581498146,
0.04162072017788887,
-0.0009716942440718412,
-0.0008795391186140478,
-0.03500114381313324,
0.02678684890270233,
-0.04162190854549408,
0.016777295619249344,
-0.023715438321232796,
-0.011243773624300957,
-0.02776557393372059,
0.01881299540400505,
-0.029291868209838867,
0.00877036340534687,
-0.028728434816002846,
0.00014104681031312793,
-0.03239577263593674,
0.029504911974072456,
-0.015282916836440563,
-0.0011101209092885256,
0.03575669601559639,
0.013885476626455784,
-0.0037595080211758614,
-0.003608838887885213,
0.03990420699119568,
-0.036659128963947296,
-0.00510950293391943,
0.04254867509007454,
0.021917032077908516,
0.006043716799467802,
-0.0029924006666988134,
-0.042819004505872726,
0.03265262022614479,
-0.062423937022686005,
-0.008339814841747284,
-0.01688672974705696,
-0.005260490346699953,
0.030272986739873886,
-0.015325209125876427,
-0.006390425376594067,
0.010908476077020168,
-0.015115059912204742,
0.00870222132652998,
-0.055809665471315384,
0.04083278402686119,
0.03127257525920868,
-0.0038483846001327038,
-0.07512194663286209,
-0.055512722581624985,
-0.014441325329244137,
-0.005062408279627562,
-0.016926206648349762,
-0.010649490170180798,
-0.01579166017472744,
-0.005411852616816759,
-0.002236975124105811,
0.014699799008667469,
0.01839510165154934,
0.0000403737103624735,
-0.01863091066479683,
0.02684827335178852,
0.0062968735583126545,
0.036605048924684525,
0.004725517239421606,
-0.014308374375104904,
0.015237604267895222,
-0.02629365585744381,
-0.023284777998924255,
0.020762406289577484,
0.07859604060649872,
-0.02153860777616501,
-0.04108550027012825,
-0.04033577814698219,
-0.01325353141874075,
0.011588172987103462,
0.006167794112116098,
-0.001182451844215393,
0.0009577562450431287,
-0.011092658154666424,
0.006392304319888353,
-0.014368574135005474,
0.0027014960069209337,
-0.022674569860100746,
0.018553975969552994,
0.05630188062787056,
-0.014193174429237843,
-0.043577466160058975,
-0.03382469713687897,
0.023625997826457024,
0.0015796461375430226,
-0.017077622935175896,
-0.037636421620845795,
0.056866180151700974,
-0.007803758140653372,
0.024749863892793655,
0.02916250377893448,
-0.005607397761195898,
-0.027712717652320862,
-0.011602104641497135,
-0.03278212249279022,
-0.007298907730728388,
-0.0231877863407135,
-0.015116069465875626,
-0.06168992444872856,
-0.017506014555692673,
0.01833578571677208,
0.0702972337603569,
0.0018040752038359642,
0.0441698282957077,
-0.026109112426638603,
-0.03617651015520096,
0.018294522538781166,
-0.02762749046087265,
-0.03355767950415611,
0.0222066268324852,
-0.020405612885951996,
0.021852267906069756,
-0.03150605782866478,
0.02819346822798252,
0.0034495170693844557,
0.055450960993766785,
0.0014299008762463927,
-0.015239708125591278,
0.017086215317249298,
0.006880148779600859,
0.036922700703144073,
0.011084594763815403,
-0.023994935676455498,
0.062409259378910065,
0.006711437366902828,
0.051799386739730835,
-0.0015390951884910464,
-0.013597724959254265,
0.03177974373102188,
-0.016601908951997757,
-0.046934451907873154,
-0.05073097348213196,
0.010231724940240383,
-0.026055697351694107,
0.005296650342643261,
0.015455172397196293,
-0.016834469512104988,
0.028699342161417007,
0.020437108352780342,
0.03379526361823082,
0.008827279321849346,
0.03200460970401764,
0.013427230529487133,
-0.025630509480834007,
0.009305334649980068,
-0.05049022287130356,
-0.04507581144571304,
0.032744232565164566,
-0.03464400768280029,
-0.0214362982660532,
-0.040400274097919464,
-0.007890925742685795,
0.0077230073511600494,
0.011484111659228802,
0.012938637286424637,
-0.001532398397102952,
0.032827895134687424,
0.02324029803276062,
0.03756363317370415,
0.0054535591043531895,
0.0024896941613405943,
0.13165433704853058,
0.03862496837973595,
0.018406866118311882,
-0.04847666248679161,
0.014114991761744022,
0.02915596030652523,
0.012872771359980106,
-0.028820781037211418,
0.018083902075886726,
-0.014116707257926464,
0.015780922025442123,
0.022447453811764717,
0.01219512801617384,
0.017687110230326653,
0.007256278768181801,
0.012620683759450912,
-0.03747710585594177,
-0.02074272744357586,
-0.0035568473394960165,
-0.013575498946011066,
-0.012583410367369652,
0.031995661556720734,
-0.032986145466566086,
0.016913747414946556,
-0.02327130176126957,
0.006130574736744165,
-0.04299783706665039,
-0.045831602066755295,
0.05209695175290108,
0.05536789074540138,
-0.031973518431186676,
0.008146775886416435,
0.020173847675323486,
0.001150861382484436,
-0.033422790467739105,
0.018227513879537582,
0.038701023906469345,
-0.0018335479544475675,
0.05249502882361412,
0.026388876140117645,
0.0028853644616901875,
-0.0156303271651268,
-0.019827034324407578,
0.009747163392603397,
-0.06578650325536728,
0.0003430378274060786,
0.009864023886620998,
0.051285721361637115,
0.006433653645217419,
-0.027540627866983414,
0.007256424520164728,
-0.022444847971200943,
0.02855042926967144,
-0.036820489913225174,
-0.01658019982278347,
0.01148615125566721,
0.013549004681408405,
-0.023559708148241043,
-0.009033799171447754,
-0.02019425667822361,
-0.003568817162886262,
0.024570750072598457,
-0.0031415587291121483,
-0.0015853127697482705,
-0.02149120531976223,
0.0034625292755663395,
-0.025179557502269745,
-0.018044723197817802,
-0.009600606746971607,
-0.033184587955474854,
0.0011579032288864255,
0.023415325209498405,
-0.04934605583548546,
-0.022883450612425804,
0.0271507129073143,
0.0016800862504169345,
0.0833478569984436,
0.015000134706497192,
-0.022820426151156425,
-0.04285694286227226,
-0.04727785289287567,
0.056690312922000885,
-0.01076311245560646,
-0.014767794869840145,
-0.0036531463265419006,
-0.0014079485554248095,
0.0022195307537913322,
-0.0008941724081523716,
-0.015311775729060173,
0.00677147414535284,
0.003949066624045372,
0.023823531344532967,
0.0007198506500571966,
-0.0008859164081513882,
-0.03966479375958443,
0.039294302463531494,
-0.018923640251159668,
0.0322638638317585,
-0.0003628180711530149,
-0.02116020955145359,
-0.0002709801192395389,
0.011730849742889404,
0.01671486534178257,
0.02637093886733055,
-0.019439799711108208,
-0.048238806426525116,
0.013376414775848389,
-0.03317677602171898,
0.008734775707125664,
0.000063952429627534,
-0.0052684820257127285,
0.023410722613334656,
-0.016917308792471886,
-0.028191452845931053,
0.016475418582558632,
0.016717897728085518,
0.058717112988233566,
0.012138314545154572,
0.03144871070981026,
-0.007550303358584642,
0.0316198393702507,
-0.018840288743376732,
-0.01238917000591755,
-0.07136084884405136,
0.022938858717679977,
0.00003425326940487139,
-0.011878049932420254,
-0.004373611882328987,
0.015327736735343933,
-0.006012827157974243,
-0.0047479248605668545,
0.005757158622145653,
0.04200616851449013,
0.011726639233529568,
0.005180947482585907,
0.03234061598777771,
0.00417972169816494,
0.023234684020280838,
0.04405271261930466,
-0.020329607650637627,
0.017377430573105812,
-0.03973553329706192,
-0.0402229018509388,
0.016088707372546196,
0.03701164573431015,
0.027632879093289375,
0.005242773797363043,
-0.019158340990543365,
-0.009751476347446442,
0.06520508974790573,
-0.039829712361097336,
0.005253206007182598,
0.01226300559937954,
-0.04187626391649246,
0.011118220165371895,
0.005796115845441818,
-0.03828388452529907,
-0.018979184329509735,
0.004320843145251274,
0.030014049261808395,
0.018301082774996758,
-0.020621221512556076,
-0.004377599339932203,
0.0031902457121759653,
-0.005561556201428175,
0.05885472521185875,
0.017296694219112396,
0.029137227684259415,
0.018582576885819435,
0.02238115854561329,
-0.011650498025119305,
0.06741276383399963,
0.024299029260873795,
0.024558238685131073,
-0.09910523891448975,
-0.03567839041352272,
0.0011962284334003925,
0.009271176531910896,
0.04106578975915909,
-0.030351651832461357,
0.0002583259774837643,
0.01773414947092533,
-0.046804334968328476,
0.030223118141293526,
-0.050586868077516556,
-0.033058032393455505,
0.0013227511662989855,
-0.019272342324256897,
-0.0334334634244442,
0.05997028201818466,
0.04898422211408615,
0.0348626971244812,
0.0486970916390419,
-0.004322264809161425,
-0.007218124344944954,
-0.030350331217050552,
-0.020496057346463203,
0.022779732942581177,
-0.02974187210202217,
0.010311012156307697,
0.054453156888484955,
-0.009975126944482327,
0.003840257413685322,
0.0020881586242467165,
-0.04541657119989395,
-0.018675444647669792,
-0.005831175018101931,
0.019897639751434326,
0.023605937138199806,
0.03096093237400055,
0.018453754484653473,
-0.041732996702194214,
-0.01996510662138462,
-0.03247538208961487,
0.010627430863678455,
0.01848038285970688,
0.001807616907171905,
-0.006256444845348597,
-0.028566325083374977,
-0.033144764602184296,
-0.0653272420167923,
0.04831109568476677,
-0.0021207125391811132,
0.0008211825625039637,
-0.024539439007639885,
0.016182314604520798,
0.0015686079859733582,
-0.03668287768959999,
-0.0018427936593070626,
-0.03772284463047981,
-0.021570688113570213,
0.01555238850414753,
-0.023520225659012794,
-0.009885650128126144,
-0.013017508201301098,
-0.025876831263303757,
-0.0690484270453453,
0.013887020759284496,
0.0055106100626289845,
-0.000891862902790308,
-0.04288599640130997,
-0.016874821856617928,
-0.016705887392163277,
-0.0011155556421726942,
-0.01035991683602333,
-0.004722108598798513,
-0.016356611624360085,
0.0175323449075222,
-0.004275902174413204,
-0.023886265233159065,
-0.06246206909418106,
-0.07603728026151657,
-0.03266790136694908,
-0.05128203332424164,
0.018166041001677513,
0.014180070720613003,
-0.03459983319044113,
-0.0318107008934021,
-0.02352694422006607,
-0.012931264005601406,
0.014278492890298367,
0.06185989826917648,
0.01642698235809803,
-0.02715199440717697,
0.03037331812083721,
-0.011485311202704906,
0.01932673342525959,
-0.039018843322992325,
-0.017048588022589684,
0.023711636662483215,
-0.0004891475546173751,
0.0011869283625856042,
0.03104116953909397,
0.0004519571375567466,
0.04945986717939377,
0.005714150611311197,
-0.0017144116573035717,
0.00427035428583622,
-0.0002972524962387979,
-0.027660654857754707,
0.03581259772181511,
0.03239200636744499,
-0.03101268596947193,
0.08379805088043213,
-0.0012538547161966562,
0.04029640555381775,
0.027492709457874298,
-0.0018610283732414246,
-0.04887640103697777,
-0.009932227432727814,
-0.012956506572663784,
-0.011849052272737026,
0.020135710015892982,
-0.002140340395271778,
0.024898486211895943,
-0.010608791373670101,
-0.007935348898172379,
0.017894938588142395,
-0.03129979968070984,
-0.028647951781749725,
0.024374665692448616,
-0.002825606381520629,
0.017421206459403038,
0.02771645039319992,
0.0036289882846176624,
0.0439375564455986,
0.019635798409581184,
0.052033282816410065,
0.07816405594348907,
-0.004444791469722986,
0.004903046414256096,
-0.0012581623159348965,
-0.003059020498767495,
-0.05880554020404816,
-0.03244764730334282,
0.0019097519107162952,
0.0026259119622409344,
-0.014906927943229675,
-0.0030623592901974916,
0.0183353740721941,
-0.02040562778711319,
-0.016053125262260437,
-0.01461122278124094,
-0.00985624734312296,
0.05530635640025139,
-0.023828059434890747,
0.05136938765645027,
-0.013981930911540985,
0.01534807775169611,
-0.02761734277009964,
0.022845562547445297,
0.017479076981544495,
0.009421717375516891,
-0.028268812224268913,
-0.027112988755106926,
-0.018555771559476852,
-0.019641755148768425,
-0.010718222707509995,
-0.046726979315280914,
-0.011254710145294666,
0.010987678542733192,
-0.02846365235745907,
-0.01955038122832775,
-0.028339680284261703,
-0.01975620537996292,
-0.031179234385490417,
0.026017561554908752,
0.03022298961877823,
0.00889493152499199,
-0.0034133053850382566,
0.004002695437520742,
-0.044999491423368454,
0.052030183374881744,
-0.06277308613061905,
-0.03290146589279175,
-0.02197856456041336,
-0.0020381840877234936,
-0.01223638653755188,
-0.0011600770521908998
] |
<p>Mass m is connected to the end of a cord at length R above its rotational axis (the axis is parallel to the horizon, the position of the mass is perpendicular to the horizon). It is given an initial velocity, V0, at a direction parallel to the horizon. The initial state is depicted at position A in the image.</p>
<p>The forces working on the mass are MG from the earth and T the tension of the cord.</p>
<p>How can I calculate the tension of the cord when the mass is at some angle $\theta$ from its initial position (position B in the image)?</p>
<p><img src="http://img535.imageshack.us/img535/8167/76300324.png" alt="image">.</p>
<p>Here's what I thought:</p>
<p>Since the mass is moving in a circle then the total force in the radial direction is T - MG*$\cos\theta$ = M*(V^2)/R</p>
<p>and so T = MG*$\cos\theta$+M*(V^2)/R</p>
<p>but since MG applies acceleration in the tangential direction then V should also be a function of $\theta$ and that is where I kind of got lost. I tried to express V as the integration of MG*$\sin\theta$, but I wasn't sure if that's the right approach.</p> | 2,019 | [
-0.005326567683368921,
-0.008046125993132591,
-0.024125300347805023,
-0.00027251572464592755,
0.02623327262699604,
-0.024799417704343796,
-0.04070566967129707,
-0.002379520796239376,
0.012607840821146965,
0.0006162227364256978,
0.03327067196369171,
0.04446316137909889,
0.06429386138916016,
0.02962552011013031,
0.030386965721845627,
-0.01903724856674671,
-0.006682421546429396,
-0.01927211321890354,
-0.0009490798111073673,
-0.027541421353816986,
-0.007693388964980841,
0.007529751397669315,
0.007517257239669561,
0.007693233899772167,
0.009087452664971352,
0.030100824311375618,
0.06625141948461533,
-0.022988712415099144,
0.001009686617180705,
0.0665040835738182,
-0.025722255930304527,
-0.018124699592590332,
-0.014258192852139473,
0.021126670762896538,
0.02097196877002716,
0.034223828464746475,
-0.06561718881130219,
-0.023675009608268738,
-0.01689276285469532,
0.04430723562836647,
-0.002378190401941538,
-0.026053819805383682,
-0.03658221289515495,
0.06949195265769958,
-0.04867061227560043,
-0.002403781283646822,
-0.010134362615644932,
0.011083156801760197,
0.08490905910730362,
-0.03732041269540787,
0.08550428599119186,
0.0037992459256201982,
0.03200514614582062,
0.01742076314985752,
0.002529947319999337,
-0.004344075918197632,
0.044026847928762436,
0.03166720271110535,
-0.029303474351763725,
-0.04598408192396164,
-0.055127158761024475,
-0.06431439518928528,
-0.04169124737381935,
-0.05200789496302605,
0.010832760483026505,
-0.001527444808743894,
0.004571741912513971,
0.028612317517399788,
0.04757465049624443,
-0.033347222954034805,
0.016665417701005936,
-0.006962880492210388,
0.02600751630961895,
-0.029238663613796234,
-0.02637675777077675,
-0.012996502220630646,
0.0031672785989940166,
0.02371971122920513,
0.0025627934373915195,
0.019145378842949867,
-0.015715118497610092,
0.0013092780718579888,
0.05477779731154442,
0.07250836491584778,
0.007525102235376835,
0.009411444887518883,
0.044666487723588943,
0.013038347475230694,
0.00821700319647789,
0.013545672409236431,
0.008632779121398926,
-0.002693353919312358,
-0.03042754717171192,
-0.014871170744299889,
-0.026868347078561783,
0.04436279833316803,
-0.02143111824989319,
0.04265330359339714,
0.008250514045357704,
-0.007611975539475679,
-0.00053812051191926,
-0.006139538250863552,
-0.00814098585397005,
0.0818653479218483,
0.008962481282651424,
-0.001979258842766285,
-0.016106203198432922,
-0.003224525600671768,
-0.004911845549941063,
-0.051307667046785355,
-0.07114715874195099,
-0.012557395733892918,
-0.004160336218774319,
-0.032580677419900894,
-0.026828909292817116,
-0.02276892215013504,
-0.010648802854120731,
-0.01322160568088293,
0.05484870448708534,
-0.0007821628823876381,
0.071738600730896,
-0.02220359817147255,
0.06007038801908493,
-0.0407230481505394,
-0.0435333289206028,
0.023017100989818573,
0.02174166403710842,
-0.04061632975935936,
-0.017324816435575485,
0.009591423906385899,
0.03274758905172348,
-0.03574374318122864,
-0.007724864408373833,
0.009697006084024906,
0.05712243542075157,
-0.026498695835471153,
-0.0859481543302536,
-0.0635562539100647,
0.03702844679355621,
-0.0006841159192845225,
0.01784975826740265,
-0.03892283886671066,
0.0018062758026644588,
0.048912279307842255,
0.08184310048818588,
0.005592335481196642,
0.02915836125612259,
0.011517561040818691,
0.04107210412621498,
-0.004297169856727123,
-0.009505964815616608,
-0.03780732303857803,
-0.0158951748162508,
-0.017576156184077263,
-0.028625711798667908,
-0.07916032522916794,
0.025727439671754837,
0.020448148250579834,
0.003523794235661626,
-0.03529614955186844,
0.07064230740070343,
0.016125446185469627,
0.023006673902273178,
0.022513266652822495,
0.0018128962256014347,
-0.011819155886769295,
0.05932451784610748,
0.005226392298936844,
-0.032060809433460236,
0.04994496330618858,
0.05256476253271103,
0.01883045956492424,
0.020663155242800713,
0.0008524974691681564,
0.032950714230537415,
-0.049131784588098526,
0.0057347798720002174,
-0.010812092572450638,
-0.018708568066358566,
0.006396738812327385,
-0.005774973891675472,
-0.10809007287025452,
-0.005626460537314415,
0.008702680468559265,
0.011794948019087315,
0.05650216341018677,
-0.015856942161917686,
-0.012437879107892513,
-0.024377668276429176,
-0.0231041070073843,
0.003524780971929431,
-0.04143047705292702,
0.04198291525244713,
-0.021198412403464317,
0.00007750718214083463,
-0.008881820365786552,
-0.002914467127993703,
0.03872325271368027,
-0.0158012043684721,
0.0033054121304303408,
0.018385786563158035,
0.02683289907872677,
-0.03102366253733635,
0.002192610874772072,
0.023859476670622826,
0.020275723189115524,
0.022866029292345047,
0.03070196881890297,
-0.0006144254584796727,
-0.014394357800483704,
-0.02628708817064762,
-0.01960606873035431,
-0.014410714618861675,
0.04072866216301918,
0.012281853705644608,
-0.0016870277468115091,
0.004351975861936808,
0.01024157740175724,
0.012442845851182938,
0.05248536542057991,
-0.016748996451497078,
0.08070573955774307,
0.06128056347370148,
0.022994738072156906,
0.030916742980480194,
0.0428469218313694,
0.030047355219721794,
0.00858383160084486,
-0.0024298641365021467,
-0.027232741937041283,
-0.04738985747098923,
0.0016047165263444185,
0.04344440624117851,
0.0125046968460083,
-0.03201831877231598,
0.014950293116271496,
0.06538816541433334,
0.048013973981142044,
0.020613383501768112,
0.018099842593073845,
-0.023177597671747208,
-0.04613832011818886,
0.0050546517595648766,
0.04663841053843498,
-0.02862805500626564,
0.0011077399831265211,
0.007868397980928421,
0.028438454493880272,
-0.010849935002624989,
0.020563628524541855,
-0.011940301395952702,
0.037057045847177505,
-0.03945546597242355,
0.008136698044836521,
-0.006393900606781244,
-0.023612022399902344,
0.08208007365465164,
-0.052105486392974854,
0.0501539520919323,
0.059561073780059814,
0.03310708329081535,
-0.015629397705197334,
-0.04818763956427574,
0.006223957985639572,
0.02214742824435234,
0.0030370077583938837,
-0.015514500439167023,
0.0016523452941328287,
0.028510652482509613,
-0.02415337972342968,
-0.001425091060809791,
-0.03564212843775749,
0.005278952419757843,
-0.043986283242702484,
0.009014955721795559,
-0.0011939997784793377,
0.033318791538476944,
0.028885168954730034,
-0.018776986747980118,
-0.0318395234644413,
-0.0056296116672456264,
-0.03400314971804619,
-0.017796654254198074,
0.03059191256761551,
-0.040538571774959564,
0.024710411205887794,
-0.01849411614239216,
-0.005436985287815332,
0.06490827351808548,
0.0056422497145831585,
-0.03163009509444237,
0.008427729830145836,
-0.0021959880832582712,
-0.018923435360193253,
-0.023591460660099983,
-0.013408191502094269,
-0.0015734991757199168,
-0.056760214269161224,
-0.004913321230560541,
0.01762266457080841,
0.029684748500585556,
-0.00996225606650114,
0.057316701859235764,
-0.05496015399694443,
-0.05257388949394226,
0.00781603716313839,
0.025918303057551384,
0.02802859991788864,
-0.030769599601626396,
0.04323067516088486,
-0.011833681724965572,
-0.011767631396651268,
-0.01160125806927681,
-0.06291748583316803,
-0.02624405175447464,
-0.02316388674080372,
0.009340889751911163,
0.029586486518383026,
0.011060811579227448,
-0.05297099053859711,
0.09211664646863937,
0.003072798717767,
-0.012597771361470222,
-0.027955830097198486,
0.009750163182616234,
0.000759728136472404,
-0.0296744704246521,
-0.012237222865223885,
0.005501968786120415,
-0.02899119257926941,
-0.03803165256977081,
0.04092172905802727,
0.0005708331009373069,
0.05257205665111542,
-0.007578530814498663,
0.010819880291819572,
0.037898894399404526,
0.014039803296327591,
-0.008039464242756367,
0.06083230674266815,
0.011187049560248852,
0.03705151379108429,
0.016213783994317055,
-0.0206198301166296,
0.026566343382000923,
-0.03167465329170227,
-0.08232367783784866,
0.03224758431315422,
-0.032900840044021606,
-0.01526651345193386,
0.0013373608235269785,
0.03343578800559044,
-0.018597999587655067,
-0.008382245898246765,
0.032413434237241745,
0.023256678134202957,
0.05324084311723709,
-0.021552016958594322,
-0.024193715304136276,
0.03701895847916603,
0.03687398135662079,
-0.017333680763840675,
-0.057191312313079834,
-0.00625190744176507,
0.0044535016641020775,
0.06118754297494888,
-0.02860988676548004,
-0.026037145406007767,
0.016591118648648262,
0.010157576762139797,
0.023462260141968727,
-0.0004954233882017434,
-0.03378397598862648,
0.008310209028422832,
-0.05429540202021599,
-0.003390856320038438,
-0.008249081671237946,
0.02681436389684677,
0.008467476814985275,
0.04419468715786934,
0.04084700718522072,
0.02113942615687847,
0.043643224984407425,
0.03069734200835228,
-0.09908842295408249,
0.021602995693683624,
-0.040664564818143845,
-0.027630044147372246,
0.009114990010857582,
-0.008418379351496696,
-0.01524489838629961,
-0.0075482758693397045,
0.018006673082709312,
0.007830717600882053,
0.0014192642411217093,
-0.06853736937046051,
0.003770642913877964,
-0.03290834277868271,
-0.005360416602343321,
-0.013458753004670143,
0.02070138230919838,
0.027647890150547028,
-0.020134111866354942,
0.02351638302206993,
0.06483113020658493,
-0.013918437995016575,
0.027404531836509705,
-0.04774836450815201,
-0.0007115336484275758,
0.013547627255320549,
0.025234274566173553,
0.03379300981760025,
0.013542236760258675,
-0.0018543732585385442,
-0.018136339262127876,
-0.023839738219976425,
0.04822757840156555,
0.007545586209744215,
0.008142680861055851,
-0.00015960994642227888,
-0.06515352427959442,
-0.01795436628162861,
-0.004514104221016169,
0.059074532240629196,
-0.022061437368392944,
-0.022450506687164307,
0.04217960312962532,
-0.016640448942780495,
0.011345316655933857,
0.023186009377241135,
0.06000804901123047,
0.0006231427541933954,
-0.035339727997779846,
-0.05176028981804848,
-0.014203389175236225,
-0.02347670868039131,
-0.021784188225865364,
-0.00587620260193944,
-0.017626749351620674,
-0.03452540561556816,
-0.010875335894525051,
0.050737105309963226,
0.028588339686393738,
0.026303879916667938,
0.021024374291300774,
-0.007135202642530203,
0.040794629603624344,
-0.007617462892085314,
-0.011630930006504059,
0.011119943112134933,
0.0140741728246212,
0.028971713036298752,
-0.008010398596525192,
-0.02158297598361969,
-0.0897158831357956,
-0.04568236321210861,
0.03593127802014351,
0.0376276932656765,
-0.0006965406937524676,
-0.04100284352898598,
-0.046805720776319504,
-0.023537088185548782,
0.07916226238012314,
-0.001395144034177065,
0.053469009697437286,
-0.005186681170016527,
0.022886812686920166,
0.0022366647608578205,
-0.052505552768707275,
-0.057343676686286926,
0.019138718023896217,
-0.013935872353613377,
0.012960563413798809,
-0.034912869334220886,
0.016368921846151352,
-0.01031098049134016,
0.012439045123755932,
0.012421377934515476,
0.01303446851670742,
0.025499608367681503,
-0.03174971044063568,
-0.017769061028957367,
-0.002343570813536644,
-0.012473542243242264,
-0.056228820234537125,
-0.0004941842053085566,
0.0014636064879596233,
-0.029703591018915176,
-0.00719053391367197,
-0.02355804666876793,
-0.04321770742535591,
0.05202895402908325,
-0.009603338316082954,
0.03593827039003372,
0.021878506988286972,
-0.03329496458172798,
0.01113203726708889,
0.047681476920843124,
-0.007485535461455584,
0.04260731488466263,
0.026408322155475616,
-0.007714754436165094,
0.005672365892678499,
0.027285609394311905,
0.02587410807609558,
-0.0005445017595775425,
-0.03290524706244469,
0.019032757729291916,
0.004748190753161907,
-0.06923326104879379,
0.04824300855398178,
0.029953474178910255,
0.015241608023643494,
-0.03224817290902138,
-0.023939041420817375,
0.011843705549836159,
0.03890152648091316,
0.024445628747344017,
-0.007713330443948507,
0.030358418822288513,
-0.0000015818696965652634,
-0.00147266685962677,
-0.023284563794732094,
-0.015506121329963207,
-0.024039026349782944,
-0.0051858993247151375,
0.03137771040201187,
-0.011348565109074116,
-0.005235024727880955,
-0.011383574455976486,
-0.016596533358097076,
0.014358188025653362,
-0.09086977690458298,
0.08069206029176712,
-0.02759726345539093,
-0.006246705073863268,
0.015679214149713516,
-0.05058471858501434,
-0.04975474998354912,
-0.008093098178505898,
0.005731134209781885,
0.01975454017519951,
-0.040363915264606476,
-0.0163804329931736,
0.008019401691854,
0.02781463786959648,
-0.05566025525331497,
-0.042526327073574066,
0.00366193731315434,
0.0037456380669027567,
-0.026160813868045807,
-0.0057583958841860294,
0.026776442304253578,
-0.025337688624858856,
-0.04488906264305115,
-0.021559225395321846,
0.05461500212550163,
-0.020545929670333862,
0.034385647624731064,
-0.0018280853983014822,
0.027156127616763115,
0.04565909132361412,
-0.0022805489134043455,
0.003659395733848214,
0.013540158048272133,
-0.026042314246296883,
0.005402728449553251,
0.008719081059098244,
0.05541844293475151,
-0.020766856148838997,
-0.04265163093805313,
-0.023530263453722,
-0.00017641126760281622,
0.030446283519268036,
0.015748461708426476,
-0.018472515046596527,
0.03199853003025055,
0.03292131423950195,
-0.00996557530015707,
-0.008941475301980972,
0.026524502784013748,
0.0294813122600317,
0.011917856521904469,
-0.023500092327594757,
0.007964443415403366,
-0.03302888572216034,
-0.03192136436700821,
0.007293621078133583,
-0.010664671659469604,
-0.01728389970958233,
-0.0074079809710383415,
0.06157872453331947,
0.00046272113104350865,
0.01913069561123848,
0.030782468616962433,
0.009501743130385876,
0.017892824485898018,
-0.0011666456703096628,
-0.027065183967351913,
0.05811652913689613,
-0.025724705308675766,
-0.04552082717418671,
-0.0102717699483037,
-0.002521699760109186,
0.01321715023368597,
0.08694499731063843,
-0.023690806701779366,
0.07048259675502777,
-0.0218556709587574,
0.015268250368535519,
0.015861105173826218,
-0.0052991886623203754,
-0.01923154480755329,
-0.0006674079340882599,
0.019782716408371925,
0.02122485637664795,
-0.024718964472413063,
0.020282024517655373,
0.029352638870477676,
0.028079651296138763,
-0.01940971054136753,
0.012900277972221375,
0.006257238332182169,
0.03482462838292122,
0.016811810433864594,
0.02284267544746399,
-0.018784377723932266,
0.004009202588349581,
0.021699069067835808,
0.05508885532617569,
-0.022100118920207024,
0.0024320033844560385,
0.04373427480459213,
0.04294554516673088,
0.02247532270848751,
-0.03580436855554581,
-0.003512784605845809,
-0.038279883563518524,
-0.0035598520189523697,
0.05424154922366142,
-0.03599025681614876,
0.009421796537935734,
0.027529893442988396,
0.013380919583141804,
-0.016531161963939667,
0.04774564877152443,
-0.03103215992450714,
-0.04253013804554939,
-0.027126789093017578,
-0.047101911157369614,
-0.08045528829097748,
0.05732778459787369,
-0.0006117349257692695,
-0.020563233643770218,
0.045007605105638504,
-0.027220845222473145,
-0.008287024684250355,
0.03604242578148842,
0.02663077600300312,
-0.002677443902939558,
0.10279284417629242,
-0.02102729119360447,
0.018411913886666298,
-0.03064926527440548,
0.013616061769425869,
0.10266504436731339,
0.04555772989988327,
0.017697632312774658,
-0.01687885820865631,
0.014282283373177052,
-0.00748467119410634,
0.005594537127763033,
-0.05179440975189209,
0.026976795867085457,
0.0011842811945825815,
-0.02715318277478218,
0.00942427758127451,
0.039605338126420975,
-0.0548827163875103,
-0.005724120885133743,
0.050361864268779755,
-0.017777400091290474,
-0.02307717688381672,
-0.02882988750934601,
0.005006580147892237,
0.008875062689185143,
0.019836245104670525,
-0.041163548827171326,
0.0466274730861187,
-0.03244509920477867,
-0.010700944811105728,
-0.033556848764419556,
-0.029666848480701447,
0.020749246701598167,
-0.03534885123372078,
-0.0594971738755703,
0.0191628597676754,
-0.004633984062820673,
-0.021745901554822922,
-0.024004606530070305,
0.014007068239152431,
0.014461178332567215,
0.01417543925344944,
0.033001914620399475,
0.031895436346530914,
-0.003484558081254363,
0.01514647901058197,
-0.002805430442094803,
-0.005151120480149984,
-0.03586363419890404,
0.010000674985349178,
-0.021605515852570534,
0.061329346150159836,
-0.003884626319631934,
0.0035515432246029377,
0.021054353564977646,
-0.004944995045661926,
0.003922960255295038,
-0.04350503906607628,
0.010025762021541595,
-0.02207380160689354,
-0.0042318664491176605,
0.007245370652526617,
0.023934917524456978,
0.005665229167789221,
0.0024489210918545723,
0.03486429899930954,
0.013036878779530525,
-0.013313530012965202,
0.014938660897314548,
-0.030959444120526314,
-0.02308553084731102,
0.061946529895067215,
-0.025824720039963722,
-0.033232469111680984,
0.017728254199028015,
-0.03495488688349724,
-0.023677034303545952,
0.01540262158960104,
-0.008589046075940132,
0.0035286233760416508,
0.021937638521194458,
0.009559678845107555,
0.0038250277284532785,
-0.004810936748981476,
-0.03952578082680702,
0.009354178793728352,
0.00910763069987297,
-0.027049127966165543,
-0.030627083033323288,
0.0034537932369858027,
0.014130319468677044,
0.019237013533711433,
-0.012011381797492504,
0.015367737039923668,
-0.00564899668097496,
0.02710685320198536,
0.01502110157161951,
-0.021641749888658524,
-0.02665126323699951,
-0.021625816822052002,
-0.0012183908838778734,
0.006608058698475361,
-0.03228452801704407,
0.01928645931184292,
0.013597294688224792,
0.043692316859960556,
-0.04647362604737282,
0.04514415189623833,
0.0075463829562067986,
0.03157348185777664,
0.00706017529591918,
-0.01946760155260563,
-0.0022753532975912094,
0.003962802700698376,
-0.014456397853791714,
-0.05002913996577263,
0.01842721737921238,
-0.008701915852725506,
-0.009924020618200302,
0.003023613942787051,
-0.0003608484985306859,
-0.02317233383655548,
0.06309029459953308,
-0.011106946505606174,
0.008903063833713531,
-0.04758601263165474,
0.02354777231812477,
-0.05088525637984276,
-0.03015066497027874,
-0.02431057021021843,
0.0003694047045428306,
-0.029406147077679634,
0.05359417200088501,
-0.05111176520586014,
-0.03534908965229988,
-0.02490164153277874,
0.021837258711457253,
-0.00856686756014824,
-0.004218938294798136,
0.007134983316063881,
0.0012347680749371648,
0.04923723638057709,
0.013012352399528027,
-0.04448379576206207,
-0.007478426210582256,
-0.0033393320627510548,
-0.0013518957421183586,
0.03259113430976868,
-0.014441587962210178,
0.06023869663476944,
0.011498135514557362,
-0.07126094400882721,
0.008485980331897736,
0.04300845041871071,
0.01863773725926876,
-0.024672146886587143,
-0.008079382590949535,
-0.060079120099544525,
-0.005325682461261749,
-0.024480246007442474,
0.010156978853046894,
-0.03458094969391823,
0.012338579632341862,
0.0035845020320266485,
0.0214527677744627,
-0.030513061210513115,
-0.00866201426833868,
0.029241900891065598,
0.01573922485113144,
0.025259384885430336,
0.021569613367319107,
0.007218158338218927,
0.06460846960544586,
0.030214853584766388,
-0.037359461188316345,
0.012728773057460785,
0.00920290406793356,
0.03217763453722,
-0.06434154510498047,
-0.02187889628112316,
0.002187000121921301,
0.01288895308971405,
0.04313268885016441,
-0.07269230484962463,
-0.011164678260684013,
0.020920448005199432,
-0.05645274370908737,
-0.022654671221971512,
-0.01209336519241333,
0.007812330964952707,
0.006661186460405588,
-0.03679283708333969,
0.022714320570230484,
0.003963216673582792,
0.017619140446186066,
0.052585847675800323,
0.017806408926844597,
0.008587361313402653,
-0.0584384948015213,
-0.045208703726530075,
0.030436323955655098,
0.030664687976241112,
-0.003768610069528222,
-0.01549717877060175,
0.08559153228998184,
-0.006220567971467972,
-0.020712830126285553,
0.01566629856824875,
-0.02200109139084816,
0.008215117268264294,
-0.0016898784087970853,
0.041335053741931915,
0.024883471429347992,
0.017985505983233452,
-0.02790233865380287,
0.0029717858415097,
0.014030965976417065,
0.01601969636976719,
0.03566167876124382,
-0.003565435763448477,
-0.04030874744057655,
-0.0074737477116286755,
0.013220379129052162,
-0.01717807911336422,
-0.05517498031258583,
0.024047598242759705,
-0.0547504723072052,
-0.013764195144176483,
0.0014655328122898936,
-0.007230775896459818,
-0.028710126876831055,
-0.04067666083574295,
-0.033458005636930466,
-0.03649718686938286,
0.026887552812695503,
0.04113006591796875,
-0.030170179903507233,
0.008638386614620686,
-0.00403250427916646,
0.010432817973196507,
-0.004428578075021505,
0.023694828152656555,
-0.017713384702801704,
-0.03364506736397743,
-0.05638732388615608,
0.021007806062698364,
-0.012144983746111393,
-0.012923750095069408,
0.014916353859007359,
-0.022813502699136734,
-0.0012965321075171232,
0.025325506925582886,
0.010865903459489346,
-0.002550760516896844,
0.01867973431944847,
-0.026847610250115395,
0.008123747073113918,
-0.09273643791675568,
0.004765798803418875,
0.00781513936817646,
-0.06959029287099838,
-0.008290747180581093,
-0.034987229853868484,
0.021844597533345222,
0.003931065090000629,
0.0380074679851532,
-0.026339929550886154,
0.0035668390337377787,
0.06307576596736908,
-0.005298876203596592,
-0.014988171868026257,
-0.03393474966287613,
0.0025199998635798693,
0.004407982341945171,
-0.009065428748726845,
0.022784952074289322,
-0.003959004767239094,
0.01574900932610035,
-0.009167096577584743,
0.00038615745143033564,
0.017234982922673225,
0.0377696193754673,
0.000284930516500026,
-0.0371345579624176,
0.003418253967538476,
-0.01906413771212101,
-0.03674556314945221,
0.08007514476776123,
0.001998845487833023,
-0.004415328148752451,
0.02039211429655552,
-0.025705179199576378,
-0.023134838789701462,
0.05297049880027771,
-0.043324194848537445,
0.0032855935860425234,
-0.017785068601369858,
-0.02018251083791256,
0.007743521127849817,
-0.04898298159241676,
-0.0288222786039114,
0.025066636502742767,
-0.040821053087711334,
0.004337305203080177,
0.04041098430752754,
0.0194895938038826,
0.03372344747185707,
-0.009944799356162548,
0.01640775427222252,
0.04415252432227135,
-0.01000011246651411,
0.010720223188400269,
0.015974977985024452,
0.023770896717905998,
-0.00813727080821991,
-0.026429129764437675,
0.05198996141552925,
-0.01786457933485508,
0.023761633783578873,
-0.01426963321864605,
0.01724107749760151,
-0.032301802188158035,
-0.03655950725078583,
-0.004679254721850157,
-0.04785028472542763,
-0.016954639926552773,
-0.004092703107744455,
-0.022047258913517,
0.038076307624578476,
-0.0012092612450942397,
-0.008204810321331024,
0.014886260963976383,
-0.004405230283737183,
-0.021198654547333717,
0.049604225903749466,
-0.0007679878617636859,
0.011476319283246994,
-0.0008513409411534667,
-0.011771748773753643,
0.0072670066729187965,
-0.038943178951740265,
0.03542627394199371,
0.028921492397785187,
0.016408095136284828,
0.025588195770978928,
-0.001428005169145763,
0.015969181433320045,
-0.05139641463756561,
-0.02833642065525055,
-0.023545745760202408,
0.07478010654449463,
0.02042345516383648,
0.010754244402050972,
-0.017494631931185722,
-0.010574650019407272,
-0.03223591670393944,
0.048408329486846924,
-0.06480859220027924,
-0.022013623267412186,
-0.002747340127825737,
0.01252913661301136,
0.011999905109405518,
-0.048596419394016266
] |
<p>In Peskin and Schroeder's QFT book, page 189, equation 6.38, how do they get from the first line to the second line?</p>
<p>In particular, I am stuck on the transition from what I perceive to be:
$$ k'_\alpha \gamma^\alpha m \gamma^\mu + m k_\alpha \gamma^\alpha \gamma^\mu $$
into:
$$ -2m(k+k')^\mu $$</p>
<p>what am I missing?</p>
<p>I thought it might be using the Dirac equation because it works on $u(p)$, but that can't be it since $k\neq p$. Also couldn't figure out how to use the anticommutation relations of the gamma matrices.</p> | 2,020 | [
0.02157306857407093,
-0.014414435252547264,
0.00481669744476676,
-0.00539783202111721,
-0.0025085138622671366,
0.01008810754865408,
-0.04380008578300476,
-0.01687195897102356,
-0.018051128834486008,
-0.054998889565467834,
0.029786288738250732,
0.0028053210116922855,
0.0557207316160202,
0.009460107423365116,
0.018218662589788437,
0.04206310585141182,
-0.025195378810167313,
-0.016627095639705658,
0.0029532131738960743,
-0.055660881102085114,
0.0031401407904922962,
0.0387762114405632,
-0.007299536373466253,
0.010188487358391285,
-0.009022950194776058,
0.0364212729036808,
-0.004707940388470888,
0.026805730536580086,
0.008261069655418396,
0.04285847768187523,
-0.028795380145311356,
-0.06624028831720352,
0.024042708799242973,
0.0002477057569194585,
0.020162949338555336,
0.02943234331905842,
0.007960574701428413,
-0.028459159657359123,
-0.007442518137395382,
0.013951089233160019,
-0.044590651988983154,
-0.033069539815187454,
-0.023252569139003754,
0.0021286916453391314,
-0.0061097294092178345,
-0.01364026591181755,
0.014986536465585232,
0.015218045562505722,
0.04668716713786125,
-0.054605163633823395,
0.08316124230623245,
0.03980400785803795,
0.005910481791943312,
0.03595840558409691,
-0.011610463261604309,
0.018347715958952904,
0.05127941444516182,
0.07204331457614899,
0.03131237253546715,
-0.03276417776942253,
-0.0017171758227050304,
-0.03271465003490448,
-0.021045321598649025,
-0.03665726259350777,
-0.026439545676112175,
0.019912047311663628,
0.017650628462433815,
0.02921251393854618,
0.035372793674468994,
0.004743080120533705,
0.01294946949928999,
0.022647196426987648,
0.06932925432920456,
-0.012717066332697868,
0.03803876414895058,
-0.020084509626030922,
-0.014588387683033943,
0.011766958050429821,
0.041244056075811386,
0.024823859333992004,
-0.002877461025491357,
0.038266364485025406,
0.011237960308790207,
-0.006037644576281309,
-0.02163161337375641,
-0.015460873022675514,
0.06925719976425171,
0.04462810605764389,
0.004765544552356005,
0.044698216021060944,
-0.017428981140255928,
0.00758036132901907,
-0.0024256811011582613,
-0.005617023445665836,
0.003130617318674922,
0.04813532531261444,
-0.004760276060551405,
0.04461061581969261,
0.01602223329246044,
-0.01304689235985279,
-0.016577990725636482,
-0.0037875317502766848,
0.030571434646844864,
0.06746772676706314,
0.017120791599154472,
0.03516640514135361,
-0.04330509155988693,
0.02637339010834694,
-0.005896652117371559,
-0.060019493103027344,
-0.03521377965807915,
-0.004918830469250679,
-0.03433974087238312,
-0.022410312667489052,
-0.01459478959441185,
-0.04855559393763542,
-0.0020929204765707254,
-0.004580031614750624,
0.05245057865977287,
0.0778777003288269,
0.017240244895219803,
-0.005694339517503977,
0.029679998755455017,
-0.04077909141778946,
-0.10633407533168793,
-0.003858688985928893,
0.05083678290247917,
-0.028425592929124832,
-0.0473698265850544,
0.0052797263488173485,
-0.01652015559375286,
-0.02150958776473999,
0.006645152345299721,
0.0011713783023878932,
0.012257338501513004,
-0.029393887147307396,
-0.10979772359132767,
-0.06390570104122162,
0.0034602333325892687,
-0.010993477888405323,
0.020804764702916145,
-0.04339002072811127,
0.005680369678884745,
0.06597231328487396,
0.108647421002388,
-0.028760742396116257,
-0.022889697924256325,
-0.007522481959313154,
0.0150581244379282,
0.00011945306323468685,
-0.008274017833173275,
-0.03180314600467682,
-0.028657205402851105,
-0.01323582511395216,
0.005844559520483017,
-0.022951243445277214,
0.02916007675230503,
0.036346450448036194,
0.012195670045912266,
-0.012671130709350109,
0.08826401829719543,
-0.012618730776011944,
0.005503815598785877,
0.00045776739716529846,
-0.025080671533942223,
-0.00910310447216034,
0.07253509014844894,
0.049561984837055206,
-0.009835567325353622,
0.023253563791513443,
0.02543875016272068,
0.013111171312630177,
-0.006119125988334417,
0.03812948241829872,
0.026205796748399734,
-0.000984523561783135,
-0.027437131851911545,
0.0009319346281699836,
0.013023316860198975,
-0.020440293475985527,
-0.041432175785303116,
-0.03245056793093681,
0.011268476955592632,
0.04257854074239731,
-0.004021572880446911,
0.0011627227067947388,
-0.03558811545372009,
0.0254460871219635,
0.0005122348084114492,
-0.04275621473789215,
-0.05265697464346886,
-0.06098473072052002,
0.015670079737901688,
-0.013164546340703964,
-0.0015636057360097766,
0.04278334230184555,
-0.01957632414996624,
0.01443446148186922,
-0.021034443750977516,
-0.0790393128991127,
0.0073350765742361546,
-0.007073559798300266,
0.014880487695336342,
-0.017374923452734947,
0.016182277351617813,
0.04100540652871132,
0.04607895761728287,
0.0035209394991397858,
0.04925572872161865,
-0.05302160233259201,
0.0335751548409462,
0.02328682877123356,
0.010343898087739944,
-0.006679120939224958,
-0.03618098795413971,
0.004687120206654072,
0.01987774483859539,
-0.002208785153925419,
0.00443556671962142,
-0.003249409841373563,
-0.046001091599464417,
0.03445848450064659,
0.05133131146430969,
0.0345105342566967,
0.013151359744369984,
0.046800803393125534,
-0.009701276198029518,
0.04113070294260979,
-0.007363947574049234,
-0.0742693692445755,
-0.021151522174477577,
-0.0042363847605884075,
0.017998727038502693,
-0.015188494697213173,
-0.04073932394385338,
0.02237040363252163,
0.00040025595808401704,
0.05556603521108627,
0.004508759826421738,
0.02123374305665493,
-0.008891494013369083,
-0.0004008589603472501,
0.004085439722985029,
-0.01550049427896738,
-0.02342621423304081,
-0.016912471503019333,
0.030353231355547905,
-0.0008467559237033129,
-0.0005670625832863152,
0.015592620708048344,
-0.03486296162009239,
0.017402634024620056,
-0.04363997280597687,
-0.010975717566907406,
-0.013838578015565872,
-0.06459959596395493,
0.035274896770715714,
-0.01727127656340599,
0.019038520753383636,
0.027569301426410675,
-0.0003319690003991127,
-0.00027484173187986016,
-0.021168263629078865,
-0.011306613683700562,
0.04028313606977463,
-0.02776927314698696,
-0.010331600904464722,
-0.012800449505448341,
0.00931569840759039,
-0.04089898243546486,
0.0003075379936490208,
0.0051063718274235725,
-0.02179611101746559,
-0.004785780794918537,
0.001704211812466383,
0.04962252452969551,
0.01813095435500145,
0.027179621160030365,
-0.035606324672698975,
-0.043176088482141495,
0.021830685436725616,
-0.004981142934411764,
0.05396796017885208,
0.047071442008018494,
-0.049386609345674515,
0.008229733444750309,
-0.0554133877158165,
-0.04578043892979622,
0.052107661962509155,
0.0006322021363303065,
0.0015913688112050295,
0.00650343531742692,
-0.01645483449101448,
-0.04082489013671875,
-0.03788736090064049,
0.008661304600536823,
-0.010223698802292347,
-0.00176796515006572,
0.02251671440899372,
0.03874592110514641,
0.032018061727285385,
-0.011957601644098759,
0.006485197693109512,
-0.03788037598133087,
-0.06061943992972374,
-0.028285328298807144,
0.014436326920986176,
0.028137385845184326,
-0.024139519780874252,
0.05349038168787956,
0.020721105858683586,
-0.026576848700642586,
0.028869621455669403,
-0.05868563801050186,
-0.008173065260052681,
0.012188652530312538,
-0.007849548012018204,
-0.012113846838474274,
-0.0025948716793209314,
-0.03397736698389053,
0.09323535114526749,
0.02963598445057869,
-0.023947186768054962,
-0.01729712262749672,
0.014066559262573719,
-0.009194822050631046,
-0.08454088121652603,
-0.01298126857727766,
0.03463657572865486,
-0.013274379074573517,
0.01800953783094883,
0.005222742445766926,
0.027429969981312752,
0.019241511821746826,
-0.031918901950120926,
-0.025241779163479805,
0.004660646431148052,
-0.022898279130458832,
0.011459678411483765,
0.019375188276171684,
-0.028513208031654358,
-0.008146032691001892,
0.0016591573366895318,
0.018546126782894135,
0.0096571184694767,
-0.009336610324680805,
-0.03384320065379143,
0.05236262455582619,
-0.0057073659263551235,
0.013339828699827194,
-0.03626926615834236,
0.01984815113246441,
0.0025168342981487513,
-0.05679623782634735,
-0.012156663462519646,
0.0034365514293313026,
0.02516012080013752,
-0.03081691823899746,
0.01285307016223669,
0.013359066098928452,
0.03275534510612488,
-0.025195548310875893,
-0.01265137828886509,
-0.025291910395026207,
-0.02883867174386978,
0.020432332530617714,
0.011002730578184128,
0.008419331163167953,
0.05689302459359169,
0.038877710700035095,
0.011225126683712006,
-0.008733398281037807,
-0.052924010902643204,
-0.02727927640080452,
-0.0434732548892498,
0.00013117252092342824,
-0.015900572761893272,
0.050173964351415634,
0.02964480035007,
0.04203016310930252,
0.052614904940128326,
0.01694784127175808,
0.010571092367172241,
0.018233846873044968,
-0.07400642335414886,
0.03597364202141762,
-0.03213631734251976,
-0.020618531852960587,
0.02686578966677189,
-0.01724838651716709,
-0.002881849417462945,
-0.016090823337435722,
-0.06028057262301445,
0.0068557714112102985,
-0.04553398862481117,
-0.0652838870882988,
0.02696698158979416,
-0.08417676389217377,
-0.011203932575881481,
0.0012812146451324224,
0.00582145107910037,
0.06304372847080231,
-0.02494807355105877,
-0.025035738945007324,
0.013417805545032024,
-0.04920676723122597,
0.015671713277697563,
-0.03084716387093067,
0.017026415094733238,
0.010482948273420334,
0.010082549415528774,
0.025159141048789024,
0.003101342124864459,
-0.013561761006712914,
0.010729447938501835,
0.0139179527759552,
0.0691465511918068,
0.010114557109773159,
-0.032825734466314316,
-0.0036975229158997536,
-0.05366140976548195,
-0.017863022163510323,
0.003536644158884883,
0.07368892431259155,
0.014261341653764248,
0.01476580835878849,
0.04900921881198883,
0.015066513791680336,
-0.018387962132692337,
0.028968999162316322,
0.07580879330635071,
0.012525638565421104,
-0.037248965352773666,
-0.03979048132896423,
-0.005303888116031885,
0.024929866194725037,
-0.009280024096369743,
-0.019181346520781517,
-0.0157408956438303,
-0.026080897077918053,
-0.008097074925899506,
0.04559064656496048,
-0.015728535130620003,
-0.019832922145724297,
-0.004082776140421629,
0.009594751521945,
-0.013919953256845474,
0.00034095911541953683,
-0.038130924105644226,
0.016889093443751335,
0.038223665207624435,
0.03168196603655815,
-0.0005813877796754241,
0.01937226951122284,
-0.033597927540540695,
-0.009393563494086266,
0.034893378615379333,
0.026507098227739334,
0.028834765776991844,
-0.033181674778461456,
-0.07900271564722061,
0.0004157444345764816,
0.02304193004965782,
0.00027865185984410346,
0.036060038954019547,
0.035467419773340225,
0.010664592497050762,
0.012854520231485367,
-0.011818252503871918,
-0.05813514068722725,
0.054785825312137604,
0.015546808019280434,
-0.0068818628787994385,
-0.0399077832698822,
0.018380915746092796,
-0.017950482666492462,
0.036319516599178314,
0.01198835764080286,
0.06706605851650238,
-0.012071041390299797,
0.008355319499969482,
0.020063500851392746,
0.021558156237006187,
-0.025661977007985115,
-0.07817960530519485,
0.023714808747172356,
0.019179336726665497,
-0.016525501385331154,
0.03483446314930916,
-0.030702756717801094,
-0.02944779396057129,
0.0204685740172863,
0.0301518477499485,
-0.009022718295454979,
-0.009970743209123611,
-0.0741603747010231,
0.07060598582029343,
0.012499512173235416,
0.007311981171369553,
0.0751267597079277,
0.01889321580529213,
-0.01278771460056305,
0.0002791575388982892,
-0.023924220353364944,
0.04314197972416878,
0.014274169690907001,
0.02855715900659561,
-0.03756525367498398,
0.010954337194561958,
-0.014881678856909275,
0.04412512108683586,
-0.009223060682415962,
0.02070106565952301,
0.0027999943122267723,
-0.02382219396531582,
-0.05517108738422394,
0.010882464237511158,
-0.038678184151649475,
0.013152185827493668,
0.017875811085104942,
0.037994157522916794,
0.02665569633245468,
-0.02148117683827877,
0.03839933127164841,
-0.023284943774342537,
0.0031989708077162504,
0.05015631020069122,
-0.020665274932980537,
0.010262384079396725,
-0.009678970091044903,
-0.0390053354203701,
-0.0053781066089868546,
-0.021434228867292404,
0.048716627061367035,
-0.013975922018289566,
-0.0487058088183403,
0.005647361744195223,
-0.013682329095900059,
-0.034022919833660126,
-0.015228117816150188,
-0.025900710374116898,
-0.00661035580560565,
-0.04520457237958908,
0.038757503032684326,
0.04308466240763664,
0.016891418024897575,
-0.09541171789169312,
-0.044117167592048645,
0.027380729094147682,
-0.013741669245064259,
-0.01861828751862049,
-0.007187897805124521,
-0.0011451739119365811,
-0.022871840745210648,
-0.041660457849502563,
0.020531151443719864,
0.015297343023121357,
-0.03257868066430092,
0.007774072233587503,
0.010376131162047386,
0.03403015434741974,
0.0225821565836668,
0.01469420362263918,
-0.002317059086635709,
0.02500317245721817,
-0.036522746086120605,
0.0015893845120444894,
0.029915079474449158,
0.04796352609992027,
0.021260477602481842,
-0.020360231399536133,
-0.03207036107778549,
0.0171482115983963,
0.026976052671670914,
-0.04572342336177826,
0.01102505624294281,
0.042164146900177,
0.025359472259879112,
0.022695990279316902,
-0.03270353376865387,
-0.03336283937096596,
0.0002912711934186518,
0.04128105193376541,
0.027384327724575996,
-0.015631435438990593,
-0.032461296766996384,
-0.023807084187865257,
0.06301075965166092,
-0.011415926739573479,
0.03501642495393753,
0.012301799841225147,
0.10428497195243835,
-0.027645723894238472,
0.0038784327916800976,
0.015815310180187225,
-0.010957475751638412,
0.018243683502078056,
0.03993493691086769,
0.02086682617664337,
0.0015462685842067003,
-0.005102618597447872,
-0.034534141421318054,
0.006186372600495815,
-0.02423376403748989,
0.0041380892507731915,
0.05841236189007759,
-0.003051990643143654,
0.033616360276937485,
0.004235382657498121,
0.003805657383054495,
0.017244284972548485,
-0.0024241297505795956,
-0.04268140345811844,
-0.011859750375151634,
0.000027098825739813037,
0.017280466854572296,
-0.03383445367217064,
0.031823523342609406,
0.012469133362174034,
0.061873454600572586,
-0.022874711081385612,
0.004960315302014351,
0.02947096712887287,
0.040436893701553345,
0.0005968550685793161,
-0.0015310619492083788,
-0.04410770162940025,
0.05701155215501785,
-0.03885994106531143,
0.03402736783027649,
0.011184855364263058,
0.014375808648765087,
0.023075025528669357,
0.04232490062713623,
0.014825277961790562,
-0.007422024384140968,
-0.024872243404388428,
-0.04597533494234085,
0.01586923561990261,
0.007100746966898441,
-0.018458865582942963,
0.027516664937138557,
0.004506605677306652,
0.03505099564790726,
-0.0076578110456466675,
0.020751353353261948,
0.01970992237329483,
0.014163687825202942,
-0.003648890880867839,
-0.06285955011844635,
-0.058674562722444534,
0.03448405861854553,
-0.030474750325083733,
-0.019185354933142662,
0.029538996517658234,
-0.023787938058376312,
0.029920421540737152,
0.005033441819250584,
0.026030654087662697,
-0.012052992358803749,
0.05597299709916115,
-0.0112886568531394,
0.0018644147785380483,
0.01164048071950674,
-0.019771993160247803,
0.11394749581813812,
0.06034800410270691,
0.008721567690372467,
-0.09547284990549088,
0.015772145241498947,
-0.015342497266829014,
0.009352387860417366,
-0.0470106415450573,
0.06350485980510712,
-0.038713302463293076,
-0.018708130344748497,
-0.01380995661020279,
0.08300217986106873,
0.017858803272247314,
0.018765075132250786,
0.04222268611192703,
-0.08066732436418533,
-0.05419445410370827,
0.025370104238390923,
-0.01207064837217331,
-0.03795768320560455,
-0.013061773963272572,
-0.012177000753581524,
0.039922796189785004,
0.010918552987277508,
0.01421376969665289,
-0.015419673174619675,
-0.008196051232516766,
0.035135265439748764,
0.006618366576731205,
-0.02654344029724598,
0.008363915607333183,
-0.004272935912013054,
0.007592242676764727,
-0.009386376477777958,
0.031134525313973427,
0.05228940024971962,
-0.03988546133041382,
0.04991603642702103,
0.011872661300003529,
0.015792924910783768,
-0.003792265197262168,
0.009600489400327206,
-0.0026764792855829,
-0.02680697850883007,
-0.0009795522782951593,
-0.023367667570710182,
0.05390717461705208,
-0.03304281830787659,
-0.02571987733244896,
0.00019986282859463245,
0.019808579236268997,
-0.007109500002115965,
-0.042273323982954025,
-0.0007268029730767012,
0.005198908969759941,
-0.0005257991142570972,
-0.01356988213956356,
0.04408780857920647,
-0.004073138348758221,
0.036876045167446136,
0.008614892140030861,
0.015418445691466331,
-0.006581708323210478,
-0.04282020404934883,
-0.013314233161509037,
-0.023114899173378944,
0.009216167964041233,
-0.02291792444884777,
0.0017703280318528414,
-0.013449997641146183,
-0.02129448764026165,
-0.03469163551926613,
-0.026568057015538216,
0.020708059892058372,
0.008676007390022278,
0.02849496714770794,
-0.010368484072387218,
-0.013818684034049511,
-0.044028185307979584,
-0.06255495548248291,
-0.0060505918227136135,
0.007054886315017939,
0.0017756110755726695,
-0.009745937772095203,
-0.010675141587853432,
0.01834530010819435,
0.04920056462287903,
-0.021745910868048668,
-0.0070565855130553246,
0.023556148633360863,
0.022673022001981735,
0.03510370850563049,
-0.025545770302414894,
0.01629883609712124,
0.005327765829861164,
-0.02320014126598835,
-0.010135415010154247,
-0.028571579605340958,
0.015998709946870804,
0.023395823314785957,
-0.004753594286739826,
-0.004697590600699186,
0.022362783551216125,
-0.035384852439165115,
-0.006584369111806154,
0.010632461868226528,
-0.034546948969364166,
0.010504821315407753,
-0.0084309671074152,
-0.017007578164339066,
-0.01742280088365078,
-0.04131065309047699,
0.008463540114462376,
0.013106242753565311,
0.044296253472566605,
0.01360535342246294,
-0.024293527007102966,
-0.008743208833038807,
-0.005971158854663372,
0.013328011147677898,
-0.008463941514492035,
-0.017210789024829865,
-0.07482041418552399,
0.03314182534813881,
-0.007442695088684559,
0.017898056656122208,
-0.03035755641758442,
0.057270314544439316,
-0.016517922282218933,
-0.01390717551112175,
0.009010814130306244,
0.026340750977396965,
-0.014253264293074608,
0.020981939509510994,
0.022819655016064644,
-0.007273258175700903,
0.013238809071481228,
0.012799413874745369,
-0.01037980243563652,
-0.014286201447248459,
-0.040072232484817505,
-0.0067029474303126335,
0.05205294117331505,
0.005720929708331823,
0.030377555638551712,
0.008846201933920383,
-0.037546973675489426,
-0.03241444751620293,
0.04542484134435654,
-0.06010908633470535,
-0.01838366873562336,
-0.009469780139625072,
-0.04219522327184677,
-0.021287795156240463,
-0.019307008013129234,
0.013105493038892746,
0.007125613745301962,
0.006523145828396082,
0.009972897358238697,
-0.009742694906890392,
-0.06073110178112984,
-0.029129721224308014,
-0.030939072370529175,
0.005833564326167107,
0.018990516662597656,
0.022023627534508705,
0.010621575638651848,
0.006243824493139982,
0.040496259927749634,
-0.01379639282822609,
0.0023999488912522793,
0.024949058890342712,
0.008751864545047283,
-0.11074236035346985,
-0.013819610700011253,
-0.004436072427779436,
0.01025717705488205,
0.07160802185535431,
-0.07930514216423035,
0.025734571740031242,
0.04911765456199646,
-0.04941241443157196,
0.018191533163189888,
-0.028116734698414803,
0.019008764997124672,
-0.012354572303593159,
0.008866161108016968,
-0.019134605303406715,
0.07583293318748474,
0.0008318761247210205,
0.022826477885246277,
0.008288813754916191,
0.0010286937467753887,
-0.029382692649960518,
-0.03167504817247391,
-0.03054189682006836,
-0.0052057658322155476,
0.0018394134240224957,
-0.024341581389307976,
0.05785183981060982,
-0.019392598420381546,
-0.04198591783642769,
0.026858029887080193,
-0.002179007278755307,
0.0005051646730862558,
-0.01800035871565342,
0.03942226991057396,
0.04303800314664841,
0.01035268884152174,
0.04903145134449005,
-0.003632665378972888,
0.014847947284579277,
0.00401453347876668,
0.03729071095585823,
0.011806045658886433,
0.004314636345952749,
0.015750732272863388,
-0.019045494496822357,
-0.03671155124902725,
-0.019741050899028778,
0.017388690263032913,
-0.06610451638698578,
-0.01958593912422657,
-0.04397844523191452,
0.006688044406473637,
-0.00048158891149796546,
-0.040280599147081375,
0.0338556282222271,
-0.02614421583712101,
-0.03872014582157135,
0.008867663331329823,
0.02021113969385624,
0.004757064860314131,
0.007271088659763336,
-0.025708293542265892,
-0.02991066500544548,
0.021221298724412918,
0.011882118880748749,
-0.010316233150660992,
-0.03310447186231613,
-0.024295514449477196,
-0.01302928663790226,
-0.0004156403592787683,
0.024493219330906868,
-0.030891135334968567,
-0.05741265416145325,
0.0030335946939885616,
0.027696266770362854,
0.0251154787838459,
-0.04000735655426979,
-0.057594072073698044,
0.006108573637902737,
-0.053805768489837646,
0.017030462622642517,
0.013566144742071629,
-0.031323909759521484,
0.004539644345641136,
-0.030194606631994247,
0.04415883496403694,
0.0015214162413030863,
0.04964679479598999,
-0.017352797091007233,
-0.04007181152701378,
-0.004912712145596743,
-0.004313392098993063,
0.03420102968811989,
-0.03169821947813034,
-0.01908218488097191,
-0.000750337727367878,
-0.011688340455293655,
-0.026439370587468147,
0.015323338098824024,
0.022946340963244438,
0.056397005915641785,
-0.021458493545651436,
0.010671916417777538,
-0.01938757672905922,
0.02584085799753666,
-0.07489599287509918,
-0.0013571309391409159,
0.020303763449192047,
-0.006998187862336636,
0.03784972056746483,
-0.0062629785388708115,
0.038862910121679306,
0.06437977403402328,
-0.014899865724146366,
-0.03565506264567375,
0.045484885573387146,
-0.028408275917172432,
-0.0012265386758372188,
-0.026027804240584373,
0.0027052925433963537,
0.04587623104453087,
-0.03193621337413788,
0.026088688522577286,
0.024359315633773804,
-0.042164113372564316,
-0.02966216765344143,
0.05521908029913902,
0.007012723479419947,
0.03689194098114967,
0.04542038217186928,
-0.0012194042792543769,
0.05684208124876022,
0.013753439299762249,
0.029251979663968086,
0.053448423743247986,
0.014218922704458237,
0.023643871769309044,
-0.0004791277169715613,
0.012597193941473961,
-0.022001689299941063,
0.015992337837815285,
-0.006692996248602867,
0.011269118636846542,
-0.008382498286664486,
0.017018048092722893,
0.012766147032380104,
-0.03254736587405205,
0.016797948628664017,
-0.0037341322749853134,
-0.05167904496192932,
0.06793797016143799,
-0.047327760607004166,
0.02372105047106743,
0.004665927961468697,
0.028055476024746895,
-0.024551669135689735,
0.02293207123875618,
0.040115971118211746,
0.04865578934550285,
0.00449483934789896,
-0.016453709453344345,
-0.02349904365837574,
0.00247503281570971,
-0.016246819868683815,
-0.023113461211323738,
-0.022080786526203156,
0.024590833112597466,
-0.015416435897350311,
-0.006880159955471754,
-0.021505262702703476,
0.010689984075725079,
-0.012373491190373898,
0.018677495419979095,
0.007260042708367109,
-0.0076806130819022655,
-0.02000371553003788,
-0.003234979696571827,
-0.033595889806747437,
0.029514413326978683,
-0.029151495546102524,
-0.0006118795135989785,
-0.022014087066054344,
0.0009018926066346467,
-0.01222976390272379,
0.00846575852483511
] |
<p>I read a lot about the classical twin paradox recently. What confuses me is that some authors claim that it can be resolved within <a href="http://en.wikipedia.org/wiki/Special_relativity">SRT</a>, others say that you need <a href="http://en.wikipedia.org/wiki/General_relativity">GRT</a>. Now, what is true (and why)? </p> | 249 | [
0.0028051361441612244,
-0.03590575233101845,
-0.005579215008765459,
-0.063487708568573,
0.0021569267846643925,
0.011670133098959923,
-0.03387074172496796,
-0.03564838692545891,
0.02221498265862465,
0.010337346233427525,
0.02513054944574833,
0.02409164234995842,
0.04482641443610191,
0.0039360434748232365,
0.0025455879513174295,
0.013639268465340137,
0.0053695025853812695,
-0.04435790330171585,
-0.01962747611105442,
-0.04003459960222244,
-0.010080808773636818,
0.002480856841430068,
0.019317632541060448,
-0.03792443871498108,
0.0001375730789732188,
0.009002895094454288,
0.001363414223305881,
-0.008573467843234539,
0.021489014849066734,
0.06090168654918671,
-0.040814004838466644,
-0.02245480939745903,
-0.042039576917886734,
0.032698776572942734,
-0.01416754350066185,
-0.011116892099380493,
-0.0198231004178524,
0.002935734810307622,
-0.020663894712924957,
-0.0031896440777927637,
-0.016131844371557236,
-0.01783248595893383,
-0.014777343720197678,
0.041665516793727875,
-0.010758335702121258,
0.03571704402565956,
0.0016282687429338694,
-0.026936890557408333,
0.06910143047571182,
-0.031906504184007645,
0.05738107115030289,
0.003215775126591325,
0.030261725187301636,
0.042046889662742615,
-0.020484982058405876,
0.019547177478671074,
0.07517365366220474,
0.07021592557430267,
-0.010868954472243786,
-0.03387037292122841,
-0.028149759396910667,
0.008795049972832203,
0.021929237991571426,
-0.016152985394001007,
-0.012722740881145,
0.035031627863645554,
0.00046096151345409453,
-0.0009417493129149079,
0.0020853898022323847,
0.001573447254486382,
0.03072383441030979,
0.0011847204295918345,
0.05623529851436615,
0.027755780145525932,
0.021335450932383537,
-0.05008813366293907,
0.003987693227827549,
-0.018926983699202538,
0.05945641174912453,
0.01767384633421898,
-0.02556448057293892,
0.029538357630372047,
0.06813465058803558,
0.007279467768967152,
-0.00848627369850874,
-0.0034404301550239325,
0.06271766126155853,
0.025957882404327393,
0.0006978624733164907,
0.047949593514204025,
-0.02498340979218483,
0.018135277554392815,
0.05199246481060982,
-0.008425915613770485,
-0.01647503301501274,
0.0627996101975441,
-0.012978192418813705,
0.060129500925540924,
-0.00045883809798397124,
-0.008178341202437878,
0.012765916995704174,
-0.0019354422111064196,
0.02116195484995842,
0.06523589789867401,
-0.0030104974284768105,
-0.021410394459962845,
-0.0231536403298378,
0.0260922871530056,
0.020123831927776337,
-0.00654884148389101,
-0.04149380326271057,
0.024978334084153175,
-0.015179759822785854,
0.025800645351409912,
0.04973649978637695,
-0.014456630684435368,
-0.0044282241724431515,
-0.0050165471620857716,
0.07459563761949539,
0.02753172628581524,
0.043061546981334686,
-0.05324471369385719,
-0.0014057562220841646,
0.01222342997789383,
-0.054398275911808014,
0.04812762141227722,
0.0043394542299211025,
-0.011763589456677437,
0.0001333403488388285,
0.028039105236530304,
-0.014095058664679527,
-0.028383243829011917,
-0.00014112926146481186,
0.00259029190056026,
0.028622377663850784,
-0.024128813296556473,
-0.12278556823730469,
-0.07073579728603363,
0.03589954227209091,
0.025111915543675423,
-0.009426227770745754,
-0.06185755133628845,
0.06021617725491524,
-0.017449934035539627,
0.10542711615562439,
-0.004129296634346247,
0.006642819382250309,
0.01629846915602684,
0.038385115563869476,
0.02239474095404148,
-0.012959059327840805,
0.005549214314669371,
0.02970067411661148,
-0.027293626219034195,
0.026275642216205597,
-0.07774461805820465,
0.007947036996483803,
0.028263013809919357,
0.02371075004339218,
-0.036713916808366776,
0.07289334386587143,
-0.001281286240555346,
-0.0025242913980036974,
0.027408283203840256,
0.012877843342721462,
-0.0115410927683115,
0.08953599631786346,
0.0016343373572453856,
-0.015579803846776485,
0.0567992627620697,
0.02552950568497181,
0.012262903153896332,
0.00159008230548352,
0.02300032414495945,
-0.01775750331580639,
-0.017961988225579262,
-0.01745353825390339,
0.05473988875746727,
-0.01977553218603134,
-0.024745440110564232,
-0.03539778292179108,
-0.03235333412885666,
0.019371064379811287,
-0.0017582704313099384,
0.006129310466349125,
0.06402504444122314,
-0.01369595155119896,
0.03594156354665756,
-0.0038541709072887897,
-0.003646537661552429,
-0.01037509273737669,
-0.034534551203250885,
0.001291204011067748,
-0.012460267171263695,
-0.034353673458099365,
0.03905339166522026,
0.008652511984109879,
0.04362437501549721,
-0.04932725429534912,
-0.06757831573486328,
-0.02890974096953869,
0.04503245651721954,
-0.004857736174017191,
-0.011762171052396297,
0.02574707567691803,
0.059464532881975174,
0.03193405643105507,
0.000693208072334528,
-0.006544100120663643,
0.011824156157672405,
-0.03304944559931755,
0.04365153983235359,
0.014638174325227737,
0.03348773345351219,
0.003173892619088292,
-0.012706466019153595,
-0.012437545694410801,
0.00901535339653492,
-0.023520493879914284,
0.03268962353467941,
-0.016638098284602165,
0.07308024913072586,
0.006449497304856777,
0.013716395013034344,
0.0055618309415876865,
0.05339478328824043,
0.004749777726829052,
0.022097796201705933,
0.00447113486006856,
-0.027150826528668404,
-0.01620093174278736,
-0.036081016063690186,
0.01806180365383625,
0.06451486796140671,
-0.033864762634038925,
0.005579520016908646,
0.04702245071530342,
0.048619989305734634,
0.0033422806300222874,
0.014912056736648083,
-0.0010465991217643023,
-0.05994863063097,
0.006046441849321127,
-0.027469713240861893,
0.011759200133383274,
0.02413780242204666,
0.015404151752591133,
0.006460677832365036,
-0.020649967715144157,
-0.0332205556333065,
-0.033277951180934906,
0.04982289671897888,
-0.00437246635556221,
-0.0028370311483740807,
0.027398275211453438,
-0.01657617837190628,
0.0288590919226408,
-0.01249934732913971,
0.04632651433348656,
0.019936781376600266,
0.008833619765937328,
-0.007749124430119991,
-0.004799536429345608,
-0.013196870684623718,
0.005118195898830891,
0.0005265030777081847,
-0.012897862121462822,
-0.014315381646156311,
0.014558191411197186,
-0.07219845056533813,
-0.009428002871572971,
-0.0058896164409816265,
-0.025942787528038025,
-0.018340766429901123,
0.009466531686484814,
0.005281760357320309,
0.011476251296699047,
0.047044333070516586,
-0.02728142961859703,
-0.020209209993481636,
-0.02249324321746826,
-0.0337725430727005,
0.0017625449690967798,
-0.014776560477912426,
-0.04291616752743721,
0.05674941465258598,
-0.03819498047232628,
-0.0036509819328784943,
0.026528550311923027,
-0.025666072964668274,
0.030264122411608696,
-0.026214634999632835,
-0.002329428680241108,
-0.04836529493331909,
-0.04733512923121452,
-0.042487867176532745,
-0.02325594611465931,
-0.038669653236866,
0.00526527501642704,
0.06839619576931,
-0.006472398526966572,
-0.03633550554513931,
-0.02227245643734932,
-0.0497455820441246,
-0.03911514952778816,
-0.02104485221207142,
0.012856893241405487,
0.01132693886756897,
-0.032583195716142654,
0.0037714620120823383,
0.0031187208369374275,
-0.053228721022605896,
-0.01929411292076111,
-0.026627348735928535,
-0.047372762113809586,
0.05518058314919472,
0.001492396928369999,
0.04514303430914879,
0.02084239013493061,
-0.010345406830310822,
0.06885737925767899,
-0.004601940978318453,
0.01049587968736887,
-0.028211114928126335,
0.020350273698568344,
0.01147947832942009,
0.026601672172546387,
0.026347605511546135,
0.03784163296222687,
0.012705039232969284,
0.011193563230335712,
0.026115281507372856,
0.027675658464431763,
0.03399055823683739,
0.03539798781275749,
-0.031311966478824615,
-0.027462374418973923,
0.018027257174253464,
0.011820990592241287,
0.05286550521850586,
0.04847750440239906,
-0.035797297954559326,
-0.016029348596930504,
-0.010853968560695648,
0.009113521315157413,
-0.012884707190096378,
-0.04321568086743355,
0.04865405708551407,
0.004879257176071405,
0.01859038881957531,
-0.01864171028137207,
-0.0059209042228758335,
0.024623870849609375,
-0.008155501447618008,
0.030260462313890457,
0.01068464107811451,
0.043502457439899445,
-0.01822885312139988,
-0.008051660843193531,
0.03758513554930687,
0.012865184806287289,
-0.02456987462937832,
-0.02884003147482872,
-0.012045531533658504,
-0.027844587340950966,
0.044267687946558,
0.0031995498575270176,
-0.014955914579331875,
0.021907903254032135,
0.02504240721464157,
0.04489975795149803,
-0.016916487365961075,
-0.05193043500185013,
-0.01821088418364525,
-0.08310480415821075,
-0.013659076765179634,
-0.003712238511070609,
0.03923321142792702,
0.008936486206948757,
0.04343267157673836,
0.016295893117785454,
0.03200094774365425,
0.021055666729807854,
-0.00685776537284255,
-0.10134643316268921,
0.03337695822119713,
-0.02906472235918045,
-0.013206418603658676,
-0.007560365367680788,
-0.03393321856856346,
-0.0046113645657896996,
-0.06835081428289413,
-0.03615524247288704,
-0.024979352951049805,
0.00029627326875925064,
-0.07722015678882599,
0.012677370570600033,
-0.0049202339723706245,
-0.025247648358345032,
0.00008523819997208193,
0.0037205361295491457,
0.02703108824789524,
-0.01691124215722084,
-0.02370624803006649,
0.04586474597454071,
-0.046691346913576126,
-0.024079913273453712,
-0.01888599433004856,
0.007609999272972345,
0.0017464971169829369,
0.06521899253129959,
0.03784767538309097,
0.005151886027306318,
-0.013261285610496998,
0.021117176860570908,
0.013673856854438782,
0.035031288862228394,
0.000633730785921216,
-0.05833474174141884,
-0.06268752366304398,
-0.01775183342397213,
-0.004348110407590866,
-0.0228023212403059,
0.05608001723885536,
-0.004173125606030226,
0.011425825767219067,
0.022663312032818794,
0.020281458273530006,
-0.00013461442722473294,
0.0006466303602792323,
0.011450151912868023,
-0.00036033400101587176,
-0.04243360832333565,
-0.034356169402599335,
-0.06173257157206535,
-0.03799090161919594,
0.026547661051154137,
0.0507640577852726,
-0.015234151855111122,
-0.04377451539039612,
-0.015437401831150055,
0.01281675323843956,
0.011985127814114094,
-0.053935468196868896,
-0.01731921173632145,
0.009774143807590008,
0.013841289095580578,
0.010133129544556141,
-0.00024040532298386097,
-0.010730247013270855,
0.006822038441896439,
0.05028979480266571,
-0.00631355494260788,
-0.0046689994633197784,
-0.058363232761621475,
0.01670760102570057,
0.02912767231464386,
0.015896271914243698,
-0.021783381700515747,
0.001275836257264018,
-0.026215100660920143,
-0.018216155469417572,
0.0318121574819088,
-0.0484437495470047,
0.0267015527933836,
0.0043622334487736225,
0.001726642600260675,
-0.03435438498854637,
-0.05099115148186684,
0.04384322464466095,
-0.002167422091588378,
-0.0004705705214291811,
0.011715737171471119,
0.029229871928691864,
0.0019235237268730998,
0.006754009984433651,
0.001979864202439785,
0.018207190558314323,
0.07081720232963562,
0.00396051025018096,
-0.01051811408251524,
-0.004393042530864477,
0.05222780257463455,
-0.0198202021420002,
-0.05682709813117981,
-0.039261989295482635,
-0.015564903616905212,
-0.03768438100814819,
0.037882983684539795,
-0.04944179207086563,
-0.06038866192102432,
0.013488780707120895,
0.000046206383558455855,
-0.0036506622564047575,
0.013410677202045918,
-0.0009124494972638786,
0.0076953512616455555,
-0.0018994107376784086,
0.01549625862389803,
0.02115044556558132,
-0.0003089687670581043,
-0.013908149674534798,
-0.01394567172974348,
-0.021584777161478996,
0.021097451448440552,
-0.04874754324555397,
0.00227158865891397,
0.016628967598080635,
-0.0019139543874189258,
-0.037557054311037064,
0.04799443483352661,
-0.018855087459087372,
0.014328265562653542,
-0.0013471483252942562,
-0.027289334684610367,
-0.016105929389595985,
0.015261330641806126,
0.007435186766088009,
0.04856434836983681,
-0.026428190991282463,
0.0020124593283981085,
-0.006873439997434616,
-0.033624064177274704,
0.012998010031878948,
0.01137325819581747,
-0.02942492626607418,
0.03287813067436218,
-0.00891114491969347,
0.03065744787454605,
-0.017304932698607445,
-0.02208688110113144,
0.043638475239276886,
-0.051104042679071426,
0.021979663521051407,
0.0013089771382510662,
-0.0040413145907223225,
0.047788094729185104,
-0.04832864925265312,
-0.033831823617219925,
-0.031046772375702858,
-0.00985582172870636,
0.03833877667784691,
-0.05053863301873207,
0.003868679516017437,
0.027888081967830658,
-0.013694368302822113,
-0.07106230407953262,
-0.05199087783694267,
0.03147551044821739,
0.027490809559822083,
-0.03912486135959625,
-0.018118221312761307,
0.016273189336061478,
-0.03595034033060074,
-0.013652983121573925,
-0.047449447214603424,
0.0848294124007225,
0.013354630209505558,
-0.05694719776511192,
-0.009097082540392876,
0.017377514392137527,
0.05773717164993286,
-0.007605391554534435,
0.017086748033761978,
0.025373663753271103,
-0.01986180804669857,
-0.01156430970877409,
0.00615753373131156,
0.038217026740312576,
0.0004228745528962463,
-0.012921181507408619,
-0.011982999742031097,
-0.0014031371101737022,
-0.00006836471584392712,
-0.0020228854846209288,
-0.01090107299387455,
0.04849746823310852,
-0.010320083238184452,
0.0028620760422199965,
-0.054946418851614,
0.023981094360351562,
0.021487858146429062,
0.01708945818245411,
-0.023879896849393845,
-0.005878151394426823,
-0.01582251861691475,
-0.03741323575377464,
0.055250007659196854,
-0.0003511793038342148,
0.003607347374781966,
-0.012211833149194717,
0.0477692186832428,
-0.0018036598339676857,
-0.010053596459329128,
0.027153853327035904,
-0.0047767190262675285,
0.009498031809926033,
-0.024132469668984413,
0.03717772290110588,
0.020037412643432617,
-0.006777201313525438,
-0.04435012862086296,
-0.036865610629320145,
-0.013155361637473106,
0.04079791158437729,
0.07313473522663116,
-0.0370427742600441,
0.07179854065179825,
0.018060125410556793,
-0.03461642190814018,
0.01377901155501604,
-0.05427449196577072,
-0.012205519713461399,
-0.004645487759262323,
0.025159072130918503,
0.036666255444288254,
-0.023626038804650307,
0.002943862695246935,
0.03504802659153938,
0.04109929874539375,
-0.02759508416056633,
0.024392053484916687,
0.00871353317052126,
0.030424272641539574,
0.009220844134688377,
0.025267131626605988,
-0.026011314243078232,
0.0023016282357275486,
0.007820329628884792,
0.006893005222082138,
-0.0007357801659964025,
0.02288799360394478,
0.024066446349024773,
0.0246400348842144,
0.018212001770734787,
-0.028244342654943466,
-0.039786066859960556,
-0.03128841146826744,
0.01567777432501316,
-0.010293865576386452,
0.005269244778901339,
0.018806420266628265,
0.0019867275841534138,
0.010838986374437809,
0.01765028014779091,
0.03513764217495918,
-0.03486198931932449,
-0.08049383014440536,
-0.05719771236181259,
-0.04530996084213257,
-0.03919617086648941,
0.0809139832854271,
0.022633232176303864,
-0.043752726167440414,
0.02425292879343033,
-0.04142042621970177,
0.01605267822742462,
0.032198216766119,
0.03571435809135437,
-0.01738801971077919,
0.08742985129356384,
0.004722383338958025,
0.002654525451362133,
-0.0012238535564392805,
0.03561968356370926,
0.11726660281419754,
0.042950186878442764,
0.012390601448714733,
-0.06969453394412994,
0.027579324319958687,
-0.038363173604011536,
-0.008307813666760921,
-0.045464400202035904,
0.049217138439416885,
-0.034546561539173126,
-0.0037122592329978943,
0.04712248221039772,
0.028145495802164078,
0.011672718450427055,
-0.02774830162525177,
0.034546419978141785,
-0.04392595961689949,
-0.020624903962016106,
0.0007765177288092673,
0.028157304972410202,
-0.012720177881419659,
-0.0037972410209476948,
0.029868433251976967,
-0.013776414096355438,
-0.045869965106248856,
-0.004030868411064148,
-0.02474246546626091,
-0.02939251810312271,
0.019841626286506653,
0.023447629064321518,
-0.05217886343598366,
0.03584779053926468,
0.03579844906926155,
-0.01824279874563217,
-0.04664134979248047,
0.0029923163820058107,
0.011830976232886314,
-0.012521475553512573,
-0.0037173829041421413,
0.01991995796561241,
-0.01648838073015213,
0.0033453337382525206,
0.005497629288583994,
0.02757747285068035,
-0.04423394054174423,
0.021140137687325478,
-0.02250242419540882,
0.05132389813661575,
-0.025739887729287148,
-0.017959026619791985,
-0.014489972032606602,
-0.021450543776154518,
0.01258434820920229,
-0.03914905712008476,
0.012433012016117573,
0.009090512059628963,
0.013495818711817265,
-0.009208722040057182,
-0.018160996958613396,
-0.03659961372613907,
0.03572756052017212,
-0.0027657062746584415,
0.03415652737021446,
-0.0010820376919582486,
0.0037544050719588995,
0.03985323756933212,
-0.012457668781280518,
-0.0036016947124153376,
0.006843658164143562,
-0.023991787806153297,
-0.06767181307077408,
0.007768796291202307,
-0.029262647032737732,
-0.021676551550626755,
0.05782291665673256,
0.02829558402299881,
0.035363614559173584,
0.01725870743393898,
-0.030724503099918365,
-0.006893041078001261,
-0.025512414053082466,
-0.00757006648927927,
-0.02515329420566559,
-0.009731460362672806,
-0.01726917363703251,
0.011368270963430405,
0.06889728456735611,
0.06322821229696274,
-0.043133512139320374,
0.02004353702068329,
-0.010707608424127102,
0.01654372364282608,
-0.000834057223983109,
-0.004454186651855707,
0.00761111406609416,
-0.01534478459507227,
-0.015592535026371479,
-0.004219888709485531,
-0.06736154854297638,
0.018022585660219193,
0.03725413605570793,
0.028259295970201492,
-0.012400374747812748,
0.013551237992942333,
0.006457366514950991,
0.03005162999033928,
0.033947307616472244,
-0.0187184177339077,
-0.019878974184393883,
0.007702890783548355,
0.018387341871857643,
-0.0026088387239724398,
0.0028298785910010338,
-0.012403602711856365,
-0.0005287668900564313,
-0.004023743327707052,
0.04394322633743286,
-0.040966108441352844,
0.028314020484685898,
0.0029888292774558067,
0.007254095748066902,
-0.03413241729140282,
0.012614644132554531,
-0.02923680655658245,
0.06136340647935867,
-0.014556868933141232,
-0.04604879021644592,
-0.03162927180528641,
0.02153397910296917,
-0.0106243547052145,
-0.009855682030320168,
0.0243340153247118,
-0.003885481972247362,
-0.00439192820340395,
0.007135703228414059,
0.03230911120772362,
0.019889455288648605,
0.037491410970687866,
-0.0354212149977684,
-0.015270059928297997,
0.02766851708292961,
-0.02608420141041279,
-0.036479607224464417,
0.03104723058640957,
-0.04100104421377182,
0.028178878128528595,
0.01562042348086834,
-0.010038970969617367,
-0.036943886429071426,
0.058087367564439774,
-0.017899394035339355,
0.01760864071547985,
0.00034393250825814903,
-0.0025804247707128525,
-0.005845477804541588,
-0.011265918612480164,
0.010690698400139809,
-0.015480732545256615,
-0.010487382300198078,
0.023595696315169334,
0.03852670267224312,
-0.00625149579718709,
0.005563130136579275,
-0.02013767883181572,
0.02514420449733734,
-0.016031742095947266,
0.0290547925978899,
-0.012643801979720592,
0.04084647819399834,
0.06586289405822754,
-0.028416236862540245,
0.02671331726014614,
0.021260546520352364,
-0.006394397001713514,
-0.09569685906171799,
-0.006516226101666689,
0.006726142950356007,
-0.010795564390718937,
0.041204772889614105,
-0.036684684455394745,
0.02540917694568634,
0.03105507791042328,
-0.060345765203237534,
0.006118817254900932,
-0.03204232454299927,
-0.043604254722595215,
-0.02099739760160446,
-0.037166982889175415,
-0.011642629280686378,
0.06911730021238327,
0.03654909133911133,
0.015440878458321095,
-0.012015135958790779,
0.020615601912140846,
-0.020192943513393402,
-0.04240407794713974,
-0.04286302253603935,
0.03077884018421173,
-0.046716976910829544,
0.0027433424256742,
0.09661227464675903,
-0.011860532686114311,
-0.04871607944369316,
0.03810008242726326,
-0.0005332758883014321,
0.00012037832493660972,
-0.0012904719915241003,
0.014792228117585182,
-0.005979521200060844,
0.04248843342065811,
0.024005861952900887,
-0.01802205666899681,
-0.009080900810658932,
0.028740203008055687,
0.011757985688745975,
0.03827778995037079,
-0.021679215133190155,
-0.039758093655109406,
-0.031796351075172424,
-0.04929109662771225,
-0.014512903057038784,
0.01895079016685486,
-0.005029960535466671,
-0.018373899161815643,
0.005892336834222078,
0.008787865750491619,
-0.014824084006249905,
-0.013585918582975864,
-0.005623517092317343,
-0.040636517107486725,
-0.014155969955027103,
0.05038200691342354,
0.006895359605550766,
0.006653343793004751,
0.014719381928443909,
-0.04041902348399162,
-0.030495930463075638,
-0.0015992062399163842,
-0.006357858888804913,
0.015110974200069904,
-0.03521107882261276,
-0.02093181386590004,
0.010269599966704845,
-0.015555220656096935,
-0.007061743177473545,
-0.04477742686867714,
-0.009161902591586113,
0.043914563953876495,
0.043214768171310425,
-0.01257800031453371,
0.008912659250199795,
-0.029727432876825333,
-0.009020018391311169,
-0.057691868394613266,
0.010215568356215954,
-0.0003695413179229945,
0.001213911920785904,
-0.059291038662195206,
-0.027307720854878426,
-0.01966155134141445,
0.01062916312366724,
0.07810050994157791,
-0.03723277151584625,
-0.011402991600334644,
0.020308494567871094,
-0.03188736364245415,
0.004309221636503935,
-0.036726709455251694,
-0.015173008665442467,
-0.012203162536025047,
-0.04854195937514305,
-0.004137395415455103,
-0.026166249066591263,
0.0025832047685980797,
-0.0052021583542227745,
-0.007697350345551968,
-0.022537725046277046,
0.06041974946856499,
0.02799401991069317,
-0.01789330318570137,
0.03561507537961006,
0.015106284990906715,
0.01906396821141243,
0.048069216310977936,
0.012372367084026337,
0.034527987241744995,
0.04236193746328354,
0.006877915933728218,
-0.042053889483213425,
0.003937074914574623,
-0.04633691534399986,
-0.026682784780859947,
-0.054333027452230453,
0.008912158198654652,
0.01142233144491911,
-0.025412188842892647,
0.0011476022191345692,
0.06270267814397812,
-0.007385806646198034,
-0.00022126735711935908,
0.05774003267288208,
-0.015591321513056755,
0.03762274235486984,
0.001730137737467885,
0.008166693150997162,
0.026326429098844528,
-0.027030345052480698,
0.0023239050060510635,
0.01859447732567787,
0.00529903220012784,
0.030300142243504524,
-0.020344795659184456,
0.034642357379198074,
-0.0015654121525585651,
0.016436263918876648,
0.010864769108593464,
0.0393214225769043,
0.0008588582277297974,
-0.017397671937942505,
-0.00005194077311898582,
-0.041572265326976776,
0.03882022574543953,
0.026500346139073372,
-0.03894343227148056,
0.053179915994405746,
-0.04547436535358429,
-0.0025122372899204493,
0.001962078968062997,
0.01474908459931612,
-0.03195181488990784,
0.020966390147805214,
0.04178553447127342,
0.0206206776201725,
-0.02130247838795185,
-0.0017904866253957152,
-0.013992058113217354,
-0.006618540734052658,
0.009923155419528484,
-0.05080852657556534,
0.025680143386125565,
-0.025807969272136688,
0.012858729809522629,
0.003202408319339156,
-0.04031972214579582,
-0.03322457894682884,
-0.018352197483181953,
0.05247723311185837,
0.04635034129023552,
0.013399804942309856,
-0.05962040647864342,
-0.004124582279473543,
0.0027727766428142786,
0.06796614080667496,
-0.06711944937705994,
-0.009647998958826065,
0.013772618025541306,
0.012542616575956345,
-0.01260330993682146,
-0.0038944045081734657
] |
<p>What are the different death scenarios for a black hole? I know they can evaporate through Hawking radiation - but is there any other way? What if you just kept shoveling more and more mass and energy into the black hole?</p> | 2,021 | [
-0.04242406040430069,
-0.07674366235733032,
-0.0038609947077929974,
-0.054009485989809036,
0.00928469281643629,
-0.0030390999745577574,
-0.04197311773896217,
-0.05408977344632149,
-0.02197888307273388,
-0.04701034724712372,
0.008068480528891087,
0.04225068911910057,
0.021728670224547386,
0.0050783781334757805,
-0.012783307582139969,
-0.005183351691812277,
0.0021851053461432457,
-0.03596626967191696,
-0.0025686731096357107,
-0.008677036501467228,
0.009804965928196907,
0.013234954327344894,
0.03203221410512924,
0.008508841507136822,
-0.025557950139045715,
0.012889131903648376,
0.010158873163163662,
-0.004393881652504206,
-0.0063588921912014484,
0.048057008534669876,
-0.013969633728265762,
-0.03353576362133026,
0.012463187798857689,
0.04416674003005028,
0.006089074537158012,
-0.030584141612052917,
-0.03166273981332779,
-0.03129924088716507,
-0.05036315694451332,
-0.0030282633379101753,
-0.027836482971906662,
-0.042306095361709595,
-0.01755022257566452,
0.06155974790453911,
-0.03114643134176731,
-0.01609061472117901,
0.0029551114421337843,
-0.037317726761102676,
0.028513537719845772,
-0.05976486951112747,
0.03677899017930031,
0.011187374591827393,
0.01857464388012886,
0.01062588207423687,
0.006093657109886408,
0.027596740052103996,
0.10108873248100281,
0.0816560834646225,
-0.03761531785130501,
-0.02426127903163433,
-0.059941601008176804,
0.002493268111720681,
-0.018386483192443848,
-0.003378656692802906,
0.007929039187729359,
0.06333956867456436,
-0.009752425365149975,
-0.03403476998209953,
0.03505678474903107,
0.00006149624095996842,
0.01191487442702055,
0.016164617612957954,
0.006541079841554165,
-0.00011386352707631886,
0.001156864920631051,
-0.02617609314620495,
0.0062408302910625935,
-0.01499133463948965,
0.04035826399922371,
0.05653830245137215,
-0.03897367790341377,
-0.0012149011017754674,
0.055717021226882935,
0.015087497420608997,
0.0015641876962035894,
0.014849243685603142,
0.10162142664194107,
0.03483296185731888,
0.018010297790169716,
0.01242097094655037,
-0.014339475892484188,
-0.007746759802103043,
0.031064234673976898,
-0.04062744975090027,
-0.019846385344862938,
-0.003959722816944122,
-0.007088143844157457,
0.0742369145154953,
-0.015886029228568077,
-0.012126018293201923,
0.024198876693844795,
0.02277751825749874,
0.010622208938002586,
0.0559292696416378,
0.03091806173324585,
-0.0066528418101370335,
-0.059760209172964096,
0.021862424910068512,
0.010731368325650692,
-0.033330440521240234,
-0.04664561152458191,
0.019395241513848305,
-0.023813392966985703,
-0.05588535591959953,
0.026104195043444633,
-0.04225124046206474,
-0.0019201405812054873,
-0.05786169320344925,
0.033630914986133575,
0.07288538664579391,
0.04382505267858505,
-0.00009677458001533523,
0.03736225143074989,
-0.024375392124056816,
-0.03475804254412651,
-0.0175845455378294,
0.0674053207039833,
-0.016702158376574516,
-0.03193921968340874,
0.0041251415386796,
-0.0023328051902353764,
-0.02276608906686306,
0.027262425050139427,
-0.0030554733239114285,
0.03021986410021782,
-0.04520095884799957,
-0.08835267275571823,
-0.0697440356016159,
0.05788683146238327,
-0.026021914556622505,
-0.014386947266757488,
-0.029564090073108673,
0.005186300724744797,
0.046020831912755966,
0.08090224862098694,
0.012330510653555393,
-0.027477076277136803,
0.018997343257069588,
0.04022141546010971,
-0.017168592661619186,
0.0014672783436253667,
0.024157555773854256,
-0.008585317991673946,
-0.008358621038496494,
0.026317687705159187,
-0.07049643993377686,
0.003115869825705886,
0.02814634144306183,
0.020351402461528778,
-0.045636534690856934,
0.06744974106550217,
-0.024143310263752937,
-0.0002032622433034703,
0.014859426766633987,
-0.029660606756806374,
-0.01345632504671812,
0.07798207551240921,
0.022032883018255234,
-0.024061646312475204,
0.01793806441128254,
0.0297123733907938,
0.05656222254037857,
0.02202482521533966,
0.023595094680786133,
0.032719194889068604,
-0.05489334464073181,
0.013067469000816345,
-0.03383420780301094,
0.026526952162384987,
0.013937175273895264,
-0.053483765572309494,
-0.0174441859126091,
0.01042089331895113,
-0.013227569870650768,
0.005928283091634512,
0.018402056768536568,
-0.00804870668798685,
-0.01881609484553337,
-0.021105295047163963,
-0.03399311751127243,
-0.012830195017158985,
-0.07153500616550446,
0.01725035160779953,
0.03867727890610695,
0.027976268902420998,
0.00531186256557703,
0.04730691388249397,
0.05731186270713806,
-0.08338867127895355,
-0.013331323862075806,
0.024694042280316353,
0.053105395287275314,
-0.02205919660627842,
-0.00870517361909151,
-0.008116093464195728,
0.05756336450576782,
0.03140170872211456,
-0.013654330745339394,
0.016468577086925507,
-0.027079330757260323,
0.007914162240922451,
-0.03126545250415802,
0.005650336388498545,
0.009792760945856571,
-0.020694730803370476,
-0.02214634418487549,
0.005761345382779837,
-0.024609267711639404,
0.01795997843146324,
0.013028077781200409,
-0.023574186488986015,
0.08158867061138153,
0.026350069791078568,
0.02994406223297119,
-0.021208517253398895,
0.0327715240418911,
0.0007925893878564239,
-0.013760852627456188,
-0.01867537386715412,
-0.031915586441755295,
-0.022066200152039528,
0.02349427342414856,
0.03206368535757065,
-0.001207228982821107,
-0.05880602449178696,
0.04826650395989418,
0.02394057624042034,
0.03496497496962547,
0.036996908485889435,
0.019611487165093422,
-0.014847726561129093,
-0.01058678887784481,
0.008240743540227413,
-0.018387852236628532,
-0.0024463925510644913,
0.013864504173398018,
0.06030835583806038,
0.012745226733386517,
-0.005878387950360775,
-0.008750061504542828,
-0.028310824185609818,
0.03548912703990936,
-0.013916910625994205,
0.012610837817192078,
0.02076086774468422,
-0.05991838499903679,
-0.018271200358867645,
-0.018345173448324203,
0.014316003769636154,
0.012665578164160252,
-0.00023704276827629656,
-0.007832430303096771,
-0.01912025175988674,
-0.010933986864984035,
0.026263108476996422,
0.02571110613644123,
0.005951241124421358,
0.00653305696323514,
0.032475169748067856,
-0.03011232055723667,
0.032087210565805435,
-0.023015156388282776,
-0.013743860647082329,
-0.02299039252102375,
0.03377561271190643,
0.022287027910351753,
-0.008283635601401329,
0.03564545512199402,
0.006550627760589123,
-0.0482257641851902,
0.004575704224407673,
-0.034010984003543854,
-0.030727693811058998,
0.02973390743136406,
-0.03157564252614975,
0.020845385268330574,
-0.007942656055092812,
-0.05707879737019539,
0.069529689848423,
-0.0056939637288451195,
0.013814748264849186,
0.023135147988796234,
-0.023641403764486313,
-0.007424796465784311,
0.022722072899341583,
0.010919230990111828,
-0.024825911968946457,
-0.027819445356726646,
0.04541138932108879,
0.06446816027164459,
-0.014046167023479939,
-0.03633420169353485,
0.026370853185653687,
-0.010965133085846901,
-0.03191758319735527,
-0.009047962725162506,
0.018008362501859665,
0.03406808525323868,
-0.016322778537869453,
0.028720801696181297,
0.015015281736850739,
-0.07200577855110168,
0.034625567495822906,
-0.02141679637134075,
-0.002941917162388563,
0.037699997425079346,
-0.005122518166899681,
-0.013001889921724796,
0.009375497698783875,
-0.009947639890015125,
0.052971258759498596,
0.030922947451472282,
-0.002488370519131422,
-0.004784114193171263,
-0.03452766314148903,
-0.0177753958851099,
0.0026874977629631758,
-0.019625255838036537,
0.003465253161266446,
-0.006229790858924389,
-0.008771960623562336,
0.05467860773205757,
0.01611323095858097,
0.01688125729560852,
-0.012820214033126831,
-0.028404206037521362,
-0.02949886955320835,
0.030719462782144547,
0.018395543098449707,
0.03582631051540375,
-0.006690915208309889,
-0.007465083617717028,
0.03129436820745468,
0.024380141869187355,
0.051053550094366074,
0.011816122569143772,
-0.050055794417858124,
0.018808461725711823,
0.004649576265364885,
0.021545158699154854,
-0.03441745042800903,
0.033485591411590576,
0.0029176955576986074,
-0.02278050221502781,
-0.0021771774627268314,
0.007954450324177742,
0.07063917815685272,
-0.01754968799650669,
0.009937645867466927,
-0.02457031048834324,
0.06154046952724457,
-0.04129583388566971,
-0.03575894981622696,
-0.01343460101634264,
-0.018310202285647392,
0.03284994512796402,
-0.005319780670106411,
0.019606251269578934,
0.039258286356925964,
-0.003939167596399784,
0.043474096804857254,
0.00515498872846365,
-0.026768073439598083,
0.010481375269591808,
-0.06585545837879181,
-0.0013263594591990113,
0.008813631720840931,
0.008349889889359474,
0.0023298158776015043,
0.00043715425999835134,
0.045375291258096695,
0.004894277546554804,
0.020763222128152847,
-0.024030478671193123,
-0.05926445126533508,
0.03504185751080513,
-0.03179231286048889,
-0.007935110479593277,
0.0035514594055712223,
0.00691002793610096,
-0.017959892749786377,
-0.022144345566630363,
-0.03904232755303383,
0.00029872250161133707,
-0.004876991268247366,
-0.042083490639925,
0.01573002152144909,
-0.05310535430908203,
-0.0314200259745121,
-0.0052165016531944275,
0.057150132954120636,
0.04209483414888382,
0.008612405508756638,
-0.005341630429029465,
0.011827424168586731,
-0.021226655691862106,
0.015169307589530945,
0.021328169852495193,
-0.0019490085542201996,
-0.011392924003303051,
0.04190424457192421,
0.00934119988232851,
-0.00128083152230829,
-0.02275831624865532,
-0.02791169472038746,
0.01845579780638218,
0.0281419288367033,
0.0017991228960454464,
-0.03165920823812485,
-0.02329370006918907,
-0.05149001255631447,
-0.015348164364695549,
-0.005300001706928015,
0.029960211366415024,
-0.0116400346159935,
0.025869786739349365,
0.027351131662726402,
-0.019917337223887444,
-0.02304054982960224,
0.028461525216698647,
0.04237918555736542,
0.010462776757776737,
-0.041901279240846634,
-0.005746066570281982,
-0.05744733661413193,
0.0035345356445759535,
0.014199264347553253,
0.011671386659145355,
0.010836903005838394,
-0.06135399639606476,
0.02822457067668438,
0.009160078130662441,
-0.004517173860222101,
-0.02997998334467411,
-0.03971297666430473,
0.015021627768874168,
0.05023835226893425,
-0.02154981903731823,
0.02458176389336586,
0.016134154051542282,
0.02034483477473259,
0.061428118497133255,
0.003052096115425229,
0.002762909047305584,
-0.045537129044532776,
0.004731365013867617,
0.03343747556209564,
0.03391936793923378,
0.03791864588856697,
-0.01540120504796505,
-0.0663895234465599,
-0.024870825931429863,
0.05627305433154106,
-0.042280737310647964,
0.014079500921070576,
0.0028743897564709187,
-0.0016205328283831477,
-0.0072375391609966755,
-0.02124190889298916,
0.017051197588443756,
0.04258447885513306,
-0.04001139476895332,
0.010474069975316525,
-0.0033992708195000887,
0.014032701961696148,
0.006142321974039078,
0.03194759786128998,
0.026824994012713432,
0.06793471425771713,
0.03309549018740654,
0.03389003127813339,
0.009758013300597668,
0.007371970918029547,
-0.025682687759399414,
-0.07264277338981628,
-0.007758272346109152,
0.020176520571112633,
-0.056172847747802734,
0.04254684969782829,
-0.041001711040735245,
-0.026991283521056175,
0.02241002395749092,
0.018391016870737076,
-0.0364544652402401,
0.005953386425971985,
-0.0651673898100853,
-0.022887784987688065,
0.007011080160737038,
-0.008559305220842361,
0.04717177897691727,
0.020738059654831886,
0.00018640258349478245,
0.0016443944768980145,
-0.02975733019411564,
0.0497719943523407,
-0.06262825429439545,
-0.008738587610423565,
-0.01637779362499714,
-0.0004517171182669699,
-0.023151634261012077,
0.0533231757581234,
0.000997735420241952,
0.01911269873380661,
0.03805699944496155,
-0.021067867055535316,
0.004839381668716669,
0.010374760255217552,
0.028871964663267136,
0.007590144407004118,
0.004864518065005541,
0.024710729718208313,
0.006056893151253462,
-0.02480274997651577,
0.015493081882596016,
-0.01746976375579834,
-0.004969804547727108,
0.043427493423223495,
-0.03744392469525337,
0.03276771679520607,
-0.020065320655703545,
0.0043859584257006645,
0.055022597312927246,
-0.032695721834897995,
0.08059818297624588,
0.001819979166612029,
-0.022056400775909424,
0.021503247320652008,
-0.04746682569384575,
0.010366834700107574,
0.0063915192149579525,
-0.00784386321902275,
0.034975357353687286,
-0.033959969878196716,
0.0686851218342781,
0.046380408108234406,
0.04517265781760216,
-0.10007961839437485,
-0.002612547716125846,
0.03604087233543396,
0.027941526845097542,
-0.0015080544399097562,
-0.03559146448969841,
0.03233885392546654,
-0.054813534021377563,
-0.041690003126859665,
-0.017307789996266365,
0.007674079854041338,
-0.03254839777946472,
0.019144445657730103,
-0.015224841423332691,
0.015480203554034233,
0.03324807435274124,
0.0065673054195940495,
-0.015788933262228966,
0.021866561844944954,
-0.010533129796385765,
0.006262813229113817,
-0.011255262419581413,
0.0404556468129158,
-0.02314363606274128,
-0.00916297547519207,
-0.008034651167690754,
-0.02206910029053688,
0.03776209428906441,
0.0034917807206511497,
0.01970530115067959,
0.04059125855565071,
0.006826066877692938,
0.014512980356812477,
0.012005147524178028,
0.0569683201611042,
-0.0394521988928318,
0.04966285452246666,
-0.018489239737391472,
-0.009337035939097404,
0.03436081483960152,
-0.07023459672927856,
0.023326585069298744,
0.012949156574904919,
0.019597548991441727,
0.013714749366044998,
0.049141112715005875,
0.0113426074385643,
-0.021401632577180862,
-0.01248107012361288,
-0.06400805711746216,
0.02158811315894127,
-0.002272985177114606,
0.018468735739588737,
0.028698062524199486,
0.009462786838412285,
-0.0027002543210983276,
-0.04509398713707924,
-0.03154653683304787,
-0.013544547371566296,
0.05168859660625458,
-0.010376475751399994,
-0.0035655777901411057,
0.03435545042157173,
-0.009983199648559093,
-0.00988094974309206,
-0.04980196803808212,
0.0023658662103116512,
0.03550519049167633,
-0.019321328029036522,
0.023234974592924118,
0.016454016789793968,
0.01177956722676754,
0.029110362753272057,
0.07351906597614288,
0.014746656641364098,
0.04899302497506142,
0.024134084582328796,
0.005313732195645571,
0.010320662520825863,
-0.0027684385422617197,
-0.033499620854854584,
0.04554219916462898,
-0.0511687807738781,
0.021256791427731514,
-0.007993759587407112,
-0.02153024449944496,
0.0072647868655622005,
-0.031199287623167038,
0.02362055890262127,
-0.012636600062251091,
-0.04377308487892151,
-0.0647309273481369,
0.021884871646761894,
-0.01644965447485447,
0.016395289450883865,
0.010205232538282871,
0.025867735967040062,
0.0030837643425911665,
-0.010194746777415276,
0.005573627073317766,
0.004715062212198973,
-0.07016471028327942,
-0.06468288600444794,
-0.017320245504379272,
-0.06233072653412819,
0.027746645733714104,
0.03597142919898033,
0.00919661857187748,
-0.022744011133909225,
-0.006411323789507151,
-0.014587977901101112,
-0.007827471941709518,
0.05115355923771858,
0.01023196056485176,
0.052507203072309494,
0.005942186340689659,
-0.006726757623255253,
-0.025940528139472008,
0.022616779431700706,
0.11055773496627808,
0.07075107097625732,
0.047603245824575424,
-0.07187873870134354,
-0.011976939626038074,
-0.02594893053174019,
0.04094533622264862,
-0.039210859686136246,
0.022809065878391266,
-0.002319908933714032,
0.015780072659254074,
0.014234155416488647,
0.041371773928403854,
-0.004949481692165136,
-0.02102251909673214,
0.06786956638097763,
-0.009974701330065727,
-0.017342979088425636,
-0.011119762435555458,
0.04126138985157013,
-0.013038008473813534,
0.006765701342374086,
-0.023264586925506592,
0.04043292626738548,
-0.002900607418268919,
-0.004845287185162306,
-0.053162019699811935,
-0.0281109306961298,
0.022872189059853554,
0.008549720980226994,
-0.05364010110497475,
-0.015384387224912643,
0.01084946095943451,
-0.00822624284774065,
-0.010837756097316742,
0.028052981942892075,
0.03244571387767792,
-0.002668164437636733,
-0.011441409587860107,
0.021895330399274826,
0.03573843836784363,
0.02212575078010559,
-0.002062141662463546,
0.03283006325364113,
-0.03809523582458496,
0.014055725187063217,
-0.0037312607746571302,
0.006068282760679722,
-0.03236794099211693,
0.023165425285696983,
-0.0290224589407444,
0.019180702045559883,
0.014222306199371815,
-0.02523873560130596,
-0.03227362781763077,
-0.02938433550298214,
0.0070044901221990585,
0.0179250817745924,
-0.040694091469049454,
-0.003739639651030302,
-0.011213758960366249,
0.02939058095216751,
0.015826664865016937,
0.020033888518810272,
0.006027618423104286,
0.00414265738800168,
-0.05376673862338066,
0.01812690682709217,
-0.04292935132980347,
0.005197541322559118,
-0.026320235803723335,
-0.008725745603442192,
-0.05025437846779823,
0.006885404232889414,
0.02636849135160446,
0.02221841551363468,
-0.007804631255567074,
0.01317716296762228,
0.02087968960404396,
-0.022167574614286423,
-0.029544545337557793,
0.030578752979636192,
-0.009411454200744629,
-0.024126050993800163,
-0.013753398321568966,
-0.009679295122623444,
-0.008596295490860939,
0.004853997379541397,
-0.032369643449783325,
0.002158639719709754,
-0.01947743445634842,
0.01936025172472,
-0.02299318090081215,
-0.005130453035235405,
0.00503250677138567,
0.016538331285119057,
-0.06340181827545166,
-0.015200838446617126,
-0.032461509108543396,
0.06459956616163254,
0.0210503451526165,
-0.03168707340955734,
0.007645171135663986,
0.00756013672798872,
-0.03849988430738449,
0.008461943827569485,
0.017504272982478142,
-0.037117503583431244,
-0.015021800063550472,
0.017603520303964615,
0.033340439200401306,
-0.024480659514665604,
-0.04473472759127617,
-0.03124966286122799,
-0.01548133697360754,
0.005756010301411152,
0.05951668322086334,
-0.022280380129814148,
0.041113853454589844,
-0.025002403184771538,
0.013805624097585678,
-0.03351978585124016,
0.007705511525273323,
-0.05075237154960632,
0.012548768892884254,
0.010954420082271099,
-0.046304479241371155,
0.01640321873128414,
-0.01215132512152195,
-0.012008076533675194,
-0.014176871627569199,
-0.014185137115418911,
0.02143426239490509,
-0.03309360891580582,
-0.005443701520562172,
0.04726242646574974,
-0.013958845287561417,
0.04062440246343613,
0.03295060619711876,
-0.022634724155068398,
0.010510485619306564,
-0.05275098979473114,
-0.026495924219489098,
0.04727380350232124,
-0.005370751954615116,
0.03897868096828461,
0.023904375731945038,
-0.04124404862523079,
-0.021583089604973793,
0.08201664686203003,
-0.04054690897464752,
-0.05280569940805435,
0.0008337278850376606,
-0.023349255323410034,
-0.03789827972650528,
0.028200726956129074,
0.015767961740493774,
-0.046892691403627396,
-0.02819177880883217,
0.029256952926516533,
0.02230001986026764,
-0.00744867417961359,
0.009733887389302254,
-0.00985807366669178,
-0.004738927353173494,
0.025569606572389603,
0.010435052216053009,
0.0017389681888744235,
0.0154516426846385,
0.0558558888733387,
-0.025720667093992233,
0.0583062507212162,
0.045989081263542175,
-0.001646375865675509,
-0.10377530008554459,
-0.009092902764678001,
0.010059249587357044,
-0.00376512692309916,
0.03065265528857708,
-0.0347948782145977,
0.013265912421047688,
0.02158021740615368,
-0.06708268076181412,
0.03352142497897148,
-0.05108102783560753,
0.005298492964357138,
-0.04725172370672226,
0.006266326643526554,
0.008727451786398888,
0.04226363077759743,
0.050408441573381424,
0.041898224502801895,
-0.007307069841772318,
-0.010908766649663448,
-0.03760622814297676,
-0.011578886769711971,
-0.020306335762143135,
0.021625617519021034,
-0.017564494162797928,
-0.015949606895446777,
0.07336924970149994,
-0.0006249189027585089,
-0.008736854419112206,
0.010512061417102814,
-0.000979135395027697,
0.0026650934014469385,
0.01558599341660738,
0.009091206826269627,
0.012293443083763123,
0.002075248397886753,
-0.0020527043379843235,
-0.014346323907375336,
-0.01544253621250391,
0.021122321486473083,
-0.004549140576273203,
0.022806739434599876,
-0.008579056710004807,
0.021744608879089355,
0.02896937169134617,
-0.039579201489686966,
-0.00806088000535965,
0.013975335285067558,
-0.03074750490486622,
-0.027933578938245773,
-0.013039343059062958,
0.00002543179834901821,
0.035016097128391266,
-0.02287364937365055,
-0.017061825841665268,
-0.026768311858177185,
0.01622512936592102,
0.007363299373537302,
0.028345836326479912,
0.0553373284637928,
0.02013476751744747,
-0.022553322836756706,
-0.005281813442707062,
-0.00895798671990633,
-0.00010550746083026752,
0.005793086253106594,
-0.029852960258722305,
0.011373619548976421,
-0.04076151177287102,
0.01353329885751009,
0.0014842355158179998,
-0.04860790818929672,
-0.014960763044655323,
0.0700724869966507,
0.007332552690058947,
0.021015290170907974,
-0.003997582942247391,
-0.04748193547129631,
-0.029592618346214294,
-0.07778241485357285,
-0.013688469305634499,
-0.047369081526994705,
0.008347230032086372,
-0.05429236590862274,
-0.03461841121315956,
0.022609876468777657,
-0.0040296646766364574,
0.052767615765333176,
-0.029948914423584938,
0.038570962846279144,
0.02294325828552246,
-0.019916299730539322,
0.006275265011936426,
-0.04117012023925781,
-0.006925452034920454,
0.004077399615198374,
-0.0626719743013382,
-0.03970658406615257,
0.029246646910905838,
-0.007166244089603424,
0.02755023166537285,
0.06139657646417618,
-0.007434356026351452,
0.05640164762735367,
0.016226032748818398,
0.016741348430514336,
0.047492239624261856,
0.013097873888909817,
0.011698664166033268,
0.041789907962083817,
-0.02410137839615345,
0.02162032760679722,
0.02349366806447506,
-0.029723946005105972,
-0.007201819214969873,
0.05138867348432541,
-0.03354549780488014,
0.009516969323158264,
0.008465235121548176,
-0.06004665046930313,
0.011264539323747158,
-0.04114362597465515,
-0.00646559614688158,
0.024959728121757507,
-0.02787032723426819,
0.0012518432922661304,
0.00807881262153387,
0.02023245394229889,
0.043139733374118805,
-0.008408390916883945,
-0.003751985728740692,
-0.016764342784881592,
0.033021435141563416,
-0.038297880440950394,
0.037554845213890076,
0.022335996851325035,
-0.02130940370261669,
0.012411855161190033,
-0.019210033118724823,
-0.01178444642573595,
-0.0073053790256381035,
-0.01243105623871088,
0.038939230144023895,
-0.046061333268880844,
-0.04687144607305527,
0.013850796036422253,
-0.02502434328198433,
0.0037111882120370865,
-0.0274929441511631,
-0.030912932008504868,
0.054562389850616455,
-0.007187430746853352,
0.021997034549713135,
-0.015346263535320759,
-0.03483308106660843,
-0.03862398862838745,
0.02506886050105095,
-0.02775350585579872,
0.08405955880880356,
0.010501082055270672,
-0.005477953236550093,
-0.01965392380952835,
0.030459130182862282,
0.040608108043670654,
-0.020572373643517494,
0.013327700085937977,
-0.003501210594549775,
0.0075926948338747025,
-0.033127009868621826,
-0.02384629286825657,
-0.005528335925191641,
-0.02086028642952442,
-0.003141482826322317,
0.015007976442575455,
0.0024760805536061525,
0.010686380788683891,
-0.019034113734960556,
-0.027295654639601707,
0.032840628176927567,
-0.023513194173574448,
-0.03451482951641083,
-0.0237099789083004,
0.05224522948265076,
-0.02764938585460186,
0.0385337695479393
] |
<p>Imagine a circuit with a voltage source, a switch and an inductivity all connected in series.</p>
<p>First, the switch is open and there's no current and no magnetic field around. If we close the switch, the potential difference of the voltage source is instantaneously applied to the inductivity. Lenz's Law tells us that the induced voltage from the inductivity will always be such that the change in the magnetic flux is reduced. And we have Faraday's Law which tells us that the induced voltage is equal to the change in the magnetic flux.</p>
<p>What is the theoretical reason why the change in magnetic flux must be smaller than the applied voltage? Why does for t -> infinity always run a current trough the inductivity as it would be just a resistor? Is it just because the wires have a resistance? What would then happen when taking superconductors instead of wires? Is it the inner resistivity of the voltage source then?</p> | 2,022 | [
-0.0011797081679105759,
-0.024832438677549362,
0.0027554724365472794,
-0.05025425925850868,
0.051543932408094406,
0.01873093843460083,
-0.045087944716215134,
-0.009180835448205471,
0.011632132343947887,
-0.009076377376914024,
0.04208741709589958,
0.018506105989217758,
0.023272771388292313,
0.01616532728075981,
0.0019003290217369795,
-0.008206559345126152,
-0.0022810851223766804,
-0.027928339317440987,
-0.032519515603780746,
-0.027579795569181442,
-0.011287283152341843,
0.03787611052393913,
0.035807546228170395,
0.015325967222452164,
-0.06231950223445892,
0.004098507575690746,
-0.007188356481492519,
0.0025062174536287785,
0.030554750934243202,
0.05263067036867142,
0.023255815729498863,
-0.020188743248581886,
-0.01600082777440548,
0.006940778810530901,
0.019423004239797592,
0.030338814482092857,
-0.04662049934267998,
-0.053637631237506866,
0.023692261427640915,
0.026469677686691284,
-0.0036875230725854635,
0.013749675825238228,
0.00027330906596034765,
0.050289180129766464,
-0.014237619005143642,
0.0068470994010567665,
0.005078095942735672,
0.02657238394021988,
0.03496265783905983,
-0.08261485397815704,
0.014660768210887909,
-0.04151442274451256,
0.05336445942521095,
0.017186643555760384,
-0.0031469594687223434,
-0.01609957590699196,
0.07539061456918716,
0.05567425861954689,
0.0002224805357400328,
-0.043062061071395874,
-0.005766569171100855,
-0.024869374930858612,
-0.029603824019432068,
-0.02538943663239479,
-0.017743434756994247,
0.06611286103725433,
0.006101952400058508,
0.02060256153345108,
-0.008128912188112736,
-0.012438326142728329,
0.003950185142457485,
0.010571747086942196,
-0.026263011619448662,
0.009064546786248684,
0.0208118949085474,
-0.004110506735742092,
0.020165324211120605,
-0.004512457177042961,
0.03989531472325325,
0.047131095081567764,
-0.02976912260055542,
0.015761546790599823,
0.027359822764992714,
0.036210570484399796,
0.017902223393321037,
-0.01309308409690857,
0.028911691159009933,
-0.023872317746281624,
0.023707857355475426,
0.03595862537622452,
0.013132425956428051,
0.031299296766519547,
0.0336492657661438,
-0.03993058204650879,
0.0007339586736634374,
0.03128889203071594,
0.011696861125528812,
0.02734321914613247,
0.02005167305469513,
-0.0007085361867211759,
0.03635193035006523,
0.00940717477351427,
0.005301665980368853,
0.052000075578689575,
0.019254950806498528,
-0.03579439967870712,
-0.025750134140253067,
0.012205702252686024,
-0.023974455893039703,
-0.041363902390003204,
-0.06343504786491394,
0.039050597697496414,
0.0028088956605643034,
0.033855684101581573,
-0.001819339580833912,
-0.04700487107038498,
0.031297050416469574,
-0.04827861860394478,
0.04730513319373131,
0.056371498852968216,
0.017944395542144775,
-0.03572032228112221,
0.025749681517481804,
-0.027529334649443626,
-0.04582582041621208,
-0.016124099493026733,
0.011127650737762451,
0.026032058522105217,
-0.00537779089063406,
0.008779472671449184,
-0.051742490381002426,
-0.025839606299996376,
-0.024084188044071198,
0.0007738832500763237,
0.032835543155670166,
-0.025974033400416374,
-0.05793650075793266,
-0.0695764496922493,
0.006754320114850998,
-0.010303780436515808,
-0.03601817041635513,
-0.0971885621547699,
-0.016384772956371307,
0.04748203977942467,
0.07130356878042221,
-0.010653028264641762,
-0.019217809662222862,
-0.015698213130235672,
0.02085988223552704,
-0.004614422097802162,
-0.02654976025223732,
-0.029170626774430275,
-0.0167916938662529,
-0.01000976376235485,
-0.014620584435760975,
-0.05439039692282677,
0.04114740341901779,
0.04666180536150932,
0.021729523316025734,
-0.023538043722510338,
0.04782457277178764,
-0.03338038921356201,
0.009987610392272472,
0.013948788866400719,
-0.038744859397411346,
-0.040957771241664886,
0.08344551175832748,
-0.002306834328919649,
0.050347961485385895,
0.05206191539764404,
0.000585049856454134,
0.010460230521857738,
-0.006711151916533709,
0.03963496908545494,
0.0260161180049181,
-0.03960153087973595,
-0.026790566742420197,
-0.0032863139640539885,
0.028171062469482422,
-0.010821041651070118,
-0.031052500009536743,
-0.009790221229195595,
-0.013026310130953789,
0.001511203940026462,
0.00015143454947974533,
0.05385774374008179,
-0.010102253407239914,
-0.03001168742775917,
-0.010898416861891747,
-0.04422752931714058,
-0.026751263067126274,
-0.02503141574561596,
0.03264082223176956,
0.007370447274297476,
-0.026709094643592834,
0.03420289605855942,
0.040728408843278885,
-0.005537092220038176,
-0.060218289494514465,
0.0018131647957488894,
0.0006126727676019073,
0.015031594783067703,
-0.011596000753343105,
-0.010672569274902344,
0.010996096767485142,
0.03103931061923504,
0.02043946087360382,
0.001050781225785613,
0.029082108289003372,
-0.023585636168718338,
-0.05900051072239876,
0.013864707201719284,
-0.03220093622803688,
0.04299382120370865,
0.028944287449121475,
0.02418464981019497,
0.008360638283193111,
-0.0006754915812052786,
-0.024847619235515594,
0.05515585094690323,
-0.014273498207330704,
0.051217351108789444,
0.05220417305827141,
0.01828230917453766,
0.0030164073687046766,
0.02677232399582863,
-0.013265763409435749,
-0.01068593468517065,
-0.009623381309211254,
-0.018929140642285347,
-0.08888129889965057,
-0.006607212591916323,
0.04498721659183502,
0.03224446251988411,
-0.026754578575491905,
-0.009408912621438503,
0.012003223411738873,
0.0418245792388916,
0.026037318632006645,
0.008444034494459629,
-0.04129011929035187,
-0.018153565004467964,
0.0025575710460543633,
-0.006706974469125271,
0.01354386005550623,
0.005085310898721218,
0.01937221735715866,
0.030164016410708427,
0.0238718930631876,
-0.009877823293209076,
-0.026589365676045418,
0.044396381825208664,
0.017327895388007164,
0.013052762486040592,
0.03480251133441925,
-0.03010786697268486,
0.022453323006629944,
-0.016207609325647354,
0.014989588409662247,
-0.020083768293261528,
-0.004100245889276266,
0.03186317905783653,
-0.020449332892894745,
-0.0027704432141035795,
0.01912236586213112,
-0.05677686259150505,
-0.012007859535515308,
-0.016391245648264885,
0.029371965676546097,
-0.05740309879183769,
0.01247042790055275,
0.003954237326979637,
0.006780622992664576,
-0.06457190960645676,
-0.006103310734033585,
-0.03673950582742691,
0.0064157904125750065,
0.05342349410057068,
-0.0474214032292366,
-0.011998521164059639,
-0.01336226798593998,
-0.03767174109816551,
0.02276509255170822,
0.04823852330446243,
-0.052183449268341064,
0.05688668042421341,
-0.031147565692663193,
-0.03134522959589958,
0.04965536668896675,
0.03269820287823677,
0.020336881279945374,
0.011824222281575203,
-0.014427883550524712,
-0.08599676936864853,
-0.0022808394860476255,
-0.018931632861495018,
0.017680026590824127,
0.0033033019863069057,
0.019678492099046707,
0.056323692202568054,
-0.0004650735354516655,
-0.0371214896440506,
0.027115197852253914,
-0.047673746943473816,
-0.031059984117746353,
0.002960645128041506,
0.023442381992936134,
-0.011923357844352722,
-0.02353774756193161,
0.02211681194603443,
0.004679318983107805,
-0.059607233852148056,
-0.03728774935007095,
-0.0619613416492939,
-0.03622235357761383,
-0.022875552996993065,
-0.017934581264853477,
0.03862753510475159,
0.000568014511372894,
-0.05292942002415657,
0.0765419602394104,
0.04672577232122421,
-0.022577067837119102,
-0.03751683235168457,
-0.020136220380663872,
-0.010490321554243565,
-0.022604960948228836,
0.018638821318745613,
0.04546113312244415,
-0.03431054949760437,
0.003519587917253375,
0.024230683222413063,
0.059226393699645996,
0.012394826859235764,
0.017771080136299133,
0.030039003118872643,
0.009211509488523006,
0.030138982459902763,
0.012815270572900772,
0.03904467076063156,
0.016256233677268028,
-0.019879093393683434,
0.020181329920887947,
0.0003657493507489562,
0.014132462441921234,
0.02450614981353283,
0.020336562767624855,
0.031480949372053146,
-0.011557083576917648,
0.0026359634939581156,
-0.04833435267210007,
0.054292768239974976,
-0.0007685752934776247,
0.019292911514639854,
-0.008708328008651733,
0.012353629805147648,
0.026069656014442444,
-0.05219454690814018,
-0.006885017734020948,
0.017407812178134918,
0.05074652284383774,
-0.023825982585549355,
-0.05757895112037659,
-0.004136927891522646,
-0.018041132017970085,
0.024683408439159393,
-0.04532705247402191,
-0.00799658615142107,
0.042356058955192566,
0.04170779138803482,
0.02286824770271778,
0.03135044872760773,
-0.017025507986545563,
-0.04059526324272156,
-0.033170975744724274,
0.008951538242399693,
-0.00005945644079474732,
0.06978044658899307,
0.026866666972637177,
0.026402009651064873,
0.010091607458889484,
0.03448529541492462,
0.0028640206437557936,
-0.015972116962075233,
-0.13049976527690887,
0.016088204458355904,
-0.07254165410995483,
-0.009005776606500149,
-0.014635242521762848,
0.03433627635240555,
-0.014382715336978436,
0.000047463348892051727,
-0.013378126546740532,
-0.04403317719697952,
-0.025634853169322014,
-0.04938230291008949,
-0.00155971001368016,
-0.02381853759288788,
-0.03222954645752907,
-0.052486635744571686,
0.018401648849248886,
0.026248568668961525,
-0.054677821695804596,
-0.017468739300966263,
-0.005635818000882864,
-0.0397501215338707,
0.018117262050509453,
-0.008370080031454563,
0.006208810955286026,
0.015069265849888325,
0.041770871728658676,
0.040330350399017334,
-0.00720073701813817,
-0.026661263778805733,
0.025515960529446602,
0.03300214186310768,
0.04521556943655014,
0.0019595324993133545,
-0.021012546494603157,
-0.017809180542826653,
-0.0576946847140789,
-0.020841266959905624,
0.014942997135221958,
0.0618111789226532,
0.004309543874114752,
0.03667398914694786,
0.02966589666903019,
0.014204457402229309,
-0.010531146079301834,
0.02431357465684414,
-0.001140096690505743,
0.005642727483063936,
-0.008933164179325104,
-0.019644103944301605,
-0.02239724062383175,
-0.0375678576529026,
-0.004951637703925371,
0.01634916476905346,
-0.0158208217471838,
-0.02817910723388195,
-0.0012270393781363964,
0.034875158220529556,
0.013725373893976212,
0.01298676896840334,
0.018130114302039146,
0.0032617326360195875,
0.006348385475575924,
0.03686109185218811,
0.013898381032049656,
0.012781836092472076,
0.009135725907981396,
0.09357321262359619,
-0.01730288751423359,
-0.024808363988995552,
-0.095323346555233,
-0.039223477244377136,
0.02285834029316902,
0.051269520074129105,
-0.0026696885470300913,
-0.018370965495705605,
-0.037261076271533966,
-0.026327379047870636,
0.03731362521648407,
-0.043674468994140625,
0.04531987011432648,
0.009762457571923733,
-0.02878464385867119,
-0.07081197202205658,
-0.054470643401145935,
0.008076215162873268,
0.04398965835571289,
0.0022157637868076563,
0.07022792100906372,
-0.00949040986597538,
-0.009609933942556381,
-0.023490171879529953,
0.014626290649175644,
0.03310530632734299,
0.04639230668544769,
-0.018470898270606995,
0.012601274065673351,
-0.007907314226031303,
0.034238655120134354,
-0.03827719762921333,
-0.060865651816129684,
0.031721629202365875,
-0.009904199279844761,
-0.023624295368790627,
0.04659731313586235,
0.014481179416179657,
-0.032916683703660965,
0.017279818654060364,
0.007979904301464558,
-0.009022445417940617,
-0.008533074520528316,
-0.01561215054243803,
0.06310757249593735,
0.03883271664381027,
0.016152579337358475,
0.04149209335446358,
0.002517380053177476,
-0.00426112674176693,
0.0015677541960030794,
0.0013768712524324656,
0.051297951489686966,
-0.002325484761968255,
0.014849669300019741,
0.002183890203014016,
0.014932725578546524,
-0.0522824190557003,
0.07287469506263733,
-0.0244487002491951,
-0.01887742429971695,
-0.04142475128173828,
0.02317744866013527,
0.012969673611223698,
-0.011071923188865185,
0.0021387403830885887,
0.001241890829987824,
-0.01796860434114933,
0.02761332131922245,
0.014226740226149559,
-0.04786810278892517,
0.03846760839223862,
-0.03015369176864624,
0.030732521787285805,
0.04385218769311905,
-0.008343946188688278,
0.024725275114178658,
-0.008121145889163017,
-0.007602727506309748,
0.005166909657418728,
-0.038669735193252563,
0.01863788068294525,
-0.009942110627889633,
-0.007908310741186142,
0.004879408981651068,
0.02148161083459854,
-0.02875363454222679,
0.016697915270924568,
-0.013642043806612492,
-0.012526171281933784,
-0.06421712785959244,
0.05276113748550415,
0.031505659222602844,
-0.017275307327508926,
-0.05854184553027153,
-0.08142049610614777,
0.02222585491836071,
0.01589518040418625,
0.015352562069892883,
-0.00011243352491874248,
-0.007723401766270399,
-0.012288476340472698,
-0.021061694249510765,
-0.004626392386853695,
0.018168188631534576,
-0.05460155010223389,
-0.008641953580081463,
0.03939743712544441,
0.01966252736747265,
0.04978063702583313,
0.01233005803078413,
-0.022252259775996208,
0.010605941526591778,
-0.025786908343434334,
0.003691024612635374,
-0.018787428736686707,
0.04284629598259926,
-0.021738091483712196,
-0.046563420444726944,
0.030679844319820404,
0.006299283821135759,
0.04834391549229622,
0.007088534999638796,
-0.0006556629086844623,
0.05644574016332626,
-0.009515137411653996,
-0.0009182541398331523,
-0.016474317759275436,
-0.006112916395068169,
0.058800507336854935,
0.04387422278523445,
0.019622063264250755,
-0.029400549829006195,
-0.04767637699842453,
-0.012972799129784107,
-0.009505159221589565,
0.03397199884057045,
-0.010153201408684254,
-0.008792288601398468,
0.06988940387964249,
-0.03429283946752548,
-0.023506470024585724,
0.018285591155290604,
-0.006151002831757069,
0.03252206742763519,
-0.005906170699745417,
-0.008100143633782864,
-0.002461368916556239,
-0.0007591008325107396,
-0.05533453822135925,
-0.035119544714689255,
-0.03766067698597908,
0.011472209356725216,
0.03282560780644417,
-0.024791697040200233,
0.04025998339056969,
0.0112671023234725,
-0.011947322636842728,
-0.02973254583775997,
-0.028492478653788567,
-0.01035275962203741,
0.0007692207582294941,
-0.030785072594881058,
-0.011934901587665081,
0.00284227984957397,
-0.01707872748374939,
0.03129586949944496,
0.037793245166540146,
-0.0629381313920021,
-0.0015131182735785842,
0.0449979305267334,
0.028078196570277214,
0.043345481157302856,
-0.015191922895610332,
-0.025146691128611565,
-0.005884974729269743,
-0.0461166650056839,
0.03442962095141411,
0.01906765252351761,
0.02197997458279133,
0.05600203573703766,
0.003288290463387966,
0.020908726379275322,
-0.04203449562191963,
-0.013850263319909573,
-0.005113663617521524,
-0.01171282958239317,
0.024504348635673523,
0.02179856225848198,
0.013786641880869865,
0.015923667699098587,
0.012753359973430634,
0.0003266899148002267,
0.021208109334111214,
0.00532932486385107,
-0.052727144211530685,
-0.03201911598443985,
-0.027472330257296562,
-0.042516082525253296,
0.044439785182476044,
0.005529151763767004,
-0.04087740182876587,
0.0037760946433991194,
-0.040327347815036774,
0.034577883780002594,
0.028664397075772285,
0.025037432089447975,
-0.009393995627760887,
0.04660510644316673,
-0.017482195049524307,
0.06967692077159882,
-0.03920622542500496,
-0.0016478040488436818,
0.12581893801689148,
0.03979646414518356,
-0.007316214963793755,
-0.039366208016872406,
0.0005004016566090286,
-0.03833475336432457,
0.010776259005069733,
-0.016774823889136314,
0.02789720892906189,
-0.011524323374032974,
0.00319552980363369,
0.021075477823615074,
0.025070317089557648,
-0.011317471973598003,
-0.016319753602147102,
0.022029606625437737,
-0.07068201154470444,
-0.008521758951246738,
-0.006056196987628937,
0.02620028704404831,
0.0008307172101922333,
0.00541335716843605,
-0.06254108995199203,
0.010028059594333172,
-0.026713622733950615,
0.018398141488432884,
-0.02457496151328087,
-0.006011139135807753,
0.02084541507065296,
0.019164590165019035,
-0.03168681263923645,
0.04464147612452507,
0.0326765812933445,
-0.022035973146557808,
-0.0424673929810524,
0.022107770666480064,
0.031180445104837418,
0.029290074482560158,
0.010265120305120945,
0.04041906073689461,
0.04426420107483864,
-0.015828179195523262,
0.021434525027871132,
0.03667723760008812,
-0.04300228878855705,
-0.004478423856198788,
-0.04809451848268509,
0.029696989804506302,
0.012838729657232761,
0.004293275065720081,
0.026602888479828835,
0.05565587431192398,
0.03652827814221382,
-0.02613116055727005,
-0.0358557291328907,
0.009703795425593853,
-0.003328145481646061,
-0.026116658002138138,
-0.020530296489596367,
-0.018266672268509865,
0.02264983579516411,
0.007032773457467556,
-0.010953303426504135,
-0.005269376561045647,
-0.007302911952137947,
0.006240904331207275,
0.02801746316254139,
0.030062999576330185,
-0.037287551909685135,
0.013446344994008541,
-0.016184937208890915,
-0.0017956598894670606,
0.011094233952462673,
-0.004850970581173897,
0.037417542189359665,
-0.01439527329057455,
0.005351158790290356,
-0.051692187786102295,
0.014385269023478031,
0.018724681809544563,
-0.049144256860017776,
0.04121510684490204,
0.01757013238966465,
0.01176377572119236,
-0.015662167221307755,
0.002680484438315034,
-0.011751154437661171,
0.029971739277243614,
-0.03257448598742485,
0.012840536423027515,
0.01121671311557293,
0.04096970707178116,
0.014799403958022594,
-0.009949667379260063,
-0.03569971024990082,
-0.004249306861311197,
-0.02843119017779827,
0.026879891753196716,
0.0363960824906826,
0.06508511304855347,
0.038440898060798645,
0.02547469176352024,
0.009261037223041058,
0.047661565244197845,
-0.018196556717157364,
0.007490783464163542,
0.012944918125867844,
-0.03711015731096268,
0.001122696092352271,
0.0012186014791950583,
0.024902313947677612,
-0.010631006211042404,
-0.025205878540873528,
-0.0025788345374166965,
0.010911259800195694,
0.0421990342438221,
0.022214150056242943,
-0.047118447721004486,
-0.030737314373254776,
-0.006707766093313694,
0.04960991442203522,
-0.023320239037275314,
-0.01772458478808403,
-0.04021042585372925,
-0.020489757880568504,
0.024481020867824554,
0.015804016962647438,
0.03898325935006142,
0.03332044184207916,
-0.022897180169820786,
-0.03261171281337738,
0.009459489956498146,
-0.0024767168797552586,
-0.028502143919467926,
-0.015767691656947136,
-0.015613301657140255,
-0.005535053554922342,
-0.004093448165804148,
-0.002588074654340744,
-0.04493860527873039,
0.029354119673371315,
-0.01919848844408989,
-0.03368960693478584,
-0.00019713275833055377,
-0.009255694225430489,
0.028467148542404175,
0.026737498119473457,
-0.007252164650708437,
-0.03298308327794075,
0.024290265515446663,
0.016726037487387657,
0.010536203160881996,
0.0019531804136931896,
-0.008218386210501194,
-0.0004905071691609919,
-0.015163364820182323,
-0.0033282889053225517,
-0.004668671637773514,
-0.0031446213833987713,
-0.011104583740234375,
0.02528381161391735,
0.010718663223087788,
-0.0311044380068779,
-0.013702133670449257,
0.002680486300960183,
-0.028438463807106018,
0.04591726139187813,
0.021790580824017525,
0.01552767027169466,
0.025055911391973495,
-0.04451592266559601,
0.021889012306928635,
-0.01503119245171547,
0.01740385964512825,
-0.09797574579715729,
0.00521897105500102,
-0.014081834815442562,
-0.0380394272506237,
-0.0028307177126407623,
-0.03213212639093399,
-0.02217700332403183,
0.029415832832455635,
-0.10195356607437134,
0.0042200032621622086,
-0.01956911012530327,
-0.029339781031012535,
-0.016894832253456116,
-0.022094357758760452,
-0.005281158722937107,
0.04411735385656357,
0.03020668402314186,
0.03591885045170784,
-0.017086928710341454,
-0.007407861761748791,
0.006081139203161001,
-0.018401162698864937,
-0.021630551666021347,
0.03467002511024475,
-0.0031872165855020285,
0.004668183159083128,
0.03740503638982773,
-0.025991830974817276,
0.02139587141573429,
0.03247242048382759,
-0.007428755518049002,
-0.006829450838267803,
0.011770994402468204,
-0.009718187153339386,
0.016085119917988777,
0.05597401782870293,
-0.018489951267838478,
0.0009264133404940367,
-0.00985445361584425,
0.023006796836853027,
0.002070660935714841,
0.030160516500473022,
0.010413303971290588,
-0.010625256225466728,
0.03533167764544487,
-0.02786070853471756,
0.018499085679650307,
0.014958846382796764,
-0.0285996925085783,
-0.025422418490052223,
-0.008341393433511257,
0.030354615300893784,
0.010730101726949215,
-0.025230692699551582,
0.0025403096806257963,
-0.0347028411924839,
-0.07428932189941406,
0.0395415723323822,
0.02899104356765747,
0.027053529396653175,
-0.0018548965454101562,
-0.02976255491375923,
-0.03519598767161369,
0.03180597722530365,
0.025191744789481163,
-0.016645735129714012,
-0.03147577866911888,
-0.008838075213134289,
0.020711630582809448,
-0.001473411568440497,
0.026799840852618217,
-0.0653228685259819,
-0.03927488625049591,
0.02812618389725685,
0.02568764239549637,
0.023629456758499146,
-0.03290187940001488,
-0.08841577172279358,
-0.05389678105711937,
-0.04670434445142746,
0.05308602377772331,
-0.03775898367166519,
-0.029712457209825516,
-0.04333896189928055,
-0.01971304602921009,
-0.01774778962135315,
0.024209914728999138,
0.055015675723552704,
0.014570693485438824,
-0.009242378175258636,
0.02355954982340336,
-0.021553391590714455,
0.03299623727798462,
-0.04219534993171692,
0.028715830296278,
0.02148648165166378,
0.005586826708167791,
0.04907432943582535,
-0.01771502196788788,
0.0006144953658804297,
0.019160419702529907,
0.004548290278762579,
0.021325118839740753,
0.023141777142882347,
-0.03478362783789635,
-0.0399874709546566,
0.013389954343438148,
0.027713993564248085,
-0.021559400483965874,
0.05211938917636871,
-0.022511735558509827,
0.01814165711402893,
-0.0410335399210453,
0.000640386191662401,
-0.05603022873401642,
0.030238686129450798,
-0.052286770194768906,
0.03984180465340614,
-0.0315621979534626,
-0.008125732652842999,
0.03612636402249336,
-0.02052444778382778,
-0.01753194071352482,
0.039983004331588745,
-0.040141742676496506,
-0.015304295346140862,
0.04390711709856987,
-0.02421920746564865,
0.01647803746163845,
-0.04214981198310852,
-0.0027321770321577787,
-0.007307287771254778,
0.010512619279325008,
0.012971318326890469,
0.040641866624355316,
0.007744613569229841,
-0.023396138101816177,
0.00948355533182621,
0.06504488736391068,
-0.008708497509360313,
0.007195144426077604,
0.002867504023015499,
0.00722548458725214,
-0.033749185502529144,
-0.03051360882818699,
0.042306240648031235,
-0.018544679507613182,
0.0009936746209859848,
0.05089640989899635,
0.004962482955306768,
0.11123008280992508,
-0.01342098880559206,
0.03627432882785797,
0.0022622733376920223,
0.0070321569219231606,
-0.02502414584159851,
0.0071647269651293755,
0.026065677404403687,
0.05329432711005211,
-0.022643081843852997,
-0.004050839226692915,
-0.025186048820614815,
-0.008117920719087124,
0.04595418646931648,
-0.028374183923006058,
0.016724668443202972,
-0.01260495837777853,
-0.017402367666363716,
-0.014828179962933064,
-0.018720582127571106,
-0.04326663538813591,
-0.04963252320885658,
0.046957504004240036,
0.03028078004717827,
0.04604765400290489,
-0.0010842237388715148,
-0.033726487308740616,
-0.029877670109272003,
0.04473582282662392,
-0.058663591742515564,
0.023946287110447884,
-0.018510760739445686,
0.03234412521123886,
0.020420057699084282,
0.009430481120944023
] |
<p>Given the solution of the Von Neumann equation
$\rho(t) = e^{-i H t/\hbar} \rho(0) e^{i H t/\hbar}$</p>
<p>How can we justify if it will be stabilized as $t\rightarrow\infty$ in general?</p>
<p>For example, $H=\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}, \rho(0)=\begin{pmatrix}\frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & \frac{1}{2}\end{pmatrix}$, it will simply be fixed? But is it normal? Shouldn't there be some wave dynamics before reaching equilibrium?</p> | 2,023 | [
-0.034851305186748505,
0.006093570496886969,
0.03020166978240013,
-0.04547686502337456,
-0.0023324156645685434,
-0.010723746381700039,
-0.03758324310183525,
0.00044387183152139187,
0.015140795148909092,
-0.04952923208475113,
-0.002301247790455818,
0.030925551429390907,
0.03839710354804993,
0.02920180931687355,
0.05665181204676628,
0.021605229005217552,
0.008227388374507427,
-0.00994837749749422,
-0.028821628540754318,
-0.0035611609928309917,
-0.017162155359983444,
0.031907740980386734,
0.0187093336135149,
-0.0214469525963068,
-0.03378545492887497,
0.035493966192007065,
0.012468323111534119,
-0.007225274574011564,
0.03824114799499512,
0.0352330319583416,
-0.03579410910606384,
-0.022191114723682404,
-0.0036346432752907276,
0.013927563093602657,
0.007955274544656277,
0.005689370911568403,
-0.02100786752998829,
-0.04362627863883972,
-0.0015633056173101068,
0.035260897129774094,
-0.04774977266788483,
0.018769316375255585,
-0.040363702923059464,
0.028764376416802406,
-0.01212981715798378,
-0.004493121523410082,
0.0279084462672472,
-0.01774466596543789,
0.047318775206804276,
-0.03385283425450325,
0.04748673364520073,
-0.0044222488068044186,
0.011839284561574459,
0.030681777745485306,
0.0010700896382331848,
-0.055710569024086,
0.06578945368528366,
0.029699303209781647,
0.0045045968145132065,
-0.018230998888611794,
-0.004204268101602793,
-0.021474676206707954,
-0.009858625940978527,
0.005368037614971399,
0.004132249858230352,
0.015084991231560707,
0.017567405477166176,
-0.02593938447535038,
0.020365919917821884,
-0.05457715317606926,
-0.0043191988952457905,
0.021592512726783752,
-0.012204263359308243,
-0.05189598351716995,
0.06518261134624481,
-0.007968666963279247,
0.007047387305647135,
0.016143208369612694,
0.00413138372823596,
0.035054706037044525,
0.031218262389302254,
-0.009499326348304749,
0.018002184107899666,
0.041664693504571915,
-0.016665462404489517,
0.01870957762002945,
0.07403981685638428,
-0.031120119616389275,
0.03302961587905884,
0.05793416500091553,
0.016316434368491173,
0.020234182476997375,
0.040780846029520035,
-0.049245256930589676,
-0.019833959639072418,
0.050029437988996506,
0.0030814148485660553,
0.04978451877832413,
0.021004632115364075,
-0.03351641073822975,
-0.008364636451005936,
-0.05815381184220314,
-0.024598509073257446,
0.022451868280768394,
0.004497314337641001,
-0.010666909627616405,
-0.06193763017654419,
0.0001330477389274165,
-0.03137527033686638,
-0.018531449139118195,
-0.033805232495069504,
0.02111334353685379,
-0.01201599184423685,
-0.00602018041536212,
-0.01225077360868454,
-0.023721598088741302,
0.022003818303346634,
-0.03800041601061821,
0.04020882397890091,
0.07495100796222687,
0.035318925976753235,
-0.030249562114477158,
0.0351654589176178,
-0.009005758911371231,
-0.0875299870967865,
0.006977003999054432,
0.014694004319608212,
-0.015811339020729065,
-0.0640479326248169,
0.004984482191503048,
0.0218666922301054,
0.001751686679199338,
0.05628244951367378,
-0.006800783798098564,
0.07335560023784637,
-0.017417537048459053,
-0.07625718414783478,
-0.036446209996938705,
0.06398478895425797,
-0.02970857359468937,
-0.02557534910738468,
-0.08619432151317596,
-0.021364672109484673,
0.05636976659297943,
0.08993418514728546,
-0.025694342330098152,
0.02071947231888771,
0.022818658500909805,
-0.012396997772157192,
0.013962303288280964,
-0.021856462582945824,
-0.04186977818608284,
0.013085676357150078,
-0.03754610940814018,
-0.027708427980542183,
-0.023826153948903084,
0.027302470058202744,
0.03634234517812729,
0.019493361935019493,
0.010020892135798931,
0.040186557918787,
0.010823617689311504,
-0.027859102934598923,
-0.007777324877679348,
-0.03823615610599518,
-0.02665787748992443,
0.08967979997396469,
0.006117822602391243,
0.028485506772994995,
-0.002824698807671666,
-0.0034532235004007816,
0.018802564591169357,
0.0036787656135857105,
0.012977932579815388,
0.013491681776940823,
-0.029459089040756226,
-0.006949163042008877,
-0.009941035881638527,
-0.0023624643217772245,
-0.00104776700027287,
-0.043499503284692764,
-0.0021176435984671116,
-0.023486243560910225,
0.03267752006649971,
0.011931224726140499,
0.02898930013179779,
-0.05036536231637001,
0.043282974511384964,
-0.007410782855004072,
-0.06928587704896927,
0.010434802621603012,
-0.03307398408651352,
0.013636485673487186,
0.01304041687399149,
-0.009979511611163616,
0.05369826778769493,
0.018002761527895927,
0.013523709028959274,
-0.020990418270230293,
-0.017378566786646843,
-0.007783209439367056,
0.022798879072070122,
0.0450410358607769,
-0.024341994896531105,
0.05182997137308121,
0.03126315027475357,
0.05133839324116707,
0.014711568132042885,
0.04306535795331001,
-0.01837773621082306,
-0.039858125150203705,
-0.01652783341705799,
-0.009990961290895939,
0.029775861650705338,
0.012324836105108261,
-0.0032467921264469624,
-0.02865118347108364,
-0.05443224683403969,
0.018162313848733902,
-0.011408466845750809,
-0.05315975844860077,
0.039719898253679276,
0.044479575008153915,
-0.008051096461713314,
0.008185464888811111,
0.019946422427892685,
0.01277382392436266,
0.010827802121639252,
0.004307496827095747,
-0.034528814256191254,
-0.02447243593633175,
0.003206066321581602,
0.018696237355470657,
0.0972026139497757,
-0.05121208727359772,
0.019086739048361778,
-0.006975770462304354,
0.020477088168263435,
0.03389415889978409,
0.018285738304257393,
-0.02930709719657898,
-0.03862924128770828,
0.04638836532831192,
0.009450986050069332,
0.004969393368810415,
0.0029324654024094343,
0.04521318897604942,
-0.012575702741742134,
-0.012045222334563732,
-0.0041730948723852634,
0.0009934311965480447,
0.02279694564640522,
0.0076459902338683605,
-0.030479246750473976,
-0.009777924045920372,
-0.005740561988204718,
0.03226307034492493,
0.012141907587647438,
-0.0013871960109099746,
0.012192665599286556,
-0.006634727120399475,
0.012710309587419033,
-0.03964144363999367,
-0.009861288592219353,
0.010640021413564682,
-0.004311316180974245,
-0.014928208664059639,
-0.04394916072487831,
0.025911075994372368,
0.006552970968186855,
-0.011814888566732407,
-0.06280779093503952,
-0.021504102274775505,
0.013155273161828518,
-0.01840836927294731,
0.06396220624446869,
0.008691948838531971,
0.002525911433622241,
-0.04253240302205086,
-0.027095548808574677,
0.012928444892168045,
-0.00033503881422802806,
0.03964286670088768,
0.030129333958029747,
-0.01207332219928503,
0.009720971807837486,
-0.031225381419062614,
0.0005022665136493742,
0.02928696572780609,
-0.006418521516025066,
0.012138472869992256,
0.013424458913505077,
-0.0044967373833060265,
-0.08239570260047913,
-0.04288214072585106,
-0.01882886327803135,
0.011876202188432217,
-0.05779452621936798,
0.006296083331108093,
0.0456213504076004,
-0.015497521497309208,
-0.003912878222763538,
0.03168702870607376,
-0.03965957835316658,
-0.02833958901464939,
0.007226946763694286,
-0.008920208550989628,
0.04673408716917038,
-0.015443825162947178,
0.062263183295726776,
0.01021749060600996,
-0.031505268067121506,
0.006262065842747688,
-0.04952399805188179,
-0.01698802225291729,
0.05134809762239456,
-0.018867140635848045,
0.041082773357629776,
0.02400418184697628,
-0.05233980715274811,
0.12160801142454147,
0.016103466972708702,
-0.003073532599955797,
0.02520734630525112,
-0.0016698386752977967,
-0.013499232940375805,
-0.03203641623258591,
0.007182637229561806,
0.03288716822862625,
0.020970236510038376,
0.0222301185131073,
0.025013480335474014,
0.029799090698361397,
0.05093124508857727,
0.00955343246459961,
-0.04024132713675499,
0.0507635734975338,
0.0177669208496809,
0.017009571194648743,
0.04513915628194809,
-0.010752798989415169,
-0.003576710121706128,
0.00381084275431931,
-0.00632083136588335,
0.008002220652997494,
0.020555395632982254,
-0.06059165298938751,
0.04372363165020943,
-0.0007492483127862215,
0.005753023084253073,
-0.025496961548924446,
0.023697273805737495,
-0.007353635039180517,
-0.03996482864022255,
-0.06218992546200752,
-0.006803600117564201,
0.04748547822237015,
-0.01381533220410347,
0.05576383322477341,
0.03672642260789871,
0.011314227245748043,
-0.005044340156018734,
-0.013740193098783493,
0.05436636880040169,
-0.021743860095739365,
0.046489961445331573,
-0.024672484025359154,
-0.07025474309921265,
0.04565143212676048,
0.018400155007839203,
-0.0112259890884161,
-0.019316701218485832,
-0.014986829832196236,
-0.022328851744532585,
-0.043740324676036835,
0.02835850976407528,
-0.010978247039020061,
0.062001410871744156,
-0.03596065193414688,
0.021939698606729507,
0.03832247853279114,
0.04518592730164528,
0.024553321301937103,
-0.013106042519211769,
-0.08787436038255692,
-0.028835788369178772,
-0.027848806232213974,
-0.013574959710240364,
0.010412877425551414,
-0.027587497606873512,
0.007417779415845871,
0.0099199702963233,
-0.025427956134080887,
-0.003200487233698368,
-0.00813845545053482,
-0.04325571656227112,
0.007190627511590719,
-0.05109455808997154,
-0.03270582854747772,
-0.018201258033514023,
0.004683333914726973,
0.03280503302812576,
-0.00453339284285903,
0.009221531450748444,
0.05425189062952995,
-0.030222831293940544,
0.0494614876806736,
-0.018277648836374283,
-0.015841543674468994,
-0.011659936048090458,
0.002780295442789793,
0.0657513439655304,
0.0067492383532226086,
-0.03017471916973591,
0.003929178696125746,
0.03941161185503006,
0.059422243386507034,
-0.00470331497490406,
0.02865634486079216,
0.017483672127127647,
-0.04088461399078369,
-0.034086767584085464,
-0.027558404952287674,
0.013945518061518669,
0.019924823194742203,
-0.0018450337229296565,
0.023870889097452164,
-0.004570094868540764,
-0.025374744087457657,
0.017085781320929527,
0.057416126132011414,
0.002670841058716178,
-0.013280997984111309,
-0.030545972287654877,
-0.014528377912938595,
0.002821051049977541,
0.02697361633181572,
-0.015709735453128815,
-0.04038611799478531,
-0.011705408804118633,
0.025105012580752373,
0.002631204668432474,
0.07328581064939499,
0.013052457943558693,
-0.025931429117918015,
0.028104091063141823,
0.02833966538310051,
0.025168169289827347,
0.0028409918304532766,
0.027959909290075302,
0.018350685015320778,
0.030449794605374336,
0.01747843809425831,
0.006519879214465618,
-0.04533833637833595,
0.01229831576347351,
-0.008761793375015259,
0.05002819001674652,
0.0197414830327034,
0.0019641381222754717,
-0.07614538818597794,
-0.019028611481189728,
0.06297890841960907,
-0.009975913912057877,
0.052984416484832764,
-0.004795733839273453,
-0.03170431777834892,
0.0070101432502269745,
-0.015353202819824219,
-0.039736662060022354,
-0.006945024710148573,
0.01541089080274105,
-0.010716564022004604,
-0.03892376646399498,
-0.012888705357909203,
-0.014017591252923012,
0.005013123154640198,
0.008075153455138206,
0.057991448789834976,
-0.00129958416800946,
-0.009957967326045036,
0.020817121490836143,
0.02886420302093029,
-0.02429843693971634,
-0.07464323937892914,
-0.020333344116806984,
0.02031233347952366,
-0.009603532962501049,
0.02082706056535244,
-0.026708416640758514,
-0.05636497586965561,
0.06109754368662834,
0.017253749072551727,
-0.03155555576086044,
0.03306315466761589,
0.007854495197534561,
0.03445574641227722,
0.010248921811580658,
-0.01948542706668377,
0.0457628034055233,
0.06107231602072716,
0.03124833293259144,
0.0024713005404919386,
-0.006834414787590504,
0.028403086587786674,
-0.04707206413149834,
0.0328587107360363,
-0.023608317598700523,
0.01582576148211956,
-0.017991993576288223,
0.025495650246739388,
0.042728669941425323,
0.015038625337183475,
0.019299698993563652,
-0.004397022537887096,
0.01662420853972435,
0.046993110328912735,
-0.039349429309368134,
-0.04088059812784195,
0.023259833455085754,
0.04173053056001663,
0.004646421875804663,
-0.039847854524850845,
-0.008002200163900852,
-0.015187699347734451,
0.0024385505821555853,
0.07678148150444031,
-0.026746802031993866,
0.03653998300433159,
-0.05135609209537506,
-0.013203245587646961,
-0.009448111057281494,
-0.030689211562275887,
0.012498058378696442,
-0.021061794832348824,
0.0350085124373436,
-0.0020259544253349304,
-0.03311360999941826,
-0.002301564672961831,
0.0029825610108673573,
0.015640782192349434,
0.022761745378375053,
-0.006011134944856167,
0.036145854741334915,
0.038648925721645355,
0.005287047475576401,
-0.08242327719926834,
-0.026167131960392,
0.0007986691198311746,
0.015069622546434402,
-0.006757526192814112,
-0.04243028908967972,
0.03410940244793892,
-0.004114270210266113,
-0.0392429418861866,
0.011566102504730225,
0.04220180958509445,
-0.019264958798885345,
-0.0013533056480810046,
0.022855741903185844,
0.032772645354270935,
0.02542613446712494,
-0.022358989343047142,
-0.023068707436323166,
0.023397959768772125,
-0.04343925416469574,
-0.012844306416809559,
0.00004868300675298087,
0.06328888982534409,
-0.022139649838209152,
-0.035756420344114304,
-0.006183725316077471,
-0.023039668798446655,
0.024383090436458588,
-0.012735920026898384,
-0.030930927023291588,
0.01862259767949581,
0.0005219062441028655,
0.026322370395064354,
-0.03935956954956055,
-0.02882661111652851,
-0.0556635782122612,
0.05058031156659126,
0.0543721579015255,
-0.008215569891035557,
-0.030742792412638664,
-0.05947096273303032,
0.014586405828595161,
0.013178328052163124,
0.004567086696624756,
0.003186465473845601,
0.061849214136600494,
-0.00579559151083231,
0.00046914719860069454,
0.0004584449634421617,
-0.014799503609538078,
0.016030196100473404,
0.017160886898636818,
-0.02258739434182644,
0.011019079945981503,
-0.014793803915381432,
-0.01110992580652237,
-0.09639455378055573,
-0.06920434534549713,
0.03770352527499199,
0.03228168562054634,
-0.010070683434605598,
0.0282325129956007,
0.016489405184984207,
0.017274294048547745,
-0.025106368586421013,
-0.012358288280665874,
-0.016910415142774582,
-0.010966948233544827,
-0.0002546424511820078,
0.0018645164091140032,
-0.04026690125465393,
-0.017635678872466087,
0.02219628356397152,
0.055631618946790695,
0.011632206849753857,
-0.003609009552747011,
0.03332105651497841,
0.023383455350995064,
0.004827507305890322,
-0.005502454936504364,
-0.019123323261737823,
0.07348814606666565,
-0.03311140090227127,
0.049197614192962646,
-0.015522148460149765,
-0.02710134908556938,
0.027632420882582664,
0.02285187505185604,
0.02778785116970539,
-0.03667190298438072,
-0.03300510346889496,
-0.023175004869699478,
0.039301998913288116,
-0.003154234727844596,
-0.013526566326618195,
0.03677880018949509,
-0.002109980210661888,
0.04091400280594826,
-0.015937333926558495,
0.01952436938881874,
-0.01914326287806034,
-0.015590786002576351,
-0.004204998258501291,
0.011192021891474724,
-0.029796628281474113,
0.021585114300251007,
0.015336534008383751,
-0.03690279275178909,
0.03794088214635849,
-0.04995453730225563,
0.014148828573524952,
0.0025428428780287504,
0.022075064480304718,
-0.008355471305549145,
0.04854593053460121,
0.02487497590482235,
0.02751760184764862,
-0.015387089923024178,
0.01028319913893938,
0.13182111084461212,
0.0696161687374115,
0.02644295245409012,
-0.037149637937545776,
-0.0003132910933345556,
0.008471999317407608,
0.020858697593212128,
-0.05999911576509476,
-0.013465624302625656,
0.020085521042346954,
0.020703045651316643,
0.008028280921280384,
0.038671836256980896,
0.014881687238812447,
0.03209114074707031,
0.007130459416657686,
-0.04826970398426056,
-0.039956241846084595,
-0.002525826683267951,
-0.00028254679637029767,
0.0024119545705616474,
0.013195282779633999,
-0.006277100183069706,
0.03650593012571335,
-0.0068124206736683846,
-0.01740921474993229,
-0.017870552837848663,
-0.013365555554628372,
0.03891398385167122,
-0.011724812909960747,
-0.05266367644071579,
0.011900488287210464,
-0.017749033868312836,
0.003433477832004428,
-0.0013754448154941201,
0.016894666478037834,
-0.012570020742714405,
0.009155704639852047,
0.029784303158521652,
0.021152082830667496,
0.0004595330683514476,
0.0019156330963596702,
0.00992689561098814,
0.000980513053946197,
-0.010937899351119995,
-0.0013820326421409845,
-0.010291806422173977,
0.06372729688882828,
-0.016634168103337288,
0.012773132883012295,
0.011026246473193169,
0.00014266785001382232,
0.0007508097914978862,
-0.015616461634635925,
-0.01589668169617653,
-0.00862928107380867,
0.010649840347468853,
0.010265858843922615,
-0.0016742987791076303,
-0.0457124337553978,
-0.018501054495573044,
-0.004450720269232988,
-0.004809243604540825,
0.00039889823528937995,
-0.02419492043554783,
-0.014547674916684628,
-0.0006190083804540336,
0.05719544738531113,
-0.0055221691727638245,
-0.005566583015024662,
-0.004498546477407217,
-0.016790900379419327,
-0.047110334038734436,
-0.03856464475393295,
0.004214470274746418,
-0.018220940604805946,
0.06827111542224884,
0.00894942507147789,
0.006089537870138884,
-0.025531936436891556,
-0.09619695693254471,
-0.007089462596923113,
0.002398903016000986,
-0.015219065360724926,
-0.01594940759241581,
-0.04474242031574249,
-0.02173609845340252,
0.030605407431721687,
-0.0282108373939991,
-0.0049606868997216225,
0.002519709523767233,
-0.010215405374765396,
0.008670725859701633,
-0.01363141555339098,
-0.056474391371011734,
-0.001081379596143961,
-0.021319745108485222,
0.05216757953166962,
-0.019853951409459114,
0.013601245358586311,
0.014111931435763836,
-0.001245044870302081,
0.012018878012895584,
0.0227340254932642,
-0.01284007728099823,
0.011988283134996891,
0.018005995079874992,
-0.013552900403738022,
0.023357881233096123,
0.031018352136015892,
0.029805216938257217,
-0.028217626735568047,
-0.03334249556064606,
-0.017589589580893517,
0.005887647159397602,
-0.03155190870165825,
0.018391229212284088,
-0.015209386125206947,
0.011674433946609497,
-0.03165172040462494,
0.029310371726751328,
-0.05794032663106918,
-0.036412499845027924,
-0.05724393203854561,
0.014677735045552254,
0.0016131836455315351,
0.02599056251347065,
0.01090132538229227,
0.02056468464434147,
0.01991971582174301,
-0.05932382121682167,
0.03088069148361683,
0.020549235865473747,
0.003958049695938826,
0.0033478422556072474,
0.0005614979309029877,
0.029028337448835373,
0.02258397825062275,
-0.01524209976196289,
-0.02962941862642765,
0.04690764471888542,
-0.023376358672976494,
-0.01448290329426527,
-0.003294162219390273,
0.02991599589586258,
0.015913894400000572,
0.014851061627268791,
-0.02842729166150093,
-0.0014975403901189566,
0.019659023731946945,
-0.029322175309062004,
0.011682786978781223,
0.04369032382965088,
-0.05195048078894615,
-0.029125237837433815,
0.005269655957818031,
0.025702789425849915,
-0.026178136467933655,
-0.0127640962600708,
0.01695375144481659,
0.08218633383512497,
-0.03103417158126831,
-0.0032383431680500507,
0.004417625721544027,
0.0022186599671840668,
0.04615837708115578,
-0.01701289974153042,
0.040459807962179184,
0.017592880874872208,
0.03233730420470238,
-0.056354694068431854,
-0.004931616131216288,
0.005130641162395477,
0.007196701131761074,
-0.0957181453704834,
-0.040414854884147644,
0.01993677206337452,
-0.04094569757580757,
0.04067551717162132,
-0.0011833858443424106,
0.011102802120149136,
0.031075110659003258,
-0.05438733845949173,
0.028533121570944786,
-0.01852763630449772,
-0.016268495470285416,
-0.0493941456079483,
-0.018234899267554283,
-0.0640048235654831,
0.035577744245529175,
0.032582975924015045,
0.04950018599629402,
-0.0009670084691606462,
0.03815802186727524,
-0.027198294177651405,
-0.01418428122997284,
-0.00550598930567503,
0.0426023043692112,
-0.007408676669001579,
0.000967365805990994,
0.05210432782769203,
-0.011774236336350441,
-0.04226028546690941,
-0.004693137481808662,
-0.027161991223692894,
-0.003769688308238983,
-0.00960620492696762,
0.01912592723965645,
-0.027601031586527824,
0.034613970667123795,
0.02261434867978096,
-0.042023222893476486,
0.0210161991417408,
0.018063558265566826,
0.0188667643815279,
-0.006770409177988768,
0.012819997034966946,
-0.004803040064871311,
0.016422461718320847,
-0.06486266851425171,
-0.048660557717084885,
0.06813840568065643,
-0.021689174696803093,
-0.0042183310724794865,
0.013972402550280094,
-0.015070762485265732,
-0.018350834026932716,
-0.028268028050661087,
0.033324796706438065,
-0.022387098520994186,
-0.0110383415594697,
0.02177456207573414,
0.04366307705640793,
-0.004330452065914869,
0.005374952685087919,
-0.03275635093450546,
-0.01728946901857853,
0.04519398510456085,
0.03039378859102726,
-0.01877138949930668,
-0.08759914338588715,
-0.04231848195195198,
0.024317670613527298,
0.0034256053622812033,
-0.00666558975353837,
-0.02018957957625389,
-0.03463941812515259,
0.04723752662539482,
-0.0001323055912507698,
0.009703883901238441,
-0.05033553019165993,
-0.042138852179050446,
-0.05322594195604324,
-0.06074347719550133,
0.017417702823877335,
-0.03160865977406502,
-0.012395946308970451,
-0.027008185163140297,
-0.04280468076467514,
-0.02577907219529152,
0.01979026198387146,
0.06410282850265503,
0.015569258481264114,
-0.007040918804705143,
0.02252247743308544,
-0.0101089458912611,
-0.021907988935709,
-0.02103339694440365,
-0.008717983961105347,
-0.0046112448908388615,
0.006339090410619974,
-0.024345699697732925,
-0.011191700585186481,
0.02514650672674179,
-0.007364349905401468,
0.003736658487468958,
0.00554525014013052,
0.034887831658124924,
-0.002325710840523243,
-0.08366627991199493,
0.02702704630792141,
0.01663592830300331,
-0.018728818744421005,
0.07770582288503647,
-0.009682424366474152,
0.004953604191541672,
0.02860759198665619,
-0.0393972247838974,
-0.0385662280023098,
0.0066735097207129,
-0.026515193283557892,
-0.002507861005142331,
-0.009755183942615986,
0.011284589767456055,
0.011868970468640327,
-0.013747616671025753,
-0.004470944404602051,
0.037624944001436234,
-0.0380561538040638,
-0.004183638375252485,
0.036231838166713715,
0.03791845217347145,
0.04038579761981964,
0.013285552151501179,
0.014481808990240097,
0.039677415043115616,
0.026376722380518913,
0.007277322933077812,
0.03816377371549606,
0.003949859645217657,
0.007796562742441893,
0.025373967364430428,
-0.0031962881330400705,
-0.07511736452579498,
0.007862089201807976,
0.00551422405987978,
-0.007547682151198387,
-0.04894789680838585,
-0.03667308762669563,
0.06418534368276596,
-0.04809689521789551,
-0.040742915123701096,
-0.003809409448876977,
-0.02413931116461754,
0.07510815560817719,
-0.03166913613677025,
0.01932004652917385,
-0.007246738765388727,
0.024988578632473946,
-0.013118666596710682,
0.004931407514959574,
-0.005341716576367617,
0.050088923424482346,
-0.028749221935868263,
0.032036472111940384,
-0.040106628090143204,
0.0007966191042214632,
-0.0000015513951439061202,
-0.048250481486320496,
-0.009446296840906143,
0.02368592843413353,
-0.0188895370811224,
-0.03655603528022766,
0.014373584650456905,
-0.03452800586819649,
-0.00006524653144879267,
-0.009553319774568081,
0.0419507771730423,
0.012546313926577568,
-0.013856198638677597,
-0.01596074365079403,
-0.0045071435160934925,
0.04241304472088814,
-0.03070983476936817,
0.011706859804689884,
-0.01843377947807312,
0.0011387967970222235,
-0.023724103346467018,
0.038807474076747894
] |
<p><img src="http://www.a-levelphysicstutor.com/images/matter/E-r-graph.jpg" alt="potential energy vs intermolecular distance r"></p>
<p>I'm trying to understand this curve better, but I can't quite figure out what "negative potential energy" means.</p>
<p>The graph should describe a molecule oscillating between $A$ and $B$, however where I'm stuck in reasoning this is that the PE is equal in $A$ and $B$, but then why does this mean $r$ will increase in $A$ (repel) and decrease in $B$?</p> | 2,024 | [
-0.03368280455470085,
-0.006278079003095627,
-0.006660149432718754,
-0.0039586895145475864,
0.010349723510444164,
0.03471950441598892,
-0.01322320755571127,
-0.01000411156564951,
0.022744938731193542,
-0.020990876480937004,
0.003919354174286127,
0.054894909262657166,
0.03531676158308983,
-0.027657313272356987,
0.021595897153019905,
-0.020813781768083572,
-0.01305841002613306,
-0.018585029989480972,
-0.0028613698668777943,
-0.028866970911622047,
0.053825218230485916,
-0.01389820221811533,
0.0592166893184185,
0.030881032347679138,
-0.02538366988301277,
0.0540328286588192,
0.060070574283599854,
-0.0339619442820549,
0.011968370527029037,
0.06962812691926956,
-0.028029998764395714,
-0.04303441569209099,
0.012713443487882614,
0.026656623929739,
0.023647606372833252,
0.013985184021294117,
-0.04413512349128723,
-0.03743484243750572,
-0.06293849647045135,
0.028465712442994118,
-0.049107637256383896,
-0.011178984306752682,
-0.005124534945935011,
0.0600743293762207,
-0.051330529153347015,
-0.023204930126667023,
0.0327979139983654,
-0.0263995174318552,
0.0483444444835186,
-0.06873650848865509,
0.0669599249958992,
0.016835711896419525,
0.04542861506342888,
0.017959296703338623,
-0.0050902944058179855,
-0.01830659992992878,
0.06862639635801315,
0.07869794964790344,
-0.03604097664356232,
-0.058167848736047745,
0.0049984036013484,
-0.023412508890032768,
-0.02711459808051586,
0.004681986756622791,
-0.025206688791513443,
0.02532906085252762,
0.014719993807375431,
0.0045106010511517525,
0.026351576671004295,
0.006799331400543451,
0.01552306767553091,
0.05457879230380058,
0.018694832921028137,
-0.04812601953744888,
0.02142258733510971,
-0.028763921931385994,
-0.019245903939008713,
0.03423275053501129,
0.03186764568090439,
0.05735868960618973,
-0.03891157731413841,
0.016954002901911736,
0.04912794753909111,
0.06844224780797958,
-0.017831232398748398,
-0.034810714423656464,
0.07010307163000107,
-0.000389543070923537,
-0.007905802689492702,
-0.01352627296000719,
-0.0060204449109733105,
0.029621735215187073,
0.03991127759218216,
-0.021647874265909195,
-0.012216762639582157,
0.016302259638905525,
0.0002656361320987344,
0.047457918524742126,
0.012544349767267704,
-0.024336840957403183,
-0.00430915504693985,
-0.05733808875083923,
0.022152669727802277,
0.053317591547966,
0.008553508669137955,
-0.0599200613796711,
-0.044940464198589325,
0.01599852927029133,
0.024151382967829704,
-0.023804301396012306,
-0.014731304720044136,
0.014073556289076805,
0.007996473461389542,
-0.006378472317010164,
0.0038967900909483433,
-0.03379939869046211,
-0.004375716671347618,
0.019448939710855484,
0.02576110139489174,
0.005684593226760626,
0.008977435529232025,
-0.03522708639502525,
0.06165526434779167,
0.005586051382124424,
-0.05242244154214859,
0.00749464426189661,
0.016057651489973068,
0.026363926008343697,
-0.030693383887410164,
0.012763867154717445,
0.0017302017658948898,
0.010185297578573227,
0.005385335069149733,
-0.002538854256272316,
0.0256618894636631,
0.028030667454004288,
-0.1105302944779396,
-0.05211057513952255,
0.04071417078375816,
-0.004092840012162924,
0.008555710315704346,
-0.06933168321847916,
-0.022934967651963234,
0.0461113303899765,
0.060583267360925674,
-0.007681409828364849,
-0.03572988137602806,
-0.01171076949685812,
0.0018375475192442536,
-0.0010083082597702742,
0.008118763566017151,
-0.02603098191320896,
-0.04961105436086655,
-0.018241850659251213,
-0.015804274007678032,
-0.06256222724914551,
0.004803171847015619,
0.04568637162446976,
-0.011081304401159286,
0.005839089397341013,
0.05142976716160774,
-0.03803934529423714,
-0.024539561942219734,
0.025447987020015717,
0.001723403693176806,
-0.006567827425897121,
0.08279827237129211,
0.030307363718748093,
-0.03296337276697159,
0.03257053345441818,
0.0008969816262833774,
0.03973127529025078,
-0.015130236744880676,
0.04715384915471077,
0.041823387145996094,
-0.02053879201412201,
-0.0012932030949741602,
-0.05048254504799843,
0.008055878803133965,
0.00039526313776150346,
-0.05275074020028114,
-0.05304739251732826,
-0.0015143647324293852,
-0.006873300299048424,
-0.0061070858500897884,
0.023827068507671356,
-0.014136843383312225,
0.006818969268351793,
0.011039393953979015,
-0.04057144373655319,
-0.03968631848692894,
-0.05431457608938217,
0.054015543311834335,
0.01605531945824623,
-0.044758304953575134,
0.034344155341386795,
0.05973181873559952,
0.024713687598705292,
-0.02086961641907692,
-0.004199172370135784,
-0.010347901843488216,
0.025120988488197327,
-0.01215514075011015,
0.004823243711143732,
0.031550344079732895,
0.0593382902443409,
0.051951706409454346,
0.02253764681518078,
0.017013194039463997,
-0.026153042912483215,
-0.027790799736976624,
0.006260700058192015,
-0.04806679114699364,
0.028594370931386948,
0.014363382011651993,
-0.038082901388406754,
-0.010260051116347313,
0.015881165862083435,
-0.00013543527165893465,
0.021600108593702316,
-0.02717210352420807,
0.03473469614982605,
0.04443427920341492,
0.05604172870516777,
-0.010073894634842873,
0.04653896763920784,
0.03744753077626228,
0.035112861543893814,
-0.03504731133580208,
-0.028080079704523087,
-0.020280130207538605,
-0.002801446011289954,
0.026508793234825134,
0.030156418681144714,
-0.04396191984415054,
-0.010278244502842426,
0.02737422287464142,
0.014391567558050156,
0.026118703186511993,
0.03920406475663185,
-0.020345544442534447,
-0.042080409824848175,
0.05034533888101578,
0.02404441311955452,
-0.019325051456689835,
-0.019093235954642296,
0.034524884074926376,
0.018543105572462082,
0.026706069707870483,
-0.022258255630731583,
-0.0034034077543765306,
0.03828590735793114,
-0.008534456603229046,
0.02711297757923603,
0.016346314921975136,
0.026559563353657722,
0.026239387691020966,
-0.03158554807305336,
0.030510494485497475,
0.01211739331483841,
-0.023224443197250366,
0.010149967856705189,
-0.02109476365149021,
-0.012588943354785442,
0.013220658525824547,
0.03657355159521103,
0.01659008301794529,
-0.006233749911189079,
-0.005950223188847303,
-0.03165427967905998,
0.03972999006509781,
0.013110998086631298,
-0.007499299943447113,
-0.03062411956489086,
-0.010216494090855122,
0.011701960116624832,
0.033699192106723785,
0.030855264514684677,
-0.02379503846168518,
-0.03232300654053688,
-0.004262789152562618,
-0.0282804723829031,
-0.013315840624272823,
-0.011365128681063652,
-0.0002616365673020482,
-0.014578516595065594,
-0.05311717092990875,
0.004036379046738148,
0.02659505605697632,
0.022911638021469116,
-0.02434402145445347,
0.017552286386489868,
0.00792242493480444,
-0.041498035192489624,
-0.03796003386378288,
-0.024592706933617592,
0.01576252281665802,
-0.029978947713971138,
-0.033890500664711,
0.0779472291469574,
-0.015338211320340633,
-0.006360851693898439,
0.030746718868613243,
-0.03599952161312103,
-0.029926879331469536,
0.010653983801603317,
-0.04332447424530983,
0.02414906583726406,
0.012390543706715107,
0.01739686168730259,
0.008546177297830582,
-0.04034261405467987,
-0.01901165395975113,
-0.04187046363949776,
-0.04257114604115486,
0.012069533579051495,
-0.015668295323848724,
0.02177039533853531,
0.014851469546556473,
-0.026448313146829605,
0.08273313194513321,
-0.01551072858273983,
-0.023646436631679535,
-0.03211658447980881,
-0.03193230554461479,
-0.05778098106384277,
-0.0074388147331774235,
0.017768507823348045,
0.04853938892483711,
0.025801625102758408,
0.03577890992164612,
-0.0009468102944083512,
0.04620853438973427,
0.03255529701709747,
-0.009065655060112476,
-0.027221759781241417,
0.03187623247504234,
-0.004698755219578743,
0.0008485100115649402,
0.05193623527884483,
-0.010507401078939438,
-0.04195152968168259,
0.042949896305799484,
0.020339515060186386,
0.027375519275665283,
0.05103793367743492,
-0.05591657757759094,
0.037966545671224594,
-0.023325949907302856,
0.02730555832386017,
-0.041280169039964676,
0.04909106716513634,
-0.0006633952143602073,
-0.025694169104099274,
0.005364022683352232,
0.0121921980753541,
0.06805543601512909,
-0.03611684963107109,
-0.023616796359419823,
0.04281226918101311,
0.013016832992434502,
-0.028803948312997818,
-0.018371643498539925,
-0.028084659948945045,
-0.008564041927456856,
0.01332207303494215,
0.02252650074660778,
-0.0593637190759182,
0.05707475170493126,
-0.014053590595722198,
0.019802501425147057,
-0.00500975688919425,
-0.0703788474202156,
-0.004329279996454716,
-0.03821643441915512,
-0.04446397349238396,
-0.0033506930340081453,
0.025236891582608223,
-0.036853864789009094,
0.05331794545054436,
-0.02029319852590561,
0.01871640235185623,
0.011268699541687965,
-0.013658581301569939,
-0.043790530413389206,
0.047934640198946,
-0.04228006303310394,
-0.018238095566630363,
-0.00014022730465512723,
-0.000715108762960881,
0.004537195432931185,
-0.039716098457574844,
-0.021186422556638718,
0.0035239197313785553,
0.015142395161092281,
-0.03518295660614967,
-0.026535773649811745,
-0.019481146708130836,
-0.021011093631386757,
-0.04459325596690178,
0.01213606633245945,
0.0029291477985680103,
-0.02985234744846821,
0.05359777435660362,
0.051461122930049896,
-0.021877840161323547,
-0.01557346060872078,
-0.03826165944337845,
-0.007482610177248716,
0.03371743857860565,
0.005725860595703125,
0.031698744744062424,
0.012205850332975388,
0.03353925794363022,
-0.026416445150971413,
-0.00533326668664813,
0.03478989005088806,
0.040423471480607986,
-0.014582921750843525,
-0.012026963755488396,
-0.04237666726112366,
-0.006236088927835226,
-0.020307501778006554,
0.04685521870851517,
0.007558517158031464,
0.037807825952768326,
-0.016142362728714943,
0.01293598860502243,
0.009218658320605755,
0.037437811493873596,
0.01301589235663414,
0.03864896297454834,
-0.012670791707932949,
-0.07544306665658951,
-0.024463554844260216,
-0.04029254987835884,
0.021843910217285156,
0.006476513110101223,
-0.009168759919703007,
-0.035665787756443024,
-0.004848056007176638,
0.025459706783294678,
0.04586133360862732,
-0.010152976028621197,
-0.022607741877436638,
-0.03582996129989624,
-0.00353327882476151,
-0.050149209797382355,
-0.024313978850841522,
0.02207460068166256,
0.012291351333260536,
0.05770452693104744,
-0.03599891811609268,
0.01698346808552742,
-0.1053430363535881,
-0.029566921293735504,
0.052070505917072296,
0.027563920244574547,
0.006957285571843386,
-0.006545082665979862,
-0.0433943085372448,
-0.008464762941002846,
0.007740656845271587,
-0.04298916831612587,
0.01201452687382698,
-0.016413887962698936,
0.044865481555461884,
-0.03715591877698898,
-0.0629773885011673,
-0.003550694789737463,
0.018917832523584366,
0.03904644399881363,
0.020833691582083702,
0.004858445841819048,
-0.021702539175748825,
-0.017220867797732353,
0.015641774982213974,
0.03294363245368004,
0.07824689894914627,
-0.028191521763801575,
-0.018011601641774178,
0.026254165917634964,
0.004851824138313532,
0.009452681988477707,
-0.08765915036201477,
-0.005983909126371145,
0.001914432505145669,
0.007821585983037949,
0.04172118008136749,
-0.051833562552928925,
-0.010681796818971634,
0.010098036378622055,
0.009146660566329956,
0.0019901429768651724,
-0.03133746609091759,
-0.03154309466481209,
0.06925758719444275,
0.06711188703775406,
-0.025999514386057854,
0.057108450680971146,
0.0407695509493351,
-0.028926482424139977,
-0.028126060962677002,
-0.05063806101679802,
0.036777280271053314,
-0.020480185747146606,
-0.025156909599900246,
-0.06405068933963776,
-0.018687844276428223,
-0.02074306644499302,
0.024949936196208,
-0.027431543916463852,
-0.0038542249239981174,
-0.03423890471458435,
-0.052860114723443985,
-0.01183179672807455,
0.034828562289476395,
-0.030373338609933853,
0.01834312453866005,
0.016387609764933586,
0.006290437653660774,
0.012560232542455196,
-0.03055214323103428,
0.016788531094789505,
-0.0019445795333012938,
-0.0031830081716179848,
0.04107416048645973,
-0.003574497764930129,
0.024525756016373634,
-0.002054565818980336,
-0.017855964601039886,
0.03088122233748436,
-0.06424456834793091,
0.0009430989739485085,
-0.0033986789640039206,
-0.013812274672091007,
0.011370014399290085,
-0.025935478508472443,
-0.03674681484699249,
0.017425470054149628,
-0.0318012498319149,
0.008503441698849201,
-0.02277989313006401,
0.024324612691998482,
0.002936445875093341,
-0.02339056134223938,
-0.0439571850001812,
-0.04430416598916054,
0.02718381956219673,
-0.017649618908762932,
-0.04413355141878128,
-0.01307950634509325,
-0.0431903637945652,
0.022406410425901413,
0.0020132451318204403,
0.024485377594828606,
0.04955747723579407,
-0.02600097469985485,
0.017580199986696243,
0.0009026496554724872,
-0.017436807975172997,
0.04735301434993744,
-0.0043025086633861065,
0.002400533063337207,
0.02996067889034748,
-0.008771760389208794,
-0.0291286651045084,
-0.00008532377978553995,
0.06851192563772202,
-0.04639901965856552,
-0.008157222531735897,
0.013184175826609135,
0.0022979883942753077,
0.03695666417479515,
-0.04220874235033989,
-0.023504728451371193,
0.011950002051889896,
0.018046341836452484,
-0.0020659263245761395,
-0.005264204926788807,
0.009782669134438038,
-0.023801663890480995,
0.013110537081956863,
0.02677406370639801,
-0.0028953601140528917,
-0.024732470512390137,
-0.046064309775829315,
-0.00006314989150268957,
0.019761977717280388,
-0.0285628791898489,
-0.0003578432952053845,
0.07908450067043304,
-0.017671039327979088,
-0.0006955256685614586,
-0.001550648594275117,
-0.040495216846466064,
0.02973337471485138,
-0.03361555188894272,
0.019025232642889023,
0.013054374605417252,
0.010776362381875515,
-0.05163956061005592,
-0.03504331037402153,
-0.05343926325440407,
-0.0073450664058327675,
0.041233353316783905,
0.004601885564625263,
0.04674492031335831,
-0.0020544733852148056,
-0.01231323555111885,
0.012079630978405476,
-0.039015114307403564,
0.000822892936412245,
-0.019617075100541115,
-0.02385900728404522,
0.0369858555495739,
-0.054787199944257736,
0.02629069797694683,
0.018968725576996803,
0.012367435730993748,
-0.017586760222911835,
0.00859034527093172,
0.04339660331606865,
0.045041780918836594,
-0.006417800672352314,
0.014566818252205849,
-0.0276105348020792,
0.032876450568437576,
0.006918211933225393,
0.043027449399232864,
0.005539375357329845,
-0.009556681849062443,
0.020724909380078316,
0.01597507856786251,
0.032372403889894485,
-0.06516280770301819,
0.040519557893276215,
-0.024969784542918205,
0.022987792268395424,
0.014847583137452602,
0.019045494496822357,
0.015792597085237503,
0.0246074590831995,
0.016047075390815735,
0.02916896715760231,
0.014599595218896866,
-0.021520545706152916,
-0.028966566547751427,
-0.00741418544203043,
-0.01261403039097786,
-0.046641867607831955,
0.003478995291516185,
-0.027631042525172234,
-0.04585862532258034,
0.03874224051833153,
-0.025444529950618744,
0.0039864592254161835,
0.008435905911028385,
-0.005809965543448925,
-0.003976142033934593,
0.08894023299217224,
0.01155181135982275,
0.027253715321421623,
-0.004850409459322691,
-0.015095612034201622,
0.12837731838226318,
0.04235079884529114,
0.004091332200914621,
-0.05247703939676285,
0.005946934688836336,
0.005111067555844784,
-0.01840892620384693,
-0.0272506270557642,
-0.004415981471538544,
0.010371997021138668,
0.0034776022657752037,
-0.0029401066713035107,
0.028019241988658905,
0.008343737572431564,
0.010112417861819267,
0.042200978845357895,
-0.01540210098028183,
-0.03652780130505562,
-0.006344258319586515,
-0.01970069855451584,
-0.00960740726441145,
0.009908798150718212,
-0.023812545463442802,
0.0025225712452083826,
-0.025764236226677895,
0.0007134252809919417,
-0.053844474256038666,
-0.03293440863490105,
0.040029678493738174,
0.009332288056612015,
-0.015191473066806793,
0.03253289684653282,
-0.020092306658625603,
-0.00019554684695322067,
0.004297854844480753,
0.007951914332807064,
0.04666827246546745,
-0.026478469371795654,
0.012520571239292622,
0.04733669012784958,
-0.01068914495408535,
-0.004646944813430309,
0.01253636833280325,
-0.0026931175962090492,
-0.04630960896611214,
-0.01640503481030464,
-0.026163902133703232,
0.033862147480249405,
-0.001491936738602817,
-0.003893172135576606,
0.0005213681724853814,
0.03032350167632103,
-0.008760238997638226,
-0.04136154428124428,
-0.04848837852478027,
-0.03728898987174034,
0.029788769781589508,
-0.003773248055949807,
-0.00159264646936208,
-0.05111793428659439,
0.008822912350296974,
0.012054641731083393,
0.008452638983726501,
-0.019313469529151917,
0.006758177652955055,
0.02139010652899742,
0.002900071442127228,
0.04873296245932579,
-0.020060352981090546,
-0.0032603552099317312,
-0.022847233340144157,
-0.0075868056155741215,
-0.04254060611128807,
-0.024440426379442215,
0.006436208728700876,
0.04965047165751457,
0.04005179926753044,
-0.002855526050552726,
-0.0015657551120966673,
-0.014785717241466045,
-0.07361896336078644,
0.037339385598897934,
-0.025162067264318466,
-0.036484505981206894,
0.00005227434303378686,
-0.0040281591936945915,
0.04566958546638489,
0.04827647656202316,
-0.03188270330429077,
0.03344336524605751,
-0.008262202143669128,
0.019755836576223373,
0.01084638200700283,
-0.016890229657292366,
-0.03361700102686882,
0.012494855560362339,
-0.058216392993927,
0.0024362036492675543,
0.038773566484451294,
0.0006588825490325689,
-0.014063099399209023,
0.01416566502302885,
0.015253379009664059,
0.024105386808514595,
-0.04181266948580742,
-0.0027419282123446465,
-0.013521751388907433,
-0.00824249442666769,
0.0016542632365599275,
-0.011737033724784851,
-0.026885485276579857,
-0.02304944209754467,
0.00008461406832793728,
-0.007509555667638779,
-0.031642477959394455,
0.041025541722774506,
0.03090335614979267,
0.005718835163861513,
-0.027438979595899582,
-0.0049614813178777695,
0.001025180914439261,
-0.048401545733213425,
-0.014350327663123608,
-0.06671852618455887,
0.023841729387640953,
0.012606360018253326,
-0.0024263642262667418,
-0.01466522179543972,
0.0013350564986467361,
-0.0022446748334914446,
0.023600753396749496,
0.0313294380903244,
0.03346490114927292,
0.0017281877808272839,
-0.0027538358699530363,
0.06766798347234726,
-0.039563268423080444,
0.06479287147521973,
-0.03451400250196457,
-0.028351064771413803,
0.04348844662308693,
-0.060784295201301575,
-0.06267888844013214,
0.024525314569473267,
-0.013741577044129372,
-0.0004687208274845034,
0.0001539309450890869,
0.00526843499392271,
0.013815037906169891,
0.015205240808427334,
0.02049217000603676,
-0.002090073423460126,
-0.007235447410494089,
-0.0302243884652853,
-0.004096889402717352,
-0.00423130439594388,
-0.005502248182892799,
-0.033099450170993805,
0.010212138295173645,
0.02744954451918602,
0.03178679198026657,
-0.018528923392295837,
-0.01732775755226612,
-0.00418817438185215,
0.0021097182761877775,
0.026719484478235245,
0.018947670236229897,
0.00969549361616373,
0.04550352320075035,
0.021133918315172195,
0.00028974772430956364,
0.035698894411325455,
0.04172661155462265,
-0.00807830411940813,
-0.0523885115981102,
0.01982295699417591,
0.00042013279744423926,
-0.01437237486243248,
0.02742691896855831,
-0.06511709094047546,
-0.004961369093507528,
0.001355443149805069,
-0.04034728929400444,
0.00983573216944933,
-0.02782610058784485,
0.004387155640870333,
0.0031479678582400084,
-0.01231541857123375,
-0.033165447413921356,
0.05983765423297882,
0.026402505114674568,
0.08319171518087387,
0.026096096262335777,
-0.00961806159466505,
-0.025476880371570587,
-0.01704522967338562,
0.022684231400489807,
0.03858518972992897,
-0.007612832821905613,
-0.03738062083721161,
0.0724167674779892,
-0.0011873896000906825,
-0.004338339902460575,
0.025529218837618828,
-0.05325688421726227,
-0.004825558513402939,
0.009172172285616398,
0.020700955763459206,
-0.004183965269476175,
0.01621447317302227,
0.005013758782297373,
-0.027880476787686348,
-0.0424983911216259,
0.01016937755048275,
0.0061871656216681,
0.03482569009065628,
-0.01650974713265896,
-0.006287857424467802,
-0.0013534434838220477,
-0.050426237285137177,
-0.009394981898367405,
0.07258633524179459,
-0.00006132930866442621,
-0.036863598972558975,
-0.004237291868776083,
0.00923237670212984,
0.010300207883119583,
-0.01950284279882908,
-0.028435541316866875,
-0.015652628615498543,
0.00423442292958498,
0.04899115115404129,
0.012783585116267204,
-0.0008381924126297235,
0.04299011453986168,
0.006708834785968065,
-0.03977196291089058,
0.026910213753581047,
-0.011230084113776684,
-0.003296514507383108,
-0.07085409015417099,
0.007797042839229107,
-0.04082426056265831,
-0.01992678828537464,
-0.019393138587474823,
-0.013207139447331429,
-0.03427648916840553,
0.023785287514328957,
0.021462582051753998,
0.0006176651804707944,
0.032485492527484894,
-0.030779575929045677,
-0.03190019726753235,
-0.06247595325112343,
0.03130427002906799,
-0.0027728918939828873,
-0.009960121475160122,
-0.050039492547512054,
-0.03835853189229965,
0.013176231645047665,
-0.0008616604027338326,
0.05402621626853943,
0.028152555227279663,
-0.029458651319146156,
0.009223872795701027,
0.017596377059817314,
0.0458078607916832,
-0.030302001163363457,
0.029270699247717857,
0.02150880917906761,
-0.006651509087532759,
0.05798576399683952,
0.019511092454195023,
-0.04175655543804169,
0.06809335201978683,
-0.013364022597670555,
-0.023914802819490433,
0.03439175710082054,
-0.017390774562954903,
-0.02033301629126072,
0.05607704445719719,
-0.009356573224067688,
-0.009098179638385773,
0.06890447437763214,
0.03950880467891693,
0.022741304710507393,
0.0019731090869754553,
-0.02837490290403366,
-0.03977106139063835,
0.024509208276867867,
-0.023022953420877457,
-0.017743708565831184,
0.024156713858246803,
-0.022752704098820686,
0.03696136549115181,
-0.060396626591682434,
-0.013018845580518246,
0.027233868837356567,
-0.02468002960085869,
-0.02002221904695034,
0.036813367158174515,
0.020827556028962135,
0.029788225889205933,
0.0038755228742957115,
0.0292543713003397,
-0.024499468505382538,
0.012818384915590286,
0.0220644474029541,
0.03420577198266983,
0.04515780881047249,
-0.007138476241379976,
-0.012343758717179298,
0.012980908155441284,
-0.0016439458122476935,
0.043483033776283264,
0.022153424099087715,
0.03782729431986809,
-0.003140954999253154,
0.0018848376348614693,
0.03390846028923988,
0.009489520452916622,
0.01929325796663761,
0.035157930105924606,
-0.013305260799825191,
0.08028769493103027,
-0.041668009012937546,
0.007129356265068054,
0.014842819422483444,
0.0058731925673782825,
-0.014392943121492863,
0.031139597296714783,
0.017615700140595436,
-0.004388638772070408,
0.005844531115144491,
-0.0241598691791296,
-0.036097440868616104,
-0.006994039751589298,
0.0033323103561997414,
-0.017173537984490395,
0.03736238554120064,
0.032014232128858566,
-0.009363503195345402,
-0.044099681079387665,
-0.028219224885106087,
0.011243308894336224,
-0.018468687310814857,
0.031023019924759865,
0.06168804317712784,
0.026621736586093903,
0.032277971506118774,
0.04076634719967842,
0.027033016085624695,
0.05058121681213379,
-0.046857208013534546,
-0.027989832684397697,
-0.0441216379404068,
-0.00338534964248538,
0.002834294456988573,
-0.01946084201335907
] |
<p>This is a question on the synchronization of clocks. If a girl on a train has the same clock that a guy has on the platform and they synchronize their clocks at 12am together when the train and the platform are both stationary with respect to each other. Then if the train runs and some time later (a random time later) the girl says, "Stop". When she says this both the guy and girl stop their clocks. They turn it off so that the clock reads the time it was at when they stopped it. Then the girl gets off the train and she compares her clock with the guy. Which one would be slow? They were both moving with respect to each other so both their clocks should run slow. I don't understand that./?</p> | 2,025 | [
-0.027018912136554718,
-0.05027664452791214,
-0.03532525151968002,
-0.03098118305206299,
0.04123412072658539,
0.0060437326319515705,
-0.019924243912100792,
-0.009701098315417767,
-0.02487146481871605,
0.03785036504268646,
0.0399479940533638,
0.03872985765337944,
0.048758167773485184,
0.03827822580933571,
0.042065177112817764,
-0.011557577177882195,
-0.002092619426548481,
0.017088886350393295,
-0.03993115946650505,
-0.047679126262664795,
0.01647341437637806,
-0.006299973931163549,
0.03819065913558006,
0.004228792153298855,
-0.054414574056863785,
0.01835334114730358,
0.027766931802034378,
-0.012623867020010948,
-0.018312549218535423,
0.02156078815460205,
-0.04232027754187584,
-0.04131524637341499,
-0.01672055386006832,
0.03180752694606781,
0.02030918188393116,
-0.010115633718669415,
-0.020561708137392998,
-0.009256337769329548,
0.006596386898308992,
0.022414812818169594,
-0.01462906040251255,
-0.0036583798937499523,
-0.010836196132004261,
0.0494924820959568,
-0.022070027887821198,
0.02242041938006878,
-0.0005604401230812073,
-0.020784951746463776,
0.08092822879552841,
-0.04260046407580376,
0.05444824695587158,
0.006494851317256689,
0.01918773353099823,
-0.0034176791086792946,
-0.0019043133361265063,
0.05080611631274223,
0.05913941562175751,
0.044562697410583496,
0.018538037315011024,
-0.030463222414255142,
-0.034799959510564804,
-0.017707128077745438,
-0.03228340670466423,
-0.011167031712830067,
-0.024241792038083076,
0.03749750182032585,
-0.03733872249722481,
-0.023424014449119568,
0.03507368639111519,
0.007561970967799425,
0.016667773947119713,
-0.0002507209137547761,
0.06629174947738647,
-0.02966287173330784,
0.014255687594413757,
-0.041140440851449966,
0.021665051579475403,
0.0560775101184845,
0.03324737027287483,
0.02999289147555828,
-0.026266975328326225,
-0.030026448890566826,
0.02557263895869255,
0.04389486834406853,
-0.026217827573418617,
-0.0397019237279892,
0.048037782311439514,
-0.0044266157783567905,
0.009030145592987537,
0.05695182830095291,
-0.020104050636291504,
0.011864837259054184,
-0.024275057017803192,
-0.0010406423825770617,
-0.011988118290901184,
0.030084839090704918,
0.016480138525366783,
0.04027273878455162,
-0.0015201650094240904,
-0.02392110973596573,
0.0079790148884058,
-0.04534388333559036,
0.03749852627515793,
0.049854181706905365,
-0.008194917812943459,
0.019333800300955772,
-0.02449982240796089,
0.004260467365384102,
-0.03288551792502403,
0.009380251169204712,
-0.050451263785362244,
-0.006097567267715931,
-0.0009475648985244334,
0.021832603961229324,
0.03721308708190918,
-0.0003726802533492446,
-0.021349569782614708,
0.006200158037245274,
0.05643180012702942,
0.026763468980789185,
0.04356428608298302,
0.00478948000818491,
0.011426946148276329,
-0.03292791545391083,
-0.07205922901630402,
0.006464411038905382,
-0.025796154513955116,
-0.01744498312473297,
0.012013377621769905,
0.04002223163843155,
0.004549027420580387,
-0.030156755819916725,
0.036253709346055984,
-0.016916275024414062,
0.07040385901927948,
-0.030153093859553337,
-0.08510403335094452,
-0.042086679488420486,
0.03412209451198578,
-0.01824193075299263,
0.010628478601574898,
-0.08949171751737595,
0.018386583775281906,
-0.031102867797017097,
0.07992307841777802,
-0.020753923803567886,
0.045752301812171936,
0.0031754726078361273,
-0.021349964663386345,
0.026800217106938362,
0.02068803459405899,
-0.005615379195660353,
0.026830574497580528,
-0.00824655219912529,
-0.001778429257683456,
-0.025785434991121292,
-0.00006850922363810241,
0.020033691078424454,
-0.03848286345601082,
-0.016124442219734192,
0.012448872439563274,
0.002627639565616846,
-0.02136237360537052,
0.04058540612459183,
0.029098274186253548,
-0.052831243723630905,
0.1063285693526268,
0.01083651464432478,
-0.010859734378755093,
0.010150572285056114,
0.05259380117058754,
0.06092564016580582,
-0.011147817596793175,
0.030834924429655075,
0.0503426119685173,
-0.019847193732857704,
-0.05881868675351143,
0.018179913982748985,
-0.00014376480248756707,
0.01926213689148426,
-0.06173991411924362,
-0.022326160222291946,
-0.011043066158890724,
-0.005057061556726694,
0.012911864556372166,
0.0251384936273098,
-0.028986738994717598,
0.030051548033952713,
0.00962051935493946,
-0.0009758396772667766,
-0.005026058293879032,
-0.08512423932552338,
0.022778719663619995,
-0.0048140776343643665,
0.008181284181773663,
0.030649082735180855,
0.005936996079981327,
0.018331613391637802,
-0.0494968518614769,
-0.02761952579021454,
-0.04157758504152298,
0.054366789758205414,
-0.024854525923728943,
-0.018886160105466843,
-0.007397977169603109,
0.10203834623098373,
0.060656532645225525,
0.009757500141859055,
0.036239463835954666,
0.002135291462764144,
-0.012675117701292038,
0.03084099106490612,
-0.014187991619110107,
-0.016924859955906868,
0.008043735288083553,
0.012232290580868721,
0.030352605506777763,
-0.007529144175350666,
-0.009145758114755154,
0.041664641350507736,
-0.03228576481342316,
0.03611554950475693,
0.0306993518024683,
-0.032681502401828766,
0.0003288916777819395,
0.008550710044801235,
0.024403192102909088,
0.04024241119623184,
0.03302150219678879,
-0.06133875995874405,
0.029572127386927605,
0.003166637849062681,
-0.02351207099854946,
-0.00013970346481073648,
-0.017987670376896858,
0.026493242010474205,
0.0492093600332737,
0.03281839191913605,
0.022241132333874702,
0.013430625200271606,
0.006628038361668587,
-0.02225419320166111,
0.003695687046274543,
-0.010323275811970234,
-0.0009972493862733245,
0.038007065653800964,
0.029726147651672363,
-0.01761518232524395,
-0.001821640762500465,
-0.00011408817226765677,
-0.05499427393078804,
0.05033461004495621,
0.01093840692192316,
0.035192009061574936,
0.00000788339639257174,
-0.03400832787156105,
0.03141060099005699,
-0.02765022963285446,
0.02117227576673031,
0.020983168855309486,
0.007919302210211754,
0.014596828259527683,
-0.01357415784150362,
-0.02826848439872265,
-0.028430713340640068,
0.006467162631452084,
-0.0342494435608387,
-0.025827445089817047,
0.010057864710688591,
-0.0234241783618927,
0.0267690010368824,
0.002650771290063858,
-0.024693677201867104,
-0.024058522656559944,
0.009937615133821964,
0.05707084387540817,
-0.012720386497676373,
-0.008801770396530628,
-0.04292852431535721,
-0.00595789635553956,
-0.02075730636715889,
-0.037925805896520615,
0.01677389070391655,
-0.018458832055330276,
-0.058974336832761765,
0.026959851384162903,
0.019019396975636482,
-0.06823110580444336,
0.001479149330407381,
0.029628489166498184,
0.059511449187994,
0.047444723546504974,
-0.029109502211213112,
-0.07954088598489761,
-0.015737615525722504,
-0.07339199632406235,
0.02344919741153717,
0.020134620368480682,
-0.012862823903560638,
0.06639761477708817,
0.005526870954781771,
-0.013170420192182064,
0.015276053920388222,
-0.04475576430559158,
-0.038777273148298264,
-0.014412637799978256,
-0.019605722278356552,
0.020656445994973183,
-0.02928825095295906,
0.004405822604894638,
0.034398190677165985,
-0.029795441776514053,
-0.04134787246584892,
-0.042099978774785995,
-0.09493253380060196,
0.030285067856311798,
0.004140058066695929,
0.03387999162077904,
0.003463310655206442,
0.010102431289851665,
0.06613482534885406,
0.05295121669769287,
-0.011231024749577045,
-0.017909187823534012,
0.01746308244764805,
-0.012770970351994038,
-0.025244031101465225,
-0.0008370972354896367,
0.03059340827167034,
-0.012941435910761356,
0.04499019309878349,
0.017352763563394547,
0.03859178349375725,
0.043567873537540436,
-0.006693914532661438,
-0.03684356436133385,
-0.02676467038691044,
0.0059106010012328625,
-0.005818314850330353,
0.05423363670706749,
0.03829957917332649,
0.0022785852197557688,
-0.010426471009850502,
-0.011459384113550186,
0.04717056080698967,
-0.006146246567368507,
-0.036944810301065445,
0.020372921600937843,
-0.021404799073934555,
0.0027232374995946884,
-0.034326255321502686,
0.0313393659889698,
-0.0184294655919075,
-0.0020150216296315193,
-0.0077814869582653046,
0.002643169369548559,
0.03948904573917389,
-0.02581445872783661,
-0.01208522543311119,
0.04057976230978966,
0.02687584049999714,
-0.051955629140138626,
-0.007171149365603924,
-0.0007737824926152825,
0.008987601846456528,
0.05609101802110672,
-0.03666304051876068,
-0.06023379787802696,
0.04195695370435715,
0.030475661158561707,
0.019783226773142815,
0.00026222923770546913,
-0.04569365829229355,
-0.027333734557032585,
-0.10961288958787918,
0.008033755235373974,
0.01042921468615532,
0.046017419546842575,
-0.004591583274304867,
0.059537943452596664,
0.02658791095018387,
0.008382370695471764,
-0.003101915353909135,
-0.009088536724448204,
-0.054054226726293564,
0.06434278190135956,
-0.04546640068292618,
-0.037450727075338364,
0.0003259344375692308,
-0.0015098664443939924,
0.01584264263510704,
-0.032574765384197235,
-0.02178024686872959,
-0.011859746649861336,
-0.006062711589038372,
-0.03932797908782959,
0.014771887101233006,
-0.013886252418160439,
-0.012463065795600414,
-0.014492606744170189,
0.013924958184361458,
0.04181365296244621,
-0.030160941183567047,
0.02652621828019619,
0.039459601044654846,
-0.047357190400362015,
-0.013892842456698418,
-0.00783125963062048,
0.0020877441857010126,
0.018732519820332527,
-0.014130664058029652,
0.03619678318500519,
-0.0022395127452909946,
-0.009480203501880169,
-0.006303847301751375,
-0.006850884296000004,
0.032690562307834625,
0.017723150551319122,
0.015097694471478462,
-0.03606228530406952,
-0.02748093754053116,
-0.005202879197895527,
0.0014626068295910954,
0.07529596239328384,
-0.008233790285885334,
-0.01463100966066122,
0.03312511742115021,
0.0252117570489645,
0.013202708214521408,
0.035173047333955765,
0.03180871903896332,
-0.001869486179202795,
0.0006014200043864548,
-0.0293835811316967,
0.024470187723636627,
-0.01949983648955822,
-0.0015074149705469608,
0.04314574971795082,
-0.005011328496038914,
0.01004188321530819,
-0.031985439360141754,
0.03434211015701294,
0.016955779865384102,
-0.008852998726069927,
0.02595761977136135,
-0.03678234666585922,
0.03539947047829628,
0.046813320368528366,
0.012825273908674717,
-0.024724122136831284,
0.026086019352078438,
0.01367862243205309,
-0.018996749073266983,
-0.014838319271802902,
-0.06661591678857803,
-0.0063776299357414246,
0.01207197830080986,
0.019987279549241066,
-0.030984658747911453,
-0.02951769158244133,
-0.04413478821516037,
-0.0012880143476650119,
0.062155917286872864,
-0.018266329541802406,
0.026476550847291946,
0.005485002417117357,
-0.022749247029423714,
-0.007871594280004501,
-0.009901662357151508,
0.002051359275355935,
0.019045496359467506,
0.0057509178295731544,
0.032186560332775116,
0.014594868756830692,
-0.027659690007567406,
-0.016353417187929153,
-0.029718130826950073,
0.04532605782151222,
0.01592646911740303,
0.03295212984085083,
0.03885394707322121,
0.025664903223514557,
0.011800883337855339,
-0.023542027920484543,
-0.0762052983045578,
0.007956251502037048,
-0.00423442991450429,
-0.0016009858809411526,
0.0452992208302021,
-0.06273889541625977,
-0.01071325596421957,
0.021824002265930176,
-0.028523819521069527,
-0.014971396885812283,
0.00290953041985631,
-0.02663969248533249,
0.04988858103752136,
0.056215815246105194,
0.01645992510020733,
0.008779126219451427,
-0.007700647693127394,
0.0015453394735231996,
-0.02704516239464283,
0.013695502653717995,
-0.010348347015678883,
-0.06482353806495667,
0.06470400094985962,
-0.008720782585442066,
0.009352564811706543,
-0.04492456838488579,
0.05872361734509468,
-0.018186034634709358,
0.00867685116827488,
-0.017891021445393562,
-0.03942450135946274,
-0.025027304887771606,
0.01262970082461834,
-0.01890058070421219,
0.020355412736535072,
-0.024040216580033302,
-0.015517284162342548,
-0.03562921658158302,
-0.002767634578049183,
0.0357334204018116,
-0.027464795857667923,
0.010570724494755268,
0.012374354526400566,
-0.016273073852062225,
0.02410649135708809,
-0.04424792155623436,
0.0040205297991633415,
-0.016560932621359825,
-0.03910130634903908,
0.0031301609706133604,
-0.016234559938311577,
-0.0009648849372752011,
0.0669110119342804,
-0.03308985009789467,
-0.05305963754653931,
-0.0022158059291541576,
-0.02897747792303562,
0.04037493094801903,
-0.03703294321894646,
0.03478516638278961,
0.03263935074210167,
-0.038240157067775726,
-0.05549651384353638,
-0.0525803342461586,
0.045337844640016556,
-0.01615430787205696,
-0.01775337941944599,
-0.037743136286735535,
0.023383282124996185,
-0.028989717364311218,
-0.01402591448277235,
-0.02243688516318798,
0.02852030284702778,
-0.026701370254158974,
-0.0163413155823946,
0.02514367550611496,
0.0052188425324857235,
0.08807932585477829,
0.01804945059120655,
-0.008271468803286552,
-0.014195962809026241,
-0.04550829157233238,
-0.021164696663618088,
-0.02710987627506256,
0.08719183504581451,
-0.02815062552690506,
-0.033575087785720825,
0.006660740356892347,
0.001546050189062953,
0.051771339029073715,
-0.015219989232718945,
0.010936410166323185,
0.04880422353744507,
0.0353897400200367,
0.015153150074183941,
-0.005102614872157574,
0.01834733411669731,
0.0025866799987852573,
0.020232873037457466,
-0.0027514540124684572,
-0.003342708572745323,
-0.00647265650331974,
-0.044620148837566376,
-0.011349066160619259,
0.005777802783995867,
-0.032389041036367416,
-0.016356050968170166,
0.054923657327890396,
-0.020745187997817993,
-0.010933690704405308,
-0.004171780776232481,
0.028798861429095268,
0.01662389002740383,
-0.024522660300135612,
-0.0036776410415768623,
-0.021220188587903976,
-0.03348413109779358,
-0.002625790424644947,
-0.003604097058996558,
-0.025911208242177963,
-0.03261266276240349,
0.057659346610307693,
-0.03609536215662956,
0.057546865195035934,
0.015070786699652672,
0.034701332449913025,
0.02463359571993351,
-0.022003866732120514,
0.020497038960456848,
0.009872381575405598,
0.014505521394312382,
-0.003308397950604558,
-0.03061467781662941,
-0.0009263264364562929,
0.03650110587477684,
0.05201609060168266,
0.0074585541151463985,
0.016816291958093643,
0.029025234282016754,
0.017316976562142372,
0.04802954941987991,
0.009595753625035286,
-0.018580248579382896,
0.030558859929442406,
0.0012096136342734098,
0.014165587723255157,
-0.02511582151055336,
0.030675392597913742,
0.0726543441414833,
0.023224255070090294,
-0.003094643587246537,
-0.051017533987760544,
-0.023795221000909805,
-0.08012306690216064,
-0.026187479496002197,
0.004066850524395704,
0.001524452120065689,
0.006821626331657171,
0.004996695090085268,
0.05458586663007736,
0.0350802056491375,
-0.001255636801943183,
-0.050554875284433365,
-0.06720523536205292,
-0.00838218443095684,
0.006695179268717766,
-0.02562502771615982,
0.04777584224939346,
-0.012286937795579433,
-0.029839154332876205,
0.014326386153697968,
-0.016808276996016502,
0.013787002302706242,
0.0011689536040648818,
0.04001042619347572,
-0.038652203977108,
0.055806905031204224,
0.001493744202889502,
0.03734689950942993,
0.005506238900125027,
-0.014479517005383968,
0.08366090059280396,
0.016416141763329506,
0.030796514824032784,
-0.06796371191740036,
0.043855197727680206,
0.014532393775880337,
-0.030585013329982758,
-0.01624186895787716,
0.0025509342085570097,
0.04861718416213989,
-0.012961504980921745,
0.040636640042066574,
0.012561927549540997,
0.04039306938648224,
-0.020973846316337585,
0.0723896250128746,
-0.013355759903788567,
-0.026603633537888527,
-0.006149176973849535,
0.01792926900088787,
0.021798044443130493,
-0.025024790316820145,
-0.010506662540137768,
0.009610398672521114,
-0.04915143549442291,
-0.015883248299360275,
-0.0314081534743309,
-0.05213242396712303,
0.013615543022751808,
0.01862078346312046,
-0.019438618794083595,
0.0725754126906395,
0.052114635705947876,
-0.022400610148906708,
-0.06135857105255127,
0.01046378631144762,
0.030407747253775597,
0.012550033628940582,
0.013758798129856586,
0.058581795543432236,
-0.0031217429786920547,
0.011319820769131184,
0.02089652419090271,
-0.03428247570991516,
-0.04854676127433777,
-0.02300240471959114,
-0.039731353521347046,
0.01599639467895031,
0.038437895476818085,
-0.026906665414571762,
0.02072812244296074,
0.025941727682948112,
-0.00006372464849846438,
-0.031917259097099304,
0.009182256646454334,
-0.019977888092398643,
0.0004441483470145613,
-0.016289709135890007,
-0.02324933186173439,
-0.06435425579547882,
0.034618254750967026,
-0.009964706376194954,
0.007176431827247143,
0.00023232994135469198,
-0.018511684611439705,
-0.005075651686638594,
-0.021316636353731155,
0.021070946007966995,
-0.013687839731574059,
-0.004389353562146425,
-0.006438695825636387,
-0.020511087030172348,
-0.016886277124285698,
0.0280532818287611,
0.041616834700107574,
0.018247872591018677,
0.033218808472156525,
0.006998579483479261,
-0.012281101197004318,
-0.012060541659593582,
-0.04417889937758446,
0.04701340198516846,
0.005674086045473814,
-0.021479161456227303,
-0.004163368605077267,
-0.0204935222864151,
0.05547326058149338,
0.047986410558223724,
0.016632264479994774,
0.03289854899048805,
0.02234276942908764,
0.028400667011737823,
0.010567612946033478,
-0.03772386163473129,
0.008902667090296745,
-0.016276760026812553,
-0.0347629077732563,
0.012086180970072746,
-0.038272056728601456,
0.029246656224131584,
0.0276583731174469,
-0.03365546464920044,
-0.007285413332283497,
-0.005530873779207468,
-0.03355991095304489,
0.000246082287048921,
-0.000866842397954315,
-0.024540390819311142,
0.011566652916371822,
0.04777006804943085,
-0.0316818505525589,
-0.021465348079800606,
-0.05058852210640907,
0.01422492228448391,
0.034715767949819565,
-0.021912407130002975,
0.018600963056087494,
-0.019868159666657448,
0.035956740379333496,
-0.020734798163175583,
0.018194613978266716,
-0.013287818990647793,
-0.0016018764581531286,
-0.06053052470088005,
-0.004307582043111324,
0.060427356511354446,
-0.008682374842464924,
-0.017641562968492508,
0.025926483795046806,
0.01586190238595009,
-0.013916585594415665,
0.0010020366171374917,
0.012883255258202553,
-0.029877284541726112,
-0.02711549773812294,
-0.006859439890831709,
0.02572331391274929,
0.044645752757787704,
-0.03802313655614853,
-0.023097405210137367,
0.017584573477506638,
-0.034054234623909,
-0.02724156528711319,
0.051990944892168045,
-0.0007472849101759493,
-0.00284266984090209,
0.022541342303156853,
-0.017465457320213318,
0.01363109890371561,
0.04489101842045784,
-0.0016433540731668472,
0.02360450103878975,
0.02562481351196766,
-0.01040838472545147,
-0.010578272864222527,
0.0178383719176054,
-0.052786875516176224,
-0.031410377472639084,
-0.025271086022257805,
0.01699422113597393,
0.040638525038957596,
-0.035953789949417114,
0.05717778205871582,
-0.07058081775903702,
0.05562082305550575,
0.012104187160730362,
0.006680660881102085,
0.003962828777730465,
0.02545406110584736,
0.02736053243279457,
-0.0305322278290987,
0.005690508522093296,
0.0067906309850513935,
-0.02337142452597618,
-0.04435716196894646,
0.003939606249332428,
0.02811211720108986,
-0.02136613056063652,
0.04369067773222923,
0.0053014494478702545,
-0.02410792000591755,
0.042174339294433594,
-0.0684344694018364,
0.0004538836656138301,
0.0024901118595153093,
-0.03459165245294571,
-0.02058502659201622,
-0.020952505990862846,
-0.006203728262335062,
0.04472053050994873,
0.013384521007537842,
0.021882284432649612,
0.0059672510251402855,
-0.01049239281564951,
0.034990426152944565,
-0.057395968586206436,
-0.004571342840790749,
0.02744707278907299,
0.034857917577028275,
0.018698671832680702,
0.04369621351361275,
-0.0680270791053772,
-0.04828200116753578,
0.05139382928609848,
-0.03254663199186325,
-0.0340317077934742,
-0.016008926555514336,
0.023928171023726463,
0.008349374867975712,
-0.00631569791585207,
-0.010474469512701035,
-0.030125007033348083,
0.008839641697704792,
0.015051818452775478,
-0.01238163560628891,
0.050765372812747955,
0.00010502643272047862,
-0.008055610582232475,
-0.009379141964018345,
-0.032858360558748245,
-0.02618470974266529,
0.02482590079307556,
0.0007128085708245635,
-0.004414588212966919,
0.024123290553689003,
-0.02188224345445633,
0.03098919801414013,
-0.037759989500045776,
-0.029669219627976418,
-0.01314650010317564,
-0.0205447506159544,
0.019832339137792587,
0.005214636214077473,
-0.017352478578686714,
-0.007112252525985241,
-0.04701120778918266,
-0.012777749449014664,
0.0033486459869891405,
0.020122632384300232,
-0.009562582708895206,
-0.013764571398496628,
0.015111353248357773,
0.03531521186232567,
0.044141389429569244,
-0.039993394166231155,
-0.058668605983257294,
-0.023449592292308807,
0.013154692016541958,
0.015981342643499374,
-0.009555524215102196,
-0.06173492968082428,
-0.037192121148109436,
-0.006667027715593576,
-0.050437554717063904,
0.004980854224413633,
0.004724238067865372,
-0.0033454985823482275,
-0.03559990972280502,
-0.024275923147797585,
-0.0380985289812088,
0.041648223996162415,
0.032891321927309036,
-0.015156379900872707,
-0.04852914810180664,
0.05152863636612892,
-0.041584763675928116,
0.017592478543519974,
-0.02662898600101471,
0.023148316890001297,
-0.0008175998227670789,
-0.00688024889677763,
0.009694844484329224,
-0.04912625998258591,
-0.05584986135363579,
0.008730011060833931,
0.012746774591505527,
0.044445157051086426,
0.014112965203821659,
0.008967334404587746,
-0.016174830496311188,
0.062266893684864044,
0.0062024230137467384,
0.031691066920757294,
0.05054137483239174,
0.03489198163151741,
-0.017342403531074524,
0.030256522819399834,
0.011187964119017124,
-0.044304009526968,
0.023165322840213776,
-0.012592719867825508,
0.014555133879184723,
-0.00028167240088805556,
-0.011164514347910881,
0.04554090276360512,
-0.03663709759712219,
0.0007786016794852912,
0.01632109470665455,
-0.0060113174840807915,
-0.010424332693219185,
0.01371336355805397,
0.019507108256220818,
0.0034616179764270782,
-0.02066092938184738,
0.04018246755003929,
0.009153910912573338,
-0.0024815485812723637,
0.04350397363305092,
0.048601385205984116,
0.001051077269949019,
-0.02362273633480072,
0.017715446650981903,
-0.015729615464806557,
-0.03527095541357994,
0.034142736345529556,
0.03052263706922531,
0.016684627160429955,
0.009713012725114822,
-0.03264341875910759,
0.04929604008793831,
-0.008994643576443195,
0.01976846531033516,
0.02291008085012436,
-0.010577401146292686,
0.036852408200502396,
-0.046660687774419785,
-0.003864152589812875,
-0.0038347237277776003,
0.01683512143790722,
-0.006552392616868019,
-0.04238094761967659,
0.034499529749155045,
-0.0026032645255327225,
-0.0019096065079793334,
-0.011252341791987419,
-0.01596837304532528,
-0.03134553134441376,
0.02659378945827484,
-0.06758855283260345,
0.023699110373854637,
-0.01382275577634573,
-0.006796038709580898,
-0.01514523196965456,
0.01206968817859888,
-0.035993900150060654,
-0.02237638272345066,
0.05671459436416626,
0.03906712681055069,
-0.01307245995849371,
-0.027940459549427032,
-0.0011783179361373186,
0.0017478691879659891,
0.031012384220957756,
-0.049047794193029404,
-0.04407934099435806,
-0.053663671016693115,
0.01365702599287033,
0.024721674621105194,
-0.03621559590101242
] |
<p>Starting with the Maxwell action for a $U(1)$ vector gauge boson with a general metric and (I'm assuming) using a plane wave ansatz for the vector, is it possible to derive the action for a massless point particle?</p>
<p>EDIT: More information on what I'm trying to do. The Maxwell action and the action for a massless point particle are written in very different language (field values integrated over spacetime vs. particle trajectory integrated over time). But if I want to follow, say, the front of an EM wave, I should be able to get the massless point particle action from Maxwell. Does anyone know if this can be done and if so where?</p> | 2,026 | [
0.015097948722541332,
0.004100913647562265,
-0.006416980177164078,
-0.023152140900492668,
0.009262144565582275,
0.02929171919822693,
-0.04307713732123375,
-0.018166331574320793,
-0.01645759679377079,
-0.049990277737379074,
0.05010945722460747,
0.02646465413272381,
0.09200961887836456,
0.008882274851202965,
0.011309350840747356,
0.0161663219332695,
0.008114303462207317,
0.001369263045489788,
-0.03060074709355831,
-0.07780437171459198,
-0.009966250509023666,
0.031387560069561005,
-0.008199251256883144,
-0.015795543789863586,
0.008546666242182255,
0.0085910614579916,
-0.004487830214202404,
0.024842457845807076,
0.0024060930591076612,
0.051959265023469925,
-0.03700030595064163,
-0.03451891988515854,
0.002486512530595064,
0.034406695514917374,
-0.0004264241433702409,
-0.023195918649435043,
-0.05751961097121239,
-0.04418697953224182,
0.010945375077426434,
-0.03332434967160225,
-0.002087049651890993,
-0.02318824641406536,
-0.033497292548418045,
0.06494853645563126,
-0.03155737742781639,
0.007143910508602858,
-0.0065700276754796505,
0.013685029000043869,
0.051085229963064194,
-0.06333842128515244,
0.07682793587446213,
0.01240269374102354,
0.022689472883939743,
-0.019829504191875458,
-0.03129442408680916,
-0.025059254840016365,
0.08211147785186768,
0.059568580240011215,
0.01465869601815939,
-0.07566343247890472,
-0.030594443902373314,
-0.019309252500534058,
-0.004856999963521957,
-0.040287043899297714,
-0.027638940140604973,
0.015402969904243946,
-0.018497399985790253,
-0.012877091765403748,
0.04024965688586235,
-0.01029759831726551,
-0.004215932916849852,
-0.00021454568195622414,
0.03220430016517639,
-0.003415993181988597,
-0.016103364527225494,
-0.012529363855719566,
0.026420697569847107,
-0.011009706184267998,
0.0538482628762722,
0.010889092460274696,
-0.04566715657711029,
0.04322846233844757,
0.025014955550432205,
0.027946453541517258,
0.010196362622082233,
-0.008102438412606716,
0.0453605055809021,
-0.01724986545741558,
-0.03268466144800186,
0.05090470239520073,
-0.04877215996384621,
-0.010754605755209923,
0.05164048448204994,
-0.0038570978213101625,
-0.03346776217222214,
0.028566844761371613,
0.01479925587773323,
0.03941388800740242,
0.04068463668227196,
-0.03881295770406723,
-0.010170449502766132,
-0.012905251234769821,
-0.02392086200416088,
0.06105218827724457,
0.006070216652005911,
0.013384892605245113,
-0.02697037160396576,
0.032855261117219925,
-0.03008112870156765,
-0.014138471335172653,
-0.06312141567468643,
0.025012439116835594,
-0.019223809242248535,
-0.027942372485995293,
0.027658382430672646,
-0.02685289829969406,
0.008750366047024727,
-0.04805844649672508,
0.061053987592458725,
0.07581757754087448,
0.05622924119234085,
-0.030167851597070694,
0.012678979896008968,
-0.028263790532946587,
-0.07264131307601929,
-0.028441060334444046,
0.023322604596614838,
0.01185013260692358,
-0.017664339393377304,
-0.0025647717993706465,
0.006627374328672886,
-0.01230628788471222,
0.01975828781723976,
-0.0006152853020466864,
0.03234044462442398,
-0.02544432505965233,
-0.08624830096960068,
-0.025201361626386642,
0.016531044617295265,
0.0005036995280534029,
0.0008328909170813859,
-0.02821188047528267,
-0.0030544507317245007,
0.023440513759851456,
0.051607292145490646,
0.00948894489556551,
0.036669716238975525,
0.015154106542468071,
0.05604355037212372,
0.01105005107820034,
0.005373888183385134,
0.00459300447255373,
-0.025072209537029266,
-0.05969688668847084,
-0.0044568548910319805,
-0.04163621738553047,
0.03754252940416336,
0.023588545620441437,
-0.025719815865159035,
0.0031287604942917824,
0.09245097637176514,
-0.001731766271404922,
0.05291616544127464,
-0.0011722410563379526,
-0.016324704512953758,
0.01173048559576273,
0.057032130658626556,
0.01576985977590084,
0.0027889511547982693,
0.017492761835455894,
-0.01193025428801775,
0.022191012278199196,
0.0033950824290513992,
0.014980868436396122,
0.046338267624378204,
-0.04948893561959267,
-0.03919556736946106,
0.01200145948678255,
0.017892595380544662,
0.017429249361157417,
0.0007851144182495773,
-0.05712771788239479,
-0.01459475513547659,
0.02428472228348255,
-0.022766131907701492,
0.03867064788937569,
-0.026099367067217827,
-0.0013005639193579555,
-0.006965894252061844,
-0.07108280062675476,
0.010563457384705544,
-0.05224136263132095,
0.02823774889111519,
0.05718468129634857,
-0.01375467237085104,
0.03119039162993431,
0.0037742534186691046,
-0.014069236814975739,
-0.04280988499522209,
-0.09580402076244354,
-0.005247444845736027,
0.043495871126651764,
-0.017042620107531548,
-0.023985307663679123,
0.004626758862286806,
0.029174644500017166,
0.0562632754445076,
-0.004452006425708532,
0.043182987719774246,
-0.0221332348883152,
-0.024546407163143158,
0.004599154926836491,
-0.024367650970816612,
0.008863032795488834,
0.016533730551600456,
0.028416963294148445,
0.02256428636610508,
-0.008620334789156914,
-0.03301624953746796,
0.025292033329606056,
-0.02385367453098297,
0.049293797463178635,
0.07564730942249298,
0.009278945624828339,
-0.006553156301379204,
0.029212670400738716,
0.04295698180794716,
0.016629274934530258,
0.02741047367453575,
-0.0010110209695994854,
-0.014299371279776096,
0.011061666533350945,
0.035670507699251175,
-0.014210478402674198,
-0.05675585940480232,
0.008898187428712845,
0.03867363557219505,
0.017758382484316826,
0.04019855707883835,
0.044385407119989395,
-0.012506159953773022,
-0.024401608854532242,
0.051362864673137665,
0.014122444204986095,
-0.021148644387722015,
-0.005092033185064793,
0.058955591171979904,
-0.002391317393630743,
0.0061286515556275845,
0.02979523502290249,
-0.03160156309604645,
0.0004886045935563743,
-0.028668053448200226,
-0.017250334843993187,
0.01397339440882206,
-0.017653455957770348,
0.019597060978412628,
-0.036972448229789734,
0.03822006657719612,
0.012794970534741879,
-0.018216634169220924,
-0.029997780919075012,
-0.03650778532028198,
-0.04044979438185692,
0.021065501496195793,
-0.007877211086452007,
-0.024221790954470634,
-0.020936211571097374,
0.03099892847239971,
-0.04020824655890465,
0.01767098158597946,
-0.001616435358300805,
-0.02775564417243004,
-0.00466382410377264,
0.01031498797237873,
0.044822562485933304,
0.03577011078596115,
0.012222159653902054,
-0.02631477080285549,
-0.044182974845170975,
0.03980233892798424,
-0.03951020538806915,
0.03184358775615692,
0.05478706955909729,
-0.04009101539850235,
0.018387390300631523,
-0.0614752359688282,
-0.030918138101696968,
0.029431307688355446,
0.023492000997066498,
-0.005162778776139021,
0.0034842719323933125,
0.007832979783415794,
-0.07784830778837204,
0.007941094227135181,
-0.02297782711684704,
0.018723299726843834,
-0.03543674200773239,
0.036537718027830124,
-0.012711050920188427,
0.019563278183341026,
-0.023478111252188683,
-0.00815920252352953,
-0.008083835244178772,
-0.052577611058950424,
-0.009062547236680984,
0.010409703478217125,
-0.00037398311542347074,
-0.04973127320408821,
0.058782633394002914,
0.03703105077147484,
-0.06088654324412346,
0.026588493958115578,
-0.06489281356334686,
-0.023634430021047592,
0.03608627989888191,
-0.0008390853181481361,
0.027530275285243988,
-0.025747336447238922,
-0.02242104895412922,
0.06784555315971375,
0.022157730534672737,
-0.047180674970149994,
-0.0002051236660918221,
0.01058900821954012,
-0.005358138587325811,
-0.012667104601860046,
-0.025095945224165916,
-0.0014586198376491666,
-0.015080226585268974,
0.020449861884117126,
0.022837456315755844,
0.008549036458134651,
0.020444851368665695,
0.054008252918720245,
-0.019638212397694588,
-0.01376188825815916,
-0.041004449129104614,
0.04676234722137451,
0.03292476385831833,
0.007241013925522566,
-0.01501466054469347,
0.03619006276130676,
0.016377735882997513,
0.004585125017911196,
0.00942175928503275,
-0.05136425793170929,
0.07629171013832092,
0.0052488576620817184,
0.009894411079585552,
-0.01949184201657772,
0.027044011279940605,
0.010815785266458988,
-0.004857548046857119,
-0.020144827663898468,
0.012478678487241268,
0.027839163318276405,
0.00406297342851758,
-0.014972997829318047,
0.03335639834403992,
0.049514587968587875,
-0.042984262108802795,
-0.03803350776433945,
0.014396212995052338,
0.005261075682938099,
0.029896289110183716,
-0.0026475705672055483,
-0.011176617816090584,
0.013900143094360828,
0.04383862018585205,
0.022326502948999405,
0.022617675364017487,
-0.037219543009996414,
-0.00009286776185035706,
-0.006573082879185677,
-0.006632313132286072,
0.017700692638754845,
0.010333254002034664,
0.003411326091736555,
0.035898055881261826,
0.023227272555232048,
0.007749778684228659,
0.043579041957855225,
0.01475027296692133,
-0.0690726488828659,
0.022031400352716446,
-0.029852014034986496,
-0.05508121848106384,
-0.031092651188373566,
-0.021003857254981995,
0.009607113897800446,
0.0034693432971835136,
-0.03984297066926956,
-0.024069376289844513,
-0.018790632486343384,
-0.059621796011924744,
0.037883926182985306,
-0.042263470590114594,
-0.04424756020307541,
-0.03676799684762955,
0.029737191274762154,
0.020157862454652786,
-0.04041167348623276,
-0.03820749372243881,
0.05293148383498192,
-0.007557542063295841,
0.018199803307652473,
0.004063241649419069,
0.016189463436603546,
0.010830830782651901,
0.005225328262895346,
0.0492112934589386,
0.02690945751965046,
-0.008718452416360378,
0.023052264004945755,
-0.0002792906016111374,
0.07450278848409653,
0.006206688936799765,
-0.019747668877243996,
-0.019689850509166718,
-0.03970463201403618,
-0.01337829977273941,
0.0059034330770373344,
0.08969290554523468,
-0.0011217372957617044,
-0.028267351910471916,
0.018917055800557137,
0.005797250661998987,
0.011205584742128849,
0.04250526428222656,
0.06842964887619019,
0.0011970341438427567,
-0.011961012147367,
-0.05142512544989586,
0.019819041714072227,
0.011034921742975712,
-0.02206074446439743,
0.0019685893785208464,
-0.007021514233201742,
-0.026946984231472015,
-0.023278333246707916,
0.01875065639615059,
0.05070022493600845,
0.009434112347662449,
-0.04968024417757988,
-0.008602120913565159,
-0.0015305562410503626,
0.0635146051645279,
-0.013742065988481045,
-0.0077392165549099445,
0.042052872478961945,
0.048989083617925644,
0.004008868243545294,
0.00001642801726120524,
-0.07401816546916962,
0.009990746155381203,
0.02316020056605339,
0.017291663214564323,
0.030836790800094604,
0.0024695906322449446,
-0.030455082654953003,
-0.011594207026064396,
0.05752785876393318,
-0.0017831901786848903,
0.010810143314301968,
0.015667466446757317,
-0.017511166632175446,
-0.00066821847576648,
-0.011350982822477818,
-0.0657038763165474,
0.002106537576764822,
-0.013842029497027397,
-0.0025141688529402018,
-0.054493680596351624,
0.013534036464989185,
-0.005701897665858269,
0.018758585676550865,
0.007004561368376017,
0.037086356431245804,
0.0409509539604187,
0.023154163733124733,
0.008057530969381332,
0.019465669989585876,
-0.016203178092837334,
-0.0921187475323677,
-0.01460987702012062,
0.03292657434940338,
-0.029447024688124657,
0.023927392438054085,
-0.01620716042816639,
-0.02866946905851364,
0.056046050041913986,
-0.03650032728910446,
0.010816375724971294,
0.015874672681093216,
-0.02033352293074131,
0.009954464621841908,
-0.002664160216227174,
-0.01708722487092018,
0.02300448715686798,
0.022316638380289078,
0.022070225328207016,
-0.024968385696411133,
-0.021221516653895378,
0.04030480608344078,
-0.002707722829654813,
-0.000860671978443861,
-0.0016831085085868835,
-0.0028615188784897327,
-0.019158998504281044,
0.042076971381902695,
0.006835926789790392,
-0.01497796829789877,
-0.04052645340561867,
-0.010923702269792557,
-0.06080590561032295,
0.005009558517485857,
0.004190461244434118,
-0.019329752773046494,
-0.022082099691033363,
0.021637622267007828,
-0.025594862177968025,
-0.014579592272639275,
-0.010889646597206593,
0.005976838991045952,
-0.006980632431805134,
0.014984417706727982,
0.03351328521966934,
0.03598330542445183,
-0.02350172959268093,
-0.01951577141880989,
0.01610753871500492,
-0.061765458434820175,
0.04436110705137253,
-0.04409009963274002,
-0.016412219032645226,
0.007404724135994911,
-0.05965755134820938,
-0.031101670116186142,
0.005934718530625105,
0.0029384305234998465,
0.022647611796855927,
-0.03931565210223198,
-0.012134354561567307,
0.03150608763098717,
0.015500214882194996,
-0.07284611463546753,
-0.03069768100976944,
-0.0027765834238380194,
0.005586319603025913,
-0.014066101983189583,
-0.029538942500948906,
0.02363508939743042,
-0.040857281535863876,
0.015770792961120605,
-0.012479090131819248,
0.04979714751243591,
-0.04171272739768028,
0.007630820851773024,
-0.013430193066596985,
0.0552302785217762,
0.04260805621743202,
-0.007973294705152512,
-0.027749134227633476,
0.04274289682507515,
-0.019285481423139572,
-0.013966166414320469,
0.011246887966990471,
0.04748440533876419,
-0.014588792808353901,
-0.03427664563059807,
-0.027611223980784416,
-0.007906508632004261,
0.01973223313689232,
-0.005985749885439873,
0.023043865337967873,
0.05163726210594177,
0.03730878606438637,
-0.014218027703464031,
-0.03946291655302048,
-0.013022230938076973,
-0.007243584841489792,
-0.02197805792093277,
-0.043566517531871796,
0.032808635383844376,
-0.007553212344646454,
-0.018324555829167366,
0.044877246022224426,
-0.0194309763610363,
0.04741889610886574,
-0.0007865783991292119,
0.043342649936676025,
0.003998392727226019,
-0.013406194746494293,
0.03852054104208946,
0.0002412013418506831,
-0.016881784424185753,
-0.018770501017570496,
0.04892389476299286,
0.014291971921920776,
-0.018782585859298706,
-0.027998074889183044,
-0.020915454253554344,
-0.02675405517220497,
0.0013365106424316764,
0.07068313658237457,
0.014610519632697105,
0.04668903350830078,
0.00919361598789692,
0.03178190439939499,
0.0006370185292325914,
0.009853031486272812,
0.013346011750400066,
0.013929230161011219,
0.01852947659790516,
0.03924354910850525,
-0.0046051181852817535,
-0.0019163768738508224,
0.004483814351260662,
0.03348710015416145,
-0.018874309957027435,
-0.001471528667025268,
0.006519199348986149,
0.0186220183968544,
0.0453617125749588,
0.022986598312854767,
-0.030898746103048325,
0.030749991536140442,
-0.012554755434393883,
0.026894094422459602,
-0.008992012590169907,
0.013128193095326424,
0.03226986899971962,
0.03679879382252693,
-0.00001621634146431461,
0.02505910024046898,
-0.01737597957253456,
-0.0585356242954731,
0.06332123279571533,
0.01448415033519268,
0.011039525270462036,
-0.0015560814645141363,
0.008089743554592133,
0.018662627786397934,
-0.025853324681520462,
-0.006116489879786968,
0.02304018661379814,
-0.04638518765568733,
-0.03230777382850647,
-0.04358604550361633,
-0.06107707694172859,
0.05656958371400833,
0.004275683779269457,
-0.011034655384719372,
0.02156251110136509,
-0.01585625857114792,
0.056875377893447876,
0.0026291708927601576,
0.03315887600183487,
-0.004136450123041868,
0.06225811317563057,
-0.0072988769970834255,
0.02865763008594513,
0.0003785798617172986,
0.0016725658206269145,
0.10177098214626312,
0.0496673509478569,
-0.004581007175147533,
-0.07504270225763321,
0.0003245655389036983,
-0.045847125351428986,
0.018345151096582413,
-0.05222208797931671,
0.03519469127058983,
-0.014854323118925095,
-0.00948184635490179,
0.01142450887709856,
0.05194705352187157,
-0.0255241971462965,
0.0076537770219147205,
0.050584521144628525,
-0.053431276232004166,
-0.05774497985839844,
0.0075978366658091545,
0.03586801514029503,
0.02567954920232296,
0.02051645517349243,
-0.021117502823472023,
0.017271699383854866,
-0.01982973888516426,
0.015146562829613686,
-0.04272530972957611,
-0.032357390969991684,
0.005575458984822035,
0.011726872995495796,
-0.04856482520699501,
-0.008401105180382729,
-0.02134946547448635,
0.001606896286830306,
-0.04357233643531799,
-0.0003543843049556017,
0.0261993408203125,
0.014688622206449509,
0.022993523627519608,
0.04089953005313873,
0.02556844986975193,
0.014298363588750362,
0.022893842309713364,
-0.010257945396006107,
-0.03718813508749008,
0.0029221628792583942,
0.001722524524666369,
0.06699713319540024,
-0.018825463950634003,
0.0029945485293865204,
-0.005852953065186739,
-0.01625395193696022,
-0.0020545462612062693,
-0.04618821665644646,
0.027232104912400246,
-0.032786499708890915,
0.04498914256691933,
0.027640867978334427,
0.04987680912017822,
-0.004195340909063816,
0.03684168681502342,
0.01915447600185871,
-0.012090069241821766,
-0.010482140816748142,
-0.0028926697559654713,
-0.001794041832908988,
-0.01191688608378172,
0.02362307347357273,
-0.0075719598680734634,
-0.05068852752447128,
-0.00140844052657485,
-0.04105639085173607,
-0.019802436232566833,
0.010877272114157677,
0.018157856538891792,
0.011471535079181194,
0.05011344701051712,
-0.015304255299270153,
0.013597151264548302,
-0.022292453795671463,
-0.08584696054458618,
0.008716396987438202,
-0.04082106798887253,
-0.04072107747197151,
-0.0011735953157767653,
0.009247871115803719,
0.02911773882806301,
0.07259483635425568,
-0.028629668056964874,
-0.0009567945380695164,
-0.016837798058986664,
0.02761288918554783,
0.037138890475034714,
-0.02231784351170063,
-0.019561175256967545,
0.0075863925740122795,
-0.010985767468810081,
-0.0023463701363652945,
-0.005129171535372734,
-0.0045651537366211414,
0.008162049576640129,
0.014763902872800827,
-0.023464234545826912,
0.031020520254969597,
-0.005485672503709793,
-0.024590248242020607,
0.009750595316290855,
-0.03787782043218613,
0.025805307552218437,
0.02029947005212307,
0.001140705542638898,
-0.04861517250537872,
-0.032094165682792664,
-0.007971064187586308,
0.008035789243876934,
-0.007481536362320185,
0.02493949420750141,
-0.03135880455374718,
0.03224522992968559,
-0.018033791333436966,
0.000429630366852507,
-0.019341591745615005,
-0.010893158614635468,
-0.030732901766896248,
0.023463847115635872,
-0.02974129468202591,
-0.009513432160019875,
0.00010422350896988064,
0.006023099645972252,
-0.0033572353422641754,
-0.006803516298532486,
-0.0030321385711431503,
0.0558038204908371,
-0.018991703167557716,
0.009172232821583748,
0.008976243436336517,
-0.02057228423655033,
0.05048074200749397,
0.013520392589271069,
-0.04387635737657547,
0.0034366226755082607,
-0.0400836244225502,
-0.011767084710299969,
0.038559719920158386,
0.0061726695857942104,
0.05590461567044258,
0.03158852085471153,
-0.03285922482609749,
-0.0024385489523410797,
0.02863951027393341,
-0.0010845167562365532,
0.017160015180706978,
0.011088418774306774,
-0.0728982463479042,
-0.04589240625500679,
-0.033624231815338135,
0.027860542759299278,
0.009610222652554512,
-0.024085860699415207,
0.021498918533325195,
-0.00035054731415584683,
-0.020090997219085693,
-0.019639180973172188,
0.024490032345056534,
-0.0285741426050663,
0.02726917527616024,
0.026368238031864166,
-0.032752711325883865,
0.013847359456121922,
0.07692070305347443,
-0.03544856235384941,
0.013361259363591671,
0.016619926318526268,
0.026618797332048416,
-0.11619938910007477,
-0.015680817887187004,
0.01290793064981699,
0.028494596481323242,
0.05243091285228729,
-0.031842369586229324,
0.022537169978022575,
0.03038637526333332,
-0.06594957411289215,
0.008479663170874119,
-0.0029607375618070364,
-0.008460186421871185,
0.0018396701198071241,
-0.013185362331569195,
-0.006095838733017445,
0.04495289549231529,
0.037769898772239685,
0.04454486444592476,
0.01107777003198862,
0.010593488812446594,
-0.011029819026589394,
-0.03925662487745285,
0.0008636611746624112,
0.022717280313372612,
0.03994590789079666,
-0.054710280150175095,
0.07015184313058853,
-0.006520244292914867,
-0.030314525589346886,
0.001329096034169197,
-0.042030345648527145,
-0.018995098769664764,
-0.0018413937650620937,
0.053214266896247864,
0.016695035621523857,
0.03151436150074005,
0.018259389325976372,
-0.001298513961955905,
0.006306021939963102,
0.024766871705651283,
0.003204851411283016,
-0.01150352880358696,
-0.04318106546998024,
0.0024223830550909042,
0.010206423699855804,
-0.025200866162776947,
-0.045917823910713196,
0.04598646238446236,
-0.043722003698349,
-0.05237752944231033,
-0.03228321671485901,
-0.03044935315847397,
-0.001067289151251316,
-0.0047336146235466,
-0.017440490424633026,
-0.07600818574428558,
-0.005189555697143078,
0.059134550392627716,
-0.008847796358168125,
-0.03103107586503029,
-0.012479732744395733,
0.013422628864645958,
-0.0359739251434803,
0.04018557444214821,
0.02664683200418949,
0.004565039649605751,
-0.06682397425174713,
-0.011741281487047672,
0.014352410100400448,
-0.009602286852896214,
0.006154876668006182,
-0.02214837074279785,
-0.023116769269108772,
-0.019644487649202347,
0.01938191056251526,
0.013782335445284843,
0.0005501612322404981,
0.036269914358854294,
-0.018408333882689476,
-0.06564430892467499,
0.041699789464473724,
0.01736770197749138,
0.004671650473028421,
0.02774333581328392,
-0.025913119316101074,
0.02046865224838257,
0.012690247036516666,
0.04813547059893608,
-0.04110085591673851,
-0.006491062697023153,
0.04025239124894142,
-0.0073134275153279305,
-0.010994933545589447,
-0.0169692263007164,
-0.026461182162165642,
-0.02176099829375744,
-0.018474506214261055,
0.0018287963466718793,
0.026831045746803284,
-0.014371797442436218,
0.03346458449959755,
0.03147093951702118,
0.0039559961296617985,
-0.012056437321007252,
-0.03595317527651787,
-0.058303333818912506,
0.04167270287871361,
0.030478088185191154,
0.013420642353594303,
0.029888391494750977,
0.006169551517814398,
0.006354488432407379,
0.03921414166688919,
-0.049805425107479095,
-0.02790934592485428,
0.02183697186410427,
-0.07420480996370316,
-0.02296309731900692,
0.002402856247499585,
0.01192157156765461,
0.007616796065121889,
-0.06240110844373703,
0.012204636819660664,
0.009820652194321156,
-0.05453535169363022,
0.0073630367405712605,
0.03535259887576103,
-0.013350335881114006,
0.007064174395054579,
0.03034534677863121,
-0.021328963339328766,
0.048906709998846054,
0.019348222762346268,
0.026318222284317017,
0.057980071753263474,
0.042166925966739655,
-0.02976386249065399,
-0.004130788613110781,
0.024610543623566628,
-0.030080927535891533,
0.013209152966737747,
0.007437586784362793,
0.02529180608689785,
-0.016702644526958466,
-0.01772245205938816,
0.03617122024297714,
-0.0086696557700634,
0.003058947157114744,
0.005917166825383902,
-0.033742621541023254,
0.056199055165052414,
-0.03914293646812439,
0.0029204143211245537,
-0.02411089651286602,
-0.009003499522805214,
-0.0013368448708206415,
0.01728130877017975,
-0.00882625300437212,
0.05664953216910362,
-0.010197090916335583,
-0.01113475114107132,
-0.03311796113848686,
-0.006882555317133665,
0.0032742966432124376,
-0.040154825896024704,
0.000020922003386658616,
0.0058268397115170956,
0.0146712027490139,
0.019864575937390327,
-0.03425156697630882,
-0.019962074235081673,
-0.019521676003932953,
-0.009591827169060707,
0.030048323795199394,
0.017386123538017273,
-0.01610870286822319,
0.020594749599695206,
-0.0566009022295475,
0.050456080585718155,
-0.049050457775592804,
-0.003299297532066703,
-0.015213013626635075,
0.010881958529353142,
-0.03220866993069649,
0.039146263152360916
] |
<p>Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that proves it?</p> | 2,027 | [
-0.05099833384156227,
0.011064043268561363,
0.007221253588795662,
-0.003922597039490938,
0.019589267671108246,
0.030301470309495926,
-0.028516806662082672,
-0.011139336042106152,
-0.021035391837358475,
-0.03250399976968765,
0.01120516937226057,
0.01966545544564724,
0.04003066569566727,
0.0077457851730287075,
-0.00890638493001461,
-0.009442061185836792,
0.0054151457734405994,
-0.019440071657299995,
-0.02764752134680748,
-0.007439321838319302,
-0.014781753532588482,
0.06336619704961777,
-0.02247222699224949,
0.02024448662996292,
-0.019054342061281204,
-0.003255626419559121,
-0.00210110773332417,
0.06253029406070709,
0.014226984232664108,
0.06378792226314545,
-0.02713719941675663,
-0.044268637895584106,
0.007785282097756863,
-0.013668213039636612,
0.013600188307464123,
0.021094946190714836,
-0.02133801020681858,
-0.034860093146562576,
0.024465521797537804,
-0.0007416673470288515,
-0.021293416619300842,
-0.009097526781260967,
-0.0007159377564676106,
0.02697530947625637,
-0.036976348608732224,
0.022714391350746155,
0.006358835846185684,
0.007094348780810833,
0.06324135512113571,
-0.049639735370874405,
0.05812038481235504,
0.026886386796832085,
0.04262322559952736,
0.015814729034900665,
-0.007921646349132061,
-0.005553625524044037,
0.02998501807451248,
0.043238554149866104,
0.033572010695934296,
-0.0516892746090889,
-0.06791465729475021,
-0.045849692076444626,
-0.0008331625140272081,
-0.0035882715601474047,
-0.030891289934515953,
0.039660606533288956,
0.026710273697972298,
0.002835427178069949,
0.019424209371209145,
-0.02228112332522869,
-0.022222768515348434,
-0.001410106779076159,
0.0528474859893322,
-0.0028271726332604885,
0.024325521662831306,
0.06045379117131233,
-0.005861509125679731,
-0.025746872648596764,
0.02908935397863388,
0.005343915428966284,
0.023828504607081413,
0.016494054347276688,
0.007740503642708063,
0.026260634884238243,
-0.017024151980876923,
0.004081930033862591,
0.06472206115722656,
0.03456060215830803,
-0.013850807212293148,
0.03608984872698784,
0.00899957213550806,
0.005832748021930456,
0.050758183002471924,
-0.03470774367451668,
-0.0008436920470558107,
0.032733213156461716,
0.01516452245414257,
0.037461552768945694,
-0.029309239238500595,
-0.009200174361467361,
-0.019016847014427185,
-0.03997357562184334,
-0.002679686527699232,
0.061978187412023544,
-0.000018635601009009406,
-0.012338544242084026,
-0.02790280058979988,
0.02873971499502659,
-0.04581020399928093,
-0.017158228904008865,
-0.005834852810949087,
0.0026331308763474226,
-0.03531227633357048,
0.006980566773563623,
-0.0025759697891771793,
-0.00042558531276881695,
-0.0077558173798024654,
-0.007336920592933893,
0.08959824591875076,
0.07087711989879608,
0.026227766647934914,
0.02361658588051796,
0.03742467239499092,
-0.02667326293885708,
-0.052232399582862854,
0.0397469699382782,
0.04788489267230034,
-0.024649281054735184,
-0.03491482511162758,
-0.02499590441584587,
0.010144766420125961,
-0.0401780940592289,
-0.022407585754990578,
-0.009959259070456028,
0.0520796962082386,
-0.009989241138100624,
-0.1240013986825943,
-0.0851864144206047,
0.040718935430049896,
0.004370409529656172,
-0.028364654630422592,
-0.047858405858278275,
0.027870770543813705,
0.05053628981113434,
0.10531673580408096,
-0.036445632576942444,
0.03066784329712391,
-0.0010964750545099378,
0.04021333530545235,
-0.0064958627335727215,
0.006552965380251408,
-0.058025460690259933,
0.04691186547279358,
-0.031702976673841476,
-0.04085645079612732,
-0.06540873646736145,
0.01791691966354847,
0.007073700428009033,
-0.0035265032202005386,
-0.028740616515278816,
0.063369981944561,
-0.010265102609992027,
0.019927220419049263,
-0.000307913200231269,
-0.01470403652638197,
-0.005204905290156603,
0.07579831033945084,
0.0305617842823267,
0.014232706278562546,
0.03458895906805992,
-0.01835516467690468,
0.01793772727251053,
0.009920814074575901,
0.012452500872313976,
0.03563674911856651,
-0.04745732992887497,
-0.0022400105372071266,
-0.0034590614959597588,
-0.011816224083304405,
-0.005492268595844507,
-0.02203558012843132,
0.006453938782215118,
0.0036114752292633057,
0.015492299571633339,
-0.02959825098514557,
-0.007072445936501026,
-0.022501224651932716,
0.0070741972886025906,
0.026305019855499268,
-0.04923465847969055,
-0.02289567142724991,
-0.04087483137845993,
-0.010814758017659187,
-0.002637275494635105,
-0.03039398416876793,
0.037434741854667664,
0.007840802893042564,
0.03390279412269592,
-0.02554360218346119,
-0.017533719539642334,
0.021616440266370773,
0.011693120934069157,
0.005252239294350147,
0.01577860862016678,
0.042427174746990204,
0.05482271686196327,
0.057487454265356064,
0.010809460654854774,
0.027381418272852898,
-0.007018755190074444,
-0.014937348663806915,
0.011040978133678436,
0.001332346466369927,
-0.0020130674820393324,
-0.05106990039348602,
0.0018215719610452652,
0.024632014334201813,
0.00648717163130641,
-0.014791877008974552,
0.044817958027124405,
-0.013304571621119976,
0.03830337151885033,
0.021862242370843887,
-0.0034586917608976364,
0.0002946328022517264,
0.025225002318620682,
0.00010937145998468623,
0.007130835670977831,
0.011799332685768604,
-0.05260609835386276,
-0.06228608638048172,
-0.03223298117518425,
0.021996332332491875,
0.036571986973285675,
-0.01784323714673519,
0.003976159729063511,
0.013364489190280437,
0.04941187798976898,
0.0001238897384610027,
0.04701356962323189,
-0.03740490600466728,
-0.04998818412423134,
0.037505555897951126,
0.011183049529790878,
0.04463978111743927,
-0.0019897324964404106,
0.017672721296548843,
-0.020061546936631203,
-0.013364989310503006,
0.022144740447402,
-0.059107597917318344,
-0.002308459719642997,
-0.0004011724086012691,
-0.014822158962488174,
-0.010107839480042458,
-0.029026012867689133,
0.007909680716693401,
-0.027182765305042267,
0.025386404246091843,
0.010684439912438393,
-0.0017306932713836432,
0.02176925167441368,
-0.015280160121619701,
-0.029900064691901207,
0.03712731972336769,
-0.03198094293475151,
-0.005404531490057707,
-0.039890483021736145,
0.0181940495967865,
-0.008040728978812695,
-0.0038846812676638365,
-0.04454904794692993,
-0.0016990076983347535,
-0.0015421545831486583,
-0.011145302094519138,
0.04060174897313118,
-0.024249425157904625,
0.020609823986887932,
-0.03228303790092468,
0.010330730117857456,
0.013568028807640076,
-0.0088725620880723,
0.015266941860318184,
0.06007986515760422,
-0.042327746748924255,
0.021579839289188385,
-0.07331466674804688,
-0.03011220693588257,
0.035610225051641464,
-0.0075402529910206795,
0.03541712462902069,
0.0068136295303702354,
0.034024592489004135,
-0.035187769681215286,
-0.010314574465155602,
-0.034492284059524536,
0.014219739474356174,
-0.016354946419596672,
-0.00901858415454626,
0.04162583872675896,
0.018148209899663925,
-0.040033698081970215,
0.024938546121120453,
-0.003678182838484645,
-0.009107962250709534,
0.005449825432151556,
0.0030562146566808224,
0.014206772670149803,
-0.018716678023338318,
0.03776658698916435,
0.012058221735060215,
-0.03941335901618004,
-0.016398422420024872,
-0.06361248344182968,
-0.03849333897233009,
-0.010208896361291409,
-0.011668930761516094,
0.045348308980464935,
0.009538926184177399,
-0.04005322977900505,
0.07606141269207001,
0.08073703944683075,
-0.006452861241996288,
0.0015708679566159844,
-0.00231558526866138,
-0.002815229818224907,
-0.05915999040007591,
0.005723161157220602,
-0.003631375264376402,
0.025339879095554352,
0.04547194764018059,
0.012901769950985909,
0.03758804872632027,
0.0009492016397416592,
0.003147422568872571,
-0.024174345657229424,
0.007727209012955427,
0.028188541531562805,
0.021440787240862846,
0.01762242801487446,
0.014291591942310333,
-0.01655966229736805,
-0.0049317628145217896,
0.03971986100077629,
0.008342080749571323,
0.010579162277281284,
-0.05572083964943886,
0.061093442142009735,
-0.02555670216679573,
0.033417876809835434,
-0.029147803783416748,
0.019165854901075363,
-0.002268394222483039,
-0.032244786620140076,
0.014638232067227364,
0.015996988862752914,
-0.00447285920381546,
-0.029317839071154594,
0.014810966327786446,
0.0005505724111571908,
0.0253386739641428,
-0.038447748869657516,
-0.022472970187664032,
-0.03704468905925751,
-0.022952450439333916,
0.056597791612148285,
-0.00878465361893177,
-0.04601740464568138,
0.037557464092969894,
0.025067077949643135,
0.028091704472899437,
-0.040285591036081314,
-0.0504189096391201,
-0.022591998800635338,
-0.040745094418525696,
0.03653724491596222,
-0.01311738695949316,
0.057875704020261765,
-0.005289699416607618,
0.05489039048552513,
0.02348802238702774,
0.011314358562231064,
-0.04798875004053116,
0.006522834300994873,
-0.0929345190525055,
0.03983481228351593,
-0.04996466264128685,
-0.007492502219974995,
-0.0019659153185784817,
-0.021447673439979553,
0.006109063513576984,
0.019587591290473938,
-0.038041308522224426,
-0.026235319674015045,
-0.01151956431567669,
-0.05272841081023216,
-0.00019551040895748883,
-0.037987466901540756,
-0.0267246812582016,
0.006542356684803963,
0.03572510927915573,
0.0732751339673996,
-0.0692673996090889,
0.02318894863128662,
0.03552332520484924,
-0.018976695835590363,
-0.030063852667808533,
-0.014127668924629688,
0.04740586131811142,
-0.014405299909412861,
0.023265529423952103,
0.013899439014494419,
0.015955833718180656,
-0.045199256390333176,
-0.02801559306681156,
0.0414065383374691,
0.06570720672607422,
-0.008995373733341694,
-0.0013426060322672129,
-0.014509928412735462,
-0.06317015737295151,
0.0002711701672524214,
0.025267496705055237,
0.05011043697595596,
0.02830646187067032,
0.021745657548308372,
0.028897734358906746,
0.04201781749725342,
-0.04277193918824196,
0.017873717471957207,
0.034535475075244904,
0.0064232246950268745,
-0.004996670875698328,
-0.005502010229974985,
0.00754693103954196,
0.0003375622909516096,
-0.03368235379457474,
0.009702125564217567,
-0.0005799385253340006,
-0.038318779319524765,
0.014300873503088951,
0.0286636371165514,
0.003962922841310501,
-0.06528110802173615,
-0.008577530272305012,
0.031237194314599037,
0.023102715611457825,
-0.01708933524787426,
0.013675672002136707,
-0.013222143985331059,
0.051244307309389114,
0.07211483269929886,
0.035659097135066986,
-0.020879186689853668,
-0.0052539450116455555,
0.03066791594028473,
0.03369073569774628,
0.02041471004486084,
0.0187889002263546,
0.021955812349915504,
-0.031972598284482956,
-0.054662544280290604,
0.04470879212021828,
-0.0075195543467998505,
0.010228931903839111,
-0.0001003445649985224,
-0.02511592023074627,
-0.019452057778835297,
-0.027001088485121727,
-0.01711091212928295,
0.020850220695137978,
0.025489090010523796,
0.007424458395689726,
-0.0015337156364694238,
0.0009051281376741827,
-0.030690696090459824,
-0.0023948156740516424,
-0.008182297460734844,
0.036603059619665146,
-0.0008051507757045329,
0.04535269737243652,
0.0025716840755194426,
0.048013098537921906,
-0.05765721946954727,
-0.0902315303683281,
-0.007959403097629547,
0.006731770001351833,
0.013864578679203987,
0.013193180784583092,
-0.04416589438915253,
-0.06878390908241272,
0.00022016078582964838,
-0.014366080984473228,
-0.013439847156405449,
-0.00021521304734051228,
-0.047355685383081436,
0.023145737126469612,
0.015286541543900967,
-0.016071392223238945,
0.07857280224561691,
0.04896251857280731,
-0.0007307951455004513,
-0.02202971652150154,
-0.00846920907497406,
0.019308414310216904,
-0.031434886157512665,
0.03487532585859299,
-0.03682558238506317,
0.003213598160073161,
-0.05786396935582161,
0.06477488577365875,
-0.040568675845861435,
0.017447784543037415,
0.008838372305035591,
-0.013555916026234627,
0.0008431081660091877,
0.04172446206212044,
0.0017831048462539911,
-0.04852713271975517,
0.00913236290216446,
0.034240465611219406,
0.012287800200283527,
-0.0415450781583786,
0.026014160364866257,
-0.02622305043041706,
-0.05115395039319992,
0.01677682437002659,
-0.0064067537896335125,
0.014688367955386639,
-0.03649183362722397,
-0.041684530675411224,
-0.011280521750450134,
-0.011665666475892067,
0.04860437288880348,
-0.005022510886192322,
0.004059399478137493,
-0.01413673348724842,
-0.05726129189133644,
-0.016430018469691277,
0.007879161275923252,
0.00893404707312584,
0.00778413750231266,
-0.04539641737937927,
0.02625594474375248,
0.01362533774226904,
0.0026874360628426075,
-0.10701363533735275,
-0.022693831473588943,
0.016953514888882637,
0.018436895683407784,
-0.02919193170964718,
-0.011188037693500519,
-0.0017669195076450706,
-0.02034543827176094,
-0.013515114784240723,
0.003988917917013168,
0.05398009344935417,
-0.025874361395835876,
0.007650462910532951,
0.019354071468114853,
0.03106362745165825,
0.005901271943002939,
-0.03960958495736122,
0.001707090763375163,
0.015362133271992207,
-0.05526004731655121,
0.01048051007091999,
0.010233446024358273,
0.025235416367650032,
-0.004471501335501671,
-0.01746063120663166,
-0.03835328295826912,
-0.012599321082234383,
0.004211084451526403,
-0.017125288024544716,
-0.0007430019322782755,
0.05958602949976921,
-0.023192839697003365,
-0.005779176950454712,
-0.049029234796762466,
-0.025134548544883728,
-0.014910955913364887,
0.05299026891589165,
-0.0007399320020340383,
-0.022420275956392288,
0.002985635306686163,
-0.014890391379594803,
0.031192179769277573,
0.009690848179161549,
-0.0019622715190052986,
0.001687322510406375,
0.06763236969709396,
-0.008209248073399067,
-0.03424086794257164,
0.015440533868968487,
-0.05044251307845116,
-0.011598296463489532,
0.002740727039054036,
0.02597595751285553,
-0.013142433948814869,
-0.0037945094518363476,
-0.04538851976394653,
-0.03358028084039688,
-0.009954891167581081,
0.008078809827566147,
0.06072096899151802,
-0.005428122356534004,
0.034758247435092926,
0.03502319008111954,
-0.041510652750730515,
-0.002246923977509141,
-0.01827220991253853,
-0.020069465041160583,
0.007467564195394516,
0.002150946296751499,
0.02741634100675583,
-0.018936647102236748,
0.01620396412909031,
0.0167420394718647,
0.0645197406411171,
0.012657669372856617,
0.025564685463905334,
0.03685816377401352,
0.020982133224606514,
0.0011918512172996998,
-0.01587591879069805,
-0.041485659778118134,
0.07046302407979965,
-0.01909421756863594,
0.0639868676662445,
0.008767838589847088,
0.01561643835157156,
0.011113313026726246,
-0.031188247725367546,
0.014135422185063362,
-0.003349944716319442,
-0.02984583005309105,
-0.049579475075006485,
0.022726470604538918,
0.005872705951333046,
0.008973957039415836,
0.02300051599740982,
0.0014956186059862375,
0.018963657319545746,
-0.009365800768136978,
-0.004037375561892986,
-0.0000370118796126917,
-0.03244636580348015,
-0.019448963925242424,
-0.014420273713767529,
-0.016475465148687363,
0.02949894592165947,
0.006084199529141188,
-0.03145701438188553,
-0.024068616330623627,
-0.017941873520612717,
0.014082036912441254,
-0.0006346784648485482,
0.025381799787282944,
-0.02460552379488945,
0.026701390743255615,
0.012188052758574486,
0.05295342206954956,
-0.006629881914705038,
0.013448162004351616,
0.1334138661623001,
0.06741988658905029,
0.0256236232817173,
-0.08585338294506073,
0.05493111163377762,
-0.01648310385644436,
0.024209415540099144,
-0.016616612672805786,
0.057965006679296494,
0.00669907359406352,
0.03810257837176323,
0.012313826940953732,
0.06434734910726547,
0.016390440985560417,
-0.003513801610097289,
0.04774714261293411,
-0.07585156708955765,
-0.04101237282156944,
-0.005695626605302095,
0.026993881911039352,
-0.008778035640716553,
-0.014429090544581413,
-0.05667813867330551,
0.016117393970489502,
-0.01100231148302555,
-0.013192815706133842,
0.004371840041130781,
-0.046494755893945694,
0.02480672486126423,
0.01740126870572567,
0.012386010028421879,
0.0032186193857342005,
0.020507147535681725,
0.006320060230791569,
-0.06820379942655563,
-0.008098842576146126,
-0.006576200947165489,
-0.011805483140051365,
0.04827005788683891,
0.05043971538543701,
0.041464030742645264,
0.013760288245975971,
-0.010945575311779976,
-0.004923026077449322,
-0.047043878585100174,
-0.011855988763272762,
-0.0232637207955122,
0.01999165490269661,
-0.031212110072374344,
-0.002140222117304802,
0.013173154555261135,
-0.032631054520606995,
-0.02416706271469593,
-0.044853415340185165,
-0.02392205037176609,
0.010877005755901337,
0.006878597661852837,
-0.030339699238538742,
0.006064347457140684,
-0.03024793602526188,
0.025905026122927666,
-0.03203265368938446,
0.001733229961246252,
0.016238585114479065,
-0.04837648943066597,
-0.02089480496942997,
-0.0009032976231537759,
0.0012740172678604722,
-0.01191585510969162,
-0.020686378702521324,
-0.052764590829610825,
-0.011732720769941807,
-0.04033065587282181,
-0.018916791304945946,
-0.013316784054040909,
-0.01051362045109272,
0.06530298292636871,
0.010817769914865494,
0.03244686499238014,
-0.02932017669081688,
-0.05325896292924881,
0.02183251641690731,
0.006813026033341885,
0.0054076300002634525,
-0.014080098830163479,
-0.015212731435894966,
0.0032679892610758543,
0.0574367456138134,
-0.047352004796266556,
-0.006368629634380341,
0.008082080632448196,
-0.022625721991062164,
0.01653442159295082,
-0.008246983401477337,
0.02343035861849785,
-0.006971454713493586,
-0.03973770514130592,
-0.023254459723830223,
-0.04933664947748184,
-0.006648501381278038,
0.04309891536831856,
0.007962366566061974,
-0.00287608546204865,
0.01486633624881506,
-0.025483662262558937,
-0.016574839130043983,
0.03641851991415024,
-0.025951331481337547,
0.025461381301283836,
0.016338955610990524,
0.01585007831454277,
-0.041745010763406754,
-0.08829078823328018,
0.006882030051201582,
-0.0042742714285850525,
0.02012687176465988,
-0.013016334734857082,
-0.053028691560029984,
-0.021232152357697487,
-0.006121722050011158,
0.042273737490177155,
-0.05005898326635361,
-0.04957212880253792,
-0.038234107196331024,
-0.003382620634511113,
0.003592071123421192,
0.01035300549119711,
-0.005793447140604258,
0.05264989659190178,
0.007340518292039633,
-0.03572976961731911,
-0.0032192447688430548,
-0.006500020157545805,
-0.0034333192743360996,
0.003851477522403002,
-0.011692344211041927,
0.01963750645518303,
0.04020268842577934,
0.017878687009215355,
-0.015116930939257145,
0.014639961533248425,
-0.057699546217918396,
-0.04531821236014366,
0.02712394669651985,
-0.0037857559509575367,
-0.01085355319082737,
-0.020483599975705147,
-0.001160472515039146,
-0.026148803532123566,
0.02182864211499691,
-0.04156363755464554,
-0.01975529082119465,
-0.014651171863079071,
-0.0384090319275856,
0.035044070333242416,
-0.023524975404143333,
0.033944062888622284,
-0.029850028455257416,
-0.010248067788779736,
0.042281623929739,
0.01855308562517166,
-0.011995849199593067,
-0.033131588250398636,
0.0014605455799028277,
0.00938549917191267,
0.04926782101392746,
0.02106183022260666,
0.04658475145697594,
0.02003217115998268,
0.06266200542449951,
-0.01645524427294731,
0.008479312993586063,
-0.0141163794323802,
-0.008726616390049458,
-0.09089343994855881,
0.013252310454845428,
0.004571064375340939,
0.005523283034563065,
-0.007453299593180418,
-0.06686019897460938,
0.040195975452661514,
0.026687365025281906,
-0.06195485591888428,
0.037859957665205,
-0.045480504631996155,
-0.011672500520944595,
-0.02944769896566868,
0.01429456751793623,
0.0003089484525844455,
0.052689824253320694,
0.056715112179517746,
0.02281089872121811,
0.0048849014565348625,
0.01663854345679283,
0.006207025144249201,
0.0286556463688612,
-0.021566839888691902,
0.034137431532144547,
-0.00888307485729456,
-0.006052653305232525,
0.004808903206139803,
0.013200994580984116,
-0.01099481526762247,
-0.015513771213591099,
-0.03499437868595123,
-0.03577790781855583,
-0.03544636070728302,
0.005479167215526104,
0.023434124886989594,
0.02285611815750599,
0.027768591418862343,
-0.0029727984219789505,
-0.006458166521042585,
-0.006531184073537588,
0.049079954624176025,
0.024936886504292488,
0.010042991489171982,
0.006038190796971321,
0.001979042775928974,
-0.029038796201348305,
-0.04225721210241318,
0.04559925198554993,
-0.012109656818211079,
-0.011024725623428822,
0.006548451259732246,
-0.014171449467539787,
-0.010399035178124905,
0.02049943059682846,
0.04731958359479904,
-0.018738197162747383,
-0.002054839627817273,
0.02106565237045288,
0.01964429020881653,
0.006173992529511452,
0.029756002128124237,
-0.007795619312673807,
-0.02260812744498253,
0.037566568702459335,
0.0220534298568964,
-0.008771956898272038,
-0.0680944174528122,
-0.001718227518722415,
-0.008101160638034344,
-0.010990466922521591,
0.027286473661661148,
-0.04499093443155289,
-0.010945416986942291,
-0.003718186402693391,
0.017375454306602478,
0.028325334191322327,
-0.028568612411618233,
-0.04989102855324745,
0.013169955462217331,
-0.057151224464178085,
0.0569746196269989,
0.019514262676239014,
0.01927940919995308,
-0.011844918131828308,
0.014900704845786095,
0.007319764234125614,
-0.005591233726590872,
0.028818409889936447,
0.02548632211983204,
-0.025802278891205788,
0.019899379462003708,
0.005476708523929119,
-0.008024254813790321,
-0.014272443018853664,
0.008202606812119484,
-0.02644980698823929,
0.005072253756225109,
-0.01609809882938862,
-0.010565130040049553,
0.0032917503267526627,
0.044800110161304474,
-0.007231653667986393,
-0.008715447038412094,
0.02587982639670372,
0.02485993690788746,
-0.0541008822619915,
0.06745961308479309,
0.014701359905302525,
-0.03586506098508835,
0.0646771639585495,
-0.017505643889307976,
0.012941456399857998,
0.016643814742565155,
0.01049988716840744,
-0.02748914808034897,
0.051357656717300415,
-0.05574316903948784,
-0.023355232551693916,
-0.0010953966993838549,
0.01768338866531849,
-0.004676423966884613,
-0.01802864298224449,
-0.0017472788458690047,
0.04402022808790207,
-0.017582155764102936,
-0.02355320379137993,
0.051353663206100464,
-0.0058059305883944035,
0.0607961006462574,
-0.0013935014139860868,
-0.015477870590984821,
0.04183174669742584,
0.01899309828877449,
-0.012072254903614521,
0.035957496613264084,
0.036746248602867126,
0.0387876071035862,
0.017072774469852448,
0.02249012514948845,
-0.028927773237228394,
0.020814400166273117,
0.017681144177913666,
0.04114922881126404,
-0.03646678477525711,
-0.015731466934084892,
0.031527988612651825,
-0.036532044410705566,
0.01584119163453579,
-0.00007898070180090144,
-0.03573823347687721,
0.06432057172060013,
-0.01869317702949047,
0.03302476182579994,
-0.01645025983452797,
0.022846847772598267,
-0.04328259825706482,
0.009025312028825283,
0.028854677453637123,
0.07598075270652771,
-0.010784211568534374,
0.01457298919558525,
-0.015809284523129463,
0.017160825431346893,
-0.01857752539217472,
-0.037900593131780624,
0.03978940472006798,
0.03356361761689186,
-0.006564259994775057,
-0.033470768481492996,
0.0034961383789777756,
-0.03511721268296242,
-0.007537653669714928,
0.026585614308714867,
0.04516386613249779,
0.0008738819160498679,
0.021004052832722664,
-0.0013151951134204865,
-0.02813406102359295,
0.06460241228342056,
-0.021894656121730804,
-0.018974965438246727,
-0.02525009959936142,
0.0028569914866238832,
-0.04684226214885712,
0.030845532193779945
] |
<p>This brand new published result (nature):</p>
<blockquote>
<p><strong>Experimental non-classicality of an indivisible quantum system</strong><br> by
Radek Lapkiewicz, Peizhe Li, Christoph Schaeff, Nathan K. Langford, Sven Ramelow, Marcin Wieśniak & Anton Zeilinger</p>
</blockquote>
<p>(see <a href="http://www.nature.com/nature/journal/v474/n7352/full/nature10119.html" rel="nofollow">here</a>, for a more popular article about it see <a href="http://www.newscientist.com/article/dn20600-quantum-magic-trick-shows-reality-is-what-you-make-it.html?DCMP=OTC-rss&nsref=physics-math" rel="nofollow">here</a>; also for a pre-print see the ArXiv <a href="http://arxiv.org/abs/1106.4481" rel="nofollow">here</a>)</p>
<p>seems to support the Copenhagen interpretation.</p>
<p><strong>My question</strong> <br>Does this definitely rule out the many-worlds interpretation - or are there still loopholes? How could a many-worlds interpretation of this experiment possibly look like (if possible)?</p>
<p>Thank you</p>
<p><strong>EDIT</strong><br>
Because I obviously created some confusion, how I came to that question: at the end of the NewScientist-article it says:</p>
<blockquote>
<p>Niels Bohr, a giant of quantum
physics, was a great proponent of the
idea that the nature of quantum
reality depends on what we choose to
measure, a notion that came to be
called the Copenhagen interpretation.
"This experiment lends more support to
the Copenhagen interpretation," says
Zeilinger.</p>
</blockquote> | 2,028 | [
-0.025663916021585464,
0.00840323232114315,
0.037613146007061005,
-0.04576607793569565,
0.07659119367599487,
-0.002423286670818925,
-0.03553696721792221,
-0.04952734708786011,
0.00037487788358703256,
-0.02550574019551277,
0.0586186908185482,
0.03380659967660904,
0.011521579697728157,
0.05649583786725998,
-0.012688505463302135,
0.016286928206682205,
-0.00747159356251359,
-0.01138581708073616,
0.02046758122742176,
-0.028943557292222977,
-0.030661525204777718,
0.04431416466832161,
0.008548709563910961,
0.008111957460641861,
-0.0058021144941449165,
0.0017538059037178755,
-0.006221296731382608,
0.001459893537685275,
0.048661019653081894,
0.04128043353557587,
0.0010200068354606628,
-0.021924450993537903,
0.014035417698323727,
0.014430801384150982,
0.011104181408882141,
0.011297601275146008,
0.002301421482115984,
-0.01299077644944191,
0.026511812582612038,
0.021437592804431915,
-0.015162047930061817,
-0.016623208299279213,
-0.006449875887483358,
0.07444897294044495,
-0.04127229377627373,
0.019020361825823784,
0.005781553220003843,
-0.005053853150457144,
0.03290465101599693,
-0.039743658155202866,
0.07012768089771271,
0.028140410780906677,
0.024256762117147446,
0.01971820555627346,
-0.02757679671049118,
0.008730982430279255,
0.08122046291828156,
0.05422617495059967,
0.027190174907445908,
-0.01784236915409565,
-0.040911659598350525,
-0.0172911137342453,
0.014073897153139114,
-0.004296388477087021,
-0.010612799786031246,
0.017866311594843864,
-0.000726614089217037,
-0.00810256414115429,
-0.025974182412028313,
-0.004831639584153891,
0.026010587811470032,
0.007593898102641106,
0.06291379034519196,
0.011038091965019703,
0.032447632402181625,
-0.0009641391807235777,
0.012553343549370766,
-0.01621866784989834,
0.02212005853652954,
0.04846303164958954,
-0.024829687550663948,
-0.016000131145119667,
0.019804222509264946,
0.037729065865278244,
0.04205379635095596,
-0.052096981555223465,
0.07174251973628998,
-0.035860877484083176,
-0.011702295392751694,
0.0011606409680098295,
0.005462417379021645,
0.017556723207235336,
0.04846905171871185,
0.024557825177907944,
-0.03417971357703209,
0.033712901175022125,
0.0014506542356684804,
0.057438965886831284,
-0.03095822036266327,
-0.021195169538259506,
-0.015251917764544487,
-0.0003523562627378851,
0.02356438711285591,
0.03396708890795708,
0.013375416398048401,
0.011295376345515251,
0.014354350976645947,
0.04474644362926483,
-0.0006429430213756859,
0.011801435612142086,
-0.04647490009665489,
0.0455198660492897,
0.024773504585027695,
-0.018095713108778,
0.012477489188313484,
-0.021718226373195648,
-0.014633395709097385,
-0.011823015287518501,
0.06294289976358414,
0.06855371594429016,
-0.004234619904309511,
-0.04170594364404678,
0.025583898648619652,
-0.036225780844688416,
-0.026819739490747452,
-0.011828003451228142,
0.04317568987607956,
0.008476394228637218,
-0.033075861632823944,
0.04017513245344162,
-0.015407714992761612,
0.002808478893712163,
0.019109338521957397,
0.01650196500122547,
0.01235626544803381,
-0.04259905591607094,
-0.13976836204528809,
-0.05016651004552841,
0.03804667294025421,
0.019367234781384468,
-0.033425260335206985,
-0.06440692394971848,
0.023357491940259933,
0.04056781902909279,
0.10147025436162949,
-0.01593613810837269,
-0.008520069532096386,
0.027717726305127144,
0.027316473424434662,
-0.00009502744796918705,
-0.019547531381249428,
0.012784718535840511,
0.027980977669358253,
-0.04674485698342323,
-0.005776251666247845,
-0.020289408043026924,
0.04021987318992615,
0.04617486894130707,
0.01317537296563387,
0.0016742227599024773,
0.05311866104602814,
0.0010508893756195903,
-0.01666664332151413,
-0.009529151022434235,
-0.023770647123456,
-0.037729717791080475,
0.07942327857017517,
0.006839132867753506,
0.001958500361070037,
0.04107429459691048,
-0.009730557911098003,
0.03635875880718231,
-0.01763852685689926,
0.047526780515909195,
-0.016993902623653412,
-0.03495696187019348,
-0.004018555395305157,
0.007445402909070253,
0.029420260339975357,
-0.02721852995455265,
-0.023515017703175545,
0.008796446025371552,
-0.03974870219826698,
0.03458062931895256,
0.01379029918462038,
0.03237619623541832,
-0.0071572959423065186,
0.005771339405328035,
0.03911152482032776,
-0.06427419930696487,
-0.040449924767017365,
-0.06413262337446213,
0.0039963792078197,
0.01460873894393444,
-0.03878060355782509,
0.03707541525363922,
0.027884062379598618,
0.020984914153814316,
-0.03295387327671051,
-0.04352083057165146,
-0.008520865812897682,
0.0304722860455513,
0.026232389733195305,
0.01640944927930832,
0.0364452600479126,
0.056869663298130035,
0.04199107736349106,
-0.011607454158365726,
0.014973209239542484,
-0.005621657706797123,
-0.05744829401373863,
0.016508080065250397,
0.000754689215682447,
0.020254334434866905,
0.004112619906663895,
-0.014139478094875813,
0.03678995370864868,
0.004864501301199198,
-0.017108554020524025,
0.019229242578148842,
-0.03190426155924797,
0.03551663085818291,
-0.021216997876763344,
0.015196180902421474,
-0.019450651481747627,
0.048380084335803986,
0.03469481319189072,
-0.010660910047590733,
0.012768787331879139,
-0.005374242085963488,
-0.03625279664993286,
-0.007768427021801472,
0.024653183296322823,
0.0448608472943306,
-0.014957389794290066,
0.02455817721784115,
-0.02270175889134407,
0.03264755755662918,
-0.0076578897424042225,
0.010741157457232475,
-0.04047640040516853,
-0.03073844127357006,
-0.0023686266504228115,
-0.004613621160387993,
0.028906092047691345,
0.0033250523265451193,
0.02591886557638645,
0.0017768493853509426,
0.031523216515779495,
-0.011644809506833553,
-0.0266841072589159,
-0.0124608613550663,
-0.061525408178567886,
-0.0022219999227672815,
-0.0241711363196373,
-0.05150054767727852,
-0.0043818713165819645,
-0.007980328984558582,
0.014316151849925518,
0.0012247886043041945,
0.007247642148286104,
0.00008119337144307792,
-0.05456016585230827,
-0.0347198024392128,
0.005486520007252693,
0.0010860712500289083,
-0.043860066682100296,
-0.017148222774267197,
0.02583162859082222,
-0.060018301010131836,
0.04725613445043564,
-0.028027281165122986,
0.01923900842666626,
-0.014354735612869263,
0.042453039437532425,
-0.0305042527616024,
-0.008340050466358662,
0.004011034499853849,
-0.07321492582559586,
-0.04741458222270012,
-0.016507187858223915,
0.002484357450157404,
-0.004824432078748941,
0.025601934641599655,
-0.05699368193745613,
0.021938467398285866,
-0.043679770082235336,
0.006536885164678097,
0.038988154381513596,
0.012579414062201977,
-0.009822758845984936,
0.02157132886350155,
-0.006163859274238348,
-0.05040113627910614,
-0.01990700699388981,
-0.011188335716724396,
0.020814353600144386,
-0.04676611348986626,
-0.006441264878958464,
0.0378250889480114,
0.02433331124484539,
-0.03690238669514656,
-0.023959897458553314,
-0.002797427587211132,
-0.06866839528083801,
0.022713128477334976,
-0.02118261530995369,
0.006553777027875185,
-0.03647427260875702,
0.025156209245324135,
-0.007522312458604574,
-0.03617013990879059,
-0.02975943684577942,
-0.044018518179655075,
-0.1002243161201477,
0.00873890332877636,
-0.04921058937907219,
0.015318285673856735,
0.005605525337159634,
0.006157826632261276,
0.061414483934640884,
-0.0003319654206279665,
-0.015581357292830944,
-0.03264050930738449,
0.010368634015321732,
-0.007103325333446264,
-0.03600615635514259,
-0.029174167662858963,
0.03739508241415024,
0.011968201026320457,
0.07116024941205978,
0.0027637931052595377,
0.028287265449762344,
0.027456561103463173,
0.010637406259775162,
-0.011597087606787682,
-0.0011318481992930174,
-0.0043807076290249825,
-0.005360218696296215,
0.060429539531469345,
-0.0009707998833619058,
-0.0059173437766730785,
0.0026110413018614054,
-0.005158036947250366,
0.025794638320803642,
0.009289456531405449,
-0.031154690310359,
0.06758476048707962,
0.026318931952118874,
0.018396427854895592,
0.009453526698052883,
-0.0023151549976319075,
-0.011616434901952744,
0.004446737002581358,
-0.000294342142296955,
0.010670226998627186,
0.045997217297554016,
0.013874229975044727,
0.01655149832367897,
0.07561741769313812,
-0.0078122676350176334,
-0.0017549964832141995,
-0.03523903712630272,
0.006834802683442831,
-0.01825859770178795,
0.03798314183950424,
-0.01011897437274456,
-0.05048491060733795,
0.025772150605916977,
-0.00399069394916296,
0.04288650304079056,
-0.028719864785671234,
-0.045129045844078064,
-0.004096690099686384,
-0.03826189413666725,
0.006163734942674637,
-0.016822976991534233,
0.02590841054916382,
0.02688273973762989,
0.026328183710575104,
0.008646449074149132,
-0.0053980108350515366,
-0.03194744139909744,
-0.04857116937637329,
-0.06721967458724976,
0.014697886072099209,
-0.03230111300945282,
0.03072105161845684,
0.008732125163078308,
-0.04645437002182007,
0.0003797470999415964,
-0.028598980978131294,
-0.019836870953440666,
-0.02711671032011509,
-0.025109488517045975,
-0.058960653841495514,
-0.02701484225690365,
-0.02520415559411049,
-0.02773773856461048,
-0.001538133597932756,
0.02990265004336834,
0.03551376983523369,
-0.019006960093975067,
0.010704818181693554,
0.010305003263056278,
-0.03244137763977051,
0.013799221254885197,
0.01376949530094862,
0.013166254386305809,
-0.006366923917084932,
0.038960788398981094,
0.009087922982871532,
0.016983386129140854,
-0.03869354724884033,
0.015517352148890495,
0.013972013257443905,
0.03719289228320122,
-0.01384794432669878,
-0.029648011550307274,
0.00406386936083436,
-0.0062870243564248085,
0.01544969342648983,
-0.008555742911994457,
0.0408204048871994,
0.007886468432843685,
0.005555612966418266,
0.040986768901348114,
-0.0008375339093618095,
-0.01040710136294365,
0.022908126935362816,
0.047188472002744675,
-0.012008428573608398,
-0.007551753427833319,
-0.015605228953063488,
-0.04487720876932144,
-0.01748647540807724,
-0.001591836684383452,
-0.003837030380964279,
0.012328814715147018,
0.012194330804049969,
-0.009098750539124012,
0.018858451396226883,
0.01927281729876995,
-0.03173546493053436,
-0.006661356892436743,
-0.036822739988565445,
-0.0017117182724177837,
-0.01693037338554859,
0.008238532580435276,
0.03541160002350807,
0.05752125754952431,
-0.0019287592731416225,
0.012313648127019405,
-0.01330425962805748,
-0.05853595957159996,
-0.028810082003474236,
0.022015158087015152,
0.037546005100011826,
0.007432521786540747,
0.007003272417932749,
-0.038864683359861374,
-0.015144402161240578,
0.04385417327284813,
-0.01920991949737072,
0.0487692691385746,
0.0022498718462884426,
0.03263363242149353,
-0.045607924461364746,
-0.007613327354192734,
0.046628713607788086,
-0.00640025082975626,
-0.003644069191068411,
0.005864364560693502,
-0.003476276295259595,
-0.015397321432828903,
-0.013668003492057323,
0.02044611983001232,
-0.02478235401213169,
0.006736488547176123,
0.0004932261654175818,
0.01180305052548647,
-0.0261954665184021,
-0.026440640911459923,
-0.028699249029159546,
-0.08590719848871231,
0.05131448060274124,
-0.0019881497137248516,
-0.02924485318362713,
0.05398043990135193,
-0.023517852649092674,
-0.07591882348060608,
-0.004361227620393038,
-0.06065027788281441,
0.001219824654981494,
0.030753038823604584,
-0.02703126147389412,
0.04206438362598419,
-0.015816206112504005,
0.01918191649019718,
0.026657244190573692,
0.009279090911149979,
-0.022126497700810432,
0.03373095393180847,
-0.013207538053393364,
0.04687869921326637,
-0.0399634949862957,
0.0013329768553376198,
-0.02551465667784214,
0.006122310180217028,
-0.02455849014222622,
0.019206000491976738,
0.00970297772437334,
0.006184449885040522,
0.010695094242691994,
-0.030490877106785774,
-0.03336147591471672,
-0.015596755780279636,
0.0026786059606820345,
-0.008897773921489716,
-0.06374812871217728,
-0.005407986231148243,
0.0011234489502385259,
-0.034580033272504807,
-0.004269765689969063,
0.009985835291445255,
0.027763383463025093,
0.024663489311933517,
0.00013715465320274234,
0.024319490417838097,
-0.0279901884496212,
-0.009602791629731655,
0.010482924059033394,
-0.035173915326595306,
0.00663810595870018,
0.002664811909198761,
-0.003295016009360552,
-0.013856358826160431,
-0.04711669683456421,
-0.034128181636333466,
-0.005448294337838888,
-0.026843464002013206,
-0.005873729009181261,
-0.03321859613060951,
0.004076515790075064,
0.0019460174953565001,
0.017160573974251747,
-0.06953265517950058,
-0.028637168928980827,
0.019742334261536598,
0.022974496707320213,
-0.0037024293560534716,
-0.014163595624268055,
-0.0017512128688395023,
-0.013694397173821926,
-0.022989550605416298,
-0.039484910666942596,
0.04291922226548195,
-0.006360126659274101,
-0.004596433602273464,
0.010154644958674908,
0.02655128575861454,
0.05115864798426628,
-0.02278255857527256,
-0.017392702400684357,
-0.037467461079359055,
-0.003041777992621064,
0.016879580914974213,
0.021396350115537643,
0.002417792333289981,
-0.018786804750561714,
-0.05565304681658745,
-0.003877730807289481,
0.02347288653254509,
0.0042793164029717445,
-0.015314864926040173,
0.0012482331367209554,
0.026123911142349243,
-0.011535044759511948,
-0.02347777970135212,
-0.028423193842172623,
-0.002313850214704871,
0.029134200885891914,
0.032675717025995255,
0.0004990624147467315,
0.021466197445988655,
0.019710280001163483,
-0.026812834665179253,
0.021974314004182816,
-0.013832074590027332,
-0.05799803510308266,
-0.0039781248196959496,
0.03031902387738228,
0.029172630980610847,
-0.014936106279492378,
-0.004421534016728401,
-0.022095853462815285,
0.002910588402301073,
-0.028137173503637314,
0.013960820622742176,
0.004721267614513636,
-0.0099048325791955,
-0.029572075232863426,
-0.04992055892944336,
-0.055475104600191116,
0.022486263886094093,
0.017991581931710243,
0.0022336470428854227,
0.024641722440719604,
0.03459940478205681,
-0.0073839155957102776,
0.023498250171542168,
0.00241422513499856,
0.041208624839782715,
0.0067532844841480255,
0.023454545065760612,
0.03939466550946236,
-0.03207038342952728,
0.009509610012173653,
0.052596770226955414,
0.03686828538775444,
-0.013459536246955395,
0.030192017555236816,
0.02958940714597702,
0.01552449632436037,
0.026212407276034355,
-0.00019935693126171827,
-0.03539410978555679,
0.034105751663446426,
-0.06895633786916733,
0.01724364049732685,
0.004800976719707251,
-0.01222678367048502,
-0.000557052728254348,
-0.01254360657185316,
-0.004080657381564379,
-0.023606110364198685,
-0.013184813782572746,
-0.0414794497191906,
-0.020820461213588715,
-0.0002596098929643631,
0.03896554186940193,
0.005439659580588341,
-0.000233423023018986,
0.003720966400578618,
0.007707227487117052,
0.01820056326687336,
-0.015556242316961288,
-0.05287342518568039,
-0.014039866626262665,
-0.03932996839284897,
0.0014649778604507446,
0.059512726962566376,
-0.008299050852656364,
-0.01150753814727068,
0.029980523511767387,
-0.025319520384073257,
0.020580628886818886,
0.05107254162430763,
0.018342237919569016,
-0.030980609357357025,
0.030596328899264336,
-0.01714671403169632,
0.03177038952708244,
-0.005453886464238167,
0.02956102415919304,
0.11940770596265793,
0.07292185723781586,
0.00948232039809227,
-0.07023490965366364,
0.02156691439449787,
-0.011037910357117653,
0.029703577980399132,
-0.009761796332895756,
0.005926832556724548,
-0.029775388538837433,
0.006536415312439203,
-0.018513740971684456,
0.0632258877158165,
0.04971040040254593,
-0.002108864253386855,
0.02244121953845024,
-0.016732752323150635,
-0.04519178718328476,
-0.0017338823527097702,
0.004110376816242933,
0.015873797237873077,
-0.04125466197729111,
-0.05792522802948952,
0.01967516914010048,
0.0012526019709184766,
0.017303865402936935,
-0.0010112691670656204,
0.011633255518972874,
0.016770631074905396,
0.06985648721456528,
-0.00877629965543747,
-0.0025118745397776365,
0.021604008972644806,
-0.012515069916844368,
-0.004231074824929237,
0.00678925309330225,
0.056987177580595016,
0.010242652148008347,
0.02925080992281437,
0.05044812709093094,
0.04571419954299927,
-0.01298624649643898,
-0.010984123684465885,
0.047307077795267105,
-0.06284406036138535,
-0.01480149757117033,
-0.0129667604342103,
0.016539860516786575,
-0.004102160222828388,
-0.028190461918711662,
-0.03371596336364746,
-0.051367051899433136,
-0.006317639723420143,
-0.02896796353161335,
0.0008034922648221254,
0.04078216105699539,
0.014779185876250267,
-0.02250717580318451,
-0.08217566460371017,
0.027601033449172974,
0.007795707322657108,
-0.01857306808233261,
0.024309180676937103,
-0.0052969129756093025,
-0.016147706657648087,
-0.016376735642552376,
-0.00746134901419282,
0.024525988847017288,
0.044764112681150436,
0.008307206444442272,
-0.05324951559305191,
0.018586257472634315,
-0.05517032742500305,
-0.06509529054164886,
0.013097941875457764,
0.006437583826482296,
0.06169323995709419,
-0.008934407494962215,
0.0018875438254326582,
-0.005656518507748842,
-0.04335338994860649,
0.02458636835217476,
-0.03821525722742081,
-0.006858140230178833,
-0.023285945877432823,
-0.029250718653202057,
0.03566720336675644,
0.0169710461050272,
-0.0059636859223246574,
0.010491952300071716,
0.018703309819102287,
0.0021434053778648376,
0.015657411888241768,
-0.03859150782227516,
0.015274662524461746,
0.009293402545154095,
-0.07809005677700043,
0.011164764873683453,
-0.05300039052963257,
0.0256664976477623,
0.041250746697187424,
0.0159293245524168,
0.023633265867829323,
0.025405142456293106,
-0.03278600424528122,
-0.047598011791706085,
0.01576681062579155,
-0.03830995038151741,
-0.004171594511717558,
0.02330106869339943,
0.0359959751367569,
-0.038328155875205994,
-0.03720493242144585,
-0.039831921458244324,
0.0020842039957642555,
0.008135398849844933,
0.02865018881857395,
-0.04240577295422554,
-0.0026470276061445475,
-0.013624461367726326,
0.021620135754346848,
0.019468409940600395,
-0.04126774147152901,
-0.06591630727052689,
-0.02267066203057766,
-0.031544279307127,
0.006340413819998503,
-0.018772201612591743,
0.006843662355095148,
0.019435912370681763,
-0.006775905843824148,
0.03752344101667404,
0.00029664175235666335,
-0.04537639021873474,
0.0017390567809343338,
0.02601841650903225,
0.0012816941598430276,
0.023584946990013123,
-0.023196814581751823,
-0.05695447325706482,
0.03675176203250885,
-0.001074551255442202,
-0.029421404004096985,
0.029308360069990158,
-0.021780142560601234,
0.047152623534202576,
0.04311509057879448,
-0.0057349917478859425,
-0.01841644011437893,
0.0417037159204483,
-0.033113498240709305,
0.013215899467468262,
0.018374668434262276,
-0.01271217130124569,
-0.005977105349302292,
-0.005742330569773912,
-0.01016219798475504,
0.025658074766397476,
-0.036879491060972214,
0.07129514217376709,
0.016283899545669556,
0.05580557882785797,
-0.006378105375915766,
0.008466070517897606,
-0.0334625169634819,
0.04057995229959488,
0.04735254868865013,
0.00646975776180625,
0.012883610092103481,
0.06731858104467392,
-0.05608236789703369,
0.04685850068926811,
0.029857296496629715,
0.01509595476090908,
-0.11781324446201324,
0.01269101444631815,
-0.014604464173316956,
0.021739741787314415,
0.029001416638493538,
-0.020463621243834496,
0.030361942946910858,
0.027074089273810387,
-0.10019132494926453,
-0.009838512167334557,
-0.03155948966741562,
-0.007796891964972019,
-0.021338678896427155,
-0.012064825743436813,
-0.06383184343576431,
0.03197953850030899,
0.0054480344988405704,
0.04890134185552597,
0.030987843871116638,
0.04677283391356468,
-0.02117844671010971,
-0.038434576243162155,
-0.0001490115828346461,
0.026886312291026115,
0.014563108794391155,
-0.0024956283159554005,
0.06128247454762459,
-0.020379288122057915,
-0.0693485215306282,
0.04949048534035683,
-0.023346703499555588,
0.02355639450252056,
-0.03884465619921684,
-0.004024572670459747,
0.04840108007192612,
0.015655381605029106,
0.06468427181243896,
-0.022793008014559746,
-0.0004922312218695879,
0.0015132729895412922,
-0.002157892333343625,
0.023420969024300575,
0.014527764171361923,
-0.03949093818664551,
0.01503040362149477,
-0.036864135414361954,
-0.02472134493291378,
0.019963841885328293,
0.015568912029266357,
0.029988666996359825,
-0.023305106908082962,
0.033397529274225235,
0.0006630956777371466,
-0.012819232419133186,
0.016094110906124115,
-0.01739000901579857,
-0.040404971688985825,
0.05075317248702049,
0.019951805472373962,
-0.006072744727134705,
-0.012994608841836452,
-0.04878485947847366,
0.009681610390543938,
0.02095462754368782,
0.010295320302248001,
-0.001534877228550613,
-0.04085966944694519,
-0.012731942348182201,
0.03710081800818443,
0.006020995322614908,
0.03526698797941208,
-0.04061947762966156,
-0.07295075058937073,
0.013591839000582695,
0.005291111301630735,
0.06953537464141846,
-0.02209804393351078,
-0.07310800999403,
-0.034539006650447845,
-0.08352820575237274,
0.09088538587093353,
0.03269506245851517,
0.03979644551873207,
-0.06305412948131561,
0.0001703224261291325,
0.009739147499203682,
-0.030082128942012787,
0.049828723073005676,
0.0016992565942928195,
0.003951402846723795,
-0.013802586123347282,
0.0271295253187418,
0.024696510285139084,
-0.04613973945379257,
0.004748689476400614,
-0.03438221290707588,
-0.0003638962807599455,
-0.005409980192780495,
-0.027091260999441147,
-0.02349874936044216,
0.03696984425187111,
0.05173390731215477,
-0.025894178077578545,
-0.015258153900504112,
0.01890399120748043,
-0.02533397451043129,
0.0481572300195694,
0.011103112250566483,
-0.004956352524459362,
0.043441563844680786,
-0.0011636775452643633,
0.03053068183362484,
0.008885031566023827,
0.012338632717728615,
-0.03136973828077316,
0.010022302158176899,
-0.0006967428489588201,
-0.02074749581515789,
0.018272854387760162,
0.025654979050159454,
0.023154037073254585,
0.009311533533036709,
0.012671840377151966,
0.021926824003458023,
-0.010415961034595966,
0.0019035476725548506,
0.04168535768985748,
-0.014010493643581867,
0.0076209548860788345,
0.012197894975543022,
0.03856104984879494,
0.025189226493239403,
0.025582928210496902,
-0.01925566792488098,
0.038535378873348236,
0.04349831864237785,
0.009399211034178734,
-0.010687592439353466,
0.06026887893676758,
-0.004772381857037544,
0.05662545934319496,
0.0005677199806086719,
0.05698883906006813,
-0.018150441348552704,
-0.009260459803044796,
0.032931189984083176,
-0.019017675891518593,
0.0016387804644182324,
-0.014575988054275513,
-0.0024086027406156063,
0.07056394964456558,
-0.018466325476765633,
0.002336512552574277,
-0.014560683630406857,
-0.014013271778821945,
-0.00009196200699079782,
-0.003621271112933755,
0.0511053204536438,
0.026987798511981964,
-0.04971805214881897,
-0.0077507710084319115,
-0.01648372784256935,
0.004368649795651436,
-0.010807658545672894,
-0.07081598043441772,
0.01746029406785965,
-0.0026592889335006475,
-0.0055333287455141544,
0.03626096248626709,
-0.012182912789285183,
-0.017964202910661697,
-0.01775328442454338,
0.048282064497470856,
0.009107034653425217,
0.025809066370129585,
-0.04588820040225983,
-0.04024083912372589,
-0.03892316669225693,
0.05145786330103874,
-0.051867563277482986,
0.01388433575630188,
-0.023294497281312943,
0.04611803591251373,
-0.02534330077469349,
0.003184521570801735
] |
<p>What is the centripetal acceleration and angular velocity of a child located 8.2 m
the center of a carousel? The speed (size of the tangential velocity) of the child is
2.1 m / s</p>
<p>A train moves in a straight path north until it turns to west.
If the road segment used to change direction is shaped like a quarter circle of radius 30 m and the train takes 30 seconds to traverse that part of the road,
What is it the speed (size of the velocity vector) and the centripetal acceleration acts on the train as it traverses the curve.</p>
<p>I am reviewing some concepts like centripet force, <code>ar = ( v^2 ) / r</code>
also this:</p>
<blockquote>
<p>The direction of the centripital
acceleration is always inwards along
the radius vector of the circular
motion. The magnitude of the
centripetal acceleration is related to
the tangential speed and angular
velocity as follows:</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/XGojw.png" alt="enter image description here"></p>
<p>Can you please guide me to solve the 2 problems above?</p>
<p>for the fisrt one is it only :</p>
<p><code>(2.1 m / s)^2 / 8.2 m</code> ?</p> | 2,029 | [
-0.031131351366639137,
-0.018176810815930367,
-0.04220245033502579,
0.02868104726076126,
0.04487951099872589,
-0.03591252863407135,
-0.033296648412942886,
-0.05393079295754433,
0.028267987072467804,
0.02082761563360691,
0.0361897312104702,
0.01920677348971367,
0.0489027164876461,
0.059133380651474,
0.04224651679396629,
0.019568748772144318,
-0.009929312393069267,
-0.008698595687747002,
0.02158241532742977,
-0.015050036832690239,
-0.021235940977931023,
-0.0270973090082407,
0.03383294865489006,
-0.007721742615103722,
0.0027210938278585672,
0.02537858858704567,
0.04694312438368797,
-0.02374548278748989,
0.012793779373168945,
0.04321388900279999,
-0.0026822739746421576,
0.016560787335038185,
0.018613390624523163,
0.00026895583141595125,
0.02450726181268692,
0.019487207755446434,
-0.07334376126527786,
-0.020208781585097313,
-0.001909974031150341,
0.024771159514784813,
0.0017108984757214785,
-0.014274870045483112,
0.014028429985046387,
0.07157891988754272,
-0.007247647736221552,
0.04545038565993309,
-0.016073398292064667,
0.0062620146200060844,
0.06818526983261108,
-0.05916392430663109,
0.08287262916564941,
0.00025328592164441943,
-0.012666323222219944,
-0.019006557762622833,
0.0017212185775861144,
0.01427062414586544,
0.027706777676939964,
0.045176103711128235,
-0.00992360059171915,
-0.027331175282597542,
-0.006546543911099434,
-0.012831318192183971,
-0.05436154454946518,
-0.04199666902422905,
-0.008734301663935184,
0.030972547829151154,
-0.007816260680556297,
-0.01644870638847351,
0.03083123452961445,
0.01016956102102995,
0.01980067789554596,
0.02121746726334095,
0.04723086953163147,
-0.01569465920329094,
0.010746614076197147,
-0.03262803331017494,
0.03230491280555725,
0.012926201336085796,
0.029622448608279228,
0.03816104680299759,
-0.015948457643389702,
0.01248080749064684,
0.022485489025712013,
0.030042830854654312,
0.04893392324447632,
-0.017825497314333916,
0.05367886647582054,
0.026061028242111206,
0.016549212858080864,
0.007036360912024975,
0.013627894222736359,
-0.012640450149774551,
0.06523051112890244,
0.011078027077019215,
0.004486695863306522,
0.02706015110015869,
0.0171843059360981,
0.02268015220761299,
0.029378216713666916,
0.008671708405017853,
-0.007591903209686279,
-0.013927806168794632,
0.029557809233665466,
0.08753158152103424,
-0.026273241266608238,
0.021110448986291885,
-0.00946645624935627,
-0.007971453480422497,
-0.010106922127306461,
-0.012602952308952808,
-0.06362766772508621,
0.009944100864231586,
-0.020115898922085762,
0.03363761678338051,
-0.0027036250103265047,
-0.014818362891674042,
-0.014172731898725033,
0.03400549292564392,
0.04002442955970764,
0.01369727123528719,
0.06171700730919838,
-0.02996586449444294,
-0.008756768889725208,
-0.03362651914358139,
-0.06476595252752304,
-0.0032239085994660854,
-0.010697579942643642,
-0.008371670730412006,
-0.02936546690762043,
0.03567860275506973,
0.0023627064656466246,
-0.0003446397604420781,
-0.02675125002861023,
-0.009338614530861378,
0.021371977403759956,
-0.014357470907270908,
-0.06610586494207382,
-0.09354512393474579,
0.025052305310964584,
0.041867200285196304,
0.0005519932601600885,
-0.07414931803941727,
0.01830984465777874,
0.0086349593475461,
0.07735386490821838,
0.017138710245490074,
0.015328273177146912,
0.0474250465631485,
0.03498198464512825,
0.03866111487150192,
-0.008672763593494892,
0.017001478001475334,
0.014233356341719627,
-0.026232367381453514,
-0.0038383426144719124,
-0.07720103114843369,
0.034562453627586365,
0.04130158573389053,
-0.015323431231081486,
-0.026881162077188492,
0.043938640505075455,
-0.01391235925257206,
0.02102966234087944,
0.002953245770186186,
-0.01692141406238079,
0.008664146065711975,
0.059926267713308334,
0.014929204247891903,
-0.009907647967338562,
0.06525761634111404,
0.027463790029287338,
0.03740357607603073,
0.012893901206552982,
-0.012937640771269798,
0.08760934323072433,
0.010694467462599277,
-0.027738552540540695,
0.0008163399179466069,
-0.028886137530207634,
0.001117259031161666,
-0.02438606321811676,
-0.051133882254362106,
-0.056472502648830414,
0.02477824129164219,
0.010105995461344719,
0.06735186278820038,
0.03126687556505203,
0.023061197251081467,
0.026114454492926598,
-0.01061780471354723,
-0.007472797762602568,
-0.06022016331553459,
0.053409118205308914,
-0.052986565977334976,
-0.02694772370159626,
-0.003135482082143426,
0.005267512984573841,
0.002206732053309679,
-0.030009593814611435,
0.0062653012573719025,
-0.015245949849486351,
0.05714996159076691,
-0.019587256014347076,
-0.006832499522715807,
-0.015465178526937962,
0.03376851975917816,
0.027694232761859894,
-0.03625841066241264,
-0.027446847409009933,
-0.01612134650349617,
0.030854279175400734,
-0.013824759982526302,
0.006412812974303961,
0.0004859910113736987,
0.002119306940585375,
-0.010819709859788418,
-0.0009679950308054686,
0.04100353270769119,
-0.005338294897228479,
0.053895123302936554,
-0.0456598699092865,
0.07849704474210739,
0.03433921933174133,
0.02238817885518074,
0.03868624195456505,
0.026342617347836494,
0.010619785636663437,
0.035072166472673416,
0.0112233217805624,
-0.013490013778209686,
-0.03868802636861801,
0.0038669100031256676,
0.023341404274106026,
0.012829023413360119,
-0.039835210889577866,
0.018848741427063942,
0.0735049843788147,
0.018982645124197006,
0.01394321396946907,
0.005073578096926212,
-0.024272706359624863,
-0.04517245292663574,
0.01676934026181698,
0.019835272803902626,
0.005048757418990135,
-0.004907403606921434,
0.004492671228945255,
0.03497571125626564,
0.036936189979314804,
0.019413115456700325,
-0.03673670068383217,
0.03796926513314247,
0.01423360500484705,
0.002854428021237254,
0.019092343747615814,
-0.024627558887004852,
0.05771764740347862,
-0.003504594322293997,
-0.011653030291199684,
0.05019150301814079,
-0.006125205662101507,
-0.005391203798353672,
-0.01352603454142809,
0.027064021676778793,
0.016572585329413414,
-0.02730436809360981,
-0.030343661084771156,
-0.01878601498901844,
0.012058407999575138,
-0.016493190079927444,
-0.010792149230837822,
0.011410444974899292,
-0.04025940224528313,
-0.042312804609537125,
0.019494887441396713,
0.03890252858400345,
-0.009091299958527088,
0.01418838370591402,
-0.02315453626215458,
0.012428472749888897,
-0.00033282817457802594,
-0.05836104974150658,
-0.00958296563476324,
-0.017375407740473747,
-0.06712446361780167,
0.05917312204837799,
-0.03959913179278374,
-0.008817176334559917,
0.04489302635192871,
0.00829097256064415,
-0.02562657929956913,
0.04051581397652626,
0.023019511252641678,
-0.0607408843934536,
-0.020635349676012993,
-0.05544497072696686,
0.024909015744924545,
-0.060028959065675735,
-0.004614157602190971,
0.03851749747991562,
0.0008660416933707893,
0.00811676774173975,
0.037629928439855576,
-0.032878369092941284,
-0.005651706829667091,
-0.03562917187809944,
0.007264116778969765,
0.016927570104599,
0.00010299659334123135,
-0.013616202399134636,
-0.003933963365852833,
0.019251005724072456,
0.025383619591593742,
-0.04697905108332634,
-0.0435781255364418,
-0.008370986208319664,
0.003359178313985467,
0.06201402470469475,
0.004379118327051401,
0.0018111503450199962,
0.05991404876112938,
0.018680592998862267,
-0.036797232925891876,
-0.03877576068043709,
0.017284907400608063,
-0.008967388421297073,
-0.016187654808163643,
-0.028148610144853592,
0.04469135403633118,
-0.030411789193749428,
-0.0450981967151165,
-0.00365145830437541,
0.018926601856946945,
0.028367381542921066,
-0.004311277065426111,
-0.0004685822350438684,
-0.020390452817082405,
0.010948306880891323,
-0.04855262115597725,
0.047678712755441666,
0.03862598165869713,
-0.03372540324926376,
0.007508359383791685,
0.005605173297226429,
0.02977873757481575,
0.001983178313821554,
-0.04714818671345711,
0.025142785161733627,
0.0069403573870658875,
-0.009607493877410889,
-0.005405766889452934,
0.011494713835418224,
0.01121163833886385,
-0.012263116426765919,
-0.02510249614715576,
0.021793721243739128,
0.031595777720212936,
-0.007773584686219692,
0.007768099661916494,
0.054070018231868744,
0.034769684076309204,
-0.031155768781900406,
-0.027960147708654404,
-0.019033854827284813,
0.015979742631316185,
0.03906711935997009,
-0.05277249217033386,
-0.012868333607912064,
0.04972183331847191,
0.03216836228966713,
0.03014438971877098,
0.009226527996361256,
-0.013933185487985611,
0.004229856189340353,
-0.04708370938897133,
0.002936338307335973,
-0.039810895919799805,
0.05110851302742958,
0.022472912445664406,
0.01903277263045311,
-0.01810515485703945,
-0.014666445553302765,
0.028675217181444168,
0.031638167798519135,
-0.05937241017818451,
0.035725463181734085,
-0.04105142503976822,
-0.037372373044490814,
0.01910688541829586,
-0.019198909401893616,
0.0008696454460732639,
-0.035415783524513245,
0.011730596423149109,
0.010753845795989037,
-0.0026909196749329567,
-0.014835840091109276,
0.0007613228517584503,
-0.02339092455804348,
-0.01587182842195034,
-0.014351378194987774,
0.021019859239459038,
0.012855174951255322,
-0.012314646504819393,
0.015292134135961533,
0.06134595721960068,
-0.03769724443554878,
-0.002150080632418394,
-0.009027557447552681,
-0.002142593963071704,
0.010515508241951466,
0.028610672801733017,
-0.009424538351595402,
0.004750736989080906,
-0.0457305870950222,
-0.004475836642086506,
0.007978742942214012,
0.027146829292178154,
0.012605056166648865,
-0.016471408307552338,
-0.06139814108610153,
-0.07616500556468964,
0.007394075393676758,
-0.023466670885682106,
0.08023180812597275,
0.007635741960257292,
-0.001464677625335753,
0.024167504161596298,
-0.00034644381958059967,
0.0029737097211182117,
-0.004191688261926174,
0.04480651393532753,
0.011247366666793823,
0.012602308765053749,
-0.04824066907167435,
-0.028039665892720222,
-0.020002664998173714,
-0.021841848269104958,
0.0048196264542639256,
-0.018935196101665497,
-0.03993839770555496,
0.0011811824515461922,
0.02539668418467045,
0.017312003299593925,
-0.001420769840478897,
0.048594243824481964,
-0.017047559842467308,
0.017292214557528496,
-0.006979364436119795,
-0.00997417513281107,
-0.01045062206685543,
0.028214719146490097,
0.03541109710931778,
-0.020999658852815628,
-0.029470162466168404,
-0.07197187095880508,
0.007109016180038452,
0.034469131380319595,
0.04110030457377434,
-0.03152281790971756,
-0.017752205953001976,
-0.028039004653692245,
0.0031603965908288956,
0.040223002433776855,
-0.05263623967766762,
0.08209653198719025,
-0.02485542558133602,
0.02591647021472454,
-0.03977915272116661,
-0.021484486758708954,
-0.04422048106789589,
-0.005737585015594959,
-0.05137646198272705,
-0.006560280919075012,
-0.055719323456287384,
-0.001980527536943555,
-0.00632315780967474,
-0.0007935973117128015,
0.032422833144664764,
0.03867311403155327,
-0.0098804896697402,
-0.03638084977865219,
0.0063078757375478745,
0.008948417380452156,
-0.03208170831203461,
-0.06623142957687378,
-0.029880693182349205,
-0.015550016425549984,
0.0021099266596138477,
0.030897947028279305,
-0.028576020151376724,
-0.04180082678794861,
0.014126001857221127,
-0.016662199050188065,
-0.030766626819968224,
0.020719975233078003,
-0.06101078540086746,
0.03667500615119934,
0.04184727743268013,
0.031148485839366913,
-0.0021229798439890146,
0.020300619304180145,
-0.032273899763822556,
-0.022583622485399246,
-0.033628374338150024,
-0.01176245603710413,
-0.0033061006106436253,
0.0016860609175637364,
-0.039651524275541306,
0.037360839545726776,
-0.006739654578268528,
0.05066918954253197,
-0.017740769311785698,
0.014921820722520351,
-0.08035282790660858,
-0.03809075430035591,
-0.01263427548110485,
0.05385615676641464,
-0.021135933697223663,
0.0070688058622181416,
0.008583171293139458,
-0.017639586701989174,
-0.025903547182679176,
-0.029923267662525177,
0.0322946198284626,
-0.02822115644812584,
-0.018223674967885017,
0.033075034618377686,
-0.004155912436544895,
0.029513297602534294,
-0.04550611600279808,
-0.010359224863350391,
-0.013170677237212658,
-0.08290673047304153,
0.0355808362364769,
0.0025983890518546104,
0.018902745097875595,
0.03605164587497711,
-0.03178735822439194,
-0.04964827746152878,
0.03260692581534386,
-0.031355760991573334,
0.044331058859825134,
-0.03249774128198624,
0.025062711909413338,
0.007607060484588146,
0.003449610434472561,
0.0024940811563283205,
-0.05117294564843178,
0.007425537798553705,
0.0073342411778867245,
-0.02822224050760269,
-0.015519876964390278,
-0.010309189558029175,
-0.022183286026120186,
-0.029857391491532326,
-0.0031632110476493835,
0.07659415900707245,
-0.041476137936115265,
0.0015388248721137643,
0.014610975049436092,
-0.009604191407561302,
0.07698876410722733,
0.029804790392518044,
0.032202284783124924,
-0.012643905356526375,
0.004014966078102589,
-0.02498983033001423,
0.02907591313123703,
0.1036703810095787,
-0.03388042747974396,
-0.054420217871665955,
-0.018068578094244003,
0.03143130615353584,
0.04113501310348511,
0.008748071268200874,
-0.009890739805996418,
-0.009305775165557861,
-0.0007159478263929486,
-0.03633610159158707,
-0.010989239439368248,
0.039503153413534164,
0.015555779449641705,
0.010076318867504597,
-0.02277316153049469,
0.008673560805618763,
-0.05789746716618538,
-0.013980605639517307,
0.005092829931527376,
-0.003392167389392853,
-0.0017077561933547258,
-0.006914264988154173,
0.06346385180950165,
-0.051018256694078445,
0.022379161790013313,
-0.011376575566828251,
0.00978556927293539,
0.04807205870747566,
-0.012608738616108894,
-0.03791079297661781,
0.002798861125484109,
-0.011256751604378223,
-0.012597362510859966,
-0.011315402574837208,
-0.013948737643659115,
0.011333527974784374,
0.03885386139154434,
-0.010904718190431595,
0.04890662059187889,
0.013507487252354622,
0.002804378978908062,
0.028123481199145317,
0.005358687601983547,
-0.0034357928670942783,
-0.01962762512266636,
0.03061860054731369,
0.060711003839969635,
-0.0004568253643810749,
-0.023731667548418045,
0.024854667484760284,
0.021354546770453453,
0.0046702963300049305,
-0.05558674782514572,
0.014740345999598503,
-0.012472467496991158,
-0.011896440759301186,
-0.018617259338498116,
-0.030466293916106224,
0.006693552248179913,
0.0071527487598359585,
0.055597588419914246,
0.01370223704725504,
-0.017142051830887794,
0.08859343826770782,
0.003086271695792675,
-0.0057309758849442005,
-0.04601935297250748,
0.025780601426959038,
-0.035569462925195694,
-0.0122643131762743,
0.0020685603376477957,
-0.026786211878061295,
-0.04848386347293854,
0.020830700173974037,
0.05338100716471672,
-0.028092622756958008,
0.018580017611384392,
-0.028268886730074883,
-0.06325756758451462,
0.012775381095707417,
-0.012924272567033768,
-0.0706067606806755,
0.011921022087335587,
0.015394719317555428,
-0.03499504551291466,
0.026895498856902122,
-0.03147156536579132,
0.033478278666734695,
0.03739037737250328,
0.03338966518640518,
-0.03527691587805748,
0.06465304642915726,
-0.018880397081375122,
-0.005594419781118631,
-0.026975221931934357,
-0.010577353648841381,
0.10751541703939438,
0.03432278707623482,
-0.04489128664135933,
-0.016230681911110878,
0.026608387008309364,
-0.03967636078596115,
0.007324683479964733,
-0.028089405968785286,
0.012114139273762703,
0.002598640974611044,
0.0055919489823281765,
0.039366237819194794,
0.00805735681205988,
0.005827362183481455,
-0.008211658336222172,
0.012692425400018692,
-0.0424293652176857,
-0.04976196959614754,
-0.039177149534225464,
0.03392456844449043,
-0.029062941670417786,
0.018306905403733253,
-0.03921474516391754,
0.015186126343905926,
-0.049446795135736465,
0.002571285702288151,
-0.02434026263654232,
-0.03337816148996353,
0.03165343776345253,
-0.028302308171987534,
-0.0532476082444191,
0.009620527736842632,
0.01267810259014368,
-0.03869973495602608,
-0.06442177295684814,
0.009404097683727741,
-0.00708697410300374,
-0.04633567854762077,
0.02624732069671154,
0.02980051562190056,
0.009477954357862473,
-0.015061788260936737,
0.0004661476705223322,
0.024976732209324837,
-0.06057445704936981,
0.02380462922155857,
-0.0403812937438488,
0.03312927857041359,
0.004088356625288725,
0.02201349101960659,
0.007468546740710735,
0.017599254846572876,
0.006003217305988073,
-0.051318295300006866,
0.025156507268548012,
0.0224270299077034,
-0.01969943568110466,
-0.03188064694404602,
0.018104160204529762,
-0.08739499747753143,
-0.0032905270345509052,
0.02434992603957653,
0.007245441898703575,
-0.007050571031868458,
0.01821894198656082,
0.0008806315599940717,
-0.027930716052651405,
0.0633552297949791,
-0.042036328464746475,
-0.009625285863876343,
0.02572948858141899,
-0.03863489255309105,
-0.025813039392232895,
0.024773430079221725,
0.022769100964069366,
-0.00003107045995420776,
0.011096984148025513,
-0.008377795107662678,
-0.03333616256713867,
0.01260373555123806,
-0.017117662355303764,
0.0059165358543396,
0.009346415288746357,
0.002358885481953621,
-0.009708253666758537,
0.016146285459399223,
0.024884473532438278,
0.004448416642844677,
-0.017244011163711548,
0.023626593872904778,
-0.022151006385684013,
0.024251682683825493,
-0.002042928012087941,
-0.02583143301308155,
-0.028885051608085632,
0.02691778540611267,
-0.008001016452908516,
0.010173183865845203,
-0.02246522530913353,
0.06549950689077377,
0.005485052242875099,
-0.007004870101809502,
-0.01742095872759819,
0.017185736447572708,
-0.0000364430743502453,
0.03746641054749489,
0.03336438164114952,
-0.03207246959209442,
-0.004635295830667019,
0.01772894896566868,
0.014999553561210632,
-0.05708931386470795,
-0.00928391795605421,
-0.0020440248772501945,
-0.039570897817611694,
0.0030625085346400738,
0.0033725083339959383,
0.005173771642148495,
0.031468912959098816,
-0.06981872022151947,
0.02495645545423031,
-0.05995958298444748,
0.0032814741134643555,
-0.03238798677921295,
-0.003391141537576914,
-0.013378354720771313,
-0.020713642239570618,
-0.020999079570174217,
0.04368666186928749,
-0.01659427024424076,
0.0036992619279772043,
0.000322366482578218,
0.03538599610328674,
-0.03145201504230499,
-0.05137023702263832,
-0.020417390391230583,
0.02761206403374672,
0.043525006622076035,
-0.013223839923739433,
-0.02943011373281479,
0.05119740590453148,
-0.006203913129866123,
-0.04739293083548546,
0.005092725623399019,
0.004064887296408415,
0.017711050808429718,
-0.007187048904597759,
-0.019309910014271736,
0.016532303765416145,
0.05465294420719147,
0.01072472520172596,
-0.014600777998566628,
-0.017870409414172173,
-0.04395347461104393,
0.006678272504359484,
-0.012138649821281433,
-0.0038672229275107384,
-0.026376081630587578,
-0.02597588673233986,
0.035154860466718674,
-0.0028441622853279114,
-0.03145406022667885,
-0.017674382776021957,
0.003234726609662175,
0.02886694297194481,
-0.002154076471924782,
0.03895115479826927,
0.014901961199939251,
0.05257934331893921,
-0.003175146412104368,
-0.0344662219285965,
0.0024156803265213966,
0.010248412378132343,
0.0009593230206519365,
-0.08166328072547913,
-0.008554843254387379,
0.027668068185448647,
0.03794414550065994,
0.032481979578733444,
-0.051380742341279984,
-0.02431371994316578,
0.03467119112610817,
-0.040925975888967514,
-0.013317693956196308,
-0.03524266183376312,
0.0012346473522484303,
-0.008336232975125313,
0.009369841776788235,
0.010507647879421711,
0.04118910804390907,
0.018839402124285698,
0.04097972437739372,
0.04473770037293434,
-0.026002151891589165,
-0.018636532127857208,
-0.045070286840200424,
0.021125059574842453,
0.05102138966321945,
-0.01294749602675438,
-0.025826945900917053,
0.04469824954867363,
-0.022505415603518486,
0.030867567285895348,
0.02729293331503868,
-0.03712401166558266,
0.02984669990837574,
-0.004437821451574564,
-0.013864404521882534,
0.007533522322773933,
0.041952185332775116,
-0.016196131706237793,
0.025386108085513115,
-0.023915952071547508,
0.0036853416822850704,
-0.00201708497479558,
0.06448265165090561,
-0.011927095241844654,
0.004902012180536985,
0.05542536452412605,
-0.001179550657980144,
0.015912769362330437,
0.08090461045503616,
-0.032914530485868454,
-0.004609508439898491,
0.004009407479315996,
0.005992847960442305,
0.00026213983073830605,
-0.016371900215744972,
0.03349487856030464,
-0.02316894382238388,
0.007020440883934498,
-0.0036046416498720646,
-0.032445766031742096,
-0.014040566980838776,
0.004700695164501667,
0.006618883460760117,
0.004168533254414797,
-0.025277063250541687,
0.004588140174746513,
0.0072371866554021835,
-0.03026135452091694,
0.01677818037569523,
0.022786390036344528,
-0.005565872881561518,
-0.011369524523615837,
-0.048400599509477615,
-0.03284924104809761,
0.041028328239917755,
0.02731086127460003,
-0.015375541523098946,
0.031070822849869728,
0.030018864199519157,
-0.023857545107603073,
-0.0683177188038826,
0.03548089414834976,
0.042459145188331604,
-0.04784896597266197,
-0.010317624546587467,
-0.032776035368442535,
-0.03727291524410248,
0.016801683232188225,
0.06831125169992447,
-0.02582246996462345,
-0.02201409637928009,
-0.0034257068764418364,
-0.015913886949419975,
0.01142396591603756,
-0.054666560143232346,
-0.0014536669477820396,
-0.008041893132030964,
-0.018297074362635612,
0.00442056730389595,
0.009799934923648834,
-0.007716034539043903,
-0.026131464168429375,
0.03703097626566887,
-0.004558528773486614,
0.05491264909505844,
0.0011192499659955502,
-0.03884683921933174,
0.012744802050292492,
-0.0028404374606907368,
-0.0036295889876782894,
0.04501274228096008,
0.00568270543590188,
0.020420154556632042,
0.0454290397465229,
-0.018606776371598244,
-0.01142914965748787,
0.027234535664319992,
-0.047263253480196,
-0.011598081327974796,
-0.01766524463891983,
-0.05087970197200775,
0.0734778568148613,
-0.06590534001588821,
0.00222153402864933,
0.040778595954179764,
-0.035435955971479416,
-0.011361123993992805,
0.034867990761995316,
0.061768267303705215,
0.01094886101782322,
-0.027381010353565216,
0.039546795189380646,
0.030650950968265533,
-0.06550333648920059,
-0.0073145111091434956,
0.0051078787073493,
0.00355574581772089,
0.005407181102782488,
0.015197464264929295,
0.06884395331144333,
-0.027380848303437233,
0.03960519656538963,
-0.012756988406181335,
0.039987798780202866,
0.007688432466238737,
-0.004323028493672609,
0.011601947247982025,
-0.020458342507481575,
0.01935008354485035,
0.04484117031097412,
-0.02939712256193161,
0.038606252521276474,
-0.005532673094421625,
0.003350490238517523,
0.008588671684265137,
-0.01914977841079235,
-0.04849904030561447,
0.0265608262270689,
-0.0013316789409145713,
0.015368921682238579,
0.0224629957228899,
-0.010495631955564022,
0.012823681347072124,
-0.0006640171050094068,
0.02978667989373207,
-0.017357107251882553,
0.03582387790083885,
-0.010844172909855843,
-0.01158340647816658,
-0.014235046692192554,
-0.022663051262497902,
-0.013623898848891258,
-0.0054405489936470985,
0.04688642919063568,
0.03869394585490227,
0.0004913325537927449,
-0.02377157285809517,
0.0016668967436999083,
0.019923973828554153,
0.0740608423948288,
-0.09091159701347351,
-0.012482043355703354,
0.0010969837894663215,
0.008238738402724266,
0.0345185361802578,
-0.040086809545755386
] |
<p>I was looking for a derivation of the expression for the energy density at any point in a static magnetic field. I do know that it is $\dfrac {1}{2 \mu_0}\left|\vec{B}\right|^2$ -- I was just wondering if there was a derivation that could be built up the way one derives the energy density $\dfrac {\epsilon_0}{2}\left|\vec{E}\right|^2$ at any point in an <em>electric</em> field, by considering the energy needed to build up a 'source' charge bit by infinitesimal bit.</p>
<p>Whatever proof I have come across seems to bring <em>inductance</em> into the picture -- is there a way of doing it without that? I ask because the corresponding proof for the electric field does not seem to need the definition of capacitance anywhere...</p>
<p>Thanks... </p> | 2,030 | [
-0.03214242681860924,
-0.0008750903652980924,
0.032636966556310654,
-0.020480327308177948,
0.01619289629161358,
0.016994155943393707,
-0.016797099262475967,
-0.002753226784989238,
0.0012210325803607702,
-0.016407279297709465,
0.025465434417128563,
0.055501215159893036,
0.059310898184776306,
0.02653900347650051,
-0.0005670373793691397,
-0.009303564205765724,
-0.01836015097796917,
0.009244337677955627,
-0.00723800715059042,
-0.056731902062892914,
0.017276952043175697,
0.01448081899434328,
0.03022146411240101,
0.0037627515848726034,
-0.01952691562473774,
0.02611321210861206,
0.009844338521361351,
0.006014540791511536,
-0.02758694253861904,
0.07627979665994644,
0.003212009323760867,
-0.0535227507352829,
0.012592630460858345,
0.002740019466727972,
0.03971032798290253,
0.004835937172174454,
-0.02284226380288601,
-0.042249422520399094,
0.002395879477262497,
0.029323715716600418,
-0.016484346240758896,
0.00022672298655379564,
-0.008048616349697113,
0.02304241992533207,
-0.014467906206846237,
-0.022057661786675453,
0.01999407261610031,
-0.022301018238067627,
0.027452757582068443,
-0.07181252539157867,
0.08175182342529297,
-0.022537607699632645,
0.06714607775211334,
0.006775781512260437,
-0.009164080023765564,
-0.002361651975661516,
0.060081254690885544,
0.05080442875623703,
-0.004626787733286619,
-0.02869274467229843,
-0.005819474346935749,
-0.021122470498085022,
-0.009892371483147144,
-0.04030635207891464,
0.014358318410813808,
0.049824994057416916,
-0.010659253224730492,
-0.016607413068413734,
0.04646822065114975,
-0.02485090121626854,
-0.003001011675223708,
0.013486374169588089,
-0.0020474432967603207,
-0.03784618526697159,
0.0013115473557263613,
0.0009124168427661061,
0.023479465395212173,
-0.013664955273270607,
0.03978591039776802,
0.05221448466181755,
-0.046463433653116226,
0.016271278262138367,
0.05559638887643814,
0.07387833297252655,
0.043021026998758316,
-0.0037333169020712376,
0.03489265590906143,
-0.0068992855958640575,
0.02497529238462448,
0.022604241967201233,
-0.010714075528085232,
0.0012583540519699454,
0.006329208612442017,
-0.04682103917002678,
-0.05233975872397423,
0.029296938329935074,
-0.031475167721509933,
0.04891113191843033,
0.0007323944009840488,
-0.026241416111588478,
0.032222066074609756,
-0.0033680549822747707,
0.028362948447465897,
0.08405245840549469,
0.010358311235904694,
-0.04327435791492462,
-0.027392160147428513,
0.03607628121972084,
-0.0035051144659519196,
-0.01220455951988697,
-0.040606539696455,
0.01867741532623768,
0.03476671501994133,
0.01784406416118145,
0.017558332532644272,
-0.06484006345272064,
0.011916241608560085,
0.0067213913425803185,
0.01365602482110262,
0.028512727469205856,
0.009926234371960163,
-0.014338701032102108,
0.024144280701875687,
-0.022361280396580696,
-0.05392385274171829,
0.03231360763311386,
0.030758842825889587,
-0.009879491291940212,
-0.04878930374979973,
0.02166098542511463,
-0.01886717788875103,
-0.0011820887448266149,
0.0016714859521016479,
0.01258914079517126,
0.019686132669448853,
-0.020469794049859047,
-0.07068344205617905,
-0.036365851759910583,
0.03647559881210327,
-0.04168073460459709,
0.009578472003340721,
-0.06951465457677841,
0.004062022548168898,
0.04616566374897957,
0.08001963794231415,
0.0027930981013923883,
0.013675093650817871,
-0.03918430581688881,
0.03133324533700943,
0.01721172407269478,
-0.033576518297195435,
-0.06002306193113327,
-0.016779959201812744,
-0.02108345739543438,
0.025379575788974762,
-0.027702875435352325,
0.05443955957889557,
0.019834468141198158,
-0.012644263915717602,
-0.022379999980330467,
0.09501542150974274,
-0.010215933434665203,
-0.036892279982566833,
-0.005050289910286665,
-0.021520094946026802,
-0.019433654844760895,
0.09725441783666611,
0.020087720826268196,
0.02430543303489685,
0.03155618906021118,
0.0074085365049541,
0.005236207041889429,
0.014881454408168793,
0.01128295436501503,
0.055825524032115936,
-0.0972982794046402,
-0.034274227917194366,
-0.031081892549991608,
0.031462885439395905,
0.019276872277259827,
-0.039803292602300644,
-0.01705591194331646,
0.012282495386898518,
-0.0038531487807631493,
0.02817351371049881,
0.02671165019273758,
-0.031954798847436905,
-0.02722799964249134,
-0.026151692494750023,
-0.029454128816723824,
0.0032584802247583866,
-0.07394515722990036,
0.04846189543604851,
-0.0035110514145344496,
-0.04938365891575813,
0.025368930771946907,
-0.01885153353214264,
0.01569201610982418,
-0.06842371821403503,
-0.030494093894958496,
0.0038391733542084694,
0.006317662075161934,
-0.007513470482081175,
-0.03097798302769661,
0.02016574703156948,
0.013287253677845001,
0.012528455816209316,
0.04620479792356491,
0.014072895981371403,
-0.003798465244472027,
-0.04861879348754883,
0.021828580647706985,
-0.04325215145945549,
0.058226730674505234,
0.02768833003938198,
-0.006212435197085142,
0.018136097118258476,
-0.006042668595910072,
-0.017091471701860428,
0.03517117723822594,
-0.026257622987031937,
0.06949751079082489,
0.059104710817337036,
0.035986367613077164,
-0.0043595414608716965,
0.061075154691934586,
0.00024809129536151886,
0.01975213550031185,
-0.023665865883231163,
-0.0318174734711647,
-0.04422223940491676,
0.029672592878341675,
0.035865239799022675,
0.02437368407845497,
-0.05448431894183159,
0.005516640841960907,
0.0357767716050148,
0.011895162053406239,
0.05144468694925308,
0.03118276596069336,
-0.028608832508325577,
-0.026502758264541626,
-0.009526720270514488,
0.012431138195097446,
-0.020852642133831978,
0.02413564920425415,
0.012772832997143269,
0.042015694081783295,
0.0032543297857046127,
0.011885419487953186,
-0.01712210848927498,
0.023110561072826385,
-0.015286753885447979,
0.01156202144920826,
0.017372455447912216,
-0.036478348076343536,
0.021459685638546944,
-0.052381761372089386,
0.04266635328531265,
0.011637412942945957,
-0.04868214577436447,
0.018466046079993248,
-0.03907245397567749,
-0.015442701056599617,
0.022101160138845444,
-0.029836304485797882,
-0.010756327770650387,
-0.017339080572128296,
0.025829480960965157,
-0.006874216720461845,
-0.0010466915555298328,
0.03919752687215805,
-0.024533087387681007,
-0.01206053327769041,
-0.000884225417394191,
0.004558043088763952,
-0.007809189613908529,
-0.011150848120450974,
-0.031589385122060776,
-0.0033038489054888487,
-0.013772907666862011,
-0.008830557577311993,
0.02135331556200981,
0.0010803377954289317,
-0.03515740483999252,
-0.015888234600424767,
-0.01543620228767395,
0.007514899596571922,
0.06988628208637238,
0.025737404823303223,
-0.027492528781294823,
0.00438452884554863,
0.012898402288556099,
-0.07541340589523315,
0.01775868609547615,
-0.008940545842051506,
0.010070602409541607,
-0.022766003385186195,
-0.004233513958752155,
0.04951363056898117,
-0.010621929541230202,
-0.033273302018642426,
0.00938824936747551,
-0.0032416186295449734,
-0.026233874261379242,
0.015073205344378948,
-0.022401435300707817,
0.021799467504024506,
-0.04776882007718086,
0.06126748025417328,
0.018210450187325478,
-0.07273293286561966,
-0.030693260952830315,
-0.03340623155236244,
-0.048646748065948486,
0.010388477705419064,
-0.009283714927732944,
0.060183923691511154,
-0.02555987983942032,
-0.0865764394402504,
0.069420225918293,
0.05605617165565491,
-0.03194420784711838,
-0.005440698005259037,
-0.048091333359479904,
0.03202739730477333,
0.000667890883050859,
-0.01988469995558262,
0.03558368980884552,
-0.014250008389353752,
-0.028619909659028053,
-0.010651271790266037,
0.029868148267269135,
0.02293924242258072,
0.0038718238938599825,
-0.014820156618952751,
0.01306127104908228,
-0.011682241223752499,
0.009266622364521027,
0.06033991649746895,
0.005255841184407473,
-0.04944756254553795,
0.008496693335473537,
0.02713640220463276,
0.029106643050909042,
0.02111317403614521,
-0.03834988921880722,
0.047205906361341476,
0.007856324315071106,
0.038057535886764526,
-0.05805891379714012,
0.030586007982492447,
0.011458097025752068,
-0.03332427889108658,
0.0259753055870533,
0.0412173718214035,
0.01857658289372921,
-0.003947283606976271,
-0.037831880152225494,
0.024980846792459488,
0.02898295223712921,
-0.012829300947487354,
-0.04551078379154205,
0.002650713548064232,
-0.006039263214915991,
0.020314520224928856,
-0.014005644246935844,
-0.030974678695201874,
0.0063301739282906055,
0.028133846819400787,
0.03592194244265556,
-0.0053837415762245655,
-0.0012465361505746841,
-0.006807386875152588,
-0.03022116981446743,
-0.00739038223400712,
-0.012660092674195766,
0.03574351221323013,
0.03639256954193115,
0.041726283729076385,
-0.015083462931215763,
-0.016164936125278473,
0.05414920672774315,
-0.023285849019885063,
-0.07876594364643097,
-0.011574294418096542,
0.005806439556181431,
-0.008998176082968712,
0.01874670572578907,
-0.0057036555372178555,
0.005582867190241814,
-0.026732783764600754,
-0.03214311972260475,
-0.03509359061717987,
0.020372042432427406,
-0.053165365010499954,
0.032760363072156906,
-0.032794032245874405,
-0.041292704641819,
-0.026126379147171974,
0.025417201220989227,
0.04359472170472145,
-0.05027032271027565,
-0.01768256537616253,
0.018893228843808174,
-0.024820098653435707,
-0.009718132205307484,
0.00984478835016489,
-0.011772182770073414,
-0.010785509832203388,
-0.002359463134780526,
0.023150548338890076,
-0.0008451964822597802,
-0.008606379851698875,
0.003985706716775894,
-0.020495641976594925,
0.05210607498884201,
0.01837620697915554,
-0.017394186928868294,
-0.027851151302456856,
-0.01692688837647438,
-0.018521053716540337,
-0.02324014902114868,
0.07082957774400711,
-0.01563708297908306,
0.00919301062822342,
0.031155623495578766,
0.032604191452264786,
-0.0018550388049334288,
0.04909680038690567,
0.037271130830049515,
0.03817597031593323,
-0.018553409725427628,
-0.06814289093017578,
0.0011934221256524324,
-0.01711726002395153,
-0.010884522460401058,
-0.006685711443424225,
-0.02254467085003853,
-0.01969343237578869,
-0.015667853876948357,
0.002693925751373172,
0.009242226369678974,
0.0346110500395298,
0.004033253528177738,
0.035915397107601166,
-0.005691392347216606,
0.022556154057383537,
-0.0034490011166781187,
0.01482515037059784,
-0.007140001282095909,
0.044305119663476944,
0.025579240173101425,
-0.013628609478473663,
-0.07855845987796783,
-0.028784118592739105,
0.035670459270477295,
0.020784776657819748,
0.02304481901228428,
-0.03132078796625137,
-0.03457960858941078,
-0.00219112541526556,
0.047970812767744064,
-0.020835798233747482,
0.04800768196582794,
0.0020735228899866343,
0.006489499472081661,
-0.028154268860816956,
-0.05042583867907524,
-0.01731170155107975,
0.041157353669404984,
-0.023829231038689613,
0.04772108793258667,
-0.022848354652523994,
-0.00042056533857248724,
-0.02581651136279106,
0.005591421853750944,
0.04238323122262955,
0.08476591110229492,
0.023319493979215622,
0.0029288800433278084,
-0.012453596107661724,
0.05306370183825493,
-0.01216959860175848,
-0.06924580037593842,
0.007488468661904335,
-0.03388770669698715,
-0.008717863820493221,
0.01747952401638031,
-0.010685903951525688,
-0.021644147112965584,
0.02255799062550068,
0.0025625862181186676,
-0.01667935401201248,
0.018571073189377785,
-0.01998106576502323,
0.1003570407629013,
0.017811786383390427,
0.02303363010287285,
0.04195300489664078,
0.012695001438260078,
-0.018307620659470558,
0.023361774161458015,
-0.03250926733016968,
0.019061770290136337,
0.010906827636063099,
-0.023388730362057686,
-0.030675305053591728,
0.05899644270539284,
-0.04135177657008171,
0.048043232411146164,
-0.025605112314224243,
0.0058849891647696495,
-0.0033971676602959633,
-0.02658531442284584,
0.0064759342931210995,
0.038926661014556885,
0.00023931496252771467,
-0.006337547674775124,
-0.0195284616202116,
0.028296781703829765,
0.019795972853899002,
-0.007741392124444246,
0.018416227772831917,
0.012240146286785603,
0.007119665388017893,
0.00564131373539567,
0.012641818262636662,
0.026487205177545547,
-0.04705174267292023,
-0.003753391094505787,
0.006772901397198439,
-0.04533456265926361,
0.06387721002101898,
-0.017568223178386688,
-0.012319370172917843,
-0.04671650752425194,
-0.049101851880550385,
-0.042555443942546844,
0.012429354712367058,
-0.0007288791821338236,
0.016209108754992485,
-0.030113954097032547,
-0.02654932253062725,
0.030978862196207047,
-0.0030105242040008307,
-0.07095663994550705,
-0.05443141236901283,
-0.006580485496670008,
0.012466197833418846,
0.014876185916364193,
-0.030881207436323166,
-0.0032652204390615225,
0.006371559575200081,
-0.030468301847577095,
0.04553381726145744,
0.01576819270849228,
-0.011915956623852253,
0.0026094706263393164,
-0.006088566035032272,
0.03062083013355732,
0.02113589644432068,
0.009283398278057575,
-0.020269468426704407,
0.029208822175860405,
-0.003493832191452384,
0.005277340300381184,
-0.01062958873808384,
0.04535242170095444,
-0.02256830409169197,
-0.005483886227011681,
0.005482673179358244,
-0.019767217338085175,
0.03183740749955177,
-0.014151529408991337,
-0.03743895888328552,
0.01686376892030239,
0.039562225341796875,
-0.03543412685394287,
-0.0051980107091367245,
-0.00363467657007277,
-0.0005927324527874589,
0.049086254090070724,
-0.011510000564157963,
-0.024691777303814888,
-0.09787699580192566,
0.007861931808292866,
0.008039343170821667,
0.018791010603308678,
0.04671403020620346,
-0.012352924793958664,
0.08525756746530533,
0.0017083482816815376,
-0.0033618949819356203,
0.03847761079668999,
-0.005314818117767572,
-0.0018677102634683251,
-0.0039656562730669975,
0.0038031002040952444,
0.007021819241344929,
0.009513162076473236,
-0.041665319353342056,
0.0008631580858491361,
-0.05545179918408394,
0.008518954738974571,
0.06321050971746445,
-0.0177559033036232,
0.040347058326005936,
-0.009558025747537613,
-0.02465883269906044,
0.01654820330440998,
0.00605050241574645,
-0.02053629420697689,
-0.03528529778122902,
-0.0013026115484535694,
0.04794410243630409,
-0.03790312632918358,
-0.037277959287166595,
0.04572182148694992,
0.036164239048957825,
-0.03443736210465431,
0.01828237622976303,
0.009829078800976276,
0.04577116668224335,
0.04082352668046951,
-0.014637904241681099,
-0.040127962827682495,
0.052176930010318756,
-0.028986839577555656,
0.004455312620848417,
0.010366090573370457,
-0.02520805224776268,
0.0452885702252388,
0.01600031740963459,
-0.008964639157056808,
0.02235575206577778,
-0.04427233710885048,
-0.028862467035651207,
0.021266646683216095,
-0.003982473164796829,
-0.015011260285973549,
-0.0007474114536307752,
0.021100791171193123,
-0.017923936247825623,
-0.0231334175914526,
0.0023980475962162018,
-0.0058989920653402805,
-0.0480494387447834,
0.013651390559971333,
-0.0228774044662714,
-0.05457417666912079,
0.021182935684919357,
-0.009837423451244831,
-0.016939133405685425,
0.027261292561888695,
-0.014361144974827766,
0.03875667601823807,
0.04166702926158905,
0.01441801618784666,
0.004647417459636927,
0.07113434374332428,
-0.012749548070132732,
-0.007774336263537407,
-0.06287016719579697,
-0.0281878300011158,
0.11955657601356506,
0.06223404034972191,
0.019003164023160934,
-0.05321873724460602,
0.017572736367583275,
-0.046987105160951614,
0.018833478912711143,
-0.03934035822749138,
0.013880720362067223,
-0.04007496312260628,
-0.031067751348018646,
0.0004377294098958373,
0.0430460162460804,
0.009560742415487766,
-0.002195895416662097,
0.02588357776403427,
-0.0008677096921019256,
-0.01816910319030285,
0.0042516994290053844,
0.041804924607276917,
-0.029976610094308853,
-0.0008660925086587667,
-0.02511945553123951,
0.00771876098588109,
-0.026028677821159363,
-0.02384701371192932,
-0.026943201199173927,
-0.023182472214102745,
0.020289916545152664,
-0.025965629145503044,
-0.05438164249062538,
-0.0029872655868530273,
0.0002711716224439442,
-0.001578936935402453,
-0.017231624573469162,
-0.021865323185920715,
0.036726877093315125,
0.029042385518550873,
0.023938415572047234,
0.018022358417510986,
0.030544575303792953,
-0.001223737490363419,
0.021589340642094612,
0.04298459738492966,
-0.020391957834362984,
-0.018042774870991707,
-0.05345623940229416,
0.052205972373485565,
-0.016163991764187813,
0.006185502745211124,
0.013251285068690777,
0.009848963469266891,
0.005879727192223072,
-0.032553136348724365,
-0.027706675231456757,
-0.012446031905710697,
0.006507640238851309,
0.00006425689934985712,
0.02227245457470417,
-0.02802649512887001,
0.03969072923064232,
0.01092612650245428,
-0.011772708967328072,
-0.013345523737370968,
-0.003558799624443054,
0.016402680426836014,
0.02181379497051239,
0.04007238522171974,
-0.009741229005157948,
-0.026080885902047157,
-0.014266734011471272,
-0.05043007805943489,
-0.029089827090501785,
-0.014033772051334381,
-0.011082921177148819,
-0.006063099019229412,
0.009433019906282425,
0.0005419363151304424,
-0.01041205320507288,
0.04202502220869064,
-0.06716267019510269,
0.028053324669599533,
0.00479567376896739,
-0.009917178191244602,
-0.006476273760199547,
0.031944066286087036,
-0.010096888989210129,
0.0555947870016098,
-0.02237842231988907,
0.01058261003345251,
0.0069395387545228004,
-0.0013825041241943836,
0.0020959987305104733,
-0.03438623622059822,
-0.020541781559586525,
-0.002528850454837084,
-0.026668952777981758,
0.033744096755981445,
0.0005525234155356884,
-0.022417763248085976,
0.005127917043864727,
0.0618252232670784,
-0.015220561064779758,
0.04195963218808174,
-0.019552530720829964,
0.003965997602790594,
-0.020945250988006592,
-0.008732502348721027,
-0.004617439582943916,
0.030326617881655693,
0.02452949434518814,
0.010762318968772888,
-0.010933797806501389,
-0.015229538083076477,
0.0323454923927784,
-0.017933011054992676,
0.012644819915294647,
-0.018068797886371613,
-0.01142840925604105,
-0.02860533818602562,
0.00799074862152338,
-0.02790992334485054,
-0.013177832588553429,
0.002282684203237295,
0.013449123129248619,
0.02520091086626053,
0.03139854967594147,
0.01261835265904665,
0.026956040412187576,
-0.014256942085921764,
0.014756710268557072,
0.030973749235272408,
0.018338482826948166,
-0.02196647599339485,
0.005848093889653683,
0.026267128065228462,
0.015001686289906502,
0.020830530673265457,
-0.023491928353905678,
-0.013695573434233665,
0.018832234665751457,
-0.014356574043631554,
-0.03991485387086868,
0.017003940418362617,
0.0015540943713858724,
0.003500558203086257,
0.02646353282034397,
0.0009255153127014637,
-0.024361414834856987,
0.04430563375353813,
0.009188396856188774,
0.007442288566380739,
0.005557394120842218,
-0.03816046938300133,
-0.023425379768013954,
-0.03283614665269852,
0.024348773062229156,
-0.01328367181122303,
0.025396300479769707,
0.015844114124774933,
-0.004631107207387686,
-0.00046748208114877343,
-0.027143623679876328,
0.024013567715883255,
0.0047893100418150425,
-0.03449363261461258,
0.02434414252638817,
-0.009105739183723927,
0.014470410533249378,
0.054594844579696655,
-0.028673585504293442,
-0.005846521817147732,
0.015663987025618553,
0.01961711049079895,
-0.08927974104881287,
-0.02439301833510399,
0.001508015557192266,
0.02583358809351921,
0.0283015388995409,
-0.04808314889669418,
0.017664795741438866,
0.029001345857977867,
-0.07807039469480515,
-0.03101525641977787,
-0.013641984201967716,
0.006799990776926279,
0.004850576166063547,
-0.022696418687701225,
-0.04347144812345505,
0.012096443213522434,
0.007876190356910229,
0.059159670025110245,
-0.0030092329252511263,
0.008356218226253986,
-0.01693161576986313,
-0.055914506316185,
-0.02777515910565853,
0.026694713160395622,
0.0017636691918596625,
-0.01006670854985714,
0.08661426603794098,
0.023449163883924484,
0.01859915442764759,
0.02888176031410694,
-0.005667183082550764,
-0.006989171728491783,
0.0015926825581118464,
0.0444796048104763,
-0.010179460979998112,
0.05917351692914963,
-0.0011214753612875938,
-0.02648281678557396,
0.0037088729441165924,
-0.04627615958452225,
0.029929013922810555,
0.007876676507294178,
-0.02932427078485489,
-0.001923124655149877,
0.04336725175380707,
0.017753636464476585,
-0.013840102590620518,
0.04755173623561859,
-0.038744211196899414,
-0.02998756244778633,
0.02400987595319748,
0.022075200453400612,
0.02666235901415348,
-0.015828337520360947,
0.03172712028026581,
-0.06431343406438828,
-0.03894408047199249,
0.026226909831166267,
-0.005198018625378609,
0.004321155603975058,
0.014460097998380661,
0.02578352950513363,
-0.04395554959774017,
0.022254176437854767,
0.05301019176840782,
-0.019258053973317146,
-0.08499346673488617,
0.0040800077840685844,
-0.0003860474389512092,
0.013658605515956879,
0.026527974754571915,
-0.07039579749107361,
-0.05163256451487541,
0.028534576296806335,
0.009987159632146358,
-0.005077518988400698,
0.014321732334792614,
-0.02793598361313343,
-0.032399021089076996,
-0.052697084844112396,
0.0349845290184021,
0.003610387910157442,
-0.022435344755649567,
-0.03429754078388214,
-0.05448796600103378,
0.006337346043437719,
0.023146530613303185,
0.0978470891714096,
-0.0004527135461103171,
-0.030998190864920616,
0.018636468797922134,
0.003151501063257456,
0.04351596161723137,
-0.09497293084859848,
-0.0030588191002607346,
0.026774490252137184,
-0.023613207042217255,
-0.003943480085581541,
0.007211595308035612,
-0.02439001575112343,
0.011067655868828297,
0.004261583089828491,
0.03350711613893509,
-0.006627166178077459,
-0.03850480169057846,
-0.006907329894602299,
0.049898091703653336,
0.011473779566586018,
-0.04167234152555466,
0.05441172793507576,
-0.021118253469467163,
0.010912472382187843,
0.015115326270461082,
-0.030926909297704697,
-0.030062219128012657,
0.01473050843924284,
-0.01799682155251503,
-0.006899442058056593,
-0.04056103155016899,
0.009559044614434242,
0.06501534581184387,
-0.057920970022678375,
-0.03117363713681698,
0.039346758276224136,
-0.06102271005511284,
-0.02507220022380352,
0.06546824425458908,
-0.020775355398654938,
0.04208105430006981,
0.018014248460531235,
0.02990097552537918,
-0.0027157871518284082,
0.016656849533319473,
0.007989554665982723,
0.013178359717130661,
0.02913707308471203,
-0.030905816704034805,
-0.0033957003615796566,
0.052200403064489365,
-0.01201336458325386,
0.017676539719104767,
0.01270745974034071,
-0.010772410780191422,
-0.04748598486185074,
-0.05843501538038254,
0.006530464626848698,
-0.000845053291413933,
-0.012449698522686958,
-0.00968927051872015,
-0.051170844584703445,
0.08428096026182175,
-0.021634267643094063,
0.0007669512997381389,
0.006161126308143139,
0.0172516331076622,
-0.01843574270606041,
0.02050560899078846,
0.01941663585603237,
0.04017825797200203,
-0.008256780914962292,
0.009911634027957916,
-0.0033327843993902206,
-0.002601141110062599,
0.044509079307317734,
-0.04126652330160141,
0.015423402190208435,
0.01985645480453968,
-0.007587464526295662,
-0.017347393557429314,
0.003177159931510687,
0.0007818122394382954,
-0.0298028402030468,
0.003918295726180077,
0.024859583005309105,
0.008931214921176434,
0.009586687199771404,
-0.0036224997602403164,
-0.008505964651703835,
0.08207862824201584,
-0.05994240567088127,
0.00886576622724533,
-0.030629204586148262,
0.02387094311416149,
-0.026663610711693764,
-0.006935704033821821
] |
<p>If p-type semiconductor and n-type semiconductor of a diode are equally doped, and if the diode is forward biased, then holes will move toward the n-type semiconductor and electrons will move toward the p-type semiconductor and they will diffuse with each other. Then will there be any electron that will go to the positive terminal of the battery if all of them have diffused with each other? I can't understand, please help me! </p> | 2,031 | [
-0.03355136141180992,
-0.0023729519452899694,
0.02920294553041458,
-0.0014756085583940148,
0.01943870633840561,
-0.01595124788582325,
-0.002149479230865836,
0.002733942586928606,
-0.006289622280746698,
-0.025887221097946167,
0.041814591735601425,
0.00966392271220684,
0.04492015391588211,
0.015341621823608875,
0.019718408584594727,
-0.001757941790856421,
-0.023979488760232925,
-0.021920882165431976,
-0.005438744556158781,
0.00754861393943429,
-0.015277317725121975,
0.018475862219929695,
-0.0008488185703754425,
0.030345752835273743,
-0.018089015036821365,
0.015667976811528206,
0.023856548592448235,
0.012140166945755482,
0.01157591212540865,
0.053840842097997665,
-0.012549947015941143,
-0.04831131175160408,
0.01582569070160389,
0.042551957070827484,
0.016900725662708282,
-0.013582690618932247,
-0.03919699788093567,
-0.04192911088466644,
-0.037406887859106064,
0.02323143184185028,
-0.00574089027941227,
-0.0027002254500985146,
0.029867231845855713,
0.025567669421434402,
-0.03344409167766571,
-0.001503186416812241,
0.03985016793012619,
-0.027425140142440796,
0.04109613969922066,
-0.08574899286031723,
0.0570291243493557,
-0.035085972398519516,
0.06325867027044296,
0.0322813056409359,
-0.00613707210868597,
0.00928796548396349,
0.07248685508966446,
0.12166812270879745,
-0.003484537824988365,
-0.0032610022462904453,
0.0024156582076102495,
-0.020566895604133606,
0.008301652036607265,
-0.05423393100500107,
-0.07550745457410812,
0.011408490128815174,
0.009544631466269493,
-0.08394470065832138,
0.024703271687030792,
0.00925915315747261,
0.019820773974061012,
0.0019441426265984774,
0.048243097960948944,
-0.046723611652851105,
-0.0035301069729030132,
-0.023934215307235718,
0.05538121610879898,
0.01568644866347313,
0.011395023204386234,
0.021513555198907852,
-0.04548496752977371,
0.01600392535328865,
-0.005876960698515177,
0.07646520435810089,
-0.006350004579871893,
-0.060456037521362305,
0.05584988370537758,
-0.04274313151836395,
0.0331660732626915,
-0.0033906560856848955,
0.01590099185705185,
-0.0011703000636771321,
0.04389689490199089,
-0.031576674431562424,
-0.024149274453520775,
0.047798581421375275,
-0.03279814124107361,
0.057647231966257095,
0.010621019639074802,
-0.004708786495029926,
0.020413417369127274,
-0.0004917751648463309,
0.04127207398414612,
0.0466894768178463,
-0.029681015759706497,
-0.042600955814123154,
-0.037456899881362915,
0.03907182440161705,
-0.00972436647862196,
0.012690837495028973,
-0.02534152753651142,
0.012068009935319424,
-0.0008124283631332219,
0.0083261514082551,
0.01400717068463564,
-0.02798553928732872,
-0.027190571650862694,
-0.00037069316022098064,
0.0330486074090004,
0.03612113371491432,
0.027917824685573578,
-0.028931550681591034,
0.034271713346242905,
-0.013782056979835033,
-0.05767884850502014,
0.02040942572057247,
0.005948803853243589,
0.011961006559431553,
0.0034128569532185793,
-0.013254471123218536,
-0.0018841037526726723,
-0.012162063270807266,
0.013090124353766441,
0.013401851989328861,
0.05912790447473526,
-0.02097768895328045,
-0.050189875066280365,
-0.03493843972682953,
0.012237782590091228,
-0.026552539318799973,
0.028261449187994003,
-0.07945839315652847,
0.005909194704145193,
0.032893721014261246,
0.07197680324316025,
-0.03920581191778183,
-0.0016940603964030743,
0.016112662851810455,
0.023991761729121208,
0.0048849876038730145,
-0.0055185421369969845,
-0.02689814753830433,
0.010812523774802685,
-0.00558885233476758,
0.026051634922623634,
-0.07721709460020065,
0.05324719846248627,
0.005919795949012041,
0.031485412269830704,
-0.030898259952664375,
0.02177176997065544,
-0.0018163196509703994,
0.006393826100975275,
0.003188406815752387,
-0.012947550043463707,
-0.01696459949016571,
0.07213008403778076,
-0.0008706413209438324,
-0.00860887672752142,
0.03863345459103584,
0.01902281492948532,
0.02753123641014099,
0.00673022260889411,
0.06970211118459702,
0.04460949823260307,
-0.0409194640815258,
-0.06135384738445282,
-0.04708964750170708,
0.03737249970436096,
-0.030732516199350357,
-0.04386277496814728,
-0.029843853786587715,
-0.003446347313001752,
0.018010487779974937,
0.0077494108118116856,
0.019669590517878532,
0.006623256951570511,
-0.020047329366207123,
-0.024209074676036835,
-0.0124185960739851,
-0.0018329215236008167,
-0.029773391783237457,
0.023268263787031174,
-0.016740862280130386,
-0.025240184739232063,
0.0255332812666893,
-0.02617756836116314,
0.038952432572841644,
-0.02860366366803646,
-0.0177910178899765,
-0.0416046641767025,
0.025694873183965683,
-0.03369202837347984,
-0.018147774040699005,
0.03214656189084053,
0.080128975212574,
0.010799580253660679,
0.017384879291057587,
0.06711212545633316,
-0.0007084287935867906,
0.004112410359084606,
0.0261521115899086,
-0.030544588342308998,
0.02962050959467888,
0.015327619388699532,
-0.007121316157281399,
0.009102188050746918,
0.0015749332960695028,
0.017228327691555023,
0.04116710647940636,
-0.016491340473294258,
0.08340577036142349,
0.06533078849315643,
-0.018436158075928688,
-0.023275252431631088,
-0.006013430189341307,
-0.005499474238604307,
-0.003099663183093071,
-0.017928391695022583,
-0.014478404074907303,
-0.052570734173059464,
-0.01619606651365757,
0.02667948044836521,
-0.006794932764023542,
-0.0472329743206501,
0.020098721608519554,
0.016490239650011063,
0.0036769916769117117,
0.029105493798851967,
0.050104763358831406,
-0.017393656075000763,
0.01863982528448105,
0.019815802574157715,
0.01055335346609354,
-0.022190984338521957,
-0.012916626408696175,
0.012904573231935501,
0.004683563020080328,
0.018681371584534645,
-0.011544782668352127,
-0.027775702998042107,
0.044192567467689514,
0.020402662456035614,
0.057545073330402374,
0.03289445862174034,
-0.043751198798418045,
0.02613595686852932,
0.0006312985788099468,
0.049219921231269836,
-0.007538304198533297,
-0.002511193510144949,
-0.013675691559910774,
0.014204845763742924,
-0.02621462568640709,
-0.003384424140676856,
0.03741876035928726,
-0.002538077300414443,
-0.013411912135779858,
0.03246964514255524,
-0.04605706036090851,
0.023288656026124954,
-0.018547242507338524,
0.015639416873455048,
-0.004314586520195007,
-0.009719803929328918,
0.055048178881406784,
0.01933293789625168,
0.020697949454188347,
-0.042243923991918564,
-0.015309475362300873,
-0.062293242663145065,
-0.030815035104751587,
0.019640697166323662,
0.007488848641514778,
-0.02218533307313919,
-0.008262031711637974,
-0.029348256066441536,
-0.05453577637672424,
0.04484504461288452,
0.025290410965681076,
0.0030703984666615725,
0.0385114960372448,
-0.042432598769664764,
-0.025617746636271477,
0.001669559278525412,
-0.00756419450044632,
0.03165575861930847,
-0.05942291021347046,
-0.005392467603087425,
0.039733562618494034,
-0.01455018948763609,
-0.04029730707406998,
0.016019318252801895,
-0.07962202280759811,
-0.033735524863004684,
0.01960102654993534,
-0.011524408124387264,
0.051083024591207504,
-0.020278697833418846,
0.04734163358807564,
0.01060744933784008,
-0.04300332069396973,
0.007524773944169283,
-0.0563870370388031,
-0.026654528453946114,
0.05839993432164192,
0.011918807402253151,
-0.008305559866130352,
-0.03483977168798447,
-0.025722825899720192,
0.0214383602142334,
0.023896701633930206,
-0.0072330511175096035,
0.01684078760445118,
-0.032255787402391434,
-0.04198857769370079,
-0.05735856667160988,
0.05953013524413109,
0.04970922693610191,
-0.009886831976473331,
0.0036051704082638025,
0.00467935623601079,
0.09612517803907394,
0.04526647552847862,
-0.02152245305478573,
-0.0038544312119483948,
0.0023749200627207756,
0.02817218378186226,
0.010014597326517105,
0.04279211536049843,
0.016821227967739105,
-0.013042294420301914,
-0.002563747577369213,
-0.01619441993534565,
0.05299612507224083,
0.047748640179634094,
-0.01188845094293356,
0.04686116799712181,
-0.013092276640236378,
0.006138701923191547,
-0.024499516934156418,
0.043745383620262146,
0.038369063287973404,
0.017787300050258636,
-0.008822058327496052,
-0.007126465439796448,
0.06317170709371567,
-0.04269298166036606,
0.015322250314056873,
0.012474572286009789,
0.009516395628452301,
-0.04283642768859863,
-0.06486363708972931,
0.0396714024245739,
-0.002088360721245408,
-0.006959137041121721,
0.01209417823702097,
-0.03295570984482765,
0.017610887065529823,
0.02105524018406868,
0.010685957036912441,
0.002373642520979047,
-0.022527044638991356,
0.011970056220889091,
-0.08686697483062744,
-0.02108926512300968,
0.028144601732492447,
0.03855346143245697,
-0.0037048261146992445,
0.056820180267095566,
0.020756173878908157,
0.022193241864442825,
0.016110090538859367,
0.007285787723958492,
-0.06893032789230347,
0.017215723171830177,
0.01779007539153099,
-0.0419946052134037,
-0.050098858773708344,
-0.04017387330532074,
-0.026483425870537758,
-0.06575536727905273,
-0.03276415541768074,
0.014807196334004402,
-0.021134331822395325,
-0.04904838278889656,
0.04440692812204361,
-0.03149278834462166,
-0.03884202241897583,
-0.04200275242328644,
0.026026790961623192,
0.024733617901802063,
-0.029347293078899384,
0.023032279685139656,
0.0040608979761600494,
-0.03677481785416603,
0.013965722173452377,
-0.03305547684431076,
0.009392819367349148,
0.007869801484048367,
0.035887014120817184,
0.033717114478349686,
0.009237188845872879,
-0.01274182554334402,
-0.023986537009477615,
0.006556999403983355,
0.07535944879055023,
0.020266780629754066,
-0.021329892799258232,
-0.012414523400366306,
-0.05169498547911644,
-0.03472602367401123,
-0.0024991354439407587,
0.03747868537902832,
-0.015157707035541534,
0.03334856033325195,
0.05191892385482788,
0.015427559614181519,
-0.03574380651116371,
0.0450398214161396,
0.029951926320791245,
0.007336799055337906,
-0.048896096646785736,
-0.032085955142974854,
-0.03140423074364662,
-0.032371729612350464,
0.008431117981672287,
0.033561550080776215,
-0.009574360214173794,
-0.020651675760746002,
-0.0034795955289155245,
0.03479199483990669,
0.017620764672756195,
-0.013372605666518211,
0.008971656672656536,
0.007043770980089903,
0.038638148456811905,
-0.009432602673768997,
-0.0034926708322018385,
0.028166795149445534,
-0.020412694662809372,
-0.003877151058986783,
0.004369558300822973,
-0.0003372452047187835,
-0.08572962880134583,
0.026756979525089264,
0.039887987077236176,
0.04859738424420357,
-0.04606534540653229,
0.01469389721751213,
-0.0508449524641037,
0.003991252742707729,
0.04506101459264755,
-0.03169475495815277,
0.023375406861305237,
-0.0034151729196310043,
-0.018684064969420433,
-0.017307307571172714,
-0.03621790558099747,
-0.03294907137751579,
0.010744335129857063,
0.005667483434081078,
0.02250880002975464,
-0.012889493256807327,
-0.011870396323502064,
-0.01058895979076624,
0.002340513514354825,
0.06358379870653152,
0.0896771103143692,
-0.003927905578166246,
0.025742875412106514,
0.008864575065672398,
0.03452841192483902,
-0.00989522784948349,
-0.0924367755651474,
0.01077301986515522,
-0.016389956697821617,
-0.006733612157404423,
0.04995132237672806,
-0.05168941989541054,
-0.05818594619631767,
0.009494383819401264,
0.030528560280799866,
0.006139985751360655,
-0.009339421056210995,
-0.05358709767460823,
0.02403704635798931,
0.0033531372901052237,
-0.006930636707693338,
0.05349193885922432,
0.014129058457911015,
-0.05299836024641991,
-0.017679907381534576,
-0.017832685261964798,
0.0393352210521698,
-0.022380905225872993,
0.025434691458940506,
0.009635505266487598,
0.03574436157941818,
0.01148978527635336,
0.028201255947351456,
0.001477884128689766,
0.02136489376425743,
0.0004656324163079262,
-0.05820191651582718,
-0.03046591393649578,
0.006617599632591009,
-0.01700819842517376,
0.002400006167590618,
-0.004061936866492033,
0.007720652502030134,
0.011204161681234837,
-0.02840091660618782,
-0.00974908284842968,
-0.01225925050675869,
0.01949305832386017,
0.01490873284637928,
-0.0036302374210208654,
0.010591553524136543,
-0.03379671275615692,
0.004231472034007311,
0.011712659150362015,
-0.007889586500823498,
0.06477253139019012,
0.012556089088320732,
-0.002717432798817754,
0.03611108660697937,
-0.05265279486775398,
-0.06026344746351242,
0.0867847129702568,
-0.00760663952678442,
-0.002259267959743738,
-0.05239782854914665,
0.040023643523454666,
0.01805719919502735,
0.003791035618633032,
-0.0769750326871872,
-0.034343134611845016,
0.008084436878561974,
-0.0016711520729586482,
-0.017808496952056885,
-0.01863504759967327,
-0.026339378207921982,
0.00997141469269991,
-0.04042107239365578,
0.023767046630382538,
0.0020155052188783884,
-0.017440224066376686,
-0.012866721488535404,
0.020922092720866203,
-0.010364936664700508,
0.07356488704681396,
-0.004267524927854538,
-0.016661299392580986,
-0.015134865418076515,
-0.042563047260046005,
-0.011287841945886612,
-0.03280745819211006,
0.026761924847960472,
-0.0020902766846120358,
-0.017018062993884087,
-0.023692309856414795,
-0.012736559845507145,
0.061490777879953384,
-0.04330174997448921,
-0.02718321420252323,
0.024827012792229652,
0.00851561687886715,
-0.004684802610427141,
-0.02472011186182499,
0.019830850884318352,
-0.014219208620488644,
0.009507772512733936,
0.007509101182222366,
0.0074964710511267185,
-0.041815850883722305,
-0.028125179931521416,
0.032913558185100555,
-0.009458610787987709,
0.006498127710074186,
-0.006678208243101835,
0.055407557636499405,
-0.001860588206909597,
-0.0011186450719833374,
0.04778660461306572,
0.003190391231328249,
0.05587174370884895,
-0.0163017176091671,
-0.002064575208351016,
-0.04358649626374245,
0.001937249326147139,
-0.004579860717058182,
-0.019836442545056343,
-0.029862748458981514,
0.001052464940585196,
0.05698347091674805,
-0.009677300229668617,
0.000914164527785033,
0.03069167397916317,
0.005083046387881041,
-0.02643240988254547,
-0.02717306651175022,
0.010740675032138824,
0.01679803803563118,
-0.0029625215101987123,
0.028596216812729836,
-0.008445633575320244,
0.004681513179093599,
0.03980531916022301,
0.04504352807998657,
-0.002267988631501794,
0.03258512541651726,
0.021931057795882225,
-0.023930266499519348,
0.05270909145474434,
0.02276824600994587,
-0.04832863807678223,
0.04120619595050812,
-0.044110946357250214,
0.026360590010881424,
-0.00887916050851345,
-0.04581286758184433,
0.061454322189092636,
-0.008227196522057056,
0.006785161793231964,
-0.011374644935131073,
-0.022984081879258156,
-0.029942229390144348,
-0.005095875356346369,
-0.015608553774654865,
0.02963227964937687,
-0.057291336357593536,
0.035554543137550354,
0.04552744701504707,
0.018881404772400856,
0.005194806959480047,
0.006792562082409859,
-0.054809730499982834,
-0.02123132534325123,
-0.03693915158510208,
-0.0019378738943487406,
0.000056118158681783825,
-0.01952946186065674,
-0.02087261714041233,
-0.015437808819115162,
-0.010767851024866104,
0.04232621565461159,
0.017550615593791008,
0.0726892277598381,
0.010820670053362846,
0.06819508224725723,
-0.013150404207408428,
0.0487741082906723,
0.004249473102390766,
-0.02266852743923664,
0.10339348763227463,
0.023660441860556602,
0.0207501370459795,
-0.0505046509206295,
-0.015543545596301556,
-0.03669341653585434,
0.00778997503221035,
0.00008804327080724761,
0.03934531286358833,
0.01084026601165533,
0.03454652056097984,
-0.006460015662014484,
0.003194857854396105,
-0.025128033012151718,
0.0063440208323299885,
0.03904321417212486,
-0.03381028026342392,
-0.06348530203104019,
0.04688210040330887,
0.029823370277881622,
-0.0034723938442766666,
0.033016055822372437,
-0.05099685862660408,
0.0048613958060741425,
-0.0367266982793808,
-0.012933864258229733,
-0.0569521002471447,
-0.036626528948545456,
0.034655340015888214,
0.02601492777466774,
-0.029531102627515793,
0.0002094739757012576,
0.01776154525578022,
-0.009836887940764427,
-0.02797035314142704,
-0.005220481660217047,
0.01688726618885994,
-0.002515022410079837,
-0.008603060618042946,
0.026707438752055168,
0.022120174020528793,
0.03586076572537422,
0.03801058232784271,
0.008825725875794888,
-0.04528403654694557,
0.030030706897377968,
0.019803326576948166,
0.028346950188279152,
-0.007625004276633263,
-0.021533461287617683,
0.014058016240596771,
0.0363817997276783,
0.005439723376184702,
-0.04551173374056816,
-0.042632732540369034,
0.008026212453842163,
0.01457798108458519,
-0.009783534333109856,
0.008547226898372173,
-0.01683790795505047,
-0.012275330722332,
-0.0018849472980946302,
-0.012767418287694454,
-0.015340163372457027,
-0.0054677072912454605,
0.026464499533176422,
-0.02881389670073986,
0.029444893822073936,
-0.017613591626286507,
-0.012672940269112587,
-0.0388350635766983,
0.009697330184280872,
-0.0390380397439003,
-0.03066975437104702,
0.01547237578779459,
0.04271451383829117,
0.012484955601394176,
0.007874094881117344,
0.002197440480813384,
0.033951617777347565,
-0.06993309408426285,
0.04758137837052345,
0.022291935980319977,
0.010176191106438637,
-0.01942955143749714,
0.031207052990794182,
0.034898675978183746,
0.020236069336533546,
-0.032052282243967056,
0.028025012463331223,
-0.006754396948963404,
0.01598355919122696,
0.010918064042925835,
-0.04455394297838211,
-0.022885236889123917,
0.0017247239593416452,
-0.03352098912000656,
0.03168024495244026,
0.015149668790400028,
0.040618326514959335,
0.003816083539277315,
-0.011083872988820076,
-0.0127500519156456,
-0.002755804220214486,
-0.0034926957450807095,
0.013694207184016705,
0.008416333235800266,
-0.014055617153644562,
0.012448405846953392,
0.0013945832615718246,
0.019623346626758575,
-0.029559394344687462,
0.0004270484787411988,
-0.028017906472086906,
0.0314752459526062,
0.039602749049663544,
0.011867537163197994,
-0.023444412276148796,
-0.014217830263078213,
-0.03899868577718735,
0.03220624476671219,
-0.02511887066066265,
-0.00553808081895113,
-0.045536965131759644,
-0.011698395945131779,
0.02021045610308647,
0.023567305877804756,
0.01047935988754034,
0.008870735764503479,
-0.028520504012703896,
-0.01944703236222267,
0.04213273897767067,
0.03288199007511139,
0.00039441490662284195,
-0.009308649227023125,
0.0476810522377491,
-0.007700531277805567,
0.04520149901509285,
-0.033987365663051605,
-0.03595579415559769,
0.053262583911418915,
-0.009422842413187027,
-0.00801440142095089,
-0.024751555174589157,
0.00527576869353652,
0.037455011159181595,
-0.003178627695888281,
-0.004025344271212816,
-0.024516994133591652,
0.06158533692359924,
-0.03279229253530502,
-0.023539666086435318,
0.035601336508989334,
-0.04604059085249901,
0.0007189256139099598,
0.012670408934354782,
-0.020584018900990486,
0.004491004161536694,
0.015491299331188202,
0.014507271349430084,
0.01695142313838005,
0.014751458540558815,
-0.019501568749547005,
0.0009140986367128789,
0.013736500404775143,
0.014830064959824085,
0.021227650344371796,
-0.02466776594519615,
-0.01091880165040493,
0.04846782237291336,
0.00005971097925794311,
0.024479197338223457,
0.01168444287031889,
0.009218253195285797,
-0.05492110550403595,
-0.020395396277308464,
0.029783427715301514,
0.013637061230838299,
0.0012486526975408196,
-0.05496858060359955,
-0.019972331821918488,
-0.0007265503518283367,
-0.07671044766902924,
0.025583036243915558,
0.01922900415956974,
-0.02806815318763256,
-0.0690474584698677,
0.016653601080179214,
-0.01472880132496357,
0.02273663319647312,
0.03496158868074417,
0.09256421774625778,
-0.005426470190286636,
-0.02031267061829567,
0.009212994948029518,
-0.021356072276830673,
-0.04577725753188133,
0.02650756575167179,
0.015398058108985424,
0.015543249435722828,
0.013850104995071888,
-0.04867376759648323,
0.007232723291963339,
0.01252049021422863,
0.006475276313722134,
-0.04117753356695175,
-0.005507230293005705,
0.01843048632144928,
0.029290780425071716,
0.04385719448328018,
-0.0275419931858778,
-0.011099258437752724,
0.015348068438470364,
0.0075787873938679695,
0.025492453947663307,
0.029072120785713196,
-0.010851223021745682,
0.03627747669816017,
0.007011622190475464,
-0.025884484872221947,
-0.0436239093542099,
0.02034190483391285,
-0.017574626952409744,
-0.0037293441127985716,
-0.001946605509147048,
0.0045191142708063126,
0.01718912273645401,
-0.0326821394264698,
-0.017057040706276894,
-0.02121216244995594,
-0.03722846508026123,
0.012213458307087421,
0.001931520993821323,
0.03877080976963043,
0.02449074760079384,
-0.0008954244549386203,
-0.019009780138731003,
0.02538081631064415,
-0.0034305399749428034,
0.008646600879728794,
-0.0673554316163063,
-0.0016047306125983596,
0.0032670756336301565,
-0.0183608029037714,
0.005917818751186132,
-0.043945107609033585,
0.00701548159122467,
0.03909961134195328,
-0.006228127982467413,
0.02118222415447235,
0.02086728624999523,
-0.06524155288934708,
0.0008051448385231197,
-0.046394575387239456,
0.027682099491357803,
-0.007411552593111992,
0.004868150223046541,
-0.053836092352867126,
-0.020896287634968758,
-0.04232478886842728,
0.050852999091148376,
0.04590732976794243,
0.00018874838133342564,
-0.017845995724201202,
0.024333281442523003,
-0.04284035786986351,
0.046460822224617004,
-0.051444392651319504,
0.011069513857364655,
-0.003706227522343397,
-0.05722063407301903,
-0.02297895960509777,
-0.020612796768546104,
-0.043994538486003876,
0.008484932594001293,
0.004892492201179266,
-0.001313274260610342,
-0.012814757414162159,
-0.022705078125,
-0.01620081625878811,
0.043922059237957,
0.006270748097449541,
0.0006506406352855265,
0.08966971933841705,
-0.02597879059612751,
0.030340828001499176,
0.032172564417123795,
-0.016898013651371002,
-0.05884072184562683,
-0.012514169327914715,
-0.039242345839738846,
0.003273868700489402,
0.006259613204747438,
-0.013395764864981174,
0.04768774285912514,
-0.035041239112615585,
-0.02491416037082672,
-0.010899784043431282,
-0.07477589696645737,
-0.011759535409510136,
0.05807698145508766,
0.008439145050942898,
0.05481459200382233,
-0.01690322905778885,
-0.008972730487585068,
-0.003863199846819043,
0.004602733068168163,
-0.022676825523376465,
0.031173044815659523,
-0.011218879371881485,
-0.005988990422338247,
-0.0015234962338581681,
0.013339505530893803,
0.0225538183003664,
0.0037758625112473965,
0.0047946712002158165,
0.012565990909934044,
-0.02544185146689415,
0.013031575828790665,
0.029262322932481766,
0.0001334409898845479,
0.04289281740784645,
-0.011025355197489262,
-0.028217852115631104,
0.04666603356599808,
-0.03631507232785225,
0.02805938571691513,
-0.012680343352258205,
0.005858988966792822,
0.008903440088033676,
0.016076330095529556,
0.0028507353272289038,
0.03628792613744736,
-0.02830454707145691,
-0.051932837814092636,
-0.008517970331013203,
0.023703251034021378,
0.028432991355657578,
-0.07031931728124619,
0.03381923958659172,
-0.018034884706139565,
-0.03630257770419121,
-0.022874977439641953,
0.03556746989488602,
-0.029389336705207825,
-0.009358997456729412,
0.01192192267626524,
0.045317720621824265,
-0.0034301376435905695,
-0.03308861330151558,
0.01891838200390339,
-0.013856497593224049,
0.04092096537351608,
-0.029290689155459404,
-0.004453148227185011,
-0.053772445768117905,
-0.0046494705602526665,
-0.02437339350581169,
-0.008914572186768055
] |
<p>The human brain is said to produce a magnetic field resulting from the action potentials released inside the brain. What's the nature of such a field in terms of size and strength, and what is the potential for manipulation of brain functions by interfering with it by means of electromagnetic radiation?</p> | 2,032 | [
-0.038091544061899185,
-0.013404708355665207,
0.005351316183805466,
-0.08843764662742615,
0.07637860625982285,
0.02507929876446724,
-0.020405307412147522,
-0.0328928679227829,
-0.000045309549022931606,
-0.028438443318009377,
0.045520979911088943,
0.05568396672606468,
0.05177314579486847,
0.008861277252435684,
0.022205524146556854,
-0.01276689488440752,
0.009857552126049995,
0.00206578872166574,
-0.02217375487089157,
-0.010411159135401249,
0.007708016782999039,
0.028955116868019104,
-0.013260227628052235,
0.01635087840259075,
-0.04539455473423004,
0.017079723998904228,
0.050717853009700775,
0.030634935945272446,
0.008652050979435444,
0.041741278022527695,
0.005755518097430468,
-0.02283969707787037,
0.0009092524414882064,
0.0046864780597388744,
0.0005488469614647329,
-0.02612708881497383,
-0.04126935452222824,
-0.04783204570412636,
-0.012732463888823986,
0.023165833204984665,
-0.014534104615449905,
-0.05884390324354172,
0.010665184818208218,
0.06397318094968796,
-0.06705892831087112,
-0.009476345032453537,
-0.008251173421740532,
-0.04442497715353966,
0.023853380233049393,
-0.06192595139145851,
0.06329361349344254,
-0.02782157063484192,
0.06175732612609863,
-0.017301227897405624,
0.006661525461822748,
-0.0023448339197784662,
0.07466752082109451,
0.051974862813949585,
0.0034707533195614815,
-0.0726490244269371,
-0.03399909660220146,
0.005527440458536148,
-0.006092161405831575,
-0.03504827618598938,
-0.052630987018346786,
0.06356798857450485,
-0.023395882919430733,
-0.0004530502774287015,
0.04935668781399727,
0.0010573109611868858,
0.0377134345471859,
0.046386417001485825,
0.006696907337754965,
0.00896476674824953,
-0.005608678795397282,
-0.043769385665655136,
0.025558101013302803,
0.010090399533510208,
0.02854495868086815,
0.03414878249168396,
0.009082180447876453,
0.0026859391946345568,
0.003419042332097888,
0.024422302842140198,
0.01896313950419426,
0.020223692059516907,
0.08763028681278229,
-0.021109677851200104,
0.04885748028755188,
0.015103517100214958,
-0.02292163483798504,
0.04147113859653473,
0.026314765214920044,
-0.02772311493754387,
-0.04569357633590698,
0.012013854458928108,
-0.032949239015579224,
0.05059564486145973,
-0.0005349116399884224,
-0.007827797904610634,
0.005994958337396383,
0.03803323954343796,
0.011224155314266682,
0.034790243953466415,
-0.0035517460200935602,
-0.04907207936048508,
-0.008326036855578423,
0.021409114822745323,
-0.01790960505604744,
-0.012177357450127602,
0.001494874246418476,
0.025891892611980438,
0.026113521307706833,
-0.02803473360836506,
0.04227880388498306,
0.012955361977219582,
-0.006055083591490984,
-0.03827979788184166,
0.04202541336417198,
0.08200833946466446,
0.02457953803241253,
-0.040158603340387344,
0.03385930135846138,
-0.024483080953359604,
-0.03958458825945854,
-0.011311597190797329,
0.01464083418250084,
0.01887253299355507,
-0.05223637819290161,
0.04459640756249428,
-0.005698380526155233,
-0.0394330695271492,
0.0009910755325108767,
-0.0028704155702143908,
0.04515558481216431,
-0.03305530175566673,
-0.10241160541772842,
-0.059164583683013916,
0.045029349625110626,
-0.01646939292550087,
-0.0022507391404360533,
-0.05902104079723358,
-0.007146739400923252,
0.04147966206073761,
0.07475978136062622,
-0.005594193469733,
-0.013768930919468403,
0.0032686335034668446,
0.04514167457818985,
0.013285554945468903,
-0.030822034925222397,
0.004643324296921492,
-0.0056326426565647125,
0.010625752620398998,
0.006182663142681122,
-0.06058153882622719,
0.03720648214221001,
0.04343552514910698,
-0.01928904466331005,
-0.0539519339799881,
0.05755118280649185,
-0.008897903375327587,
0.011370081454515457,
0.0015630488051101565,
-0.03717748820781708,
-0.02608458325266838,
0.08896602690219879,
-0.008706238120794296,
0.019763322547078133,
0.04624635726213455,
0.007028188556432724,
0.05072673782706261,
0.02098509855568409,
0.023988787084817886,
0.019085794687271118,
-0.028112690895795822,
-0.00011097794049419463,
-0.013583923690021038,
0.02630348689854145,
0.0016959713539108634,
-0.04551219940185547,
-0.008184274658560753,
-0.012915946543216705,
0.020444463938474655,
0.0029045999981462955,
0.057619258761405945,
-0.026259643957018852,
-0.031490348279476166,
0.0017320928163826466,
-0.02899218536913395,
0.003652111627161503,
-0.03389671444892883,
0.06169068068265915,
-0.018086791038513184,
-0.019456040114164352,
0.03388265520334244,
-0.016926590353250504,
0.030475175008177757,
-0.05453839898109436,
-0.05716189369559288,
-0.0012860120041295886,
0.014146482571959496,
0.016601422801613808,
0.030052345246076584,
0.01728726178407669,
0.054721347987651825,
-0.0018208340043202043,
0.011027751490473747,
0.05539322271943092,
-0.035030752420425415,
-0.0746360570192337,
0.0033701176289469004,
-0.022664839401841164,
0.04473583400249481,
0.05123808607459068,
-0.011112287640571594,
-0.013265830464661121,
0.008285708725452423,
-0.014921839348971844,
0.019797326996922493,
-0.012581788003444672,
0.101530060172081,
0.0258957426995039,
0.00023068769951350987,
0.017910439521074295,
0.04080548882484436,
0.018261604011058807,
-0.05070514231920242,
-0.004970161244273186,
-0.02821623906493187,
-0.06295958906412125,
0.0031074993312358856,
0.053758054971694946,
0.01669393666088581,
-0.031232185661792755,
0.030501728877425194,
-0.024939540773630142,
0.04019792005419731,
0.044076234102249146,
0.027575276792049408,
-0.039017558097839355,
-0.04754873737692833,
0.0008058308740146458,
0.003949945792555809,
-0.017185403034090996,
0.016363458707928658,
0.02623390033841133,
0.03412098437547684,
-0.00955046433955431,
0.020731467753648758,
-0.025555551052093506,
0.06514099985361099,
-0.043379027396440506,
0.00483444519340992,
0.0061025237664580345,
-0.045670635998249054,
0.015520414337515831,
-0.03547856584191322,
0.013304629363119602,
-0.020852044224739075,
-0.0275430791079998,
-0.01215820387005806,
-0.0073370314203202724,
-0.024344297125935555,
0.007010843139141798,
-0.004953947849571705,
-0.009942297823727131,
-0.009903568774461746,
0.029648231342434883,
-0.052462026476860046,
-0.009922710247337818,
-0.001410654396750033,
0.0026346591766923666,
-0.025730207562446594,
-0.014298693276941776,
0.011608566157519817,
-0.012403149157762527,
0.04721590504050255,
-0.008559360168874264,
-0.02768530882894993,
0.005607894156128168,
-0.03939756751060486,
-0.004797369707375765,
0.012160136364400387,
-0.048820581287145615,
0.015183706767857075,
-0.006083558313548565,
0.005727657116949558,
0.05288112536072731,
-0.016124362125992775,
0.03762110695242882,
0.02763255126774311,
-0.00042863821727223694,
-0.07633332163095474,
-0.016744399443268776,
-0.017558759078383446,
0.02733018435537815,
0.04444590583443642,
-0.0008754547452554107,
0.03577151522040367,
0.004033199045807123,
-0.015540936961770058,
0.020947987213730812,
0.00192583620082587,
-0.0165171567350626,
0.0026217284612357616,
0.003391010221093893,
0.03178977593779564,
-0.01174046378582716,
-0.002411254681646824,
0.010962478816509247,
-0.09698090702295303,
0.004795500077307224,
-0.04790779575705528,
-0.05471042916178703,
0.024324355646967888,
-0.01713412068784237,
0.03079207055270672,
-0.01873835362493992,
-0.03296474739909172,
0.059886619448661804,
0.011534885503351688,
-0.04085313528776169,
-0.034606315195560455,
-0.04503214359283447,
-0.023959174752235413,
-0.029545441269874573,
0.025409486144781113,
0.08417373895645142,
-0.005221252795308828,
0.04384955018758774,
0.010439962148666382,
-0.0017350036650896072,
0.017551252618432045,
0.02854551188647747,
-0.06901533156633377,
0.023696333169937134,
-0.04673938453197479,
-0.014902041293680668,
0.024040454998612404,
-0.002915123011916876,
-0.03076787479221821,
0.04507497698068619,
0.00321730924770236,
0.03263026848435402,
0.00433716457337141,
0.014300924725830555,
0.039204709231853485,
-0.019597405567765236,
0.011425156146287918,
-0.04811714589595795,
0.059708185493946075,
-0.037576958537101746,
0.013461821712553501,
0.007005013059824705,
0.012108218856155872,
0.019306495785713196,
-0.028544850647449493,
0.016476837918162346,
0.026056967675685883,
0.02956346794962883,
-0.005992332473397255,
-0.02527422457933426,
-0.00110026600304991,
0.018281403928995132,
-0.014438125304877758,
-0.026345551013946533,
-0.012323612347245216,
0.03248130902647972,
0.03223222866654396,
0.017422931268811226,
0.0005642729229293764,
0.004538508132100105,
-0.011454151943325996,
-0.03124908357858658,
0.005841521080583334,
-0.01881561055779457,
0.02252664603292942,
0.010645187459886074,
0.030070675536990166,
0.028571132570505142,
-0.02644118294119835,
0.012786702252924442,
-0.0001711822405923158,
-0.052786048501729965,
0.017296332865953445,
-0.03807655721902847,
0.015163510106503963,
-0.017664356157183647,
-0.0016364483162760735,
0.0012085746275261045,
0.0025130282156169415,
-0.011137533001601696,
-0.036568157374858856,
-0.04570084437727928,
-0.05467885360121727,
0.0044777411967515945,
-0.027297187596559525,
0.00818774476647377,
-0.029490405693650246,
0.020391952246427536,
0.0158523116260767,
-0.010859298519790173,
-0.015765808522701263,
-0.0032354455906897783,
-0.02616449072957039,
0.018225373700261116,
-0.009437745437026024,
-0.005384383723139763,
0.007330059073865414,
0.03927268087863922,
0.01295129768550396,
-0.027485357597470284,
-0.018511058762669563,
0.02055862918496132,
-0.010109511204063892,
0.03159238025546074,
0.03642639145255089,
0.02166372537612915,
-0.03460180386900902,
-0.06573448330163956,
0.016407661139965057,
-0.03645795211195946,
0.04018980264663696,
-0.008571308106184006,
0.027821647003293037,
0.041954442858695984,
0.006816957611590624,
-0.04136674478650093,
0.018292242661118507,
0.055570632219314575,
0.002882912289351225,
-0.014417117461562157,
-0.05926768109202385,
-0.018362857401371002,
-0.023573732003569603,
0.011821080930531025,
0.032911624759435654,
-0.03893024101853371,
-0.028015250340104103,
0.013490612618625164,
0.03586293011903763,
-0.01544912438839674,
-0.026457196101546288,
-0.025279445573687553,
0.01701327972114086,
0.004736765753477812,
0.001336562680080533,
0.004172417335212231,
-0.0017646686173975468,
0.016799980774521828,
0.08315666764974594,
0.009342056699097157,
-0.04472111910581589,
-0.08401955664157867,
-0.0016721399733796716,
0.04322446510195732,
0.0404888391494751,
0.024066966027021408,
0.01352998148649931,
-0.04240290820598602,
-0.0015258843777701259,
0.04754580184817314,
-0.0531700998544693,
0.02465066686272621,
-0.015674764290452003,
-0.012960905209183693,
-0.03197900205850601,
-0.004485161975026131,
-0.02505584992468357,
0.02627650275826454,
-0.006960221566259861,
0.03358098864555359,
-0.012749038636684418,
-0.004040637984871864,
0.0057855164632201195,
0.031071379780769348,
0.03580041229724884,
0.045587606728076935,
0.04422539472579956,
-0.014851444400846958,
0.012315771542489529,
0.010276047512888908,
-0.03521357476711273,
-0.0603661946952343,
-0.008804313838481903,
0.022826673462986946,
-0.03384954482316971,
0.059556085616350174,
-0.03102520853281021,
-0.025571398437023163,
-0.00011758286564145237,
0.0059334575198590755,
-0.0034153852611780167,
-0.01507924497127533,
-0.029436144977808,
0.05270791053771973,
0.027718346565961838,
0.01229641493409872,
0.0664423257112503,
-0.004800043068826199,
-0.02939317375421524,
-0.0018811492482200265,
-0.015509660355746746,
0.058408793061971664,
-0.012264447286725044,
0.0027481429278850555,
0.009141967631876469,
0.007289694156497717,
-0.020545469596982002,
0.06726397573947906,
-0.02416394278407097,
-0.008946752175688744,
-0.01752830296754837,
-0.009658793918788433,
-0.04965374618768692,
0.010538579896092415,
-0.004454322624951601,
-0.03609457612037659,
0.004186051897704601,
0.023962823674082756,
0.0041834344156086445,
-0.013294525444507599,
0.04685119539499283,
-0.018453489989042282,
0.03705344349145889,
0.03711608797311783,
-0.04395637661218643,
-0.024357305839657784,
-0.026509534567594528,
-0.03577936068177223,
0.00883442722260952,
-0.03599100187420845,
0.0415986105799675,
-0.04605649784207344,
-0.034741852432489395,
0.03044898808002472,
-0.07645907253026962,
-0.048523809760808945,
0.009850946255028248,
-0.03164766728878021,
0.06229938939213753,
-0.01614890620112419,
0.0351821593940258,
-0.01391509734094143,
0.01610066555440426,
-0.05633816868066788,
-0.055886659771203995,
0.02986251935362816,
0.015315000899136066,
0.020915275439620018,
0.006524842698127031,
0.017318950966000557,
-0.014661505818367004,
-0.03551642596721649,
-0.001720583881251514,
0.02968178503215313,
-0.037636835128068924,
0.032044097781181335,
0.013576295226812363,
-0.017285123467445374,
0.035261332988739014,
0.01565960794687271,
-0.04089390113949776,
0.046687155961990356,
-0.04908590763807297,
-0.012932094745337963,
-0.034666746854782104,
0.03915416821837425,
-0.002577613340690732,
-0.030507365241646767,
-0.003861373057588935,
0.00798364169895649,
0.020272789523005486,
-0.013910279609262943,
-0.024805571883916855,
0.04384943097829819,
0.022225499153137207,
-0.010407183319330215,
-0.028580989688634872,
0.029198123142123222,
0.0069517707452178,
0.05451741814613342,
0.00964155700057745,
-0.02004260942339897,
-0.033969517797231674,
-0.036720696836709976,
0.045221906155347824,
0.04980362951755524,
0.004933575168251991,
0.01264553889632225,
0.05443837493658066,
-0.006026608869433403,
0.003950722049921751,
-0.004381765145808458,
-0.00036026776069775224,
0.023969609290361404,
-0.027706047520041466,
0.016064899042248726,
0.0038535178173333406,
0.02283124439418316,
-0.04580722004175186,
-0.03260662779211998,
-0.014956697821617126,
-0.0007268065819516778,
0.046028342097997665,
-0.019623611122369766,
0.01939779706299305,
0.01754070445895195,
-0.009387305937707424,
-0.036334000527858734,
-0.035795681178569794,
0.0010245183948427439,
0.03398030251264572,
-0.03044249303638935,
0.01749947853386402,
-0.008589094504714012,
0.025149742141366005,
0.021653231233358383,
0.03465664014220238,
-0.04091185703873634,
0.017354026436805725,
0.06569645553827286,
0.04978945106267929,
0.04745922610163689,
-0.016804104670882225,
-0.04909360036253929,
0.022002870216965675,
-0.05916373431682587,
0.010362669825553894,
0.01242087036371231,
-0.0008628860814496875,
0.06293428689241409,
-0.011202218011021614,
0.019267547875642776,
-0.010351876728236675,
0.0001491611183155328,
-0.011526470072567463,
-0.01030314713716507,
-0.01172366738319397,
-0.008609813638031483,
0.02159780077636242,
-0.013242632150650024,
0.011328327469527721,
-0.01815626583993435,
-0.03350270166993141,
0.01789136230945587,
-0.0902935042977333,
-0.04272687807679176,
-0.02887345664203167,
-0.06003918871283531,
0.06893527507781982,
0.023972030729055405,
-0.04405314475297928,
0.029848672449588776,
-0.028030985966324806,
0.02701861597597599,
-0.004065998364239931,
0.016262389719486237,
-0.017792288213968277,
0.05037304013967514,
-0.011558814905583858,
-0.015553883276879787,
-0.017629455775022507,
0.010044436901807785,
0.09231046587228775,
0.05357955023646355,
-0.00016240417608059943,
-0.09929077327251434,
0.0284525528550148,
-0.05115397274494171,
-0.03197592496871948,
-0.03679382801055908,
0.01068093441426754,
-0.040542446076869965,
0.023513829335570335,
0.027165548875927925,
0.012488034553825855,
0.02614232338964939,
0.009479193948209286,
0.060024674981832504,
-0.012396753765642643,
-0.0377035066485405,
0.01383599266409874,
0.016532855108380318,
-0.01673063077032566,
0.010451331734657288,
-0.03874008730053902,
0.0199319738894701,
-0.0667291209101677,
-0.004046282265335321,
-0.01249197218567133,
-0.017772046849131584,
0.053426098078489304,
-0.0064140185713768005,
-0.013498270884156227,
-0.03831453248858452,
-0.024615172296762466,
0.023277632892131805,
-0.04492292180657387,
-0.0025295100640505552,
0.058828216046094894,
0.010737422853708267,
-0.02968442626297474,
0.020834624767303467,
0.02150155045092106,
-0.01820329762995243,
0.008342307060956955,
0.022944288328289986,
-0.025928514078259468,
-0.01195730734616518,
-0.009276586584746838,
0.03590526059269905,
0.00538978585973382,
0.03159943222999573,
0.00880581233650446,
0.035889748483896255,
-0.013044080697000027,
-0.024504108354449272,
-0.041386596858501434,
-0.004588719457387924,
0.03377121686935425,
0.0009637533221393824,
-0.004486194811761379,
-0.03769546374678612,
0.04092663526535034,
-0.021152961999177933,
0.05133672058582306,
-0.009283555671572685,
0.025677915662527084,
0.015354061499238014,
0.0024821837432682514,
0.004654612857848406,
0.000987563282251358,
-0.006769848056137562,
-0.03172529116272926,
-0.02963353879749775,
-0.017361588776111603,
0.02318865992128849,
0.024729494005441666,
0.007775944657623768,
-0.003645571880042553,
0.019805429503321648,
-0.027380792424082756,
-0.0010555018670856953,
-0.06315593421459198,
0.03184701129794121,
-0.03009682334959507,
-0.0006434140377677977,
-0.005408539902418852,
-0.014821289107203484,
0.04634873569011688,
0.027497999370098114,
-0.00641125813126564,
0.02799312397837639,
-0.028079701587557793,
-0.019957194104790688,
0.01736578531563282,
-0.02515069581568241,
-0.028928611427545547,
0.007138072978705168,
-0.03319922089576721,
0.006327280309051275,
-0.00899515487253666,
0.04412511736154556,
0.0016284049488604069,
-0.010172623209655285,
0.0027303630486130714,
0.026516377925872803,
-0.010116558521986008,
-0.021830180659890175,
0.021987244486808777,
-0.050037138164043427,
-0.0443047396838665,
-0.014754893258213997,
0.003922299016267061,
-0.03426113352179527,
-0.012230622582137585,
-0.02147582918405533,
-0.008717106655240059,
0.015010489150881767,
0.04656212404370308,
-0.004956012591719627,
-0.0048796795308589935,
0.029743893072009087,
0.018435509875416756,
-0.009702860377728939,
0.0071092513389885426,
-0.040132686495780945,
0.025208598002791405,
0.019423730671405792,
-0.02211945317685604,
0.0037666629068553448,
0.02799859642982483,
-0.02574908547103405,
-0.004280776716768742,
0.021199099719524384,
0.005276658106595278,
0.01038819644600153,
0.02951395884156227,
0.004300926346331835,
0.018709706142544746,
0.07951060682535172,
-0.010616498067975044,
-0.0227112527936697,
0.055129874497652054,
-0.07537927478551865,
-0.030458370223641396,
0.0072967796586453915,
-0.046619247645139694,
0.03255319595336914,
0.05357600376009941,
-0.007682235445827246,
-0.013897146098315716,
0.0404512844979763,
-0.011299011297523975,
-0.005234678741544485,
-0.0003005963226314634,
0.011083823628723621,
-0.015191566199064255,
0.010698940604925156,
0.0077236611396074295,
-0.0037822932936251163,
-0.023909607902169228,
0.016622120514512062,
0.03025222197175026,
0.017733527347445488,
-0.0017680368619039655,
0.001162064028903842,
-0.004426202736794949,
-0.022358432412147522,
-0.012769089080393314,
-0.025233985856175423,
0.04320827126502991,
0.029773958027362823,
-0.024273676797747612,
0.03149132430553436,
0.00751696340739727,
0.005160950589925051,
-0.1057458147406578,
-0.012318876571953297,
-0.007086551748216152,
-0.007631843909621239,
0.0437634103000164,
-0.03334994614124298,
-0.0026755165308713913,
0.026162294670939445,
-0.06876526027917862,
-0.0015396778471767902,
-0.024023374542593956,
-0.03598759323358536,
0.0042882999405264854,
0.021604452282190323,
-0.003594788257032633,
0.029684118926525116,
0.010613839142024517,
0.04075741022825241,
0.010129607282578945,
-0.013788622803986073,
-0.020953688770532608,
-0.010904808528721333,
-0.007138911634683609,
0.03955251723527908,
0.0062741003930568695,
-0.003197869285941124,
0.04929080232977867,
-0.0018007885664701462,
-0.02272423543035984,
0.029687296599149704,
-0.007900796830654144,
0.033115651458501816,
0.016113780438899994,
0.00617418996989727,
0.04060971736907959,
0.03680426999926567,
0.003940317314118147,
-0.016234371811151505,
0.014777883887290955,
0.013427547179162502,
0.018109921365976334,
0.041098956018686295,
0.0030230607371777296,
0.0073074777610599995,
0.013161852024495602,
-0.013301096856594086,
0.020993297919631004,
0.018016915768384933,
-0.022327862679958344,
-0.00372317829169333,
-0.02646634913980961,
0.02341550774872303,
0.02286478877067566,
-0.030606502667069435,
0.019467025995254517,
-0.04998592659831047,
-0.045897506177425385,
-0.00005857711948920041,
0.0019421471515670419,
0.0062371292151510715,
0.05166323482990265,
-0.013487149961292744,
-0.009307211264967918,
-0.0014358279295265675,
0.009907368570566177,
0.009348898194730282,
-0.035167522728443146,
0.04043815657496452,
0.010785441845655441,
0.01416043285280466,
0.02411395125091076,
-0.026567067950963974,
-0.03802807629108429,
0.021949440240859985,
0.013343502767384052,
0.025319883599877357,
0.003172819735482335,
-0.054347407072782516,
-0.004811951890587807,
-0.03039647825062275,
0.021616948768496513,
-0.036835696548223495,
-0.012251430191099644,
-0.05060422420501709,
-0.06096186488866806,
0.018455790355801582,
0.019206365570425987,
0.034816674888134,
-0.021125705912709236,
-0.023019375279545784,
0.0034510798286646605,
0.001118863932788372,
0.018705788999795914,
-0.05792979151010513,
0.009919690899550915,
0.014152409508824348,
-0.026912683621048927,
-0.012244079262018204,
-0.0013334351824596524,
0.006812207866460085,
0.005713514052331448,
-0.014424494467675686,
0.05207715928554535,
0.01613558642566204,
-0.00851692259311676,
-0.022749770432710648,
0.05104135721921921,
0.022194456309080124,
-0.028028862550854683,
0.025664838030934334,
-0.041762575507164,
0.014189038425683975,
-0.0035555867943912745,
0.008172973059117794,
-0.04447399452328682,
0.009601629339158535,
-0.005824018269777298,
0.02811002917587757,
0.007012166548520327,
0.002678581513464451,
0.0720231756567955,
-0.03748323768377304,
-0.019891556352376938,
0.059734880924224854,
-0.029627269133925438,
0.02144802361726761,
0.0654938668012619,
0.02011302299797535,
0.025879546999931335,
-0.002550482517108321,
0.020084142684936523,
-0.0032958087977021933,
0.005355242174118757,
-0.023803235962986946,
0.048557382076978683,
0.0018203260842710733,
-0.02030155062675476,
0.01072823815047741,
0.04362928867340088,
-0.025627821683883667,
0.006959560792893171,
0.023700589314103127,
0.023513667285442352,
-0.03920157998800278,
-0.047606129199266434,
0.010438448749482632,
0.0018513236427679658,
-0.0011746493401005864,
0.00873807817697525,
0.00013941795623395592,
0.10086312144994736,
-0.020241452381014824,
0.0030953465029597282,
-0.012434208765625954,
-0.0018736381316557527,
0.004586110357195139,
0.013462795875966549,
0.018509576097130775,
0.04789964109659195,
-0.0028630797751247883,
0.00007773162360535935,
-0.010066917166113853,
0.007009850814938545,
0.031152525916695595,
-0.04967336356639862,
0.023989520967006683,
-0.021388087421655655,
-0.001776865217834711,
-0.03860965371131897,
-0.020365305244922638,
-0.043471649289131165,
-0.036762725561857224,
0.02476702444255352,
0.0345865823328495,
0.03142862021923065,
-0.007520569488406181,
0.002192640909925103,
-0.030509956181049347,
0.017674565315246582,
-0.07915667444467545,
0.006288167554885149,
-0.03462480008602142,
0.05406773090362549,
-0.028907056897878647,
0.018417781218886375
] |
<p>Hi I'm trying to solve this textbook example but I don't know where to begin;</p>
<blockquote>
<p><em>NASA has decided to send an experimental probe to Mars. Its weight on earth is $40 kg_f$. When the probe is near the planet it will be
attracted by the its gravitational field ($g_{Mars} = 3.75\ m/s^2$). Determine the parachute’s diameter so that the probe will touch Mars’ surface with a velocity of $3 m/s$ (which is equivalent of dropping the probe from 0.5 m height on Earth). ($A_{chute} = π \frac{D^2}{4}, C_D = 1.4$, the density of Mars’ atmosphere is $\frac{2}{3}$ of Earth’s).</em></p>
<p><em>[$C_D$ is the drag coefficient of the parachute $C_D = 1.4$ (no dimensions, dimensionless number, or clear number,) and where $A$ is the projected area of the solid on a plane perpendicular to the body’s motion.]</em></p>
</blockquote>
<p>My knowledge of phyics is still at a beginner-intermediate level. I've been working on this problem for more than an hour and understand the concepts of drag coefficient, and force of a falling object.
What I don't understand, and couldn't find good resources for, is how to measure the speed of a falling object attached to a parachute (aka calculate the drag the parachute has on the fall), how to figure the density of Earth's atmosphere (isn't it different everywhere?) and how to figure out what the speed of the probe would be without a parachute. </p> | 2,033 | [
0.00548403849825263,
-0.0027449640911072493,
-0.03888268768787384,
0.013295714743435383,
0.036546770483255386,
-0.005727889947593212,
-0.001973856706172228,
-0.007607096806168556,
0.03736932948231697,
-0.00865534134209156,
0.01568739116191864,
0.039048582315444946,
0.05806490778923035,
0.0077860429883003235,
0.05869486182928085,
0.008789172396063805,
-0.03156290575861931,
-0.00978569034487009,
0.03250712901353836,
-0.005221281200647354,
0.016768397763371468,
0.004206424579024315,
0.033465348184108734,
-0.030555861070752144,
0.00025078572798520327,
0.0003003684105351567,
0.023369882255792618,
-0.039281681180000305,
0.0168773103505373,
0.04994210600852966,
-0.0022850781679153442,
0.003447943599894643,
0.02182399109005928,
-0.02191103622317314,
-0.011918745003640652,
0.008971166796982288,
-0.0680108368396759,
-0.002898524748161435,
0.021351788192987442,
0.0457560271024704,
-0.012765779159963131,
-0.02349219098687172,
-0.009874856099486351,
0.04478100314736366,
-0.0028322513680905104,
-0.0071595883928239346,
0.03660120815038681,
-0.047499075531959534,
0.04744754731655121,
-0.08096321672201157,
0.07355422526597977,
0.03618886321783066,
0.04645911231637001,
0.047866396605968475,
-0.002088647335767746,
-0.03709686920046806,
0.02253662422299385,
0.0749845802783966,
-0.018109597265720367,
-0.027091683819890022,
-0.030059827491641045,
-0.06130538508296013,
0.004370860289782286,
-0.005400158930569887,
-0.00533728301525116,
0.0340762585401535,
-0.050429780036211014,
0.005496132653206587,
-0.004563812166452408,
-0.009934583678841591,
0.053502295166254044,
-0.003218970261514187,
0.004784911405295134,
-0.00018840092525351793,
-0.007918796502053738,
0.0007327374769374728,
-0.0010064963717013597,
0.030502717941999435,
0.04045962914824486,
0.026198558509349823,
0.005560879595577717,
0.031120559200644493,
0.029495906084775925,
0.03730519115924835,
0.010709642432630062,
-0.0038728294894099236,
0.07631685584783554,
0.007897835224866867,
0.006864799652248621,
-0.004061123821884394,
-0.006329820491373539,
-0.04213545098900795,
-0.0052489968948066235,
-0.004161137621849775,
-0.021488908678293228,
0.01928580366075039,
-0.027827538549900055,
0.05881785973906517,
0.0031861423049122095,
-0.028463350608944893,
-0.030054504051804543,
-0.013386589474976063,
0.014602352865040302,
0.07796940207481384,
0.00030299072386696935,
-0.0027568840887397528,
-0.03186563774943352,
0.01302972249686718,
0.0008881234098225832,
-0.02208925224840641,
-0.01981363259255886,
0.013938898220658302,
-0.015326305292546749,
-0.012707596644759178,
0.011624110862612724,
-0.005532755050808191,
-0.012277116999030113,
-0.03215404972434044,
0.018811026588082314,
0.018353501334786415,
0.04098770022392273,
-0.028737805783748627,
0.02346491627395153,
-0.04064977541565895,
-0.036913882941007614,
0.04700003191828728,
0.035533513873815536,
-0.025634992867708206,
-0.004460971802473068,
0.015430397354066372,
0.008185276761651039,
-0.02917112410068512,
-0.03951282426714897,
0.0007713131490163505,
0.034158363938331604,
0.018064221367239952,
-0.09380929917097092,
-0.04756149277091026,
0.023312054574489594,
0.021129904314875603,
-0.005157043691724539,
-0.078316330909729,
-0.006206934805959463,
0.016155589371919632,
0.056698210537433624,
-0.0011767006944864988,
0.03420140594244003,
-0.004585818387567997,
0.024188615381717682,
-0.003699785564094782,
-0.026410428807139397,
-0.004250544589012861,
-0.025114409625530243,
-0.0533226877450943,
-0.024057524278759956,
-0.055572617799043655,
0.011660519056022167,
-0.00008230603998526931,
0.02594715729355812,
-0.06135951355099678,
0.028739746659994125,
-0.004105134401470423,
-0.009042063727974892,
0.022256430238485336,
0.004938399884849787,
0.002558337990194559,
0.06369738280773163,
0.021706346422433853,
-0.03380756080150604,
0.03840191662311554,
0.03047015331685543,
-0.008050677366554737,
-0.014099836349487305,
-0.010565091855823994,
0.04725465551018715,
-0.030981114134192467,
-0.013951490633189678,
-0.047418203204870224,
-0.021515121683478355,
-0.0005870966706424952,
-0.03387201204895973,
-0.042616695165634155,
0.015639502555131912,
0.021292921155691147,
0.009380301460623741,
0.03277749568223953,
0.04180826246738434,
-0.013080916367471218,
-0.01025503221899271,
-0.013189167715609074,
-0.0023337278980761766,
-0.047184061259031296,
0.0225653275847435,
-0.026692619547247887,
0.005433997139334679,
0.022585920989513397,
0.029229646548628807,
0.016002053394913673,
-0.02614547312259674,
-0.027178820222616196,
0.014894344843924046,
0.011958085000514984,
0.009252526797354221,
0.0001224141742568463,
-0.004500160925090313,
0.05001209303736687,
0.04038316756486893,
0.007799079176038504,
-0.01168526615947485,
0.015821391716599464,
-0.012506366707384586,
-0.02859555184841156,
-0.00564203504472971,
0.0120980404317379,
-0.0054929074831306934,
0.020302698016166687,
0.03667088598012924,
-0.004590969532728195,
0.026053937152028084,
0.024424564093351364,
-0.01406792737543583,
0.08888514339923859,
0.04658560827374458,
0.002563721500337124,
0.0031796135008335114,
0.00280464137904346,
0.008938878774642944,
0.007106294389814138,
-0.010452212765812874,
0.004455945920199156,
-0.039853569120168686,
-0.012846129015088081,
0.011045200750231743,
0.03662562370300293,
-0.03576274961233139,
0.003009951673448086,
0.06217311695218086,
0.003803110681474209,
0.06004954129457474,
0.02711927518248558,
0.011546347290277481,
-0.03748006373643875,
0.040791694074869156,
0.021848635748028755,
-0.02024209126830101,
0.00635812571272254,
-0.010828467085957527,
0.04225616157054901,
0.006323196459561586,
-0.00845419056713581,
-0.014401714317500591,
0.021207613870501518,
-0.0003964552888646722,
0.02847471833229065,
-0.004057169891893864,
0.013291177339851856,
0.05417259782552719,
-0.024244248867034912,
0.0007928648265078664,
0.049806345254182816,
0.010729042813181877,
0.017788708209991455,
-0.04554775729775429,
-0.030117075890302658,
0.0510808527469635,
0.03279266878962517,
-0.012476564384996891,
-0.005814519710838795,
0.03139998018741608,
-0.044553376734256744,
0.006229113787412643,
-0.013477903790771961,
0.018347514793276787,
-0.03205389156937599,
0.007012011017650366,
0.006556584034115076,
0.021584710106253624,
0.03244438022375107,
0.01446736790239811,
-0.034912727773189545,
-0.03249331936240196,
-0.020729899406433105,
0.0016031700652092695,
0.0323977991938591,
-0.04562388360500336,
0.03329851105809212,
-0.046397775411605835,
-0.030782917514443398,
0.04669024795293808,
0.022581797093153,
-0.022130681201815605,
0.004093346651643515,
-0.02309187687933445,
-0.014463764615356922,
0.004914507269859314,
0.0043960511684417725,
0.01261014025658369,
-0.028372302651405334,
0.02574547380208969,
0.04233657568693161,
-0.016683224588632584,
0.0062513709999620914,
0.06426119804382324,
-0.05670515075325966,
-0.028685610741376877,
-0.02060415968298912,
-0.0038042068481445312,
-0.0031323733273893595,
-0.04233667626976967,
0.023874884471297264,
0.004230420105159283,
0.002702435478568077,
-0.020001031458377838,
-0.04190963879227638,
-0.04087837040424347,
-0.005585587117820978,
0.006909709423780441,
0.06269095093011856,
-0.008015433326363564,
-0.054236188530921936,
0.07723305374383926,
0.0031141662038862705,
-0.0033664172515273094,
-0.03629857674241066,
0.004885595291852951,
-0.011469533666968346,
-0.054611291736364365,
0.0061763194389641285,
0.019733570516109467,
-0.016480524092912674,
-0.016631778329610825,
0.006612319964915514,
0.010555586777627468,
0.04376434162259102,
0.0170234814286232,
0.02903846465051174,
0.0045900894328951836,
0.03224419429898262,
-0.010360476560890675,
0.06804636120796204,
0.03988169878721237,
-0.0075627402402460575,
0.020183080807328224,
-0.04178677871823311,
0.042249903082847595,
0.007297731004655361,
-0.05652429908514023,
0.019929273054003716,
-0.04235246032476425,
-0.041847094893455505,
0.006972939241677523,
0.012133247219026089,
0.012753702700138092,
-0.025305036455392838,
0.02312926948070526,
0.032542161643505096,
0.03895959258079529,
-0.027945570647716522,
-0.022101817652583122,
0.06526962667703629,
0.03203767165541649,
-0.04969380795955658,
-0.04916994273662567,
0.012177934870123863,
-0.027905641123652458,
0.04431668296456337,
-0.010087361559271812,
0.007653732784092426,
0.01717771403491497,
0.013093587942421436,
0.041082900017499924,
-0.02724645845592022,
-0.04010840132832527,
0.026576662436127663,
-0.0330648198723793,
-0.014927498996257782,
0.01932390220463276,
0.044046517461538315,
0.0072138081304728985,
0.053173553198575974,
0.03304558992385864,
0.03888208419084549,
0.03367217630147934,
0.019734103232622147,
-0.0795111358165741,
0.045043401420116425,
-0.01514215487986803,
-0.053426142781972885,
0.007928860373795033,
0.01273330394178629,
-0.0012603357899934053,
-0.01978081464767456,
-0.0018442529253661633,
-0.001623292570002377,
0.012312402948737144,
-0.03694894537329674,
0.019404131919145584,
-0.0326070599257946,
-0.013149617239832878,
-0.0017438859213143587,
0.07059571146965027,
0.03148422762751579,
0.000597102043684572,
0.0056786444038152695,
0.058657508343458176,
-0.007379463408142328,
-0.04976709559559822,
-0.018948260694742203,
-0.04096995294094086,
-0.011894439347088337,
0.03119535744190216,
0.04182681068778038,
0.008059765212237835,
-0.02968641370534897,
0.027930114418268204,
0.012382625602185726,
0.057329364120960236,
-0.06190088763833046,
-0.005914866924285889,
-0.028522411361336708,
-0.05629147216677666,
0.0025638386141508818,
-0.010216183960437775,
0.01449285913258791,
-0.02804308570921421,
0.028201401233673096,
0.028093872591853142,
0.017676718533039093,
0.0035490673035383224,
0.05602779611945152,
0.05215110629796982,
-0.020634062588214874,
0.00832635723054409,
-0.028762085363268852,
-0.010659859515726566,
-0.04924881085753441,
-0.019982272759079933,
0.03451162204146385,
0.057889483869075775,
-0.02622990310192108,
-0.010351469740271568,
0.053158845752477646,
-0.009619774296879768,
0.005044105928391218,
0.007717707194387913,
-0.007885633036494255,
0.008205405436456203,
-0.04773521050810814,
-0.04770887270569801,
-0.01886281557381153,
0.03657970204949379,
0.031165631487965584,
-0.014970732852816582,
0.012591585516929626,
-0.0853496640920639,
-0.03106403909623623,
-0.0004730175423901528,
0.05307401344180107,
-0.039628226310014725,
0.0012563570635393262,
-0.03501906991004944,
-0.0314895324409008,
0.04291698336601257,
-0.040567122399806976,
0.038344625383615494,
-0.011775804683566093,
0.042637426406145096,
-0.018731385469436646,
0.01895737648010254,
-0.039531368762254715,
0.01456963550299406,
-0.012359247542917728,
0.00318617164157331,
-0.020200461149215698,
-0.02692762017250061,
-0.0019853883422911167,
-0.0023894452024251223,
0.05873626098036766,
0.06689080595970154,
0.029545798897743225,
-0.00516971992328763,
0.009964516386389732,
-0.02668369933962822,
-0.0597718171775341,
-0.04204947128891945,
-0.020209727808833122,
-0.022353684529662132,
-0.02062675543129444,
0.002419881522655487,
-0.033743396401405334,
-0.053263381123542786,
0.030811676755547523,
0.01876985654234886,
-0.01881532371044159,
-0.0029650337528437376,
-0.02908310852944851,
0.024927370250225067,
0.049102284014225006,
-0.015730097889900208,
0.04048044979572296,
0.017540844157338142,
-0.01387679111212492,
0.030530467629432678,
-0.023809542879462242,
-0.006970141548663378,
-0.011441312730312347,
-0.013877378776669502,
-0.018611954525113106,
0.01572304032742977,
-0.03381069377064705,
0.03581031784415245,
0.0027036957908421755,
0.0313076488673687,
-0.006571178790181875,
-0.04090188816189766,
0.013090994209051132,
0.007244262844324112,
-0.01081646978855133,
0.017068587243556976,
0.011062790639698505,
0.007549918256700039,
-0.0022622926626354456,
-0.029077958315610886,
-0.02220452018082142,
0.037491027265787125,
-0.01180428545922041,
-0.019205791875720024,
-0.007504096254706383,
0.009269739501178265,
-0.03362894058227539,
-0.038406651467084885,
-0.00968056172132492,
-0.0668952539563179,
0.06884238868951797,
-0.016026025637984276,
-0.001739592058584094,
0.007475541904568672,
-0.034480880945920944,
-0.03000316396355629,
0.01589612476527691,
0.019767049700021744,
0.03722661733627319,
-0.06164078786969185,
-0.009196613915264606,
-0.023244276642799377,
0.04087161645293236,
-0.03958998620510101,
0.0036185963544994593,
0.018208513036370277,
0.006681586615741253,
-0.016961239278316498,
-0.03324674442410469,
-0.020316191017627716,
-0.025093993172049522,
-0.07078646123409271,
0.017828242853283882,
0.06303125619888306,
-0.032315943390131,
0.0027702506631612778,
0.017986107617616653,
0.026235835626721382,
0.04714410379528999,
-0.03574417158961296,
0.006877588573843241,
-0.028784336522221565,
0.015028121881186962,
-0.025686446577310562,
-0.030324546620249748,
0.04043719545006752,
-0.03927890583872795,
-0.020637866109609604,
-0.01303504966199398,
-0.0440659336745739,
-0.0016090081771835685,
-0.04440693557262421,
-0.005335174035280943,
0.019515782594680786,
0.017890620976686478,
-0.031060190871357918,
-0.020685354247689247,
0.006695285905152559,
-0.0020245746709406376,
0.02188776433467865,
-0.04078906401991844,
0.018376033753156662,
-0.03651172295212746,
-0.03185223042964935,
0.028021348640322685,
-0.03198520094156265,
0.03032606840133667,
-0.0008814124739728868,
0.09305469691753387,
-0.007884116843342781,
-0.007969378493726254,
0.03922819718718529,
0.0038815864827483892,
0.02394110895693302,
0.01476591918617487,
-0.009536515921354294,
0.034619465470314026,
-0.014552702195942402,
-0.014693092554807663,
-0.02735259011387825,
-0.03808179870247841,
-0.023584919050335884,
0.068178191781044,
-0.039929065853357315,
0.05363985523581505,
0.030624067410826683,
0.012462368234992027,
0.008753915317356586,
0.010491754859685898,
-0.0284646674990654,
0.010815580375492573,
0.01995253562927246,
0.05369897186756134,
0.012590321712195873,
-0.03154629096388817,
0.041865576058626175,
-0.009892718866467476,
-0.026400288566946983,
0.03509772568941116,
0.029353052377700806,
0.01205422356724739,
0.04055345430970192,
-0.023084038868546486,
0.010927560739219189,
0.024893300607800484,
0.008287903852760792,
0.03822515532374382,
-0.020517461001873016,
-0.01937888190150261,
0.03152893856167793,
0.025278691202402115,
0.011669391766190529,
-0.055849120020866394,
-0.034027308225631714,
-0.03570365160703659,
0.008159387856721878,
0.05577923730015755,
-0.017744112759828568,
0.017715949565172195,
-0.005139973014593124,
0.06450274586677551,
0.00482143322005868,
0.04562818631529808,
-0.01488004345446825,
-0.007610187400132418,
-0.0361279621720314,
-0.03328436240553856,
-0.015594029799103737,
0.023145675659179688,
0.01389140821993351,
-0.050162963569164276,
0.009786971844732761,
-0.008149378933012486,
0.008648836053907871,
-0.00320065813139081,
0.013794762082397938,
-0.025637464597821236,
0.08533946424722672,
-0.024054042994976044,
-0.019353870302438736,
-0.017475757747888565,
-0.005491747986525297,
0.09532996267080307,
0.07141873240470886,
0.023376841098070145,
-0.053100407123565674,
0.002446412341669202,
-0.003924524877220392,
0.025090018287301064,
-0.03627751022577286,
0.013047349639236927,
0.0010697393445298076,
0.013619457371532917,
0.020059853792190552,
0.01701994426548481,
-0.026133235543966293,
-0.00706134969368577,
0.03214956820011139,
-0.02401128038764,
-0.03105255775153637,
-0.022782592102885246,
0.00036859800457023084,
-0.05836281552910805,
0.015503455884754658,
-0.0003235523181501776,
0.02274228073656559,
-0.018594764173030853,
-0.0013174416963011026,
-0.03830913454294205,
-0.028959907591342926,
0.018980272114276886,
-0.05233924463391304,
-0.06655394285917282,
0.02894764021039009,
-0.0373290590941906,
-0.025011269375681877,
-0.030156278982758522,
0.03595586493611336,
-0.0063618989661335945,
-0.027190465480089188,
-0.022151071578264236,
0.036213282495737076,
-0.036872878670692444,
-0.0032413939479738474,
0.025779027491807938,
0.02282804436981678,
-0.033334121108055115,
-0.005879153031855822,
-0.02230503037571907,
0.06816799193620682,
-0.042735546827316284,
0.013435103930532932,
0.0023955884389579296,
-0.0003557203453965485,
-0.02816164493560791,
-0.07301107794046402,
-0.01475959736853838,
-0.01305534690618515,
0.04162447527050972,
-0.04872572049498558,
0.0017916078213602304,
0.03201899304986,
0.0017090949695557356,
0.017452774569392204,
0.022834211587905884,
0.006720960605889559,
0.0316026397049427,
0.014254475012421608,
-0.03309701755642891,
0.0465596541762352,
-0.02504376880824566,
-0.015824446454644203,
-0.039648331701755524,
0.014190161600708961,
-0.02392939291894436,
0.003576518502086401,
0.022717686370015144,
0.03212021663784981,
-0.006742578931152821,
-0.0022990212310105562,
-0.007508126087486744,
-0.030901821330189705,
-0.019421527162194252,
0.04762210696935654,
-0.01374768652021885,
-0.008598119020462036,
-0.046981893479824066,
-0.03419770672917366,
0.030165521427989006,
0.05380292236804962,
-0.02909817546606064,
-0.017477940768003464,
-0.0077260262332856655,
0.021230783313512802,
0.020573273301124573,
-0.028479717671871185,
0.011532116681337357,
0.02495415322482586,
-0.03611064702272415,
0.011387007310986519,
0.01016968209296465,
0.01722552254796028,
0.04611481353640556,
0.021063514053821564,
-0.00672048470005393,
-0.0005950755439698696,
-0.06163439154624939,
0.06774318963289261,
0.03490886092185974,
-0.008004691451787949,
-0.03207886964082718,
0.03142641484737396,
0.007549690548330545,
-0.03779228404164314,
-0.008911922574043274,
-0.06384821981191635,
-0.022995876148343086,
-0.019079582765698433,
-0.011045563966035843,
-0.01205412670969963,
0.036219049245119095,
-0.020258892327547073,
0.015314324758946896,
-0.03735243156552315,
0.013835888355970383,
-0.061521414667367935,
0.006386277731508017,
0.014238455332815647,
-0.01674085669219494,
-0.028690626844763756,
0.006311470177024603,
-0.0509122759103775,
-0.0059368968941271305,
0.003296371316537261,
0.034962646663188934,
-0.011103048920631409,
-0.033255115151405334,
0.02202465943992138,
0.017156999558210373,
0.048273395746946335,
-0.01439776923507452,
-0.01724061369895935,
0.055887628346681595,
-0.06487275660037994,
-0.0681094154715538,
0.05508981645107269,
0.00823677983134985,
0.07849856466054916,
0.026198765262961388,
-0.016009395942091942,
-0.02521699294447899,
0.05418474227190018,
-0.015459774993360043,
0.018261542543768883,
-0.0354856438934803,
-0.04592517018318176,
-0.02625429444015026,
-0.024746812880039215,
0.039763789623975754,
-0.06083754822611809,
0.015841549262404442,
0.04359480366110802,
-0.011241595260798931,
-0.00031358120031654835,
0.03435692936182022,
0.04497252777218819,
-0.010104306973516941,
-0.012567385099828243,
0.018440209329128265,
0.015475844033062458,
0.031797926872968674,
0.07402857393026352,
-0.027054177597165108,
0.04112047702074051,
0.003299577860161662,
0.022780144587159157,
-0.11231234669685364,
0.0074782767333090305,
-0.0064866808243095875,
0.014093901962041855,
0.04060851037502289,
-0.09006460011005402,
-0.01455221138894558,
0.03805496171116829,
-0.020679453387856483,
-0.0012238448252901435,
-0.06618858128786087,
0.0026272088289260864,
-0.023127054795622826,
-0.017403190955519676,
0.03806978464126587,
0.022684838622808456,
-0.006818615831434727,
0.028699368238449097,
-0.005487403366714716,
0.014905319549143314,
-0.023947572335600853,
-0.015503903850913048,
0.02558175101876259,
0.03408777713775635,
-0.03343271464109421,
0.0005597255658358335,
0.06833039224147797,
0.012875313870608807,
0.015253967605531216,
0.034041572362184525,
0.0019154901383444667,
0.036259714514017105,
-0.006544345989823341,
-0.00368326879106462,
-0.01648259535431862,
0.01908678002655506,
0.017717299982905388,
0.0014035177882760763,
0.004851263482123613,
0.024622270837426186,
0.035884030163288116,
0.007661766372621059,
0.0010629297466948628,
0.0058888220228254795,
0.030216991901397705,
0.003854981157928705,
-0.015436883084475994,
0.024930017068982124,
-0.020538421347737312,
-0.008938001468777657,
0.034611206501722336,
-0.022997865453362465,
0.012857741676270962,
-0.04079772159457207,
0.012875988148152828,
-0.04832058772444725,
0.010235834866762161,
0.017851777374744415,
-0.01612953469157219,
-0.008919325657188892,
0.030862782150506973,
-0.04232030361890793,
-0.005571463145315647,
0.0044136312790215015,
-0.015240100212395191,
-0.009889056906104088,
-0.005716654006391764,
-0.00836943183094263,
-0.02343023754656315,
-0.006115424446761608,
0.016353914514183998,
-0.02531968615949154,
-0.015444964170455933,
0.02564573846757412,
0.03354352340102196,
-0.000849448493681848,
-0.023914137855172157,
0.012400949373841286,
0.012733757495880127,
-0.08371452242136002,
0.03134048730134964,
-0.006746827624738216,
-0.08015204221010208,
-0.019765013828873634,
0.005862177349627018,
-0.028470713645219803,
0.024976875633001328,
0.03048776276409626,
-0.03988920524716377,
0.0003761796106118709,
-0.0023712655529379845,
-0.005925900302827358,
-0.019000571221113205,
-0.07388495653867722,
-0.017901549115777016,
0.024561041966080666,
-0.02729414962232113,
0.0013265290763229132,
0.016889048740267754,
0.026541050523519516,
0.005552529823035002,
0.0031169161666184664,
0.05395034700632095,
0.056589510291814804,
-0.013286811299622059,
-0.03078318014740944,
0.015444730408489704,
0.027445631101727486,
0.003945447038859129,
0.06024625152349472,
0.01582544669508934,
0.005322309210896492,
0.0019498502369970083,
-0.02351277694106102,
-0.035795051604509354,
0.0644221305847168,
-0.005766277201473713,
-0.027760321274399757,
-0.027359018102288246,
-0.03960150480270386,
-0.02025316283106804,
-0.07846890389919281,
-0.024475600570440292,
0.03862766548991203,
-0.0368446484208107,
-0.005320106167346239,
0.022445781156420708,
0.06308877468109131,
0.04824666306376457,
-0.04476484656333923,
0.018165862187743187,
0.019273601472377777,
-0.020525671541690826,
-0.05050073564052582,
0.003222947707399726,
0.05265217274427414,
0.012920326553285122,
0.002862569410353899,
0.05062825605273247,
0.008638730272650719,
-0.018623080104589462,
0.029443206265568733,
-0.013934491202235222,
0.017134834080934525,
-0.021934067830443382,
-0.015614477917551994,
0.015304322354495525,
-0.008491778746247292,
0.010403658263385296,
-0.013417933136224747,
0.06959912925958633,
-0.019416457042098045,
0.0009627403924241662,
-0.0029211873188614845,
0.002160170115530491,
-0.03151645511388779,
0.024884801357984543,
-0.006442549172788858,
0.012403351254761219,
0.01098852138966322,
-0.02859528176486492,
0.0010983136016875505,
-0.00047742307651787996,
0.02871745266020298,
0.0300948154181242,
0.04864909499883652,
-0.005737774074077606,
0.004986338317394257,
-0.004791125655174255,
-0.05322860926389694,
-0.041087545454502106,
-0.04889317974448204,
0.04771585017442703,
0.0082773482427001,
0.0050836969166994095,
0.0025311221834272146,
-0.0009798977989703417,
0.006572631187736988,
0.0931711420416832,
-0.04310164228081703,
-0.05215684697031975,
0.006515693385154009,
0.0320005938410759,
0.01590746082365513,
0.008579268120229244
] |
<p>This was another question from my son's workbook. It said:</p>
<pre><code>Ever jumped into a pool on a warm day and still felt cold, even after measuring the
temperature of the water with a thermometer and finding that it is the same temperature as
the air? Would this be conduction, convection or radiation then?
</code></pre>
<p>Interesting question. When he asked me, I immediately thought of convection, as that is 'conduction' of fluids, right? But I wasn't too sure, and I asked some friends. Both conduction and convection came as answers.</p>
<p>Which one is it? Why?</p> | 2,034 | [
-0.03224264457821846,
-0.014957181178033352,
-0.007425593212246895,
0.01681627333164215,
0.02061956748366356,
0.01068941131234169,
-0.004784040153026581,
0.004294128157198429,
0.01381497923284769,
-0.021472616121172905,
0.06803939491510391,
0.023874271661043167,
0.015667203813791275,
0.019173139706254005,
0.06399789452552795,
0.027697324752807617,
0.012083286419510841,
0.01065132673829794,
0.037225205451250076,
0.002839059568941593,
-0.03446529433131218,
-0.016029678285121918,
-0.019252004101872444,
0.000555371108930558,
-0.054394710808992386,
0.03761342912912369,
0.0026071611791849136,
-0.012087268754839897,
-0.015790462493896484,
-0.0008340409258380532,
-0.03731762617826462,
-0.01976681686937809,
-0.0027678869664669037,
-0.04194915294647217,
0.0446128286421299,
0.006110892165452242,
-0.05175739899277687,
0.0015574860153719783,
-0.04531369358301163,
0.02545788511633873,
0.028024137020111084,
-0.03615117073059082,
0.002384308259934187,
0.014351541176438332,
-0.013947107829153538,
-0.021612683311104774,
0.03651529923081398,
-0.012941021472215652,
0.022136034443974495,
-0.05297694727778435,
0.023188279941678047,
-0.013705074787139893,
0.05242905765771866,
0.016812892630696297,
-0.018761046230793,
0.032470859587192535,
0.0688982903957367,
0.0380047932267189,
-0.013240735046565533,
-0.04517216607928276,
0.013510636053979397,
-0.0030850283801555634,
-0.03009733557701111,
-0.00417904881760478,
-0.03630683943629265,
-0.0016864354256540537,
0.0027885916642844677,
-0.04683557152748108,
0.014807283878326416,
-0.003985411487519741,
-0.009873258881270885,
-0.0004705814935732633,
0.02103407308459282,
-0.009473736397922039,
0.028162319213151932,
-0.015756970271468163,
0.011250775307416916,
0.020799344405531883,
0.04072751849889755,
0.01316794753074646,
-0.005356016103178263,
0.03978830575942993,
0.011104135774075985,
0.0038652948569506407,
-0.001423293142579496,
-0.02169603481888771,
0.06252217292785645,
-0.009111421182751656,
0.034771088510751724,
0.009542262181639671,
-0.00849905051290989,
-0.0070772552862763405,
-0.021919015794992447,
0.03067033179104328,
0.012937137857079506,
0.007671703118830919,
-0.005880378186702728,
0.03540879860520363,
0.03129609301686287,
-0.0570964440703392,
0.016980865970253944,
0.010301563888788223,
0.03145381063222885,
0.08486764878034592,
-0.014899475499987602,
-0.014654752798378468,
-0.048245348036289215,
-0.001276779337786138,
-0.029065538197755814,
-0.009745578281581402,
-0.03782791644334793,
0.0036923198495060205,
-0.009744305163621902,
0.005350351333618164,
0.02159804292023182,
-0.015480151399970055,
0.031775303184986115,
-0.0019059544429183006,
0.03359588608145714,
0.04375334084033966,
0.04419907182455063,
-0.041282862424850464,
0.04524046555161476,
0.0012197645846754313,
-0.044806018471717834,
0.007035211194306612,
0.0005889927269890904,
-0.0024472142104059458,
-0.025966951623558998,
0.04047657921910286,
-0.033123038709163666,
0.01490638218820095,
-0.013268725946545601,
0.004930260591208935,
0.007783893030136824,
-0.012523772194981575,
-0.06437800824642181,
-0.06779815256595612,
0.04109404981136322,
-0.0016860859468579292,
-0.05754614993929863,
-0.05928319692611694,
-0.0001389288663631305,
0.06356214731931686,
0.06528069078922272,
0.016937674954533577,
0.013681959360837936,
0.00868249125778675,
0.0332702212035656,
-0.002554243430495262,
-0.0006042408058419824,
-0.02802990935742855,
-0.010274481028318405,
-0.044887520372867584,
-0.00807253923267126,
-0.03177495673298836,
-0.007453705184161663,
0.04917106404900551,
-0.010793864727020264,
0.009999264031648636,
0.022411083802580833,
-0.030123403295874596,
-0.023392358794808388,
0.0252278633415699,
-0.000031290830520447344,
-0.03388068079948425,
0.06505206227302551,
0.029852064326405525,
0.02351974882185459,
0.03316161036491394,
0.029310084879398346,
0.01533233281224966,
-0.004466799087822437,
0.03177490085363388,
0.05690131336450577,
-0.0049030110239982605,
-0.030958229675889015,
0.00012261071242392063,
0.02027982473373413,
-0.005638172384351492,
-0.06309311836957932,
0.014098466373980045,
0.009656858630478382,
-0.00743924779817462,
0.0001075180625775829,
0.07751034200191498,
0.03224501013755798,
-0.014969347044825554,
0.03281720355153084,
-0.024401916190981865,
-0.014938916079699993,
-0.03645388036966324,
0.004156060982495546,
-0.02148350514471531,
0.005501185078173876,
-0.012718670070171356,
0.009788008406758308,
0.03530435264110565,
-0.007863368839025497,
-0.031945958733558655,
-0.0036644870415329933,
0.0005815648473799229,
0.010365752503275871,
-0.002113773487508297,
0.002476457506418228,
0.035257987678050995,
0.027606967836618423,
-0.016934575513005257,
-0.0011883004335686564,
-0.02880946919322014,
-0.006393903866410255,
-0.04439754784107208,
-0.02604863792657852,
0.014153577387332916,
-0.014687130227684975,
-0.022935936227440834,
0.006967061199247837,
0.0034028380177915096,
-0.018428966403007507,
0.021646693348884583,
-0.040343716740608215,
0.05751485377550125,
0.0017225603805854917,
0.009981761686503887,
0.001752659329213202,
0.02796788699924946,
-0.004286086652427912,
0.0070000323466956615,
0.01464475691318512,
-0.020618664100766182,
-0.055097922682762146,
-0.006587705109268427,
0.045767415314912796,
0.01108215656131506,
-0.029808515682816505,
-0.0022336826659739017,
0.03008810244500637,
0.055356863886117935,
0.013352811336517334,
0.009833195246756077,
-0.0015099674928933382,
-0.03675374761223793,
0.014428644441068172,
0.045543208718299866,
0.03876692056655884,
0.053768087178468704,
0.04747021198272705,
0.04150421544909477,
0.028234459459781647,
-0.027131211012601852,
-0.020371343940496445,
0.06394454836845398,
0.0005868334555998445,
0.03155327960848808,
-0.03354233503341675,
-0.044283486902713776,
0.01053000707179308,
-0.022852232679724693,
0.015311743132770061,
0.009172669611871243,
0.010775587521493435,
-0.022071467712521553,
-0.02680392563343048,
-0.0021572380792349577,
0.014402763918042183,
0.01478094607591629,
-0.02851075679063797,
-0.006704041268676519,
0.03081130050122738,
-0.050019990652799606,
0.015631679445505142,
-0.03816301003098488,
0.02078884281218052,
-0.048770494759082794,
-0.012516484595835209,
0.005475150886923075,
-0.0013622961705550551,
0.010078397579491138,
-0.046054329723119736,
-0.020757267251610756,
-0.010192329995334148,
-0.044857852160930634,
-0.01902828738093376,
-0.00077059306204319,
-0.0512164942920208,
-0.013095870614051819,
-0.0344739705324173,
-0.024409150704741478,
0.04982437565922737,
0.014334128238260746,
-0.03892024606466293,
0.025099482387304306,
-0.007490641437470913,
-0.00982517097145319,
-0.0006683446117676795,
-0.031338971108198166,
0.032280173152685165,
-0.039100077003240585,
0.009365107864141464,
0.08643682301044464,
-0.0740351602435112,
-0.04818223416805267,
0.013394131325185299,
-0.055102940648794174,
-0.06965146213769913,
-0.006485617719590664,
-0.03245314583182335,
0.02920287847518921,
0.0041030640713870525,
0.016975298523902893,
0.018863646313548088,
-0.008973355405032635,
0.013701054267585278,
-0.040962476283311844,
-0.024914927780628204,
0.028845462948083878,
-0.03696497902274132,
0.022173218429088593,
0.020432820543646812,
-0.04945220425724983,
-0.0024460761342197657,
-0.007273728493601084,
-0.009191786870360374,
-0.010209689848124981,
0.024626074358820915,
-0.0321611724793911,
-0.05453251302242279,
0.012662535533308983,
0.041382867842912674,
-0.0320604182779789,
-0.023104319348931313,
0.016544342041015625,
0.03406576067209244,
0.018413633108139038,
-0.01364089921116829,
0.020783722400665283,
0.000738090428058058,
0.025449508801102638,
-0.0005410856101661921,
0.039441581815481186,
-0.006492572370916605,
-0.019204195588827133,
0.015316289849579334,
-0.020144611597061157,
0.005672767758369446,
0.05726880207657814,
-0.006041269749403,
0.0478760302066803,
0.026624755933880806,
0.02409697137773037,
-0.06655682623386383,
0.03545413911342621,
-0.007449971046298742,
-0.010302851907908916,
-0.005569503176957369,
0.029821880161762238,
0.026404861360788345,
-0.016709113493561745,
0.004804257769137621,
0.04235949367284775,
0.04098886623978615,
-0.020789191126823425,
-0.018408751115202904,
0.011837156489491463,
0.003476895159110427,
0.014025645330548286,
-0.025207962840795517,
-0.0020452633034437895,
0.0891311764717102,
0.01473025232553482,
0.04892093688249588,
0.03390619158744812,
-0.03687199205160141,
-0.030744928866624832,
-0.03804931417107582,
-0.01647575944662094,
-0.013292263261973858,
0.06661097705364227,
-0.004047197289764881,
0.03800055384635925,
0.023830151185393333,
0.044778283685445786,
0.04999472573399544,
0.009294506162405014,
-0.09119148552417755,
0.029266640543937683,
-0.0318857803940773,
-0.005411766469478607,
-0.0360778272151947,
0.0007049311534501612,
-0.004082942847162485,
-0.05266645550727844,
-0.020081927999854088,
0.03576652333140373,
-0.04760264605283737,
-0.008564549498260021,
0.05752294138073921,
-0.013511489145457745,
-0.06376871466636658,
-0.03273123875260353,
-0.005509975366294384,
0.01731538586318493,
-0.009964427910745144,
0.05141550302505493,
0.04243571683764458,
0.019654911011457443,
-0.00005259650788502768,
-0.047791946679353714,
-0.00239985017105937,
0.02116083726286888,
0.016764704138040543,
-0.010250244289636612,
0.011340568773448467,
-0.035329654812812805,
-0.0017408669227734208,
0.021975912153720856,
-0.009019247256219387,
-0.004689608234912157,
-0.02823447994887829,
-0.04268670827150345,
-0.05050889402627945,
0.0020888755097985268,
0.012094663456082344,
-0.005686595570296049,
0.01022321917116642,
0.025151079520583153,
-0.01985948160290718,
0.00710677495226264,
-0.015531152486801147,
0.04537668451666832,
0.05256577953696251,
0.018495120108127594,
-0.025849752128124237,
-0.006090867333114147,
-0.02258886955678463,
-0.030512908473610878,
-0.006737211253494024,
0.048445217311382294,
0.024581944569945335,
-0.00598034868016839,
-0.02867649681866169,
0.012040823698043823,
-0.02403585985302925,
0.03100193478167057,
0.005589629523456097,
0.0016433221753686666,
0.01706724241375923,
-0.01987374573945999,
-0.01487843506038189,
0.01133823860436678,
0.05732819065451622,
0.05629897862672806,
0.011493364349007607,
-0.03749096393585205,
-0.09827249497175217,
0.008406792767345905,
0.04918011277914047,
0.053838010877370834,
-0.03398459777235985,
-0.01435414981096983,
-0.0640045553445816,
-0.016763269901275635,
0.03902386501431465,
-0.030554955825209618,
0.03933582082390785,
-0.017151828855276108,
0.018604857847094536,
-0.0015829498879611492,
-0.04626952111721039,
-0.017650360241532326,
0.036170441657304764,
0.011877814307808876,
0.04519382491707802,
-0.05943846330046654,
-0.022932274267077446,
0.011396008543670177,
-0.019598504528403282,
0.017798202112317085,
0.04264955595135689,
-0.033567287027835846,
0.0018966965144500136,
-0.019560331478714943,
-0.02513871341943741,
-0.03224283829331398,
-0.08958052098751068,
-0.036631859838962555,
0.038772400468587875,
-0.02890378050506115,
0.024993890896439552,
-0.021221676841378212,
-0.06067813187837601,
0.024483568966388702,
0.001180292689241469,
-0.025796685367822647,
-0.006551804486662149,
-0.07608353346586227,
0.05876957252621651,
0.022209424525499344,
0.03322392329573631,
0.04980028048157692,
0.014543190598487854,
-0.03084397502243519,
-0.05292851850390434,
-0.014690560288727283,
0.005140471737831831,
-0.030330630019307137,
-0.02847493812441826,
-0.01594764180481434,
-0.016926787793636322,
-0.04950353503227234,
0.05127234384417534,
0.020447125658392906,
0.01059782411903143,
-0.00990369450300932,
0.0022280814591795206,
-0.013477060943841934,
0.027021251618862152,
-0.01636377163231373,
-0.022570954635739326,
0.01608806662261486,
0.019338790327310562,
-0.028299108147621155,
-0.025667332112789154,
0.027012687176465988,
-0.007433807943016291,
0.020544296130537987,
0.06604217737913132,
-0.0019660559482872486,
0.052823495119810104,
-0.01674550026655197,
0.021094530820846558,
-0.012138781137764454,
-0.03462735190987587,
0.027937566861510277,
0.015700260177254677,
-0.00120968755800277,
0.03192119672894478,
-0.06768086552619934,
-0.014556445181369781,
0.03861331567168236,
0.030685968697071075,
-0.0030363427940756083,
-0.008319279178977013,
0.05583368241786957,
0.028864016756415367,
-0.021620983257889748,
-0.08955458551645279,
-0.0371667817234993,
0.026092225685715675,
0.041039030998945236,
-0.0233036857098341,
-0.05286931246519089,
-0.016501260921359062,
-0.03461494669318199,
-0.07051946967840195,
0.007361339405179024,
0.015292515978217125,
-0.018380042165517807,
-0.025269880890846252,
0.05652198940515518,
0.03231729194521904,
0.051735274493694305,
-0.02771703712642193,
-0.002406821819022298,
0.0005977177061140537,
-0.01230909489095211,
-0.025961831212043762,
0.016205741092562675,
0.065669484436512,
-0.027540165930986404,
-0.012632830999791622,
0.006393705494701862,
0.006283195223659277,
0.06688226014375687,
0.022431276738643646,
-0.018953094258904457,
0.025795847177505493,
0.010303331539034843,
-0.0452374592423439,
-0.03839287534356117,
0.03452916070818901,
-0.007950644940137863,
0.008983928710222244,
-0.02147858589887619,
0.014261740259826183,
-0.028291212394833565,
0.0038959351368248463,
0.009344685822725296,
-0.007120661903172731,
-0.006411164067685604,
0.004959907848387957,
0.05506559833884239,
-0.05146121606230736,
-0.00033940901630558074,
-0.0046005710028111935,
0.04406381770968437,
0.04177023097872734,
0.03568863496184349,
-0.03772509843111038,
-0.01538870483636856,
0.035156261175870895,
-0.028461879119277,
0.007706740405410528,
-0.02102050371468067,
0.006570328958332539,
0.06517910957336426,
-0.013584475964307785,
0.0738922506570816,
0.055355556309223175,
0.007828375324606895,
0.04321601986885071,
0.01584375463426113,
-0.015208659693598747,
0.03471683710813522,
-0.013226034119725227,
0.04454370215535164,
-0.039677783846855164,
0.0039044234436005354,
0.037925999611616135,
0.010814614593982697,
-0.003776181722059846,
0.0063832481391727924,
-0.009825579822063446,
-0.0006861523725092411,
-0.02233102358877659,
-0.024306759238243103,
-0.03248095512390137,
0.01486809179186821,
-0.03158240020275116,
0.054126057773828506,
0.007273574825376272,
-0.004661788698285818,
0.05593262240290642,
0.0051025403663516045,
-0.004691396374255419,
-0.051761869341135025,
0.022920530289411545,
-0.05609956756234169,
-0.010514686815440655,
0.0083040501922369,
0.031480275094509125,
-0.010664875619113445,
0.01297510415315628,
0.03130430355668068,
-0.014549130573868752,
0.0013609931338578463,
0.010316896252334118,
-0.03429805487394333,
0.012032059021294117,
0.005653660744428635,
0.0003329591709189117,
0.06280363351106644,
-0.008664281107485294,
-0.046183373779058456,
-0.012282655574381351,
-0.01476982794702053,
0.007368125021457672,
0.04136878624558449,
0.05163036659359932,
-0.03652917221188545,
0.02373303472995758,
-0.04157636687159538,
0.014530682004988194,
-0.027479499578475952,
0.004384333733469248,
0.12795107066631317,
0.06349156051874161,
0.001836969400756061,
-0.03391711786389351,
-0.015355202369391918,
-0.04619612544775009,
0.005529097747057676,
-0.015412340871989727,
0.0032767299562692642,
-0.022968895733356476,
0.04398173466324806,
0.02826455794274807,
0.06377533823251724,
0.016471778973937035,
0.0000285063488263404,
0.017178643494844437,
-0.03661003336310387,
-0.006590696983039379,
-0.02530699037015438,
0.0019520301138982177,
-0.026631126180291176,
0.035038094967603683,
-0.05606726184487343,
0.008096660487353802,
-0.007826688699424267,
0.0006608255207538605,
-0.05566811561584473,
-0.02848665416240692,
0.0406477116048336,
-0.01627703569829464,
-0.0575309619307518,
-0.008511453866958618,
0.00047430492122657597,
-0.025634516030550003,
-0.028969528153538704,
0.009363328106701374,
0.03527336195111275,
-0.013699192553758621,
0.01955161616206169,
0.031822510063648224,
0.04795517027378082,
-0.011060090735554695,
0.002410317538306117,
0.07149844616651535,
-0.03238048031926155,
-0.0031970266718417406,
-0.03500474989414215,
0.01351121161133051,
0.008777689188718796,
0.002426151419058442,
0.0029587114695459604,
0.018417010083794594,
-0.0011433357140049338,
-0.04232148453593254,
-0.011729616671800613,
0.008216405287384987,
0.0462217815220356,
-0.03166307508945465,
-0.03749878332018852,
-0.026029951870441437,
0.003329344093799591,
-0.007405356038361788,
0.0029680640436708927,
0.0005634513217955828,
0.02117343433201313,
0.020381154492497444,
0.007838383316993713,
0.0629110112786293,
-0.012058824300765991,
0.013253818266093731,
-0.031191887333989143,
-0.017939329147338867,
-0.013066663406789303,
-0.0027060103602707386,
0.01943117380142212,
0.021338650956749916,
0.02571217715740204,
0.023500002920627594,
-0.0030970924999564886,
-0.008481305092573166,
-0.027874257415533066,
0.012515585869550705,
0.031679049134254456,
0.035820987075567245,
-0.016577936708927155,
-0.01497660018503666,
-0.03817085921764374,
0.05091659352183342,
0.002946123480796814,
-0.009702141396701336,
0.03633364289999008,
0.027612822130322456,
0.02236899733543396,
-0.017231883481144905,
-0.010055214166641235,
-0.0076364148408174515,
-0.044521596282720566,
0.01878124289214611,
0.0020376951433718204,
0.06182720512151718,
0.009828614071011543,
0.03006035089492798,
-0.00009965224307961762,
-0.012062998488545418,
-0.05599498748779297,
0.02054431475698948,
0.03975672647356987,
0.023016899824142456,
-0.026520488783717155,
-0.010839822702109814,
-0.027547186240553856,
-0.004087250679731369,
-0.018338508903980255,
-0.043616607785224915,
0.006818385794758797,
-0.005961439106613398,
0.05798691511154175,
-0.024436816573143005,
0.03085051290690899,
-0.029590947553515434,
0.013009783811867237,
-0.03656032681465149,
-0.0003083041519857943,
-0.0704481303691864,
-0.012148392386734486,
0.02127234824001789,
-0.018012674525380135,
-0.02237016148865223,
0.021359283477067947,
-0.05536859482526779,
0.007670963648706675,
0.018811417743563652,
0.01264196913689375,
-0.011875715106725693,
-0.027147602289915085,
0.02207086980342865,
-0.04412974417209625,
0.05480176582932472,
-0.017938217148184776,
-0.0467088483273983,
0.07722920924425125,
-0.03837665542960167,
-0.02728072553873062,
0.037013087421655655,
0.0069797285832464695,
0.023842940106987953,
0.01856793463230133,
0.009031148627400398,
0.027852818369865417,
0.06793364882469177,
-0.014772804453969002,
-0.0038973663467913866,
-0.013164512813091278,
-0.0383165180683136,
0.02062612771987915,
-0.034148018807172775,
0.028587929904460907,
-0.010308468714356422,
-0.036101993173360825,
0.02301696501672268,
0.024158712476491928,
0.02066640555858612,
-0.008329944685101509,
-0.02787710353732109,
-0.014641343615949154,
-0.007322457153350115,
0.049452055245637894,
0.013059903867542744,
0.0040043736808001995,
0.03229808807373047,
-0.026568064466118813,
0.035221848636865616,
0.0028313621878623962,
0.01409557182341814,
-0.11000432819128036,
0.0038017232436686754,
0.024723289534449577,
0.019484560936689377,
-0.011496387422084808,
-0.05019163712859154,
-0.006666064262390137,
0.015563898719847202,
-0.06378122419118881,
0.0182652547955513,
-0.010952088050544262,
0.019006414338946342,
-0.025334827601909637,
0.01342384796589613,
-0.05286593362689018,
0.016116201877593994,
0.041605014353990555,
0.014799566008150578,
-0.03257756307721138,
0.022128354758024216,
-0.011999099515378475,
-0.00026149992481805384,
-0.03104822151362896,
0.028106186538934708,
-0.029618466272950172,
-0.0014395444886758924,
0.012063143774867058,
0.013197372667491436,
0.0019551904406398535,
-0.019387565553188324,
-0.04886781796813011,
-0.005530975293368101,
-0.0018958533182740211,
0.007304425351321697,
-0.024096159264445305,
-0.001392630860209465,
-0.00504743866622448,
-0.01477113738656044,
-0.02797236293554306,
0.021351514384150505,
0.05561167746782303,
0.04470138996839523,
-0.013554194942116737,
-0.0059958030469715595,
0.027243761345744133,
-0.041748594492673874,
-0.04069026559591293,
0.04069636017084122,
-0.018751954659819603,
0.026981258764863014,
0.010458382777869701,
0.004169277381151915,
0.027345411479473114,
0.025419676676392555,
-0.02983184903860092,
-0.050513483583927155,
-0.009714549407362938,
0.01011627446860075,
0.01304177101701498,
-0.0033318146597594023,
-0.005926094483584166,
-0.0004233139334246516,
0.0005836445488967001,
-0.01063087023794651,
-0.013830732554197311,
-0.019549228250980377,
-0.018179267644882202,
-0.031848691403865814,
0.01160084642469883,
0.02161298505961895,
-0.028013212606310844,
-0.029117809608578682,
-0.03108261525630951,
0.030988356098532677,
0.05189117044210434,
0.0012648944975808263,
0.014505315572023392,
-0.0335671603679657,
-0.021529221907258034,
-0.05700419098138809,
0.018165141344070435,
0.004492456093430519,
-0.01169445738196373,
-0.04722503945231438,
-0.0068979281932115555,
-0.047479357570409775,
0.05165804922580719,
0.09845399111509323,
-0.001721069449558854,
-0.003937021363526583,
0.006199404131621122,
0.0017561470158398151,
0.041338421404361725,
-0.08405513316392899,
-0.0008796307956799865,
0.0037867273204028606,
-0.036558642983436584,
0.03875564783811569,
0.011726349592208862,
-0.052353955805301666,
-0.016304239630699158,
0.02481911890208721,
-0.02815583162009716,
0.033489204943180084,
-0.023282289505004883,
-0.011552846990525723,
0.02071112021803856,
0.044024042785167694,
-0.008828285150229931,
0.04209331050515175,
-0.009719396010041237,
-0.026063337922096252,
0.04498525336384773,
-0.01081894151866436,
-0.005420172121375799,
0.04905392602086067,
-0.006917156279087067,
0.0206467118114233,
0.030184602364897728,
-0.030285146087408066,
0.03587011620402336,
-0.04630361124873161,
-0.007823663763701916,
0.028874071314930916,
-0.041646674275398254,
-0.051739875227212906,
0.04347037523984909,
0.02055794931948185,
0.022039745002985,
-0.021640537306666374,
0.009476473554968834,
0.00019859717576764524,
-0.009350699372589588,
-0.022139761596918106,
0.06235979497432709,
0.0500478632748127,
-0.031322646886110306,
-0.0030186024960130453,
0.04085807874798775,
0.011355239897966385,
0.024887477979063988,
0.002949228510260582,
0.010279916226863861,
-0.053873538970947266,
-0.014029862359166145,
0.03148961439728737,
0.02364177629351616,
-0.041907235980033875,
0.007650925777852535,
-0.0201976727694273,
0.07527180761098862,
-0.020154234021902084,
-0.0008723753271624446,
-0.04993733391165733,
-0.011033945716917515,
-0.019490238279104233,
0.03918905183672905,
0.03796525299549103,
0.05139372870326042,
-0.008242330513894558,
-0.015305986627936363,
-0.02130446955561638,
-0.012038935907185078,
0.03543427214026451,
-0.022970812395215034,
0.021558240056037903,
-0.03303217142820358,
0.016150975599884987,
-0.020673472434282303,
0.016867779195308685,
0.010729811154305935,
0.03666539117693901,
0.0473656952381134,
0.025848032906651497,
-0.0005932868807576597,
0.01908252201974392,
-0.018674449995160103,
-0.006840044632554054,
0.0655570849776268,
-0.06286068260669708,
-0.05051255226135254,
-0.012890913523733616,
0.06757815182209015,
0.003968548029661179,
-0.032280661165714264
] |
<p>Assuming that I calculated the electric field in a single point between a uniform charged positive sphere and an infinite long wire charged positive uniformly.
Now, I want to calculate the velocity of a given particle q+ which will be set free from the point (A) which I calculated the field at, while hitting the surface of the sphere.
It is very clear that the electric field will change at any point during the particle q movement, but can I still use the Line Integral of the electric field in point A to calculate the Voltage between point A and the surface of the sphere? or do I need to calculate individualy the potential of the wire and sphere and these 2 points?</p>
<p><img src="http://i.stack.imgur.com/ciIzD.gif" alt="enter image description here"></p> | 2,035 | [
0.00691378116607666,
0.008642038330435753,
-0.00439870310947299,
0.0010743474122136831,
0.02788020856678486,
-0.023793837055563927,
-0.031645268201828,
-0.03756537660956383,
0.0013209787430241704,
-0.013047883287072182,
0.04688470438122749,
0.024249210953712463,
0.07411216199398041,
0.03504634648561478,
0.024225007742643356,
-0.01383222732692957,
0.001325039193034172,
-0.02225053869187832,
-0.007506924215704203,
-0.038195207715034485,
-0.01530963834375143,
0.029972510412335396,
0.016016503795981407,
0.016918711364269257,
0.0009226419497281313,
0.02532750740647316,
0.04749247804284096,
-0.033419910818338394,
0.005610224325209856,
0.057501453906297684,
-0.0066119348630309105,
-0.029660414904356003,
0.045119334012269974,
0.03208433836698532,
0.03515787050127983,
0.02621188387274742,
-0.05469830334186554,
-0.04542160406708717,
-0.0020639796275645494,
-0.002452468266710639,
0.0055443476885557175,
0.011437637731432915,
-0.0023180777207016945,
0.08935419470071793,
-0.004241221584379673,
0.023425474762916565,
0.0018313172040507197,
-0.00885184295475483,
0.04456428438425064,
-0.06677135080099106,
0.01796991191804409,
0.0030431682243943214,
0.05801412835717201,
0.02406921423971653,
0.014591779559850693,
-0.030731506645679474,
0.05483100190758705,
0.06256434321403503,
0.003867129795253277,
-0.052172672003507614,
-0.00027920471620745957,
-0.02433277666568756,
-0.02858232706785202,
-0.039620209485292435,
-0.024041302502155304,
0.022721009328961372,
-0.0019458146998658776,
-0.03943518176674843,
0.008743339218199253,
-0.009255674667656422,
0.011564814485609531,
0.02519925870001316,
0.022501083090901375,
-0.009996563196182251,
0.041111674159765244,
-0.005200876854360104,
0.031726256012916565,
0.013402339071035385,
-0.00239916006103158,
0.03378752991557121,
-0.029326792806386948,
0.009559004567563534,
0.06905405223369598,
0.02264626882970333,
0.03156047686934471,
-0.031131304800510406,
0.019504476338624954,
-0.0032050451263785362,
0.00533867534250021,
0.01296076737344265,
-0.030708983540534973,
0.018671225756406784,
0.016400901600718498,
-0.007469422649592161,
-0.014248237013816833,
0.0004765480989590287,
0.005366020370274782,
0.02861546166241169,
0.008026234805583954,
-0.031550824642181396,
-0.0073712714947760105,
-0.03921641409397125,
0.025357799604535103,
0.08790458738803864,
0.002687083324417472,
-0.024006742984056473,
0.021144390106201172,
-0.018676957115530968,
-0.011527894996106625,
-0.025863515213131905,
-0.05041557550430298,
0.0161184910684824,
0.0198033656924963,
0.017460254952311516,
0.00942078884691,
-0.01669103093445301,
-0.01579703576862812,
-0.008998137898743153,
0.031510334461927414,
0.00864914059638977,
0.03889979049563408,
-0.06087920442223549,
0.007555943448096514,
-0.02331491932272911,
-0.02193957194685936,
0.03810865432024002,
0.004347901325672865,
0.02364118956029415,
-0.023189973086118698,
0.015081282705068588,
0.02577832154929638,
0.005666066892445087,
0.0012520222226157784,
0.02274065837264061,
0.030043095350265503,
-0.018572131171822548,
-0.08711913228034973,
-0.048381637781858444,
0.03699793294072151,
-0.015369564294815063,
0.028608093038201332,
-0.08398815244436264,
-0.035633720457553864,
0.03277026489377022,
0.07853447645902634,
-0.010527596808969975,
-0.0011792004806920886,
-0.017250725999474525,
0.04046899080276489,
-0.001148141804151237,
-0.01759576052427292,
-0.0032314967829734087,
-0.006918512284755707,
-0.03731817379593849,
0.03997248038649559,
-0.04732904210686684,
0.021575121209025383,
0.04261358454823494,
-0.0032150691840797663,
-0.01753409579396248,
0.07412537187337875,
-0.006868442986160517,
0.043639637529850006,
0.0005257298471406102,
0.0016990565927699208,
-0.007943407632410526,
0.04676373675465584,
-0.0032105259597301483,
-0.007033321540802717,
0.048938777297735214,
0.00029685118352063,
0.03183247521519661,
-0.0417681485414505,
0.005690897814929485,
0.06616315245628357,
-0.026350311934947968,
0.0023328254465013742,
-0.0508149191737175,
0.029390189796686172,
-0.014772750437259674,
-0.02790333889424801,
-0.04465233162045479,
-0.003377558197826147,
0.018681123852729797,
0.006400321144610643,
0.06743568927049637,
-0.008280019275844097,
0.01619347557425499,
-0.02463158778846264,
0.00843846332281828,
-0.039975881576538086,
-0.038486916571855545,
0.07080868631601334,
0.04007682204246521,
-0.039367083460092545,
0.01265076082199812,
0.0062956614419817924,
0.022275874391198158,
-0.048578422516584396,
0.002150499727576971,
-0.028175150975584984,
0.050059713423252106,
-0.018135424703359604,
-0.039480339735746384,
0.017110003158450127,
0.06733905524015427,
0.03369550034403801,
0.001885030185803771,
0.014879949390888214,
-0.054779160767793655,
0.019142042845487595,
-0.02764361910521984,
-0.01992696523666382,
0.04836217314004898,
0.0588594414293766,
-0.002811030950397253,
0.004953400697559118,
0.022974194958806038,
-0.005338979419320822,
0.037569135427474976,
-0.02883131243288517,
0.0744033232331276,
0.060602858662605286,
0.005034125410020351,
-0.03782567381858826,
0.029565120115876198,
0.0162312351167202,
-0.0020271034445613623,
0.019063880667090416,
-0.04041561111807823,
-0.04262078180909157,
0.004549071192741394,
0.03648391366004944,
0.02017657272517681,
-0.039510324597358704,
-0.037570513784885406,
0.036386094987392426,
0.008211697451770306,
0.022681789472699165,
0.04462536424398422,
-0.031062869355082512,
-0.036465127021074295,
0.027167825028300285,
0.029580486938357353,
-0.02602229081094265,
-0.010712025687098503,
0.03317585960030556,
0.014101503416895866,
0.04662912338972092,
-0.009975805878639221,
-0.02545863576233387,
0.014717966318130493,
-0.008572833612561226,
0.00802373606711626,
0.011676495894789696,
-0.013178304769098759,
0.019646430388092995,
-0.027345607057213783,
0.05552459508180618,
-0.008858920074999332,
0.00034141389187425375,
-0.0065681482665240765,
-0.024432804435491562,
-0.01739179901778698,
0.038379643112421036,
-0.0038710199296474457,
-0.006449914071708918,
-0.013318771496415138,
0.011811317875981331,
-0.014618774875998497,
0.011244169436395168,
0.00650920532643795,
-0.008502272889018059,
0.004894462879747152,
-0.004180575255304575,
-0.0061566149815917015,
0.0224520992487669,
0.024263428524136543,
-0.040517888963222504,
-0.03384412080049515,
-0.005152284633368254,
-0.03814932331442833,
-0.004239875357598066,
0.059531573206186295,
-0.042356256395578384,
-0.00029901674133725464,
-0.029828213155269623,
-0.044897690415382385,
0.050700195133686066,
-0.0016880815383046865,
0.0194111205637455,
0.04927017539739609,
0.0005813335883431137,
-0.07734304666519165,
0.022435320541262627,
-0.005888547748327255,
0.03802614286541939,
-0.018730195239186287,
-0.003438142128288746,
0.029847687110304832,
0.01077024731785059,
-0.043122656643390656,
0.008250992745161057,
-0.0718507170677185,
-0.04797418415546417,
-0.007077626883983612,
0.008918686769902706,
0.057870473712682724,
-0.01993277668952942,
0.008315106853842735,
0.011926387436687946,
-0.05536111071705818,
-0.027305906638503075,
-0.04428388550877571,
-0.055368032306432724,
0.00418942840769887,
-0.020112361758947372,
0.014845593832433224,
-0.03779539838433266,
-0.049456484615802765,
0.059440165758132935,
0.06254091113805771,
-0.05220413953065872,
-0.027529174461960793,
-0.03689999505877495,
-0.03011113964021206,
-0.011924528516829014,
-0.0014752703718841076,
0.005188445094972849,
-0.05276253819465637,
-0.00259660417214036,
0.015684891492128372,
0.019792145118117332,
0.02480016089975834,
0.020661843940615654,
0.02581874467432499,
-0.011171898804605007,
0.02233051136136055,
0.0016570836305618286,
0.05294937640428543,
0.000291052128886804,
-0.03384598717093468,
0.012089663185179234,
-0.020019598305225372,
0.04021163657307625,
0.035039741545915604,
-0.0018534762784838676,
0.022648843005299568,
-0.011162854731082916,
0.029650907963514328,
-0.02125750295817852,
0.029188863933086395,
0.012382806278765202,
0.0016597142675891519,
-0.00879226066172123,
-0.03353205323219299,
0.031759969890117645,
-0.007938549853861332,
-0.012700580060482025,
-0.014282380230724812,
0.03946229815483093,
-0.020522261038422585,
-0.05175340175628662,
0.00694740004837513,
0.0025213828776031733,
0.025674978271126747,
-0.046199820935726166,
-0.035629622638225555,
0.04752224683761597,
0.04999365657567978,
0.011010725982487202,
0.008263129740953445,
-0.03032875806093216,
-0.006117604207247496,
-0.060573022812604904,
0.01933433674275875,
0.023909689858555794,
0.049789588898420334,
0.027230361476540565,
0.061140380799770355,
-0.0005379901849664748,
0.01599164679646492,
0.0001364462950732559,
0.02182934805750847,
-0.08622897416353226,
0.03566479682922363,
-0.046680252999067307,
-0.044389527291059494,
-0.04417318478226662,
-0.04510917142033577,
-0.020895011723041534,
-0.02025153674185276,
-0.015276893973350525,
-0.010488657280802727,
-0.019011741504073143,
-0.04704384505748749,
-0.005171663127839565,
-0.035448912531137466,
-0.008421718142926693,
-0.06597620248794556,
0.055701691657304764,
0.008346873335540295,
-0.07535518705844879,
0.035221897065639496,
0.035164304077625275,
-0.04011385515332222,
-0.0075526731088757515,
-0.005352416075766087,
-0.0032166813034564257,
0.012251448817551136,
0.04873805120587349,
-0.022809728980064392,
0.043230198323726654,
-0.019066572189331055,
0.045821525156497955,
0.010084007866680622,
0.049834828823804855,
-0.003973419312387705,
-0.00967576913535595,
-0.04607498645782471,
-0.049295973032712936,
0.009589522145688534,
-0.023795895278453827,
0.07103852182626724,
-0.03395820036530495,
-0.007266124710440636,
0.05096927657723427,
-0.022921964526176453,
-0.007613756228238344,
0.01024756021797657,
0.06083311513066292,
0.02295858785510063,
0.007617216091603041,
-0.045053258538246155,
-0.003705557668581605,
-0.00735080661252141,
-0.018804941326379776,
0.023981716483831406,
-0.0012349053286015987,
-0.011138161644339561,
-0.0005646879435516894,
0.037268489599227905,
0.034702327102422714,
-0.008811406791210175,
0.00991816632449627,
0.008901482447981834,
0.00706075644120574,
-0.0021820387337356806,
-0.024768441915512085,
0.027847185730934143,
-0.006419910117983818,
0.03209588676691055,
0.016116490587592125,
-0.003531583584845066,
-0.0810384452342987,
-0.04433887451887131,
0.05168044567108154,
0.05780830606818199,
0.026983750984072685,
-0.0161574799567461,
-0.05899164080619812,
-0.0059740375727415085,
0.07780995965003967,
-0.01186350081115961,
0.017440786585211754,
0.007573856972157955,
-0.0023804435040801764,
-0.02106877975165844,
-0.060844484716653824,
-0.05850746110081673,
0.03588235378265381,
-0.010043433867394924,
0.038259368389844894,
-0.04934732988476753,
0.0068876068107783794,
0.017103638499975204,
0.034284401684999466,
0.017079152166843414,
0.06517892330884933,
0.015532318502664566,
0.01583808660507202,
0.013748903758823872,
-0.01301950216293335,
-0.013744798488914967,
-0.08131232857704163,
0.010193939320743084,
0.0062339529395103455,
0.024201134219765663,
0.04603252559900284,
-0.012880989350378513,
-0.018519733101129532,
0.036967694759368896,
-0.0017972388304769993,
0.027034981176257133,
-0.008745169267058372,
-0.03521357476711273,
0.039016492664813995,
0.023233605548739433,
0.002859456231817603,
0.04700377210974693,
0.020702887326478958,
-0.023093901574611664,
-0.025390226393938065,
-0.01680021360516548,
0.04424245283007622,
0.009638450108468533,
-0.04298757389187813,
0.005744116846472025,
0.012327422387897968,
-0.02291589044034481,
0.043773580342531204,
-0.008169603534042835,
0.0016683547291904688,
-0.04666316881775856,
0.007721183355897665,
-0.0052949534729123116,
0.019362064078450203,
0.01466809306293726,
0.019318649545311928,
-0.0396123081445694,
0.014388224110007286,
-0.0008182533783838153,
-0.03865045681595802,
-0.021622035652399063,
0.002439086325466633,
0.004501580726355314,
0.02465650998055935,
-0.0037214169278740883,
-0.006340899039059877,
0.023316342383623123,
-0.040315933525562286,
-0.011705278418958187,
-0.09281867742538452,
0.0612676776945591,
-0.01931576058268547,
-0.02829871140420437,
0.03249415382742882,
-0.08196164667606354,
-0.02627180702984333,
0.015012470073997974,
0.0051791006699204445,
0.00803331658244133,
-0.06925249099731445,
0.027809249237179756,
-0.004401387181133032,
0.04453205689787865,
-0.037632983177900314,
-0.05278230085968971,
-0.014136778190732002,
-0.006893062964081764,
0.0101169990375638,
-0.02730722352862358,
-0.006666084751486778,
-0.02418121136724949,
-0.012917225249111652,
-0.0009530165116302669,
0.030719328671693802,
-0.018558910116553307,
-0.0010166645515710115,
0.03824404254555702,
0.032156143337488174,
0.04024830460548401,
0.02931039035320282,
0.021387310698628426,
0.02090492844581604,
-0.029934529215097427,
-0.007134412415325642,
-0.008605074137449265,
0.06869392842054367,
-0.026158122345805168,
-0.035328999161720276,
-0.005137982312589884,
-0.02346429042518139,
0.02885211445391178,
-0.021139441058039665,
-0.03844546526670456,
0.025159655138850212,
0.02488182671368122,
-0.004554735962301493,
-0.008477342315018177,
0.0009509156225249171,
0.027422722429037094,
0.017906468361616135,
-0.0024493541568517685,
-0.0027619097381830215,
-0.029066018760204315,
-0.013309584930539131,
0.012215354479849339,
0.004457535687834024,
0.008196798153221607,
-0.005540370475500822,
0.042303793132305145,
-0.04757474362850189,
-0.024423327296972275,
0.01947651244699955,
0.007482658140361309,
0.011285624466836452,
-0.06511549651622772,
-0.03515373170375824,
0.003604964353144169,
-0.004721167962998152,
-0.030264945700764656,
-0.004868514370173216,
-0.04728551581501961,
-0.009197523817420006,
0.055326610803604126,
-0.012322680093348026,
0.007785028778016567,
0.03919963538646698,
0.0426081046462059,
-0.028924113139510155,
-0.027413615956902504,
-0.03606769070029259,
-0.004699795041233301,
-0.0034443670883774757,
0.002500695176422596,
-0.0077034300193190575,
0.006649656221270561,
0.02319931611418724,
0.03182302042841911,
-0.045937616378068924,
0.022104335948824883,
0.011386767029762268,
0.030694758519530296,
0.029683616012334824,
0.020059632137417793,
-0.03093370795249939,
-0.012606332078576088,
-0.04027416184544563,
0.05197842791676521,
-0.026235390454530716,
-0.019670289009809494,
0.07850410789251328,
0.031933993101119995,
-0.010946935042738914,
-0.026326855644583702,
0.0021078872960060835,
-0.0001688436750555411,
0.03758389502763748,
0.010203873738646507,
-0.008770134299993515,
-0.010068383999168873,
0.020155493170022964,
0.016549764201045036,
-0.0019627721048891544,
-0.0004575275524985045,
-0.029510848224163055,
-0.07855181396007538,
-0.032291095703840256,
-0.05910966172814369,
-0.05381305143237114,
0.06167939305305481,
-0.001932462677359581,
-0.02859189175069332,
0.012810612097382545,
-0.0172769483178854,
0.054479680955410004,
0.02490110509097576,
0.03900190070271492,
-0.038404908031225204,
0.0781700611114502,
-0.02793646790087223,
0.040787164121866226,
-0.04020339995622635,
0.01684669777750969,
0.1028912365436554,
0.019619295373558998,
-0.02327822707593441,
-0.05067167058587074,
-0.00035484612453728914,
-0.03698652610182762,
0.03772197663784027,
-0.04445679858326912,
-0.03685496374964714,
-0.05610309913754463,
-0.031858328729867935,
0.02831355854868889,
0.02178381197154522,
-0.012391156516969204,
-0.00815853662788868,
0.015371480025351048,
-0.02768811583518982,
-0.05107438191771507,
0.013882727362215519,
0.04585389420390129,
-0.023064740002155304,
0.05366654321551323,
-0.03221305087208748,
0.015091964043676853,
-0.04788067936897278,
-0.005899304058402777,
-0.04105457291007042,
-0.006310218013823032,
0.027452519163489342,
-0.005947019439190626,
-0.07172609865665436,
0.004444427322596312,
0.03839975968003273,
-0.014111720956861973,
-0.056588467210531235,
0.020699989050626755,
0.03288106620311737,
-0.014018897898495197,
0.008145937696099281,
0.027668870985507965,
0.016522040590643883,
0.009222473949193954,
0.021729886531829834,
0.00897538848221302,
-0.039656445384025574,
-0.019216516986489296,
-0.03621344268321991,
0.0476684644818306,
-0.012563485652208328,
0.020611170679330826,
0.004896863829344511,
0.017192112281918526,
0.03745700418949127,
-0.05081247538328171,
-0.03599498048424721,
-0.03939257934689522,
0.032310668379068375,
0.016362575814127922,
0.016087595373392105,
-0.012799881398677826,
0.019645582884550095,
0.013288095593452454,
-0.0043362719006836414,
0.017716027796268463,
-0.004353503230959177,
-0.0011531562777236104,
0.030284952372312546,
0.03510332480072975,
-0.026045093312859535,
-0.03149349242448807,
0.007795354351401329,
-0.01271506492048502,
-0.021600527688860893,
0.001672017271630466,
0.014652126468718052,
0.024476131424307823,
0.021801698952913284,
-0.02809581533074379,
-0.006921677850186825,
0.0008151348447427154,
-0.08521588891744614,
0.04003138467669487,
0.01970187947154045,
-0.012552987784147263,
-0.020819352939724922,
-0.004144963808357716,
0.04222197085618973,
0.04480137676000595,
-0.0051374551840126514,
-0.012392198666930199,
-0.010899788700044155,
0.03203583508729935,
0.027185847982764244,
-0.019150996580719948,
-0.023070422932505608,
-0.006157894618809223,
-0.03165483474731445,
0.017127135768532753,
-0.0447024405002594,
0.032688699662685394,
0.003491858020424843,
0.03179822862148285,
-0.027703063562512398,
0.04172656685113907,
-0.03441312536597252,
0.024039730429649353,
-0.010330033488571644,
0.017235230654478073,
-0.02735270746052265,
0.03868811950087547,
0.011012532748281956,
0.0021364595741033554,
0.006742051802575588,
-0.029488055035471916,
-0.013583801686763763,
0.009374257177114487,
-0.007922525517642498,
-0.05263214185833931,
0.002709170337766409,
-0.022484082728624344,
0.0254511795938015,
-0.026586191728711128,
0.03604191914200783,
-0.03304850310087204,
-0.011913608759641647,
0.00842223223298788,
0.010249120183289051,
-0.019985588267445564,
0.020268814638257027,
-0.040567442774772644,
-0.0008273223065771163,
0.03267031908035278,
0.0032006758265197277,
0.024725807830691338,
-0.004305073991417885,
0.008149756118655205,
-0.01193229015916586,
0.050312165170907974,
0.012697777710855007,
-0.03107878379523754,
0.0015404692385345697,
-0.016844626516103745,
-0.01976790651679039,
0.033674292266368866,
0.009283948689699173,
0.04099854454398155,
0.0528985857963562,
-0.020364362746477127,
-0.031722210347652435,
0.0586373470723629,
0.002062719315290451,
-0.017402976751327515,
0.0005220983875915408,
-0.0877063199877739,
-0.02026425115764141,
-0.027015021070837975,
0.023143237456679344,
0.01699957810342312,
0.007551704533398151,
0.005603638011962175,
0.007975710555911064,
-0.03155577927827835,
-0.003917553462088108,
0.028942802920937538,
0.0064386301673948765,
0.01840711198747158,
0.06713671237230301,
-0.008520275354385376,
0.05043599754571915,
0.07431821525096893,
-0.012708508409559727,
0.0027197368908673525,
0.006394145544618368,
-0.003178650513291359,
-0.07817412167787552,
-0.0006220675422810018,
-0.00032750971149653196,
0.021239403635263443,
0.03527136892080307,
-0.08114752918481827,
-0.008073505014181137,
0.06610880047082901,
-0.07731912285089493,
0.009134952910244465,
-0.01816045306622982,
-0.00037507255910895765,
-0.027968941256403923,
-0.005443227011710405,
0.013420913368463516,
0.028194792568683624,
0.03844472020864487,
0.029653377830982208,
0.031582269817590714,
0.001725563663057983,
-0.014963516034185886,
-0.04764965549111366,
-0.012821635231375694,
0.04684370756149292,
0.006047750357538462,
-0.03448573499917984,
0.03985454514622688,
-0.04036109521985054,
-0.02131875604391098,
-0.0036843051202595234,
-0.026622360572218895,
0.024182751774787903,
-0.0062923855148255825,
0.02200021781027317,
0.028759058564901352,
0.03715816140174866,
0.001889980398118496,
-0.0024760642554610968,
-0.011721543036401272,
0.010892767459154129,
0.017800062894821167,
-0.0014811033615842462,
-0.029717078432440758,
0.0038384271319955587,
0.007430332712829113,
-0.013306901790201664,
-0.03901088610291481,
0.049800727516412735,
-0.023677630349993706,
-0.0022129181306809187,
-0.026845604181289673,
0.016946803778409958,
0.027692988514900208,
-0.009083704091608524,
-0.03126177564263344,
-0.027112986892461777,
-0.0001495733595220372,
0.04279940947890282,
-0.014606981538236141,
0.01324665080755949,
-0.009778076782822609,
0.010894508101046085,
-0.04504043608903885,
0.030902791768312454,
-0.00451014144346118,
-0.016550879925489426,
-0.08176800608634949,
-0.020879780873656273,
0.022048037499189377,
-0.016912512481212616,
0.005463308189064264,
-0.004884712398052216,
-0.01550338789820671,
-0.029665561392903328,
0.015998410061001778,
0.025701310485601425,
0.01595565490424633,
-0.012938007712364197,
-0.010037182830274105,
-0.0495898574590683,
0.04518963769078255,
-0.004501789808273315,
-0.05068947747349739,
-0.01744716241955757,
-0.053731780499219894,
0.011154070496559143,
0.033419400453567505,
0.06990096718072891,
-0.03111841529607773,
0.01637313701212406,
0.0398525595664978,
-0.004620538558810949,
0.04066663980484009,
-0.048047181218862534,
-0.012936203740537167,
-0.00883792620152235,
0.005537804216146469,
0.032446619123220444,
0.01731439121067524,
-0.021814804524183273,
0.05025642365217209,
0.02779022604227066,
-0.005228155758231878,
0.0009850625647231936,
-0.001953204395249486,
-0.03362086042761803,
0.0017292093252763152,
0.026419293135404587,
-0.012501083314418793,
0.045372072607278824,
0.008486680686473846,
0.0009817396057769656,
-0.012843037955462933,
-0.024363119155168533,
0.0034698413219302893,
0.010717037133872509,
-0.05438017100095749,
-0.0056975772604346275,
-0.015441731549799442,
0.0020147557370364666,
0.007597107905894518,
-0.06993790715932846,
-0.0017367207910865545,
0.01712716557085514,
-0.031149618327617645,
-0.016183435916900635,
0.05778609216213226,
-0.011503933928906918,
0.016948143020272255,
0.02200804091989994,
0.018745427951216698,
0.014812163077294827,
-0.0073371222242712975,
-0.017428062856197357,
0.026078451424837112,
0.009648253209888935,
-0.01312018558382988,
0.015407105907797813,
0.05449531227350235,
0.04705449566245079,
-0.008216881193220615,
-0.009404291398823261,
0.008614670485258102,
-0.02613724395632744,
0.0013111282605677843,
0.006557533983141184,
-0.017398400232195854,
0.016457075253129005,
0.030538281425833702,
-0.02090095914900303,
0.08146179467439651,
-0.03985302150249481,
0.004536102991551161,
0.018754884600639343,
-0.010994362644851208,
-0.000575255777221173,
0.008748786523938179,
0.0018278893548995256,
0.03119678981602192,
-0.004899951163679361,
-0.04006153717637062,
0.006435150746256113,
-0.0062510548159480095,
0.018532635644078255,
-0.034985028207302094,
0.038830555975437164,
0.0167087335139513,
0.004406140185892582,
-0.03916209563612938,
-0.004034786485135555,
-0.01659139059484005,
0.012049558572471142,
0.007285562809556723,
0.05135070160031319,
0.02194260060787201,
0.0037652484606951475,
0.00356824672780931,
-0.03630634769797325,
0.041289377957582474,
-0.04833424091339111,
0.011564555577933788,
-0.024699795991182327,
0.015307696536183357,
0.020597847178578377,
0.02690572291612625
] |
<p>We typically say that forces cause acceleration inversely proportionate to mass. Would it be any less correct to say that acceleration causes forces proportionate to mass? Why?</p>
<p>(Note that the underlying question in my mind - essentially, what distinguishes cause from effect - is far more general. But this seems like a good place to start.)</p> | 2,036 | [
-0.026682227849960327,
0.00797917228192091,
-0.0189192034304142,
-0.009507831186056137,
0.01585478149354458,
0.0008300197659991682,
-0.010034562088549137,
0.00987972877919674,
0.0032993596978485584,
0.00818108394742012,
0.022489221766591072,
-0.019360393285751343,
0.06443747878074646,
-0.01745348796248436,
0.00029217597329989076,
0.03414229676127434,
-0.016364114359021187,
0.026641588658094406,
0.0065567041747272015,
-0.03644954040646553,
-0.015062359161674976,
0.0005289604887366295,
0.0033156471326947212,
0.009334047324955463,
-0.014115029945969582,
0.02089005708694458,
0.03655153140425682,
-0.0070562842302024364,
0.008659092709422112,
0.016799960285425186,
-0.0015023174928501248,
0.014023496769368649,
0.022507650777697563,
0.04133119061589241,
0.02064554952085018,
0.016268359497189522,
-0.016050269827246666,
0.008194202557206154,
0.005923580378293991,
0.03664544224739075,
-0.014834458939731121,
-0.01777815632522106,
0.0040742941200733185,
0.04324819892644882,
-0.021554529666900635,
0.012859447859227657,
0.0019396160496398807,
0.002989784348756075,
0.046216197311878204,
-0.0374872051179409,
0.08957388252019882,
-0.006233442109078169,
0.021085025742650032,
0.018491266295313835,
-0.005585553590208292,
-0.024656102061271667,
0.06897227466106415,
0.05193794518709183,
-0.020905552431941032,
-0.059034787118434906,
-0.021756978705525398,
-0.015218613669276237,
-0.04346287623047829,
-0.017667356878519058,
0.008990075439214706,
0.045492492616176605,
-0.018207402899861336,
-0.013443714939057827,
0.0367744043469429,
0.029478177428245544,
0.012568817473948002,
0.00890957098454237,
0.038516804575920105,
0.008150623179972172,
-0.02692517451941967,
-0.05420607328414917,
0.0393160916864872,
-0.009517308324575424,
0.01619526371359825,
0.03757832944393158,
-0.01463248673826456,
0.0033717353362590075,
0.047381285578012466,
0.04884995520114899,
0.025159386917948723,
-0.012899290770292282,
0.05665472522377968,
-0.025010641664266586,
0.0284395944327116,
0.030832355841994286,
-0.042552825063467026,
0.01239357702434063,
0.004842553287744522,
-0.010994579643011093,
0.019951779395341873,
0.037585314363241196,
-0.004684900399297476,
0.024833306670188904,
0.0411374606192112,
0.023855671286582947,
-0.024683592841029167,
-0.013728611171245575,
0.018229668959975243,
0.053932443261146545,
0.005508131813257933,
-0.002953293500468135,
-0.058246124535799026,
0.05729779228568077,
-0.04746082052588463,
-0.021440237760543823,
-0.03050869144499302,
0.031229568645358086,
-0.0055607957765460014,
0.00531241437420249,
0.015142163261771202,
-0.006895570084452629,
0.027705539017915726,
0.0032798643223941326,
0.07877224683761597,
0.05312230437994003,
0.03849848359823227,
-0.05196173116564751,
0.02313336357474327,
-0.009520494379103184,
-0.0240609310567379,
-0.00008554486703360453,
0.02275008335709572,
-0.0409005768597126,
0.008725850842893124,
0.054822005331516266,
0.010407835245132446,
-0.03103048726916313,
-0.026975780725479126,
-0.00183029321487993,
0.024913450703024864,
0.010966557078063488,
-0.09578566253185272,
-0.054353922605514526,
0.034979548305273056,
0.028859496116638184,
-0.0058002769947052,
-0.0658450797200203,
0.00393076753243804,
0.05735475569963455,
0.07773810625076294,
0.029387440532445908,
0.011541418731212616,
0.03297839313745499,
0.02920210361480713,
0.00804886594414711,
0.019150251522660255,
-0.03252628818154335,
-0.008562088012695312,
-0.04580096900463104,
-0.0007953703752718866,
-0.07129883021116257,
0.030442746356129646,
0.019096123054623604,
0.012602860108017921,
-0.002837018808349967,
0.03700481727719307,
-0.022066332399845123,
0.00007193623605417088,
0.035116784274578094,
0.02235475368797779,
-0.013088620267808437,
0.02661411091685295,
0.023235369473695755,
-0.014679957181215286,
0.05413467809557915,
0.036800943315029144,
0.025716012343764305,
0.03410074859857559,
0.012827872298657894,
0.039101358503103256,
-0.026582369580864906,
-0.02698563039302826,
-0.019682079553604126,
-0.013547493144869804,
-0.007419230416417122,
-0.02705681510269642,
-0.05126786604523659,
-0.03503769263625145,
-0.03027474693953991,
0.007521331310272217,
0.025706084445118904,
0.018546810373663902,
0.012022758834064007,
0.032331451773643494,
-0.0026477756910026073,
-0.011033185757696629,
-0.1103590801358223,
0.03753744065761566,
-0.0077333818189799786,
0.0073579465970396996,
0.03640348091721535,
0.004925729241222143,
-0.009462307207286358,
-0.02795921079814434,
0.03022831864655018,
0.032657135277986526,
-0.0013624749844893813,
0.005574310198426247,
-0.02987903170287609,
0.018525969237089157,
0.049976661801338196,
0.01908140815794468,
0.01127517968416214,
0.013692776672542095,
0.0018286375561729074,
-0.05044709891080856,
0.036808695644140244,
-0.02505739964544773,
0.006052973214536905,
-0.011827419511973858,
0.013978930190205574,
0.012427352368831635,
-0.03591277077794075,
-0.03740951418876648,
0.051258161664009094,
-0.060012876987457275,
0.11702343076467514,
0.037759941071271896,
0.003927615471184254,
0.008086948655545712,
0.05892513319849968,
0.03576338663697243,
0.0005118342232890427,
-0.006632887292653322,
-0.006075186654925346,
-0.04754340276122093,
-0.0018803421407938004,
0.02105896547436714,
0.04065103083848953,
-0.04984639957547188,
0.031659629195928574,
0.04050913825631142,
0.04831391200423241,
0.008993582800030708,
0.04888783395290375,
-0.013779021799564362,
-0.05556413531303406,
0.05337674543261528,
-0.008028638549149036,
0.029819956049323082,
0.005532342474907637,
0.03131914138793945,
0.02108086459338665,
-0.00371133117005229,
0.014350843615829945,
0.01605488918721676,
0.014262485317885876,
0.016416030004620552,
0.0333026647567749,
0.009709404781460762,
-0.03422541916370392,
0.023829054087400436,
0.006401621736586094,
0.026339927688241005,
0.012548990547657013,
-0.030849505215883255,
-0.01989462785422802,
-0.029081184417009354,
-0.0058668083511292934,
0.0036772130988538265,
-0.023514319211244583,
-0.04686534404754639,
-0.03951151296496391,
0.03136824071407318,
-0.0732087790966034,
0.005230121314525604,
-0.03655654191970825,
-0.03140223026275635,
-0.04085835441946983,
-0.010862590745091438,
0.016187142580747604,
0.008638929575681686,
0.047805752605199814,
-0.027570905163884163,
0.016169026494026184,
0.02293446473777294,
-0.04686364531517029,
0.006837892811745405,
0.023242011666297913,
-0.035449232906103134,
0.02450740337371826,
-0.05188685283064842,
-0.052106864750385284,
0.057676445692777634,
-0.015231452882289886,
-0.00012206893734401092,
0.03964630141854286,
0.024020858108997345,
-0.02065890282392502,
0.0007871828856877983,
-0.06423402577638626,
-0.01435078028589487,
-0.026218842715024948,
-0.015334125608205795,
0.05130518227815628,
-0.010433652438223362,
-0.032676421105861664,
0.0034399714786559343,
-0.028298620134592056,
-0.0044540707021951675,
-0.006901009473949671,
-0.0006812416249886155,
-0.006323898211121559,
-0.00801821704953909,
0.00901749636977911,
0.02892150543630123,
-0.04296122491359711,
-0.014908838085830212,
-0.046591464430093765,
-0.056479718536138535,
0.012585047632455826,
0.0036263945512473583,
0.08627943694591522,
0.024221746250987053,
-0.023807203397154808,
0.06896549463272095,
0.03776334971189499,
-0.004901720676571131,
-0.03310541436076164,
-0.04918192699551582,
0.014090466313064098,
-0.017785130068659782,
0.01916985958814621,
0.029101721942424774,
0.01834699884057045,
0.011606791988015175,
0.03676614165306091,
0.06478996574878693,
-0.023095186799764633,
-0.00043709788587875664,
-0.0029503542464226484,
0.00019549662829376757,
0.021442649886012077,
-0.02989487536251545,
-0.009691944345831871,
0.03549959510564804,
-0.014087832532823086,
0.011613233014941216,
0.006546620279550552,
0.03671901673078537,
-0.022036951035261154,
-0.05263836309313774,
0.018810493871569633,
-0.00352573418058455,
0.013150336220860481,
-0.05519607290625572,
0.03622494637966156,
-0.014238103292882442,
-0.0029587759636342525,
0.02664526179432869,
-0.009853161871433258,
0.020250830799341202,
-0.04315611720085144,
0.028573662042617798,
0.0442652590572834,
0.04864180460572243,
-0.02143133245408535,
-0.03681480139493942,
0.014582602307200432,
-0.009209224954247475,
0.020197613164782524,
-0.0180512685328722,
0.014966429211199284,
0.0294303297996521,
-0.004242210648953915,
0.03491603955626488,
0.011411952786147594,
-0.05457361415028572,
0.02050236240029335,
-0.06183457374572754,
0.003293402260169387,
-0.04886835440993309,
0.03327256068587303,
-0.02362578921020031,
0.049422625452280045,
0.023423152044415474,
0.0190968606621027,
0.002703360514715314,
-0.014062780886888504,
-0.10297400504350662,
0.022176310420036316,
-0.0609435997903347,
-0.0014781842473894358,
-0.019351975992321968,
-0.025516198948025703,
-0.03174275532364845,
-0.10165098309516907,
-0.021949652582406998,
-0.018692653626203537,
0.002887965179979801,
-0.02422594651579857,
0.007283722050487995,
-0.06130516529083252,
-0.061848968267440796,
0.017848480492830276,
-0.018593454733490944,
0.02011183835566044,
-0.034249477088451385,
0.030149592086672783,
0.027181394398212433,
-0.016328195109963417,
-0.05050325766205788,
-0.026002176105976105,
0.0290713869035244,
0.00252859597094357,
0.02980811893939972,
0.028097663074731827,
0.015109643340110779,
-0.03661610558629036,
0.05298134312033653,
-0.001674293540418148,
0.044679414480924606,
0.01000820193439722,
-0.0273202583193779,
-0.05136699974536896,
-0.03019084967672825,
-0.025968439877033234,
0.017360128462314606,
0.03187348693609238,
0.018065162003040314,
-0.00045218298328109086,
0.00981353223323822,
0.010246573016047478,
0.027742071077227592,
0.06542853266000748,
0.020108388736844063,
0.028023362159729004,
-0.004902219399809837,
-0.0744423195719719,
0.021554527804255486,
-0.004111617337912321,
-0.011834727600216866,
0.03118021972477436,
0.0020042320247739553,
-0.02851138450205326,
0.019199378788471222,
0.0008190867374651134,
0.021614763885736465,
-0.007756839040666819,
0.02873663231730461,
-0.024445485323667526,
0.058442309498786926,
0.017635580152273178,
0.005996741354465485,
0.009697114117443562,
0.006587937939912081,
0.047011055052280426,
0.04521440714597702,
-0.035981014370918274,
-0.09231109917163849,
0.017909027636051178,
0.04471868649125099,
0.011366029269993305,
-0.06975611299276352,
0.01947084441781044,
-0.006416776683181524,
-0.015384959056973457,
0.03190736100077629,
-0.027794895693659782,
0.00846218504011631,
-0.037904996424913406,
0.032235972583293915,
-0.004294467158615589,
-0.031316451728343964,
-0.020578421652317047,
0.02743968740105629,
0.017371850088238716,
-0.023867357522249222,
-0.03215598687529564,
0.004459932446479797,
-0.031411852687597275,
0.0010079246712848544,
0.06994571536779404,
0.019412517547607422,
0.011752509512007236,
-0.0363147109746933,
-0.035178862512111664,
0.006474941968917847,
-0.0432366281747818,
-0.05459689348936081,
0.0019416639115661383,
-0.01250668428838253,
-0.014399716630578041,
-0.0005098447436466813,
-0.031646255403757095,
-0.014552452601492405,
0.03416174277663231,
-0.011551872827112675,
-0.029570339247584343,
-0.025497589260339737,
-0.03424154222011566,
0.026791052892804146,
0.024959631264209747,
0.013136932626366615,
0.04996546357870102,
0.053162749856710434,
-0.054074011743068695,
-0.018868548795580864,
-0.00461993645876646,
0.021748486906290054,
-0.06469299644231796,
-0.0007069001439958811,
-0.03606407716870308,
0.0105442451313138,
-0.03320842608809471,
0.0473000705242157,
0.02054973691701889,
0.02340497449040413,
-0.012606634758412838,
-0.038393534719944,
-0.011714172549545765,
0.030048277229070663,
0.018580954521894455,
-0.006364493165165186,
-0.000008407235327467788,
0.036886658519506454,
-0.010053085163235664,
-0.04754503816366196,
-0.0000858505954965949,
0.045651912689208984,
0.020339375361800194,
0.022284068167209625,
-0.02143707312643528,
0.03508499637246132,
-0.0063818758353590965,
-0.027456562966108322,
0.02165423333644867,
-0.021556038409471512,
0.06100430339574814,
-0.01483533438295126,
-0.013710093684494495,
-0.0009037325507961214,
-0.05618394911289215,
-0.028399761766195297,
0.016447436064481735,
0.013093413785099983,
0.027512257918715477,
-0.0391223318874836,
0.022213662043213844,
0.008502115495502949,
-0.0038384294603019953,
-0.08234697580337524,
-0.0505845732986927,
-0.00043380915303714573,
0.017693864181637764,
0.02918328531086445,
-0.010417971760034561,
0.003972082864493132,
-0.05337836220860481,
-0.04259413480758667,
0.00011570659989956766,
0.08070523291826248,
-0.04350731521844864,
-0.013756723143160343,
0.006009378936141729,
-0.009576884098351002,
0.04036732763051987,
-0.020027827471494675,
-0.03830219805240631,
-0.00774827366694808,
-0.00584076065570116,
-0.009798699989914894,
-0.0264732763171196,
0.07251029461622238,
-0.019635027274489403,
-0.013411461375653744,
0.01045452430844307,
-0.020395873114466667,
0.016116702929139137,
-0.020877854898571968,
-0.037452321499586105,
0.04329850524663925,
0.00972544401884079,
-0.01005357876420021,
-0.042302653193473816,
0.013002987019717693,
0.01685297302901745,
0.020640376955270767,
0.029024438932538033,
-0.0007227862370200455,
-0.01821981742978096,
-0.030571462586522102,
0.018273068591952324,
0.006842678878456354,
-0.002877766266465187,
0.019601307809352875,
0.043682247400283813,
-0.023779841139912605,
0.007149766199290752,
-0.0035637870896607637,
-0.016366498544812202,
0.050402313470840454,
-0.011978468857705593,
0.00006952005787752569,
0.010918568819761276,
-0.03171269968152046,
-0.023628514260053635,
-0.02146444283425808,
-0.02131880819797516,
-0.004499940667301416,
0.08224566280841827,
-0.010509463958442211,
0.060436420142650604,
0.016878942027688026,
0.007713858503848314,
0.005380915477871895,
-0.015429583378136158,
0.009381131269037724,
-0.005262611899524927,
0.034305639564991,
0.022673044353723526,
-0.06379267573356628,
-0.0013025690568611026,
0.030765051022171974,
0.03140502795577049,
-0.01402315404266119,
-0.007349736988544464,
0.029960446059703827,
0.04429309442639351,
-0.0007957954658195376,
0.0007013424765318632,
-0.02835124358534813,
0.025345930829644203,
-0.039710916578769684,
0.008748135529458523,
-0.04876282811164856,
-0.009581689722836018,
0.046995289623737335,
0.011822616681456566,
-0.026455789804458618,
-0.057131920009851456,
0.012123854830861092,
-0.027958093211054802,
-0.007496815640479326,
0.009963897056877613,
0.027233611792325974,
0.0038393866270780563,
-0.009996249340474606,
0.030346738174557686,
0.0001045953540597111,
0.012527573853731155,
0.016036788001656532,
-0.06548280268907547,
-0.026946276426315308,
-0.028486916795372963,
-0.023620672523975372,
-0.018750956282019615,
-0.028700795024633408,
-0.057865120470523834,
0.0027798209339380264,
-0.036757778376340866,
0.006679083686321974,
0.018287507817149162,
0.024846170097589493,
-0.014046513475477695,
0.059712689369916916,
-0.02677614986896515,
-0.005236579570919275,
-0.025946732610464096,
0.008251498453319073,
0.1072944924235344,
0.06730605661869049,
0.028182432055473328,
-0.029774148017168045,
0.02752157859504223,
-0.004398133140057325,
0.005165242590010166,
0.007337536662817001,
-0.017124542966485023,
-0.019545482471585274,
-0.0011853750329464674,
0.02309625782072544,
0.04707115888595581,
0.01936342380940914,
-0.025458533316850662,
0.07433942705392838,
-0.03475189954042435,
-0.01289529912173748,
-0.03283359110355377,
0.010790707543492317,
0.000951366382651031,
0.03440439701080322,
-0.007318465504795313,
0.005497912410646677,
-0.02362808585166931,
0.0038144071586430073,
-0.020880358293652534,
-0.008398270234465599,
-0.03306777775287628,
0.0393928587436676,
-0.06036898493766785,
0.006036162842065096,
0.03512754291296005,
-0.043163999915122986,
-0.07796018570661545,
0.01194827165454626,
-0.027271000668406487,
-0.026133328676223755,
-0.00406876252964139,
0.03950818255543709,
0.025039993226528168,
0.0335138775408268,
0.008723728358745575,
0.03291122615337372,
-0.06937594711780548,
0.022377004846930504,
-0.01983806863427162,
0.02578006312251091,
-0.016703519970178604,
0.021833859384059906,
0.009019004181027412,
-0.011661140248179436,
-0.005731666926294565,
-0.054438699036836624,
-0.023783907294273376,
-0.019571959972381592,
0.03024640679359436,
-0.013626109808683395,
-0.016879674047231674,
-0.02040902152657509,
0.018963174894452095,
-0.023817645385861397,
0.03773754462599754,
0.022648680955171585,
-0.006554645020514727,
-0.009701061993837357,
0.015196651220321655,
0.046770889312028885,
-0.027712849900126457,
-0.010942293331027031,
-0.009623853489756584,
-0.02595507726073265,
-0.0574103407561779,
-0.00918199960142374,
-0.00964009203016758,
0.05018480867147446,
0.043185822665691376,
0.03567766770720482,
0.009664182551205158,
-0.07333692908287048,
-0.027813466265797615,
0.03586719557642937,
-0.016044337302446365,
-0.011583548039197922,
-0.03914903849363327,
-0.00285698683001101,
0.008286436088383198,
0.0345936082303524,
-0.041066478937864304,
0.011320638470351696,
0.006010100711137056,
0.021932251751422882,
-0.0001510936563136056,
-0.022992447018623352,
-0.002989805769175291,
0.02999921515583992,
-0.012377276085317135,
0.0015697167254984379,
0.044033173471689224,
0.019846484065055847,
0.017464647069573402,
-0.005925528705120087,
-0.002116038929671049,
0.03104114718735218,
-0.0020731277763843536,
0.037919096648693085,
0.03732038661837578,
-0.007126749958842993,
-0.011314159259200096,
0.024660775437951088,
0.009923010133206844,
-0.03937632218003273,
-0.031373701989650726,
-0.024433497339487076,
-0.0104770977050066,
-0.007307413965463638,
0.024105830118060112,
0.005021021701395512,
0.04514758661389351,
-0.03216414898633957,
0.04063807427883148,
-0.06004184111952782,
-0.028834111988544464,
-0.06236032024025917,
-0.02655297890305519,
0.01408306322991848,
-0.04032701626420021,
-0.03628907352685928,
0.033019598573446274,
-0.02697741985321045,
-0.00013107254926580936,
-0.01645084284245968,
-0.00044211966451257467,
-0.005705232731997967,
-0.03269951418042183,
0.031877320259809494,
-0.05436168611049652,
0.04520415514707565,
-0.00915609486401081,
-0.005687539465725422,
0.029348693788051605,
-0.030494051054120064,
-0.05253653973340988,
0.0114102428779006,
-0.013792550191283226,
0.02703351341187954,
0.009640208445489407,
-0.004893050063401461,
-0.02661135420203209,
0.06681296974420547,
-0.021631160750985146,
0.0023493028711527586,
-0.011665862053632736,
-0.019231323152780533,
-0.04869704321026802,
-0.009805663488805294,
-0.006429783068597317,
-0.022292697802186012,
-0.0028367789927870035,
0.03321778401732445,
0.04683297500014305,
-0.013344637118279934,
-0.025584973394870758,
0.011615567840635777,
-0.015655456110835075,
-0.003951362334191799,
-0.000921932514756918,
0.026651954278349876,
0.02229679562151432,
0.030827533453702927,
-0.04918527230620384,
0.027011334896087646,
-0.009522129781544209,
0.004742308519780636,
-0.07828878611326218,
-0.0170107614248991,
-0.0065103936940431595,
-0.003547873580828309,
0.001063160365447402,
-0.023529013618826866,
0.018196754157543182,
-0.014653578400611877,
-0.039011236280202866,
0.023476259782910347,
-0.03424284607172012,
-0.017100734636187553,
-0.007746705319732428,
-0.012903345748782158,
0.009493623860180378,
0.02485264278948307,
0.03079703263938427,
0.045941296964883804,
-0.007602832745760679,
0.0022407223004847765,
0.00006333422061288729,
-0.006958628073334694,
0.005256307311356068,
0.0297059528529644,
0.003526357002556324,
-0.009919832460582256,
0.07144853472709656,
0.0035772204864770174,
-0.019169146195054054,
0.03851370885968208,
0.03383626788854599,
0.035915110260248184,
-0.008552372455596924,
0.0226494912058115,
-0.0006111117545515299,
0.06361643970012665,
-0.022167246788740158,
-0.021096400916576385,
-0.02496519312262535,
0.050826895982027054,
0.008813711814582348,
0.04636859893798828,
-0.015376236289739609,
-0.016616107895970345,
0.029905013740062714,
-0.027364937588572502,
-0.022705480456352234,
0.0038293092511594296,
0.008771184831857681,
-0.03843650221824646,
-0.014521830715239048,
0.021059563383460045,
0.0020402120426297188,
-0.00769250700250268,
0.03238346055150032,
-0.05346159636974335,
-0.027276568114757538,
0.04427278786897659,
-0.018108556047081947,
-0.04010768234729767,
0.02977144718170166,
0.013376806862652302,
0.028602149337530136,
-0.03665776550769806,
0.021746916696429253,
0.022312628105282784,
-0.04418528825044632,
0.015974093228578568,
-0.011003372259438038,
0.005172380246222019,
-0.02685064822435379,
-0.04772739112377167,
-0.032089099287986755,
0.04416396841406822,
0.012034048326313496,
0.02021840214729309,
0.005697447806596756,
-0.027667513117194176,
-0.018248016014695168,
-0.051992520689964294,
0.03319818526506424,
0.025800669565796852,
-0.02837597206234932,
-0.03520229831337929,
-0.014036890119314194,
0.03843674063682556,
0.005446190480142832,
0.051320865750312805,
-0.0012444882886484265,
-0.05322558805346489,
0.024084733799099922,
0.006553090177476406,
0.017030371353030205,
-0.020314624533057213,
0.015885965898633003,
-0.0016224608989432454,
-0.04135304316878319,
-0.0018341082613915205,
0.007978817448019981,
-0.003095072926953435,
0.004170282743871212,
-0.010548909194767475,
-0.0146315423771739,
0.046471744775772095,
-0.01618846133351326,
-0.047918759286403656,
0.060031596571207047,
0.03578576445579529,
-0.002957613905891776,
0.0594218410551548,
-0.015277625061571598,
0.02146049216389656,
0.020966678857803345,
-0.02291383221745491,
-0.06381309032440186,
0.03418702259659767,
-0.03845350444316864,
0.0020301181357353926,
0.004863005597144365,
0.0004710405773948878,
0.010843734256923199,
-0.021224813535809517,
0.014196318574249744,
0.05103366822004318,
-0.06644313037395477,
-0.0009369254112243652,
0.003982828930020332,
0.02403363026678562,
0.05228894203901291,
0.0013035089941695333,
0.018101923167705536,
0.015851560980081558,
-0.013385661877691746,
0.01950702629983425,
0.02804741822183132,
0.04559401050209999,
0.006638490129262209,
-0.023444339632987976,
0.0802883505821228,
-0.015841176733374596,
0.020419614389538765,
0.010118234902620316,
0.012558107264339924,
-0.0342341847717762,
-0.02930355630815029,
0.009661497548222542,
-0.034705646336078644,
0.058179546147584915,
0.04521754011511803,
-0.0010206939186900854,
0.05286465585231781,
-0.006040067877620459,
-0.000023208292986964807,
-0.020669184625148773,
0.0021411217749118805,
-0.012484020553529263,
-0.012043336406350136,
-0.01103492546826601,
0.01687357947230339,
0.020708613097667694,
-0.022974764928221703,
0.006045192014425993,
-0.035429034382104874,
0.008878637105226517,
0.009711851365864277,
-0.0065907384268939495,
0.005949647165834904,
-0.018389644101262093,
0.00017899730300996453,
-0.01095826830714941,
-0.04144259914755821,
-0.016116494312882423,
0.07690729200839996,
0.04152374342083931,
0.028915809467434883,
-0.010401464067399502,
-0.02153863199055195,
-0.030142150819301605,
0.03907286375761032,
-0.07062491774559021,
-0.04712614044547081,
-0.03572939708828926,
0.022241029888391495,
0.006343090906739235,
-0.016825389117002487
] |
<p>From a paper on tunnel design I've been reading: (<a href="http://www.sciencedirect.com/science/article/pii/0886779887900113" rel="nofollow">http://www.sciencedirect.com/science/article/pii/0886779887900113</a>)</p>
<blockquote>
<p>In the present application, the solu-
tion corresponding to a sinusoidal load
in an infinite elastic medium is sought.
Since no closed-form solution to this
problem exists, a numerical procedure
should be used. The procedure involves,
first, deriving the solution to the case of
a constant pressure applied to a finite
strip in an infinite body. The solution
for a sinusoidal distribution of loading
then can be found by dividing the
wavelength into several segments and
assuming the pressure on each segment
to be constant. In the present case, this
procedure is applied to calculate the
displacements under a sinusoidal line
load. Each wavelength was divided in 10
and 20 segments and a line load of 4, 6, 8
and 10 wavelengths were considered. It
was found that the calculated displace-
ments became insensitive to the number
of wavelengths when the latter exceeded
6, and that 10 segments were enough to
represent each wavelength.
As a result of this analysis, the vertical
displacement under a sinusoidal load
may be approximated by</p>
<p>$$u_y = \frac{(3-4\nu)}{16\pi(1-4\nu)G}\sigma L\sin\frac{2\pi x}{L}$$</p>
</blockquote>
<p>The authors refer to the plane strain solution to Kelvin's problem before this.</p>
<p>Can you suggest how I would go about deriving this as mentioned in the paper—from going for a finite strip in an infinite body to applying a <em>numerical</em> solution and getting the result for displacement?</p>
<p>Note: $\nu$ poisson's ratio, $L$ Length of strip, $G$ is the shear modulus.</p> | 2,037 | [
0.016919130459427834,
-0.017454979941248894,
-0.0016994972247630358,
-0.022065965458750725,
0.08279892057180405,
-0.02612571232020855,
0.010327897034585476,
-0.02572171576321125,
0.002950087422505021,
-0.019743334501981735,
0.013034917414188385,
0.013355438597500324,
0.02741987258195877,
0.012050816789269447,
0.016621924936771393,
-0.0036038465332239866,
-0.025995230302214622,
-0.008666911162436008,
-0.007649517152458429,
-0.07390903681516647,
0.013684379868209362,
-0.0055106934159994125,
-0.05397796630859375,
-0.015384325757622719,
-0.03174647316336632,
0.05571670085191727,
0.028930796310305595,
-0.01332002691924572,
0.002804326359182596,
0.01665300503373146,
-0.031193898990750313,
-0.01172974519431591,
0.010280994698405266,
0.034747399389743805,
-0.007854956202208996,
-0.02111618034541607,
-0.04459530860185623,
-0.036880556493997574,
-0.00898918230086565,
0.011524214409291744,
-0.02801876701414585,
0.04046933352947235,
-0.02157796546816826,
0.010311320424079895,
0.01122775487601757,
0.04249335080385208,
0.006653240881860256,
-0.0023230304941534996,
0.023770932108163834,
-0.0373033806681633,
0.08090932667255402,
-0.008133682422339916,
0.03820561245083809,
-0.017485348507761955,
-0.040985818952322006,
-0.028636768460273743,
0.03747638687491417,
0.0741514340043068,
-0.015147802419960499,
-0.029333315789699554,
0.007932626642286777,
-0.01883537508547306,
-0.054245173931121826,
-0.02370375208556652,
0.001964168855920434,
-0.002900482388213277,
-0.02391262724995613,
-0.006867666728794575,
-0.004284659866243601,
-0.008174613118171692,
0.014177659526467323,
0.001429918222129345,
0.01571006327867508,
-0.04197565093636513,
-0.030160298570990562,
0.006229822989553213,
0.0012138831662014127,
0.039979904890060425,
0.024148501455783844,
0.028103407472372055,
-0.038980428129434586,
0.002133239759132266,
0.02599201537668705,
0.04262537881731987,
-0.007611445151269436,
-0.032943613827228546,
0.10080811381340027,
-0.019824545830488205,
0.0209669079631567,
-0.0075442250818014145,
0.030580483376979828,
-0.002449479652568698,
0.040048323571681976,
0.021467551589012146,
-0.010071900673210621,
0.0025281929410994053,
0.008248123340308666,
0.025579508394002914,
0.011745325289666653,
-0.010934115387499332,
0.04613220691680908,
-0.032362207770347595,
0.049584005028009415,
0.057885486632585526,
0.00023447131388820708,
-0.014094078913331032,
-0.007448877673596144,
0.021022189408540726,
-0.003110965946689248,
-0.04649268463253975,
-0.02103869430720806,
0.03765430301427841,
-0.030170580372214317,
0.03765103220939636,
-0.019219079986214638,
-0.005853496491909027,
0.03373689204454422,
0.0011550940107554197,
0.02920341305434704,
0.07473362982273102,
0.035463448613882065,
-0.05271754786372185,
0.035764407366514206,
-0.01515891868621111,
-0.0796608105301857,
0.006927743554115295,
0.006684579886496067,
-0.02631864883005619,
-0.05326734855771065,
0.022485276684165,
0.04421309009194374,
0.01567537523806095,
0.02347330003976822,
0.022614499554038048,
0.00508037069812417,
0.0016001883195713162,
-0.09195366501808167,
-0.0744403749704361,
0.058740295469760895,
-0.005016467999666929,
0.02001325786113739,
-0.04074493423104286,
-0.025229696184396744,
0.014686252921819687,
0.0761127769947052,
0.009678118862211704,
0.027934355661273003,
-0.026979699730873108,
0.04903019964694977,
-0.000021295778424246237,
-0.011957880109548569,
-0.002217325149103999,
0.001087970333173871,
-0.04721614345908165,
-0.008935611695051193,
-0.06490771472454071,
0.027396023273468018,
0.02626926265656948,
0.011984357610344887,
0.005210750736296177,
0.010718650184571743,
-0.02171037346124649,
-0.013122349977493286,
0.01474850531667471,
-0.014568688347935677,
-0.03990742564201355,
0.0482783317565918,
0.004046597983688116,
-0.0332091823220253,
0.01692650094628334,
0.014929340220987797,
-0.045012217015028,
0.007961946539580822,
0.03841238468885422,
0.04563149809837341,
-0.014504999853670597,
0.06292445957660675,
-0.08018682152032852,
-0.003848963649943471,
-0.020649492740631104,
0.019442331045866013,
-0.04322173446416855,
-0.002716213697567582,
0.033400412648916245,
0.0526655949652195,
0.058176301419734955,
-0.011672238819301128,
0.028810281306505203,
0.04319353029131889,
-0.07149535417556763,
-0.01001321617513895,
-0.0063819983042776585,
0.08393297344446182,
-0.006198592949658632,
-0.013545816764235497,
-0.008683250285685062,
-0.015831418335437775,
-0.0005876271752640605,
-0.026696665212512016,
-0.02730383910238743,
-0.002966060768812895,
0.01223604753613472,
0.04373913258314133,
-0.0016005361685529351,
-0.00014370345161296427,
0.031059283763170242,
0.02569030225276947,
0.029026418924331665,
0.023023396730422974,
-0.05802338942885399,
-0.026303879916667938,
0.007031760178506374,
-0.014481973834335804,
0.07564548403024673,
0.004590101074427366,
-0.003208502195775509,
-0.009260333143174648,
-0.005908009130507708,
-0.027600716799497604,
0.04297229275107384,
-0.04108573496341705,
0.044513456523418427,
0.08897936344146729,
0.036638833582401276,
-0.018614035099744797,
0.035396844148635864,
-0.01718004047870636,
0.02414310909807682,
0.013343101367354393,
-0.052437301725149155,
-0.06155093386769295,
0.0028670774772763252,
0.020499100908637047,
0.03951996564865112,
-0.01888871379196644,
-0.05140896514058113,
0.017223572358489037,
0.035435017198324203,
0.05621333047747612,
0.0008198475698009133,
-0.01494826190173626,
-0.03468387573957443,
0.018026752397418022,
0.03679656982421875,
0.03442464768886566,
-0.02862164005637169,
0.03765065222978592,
0.04213990643620491,
0.042512472718954086,
0.020148834213614464,
0.03123258426785469,
0.004614672157913446,
0.01910211890935898,
0.0506478026509285,
0.022851234301924706,
0.02920851670205593,
0.06281017512083054,
-0.036582447588443756,
0.024051928892731667,
0.06328029185533524,
-0.02849567122757435,
-0.0053685554303228855,
-0.011486598290503025,
0.007039762567728758,
0.03057493083178997,
-0.031984858214855194,
-0.0227529164403677,
-0.014121923595666885,
0.008455718867480755,
-0.04091763123869896,
0.006672432646155357,
-0.04376241937279701,
-0.005754634737968445,
-0.02227133885025978,
-0.011022296734154224,
0.02008647285401821,
0.026252180337905884,
0.031256988644599915,
-0.051765359938144684,
0.01166127435863018,
0.003911181818693876,
0.026711266487836838,
-0.0006170229753479362,
-0.001734100398607552,
-0.033671293407678604,
-0.03205456584692001,
-0.029526060447096825,
-0.027379345148801804,
0.036309462040662766,
-0.0002291716227773577,
-0.01649102196097374,
0.0019644189160317183,
-0.007946853525936604,
-0.05262953042984009,
0.012245123274624348,
-0.01315624825656414,
0.027687743306159973,
-0.029767179861664772,
-0.015041543170809746,
0.04231409355998039,
-0.03138793632388115,
-0.04205022379755974,
0.02694622054696083,
-0.050734423100948334,
-0.021984215825796127,
-0.02203284204006195,
0.017690131440758705,
-0.028963811695575714,
-0.0003192461736034602,
0.028264211490750313,
0.014805682934820652,
-0.021259654313325882,
-0.0033766920678317547,
-0.03725191205739975,
-0.06634081155061722,
-0.0016814355039969087,
-0.0072451867163181305,
0.06736728549003601,
-0.020140210166573524,
-0.025581860914826393,
0.07143820822238922,
0.012212778441607952,
-0.04503554105758667,
0.00035258475691080093,
0.027291076257824898,
0.018034886568784714,
0.015612552873790264,
-0.004741792567074299,
0.0187925286591053,
-0.009462893940508366,
0.011010671965777874,
-0.007768439128994942,
0.02519076131284237,
0.07290319353342056,
0.03427716717123985,
-0.019230937585234642,
0.017564404755830765,
0.019648704677820206,
-0.005190345458686352,
0.013065282255411148,
0.03070938028395176,
-0.0007532132440246642,
0.01318042166531086,
-0.04796946048736572,
0.009947013109922409,
0.023604394868016243,
-0.08077877759933472,
0.014325389638543129,
0.0005279736360535026,
-0.03408811613917351,
-0.0312763974070549,
0.013682977296411991,
0.010416926816105843,
-0.01871359534561634,
-0.021686214953660965,
0.06466223299503326,
0.04900110140442848,
-0.030354101210832596,
-0.03318221867084503,
0.04155278205871582,
0.03764702379703522,
0.000453905580798164,
-0.026801729574799538,
0.011685025878250599,
-0.028133803978562355,
0.03588045388460159,
-0.030355023220181465,
-0.04087069258093834,
0.0023369411937892437,
0.0375312939286232,
-0.0010086291003972292,
0.00045931764179840684,
-0.017563825473189354,
0.013899635523557663,
-0.050137415528297424,
-0.00933082029223442,
-0.019322393462061882,
0.043139684945344925,
0.02475394494831562,
0.04455268383026123,
-0.004435254260897636,
0.0019356796983629465,
0.04472648352384567,
0.022775793448090553,
-0.09386102110147476,
-0.01660812273621559,
-0.01883663237094879,
0.005410771816968918,
0.019174328073859215,
-0.04490385577082634,
0.0007948802667669952,
-0.032747771590948105,
-0.0063501703552901745,
0.003908700775355101,
-0.012764440849423409,
-0.034987397491931915,
0.025959838181734085,
0.004088385496288538,
-0.05002903193235397,
-0.015918098390102386,
0.01945222169160843,
0.03418872505426407,
-0.025445211678743362,
-0.0019386012572795153,
0.047127824276685715,
-0.031718432903289795,
-0.022383490577340126,
-0.011442343704402447,
0.014929364435374737,
-0.009888148866593838,
0.009067961014807224,
0.008277497254312038,
0.017466558143496513,
-0.011696599423885345,
-0.012902235612273216,
-0.029050728306174278,
0.019104773178696632,
0.030427005141973495,
0.009385702200233936,
-0.002055889694020152,
-0.0275141391903162,
0.029749078676104546,
0.01388790737837553,
0.058418240398168564,
0.007237133104354143,
0.007849637418985367,
0.05142010375857353,
-0.0020438088104128838,
0.0015646996907889843,
0.07036030292510986,
0.03725696727633476,
-0.0005270096589811146,
-0.00045529857743531466,
-0.02610239014029503,
-0.009271783754229546,
0.0045448848977684975,
-0.0042484719306230545,
0.01638755202293396,
0.01730215549468994,
-0.012760250829160213,
0.02059435285627842,
0.0740869864821434,
0.03292536735534668,
0.016971183940768242,
0.025476966053247452,
-0.03669348359107971,
0.00007510982686653733,
-0.04202947020530701,
-0.0067835357040166855,
0.02230636402964592,
-0.007035724353045225,
0.06523668020963669,
0.020075105130672455,
-0.008701493963599205,
-0.11066610366106033,
-0.039102837443351746,
0.01597673073410988,
0.026924695819616318,
0.012585213407874107,
0.0060755303129553795,
-0.057217903435230255,
-0.04620194435119629,
0.03795742243528366,
-0.022338762879371643,
0.013690595515072346,
-0.03133060038089752,
0.017644986510276794,
-0.03432605043053627,
-0.041425175964832306,
-0.02403130568563938,
-0.008157484233379364,
-0.01596880331635475,
0.0027333286125212908,
-0.0011943398276343942,
-0.014360057190060616,
0.005500570870935917,
0.007411092985421419,
0.023712584748864174,
0.029448021203279495,
0.006952127441763878,
-0.047509826719760895,
0.000030086930564721115,
0.012840358540415764,
-0.032686926424503326,
-0.055093199014663696,
0.0003538074379321188,
0.007484836038202047,
0.03228336572647095,
0.009329291060566902,
-0.023838622495532036,
-0.06161023676395416,
0.04735388979315758,
0.017002834007143974,
-0.02292284183204174,
0.005192650482058525,
-0.03991050273180008,
0.09618180990219116,
0.045154742896556854,
-0.002051188610494137,
0.05827537551522255,
0.017578380182385445,
-0.03728160262107849,
0.029558656737208366,
-0.008557623252272606,
0.03772265836596489,
-0.012387052178382874,
0.029745114967226982,
0.018828019499778748,
0.07577119767665863,
-0.025652587413787842,
0.06829765439033508,
0.004670934285968542,
0.019020656123757362,
0.0029781742487102747,
-0.01918412372469902,
0.023393450304865837,
-0.0007513201562687755,
-0.02026405930519104,
0.032719019800424576,
-0.004859624896198511,
-0.0007701196591369808,
-0.002878689207136631,
-0.04570896923542023,
0.014481025747954845,
-0.007362792268395424,
0.024172550067305565,
0.015036128461360931,
0.010084215551614761,
0.007073994725942612,
-0.01620958372950554,
0.00925681833177805,
0.011898921802639961,
-0.0630083978176117,
0.06673183292150497,
-0.017647892236709595,
0.033541224896907806,
-0.003591503482311964,
-0.0007489983690902591,
-0.00871945545077324,
0.030090853571891785,
-0.016183122992515564,
0.03588427975773811,
-0.009969404898583889,
0.005192905198782682,
-0.006970400456339121,
0.006840603891760111,
-0.01459252554923296,
-0.02829299494624138,
0.025601742789149284,
0.05158216506242752,
-0.021176878362894058,
-0.05301922187209129,
-0.03349529206752777,
0.01284648198634386,
-0.04669371619820595,
0.011237611062824726,
0.05278882756829262,
-0.023689132183790207,
-0.019814347848296165,
0.023048538714647293,
0.026338448747992516,
0.08143876492977142,
-0.02210512012243271,
-0.014703357592225075,
0.005402747541666031,
-0.007576183415949345,
-0.022699087858200073,
-0.01852455362677574,
0.013732562772929668,
-0.032562028616666794,
-0.043883953243494034,
-0.013661940582096577,
-0.006854483392089605,
0.030726542696356773,
-0.017657317221164703,
-0.048790883272886276,
-0.011612162925302982,
-0.00039352569729089737,
-0.014631860889494419,
-0.009298913180828094,
0.006751879118382931,
-0.018974609673023224,
0.0036050337366759777,
-0.03215019777417183,
-0.0036328050773590803,
-0.04807824641466141,
0.0028683384880423546,
-0.017997032031416893,
0.025228071957826614,
0.006476989947259426,
0.030071130022406578,
0.08810187876224518,
-0.010995883494615555,
-0.024318287149071693,
0.025451436638832092,
-0.01508595421910286,
0.03350001201033592,
0.010072366334497929,
0.0002532436337787658,
-0.0012990387622267008,
0.01886117272078991,
-0.00349977845326066,
-0.045035552233457565,
-0.014086435548961163,
-0.01870029605925083,
0.06642225384712219,
-0.04030653089284897,
0.035899292677640915,
0.01652350462973118,
-0.04447032883763313,
0.002612366806715727,
0.004346845205873251,
-0.010827464051544666,
0.0031033277045935392,
-0.010367773473262787,
0.030997613444924355,
-0.02501121535897255,
-0.027424979954957962,
0.009894956834614277,
0.0017749926773831248,
-0.01072200108319521,
-0.0008587762131355703,
-0.008763567544519901,
-0.0023903348483145237,
-0.017641449347138405,
-0.05097406730055809,
-0.05587536096572876,
0.026416437700390816,
-0.02549631893634796,
0.0346318744122982,
0.021009718999266624,
0.01598949357867241,
0.04856790602207184,
0.03665250912308693,
0.04471827670931816,
-0.009385374374687672,
0.0017147990874946117,
-0.007811672519892454,
0.030528565868735313,
0.0010109796421602368,
-0.0027726825792342424,
0.01683858223259449,
-0.005182819906622171,
0.019122052937746048,
0.021842697635293007,
0.04256395250558853,
-0.04996371641755104,
-0.025329869240522385,
-0.018219804391264915,
-0.033073727041482925,
-0.05285356193780899,
0.054141271859407425,
0.0020482302643358707,
-0.03230143338441849,
0.051097191870212555,
-0.02908235602080822,
0.04601077362895012,
0.016400441527366638,
-0.015550414100289345,
-0.009270412847399712,
0.07746158540248871,
-0.025138426572084427,
-0.021355241537094116,
-0.015985732898116112,
0.01407758891582489,
0.1347670704126358,
0.07319068908691406,
0.05254938080906868,
-0.027998803183436394,
0.027318011969327927,
-0.0305157620459795,
-0.05470988154411316,
-0.03807023912668228,
-0.00895981676876545,
0.00988672487437725,
-0.03876359760761261,
-0.015028365887701511,
0.02012138068675995,
-0.027331221848726273,
-0.011131645180284977,
0.0319596603512764,
-0.05673547834157944,
-0.031222378835082054,
0.019693804904818535,
-0.017422515898942947,
-0.018179256469011307,
0.003554279450327158,
-0.019416093826293945,
0.030874304473400116,
-0.011496276594698429,
-0.004686453379690647,
-0.05065739154815674,
-0.00769798131659627,
0.04028156399726868,
-0.01026923768222332,
-0.06090262904763222,
0.01358481589704752,
-0.0023927693255245686,
-0.05223802104592323,
0.004579485394060612,
0.037748996168375015,
-0.015587992034852505,
-0.03019237145781517,
0.026455212384462357,
0.008586371317505836,
-0.022056374698877335,
0.010646744631230831,
-0.010161875747144222,
0.018339788541197777,
-0.009949917905032635,
-0.015660762786865234,
-0.03280029073357582,
0.03359871357679367,
0.008249321021139622,
-0.040844764560461044,
0.013155235908925533,
0.015369614586234093,
-0.03225686028599739,
-0.02374134212732315,
-0.013420787639915943,
0.0014358938205987215,
0.060967862606048584,
-0.0009202937944792211,
-0.03344300761818886,
0.03595627471804619,
-0.008321349509060383,
0.04412547126412392,
0.015877822414040565,
0.014513571746647358,
-0.009541216306388378,
0.014184693805873394,
0.008021580055356026,
0.0865088403224945,
0.00850287638604641,
-0.011624309234321117,
-0.04343973100185394,
0.007896547205746174,
-0.033768292516469955,
0.0010808856459334493,
-0.02267618477344513,
0.0211965199559927,
0.028868041932582855,
-0.022860517725348473,
-0.018625762313604355,
-0.03734998777508736,
-0.026853350922465324,
0.00421261228621006,
0.0034240547101944685,
-0.02494332194328308,
0.010209965519607067,
-0.031286146491765976,
-0.0042917258106172085,
0.05316195264458656,
-0.011743126437067986,
0.02212364599108696,
0.004120639991015196,
0.015817617997527122,
0.02315179631114006,
-0.02561190538108349,
-0.05658912658691406,
-0.026090243831276894,
-0.030787289142608643,
0.04096057265996933,
0.003788289614021778,
0.03532590717077255,
0.025115372613072395,
0.04930124431848526,
-0.005349007900804281,
0.0567195750772953,
-0.03690718114376068,
-0.028986429795622826,
-0.0012256433255970478,
-0.021665209904313087,
0.0240388885140419,
0.03367554396390915,
0.027596373111009598,
-0.0742688924074173,
-0.013933360576629639,
0.0010525973048061132,
-0.04482034966349602,
0.02536665089428425,
-0.018588995561003685,
-0.05139489099383354,
0.021007807925343513,
-0.04056873917579651,
-0.01981944777071476,
-0.01233141403645277,
-0.002855765400454402,
-0.02705034427344799,
-0.04030831530690193,
-0.012227687984704971,
0.010843951255083084,
-0.03195393085479736,
-0.0010272355284541845,
-0.08363344520330429,
-0.01981288194656372,
0.03811734914779663,
-0.0044942027889192104,
0.010431692004203796,
-0.01865614391863346,
0.007376994471997023,
0.02287917397916317,
0.04023391008377075,
-0.005385562311857939,
-0.006298345979303122,
0.0022718554828315973,
0.0024915433023124933,
-0.034541938453912735,
0.04274094104766846,
-0.02872435562312603,
0.019679704681038857,
-0.03118075616657734,
0.01810557395219803,
-0.009809084236621857,
0.03474215790629387,
-0.023011133074760437,
-0.005083284806460142,
-0.03272887319326401,
-0.0027274165768176317,
-0.001992597011849284,
-0.053663600236177444,
-0.01013435609638691,
0.0052292728796601295,
0.015443756245076656,
-0.00010518431372474879,
0.02059234492480755,
0.023002272471785545,
-0.013533558696508408,
0.01063759345561266,
-0.018742412328720093,
-0.0023336736485362053,
0.017385445535182953,
0.009602239355444908,
-0.004993106704205275,
0.047143660485744476,
-0.05717456340789795,
0.019255083054304123,
0.024964818730950356,
-0.004973138216882944,
-0.07715117931365967,
-0.033623289316892624,
0.027290014550089836,
0.020526006817817688,
0.057819951325654984,
-0.0792984738945961,
-0.017045726999640465,
0.00684641906991601,
-0.04203515499830246,
0.027788029983639717,
-0.0388798825442791,
-0.0050883605144917965,
-0.048919398337602615,
-0.015478783287107944,
-0.01071866974234581,
-0.021074887365102768,
0.04076468199491501,
0.047958314418792725,
-0.011314598843455315,
0.02040047198534012,
-0.01651526801288128,
-0.050444431602954865,
0.03204107657074928,
0.016569551080465317,
0.010563916526734829,
-0.009537865407764912,
0.06821879744529724,
-0.026299864053726196,
-0.029119431972503662,
0.03622102737426758,
-0.033192768692970276,
0.013420000672340393,
-0.00437696510925889,
0.006623892113566399,
-0.042037658393383026,
0.07290803641080856,
0.01603694073855877,
0.042359039187431335,
0.004679246339946985,
0.007229890674352646,
-0.016837267205119133,
-0.03413424268364906,
-0.01804456114768982,
-0.003167335642501712,
0.026803234592080116,
-0.030779581516981125,
0.018727267161011696,
0.05012163892388344,
-0.01791645772755146,
-0.00040233347681351006,
0.010669773444533348,
0.0044745891354978085,
0.014078451320528984,
-0.02429964579641819,
0.0074746375903487206,
-0.02443520911037922,
-0.01454300619661808,
0.007112839259207249,
0.015060785226523876,
-0.02737571857869625,
-0.002054421929642558,
0.01704566739499569,
-0.03579012304544449,
-0.001468256232328713,
-0.036562517285346985,
-0.05425417795777321,
-0.04462722688913345,
0.0020453492179512978,
-0.02965664491057396,
-0.032103948295116425,
-0.0252432432025671,
0.03369870409369469,
-0.014391953125596046,
-0.010604405775666237,
0.016704430803656578,
0.019880102947354317,
-0.007075370289385319,
-0.042833730578422546,
0.0009520410094410181,
-0.04188208654522896,
0.02720288746058941,
0.0316363126039505,
-0.0032835223246365786,
-0.022244682535529137,
-0.04041178151965141,
-0.03330622613430023,
0.03801458328962326,
0.08311782777309418,
-0.02211030386388302,
-0.039125554263591766,
0.0004891786957159638,
-0.0003892017703037709,
0.026712361723184586,
-0.010251585394144058,
-0.0029722771141678095,
0.027548789978027344,
-0.024101564660668373,
-0.016203731298446655,
-0.006689359433948994,
0.004876998718827963,
-0.016532067209482193,
0.013271034695208073,
0.02332690730690956,
0.025016814470291138,
-0.0009775315411388874,
0.009317786432802677,
0.00019312997756060213,
0.004929537419229746,
0.0014854456530883908,
0.041577354073524475,
-0.0036874290090054274,
-0.010344836860895157,
-0.004369952715933323,
0.00746389664709568,
-0.08831270784139633,
0.017256738618016243,
-0.01995975710451603,
0.026074128225445747,
-0.029669545590877533,
0.007979207672178745,
0.05134521424770355,
-0.0660957470536232,
0.01053845789283514,
0.05538026988506317,
-0.01030556671321392,
-0.009531043469905853,
0.03433815762400627,
0.02541283890604973,
0.017375249415636063,
0.013611583039164543,
-0.01792752929031849,
0.015540977008640766,
-0.03382665291428566,
-0.006709532346576452,
0.0036028430331498384,
0.021727005019783974,
-0.0006247709388844669,
-0.021498672664165497,
0.01832559145987034,
-0.0068894135765731335,
0.03247992694377899,
0.021503662690520287,
0.011496209539473057,
-0.009859575890004635,
-0.03334520757198334,
0.018103089183568954,
0.021752791479229927,
-0.05020344629883766,
0.044143665581941605,
-0.0002040749677689746,
0.07598656415939331,
0.02994309365749359,
0.03488853573799133,
-0.029141146689653397,
-0.02901497296988964,
0.034448835998773575,
0.03067759796977043,
-0.0002912133058998734,
0.0018128007650375366,
-0.017170816659927368,
0.0069040036760270596,
-0.011539196595549583,
-0.015574193559587002,
0.025809859856963158,
-0.06225821003317833,
-0.006245868280529976,
-0.011017330922186375,
0.00018122774781659245,
0.015534243546426296,
-0.024043627083301544,
-0.005169700365513563,
0.03547772392630577,
0.03699261322617531,
0.05045311152935028,
-0.004506845958530903,
0.009370137006044388,
0.06855937838554382,
-0.0072537693195044994,
0.027970312163233757,
-0.04172750934958458,
0.015977639704942703,
0.005695919971913099,
0.02731722593307495,
0.014940731227397919,
-0.01575208082795143
] |
<p>I need to find a parachutist's displacement after a given height (nearly 37000m) and at a given latitude. I have his mass, area, parachute area, drop height, parachute deployment height, data about the atmosphere, and other assorted values. I don't have velocity and Temperature so I'm stuck. Please help.</p>
<p>My issues:</p>
<p>finding pressure change without temperature: $V(dP/dt) = nR(PV/NR)$ (doing that would result in the original pressure for pressure change...)?</p>
<p>using pressure change to find density change: again, no temperature, and if you substitute temp for PV/NR you end up canceling the pressure terms making using the pressure derivative futile? $ Density = (P*Mw)/(RT)$</p>
<p>using density change to find drag change: No velocity given so what do I do?
$Drag = Cd*A*.5*r*v^2$, where $r = drag$</p>
<p>using drag to net force to find acceleration: $drag/m = a$? </p>
<p>repeat last few steps for the parachute:...</p>
<p>Find how fast the earth rotates, and use the two velocities (earth/person) to find salient times: ?</p>
<p>Use the above to find: total displacement</p>
<p><em>Note</em> I'd need to stick to the above process and I didn't give values because I'd prefer to get help with strategies. </p> | 2,038 | [
-0.012221088632941246,
-0.012902498245239258,
-0.024342859163880348,
0.04148564487695694,
0.04074383154511452,
-0.029247138649225235,
-0.037596795707941055,
-0.037318155169487,
0.016117123886942863,
-0.02506868913769722,
0.0253575649112463,
0.03308689966797829,
0.0547860749065876,
0.03153664618730545,
0.036113232374191284,
-0.022230196744203568,
-0.020646074786782265,
-0.004064516630023718,
0.03625654801726341,
-0.004182595293968916,
-0.008082566782832146,
0.0004006877134088427,
0.01438027061522007,
-0.041486795991659164,
0.013005323708057404,
0.007162406574934721,
0.04510028660297394,
-0.01487814262509346,
-0.025862164795398712,
0.07292161136865616,
-0.03755057230591774,
-0.02279185689985752,
0.03284386917948723,
0.002263105707243085,
0.008744215592741966,
0.020272932946681976,
-0.07546234130859375,
-0.002348927315324545,
0.0100790336728096,
0.03604397550225258,
-0.01306262519210577,
-0.012604313902556896,
0.005960345268249512,
0.04253385588526726,
-0.007613607216626406,
0.023272302001714706,
0.019229523837566376,
-0.002211961429566145,
0.07453744858503342,
-0.05974488705396652,
0.048488885164260864,
0.023360559716820717,
0.042859043926000595,
0.048204995691776276,
-0.02671920135617256,
0.007214654237031937,
0.05417356267571449,
0.04896961525082588,
-0.01104770228266716,
-0.0536087267100811,
-0.015214410610496998,
-0.05854622274637222,
-0.007448748219758272,
-0.01901189051568508,
0.0033842134289443493,
0.007214620243757963,
-0.022841835394501686,
0.016157492995262146,
0.02076047472655773,
-0.02788402885198593,
0.01512173842638731,
-0.01802995428442955,
-0.0029841477517038584,
-0.025919277220964432,
0.01935502141714096,
-0.029452094808220863,
0.014561211690306664,
0.008979033678770065,
0.03891780227422714,
0.053969770669937134,
-0.021512387320399284,
0.03652913495898247,
0.04485360532999039,
0.005135308485478163,
0.012605163268744946,
-0.008037576451897621,
0.0605698823928833,
0.01573268696665764,
-0.01670685224235058,
0.0031034040730446577,
-0.001901488285511732,
-0.014152592979371548,
0.010588083416223526,
-0.019860392436385155,
-0.0013135888148099184,
0.028638387098908424,
-0.007251884322613478,
0.057780127972364426,
0.005813888274133205,
-0.05849925056099892,
-0.025450536981225014,
-0.04022727161645889,
0.01634947583079338,
0.0604923851788044,
-0.01705360785126686,
-0.0015341804828494787,
-0.019929341971874237,
-0.03333599492907524,
0.009059859439730644,
-0.05239921808242798,
-0.0353342667222023,
-0.0006200216012075543,
-0.04532139003276825,
-0.05682062357664108,
-0.0031894848216325045,
-0.026709625497460365,
-0.01129352580755949,
-0.026192832738161087,
0.037388287484645844,
0.010654805228114128,
0.09300556033849716,
0.00831802748143673,
0.022216396406292915,
-0.013767999596893787,
-0.054116278886795044,
0.01672147773206234,
0.031194407492876053,
-0.006752105429768562,
-0.036574553698301315,
0.014427986927330494,
-0.006116053555160761,
-0.03895680606365204,
0.017336539924144745,
-0.022161997854709625,
0.021478530019521713,
0.011452505365014076,
-0.08755839616060257,
-0.06117317080497742,
0.00677459966391325,
0.001966268289834261,
0.0013006891822442412,
-0.05783383175730705,
-0.006265288218855858,
-0.004572284873574972,
0.0807686373591423,
0.008726916275918484,
0.029292630031704903,
-0.014628451317548752,
0.02254926972091198,
-0.01073493342846632,
-0.029965007677674294,
0.003939816262573004,
0.01708304136991501,
-0.045054662972688675,
-0.023787394165992737,
-0.08282974362373352,
0.040252503007650375,
0.006446674931794405,
-0.007881008088588715,
-0.022474775090813637,
0.035932861268520355,
-0.014561749994754791,
0.00535288592800498,
-0.02007340081036091,
0.03228569030761719,
-0.0010708972113206983,
0.06795831769704819,
0.012095103040337563,
-0.025452448055148125,
0.03131232038140297,
0.023863285779953003,
0.019019851461052895,
0.012267372570931911,
-0.009462011978030205,
0.07606577128171921,
-0.01929929107427597,
0.026726683601737022,
-0.03546656295657158,
0.0041856588795781136,
-0.026675699278712273,
-0.03603336960077286,
-0.04129220172762871,
-0.012791943736374378,
0.019489727914333344,
-0.005979356821626425,
0.05271419510245323,
0.014326435513794422,
0.0003481648745946586,
-0.0016088656848296523,
-0.0340224951505661,
-0.007414799649268389,
-0.0602416954934597,
0.01576157845556736,
-0.02374492771923542,
0.00872824341058731,
0.01145025622099638,
0.013911508955061436,
0.05102039873600006,
-0.010015185922384262,
-0.03272753953933716,
0.02040301077067852,
0.02596658281981945,
0.04499530419707298,
0.008300159126520157,
0.00017106342420447618,
0.049915459007024765,
0.031283311545848846,
0.00873718410730362,
-0.002205281751230359,
-0.010514382272958755,
-0.017926784232258797,
0.0039901407435536385,
-0.02465023100376129,
0.0010896528838202357,
0.012839794158935547,
-0.017128825187683105,
0.009981432929635048,
0.031028013676404953,
-0.002510967431589961,
0.0035988534800708294,
-0.01753745786845684,
0.09100299328565598,
0.06937841325998306,
0.005088062956929207,
0.02491307258605957,
0.043003782629966736,
0.021845197305083275,
-0.009216474369168282,
0.0061093163676559925,
-0.022751402109861374,
-0.04197471961379051,
-0.00710478937253356,
0.018346596509218216,
0.01204393245279789,
-0.022663723677396774,
0.02902103401720524,
0.06141357123851776,
0.004618389066308737,
0.04524792730808258,
0.04055624082684517,
0.00763677665963769,
-0.02429019659757614,
0.01294231228530407,
0.011862397193908691,
-0.00829983502626419,
0.017401330173015594,
-0.023680616170167923,
0.03341885656118393,
0.042774345725774765,
-0.019065894186496735,
0.01938518136739731,
0.042111266404390335,
0.016715120524168015,
0.000987136852927506,
0.019213367253541946,
-0.00546619575470686,
0.04224677011370659,
0.004924716427922249,
0.000015451643776032142,
0.06453189998865128,
0.03222625330090523,
-0.013854587450623512,
-0.024953074753284454,
-0.009735668078064919,
0.042194075882434845,
0.01860879920423031,
-0.023796681314706802,
0.013321210630238056,
0.02699049562215805,
-0.05545506626367569,
-0.013019029051065445,
-0.025498006492853165,
0.024241404607892036,
-0.06538453698158264,
0.0018092452082782984,
-0.002406157087534666,
0.011681879870593548,
0.035048846155405045,
-0.0010213048662990332,
-0.016926448792219162,
-0.015976453199982643,
-0.04745358228683472,
-0.011255687102675438,
-0.014822783879935741,
-0.07017649710178375,
0.02216191403567791,
-0.0028486549854278564,
-0.03735114634037018,
0.060333944857120514,
-0.006619252264499664,
-0.04013633728027344,
0.018291916698217392,
-0.015250076539814472,
-0.02533634379506111,
-0.0007758648716844618,
-0.011377527378499508,
0.012872879393398762,
-0.05291924625635147,
-0.03929092362523079,
0.07065596431493759,
-0.016876719892024994,
-0.008224320597946644,
0.04136356711387634,
-0.03292416036128998,
-0.03927101939916611,
-0.027715468779206276,
-0.000214099301956594,
0.01155352033674717,
-0.018211575224995613,
0.0048047699965536594,
-0.0021103941835463047,
0.01042474340647459,
0.011788919568061829,
-0.06022518873214722,
-0.038685888051986694,
-0.007699707057327032,
0.0204393919557333,
0.0518350675702095,
-0.001468509086407721,
-0.016483698040246964,
0.05822877213358879,
0.018334534019231796,
-0.021567992866039276,
-0.04029369354248047,
0.04056370630860329,
-0.027322428300976753,
-0.010810998268425465,
0.004722520709037781,
-0.0050290790386497974,
-0.030672941356897354,
-0.020391780883073807,
-0.008440048433840275,
-0.0032696365378797054,
0.039242081344127655,
0.0282138679176569,
0.0008985416498035192,
0.015936458483338356,
0.02565237134695053,
0.002974336501210928,
0.07482828199863434,
0.010926436632871628,
-0.031097542494535446,
0.021286476403474808,
-0.027250807732343674,
0.021626301109790802,
0.006846755277365446,
-0.0670897513628006,
0.04211251065135002,
0.008757669478654861,
-0.02365132048726082,
-0.008140932768583298,
0.03137318044900894,
0.008489980362355709,
-0.022888220846652985,
-0.002362751867622137,
0.026682764291763306,
0.022854328155517578,
-0.012654520571231842,
-0.013670499436557293,
0.05136713758111,
0.04118272662162781,
-0.03862330690026283,
-0.033902857452631,
-0.028270015493035316,
-0.013365146704018116,
0.024248162284493446,
-0.00013799658336210996,
-0.04724108427762985,
0.05867637321352959,
0.04236163571476936,
0.04920167475938797,
0.0020997878164052963,
-0.029253358021378517,
0.04054701700806618,
-0.06472670286893845,
0.0063776131719350815,
0.0050354874692857265,
0.06402219086885452,
-0.019454682245850563,
0.06333325803279877,
0.04423482343554497,
0.04023627191781998,
0.03406214341521263,
0.03529492765665054,
-0.06240127980709076,
0.05529290810227394,
-0.03620380908250809,
-0.023627249523997307,
0.003505771979689598,
0.013339568860828876,
0.0059652142226696014,
-0.04838283360004425,
-0.0050537376664578915,
0.01702999509871006,
0.020441671833395958,
-0.06422258913516998,
0.01214964035898447,
-0.04866723343729973,
-0.004386006388813257,
-0.01846887543797493,
0.01857423409819603,
0.03723466768860817,
0.0013091786531731486,
0.04917801171541214,
0.07871459424495697,
-0.006102452054619789,
0.014591456390917301,
-0.045248474925756454,
-0.012123246677219868,
0.00427766889333725,
0.06597580015659332,
0.009836651384830475,
0.00492451386526227,
0.009245135821402073,
0.021449001505970955,
-0.028020566329360008,
0.02987404353916645,
-0.012225205078721046,
0.027001578360795975,
-0.00912313349545002,
-0.05553437024354935,
0.0011556186946108937,
0.015913231298327446,
0.024830374866724014,
-0.01316912192851305,
0.015662984922528267,
0.03621674329042435,
-0.0009276079363189638,
0.014942090958356857,
0.040047261863946915,
0.06320390105247498,
-0.05473514273762703,
0.006085970904678106,
-0.02801959030330181,
-0.019839689135551453,
-0.035525184124708176,
-0.04690711572766304,
0.0029458622448146343,
0.033320482820272446,
0.0006542421760968864,
-0.035350531339645386,
0.05483061075210571,
-0.04657335579395294,
-0.009164808318018913,
0.0317780002951622,
0.028105292469263077,
0.03902212530374527,
-0.03704143315553665,
-0.028333822265267372,
0.004895141813904047,
0.024594230577349663,
0.05259593948721886,
-0.05318037047982216,
0.014715303666889668,
-0.09706620126962662,
-0.009555519558489323,
0.028455497696995735,
0.07245095819234848,
-0.018561499193310738,
0.01974300481379032,
-0.052185580134391785,
-0.043058909475803375,
0.05843481793999672,
-0.018942473456263542,
0.021654268726706505,
0.005359319970011711,
0.0425160713493824,
0.006818036548793316,
-0.04075581207871437,
-0.033388327807188034,
0.01094105839729309,
-0.020324325188994408,
0.0163193978369236,
-0.02658802643418312,
0.0018315052147954702,
-0.013015187345445156,
-0.014323724433779716,
0.04365835711359978,
0.04640048369765282,
0.030863314867019653,
-0.018527915701270103,
-0.019751274958252907,
-0.02326327934861183,
-0.03515903651714325,
-0.06682944297790527,
-0.026207752525806427,
-0.008034534752368927,
-0.01917865313589573,
0.007671777158975601,
-0.004906665068119764,
-0.06494491547346115,
0.04208652302622795,
0.01660582236945629,
-0.03587591275572777,
-0.014804375357925892,
-0.058083564043045044,
0.02864205464720726,
0.02599876932799816,
0.019236663356423378,
0.018617140129208565,
0.03998400643467903,
0.002913504606112838,
0.02128538303077221,
-0.011815042234957218,
0.0002727401733864099,
-0.01777924783527851,
0.0067957928404212,
-0.02677537128329277,
0.0082272719591856,
-0.04154050350189209,
0.010868861339986324,
0.008674721233546734,
0.019649162888526917,
-0.015195022337138653,
-0.024489590898156166,
0.0027167925145477057,
0.020649142563343048,
-0.0010718218982219696,
0.025502072647213936,
0.004388542380183935,
-0.03222506493330002,
-0.00431293249130249,
-0.03152706101536751,
-0.0006486564525403082,
0.033729586750268936,
-0.004530311096459627,
0.016415119171142578,
-0.005141971167176962,
0.001465948997065425,
-0.033210720866918564,
-0.007065534591674805,
0.01598447374999523,
-0.06516499817371368,
0.062121257185935974,
-0.00381496106274426,
0.02695504017174244,
0.03953922912478447,
-0.051587287336587906,
-0.0430050790309906,
0.019896693527698517,
0.02893046662211418,
-0.0216009970754385,
-0.05861804634332657,
-0.0009465533657930791,
0.0029800257179886103,
0.034467682242393494,
-0.030786151066422462,
-0.03189732879400253,
0.028394926339387894,
0.01990206353366375,
-0.015941692516207695,
-0.04792710021138191,
0.00005566052277572453,
-0.05013834685087204,
-0.04096991941332817,
-0.0027223301585763693,
0.05526772513985634,
-0.010852993465960026,
0.016386793926358223,
0.01913127303123474,
0.030077824369072914,
0.09546662867069244,
-0.03004002384841442,
0.04332093521952629,
0.006157624535262585,
0.011134820058941841,
-0.019715704023838043,
-0.028959020972251892,
0.04095856100320816,
-0.03910849988460541,
-0.01994463987648487,
0.005818159319460392,
-0.019072217866778374,
0.02184530720114708,
-0.020170269533991814,
0.005832978058606386,
0.02634315751492977,
0.004551106132566929,
-0.008606195449829102,
-0.028602201491594315,
0.023830533027648926,
-0.0029294725973159075,
0.0113176004961133,
-0.027689294889569283,
0.02226635068655014,
-0.011384943500161171,
-0.014028406701982021,
0.0010303963208571076,
0.004507292062044144,
0.018636109307408333,
0.012681979686021805,
0.07193953543901443,
-0.028548192232847214,
0.004223302472382784,
0.055070213973522186,
0.011358467862010002,
0.04600163549184799,
0.03539295494556427,
-0.05528953671455383,
0.01068863831460476,
-0.010815436951816082,
-0.024500295519828796,
-0.020646100863814354,
-0.0061821648851037025,
-0.0049436395056545734,
0.08242359012365341,
-0.03779095783829689,
0.039739955216646194,
-0.013503793627023697,
0.012737924233078957,
0.02385741099715233,
0.0006113669369369745,
-0.033752430230379105,
-0.012206640094518661,
-0.013907027430832386,
0.05021795630455017,
0.008263970725238323,
0.006334351841360331,
0.023362623527646065,
0.025664139539003372,
0.012859152629971504,
0.021138247102499008,
-0.0020527872256934643,
-0.010774081572890282,
0.014744620770215988,
-0.023405080661177635,
-0.03419395163655281,
-0.004778186324983835,
-0.02023432031273842,
0.038752421736717224,
-0.04533118009567261,
-0.0220023225992918,
0.04931579902768135,
0.019269945099949837,
0.011697887443006039,
-0.05035661160945892,
-0.0148503752425313,
-0.045265696942806244,
-0.02043461799621582,
0.028578074648976326,
-0.020913414657115936,
0.009216897189617157,
0.025163952261209488,
0.08168094605207443,
-0.012179362587630749,
0.029660340398550034,
-0.030241169035434723,
-0.024734843522310257,
-0.01670258678495884,
-0.03710252791643143,
-0.05755750834941864,
0.05333622172474861,
0.0047409976832568645,
-0.04321989417076111,
0.048039816319942474,
0.02968723326921463,
0.006873919162899256,
0.030687585473060608,
0.006501264404505491,
-0.02575056254863739,
0.08727356791496277,
-0.007090623490512371,
-0.03418001905083656,
-0.004649756476283073,
-0.003318501403555274,
0.11432714015245438,
0.04069021716713905,
0.02605357952415943,
-0.022087115794420242,
0.013540273532271385,
-0.015165944583714008,
0.02331332303583622,
-0.01691654697060585,
0.009162265807390213,
0.013165508396923542,
0.007507493253797293,
0.017578279599547386,
0.0278644859790802,
-0.007585862185806036,
-0.013990423642098904,
0.01760663278400898,
-0.03760222718119621,
-0.026627788320183754,
0.011167846620082855,
0.004860597662627697,
-0.02638968452811241,
-0.007352402899414301,
-0.027079302817583084,
0.03598976135253906,
-0.05202977731823921,
-0.006726284511387348,
-0.04186330735683441,
-0.0534052699804306,
0.016127321869134903,
0.0023531520273536444,
-0.0749981477856636,
0.015418969094753265,
0.01681273803114891,
0.005207001697272062,
-0.041052114218473434,
0.01787312515079975,
-0.023281682282686234,
-0.036378152668476105,
0.0163993202149868,
0.04899081587791443,
0.008061106316745281,
0.0000032680998174328124,
0.014287460595369339,
0.007978689856827259,
-0.02885318361222744,
0.003461994929239154,
-0.026267629116773605,
0.03765854611992836,
-0.0014046740252524614,
-0.0034559702035039663,
0.0038507296703755856,
-0.02852221392095089,
-0.030533218756318092,
-0.04271584004163742,
-0.0022587620187550783,
-0.0008156342664733529,
0.013661084696650505,
0.006761600729078054,
-0.008003861643373966,
-0.007537674158811569,
-0.00883663259446621,
0.017074452713131905,
0.003802441293373704,
-0.013337312266230583,
0.03214074671268463,
-0.016104338690638542,
-0.012420346960425377,
0.07583308964967728,
-0.05445513501763344,
-0.0198399368673563,
-0.045140184462070465,
-0.023538021370768547,
-0.022117825224995613,
0.00036889282637275755,
0.028190668672323227,
-0.00832606665790081,
-0.018900925293564796,
-0.00791310053318739,
-0.008188286796212196,
-0.03532368689775467,
-0.04242602363228798,
0.01971341483294964,
0.0017162688309326768,
-0.016287222504615784,
-0.025480924174189568,
-0.019046960398554802,
0.032335277646780014,
0.01190709974616766,
0.023051470518112183,
-0.004480733070522547,
-0.016819505020976067,
0.06166424974799156,
0.03618760406970978,
-0.05094252526760101,
-0.034227222204208374,
0.012760586105287075,
-0.033614739775657654,
0.03080919198691845,
-0.02093038521707058,
0.05178341642022133,
0.03782954066991806,
-0.0009878936689347029,
-0.026408199220895767,
-0.01884848065674305,
-0.02689911238849163,
0.034571096301078796,
0.01626027189195156,
-0.011903111822903156,
-0.012709719128906727,
0.02860543690621853,
0.020275337621569633,
-0.010257016867399216,
-0.01736794412136078,
-0.027520939707756042,
0.008201646618545055,
-0.004834780003875494,
-0.015856748446822166,
-0.011480551213026047,
0.009536578319966793,
-0.02790580317378044,
0.018491484224796295,
-0.0203364510089159,
0.06159742921590805,
-0.04596966132521629,
0.003471619915217161,
-0.01473053265362978,
0.0038953626062721014,
-0.008747648447751999,
0.00210671778768301,
-0.058289170265197754,
-0.024352235719561577,
0.015748141333460808,
0.049272242933511734,
0.0104026785120368,
-0.01653783954679966,
-0.0028670188039541245,
0.00367914792150259,
0.05144215747714043,
-0.02120513655245304,
-0.04584237188100815,
0.04903081804513931,
-0.02505643479526043,
-0.07556189596652985,
0.05341265723109245,
0.001188160851597786,
0.09030195325613022,
-0.00971738900989294,
-0.013839525170624256,
-0.015501790679991245,
0.07203461229801178,
-0.013057040981948376,
0.010800031013786793,
-0.008215213194489479,
-0.04779186472296715,
-0.007379619404673576,
-0.03572908416390419,
0.008769946172833443,
-0.03073720447719097,
-0.00468862522393465,
0.03485382720828056,
0.005843489896506071,
-0.01898154802620411,
0.027497367933392525,
0.025875629857182503,
0.01971869356930256,
0.0007961289375089109,
0.026428913697600365,
-0.020844047889113426,
0.0246199369430542,
0.037477198988199234,
-0.013757798820734024,
0.004852294456213713,
-0.009592514485120773,
0.03343363478779793,
-0.10552463680505753,
0.01882648468017578,
0.0044828434474766254,
0.011979244649410248,
0.03934425488114357,
-0.08169513940811157,
0.002911292714998126,
0.035766422748565674,
-0.027543291449546814,
-0.009253285825252533,
-0.04985613003373146,
0.0013566542183980346,
0.020401207730174065,
0.003506405046209693,
0.014175140298902988,
-0.0013911898713558912,
0.04495399817824364,
0.02203892543911934,
-0.011735910549759865,
0.015652913600206375,
-0.0075844223611056805,
-0.03841657191514969,
0.0035737392026931047,
0.019859394058585167,
0.0032882357481867075,
-0.027814999222755432,
0.020212149247527122,
-0.006281556561589241,
-0.007995461113750935,
0.01793500781059265,
-0.0566147081553936,
0.039936795830726624,
-0.015203289687633514,
0.01513783261179924,
-0.005395254585891962,
0.030899574980139732,
0.03434041142463684,
0.0029362617060542107,
-0.006651362404227257,
0.022075684741139412,
0.0232074037194252,
0.042341653257608414,
-0.04462556540966034,
-0.0154854916036129,
-0.0006707872962579131,
0.002709972206503153,
-0.01682828553020954,
0.03496389463543892,
-0.02093731425702572,
-0.006797350011765957,
0.03251342475414276,
0.0015751796308904886,
-0.0003090727550443262,
-0.04139294847846031,
0.0069812568835914135,
-0.04055323079228401,
0.019112927839159966,
0.0149197643622756,
-0.024125097319483757,
0.0021102996543049812,
0.026934035122394562,
0.008383611217141151,
-0.03481997922062874,
-0.007623234298080206,
-0.028133763000369072,
-0.039041340351104736,
-0.02111305668950081,
0.020326605066657066,
-0.00703119020909071,
-0.04059296101331711,
-0.025253714993596077,
0.006642001215368509,
-0.047380927950143814,
0.027645250782370567,
0.02603132277727127,
-0.001115823513828218,
0.003872618079185486,
0.018638355657458305,
0.03012414462864399,
-0.09237277507781982,
0.02512270025908947,
0.00974295474588871,
-0.04741346836090088,
-0.049949537962675095,
-0.022959014400839806,
0.01423072163015604,
0.034072406589984894,
0.06314432621002197,
-0.03694175183773041,
0.019325247034430504,
0.028333045542240143,
-0.03049335442483425,
-0.001472158939577639,
-0.05042203888297081,
0.04426481947302818,
-0.005460689309984446,
-0.04853147268295288,
0.022416871041059494,
-0.024530718103051186,
-0.007486382964998484,
0.007226950488984585,
0.01829598657786846,
0.01282016932964325,
0.0422852486371994,
0.02318088337779045,
0.004276863299310207,
0.018205657601356506,
-0.002740646479651332,
0.009684544987976551,
0.03990483283996582,
0.006894425489008427,
0.0015460732392966747,
0.01686745509505272,
0.032103829085826874,
-0.035215336829423904,
0.08790548145771027,
-0.021146045997738838,
-0.05748458951711655,
-0.0010781125165522099,
-0.047715671360492706,
0.007847846485674381,
-0.07432905584573746,
0.0021151299588382244,
0.03369172662496567,
-0.021850507706403732,
0.003827302949503064,
0.03907380253076553,
0.00881845224648714,
0.023422423750162125,
-0.03294447436928749,
0.023437896743416786,
0.03522661328315735,
-0.05816539004445076,
0.005204566288739443,
0.0003023800964001566,
0.045463334769010544,
-0.009893990121781826,
0.020793015137314796,
0.03907492756843567,
0.0065885549411177635,
0.016467072069644928,
0.00628121942281723,
0.018140699714422226,
-0.007373821921646595,
-0.015194298699498177,
0.009498241357505322,
-0.03197237849235535,
-0.012979552149772644,
-0.0005387580604292452,
-0.031102726235985756,
0.04356703162193298,
-0.025162970647215843,
0.02720528654754162,
-0.008513974025845528,
-0.005505403503775597,
-0.05399591848254204,
0.020610706880688667,
0.0018586337100714445,
-0.0025719187688082457,
0.011876705102622509,
-0.028187919408082962,
-0.007666957564651966,
-0.0011990874772891402,
0.030110368505120277,
-0.015221668407320976,
0.04568008705973625,
-0.007795695681124926,
-0.025982040911912918,
-0.0030487203039228916,
-0.050099682062864304,
-0.027246776968240738,
-0.02772662788629532,
0.048341091722249985,
0.012968536466360092,
0.008900082670152187,
-0.011741367168724537,
-0.04260917007923126,
-0.010463993065059185,
0.05799601599574089,
-0.03770538792014122,
-0.04068875312805176,
-0.0015186049276962876,
0.02059691585600376,
-0.0042044613510370255,
-0.01829199120402336
] |
<p>The eigenfunctions of a Hermitian operator are real. But consider a function $\psi(x)=e^{-\kappa x}$, $x\in\mathbb{R}$, where $\kappa$ is a real constant. Then, $$\hat p \psi(x)=-i\hbar \frac{d}{dx}e^{-\kappa x}=i\kappa \hbar \psi(x).$$ This gives a pure imaginary eigenvalue. Is it not a contradiction? Or am I missing some crucial point?</p> | 2,039 | [
-0.00792611949145794,
-0.00871986709535122,
-0.016591040417551994,
-0.061289168894290924,
0.0353144146502018,
-0.015018496662378311,
-0.042449209839105606,
-0.02062155492603779,
0.01979527249932289,
-0.04070140793919563,
0.030388163402676582,
0.03451824188232422,
0.06384995579719543,
0.00011052012268919498,
-0.006933930795639753,
0.04541577771306038,
-0.0420871339738369,
-0.016282904893159866,
-0.01948097161948681,
0.014394625090062618,
-0.01005643792450428,
0.06899632513523102,
0.03294381499290466,
-0.01668117754161358,
0.0017242218600586057,
0.033348046243190765,
0.005430185701698065,
0.043315496295690536,
-0.005675085820257664,
0.06245250999927521,
-0.019270507618784904,
-0.0053737591952085495,
0.017853567376732826,
0.04965175688266754,
0.014509360305964947,
-0.020827947184443474,
-0.024110088124871254,
-0.024658629670739174,
-0.005468736402690411,
0.024700159206986427,
-0.033938467502593994,
-0.017782296985387802,
-0.0023816486354917288,
0.02156173065304756,
0.04053286090493202,
0.011026779189705849,
-0.007822767831385136,
-0.042534757405519485,
0.03220699727535248,
-0.049588315188884735,
0.06659887731075287,
-0.007651147898286581,
0.04040227830410004,
0.04378873109817505,
0.005363612901419401,
0.0020664059557020664,
0.07423432916402817,
0.06534060090780258,
-0.008296018466353416,
-0.0568494014441967,
0.0003167965915054083,
-0.020865682512521744,
-0.0011663481127470732,
-0.003007024759426713,
-0.04811376705765724,
-0.0016907076351344585,
0.020486628636717796,
-0.024571284651756287,
0.008847584016621113,
-0.0050506978295743465,
0.008819141425192356,
0.017692646011710167,
0.009829595685005188,
-0.02805410511791706,
0.027070753276348114,
-0.04243044927716255,
0.012970371171832085,
0.036107007414102554,
0.043144356459379196,
0.02008097805082798,
0.0250100065022707,
0.03229245916008949,
0.021243872120976448,
0.0012422763975337148,
0.017459576949477196,
0.04542029649019241,
0.0838799774646759,
-0.003491414012387395,
0.0017484918935224414,
0.04980694502592087,
0.0299167912453413,
0.009691904298961163,
0.03659946843981743,
-0.01977471448481083,
0.0034229320008307695,
0.013555647805333138,
-0.0003939822199754417,
0.025303952395915985,
-0.021644705906510353,
-0.037034690380096436,
0.004130620509386063,
-0.020495163276791573,
0.03676300868391991,
0.030959147959947586,
-0.010953494347631931,
-0.002842632122337818,
-0.023366617038846016,
0.012226331047713757,
0.01792862080037594,
-0.016288600862026215,
-0.053128816187381744,
0.02111539989709854,
-0.04205692186951637,
0.04166087880730629,
0.01927214302122593,
-0.01843305490911007,
0.01908661425113678,
-0.012384438887238503,
0.038739703595638275,
0.06377366930246353,
0.011514083482325077,
-0.031053390353918076,
0.026884369552135468,
-0.04641582444310188,
-0.049559999257326126,
0.054434869438409805,
0.00800826121121645,
0.017372818663716316,
-0.0870589017868042,
-0.011552314274013042,
0.0027234170120209455,
-0.010379220359027386,
0.027790717780590057,
0.020102592185139656,
0.041196901351213455,
-0.01860307715833187,
-0.11751769483089447,
-0.06543474644422531,
0.0009111084509640932,
-0.014554510824382305,
-0.007996409200131893,
-0.09831477701663971,
-0.015114065259695053,
0.03999993950128555,
0.06985555589199066,
0.01213531382381916,
0.0015776382060721517,
-0.033401958644390106,
0.005880238488316536,
0.032621029764413834,
-0.004996237810701132,
-0.06423590332269669,
0.006895157508552074,
-0.06482266634702682,
-0.009752877056598663,
-0.028848182410001755,
0.0013912334106862545,
0.02605159394443035,
0.018393434584140778,
-0.004905433859676123,
0.04432417452335358,
-0.04149443656206131,
0.0008607383933849633,
-0.0033005469013005495,
-0.01629205420613289,
-0.04031562805175781,
0.07748214900493622,
0.03005513921380043,
0.030204007402062416,
0.0009627561084926128,
-0.0038303714245557785,
0.03525853157043457,
0.0037794909439980984,
0.01784525066614151,
-0.006757102441042662,
-0.05100896582007408,
-0.03314189985394478,
-0.05398566275835037,
0.032935209572315216,
0.00018214645388070494,
-0.030051426962018013,
-0.00429421616718173,
-0.014594453386962414,
0.0062051028944551945,
-0.0008102613501250744,
0.05005990341305733,
-0.00975274108350277,
-0.002285116584971547,
0.0049014645628631115,
-0.056461237370967865,
-0.008006160147488117,
-0.03005659207701683,
0.04489786922931671,
0.04465717077255249,
-0.013762974180281162,
0.043317317962646484,
0.03687455877661705,
0.01595316454768181,
-0.027343086898326874,
-0.05211969092488289,
0.011015059426426888,
0.011044892482459545,
0.03376193717122078,
-0.06396109610795975,
0.043207231909036636,
0.03052746132016182,
0.03490583971142769,
0.014221777208149433,
0.06754332780838013,
-0.028903493657708168,
-0.027231762185692787,
0.031882427632808685,
-0.02749975398182869,
0.022073013707995415,
0.009801436215639114,
0.023384233936667442,
-0.003536967094987631,
-0.048508815467357635,
-0.024360790848731995,
0.016531525179743767,
-0.04206927865743637,
0.05832182243466377,
0.02850760892033577,
0.01928451843559742,
0.004117256496101618,
0.015660647302865982,
0.023684168234467506,
0.021056782454252243,
-0.016183217987418175,
-0.05326048657298088,
-0.008107481524348259,
0.02643638290464878,
0.013296734541654587,
0.049414798617362976,
-0.0570145882666111,
0.04496600106358528,
0.01630430854856968,
0.05406590923666954,
0.022379210218787193,
0.006368802394717932,
-0.02267843298614025,
0.0025662670377641916,
0.013787396252155304,
0.024248763918876648,
0.014207941479980946,
0.038529232144355774,
0.02107881009578705,
-0.011901363730430603,
0.028216253966093063,
-0.009728381410241127,
0.017521655187010765,
0.045260198414325714,
-0.06363777816295624,
-0.0038109177257865667,
0.0039641293697059155,
-0.0007496406324207783,
0.03591933101415634,
-0.04336558282375336,
0.001353538827970624,
0.02072860673069954,
-0.03552480787038803,
-0.017142070457339287,
-0.020774034783244133,
-0.0018378086388111115,
0.030381368473172188,
0.008290424942970276,
-0.0421917699277401,
-0.015326506458222866,
0.01950741931796074,
-0.016157975420355797,
0.016084175556898117,
-0.06307618319988251,
-0.0021129646338522434,
-0.0041387202218174934,
-0.00001516600968898274,
0.04901626706123352,
0.03617016598582268,
0.039156798273324966,
-0.038310691714286804,
-0.0491490364074707,
-0.0012690714793279767,
-0.0457661934196949,
0.006576266605407,
0.024432921782135963,
-0.05929972603917122,
0.03509858623147011,
-0.07806351035833359,
-0.016062725335359573,
0.03398566693067551,
0.019024735316634178,
0.03220271319150925,
-0.015452969819307327,
-0.03649791330099106,
-0.047151677310466766,
-0.017480961978435516,
-0.025013422593474388,
-0.0009827751200646162,
-0.04088728502392769,
0.014733335003256798,
0.011951267719268799,
-0.03819526731967926,
0.008916483260691166,
0.0013610554160550237,
0.024432837963104248,
-0.07240259647369385,
-0.006267201621085405,
-0.044047486037015915,
0.04005294293165207,
-0.018745562061667442,
0.0115126334130764,
0.009627736173570156,
-0.04414850473403931,
0.01279980968683958,
-0.03465750068426132,
-0.050581809133291245,
0.04884348064661026,
0.014852422289550304,
0.014589779078960419,
0.03379590064287186,
-0.0016472369898110628,
0.0895501971244812,
0.02694854699075222,
-0.010339224711060524,
-0.015762027353048325,
-0.01456774678081274,
-0.03401848301291466,
-0.02994159236550331,
-0.028980037197470665,
0.02646023780107498,
-0.031533144414424896,
0.05912349000573158,
0.0009241458610631526,
0.012303214520215988,
0.02581903338432312,
-0.014065260998904705,
-0.027037231251597404,
0.043548546731472015,
-0.006346340291202068,
0.007882596924901009,
0.0651450902223587,
-0.0047124046832323074,
-0.009996144101023674,
0.0019489024998620152,
0.00569965410977602,
0.01860598288476467,
-0.027167832478880882,
-0.029335668310523033,
0.052368491888046265,
-0.03468051552772522,
0.05614173039793968,
-0.026465266942977905,
0.06362078338861465,
0.007564625237137079,
-0.0011731336126103997,
-0.0382051058113575,
0.024737292900681496,
0.060796093195676804,
-0.054800573736429214,
0.0100892698392272,
0.038300976157188416,
-0.02875344455242157,
-0.013861985877156258,
0.01389457006007433,
-0.006843614857643843,
-0.03219306841492653,
0.02707398124039173,
-0.04485208913683891,
-0.07491723448038101,
0.06676134467124939,
0.011202114634215832,
0.02306201495230198,
-0.019185837358236313,
-0.04666561633348465,
-0.0013604742707684636,
-0.007856354117393494,
0.019327955320477486,
-0.0037378259003162384,
0.032600559294223785,
-0.008953843265771866,
0.03983507677912712,
0.05674586817622185,
-0.009477860294282436,
-0.010761869139969349,
0.00015027244808152318,
-0.04612768068909645,
0.007352704647928476,
-0.02717689238488674,
0.002198962727561593,
0.003135781502351165,
-0.013096025213599205,
0.0005474761710502207,
-0.038944024592638016,
-0.03431907668709755,
-0.009197462350130081,
-0.03744044527411461,
-0.036167871206998825,
0.030114687979221344,
-0.03650931268930435,
-0.0375632680952549,
-0.03548116609454155,
-0.005493649747222662,
0.018021581694483757,
0.0054116505198180676,
-0.01082555204629898,
0.026028549298644066,
-0.0449683740735054,
0.012841129675507545,
-0.026070808991789818,
0.003313144901767373,
0.027136852964758873,
0.017047777771949768,
0.06029166281223297,
0.007552371826022863,
-0.0024217560421675444,
0.006958454381674528,
-0.014118880033493042,
0.06185135617852211,
0.020688911899924278,
-0.042058493942022324,
0.021332019940018654,
-0.03972078487277031,
0.0025707893073558807,
0.0017968951724469662,
0.06295346468687057,
-0.020297996699810028,
0.008001930080354214,
0.015354841947555542,
-0.0021823891438543797,
-0.011058744974434376,
0.016843745484948158,
0.03669902682304382,
0.03433796018362045,
0.0013534188037738204,
-0.05824773758649826,
0.002754181856289506,
-0.018027713522315025,
0.007561852689832449,
-0.018510421738028526,
-0.037283629179000854,
-0.02459905669093132,
0.01713707111775875,
0.027320552617311478,
-0.028643114492297173,
0.023489227518439293,
-0.009582278318703175,
0.025997914373874664,
0.004773336928337812,
-0.03420029953122139,
-0.01438161451369524,
0.028106147423386574,
0.06410091370344162,
0.0538838766515255,
0.03584505245089531,
-0.0018705443944782019,
-0.04900265112519264,
0.004165250808000565,
0.07095502316951752,
0.029546141624450684,
0.002063704887405038,
-0.020266640931367874,
-0.014453181996941566,
-0.033541545271873474,
0.037651460617780685,
-0.0028788361232727766,
0.048824064433574677,
-0.026848994195461273,
-0.015353536233305931,
0.015474710613489151,
-0.03781874105334282,
-0.01596944034099579,
0.02977403998374939,
0.010484966449439526,
0.015852520242333412,
-0.03345399722456932,
-0.0029054833576083183,
-0.03559653460979462,
0.029640864580869675,
0.018919985741376877,
0.06623780727386475,
0.02355225756764412,
-0.0010594461346045136,
0.00898074172437191,
0.03891459479928017,
-0.008488382212817669,
-0.0805201381444931,
0.015986299142241478,
-0.020870713517069817,
0.0056725735776126385,
0.019394276663661003,
-0.016875140368938446,
-0.038637761026620865,
0.010812177322804928,
0.03187895193696022,
-0.010192634537816048,
0.03616312891244888,
0.0074430713430047035,
0.05437257140874863,
0.036153893917798996,
0.01945485547184944,
0.036880284547805786,
0.04461660608649254,
-0.0029685734771192074,
-0.000997616327367723,
-0.05050886794924736,
0.030815355479717255,
-0.010852601379156113,
-0.013640526682138443,
-0.0387568436563015,
-0.018360307440161705,
-0.019939282909035683,
0.017798811197280884,
0.01239578053355217,
0.0029981688130646944,
0.011982733383774757,
0.0054475488141179085,
-0.006146247498691082,
0.02489420771598816,
-0.05286362022161484,
-0.015652993693947792,
-0.004283190239220858,
0.04706719517707825,
0.0075259217992424965,
-0.020120039582252502,
-0.0010216133669018745,
-0.005057380069047213,
-0.009791982360184193,
0.04009377583861351,
-0.01001425925642252,
0.049836620688438416,
-0.040539439767599106,
-0.023877611383795738,
-0.00392277492210269,
-0.04668483883142471,
0.0019037354504689574,
-0.0253156628459692,
0.014683797955513,
0.0015161236515268683,
-0.04273400828242302,
0.0006276863277889788,
0.0010103340027853847,
-0.010100473649799824,
0.0016211161855608225,
-0.049022018909454346,
0.012140030041337013,
-0.00293812551535666,
-0.009353779256343842,
-0.08421113342046738,
-0.023980509489774704,
0.023819204419851303,
0.00454241456463933,
-0.02623864635825157,
-0.03053675964474678,
-0.006426911801099777,
-0.013589994981884956,
-0.004076414741575718,
0.010416146367788315,
0.008183355443179607,
-0.0387880839407444,
-0.0059099020436406136,
0.02436603605747223,
-0.0010358387371525168,
0.06464365124702454,
-0.027396036311984062,
0.00590095017105341,
-0.014414608478546143,
-0.026800941675901413,
0.012048037722706795,
0.028994711115956306,
0.06006789207458496,
-0.02064918354153633,
-0.013481576927006245,
-0.003912660758942366,
-0.0322212353348732,
0.027082134038209915,
0.009202921763062477,
-0.02617286518216133,
0.0034327127505093813,
0.009093129076063633,
0.03891267254948616,
0.004919309169054031,
0.02488582208752632,
-0.0013517107581719756,
0.026419557631015778,
0.028647294268012047,
-0.007984740659594536,
-0.02534850314259529,
-0.04669007286429405,
0.003996479324996471,
-0.003828145796433091,
0.007922317832708359,
0.003971040714532137,
0.05175565555691719,
-0.030541643500328064,
0.018177544698119164,
0.013540802523493767,
-0.02050543576478958,
-0.025331048294901848,
-0.013082107529044151,
0.005391595885157585,
-0.027256427332758904,
-0.010950236581265926,
-0.03818422928452492,
-0.04509503021836281,
-0.04858703166246414,
0.037333469837903976,
0.02419763058423996,
0.0458524152636528,
0.04442177712917328,
0.027579018846154213,
-0.0019653779454529285,
-0.031336527317762375,
0.005015047267079353,
-0.017631709575653076,
0.007075130008161068,
-0.021060023456811905,
-0.008139100857079029,
-0.04348331689834595,
0.009811022318899632,
0.011840593069791794,
0.06291615962982178,
-0.018093936145305634,
-0.010213634930551052,
0.023968080058693886,
0.037859175354242325,
-0.007493722718209028,
0.023514920845627785,
-0.021606331691145897,
0.015440444462001324,
-0.019607223570346832,
0.03480549529194832,
0.017292896285653114,
-0.01287105306982994,
0.003913670778274536,
-0.01138237863779068,
0.0062531353905797005,
-0.014469816349446774,
-0.0351446159183979,
-0.03724896162748337,
0.024225695058703423,
0.0011052008485421538,
0.01078968308866024,
0.005246583838015795,
-0.0015951975947245955,
0.0008376699406653643,
0.018356287851929665,
0.027060022577643394,
-0.01650424674153328,
-0.05957961082458496,
-0.04891132563352585,
-0.04345110058784485,
-0.02958187460899353,
0.02127941884100437,
0.0020169939380139112,
-0.010975595563650131,
0.03185492753982544,
-0.012174798175692558,
0.028658725321292877,
0.03397325053811073,
0.009588024578988552,
-0.008142467588186264,
0.03134028613567352,
0.04252046346664429,
-0.0034603564999997616,
0.03542141616344452,
0.02449261024594307,
0.11578868329524994,
0.0356135293841362,
0.03569010645151138,
-0.040779128670692444,
0.015556739643216133,
-0.00927602406591177,
0.04135362431406975,
-0.031096192076802254,
0.01574627123773098,
0.0057801753282547,
-0.006418912671506405,
-0.019990358501672745,
0.06197664886713028,
0.020161181688308716,
0.008961748331785202,
0.02188451588153839,
-0.025552403181791306,
-0.06748111546039581,
-0.008787346072494984,
0.028584396466612816,
-0.02152005396783352,
-0.011865619570016861,
-0.008418165147304535,
-0.005957469809800386,
-0.045481082051992416,
0.01615768112242222,
-0.003534770803526044,
-0.03355211392045021,
0.008388923481106758,
-0.006117488257586956,
-0.06936556100845337,
-0.03472864627838135,
0.005534667521715164,
-0.03391262888908386,
-0.010439337231218815,
0.025371624156832695,
0.008695142343640327,
0.000996004673652351,
0.02928336150944233,
0.02455109916627407,
0.007027450017631054,
-0.023316487669944763,
0.019722240045666695,
-0.011729375459253788,
-0.02840028516948223,
-0.014684426598250866,
-0.035539377480745316,
0.05153876170516014,
-0.03887851536273956,
0.027452532202005386,
0.005937456618994474,
-0.03978080302476883,
-0.012179256416857243,
-0.055274415761232376,
-0.012974574230611324,
-0.018637530505657196,
0.0238166656345129,
-0.015868086367845535,
-0.0011329230619594455,
-0.03184335306286812,
0.02736835554242134,
0.032048437744379044,
0.02773302048444748,
-0.015776628628373146,
-0.03975502774119377,
0.014006565324962139,
-0.013790486380457878,
0.035186417400836945,
-0.006847665645182133,
-0.004895657766610384,
0.008493022061884403,
-0.01847299188375473,
-0.05024389550089836,
-0.07210839539766312,
0.01323886401951313,
0.01740015298128128,
0.07305087149143219,
-0.020402997732162476,
-0.013014753349125385,
-0.04403218626976013,
-0.058483872562646866,
-0.021873751655220985,
0.00017875805497169495,
-0.024491971358656883,
-0.004427098203450441,
0.01240366417914629,
0.03910159692168236,
0.058850426226854324,
-0.031364940106868744,
0.009956128895282745,
-0.007677377201616764,
0.007176343817263842,
0.008394376374781132,
-0.03773253411054611,
-0.04309313744306564,
-0.0056528919376432896,
-0.05826931819319725,
0.029203863814473152,
-0.001928928541019559,
-0.021205147728323936,
0.010932971723377705,
0.041758786886930466,
-0.020345255732536316,
0.0424838624894619,
-0.031238310039043427,
-0.0029015911277383566,
0.02823640964925289,
-0.008671358227729797,
0.017331410199403763,
0.04386633634567261,
0.028926117345690727,
-0.04715511575341225,
-0.07780643552541733,
-0.07141047716140747,
0.02123193070292473,
-0.0070383730344474316,
0.02143198996782303,
-0.03767753764986992,
-0.022341594099998474,
0.014028566889464855,
0.01418757438659668,
-0.04416614770889282,
-0.0033558157738298178,
-0.06507427990436554,
0.028904946520924568,
0.03412991017103195,
-0.005055147688835859,
-0.012477175332605839,
-0.0008212592219933867,
-0.0002439494855934754,
-0.010565940290689468,
0.05361420288681984,
0.028298353776335716,
-0.015194284729659557,
0.0027651928830891848,
0.029890265315771103,
0.021555040031671524,
0.021804073825478554,
-0.0012257054913789034,
0.01244838535785675,
0.03461582958698273,
-0.035789575427770615,
-0.03708841651678085,
0.00020254193805158138,
-0.033450447022914886,
0.0031017630826681852,
0.026165487244725227,
-0.02564207650721073,
-0.01594178006052971,
0.017102858051657677,
-0.023206522688269615,
-0.02087036892771721,
-0.008065510541200638,
0.007195332553237677,
-0.001424491056241095,
0.006041389890015125,
0.009616971015930176,
-0.00045266037341207266,
0.017288420349359512,
0.012806319631636143,
0.020547788590192795,
0.01382285077124834,
-0.023440726101398468,
0.015834905207157135,
0.013527091592550278,
0.00831963587552309,
0.02621454745531082,
0.020499134436249733,
0.03017413057386875,
0.04560703784227371,
-0.06699682027101517,
0.0317569226026535,
0.02185683511197567,
0.016197605058550835,
-0.10189120471477509,
-0.01407988928258419,
0.0014454717747867107,
-0.011665587313473225,
0.03312673792243004,
-0.03143608197569847,
0.005249475594609976,
0.043600358068943024,
-0.07264970242977142,
0.02450801245868206,
-0.06393653899431229,
-0.011493600904941559,
-0.03268517553806305,
0.005072733387351036,
-0.03270464763045311,
0.010055212303996086,
0.056604526937007904,
0.06031821668148041,
0.016462212428450584,
0.002806390170007944,
0.04944410175085068,
0.00043776159873232245,
-0.0011466279393061996,
0.032614320516586304,
-0.030359504744410515,
-0.025363733991980553,
0.0897579938173294,
-0.03390079736709595,
-0.0024030187632888556,
0.023006567731499672,
-0.020142965018749237,
-0.02439071424305439,
-0.000012964522284164559,
0.012614921666681767,
0.006360209081321955,
0.03346220403909683,
0.04674959182739258,
-0.02857309579849243,
-0.014405885711312294,
0.005897180177271366,
0.02593201771378517,
0.028477435931563377,
-0.025760525837540627,
0.007393438369035721,
-0.01758195273578167,
-0.048804350197315216,
-0.018334830179810524,
0.01527897547930479,
-0.006770563777536154,
-0.02335813082754612,
-0.009238611906766891,
-0.007015629205852747,
-0.007409695070236921,
-0.03732770308852196,
0.06806696206331253,
-0.04390812665224075,
-0.013294670730829239,
0.007486382033675909,
0.0497012734413147,
-0.027806704863905907,
-0.013343445025384426,
0.011125870980322361,
-0.05990872159600258,
0.026806021109223366,
0.037028953433036804,
-0.02386479824781418,
-0.06950659304857254,
0.008866428397595882,
0.013999531045556068,
0.005469151772558689,
0.027378607541322708,
-0.04274518042802811,
-0.05493631958961487,
0.027300860732793808,
-0.007353527937084436,
0.007009660359472036,
-0.010976654477417469,
-0.020601287484169006,
-0.037651363760232925,
-0.040648337453603745,
0.0369638130068779,
0.019271867349743843,
-0.0023988184984773397,
0.0027828258462250233,
0.003193662967532873,
-0.004501016344875097,
-0.0025066928938031197,
0.042482249438762665,
-0.019097961485385895,
-0.021102113649249077,
0.0037482299376279116,
-0.020260898396372795,
0.0016369367949664593,
-0.04139534384012222,
-0.0038199075497686863,
-0.007352359127253294,
-0.028909623622894287,
-0.007967788726091385,
0.033540088683366776,
-0.022454923018813133,
0.054817527532577515,
0.024372566491365433,
-0.007411620579659939,
0.027455639094114304,
0.023036044090986252,
-0.05218072235584259,
0.07037345319986343,
0.04221345856785774,
0.005400052759796381,
0.08065597712993622,
0.011652213521301746,
0.019898101687431335,
0.03497401997447014,
-0.022730374708771706,
-0.012284002266824245,
0.024313436821103096,
-0.010864838026463985,
-0.030434638261795044,
0.006192701868712902,
0.028127213940024376,
-0.00045542657608166337,
-0.004148503299802542,
-0.01949872262775898,
0.03715040907263756,
-0.03553372994065285,
-0.02797868475317955,
-0.0032468566205352545,
0.0018991606775671244,
0.030726373195648193,
0.0477011539041996,
0.02655697800219059,
0.03140567988157272,
0.012736596167087555,
0.04249999672174454,
0.027150854468345642,
0.0046162791550159454,
-0.021417243406176567,
0.04386215656995773,
0.027091702446341515,
-0.030902106314897537,
0.04195641726255417,
-0.020182883366942406,
0.06128702685236931,
-0.03195037320256233,
-0.034835271537303925,
0.011762980371713638,
-0.020429860800504684,
0.02396106906235218,
0.021236438304185867,
-0.018863670527935028,
0.07272203266620636,
0.0024404835421591997,
0.04759806767106056,
-0.013405503705143929,
-0.00884214136749506,
-0.013116232119500637,
-0.012026187963783741,
0.04823894798755646,
0.022705351933836937,
-0.043647658079862595,
-0.02434343658387661,
-0.02952118217945099,
-0.006042085122317076,
-0.01310645043849945,
-0.060879237949848175,
0.01590069755911827,
0.01386328786611557,
-0.018716029822826385,
-0.044285956770181656,
-0.028889918699860573,
0.0032544529531151056,
-0.014270588755607605,
0.017639577388763428,
0.07240811735391617,
0.008536511100828648,
-0.0101518165320158,
-0.030645664781332016,
-0.014598323032259941,
0.03758886083960533,
-0.05260419845581055,
-0.0030945162288844585,
0.01000335905700922,
0.02027653343975544,
0.018743347376585007,
0.003927161917090416
] |
<p>On page 160 Peskin & Schroeder, they say: </p>
<blockquote>
<p>Therefore we expect $\mathcal{M}^\mu(k)$ to be given by a matrix element of the Heisenberg field $j^\mu$: $$\mathcal{M}^\mu(k) = \int \mathrm{d^4}x \; \exp(\mathrm{i}k \cdot x)\langle f | j^\mu(x) | i\rangle.$$</p>
</blockquote>
<p>Why do they expect that?
Where does this come from? I've seen similar expressions with e.g. two Lorentz indices and so on. I've been taught (obviously not enough) qft through path integrals and have a hard time to make connections between the different formalisms. </p> | 2,040 | [
0.013829324394464493,
-0.01905321143567562,
0.024579016491770744,
-0.02698785997927189,
0.021036162972450256,
0.011444061994552612,
-0.01632091961801052,
-0.024646155536174774,
-0.0073354654014110565,
-0.0019699756521731615,
0.034640323370695114,
0.011316892690956593,
0.09232961386442184,
0.002942908788099885,
0.0009178647887893021,
0.05749383568763733,
-0.027080193161964417,
-0.024485396221280098,
-0.005026022903621197,
-0.02984367124736309,
-0.01811002567410469,
0.06675563752651215,
-0.011590824462473392,
-0.0005878977244719863,
0.007053842768073082,
0.02085794322192669,
-0.022824857383966446,
0.023369504138827324,
0.02005242370069027,
0.0451076403260231,
-0.0013946148101240396,
-0.05031157284975052,
0.02521716058254242,
0.00020672126265708357,
-0.00629730150103569,
0.01828506961464882,
-0.024812957271933556,
-0.018671587109565735,
0.01004498079419136,
0.028873952105641365,
-0.04272141680121422,
-0.03305982053279877,
-0.02439228817820549,
0.002623582724481821,
-0.024365926161408424,
0.03855205699801445,
0.014198282733559608,
-0.03015546314418316,
0.061328403651714325,
-0.05162960663437843,
0.06895441561937332,
0.0468379482626915,
0.0271060261875391,
0.019411679357290268,
-0.01568741165101528,
0.013948861509561539,
0.053210679441690445,
0.06483357399702072,
0.03541859611868858,
-0.06374067068099976,
-0.05845312029123306,
-0.026283426210284233,
0.013914130628108978,
-0.055488165467977524,
0.019985543563961983,
0.004319069441407919,
0.024958595633506775,
-0.013664936646819115,
0.046337518841028214,
-0.007081655319780111,
-0.0027366946451365948,
0.016884250566363335,
0.055403806269168854,
-0.01681174710392952,
0.008039237931370735,
-0.0025802042800933123,
-0.017761914059519768,
-0.013760280795395374,
0.05137599632143974,
-0.014596374705433846,
0.0022799151483923197,
0.005576747003942728,
0.01821974478662014,
0.02500087395310402,
0.006389202084392309,
0.01958129182457924,
0.07087394595146179,
0.009388560429215431,
0.028568094596266747,
-0.003998941741883755,
-0.0217138659209013,
0.03138737380504608,
0.04135116934776306,
-0.03874699026346207,
-0.01853901706635952,
0.03987975791096687,
0.008962656371295452,
0.03044598177075386,
-0.012092286720871925,
0.015689866617321968,
-0.037477198988199234,
-0.008245601318776608,
0.021035047248005867,
0.028341764584183693,
0.03247259557247162,
0.016865605488419533,
-0.009836013428866863,
0.03864419087767601,
-0.02737671509385109,
-0.024990126490592957,
-0.026740742847323418,
0.013843330554664135,
-0.02902250364422798,
0.027850423008203506,
0.01294315978884697,
-0.018975289538502693,
0.0012764548882842064,
0.016575897112488747,
0.043143294751644135,
0.08201207965612411,
0.015819016844034195,
-0.025126377120614052,
0.010907093994319439,
-0.08723360300064087,
-0.0922585055232048,
0.02453051134943962,
0.029995840042829514,
0.013414368964731693,
-0.0604686476290226,
-0.0006984748179093003,
0.028797119855880737,
0.004806110635399818,
-0.004770913161337376,
0.02910996414721012,
0.0023709696251899004,
-0.05612372234463692,
-0.08893375098705292,
-0.06946595758199692,
0.060916393995285034,
-0.022185925394296646,
0.0018957428401336074,
-0.06263094395399094,
0.006049833260476589,
0.04880019277334213,
0.099869504570961,
-0.020780134946107864,
0.01163362804800272,
0.007929190993309021,
0.035891901701688766,
0.021047204732894897,
-0.012708951719105244,
-0.05284462869167328,
-0.04739910736680031,
-0.029105214402079582,
-0.009116561152040958,
-0.029329409822821617,
0.013658398762345314,
0.04789779707789421,
-0.005473793018609285,
-0.005695083644241095,
0.07659893482923508,
-0.0005851517198607326,
-0.005534833297133446,
0.032426416873931885,
-0.016776157543063164,
-0.012178998440504074,
0.05515131726861,
0.02914036437869072,
0.029576068744063377,
0.04051763564348221,
-0.0011863679392263293,
0.016562091186642647,
0.006565491668879986,
0.07346896082162857,
-0.009160839952528477,
-0.03756946697831154,
-0.015666380524635315,
0.006742434576153755,
0.0362289659678936,
-0.021108034998178482,
-0.0482996366918087,
-0.030339300632476807,
-0.002552078105509281,
0.00722354743629694,
-0.009373772889375687,
0.009629654698073864,
0.0008740838384255767,
0.027993064373731613,
-0.0009749545715749264,
-0.021018946543335915,
-0.018735477700829506,
-0.029168924316763878,
0.02558978646993637,
0.0019025931833311915,
-0.01702275685966015,
0.05967438220977783,
-0.02280735783278942,
0.016119221225380898,
-0.006059280596673489,
-0.053822387009859085,
0.006812111474573612,
-0.006375686731189489,
5.426860525403754e-7,
0.008468136191368103,
0.010113301686942577,
0.029958995059132576,
0.0187663733959198,
0.023350350558757782,
0.03269059956073761,
-0.04913990944623947,
-0.04723415523767471,
0.02033623680472374,
0.0032199693378061056,
-0.010230615735054016,
0.0018760360544547439,
-0.03044312261044979,
0.0038057707715779543,
-0.021584732457995415,
0.00020952611521352082,
0.013998528011143208,
-0.015051948837935925,
0.04525277018547058,
0.03807421401143074,
0.012896840460598469,
-0.0024086786434054375,
0.041502390056848526,
0.010205021128058434,
0.0010314700193703175,
-0.018053164705634117,
-0.05427836999297142,
-0.007617021910846233,
-0.013983888551592827,
0.024625787511467934,
0.03279518708586693,
-0.030749155208468437,
0.01823241077363491,
0.02640708163380623,
0.03759967163205147,
0.01218114048242569,
0.019148411229252815,
-0.010720864869654179,
-0.024819469079375267,
-0.012985972687602043,
-0.011981918476521969,
-0.01908854767680168,
-0.016921328380703926,
0.008781478740274906,
-0.009216497652232647,
0.0061379908584058285,
-0.0008410525042563677,
-0.019845059141516685,
0.02107497863471508,
-0.0834423080086708,
0.019294654950499535,
-0.01156314741820097,
-0.01975642889738083,
0.005852010566741228,
-0.02027421072125435,
0.017062310129404068,
0.042692720890045166,
-0.015626875683665276,
-0.03171652927994728,
-0.0336356945335865,
-0.04886191710829735,
0.028538860380649567,
-0.0273578017950058,
-0.058896441012620926,
-0.04998316243290901,
0.015267240814864635,
-0.007966706529259682,
0.02318345569074154,
-0.003411681391298771,
0.010774017311632633,
0.005191757809370756,
0.028721598908305168,
0.02342107892036438,
-0.0009042739984579384,
0.03530936315655708,
-0.02391335554420948,
-0.03426619991660118,
0.01978156343102455,
-0.03456926345825195,
0.02500130794942379,
0.039563022553920746,
-0.03229723870754242,
0.015418094582855701,
-0.04616741091012955,
-0.04111405462026596,
0.027157455682754517,
-0.0073449090123176575,
-0.002966483123600483,
-0.003370557213202119,
-0.004824599716812372,
-0.011953171342611313,
-0.03077445738017559,
0.0069119310937821865,
0.01026774849742651,
0.0027989675290882587,
-0.0056074573658406734,
0.01656009815633297,
-0.0017342559294775128,
-0.02451545000076294,
0.025469515472650528,
0.012409891933202744,
-0.05457967147231102,
-0.03969378024339676,
-0.01302964985370636,
0.015281081199645996,
-0.015496278181672096,
0.004517300985753536,
0.032124266028404236,
-0.052344534546136856,
-0.020073434337973595,
-0.04114722087979317,
-0.008326707407832146,
0.02649877592921257,
-0.005563618615269661,
0.003565708175301552,
0.02756630815565586,
-0.03271730989217758,
0.09977751225233078,
0.04322981461882591,
-0.015263439156115055,
-0.03480071946978569,
-0.0003973467682953924,
-0.016740206629037857,
-0.060920700430870056,
-0.0037558297626674175,
-0.001298055867664516,
-0.0020516151562333107,
0.05920971557497978,
-0.008230273611843586,
-0.007501248735934496,
0.04032856971025467,
-0.032615937292575836,
-0.005235916934907436,
-0.0016566383419558406,
-0.041742149740457535,
-0.015373335219919682,
0.07572119683027267,
-0.0009019013959914446,
0.014563857577741146,
-0.0055077518336474895,
-0.003551420522853732,
0.018942587077617645,
0.008182183839380741,
-0.03164432942867279,
0.07120918482542038,
-0.0020100257825106382,
-0.006616226863116026,
-0.052560772746801376,
0.04713072255253792,
0.009034890681505203,
-0.0350242480635643,
0.012498900294303894,
0.007580895908176899,
-0.012804641388356686,
-0.033604640513658524,
0.011363907717168331,
0.013799118809401989,
0.005983888171613216,
-0.04115132987499237,
0.006800728850066662,
-0.027348211035132408,
-0.01159043051302433,
0.007711998652666807,
-0.04611789062619209,
-0.044170621782541275,
0.04353823512792587,
0.02222602069377899,
0.0014598191482946277,
-0.03748416155576706,
-0.054947879165410995,
-0.031223701313138008,
-0.06355591118335724,
-0.016464700922369957,
0.0021706700790673494,
0.04216760769486427,
0.02995453029870987,
0.053566474467515945,
0.017259197309613228,
0.013615940697491169,
0.012294426560401917,
0.006801907438784838,
-0.06533623486757278,
-0.006338522769510746,
-0.027361197397112846,
0.015570851974189281,
-0.009788825176656246,
-0.06113310158252716,
0.03276454657316208,
-0.023739043623209,
-0.01983177289366722,
0.015001527033746243,
-0.04606367647647858,
-0.053117536008358,
0.02900075912475586,
-0.021485580131411552,
-0.021773988381028175,
-0.02955072559416294,
0.02133992128074169,
0.06725944578647614,
-0.03363291174173355,
-0.00808409322053194,
0.03693341091275215,
-0.03918472304940224,
-0.002603883622214198,
-0.0014075783547013998,
0.029414799064397812,
0.01755508780479431,
0.020761560648679733,
0.043929748237133026,
-0.019587229937314987,
-0.019603867083787918,
0.010144424624741077,
0.01833801344037056,
0.0940757468342781,
0.01094154641032219,
-0.03660799190402031,
0.013146776705980301,
-0.057915233075618744,
0.012731606140732765,
-0.0008214630652219057,
0.07693053036928177,
-0.002910682698711753,
0.015866216272115707,
0.0567094162106514,
0.0034446960780769587,
-0.013092922046780586,
0.01771651953458786,
0.05297764390707016,
0.004533908795565367,
-0.0069028758443892,
-0.02042052336037159,
0.028313130140304565,
0.017668893560767174,
-0.009848175570368767,
-0.00495523726567626,
-0.0181193258613348,
0.01466691866517067,
-0.006419074255973101,
0.03669995442032814,
-0.04230896383523941,
-0.019863702356815338,
0.004371644929051399,
0.03341729938983917,
0.0012007419718429446,
0.0026425132527947426,
-0.02212882973253727,
-0.012783643789589405,
0.05364394560456276,
0.021563468500971794,
0.008268672972917557,
-0.011486713774502277,
-0.04919779300689697,
-0.0007849059766158462,
0.0309977475553751,
0.027786262333393097,
0.01466673705726862,
-0.008407891727983952,
-0.04286741837859154,
-0.007671349216252565,
0.024758273735642433,
0.012310606427490711,
0.030816206708550453,
0.008630328811705112,
0.028689373284578323,
-0.027150072157382965,
-0.014442184939980507,
-0.0007869412656873465,
0.03837303817272186,
0.024097999557852745,
-0.014702086336910725,
-0.03067234717309475,
0.004409872926771641,
-0.00514259422197938,
0.035777222365140915,
-0.0010405885986983776,
0.04305227845907211,
0.02493228204548359,
-0.02104789763689041,
0.016476815566420555,
0.011779609136283398,
-0.03511571139097214,
-0.12104755640029907,
0.006019876804202795,
0.00012386533489916474,
-0.017017172649502754,
0.02866031974554062,
-0.026326201856136322,
-0.030333561822772026,
0.023930056020617485,
0.005044827703386545,
-0.014447376132011414,
0.02929927594959736,
-0.047141190618276596,
0.04702901840209961,
0.004727862309664488,
-0.013312931172549725,
0.05952543392777443,
0.030088277533650398,
0.017871124669909477,
0.011832175776362419,
-0.011869865469634533,
0.05707908421754837,
-0.0170857273042202,
-0.000262203102465719,
-0.04319429025053978,
-0.012509963475167751,
-0.040215279906988144,
0.04926961287856102,
-0.005232721101492643,
0.029472557827830315,
-0.011649813503026962,
-0.04735659062862396,
-0.03359035775065422,
0.009489359334111214,
-0.02396950125694275,
-0.02688022330403328,
-0.0018644846277311444,
0.032147858291864395,
0.01001760270446539,
-0.020299984142184258,
0.0405535027384758,
0.0005448676529340446,
-0.0010663712164387107,
0.04130961373448372,
-0.0019693830981850624,
0.00615077605471015,
-0.005961219314485788,
-0.03893899545073509,
0.011268392205238342,
-0.02735988423228264,
0.006371856201440096,
-0.02758949063718319,
-0.025243045762181282,
0.003557820338755846,
-0.02863796055316925,
-0.017261197790503502,
-0.02676508203148842,
-0.028198398649692535,
0.015279457904398441,
-0.028208108618855476,
0.024931341409683228,
0.01558475662022829,
0.018046163022518158,
-0.09142494201660156,
-0.010924896225333214,
-0.022728051990270615,
-0.02162875235080719,
-0.03362765163183212,
-0.009960359893739223,
-0.0044622523710131645,
-0.039908528327941895,
-0.028090257197618484,
0.023423630744218826,
0.051315389573574066,
-0.01432814821600914,
-0.021119872108101845,
0.011328771710395813,
0.024526765570044518,
0.015410388819873333,
-0.0070067779161036015,
-0.02454397641122341,
0.023405494168400764,
-0.0027378415688872337,
0.012437514029443264,
0.009850254282355309,
0.0567857101559639,
0.005708758719265461,
-0.003693735459819436,
-0.042235665023326874,
-0.01821817271411419,
0.020504102110862732,
-0.022497862577438354,
0.021473031491041183,
0.04342491552233696,
0.06286939233541489,
0.035109225660562515,
-0.01894609071314335,
-0.01505889743566513,
0.0036954074166715145,
0.050582751631736755,
0.02613741345703602,
0.007742940913885832,
-0.019572004675865173,
-0.0010022656060755253,
0.05375281348824501,
-0.02689974755048752,
0.03135036304593086,
-0.008504614233970642,
0.07902328670024872,
-0.03728610649704933,
0.018051307648420334,
0.01624300144612789,
0.020039668306708336,
-0.011943086981773376,
-0.029601121321320534,
0.033404525369405746,
0.0022740245331078768,
0.016053110361099243,
-0.02344047650694847,
-0.029039567336440086,
-0.06654088199138641,
0.03942522779107094,
0.040828440338373184,
-0.03871836140751839,
0.01489331666380167,
0.025191599503159523,
-0.0431467704474926,
0.01257967296987772,
-0.01760336011648178,
-0.011042739264667034,
0.018010858446359634,
-0.019760189577937126,
0.054248154163360596,
-0.052622806280851364,
-0.02550843171775341,
0.03798897936940193,
0.06576360017061234,
-0.034501124173402786,
-0.0016935026505962014,
0.010399234481155872,
0.04597931355237961,
0.033912431448698044,
0.018643870949745178,
-0.06028933823108673,
0.049464911222457886,
-0.0234955046325922,
0.02507316879928112,
-0.008520223200321198,
0.002091238973662257,
0.014441682025790215,
0.031700823456048965,
-0.010744510218501091,
0.005869235377758741,
-0.008358627557754517,
-0.055528201162815094,
0.002984679536893964,
0.05354219675064087,
-0.007035085931420326,
0.01672554202377796,
0.006458871066570282,
0.011366628110408783,
0.00742377107962966,
-0.009264795109629631,
0.02101987414062023,
-0.024180125445127487,
-0.013905003666877747,
-0.05870893597602844,
-0.05065089836716652,
0.014441593550145626,
-0.040615808218717575,
-0.06452305614948273,
0.00788411870598793,
-0.03309693560004234,
0.038442209362983704,
-0.013227373361587524,
0.01974884234368801,
-0.023107584565877914,
0.06554202735424042,
0.016187435016036034,
-0.0002541513240430504,
-0.0071714939549565315,
-0.003946521785110235,
0.10848250985145569,
0.0484590046107769,
0.02070385403931141,
-0.08972780406475067,
-0.02034185081720352,
-0.02105025388300419,
0.017002064734697342,
-0.04982578381896019,
0.038046158850193024,
-0.026358749717473984,
-0.008312294259667397,
-0.04086926206946373,
0.07869771122932434,
0.007379728369414806,
0.023647084832191467,
0.031223295256495476,
-0.05770397186279297,
-0.03476347401738167,
-0.0025294485967606306,
-0.00866066012531519,
-0.027826091274619102,
0.0017980773700401187,
-0.036742232739925385,
0.006414615083485842,
0.0054241050966084,
0.04131874442100525,
0.008722714148461819,
-0.005651275161653757,
0.013053376227617264,
-0.015004691667854786,
-0.03429623320698738,
-0.006496869958937168,
0.00693782651796937,
-0.004614057019352913,
-0.0265621617436409,
-0.004003605805337429,
0.0281072985380888,
-0.006319201085716486,
0.04737930744886398,
0.024798255413770676,
-0.01074066013097763,
-0.020139863714575768,
0.03798289597034454,
-0.006771464366465807,
-0.008944137021899223,
-0.03870609775185585,
-0.024497414007782936,
0.07380416244268417,
-0.008022835478186607,
-0.02016754262149334,
-0.006546728312969208,
-0.02640818990767002,
-0.018675917759537697,
-0.05733392760157585,
0.006753185298293829,
-0.037575092166662216,
0.03492842614650726,
-0.03223629295825958,
0.03967495635151863,
-0.02409329079091549,
0.0362686812877655,
0.00658476771786809,
0.025827838107943535,
-0.03255925327539444,
-0.02917766012251377,
-0.012147696688771248,
-0.001088608056306839,
0.003137432737275958,
-0.035852812230587006,
-0.014430375769734383,
-0.003410420613363385,
-0.018510594964027405,
-0.0384923592209816,
-0.04339338466525078,
0.028056422248482704,
-0.003726234659552574,
0.05755440890789032,
-0.005414387211203575,
0.028064144775271416,
-0.017182715237140656,
-0.04400867596268654,
-0.00820673443377018,
0.010751305148005486,
-0.022434815764427185,
-0.012560506351292133,
-0.0003563741047400981,
0.03741392493247986,
0.06269974261522293,
-0.0024097717832773924,
-0.031215619295835495,
0.005897603463381529,
0.010518284514546394,
0.014429756440222263,
-0.02149522304534912,
0.01115806121379137,
0.020329227671027184,
-0.013269088231027126,
0.012129154987633228,
-0.0383492112159729,
-0.028859831392765045,
0.015552238561213017,
0.005682329181581736,
-0.03550272807478905,
0.02871582843363285,
0.01326705515384674,
-0.0015058297431096435,
0.020993847399950027,
-0.03286837413907051,
0.00823280494660139,
0.04391242191195488,
-0.004624894354492426,
-0.042919352650642395,
-0.03508982062339783,
-0.004205658100545406,
0.006119654513895512,
-0.0022378270514309406,
0.03545685485005379,
-0.03219594433903694,
-0.04402339458465576,
-0.01950925961136818,
0.05075766518712044,
-0.03525993973016739,
-0.018662432208657265,
-0.06862330436706543,
0.05040213465690613,
0.011095953173935413,
0.00035024492535740137,
-0.02408306486904621,
0.006557875778526068,
-0.0036024015862494707,
-0.006944507360458374,
0.024632642045617104,
0.025466084480285645,
-0.02128382958471775,
0.018113816156983376,
-0.009061667136847973,
-0.020370369777083397,
0.0013274262892082334,
0.026092631742358208,
-0.003943599294871092,
0.009542805142700672,
-0.049326665699481964,
-0.029665807262063026,
0.07283980399370193,
0.008945428766310215,
0.02533857524394989,
0.05533449351787567,
-0.010221069678664207,
-0.07443056255578995,
0.008181883953511715,
-0.038388267159461975,
-0.009193253703415394,
0.014307920821011066,
-0.051104988902807236,
-0.01764705218374729,
-0.035044457763433456,
0.007173178717494011,
0.02611772157251835,
-0.002211694372817874,
0.033301107585430145,
0.008282284252345562,
-0.016931671649217606,
-0.007882337085902691,
0.019702183082699776,
0.01767001487314701,
0.03795516490936279,
0.02891954779624939,
0.0021628018002957106,
0.029041416943073273,
0.04752229526638985,
-0.008258921094238758,
0.018566839396953583,
0.019327988848090172,
0.03661942854523659,
-0.09520117193460464,
-0.019924236461520195,
0.010422462597489357,
0.030353030189871788,
0.04520193114876747,
-0.04622972756624222,
0.018292700871825218,
0.01546461507678032,
-0.07763002067804337,
-0.013955394737422466,
-0.022536801174283028,
-0.015996189787983894,
-0.004209942650049925,
0.015318768098950386,
-0.0007146919379010797,
0.04198317974805832,
0.013349167071282864,
0.018032902851700783,
0.0024814631324261427,
0.021595461294054985,
0.004802022594958544,
0.022764433175325394,
-0.03801506385207176,
0.025362933054566383,
-0.010770234279334545,
-0.020367808640003204,
0.061957452446222305,
-0.00655902735888958,
-0.06798164546489716,
0.03545461222529411,
0.008917854167521,
-0.038269709795713425,
-0.008379818871617317,
0.046975888311862946,
0.05046992748975754,
0.036099307239055634,
0.021731818094849586,
-0.0416867770254612,
0.05761609598994255,
-0.016421323642134666,
0.02789223939180374,
0.006013892125338316,
0.0015634510200470686,
-0.019347963854670525,
0.024026265367865562,
-0.028743360191583633,
-0.03134865686297417,
0.03530779853463173,
-0.012625062838196754,
-0.05537686124444008,
-0.051567092537879944,
-0.01896260865032673,
0.01612047106027603,
-0.044386543333530426,
0.0695408433675766,
-0.021519966423511505,
0.0014852292370051146,
-0.008952743373811245,
-0.0022221410181373358,
-0.00957441609352827,
0.025122512131929398,
0.011700271628797054,
-0.006510087288916111,
0.04474577680230141,
0.023295560851693153,
-0.025882594287395477,
-0.052379269152879715,
-0.028884822502732277,
0.02636680379509926,
0.017258090898394585,
0.014112216420471668,
-0.03947339951992035,
-0.04769354686141014,
-0.005812843330204487,
0.015456723049283028,
0.057931821793317795,
-0.034855250269174576,
-0.026800697669386864,
0.016119927167892456,
-0.055857229977846146,
0.04348117858171463,
0.031068582087755203,
-0.009443593211472034,
0.005630151368677616,
-0.021279504522681236,
0.04579281434416771,
0.0006573792779818177,
0.05725160241127014,
-0.003058985574170947,
-0.05240735784173012,
-0.001350690028630197,
-0.012616217136383057,
0.008413390256464481,
-0.033555492758750916,
0.0072646671906113625,
-0.030722038820385933,
0.0007927388069219887,
-0.011473509483039379,
-0.012279404327273369,
-0.006644892040640116,
0.037955284118652344,
-0.009286396205425262,
-0.0046248650178313255,
-0.012148026376962662,
0.005989010911434889,
-0.01900855265557766,
0.024810612201690674,
0.027947986498475075,
-0.012075706385076046,
0.040020085871219635,
0.02054755948483944,
0.03827422857284546,
0.037402570247650146,
-0.012821638956665993,
-0.02159426361322403,
0.03357837349176407,
-0.017527857795357704,
-0.032403163611888885,
0.007220032159239054,
-0.01760105788707733,
0.04747721180319786,
-0.03669881820678711,
0.007119545713067055,
0.03999536484479904,
-0.044599749147892,
-0.03360971063375473,
0.0744938999414444,
0.039920490235090256,
0.052352823317050934,
0.05791496858000755,
0.007081951946020126,
0.0567484088242054,
0.013924604281783104,
-0.013163363561034203,
0.04269136115908623,
0.04073215648531914,
-0.002592791337519884,
-0.010906447656452656,
0.002257591113448143,
-0.019777489826083183,
0.0025317384861409664,
0.021547120064496994,
0.014825611375272274,
-0.023990077897906303,
-0.01602952927350998,
0.022450724616646767,
-0.029558314010500908,
0.008820326998829842,
0.03483732417225838,
-0.03450288251042366,
0.06670825928449631,
-0.023511873558163643,
-0.01412096805870533,
-0.03730541467666626,
0.023062309250235558,
0.009182620793581009,
0.007412169594317675,
0.05012517794966698,
0.04255036264657974,
-0.009769991040229797,
-0.027001211419701576,
-0.040027912706136703,
0.021658241748809814,
0.005180602427572012,
-0.060505613684654236,
-0.0003274861956015229,
0.02251341938972473,
-0.034164294600486755,
-0.0022225319407880306,
-0.037133123725652695,
0.015636442229151726,
0.0022548420820385218,
0.010830127634108067,
0.016720911487936974,
-0.0014906529104337096,
0.009707004763185978,
-0.011632504872977734,
-0.006791363004595041,
0.06157084181904793,
-0.052070677280426025,
0.015182808972895145,
-0.03156447783112526,
0.00945583451539278,
0.025748515501618385,
0.021061299368739128
] |
<p>In quantization of scalar field theory we impose commutation relation between the field operators <strong>by hand</strong> and similarly we impose anti-commutation relation between Dirac field operators <strong>by hand</strong>. As a consequence one gets Bose-statistics (two-particle wavefuction is symmetric) in the first case and the Fermi statistics (two-particle wavefuction is anti-symmetric) in the second case. But does it really <strong>prove</strong> the <a href="http://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem" rel="nofollow">spin-statistics theorem</a>?</p> | 2,041 | [
-0.03800635039806366,
-0.045733578503131866,
0.019149649888277054,
-0.032963767647743225,
0.04665898159146309,
-0.0008229399682022631,
0.0142966378480196,
0.002302300650626421,
-0.00679825572296977,
-0.04500163346529007,
0.009347409009933472,
0.007073790300637484,
0.0701233521103859,
0.015550955198705196,
0.046744246035814285,
0.014823430217802525,
-0.01332415547221899,
0.0017414911417290568,
-0.030016109347343445,
-0.013521663844585419,
-0.006192154251039028,
0.049846306443214417,
0.005909041967242956,
-0.01190250925719738,
-0.01272635068744421,
0.00983515102416277,
-0.009705930948257446,
0.02338303253054619,
-0.00008186915511032566,
0.06472254544496536,
-0.012388196773827076,
-0.013427335768938065,
-0.005269762594252825,
0.0303297508507967,
0.047292761504650116,
-0.01721358858048916,
-0.005994783248752356,
-0.04896114394068718,
0.02220953069627285,
0.006523679941892624,
-0.043888188898563385,
-0.02269364707171917,
-0.04401583597064018,
0.012101338244974613,
-0.015482984483242035,
0.01562353502959013,
0.0007020753691904247,
0.0019145460100844502,
0.040979329496622086,
-0.03283284232020378,
0.05219574272632599,
0.007870331406593323,
0.03471570089459419,
0.0016028906684368849,
-0.009139020927250385,
-0.017494911327958107,
0.04843635857105255,
0.04155277833342552,
0.010864851996302605,
-0.018896427005529404,
-0.013420812785625458,
0.0007994066108949482,
-0.00047797057777643204,
-0.00024355437199119478,
-0.04711679369211197,
0.03358384221792221,
0.04595759138464928,
-0.009141028858721256,
0.02589508332312107,
0.003064015880227089,
-0.01184060238301754,
-0.0007569683948531747,
0.0492568239569664,
-0.0189463272690773,
0.012227729894220829,
-0.004076071549206972,
0.023979967460036278,
0.0373900830745697,
0.014391357079148293,
0.02797403186559677,
-0.0034117335453629494,
0.06809242069721222,
0.0073731136508286,
0.022418048232793808,
0.01774425618350506,
-0.012665955349802971,
0.03672639653086662,
0.026622720062732697,
0.0016290682833641768,
0.027704153209924698,
0.001557162031531334,
-0.02656630054116249,
0.03702656924724579,
-0.00927977729588747,
-0.06801879405975342,
0.03539549931883812,
-0.006480872165411711,
0.04613039270043373,
-0.02265034057199955,
-0.04309729114174843,
-0.04648948088288307,
-0.04062705487012863,
0.03163903206586838,
0.059407543390989304,
-0.017983274534344673,
-0.021490296348929405,
-0.012574687600135803,
0.03554083779454231,
-0.04847775027155876,
-0.01210201345384121,
-0.02517818659543991,
0.00818836223334074,
-0.0035285933408886194,
-0.024664398282766342,
0.00851299799978733,
-0.023404758423566818,
0.0013889508554711938,
-0.010685409419238567,
0.04464467987418175,
0.08714955300092697,
0.05020741745829582,
-0.00943536777049303,
-0.0010095275938510895,
-0.035034291446208954,
-0.03623121231794357,
0.013876991346478462,
0.055849190801382065,
-0.0170354712754488,
-0.055902305990457535,
0.03927737846970558,
0.009125562384724617,
-0.005757427308708429,
-0.0064656841568648815,
0.006976307835429907,
0.017952265217900276,
0.0003317897499073297,
-0.1109786257147789,
-0.044144392013549805,
0.04161379858851433,
-0.008211381733417511,
-0.03379646688699722,
-0.04645123332738876,
0.025694767013192177,
0.02825205773115158,
0.09508416056632996,
-0.029554227367043495,
0.06306438893079758,
-0.031660549342632294,
0.019125627353787422,
0.031002286821603775,
0.010064159519970417,
-0.0316145233809948,
0.021266721189022064,
-0.008351637050509453,
-0.05003757402300835,
-0.06873546540737152,
0.021161427721381187,
-0.00617150217294693,
-0.037736743688583374,
-0.011193945072591305,
0.0373225137591362,
-0.00579240033403039,
-0.004643700085580349,
-0.01439939346164465,
0.021827436983585358,
-0.039237916469573975,
0.06876916438341141,
0.026295842602849007,
0.006845602300018072,
0.02704792097210884,
-0.057815637439489365,
0.0033182937186211348,
0.000266103888861835,
0.02905956283211708,
-0.0021454927045851946,
-0.065594881772995,
-0.0169645007699728,
0.011330476962029934,
0.0052905515767633915,
-0.0009192107827402651,
-0.04614260047674179,
-0.007989185862243176,
-0.03347954899072647,
0.05018891394138336,
-0.01908230595290661,
0.02694716490805149,
0.03153276443481445,
-0.015388772822916508,
0.03253991901874542,
-0.05907023698091507,
0.004768402315676212,
-0.07790175080299377,
-0.008283657021820545,
0.008887037634849548,
-0.06643181294202805,
0.030182339251041412,
0.021356064826250076,
0.03138130530714989,
-0.028691403567790985,
-0.0587819404900074,
0.023033631965517998,
0.05275971069931984,
0.0014944258145987988,
0.009771253913640976,
0.012119313701987267,
0.04645490646362305,
0.04258096218109131,
-0.02235194854438305,
0.037069909274578094,
-0.003901796182617545,
-0.06397295743227005,
0.039119068533182144,
-0.009928423911333084,
-0.006580775137990713,
0.052934568375349045,
-0.032982926815748215,
0.006417973432689905,
-0.01084137987345457,
-0.044914133846759796,
0.02508886344730854,
-0.033743713051080704,
0.043612461537122726,
-0.0030619949102401733,
-0.009519634768366814,
-0.006158551666885614,
0.049080345779657364,
0.034395456314086914,
0.03924970701336861,
0.011134056374430656,
-0.012061798945069313,
-0.017374128103256226,
0.012256317771971226,
0.03783034160733223,
0.03239591047167778,
-0.027332670986652374,
0.026508839800953865,
0.014063660055398941,
0.006289507262408733,
0.011737137101590633,
0.01636331155896187,
-0.033138953149318695,
-0.04583656042814255,
0.02179965190589428,
0.011412945576012135,
0.01743682660162449,
-0.008591706864535809,
-0.015927890315651894,
-0.01148244459182024,
-0.006718246266245842,
0.008412467315793037,
-0.059358399361371994,
0.0030055150855332613,
-0.009440625086426735,
-0.006824573967605829,
0.01843852736055851,
-0.048774488270282745,
0.010078009217977524,
0.009953253902494907,
0.024634066969156265,
0.005473535507917404,
-0.03939058631658554,
0.014765754342079163,
-0.016613634303212166,
-0.034560538828372955,
0.021341273561120033,
-0.03589925169944763,
-0.02462192252278328,
-0.0017235289560630918,
0.010999987833201885,
-0.02230418100953102,
-0.048532359302043915,
-0.007463216781616211,
-0.013847860507667065,
-0.03395744785666466,
-0.027306586503982544,
0.03347202390432358,
0.007610585540533066,
0.024167027324438095,
-0.0027192458510398865,
-0.01583479717373848,
0.00887629296630621,
0.0030962128657847643,
0.030621374025940895,
0.05283685028553009,
-0.023178881034255028,
0.034929729998111725,
-0.048807818442583084,
-0.0435815304517746,
0.0544317252933979,
-0.013450887985527515,
0.03781966492533684,
0.008953612297773361,
-0.0065722959116101265,
-0.04275195300579071,
-0.020417891442775726,
-0.023656990379095078,
0.032574985176324844,
-0.052003663033246994,
-0.024255603551864624,
0.0407843180000782,
-0.02999153360724449,
-0.009575717151165009,
0.023520594462752342,
0.009641824290156364,
-0.08071105927228928,
0.013728638179600239,
0.0038933344185352325,
0.014282621443271637,
-0.03750337287783623,
0.0280672125518322,
0.06085582822561264,
-0.04521698132157326,
-0.04956955835223198,
-0.06674908846616745,
-0.03219776228070259,
0.02399412728846073,
-0.007390061393380165,
0.003359941067174077,
0.00098334439098835,
-0.03519512712955475,
0.0447300486266613,
0.03602037578821182,
-0.035643864423036575,
-0.0027943395543843508,
0.03494200482964516,
-0.0183554757386446,
0.005934924818575382,
0.011440289206802845,
0.03303990513086319,
0.024277249351143837,
0.07436298578977585,
0.05602797865867615,
0.009838765487074852,
-0.00239573628641665,
0.017103157937526703,
-0.0219868253916502,
-0.010839761234819889,
0.0038702322635799646,
0.019003989174962044,
0.04897454380989075,
0.00009887577471090481,
-0.013717824593186378,
0.0005822231760248542,
0.0013275413075461984,
0.015562132000923157,
0.04008350521326065,
-0.04289591312408447,
0.05329848825931549,
0.023511100560426712,
0.03893602266907692,
-0.05179997533559799,
0.03756190091371536,
0.023551292717456818,
-0.02252049185335636,
0.01713673397898674,
0.0017220349982380867,
-0.001673308783210814,
-0.0008298291359096766,
-0.005814947187900543,
0.017417291179299355,
0.06600509583950043,
-0.0276943389326334,
-0.029211578890681267,
-0.0446939617395401,
-0.013424904085695744,
0.0538947731256485,
-0.0408441536128521,
-0.048654526472091675,
0.037324175238609314,
0.06589551270008087,
0.001530438312329352,
-0.006203049793839455,
-0.019306644797325134,
0.005136463791131973,
-0.035324033349752426,
0.018602965399622917,
-0.007287095300853252,
0.04891509935259819,
-0.0019854065030813217,
0.06801605224609375,
0.02582106553018093,
0.011297930963337421,
-0.014206107705831528,
-0.017129963263869286,
-0.07206129282712936,
-0.009828255511820316,
-0.013844240456819534,
-0.014880068600177765,
0.011365460231900215,
-0.04723548889160156,
-0.01088537648320198,
-0.009969730861485004,
-0.03179547190666199,
-0.03826414793729782,
0.009976768866181374,
-0.048943620175123215,
0.01714218221604824,
-0.06747417151927948,
-0.05774160102009773,
-0.009081413969397545,
0.034946974366903305,
0.030221031978726387,
-0.02521602064371109,
0.01683979667723179,
0.028848448768258095,
-0.055190879851579666,
0.018532346934080124,
-0.023655714467167854,
0.03231153264641762,
0.020774079486727715,
0.0032167281024158,
0.057791899889707565,
0.00018186893430538476,
-0.035099636763334274,
-0.024791378527879715,
0.007029315922409296,
0.07215597480535507,
0.02380579523742199,
-0.012105417437851429,
0.004441817756742239,
-0.022156067192554474,
-0.021377326920628548,
0.005077339243143797,
0.058004580438137054,
0.01446162536740303,
-0.0032313030678778887,
0.04531174898147583,
0.013439788483083248,
-0.027094554156064987,
0.025700684636831284,
0.0866650864481926,
0.0032601403072476387,
0.014125791378319263,
-0.023446818813681602,
-0.0004487773112487048,
0.0012731340248137712,
-0.0390937440097332,
0.0149111058562994,
0.009337995201349258,
-0.027712590992450714,
0.01374579407274723,
0.03627774491906166,
0.07385862618684769,
-0.05433546006679535,
0.014050296507775784,
-0.027794688940048218,
0.008200199343264103,
0.01505272276699543,
-0.0018021627329289913,
-0.006771990563720465,
0.05065656453371048,
0.016760770231485367,
0.053430259227752686,
-0.010606762021780014,
-0.01160776149481535,
0.006291573401540518,
0.04598275199532509,
-0.009119022637605667,
0.0048271482810378075,
0.01893145591020584,
-0.018355954438447952,
-0.01257307268679142,
0.03552502393722534,
-0.016739580780267715,
0.030907126143574715,
-0.0011130510829389095,
-0.020386401563882828,
-0.031748149544000626,
-0.02045014686882496,
-0.022928394377231598,
0.04879048839211464,
-0.021576305851340294,
-0.019949475303292274,
-0.021303579211235046,
-0.03374939784407616,
-0.022481907159090042,
-0.014589616097509861,
0.017915816977620125,
0.05138648301362991,
-0.011257516220211983,
0.015047306194901466,
-0.010627534240484238,
0.046228356659412384,
-0.038112252950668335,
-0.08933747559785843,
-0.011227421462535858,
-0.012420319020748138,
-0.017652636393904686,
0.05012175440788269,
-0.016665058210492134,
-0.009532797150313854,
0.013836939819157124,
-0.01210037712007761,
-0.02399335987865925,
0.038326241075992584,
-0.048678260296583176,
0.027361521497368813,
0.020392892882227898,
0.011621938087046146,
0.037830375134944916,
0.004860389046370983,
-0.0018451942596584558,
0.003715124214068055,
-0.003676084103062749,
0.017716331407427788,
-0.0002602911554276943,
0.01838098093867302,
-0.04160073399543762,
-0.012957369908690453,
-0.031040942296385765,
-0.01317690871655941,
-0.027802864089608192,
0.005808801390230656,
0.014498253352940083,
-0.017583830282092094,
-0.019502239301800728,
-0.011540298350155354,
0.00031563203083351254,
-0.009611188434064388,
-0.02373243123292923,
0.03113815374672413,
-0.0058431015349924564,
-0.05521301552653313,
0.006839234847575426,
-0.008524013683199883,
-0.030456101521849632,
0.0335659496486187,
0.008696531876921654,
0.03331545740365982,
-0.046970345079898834,
-0.001615070505067706,
-0.02743544615805149,
-0.03605049103498459,
0.006896082311868668,
-0.013784186914563179,
0.02631370723247528,
-0.018128879368305206,
0.01969357579946518,
-0.035678327083587646,
0.03854779526591301,
-0.003992402460426092,
0.0021081918384879827,
-0.05042696371674538,
-0.02072221413254738,
0.03852567821741104,
-0.01658312976360321,
-0.06575080752372742,
-0.0812271386384964,
0.018337229266762733,
0.019310006871819496,
-0.04153870791196823,
-0.011700029484927654,
-0.011848947033286095,
-0.006136205047369003,
-0.014450940303504467,
-0.0009419341804459691,
0.013752039521932602,
-0.010777139104902744,
-0.017073607072234154,
0.012112930417060852,
-0.014036061242222786,
0.042995385825634,
-0.024805497378110886,
-0.01117676217108965,
-0.015961872413754463,
-0.034093987196683884,
0.017642928287386894,
0.024924490600824356,
0.013309808447957039,
-0.0027824300341308117,
-0.05434189736843109,
-0.019748017191886902,
0.012903302907943726,
-0.00024713450693525374,
-0.015357308089733124,
-0.02758895419538021,
0.022753292694687843,
0.04557763785123825,
-0.0034475557040423155,
-0.010086060501635075,
-0.004629033152014017,
-0.010691086761653423,
0.04268480837345123,
0.0014371785800904036,
0.007384657859802246,
-0.041244298219680786,
-0.02525775134563446,
0.019605424255132675,
-0.016780124977231026,
-0.006846723612397909,
0.005873736925423145,
0.01941824145615101,
0.00472688814625144,
0.01192560140043497,
0.0052340771071612835,
-0.023182058706879616,
0.0020926715806126595,
-0.023504696786403656,
0.0031888626981526613,
0.0056380536407232285,
0.027435194700956345,
0.023020334541797638,
-0.01075020246207714,
-0.02750800922513008,
0.0506831556558609,
0.07053378224372864,
0.02750425599515438,
0.049625564366579056,
0.04079913720488548,
0.012581409886479378,
-0.028104791417717934,
-0.013508042320609093,
-0.013073376379907131,
-0.023186324164271355,
0.00506439246237278,
0.025701314210891724,
-0.041623033583164215,
0.037573911249637604,
0.06086648628115654,
0.05315372347831726,
-0.01681211218237877,
0.002347727073356509,
0.00660286657512188,
0.016054939478635788,
0.005889350548386574,
-0.011343521997332573,
-0.03580476716160774,
0.059884168207645416,
-0.040830790996551514,
0.05029313638806343,
-0.016352569684386253,
-0.0013801292516291142,
0.03077755495905876,
-0.00607014074921608,
0.011381492018699646,
0.0064798761159181595,
-0.05134503170847893,
-0.04958246648311615,
-0.00486267963424325,
-0.0016860465984791517,
0.025967683643102646,
0.0002870929311029613,
0.002506809774786234,
0.04272067919373512,
0.044676970690488815,
0.023771217092871666,
-0.018868600949645042,
-0.04784729704260826,
0.0009120946633629501,
-0.0275998804718256,
-0.04739241674542427,
0.0445408895611763,
0.010012776590883732,
-0.04428448528051376,
0.011177673004567623,
-0.02406022697687149,
0.042027875781059265,
0.03450750559568405,
0.022211069241166115,
-0.0313887745141983,
0.03695065528154373,
0.004727238789200783,
0.03379927948117256,
0.031065020710229874,
0.00032252774690277874,
0.1255030632019043,
0.019158272072672844,
0.017640402540564537,
-0.04606868699193001,
0.02030300535261631,
0.025102227926254272,
0.017551155760884285,
-0.012998904101550579,
0.013320159167051315,
-0.012890937738120556,
0.014401532709598541,
-0.012032117694616318,
0.05448726564645767,
0.02099708467721939,
-0.04470916837453842,
0.027893660590052605,
-0.04559309408068657,
-0.03482350334525108,
-0.005018275696784258,
0.013647366315126419,
0.005635537672787905,
-0.002717019757255912,
-0.060335736721754074,
-0.03843662515282631,
-0.028931453824043274,
0.018091220408678055,
-0.010828165337443352,
-0.030870048329234123,
0.01264956034719944,
0.02187018096446991,
-0.02440367452800274,
-0.008871990256011486,
0.03179870918393135,
-0.009612146764993668,
-0.04287078604102135,
-0.018806908279657364,
0.02659805491566658,
-0.02043849788606167,
0.041434675455093384,
0.013050981797277927,
-0.013869347982108593,
0.025656957179307938,
0.010135515592992306,
0.029099933803081512,
-0.03970774635672569,
0.024996137246489525,
-0.01977238617837429,
0.05768416449427605,
-0.02873975783586502,
-0.006555998232215643,
0.021443290635943413,
-0.04593672603368759,
0.03208649158477783,
-0.03732486814260483,
0.0061721052043139935,
-0.012624569237232208,
0.030568063259124756,
-0.03177229315042496,
-0.010423301719129086,
-0.03939954936504364,
0.059093404561281204,
-0.017367491498589516,
0.011350397951900959,
-0.01843150705099106,
-0.054151687771081924,
-0.016007982194423676,
0.010900124907493591,
0.051425665616989136,
0.0032217155676335096,
-0.01429748348891735,
0.015688398852944374,
-0.017894215881824493,
-0.03419800475239754,
-0.007578229997307062,
0.022265244275331497,
0.013857838697731495,
0.05553288012742996,
0.012189343571662903,
-0.022344551980495453,
0.01065806020051241,
-0.06277745962142944,
-0.0037985180970281363,
-0.055568259209394455,
-0.038347937166690826,
-0.014486899599432945,
0.0053058466874063015,
0.021207295358181,
0.05775739625096321,
-0.04025102034211159,
-0.020114583894610405,
0.02265106700360775,
-0.0002796456392388791,
0.016520146280527115,
-0.06092017516493797,
0.011103445664048195,
-0.009892934001982212,
-0.024599231779575348,
-0.010166463442146778,
-0.01801377534866333,
-0.01986744813621044,
0.03779315575957298,
0.005906326696276665,
-0.012347020208835602,
0.02433844283223152,
0.007810489274561405,
-0.013909302651882172,
0.02152528427541256,
-0.02391699142754078,
0.0018256156472489238,
0.04395752400159836,
-0.008885826915502548,
-0.020261984318494797,
-0.03402028977870941,
-0.013096016831696033,
0.013885841704905033,
0.0065569751895964146,
-0.00356883043423295,
-0.04824355989694595,
-0.028479186818003654,
0.005939873866736889,
0.046980053186416626,
-0.03647628799080849,
0.004138056188821793,
-0.026824485510587692,
0.03105645440518856,
0.008973058313131332,
0.01823684200644493,
-0.05242503434419632,
0.05436621606349945,
0.0014624183531850576,
-0.019501155242323875,
0.020245395600795746,
0.0404830276966095,
-0.05472860857844353,
-0.0182205643504858,
0.06936471164226532,
-0.00003262342215748504,
0.027582326903939247,
0.009003311395645142,
0.0034170865546911955,
0.03549953177571297,
-0.05508719012141228,
-0.04410551115870476,
0.04250580817461014,
-0.04083702713251114,
0.028379717841744423,
0.002859476488083601,
-0.013994727283716202,
0.001281455159187317,
0.010039293207228184,
-0.046083636581897736,
-0.014188092201948166,
-0.019829729571938515,
-0.02836782857775688,
-0.0010353418765589595,
0.0032139280810952187,
0.05344076827168465,
0.014769687317311764,
-0.009779734537005424,
0.03330472111701965,
0.046428266912698746,
-0.02593538910150528,
0.006889162585139275,
0.005891371984034777,
0.025868093594908714,
0.038709260523319244,
0.01464226096868515,
-0.03149382397532463,
0.007868096232414246,
0.06725547462701797,
-0.024867914617061615,
0.03103533759713173,
-0.03156305104494095,
0.02112230472266674,
-0.09819138795137405,
-0.02911313623189926,
0.03323838859796524,
0.007407862227410078,
0.04615721479058266,
-0.03345101699233055,
0.04899069294333458,
0.01085385587066412,
-0.05273675546050072,
0.025468813255429268,
-0.02214217185974121,
-0.010504025965929031,
-0.053648144006729126,
-0.01463244203478098,
-0.06773758679628372,
0.093218132853508,
-0.024019155651330948,
0.03919067233800888,
0.004294335376471281,
0.040231771767139435,
0.005261072423309088,
-0.032453205436468124,
-0.05590593069791794,
-0.027053628116846085,
0.027345046401023865,
-0.0017397637711837888,
0.06832316517829895,
-0.013691446743905544,
-0.014113499782979488,
0.03265883028507233,
-0.012678570114076138,
-0.01846875622868538,
-0.0015073628164827824,
0.03696155175566673,
-0.0015164273791015148,
0.01267659105360508,
0.009223333559930325,
-0.01605396904051304,
-0.0066788955591619015,
-0.0041024573147296906,
0.02455103024840355,
0.020330222323536873,
-0.020582446828484535,
0.008755955845117569,
0.009938020259141922,
-0.03975405544042587,
-0.03343029320240021,
0.04213770106434822,
0.008987883105874062,
-0.029165254905819893,
-0.012150521390140057,
-0.0005525541491806507,
-0.013128584250807762,
0.010438933968544006,
0.07144235074520111,
-0.041870567947626114,
0.034140028059482574,
0.016760194674134254,
0.01579440012574196,
-0.011988273821771145,
0.031950585544109344,
-0.009212448261678219,
-0.012013678438961506,
0.025862539187073708,
0.006722093094140291,
0.009672891348600388,
-0.032169144600629807,
-0.008613839745521545,
0.02893943339586258,
0.03517359495162964,
0.01688074879348278,
-0.07409080862998962,
-0.02699161134660244,
0.0030230882111936808,
-0.003260368946939707,
0.023555487394332886,
-0.049562565982341766,
-0.0030410795006901026,
0.02374429814517498,
-0.10608082264661789,
0.03173055872321129,
0.027629168704152107,
0.0208792332559824,
-0.04314451664686203,
0.010044830851256847,
0.010441498830914497,
-0.019566304981708527,
0.00965517945587635,
0.004067948553711176,
-0.02835969254374504,
0.021373983472585678,
0.0018907655030488968,
0.00026031603920273483,
-0.01707352325320244,
0.025393174961209297,
-0.0344611257314682,
-0.01399014238268137,
0.008961084298789501,
-0.0014255084097385406,
-0.00492148008197546,
0.0008016460342332721,
-0.021290170028805733,
-0.01788950152695179,
-0.0035880107898265123,
0.03252623230218887,
-0.06508354842662811,
0.06585363298654556,
-0.0007827899535186589,
0.04293885454535484,
0.06738029420375824,
-0.022245017811655998,
0.03064160794019699,
0.04238610342144966,
-0.05142131820321083,
-0.012781757861375809,
0.053174957633018494,
-0.0049397447146475315,
-0.04399901255965233,
-0.012406975962221622,
0.005129894241690636,
0.012998132966458797,
-0.008679843507707119,
-0.018335668370127678,
0.03178039565682411,
-0.04782122001051903,
-0.030584683641791344,
0.05067581310868263,
0.02132667601108551,
0.027440529316663742,
0.011211012490093708,
0.01407410018146038,
0.021008707582950592,
0.020258935168385506,
0.016809411346912384,
0.053254030644893646,
0.008093580603599548,
0.031170057132840157,
0.034870654344558716,
0.038414761424064636,
-0.012526541948318481,
0.030631570145487785,
0.03848344087600708,
0.046146832406520844,
-0.03142610192298889,
0.01591002382338047,
0.033629439771175385,
-0.02795642986893654,
0.03259526938199997,
0.017945680767297745,
-0.045703571289777756,
0.10364998131990433,
-0.018096890300512314,
0.014469060115516186,
-0.039868373423814774,
-0.006694685202091932,
-0.033108897507190704,
-0.027647271752357483,
0.0006449485081247985,
0.016748622059822083,
-0.0442754365503788,
-0.008300959132611752,
-0.03431733697652817,
0.03297622501850128,
0.023049084469676018,
-0.03738147392868996,
-0.007799839600920677,
0.0026254933327436447,
-0.02498278021812439,
0.011692827567458153,
0.004872793797403574,
-0.02177353762090206,
-0.0026333683636039495,
0.018096573650836945,
0.018631065264344215,
0.01755075342953205,
-0.002902750624343753,
-0.005566053092479706,
-0.010026078671216965,
0.03557233884930611,
-0.05796370282769203,
-0.008343937806785107,
-0.01827068068087101,
0.03276098892092705,
-0.028483344241976738,
-0.016492608934640884
] |
<p>Where can one find some concrete physical problems (with solutions) that illustrates the uselfullness and power of QFT? These must not be solvable by QM or SR alone.</p>
<p>It would be good if the problem utilizes the most central QFT concepts. I am trying to learn QFT but it looks like only some mathematical definitions.</p>
<p>Concrete QFT calculations which shows agreement with physical experiment to high accuracy.</p> | 2,042 | [
0.011496247723698616,
-0.006017024163156748,
-0.02616736851632595,
-0.039664581418037415,
0.026344643905758858,
0.015806598588824272,
-0.0029322411864995956,
-0.04138750210404396,
-0.010846764780580997,
-0.0428813099861145,
0.034374188631772995,
0.03183813765645027,
0.025677217170596123,
-0.003983211703598499,
0.012025563977658749,
0.007595180068165064,
-0.012179735116660595,
-0.04979942366480827,
-0.016148900613188744,
-0.004783343989402056,
0.0009779160609468818,
0.055401913821697235,
0.0225943922996521,
-0.0020661097951233387,
-0.00543116545304656,
0.03720127418637276,
-0.002122810808941722,
0.02255922555923462,
0.028814565390348434,
0.0672031044960022,
-0.029779285192489624,
-0.04966731369495392,
0.0263285581022501,
0.01623232662677765,
0.0012890854850411415,
0.025612102821469307,
-0.004028100520372391,
-0.0015407779719680548,
-0.0038585886359214783,
-0.03385793790221214,
-0.0386042557656765,
-0.024925418198108673,
-0.006235357839614153,
0.04003177583217621,
-0.013270287774503231,
0.026426708325743675,
0.013159275986254215,
-0.029329761862754822,
0.07337816059589386,
-0.08249987661838531,
0.06086442619562149,
0.012497618794441223,
0.03776019066572189,
0.03214544430375099,
0.01193014532327652,
-0.009156335145235062,
0.07225676625967026,
0.06775575131177902,
0.006483183708041906,
-0.06450065225362778,
-0.011510927230119705,
-0.013899357058107853,
-0.010611869394779205,
-0.04834332317113876,
-0.024178877472877502,
0.04554496333003044,
-0.010153312236070633,
0.01679355278611183,
-0.007248410955071449,
-0.015701167285442352,
0.01135384850203991,
0.043243955820798874,
0.04066120460629463,
0.013825148344039917,
-0.010649872943758965,
0.0051636784337460995,
0.007650390733033419,
-0.01613611914217472,
0.046794600784778595,
0.019475329667329788,
-0.021002601832151413,
0.006601187400519848,
0.015660611912608147,
0.006054118275642395,
-0.010954667814075947,
-0.02919645980000496,
0.0687907487154007,
0.013287010602653027,
-0.0032111459877341986,
-0.006216107401996851,
-0.012276658788323402,
-0.011225992813706398,
0.046870775520801544,
0.0050696926191449165,
-0.042578939348459244,
0.01964433118700981,
0.027030006051063538,
0.04387064650654793,
0.0021221651695668697,
-0.030078092589974403,
0.0046144104562699795,
-0.02284284494817257,
0.02938990853726864,
0.1009427011013031,
-0.019380459561944008,
-0.004113406874239445,
-0.015111374668776989,
0.009184732101857662,
0.019717885181307793,
-0.0032022574450820684,
-0.01852205954492092,
0.02342379465699196,
-0.009647774510085583,
0.008419651538133621,
-0.02063678950071335,
-0.04526788368821144,
-0.015330890193581581,
-0.01948520354926586,
0.06137057766318321,
0.06721577048301697,
0.03998083248734474,
-0.055850062519311905,
0.02042030356824398,
-0.027325257658958435,
-0.0694766491651535,
0.01663881167769432,
0.04203944653272629,
-0.03593135625123978,
-0.05035749450325966,
0.03439662232995033,
0.006003184709697962,
-0.02816854976117611,
-0.016428090631961823,
-0.018270347267389297,
0.054713133722543716,
-0.03889790549874306,
-0.10478020459413528,
-0.060090139508247375,
0.038719624280929565,
-0.02085024118423462,
-0.025423381477594376,
-0.03674411028623581,
0.05351412296295166,
0.03714065998792648,
0.05493871867656708,
-0.004457041155546904,
-0.010445215739309788,
-0.0264380294829607,
0.0348983034491539,
0.0074965800158679485,
-0.034748051315546036,
0.016473347321152687,
0.008859601803123951,
-0.03418685495853424,
-0.007919886149466038,
-0.03664333373308182,
0.0052340105175971985,
0.01248543243855238,
0.0027364862617105246,
-0.04698910191655159,
0.0846400037407875,
-0.007198809180408716,
0.00792256835848093,
0.005804733373224735,
-0.03903765603899956,
-0.008315612562000751,
0.06790667772293091,
0.0036627568770200014,
0.014845671132206917,
0.05474865809082985,
-0.010479332879185677,
0.007315413095057011,
0.022524049505591393,
-0.009288391098380089,
0.008281156420707703,
-0.015492933802306652,
0.012911343015730381,
0.0035152235068380833,
0.0037762236315757036,
-0.02232465334236622,
-0.03241533413529396,
-0.011107760481536388,
-0.022886984050273895,
0.002771692117676139,
-0.025476304814219475,
0.020389264449477196,
-0.004251094534993172,
0.009501523338258266,
0.015826694667339325,
-0.04820750281214714,
-0.01895417459309101,
-0.07457567006349564,
0.0422377809882164,
-0.020134203135967255,
-0.011550392024219036,
0.033661432564258575,
0.016866127029061317,
0.03472656011581421,
-0.06802660971879959,
-0.06143728271126747,
-0.010936896316707134,
0.0432359054684639,
-0.005868702195584774,
0.005242764484137297,
0.04069727659225464,
0.04761199280619621,
0.03454047441482544,
-0.018394438549876213,
0.027538487687706947,
-0.014582935720682144,
-0.021706923842430115,
-0.00875048991292715,
-0.026786530390381813,
0.01267998293042183,
-0.01557641476392746,
0.006691176909953356,
-0.002564622089266777,
-0.005841394886374474,
-0.003020979231223464,
0.02501651644706726,
-0.014204559847712517,
0.0850721076130867,
0.04579499736428261,
0.030496859923005104,
-0.0006349248578771949,
0.02412448823451996,
0.004154703579843044,
-0.005882185883820057,
0.016346881166100502,
-0.02732936292886734,
-0.040858957916498184,
-0.021722666919231415,
0.07529140263795853,
0.03649287670850754,
-0.031087100505828857,
0.01940934732556343,
0.013118894770741463,
0.025797894224524498,
0.03480521962046623,
0.03368061035871506,
-0.05283995345234871,
-0.026825644075870514,
0.011724734678864479,
-0.030197713524103165,
0.040327996015548706,
0.01724201813340187,
0.00253861746750772,
0.0348154678940773,
-0.010115631856024265,
-0.0005545833264477551,
-0.04390436038374901,
0.04684949293732643,
-0.04802222177386284,
-0.015436719171702862,
-0.0011243936605751514,
-0.05625114589929581,
0.023439886048436165,
-0.03784967586398125,
0.016382886096835136,
-0.0039802612736821175,
-0.033681176602840424,
0.03248659893870354,
-0.012192942202091217,
-0.04526469483971596,
0.039635539054870605,
-0.010613816790282726,
-0.01798211969435215,
0.006755726411938667,
0.021428003907203674,
-0.03675084933638573,
-0.00499104056507349,
-0.014900950714945793,
-0.0056131561286747456,
-0.01375508401542902,
-0.009368318133056164,
0.03150780498981476,
-0.007758136373013258,
0.03866807371377945,
-0.025225328281521797,
-0.026614833623170853,
-0.006197088398039341,
-0.0230174008756876,
-0.010707403533160686,
0.013723154552280903,
-0.03499172627925873,
0.018438374623656273,
-0.045067571103572845,
-0.05786257982254028,
0.04503614082932472,
-0.039801403880119324,
0.000951424241065979,
0.023843159899115562,
0.004499519243836403,
-0.03568989410996437,
0.004720616154372692,
-0.038192715495824814,
0.015654440969228745,
-0.011524665169417858,
0.026456234976649284,
0.05803975462913513,
-0.00006043816756573506,
-0.024631859734654427,
0.016211284324526787,
0.0015419976552948356,
-0.03885854780673981,
-0.0165813360363245,
0.007273913826793432,
0.030830636620521545,
-0.01542967651039362,
0.03763160854578018,
0.0064443740993738174,
-0.05701379477977753,
-0.022810157388448715,
-0.0280938521027565,
-0.030698511749505997,
0.01439092680811882,
0.01211019977927208,
0.04473869502544403,
-0.009750722907483578,
-0.03356487676501274,
0.08488207310438156,
0.02894817478954792,
-0.06278552114963531,
-0.003262853715568781,
-0.014949072152376175,
-0.011530597694218159,
0.025255346670746803,
0.007205937057733536,
0.0050851814448833466,
-0.020029863342642784,
0.03969205170869827,
0.015601213090121746,
0.004037513397634029,
0.007434643339365721,
0.03469863533973694,
-0.03556797280907631,
0.007526301313191652,
-0.00031080562621355057,
0.020718229934573174,
0.05504525452852249,
0.00972943939268589,
-0.06510791182518005,
0.00231122481636703,
0.01996513456106186,
-0.013598538935184479,
0.0024643181823194027,
-0.01751469075679779,
0.04925476387143135,
0.0018202613573521376,
0.019773324951529503,
-0.0477491095662117,
0.038583435118198395,
-0.026572899892926216,
-0.016549544408917427,
0.005771635565906763,
0.03127998113632202,
-0.006676103454083204,
-0.006145433988422155,
0.023690178990364075,
0.007007160689681768,
0.041643593460321426,
-0.04229710251092911,
-0.04893529415130615,
-0.023180916905403137,
-0.009427689015865326,
0.02910497412085533,
-0.03757532313466072,
-0.027185656130313873,
0.03561611846089363,
0.04828639328479767,
0.04468335211277008,
-0.026435280218720436,
-0.019940562546253204,
-0.02128138393163681,
-0.06617244333028793,
-0.023879969492554665,
-0.04907061159610748,
0.061530403792858124,
0.0020300198812037706,
0.06296926736831665,
-0.012341488152742386,
-0.015460966154932976,
0.023518871515989304,
0.01448983233422041,
-0.07351554185152054,
0.024043990299105644,
-0.007587293162941933,
-0.005956942681223154,
0.00115198886487633,
0.010324206203222275,
0.008735394105315208,
-0.008219508454203606,
-0.043464675545692444,
-0.021228333935141563,
0.012773977592587471,
-0.034617651253938675,
-0.037606485188007355,
-0.021536976099014282,
-0.017267528921365738,
-0.020394625142216682,
0.022904405370354652,
0.05566388741135597,
-0.050444453954696655,
-0.011111093685030937,
0.039242129772901535,
-0.07570218294858932,
-0.028715090826153755,
0.0003470131487119943,
0.014269360341131687,
-0.0008516176603734493,
0.031264372169971466,
0.016873523592948914,
0.02853333204984665,
-0.027694450691342354,
0.01705794595181942,
-0.007286834996193647,
0.08332528173923492,
-0.011045384220778942,
-0.02302895113825798,
-0.008855183608829975,
-0.04340102896094322,
-0.0021956083364784718,
-0.0017308605602011085,
0.04770016297698021,
0.009471350349485874,
-0.012819579802453518,
0.04017559066414833,
-0.004752808716148138,
-0.019927917048335075,
0.032762132585048676,
0.04275471344590187,
0.013606439344584942,
-0.02957196906208992,
-0.014838450588285923,
-0.039122723042964935,
-0.016775809228420258,
0.0022587028797715902,
0.02538805827498436,
-0.004558186046779156,
-0.0019511595601215959,
0.016450701281428337,
-0.01046059187501669,
0.03008890338242054,
-0.03485020995140076,
0.008978289552032948,
0.027535727247595787,
0.015955617651343346,
-0.002074948512017727,
-0.005570963956415653,
0.010342657566070557,
0.03713586553931236,
0.042932648211717606,
0.018400730565190315,
-0.013474197126924992,
-0.04474017396569252,
0.03875221312046051,
0.06822141259908676,
0.01386140938848257,
0.03637577220797539,
0.0031387112103402615,
-0.014810847118496895,
-0.004897296894341707,
0.04205060377717018,
-0.046700723469257355,
0.034952469170093536,
-0.01039935927838087,
-0.0021476189140230417,
-0.021196799352765083,
-0.013424803502857685,
0.00164695642888546,
0.021546103060245514,
0.010037505999207497,
0.014820123091340065,
-0.029362235218286514,
0.009730910882353783,
-0.008646021597087383,
0.028211181983351707,
0.030009008944034576,
0.060212135314941406,
0.00036937984987162054,
0.012508061714470387,
0.02530020661652088,
0.015173057094216347,
-0.03908697888255119,
-0.08111261576414108,
-0.009308932349085808,
0.019796188920736313,
-0.007976793684065342,
0.022136738523840904,
-0.04774901270866394,
-0.07781535387039185,
0.0031203399412333965,
0.004363775718957186,
-0.027883008122444153,
-0.006285571493208408,
-0.05355219542980194,
0.04427803307771683,
0.007080713752657175,
0.043404221534729004,
0.03839676082134247,
0.03663202375173569,
-0.034556858241558075,
-0.0313093438744545,
0.010311782360076904,
0.015279863029718399,
0.0006254521431401372,
0.02295578457415104,
-0.031685102730989456,
0.004585229326039553,
-0.04157496988773346,
0.06368838995695114,
-0.03362968564033508,
0.02730226330459118,
-0.016594642773270607,
-0.004730287939310074,
-0.03433941677212715,
0.0182737298309803,
-0.004831109661608934,
-0.008212543092668056,
0.0063904281705617905,
0.010652480646967888,
0.01998918130993843,
-0.02389094978570938,
0.009999629110097885,
0.04587377980351448,
-0.019581446424126625,
0.03467659279704094,
-0.01266574952751398,
-0.0013171567115932703,
-0.02903061732649803,
-0.011416099034249783,
0.005184009671211243,
-0.040994904935359955,
0.04971519485116005,
-0.013061669655144215,
-0.025690557435154915,
0.026583857834339142,
-0.08510588854551315,
-0.045365624129772186,
0.02019820362329483,
0.016040315851569176,
0.0387040413916111,
-0.00317896855995059,
-0.0038179487455636263,
0.008681703358888626,
0.01656115986406803,
-0.07352697849273682,
-0.054044343531131744,
0.028362927958369255,
0.020422032102942467,
-0.006942729000002146,
-0.029910555109381676,
0.016691353172063828,
-0.029913047328591347,
-0.012595253996551037,
0.005204704590141773,
0.035623468458652496,
-0.00846205186098814,
-0.0031599474605172873,
0.015929289162158966,
0.012581034563481808,
0.03769977018237114,
0.008669992908835411,
0.001281139673665166,
0.004024677909910679,
-0.0022342645097523928,
-0.026293253526091576,
0.006531592458486557,
-0.01212125550955534,
-0.01593826524913311,
-0.0544375479221344,
-0.018659327179193497,
0.010791821405291557,
-0.00675000436604023,
-0.01697697676718235,
0.0025289494078606367,
0.017632989212870598,
0.015351416543126106,
-0.019641757011413574,
-0.036283254623413086,
0.013685880228877068,
0.012441533617675304,
0.05811529606580734,
-0.003860575845465064,
-0.007385445758700371,
-0.01565481349825859,
-0.07329729199409485,
0.01983749121427536,
-0.006215388886630535,
-0.018687019124627113,
0.026257850229740143,
0.06642140448093414,
0.0003296121722087264,
-0.012276463210582733,
0.010314660146832466,
-0.006526987534016371,
-0.008391599170863628,
-0.01084398478269577,
0.02075853757560253,
-0.0034300722181797028,
0.04614316299557686,
-0.04386317729949951,
-0.04824257269501686,
-0.009883386082947254,
-0.008973035030066967,
0.056899864226579666,
-0.001615268411114812,
0.07411383092403412,
0.03750918433070183,
-0.033300284296274185,
-0.004725362174212933,
0.048269208520650864,
-0.008527657948434353,
-0.0009692786843515933,
0.02578275464475155,
0.012226046063005924,
-0.019463924691081047,
0.0097957793623209,
0.00497393636032939,
0.046658195555210114,
-0.027980362996459007,
0.03294741362333298,
0.026130691170692444,
0.05980789288878441,
0.03209838271141052,
-0.045714471489191055,
-0.03135588765144348,
0.05016176775097847,
-0.032996855676174164,
0.029949288815259933,
0.01431105937808752,
0.02664485201239586,
0.040109310299158096,
0.01022157073020935,
-0.015569736249744892,
0.007080193143337965,
-0.02828049473464489,
-0.049190256744623184,
0.010783162899315357,
0.01151273027062416,
-0.009067279286682606,
-0.0002889537427108735,
-0.005431234370917082,
0.013656332157552242,
-0.006903305649757385,
0.01909697987139225,
0.018472271040081978,
-0.05213964730501175,
-0.04318637400865555,
-0.03754078224301338,
-0.04357951134443283,
0.05702545866370201,
0.00923241674900055,
-0.03510311618447304,
0.004346686415374279,
-0.03291510418057442,
0.02951224520802498,
0.009522969834506512,
0.011394871398806572,
-0.04648646339774132,
0.06815670430660248,
-0.02528860792517662,
0.023737842217087746,
-0.017270252108573914,
0.024081053212285042,
0.11239197850227356,
0.07348747551441193,
0.006413517985492945,
-0.07408619672060013,
0.0058980947360396385,
-0.0273827463388443,
0.03225310519337654,
-0.052272774279117584,
0.035069018602371216,
-0.0303694736212492,
0.020897049456834793,
0.019861139357089996,
0.05463127791881561,
0.02278086356818676,
0.019020913168787956,
0.058716434985399246,
-0.07062321156263351,
-0.05219188332557678,
0.0009682499221526086,
0.022996146231889725,
-0.02438674308359623,
0.007124549243599176,
-0.061553530395030975,
0.007449937053024769,
-0.05777132138609886,
-0.0017499421956017613,
-0.023110345005989075,
-0.01893356442451477,
0.04425825551152229,
0.00243289559148252,
-0.03862524405121803,
-0.013720591552555561,
-0.008137576282024384,
-0.004422890488058329,
-0.027147922664880753,
0.010770993307232857,
0.017817001789808273,
-0.028245072811841965,
0.009382026270031929,
0.05574033036828041,
0.022993549704551697,
0.0042649442330002785,
-0.043294332921504974,
0.0069480533711612225,
-0.04235247150063515,
-0.0029399108607321978,
-0.030014842748641968,
0.048850759863853455,
-0.031224796548485756,
0.002478290582075715,
-0.009680601768195629,
0.03133787959814072,
-0.017237382009625435,
-0.023685356602072716,
-0.028062311932444572,
0.006789189297705889,
0.03589751198887825,
-0.053355176001787186,
0.007110862992703915,
-0.03281183913350105,
0.047882966697216034,
-0.028276395052671432,
0.006949585862457752,
-0.011338063515722752,
-0.015350325033068657,
-0.0014766213716939092,
-0.004793391562998295,
0.01701696775853634,
-0.02190443128347397,
-0.02164245955646038,
-0.04492846503853798,
-0.016813119873404503,
-0.030405551195144653,
-0.022155027836561203,
0.025537259876728058,
0.037282783538103104,
0.04727969691157341,
-0.009119353257119656,
0.010041359812021255,
-0.0007490619318559766,
-0.050565898418426514,
0.02884485200047493,
-0.010309825651347637,
-0.014168855734169483,
0.01162777654826641,
-0.00014508394815493375,
0.02791348099708557,
0.03916575387120247,
0.0007307197665795684,
-0.0281959380954504,
-0.03276451677083969,
-0.007084062322974205,
0.03608217090368271,
-0.020870506763458252,
-0.02623097412288189,
-0.018921809270977974,
-0.02014308050274849,
0.022571809589862823,
-0.012316488660871983,
-0.005843319930136204,
0.045495178550481796,
-0.0011086069280281663,
0.017713496461510658,
0.04462061822414398,
-0.02027488313615322,
-0.0034416704438626766,
0.03156130388379097,
-0.02899295464158058,
-0.011270915158092976,
0.016473930329084396,
0.01988421194255352,
-0.02219581976532936,
-0.06505090743303299,
0.007382040843367577,
-0.005186242051422596,
-0.011680133640766144,
0.031209424138069153,
-0.0312591977417469,
-0.002147067803889513,
-0.011508023366332054,
-0.00011432825704105198,
-0.06819497793912888,
-0.010872670449316502,
-0.05391135811805725,
0.010395534336566925,
0.0016607060097157955,
-0.015707800164818764,
-0.010829859413206577,
0.0003378992259968072,
-0.004916295874863863,
-0.0294931810349226,
0.021022634580731392,
-0.005976860411465168,
-0.01062063779681921,
0.023884600028395653,
0.013412661850452423,
0.02663818746805191,
0.022257769480347633,
-0.0054990206845104694,
-0.00819165538996458,
0.033632200211286545,
-0.044650495052337646,
-0.05211475491523743,
0.008383495733141899,
-0.02016100101172924,
0.013699633069336414,
0.048949915915727615,
0.0006942882901057601,
-0.04864104837179184,
0.029170596972107887,
-0.017295220866799355,
-0.0070458101108670235,
0.0032906164415180683,
0.0011596187250688672,
-0.020309800282120705,
-0.014855953864753246,
0.03717624768614769,
-0.02373013086616993,
-0.015765678137540817,
-0.0032231868244707584,
0.02961587719619274,
0.030821314081549644,
-0.0070998575538396835,
0.020319713279604912,
0.023409152403473854,
-0.0029613939113914967,
0.0625540241599083,
-0.021751247346401215,
0.03774752840399742,
0.05538215860724449,
-0.04218927398324013,
0.02407643012702465,
0.013735707849264145,
0.005542421713471413,
-0.10438256710767746,
0.006626354530453682,
0.029371820390224457,
0.0006572680431418121,
0.05906638875603676,
-0.06007085368037224,
0.03419357165694237,
0.02995871752500534,
-0.08454719185829163,
0.05634637176990509,
-0.040919702500104904,
-0.027217958122491837,
-0.0034389107022434473,
0.003029485698789358,
-0.02896811254322529,
0.08451258391141891,
0.006283446680754423,
0.02418268285691738,
0.000016903346477192827,
0.036914873868227005,
0.025168439373373985,
0.021857712417840958,
-0.019412171095609665,
0.04496831074357033,
-0.022291501984000206,
-0.0050881244242191315,
0.06231219321489334,
0.017190424725413322,
-0.00152890058234334,
0.005861141253262758,
-0.012772900052368641,
-0.013238029554486275,
-0.02754722163081169,
0.011158451437950134,
-0.010964608751237392,
0.06322735548019409,
0.04582777991890907,
0.008486294187605381,
-0.00362632074393332,
0.011285880580544472,
0.026215512305498123,
0.025705035775899887,
0.020556151866912842,
0.009332952089607716,
0.025069253519177437,
-0.037809040397405624,
-0.03720436245203018,
0.03877972811460495,
0.01881173625588417,
-0.014001289382576942,
-0.003515600459650159,
-0.020911505445837975,
-0.003963963128626347,
0.0029815041925758123,
0.018723541870713234,
-0.05433757230639458,
-0.004632678814232349,
0.01944596879184246,
0.010587580502033234,
0.0046608042903244495,
0.035581015050411224,
0.010968317277729511,
-0.027788126841187477,
0.03111918456852436,
0.015948116779327393,
0.01243442203849554,
-0.0713568925857544,
0.0026282158214598894,
0.02062620408833027,
-0.008239446207880974,
0.010590857826173306,
-0.05735402554273605,
-0.052427757531404495,
0.021555572748184204,
0.015032055787742138,
0.023875389248132706,
-0.0327620729804039,
-0.020648669451475143,
-0.01796882227063179,
-0.060999415814876556,
0.041002340614795685,
-0.0030824646819382906,
-0.00003024445686605759,
-0.026387043297290802,
0.014176275581121445,
0.013516438193619251,
0.019185369834303856,
0.03016776032745838,
-0.045412108302116394,
-0.028981249779462814,
-0.006691342685371637,
-0.014586254954338074,
0.015334658324718475,
-0.05348962917923927,
-0.02338089421391487,
-0.02821783348917961,
-0.036041684448719025,
-0.026668397709727287,
-0.027422156184911728,
0.00219510355964303,
0.02986937388777733,
0.03395209088921547,
-0.0005033300258219242,
0.012091705575585365,
0.009341220371425152,
-0.03260662779211998,
0.0795913115143776,
0.01540831197053194,
0.0025412095710635185,
0.05817783996462822,
-0.024768341332674026,
0.014852809719741344,
0.012411794625222683,
-0.03944230452179909,
-0.009424575604498386,
0.0285430159419775,
-0.049762021750211716,
-0.02226863242685795,
-0.007428093813359737,
-0.004080300219357014,
0.026123903691768646,
-0.04634982720017433,
-0.008869620971381664,
0.05035660043358803,
-0.05051726847887039,
-0.0015129813691601157,
0.05467357486486435,
0.03056972287595272,
0.051567140966653824,
-0.0014378922060132027,
0.002631230978295207,
0.016780711710453033,
0.01897977665066719,
-0.012088709510862827,
0.021736597642302513,
0.03633835166692734,
-0.008842497132718563,
0.024736570194363594,
0.04472576826810837,
-0.0032630437053740025,
0.01902059279382229,
0.027306528761982918,
0.015005361288785934,
-0.03668768331408501,
0.0016508267726749182,
0.01927596516907215,
-0.022801324725151062,
0.024887720122933388,
0.008478456176817417,
-0.03994304686784744,
0.08084935694932938,
-0.04774514213204384,
-0.0010849474929273129,
-0.021248461678624153,
0.004710821434855461,
-0.02135840430855751,
0.010068811476230621,
0.027574311941862106,
0.08500946313142776,
-0.040823038667440414,
0.0029822213109582663,
0.003287574974820018,
0.03267689049243927,
-0.008536078967154026,
-0.030446987599134445,
0.010110897943377495,
-0.006293689366430044,
-0.015974830836057663,
0.0026580148842185736,
-0.0037795554380863905,
-0.00683865649625659,
-0.001440698280930519,
0.03160657361149788,
0.04834873229265213,
-0.0006021454464644194,
-0.0025440691970288754,
0.0020228789653629065,
-0.011634288355708122,
0.06222299113869667,
-0.05223860964179039,
0.02267381176352501,
-0.007295321673154831,
0.024712268263101578,
-0.03439131751656532,
0.018959496170282364
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/2175/is-it-possible-for-information-to-be-transmitted-faster-than-light-by-using-a-ri">Is it possible for information to be transmitted faster than light by using a rigid pole?</a> </p>
</blockquote>
<p>On one episode of <a href="http://www.qi.com/" rel="nofollow">QI</a> they asked the question, "How fast do electrons move travelling around an electric current."</p>
<p>The answer is (more or less) "very slowly", with the explanation that it's not the electrons that move fast, it's the force (I think). They likened it to pushing on one end of a long tube of touching marbles and observing how quickly one fell out the other end.</p>
<p>This made me think about the tube. I realise that this tube cannot allow a force to propagate through the tube instantaneously because that would be faster than the speed of light, so my question is, why not?</p>
<hr>
<p><strong>TL;DR;</strong> Why doesn't a marble exit a long tube filled with touching marbles immediately when a force is applied to the marble at the other end?</p> | 4 | [
-0.02983108162879944,
-0.019781464710831642,
0.002339086262509227,
-0.09036342799663544,
0.009979435242712498,
-0.02472270466387272,
0.02559809945523739,
-0.0160423144698143,
-0.008464816957712173,
0.011855145916342735,
0.040690891444683075,
0.03743036836385727,
0.06214473024010658,
0.00005598115239990875,
0.02239539660513401,
0.01258291769772768,
0.014802470803260803,
-0.006466500926762819,
0.012958602048456669,
-0.02619638666510582,
-0.014133588410913944,
0.03865595534443855,
-0.02262858673930168,
0.012385256588459015,
-0.008301991969347,
-0.015992701053619385,
0.03205118700861931,
0.006391302216798067,
-0.011345862410962582,
0.03816348686814308,
-0.010195987299084663,
-0.005585826002061367,
-0.0006053677061572671,
-0.006043991073966026,
0.03987511992454529,
-0.009572780691087246,
-0.03421088680624962,
-0.025703569874167442,
-0.0030387751758098602,
-0.0007520463550463319,
-0.003331004176288843,
0.009768086485564709,
0.007706745993345976,
0.04604102298617363,
-0.05263744667172432,
0.039392512291669846,
0.03699323534965515,
-0.02517462708055973,
0.04755326732993126,
-0.055749453604221344,
0.01346528809517622,
0.0021347205620259047,
0.018997056409716606,
0.015760213136672974,
-0.0019557508639991283,
-0.02920006401836872,
0.049738410860300064,
0.058173783123493195,
-0.05853504687547684,
-0.034317467361688614,
-0.008521093986928463,
-0.0007739439606666565,
-0.03692528232932091,
-0.02580072358250618,
-0.020928343757987022,
0.038592178374528885,
-0.016364961862564087,
-0.003916735295206308,
0.04402569308876991,
0.007221141830086708,
0.003163889516144991,
0.011768407188355923,
0.03202371299266815,
0.03263326734304428,
-0.013598967343568802,
-0.0018822760321199894,
-0.004447115119546652,
-0.0019472630228847265,
0.017441535368561745,
0.054058559238910675,
-0.01911279372870922,
-0.007987401448190212,
0.04795784130692482,
0.07113398611545563,
0.027097320184111595,
-0.015503774397075176,
0.021733928471803665,
-0.019227731972932816,
-0.013513242825865746,
0.05202830955386162,
-0.028875669464468956,
-0.010245605371892452,
0.013957160525023937,
0.026421230286359787,
0.0008782301447354257,
0.011016814969480038,
-0.0008244771743193269,
0.06641082465648651,
0.04487528279423714,
0.0063851154409348965,
0.00209560408256948,
-0.02144174464046955,
0.031119275838136673,
0.08082101494073868,
-0.0038251967635005713,
-0.034500449895858765,
-0.0010659360559657216,
-0.008781934157013893,
-0.042281508445739746,
-0.004196752328425646,
-0.0027320529334247112,
-0.027142135426402092,
-0.0001522260281490162,
-0.008640050888061523,
-0.018696555867791176,
-0.01930282637476921,
-0.013111435808241367,
-0.016286833211779594,
0.05089849233627319,
0.04893256723880768,
0.013830036856234074,
-0.040539514273405075,
-0.01870621368288994,
-0.06937278807163239,
-0.017955442890524864,
0.007911897264420986,
-0.00013392175605986267,
-0.0034792146179825068,
-0.0029385124798864126,
0.04545525088906288,
0.021987471729516983,
0.0017308180686086416,
-0.041555386036634445,
-0.03248217701911926,
0.046088386327028275,
-0.014782719314098358,
-0.10645721107721329,
-0.06448263674974442,
0.059229619801044464,
0.0072426158003509045,
-0.013989469967782497,
-0.11528918147087097,
0.0019267642637714744,
0.013530745171010494,
0.07342708855867386,
-0.004019783344119787,
0.015396303497254848,
-0.008243069052696228,
0.03687799721956253,
-0.003321202239021659,
-0.009733959101140499,
0.0054648397490382195,
0.016983158886432648,
0.009954791516065598,
0.020482007414102554,
-0.04904218763113022,
0.020592456683516502,
0.025436216965317726,
0.0069800084456801414,
-0.008626704104244709,
-0.00027145480271428823,
-0.01879519410431385,
0.024634044617414474,
0.005827864166349173,
-0.021558579057455063,
-0.02007460966706276,
0.09027080982923508,
0.028821373358368874,
-0.017237840220332146,
0.04485023021697998,
0.029431570321321487,
0.0263985563069582,
-0.023222995921969414,
0.004039134364575148,
0.00004517655906965956,
-0.028431544080376625,
0.006345134694129229,
-0.024318192154169083,
-0.0003836022806353867,
0.019096363335847855,
-0.04210099205374718,
-0.03448738157749176,
-0.013363046571612358,
0.0008840837399475276,
0.018356231972575188,
0.047920484095811844,
0.007384589407593012,
-0.008625329472124577,
-0.015365076251327991,
-0.04564690589904785,
-0.02386135421693325,
-0.034341633319854736,
0.054958127439022064,
-0.0019111032597720623,
-0.003547602565959096,
0.0029880315996706486,
-0.014057911932468414,
0.022473372519016266,
0.010931013152003288,
0.0028346050530672073,
-0.029266569763422012,
-0.008971347473561764,
0.011425650678575039,
-0.0024536491837352514,
-0.0013791872188448906,
0.046937502920627594,
0.0320616289973259,
0.016053102910518646,
-0.001256447983905673,
-0.00018214037118013948,
-0.010624032467603683,
0.0057100532576441765,
0.008548582904040813,
0.03739950805902481,
0.022687992081046104,
-0.004080337937921286,
0.015564442612230778,
0.001871217624284327,
-0.026299843564629555,
0.02049735188484192,
-0.024461813271045685,
0.10693170130252838,
0.02538829855620861,
-0.012873226776719093,
0.021554285660386086,
0.02671736478805542,
0.022192643955349922,
0.0018634835723787546,
-0.034435030072927475,
-0.04676859453320503,
-0.037893667817115784,
-0.007955562323331833,
0.015148895792663097,
0.01496916078031063,
-0.020469041541218758,
0.020649567246437073,
0.0049130613915622234,
0.03777877241373062,
0.010760226286947727,
0.034575462341308594,
-0.013509977608919144,
-0.025811292231082916,
0.044170279055833817,
0.0032035131007432938,
-0.04855869710445404,
0.006501991767436266,
0.03661835566163063,
0.01774205081164837,
0.009268863126635551,
0.0040601762011647224,
0.02504546381533146,
-0.01128910481929779,
-0.010745839215815067,
0.020870165899395943,
0.04245247691869736,
-0.05087626725435257,
0.060111746191978455,
-0.0050028045661747456,
0.004215937573462725,
-0.002036724705249071,
0.019434725865721703,
0.013156689703464508,
-0.059318315237760544,
0.004800280090421438,
-0.03543173521757126,
0.007772619370371103,
-0.0012048531789332628,
-0.021343696862459183,
0.03494652733206749,
-0.04462935030460358,
0.0011561629362404346,
-0.0021931605879217386,
-0.030000589787960052,
-0.019108742475509644,
0.0024334799963980913,
0.013125445693731308,
0.03821740671992302,
0.03430230915546417,
-0.09497685730457306,
-0.025102587416768074,
-0.027281682938337326,
-0.02557113766670227,
0.011409423314034939,
0.03278379142284393,
-0.016745327040553093,
0.02508017234504223,
-0.03295646607875824,
-0.03454853966832161,
0.05409867689013481,
-0.044500693678855896,
-0.023206183686852455,
0.00017201770970132202,
-0.013019916601479053,
-0.026233980432152748,
-0.010274150408804417,
-0.03259147331118584,
0.029584908857941628,
-0.01861148327589035,
0.007623765151947737,
0.08797154575586319,
-0.01961343176662922,
-0.04817015677690506,
0.00813404843211174,
-0.03222237154841423,
-0.036750197410583496,
0.0331711545586586,
0.021815724670886993,
-0.0041243634186685085,
-0.03604014590382576,
0.013017470017075539,
0.018745504319667816,
-0.05700111389160156,
-0.044859349727630615,
-0.052802298218011856,
-0.040497392416000366,
0.03468427062034607,
0.0075917630456388,
0.056548405438661575,
0.010321051813662052,
-0.02263450436294079,
0.045348409563302994,
0.011343438178300858,
-0.04242710769176483,
0.003940298687666655,
-0.018682828173041344,
-0.06766919791698456,
-0.056680936366319656,
0.0037226194981485605,
0.0429748073220253,
-0.01728345826268196,
-0.0005102790892124176,
0.008252525702118874,
0.07169710844755173,
-0.023758312687277794,
0.018289199098944664,
-0.017251919955015182,
-0.008469491265714169,
0.0142666632309556,
-0.03940223529934883,
0.025394467636942863,
0.08120635151863098,
-0.01987508498132229,
-0.0016030366532504559,
-0.0323999747633934,
0.03657929599285126,
0.02975492924451828,
-0.05089079588651657,
0.07091491669416428,
0.01017007976770401,
-0.0008243381744250655,
-0.043914422392845154,
0.03403940796852112,
-0.0314629003405571,
-0.03234126791357994,
-0.02049659565091133,
0.020611895248293877,
0.05088088661432266,
-0.010166598483920097,
0.021904055029153824,
0.048612140119075775,
0.04768456146121025,
-0.028083661571145058,
-0.000025160199584206566,
-0.024236856028437614,
-0.012515840120613575,
0.018696637824177742,
0.01596939004957676,
0.005818680394440889,
0.017727036029100418,
0.03217236325144768,
0.007935351692140102,
0.022969746962189674,
0.005395432934165001,
-0.030762851238250732,
-0.02982373908162117,
-0.005703428760170937,
0.006006818730384111,
0.050517354160547256,
0.05517031252384186,
0.06980465352535248,
0.0559074804186821,
0.03307163715362549,
-0.020212076604366302,
-0.0007312658708542585,
-0.09386047720909119,
0.02949579618871212,
-0.019473303109407425,
-0.03352917358279228,
-0.022812845185399055,
-0.038568802177906036,
-0.01260608620941639,
-0.0016020180191844702,
-0.02198120392858982,
-0.008422122336924076,
0.016558893024921417,
-0.0390954464673996,
0.011691472493112087,
-0.02862764149904251,
0.005807321984320879,
-0.01905789226293564,
0.034474242478609085,
0.04541761055588722,
-0.017357001081109047,
0.02945401892066002,
0.022905252873897552,
-0.050200968980789185,
-0.01889081858098507,
-0.012922147288918495,
0.015368211083114147,
0.032457385212183,
0.011876448057591915,
0.023522567003965378,
0.016677631065249443,
-0.03592708334326744,
-0.03266771137714386,
0.04487273842096329,
0.014501428231596947,
-0.024587886407971382,
0.012395819649100304,
-0.03850247338414192,
-0.029762474820017815,
0.020687630400061607,
0.003693836275488138,
0.07250062376260757,
-0.04226182773709297,
0.0010217520175501704,
-0.0030805764254182577,
-0.022917281836271286,
-0.0029321264009922743,
0.036738116294145584,
-0.0011214443948119879,
0.0013820312451571226,
-0.027656011283397675,
-0.057627204805612564,
-0.0076266322284936905,
-0.019719233736395836,
0.02221124805510044,
-0.004547846503555775,
0.016327189281582832,
-0.025589894503355026,
-0.006670054979622364,
0.004413919523358345,
0.03449459746479988,
-0.015890510752797127,
0.010274422354996204,
-0.005394043866544962,
0.01053651049733162,
-0.02543204091489315,
0.009265388362109661,
-0.010269318707287312,
0.025709884241223335,
0.006517867092043161,
0.011327392421662807,
-0.014433284290134907,
-0.07156610488891602,
-0.023579562082886696,
0.02903791330754757,
0.05745593085885048,
-0.01285581011325121,
0.014674318954348564,
-0.04429418221116066,
0.01060456968843937,
0.030521046370267868,
-0.009536482393741608,
-0.000030425477234530263,
-0.0274457186460495,
-0.009716802276670933,
-0.020077776163816452,
-0.09587489813566208,
-0.020158473402261734,
-0.016952641308307648,
-0.03630279749631882,
0.004308517090976238,
0.01454923115670681,
-0.04335806891322136,
0.0214089322835207,
-0.012387902475893497,
0.03197085112333298,
0.029489194974303246,
0.009564010426402092,
0.022544879466295242,
0.017070267349481583,
0.00321884173899889,
-0.038038719445466995,
-0.06717624515295029,
0.02951653115451336,
-0.040142402052879333,
-0.02964555099606514,
0.01931927539408207,
-0.08544523268938065,
-0.02685781940817833,
0.02726701833307743,
0.01655677892267704,
0.031016582623124123,
0.024550452828407288,
-0.05892406404018402,
0.03813857212662697,
0.011719850823283195,
0.009837659075856209,
0.02444283291697502,
0.02401966229081154,
-0.018778182566165924,
0.01779128424823284,
-0.024338312447071075,
0.004890829790383577,
-0.024278784170746803,
0.007064207922667265,
-0.021009625867009163,
0.049701496958732605,
-0.0107705844566226,
0.050893720239400864,
0.019786572083830833,
0.023240653797984123,
-0.009710417129099369,
-0.04111167788505554,
-0.00237168837338686,
0.022251510992646217,
-0.011896390467882156,
0.029180914163589478,
-0.05461109057068825,
-0.003478653496131301,
-0.012045889161527157,
-0.0456191748380661,
0.030050164088606834,
-0.015047254040837288,
0.02263975888490677,
0.04330483824014664,
0.012338876724243164,
-0.030237676575779915,
-0.03904535248875618,
-0.01888473704457283,
0.016902940347790718,
-0.029445897787809372,
0.03975006192922592,
-0.01829133741557598,
0.026199158281087875,
0.008565597236156464,
-0.024470359086990356,
-0.01978437229990959,
0.01794186420738697,
-0.031498633325099945,
0.0037265680730342865,
-0.03216785192489624,
0.03169639781117439,
-0.001243807841092348,
-0.005303948186337948,
-0.02164599299430847,
-0.04900508001446724,
0.006214471999555826,
-0.002804472576826811,
-0.012305519543588161,
0.007991788908839226,
-0.005544924642890692,
-0.03195033222436905,
-0.04170094430446625,
-0.00005442019028123468,
0.023378964513540268,
-0.028592342510819435,
0.02653401345014572,
0.05753776431083679,
-0.007661778945475817,
0.03206448256969452,
-0.016808252781629562,
-0.04362377151846886,
0.008878995664417744,
-0.018686985597014427,
-0.014367579482495785,
-0.012244636192917824,
0.04078822582960129,
-0.040576815605163574,
-0.049491509795188904,
0.013712742365896702,
-0.0025930546689778566,
0.04196913540363312,
0.008477802388370037,
0.04304961860179901,
0.02704271301627159,
0.010102231986820698,
-0.022844620048999786,
0.02265811525285244,
0.051881540566682816,
0.03733057901263237,
0.026635944843292236,
-0.027630889788269997,
0.0012990909162908792,
-0.06580282747745514,
-0.05437065660953522,
0.03132554516196251,
-0.014058390632271767,
0.020997196435928345,
0.0004999378579668701,
0.035447705537080765,
-0.011258702725172043,
-0.026614412665367126,
0.007202448323369026,
-0.008471972309052944,
0.04974905401468277,
-0.013258521445095539,
-0.005562315229326487,
-0.049526751041412354,
-0.014970093034207821,
-0.011837233789265156,
-0.028304271399974823,
0.009283694438636303,
0.014139469712972641,
0.04186743497848511,
-0.018475716933608055,
0.06891278922557831,
-0.020093455910682678,
-0.041386138647794724,
-0.02388906292617321,
0.0032180692069232464,
-0.026227569207549095,
0.030361047014594078,
0.020191652700304985,
0.015755120664834976,
-0.01817241869866848,
0.014872160740196705,
0.017286570742726326,
0.05488630756735802,
-0.0019151560263708234,
-0.0067413379438221455,
0.057888567447662354,
0.008794660679996014,
0.05048338696360588,
-0.030866213142871857,
0.0016041493508964777,
0.05023963376879692,
-0.0553438737988472,
0.042681917548179626,
0.0012305000564083457,
-0.011230704374611378,
0.03657728061079979,
0.012682126834988594,
-0.009096105583012104,
-0.03915596380829811,
0.004152607638388872,
-0.03731150925159454,
-0.01311295386403799,
0.021057626232504845,
0.02943110093474388,
-0.003920656628906727,
-0.01384599320590496,
0.029149366542696953,
0.03246761113405228,
0.013005331158638,
0.012820262461900711,
-0.06469761580228806,
-0.026590468361973763,
-0.04765310510993004,
-0.017046574503183365,
0.06262993812561035,
0.02820190228521824,
-0.0013775023398920894,
0.011062119156122208,
-0.07467053830623627,
0.022329360246658325,
-0.0027989197988063097,
0.013913478702306747,
-0.02940264344215393,
0.09615149348974228,
-0.017300011590123177,
0.009099828079342842,
-0.023976357653737068,
-0.004829385317862034,
0.11617566645145416,
0.015330919064581394,
0.005148968659341335,
-0.030402425676584244,
0.018655329942703247,
-0.00041856092866510153,
0.010735118761658669,
-0.026170456781983376,
-0.031148061156272888,
0.013338943012058735,
0.0023139233235269785,
0.0209871344268322,
0.0725882276892662,
-0.03501347452402115,
0.01995769515633583,
0.043957266956567764,
-0.06115584820508957,
-0.01239696517586708,
-0.006013857200741768,
0.009728854522109032,
-0.02141258865594864,
-0.0005667967488989234,
-0.017196502536535263,
0.014325667172670364,
-0.054325003176927567,
-0.032268378883600235,
-0.0270093884319067,
-0.01656125858426094,
0.015416421927511692,
0.011508633382618427,
-0.05887695029377937,
-0.007401537615805864,
0.003559121862053871,
-0.02547927387058735,
-0.011201707646250725,
0.051111429929733276,
0.04616664722561836,
0.0011375545291230083,
0.04362431541085243,
0.03929046541452408,
0.020459216088056564,
0.00892165582627058,
0.04837793856859207,
0.03170320764183998,
-0.05273394286632538,
-0.017931537702679634,
-0.02790829911828041,
0.006477648857980967,
-0.0006932744290679693,
-0.01480808760970831,
0.03701646253466606,
-0.022316986694931984,
0.010152039118111134,
-0.008478529751300812,
0.015464733354747295,
-0.019703732803463936,
0.027000484988093376,
0.02933502197265625,
-0.0006187967373989522,
-0.002697065006941557,
0.007249595131725073,
-0.0022375015541911125,
0.0042915004305541515,
0.011929567903280258,
-0.005716747138649225,
-0.010811803862452507,
0.01494837086647749,
-0.02307748794555664,
-0.016924194991588593,
-0.028439730405807495,
-0.034564308822155,
0.0010813623666763306,
-0.07859542220830917,
0.033987052738666534,
0.009019199758768082,
0.052620287984609604,
0.05235443264245987,
0.006057508289813995,
-0.023422205820679665,
-0.032742105424404144,
-0.03938761353492737,
0.05807457119226456,
-0.007920043542981148,
-0.03202991187572479,
-0.007797613274306059,
-0.023516252636909485,
0.01915692538022995,
0.025323156267404556,
-0.03198305517435074,
-0.013764744624495506,
-0.01979553885757923,
0.038023706525564194,
0.013162422925233841,
-0.030389366671442986,
-0.031145501881837845,
-0.007986491546034813,
-0.022035835310816765,
0.00921585038304329,
-0.0038419796619564295,
0.006625411566346884,
0.021750235930085182,
0.03239487111568451,
-0.005800265818834305,
-0.016566166654229164,
-0.006688388995826244,
-0.0024958564899861813,
0.06291196495294571,
-0.0006871673977002501,
0.0016485805390402675,
0.005179997533559799,
-0.025087734684348106,
-0.02012818492949009,
-0.03483866900205612,
-0.002560846507549286,
-0.019214384257793427,
0.002519500907510519,
0.03510430455207825,
0.0037255892530083656,
0.023606006056070328,
-0.015630243346095085,
0.01114081870764494,
-0.0036698738113045692,
0.010901439003646374,
-0.02365323156118393,
-0.03335053473711014,
-0.034088291227817535,
-0.01090452540665865,
-0.043885357677936554,
0.04847455024719238,
-0.01910652592778206,
-0.01314243022352457,
-0.015410052612423897,
0.012439488433301449,
-0.03461230546236038,
-0.008368144743144512,
-0.0053040203638374805,
0.01674508862197399,
0.022458570078015327,
-0.006671668961644173,
-0.005414151586592197,
0.06286231428384781,
-0.02383255399763584,
-0.07704715430736542,
0.03196050599217415,
-0.013102339580655098,
0.026028411462903023,
0.03627914935350418,
-0.012116126716136932,
0.005511707626283169,
0.0867723673582077,
-0.004966161213815212,
-0.005357210990041494,
0.0123443603515625,
-0.06987495720386505,
-0.015055815689265728,
-0.03405241295695305,
-0.004078418016433716,
-0.012667253613471985,
0.021346688270568848,
0.016129573807120323,
0.014371341094374657,
0.018238181248307228,
0.02345103956758976,
-0.00810087937861681,
0.010353474877774715,
-0.011943495832383633,
0.02538912370800972,
-0.0061379955150187016,
0.016014957800507545,
0.056812647730112076,
-0.023748936131596565,
0.04974996671080589,
-0.042917121201753616,
-0.007864497601985931,
-0.10539622604846954,
0.02150481566786766,
-0.021248338744044304,
-0.008725651539862156,
0.020360449329018593,
-0.06306612491607666,
-0.0014179314021021128,
0.03623063862323761,
-0.07815703749656677,
-0.00636901194229722,
-0.01637144573032856,
-0.012155238538980484,
-0.024930106475949287,
0.034496814012527466,
-0.021978583186864853,
0.03554551675915718,
0.0662376657128334,
0.04787247255444527,
0.018448716029524803,
0.012198297306895256,
-0.013030382804572582,
-0.021517382934689522,
-0.010830607265233994,
0.06219077855348587,
-0.04998381435871124,
0.05368513613939285,
0.09014622867107391,
-0.008140337653458118,
0.035421207547187805,
0.013859842903912067,
-0.04665832594037056,
0.0297416839748621,
0.0034938594326376915,
-0.01111625600606203,
0.04084301367402077,
0.026331540197134018,
-0.004518465138971806,
0.0022516436874866486,
0.007024753838777542,
0.041514378041028976,
0.016014065593481064,
0.038685623556375504,
-0.040579281747341156,
-0.015549457632005215,
0.02203121781349182,
-0.01409502699971199,
0.0033880218397825956,
0.009734665043652058,
-0.028414377942681313,
0.017851296812295914,
0.02863825298845768,
0.017511948943138123,
0.03387722745537758,
-0.05083983764052391,
-0.015403288416564465,
0.012346615083515644,
0.015508404932916164,
-0.013770014978945255,
0.0149424122646451,
-0.00291522522456944,
0.0377054437994957,
-0.013521036133170128,
-0.008224993012845516,
-0.016670534387230873,
-0.008615875616669655,
0.031188759952783585,
-0.03412748500704765,
-0.04426250234246254,
0.002552296733483672,
0.025355743244290352,
0.02546580135822296,
-0.05556803196668625,
-0.03674619644880295,
0.022313686087727547,
0.026107899844646454,
0.02988525852560997,
0.029006853699684143,
-0.00021804793504998088,
0.010590207763016224,
-0.07111122459173203,
-0.001162598724476993,
0.01215742714703083,
0.03277016803622246,
-0.0498836450278759,
-0.07593439519405365,
0.006580592133104801,
0.033779531717300415,
0.09798015654087067,
0.0009646020480431616,
0.0020408923737704754,
0.08162946999073029,
-0.019950658082962036,
0.027772117406129837,
-0.020931629464030266,
-0.025291768833994865,
-0.0055004446767270565,
0.012601395137608051,
0.002278077881783247,
0.028070544824004173,
-0.012552288360893726,
-0.0015057075070217252,
0.011144016869366169,
-0.0034415251575410366,
0.023719623684883118,
-0.011956078931689262,
-0.04260462895035744,
0.025534257292747498,
0.03191942721605301,
0.0025168152060359716,
0.04255696386098862,
0.02335970662534237,
0.003189152106642723,
0.034252800047397614,
-0.04196431115269661,
-0.040977682918310165,
0.042476970702409744,
-0.019853610545396805,
0.019005397334694862,
-0.02356169931590557,
-0.004381026141345501,
-0.007510287221521139,
-0.052409712225198746,
-0.009678063914179802,
0.03504137322306633,
-0.03767290711402893,
-0.017091702669858932,
0.024946104735136032,
-0.014506306499242783,
0.04401339590549469,
-0.02158496156334877,
0.004975639283657074,
0.0039298757910728455,
0.01774802803993225,
0.007987224496901035,
0.012603803537786007,
0.013343749567866325,
-0.01482069119811058,
-0.028561197221279144,
0.059997640550136566,
-0.0032285605557262897,
-0.0209549218416214,
0.011448157019913197,
0.04669930785894394,
0.018511293455958366,
-0.042536478489637375,
-0.019208578392863274,
-0.009103905409574509,
-0.010500800795853138,
0.04884190484881401,
-0.013713193126022816,
0.06582344323396683,
-0.03394569829106331,
0.029317239299416542,
-0.004992973525077105,
0.05213869735598564,
0.018471132963895798,
0.016920585185289383,
-0.0021282725501805544,
-0.018635550513863564,
-0.03331040218472481,
-0.009774046018719673,
-0.01608124189078808,
-0.031451962888240814,
0.009803080931305885,
-0.029392041265964508,
-0.01967320777475834,
0.021152982488274574,
-0.026447683572769165,
-0.03605298325419426,
-0.040153078734874725,
-0.01622140035033226,
-0.01002501044422388,
0.06495481729507446,
0.009111902676522732,
-0.016382968053221703,
-0.029305405914783478,
0.04046984389424324,
0.015160639770328999,
0.06914328783750534,
-0.05004490539431572,
0.0172073133289814,
-0.028953708708286285,
0.03278385475277901,
-0.0158236101269722,
0.0044667962938547134
] |
<p>Considering the fact that electrons tend to take the maximum conductance path to flow from A to B. This is justified by saying that $\vec{E}$ is larger in conductors. But once similarly it was thought for gravitation, that if in a region the gravity was stronger, the mass more likely took that path, then later it was found it is actually a geodesic in space time as gravity curves space time. So is there some underlying geodesic for motion caused by electromagnetic force?</p> | 543 | [
-0.02405768819153309,
0.009648681618273258,
0.005179623607546091,
-0.025699255988001823,
0.0022579270880669355,
0.047533415257930756,
-0.018298421055078506,
-0.005254863761365414,
-0.007107042707502842,
-0.005470056086778641,
0.0323932021856308,
0.0033267538528889418,
0.0866304412484169,
0.013513786718249321,
0.045004505664110184,
0.017717143520712852,
-0.007097069639712572,
0.045934852212667465,
-0.001034504035487771,
-0.0758916363120079,
-0.015965553000569344,
0.04020276665687561,
0.00667373975738883,
-0.028967194259166718,
-0.0069978078827261925,
-0.0069094086065888405,
0.024869978427886963,
0.014861189760267735,
-0.022632453590631485,
0.04302849620580673,
-0.009805481880903244,
-0.027738060802221298,
0.006719075608998537,
0.041928622871637344,
0.049160610884428024,
-0.00028938049217686057,
-0.03864903748035431,
-0.03612534701824188,
-0.006030196789652109,
0.002002713503316045,
-0.019648363813757896,
-0.049964312463998795,
-0.006466356106102467,
0.04929632693529129,
-0.006284431554377079,
0.028384478762745857,
0.04366440698504448,
-0.008138950914144516,
0.059979408979415894,
-0.0569760836660862,
0.07087960094213486,
-0.02828718163073063,
0.027864152565598488,
-0.016464712098240852,
-0.009527649730443954,
-0.02710486575961113,
0.06501685082912445,
0.03794803470373154,
-0.008158584125339985,
-0.037277426570653915,
-0.014346989803016186,
-0.02651234343647957,
0.01512672659009695,
-0.04403981938958168,
-0.009039237163960934,
0.05845511704683304,
-0.020792881026864052,
-0.018917646259069443,
0.030336542055010796,
0.006950580980628729,
-0.0304070096462965,
-0.00023048685397952795,
0.0031116227619349957,
0.01858319714665413,
0.01401390228420496,
-0.0012023687595501542,
0.016732599586248398,
0.0022068731486797333,
0.03452247008681297,
0.002009946620091796,
-0.035510435700416565,
0.004930937197059393,
0.0351581908762455,
0.019250135868787766,
-0.026248281821608543,
0.010536090470850468,
0.031492963433265686,
-0.045613016933202744,
-0.010117079131305218,
0.03264382481575012,
-0.03772444278001785,
0.0006605664966627955,
0.026021922007203102,
-0.011298724450170994,
-0.04272548854351044,
0.008585719391703606,
-0.013256911188364029,
-0.002428254811093211,
0.015944769605994225,
-0.004376737866550684,
-0.007415784522891045,
-0.011571328155696392,
0.0013951509026810527,
0.11064804345369339,
0.02611042745411396,
-0.013217324391007423,
-0.03418959304690361,
-0.0018589411629363894,
-0.024799523875117302,
-0.0103611433878541,
-0.02210414409637451,
0.01662960834801197,
0.02320265583693981,
0.007012078072875738,
0.02042778581380844,
-0.03241173177957535,
0.02736993320286274,
-0.028381777927279472,
0.023852713406085968,
0.07233014702796936,
0.033966731280088425,
-0.04599912837147713,
0.05552243813872337,
-0.014763322658836842,
-0.02518502064049244,
0.0051476857624948025,
0.05981003865599632,
0.009193723089993,
-0.0010382655309513211,
0.037271205335855484,
-0.011295762844383717,
0.004111985210329294,
0.010570165701210499,
0.0199629794806242,
0.03343035280704498,
-0.010251070372760296,
-0.09379111230373383,
-0.03207044303417206,
0.05108054354786873,
-0.008307076059281826,
0.01676773466169834,
-0.0466449074447155,
0.00944901816546917,
0.02158738486468792,
0.08596451580524445,
0.036223240196704865,
0.013634325005114079,
-0.00035071291495114565,
0.07516249269247055,
0.01914081908762455,
-0.003979323897510767,
-0.03238602727651596,
0.0008594808750785887,
-0.01759963296353817,
0.01509634219110012,
-0.0692472755908966,
0.020286541432142258,
-0.004682658240199089,
-0.009908904321491718,
0.00039137364365160465,
0.08099628239870071,
-0.0014760966878384352,
0.01660737581551075,
-0.0049062068574130535,
0.016018912196159363,
0.0030742029193788767,
0.06463482230901718,
0.037610989063978195,
-0.014620862901210785,
0.04794299975037575,
0.0301958080381155,
0.0432903990149498,
0.039742425084114075,
-0.014792926609516144,
0.024951253086328506,
-0.06313931196928024,
-0.004993119742721319,
0.006352709606289864,
0.010490206070244312,
-0.010796775110065937,
-0.030713090673089027,
-0.040307752788066864,
-0.014844268560409546,
-0.03681366890668869,
-0.017784036695957184,
0.03917631134390831,
-0.029410412535071373,
-0.013923405669629574,
0.011612491682171822,
-0.02630646526813507,
0.01767711155116558,
-0.04422338306903839,
0.021212656050920486,
-0.00392034649848938,
-0.029147475957870483,
0.001917267101816833,
-0.010665169917047024,
-0.005695557687431574,
-0.040062159299850464,
-0.020665736868977547,
0.008276239037513733,
0.020270448178052902,
-0.05182516947388649,
-0.036352306604385376,
0.005252527073025703,
0.04252012073993683,
0.001132652279920876,
0.005363053176552057,
0.007902868092060089,
-0.013803134672343731,
-0.05362847074866295,
0.014429132454097271,
-0.04247787594795227,
0.047720786184072495,
0.016334813088178635,
-0.03011082485318184,
-0.015514128841459751,
-0.0005260924226604402,
-0.038490768522024155,
0.03959864377975464,
-0.04651004821062088,
0.07942583411931992,
0.07648259401321411,
0.018771260976791382,
-0.0005086520104669034,
0.06331910938024521,
0.007935424335300922,
-0.010004843585193157,
-0.016493307426571846,
-0.05509280040860176,
-0.05659272149205208,
-0.0003428860509302467,
0.03017321601510048,
0.02369462512433529,
-0.026973402127623558,
0.01787685602903366,
0.03230150789022446,
0.054406315088272095,
0.0176527239382267,
0.04852983355522156,
-0.004964287858456373,
-0.05650277063250542,
0.029552632942795753,
0.009863963350653648,
0.0023087786976248026,
0.0063470941968262196,
0.035876452922821045,
0.01839430071413517,
-0.021876854822039604,
-0.023931480944156647,
-0.027563417330384254,
0.02849048189818859,
-0.021114088594913483,
0.026560528203845024,
0.008835148997604847,
-0.01646972820162773,
0.03733889386057854,
-0.02766801044344902,
0.04323214292526245,
0.02250899374485016,
-0.013470846228301525,
-0.004325029440224171,
-0.06322017312049866,
-0.0005945635493844748,
0.024002086371183395,
-0.01860385201871395,
-0.011793776415288448,
-0.004656285513192415,
0.031117627397179604,
-0.06916861981153488,
0.006182593759149313,
-0.03129303827881813,
0.004333804827183485,
-0.022322168573737144,
-0.009433657862246037,
0.038703761994838715,
0.03097749873995781,
0.006748470012098551,
-0.016509385779500008,
-0.023110056295990944,
0.005119266454130411,
-0.034645020961761475,
-0.003560981247574091,
0.029514338821172714,
-0.04280824214220047,
0.0252090897411108,
-0.031377822160720825,
-0.027904924005270004,
0.0940212681889534,
-0.0008972770301625133,
0.016890903934836388,
0.030755184590816498,
0.006559194531291723,
-0.028819490224123,
0.005080924369394779,
-0.008249430917203426,
-0.016747962683439255,
-0.019572032615542412,
0.0042072501964867115,
0.04241612181067467,
-0.02161150798201561,
-0.03643808513879776,
-0.0009321122197434306,
-0.0177494864910841,
-0.08425262570381165,
0.002419593045488,
-0.010336974635720253,
-0.004010734148323536,
-0.004059131722897291,
0.05544399097561836,
0.041755612939596176,
-0.035363201051950455,
-0.03312167525291443,
-0.04924030974507332,
-0.010884905233979225,
0.06858107447624207,
-0.03826803341507912,
0.040829092264175415,
-0.010579269379377365,
-0.04106277599930763,
0.05841195955872536,
0.052449487149715424,
-0.00041400539339520037,
-0.024981601163744926,
-0.03330413997173309,
-0.005682277027517557,
0.00863125640898943,
0.012189318425953388,
0.035872507840394974,
0.006954942364245653,
-0.0008517208625562489,
0.04498061537742615,
0.038045626133680344,
0.000573415425606072,
-0.021825503557920456,
0.007616031914949417,
0.015492519363760948,
0.0022000567987561226,
-0.00169698940590024,
0.029430288821458817,
0.027056660503149033,
-0.02399214543402195,
0.02637900784611702,
0.012579900212585926,
0.04074523597955704,
-0.006364334374666214,
-0.024261970072984695,
0.04904940351843834,
0.004433278925716877,
0.034796878695487976,
-0.005427749827504158,
-0.002946496708318591,
-0.018656566739082336,
-0.01233366783708334,
-0.024941345676779747,
0.05163508653640747,
0.026212457567453384,
0.010764515027403831,
0.013327423483133316,
0.018029849976301193,
0.032386664301157,
-0.04446358233690262,
-0.02285064570605755,
-0.013070386834442616,
0.004314829129725695,
0.03110422007739544,
-0.007730364333838224,
-0.01731126569211483,
0.027339180931448936,
0.02268463745713234,
-0.0038405461236834526,
0.01773691177368164,
-0.045043569058179855,
-0.03458227962255478,
-0.04893466830253601,
-0.02438873052597046,
0.02494954690337181,
0.048085518181324005,
-0.008282877504825592,
0.014622769318521023,
0.04028652235865593,
0.019075078889727592,
-0.012483685277402401,
-0.0018438842380419374,
-0.14735041558742523,
0.004165624268352985,
-0.056915007531642914,
-0.020393699407577515,
-0.004709657747298479,
-0.021891525015234947,
-0.03056478127837181,
-0.01015842892229557,
-0.02306355908513069,
-0.011189240030944347,
0.0024981405586004257,
-0.06776098161935806,
0.0068932087160646915,
-0.047981034964323044,
-0.03460732847452164,
-0.025540925562381744,
0.007721077650785446,
0.028787504881620407,
-0.05057907477021217,
-0.015297957696020603,
0.020491864532232285,
-0.03284939005970955,
-0.030576298013329506,
-0.0002096862008329481,
0.025307822972536087,
0.00211994256824255,
-0.019636446610093117,
0.007439628709107637,
-0.01583733595907688,
-0.018135780468583107,
0.026284586638212204,
0.001439262880012393,
0.041852403432130814,
0.00893739890307188,
-0.023709937930107117,
-0.02669540047645569,
-0.037023670971393585,
-0.02134539745748043,
-0.01051170565187931,
0.06356602162122726,
0.031167395412921906,
-0.026452187448740005,
0.03406132757663727,
0.0066110859625041485,
-0.00005757954204455018,
0.05069116875529289,
0.044959183782339096,
0.0318814255297184,
-0.03734886646270752,
-0.055009808391332626,
-0.025628160685300827,
-0.024032019078731537,
-0.00722470274195075,
0.06106061115860939,
-0.03134846314787865,
-0.02442675083875656,
0.024609500542283058,
0.006873833481222391,
0.03321012482047081,
-0.003259167540818453,
-0.032049357891082764,
0.023258330300450325,
0.027010105550289154,
0.021998299285769463,
-0.01665314845740795,
-0.0006222467636689544,
0.013575018383562565,
0.0585261769592762,
-0.0006819901755079627,
0.003415067447349429,
-0.08750325441360474,
0.0008954461081884801,
0.03357478231191635,
0.015054856427013874,
-0.04233995079994202,
0.01704166829586029,
-0.06400918960571289,
0.0007813775446265936,
0.029919585213065147,
0.023542169481515884,
0.0186470914632082,
-0.011507014743983746,
-0.008979585953056812,
-0.035926759243011475,
-0.04098927229642868,
-0.03554830700159073,
0.027264509350061417,
0.011932382360100746,
-0.007435639388859272,
-0.025187095627188683,
0.016848262399435043,
0.018478838726878166,
0.012170456349849701,
0.022616246715188026,
0.06656117737293243,
0.024361226707696915,
0.033385392278432846,
0.008101983927190304,
0.012634792365133762,
-0.017111174762248993,
-0.10254404693841934,
-0.015037707053124905,
0.026243841275572777,
-0.017056254670023918,
-0.007586509454995394,
-0.03825083002448082,
-0.026163877919316292,
0.02947266586124897,
-0.03273959830403328,
0.013273569755256176,
-0.007698582485318184,
-0.012533345259726048,
0.024554170668125153,
0.01631014049053192,
-0.0316116102039814,
0.034158531576395035,
-0.015145224519073963,
-0.02018825151026249,
-0.017575250938534737,
-0.0048339175991714,
0.07626387476921082,
-0.038132138550281525,
-0.024518458172678947,
0.005655627232044935,
0.012508461251854897,
-0.025335196405649185,
0.048739831894636154,
0.03688103333115578,
-0.003240859368816018,
-0.021423405036330223,
-0.0436365082859993,
-0.04254299774765968,
0.02958632819354534,
0.012888018041849136,
-0.015611624345183372,
0.005845239385962486,
0.02789207547903061,
-0.0016643794951960444,
-0.009892866015434265,
0.005420086905360222,
0.003111589001491666,
0.015117189846932888,
0.060032691806554794,
-0.0019755461253225803,
-0.019607054069638252,
-0.025435002520680428,
-0.0094090411439538,
0.0013466529780998826,
-0.06461581587791443,
0.04521554335951805,
-0.019633224233984947,
-0.036383990198373795,
0.04130282253026962,
-0.04295400530099869,
-0.028721682727336884,
0.00963589921593666,
-0.01125225517898798,
0.01922612264752388,
-0.04828427731990814,
-0.021939238533377647,
0.04514842852950096,
0.015040980651974678,
-0.10123975574970245,
-0.04220084100961685,
0.019475197419524193,
0.003911426756531,
-0.010114467702805996,
-0.026227068156003952,
0.009667607955634594,
-0.08277598023414612,
-0.022816447541117668,
0.020703470334410667,
0.05571888014674187,
-0.01625712960958481,
-0.020507074892520905,
-0.014584194868803024,
0.022353360429406166,
0.020599892362952232,
-0.014423957094550133,
0.005835799966007471,
0.019026760011911392,
-0.0008504699799232185,
0.03689482808113098,
-0.019542450085282326,
0.051626041531562805,
-0.016652008518576622,
-0.002025644527748227,
-0.005167636089026928,
-0.0345759280025959,
-0.0027533071115612984,
-0.006990890018641949,
-0.010013007558882236,
0.06393177807331085,
0.00993682723492384,
-0.0033764883410185575,
-0.008815773762762547,
0.028829773887991905,
-0.009841442108154297,
0.013685407117009163,
0.004478359594941139,
0.014757150784134865,
-0.002990227658301592,
-0.04678509384393692,
0.04776661470532417,
0.026242472231388092,
-0.017987580969929695,
0.015692835673689842,
0.032516080886125565,
0.019007232040166855,
-0.02683432772755623,
0.019961874932050705,
-0.0013470445992425084,
0.0008774248999543488,
-0.020501254126429558,
0.007511288393288851,
0.01706763170659542,
0.012151424773037434,
-0.02083420194685459,
-0.024660877883434296,
-0.025489410385489464,
0.02786121517419815,
0.06799645721912384,
-0.02604757994413376,
0.044998303055763245,
0.01579882577061653,
-0.011293488554656506,
-0.013734648935496807,
-0.008812804706394672,
-0.01093251258134842,
0.012818245217204094,
-0.03361203148961067,
0.029442790895700455,
-0.016159437596797943,
-0.0013155938358977437,
0.02646602690219879,
0.03586769104003906,
-0.046153102070093155,
-0.0212294589728117,
-0.0028433077968657017,
0.03459049016237259,
0.025945786386728287,
0.00775300245732069,
-0.0116726690903306,
0.039621468633413315,
-0.030246561393141747,
0.04420030862092972,
-0.012289430946111679,
-0.012230034917593002,
0.01869739405810833,
0.02560868114233017,
-0.014074898324906826,
0.017456337809562683,
-0.014870136976242065,
-0.05580805987119675,
0.04907272756099701,
0.02939920499920845,
0.028130032122135162,
0.010831219144165516,
0.0262095145881176,
0.03248358890414238,
-0.017362669110298157,
0.00990078505128622,
0.026170803233981133,
-0.07047919929027557,
-0.014791954308748245,
-0.03334420919418335,
-0.008467544801533222,
0.050122298300266266,
0.00335121201351285,
-0.02784823067486286,
0.019598660990595818,
-0.020086620002985,
0.03188430145382881,
0.04381299018859863,
0.051537394523620605,
-0.016486892476677895,
0.08613072335720062,
-0.030226286500692368,
0.00009648126433603466,
-0.031881071627140045,
-0.01129810232669115,
0.11915063858032227,
0.05542770028114319,
0.016991352662444115,
-0.03483424335718155,
0.013506947085261345,
-0.005543071310967207,
0.0015813993522897363,
-0.03184123337268829,
0.02831008844077587,
-0.00932490173727274,
0.025082038715481758,
0.014335723593831062,
0.03152180463075638,
0.010857992805540562,
-0.04670492559671402,
0.06288006901741028,
-0.04105444997549057,
-0.026115650311112404,
-0.0023264100309461355,
-0.0008190700318664312,
-0.009729672223329544,
0.016369232907891273,
-0.04560655355453491,
0.026119006797671318,
-0.08190281689167023,
-0.016433240845799446,
-0.028979146853089333,
-0.020236879587173462,
-0.018893221393227577,
-0.012707885354757309,
-0.053881123661994934,
-0.013398251496255398,
0.01418668869882822,
-0.01656385138630867,
-0.0435204841196537,
-0.002110290341079235,
0.03461836278438568,
-0.005324361380189657,
0.037311479449272156,
0.017338063567876816,
-0.02292231097817421,
0.022467434406280518,
-0.001580632640980184,
0.01724993623793125,
-0.04227486997842789,
0.034271884709596634,
-0.027080349624156952,
0.03341589868068695,
0.001960506895557046,
0.05442778021097183,
0.03818202391266823,
0.006802463438361883,
0.002579140942543745,
-0.020062249153852463,
0.014749337919056416,
-0.027252035215497017,
0.010691514238715172,
0.007627681829035282,
-0.008906289003789425,
-0.005755424499511719,
0.0031093587167561054,
0.006704051047563553,
0.0016716716345399618,
0.004304836038500071,
0.01335709448903799,
0.02053014002740383,
0.0003301042888779193,
0.07583501935005188,
0.012899836525321007,
-0.03531450033187866,
-0.018627937883138657,
-0.05866662412881851,
-0.03200610354542732,
-0.012291737832129002,
0.003259306540712714,
0.020637894049286842,
-0.01280276570469141,
0.025293828919529915,
-0.008383912034332752,
0.024867672473192215,
-0.06387139111757278,
0.04351738467812538,
0.004446173086762428,
0.008847206830978394,
-0.03660621494054794,
0.005034516099840403,
0.022318294271826744,
0.010654404759407043,
0.014378517866134644,
-0.009579155594110489,
0.019841965287923813,
0.005084378644824028,
0.000965505838394165,
-0.03488945960998535,
0.02730051428079605,
-0.03746308386325836,
-0.0124517772346735,
-0.015712762251496315,
-0.01537403091788292,
0.004921548068523407,
-0.0160603616386652,
0.00010176349314861,
0.003804839449003339,
0.022161409258842468,
-0.008497911505401134,
0.019821664318442345,
0.028902361169457436,
-0.019177798181772232,
-0.026614144444465637,
0.010108940303325653,
-0.03284675255417824,
-0.06090161204338074,
-0.0339382141828537,
0.0006271156598813832,
0.009547323919832706,
-0.0030498383566737175,
0.010001099668443203,
-0.016254281625151634,
0.05689018592238426,
-0.011023024097084999,
0.009669472463428974,
-0.05495006591081619,
-0.004293843172490597,
-0.04090132936835289,
0.0006901405868120492,
-0.030946388840675354,
-0.018802357837557793,
0.002546065952628851,
0.0214596726000309,
-0.019355392083525658,
-0.02258801832795143,
-0.025312509387731552,
0.030281543731689453,
0.006236011628061533,
0.008884796872735023,
0.05596335232257843,
-0.049837931990623474,
0.06779322028160095,
-0.031729765236377716,
-0.03560623526573181,
0.01955415867269039,
-0.038409698754549026,
-0.036001868546009064,
0.029927261173725128,
-0.029617412015795708,
0.02159377560019493,
0.013479527086019516,
-0.013649765402078629,
0.029900062829256058,
0.04362598806619644,
0.005092639476060867,
0.019825909286737442,
-0.006045455113053322,
-0.047996558248996735,
-0.036717724055051804,
-0.026440413668751717,
0.029034828767180443,
-0.03100133128464222,
0.013513738289475441,
0.007635416928678751,
0.01593075506389141,
-0.010871180333197117,
-0.01757422834634781,
0.025297317653894424,
-0.04792439937591553,
0.0000449592262157239,
0.02698463574051857,
0.0028879656456410885,
0.04098149761557579,
0.03581934794783592,
-0.020981956273317337,
-0.004529666155576706,
0.015598616562783718,
0.035325683653354645,
-0.08368466049432755,
-0.0413162000477314,
0.0005567774642258883,
-0.005149581469595432,
0.04844260960817337,
-0.04247400909662247,
0.01678154617547989,
-0.010667718946933746,
-0.05642310902476311,
0.03646204620599747,
-0.006038551684468985,
0.008079888299107552,
-0.040791358798742294,
-0.04737536236643791,
-0.0071611893363296986,
0.05600760504603386,
0.04778270423412323,
0.04873635247349739,
-0.004296914208680391,
0.01432834193110466,
-0.005411074031144381,
-0.028235334903001785,
-0.04873935505747795,
0.029191067442297935,
-0.02719900570809841,
-0.04553438350558281,
0.05281593278050423,
0.0031992001459002495,
-0.030922839418053627,
0.031004393473267555,
0.02687346749007702,
-0.005774849094450474,
-0.024938002228736877,
0.01323134545236826,
0.006178019102662802,
0.021635962650179863,
0.018458586186170578,
-0.014611667953431606,
0.007716876454651356,
0.019251713529229164,
-0.0023963034618645906,
0.028504010289907455,
-0.017539771273732185,
-0.0027855983935296535,
0.017298981547355652,
-0.027907757088541985,
-0.013821564614772797,
0.016624815762043,
-0.012701154686510563,
-0.046448513865470886,
0.008420714177191257,
0.0345272533595562,
-0.0060017225332558155,
-0.024816690012812614,
0.025575924664735794,
-0.04697379842400551,
-0.002756394213065505,
0.02013295888900757,
-0.005430169403553009,
-0.0023126844316720963,
0.017421666532754898,
0.02116500213742256,
-0.011260809376835823,
-0.017240038141608238,
-0.005167155060917139,
0.03726496919989586,
-0.0520373173058033,
0.002632838673889637,
-0.02482871524989605,
0.011963901109993458,
-0.0023373605217784643,
-0.05880576744675636,
-0.0173809714615345,
0.04910577833652496,
0.033477697521448135,
0.027991831302642822,
0.016900766640901566,
-0.004174886271357536,
-0.0091465525329113,
-0.04503750056028366,
0.028497712686657906,
-0.02726116217672825,
0.012842458672821522,
-0.021579964086413383,
-0.02827591449022293,
0.006371216848492622,
0.019597506150603294,
0.07407067716121674,
-0.021771902218461037,
-0.011627611704170704,
0.04637277498841286,
-0.019967930391430855,
0.005502085667103529,
-0.023505588993430138,
-0.0050701601430773735,
-0.01402596477419138,
-0.038973890244960785,
0.013988110236823559,
0.01987471804022789,
-0.004009010270237923,
0.016577990725636482,
-0.025307120755314827,
0.016784001141786575,
0.052223026752471924,
-0.008592228405177593,
-0.016708694398403168,
0.05009939521551132,
0.07070426642894745,
-0.004272385034710169,
0.07193543016910553,
0.0023576277308166027,
0.002740949857980013,
-0.012928062118589878,
-0.04644718021154404,
-0.031369730830192566,
0.025946613401174545,
-0.004949551075696945,
-0.0010558777721598744,
-0.028365308418869972,
-0.031461201608181,
0.010131425224244595,
-0.052387792617082596,
-0.025640636682510376,
0.031676582992076874,
-0.05373687669634819,
0.015599201433360577,
0.05356385186314583,
-0.011604677885770798,
0.03528384864330292,
0.006422227248549461,
0.03773195296525955,
0.005216083023697138,
-0.01936032436788082,
-0.0030508977361023426,
0.04639674350619316,
0.01981472223997116,
-0.0017335457960143685,
-0.005316390190273523,
0.06001009792089462,
-0.014680149964988232,
0.029296010732650757,
0.02799423225224018,
0.02041183039546013,
-0.035380955785512924,
0.01469169370830059,
0.04121231660246849,
-0.004719713237136602,
-0.0022151272278279066,
0.00808681733906269,
-0.021992409601807594,
0.08192013204097748,
-0.06689461320638657,
-0.026182984933257103,
0.009291416965425014,
0.0030806029681116343,
0.007276386953890324,
0.04765211418271065,
-0.008531964384019375,
0.02838113158941269,
0.03267290070652962,
-0.011801599524915218,
0.011312799528241158,
-0.016120390966534615,
-0.011406672187149525,
-0.010447252541780472,
0.03730558604001999,
0.02825237438082695,
-0.01781591959297657,
0.01610448583960533,
-0.02482232265174389,
-0.05204629898071289,
-0.04852042719721794,
0.022963449358940125,
0.03895041346549988,
0.03632621094584465,
-0.029477432370185852,
-0.009709592908620834,
-0.04261040687561035,
0.06572168320417404,
-0.06820710003376007,
-0.03506438434123993,
-0.029186541214585304,
0.04974066838622093,
-0.028094954788684845,
0.011185461655259132
] |
<p>Hi, I am thinking about acceleration. Let's think we have a force of $1$ N and a particle of $1$ kg, then acceleration will be $1$. So the speed gets higher every second and $c$ seconds later, <em>in Newtonian mechanics</em>, the particle will reach the speed of light. In relativity, of course, something like that cannot happen. So, what are the equations that describe acceleration in relativity?</p> | 37 | [
0.00005608175342786126,
-0.04525189474225044,
-0.03001009114086628,
-0.022729262709617615,
0.048741769045591354,
-0.008114409632980824,
-0.03590792790055275,
-0.01004030741751194,
-0.008600324392318726,
-0.03226195275783539,
0.03390961140394211,
0.049718841910362244,
0.06343314051628113,
0.004776945803314447,
0.018346566706895828,
-0.0010008754907175899,
-0.004520154558122158,
-0.016763858497142792,
-0.005404853727668524,
-0.04610511660575867,
0.029497424140572548,
0.01059053186327219,
0.012140846811234951,
0.006071121897548437,
-0.02105890028178692,
0.02949467860162258,
0.04203898832201958,
0.015787610784173012,
0.01853257603943348,
0.026691142469644547,
0.011429663747549057,
-0.0054657780565321445,
-0.008188080973923206,
0.02154083549976349,
0.0047334642149508,
0.01208868995308876,
-0.03914479911327362,
-0.034432437270879745,
0.018130293115973473,
-0.008084728382527828,
-0.04347610846161842,
-0.04303852468729019,
0.0007514343596994877,
0.03593062981963158,
-0.02683286927640438,
0.009196225553750992,
0.03136859089136124,
-0.0010801736498251557,
0.04893534630537033,
-0.05690882354974747,
0.09700889885425568,
0.018744368106126785,
0.03950488567352295,
-0.003267117077484727,
0.013147764839231968,
0.012445290572941303,
0.07795639336109161,
0.05016095191240311,
-0.001077927416190505,
-0.0457405149936676,
-0.023931171745061874,
-0.013265089131891727,
0.0023048908915370703,
-0.03921040892601013,
0.017465196549892426,
0.0696808472275734,
-0.058293212205171585,
-0.02589123323559761,
0.006074859760701656,
0.0076332371681928635,
0.003344279481098056,
-0.004044255707412958,
0.05434724688529968,
-0.01235173735767603,
-0.021522095426917076,
-0.031121879816055298,
0.032788898795843124,
-0.0017002120148390532,
0.04109509661793709,
0.06262080371379852,
-0.03261549770832062,
0.026346616446971893,
0.030428646132349968,
0.03651365265250206,
-0.0040215784683823586,
-0.016930392012000084,
0.06526147574186325,
0.02515493519604206,
0.023614641278982162,
0.02732709050178528,
-0.028515007346868515,
0.022996405139565468,
0.012642321176826954,
-0.019346561282873154,
-0.004949660040438175,
0.00686905812472105,
0.011584823951125145,
0.041184503585100174,
0.021666033193469048,
-0.005324146710336208,
0.02879003807902336,
-0.013845988549292088,
-0.008974099531769753,
0.06018715351819992,
0.00846010260283947,
-0.00760012399405241,
-0.03516390174627304,
0.0028864664491266012,
-0.052488502115011215,
0.0017428140854462981,
-0.024211138486862183,
0.019969403743743896,
-0.0010601262329146266,
0.008757269941270351,
0.02766386978328228,
-0.0195867158472538,
-0.004133972339332104,
-0.03324272111058235,
0.0708475112915039,
0.060821570456027985,
0.04647555574774742,
-0.021198751404881477,
0.04041782021522522,
0.004001010674983263,
-0.04684300348162651,
-0.005433628335595131,
0.013681448996067047,
-0.014895759522914886,
0.0036896613892167807,
-0.000035192111681681126,
-0.004983787890523672,
-0.06849977374076843,
-0.0181032195687294,
0.01763114705681801,
0.05039230361580849,
-0.025054331868886948,
-0.09837787598371506,
-0.07574198395013809,
0.04635397717356682,
-0.0010868540266528726,
-0.008183413185179234,
-0.09033842384815216,
0.04528596252202988,
0.015412315726280212,
0.09809933602809906,
0.03948569297790527,
-0.004559284541755915,
0.02718367613852024,
0.005654496606439352,
0.01690085604786873,
-0.018855709582567215,
-0.014873662032186985,
0.01803082972764969,
-0.025424955412745476,
0.001406502677127719,
-0.07634229212999344,
0.03160780668258667,
0.02087731473147869,
0.013166559860110283,
-0.023496614769101143,
0.07539631426334381,
-0.04413706064224243,
0.017319418489933014,
0.01704338751733303,
0.021985884755849838,
-0.00041513031465001404,
0.06163095310330391,
0.02817404456436634,
-0.007911132648587227,
0.06492926925420761,
0.054135166108608246,
0.02676386386156082,
0.01339657511562109,
0.016691239550709724,
0.051099956035614014,
-0.04828067868947983,
-0.04517645761370659,
0.014135726727545261,
-0.028162486851215363,
-0.002020625164732337,
-0.023757819086313248,
-0.03268193453550339,
-0.004274482373148203,
-0.0037703863345086575,
-0.01760931871831417,
0.03243416175246239,
-0.0004240218549966812,
0.03903185948729515,
-0.040947720408439636,
-0.0037028659135103226,
0.020698735490441322,
-0.09617815911769867,
0.028704306110739708,
-0.0012183532817289233,
0.007265823893249035,
0.029790984466671944,
0.010702639818191528,
0.027585212141275406,
-0.011707459576427937,
-0.005561507772654295,
-0.024618692696094513,
0.0609670914709568,
-0.02460007183253765,
-0.03540898114442825,
0.007556977681815624,
0.03991807997226715,
0.02341434173285961,
0.02049926295876503,
0.007961738854646683,
0.02346220798790455,
-0.0056226528249681,
0.02423233911395073,
-0.027254940941929817,
0.0071811797097325325,
-0.014453481882810593,
0.00021962006576359272,
0.02598300389945507,
-0.04229428246617317,
0.014246721751987934,
0.03733796253800392,
-0.02250087261199951,
0.07667044550180435,
0.009206968359649181,
0.019123654812574387,
0.005245750769972801,
0.05528217554092407,
-0.007428113371133804,
-0.011413748376071453,
0.0015538402367383242,
-0.03267724812030792,
0.006022735498845577,
-0.03714071586728096,
0.030325254425406456,
0.040787748992443085,
-0.05156391113996506,
-0.0010648831957951188,
0.05421985685825348,
0.05474727600812912,
0.040598634630441666,
0.026327641680836678,
-0.03313184157013893,
-0.048041582107543945,
0.00930854119360447,
0.022669430822134018,
-0.007750079035758972,
0.0010196531657129526,
0.025117218494415283,
0.021118372678756714,
0.011608552187681198,
0.005088502075523138,
-0.01728706993162632,
0.017864326015114784,
-0.006307829171419144,
-0.01327684335410595,
0.02687452733516693,
-0.061323922127485275,
0.03634360060095787,
-0.00128180009778589,
0.004623053595423698,
0.03555795177817345,
0.0022126007825136185,
-0.009470012038946152,
-0.0096231484785676,
0.00025346697657369077,
0.012791246175765991,
-0.022607384249567986,
-0.017891259863972664,
-0.042745091021060944,
0.02026762068271637,
-0.03910699859261513,
0.03887808322906494,
-0.018714550882577896,
-0.01961762271821499,
-0.037337590008974075,
-0.012232238426804543,
-0.0008774151210673153,
0.014220604673027992,
0.03772090747952461,
-0.009842291474342346,
-0.03355209156870842,
0.014842675067484379,
-0.05471370741724968,
0.03124268352985382,
0.0262239221483469,
-0.0466407872736454,
0.07138988375663757,
-0.04380066320300102,
-0.06858944892883301,
0.06966086477041245,
0.0009982677875086665,
0.02215847559273243,
0.0750982016324997,
-0.029534494504332542,
-0.05369263514876366,
-0.0108257457613945,
-0.03701988607645035,
-0.004915270954370499,
-0.020830916240811348,
0.01687896065413952,
0.0392017662525177,
-0.0017598764970898628,
-0.022164516150951385,
0.007648349739611149,
-0.05036159232258797,
-0.020614413544535637,
-0.04200923442840576,
0.02747957780957222,
0.0003572884888853878,
-0.03584727272391319,
0.018981795758008957,
0.025299375876784325,
-0.02831365540623665,
0.0034441999159753323,
-0.05587485060095787,
-0.03898145630955696,
0.038775891065597534,
0.014533326029777527,
0.0435631088912487,
0.002338900463655591,
-0.018749946728348732,
0.05931438133120537,
0.02240646630525589,
-0.027249885722994804,
-0.03967519849538803,
0.006496536545455456,
0.023323511704802513,
-0.025750959292054176,
0.012297666631639004,
0.022139959037303925,
-0.006896271836012602,
-0.002661005361005664,
0.027098659425973892,
0.00830320455133915,
0.028038809075951576,
0.010178727097809315,
-0.003279336029663682,
-0.010377837345004082,
-0.006703673396259546,
0.012196885421872139,
0.01629672944545746,
0.02934352494776249,
-0.032862454652786255,
0.04899469017982483,
0.018332291394472122,
0.038800470530986786,
0.0061842468567192554,
-0.03817666694521904,
0.03541065752506256,
0.026973888278007507,
-0.024255631491541862,
-0.04234398528933525,
-0.005257584620267153,
0.019376641139388084,
0.0013218504609540105,
0.02568884938955307,
0.05457978695631027,
0.023314181715250015,
-0.035080600529909134,
0.029783720150589943,
0.0061547947116196156,
0.02589934691786766,
-0.053558796644210815,
-0.03240448608994484,
0.02622239477932453,
-0.009905608370900154,
0.03154665231704712,
-0.04308491572737694,
0.023227578029036522,
0.04093065857887268,
-0.00839622039347887,
0.018301133066415787,
0.013400350697338581,
-0.022277604788541794,
0.039045192301273346,
-0.06240399554371834,
-0.014421727508306503,
0.010978763923048973,
0.03609590604901314,
0.0033400848042219877,
0.07161960750818253,
0.02051267959177494,
0.01891207881271839,
0.07370058447122574,
-0.0013596063945442438,
-0.09443971514701843,
0.047665465623140335,
-0.05050280690193176,
-0.03712137043476105,
-0.02255636639893055,
-0.014665250666439533,
-0.02651197835803032,
-0.04397808387875557,
-0.02360452711582184,
-0.023478873074054718,
-0.01311466097831726,
-0.039702240377664566,
0.01082631852477789,
-0.051911018788814545,
-0.0512876957654953,
0.003291917033493519,
0.037688858807086945,
0.04876024276018143,
-0.025078143924474716,
-0.0034307294990867376,
0.054458875209093094,
-0.028562983497977257,
-0.010121193714439869,
-0.009284504689276218,
-0.01887204684317112,
0.03508436307311058,
0.03013751469552517,
0.0430520735681057,
0.0005021278047934175,
-0.015690356492996216,
0.02519334852695465,
0.016913050785660744,
0.05100461095571518,
0.0440550222992897,
-0.008796349167823792,
-0.05185339227318764,
-0.052415210753679276,
-0.0027497385162860155,
-0.016045311465859413,
0.05768459290266037,
-0.008147773332893848,
0.003492712741717696,
0.02435975894331932,
0.008022994734346867,
0.005940227769315243,
0.04082198441028595,
0.05230056494474411,
0.00925626140087843,
-0.02101312205195427,
-0.02029154822230339,
-0.0066935173235833645,
-0.015083284117281437,
-0.0007666461169719696,
0.029133126139640808,
-0.0023458239156752825,
-0.022295178845524788,
0.023805588483810425,
0.012006529606878757,
-0.021551866084337234,
-0.025352390483021736,
-0.025110432878136635,
-0.002640462713316083,
0.02276885323226452,
0.0389707051217556,
-0.014933937229216099,
-0.039830565452575684,
0.024836311116814613,
0.047722239047288895,
-0.019231881946325302,
0.004645021632313728,
-0.08343689888715744,
-0.008581310510635376,
0.0195617713034153,
-0.0009056026465259492,
-0.051350705325603485,
-0.000028201568056829274,
-0.0489824153482914,
0.0022741721477359533,
0.04718882590532303,
-0.04588320851325989,
0.0071774437092244625,
0.012948580086231232,
0.0029478089418262243,
-0.014621599577367306,
0.00030748933204449713,
-0.032612334936857224,
0.0021347850561141968,
-0.01677342876791954,
-0.029130443930625916,
-0.03489440679550171,
0.027409279718995094,
0.004751872271299362,
0.02917323261499405,
0.03480641171336174,
0.032095637172460556,
0.012223631143569946,
-0.005386401433497667,
-0.011856123805046082,
0.01690862514078617,
-0.017777007073163986,
-0.06632566452026367,
-0.008111021481454372,
0.028431929647922516,
-0.01336124911904335,
0.03440919518470764,
-0.04428105428814888,
-0.028882045298814774,
0.028670474886894226,
-0.006734317168593407,
-0.020071886479854584,
-0.02615276537835598,
-0.07928665727376938,
0.014629928395152092,
0.008263252675533295,
-0.006241557653993368,
0.024847878143191338,
0.025470174849033356,
-0.027015652507543564,
-0.010195866227149963,
-0.003963002935051918,
0.029370183125138283,
-0.03857539966702461,
-0.004986382555216551,
-0.0022400773596018553,
-0.0030008102767169476,
-0.030827686190605164,
0.07171721756458282,
-0.013150360435247421,
0.011149248108267784,
-0.007326459512114525,
-0.04185732454061508,
-0.009150463156402111,
0.04535403847694397,
0.02103452757000923,
0.022770840674638748,
-0.012560364790260792,
-0.006633476819843054,
0.0010242013959214091,
-0.04043269157409668,
0.007296808995306492,
0.0029975110664963722,
-0.027828609570860863,
0.026028791442513466,
-0.001677260035648942,
0.004962385166436434,
-0.005059481132775545,
-0.006746942643076181,
0.011833726428449154,
-0.03193642944097519,
0.06288129836320877,
-0.0008520702249370515,
-0.00005689501267625019,
0.00038855100865475833,
-0.020365413278341293,
-0.05389001965522766,
-0.012636123225092888,
0.0009203428635373712,
0.05227447301149368,
-0.05430592596530914,
0.006347095128148794,
0.006647062953561544,
0.03160446137189865,
-0.06895902752876282,
-0.05922791361808777,
0.0544455461204052,
-0.040272027254104614,
0.0034756609238684177,
-0.03297178074717522,
0.013574441894888878,
-0.06968753784894943,
-0.027784563601017,
0.01068958267569542,
0.07145120948553085,
-0.02148890122771263,
-0.030575012788176537,
-0.003760978579521179,
-0.021767819300293922,
-0.0017048293957486749,
-0.015747379511594772,
-0.011082148179411888,
-0.021223854273557663,
-0.01164061576128006,
-0.0008291659760288894,
-0.00786919891834259,
0.08413456380367279,
-0.012399023398756981,
-0.00950641930103302,
-0.03519739583134651,
-0.008425319567322731,
0.0025578055065125227,
-0.027672871947288513,
-0.0015718616778030992,
0.07128304988145828,
0.03015219233930111,
-0.03028324991464615,
-0.033515941351652145,
0.017538229003548622,
-0.008715897798538208,
0.026176979765295982,
0.01452453713864088,
-0.025181438773870468,
-0.023990454152226448,
-0.04470421373844147,
0.034347906708717346,
0.0009655880858190358,
0.031269002705812454,
0.004346202593296766,
0.037473008036613464,
-0.019983693957328796,
-0.010408702306449413,
0.012402788735926151,
-0.0019407423678785563,
0.042609598487615585,
-0.015335511416196823,
-0.0036064644809812307,
0.021181242540478706,
-0.02952411212027073,
-0.022599898278713226,
-0.019522443413734436,
-0.022732429206371307,
-0.031084435060620308,
0.08158454298973083,
-0.031035255640745163,
0.03834320604801178,
0.004910988267511129,
0.011550087481737137,
-0.005344973411411047,
0.0053203473798930645,
-0.021483629941940308,
0.02188715897500515,
0.0032775443978607655,
0.05438274145126343,
-0.01558343879878521,
-0.000355887837940827,
0.03204229474067688,
0.05842558667063713,
0.010692260228097439,
0.006051421631127596,
0.004398981109261513,
0.025239307433366776,
-0.006896562408655882,
0.017371274530887604,
-0.03271384909749031,
0.02766457386314869,
-0.005547403357923031,
0.006140187848359346,
0.005746620707213879,
-0.016284208744764328,
0.03930863365530968,
0.01890086755156517,
0.007099791429936886,
-0.0037893960252404213,
-0.014126818627119064,
-0.03402857109904289,
0.01551763340830803,
0.03671161085367203,
0.002398862037807703,
-0.022839663550257683,
0.01061377301812172,
0.027934622019529343,
0.012792537920176983,
0.02395661734044552,
-0.002034509088844061,
-0.06420458108186722,
-0.026844680309295654,
-0.058123793452978134,
-0.06191219761967659,
-0.009906665422022343,
0.022470535710453987,
-0.02995484694838524,
-0.00089598901104182,
-0.021768156439065933,
0.022272277623414993,
0.025354014709591866,
0.034464336931705475,
0.03655030578374863,
0.08037906140089035,
-0.028275972232222557,
-0.02261967584490776,
0.000619426544290036,
0.013103046454489231,
0.08284533768892288,
0.05663565918803215,
-0.013411756604909897,
-0.054447565227746964,
0.008524308912456036,
-0.020608048886060715,
-0.007097853813320398,
-0.05158216133713722,
0.05729525163769722,
-0.0026549312751740217,
0.001149926334619522,
0.01946045085787773,
0.0602317750453949,
-0.011019915342330933,
-0.0005764381494373083,
0.05965293198823929,
-0.01518719270825386,
-0.02428431250154972,
-0.01915532909333706,
0.022678960114717484,
0.002262330148369074,
0.018347295001149178,
-0.0021712160669267178,
0.01157835777848959,
-0.01756066456437111,
-0.0041329325176775455,
-0.04687134921550751,
-0.020263874903321266,
0.03719112277030945,
-0.018825463950634003,
-0.07557651400566101,
-0.006269761826843023,
-0.012670517899096012,
-0.030196096748113632,
-0.06156820058822632,
0.016011521220207214,
-0.00463118078187108,
-0.005844391882419586,
0.03288363665342331,
0.010577689856290817,
0.029766393825411797,
0.047609418630599976,
0.01903209462761879,
-0.014542634598910809,
-0.04711509868502617,
0.01609201356768608,
-0.0301114059984684,
0.03224685788154602,
-0.021031498908996582,
0.006222283933311701,
0.014482272788882256,
0.03408461809158325,
0.008326778188347816,
-0.04761623591184616,
-0.03345182165503502,
-0.011066876351833344,
0.017924221232533455,
-0.001996054546907544,
0.01681673899292946,
-0.07172031700611115,
0.006277286913245916,
-0.010056668892502785,
-0.0006225709803402424,
-0.0037610111758112907,
-0.020709889009594917,
0.03552187979221344,
-0.02873881347477436,
0.03356796130537987,
-0.05939405411481857,
-0.03805981203913689,
-0.013515349477529526,
-0.0024407010059803724,
-0.0341821052134037,
0.014341097325086594,
0.03008143976330757,
0.035862140357494354,
0.006864978466182947,
-0.008517581038177013,
-0.007110071834176779,
-0.022308815270662308,
-0.05750679597258568,
0.02377709187567234,
-0.020857425406575203,
-0.014735241420567036,
-0.013621585443615913,
-0.019599316641688347,
0.025497743859887123,
0.02517389878630638,
-0.02145671471953392,
0.01617809385061264,
-0.02757326513528824,
-0.012770731933414936,
0.03729904815554619,
-0.019679704681038857,
0.0231346245855093,
0.01471624057739973,
-0.007631778251379728,
-0.02597804367542267,
-0.034654077142477036,
0.042766593396663666,
0.0342467799782753,
-0.01285136491060257,
-0.010224842466413975,
0.033745136111974716,
-0.038776155561208725,
-0.011691063642501831,
0.023526612669229507,
-0.02161109633743763,
0.026546547189354897,
0.005808037240058184,
0.053262244910001755,
-0.05487322434782982,
-0.03527243807911873,
-0.01894075982272625,
-0.0017885015113279223,
-0.038296427577733994,
0.02199644222855568,
-0.017195535823702812,
0.021893614903092384,
-0.01037389226257801,
0.020635051652789116,
-0.027313390746712685,
0.016404222697019577,
-0.03779995068907738,
0.05189031362533569,
0.0074793025851249695,
-0.025754593312740326,
-0.03462989628314972,
0.04437750205397606,
-0.010536525398492813,
-0.010238050483167171,
0.004064588807523251,
0.014396307989954948,
-0.0028653484769165516,
-0.015097583644092083,
0.02723093144595623,
-0.03370513394474983,
0.017317352816462517,
-0.003660527290776372,
-0.02120552770793438,
0.012374517507851124,
-0.05431821569800377,
-0.02893694117665291,
0.04591575264930725,
-0.027088463306427002,
0.012385614216327667,
0.02531266398727894,
-0.028057172894477844,
-0.01759251579642296,
0.08471142500638962,
-0.034549154341220856,
0.019509509205818176,
0.01537058874964714,
-0.025510825216770172,
-0.03211062774062157,
0.0024290771689265966,
0.01649991050362587,
-0.01112667378038168,
-0.013031900860369205,
0.03917365521192551,
0.048036545515060425,
-0.05477159097790718,
0.022459451109170914,
0.002428375417366624,
-0.01831458881497383,
-0.0005269484827294946,
0.01459354069083929,
-0.007296707946807146,
-0.0018207161920145154,
0.06666634976863861,
-0.03319748863577843,
0.03155462443828583,
0.011573802679777145,
0.024867739528417587,
-0.09099765121936798,
0.007110771723091602,
-0.00963255763053894,
0.012585209682583809,
0.036750294268131256,
-0.03771758824586868,
0.03700484335422516,
0.023255346342921257,
-0.05735239386558533,
0.005081364884972572,
-0.051400359719991684,
0.0006508050137199461,
0.001459623803384602,
-0.008404012769460678,
0.019046764820814133,
0.04731578379869461,
0.026423336938023567,
0.03433620184659958,
0.02709909901022911,
-0.01187880802899599,
-0.013870032504200935,
-0.016441818326711655,
0.017498934641480446,
0.03286159783601761,
0.005910418462008238,
-0.002701309509575367,
0.06438150256872177,
-0.02526390738785267,
-0.03677833825349808,
0.01833030954003334,
0.017435748130083084,
-0.004101885482668877,
0.004514610394835472,
0.008477116003632545,
-0.0009131446713581681,
0.018602540716528893,
-0.023939471691846848,
-0.015737025067210197,
-0.010660074651241302,
0.05400221049785614,
0.007559299934655428,
0.021115019917488098,
-0.04031359404325485,
-0.014246764592826366,
0.018977828323841095,
-0.022629598155617714,
-0.03635116294026375,
0.03360496833920479,
0.011726989410817623,
-0.03158972039818764,
-0.014144787564873695,
0.00807033758610487,
0.004200274124741554,
-0.020900815725326538,
0.011524204164743423,
-0.0322028212249279,
0.0040693506598472595,
-0.004280175548046827,
-0.03661094978451729,
-0.017500173300504684,
0.004684872459620237,
-0.02825808897614479,
0.017407625913619995,
-0.009314225055277348,
0.01630459539592266,
-0.012350235134363174,
-0.06723910570144653,
-0.0061153629794716835,
0.017565330490469933,
-0.022908231243491173,
-0.009357629343867302,
-0.042094599455595016,
-0.009299452416598797,
0.058879513293504715,
0.025535838678479195,
0.008203386329114437,
-0.007137596607208252,
-0.020822299644351006,
-0.012614285573363304,
-0.056025370955467224,
-0.006458400283008814,
0.006355510093271732,
-0.00039057573303580284,
-0.04233101010322571,
-0.010203374549746513,
-0.018866024911403656,
0.007128111552447081,
0.06748075038194656,
-0.023120593279600143,
-0.04014743119478226,
0.021952949464321136,
0.006535142194479704,
-0.0012536854483187199,
-0.034853626042604446,
-0.00012214189337100834,
-0.03416197746992111,
-0.01993405632674694,
-0.06275036931037903,
0.008143787272274494,
-0.021931935101747513,
0.03004905954003334,
-0.00277369050309062,
0.00538065517321229,
0.06585968285799026,
-0.012989329174160957,
-0.04265955835580826,
0.04716241732239723,
0.029004689306020737,
-0.009848935529589653,
0.07601992785930634,
-0.02631480246782303,
0.02146313525736332,
0.048892851918935776,
-0.00436409842222929,
-0.03745187819004059,
0.02460799738764763,
-0.011631915345788002,
0.004631113726645708,
-0.030351730063557625,
0.006258300505578518,
0.01900666207075119,
-0.07914406061172485,
0.0179184228181839,
0.037662822753190994,
-0.04170162230730057,
0.006939120125025511,
0.038823992013931274,
0.012638047337532043,
0.011637985706329346,
0.009594614617526531,
0.010517686605453491,
0.017056619748473167,
0.012489358894526958,
-0.013233352452516556,
0.050288084894418716,
0.02798083983361721,
-0.02276599407196045,
0.027656158432364464,
0.04659947380423546,
-0.006353468634188175,
0.02555265463888645,
0.020708970725536346,
0.01251180935651064,
-0.017965413630008698,
0.010721593163907528,
-0.018071860074996948,
-0.029312739148736,
0.05307774245738983,
0.026199769228696823,
-0.01696881279349327,
0.07389190047979355,
-0.055329762399196625,
0.005993344821035862,
-0.004326956812292337,
0.020617401227355003,
-0.02557183988392353,
-0.004647557623684406,
-0.01904098130762577,
0.050046101212501526,
0.009669540449976921,
-0.0029542462434619665,
-0.0035418206825852394,
-0.01724286936223507,
0.018536042422056198,
-0.03832226246595383,
0.0032724204938858747,
0.01323134545236826,
-0.021934084594249725,
-0.009085769765079021,
-0.0133661525323987,
-0.011959167197346687,
-0.006327130366116762,
0.03331131488084793,
-0.00247434270568192,
0.03401919826865196,
-0.0044114612974226475,
0.021365344524383545,
-0.013986312784254551,
0.05805554240942001,
-0.07656063884496689,
-0.030329953879117966,
-0.01714775152504444,
0.015471725724637508,
-0.05323450639843941,
-0.0014950042823329568
] |
<p>Is there any reason for the names of the decay chains? As shown in this chart (<a href="http://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Radioactive_decay_chains_diagram.svg/2000px-Radioactive_decay_chains_diagram.svg.png" rel="nofollow">larger version here</a>):
<img src="http://i.stack.imgur.com/0LVtw.png" alt="enter image description here"></p>
<p>only the Thorium chain starts on an isotope of the element it takes its name from, and it can also start from Uranium.</p>
<p>My bet is that they were given that name because it was thought those were the starting elements, and it was later discovered that there were parent isotopes. Am I right?</p> | 2,043 | [
0.006705434527248144,
-0.03415612131357193,
-0.013144033960998058,
0.02248959243297577,
-0.007882904261350632,
0.0012345444411039352,
-0.04701098054647446,
-0.02802257426083088,
0.017099903896450996,
-0.04786377400159836,
0.03147964924573898,
0.002993971109390259,
0.04388563707470894,
0.004153628367930651,
0.014785720966756344,
0.04715830460190773,
0.013854854740202427,
-0.03234851360321045,
-0.028548050671815872,
-0.025814823806285858,
0.029221875593066216,
-0.024051865562796593,
0.0144348768517375,
0.05162094533443451,
-0.0006331627955660224,
0.06273575127124786,
-0.00554063031449914,
0.049045585095882416,
0.04978664219379425,
0.018599895760416985,
0.0033149877563118935,
-0.05690701678395271,
0.025125188753008842,
-0.04665787145495415,
0.030677208676934242,
-0.031925566494464874,
-0.0014241287717595696,
-0.006658195983618498,
-0.013674161396920681,
0.0479079894721508,
-0.03823576122522354,
-0.05218353867530823,
-0.025046832859516144,
0.024349477142095566,
-0.0007258234545588493,
-0.020221814513206482,
-0.019730964675545692,
0.0011227091308683157,
0.04767753928899765,
-0.02919478714466095,
0.04846186935901642,
-0.008339949883520603,
0.03343131020665169,
0.025223365053534508,
0.012612646445631981,
0.010337927378714085,
0.03215399757027626,
0.05121511220932007,
0.0038271683733910322,
-0.017525076866149902,
-0.0014438824728131294,
-0.022760840132832527,
0.0007067479891702533,
0.022046837955713272,
-0.011398671194911003,
0.039689525961875916,
0.0038784132339060307,
-0.011579430662095547,
0.026145340874791145,
0.05622359365224838,
0.06561708450317383,
0.007994119077920914,
0.016710594296455383,
-0.0261624064296484,
-0.011011212132871151,
-0.008374040946364403,
0.013994554057717323,
-0.006803223863244057,
0.05123615264892578,
0.021139830350875854,
0.0023884319234639406,
0.01812104322016239,
0.00011305691441521049,
0.0033048600889742374,
-0.0398794561624527,
0.03311202675104141,
0.05636341869831085,
-0.03144775703549385,
-0.008746331557631493,
0.0205415990203619,
0.019510257989168167,
0.014336765743792057,
0.04853426665067673,
0.0513874851167202,
-0.0017172497464343905,
0.051677703857421875,
-0.006587595213204622,
0.031961727887392044,
0.028702719137072563,
0.015844233334064484,
0.0342831090092659,
-0.0023023851681500673,
0.037883371114730835,
0.06167581304907799,
-0.0021534946281462908,
0.0023716753348708153,
-0.05879295989871025,
0.030351046472787857,
-0.04643499478697777,
-0.001780397375114262,
-0.062398768961429596,
-0.005419788416475058,
-0.01857670210301876,
0.031232649460434914,
-0.010363607667386532,
-0.018678193911910057,
0.021494437009096146,
0.015767861157655716,
0.029765209183096886,
0.04246239736676216,
0.058503102511167526,
-0.03214624524116516,
0.059125371277332306,
-0.01797652617096901,
-0.09022865444421768,
-0.01799805834889412,
0.038267046213150024,
0.0049672806635499,
-0.000697274983394891,
0.03218362107872963,
-0.01618005894124508,
-0.030135206878185272,
0.030872831121087074,
0.01136497501283884,
0.08553136885166168,
0.007361266762018204,
-0.11861278116703033,
-0.060653477907180786,
0.004366899840533733,
-0.012430792674422264,
-0.04458620771765709,
-0.0750511884689331,
0.009015980176627636,
0.01942361146211624,
0.017744285985827446,
-0.03076731599867344,
-0.02930137701332569,
-0.006065339781343937,
0.025333184748888016,
-0.0038636489771306515,
-0.00287052639760077,
-0.028583426028490067,
0.029945913702249527,
-0.04860896244645119,
-0.009097092784941196,
-0.06980812549591064,
0.00996879581362009,
-0.002215426182374358,
-0.0030506495386362076,
-0.019962230697274208,
0.04857353866100311,
-0.037974629551172256,
0.06973645091056824,
0.006395877804607153,
-0.024212131276726723,
-0.03232073783874512,
0.07848165184259415,
0.04124118760228157,
-0.008618438616394997,
0.059220295399427414,
-0.01965954527258873,
0.042968232184648514,
0.02872001752257347,
0.06020127981901169,
0.05097222328186035,
-0.03837790712714195,
-0.0472823865711689,
-0.005438062362372875,
0.015559080056846142,
-0.003941149450838566,
-0.03156173229217529,
-0.021048227325081825,
0.012225930579006672,
-0.002378623466938734,
0.0012166794622316957,
0.03451990336179733,
-0.0126894386485219,
-0.044372331351041794,
0.05064981430768967,
-0.0435589924454689,
-0.0254807211458683,
-0.0188580434769392,
-0.010226252488791943,
-0.06941268593072891,
-0.01446959376335144,
0.0016035883454605937,
-0.013740846887230873,
-0.005250596906989813,
-0.013721995055675507,
-0.015383841469883919,
-0.031508658081293106,
0.05648653954267502,
-0.0066770571283996105,
0.015439779497683048,
0.019546275958418846,
0.05604242533445358,
0.031012631952762604,
0.006987802684307098,
0.025283774361014366,
-0.03219481185078621,
-0.014608723111450672,
-0.009441785514354706,
0.004966724198311567,
0.0021843777503818274,
-0.028137462213635445,
-0.009527589194476604,
-0.019038178026676178,
-0.002883391221985221,
-0.008130067028105259,
0.0185506884008646,
-0.04001789912581444,
0.08119547367095947,
-0.005419274792075157,
0.029718033969402313,
-0.010219389572739601,
0.02674243226647377,
0.038989271968603134,
0.07058074325323105,
-0.02811649814248085,
-0.023838259279727936,
-0.043926138430833817,
-0.02483941987156868,
0.039167530834674835,
0.021760541945695877,
-0.03178868815302849,
0.015876416116952896,
-0.017764857038855553,
0.057681456208229065,
0.010504969395697117,
0.018458537757396698,
-0.017486747354269028,
-0.04207053408026695,
-0.04554380476474762,
0.06124499440193176,
-0.014661809429526329,
0.0301260557025671,
0.02252393774688244,
-0.0011051945621147752,
0.013769586570560932,
-0.04414381831884384,
-0.04602985084056854,
0.01595134101808071,
-0.027542315423488617,
0.0026794320438057184,
-0.006242212373763323,
-0.04929884523153305,
0.04667653515934944,
-0.026718897745013237,
0.03889515623450279,
0.014835541136562824,
0.012705896981060505,
-0.022420059889554977,
-0.011739108711481094,
-0.027741730213165283,
0.01730666495859623,
0.021610507741570473,
-0.04148835316300392,
0.009490926750004292,
0.020955467596650124,
-0.01349083986133337,
0.03499320149421692,
-0.05810396745800972,
-0.03298875689506531,
-0.013333447277545929,
-0.01353142224252224,
0.025797752663493156,
0.008260741829872131,
0.0518902912735939,
-0.028732052072882652,
-0.035198986530303955,
-0.006329711992293596,
-0.03820224478840828,
-0.02537425234913826,
0.027144676074385643,
-0.042446814477443695,
0.04901287704706192,
-0.02210652083158493,
-0.005710070487111807,
0.050549935549497604,
0.020132167264819145,
-0.012115134857594967,
0.02090604230761528,
0.004333871882408857,
-0.028071142733097076,
-0.033628880977630615,
-0.02641022764146328,
0.03270314633846283,
0.038955964148044586,
0.0452425554394722,
0.024700434878468513,
-0.004654900636523962,
-0.0003157583123538643,
0.03324328735470772,
-0.08546553552150726,
-0.0045710778795182705,
-0.002590049523860216,
-0.001386771211400628,
-0.02069375291466713,
0.025111258029937744,
0.013821297325193882,
0.03238185495138168,
-0.05184904485940933,
-0.02263919822871685,
-0.004813003353774548,
-0.023324117064476013,
0.029962817206978798,
-0.010229906067252159,
0.045134536921978,
0.02433962933719158,
0.004475750029087067,
0.08074444532394409,
0.06980714946985245,
-0.029402006417512894,
-0.0016956401523202658,
0.000495517801027745,
-0.011333838105201721,
-0.039433617144823074,
0.02162707969546318,
0.013669196516275406,
0.046542007476091385,
0.01614850014448166,
0.0331350639462471,
0.03085322305560112,
0.020754827186465263,
-0.017267633229494095,
0.019900191575288773,
0.02430027350783348,
0.021858789026737213,
-0.021066460758447647,
0.03667948767542839,
0.010383662767708302,
-0.03881543129682541,
-0.003927681129425764,
-0.02541881985962391,
0.06000747159123421,
-0.027753939852118492,
-0.06242453679442406,
0.03400742635130882,
0.02455722540616989,
0.0014906899305060506,
0.004183399025350809,
-0.021893078461289406,
-0.012197943404316902,
-0.021343709900975227,
-0.02367192693054676,
0.031715795397758484,
0.049261756241321564,
-0.02522057108581066,
0.019347410649061203,
0.008660286664962769,
0.05124694108963013,
-0.03325730562210083,
0.0013095939066261053,
0.0009083806653507054,
-0.028993049636483192,
0.0321485698223114,
0.002836800878867507,
-0.025169597938656807,
0.03829347714781761,
0.04328303784132004,
0.028772452846169472,
0.03785760700702667,
-0.05202632397413254,
-0.008511894382536411,
-0.058887284249067307,
-0.00874284841120243,
0.002886735135689378,
0.02216416969895363,
-0.0009628126863390207,
0.05470508709549904,
0.012647784315049648,
0.021761909127235413,
-0.027977721765637398,
0.001940363203175366,
-0.08149322867393494,
-0.0011342334328219295,
-0.07125827670097351,
-0.04967711120843887,
-0.017108380794525146,
-0.024540087208151817,
-0.03156440705060959,
-0.016215384006500244,
-0.02149759978055954,
-0.0021036851685494184,
-0.026142360642552376,
-0.059702206403017044,
0.02673313580453396,
-0.013957524672150612,
-0.004227355122566223,
-0.021137328818440437,
0.041992541402578354,
0.03439370542764664,
0.03368226811289787,
0.03365044668316841,
-0.005762582179158926,
-0.02069101482629776,
-0.005365136545151472,
-0.026462653651833534,
0.009105244651436806,
0.01059209555387497,
-0.020437324419617653,
0.038254424929618835,
0.0336734764277935,
-0.06093573942780495,
-0.03741146996617317,
0.005302751902490854,
0.06546257436275482,
0.012758624739944935,
-0.02309703640639782,
0.002154030604287982,
-0.06854254752397537,
0.004972993861883879,
0.059472739696502686,
-0.0015731006860733032,
0.017869435250759125,
0.04713258892297745,
0.03797366842627525,
-0.00016064972442109138,
0.012428142130374908,
0.04246816039085388,
0.03210914880037308,
0.009169512428343296,
-0.03258055821061134,
-0.011658311821520329,
0.009840568527579308,
-0.003587433835491538,
-0.011496891267597675,
-0.014175823889672756,
0.028164247050881386,
-0.022774193435907364,
0.014328607358038425,
0.015146157704293728,
0.018557164818048477,
-0.0031737566459923983,
0.01263168640434742,
-0.015563351102173328,
0.05951302871108055,
-0.0006189503474161029,
-0.016197003424167633,
-0.0020697000436484814,
0.004513465333729982,
0.03827020153403282,
-0.014116591773927212,
0.010576771572232246,
-0.05947398766875267,
0.007107422687113285,
0.013516576960682869,
0.05568787828087807,
-0.03304938226938248,
-0.04191597178578377,
-0.014407545328140259,
-0.01652035303413868,
0.08214058727025986,
-0.038944341242313385,
0.05562843754887581,
-0.04312396049499512,
-0.025657420977950096,
0.013924569822847843,
-0.041095662862062454,
0.020339151844382286,
0.00429389625787735,
0.018436860293149948,
-0.00343428086489439,
-0.016919272020459175,
0.01748669520020485,
-0.0012397094396874309,
0.008429640904068947,
-0.015333198942244053,
0.03547680005431175,
-0.003920592833310366,
-0.0026726974174380302,
0.004132372792810202,
0.030026685446500778,
0.008793452754616737,
-0.0612129271030426,
-0.008006278425455093,
-0.02311304211616516,
0.009078779257833958,
0.01796909049153328,
-0.041483934968709946,
-0.09572161734104156,
0.0235463697463274,
0.043751392513513565,
-0.005681387614458799,
-0.02359919250011444,
-0.02994498983025551,
0.010003947652876377,
0.08148649334907532,
-0.030162885785102844,
0.058226294815540314,
0.05820133164525032,
-0.03890352323651314,
0.0021729515865445137,
-0.035031139850616455,
0.03424222767353058,
-0.0406469888985157,
0.00847727432847023,
-0.023243185132741928,
0.031456220895051956,
-0.014545570127665997,
0.06456077098846436,
-0.013510381802916527,
0.01728002354502678,
-0.012575598433613777,
0.006201197858899832,
-0.010450726374983788,
0.02689950354397297,
-0.013584933243691921,
0.0036321307998150587,
-0.018402988091111183,
0.022561049088835716,
0.0018843377474695444,
-0.01830635406076908,
0.01835954561829567,
-0.028004566207528114,
0.018882017582654953,
-0.0064540160819888115,
0.02152547426521778,
0.03666798770427704,
-0.04857810214161873,
-0.01546018011868,
0.05047071352601051,
-0.018647439777851105,
0.009809227660298347,
0.02249222621321678,
-0.01507091149687767,
0.01885267160832882,
-0.07005249708890915,
-0.03891412913799286,
0.01413742732256651,
-0.022756198421120644,
0.03613797947764397,
-0.026366064324975014,
0.07322540879249573,
0.018035193905234337,
0.017409276217222214,
-0.05421534925699234,
-0.022279798984527588,
-0.008552979677915573,
0.012283810414373875,
-0.03806626796722412,
-0.0195090863853693,
0.028354259207844734,
-0.00823940709233284,
-0.025305218994617462,
0.005948634352535009,
0.05415046215057373,
-0.04019373655319214,
-0.030879609286785126,
0.014654235914349556,
0.025802144780755043,
0.05347595736384392,
0.018657168373465538,
0.0034001211170107126,
-0.0037562043871730566,
0.019831720739603043,
0.02776515856385231,
0.023119250312447548,
0.03575030341744423,
-0.012223399244248867,
-0.046257540583610535,
0.02043372020125389,
0.03340812772512436,
0.04565979167819023,
-0.037750955671072006,
-0.023225931450724602,
0.0099794315174222,
-0.009441405534744263,
0.022389430552721024,
-0.029837025329470634,
0.024538224563002586,
-0.027893800288438797,
-0.01592489890754223,
0.03050343319773674,
0.02043091133236885,
0.008208568207919598,
-0.03926565870642662,
0.02739119902253151,
-0.017842495813965797,
0.029212825000286102,
0.0281351450830698,
-0.0006794790970161557,
-0.01033789198845625,
-0.0061248778365552425,
0.00464059691876173,
-0.01932547613978386,
0.013503575697541237,
0.001759057748131454,
0.013578233309090137,
0.035054903477430344,
-0.01806006394326687,
-0.010777859948575497,
-0.020299918949604034,
-0.02651968039572239,
0.010777893476188183,
0.06395210325717926,
-0.018336530774831772,
0.01606159098446369,
0.0027626908849924803,
-0.03570743650197983,
0.05724981054663658,
0.0122816301882267,
-0.02227691188454628,
-0.02276446856558323,
0.015975967049598694,
0.010149098932743073,
-0.03563174232840538,
0.019771208986639977,
0.005340635776519775,
0.009842717088758945,
0.003085547359660268,
0.007797857280820608,
0.0037943762727081776,
-0.01735534891486168,
-0.02220219373703003,
0.007488499395549297,
-0.02295929193496704,
0.02674943581223488,
-0.00874998327344656,
0.006621570326387882,
0.035111188888549805,
-0.02470078505575657,
0.03128601238131523,
-0.011939276941120625,
-0.020952314138412476,
-0.05351348966360092,
-0.013637685216963291,
-0.054073575884103775,
0.025902235880494118,
0.013209671713411808,
0.017295552417635918,
-0.006203202530741692,
-0.008569072000682354,
0.0271307360380888,
-0.0023328831885010004,
0.021626917645335197,
0.005239567253738642,
-0.0563533715903759,
-0.01163986325263977,
-0.01708737015724182,
-0.06081226095557213,
0.03582194074988365,
-0.06413143873214722,
-0.058342255651950836,
-0.03779967129230499,
-0.025640081614255905,
-0.0024098893627524376,
-0.010350629687309265,
0.010583586990833282,
-0.03159789368510246,
0.032116230577230453,
-0.0137491375207901,
0.029435276985168457,
0.04613232612609863,
-0.022255009040236473,
0.12822382152080536,
0.017630835995078087,
0.017966290935873985,
-0.04076724499464035,
-0.003936207387596369,
-0.00626772316172719,
0.014078819192945957,
-0.002814193954691291,
0.03568877652287483,
0.03801070153713226,
0.03226028382778168,
0.005508665926754475,
0.025926535949110985,
0.005763620603829622,
0.027454592287540436,
0.03405807912349701,
-0.009904316626489162,
-0.05691740661859512,
-0.0010209365282207727,
-0.013007034547626972,
-0.02971726842224598,
-0.019208721816539764,
-0.03765386343002319,
0.008674006909132004,
0.027711432427167892,
0.022546162828803062,
-0.025793857872486115,
-0.0077052004635334015,
0.04637310653924942,
0.048491887748241425,
-0.0030864952132105827,
-0.0031989377457648516,
0.035655390471220016,
0.006709373090416193,
-0.03139288350939751,
-0.001138491090387106,
0.007220668252557516,
-0.01918167434632778,
0.04323318973183632,
0.028229016810655594,
0.014719602651894093,
-0.031724680215120316,
-0.024071140214800835,
0.014644870534539223,
-0.048124492168426514,
-0.003914552740752697,
-0.0003894820692948997,
-0.0029443090315908194,
-0.03914415463805199,
0.018184645101428032,
-0.03370872139930725,
0.012707788497209549,
0.00898657739162445,
-0.03866457939147949,
0.011803323403000832,
-0.028460226953029633,
0.0251300148665905,
-0.054151639342308044,
-0.03405039384961128,
-0.05553816258907318,
0.008147700689733028,
-0.0010923711815848947,
0.038485631346702576,
0.0055419509299099445,
-0.015988849103450775,
0.018980829045176506,
-0.05592287331819534,
0.000582459440920502,
0.0061379363760352135,
0.021533643826842308,
-0.006235190667212009,
0.019619761034846306,
-0.06106747314333916,
-0.004708535503596067,
0.038661520928144455,
0.029711902141571045,
0.07658448815345764,
0.0411401130259037,
-0.003320976858958602,
0.0035561141557991505,
-0.016372712329030037,
0.05044925585389137,
-0.01633709855377674,
-0.023875772953033447,
-0.03245638683438301,
-0.0026346175000071526,
-0.0037709095049649477,
0.014538947492837906,
-0.03509509190917015,
0.05739561840891838,
0.008234875276684761,
0.013413134962320328,
-0.009191400371491909,
-0.030962413176894188,
0.005142266862094402,
0.03710274025797844,
-0.02680424600839615,
-0.014265518635511398,
-0.022703297436237335,
0.03946112096309662,
0.031375691294670105,
-0.011267192661762238,
0.016245732083916664,
0.016925698146224022,
0.008961047045886517,
0.007748500443994999,
0.024611903354525566,
-0.045996811240911484,
0.03330707177519798,
-0.015563818626105785,
-0.028306324034929276,
-0.04706596955657005,
-0.03769390285015106,
0.002067123306915164,
0.004253934603184462,
0.04874826967716217,
0.01563364267349243,
-0.020824521780014038,
0.0022779691498726606,
-0.08891204744577408,
0.012554830871522427,
-0.016686346381902695,
-0.009781570173799992,
-0.06494047492742538,
-0.008581587113440037,
-0.0017975741066038609,
-0.027274848893284798,
-0.030659856274724007,
0.033034373074769974,
0.005911522079259157,
0.0006458174902945757,
0.043196409940719604,
0.019010288640856743,
-0.047553397715091705,
-0.04514067992568016,
-0.004884445574134588,
0.00562317157164216,
0.019031120464205742,
-0.0046586510725319386,
0.03796787187457085,
0.010940316133201122,
-0.007660709787160158,
-0.04571232572197914,
0.030879421159625053,
0.01488508377224207,
-0.002448177197948098,
0.009542250074446201,
0.003649595659226179,
-0.005126572214066982,
0.0651182234287262,
-0.0620032362639904,
-0.008156144991517067,
0.03098665550351143,
0.03391260653734207,
0.0025017433799803257,
0.0032342493068426847,
-0.01174013502895832,
0.005004402250051498,
0.005121306516230106,
0.008736875839531422,
0.016803648322820663,
0.0031667021103203297,
-0.002737195696681738,
-0.03987817093729973,
-0.011832698248326778,
0.037967730313539505,
-0.017751125618815422,
0.04211418330669403,
0.028589287772774696,
-0.012931862846016884,
-0.04586267098784447,
0.058886073529720306,
0.03683736175298691,
0.000761591421905905,
-0.06253539770841599,
-0.004204078111797571,
-0.003191858297213912,
-0.002389617497101426,
-0.00046312142512761056,
-0.04416583478450775,
-0.008326839655637741,
-0.0001349297963315621,
-0.051937300711870193,
0.0011443441035225987,
-0.014242815785109997,
-0.03980904445052147,
-0.03149037063121796,
-0.04188891500234604,
0.009542874991893768,
0.061541926115751266,
0.032770343124866486,
0.03588561713695526,
0.04076647013425827,
-0.029927430674433708,
-0.03489631786942482,
-0.004935831297188997,
-0.06382408738136292,
-0.011059314012527466,
-0.04021092876791954,
-0.026063222438097,
0.036738283932209015,
-0.002031821757555008,
-0.010083602741360664,
0.008747509680688381,
0.03131283447146416,
0.02737358771264553,
-0.006431099958717823,
0.0006793111679144204,
-0.028518425300717354,
0.006025329232215881,
0.013271470554172993,
-0.017557648941874504,
-0.029636362567543983,
0.02243979275226593,
0.014879210852086544,
0.026749104261398315,
0.030041467398405075,
-0.028458816930651665,
-0.007863625884056091,
-0.0482902005314827,
-0.0628419741988182,
0.016955506056547165,
0.011781499721109867,
-0.009479456581175327,
-0.02703861892223358,
0.01299761887639761,
-0.013866164721548557,
-0.03155720233917236,
-0.045737169682979584,
-0.036123309284448624,
-0.03364330902695656,
0.00961386226117611,
-0.006526636425405741,
0.019075946882367134,
0.022151567041873932,
-0.007831268012523651,
-0.042997535318136215,
-0.009753137826919556,
0.030346540734171867,
-0.017811665311455727,
-0.018180962651968002,
0.03175816684961319,
0.017436066642403603,
0.005939406808465719,
-0.010333484970033169,
-0.028295189142227173,
-0.0443548746407032,
0.06177055835723877,
0.014517470262944698,
0.017568914219737053,
-0.029052678495645523,
-0.04010045900940895,
-0.0011232455726712942,
-0.03391271457076073,
0.04228157922625542,
-0.017424380406737328,
-0.004435312934219837,
-0.04273652657866478,
-0.007587714586406946,
0.00931747816503048,
0.019032636657357216,
0.03772162273526192,
0.01638100855052471,
0.0044026002287864685,
0.005426682066172361,
0.007350040599703789,
0.02463550493121147,
-0.033527567982673645,
0.012802721001207829,
0.02003278024494648,
-0.019726112484931946,
0.011855521239340305,
0.0024586098734289408,
0.0035717894788831472,
0.04453544318675995,
0.0016359076835215092,
0.01679149456322193,
-0.04450414702296257,
-0.023081259801983833,
0.010997062548995018,
0.03548857942223549,
-0.04385199770331383,
-0.03756524994969368,
0.07202548533678055,
0.0015107323415577412,
-0.01711430586874485,
0.04689261317253113,
-0.025149738416075706,
-0.026608478277921677,
0.0679372251033783,
-0.010794571600854397,
-0.017801394686102867,
-0.004191695246845484,
-0.04072342813014984,
0.02786005474627018,
-0.033319488167762756,
0.0044720908626914024,
0.021369796246290207,
-0.025006774812936783,
-0.0036746941041201353,
0.029043253511190414,
0.00943207461386919,
0.02862394228577614,
0.03178424388170242,
0.02283088117837906,
0.01293217483907938,
-0.028411325067281723,
0.016480164602398872,
0.05885182321071625,
0.02301776222884655,
0.0070745088160037994,
0.007447806186974049,
-0.018037403002381325,
-0.03907989710569382,
0.012934361584484577,
-0.008984616957604885,
0.013571314513683319,
-0.031702809035778046,
-0.0017318851314485073,
0.028187043964862823,
-0.03885814547538757,
-0.01329588983207941,
0.05020717531442642,
-0.06162213161587715,
0.06974902004003525,
-0.024885207414627075,
0.024301419034600258,
-0.00027783738914877176,
0.011545157991349697,
-0.013052459806203842,
0.02013055793941021,
-0.011168759316205978,
-0.0004551795427687466,
-0.03857262432575226,
0.013058695942163467,
-0.017231842502951622,
0.01448747981339693,
0.022421197965741158,
-0.05591891333460808,
-0.012755310162901878,
-0.018238332122564316,
0.017142726108431816,
-0.025812214240431786,
0.011968874372541904,
-0.0452704019844532,
-0.05557369440793991,
0.029303524643182755,
0.08994057774543762,
0.03564143180847168,
0.0004320031439419836,
-0.05604713782668114,
-0.03590606153011322,
0.05741792917251587,
-0.010262406431138515,
-0.011632551439106464,
-0.008584227412939072,
-0.004595817532390356,
-0.014681033790111542,
-0.010808616876602173
] |
<p>I have two coherent point sources of light, $A$ and $B$, separated by a distance $L$, which I focus down to the diffraction limit using a high-powered objective (e.g. a $\approx 100x$ objective). If I turn on $A$ and turn off $B$, I have an Airy disk at position $c_1$, and I turn off $A$ and I turn on $B$, I have an Airy disk at position $c_2$. Given that both light sources are sent through the same objective, what is the minimum distance between $c_1$ and $c_2$? Is it simply $L$ scaled down by the objective (i.e. $\frac{L}{100}$)? Or does something odd happen because of e.g. curvature of the lens in the objective?</p>
<p>EDIT: A restatement of this question would be the following - Assuming all of the optics are perfect, if I shine a laser at a point (x,y) on an objective, and then shine the laser at a point (x2,y2), will the peak of the Airy disk move the same distance?</p> | 2,044 | [
-0.026842115446925163,
-0.0024857004173099995,
-0.010388822294771671,
-0.024138430133461952,
0.026426786556839943,
0.002179425209760666,
-0.04972847178578377,
-0.028767848387360573,
0.008953833021223545,
0.0007259397534653544,
0.0387667641043663,
0.03518544137477875,
0.07352820038795471,
-0.006710323505103588,
0.02443128265440464,
-0.026454539969563484,
-0.006340544205158949,
0.005920208524912596,
0.008519330061972141,
-0.005333464592695236,
0.0103623541072011,
0.028140630573034286,
0.019075704738497734,
-0.007461513392627239,
-0.04828879237174988,
0.013820000924170017,
-0.004948969464749098,
-0.007221453823149204,
-0.028378672897815704,
0.041997604072093964,
-0.02491353265941143,
-0.039701178669929504,
-0.012428361922502518,
0.025374114513397217,
0.0017996272072196007,
-0.026085810735821724,
-0.02921592816710472,
-0.020306335762143135,
-0.015036196447908878,
0.022220460698008537,
-0.05373792722821236,
-0.02562776766717434,
-0.00025953949079848826,
0.06541621685028076,
-0.007551932707428932,
-0.004829231183975935,
-0.023853357881307602,
-0.01917714811861515,
0.03781964257359505,
-0.029840117320418358,
0.08202055096626282,
0.009769287891685963,
0.02484782785177231,
0.030884817242622375,
-0.007839389145374298,
0.017204567790031433,
0.0790875181555748,
0.04889645799994469,
-0.01820414885878563,
-0.02651645429432392,
-0.04125633090734482,
-0.005217461846768856,
-0.0017362418584525585,
-0.012295826338231564,
-0.031378280371427536,
0.024063246324658394,
-0.01667213626205921,
0.013844374567270279,
0.016684720292687416,
-0.002274170285090804,
-0.020431600511074066,
0.037485718727111816,
0.054339449852705,
-0.023893851786851883,
0.04105927422642708,
-0.0223151296377182,
0.04815175011754036,
0.0008714613504707813,
0.02564080059528351,
0.026005033403635025,
-0.01879964768886566,
0.01258959248661995,
-0.0028999231290072203,
0.05630671977996826,
0.024394774809479713,
0.023266855627298355,
0.05693333223462105,
-0.012456671334803104,
0.029397564008831978,
0.020951485261321068,
0.019476300105452538,
0.025878187268972397,
0.039492569863796234,
0.005050604697316885,
0.015104918740689754,
0.02897733263671398,
-0.014537110924720764,
0.051342159509658813,
-0.015925249084830284,
-0.01687544584274292,
-0.0012054897379130125,
-0.0016152402386069298,
0.016607040539383888,
0.04863009229302406,
0.006211690604686737,
-0.03527835011482239,
-0.007810089737176895,
0.057547081261873245,
-0.0647936463356018,
-0.004613441880792379,
-0.026364389806985855,
0.042988572269678116,
-0.0063813235610723495,
0.029731862246990204,
0.04242704063653946,
-0.020149018615484238,
0.015395515598356724,
-0.04965836554765701,
0.07619019597768784,
0.033856723457574844,
0.05773549526929855,
-0.025583965703845024,
-0.008767466060817242,
-0.010475237853825092,
-0.018966680392622948,
-0.002460571238771081,
0.07215409725904465,
-0.0051173195242881775,
-0.05261460319161415,
-0.0023328110110014677,
-0.010222380049526691,
0.013668994419276714,
0.00611899746581912,
0.0033331254962831736,
-0.013371809385716915,
-0.032870471477508545,
-0.0750245451927185,
-0.017320165410637856,
0.019992928951978683,
0.024263018742203712,
0.005322635173797607,
-0.06975536048412323,
-0.010972490534186363,
0.02855907566845417,
0.10203199833631516,
-0.016603508964180946,
-0.01151056308299303,
0.0004371930845081806,
0.06880251318216324,
-0.03584323078393936,
-0.015164091251790524,
0.015348059125244617,
-0.003627106314525008,
-0.04467598348855972,
-0.0014404745306819677,
-0.06124920770525932,
-0.0016278629191219807,
0.05889211967587471,
0.01612197421491146,
-0.02851240523159504,
0.04787265509366989,
-0.012353254482150078,
0.0225256085395813,
-0.00917223934084177,
0.04715173691511154,
-0.010694775730371475,
0.0643187165260315,
0.036779746413230896,
-0.006429318804293871,
0.06265968829393387,
0.00414580013602972,
0.021900005638599396,
-0.01253607776015997,
0.009005624800920486,
0.06131665036082268,
-0.02638883888721466,
0.00223917025141418,
-0.02779083512723446,
0.014161757193505764,
0.043557144701480865,
-0.027977177873253822,
-0.038297779858112335,
-0.010078956373035908,
-0.008870517835021019,
0.00865236483514309,
0.05447845533490181,
-0.02446444146335125,
0.018307263031601906,
-0.004982857033610344,
-0.04169182479381561,
0.011049900203943253,
-0.03758474066853523,
0.029298610985279083,
0.040058840066194534,
0.016702312976121902,
0.049211736768484116,
-0.007826900109648705,
-0.008607890456914902,
-0.0007320963777601719,
-0.0069654942490160465,
-0.011359785683453083,
0.03954127058386803,
-0.0010375831043347716,
0.008576239459216595,
0.057109665125608444,
0.09350723028182983,
0.04372517019510269,
0.03084443509578705,
0.024702364578843117,
-0.04471176490187645,
-0.010622304864227772,
0.018737496808171272,
-0.018870750442147255,
0.022099124267697334,
0.011810359545052052,
0.02039361745119095,
-0.00944118294864893,
0.028360186144709587,
0.02064901404082775,
0.010947953909635544,
-0.033680547028779984,
0.054072003811597824,
0.06403429806232452,
-0.013570956885814667,
0.00304432469420135,
0.028196929022669792,
0.003057565540075302,
-0.012129268608987331,
-0.0004420326731633395,
-0.03428293392062187,
-0.05016304552555084,
0.01803683489561081,
0.016246018931269646,
0.040674708783626556,
-0.028141610324382782,
0.03887524828314781,
0.031698521226644516,
0.019108794629573822,
0.03863674774765968,
0.03520580381155014,
-0.04810456559062004,
-0.027798360213637352,
0.018028326332569122,
0.057888153940439224,
-0.022777317091822624,
0.003253268776461482,
0.007233844604343176,
0.01206163875758648,
0.034875545650720596,
0.015291471034288406,
-0.005763963330537081,
0.01379790622740984,
-0.003102216636762023,
-0.015303339809179306,
-0.03322998434305191,
0.03241727873682976,
0.04491613805294037,
-0.022205164656043053,
0.01010141335427761,
0.0003758838283829391,
-0.02478894405066967,
-0.02116106078028679,
-0.049988579005002975,
-0.020156722515821457,
0.03057461977005005,
0.011719943955540657,
-0.015868600457906723,
-0.0005359985516406596,
0.017860934138298035,
-0.01765703596174717,
0.012725706212222576,
-0.045524585992097855,
0.006009649485349655,
-0.019471174106001854,
-0.013657684437930584,
0.0020386099349707365,
0.06588972359895706,
0.03316823020577431,
-0.05447348952293396,
-0.0653323233127594,
-0.05692628026008606,
-0.035271286964416504,
0.026101086288690567,
0.01144405361264944,
-0.033867307007312775,
-0.001271713525056839,
-0.01989094540476799,
-0.014920596964657307,
0.019686495885252953,
-0.013987609185278416,
0.036006420850753784,
0.013856671750545502,
-0.017557475715875626,
-0.06224220618605614,
0.02262636087834835,
-0.016517583280801773,
0.01885978691279888,
-0.016885265707969666,
0.008423740975558758,
-0.006424786057323217,
-0.008063172921538353,
-0.03151795268058777,
-0.008337692357599735,
-0.0197349451482296,
-0.007581513840705156,
-0.02131684683263302,
0.014825159683823586,
-0.0005059051909483969,
-0.02591276541352272,
0.0024411471094936132,
0.00800950825214386,
-0.0061395419761538506,
0.00866619311273098,
-0.06004728749394417,
-0.03774154931306839,
0.061912328004837036,
-0.029850659891963005,
0.021785736083984375,
-0.05024589225649834,
-0.006659054663032293,
0.04837331920862198,
0.02189752459526062,
-0.05136462673544884,
-0.026583319529891014,
-0.006148102227598429,
0.02306622639298439,
0.021227924153208733,
-0.026914851740002632,
0.0010395158315077424,
-0.0019166189013049006,
0.08196862041950226,
0.02036113291978836,
0.003985594492405653,
0.03036392480134964,
0.02807774394750595,
-0.0004399032040964812,
-0.00582923972979188,
0.030934657901525497,
-0.02925189584493637,
0.019020330160856247,
0.03346670791506767,
-0.01614752598106861,
0.0395110547542572,
-0.038140565156936646,
0.02917373739182949,
0.022003235295414925,
-0.02845887467265129,
0.043350543826818466,
-0.026108304038643837,
-0.011870536021888256,
0.02754788286983967,
0.04670440033078194,
0.012821328826248646,
0.005180890206247568,
-0.01684604212641716,
0.02991580404341221,
0.04502546414732933,
-0.029466155916452408,
-0.03669380396604538,
0.03637236729264259,
0.04358586296439171,
0.010336635634303093,
-0.022266125306487083,
-0.011180552653968334,
-0.008458265103399754,
0.006540827918797731,
-0.013702220283448696,
-0.043418411165475845,
0.02640325389802456,
0.0013812747783958912,
-0.015817193314433098,
-0.0009526580106467009,
-0.02190840244293213,
0.036586612462997437,
-0.05902167782187462,
-0.001197823672555387,
0.004418416880071163,
0.02273385226726532,
0.004939518868923187,
0.01100833434611559,
0.05471033975481987,
0.017133040353655815,
-0.0009395730448886752,
-0.017571991309523582,
-0.068930484354496,
0.0076163350604474545,
-0.051985472440719604,
-0.022743433713912964,
-0.012348653748631477,
0.003869313281029463,
0.012980995699763298,
-0.019385643303394318,
0.0036030220799148083,
-0.04581940919160843,
0.017262311652302742,
-0.021075701341032982,
0.011705774813890457,
-0.05020952597260475,
-0.05625990405678749,
0.00864484254270792,
0.017458977177739143,
0.008059625513851643,
-0.016474585980176926,
0.04445187374949455,
-0.0024129822850227356,
-0.01900234818458557,
-0.0033193060662597418,
0.010972662828862667,
0.021259505301713943,
-0.03629801422357559,
0.025522248819470406,
0.045898012816905975,
0.06300479918718338,
-0.029290582984685898,
0.031085673719644547,
-0.0016886905068531632,
0.07220718264579773,
-0.0097124595195055,
-0.015451552346348763,
-0.037837881594896317,
-0.05135029926896095,
-0.03366376459598541,
-0.0067934924736619,
0.07237134128808975,
-0.02949872799217701,
-0.005495409015566111,
0.027744373306632042,
0.022809600457549095,
0.018773818388581276,
0.03284646198153496,
-0.0005575089016929269,
0.020670277997851372,
-0.0022212336771190166,
-0.04685933142900467,
-0.01706070639193058,
-0.02193707786500454,
0.024855993688106537,
0.057437825947999954,
-0.014236061833798885,
0.017749689519405365,
0.007294150069355965,
0.02804720215499401,
0.05329526215791702,
-0.015433021821081638,
0.03497753292322159,
-0.020394394174218178,
0.017972465604543686,
-0.015027284622192383,
0.010985597036778927,
-0.006119837984442711,
-0.0041409884579479694,
0.03236471116542816,
0.006867754273116589,
0.01854781247675419,
-0.06106606870889664,
-0.02238639071583748,
0.0318567231297493,
0.012015449814498425,
-0.031839337199926376,
-0.015058398246765137,
-0.023379161953926086,
-0.05465775728225708,
0.033236779272556305,
-0.02662326768040657,
0.04262237995862961,
-0.015530471689999104,
-0.027165016159415245,
0.00448443740606308,
-0.005326603539288044,
-0.05614911764860153,
0.03631669655442238,
0.01614941842854023,
0.007153987884521484,
-0.04268757253885269,
-0.006855430547147989,
0.010180885903537273,
0.017751509323716164,
0.036600589752197266,
0.05863006040453911,
-0.021033136174082756,
-0.03385908901691437,
0.0057548703625798225,
0.02065790444612503,
0.02018507570028305,
-0.04312954843044281,
0.01851542480289936,
0.02332940883934498,
-0.034636422991752625,
0.03774913400411606,
0.0050806947983801365,
0.0035717531573027372,
0.03603179380297661,
0.0023426164407283068,
-0.005702170077711344,
0.023918166756629944,
0.032069627195596695,
0.022826623171567917,
0.046547140926122665,
-0.003527518594637513,
0.06492780894041061,
-0.006114550866186619,
-0.05788855254650116,
-0.03175649046897888,
-0.014150979928672314,
0.06625574827194214,
-0.0348312146961689,
-0.0063375202007591724,
-0.025688545778393745,
0.013374438509345055,
-0.03864545002579689,
0.08460932970046997,
-0.03154062479734421,
-0.0017850515432655811,
0.010177938267588615,
0.003575419308617711,
-0.0028879032470285892,
0.042062822729349136,
0.007035721093416214,
0.015216398984193802,
0.009999201633036137,
0.051244113594293594,
0.0413859486579895,
-0.02042548917233944,
-0.012722373940050602,
-0.024577897042036057,
0.011547133326530457,
0.010393430478870869,
0.006787238642573357,
0.04179638624191284,
-0.06536918133497238,
-0.010165780782699585,
-0.0002005128626478836,
-0.03329691290855408,
0.039767052978277206,
-0.021000061184167862,
0.008678529411554337,
0.016686193645000458,
-0.05339937284588814,
-0.019981130957603455,
-0.012372100725769997,
-0.027031593024730682,
0.01057298481464386,
-0.053206667304039,
0.02620387263596058,
-0.014583433046936989,
-0.0291790459305048,
-0.060685355216264725,
-0.01627746783196926,
-0.008077571168541908,
0.04261237382888794,
0.02076422981917858,
-0.04466674104332924,
0.005173138342797756,
-0.038343656808137894,
-0.014696239493787289,
-0.017423905432224274,
0.043309714645147324,
-0.016340170055627823,
-0.04017317295074463,
0.01755448244512081,
-0.030871843919157982,
0.009953685104846954,
-0.025777338072657585,
-0.03838383033871651,
0.0004826441581826657,
0.015599209815263748,
-0.03156604617834091,
0.0037636440247297287,
0.0674816370010376,
-0.04035121202468872,
-0.05210678651928902,
-0.03477529436349869,
-0.017957566305994987,
0.045000310987234116,
-0.04858680069446564,
-0.02228916808962822,
-0.0009371741907671094,
0.012348405085504055,
0.03290208801627159,
0.01423033606261015,
-0.009327723644673824,
-0.028930172324180603,
-0.0010980995139107108,
0.00046419110731221735,
-0.02463502623140812,
-0.034002818167209625,
-0.06800031661987305,
0.023080982267856598,
0.030394306406378746,
0.02962828427553177,
-0.022673672065138817,
0.03957332298159599,
-0.014522885903716087,
-0.02430741675198078,
-0.0032780312467366457,
0.0002634882985148579,
0.038440950214862823,
-0.00937575288116932,
0.009609546512365341,
0.008443820290267467,
0.007044905796647072,
-0.019770240411162376,
-0.050311554223299026,
-0.013714971020817757,
0.015519176609814167,
0.0829901173710823,
-0.005587882362306118,
0.04470311477780342,
0.03851738199591637,
-0.019205037504434586,
-0.01045280508697033,
-0.01780303567647934,
0.009991573169827461,
0.016552027314901352,
-0.00007207591988844797,
0.029747413471341133,
-0.056329015642404556,
-0.0062385364435613155,
0.03623679280281067,
0.06043769419193268,
-0.00013857938756700605,
-0.0028853032272309065,
0.016668008640408516,
0.06266164034605026,
0.02273145131766796,
-0.047283872961997986,
-0.035646166652441025,
0.042378127574920654,
-0.06518577039241791,
0.007354802917689085,
0.003408630145713687,
-0.008932676166296005,
0.011206910945475101,
0.01850348711013794,
0.02421598881483078,
-0.04973800107836723,
-0.046690020710229874,
-0.038826968520879745,
0.002858952386304736,
-0.017283057793974876,
0.026454763486981392,
0.014106565155088902,
0.01302841305732727,
-0.02511076256632805,
-0.0018859806004911661,
0.031188640743494034,
-0.01818200573325157,
-0.0692685917019844,
-0.06134021654725075,
-0.01767289824783802,
-0.05917293205857277,
0.011009479872882366,
-0.012718516401946545,
-0.02191234566271305,
0.034262608736753464,
-0.0358310341835022,
0.0029503267724066973,
0.052658550441265106,
0.01716240495443344,
0.009262517094612122,
0.05373143032193184,
0.01977851614356041,
0.020856142044067383,
-0.005255577620118856,
0.017242440953850746,
0.10820486396551132,
0.026189645752310753,
0.0011074012145400047,
-0.09164009243249893,
-0.008021869696676731,
-0.0005507865571416914,
0.0033811675384640694,
-0.06426175683736801,
0.014905949123203754,
-0.016894064843654633,
-0.0020003977697342634,
0.054095324128866196,
0.02623448334634304,
0.04389925301074982,
-0.010202494449913502,
0.03163512051105499,
-0.01900164596736431,
-0.009360353462398052,
0.03448157384991646,
0.0093870023265481,
0.015293763019144535,
0.01368778757750988,
0.00853309128433466,
0.013879174366593361,
-0.05001566559076309,
0.004994636867195368,
0.01225859671831131,
-0.05776296183466911,
0.00700130732730031,
0.015884989872574806,
-0.027061035856604576,
0.0014190123183652759,
0.008504916913807392,
-0.031832076609134674,
-0.06727098673582077,
0.03662363812327385,
0.03034220077097416,
-0.0007788802031427622,
-0.03461207449436188,
0.04763394594192505,
0.00795662123709917,
0.047744181007146835,
0.025794653221964836,
0.009611082263290882,
-0.040586020797491074,
-0.03779768943786621,
-0.0294355358928442,
0.02691613882780075,
-0.013999059796333313,
0.030303165316581726,
0.01982194371521473,
-0.0233047716319561,
0.025779670104384422,
-0.04360038414597511,
0.011394272558391094,
0.019671330228447914,
-0.006933124270290136,
-0.01749357394874096,
-0.024270690977573395,
-0.010465728119015694,
0.057068582624197006,
0.02169668860733509,
-0.004391874186694622,
0.0013952477602288127,
-0.006151059176772833,
-0.015671223402023315,
0.017534710466861725,
0.06123441830277443,
0.006223202683031559,
-0.05551677569746971,
-0.04264708235859871,
0.03899877145886421,
0.01901094801723957,
-0.007575736381113529,
0.010184881277382374,
0.014161558821797371,
0.024142378941178322,
0.016349924728274345,
-0.024550529196858406,
-0.02479756623506546,
-0.09252478182315826,
-0.0017507618758827448,
-0.011493874713778496,
-0.02091388776898384,
-0.01088147982954979,
-0.0014240463497117162,
0.02502560429275036,
0.03391747549176216,
0.007672578562051058,
-0.030336780473589897,
-0.028356563299894333,
0.04946570098400116,
0.01886129379272461,
-0.013977866619825363,
-0.038392432034015656,
0.008122799918055534,
-0.05046024173498154,
-0.016756758093833923,
-0.011276512406766415,
0.04871732369065285,
-0.022219602018594742,
0.02639150619506836,
0.005487959366291761,
0.013134850189089775,
-0.07194412499666214,
-0.0008082155254669487,
0.021177329123020172,
-0.03435393422842026,
0.0027750409208238125,
-0.006165051832795143,
-0.011789452284574509,
-0.023016266524791718,
-0.042666517198085785,
-0.02100983075797558,
-0.04011175036430359,
-0.002969104563817382,
-0.006156416144222021,
0.025651922449469566,
-0.0029660614673048258,
0.0007104753749445081,
-0.014972812496125698,
-0.023148683831095695,
-0.03200812637805939,
-0.01627226360142231,
0.02534959279000759,
0.04008666053414345,
0.01899472437798977,
0.012137627229094505,
0.013303474523127079,
0.0028151324950158596,
-0.0713554248213768,
-0.025536084547638893,
0.03985900431871414,
0.017918817698955536,
-0.00426898617297411,
0.024783167988061905,
0.0183925312012434,
0.04461583122611046,
-0.01854431815445423,
-0.046408262103796005,
0.04606525972485542,
-0.036428503692150116,
-0.05694098025560379,
0.03890879452228546,
-0.044696297496557236,
0.031647346913814545,
0.024934852495789528,
-0.007988655008375645,
-0.03561333194375038,
0.08057144284248352,
0.03453143686056137,
-0.02944529801607132,
0.009667733684182167,
-0.005266502033919096,
0.02303878404200077,
0.047314003109931946,
0.019916070625185966,
-0.020646901801228523,
-0.027112234383821487,
0.03501065820455551,
0.029105626046657562,
-0.06326764076948166,
0.010232491418719292,
0.01842336542904377,
-0.011440753936767578,
-0.01662265509366989,
-0.024594957008957863,
0.017890674993395805,
0.04633713886141777,
0.04344821721315384,
0.016585610806941986,
0.013804314658045769,
0.038027435541152954,
0.022502480074763298,
-0.10579445213079453,
-0.004043615888804197,
0.011702647432684898,
-0.007054799702018499,
0.012449238449335098,
-0.04801354929804802,
0.032436735928058624,
0.033589862287044525,
-0.06406011432409286,
0.00937693938612938,
-0.023852940648794174,
-0.016209745779633522,
-0.08669108897447586,
-0.0020565520972013474,
-0.006085524335503578,
0.004200487397611141,
0.020173512399196625,
0.04507406800985336,
0.01787581294775009,
0.017835091799497604,
-0.008951457217335701,
-0.030019676312804222,
-0.022185305133461952,
-0.0012590709375217557,
0.0027849841862916946,
-0.022667881101369858,
0.02433830499649048,
-0.013610590249300003,
-0.03816995397210121,
0.015618412755429745,
-0.03029087744653225,
0.0028161408845335245,
0.003652285784482956,
0.004734863992780447,
0.013962666504085064,
0.025880293920636177,
0.005118922796100378,
0.0315980426967144,
0.0026416978798806667,
0.01770707219839096,
-0.014923461712896824,
-0.0029425944667309523,
-0.04555753991007805,
0.017492253333330154,
0.041945718228816986,
-0.0603153295814991,
-0.029909629374742508,
0.040226954966783524,
0.0028526245150715113,
-0.016585998237133026,
0.01965988613665104,
0.016320152208209038,
0.030992552638053894,
-0.034692808985710144,
0.03789649158716202,
-0.053488969802856445,
-0.020688224583864212,
0.008786438032984734,
0.00834828894585371,
-0.031791478395462036,
0.012802338227629662,
-0.03659664839506149,
-0.03593643382191658,
0.016177823767066002,
-0.00201985496096313,
-0.01800212636590004,
-0.03403056412935257,
-0.033766016364097595,
-0.013899675570428371,
-0.0015442430740222335,
0.010954994708299637,
-0.04304220899939537,
-0.05010512098670006,
0.012698029167950153,
0.010895350947976112,
0.019692670553922653,
0.018221529200673103,
0.027165763080120087,
-0.07718437165021896,
-0.07764924317598343,
-0.006152067333459854,
-0.024202533066272736,
0.021414170041680336,
-0.042643412947654724,
0.005960776936262846,
-0.019451042637228966,
0.01474529318511486,
0.01627681404352188,
0.015930822119116783,
-0.027765322476625443,
0.03803233802318573,
-0.02000771276652813,
0.0007696370012126863,
-0.022920414805412292,
-0.009297236800193787,
0.011899950914084911,
-0.0075456625781953335,
-0.020769912749528885,
0.011494593694806099,
-0.03888864815235138,
0.025870583951473236,
0.007436067797243595,
0.008552356623113155,
0.028865568339824677,
-0.015256591141223907,
-0.03366423770785332,
0.039273183792829514,
-0.01991373859345913,
0.00403667101636529,
0.04586794227361679,
0.044783756136894226,
-0.014592776075005531,
-0.004560535307973623,
-0.021103424951434135,
-0.0416673868894577,
0.0622965469956398,
-0.058081042021512985,
-0.010904617607593536,
-0.02190990187227726,
0.011423690244555473,
0.01546846330165863,
-0.06638722121715546,
0.009059949778020382,
-0.004194983746856451,
-0.031687673181295395,
-0.02405739761888981,
0.02180033177137375,
-0.0095394691452384,
0.004881152417510748,
-0.008524620905518532,
0.011771474033594131,
0.0009880948346108198,
0.004119153134524822,
0.004037274047732353,
0.05408496782183647,
0.020832112058997154,
0.047598496079444885,
0.021541208028793335,
0.007218811195343733,
0.007760314736515284,
0.02700021304190159,
-0.05013785883784294,
0.0404345728456974,
0.013983422890305519,
-0.03591661900281906,
0.01331099309027195,
0.00036449823528528214,
-0.012719557620584965,
0.019043000414967537,
0.00867089070379734,
0.04583870992064476,
-0.03685571625828743,
0.02207573503255844,
-0.07861398160457611,
0.020233487710356712,
0.010664407163858414,
0.005219177342951298,
-0.005312911234796047,
0.04149559140205383,
0.00274745118804276,
0.0011481571709737182,
0.0036481539718806744,
-0.01930108852684498,
-0.0041419644840061665,
-0.03863111510872841,
0.02443423494696617,
-0.01245261263102293,
-0.016853520646691322,
0.008919336833059788,
-0.017670707777142525,
-0.03680289909243584,
-0.04764774814248085,
0.0034583655651658773,
0.05037970468401909,
0.039539631456136703,
0.02503681369125843,
-0.02804582752287388,
0.009305345825850964,
0.04932957515120506,
-0.0871070995926857,
0.0003312840417493135,
0.020963674411177635,
0.020167334005236626,
-0.01739989034831524,
-0.027853161096572876
] |
<p>I read in wiki that the speed of light is 88km/s slower in air than it is in a vacuum.</p>
<p>Do neutrinos travel faster than light in air?</p> | 2,045 | [
-0.015264632180333138,
-0.062441494315862656,
-0.014846236445009708,
-0.04090240225195885,
0.042975716292858124,
-0.007110318168997765,
-0.02435579150915146,
-0.03705457225441933,
0.02213052473962307,
-0.010316573083400726,
0.044986944645643234,
0.04430452361702919,
0.04240189865231514,
-0.004087557550519705,
-0.00844242237508297,
0.007806706707924604,
-0.021945811808109283,
0.020568987354636192,
-0.013744272291660309,
-0.04330481216311455,
-0.009678891859948635,
-0.002094726078212261,
-0.013819374144077301,
0.026831455528736115,
-0.02529129758477211,
0.0390382744371891,
0.01622934080660343,
0.01284165121614933,
0.022530199959874153,
0.01341425534337759,
0.028695641085505486,
0.005244965199381113,
0.03592580556869507,
0.025671012699604034,
0.03781842812895775,
-0.0006689861183986068,
-0.02615049108862877,
-0.02940373681485653,
-0.018072478473186493,
0.017651764675974846,
-0.003655420383438468,
-0.03332792967557907,
-0.008210978470742702,
0.014852426014840603,
-0.00905567966401577,
0.03937206789851189,
0.029569512233138084,
-0.013413605280220509,
0.062156327068805695,
-0.0842830091714859,
0.04595211148262024,
0.009547758847475052,
0.010378965176641941,
0.03182990476489067,
-0.004053852986544371,
-0.003206600435078144,
0.10400521755218506,
0.06937798112630844,
-0.01563018187880516,
-0.04799460247159004,
0.019306020811200142,
-0.018854064866900444,
-0.012706819921731949,
-0.026980483904480934,
-0.01909276843070984,
0.03423260152339935,
-0.06602423638105392,
-0.015768911689519882,
0.013418452814221382,
0.03218381851911545,
0.0043413941748440266,
0.020669592544436455,
0.03203006461262703,
-0.0016347226919606328,
0.010875815525650978,
-0.03297291323542595,
0.006552782841026783,
0.008637459017336369,
0.047191351652145386,
0.06687995046377182,
-0.0149706294760108,
0.005928826052695513,
0.03538325056433678,
-0.010865488089621067,
0.0056855217553675175,
-0.01777496561408043,
0.0702701210975647,
-0.012498403899371624,
-0.030559955164790154,
0.012504697777330875,
-0.016830764710903168,
-0.02412157505750656,
0.001964850816875696,
0.025535166263580322,
0.01642906293272972,
0.01622774824500084,
-0.00981704518198967,
0.035424116998910904,
0.01942775398492813,
-0.03578393533825874,
-0.0007675911765545607,
0.02542511373758316,
0.03978162631392479,
0.07162152975797653,
-0.0022487046662718058,
-0.030380399897694588,
-0.04363999143242836,
0.01885746233165264,
-0.04277636110782623,
0.011072561144828796,
-0.06116125360131264,
0.0011936554219573736,
-0.02768743969500065,
0.02008882723748684,
0.015252482146024704,
-0.044756822288036346,
0.0171066764742136,
-0.018469182774424553,
0.09510941803455353,
0.0843830332159996,
0.03309628367424011,
-0.027560286223888397,
-0.002950462279841304,
0.0074114263989031315,
-0.03336883708834648,
0.040557850152254105,
0.023002637550234795,
-0.004356237128376961,
-0.028534913435578346,
0.010033207014203072,
-0.03279052674770355,
0.01366416085511446,
0.01700604520738125,
-0.03802316635847092,
0.03811754286289215,
-0.022903086617588997,
-0.11354391276836395,
-0.07551246136426926,
0.05796626955270767,
0.019971156492829323,
-0.023165037855505943,
-0.08741753548383713,
0.016987523064017296,
-0.007457562256604433,
0.09090787917375565,
0.024155933409929276,
-0.006792082916945219,
-0.038811735808849335,
0.01593148522078991,
-0.006529254838824272,
-0.023893460631370544,
0.002785648684948683,
0.046265993267297745,
-0.05366269499063492,
0.029589535668492317,
-0.07846182584762573,
0.00021838619431946427,
0.04503055289387703,
0.009476615116000175,
-0.014689144678413868,
0.05850108712911606,
-0.033823639154434204,
0.04232301190495491,
-0.01786106452345848,
-0.0024350727908313274,
-0.054871201515197754,
0.07377074658870697,
0.030732324346899986,
0.025888074189424515,
0.04029643535614014,
-0.008856398053467274,
0.043481748551130295,
-0.028043147176504135,
-0.019718440249562263,
0.0579969584941864,
-0.023672668263316154,
-0.031013811007142067,
-0.021555820479989052,
0.001043093390762806,
0.010674450546503067,
-0.05246969312429428,
-0.0241763386875391,
-0.012369444593787193,
0.02868890017271042,
0.02167259342968464,
0.05783139169216156,
-0.010858078487217426,
-0.02645890973508358,
0.012500783428549767,
-0.0464545302093029,
-0.0027015109080821276,
-0.044818442314863205,
-0.004216556902974844,
0.02886011451482773,
0.01762307807803154,
-0.011491783894598484,
0.02359553799033165,
0.018496455624699593,
-0.05062558129429817,
-0.014194485731422901,
-0.01805248111486435,
0.03454722464084625,
-0.006913412362337112,
-0.01809048466384411,
0.0034044431522488594,
0.05875806510448456,
0.007383431773632765,
-0.031674936413764954,
0.008317392319440842,
-0.0012813826324418187,
-0.007493459153920412,
0.0022343227174133062,
-0.02101772651076317,
0.002818870358169079,
-0.008561006747186184,
0.019774338230490685,
0.03401179239153862,
0.03381025791168213,
0.00010008381650550291,
0.017432216554880142,
0.0018009847262874246,
0.08381979167461395,
0.05634108930826187,
0.009104084223508835,
0.007385942153632641,
0.012560763396322727,
0.022815581411123276,
0.006684968713670969,
0.005012305453419685,
-0.03437139093875885,
-0.05247654765844345,
-0.015213394537568092,
0.07309410721063614,
-0.031291645020246506,
-0.040850333869457245,
0.012557289563119411,
0.02390117384493351,
0.05221491679549217,
0.045557618141174316,
0.02020927146077156,
-0.01835983619093895,
-0.06553330272436142,
-0.016145342960953712,
0.029243212193250656,
0.020882707089185715,
0.025973739102482796,
0.03895660117268562,
-0.007058355025947094,
0.07413102686405182,
-0.04423244297504425,
-0.021724587306380272,
0.00375935435295105,
-0.012460038997232914,
0.017651449888944626,
0.005268031265586615,
-0.03673570230603218,
0.03906496614217758,
-0.05012459307909012,
0.027129381895065308,
-0.004009843338280916,
0.01302158460021019,
0.03745301812887192,
0.0023613320663571358,
0.008619321510195732,
0.03387930616736412,
0.012525982223451138,
-0.0020412050653249025,
0.008412208408117294,
0.03317398205399513,
-0.047974929213523865,
0.029769523069262505,
-0.04603463411331177,
0.000036140208976576105,
-0.024913454428315163,
0.016536930575966835,
0.02978670410811901,
0.02294779382646084,
0.030148392543196678,
0.0015743752010166645,
-0.04027053713798523,
-0.003948134370148182,
-0.05687176063656807,
-0.027864031493663788,
0.0470891110599041,
-0.007224137894809246,
0.059653107076883316,
-0.01861567609012127,
-0.045389749109745026,
0.01505946833640337,
-0.010058959946036339,
-0.0019018533639609814,
0.025541111826896667,
-0.02350245602428913,
-0.04041600227355957,
0.004808624740689993,
-0.04100221022963524,
0.013593127019703388,
-0.012980520725250244,
-0.0015034907264634967,
0.04515577480196953,
-0.005855726543813944,
-0.015907427296042442,
0.015423581004142761,
-0.021554376929998398,
-0.043051138520240784,
-0.04828415811061859,
0.012830940075218678,
-0.0020840447396039963,
-0.06348875910043716,
0.014022566378116608,
0.00039978031418286264,
-0.049562472850084305,
0.009551082737743855,
-0.02538766711950302,
-0.058343835175037384,
0.03361005708575249,
-0.00035299244336783886,
0.02712966315448284,
-0.0030456751119345427,
-0.051635488867759705,
0.054125018417835236,
0.038180381059646606,
0.009556894190609455,
-0.003833790309727192,
-0.0198783278465271,
-0.03830089420080185,
-0.040546830743551254,
-0.012528550811111927,
0.012544144876301289,
-0.013364310376346111,
0.007214418612420559,
0.012522145174443722,
0.05437912419438362,
0.00666090426966548,
0.0002854631165973842,
-0.010487825609743595,
-0.03933170810341835,
0.016698012128472328,
-0.007292082067579031,
0.0622972697019577,
0.0074937292374670506,
-0.0011413018219172955,
0.015835246071219444,
-0.026728879660367966,
0.05326123163104057,
0.04111485928297043,
-0.0495237372815609,
0.05796446651220322,
0.006079811602830887,
0.005321275442838669,
-0.04990919679403305,
0.006539749447256327,
0.02765662968158722,
0.019253568723797798,
0.002997913397848606,
0.013965669088065624,
0.035688333213329315,
0.018000081181526184,
0.0038149040192365646,
0.013029786758124828,
0.0958232581615448,
-0.01239468902349472,
-0.031492698937654495,
-0.011325884610414505,
0.008677021600306034,
0.031871527433395386,
-0.022498128935694695,
-0.010175801813602448,
0.06969624757766724,
0.05856146290898323,
-0.01300125103443861,
-0.013589873909950256,
-0.030526844784617424,
0.00834930595010519,
-0.050414878875017166,
0.018035314977169037,
0.01703638583421707,
-0.0008677442674525082,
-0.0029403504449874163,
0.011338344775140285,
0.008236600086092949,
0.004846366122364998,
0.01218409463763237,
-0.023748653009533882,
-0.05931305140256882,
0.015112071298062801,
-0.03957400098443031,
-0.03635888546705246,
-0.01545193511992693,
-0.044341590255498886,
-0.06372900307178497,
-0.008444640785455704,
-0.0036400104872882366,
-0.020197663456201553,
-0.009258311241865158,
-0.0360751673579216,
0.003887747647240758,
-0.02742338739335537,
-0.03776496648788452,
-0.0017887852154672146,
0.027951737865805626,
0.002993499394506216,
-0.007462936453521252,
0.009221818298101425,
0.03930963575839996,
-0.0518573634326458,
0.011582834646105766,
-0.012616940774023533,
0.04531489312648773,
0.01918906159698963,
0.005476239137351513,
0.027895184233784676,
-0.020814750343561172,
-0.033772584050893784,
0.011547297239303589,
0.012982793152332306,
0.023062879219651222,
-0.015584287233650684,
-0.01831424981355667,
-0.06318245083093643,
-0.02196391671895981,
-0.03268539160490036,
-0.005519025027751923,
0.04317374527454376,
-0.002312196884304285,
0.01990477368235588,
0.016690636053681374,
-0.02314833551645279,
-0.01702040620148182,
0.03591683879494667,
0.03002336621284485,
-0.007216006051748991,
0.008254674263298512,
-0.05915955454111099,
-0.014705618843436241,
-0.017863081768155098,
0.008954619988799095,
0.01711198315024376,
0.018706874921917915,
-0.039591047912836075,
-0.025094421580433846,
0.012192807160317898,
0.0176641084253788,
-0.021062826737761497,
0.030113158747553825,
-0.009794422425329685,
-0.026100002229213715,
-0.019468897953629494,
-0.003000679425895214,
-0.013712913729250431,
0.03769964352250099,
0.017411893233656883,
0.01562759466469288,
0.00043123753857798874,
-0.0794728547334671,
-0.011522267945110798,
0.04443042352795601,
0.041117534041404724,
-0.004634357988834381,
-0.015214942395687103,
-0.08559578657150269,
-0.0020491783507168293,
0.02406015805900097,
-0.03491408750414848,
0.031646598130464554,
-0.014155489392578602,
-0.014695431105792522,
-0.0074457707814872265,
-0.019851047545671463,
0.02551683411002159,
0.04882877320051193,
0.009373907931149006,
-0.0015024279709905386,
-0.01120380312204361,
0.00126107526011765,
-0.03082522377371788,
0.025048619136214256,
0.04548076540231705,
0.06131625175476074,
0.036176204681396484,
0.02208334393799305,
-0.00432177446782589,
-0.027256950736045837,
-0.04109048470854759,
-0.060723066329956055,
0.008914733305573463,
0.02761157602071762,
0.0006730112945660949,
0.03404131531715393,
0.004765524994581938,
-0.032056838274002075,
0.03988512232899666,
0.02032642439007759,
-0.02560119330883026,
-0.026630504056811333,
-0.07068642228841782,
0.03241652995347977,
0.016161199659109116,
-0.024169012904167175,
0.023196479305624962,
0.03217275068163872,
-0.05157959461212158,
0.0005585934268310666,
-0.01318690087646246,
0.0725567564368248,
-0.02458820305764675,
0.0011632738169282675,
0.013695331290364265,
-0.02095511555671692,
0.0030650857370346785,
0.06806065142154694,
-0.010027546435594559,
0.03873516246676445,
0.012367863208055496,
-0.05840997397899628,
-0.029916254803538322,
0.019278934225440025,
0.04016384109854698,
0.0018677300540730357,
-0.04261942580342293,
0.006451731082051992,
0.010469731874763966,
-0.02718115970492363,
0.033443383872509,
0.017903724685311317,
0.009009410627186298,
0.022034645080566406,
0.017800070345401764,
0.012361716479063034,
-0.05363898724317551,
-0.02507295273244381,
0.0028194778133183718,
-0.04225243628025055,
0.02053050324320793,
-0.0011962206335738301,
-0.05253076180815697,
0.014195764437317848,
-0.04499543085694313,
-0.04527861624956131,
0.0029603687580674887,
-0.01831018179655075,
0.04880738630890846,
-0.0802016407251358,
0.04914766922593117,
0.022571729496121407,
0.02517196349799633,
-0.05469179525971413,
-0.046683359891176224,
0.004403943195939064,
0.005094442516565323,
0.0036600728053599596,
-0.04845896363258362,
-0.01493760198354721,
-0.05716029554605484,
-0.05564458668231964,
-0.0073831710033118725,
0.05072488635778427,
-0.03305745869874954,
-0.019223053008317947,
-0.0031425580382347107,
-0.004452188964933157,
0.06267015635967255,
0.013604682870209217,
-0.019026080146431923,
0.024391425773501396,
0.007820996455848217,
-0.02804435044527054,
0.0019535727333277464,
0.057566508650779724,
0.0030494609382003546,
-0.03310859948396683,
-0.0029510916210711002,
0.0022266318555921316,
0.019584279507398605,
-0.010751765221357346,
0.014275927096605301,
0.031422968953847885,
0.008105816319584846,
-0.00010738697892520577,
0.012147234752774239,
0.04716195911169052,
0.015932274982333183,
0.0189987700432539,
-0.01652553305029869,
-0.010849788784980774,
-0.04367661103606224,
-0.02094496414065361,
0.0261776614934206,
0.01168579887598753,
0.04428759217262268,
-0.01931053027510643,
0.05090997368097305,
-0.03480850160121918,
-0.014024474658071995,
0.003364867065101862,
-0.03697451949119568,
-0.02234031818807125,
0.007975023239850998,
-0.016717391088604927,
-0.001801946316845715,
-0.003129943972453475,
-0.014235827140510082,
-0.024752898141741753,
-0.022926267236471176,
-0.030826322734355927,
0.03586636111140251,
-0.01368601992726326,
0.029904717579483986,
0.006722245831042528,
0.007665176410228014,
0.006207854487001896,
-0.04239499941468239,
-0.003039747476577759,
0.03345737233757973,
0.012342637404799461,
0.023113451898097992,
0.00703120743855834,
0.024860074743628502,
0.03344881907105446,
0.03619014844298363,
0.03425679728388786,
-0.012608872726559639,
0.017493868246674538,
0.025521671399474144,
-0.003520933212712407,
0.012690515257418156,
-0.04225084185600281,
0.03590403124690056,
-0.05519205704331398,
0.04064669460058212,
-0.005817631725221872,
0.007538286969065666,
0.04353474825620651,
-0.017106132581830025,
0.0007120128720998764,
-0.0029019988141953945,
-0.022100703790783882,
-0.03646470233798027,
0.001393588725477457,
-0.01719970814883709,
0.022514106705784798,
-0.018649209290742874,
0.008193226531147957,
0.06435254216194153,
0.009369582869112492,
0.01217842660844326,
-0.013145344331860542,
-0.05129507556557655,
-0.02880159579217434,
-0.027839554473757744,
-0.036450304090976715,
0.01948985643684864,
0.0040410528890788555,
-0.05699799209833145,
0.014673705212771893,
-0.026183990761637688,
0.035526737570762634,
0.017446940764784813,
0.027658576145768166,
-0.018756765872240067,
0.04628229886293411,
-0.01608368195593357,
0.012611226178705692,
0.007329448591917753,
0.012496978044509888,
0.10820510238409042,
0.027441341429948807,
0.008805657736957073,
-0.05086103081703186,
-0.003268076106905937,
-0.026203518733382225,
0.04279773682355881,
-0.052164629101753235,
-0.009019588120281696,
-0.023582926020026207,
0.029796263203024864,
0.030935775488615036,
0.04603055119514465,
0.01385845709592104,
-0.0008067807648330927,
0.01868959702551365,
-0.035974398255348206,
-0.02911214530467987,
0.03311725705862045,
0.03383490443229675,
-0.012095079757273197,
0.022427981719374657,
-0.025151265785098076,
0.048614222556352615,
-0.03705405443906784,
-0.004821235779672861,
-0.03221471235156059,
-0.031635429710149765,
0.034632548689842224,
-0.035273365676403046,
-0.08432203531265259,
-0.03212679177522659,
0.036760296672582626,
-0.05672137066721916,
-0.048336613923311234,
0.0036605552304536104,
0.025950314477086067,
0.0033450471237301826,
0.01630176603794098,
0.022023236379027367,
0.04147620499134064,
0.008849464356899261,
-0.016657942906022072,
0.03303229808807373,
-0.07623162120580673,
0.00995579268783331,
-0.0017673363909125328,
0.028860416263341904,
0.0015508871292695403,
0.019151153042912483,
0.019603997468948364,
0.04709387570619583,
0.01733982376754284,
-0.08035239577293396,
-0.005299334414303303,
0.0009509482188150287,
0.0010204847203567624,
-0.015792494639754295,
-0.017787540331482887,
-0.030042633414268494,
0.005773406010121107,
-0.00028160325018689036,
0.03278563916683197,
-0.03429153189063072,
0.011521240696310997,
0.0015387997264042497,
-0.0016558089992031455,
-0.021845202893018723,
-0.059497036039829254,
-0.04072444140911102,
0.002384921070188284,
0.017259716987609863,
-0.030484693124890327,
-0.008161417208611965,
0.05532683804631233,
0.02079491876065731,
0.02632424421608448,
0.006927811540663242,
-0.011916601099073887,
-0.01014030259102583,
-0.04350542277097702,
0.039698898792266846,
-0.02751714177429676,
-0.021274913102388382,
-0.011185460723936558,
-0.027214812114834785,
0.024626951664686203,
0.02523416467010975,
-0.02228846400976181,
0.011099963448941708,
-0.01119944080710411,
0.01009885873645544,
0.022175099700689316,
-0.03255080431699753,
-0.024817651137709618,
0.002330152317881584,
-0.021485863253474236,
0.011179277673363686,
-0.049701906740665436,
0.04606366157531738,
0.029359547421336174,
-0.013513670302927494,
0.010678407736122608,
0.009184619411826134,
-0.014774159528315067,
-0.023314669728279114,
0.0015565314097329974,
-0.018435070291161537,
-0.0008285237709060311,
-0.0025405799970030785,
0.0377638004720211,
-0.024743875488638878,
-0.016892626881599426,
-0.046268608421087265,
0.002247465308755636,
0.012839926406741142,
-0.009413124062120914,
0.0019865359645336866,
0.05171778053045273,
-0.04256163537502289,
0.01124928891658783,
-0.03044726885855198,
-0.010152176953852177,
-0.00711511354893446,
0.01870870776474476,
-0.010891090147197247,
-0.020366717129945755,
0.004144323989748955,
0.009703114628791809,
-0.055383697152137756,
0.04249025136232376,
0.02080310508608818,
0.013950060121715069,
0.005448279436677694,
-0.0017101283883675933,
0.0308633204549551,
0.005026053171604872,
0.026067793369293213,
-0.018596384674310684,
-0.018784109503030777,
0.0643119141459465,
0.00902022235095501,
-0.07150425761938095,
0.04879038780927658,
-0.017637139186263084,
0.027554882690310478,
0.02313660830259323,
-0.01965605840086937,
0.013387491926550865,
0.08460157364606857,
-0.023776572197675705,
-0.023670755326747894,
0.002669307868927717,
-0.03880938142538071,
-0.005757312290370464,
-0.010694271884858608,
0.025247929617762566,
-0.016940681263804436,
-0.030047034844756126,
0.036218203604221344,
0.018417663872241974,
-0.03350730985403061,
0.020883914083242416,
-0.0124166589230299,
-0.05541740357875824,
-0.010536960326135159,
0.01876838132739067,
0.017837343737483025,
0.008848981000483036,
0.058148182928562164,
-0.0011951308697462082,
0.05138874799013138,
0.020649809390306473,
-0.02609354630112648,
-0.13645729422569275,
0.0032976821530610323,
-0.004004138521850109,
0.035020384937524796,
0.022563153877854347,
-0.030762499198317528,
0.04485538229346275,
0.04019413888454437,
-0.05031497776508331,
0.003448714269325137,
-0.005957585759460926,
-0.027033668011426926,
-0.07318180799484253,
0.020240703597664833,
0.00014950946206226945,
0.05920533835887909,
0.033047161996364594,
0.039667461067438126,
0.015546937473118305,
0.010878637433052063,
-0.011113261803984642,
-0.03342340141534805,
-0.019481349736452103,
0.033016614615917206,
0.03462427854537964,
0.0007913197623565793,
0.013775289058685303,
-0.018438484519720078,
0.05185556784272194,
0.017157182097434998,
0.006712356582283974,
0.015477859415113926,
0.01674583926796913,
-0.0028534773737192154,
0.0293396208435297,
0.0063475994393229485,
0.028856810182332993,
-0.002447343897074461,
-0.009277606382966042,
0.02432449348270893,
-0.007355073466897011,
0.045528560876846313,
-0.03840082138776779,
-0.0005678825546056032,
0.016150370240211487,
-0.03529316559433937,
-0.03158107027411461,
0.01973203383386135,
-0.01810881495475769,
-0.00796599593013525,
0.020296022295951843,
-0.0016848674276843667,
0.0009325056453235447,
-0.02570071630179882,
-0.0032516345381736755,
-0.03769207000732422,
0.006358917336910963,
-0.005369388964027166,
-0.006830361671745777,
-0.0327383317053318,
0.019893424585461617,
0.004826126620173454,
-0.008764221332967281,
-0.01410629041492939,
0.0017899973317980766,
0.04259025678038597,
-0.04704687371850014,
-0.019922705367207527,
0.003738834522664547,
-0.007271345239132643,
0.018094301223754883,
-0.033607106655836105,
-0.009477823041379452,
0.01968490518629551,
0.037282999604940414,
0.0008035515784285963,
0.013688167557120323,
-0.0036243076901882887,
-0.03455178067088127,
-0.06269001960754395,
0.0063147274777293205,
-0.015879293903708458,
0.013941691257059574,
-0.06024903804063797,
-0.0017220212612301111,
-0.002189100021496415,
0.019684502854943275,
0.05245216190814972,
-0.007815800607204437,
-0.01562601886689663,
0.010224796831607819,
-0.018336564302444458,
-0.002992468886077404,
-0.040389444679021835,
0.020641911774873734,
-0.0015947887441143394,
-0.04913020506501198,
0.007861582562327385,
-0.003053494496271014,
-0.012643266469240189,
0.021179992705583572,
0.042738065123558044,
0.000003821429800154874,
0.02286151424050331,
-0.006179514806717634,
-0.038584642112255096,
0.038144372403621674,
0.018422439694404602,
-0.0038691321387887,
0.07119470089673996,
-0.02000771276652813,
0.012502663768827915,
0.02574116736650467,
-0.019122397527098656,
-0.02869265340268612,
0.023104095831513405,
0.0029298511799424887,
0.02779003605246544,
-0.004434332717210054,
-0.012380889616906643,
0.02186085470020771,
-0.0469466969370842,
0.01787377893924713,
0.03543029725551605,
-0.042102571576833725,
-0.005513676907867193,
0.06204769015312195,
0.012152878567576408,
0.030251534655690193,
-0.009890167973935604,
0.04008673503994942,
0.026820389553904533,
-0.010416500270366669,
-0.014827894046902657,
0.04377581179141998,
0.007158092688769102,
0.01886684261262417,
0.02498568408191204,
0.005117840599268675,
0.03895266726613045,
0.0431986004114151,
-0.002804107964038849,
0.026216791942715645,
-0.010758408345282078,
-0.018299123272299767,
0.008890021592378616,
0.012735851109027863,
-0.009400276467204094,
0.024327818304300308,
-0.017783796414732933,
0.04808376729488373,
-0.030657723546028137,
0.014345822855830193,
0.012017047964036465,
-0.010502814315259457,
-0.026131659746170044,
0.024876508861780167,
-0.004132202826440334,
0.011662106961011887,
0.008642722852528095,
0.013018302619457245,
-0.02011782117187977,
0.009474316611886024,
0.03594794496893883,
-0.0641559287905693,
-0.007066631689667702,
-0.01897377334535122,
0.007869734428822994,
-0.01499346736818552,
-0.02529410645365715,
0.019054779782891273,
0.009359803982079029,
-0.021816106513142586,
0.003280472941696644,
-0.002480866154655814,
-0.023424595594406128,
-0.04558796435594559,
0.011278684251010418,
0.0883408710360527,
-0.03212584927678108,
0.008141783066093922,
-0.040645841509103775,
0.0368172787129879,
-0.025298088788986206,
-0.022854158654808998
] |
<p>A lot of textbooks and exam boards claim that light incident at exactly the critical angle is transmitted along the media boundary (i.e. at right-angles to the normal), but this seems to violate the principle of reversibility in classical physics. How would a photon or ray travelling in the reverse direction "know" when to enter the higher refracting medium? It can't know, so I conclude that such light is simply reflected?</p>
<p>Is this correct?</p> | 722 | [
-0.031324539333581924,
-0.05737266317009926,
0.01101101003587246,
-0.011201644316315651,
0.012160194106400013,
0.02828482910990715,
-0.0016325284959748387,
-0.0005533061921596527,
-0.016540460288524628,
-0.023697104305028915,
0.03929861634969711,
0.019293218851089478,
0.0010173864429816604,
0.046458903700113297,
0.04579329490661621,
0.02206827513873577,
-0.018109411001205444,
0.015004666522145271,
0.0038529883604496717,
-0.03373024985194206,
-0.03176127374172211,
0.026779331266880035,
-0.007155516650527716,
0.008205324411392212,
-0.0448809415102005,
0.004892100114375353,
0.0021495723631232977,
-0.030807960778474808,
0.05777709558606148,
0.013976621441543102,
0.025118904188275337,
0.01865246333181858,
0.014897715300321579,
0.013243716210126877,
-0.002600958803668618,
-0.009560923092067242,
-0.001502815168350935,
-0.022556636482477188,
-0.02257883921265602,
-0.00974939577281475,
0.006904075853526592,
-0.0027765538543462753,
0.001397368498146534,
0.05122007057070732,
-0.002662349957972765,
0.009031631052494049,
-0.014007458463311195,
-0.01193426176905632,
0.03532354533672333,
-0.0653679147362709,
0.046651650220155716,
-0.014306657947599888,
-0.021243946626782417,
0.013808674179017544,
-0.012671470642089844,
-0.04009214788675308,
0.08599086105823517,
0.0587339848279953,
0.0028801944572478533,
-0.051035866141319275,
0.012419194914400578,
-0.03066638857126236,
-0.055252548307180405,
0.02961783856153488,
-0.0528114028275013,
-0.021175142377614975,
-0.0033332251477986574,
-0.023328371345996857,
0.03904547914862633,
-0.0019013113342225552,
-0.02454276941716671,
0.01110053900629282,
0.028524918481707573,
0.024568520486354828,
0.007314835209399462,
-0.01745588518679142,
0.013065186329185963,
0.03785945847630501,
0.026020603254437447,
0.013904173858463764,
0.009585770778357983,
0.00942546222358942,
0.011130068451166153,
0.05268304795026779,
-0.0025867936201393604,
-0.002035250188782811,
0.052042409777641296,
0.005452783778309822,
0.02704865299165249,
0.07038754224777222,
-0.02652987278997898,
0.032280679792165756,
-0.028686052188277245,
-0.007520680315792561,
-0.03791402652859688,
0.027961483225226402,
-0.019717613235116005,
0.04463111236691475,
-0.02036137320101261,
-0.012852638959884644,
-0.03779803588986397,
-0.02322307601571083,
0.01870195008814335,
0.04648243263363838,
-0.003522101091220975,
-0.03138623386621475,
-0.050095751881599426,
0.017320353537797928,
-0.0021050088107585907,
-0.0006226160912774503,
-0.032018862664699554,
0.0038307493086904287,
-0.028812015429139137,
0.04030880704522133,
0.016202406957745552,
-0.009444784373044968,
0.02735114097595215,
-0.026199018582701683,
0.08425399661064148,
0.04100797325372696,
0.04616040736436844,
0.001454525743611157,
0.0029142112471163273,
-0.020645692944526672,
-0.058531828224658966,
0.039103973656892776,
0.030310209840536118,
-0.008012219332158566,
-0.024660570546984673,
0.023113757371902466,
0.024938540533185005,
-0.02650909125804901,
-0.022645413875579834,
-0.007099485956132412,
0.019190162420272827,
-0.02872808463871479,
-0.10494795441627502,
-0.07733254134654999,
0.013607585802674294,
0.01332707330584526,
-0.0538150779902935,
-0.07438412308692932,
0.025588445365428925,
0.04522343724966049,
0.06646300852298737,
-0.005511559080332518,
0.02865120954811573,
-0.013824144378304482,
0.037126850336790085,
-0.025113970041275024,
0.010358259081840515,
0.0022004118654876947,
0.01146027073264122,
-0.029505593702197075,
0.001902666874229908,
-0.07299266010522842,
-0.0016205422580242157,
0.038644857704639435,
-0.014476551674306393,
-0.04102405533194542,
0.04032628610730171,
-0.055311158299446106,
0.01731962524354458,
0.03611834719777107,
-0.05669942870736122,
-0.041933998465538025,
0.10566610842943192,
0.03039148822426796,
0.016593104228377342,
0.003203402040526271,
0.018284248188138008,
0.034185439348220825,
-0.04823153838515282,
0.015511013567447662,
0.019643515348434448,
-0.0179989505559206,
0.009294203482568264,
-0.013109086081385612,
0.009959046728909016,
0.005115728825330734,
-0.004050121642649174,
-0.010003211908042431,
0.03208983317017555,
0.006579103413969278,
-0.02163991890847683,
0.04423629492521286,
-0.008839147165417671,
-0.018751848489046097,
0.012947429902851582,
-0.052474167197942734,
0.015362787060439587,
0.025228725746273994,
0.059673406183719635,
-0.008301857858896255,
-0.004022635519504547,
-0.007274979259818792,
0.00624585198238492,
0.03579838201403618,
-0.034920211881399155,
-0.018904322758316994,
-0.0053655537776649,
0.02005056105554104,
0.02329961210489273,
-0.008752663619816303,
0.024813994765281677,
0.050298724323511124,
0.04504628852009773,
0.004409635905176401,
0.0005532717332243919,
-0.03432683274149895,
-0.021461112424731255,
0.0007090462022460997,
0.010433400049805641,
0.03858749568462372,
0.00005764941670349799,
-0.008041036315262318,
0.0049165599048137665,
0.013615035451948643,
-0.018545400351285934,
0.021215185523033142,
-0.04101642966270447,
0.03862108290195465,
0.042325086891651154,
0.006763032637536526,
-0.008865210227668285,
0.035792745649814606,
-0.03479856252670288,
0.007755053695291281,
-0.004956969991326332,
-0.022622868418693542,
-0.03905966877937317,
-0.02131185494363308,
0.028868773952126503,
-0.02179183065891266,
-0.07341267913579941,
0.01998835988342762,
0.022290946915745735,
0.028972866013646126,
0.05769388750195503,
0.045911215245723724,
0.008515516296029091,
-0.07306379824876785,
0.0089957844465971,
0.01855739764869213,
0.028536582365632057,
0.01884828694164753,
0.025957191362977028,
0.003862073179334402,
0.01845603808760643,
-0.02552206441760063,
-0.024112217128276825,
-0.006017305422574282,
0.0018533890834078193,
0.020157648250460625,
-0.011243967339396477,
-0.010225193575024605,
0.025209546089172363,
-0.006498105823993683,
0.019831132143735886,
0.007403692230582237,
-0.018376754596829414,
0.014612420462071896,
-0.036879993975162506,
0.01776050217449665,
-0.009156795218586922,
0.021454237401485443,
-0.03677583858370781,
-0.004127493593841791,
0.03825948387384415,
-0.026480436325073242,
0.01088668778538704,
-0.04482267424464226,
-0.021032553166151047,
-0.027631856501102448,
-0.026973159983754158,
0.002564824651926756,
0.02967105805873871,
0.04121784865856171,
-0.03309474512934685,
-0.04179149493575096,
0.011302713304758072,
-0.02870555967092514,
0.005399275105446577,
0.028741363435983658,
0.0004904908128082752,
0.03601381555199623,
-0.035326045006513596,
-0.02899518422782421,
0.0020208971109241247,
-0.01369725912809372,
0.03567402437329292,
-0.013451999984681606,
-0.027123846113681793,
-0.05684363842010498,
-0.038869164884090424,
0.0002713658905122429,
-0.04488076642155647,
-0.012000221759080887,
0.003350565442815423,
0.061007287353277206,
0.004302537068724632,
-0.017832154408097267,
-0.016165299341082573,
-0.029796993359923363,
-0.0444917231798172,
-0.003842815989628434,
-0.025063734501600266,
0.006347188260406256,
-0.04781796783208847,
0.010968141257762909,
0.004568345379084349,
-0.06093105301260948,
-0.009894481860101223,
-0.030069991946220398,
-0.07940524071455002,
0.030995314940810204,
-0.025225438177585602,
0.020498335361480713,
-0.019709009677171707,
0.0031704155262559652,
0.028869779780507088,
0.027428656816482544,
-0.021264826878905296,
-0.01891515962779522,
-0.004622976295650005,
0.003637532936409116,
-0.06454150378704071,
-0.013627137057483196,
0.03569575026631355,
-0.009888600558042526,
0.05350081995129585,
-0.02524358406662941,
0.015467535704374313,
0.0054777199402451515,
0.026197336614131927,
-0.017171788960695267,
0.010594716295599937,
-0.005166124552488327,
-0.00330447219312191,
0.022305289283394814,
0.008486922830343246,
-0.051606614142656326,
0.014266030862927437,
0.0025451206602156162,
0.05249964818358421,
0.021931296214461327,
-0.05181361362338066,
0.06982307881116867,
-0.010736656375229359,
0.031246500089764595,
0.03465462476015091,
0.01338039431720972,
0.007785339839756489,
0.011372317560017109,
0.004862050525844097,
0.022586751729249954,
0.040937405079603195,
-0.011652987450361252,
-0.03621063753962517,
-0.026826921850442886,
0.058674123138189316,
-0.005787819158285856,
-0.005772549659013748,
0.003471313277259469,
0.000731759995687753,
0.04103446006774902,
-0.02200915291905403,
0.00472744507715106,
0.06539487093687057,
0.010958204045891762,
0.014259148389101028,
0.03018144890666008,
-0.07388637959957123,
-0.026491064578294754,
-0.008358974941074848,
0.016849923878908157,
-0.008669634349644184,
0.005039848852902651,
-0.006009956356137991,
0.04406597465276718,
0.058554135262966156,
0.05805040895938873,
0.03787848725914955,
0.02510259300470352,
-0.11548450589179993,
-0.005805571097880602,
-0.029933014884591103,
-0.0015667692059651017,
-0.021824389696121216,
-0.004466811195015907,
0.02482844889163971,
-0.006339647341519594,
-0.03240041807293892,
-0.013351134955883026,
-0.02670707181096077,
-0.049078989773988724,
0.03675447776913643,
-0.02919677272439003,
-0.03603556007146835,
-0.010380545631051064,
0.016146749258041382,
0.015085974708199501,
-0.0387001670897007,
0.009027399122714996,
0.051911886781454086,
-0.04815305024385452,
0.010726588778197765,
0.00036671891575679183,
0.032211899757385254,
0.013348769396543503,
0.04588434845209122,
0.05456005036830902,
0.008041244000196457,
-0.01941380836069584,
0.05986233055591583,
0.0018219825578853488,
0.035143230110406876,
-0.02727806754410267,
-0.021037794649600983,
-0.03330526500940323,
-0.03269040212035179,
-0.029680104926228523,
-0.03222925588488579,
0.052893251180648804,
-0.009928938932716846,
0.0036531449295580387,
0.026010729372501373,
-0.011316855438053608,
-0.03667730093002319,
0.006157638970762491,
-0.041733019053936005,
0.01812807098031044,
-0.014877074398100376,
-0.0327194407582283,
-0.011756762862205505,
-0.025830872356891632,
-0.009639003314077854,
0.016449453309178352,
0.009522798471152782,
-0.023989295586943626,
-0.033993639051914215,
0.005075844936072826,
0.0281009953469038,
0.015746131539344788,
0.05077735707163811,
-0.028637386858463287,
-0.025034256279468536,
0.02939256839454174,
0.001984252594411373,
0.012537205591797829,
0.008794808760285378,
0.03942697122693062,
-0.0025912667624652386,
-0.0029662877786904573,
-0.046974048018455505,
-0.03154997155070305,
0.02491646632552147,
0.035462457686662674,
-0.02841140516102314,
-0.006346803158521652,
-0.07223629951477051,
-0.02619479037821293,
0.004634907469153404,
-0.00009804297587834299,
0.045876648277044296,
-0.03159087896347046,
0.017237571999430656,
-0.01765758916735649,
-0.007345650345087051,
-0.031895723193883896,
0.034148138016462326,
0.03372291848063469,
-0.008847466669976711,
-0.014194532297551632,
-0.0061742584221065044,
-0.03513823822140694,
-0.0050347005017101765,
-0.012746334075927734,
0.040032655000686646,
-0.009896835312247276,
0.030529022216796875,
0.027880696579813957,
0.0019348588539287448,
-0.03303547948598862,
-0.07599656283855438,
0.00038406928069889545,
0.02489306777715683,
0.02011825144290924,
0.07082537561655045,
-0.015497489832341671,
-0.021586010232567787,
0.044715024530887604,
0.038005731999874115,
0.0006238798960112035,
0.017783982679247856,
-0.021614352241158485,
0.0363161601126194,
0.003233053255826235,
-0.002378883073106408,
0.05625305697321892,
0.035991329699754715,
0.006501380819827318,
-0.04909448325634003,
0.00240236334502697,
0.03562174364924431,
-0.025137770920991898,
-0.022597623988986015,
0.0033460468985140324,
0.0058618225157260895,
-0.033653609454631805,
0.06938321888446808,
-0.008446929976344109,
0.006291107274591923,
0.019301224499940872,
-0.035381805151700974,
0.0065919095650315285,
0.004134968854486942,
-0.007632839493453503,
0.014569363556802273,
-0.026969140395522118,
0.011848595924675465,
-0.011278435587882996,
-0.002981803612783551,
-0.0009406585595570505,
-0.026290781795978546,
0.020046986639499664,
0.03730273246765137,
0.001450839452445507,
-0.008619518019258976,
-0.03652132675051689,
-0.014810309745371342,
-0.04716740921139717,
-0.04222733899950981,
0.041831571608781815,
-0.0022461849730461836,
0.00422408664599061,
0.030691584572196007,
-0.03793676570057869,
0.0030453030485659838,
0.012582906521856785,
-0.018339885398745537,
0.017096800729632378,
-0.059381600469350815,
0.020307481288909912,
0.028819458559155464,
0.02517920359969139,
-0.04174189642071724,
-0.050180986523628235,
0.010212292894721031,
0.03452824428677559,
-0.025220109149813652,
0.006296759936958551,
0.004854523576796055,
-0.020036084577441216,
-0.05553172156214714,
0.0001222073333337903,
0.027511360123753548,
-0.028327489271759987,
-0.008053005672991276,
0.03200898319482803,
0.035066623240709305,
0.013673072680830956,
-0.03682291507720947,
-0.04638740047812462,
0.019017959013581276,
-0.016287552192807198,
-0.020596465095877647,
-0.0013611980248242617,
0.05832871422171593,
0.0002627988578751683,
-0.04103357717394829,
-0.008821148425340652,
0.024235332384705544,
0.0199740007519722,
0.010819974355399609,
-0.005008512642234564,
0.02240750752389431,
-0.01150585152208805,
-0.0002074811200145632,
-0.013452020473778248,
0.001112413010559976,
0.023381104692816734,
0.019199425354599953,
0.006546352989971638,
-0.02425459586083889,
-0.05244424194097519,
-0.04639989882707596,
0.05366450175642967,
0.007968823425471783,
0.05537382885813713,
0.001323113334365189,
0.09225854277610779,
-0.0030517210252583027,
-0.03079489804804325,
-0.02504330687224865,
-0.023965509608387947,
-0.0011041865218430758,
-0.008102735504508018,
0.022867612540721893,
0.030295763164758682,
0.01630488783121109,
-0.025996247306466103,
-0.04935899376869202,
-0.042154207825660706,
0.011517269536852837,
0.09514392167329788,
-0.03465656936168671,
0.042277973145246506,
-0.017084386199712753,
0.011498025618493557,
-0.0285808015614748,
-0.006933628581464291,
0.003777426900342107,
0.012051999568939209,
-0.007285445928573608,
0.046161044389009476,
-0.03593791276216507,
-0.00038240558933466673,
-0.007101802621036768,
0.05723288282752037,
-0.006915256381034851,
0.0037869613151997328,
0.017019620165228844,
0.03916918486356735,
0.05702207237482071,
0.017967788502573967,
-0.04035279154777527,
0.044177886098623276,
-0.055028192698955536,
0.02915702760219574,
0.0025686935987323523,
-0.002086897613480687,
0.05227167531847954,
0.013573856092989445,
0.051652342081069946,
-0.035977356135845184,
-0.017002200707793236,
-0.036776959896087646,
0.007555780466645956,
-0.026858802884817123,
0.02507265843451023,
-0.018773015588521957,
-0.005965155083686113,
0.02609935589134693,
-0.011739679612219334,
0.02073047123849392,
0.011307597160339355,
-0.0443529337644577,
-0.01830224134027958,
-0.0318371020257473,
-0.04674675315618515,
0.042926233261823654,
0.018807653337717056,
0.025595229119062424,
0.0323268286883831,
-0.05289991572499275,
0.009423498995602131,
0.03951059281826019,
0.0430273599922657,
0.03373836725950241,
0.03747038170695305,
-0.013796149753034115,
0.04074763506650925,
-0.01951073482632637,
0.007925373502075672,
0.12838208675384521,
0.0671801045536995,
-0.025500977411866188,
-0.061561502516269684,
0.03245488181710243,
-0.04920453205704689,
0.0485643669962883,
-0.03484930098056793,
0.00394256878644228,
-0.029654670506715775,
0.00806282740086317,
0.04707932472229004,
0.04738291725516319,
0.012876946479082108,
-0.01352057233452797,
0.01713409088551998,
-0.05648631602525711,
-0.054729171097278595,
0.012979176826775074,
0.017849627882242203,
-0.004366087261587381,
0.027728721499443054,
-0.00621290085837245,
-0.0019788460340350866,
-0.03895707428455353,
0.0015660463832318783,
0.010859324596822262,
-0.040512215346097946,
0.03753523901104927,
0.013374071568250656,
-0.017717566341161728,
-0.00022952219296712428,
0.03800011798739433,
-0.022293178364634514,
-0.03929375857114792,
0.043367814272642136,
0.037806734442710876,
0.012842893600463867,
0.018459437415003777,
0.0019262125715613365,
0.022562799975275993,
0.022505750879645348,
0.017439600080251694,
0.03397029638290405,
-0.053563471883535385,
-0.025039177387952805,
0.0024839872494339943,
0.04037809744477272,
-0.05897720158100128,
-0.004689784720540047,
-0.0060630314983427525,
-0.03872518986463547,
0.02576032467186451,
-0.039316415786743164,
-0.016301019117236137,
0.0031588729470968246,
-0.0039582401514053345,
0.004430168308317661,
-0.01944061554968357,
0.017756391316652298,
0.0263893473893404,
0.006683980114758015,
0.014717058278620243,
-0.010959991253912449,
-0.03760400786995888,
-0.001031208666972816,
-0.001443023793399334,
0.025466954335570335,
-0.023890463635325432,
-0.05545738711953163,
-0.05881357938051224,
-0.0016090767458081245,
-0.044910676777362823,
-0.0007387837977148592,
0.014239940792322159,
0.020913217216730118,
0.01630467362701893,
0.0041517699137330055,
-0.02969914861023426,
-0.056713737547397614,
-0.06914284080266953,
0.020198620855808258,
-0.019867492839694023,
0.00015385673032142222,
-0.037415869534015656,
0.0026596663519740105,
0.020420484244823456,
0.0800798311829567,
-0.005953976418823004,
-0.023829780519008636,
0.01988956145942211,
-0.00441147992387414,
0.031052621081471443,
0.0019329068018123507,
-0.03470771759748459,
0.02135605551302433,
-0.027005046606063843,
-0.01835222728550434,
0.0031109813135117292,
0.023887893185019493,
0.03212619572877884,
0.019933288916945457,
-0.007313643582165241,
0.03463434800505638,
-0.02432417869567871,
0.0028397475834935904,
-0.008094100281596184,
-0.010829242877662182,
0.025586741045117378,
-0.0017935576615855098,
0.009413582272827625,
-0.019909478724002838,
-0.013474538922309875,
-0.020725583657622337,
-0.005143351387232542,
-0.03890005499124527,
-0.0019980163779109716,
0.01193278655409813,
-0.02303355373442173,
-0.023785607889294624,
0.019983883947134018,
-0.003865657141432166,
-0.02646457962691784,
-0.0072892801836133,
0.0030351821333169937,
0.020746903494000435,
-0.008547225035727024,
-0.03370630741119385,
0.0517670139670372,
0.02560553513467312,
-0.011909645050764084,
-0.0035383328795433044,
0.045178867876529694,
-0.008405866101384163,
-0.012303480878472328,
-0.002357195597141981,
0.015758993104100227,
0.028742974624037743,
-0.03230132907629013,
-0.04240342602133751,
0.05186218395829201,
-0.021751768887043,
-0.031738195568323135,
0.024521008133888245,
0.010815490037202835,
0.019857173785567284,
0.024253791198134422,
0.003284648060798645,
0.03522998467087746,
0.05926485359668732,
0.015841711312532425,
-0.03047712706029415,
0.009329537861049175,
-0.021810539066791534,
0.029761048033833504,
-0.013127187266945839,
0.04529823362827301,
-0.049121227115392685,
-0.015114421024918556,
0.037915680557489395,
-0.003618803806602955,
-0.009173240512609482,
-0.0031297216191887856,
0.016249708831310272,
-0.04229277744889259,
-0.012718734331429005,
0.03405366092920303,
-0.01552126370370388,
0.01774878427386284,
0.06371287256479263,
-0.015185055322945118,
0.057482630014419556,
0.05161067098379135,
-0.02458997815847397,
-0.09486191719770432,
-0.005998208187520504,
0.03034469671547413,
0.012103753164410591,
0.011891125701367855,
-0.03400183469057083,
0.029301045462489128,
0.054032523185014725,
-0.07102716714143753,
0.02430862747132778,
-0.011399179697036743,
-0.031849950551986694,
-0.03944804146885872,
0.030939679592847824,
0.0062581575475633144,
0.0638696700334549,
0.010679220780730247,
-0.006310196127742529,
0.01229841262102127,
-0.004090047907084227,
-0.044660795480012894,
-0.0234226044267416,
0.003209020011126995,
0.03314824402332306,
-0.029569555073976517,
0.004324452485889196,
0.06204912066459656,
0.007135006599128246,
-0.036355070769786835,
0.020706212148070335,
-0.01208224892616272,
0.0221230611205101,
0.016982514411211014,
-0.013631714507937431,
0.006334007252007723,
0.027368078008294106,
0.012367906980216503,
-0.01853211782872677,
-0.021332629024982452,
0.006442380137741566,
0.06416093558073044,
0.004012905061244965,
-0.029337432235479355,
-0.007109274622052908,
0.013835492543876171,
-0.056528519839048386,
-0.02441580221056938,
0.004674636758863926,
-0.0361395925283432,
0.02262924052774906,
-0.0011368734994903207,
0.004261419642716646,
0.0015114303678274155,
-0.007098978850990534,
-0.0008297032909467816,
-0.05793001130223274,
-0.03371666371822357,
0.012448308058083057,
0.023679127916693687,
-0.033945176750421524,
-0.0015551320975646377,
-0.02388906106352806,
-0.04765797406435013,
0.0572819858789444,
-0.02030874229967594,
0.016444526612758636,
-0.02153843641281128,
-0.028916791081428528,
-0.018543843179941177,
-0.016361767426133156,
-0.00276515306904912,
-0.025990447029471397,
-0.03899109363555908,
0.032275404781103134,
0.011560202576220036,
0.015723248943686485,
-0.012341228313744068,
-0.04871894419193268,
-0.039378292858600616,
-0.06317474693059921,
0.023494942113757133,
0.00813639909029007,
0.004246147815138102,
-0.045808810740709305,
-0.013526326976716518,
-0.04865504056215286,
0.0010587102733552456,
0.10111325234174728,
0.030210714787244797,
-0.011978504247963428,
-0.025553137063980103,
0.007750977296382189,
0.0390959195792675,
-0.042444858700037,
-0.015503267757594585,
-0.00457676500082016,
-0.04309187829494476,
-0.005471347365528345,
0.007470920216292143,
-0.010705474764108658,
-0.005315091926604509,
-0.01633712649345398,
-0.024272184818983078,
0.009481891989707947,
0.007528539281338453,
0.001709019998088479,
0.021649107336997986,
0.011386499740183353,
0.007946653291583061,
0.0766899436712265,
-0.016812602058053017,
0.03405362740159035,
0.046658892184495926,
-0.04532957449555397,
-0.06322380155324936,
0.00353905837982893,
-0.05041146278381348,
-0.02601802349090576,
-0.014680534601211548,
0.03050159104168415,
0.026955096051096916,
-0.0019594549667090178,
-0.012620190158486366,
0.05549022927880287,
-0.07213850319385529,
-0.014834091998636723,
0.050617508590221405,
-0.013799739070236683,
-0.007794173434376717,
-0.025564657524228096,
0.03151368349790573,
0.05153212323784828,
0.004891820251941681,
0.01165416743606329,
0.05301530286669731,
0.00569858169183135,
-0.0002572391531430185,
0.009430515579879284,
0.06393367797136307,
0.008719787001609802,
0.027777763083577156,
0.001453087548725307,
0.047861624509096146,
-0.01843743957579136,
0.0017881676321849227,
0.03299309313297272,
0.0029011545702815056,
-0.00032660565921105444,
0.04736657813191414,
0.024286523461341858,
0.05080978572368622,
-0.006866468582302332,
0.033518679440021515,
-0.018123330548405647,
0.022928765043616295,
0.00814145803451538,
-0.00839417427778244,
0.06767614930868149,
0.012857163324952126,
-0.0037786290049552917,
-0.020029745995998383,
-0.025106113404035568,
-0.02993941120803356,
0.03210613504052162,
-0.016142962500452995,
0.00628287810832262,
-0.021512340754270554,
0.005009735934436321,
0.02835354022681713,
-0.05525980517268181,
-0.007903658784925938,
-0.04759872704744339,
0.004248007200658321,
0.01056369487196207,
0.03760357201099396,
0.04834751784801483,
0.044498492032289505,
-0.010432522743940353,
0.03596758097410202,
-0.09426330775022507,
-0.010073631070554256,
0.005617609713226557,
0.03909912332892418,
0.005736561492085457,
-0.006650410592556
] |
<p>RHIC has been the dominant player in heavy ion physics, producing tantalizing evidence in support of the entropy/viscocity formula from AdS/CFT.
What's the potential of the LHC's Pb ion collsions? What can it achieve which RHIC can't? What measurements will be improved?</p> | 2,046 | [
-0.02413487248122692,
-0.022792570292949677,
-0.016577158123254776,
-0.042938731610774994,
0.046638764441013336,
0.03650054335594177,
-0.015377952717244625,
-0.008863280527293682,
-0.0007369749364443123,
-0.03665432706475258,
0.03588434308767319,
0.05000346153974533,
0.01963222771883011,
0.04072630777955055,
0.0065582748502492905,
-0.005262698978185654,
0.031333696097135544,
-0.030950279906392097,
0.016757026314735413,
-0.02284809947013855,
0.0355815626680851,
0.01717890053987503,
0.014231675304472446,
0.05006929114460945,
-0.0038372271228581667,
0.011791571974754333,
-0.015612466260790825,
0.001102045876905322,
0.016179829835891724,
0.029882464557886124,
-0.011251483112573624,
-0.029345408082008362,
0.037096407264471054,
-0.013775350525975227,
0.034947559237480164,
0.009224877692759037,
-0.015671057626605034,
-0.02988475374877453,
-0.03761567547917366,
0.014025826938450336,
-0.065416619181633,
-0.031733911484479904,
0.0013725620228797197,
0.05355909839272499,
0.012664158828556538,
-0.006282523274421692,
-0.0046599549241364,
0.016890428960323334,
0.06111506372690201,
-0.09081447869539261,
0.014508707448840141,
0.015618471428751945,
0.03431076183915138,
0.01515168882906437,
-0.02026723138988018,
-0.032100748270750046,
0.030102243646979332,
0.07974229007959366,
-0.00010602017573546618,
-0.059575945138931274,
-0.013029110617935658,
0.01472732424736023,
0.022952372208237648,
0.00023720318858977407,
-0.027149096131324768,
0.03551048785448074,
0.016252491623163223,
-0.0013763708993792534,
0.012312815524637699,
-0.025704234838485718,
0.044012781232595444,
0.03308138996362686,
-0.010791304521262646,
0.007721147034317255,
0.028413040563464165,
-0.016437912359833717,
-0.01585017330944538,
-0.009568951092660427,
0.022648172453045845,
0.044619955122470856,
-0.032755278050899506,
0.002952040871605277,
0.007244487293064594,
0.05449065566062927,
-0.00039871613262221217,
-0.024887243285775185,
0.0627422109246254,
-0.04446667060256004,
-0.022952238097786903,
0.018524158746004105,
-0.020228184759616852,
0.02319394424557686,
0.04128824919462204,
0.004240828566253185,
-0.041203442960977554,
0.021501081064343452,
-0.016278594732284546,
0.059200506657361984,
-0.04144122079014778,
-0.03878449648618698,
0.033143483102321625,
-0.0032867547124624252,
-0.012101216241717339,
0.06684691458940506,
-0.012681917287409306,
-0.007278787437826395,
-0.007449209224432707,
0.0060570682398974895,
-0.03966637700796127,
-0.03248470649123192,
-0.05786861851811409,
0.0026712059043347836,
0.008848991245031357,
-0.006204893812537193,
0.012459315359592438,
-0.07455216348171234,
-0.020948292687535286,
0.005531794391572475,
0.04895057529211044,
0.06217198818922043,
0.04314413294196129,
-0.005501586478203535,
0.02319277450442314,
-0.03762088716030121,
-0.058978524059057236,
0.00784351211041212,
0.05066915974020958,
-0.009139837697148323,
-0.01642058603465557,
0.039378032088279724,
-0.03824978321790695,
0.019844433292746544,
-0.004837528802454472,
-0.0045632487162947655,
0.044309522956609726,
-0.03087714873254299,
-0.08479022979736328,
-0.06127411872148514,
0.06834089756011963,
0.014974910765886307,
-0.059948209673166275,
-0.05997425317764282,
-0.011073006317019463,
-0.0026554770302027464,
0.06382643431425095,
-0.026036923751235008,
-0.0013612910406664014,
0.022591397166252136,
0.05051952600479126,
0.023566769436001778,
-0.04550345987081528,
-0.02133108675479889,
0.009178461506962776,
0.000997478375211358,
0.0039168163202703,
-0.08077339828014374,
-0.016167936846613884,
0.0487820990383625,
-0.0030236036982387304,
-0.01441124640405178,
0.03603670746088028,
0.007296935189515352,
-0.009490118362009525,
0.0013136103516444564,
-0.04045138880610466,
-0.02463286556303501,
0.05548389256000519,
-0.02083365060389042,
0.04164247587323189,
0.023798149079084396,
0.031069302931427956,
0.017688840627670288,
0.02701544016599655,
-0.017845692113041878,
0.025834854692220688,
-0.023963486775755882,
-0.03754035383462906,
0.023191167041659355,
-0.015110061503946781,
-0.02249191515147686,
-0.014644295908510685,
-0.023232487961649895,
-0.05009641870856285,
-0.019306572154164314,
-0.03160638362169266,
0.02213890664279461,
-0.021091623231768608,
-0.006734031252563,
0.028923561796545982,
-0.06249905750155449,
-0.06775031238794327,
-0.07283344864845276,
0.011367331258952618,
0.011138960719108582,
-0.0035578315146267414,
0.06912161409854889,
-0.0018640909111127257,
0.012379465624690056,
0.025679951533675194,
-0.021095307543873787,
-0.02186109870672226,
0.057262126356363297,
0.03716014325618744,
0.004717221949249506,
0.02135375328361988,
0.04145708680152893,
0.024779411032795906,
0.0001375216816086322,
0.02161421999335289,
-0.017517071217298508,
-0.08351995050907135,
-0.016156205907464027,
0.010041766799986362,
0.013820513151586056,
0.000036991645174566656,
-0.020150132477283478,
0.012030021287500858,
-0.05696165934205055,
-0.033916834741830826,
0.007172692567110062,
0.00770049262791872,
0.08617966622114182,
0.019547253847122192,
0.02690351940691471,
-0.0034906980581581593,
0.030910978093743324,
0.013383306562900543,
0.013562390580773354,
0.019631996750831604,
-0.006052454933524132,
-0.05183300003409386,
-0.005051836371421814,
0.005762994289398193,
0.07515648007392883,
-0.04768873378634453,
0.04446478188037872,
0.022879987955093384,
0.01131923496723175,
0.00056376465363428,
-0.00830700621008873,
-0.040993548929691315,
-0.023020636290311813,
0.035581912845373154,
0.013328504748642445,
-0.010842176154255867,
-0.03337855264544487,
0.050989989191293716,
-0.021202828735113144,
-0.01720362715423107,
-0.014367716386914253,
-0.03545384481549263,
0.0010042664362117648,
-0.0011156039545312524,
-0.0008539840346202254,
0.005560507532209158,
-0.06690376996994019,
0.018027568235993385,
-0.003539761295542121,
0.0159421619027853,
0.009978286921977997,
-0.008300486020743847,
0.008743789047002792,
-0.0028375638648867607,
-0.004579655360430479,
-0.011277608573436737,
0.0038982790429145098,
-0.027262551710009575,
-0.03227698802947998,
0.0362844243645668,
-0.05045686662197113,
0.05837343633174896,
-0.026073278859257698,
0.0024924029130488634,
-0.023409908637404442,
0.03377819061279297,
0.018296178430318832,
-0.00389755773358047,
0.003944248892366886,
-0.027730204164981842,
-0.014150401577353477,
0.0533844418823719,
0.008707625791430473,
-0.042985718697309494,
0.07540556788444519,
-0.04999028146266937,
0.011413137428462505,
-0.016204454004764557,
-0.005330276675522327,
0.026510072872042656,
0.008791076950728893,
0.025543002411723137,
0.02138466201722622,
0.004999874625355005,
-0.03520575538277626,
-0.005669764243066311,
0.0407564714550972,
0.0526728518307209,
-0.06365996599197388,
0.012586493976414204,
-0.006284673232585192,
-0.011042512953281403,
-0.020573286339640617,
-0.011924904771149158,
-0.015603369101881981,
0.020801139995455742,
0.005056204739958048,
-0.000796013162471354,
-0.00797534454613924,
-0.015058578923344612,
0.0586739107966423,
0.004012912977486849,
-0.0388980507850647,
-0.011923194862902164,
-0.022388217970728874,
-0.00898537877947092,
0.03386237472295761,
-0.01932624541223049,
0.00013877805031370372,
-0.003091340884566307,
-0.030747264623641968,
0.0635821521282196,
0.015625152736902237,
-0.04634207859635353,
-0.004845892079174519,
-0.03279254585504532,
-0.04659031331539154,
-0.025664815679192543,
0.045121341943740845,
0.022265948355197906,
-0.011241128668189049,
-0.01718059554696083,
0.007121427450329065,
0.012589552439749241,
0.03834483027458191,
0.04492064192891121,
-0.024683013558387756,
0.04110917076468468,
0.02180374041199684,
0.014381096698343754,
-0.011658329516649246,
0.012757289223372936,
-0.03114289417862892,
0.013315574266016483,
0.009257589466869831,
0.014425812289118767,
0.034845829010009766,
-0.0461270809173584,
0.039657112210989,
0.024983441457152367,
0.026000168174505234,
-0.012617867439985275,
0.008932582102715969,
-0.05710892751812935,
-0.013377764262259007,
-0.023490138351917267,
0.012129656039178371,
0.012667910195887089,
0.015049646608531475,
-0.0034876130521297455,
0.013568584807217121,
0.04823870584368706,
-0.026208285242319107,
-0.020612623542547226,
-0.03980034217238426,
-0.04134081304073334,
0.02425788901746273,
-0.0153203085064888,
-0.017643725499510765,
0.0024911377113312483,
0.014627540484070778,
-0.00934306625276804,
-0.03757793828845024,
-0.011613146401941776,
0.010787907056510448,
-0.08501772582530975,
0.028266331180930138,
-0.042108599096536636,
0.034186799079179764,
0.02462155558168888,
0.04542539641261101,
0.01388455182313919,
-0.003866138868033886,
0.009694994427263737,
-0.03722608834505081,
-0.09351292997598648,
0.02987179532647133,
-0.039035599678754807,
0.026608718559145927,
-0.021290147677063942,
-0.012235774658620358,
-0.004735182039439678,
-0.03266045078635216,
-0.03288303688168526,
-0.039576608687639236,
0.032053492963314056,
-0.0085501903668046,
0.006933604832738638,
-0.04691789299249649,
-0.03782999888062477,
-0.011317282915115356,
0.025881452485919,
0.04532577097415924,
-0.02325752191245556,
0.057278551161289215,
0.002452337881550193,
-0.027395857498049736,
0.00170590088237077,
-0.016933878883719444,
0.046590354293584824,
-0.026883795857429504,
0.08433829247951508,
0.014283152297139168,
-0.006253782659769058,
-0.03655752167105675,
0.0025717243552207947,
0.02671118825674057,
0.025247592478990555,
-0.01019683200865984,
-0.03637129068374634,
-0.0017837678315117955,
-0.06689152121543884,
-0.011379982344806194,
-0.015029335394501686,
0.044198259711265564,
0.0328887514770031,
-0.005898203235119581,
0.04900798946619034,
-0.005954383406788111,
-0.030101368203759193,
0.018046462908387184,
0.04421453922986984,
0.03184312954545021,
-0.04067598283290863,
-0.03731992468237877,
-0.028680577874183655,
0.005474751349538565,
-0.0026027869898825884,
0.032911449670791626,
-0.006747912615537643,
-0.010562676936388016,
0.045889951288700104,
0.01373816467821598,
0.014336757361888885,
-0.06705766171216965,
-0.018077095970511436,
0.0011783047812059522,
-0.00023547234013676643,
-0.01572565920650959,
0.01838529482483864,
0.004952825605869293,
0.02440521866083145,
0.024484198540449142,
0.007176320534199476,
0.01194755733013153,
-0.09196338802576065,
-0.0032015061005949974,
0.0177947785705328,
0.05736956745386124,
-0.009218459017574787,
-0.012324506416916847,
-0.024348611012101173,
0.011761773377656937,
0.07945661246776581,
-0.022363701835274696,
0.008884459733963013,
-0.00127338245511055,
0.03138041868805885,
-0.011064949445426464,
0.0039007968734949827,
-0.040522441267967224,
0.04639759287238121,
0.014603945426642895,
-0.028780462220311165,
-0.01174441073089838,
-0.009129013866186142,
0.002782703610137105,
0.06141934543848038,
0.007918505929410458,
0.04487413167953491,
0.02059699036180973,
0.06237785145640373,
-0.007118909619748592,
0.011147893965244293,
0.0037914218846708536,
-0.07458766549825668,
-0.012861362658441067,
-0.013851245865225792,
-0.025742780417203903,
0.0037020400632172823,
-0.0014121616259217262,
-0.049195483326911926,
0.010344456881284714,
0.013488473370671272,
-0.004277811385691166,
0.004190539941191673,
-0.053619250655174255,
0.024289174005389214,
0.0450209341943264,
0.01028054766356945,
0.030468910932540894,
-0.008076446130871773,
0.007071522064507008,
0.006865649949759245,
0.0030037774704396725,
0.07262678444385529,
0.03302522376179695,
0.032346781343221664,
0.030865442007780075,
-0.007970358245074749,
-0.03690733760595322,
0.08338631689548492,
-0.0071635739877820015,
0.021390043199062347,
0.00484837219119072,
-0.03545311838388443,
-0.016334040090441704,
0.016354035586118698,
0.007498421240597963,
-0.016954496502876282,
0.037812232971191406,
0.007338378112763166,
-0.018523424863815308,
-0.020924659445881844,
0.00469062477350235,
-0.010296213440597057,
0.016423257067799568,
-0.01698444038629532,
-0.024417048320174217,
0.050103697925806046,
-0.014209735207259655,
0.025522513315081596,
0.02002396248281002,
-0.01913011074066162,
0.070644311606884,
0.011130291037261486,
-0.004195728804916143,
0.004306028131395578,
-0.05774766951799393,
0.007452742196619511,
-0.029882626608014107,
0.007026018109172583,
-0.011140646412968636,
-0.026882443577051163,
0.042504407465457916,
-0.015034079551696777,
0.00742057990282774,
-0.07446246594190598,
-0.029642734676599503,
-0.0030588798690587282,
-0.0011621288722380996,
-0.03218953683972359,
-0.017661387100815773,
0.020551009103655815,
-0.010090305469930172,
-0.007650901097804308,
-0.0695539116859436,
0.07142533361911774,
-0.04075132682919502,
0.003635158995166421,
-0.002579848049208522,
0.02849799394607544,
0.02523765340447426,
0.005592347122728825,
-0.04192744567990303,
0.021210120990872383,
-0.009150112047791481,
0.02898603491485119,
-0.029020681977272034,
0.03370141610503197,
0.008883822709321976,
-0.037722472101449966,
0.03481810912489891,
0.004501751624047756,
0.034953389316797256,
0.0006344116409309208,
0.033345676958560944,
0.02682175487279892,
-0.0153731107711792,
0.014358827844262123,
0.013818565756082535,
0.015042652375996113,
-0.009400447830557823,
0.043192796409130096,
-0.018452584743499756,
-0.00925114843994379,
0.00609514769166708,
-0.024747401475906372,
0.03297927975654602,
0.04761086404323578,
0.0025752040091902018,
-0.021874547004699707,
0.0018191919662058353,
0.01059152651578188,
0.0006372756906785071,
-0.0221244003623724,
-0.01379503682255745,
0.013531334698200226,
-0.03936208039522171,
0.01390375941991806,
0.005961005575954914,
-0.02907002530992031,
-0.04560369253158569,
-0.06088237091898918,
-0.045170340687036514,
-0.0170028917491436,
0.05168953537940979,
-0.008451185189187527,
0.051937658339738846,
-0.009252585470676422,
-0.03608810156583786,
0.014269039034843445,
-0.021312372758984566,
0.008797488175332546,
0.01692453771829605,
0.0009774534264579415,
0.009878928773105145,
-0.02489849179983139,
-0.011052846908569336,
-0.006125209387391806,
0.048902928829193115,
0.0031360911671072245,
-0.029219016432762146,
0.05545850470662117,
0.03944963961839676,
0.017362097278237343,
-0.02198919653892517,
-0.037228260189294815,
0.057945460081100464,
-0.049168698489665985,
-0.02803776226937771,
-0.009163259528577328,
0.006856790278106928,
0.0513903871178627,
-0.02151782624423504,
0.025200270116329193,
0.024040451273322105,
-0.023016007617115974,
-0.05606549233198166,
0.0113905668258667,
0.03894598037004471,
0.0010823562042787671,
-0.0009862625738605857,
-0.01859353296458721,
0.007765906862914562,
0.02435874752700329,
0.0033991073723882437,
0.016108570620417595,
-0.08288857340812683,
0.009959111921489239,
0.013642599806189537,
-0.03798740357160568,
0.04202727973461151,
0.018457751721143723,
-0.0008452645852230489,
0.030822675675153732,
0.004173805937170982,
0.03237297013401985,
0.032155588269233704,
0.007838231511414051,
0.012454225681722164,
0.015254642814397812,
-0.03356127068400383,
0.045187827199697495,
-0.022729327902197838,
0.007898588664829731,
0.13800247013568878,
0.029589170590043068,
0.0013374016853049397,
-0.07665503025054932,
-0.002261197427287698,
-0.0009787308517843485,
0.018585965037345886,
-0.024105949327349663,
0.018353627994656563,
0.012372597120702267,
-0.003448090050369501,
0.029342664405703545,
0.03628118708729744,
0.009900125674903393,
0.01379823125898838,
0.024658380076289177,
-0.0677349865436554,
-0.022527147084474564,
-0.0022067083045840263,
0.02311050146818161,
-0.03217732161283493,
-0.00983849260956049,
-0.029304778203368187,
-0.012193134054541588,
-0.012594922445714474,
0.0001624729484319687,
-0.03916575387120247,
-0.04887528717517853,
-0.00290873390622437,
-0.00104679842479527,
0.019334465265274048,
0.013888189569115639,
0.001094246283173561,
0.012519774958491325,
-0.0049070087261497974,
-0.013146888464689255,
-0.004692838527262211,
0.02550259605050087,
-0.013122360222041607,
0.010145663283765316,
0.04880125820636749,
-0.01329726167023182,
-0.047178614884614944,
0.048598211258649826,
-0.03596343845129013,
-0.0355471670627594,
0.021163763478398323,
0.030726326629519463,
-0.0488656684756279,
-0.004702412057667971,
-0.037556763738393784,
-0.003023180877789855,
-0.023494290187954903,
-0.016111940145492554,
-0.03266897797584534,
0.015187342651188374,
0.015622388571500778,
-0.005253347102552652,
-0.01517334021627903,
-0.032145850360393524,
0.018636206164956093,
-0.03560933843255043,
0.032344087958335876,
-0.0197452399879694,
0.01431581936776638,
0.013367332518100739,
0.006108393426984549,
0.06660208851099014,
-0.01148984394967556,
0.0034402012825012207,
-0.04911136254668236,
0.0647626519203186,
-0.06167934834957123,
-0.005908952094614506,
0.009422187693417072,
0.008332652039825916,
0.02801533043384552,
0.023889780044555664,
-0.008826253935694695,
-0.055723778903484344,
-0.0286217350512743,
0.05223367363214493,
-0.02236577868461609,
-0.008306339383125305,
-0.037280160933732986,
0.02507544308900833,
0.027216091752052307,
0.04204711690545082,
-0.016559014096856117,
-0.011248830705881119,
-0.015024562366306782,
0.039327770471572876,
-0.025646736845374107,
0.0026012693997472525,
-0.0077177551575005054,
-0.00791958812624216,
-0.039715416729450226,
0.007831431925296783,
0.003974586259573698,
0.012573651038110256,
0.019273977726697922,
-0.017230046913027763,
-0.005557139404118061,
-0.001786775072105229,
-0.030948596075177193,
0.03633854538202286,
0.050781428813934326,
-0.02848641388118267,
-0.053975481539964676,
-0.000085530846263282,
0.03702659159898758,
-0.02305874228477478,
-0.036824461072683334,
-0.040220700204372406,
-0.008634667843580246,
0.01373705081641674,
0.025939011946320534,
-0.03885797783732414,
0.030170463025569916,
0.00968337245285511,
-0.005325790960341692,
-0.048118866980075836,
0.013205043971538544,
-0.052369046956300735,
0.015810707584023476,
-0.020029772073030472,
0.025107158347964287,
0.01882091723382473,
0.017376404255628586,
-0.029585381969809532,
-0.03668254613876343,
-0.002715102629736066,
-0.03360925242304802,
-0.013037844561040401,
0.004124680999666452,
0.010807506740093231,
0.02672616019845009,
0.03252951055765152,
0.013705442659556866,
-0.04319888725876808,
0.025745859369635582,
0.008617701940238476,
-0.058881454169750214,
0.020816966891288757,
-0.00404516514390707,
0.011840350925922394,
0.04444152116775513,
0.014017906971275806,
-0.03125486150383949,
0.011328572407364845,
-0.030361700803041458,
-0.028276726603507996,
-0.008497267961502075,
-0.03586120530962944,
-0.007144102361053228,
0.025204382836818695,
0.0199078731238842,
-0.03305098041892052,
0.00478957686573267,
0.049571484327316284,
0.06165460869669914,
-0.012021164409816265,
0.011374128051102161,
-0.04433400183916092,
-0.010256660170853138,
0.04030581936240196,
0.0067980545572936535,
-0.018582234159111977,
0.015939297154545784,
0.023196203634142876,
-0.01294823456555605,
0.01142046321183443,
0.02435752935707569,
-0.005561503116041422,
-0.09647299349308014,
-0.007897958159446716,
0.004185763653367758,
-0.027541495859622955,
0.010941463522613049,
-0.04485291987657547,
0.029170801863074303,
0.014979742467403412,
-0.057692695409059525,
0.04249143600463867,
-0.03334410488605499,
-0.045734506100416183,
-0.02957092598080635,
0.007059508003294468,
-0.019533440470695496,
0.07713036984205246,
0.03315333276987076,
0.044602490961551666,
-0.001676106359809637,
0.007486740127205849,
0.039241280406713486,
-0.008716464042663574,
0.004607134032994509,
0.015496687032282352,
-0.0007719973800703883,
0.0003129232209175825,
0.08178047090768814,
0.0012599629117175937,
-0.014173122122883797,
0.0057319593615829945,
0.02775348350405693,
0.010639273561537266,
-0.003663531504571438,
-0.00738363666459918,
-0.014881225302815437,
0.05915042757987976,
0.024529647082090378,
-0.014778776094317436,
-0.01695835590362549,
-0.010681359097361565,
0.004302217625081539,
0.029567033052444458,
-0.008232936263084412,
0.018212929368019104,
0.015304322354495525,
0.007738352753221989,
0.011315329000353813,
0.03192054480314255,
-0.007898542098701,
-0.004494864959269762,
-0.0015250376891344786,
-0.012280745431780815,
0.013997401110827923,
0.004871007055044174,
0.021488353610038757,
-0.026775198057293892,
0.004287916701287031,
0.011173768900334835,
-0.008076387457549572,
-0.0160991083830595,
0.00665833055973053,
-0.017134634777903557,
0.010819834657013416,
0.006746831350028515,
0.03736061975359917,
-0.010249622166156769,
-0.04334086924791336,
-0.034035757184028625,
0.030700670555233955,
0.03701344132423401,
0.010251328349113464,
-0.03391636535525322,
-0.03143195062875748,
0.06651540100574493,
0.008850892074406147,
0.02601172775030136,
0.007840997539460659,
-0.030206112191081047,
-0.0529145747423172,
-0.05260755866765976,
0.02410455234348774,
-0.017997363582253456,
0.0032924427650868893,
-0.007497704587876797,
-0.047457676380872726,
0.007606515195220709,
0.004588785581290722,
0.07901323586702347,
-0.02566179819405079,
0.00387088512070477,
0.020136399194598198,
0.0029615829698741436,
-0.006448462605476379,
-0.004511399194598198,
-0.02808043360710144,
-0.010268528014421463,
-0.0008444445556961,
-0.039001598954200745,
-0.009168718010187149,
0.003371761180460453,
0.05022246390581131,
0.03861785680055618,
0.015037559904158115,
0.0037659115623682737,
-0.01227887999266386,
-0.03592582419514656,
0.08304663747549057,
-0.010476452298462391,
0.013666223734617233,
0.04309885576367378,
-0.019442319869995117,
0.046487998217344284,
-0.01257295161485672,
-0.0026461060624569654,
0.015745459124445915,
0.057282835245132446,
-0.02009829506278038,
-0.049082573503255844,
0.005499932449311018,
0.019740121439099312,
-0.008613833226263523,
-0.024302901700139046,
0.02723555453121662,
0.01077939011156559,
-0.06921759247779846,
-0.02843608893454075,
0.044436462223529816,
0.003338131820783019,
0.023487970232963562,
0.0026386312674731016,
-0.009458650834858418,
0.026591680943965912,
0.01041927095502615,
-0.025880077853798866,
0.05207999423146248,
0.05888869985938072,
0.02275928296148777,
0.0205154400318861,
0.021639011800289154,
-0.0035816477611660957,
-0.001813265378586948,
0.03590008243918419,
0.04941261559724808,
-0.009078570641577244,
-0.02996974252164364,
0.008076461032032967,
-0.05730156973004341,
0.029138809069991112,
0.04461554437875748,
-0.02162567712366581,
0.1030084639787674,
-0.05642344430088997,
-0.010860763490200043,
-0.037700146436691284,
-0.06435874104499817,
0.011857346631586552,
0.006664755754172802,
-0.028451723977923393,
0.06229056790471077,
-0.005273849703371525,
-0.03463421016931534,
-0.008829018101096153,
0.0076597933657467365,
0.0038544628769159317,
-0.02885681949555874,
-0.021172715350985527,
0.002402340527623892,
0.04061049222946167,
-0.0315571203827858,
-0.010003337636590004,
-0.031007155776023865,
-0.011970007792115211,
-0.0013845700304955244,
0.04182879254221916,
0.030384885147213936,
0.006306331139057875,
-0.019153712317347527,
-0.03664536401629448,
0.022133521735668182,
0.0028316224925220013,
0.037115078419446945,
-0.03348054736852646,
0.02629566565155983,
-0.029203664511442184,
0.01559517253190279
] |
<p>I don't know how this "paradox" can be solved. I'm given the following system: A permanent magnet with a magnetic field given by ($\hat{a}$ are unit vectors in the x and y directions)</p>
<p>$$\vec{H}=H_0\hat{a}_y$$</p>
<p>and a parallel plane capacitor with an electric field</p>
<p>$$\vec{E}=E_0\hat{a}_x$$</p>
<p>Poynting's vector is given by:</p>
<p>$$\vec{S}=\vec{E}\times\vec{H}=H_0E_0\hat{a}_z \neq 0$$</p>
<p>The funny part comes when the professor told that in a system like that "clearly" there is not propagation (wich I know will imply some short of energy flux) in the $z$ direction, hence the "paradox". Is there or is there not propagation of energy?</p>
<p>Any hint will be appreciated, thank you for your time.</p> | 2,047 | [
-0.04539988189935684,
-0.03623020276427269,
0.010613343678414822,
-0.054697148501873016,
0.0556817427277565,
0.0015366438310593367,
-0.031060175970196724,
-0.005234877113252878,
0.005938661750406027,
0.012095042504370213,
-0.007507129106670618,
0.061054397374391556,
0.08830475807189941,
0.05850403383374214,
-0.010871130041778088,
-0.015254903584718704,
-0.03650489076972008,
-0.0012616025051102042,
0.01831977628171444,
-0.038749922066926956,
0.011185456067323685,
0.045091062784194946,
0.0038055088371038437,
-0.01089094951748848,
-0.007267798762768507,
0.02638816274702549,
0.007788368500769138,
0.0167720764875412,
0.00888938270509243,
0.0622396245598793,
-0.014379621483385563,
-0.02564564347267151,
-0.006080511026084423,
0.016848234459757805,
0.020243454724550247,
-0.0121007040143013,
-0.024932825937867165,
-0.04891734570264816,
-0.004066598601639271,
0.009965366683900356,
0.010446390137076378,
-0.009576349519193172,
-0.023050803691148758,
0.0950339064002037,
-0.01511137094348669,
-0.024644533172249794,
0.020668385550379753,
0.0035286513157188892,
0.06571120023727417,
-0.01834271103143692,
0.053002599626779556,
-0.011441647075116634,
0.03648502752184868,
0.016999177634716034,
-0.00821202713996172,
-0.00474590016528964,
0.0645037293434143,
0.10516124963760376,
-0.04223329946398735,
-0.03041241131722927,
-0.007076279725879431,
-0.019919894635677338,
-0.024065114557743073,
-0.04777749627828598,
-0.032404571771621704,
0.03057018853724003,
0.0072004953399300575,
-0.05387416481971741,
0.008914319798350334,
0.005568261258304119,
0.014682982116937637,
0.01690002903342247,
0.016304686665534973,
-0.001380094443447888,
0.003736262209713459,
-0.012047989293932915,
0.031553640961647034,
0.0408688522875309,
0.02571684867143631,
0.03035704791545868,
-0.03490320220589638,
0.01345463003963232,
0.021126803010702133,
0.09655461460351944,
0.03093715012073517,
-0.012340210378170013,
0.014329429715871811,
-0.0317409485578537,
0.00585738243535161,
0.04066086933016777,
-0.018218541517853737,
-0.005514162126928568,
0.02856419049203396,
-0.006647593341767788,
-0.006566713098436594,
0.04307621717453003,
-0.030190682038664818,
0.059583112597465515,
0.017300257459282875,
-0.03767242282629013,
0.03747143968939781,
-0.0002952339709736407,
0.012091118842363358,
0.032007742673158646,
0.04932749643921852,
-0.02506590448319912,
-0.005531564820557833,
0.019312161952257156,
-0.029298115521669388,
-0.015814514830708504,
-0.030879292637109756,
0.026082241907715797,
0.02336377091705799,
0.019124815240502357,
-0.0062625231221318245,
-0.027215486392378807,
0.016721585765480995,
-0.01378039550036192,
0.0411466509103775,
0.057818587869405746,
0.019535085186362267,
-0.03267403319478035,
0.01650237664580345,
-0.035783551633358,
-0.10444795340299606,
0.006629072595387697,
0.006320376414805651,
-0.022968558594584465,
-0.026796920225024223,
0.02617655321955681,
0.0143126817420125,
0.006930653937160969,
-0.015160888433456421,
-0.030226388946175575,
0.04433172196149826,
-0.014014828950166702,
-0.0887049213051796,
-0.0718778669834137,
0.027725713327527046,
-0.0051612090319395065,
0.029241804033517838,
-0.061544813215732574,
-0.019764600321650505,
0.040515169501304626,
0.07066164165735245,
0.000894225318916142,
-0.019675593823194504,
-0.025345364585518837,
0.0753709152340889,
0.0058845276944339275,
-0.022600211203098297,
-0.03874838724732399,
-0.04390633851289749,
-0.061355963349342346,
0.06218479946255684,
-0.046393632888793945,
0.04553269222378731,
0.02858112007379532,
0.018394021317362785,
-0.0003638907801359892,
0.03658158704638481,
-0.005830221809446812,
0.00007864454528316855,
0.009169500321149826,
-0.023093322291970253,
-0.035933028906583786,
0.08788847923278809,
0.00849760603159666,
0.030672920867800713,
0.02324630506336689,
-0.006684113759547472,
-0.007500847801566124,
-0.02000666968524456,
0.03973178565502167,
0.05732963606715202,
-0.0552699901163578,
-0.04514183849096298,
-0.03953254967927933,
0.007867025211453438,
0.001210344024002552,
-0.0720738023519516,
-0.052464403212070465,
-0.0041982741095125675,
0.016813363879919052,
0.01312041562050581,
0.04395141080021858,
-0.014244426041841507,
-0.006467211991548538,
-0.034947898238897324,
-0.022918639704585075,
-0.03747495636343956,
-0.07015234231948853,
0.04257577657699585,
0.01014795619994402,
0.000882490596268326,
0.028637532144784927,
-0.01898159831762314,
0.009071293286979198,
-0.06949291378259659,
-0.042482566088438034,
0.011300863698124886,
0.0038317760918289423,
0.013196566142141819,
-0.01109733060002327,
0.019181007519364357,
0.036036502569913864,
0.04443054273724556,
0.030028996989130974,
0.018612105399370193,
-0.003610032144933939,
-0.030057407915592194,
0.021538814529776573,
-0.01088035013526678,
0.000675519579090178,
0.030143536627292633,
0.02677200362086296,
0.009226392954587936,
0.02274603210389614,
-0.0019300540443509817,
0.04460997134447098,
-0.01899236999452114,
0.036950837820768356,
0.07673443108797073,
-0.0012163969222456217,
0.016200903803110123,
0.03918232396245003,
0.001501235761679709,
0.023532813414931297,
-0.05168222635984421,
-0.04510752856731415,
-0.04688261076807976,
0.035451192408800125,
0.02915409579873085,
-0.006203383207321167,
-0.051867179572582245,
0.037145063281059265,
0.04212968423962593,
0.018470032140612602,
0.038018543273210526,
0.0368175208568573,
0.009282550774514675,
-0.013117408379912376,
0.004159788601100445,
0.0030305434484034777,
0.014661558903753757,
0.03423227369785309,
0.011331443674862385,
0.0018878914415836334,
-0.011920703575015068,
0.014307894743978977,
-0.016749870032072067,
0.01808098703622818,
-0.012429078109562397,
0.023102618753910065,
0.039415355771780014,
-0.04696182906627655,
0.023953206837177277,
-0.030647551640868187,
0.01946987211704254,
0.023729396983981133,
0.008632561191916466,
-0.023177092894911766,
-0.026379423215985298,
0.000906233093701303,
-0.0029480464290827513,
-0.006092408671975136,
-0.020477257668972015,
-0.031349122524261475,
0.0121145686134696,
-0.01467672735452652,
0.00046106986701488495,
-0.003422400215640664,
-0.010001493617892265,
-0.003969625104218721,
-0.01796780154109001,
0.05247239023447037,
0.04867806285619736,
0.017667096108198166,
-0.04619693011045456,
-0.04544315114617348,
-0.027730470523238182,
-0.04259965196251869,
0.017533352598547935,
0.031148850917816162,
-0.029881997033953667,
-0.022679487243294716,
-0.0580260194838047,
-0.045182619243860245,
0.054638173431158066,
-0.0031638555228710175,
0.010180564597249031,
0.014999935403466225,
-0.006233260966837406,
-0.04709625244140625,
-0.04259485378861427,
-0.024220310151576996,
0.00919394288212061,
-0.04352887347340584,
0.00543059641495347,
0.07408933341503143,
-0.013121474534273148,
-0.040800292044878006,
0.005335052963346243,
-0.014896604232490063,
-0.05271788686513901,
0.0113765774294734,
-0.03542207553982735,
0.02639763057231903,
-0.02718956582248211,
0.03917213901877403,
0.014052305370569229,
-0.03256434202194214,
-0.014903334900736809,
-0.027837654575705528,
-0.05346769466996193,
0.03137573227286339,
-0.026547277346253395,
0.030985025689005852,
-0.0075022196397185326,
-0.01819118857383728,
0.07785715162754059,
0.02251453325152397,
-0.0059503368102014065,
-0.004115566611289978,
-0.017910689115524292,
0.014595095999538898,
-0.05952662229537964,
-0.005028200801461935,
0.04423713684082031,
-0.00565807381644845,
0.022477146238088608,
0.0333542600274086,
0.0422959104180336,
-0.002478630980476737,
-0.008292148821055889,
-0.024430833756923676,
-0.018122000619769096,
0.03781662881374359,
0.013643540441989899,
0.058997660875320435,
0.028242355212569237,
-0.06034586951136589,
-0.011585897766053677,
0.01269532646983862,
0.03682385012507439,
0.010600902140140533,
-0.03391997888684273,
0.054401565343141556,
-0.013257495127618313,
0.030843758955597878,
-0.023671954870224,
0.05849670246243477,
0.02144414372742176,
-0.0042681582272052765,
0.008828227408230305,
0.027641616761684418,
0.08457624167203903,
-0.04241825267672539,
0.015753164887428284,
0.055872246623039246,
-0.016746189445257187,
-0.014402121305465698,
-0.014773753471672535,
-0.01180710643529892,
0.014405522495508194,
-0.017603205516934395,
-0.0008122451254166663,
-0.06401976197957993,
0.05825686454772949,
0.03058936819434166,
0.013385934755206108,
0.010852117091417313,
-0.04608306288719177,
0.0105095524340868,
-0.0237629022449255,
0.025106234475970268,
-0.005791935604065657,
0.00933930929750204,
0.022412769496440887,
0.022731292992830276,
0.023886939510703087,
0.014034708961844444,
-0.0011989555787295103,
-0.03419308364391327,
-0.08987617492675781,
0.0027332105673849583,
0.0022937164176255465,
-0.03763500228524208,
-0.03461050987243652,
-0.007029163651168346,
-0.035230882465839386,
-0.016441667452454567,
0.011052223853766918,
-0.0009039246942847967,
-0.010286475531756878,
-0.0663234293460846,
0.02825613133609295,
-0.026269273832440376,
-0.06311661750078201,
-0.037350594997406006,
-0.025407936424016953,
0.05161614716053009,
-0.057069890201091766,
0.0031887402292340994,
0.0187233779579401,
-0.07452119886875153,
0.014747321605682373,
-0.021326318383216858,
0.025905385613441467,
0.006350889336317778,
0.021115919575095177,
0.001242263475432992,
-0.0000060260072132223286,
0.006351981777697802,
0.030015725642442703,
0.011818994767963886,
0.03734126314520836,
-0.020234758034348488,
-0.03066909685730934,
-0.03211747482419014,
-0.005875880364328623,
-0.01781049743294716,
-0.011456778272986412,
0.05750873312354088,
0.01985241286456585,
0.018944038078188896,
0.01985858380794525,
0.04767540842294693,
0.0001374536514049396,
0.020337799564003944,
-0.0022710533812642097,
0.0033099364954978228,
-0.03246030956506729,
-0.04650968685746193,
-0.0034992399159818888,
-0.026134701445698738,
-0.017601439729332924,
0.03161652013659477,
-0.030133912339806557,
-0.024590177461504936,
-0.035045232623815536,
-0.009328898042440414,
0.02989693358540535,
0.014496794901788235,
0.045953668653964996,
-0.017336338758468628,
-0.024678584188222885,
0.009044190868735313,
-0.002082750666886568,
-0.012718996033072472,
0.020962512120604515,
0.015834512189030647,
-0.0004498557245824486,
-0.045115336775779724,
-0.04709922522306442,
0.019445519894361496,
0.036446284502744675,
0.02630443125963211,
-0.008483861573040485,
-0.007347918581217527,
-0.026090877130627632,
-0.05571281909942627,
0.047560300678014755,
-0.04136533662676811,
0.017886674031615257,
-0.05582926422357559,
-0.012053662911057472,
-0.005707231815904379,
-0.05251391977071762,
-0.05494845658540726,
0.029941139742732048,
0.0022073695436120033,
0.03676304593682289,
0.010523627512156963,
-0.018723344430327415,
0.006304784677922726,
-0.017197374254465103,
0.04257072135806084,
0.05898277088999748,
-0.004793726373463869,
-0.005051330663263798,
-0.009707743301987648,
0.034129396080970764,
0.02468438632786274,
-0.08311524242162704,
-0.016802186146378517,
0.002137424424290657,
-0.03457007557153702,
0.02968646213412285,
-0.04526776820421219,
-0.05967412143945694,
0.012618103064596653,
0.029819093644618988,
0.010384771041572094,
0.005445525981485844,
0.00009209010750055313,
0.05507766455411911,
0.02470254711806774,
-0.02351871319115162,
0.025355353951454163,
0.017384938895702362,
-0.033340100198984146,
-0.02002854272723198,
-0.019725147634744644,
0.00357358087785542,
-0.022955773398280144,
0.0007484856760129333,
-0.02401178888976574,
0.03888982906937599,
-0.0185975581407547,
0.0505867563188076,
0.005273458547890186,
-0.005047515034675598,
-0.042238473892211914,
-0.032391972839832306,
0.018036222085356712,
-0.003865285310894251,
-0.03088446334004402,
-0.00977872684597969,
-0.0477028526365757,
0.02129862643778324,
0.012090299278497696,
0.000013016635421081446,
-0.023973265662789345,
0.0019017898011952639,
-0.0025164552498608828,
0.03346976265311241,
0.007450422737747431,
-0.01147542055696249,
-0.03043440543115139,
-0.008007381111383438,
0.039802394807338715,
-0.055961910635232925,
0.013306302018463612,
-0.01968480460345745,
-0.011102890595793724,
0.011337717063724995,
-0.030154680833220482,
-0.056592848151922226,
0.013773034326732159,
-0.004146297927945852,
0.011256100609898567,
-0.0478798970580101,
-0.03894471377134323,
0.011944894678890705,
0.022941777482628822,
-0.04302362725138664,
-0.036335479468107224,
-0.016277186572551727,
0.035320110619068146,
0.011804505251348019,
-0.02706608735024929,
-0.047218870371580124,
-0.015192200429737568,
-0.006832239218056202,
-0.008880372159183025,
-0.009474677965044975,
-0.04152673855423927,
0.00990462489426136,
0.025133315473794937,
0.008303048089146614,
0.05457330122590065,
-0.0035734365228563547,
-0.021815596148371696,
0.0283067487180233,
-0.02291794866323471,
-0.029045317322015762,
-0.004451222252100706,
0.04178760200738907,
-0.013062276877462864,
-0.0486207939684391,
0.04213162511587143,
0.0016211133915930986,
0.04685782268643379,
-0.0129851084202528,
-0.0046761734411120415,
0.024772297590970993,
0.015433980152010918,
-0.021115900948643684,
-0.01552539598196745,
0.04277922585606575,
0.0036471860948950052,
-0.0008380087092518806,
0.013275633566081524,
-0.044702231884002686,
-0.052907757461071014,
-0.007885792292654514,
-0.0013251964701339602,
0.033997148275375366,
0.017117565497756004,
-0.013333930633962154,
0.04904617369174957,
-0.008145864121615887,
0.006370233371853828,
0.03750241547822952,
0.009473719634115696,
0.02580096572637558,
0.013822180218994617,
-0.010356065817177296,
0.014412559568881989,
0.0003727882867679,
0.011770728975534439,
-0.004934902302920818,
-0.049809835851192474,
0.05504946410655975,
0.036155324429273605,
0.004813089966773987,
0.034631386399269104,
-0.01301611214876175,
0.014455607160925865,
-0.03149137645959854,
-0.0004666748864110559,
-0.015394110232591629,
0.028251152485609055,
0.015507827512919903,
0.02241775393486023,
-0.017332343384623528,
0.005062971729785204,
0.05829811096191406,
0.034612126648426056,
-0.019592173397541046,
0.007985318079590797,
0.019429443404078484,
0.054641418159008026,
0.034453533589839935,
0.017790162935853004,
-0.03741129860281944,
0.026185955852270126,
-0.03290974721312523,
0.006082281470298767,
-0.004650515038520098,
-0.012282278388738632,
0.03195054084062576,
0.021983958780765533,
-0.02343263104557991,
-0.04023385047912598,
-0.007004044484347105,
-0.03339356929063797,
0.005833109840750694,
-0.022923192009329796,
0.03429793938994408,
-0.0035014129243791103,
0.01056454237550497,
0.020992955192923546,
-0.0031792535446584225,
0.03532436490058899,
-0.008263845928013325,
-0.07053132355213165,
-0.02922588586807251,
-0.016487080603837967,
-0.034929368644952774,
0.039160363376140594,
0.023007644340395927,
0.007620863150805235,
-0.003437846200540662,
-0.03218487277626991,
0.00011194319813512266,
-0.004188500344753265,
0.028535500168800354,
0.0162238460034132,
0.07245675474405289,
0.013922279700636864,
0.012945203110575676,
-0.03690868243575096,
0.018349437043070793,
0.11200549453496933,
0.002373450668528676,
0.029716257005929947,
-0.04024922847747803,
0.04275810718536377,
-0.0525856614112854,
-0.012990795075893402,
-0.06282759457826614,
0.0629681870341301,
-0.005337366834282875,
-0.0019851624965667725,
0.02139318361878395,
0.046753186732530594,
0.0077811055816709995,
-0.0013494965387508273,
0.06307689100503922,
-0.040020085871219635,
0.005197813268750906,
-0.02384583279490471,
0.03261691331863403,
-0.006658161990344524,
0.005199763923883438,
-0.010189643129706383,
0.015169937163591385,
-0.049829207360744476,
0.007379590999335051,
-0.013802528381347656,
-0.0071045043878257275,
0.00944127980619669,
0.007971576415002346,
-0.039043623954057693,
0.020415296778082848,
0.023124463856220245,
-0.010282550007104874,
-0.02049674279987812,
0.0009052944369614124,
0.04863186925649643,
0.03952573984861374,
0.02221766673028469,
-0.011381255462765694,
0.0061462875455617905,
0.012274966575205326,
0.032745905220508575,
0.012355831451714039,
-0.024453623220324516,
0.013670533895492554,
-0.03285546228289604,
0.06763481348752975,
0.028590405359864235,
0.01058601401746273,
0.01237668190151453,
-0.007844665087759495,
0.01566501148045063,
-0.04282534494996071,
-0.008315302431583405,
-0.012393352575600147,
0.023076258599758148,
-0.01430541928857565,
-0.014510219916701317,
-0.002564186230301857,
-0.009043888188898563,
-0.014778909273445606,
0.023539137095212936,
0.017585692927241325,
-0.00685524195432663,
0.030660662800073624,
0.019321030005812645,
0.03902032598853111,
0.00032744425698183477,
-0.01992270164191723,
-0.025935005396604538,
-0.044329699128866196,
-0.02268061973154545,
0.006394922733306885,
0.029589880257844925,
-0.007104470394551754,
0.015503368340432644,
0.009638600051403046,
-0.011857107281684875,
0.024957874789834023,
-0.04052218422293663,
0.02056385576725006,
0.03892151638865471,
-0.011187611147761345,
0.011160323396325111,
-0.005401449277997017,
-0.0030506784096360207,
0.05646652728319168,
-0.03793182224035263,
-0.013647504150867462,
0.0073483469896018505,
0.016258573159575462,
0.019328400492668152,
0.0014631031081080437,
-0.01804494485259056,
-0.023946573957800865,
-0.05806864798069,
0.021898092702031136,
0.005595721770077944,
0.003034174907952547,
0.02835838496685028,
0.053417522460222244,
-0.006274836603552103,
0.020963475108146667,
-0.02756044827401638,
-0.02204110659658909,
0.040967125445604324,
-0.03544706478714943,
0.0028884573839604855,
0.009362888522446156,
-0.012766816653311253,
-0.02510950341820717,
-0.026422349736094475,
-0.01773620769381523,
0.018383726477622986,
0.01721859909594059,
0.035386502742767334,
-0.008453945629298687,
0.010392295196652412,
-0.050236206501722336,
0.02521122619509697,
-0.022504033520817757,
0.0247796643525362,
-0.027714142575860023,
0.0044971914030611515,
0.05096400901675224,
-0.018546026200056076,
-0.018857283517718315,
0.0488169826567173,
-0.04318830370903015,
0.013272924348711967,
0.030925951898097992,
0.04313213378190994,
-0.006430109962821007,
0.02586590312421322,
0.037511393427848816,
0.03278908506035805,
0.04011349752545357,
-0.005581659264862537,
-0.046704892069101334,
0.03334394842386246,
-0.025424782186746597,
-0.032797541469335556,
-0.0028164363466203213,
-0.00710583571344614,
0.034008633345365524,
0.019371673464775085,
-0.03830462321639061,
-0.03481677919626236,
0.09261392802000046,
-0.00915102381259203,
0.005142850801348686,
0.003444046713411808,
-0.04488986358046532,
-0.04142540320754051,
0.005015375092625618,
0.013198841363191605,
-0.005797294434159994,
-0.002498416230082512,
0.014821058139204979,
0.02488720417022705,
0.0260208360850811,
-0.028517160564661026,
-0.003684047842398286,
0.006327782291918993,
-0.06257686018943787,
0.018299035727977753,
-0.008833578787744045,
0.024219030514359474,
0.07795057445764542,
-0.018748123198747635,
0.00571709917858243,
0.035199105739593506,
0.049890872091054916,
-0.09067749977111816,
0.023161090910434723,
0.0023561129346489906,
0.007316616829484701,
0.0046713100746273994,
-0.03893804922699928,
0.009341049939393997,
0.028885602951049805,
-0.09775538742542267,
0.017306692898273468,
-0.017503399401903152,
-0.0040296888910233974,
-0.03761301562190056,
-0.0038326086942106485,
-0.008300870656967163,
0.06070505082607269,
0.032711464911699295,
0.05999802425503731,
0.000010383409062342253,
0.014101226814091206,
-0.015452925115823746,
-0.04824049025774002,
-0.033140864223241806,
0.04857052117586136,
-0.020550360903143883,
-0.003141700057312846,
0.07483626902103424,
-0.0031227741856127977,
-0.0118991918861866,
0.012121140956878662,
-0.0312982052564621,
0.00044898196938447654,
0.0035045284312218428,
0.034188736230134964,
0.02700618840754032,
0.04167495667934418,
-0.021898716688156128,
-0.019586719572544098,
-0.01395556703209877,
-0.016744377091526985,
0.017577296122908592,
0.01878741942346096,
0.016310200095176697,
0.011566989123821259,
0.014481144957244396,
-0.024262908846139908,
-0.04527810961008072,
0.015374595299363136,
-0.02970343828201294,
-0.006826390977948904,
0.03153013810515404,
0.00021421004203148186,
0.05737901106476784,
0.005541498307138681,
-0.017392385751008987,
-0.035486042499542236,
-0.0638614296913147,
0.031681936234235764,
0.006391876842826605,
0.025449829176068306,
0.015762941911816597,
-0.037265922874212265,
-0.044067323207855225,
0.028426043689250946,
0.0050659398548305035,
-0.003525389824062586,
-0.045152369886636734,
0.00402076356112957,
-0.023911243304610252,
-0.005467470269650221,
0.006885060574859381,
-0.04672994092106819,
-0.04453575983643532,
0.010823914781212807,
0.03947138786315918,
0.02581535093486309,
0.00763598782941699,
-0.021692907437682152,
-0.02022429369390011,
-0.06213587522506714,
0.03954331576824188,
-0.03218167647719383,
-0.013156373053789139,
-0.05948442220687866,
-0.03304016962647438,
-0.030305087566375732,
0.003083245363086462,
0.08457061648368835,
-0.01966942474246025,
-0.011533090844750404,
0.024852927774190903,
-0.022135302424430847,
0.005788829177618027,
-0.0781237781047821,
-0.001275551738217473,
0.012807448394596577,
-0.022102992981672287,
0.03635912388563156,
-0.007251580711454153,
-0.021454332396388054,
-0.002221834147349,
0.011981883086264133,
0.009931218810379505,
0.012305129319429398,
0.021262310445308685,
-0.03849087655544281,
0.046282749623060226,
-0.001962462440133095,
-0.04003595933318138,
0.0492430180311203,
0.007882076315581799,
0.0006854904349893332,
0.010358200408518314,
-0.018453191965818405,
-0.021712088957428932,
0.014939277432858944,
-0.05225639417767525,
0.020820870995521545,
-0.03332912549376488,
0.011151748709380627,
0.03999435156583786,
-0.0462837815284729,
-0.029737459495663643,
0.028590532019734383,
-0.042108435183763504,
0.0041193887591362,
0.0312352254986763,
-0.012630468234419823,
0.03233923017978668,
-0.016344280913472176,
0.000620297621935606,
-0.021709397435188293,
0.02182849310338497,
-0.0009149948018603027,
0.044297002255916595,
0.022166747599840164,
0.003978630993515253,
-0.01777665689587593,
0.008879114873707294,
-0.023560475558042526,
0.027824753895401955,
0.022203700616955757,
0.008774294517934322,
-0.02637282945215702,
0.005310941953212023,
0.016170766204595566,
-0.001711348770186305,
-0.020704086869955063,
0.03479987755417824,
-0.01657494716346264,
0.07372812926769257,
0.002894517732784152,
0.03351899981498718,
-0.0061233388260006905,
0.030232548713684082,
-0.016773389652371407,
0.031272102147340775,
0.0011895018396899104,
0.03467865660786629,
-0.014860779978334904,
-0.011919518001377583,
-0.015565535984933376,
-0.012818364426493645,
0.015342425554990768,
-0.027139874175190926,
-0.02221967652440071,
-0.019124649465084076,
-0.058060988783836365,
0.01283099316060543,
0.0065546901896595955,
-0.014743568375706673,
0.0064263008534908295,
0.031662628054618835,
0.028142737224698067,
-0.015685146674513817,
-0.045482177287340164,
0.014412720687687397,
-0.020858662202954292,
0.04320085793733597,
-0.0555805005133152,
0.003640569280833006,
0.0022090121638029814,
0.033391598612070084,
0.013093647547066212,
-0.017249658703804016
] |
<p>The only explicit computation I have seen is the planar 1-loop one, but there should be a way to write the multi-loop case in terms of boundary states as well. </p> | 2,048 | [
-0.01757367141544819,
0.002397820819169283,
0.014299724251031876,
0.007370667532086372,
0.02247406542301178,
-0.00046096276491880417,
-0.032519131898880005,
-0.03902675211429596,
-0.011314497329294682,
-0.004173708148300648,
0.024825558066368103,
-0.004987637046724558,
0.03333129361271858,
0.03484757989645004,
0.0290281530469656,
-0.000479274574900046,
0.022305287420749664,
-0.02765689790248871,
0.0455470010638237,
-0.06264516711235046,
0.006582339759916067,
0.0362723208963871,
0.0006914648693054914,
-0.011107789352536201,
-0.01555368211120367,
0.02571062184870243,
0.046825677156448364,
-0.0064027863554656506,
0.030948316678404808,
0.07080163061618805,
-0.04012337327003479,
-0.06528989970684052,
0.017677167430520058,
0.07077932357788086,
0.009781192988157272,
0.016321664676070213,
-0.048048146069049835,
-0.03453122079372406,
-0.03486334905028343,
0.017986638471484184,
-0.014010541141033173,
-0.022845113649964333,
-0.04417864605784416,
0.03816322982311249,
0.03473764657974243,
-0.010074193589389324,
-0.030692074447870255,
0.01215500570833683,
0.044516921043395996,
-0.08534209430217743,
0.10758350789546967,
-0.014414268545806408,
0.04783770069479942,
-0.01863742806017399,
0.0027093631215393543,
0.03600269928574562,
0.06565706431865692,
0.04205816239118576,
0.022092297673225403,
-0.04513213038444519,
-0.021085603162646294,
-0.026384050026535988,
-0.006417291704565287,
-0.01557394303381443,
-0.014908644370734692,
-0.04583584517240524,
-0.012698596343398094,
-0.017407216131687164,
0.00019354003597982228,
-0.00348019041121006,
-0.039186347275972366,
0.0028565055690705776,
0.04529699683189392,
-0.019197486340999603,
0.028559522703289986,
0.03201986476778984,
0.011500321328639984,
0.013114262372255325,
0.008503946475684643,
0.028326230123639107,
-0.04613383859395981,
0.020865563303232193,
0.028246553614735603,
0.038722697645425797,
-0.02059325948357582,
-0.024727895855903625,
0.055945590138435364,
-0.015805788338184357,
-0.012592109851539135,
0.012955213896930218,
0.015568087808787823,
-0.030091743916273117,
0.05768590047955513,
0.014434874057769775,
-0.04779744893312454,
0.018834572285413742,
0.036922574043273926,
0.05752134323120117,
0.0071340822614729404,
-0.04158833622932434,
-0.040073346346616745,
-0.023300210013985634,
-0.02919766493141651,
0.10245347023010254,
0.006229917053133249,
0.04892817139625549,
-0.00781283713877201,
0.039045535027980804,
0.017681024968624115,
0.00679413415491581,
-0.06751604378223419,
-0.0024208882823586464,
-0.006266819778829813,
-0.0008275630534626544,
-0.00824870727956295,
-0.06869172304868698,
-0.038200121372938156,
-0.005734449718147516,
-0.017289873212575912,
0.058941956609487534,
0.012526474893093109,
-0.040804918855428696,
0.007201632484793663,
-0.034648265689611435,
-0.1039913222193718,
0.007609173655509949,
0.03367258980870247,
-0.02322772704064846,
-0.03404611721634865,
0.030920961871743202,
-0.0034302996937185526,
0.005340889561921358,
0.0296329315751791,
0.003527789143845439,
0.032899778336286545,
-0.02053072862327099,
-0.06069111078977585,
-0.084148108959198,
0.019809944555163383,
-0.035012729465961456,
0.0015022078296169639,
-0.030901804566383362,
0.019748413935303688,
0.042866531759500504,
0.08207785338163376,
-0.01893659494817257,
0.015162823721766472,
0.02787693403661251,
0.017340023070573807,
0.0008392916643060744,
-0.03665534406900406,
0.0038224905729293823,
-0.014555060304701328,
-0.05131366848945618,
-0.02004130184650421,
-0.05241483449935913,
0.03362375125288963,
0.05364621803164482,
-0.026320848613977432,
0.02817969210445881,
0.06518357992172241,
-0.01127994991838932,
-0.00210033031180501,
0.006745595950633287,
-0.0002834905462805182,
-0.028351372107863426,
0.07924670726060867,
-0.01889258809387684,
-0.01617947407066822,
0.037125542759895325,
-0.012560860253870487,
-0.04156576842069626,
-0.027751488611102104,
0.020445557311177254,
0.05033349618315697,
-0.03252405673265457,
-0.011588751338422298,
0.0004331902018748224,
0.0188734270632267,
0.018588662147521973,
0.01784704066812992,
-0.019855573773384094,
-0.013579907827079296,
0.013899492099881172,
-0.0030530348885804415,
0.02585129253566265,
-0.03701211139559746,
-0.007212339900434017,
0.007723383605480194,
-0.05975022912025452,
-0.004515222739428282,
-0.04176556318998337,
0.02049439214169979,
0.02783237025141716,
-0.005183597095310688,
0.023387305438518524,
0.006118108052760363,
-0.0069920639507472515,
-0.005089094862341881,
-0.09061244130134583,
-0.03810587152838707,
0.03387829288840294,
-0.0030088378116488457,
-0.024381252005696297,
-0.012309731915593147,
0.05657379329204559,
0.05779542028903961,
-0.010871709324419498,
0.06607373803853989,
-0.060050275176763535,
0.024799758568406105,
-0.016539329662919044,
-0.058138228952884674,
0.0348222590982914,
-0.0060858093202114105,
-0.010241428390145302,
-0.005728679709136486,
-0.0164412222802639,
0.010597172193229198,
0.019939778372645378,
-0.033178091049194336,
0.06238783523440361,
0.08080899715423584,
0.04400162398815155,
0.008613376878201962,
0.004049693234264851,
-0.007893387228250504,
-0.006174418143928051,
0.007413852959871292,
-0.034070346504449844,
-0.04536203667521477,
-0.03918691352009773,
0.004968815483152866,
0.03684733062982559,
-0.02023400366306305,
-0.007278822362422943,
0.03350716084241867,
0.04839739948511124,
0.03344452753663063,
0.02115318924188614,
-0.0031507927924394608,
0.014679575338959694,
0.029790310189127922,
0.035799577832221985,
0.015856372192502022,
-0.024373944848775864,
0.03586769104003906,
0.018047528341412544,
0.0038648410700261593,
-0.03495795652270317,
-0.04107685014605522,
0.0195578895509243,
-0.0278325118124485,
0.005968807730823755,
0.021861957386136055,
-0.040040552616119385,
0.025311864912509918,
-0.02280142717063427,
0.020529353991150856,
0.042698729783296585,
-0.014415395446121693,
-0.002292838180437684,
-0.001160697778686881,
-0.005232083611190319,
0.03541622310876846,
-0.01351251546293497,
0.004497597459703684,
0.004709675908088684,
0.03791783004999161,
-0.010970448143780231,
0.06367400288581848,
-0.03173426538705826,
-0.02048647589981556,
0.007596986368298531,
0.0443403422832489,
0.017321808263659477,
-0.00833899062126875,
0.007706128526479006,
-0.05754711478948593,
-0.007692156825214624,
0.015385597012937069,
-0.0002019952080445364,
0.021078065037727356,
0.02192939631640911,
-0.046321969479322433,
0.01601247675716877,
-0.07920221239328384,
-0.04275140166282654,
0.03245551139116287,
0.010659267194569111,
-0.05061880126595497,
0.004809733480215073,
0.006438576150685549,
-0.028378967195749283,
-0.007616037968546152,
-0.03182095289230347,
0.010192601010203362,
-0.030385924503207207,
0.014540229924023151,
0.029711376875638962,
0.016500893980264664,
-0.05593542754650116,
0.012222842313349247,
0.010726159438490868,
-0.008529655635356903,
-0.013347264379262924,
-0.012935652397572994,
-0.0027240028139203787,
-0.030519120395183563,
0.04436417669057846,
0.027462897822260857,
-0.03351524472236633,
0.007359754294157028,
-0.03908342868089676,
-0.04641866311430931,
0.0091283293440938,
0.006749914493411779,
0.04948768392205238,
-0.021386364474892616,
-0.04528682306408882,
0.07644427567720413,
-0.015112905763089657,
-0.02528814598917961,
0.006293941289186478,
0.011476976796984673,
0.00752988550812006,
0.013493241742253304,
-0.012025154195725918,
0.016279311850667,
-0.07253815233707428,
0.021732395514845848,
0.015381701290607452,
0.029118193313479424,
0.05467400327324867,
0.011975680477917194,
-0.014262697659432888,
0.04441482201218605,
-0.005507724825292826,
0.004679183010011911,
0.04228992387652397,
-0.01237710751593113,
0.01936231553554535,
0.014826259575784206,
-0.0022870206739753485,
-0.04265105724334717,
0.002433343790471554,
-0.032200515270233154,
0.047067299485206604,
-0.008286948315799236,
0.00825137086212635,
-0.029865577816963196,
0.011998974718153477,
-0.01569257490336895,
-0.03665429726243019,
-0.022803734987974167,
0.06216716393828392,
0.06013629212975502,
-0.0103091886267066,
-0.009394907392561436,
0.0029127185698598623,
0.041143253445625305,
-0.013010600581765175,
-0.036056987941265106,
0.03024972788989544,
-0.02762436494231224,
0.026193998754024506,
-0.0531005784869194,
-0.03348088636994362,
0.03620215877890587,
0.042191099375486374,
0.010731106624007225,
0.013454250991344452,
-0.010197991505265236,
0.032283104956150055,
-0.0883740559220314,
-0.03009786643087864,
-0.02479635179042816,
0.06240076199173927,
0.015058270655572414,
-0.003637803951278329,
-0.012608654797077179,
0.006032935343682766,
0.031063036993145943,
0.0032825989183038473,
-0.0509667806327343,
-0.02740226872265339,
-0.05549284443259239,
0.012650281190872192,
0.015528310090303421,
-0.009696373715996742,
0.05635768175125122,
-0.018755875527858734,
-0.010798194445669651,
-0.00308560230769217,
-0.011204707436263561,
-0.05221535637974739,
0.0009983772179111838,
-0.003381321905180812,
-0.03134656697511673,
-0.028739070519804955,
0.04682129621505737,
0.0351673923432827,
-0.03072289563715458,
0.009899095632135868,
0.02440282702445984,
-0.035371989011764526,
0.013651667162775993,
-0.01968218758702278,
0.04243357852101326,
-0.016594909131526947,
0.046646326780319214,
0.047064024955034256,
0.010759691707789898,
-0.023528549820184708,
-0.030219897627830505,
0.007885510101914406,
0.05137162655591965,
0.01819043606519699,
-0.01076415739953518,
0.02447395585477352,
-0.058559756726026535,
-0.014618061482906342,
0.006838820409029722,
0.07825779169797897,
-0.019981607794761658,
0.03199468180537224,
0.017477238550782204,
0.014090411365032196,
-0.04032866284251213,
0.0436263270676136,
0.06429780274629593,
-0.01447240449488163,
-0.030430760234594345,
-0.01209572609513998,
-0.006285935640335083,
0.01989525929093361,
0.005277681164443493,
-0.0010619633831083775,
0.006660694722086191,
-0.025752313435077667,
0.03508083149790764,
0.044207025319337845,
0.011000140570104122,
0.005801775958389044,
-0.010181822814047337,
-0.026847757399082184,
0.05300450697541237,
-0.01441492885351181,
0.020599419251084328,
0.007831902243196964,
0.028954116627573967,
0.006043827626854181,
0.027456672862172127,
-0.008785275742411613,
-0.06022884324193001,
-0.018003297969698906,
0.028846299275755882,
0.026262834668159485,
0.0475570484995842,
-0.017167435958981514,
-0.04770834743976593,
0.008960026316344738,
0.06213194131851196,
0.006366928108036518,
0.05069780349731445,
0.011359725147485733,
-0.0008853114559315145,
-0.005007307976484299,
-0.01791759766638279,
-0.042336367070674896,
0.027601387351751328,
-0.015604289248585701,
0.00044219320989213884,
-0.03578608110547066,
0.03307003527879715,
-0.0032414111774414778,
0.00740351527929306,
0.020727412775158882,
0.05238689109683037,
0.016100510954856873,
0.014021242968738079,
0.00682721147313714,
0.03944304957985878,
-0.06333790719509125,
-0.05826928839087486,
0.022006940096616745,
0.01600538194179535,
0.012552349828183651,
0.05068385601043701,
-0.019470717757940292,
-0.024707676842808723,
0.0033018612302839756,
0.006016950588673353,
0.03265384957194328,
-0.00007462227222276852,
-0.009862902574241161,
0.05481333285570145,
0.03248075023293495,
-0.02779853530228138,
0.0297293309122324,
0.0368061326444149,
-0.007601811084896326,
-0.003228330984711647,
0.0244353786110878,
0.015851426869630814,
-0.008279974572360516,
0.011824124492704868,
0.0019092931179329753,
0.009677883237600327,
-0.020980769768357277,
0.03777656704187393,
-0.041556380689144135,
0.037045080214738846,
-0.0023378098849207163,
-0.03636258468031883,
-0.04877416417002678,
0.01748156175017357,
-0.033016402274370193,
-0.029448801651597023,
0.012935912236571312,
-0.0011561675928533077,
0.01971716247498989,
-0.029421208426356316,
0.030276546254754066,
-0.004330856259912252,
0.02806069701910019,
0.03367678448557854,
0.00307106995023787,
-0.010972120799124241,
-0.04745527729392052,
-0.005008120555430651,
-0.012875813990831375,
-0.06533016264438629,
0.051830872893333435,
-0.059717778116464615,
-0.011164884082973003,
-0.011416883207857609,
-0.031026160344481468,
0.012433881871402264,
0.004354518372565508,
0.0003237343917135149,
0.013290216214954853,
-0.0114767299965024,
0.003501805942505598,
-0.008571181446313858,
0.0014229898806661367,
-0.0593530535697937,
-0.04899505153298378,
0.02345838025212288,
0.008493224158883095,
0.008475134149193764,
-0.061448052525520325,
-0.01642884686589241,
-0.041205812245607376,
-0.02888488955795765,
-0.011101271025836468,
0.03721050173044205,
-0.07258106023073196,
0.008375768549740314,
0.004472554661333561,
0.03462933003902435,
0.04771219566464424,
0.031411752104759216,
0.0027747470885515213,
0.01285091508179903,
-0.06307981163263321,
-0.02568748965859413,
-0.02605508826673031,
0.014629065990447998,
-0.03453703969717026,
-0.021141426637768745,
-0.013848559930920601,
0.013358241878449917,
0.06252530962228775,
-0.014470528811216354,
0.0045076701790094376,
0.020736290141940117,
0.01829463243484497,
-0.014721107669174671,
-0.019085412845015526,
-0.04127788916230202,
-0.03409895673394203,
0.02365870214998722,
-0.012464353814721107,
-0.0004721380537375808,
-0.029847629368305206,
-0.006486090831458569,
0.005629647523164749,
0.02278945967555046,
-0.035536881536245346,
-0.01929926685988903,
0.09254949539899826,
0.03568502515554428,
-0.02964097447693348,
0.01987905614078045,
-0.03757571429014206,
-0.0007234493386931717,
-0.028885504230856895,
0.007184165995568037,
0.054919831454753876,
-0.0047425017692148685,
-0.028688965365290642,
-0.03238748386502266,
-0.035103779286146164,
0.005821638274937868,
0.024894196540117264,
-0.01941712014377117,
0.028260229155421257,
0.021648496389389038,
0.006387701258063316,
0.005104356911033392,
0.01677335426211357,
-0.04633471742272377,
0.037549860775470734,
-0.00020779164333362132,
0.07354635745286942,
-0.019183309748768806,
-0.0017600877908989787,
0.01853748969733715,
0.0226273313164711,
-0.007586517836898565,
-0.03477877750992775,
-0.001047460362315178,
-0.026242664083838463,
0.04246148467063904,
-0.028621766716241837,
-0.011948293074965477,
0.04882397502660751,
-0.01033461932092905,
0.019732050597667694,
-0.02032371424138546,
0.0016245236620306969,
0.06861361861228943,
0.016058936715126038,
0.01824789308011532,
-0.00028873884002678096,
-0.03246526047587395,
-0.023516636341810226,
0.015559598803520203,
-0.015152006410062313,
0.0190264992415905,
-0.0017448239959776402,
0.01091857347637415,
0.034961044788360596,
0.014307690784335136,
0.0026522106491029263,
-0.016476908698678017,
-0.01411935780197382,
-0.021064450964331627,
-0.020353149622678757,
-0.051200851798057556,
0.03852567821741104,
0.03432349115610123,
-0.016579685732722282,
0.06218191608786583,
0.02672896906733513,
0.0331590436398983,
0.012422571890056133,
0.04504832997918129,
-0.01312023401260376,
0.03961654379963875,
-0.012806110084056854,
0.02549394778907299,
-0.0026933299377560616,
0.005995363462716341,
0.1160309687256813,
0.07561428844928741,
0.01909295655786991,
-0.10174745321273804,
0.022668110206723213,
-0.011182545684278011,
0.0032524773851037025,
-0.043332334607839584,
0.02348809875547886,
0.03037370927631855,
-0.031145086511969566,
-0.008318602107465267,
0.03298607096076012,
-0.040368854999542236,
0.0069344136863946915,
0.047837212681770325,
-0.010123949497938156,
-0.01396985910832882,
0.040699414908885956,
0.031258415430784225,
-0.0077605354599654675,
0.011923031881451607,
-0.04415501654148102,
0.012675573118031025,
-0.02208571694791317,
-0.0022966850083321333,
-0.06747448444366455,
-0.03727329149842262,
0.0488838329911232,
-0.004635408986359835,
-0.03984404727816582,
0.013360202312469482,
-0.029740333557128906,
-0.004010268487036228,
-0.01924307830631733,
0.04130854830145836,
0.024370651692152023,
0.004961729049682617,
0.05554555729031563,
0.06595893204212189,
0.01640673540532589,
-0.0017368620028719306,
-0.004225194454193115,
0.003062025411054492,
-0.028772171586751938,
-0.016794772818684578,
-0.024483637884259224,
0.03780338540673256,
-0.01824176125228405,
0.003839547745883465,
-0.008454353548586369,
-0.014093401841819286,
0.02170204371213913,
-0.017689824104309082,
-0.009366502985358238,
-0.013084587641060352,
0.034373775124549866,
-0.013701147399842739,
0.02952469512820244,
0.018237629905343056,
0.0013258347753435373,
0.03401266038417816,
-0.030133014544844627,
-0.03818264231085777,
-0.019045846536755562,
0.020039893686771393,
-0.014733233489096165,
0.06274674087762833,
0.003450332675129175,
-0.032285578548908234,
-0.0031900585163384676,
0.0007009132532402873,
0.010126523673534393,
-0.011734293773770332,
-0.0004968316643498838,
-0.009490025229752064,
0.03144897148013115,
0.012730622664093971,
-0.027480604127049446,
-0.007085798308253288,
-0.03543242812156677,
-0.021666347980499268,
-0.04664536193013191,
-0.03349808603525162,
-0.028592301532626152,
-0.016276998445391655,
0.04324942082166672,
0.029552550986409187,
0.00463468860834837,
0.011033405549824238,
-0.016705021262168884,
0.01553928479552269,
0.005754977464675903,
-0.03717943653464317,
-0.008812567219138145,
-0.01439394149929285,
-0.043345995247364044,
0.007654318120330572,
-0.04215428605675697,
0.012246721424162388,
0.012159963138401508,
0.04311699792742729,
-0.019758515059947968,
0.08285065740346909,
0.0017136649694293737,
-0.009946650825440884,
-0.0000478273541375529,
-0.028723029419779778,
0.015780476853251457,
-0.013982901349663734,
0.0011829895665869117,
-0.0667414739727974,
-0.020554523915052414,
-0.020245278254151344,
0.003415297484025359,
0.02051653154194355,
-0.007125962059944868,
-0.021410640329122543,
-0.01578076370060444,
-0.02664834074676037,
0.004993687383830547,
-0.035252805799245834,
0.01863819919526577,
-0.016265185549855232,
0.019053936004638672,
-0.00392062496393919,
0.004656994715332985,
-0.012630453333258629,
-0.000006667165962426225,
0.002954480005428195,
0.0038303460460156202,
0.008839372545480728,
0.028128569945693016,
0.003965090028941631,
-0.017978910356760025,
0.03444267436861992,
0.01226034201681614,
0.006054739002138376,
0.004271980375051498,
-0.0412190817296505,
0.018321147188544273,
-0.05454150587320328,
0.011029750108718872,
0.015617113560438156,
0.0012625680537894368,
0.031134622171521187,
0.029369421303272247,
-0.03481273725628853,
-0.032872024923563004,
0.01737048104405403,
-0.01602640375494957,
-0.014489889144897461,
-0.004948070738464594,
-0.00402103690430522,
0.02009299397468567,
-0.03134840726852417,
0.019891247153282166,
-0.019099341705441475,
-0.006301983259618282,
-0.02192900888621807,
-0.012814546003937721,
-0.007920066826045513,
0.0008653263794258237,
-0.008597836829721928,
0.000781053036917001,
0.043043918907642365,
0.045967068523168564,
0.002407983411103487,
0.024485258385539055,
0.03627467900514603,
-0.005269302520900965,
-0.005825246684253216,
0.0020358304027467966,
0.013756567612290382,
-0.05728495121002197,
0.003941231872886419,
-0.01052804384380579,
-0.012771871872246265,
0.0378091037273407,
-0.06890025734901428,
0.02149786800146103,
0.012846582569181919,
-0.06338606029748917,
-0.007490239106118679,
0.004259384237229824,
0.00013938953634351492,
-0.054405126720666885,
-0.03241411969065666,
-0.05939238518476486,
0.05267433449625969,
0.03242064639925957,
0.033504366874694824,
-0.011576990596950054,
-0.01922745816409588,
-0.043209321796894073,
-0.031537167727947235,
-0.007437885273247957,
-0.00965234637260437,
0.00503674428910017,
-0.07252621650695801,
0.025933166965842247,
-0.045224033296108246,
-0.035790421068668365,
0.014508911408483982,
-0.0321291945874691,
-0.011908089742064476,
-0.0438406802713871,
0.020425468683242798,
0.0035249420907348394,
0.0365108922123909,
0.002628170419484377,
0.014127805829048157,
0.012266029603779316,
0.047536853700876236,
-0.007171297911554575,
0.0058706896379590034,
-0.030103126540780067,
0.0299342330545187,
0.009169702418148518,
-0.03651713207364082,
-0.06772415339946747,
0.04179612174630165,
-0.007725543808192015,
-0.01827525720000267,
-0.04309103265404701,
-0.019560927525162697,
0.037994686514139175,
-0.02541077882051468,
0.0058612520806491375,
-0.04539226368069649,
0.013133665546774864,
0.014576266519725323,
-0.015892263501882553,
-0.006599124521017075,
0.018461618572473526,
0.0008068823954090476,
-0.03950364887714386,
0.025634801015257835,
-0.006859276909381151,
-0.037306804209947586,
-0.04922105371952057,
-0.012399419210851192,
0.01254978682845831,
-0.002865706803277135,
-0.007098194677382708,
-0.027247438207268715,
-0.0019329137867316604,
-0.0029507430735975504,
0.0013708252226933837,
0.04382013529539108,
-0.019333457574248314,
-0.030546050518751144,
-0.01618262380361557,
-0.020140236243605614,
0.049783337861299515,
0.00933898240327835,
-0.009752251207828522,
-0.018269265070557594,
-0.025398269295692444,
0.026414206251502037,
0.016738001257181168,
0.04072099179029465,
-0.022995248436927795,
-0.03210093826055527,
0.014176664873957634,
-0.0011533048236742616,
-0.004303302615880966,
-0.04440122842788696,
-0.0034525003284215927,
-0.013925241306424141,
0.0009500504820607603,
-0.002304869005456567,
-0.03276865556836128,
-0.010009988211095333,
0.027296029031276703,
0.02261143922805786,
0.021869994699954987,
-0.036768779158592224,
-0.04510098695755005,
-0.014405051246285439,
0.004427195526659489,
-0.006542676594108343,
-0.011844249442219734,
0.10189009457826614,
0.005390270613133907,
0.006361949257552624,
0.007481472101062536,
-0.03184044733643532,
-0.0049127922393381596,
0.024247080087661743,
-0.03962346538901329,
-0.01449597254395485,
-0.03931115195155144,
-0.0328337736427784,
0.015395512804389,
-0.021750451996922493,
0.013960901647806168,
0.02259145863354206,
-0.01688188500702381,
-0.025146769359707832,
0.05359392240643501,
0.0164395309984684,
0.030941549688577652,
-0.040732190012931824,
0.004225392825901508,
0.026051560416817665,
0.00537403067573905,
0.02286907471716404,
0.025440040975809097,
0.029948879033327103,
0.02522457204759121,
0.0029594553634524345,
0.004679194185882807,
-0.015629658475518227,
0.04296554997563362,
0.032412778586149216,
-0.0027423386927694082,
0.008295568637549877,
-0.004582322668284178,
0.058120790868997574,
-0.019018400460481644,
0.01613708958029747,
0.015281610190868378,
-0.04597686976194382,
0.09128794819116592,
-0.010064790025353432,
0.04680025577545166,
-0.027820361778140068,
0.0011624047765508294,
0.051781442016363144,
0.0031048422679305077,
0.023258429020643234,
0.08613155037164688,
-0.0335574671626091,
-0.009146317839622498,
-0.011282872408628464,
0.011984847486019135,
0.021460995078086853,
-0.057974547147750854,
0.013351619243621826,
0.021548306569457054,
-0.007282063830643892,
0.014019697904586792,
-0.014662791043519974,
0.009021716192364693,
0.004107448272407055,
0.03145863860845566,
0.037771422415971756,
0.010755886323750019,
0.017285941168665886,
0.04416238144040108,
0.0010360776213929057,
0.054533086717128754,
-0.03203530237078667,
-0.009331971406936646,
-0.021114809438586235,
0.02071130834519863,
-0.0031467131339013577,
0.05059881880879402
] |
<p>I had a test on Quantum mechanics a few days ago, and there was a problem which I had no clue how to solve. Could you please explain me?</p>
<p>The problem is:</p>
<blockquote>
<p>Let's look at the $\hat H=E_0[|1 \rangle \langle 2| + |2 \rangle \langle1|]$ two-state quantum system, where $E_0$ is a constant, and $\langle i|j \rangle=\delta_{ij}$ $(i,j=1,2)$.
\begin{equation}
\hat O= \Omega_0 [3 |1 \rangle \langle1|- |2 \rangle \langle2|]
\end{equation}
is an observable quantity, and its expectation value at $t=0$ is: $\langle \hat O \rangle =-\Omega_0$, where $\Omega_o$ is a constant.
What is the $|\psi(0) \rangle$ state of the system at $t=0$, and what is the minimum $t>0$ time, that is needed for the system to be in the state: $|\psi(t) \rangle =|1 \rangle$?</p>
</blockquote>
<p>I never came across a problem like this, I tried to construct the time evolution operator, $\hat U$, but I couldn't, and I have no idea how to start. </p> | 2,049 | [
0.008806089870631695,
-0.05533159151673317,
0.009931754320859909,
-0.013013404794037342,
-0.006686252076178789,
-0.029502704739570618,
-0.044889070093631744,
-0.014342389069497585,
0.003950410522520542,
-0.0015148844104260206,
0.01881997659802437,
0.06329640001058578,
0.04629551246762276,
-0.026572469621896744,
0.019961675629019737,
0.011193039827048779,
0.001157391699962318,
-0.012067883275449276,
-0.05051635578274727,
-0.02791162207722664,
0.03029954805970192,
0.025648634880781174,
0.018851162865757942,
0.0006048508221283555,
-0.03660177066922188,
0.021125363186001778,
0.038551509380340576,
0.017097415402531624,
0.03139742836356163,
0.05439586192369461,
-0.05428620055317879,
-0.06421022862195969,
0.018924519419670105,
0.02526474930346012,
-0.0006873495876789093,
0.00438203988596797,
-0.04349173605442047,
-0.04875575006008148,
0.0018294649198651314,
0.006826127879321575,
-0.03282085433602333,
-0.020939350128173828,
-0.0005136581021361053,
0.017771657556295395,
0.00394592946395278,
-0.004882955923676491,
0.004866963718086481,
0.0003833367663901299,
0.03872351720929146,
-0.038665011525154114,
0.07017301768064499,
0.012918406166136265,
0.027828721329569817,
0.0021622732747346163,
-0.01870126836001873,
0.0006792576750740409,
0.05846735090017319,
0.08427596092224121,
0.006155420560389757,
-0.03471717983484268,
-0.04124031960964203,
-0.05604696646332741,
-0.007663307245820761,
-0.022533509880304337,
-0.014333721250295639,
0.0120539590716362,
0.006341204512864351,
0.028356054797768593,
0.01689300686120987,
-0.011446013115346432,
0.009470350109040737,
-0.033051904290914536,
0.04731864482164383,
-0.021923774853348732,
0.04596390202641487,
-0.023951146751642227,
0.010823095217347145,
0.038758110255002975,
0.036267369985580444,
0.024527087807655334,
-0.000009551078619551845,
0.0000212504619412357,
0.019748052582144737,
0.04201537370681763,
-0.038975790143013,
0.0057106767781078815,
0.09171183407306671,
-0.009675253182649612,
-0.004339788109064102,
0.05315430089831352,
-0.04079248011112213,
0.03293450549244881,
0.018907830119132996,
-0.02525317668914795,
0.02938738837838173,
0.024655835703015327,
0.016383616253733635,
0.05565713346004486,
0.013830307871103287,
-0.03357996046543121,
0.02223292551934719,
-0.0916680172085762,
0.02982931397855282,
0.05614089220762253,
0.013122905977070332,
0.014800501987338066,
-0.05554596707224846,
0.00037608930142596364,
-0.02570444531738758,
-0.012129838578402996,
-0.04126928001642227,
0.04080976918339729,
-0.016618285328149796,
0.02373737283051014,
-0.0366351492702961,
-0.03650853782892227,
0.029279114678502083,
-0.01738525927066803,
0.053063761442899704,
0.036036763340234756,
0.04393995553255081,
-0.01409598533064127,
0.006982946302741766,
-0.03631923347711563,
-0.09600795060396194,
0.03151746094226837,
0.021456992253661156,
-0.00019731593783944845,
-0.04578813537955284,
0.019919317215681076,
-0.0024109322112053633,
-0.011762983165681362,
0.045927584171295166,
0.003033682703971863,
0.03709746152162552,
-0.04594266414642334,
-0.13266728818416595,
-0.052602604031562805,
-0.021546637639403343,
-0.028426358476281166,
-0.03628436103463173,
-0.08434315770864487,
0.009745120070874691,
0.046282727271318436,
0.06200871989130974,
-0.007800468243658543,
0.011279014870524406,
0.02028576284646988,
0.011359142139554024,
0.008321115747094154,
-0.0028582075610756874,
-0.025832531973719597,
-0.018356017768383026,
-0.019461143761873245,
0.02971855364739895,
-0.015857722610235214,
0.0263203214854002,
0.03115462325513363,
0.005266315769404173,
-0.007608174812048674,
0.08933434635400772,
-0.009889918379485607,
0.02105526626110077,
0.02261458896100521,
-0.022513216361403465,
-0.03562429919838905,
0.09065712243318558,
0.003478260710835457,
0.0059304735623300076,
0.028153687715530396,
-0.0058679161593317986,
0.008756271563470364,
-0.02462494559586048,
0.02811366692185402,
0.022705692797899246,
-0.0667661651968956,
-0.02581719681620598,
-0.028915489092469215,
-0.023304490372538567,
0.01810954324901104,
0.015091466717422009,
-0.01775369979441166,
0.01296611875295639,
-0.014356408268213272,
0.010114820674061775,
0.006460925564169884,
-0.005318090319633484,
0.02398284152150154,
-0.02824530564248562,
-0.03759343922138214,
-0.024300266057252884,
-0.03594856336712837,
-0.004332139156758785,
0.050584468990564346,
-0.0006476087146438658,
0.04805062338709831,
0.006173565983772278,
0.0023736213333904743,
-0.037044595927000046,
-0.03587314859032631,
-0.026647726073861122,
0.01844153180718422,
0.006756927818059921,
-0.035995785146951675,
0.048017241060733795,
0.07636565715074539,
0.040612053126096725,
0.0016303705051541328,
0.01934216171503067,
-0.030459251254796982,
-0.007865392602980137,
-0.0025858627632260323,
0.01514335349202156,
0.026574188843369484,
0.020173881202936172,
0.021904634311795235,
-0.00939639750868082,
-0.04421238973736763,
0.02082153409719467,
-0.02015257254242897,
-0.01100342720746994,
0.06368114054203033,
0.02597680687904358,
-0.011408397927880287,
0.009845802560448647,
0.03668797016143799,
0.02455284632742405,
0.043910007923841476,
-0.00020320579642429948,
-0.015833964571356773,
-0.04728741943836212,
0.023820744827389717,
0.03915092721581459,
0.04085557907819748,
-0.04432272911071777,
-0.003547410946339369,
-0.005115997511893511,
0.019602254033088684,
0.037441276013851166,
-0.004194657318294048,
-0.013775577768683434,
0.003141887253150344,
0.011486807838082314,
-0.004312217701226473,
-0.02274988405406475,
0.02163315750658512,
0.03678250312805176,
0.026765329763293266,
0.01371762529015541,
0.011655448004603386,
-0.026197776198387146,
0.04669501632452011,
-0.01093718409538269,
0.017311427742242813,
-0.0037440808955579996,
-0.014496926218271255,
-0.00013650803884956986,
-0.019626839086413383,
0.049993228167295456,
0.02577938698232174,
-0.026655910536646843,
0.004148653708398342,
0.005000258330255747,
-0.04752057418227196,
0.006280729081481695,
-0.0025540615897625685,
0.003908930346369743,
-0.02141941897571087,
0.014614338986575603,
-0.024593908339738846,
0.0002178936847485602,
-0.01489402074366808,
-0.020290479063987732,
-0.058793745934963226,
-0.00842860247939825,
0.04459640011191368,
0.0103585384786129,
-0.0024429219774901867,
-0.05320452153682709,
-0.02183546870946884,
-0.013118944130837917,
0.00047497006016783416,
0.03385736048221588,
0.012092959135770798,
-0.038748983293771744,
0.02100931480526924,
-0.04066792130470276,
-0.043341271579265594,
0.056061867624521255,
0.0014236540300771594,
0.004387140739709139,
0.008137528784573078,
-0.007775857578963041,
-0.03871627151966095,
-0.05820780247449875,
-0.04569664224982262,
0.026809174567461014,
-0.026148509234189987,
-0.012594490312039852,
0.0510842390358448,
-0.026567919179797173,
-0.056179970502853394,
0.04438275098800659,
-0.05251877009868622,
-0.05971962586045265,
-0.02554735727608204,
0.008712949231266975,
0.029199449345469475,
-0.04318331182003021,
0.046541567891836166,
0.008307874202728271,
-0.009439647197723389,
0.0017062139231711626,
-0.06871186196804047,
-0.044398900121450424,
0.03391090780496597,
0.030130606144666672,
0.040896784514188766,
0.012165691703557968,
-0.031615812331438065,
0.06962360441684723,
0.020581694319844246,
-0.013364680111408234,
-0.016896476969122887,
0.021397236734628677,
0.000223662267671898,
-0.038670144975185394,
0.015338810160756111,
0.036599572747945786,
0.005663099233061075,
0.01992942951619625,
-0.01899850182235241,
0.05438297241926193,
0.026623867452144623,
0.010135335847735405,
-0.023525144904851913,
0.021902834996581078,
0.01188928633928299,
0.018793070688843727,
0.0546734519302845,
-0.01116170734167099,
-0.004030448850244284,
0.010217554867267609,
-0.015005922876298428,
0.040127232670784,
-0.027552243322134018,
-0.05111343041062355,
0.05589618533849716,
-0.00594139751046896,
0.005082243122160435,
0.010573242790997028,
0.06217913702130318,
-0.028123309835791588,
-0.015276679769158363,
-0.005729084834456444,
0.01697799190878868,
0.03892388939857483,
-0.005863603204488754,
0.011486073955893517,
0.05429833382368088,
-0.0013169837184250355,
-0.02590923197567463,
-0.019473347812891006,
-0.018970204517245293,
-0.006560847628861666,
0.02937404066324234,
-0.04845069348812103,
-0.05759548395872116,
0.030506057664752007,
0.030261505395174026,
0.01152967568486929,
-0.0019781843293458223,
-0.05286165326833725,
-0.049284927546978,
-0.02765086479485035,
-0.00046945843496359885,
0.02840897999703884,
0.06850667297840118,
0.003803187282755971,
0.06582608819007874,
0.03420509397983551,
0.028794685378670692,
0.02977241389453411,
-0.02525734342634678,
-0.04326724261045456,
0.03543003648519516,
-0.04489947855472565,
-0.008383212611079216,
-0.014801288954913616,
0.011624661274254322,
0.031872719526290894,
-0.05396529287099838,
0.0052247303538024426,
0.014867610298097134,
-0.023193109780550003,
-0.028294768184423447,
0.010967434383928776,
-0.015253341756761074,
0.01576640084385872,
-0.027510805055499077,
0.005025720689445734,
0.027473125606775284,
0.013087349943816662,
0.008718456141650677,
0.05525219440460205,
-0.02558625489473343,
0.034460291266441345,
-0.011550112627446651,
-0.021338891237974167,
0.03313617408275604,
0.020959120243787766,
0.042460061609745026,
0.014018567278981209,
0.013458718545734882,
0.016392266377806664,
-0.027125027030706406,
0.045835815370082855,
0.008798598311841488,
-0.026868676766753197,
0.034855958074331284,
-0.0184027012437582,
0.013246212154626846,
0.014215313829481602,
0.07069768756628036,
0.0011927546001970768,
0.02812020666897297,
0.006637084763497114,
0.016727237030863762,
-0.010101860389113426,
0.002590630669146776,
0.0675237774848938,
-0.011219085194170475,
0.0014432021416723728,
-0.06029637157917023,
-0.03373916447162628,
-0.050075750797986984,
0.003397373016923666,
-0.010440520942211151,
-0.01049256045371294,
-0.02730065956711769,
-0.004035514779388905,
0.015020223334431648,
0.011965306475758553,
0.018121737986803055,
-0.02555069327354431,
0.02883763611316681,
0.005573700647801161,
0.015924731269478798,
-0.0070878867991268635,
0.012953286990523338,
0.038707055151462555,
0.01457565650343895,
-0.0019735763780772686,
0.027757620438933372,
-0.04672236740589142,
-0.03467267006635666,
0.015784254297614098,
0.033857766538858414,
0.015263689681887627,
-0.010572835803031921,
-0.062242697924375534,
-0.03613676503300667,
0.026183711364865303,
-0.058063872158527374,
0.046651896089315414,
0.002330991206690669,
-0.051735132932662964,
-0.0018300152150914073,
-0.047127965837717056,
-0.019648393616080284,
0.021796392276883125,
-0.0081483144313097,
0.021298805251717567,
-0.011150890961289406,
-0.001021046657115221,
-0.01976822130382061,
0.006399308796972036,
0.02298661507666111,
0.04329146072268486,
-0.020959893241524696,
0.0066802953369915485,
0.02222830429673195,
0.025593943893909454,
-0.05148319900035858,
-0.06261732429265976,
-0.017674393951892853,
0.003986147232353687,
-0.009798115119338036,
0.01485168095678091,
-0.05139439180493355,
-0.040467824786901474,
0.013461955823004246,
0.03136537969112396,
-0.014709176495671272,
0.027669569477438927,
-0.03269857540726662,
0.04230879992246628,
0.007437645457684994,
-0.0193913746625185,
0.014429760165512562,
0.01597517542541027,
0.009227972477674484,
0.018342534080147743,
-0.03268110752105713,
0.01633969135582447,
-0.03813623636960983,
0.025779077783226967,
-0.030283337458968163,
0.0024531984236091375,
-0.020525267347693443,
0.0416727215051651,
-0.025395983830094337,
0.004060951992869377,
0.0030884642619639635,
-0.038102976977825165,
0.002394226612523198,
0.016621489077806473,
0.011934946291148663,
-0.010585257783532143,
-0.008181697688996792,
-0.008669869042932987,
0.029743986204266548,
-0.027430618181824684,
-0.0037324249278753996,
-0.033900223672389984,
0.013688812032341957,
0.05347958207130432,
-0.02461105026304722,
0.07433542609214783,
-0.031077690422534943,
-0.04623984917998314,
-0.013128909282386303,
-0.07347667962312698,
0.032755568623542786,
-0.023311950266361237,
0.01501207984983921,
0.0025365969631820917,
0.010585835203528404,
-0.03577909246087074,
0.005704844836145639,
-0.008532349020242691,
0.019831150770187378,
-0.02723647840321064,
0.0073345680721104145,
0.037871092557907104,
0.021233834326267242,
-0.06283168494701385,
-0.049758829176425934,
-0.0024404008872807026,
0.019777769222855568,
-0.038019679486751556,
-0.02304692566394806,
0.014030953869223595,
-0.007601037155836821,
-0.007612147834151983,
-0.011394002474844456,
0.022758105769753456,
-0.0003712538746185601,
-0.013496595434844494,
0.019752133637666702,
0.05969737097620964,
0.030401239171624184,
0.017703823745250702,
-0.007051896769553423,
0.0034531226847320795,
-0.013871795497834682,
-0.052520547062158585,
0.02305096760392189,
0.05630628019571304,
-0.027077825739979744,
-0.04350753128528595,
-0.021367982029914856,
0.015009574592113495,
0.030517026782035828,
-0.032061416655778885,
-0.01000173669308424,
0.040446821600198746,
0.008584537543356419,
0.027836091816425323,
-0.04436343163251877,
0.01938658393919468,
-0.024756979197263718,
-0.0029255400877445936,
0.018630623817443848,
-0.010518806055188179,
-0.053555961698293686,
-0.045518167316913605,
0.0250509325414896,
-0.015905989333987236,
-0.008745217695832253,
-0.009745355695486069,
0.04762663692235947,
0.026071801781654358,
0.009887120686471462,
0.041710324585437775,
-0.01975480280816555,
0.00006664478132734075,
0.019867340102791786,
-0.020764203742146492,
0.025643520057201385,
-0.00014653710240963846,
-0.03986088186502457,
-0.01185374055057764,
-0.04659102484583855,
0.03383582830429077,
0.05466388911008835,
0.004910530988126993,
0.06315762549638748,
0.020797334611415863,
0.026672950014472008,
-0.025915779173374176,
-0.0005001684767194092,
-0.03720888867974281,
0.018312668427824974,
-0.008673056028783321,
0.024297749623656273,
0.004610635805875063,
0.03223651647567749,
0.03141305223107338,
0.022511117160320282,
-0.017996082082390785,
0.030929112806916237,
0.03835388645529747,
0.02717982605099678,
0.0311605054885149,
-0.026592131704092026,
-0.01857049949467182,
0.029568621888756752,
-0.022403663024306297,
0.020179646089673042,
-0.004423316102474928,
-0.048940517008304596,
-0.004725472070276737,
0.02694704942405224,
0.013833634555339813,
-0.03550516813993454,
0.004880748689174652,
-0.039775412529706955,
0.013146856799721718,
0.007272706367075443,
-0.012334424071013927,
-0.010827407240867615,
0.025611983612179756,
0.01668957620859146,
0.01196092739701271,
0.05443274974822998,
-0.015023618936538696,
-0.02019142545759678,
0.007365171331912279,
-0.026737235486507416,
-0.024992790073156357,
-0.0006281412206590176,
0.0019372000824660063,
0.005405659321695566,
0.025430982932448387,
-0.012928047217428684,
-0.0031959498301148415,
0.005366448312997818,
0.038402944803237915,
-0.02471969462931156,
0.07841301709413528,
0.04076018184423447,
0.01612217351794243,
-0.0004932248266413808,
0.01762491464614868,
0.10848654061555862,
0.08329431712627411,
0.022030077874660492,
-0.058531735092401505,
-0.0004342985921539366,
-0.011177954263985157,
0.014900917187333107,
-0.03367829695343971,
0.03729510307312012,
-0.009494383819401264,
0.012026755139231682,
-0.0230831541121006,
0.025754710659384727,
0.0005091008497402072,
0.006202705670148134,
0.05456085130572319,
-0.04417583346366882,
-0.027339255437254906,
-0.015150400809943676,
0.006715795490890741,
0.00327051873318851,
-0.004301947075873613,
-0.01843281090259552,
0.0314490869641304,
-0.029064519330859184,
-0.002623093780130148,
0.0003143172652926296,
-0.02362130396068096,
0.03472679853439331,
-0.034453798085451126,
-0.005828814581036568,
0.007617541588842869,
-0.021809309720993042,
-0.04170628637075424,
-0.03733642399311066,
0.026734517887234688,
-0.012597878463566303,
-0.012574402615427971,
0.02495984174311161,
0.03255387023091316,
0.03424211964011192,
0.0018805803265422583,
0.021546833217144012,
-0.03143123909831047,
0.004411808680742979,
-0.017522074282169342,
-0.007162155583500862,
0.11276857554912567,
-0.02719848044216633,
-0.02102138288319111,
-0.007002107333391905,
-0.007654230576008558,
-0.03390441834926605,
-0.07442092150449753,
-0.02910543978214264,
-0.015298623591661453,
0.04311325401067734,
0.006917419843375683,
0.007184430491179228,
-0.02959577925503254,
0.002597444923594594,
0.0011345383245497942,
0.02723528817296028,
-0.0021290378645062447,
0.004216461442410946,
-0.004896010737866163,
-0.0011173426173627377,
0.018743878230452538,
0.006045273505151272,
-0.009820706211030483,
-0.019515223801136017,
-0.01053021289408207,
-0.05680706724524498,
-0.001703543122857809,
0.069686658680439,
-0.023540355265140533,
0.06197866052389145,
0.014625516720116138,
-0.03176550939679146,
-0.02134421467781067,
-0.10445700585842133,
-0.01620296947658062,
0.007806381210684776,
-0.04193767160177231,
-0.0005143102025613189,
-0.020257649943232536,
0.018772980198264122,
0.046672508120536804,
-0.0014489958994090557,
-0.0013355620903894305,
0.04053331911563873,
0.020127730444073677,
0.021562352776527405,
-0.012256414629518986,
-0.014844371937215328,
0.025771113112568855,
-0.014844100922346115,
0.02034268155694008,
-0.04160872474312782,
0.015887537971138954,
0.01361190527677536,
-0.003255838993936777,
0.006144593004137278,
0.009742610156536102,
-0.050450678914785385,
0.00048251982661895454,
0.01755528151988983,
-0.03710327669978142,
-0.005419165827333927,
0.007936612702906132,
0.0058430265635252,
-0.029449287801980972,
-0.03981455788016319,
-0.029100796207785606,
0.04093942046165466,
-0.00497452262789011,
-0.013362172991037369,
-0.017456000670790672,
0.03418353945016861,
-0.03755120933055878,
0.03278159350156784,
-0.02757064625620842,
0.019150493666529655,
-0.024788908660411835,
0.0050210910849273205,
0.000002877453425753629,
0.011838632635772228,
-0.02830517292022705,
0.028300205245614052,
0.03097408264875412,
-0.02732325717806816,
0.024813096970319748,
0.06068722531199455,
-0.01315406896173954,
0.008628292940557003,
-0.00999642163515091,
0.02250552549958229,
0.027965964749455452,
-0.004841105546802282,
-0.02337954193353653,
0.03949173167347908,
-0.03438181430101395,
-0.0014082358684390783,
0.0354577973484993,
0.04855797439813614,
0.02593952976167202,
0.04027024656534195,
-0.04294032230973244,
-0.016582287847995758,
0.04059674218297005,
-0.024454260244965553,
-0.003950478043407202,
0.023943975567817688,
-0.02263575606048107,
-0.018321361392736435,
-0.008222505450248718,
-0.00619426229968667,
0.00420825881883502,
-0.005282625090330839,
-0.0010253540240228176,
0.02455403283238411,
0.0017108111642301083,
0.021132510155439377,
-0.02169535495340824,
0.03568917140364647,
0.038041599094867706,
0.054931432008743286,
-0.02426878735423088,
0.021289845928549767,
0.06629558652639389,
-0.0387040451169014,
0.044591471552848816,
0.03417222201824188,
0.0014239302836358547,
-0.09804460406303406,
-0.023079974576830864,
0.0010219549294561148,
0.020082639530301094,
0.06003187969326973,
-0.03985128179192543,
0.013393275439739227,
0.06327452510595322,
-0.01684984378516674,
0.04114215075969696,
-0.03994852304458618,
0.02153087593615055,
-0.012212110683321953,
-0.026059569790959358,
-0.03550522029399872,
0.035359807312488556,
0.013670966029167175,
0.016953136771917343,
0.011735483072698116,
0.023723872378468513,
-0.017294568940997124,
-0.04777296259999275,
-0.0047209616750478745,
0.033510107547044754,
0.013673829846084118,
-0.011648861691355705,
0.035706158727407455,
-0.04722774028778076,
-0.02705078013241291,
0.03188671916723251,
-0.0025365191977471113,
-0.027183882892131805,
-0.030335385352373123,
0.01822729967534542,
-0.0065070646815001965,
0.03968873247504234,
0.03141855075955391,
-0.03427869826555252,
0.024850506335496902,
-0.01286478154361248,
0.008427685126662254,
-0.009256573393940926,
-0.008649508468806744,
-0.018779095262289047,
-0.01009313203394413,
-0.05347078666090965,
-0.08535149693489075,
0.03689143434166908,
0.03260985016822815,
0.005169994197785854,
0.021784707903862,
-0.01893596723675728,
-0.0012364578433334827,
-0.03406344726681709,
-0.0052417791448533535,
-0.003691326128318906,
-0.01809603162109852,
0.037211380898952484,
0.04087468609213829,
-0.009598029777407646,
-0.020427962765097618,
-0.03834925964474678,
-0.026840392500162125,
0.04264237359166145,
-0.0032377978786826134,
-0.051881611347198486,
-0.05935106426477432,
-0.023660626262426376,
-0.002713800873607397,
0.03210487589240074,
-0.002724692225456238,
-0.03585013002157211,
-0.05440794676542282,
0.007308213505893946,
-0.02040289156138897,
-0.024815909564495087,
-0.005104408599436283,
-0.016037672758102417,
-0.03668665885925293,
-0.06444521248340607,
0.04549200087785721,
0.015689026564359665,
-0.0038713812828063965,
-0.03228050842881203,
-0.03419956937432289,
-0.05397191271185875,
0.031864237040281296,
0.04884352162480354,
0.021668963134288788,
-0.057935360819101334,
0.0016170479357242584,
-0.005550385918468237,
0.04514791816473007,
-0.00775141129270196,
0.02153475396335125,
-0.02849908545613289,
-0.02006741613149643,
0.005527921952307224,
-0.0017887031426653266,
0.01133786141872406,
-0.010459685698151588,
0.0192970372736454,
-0.012776178307831287,
-0.028087565675377846,
-0.004355353303253651,
-0.04812975972890854,
0.04211439564824104,
-0.019348228350281715,
0.014713592827320099,
0.07085784524679184,
-0.0031382825691252947,
0.033110033720731735,
0.015862299129366875,
-0.038287676870822906,
-0.054999884217977524,
0.030438100919127464,
-0.036312609910964966,
-0.02086903713643551,
-0.01868215575814247,
-0.020776137709617615,
0.02708590030670166,
-0.025398677214980125,
-0.043223775923252106,
0.03238300234079361,
0.010660258121788502,
0.010836984030902386,
0.003486053319647908,
0.00731987738981843,
0.06700371205806732,
-0.0082852179184556,
0.017039641737937927,
0.022054312750697136,
-0.006877855397760868,
0.035874005407094955,
0.06800823658704758,
0.017839699983596802,
-0.0012760133249685168,
0.03977680206298828,
0.031081639230251312,
-0.04738247022032738,
0.015866035595536232,
0.017112448811531067,
0.007302870973944664,
-0.03141710162162781,
-0.002296542515978217,
0.050617240369319916,
-0.005662485957145691,
-0.042134612798690796,
-0.0007301628356799483,
-0.02204335853457451,
0.05919385328888893,
-0.000678809592500329,
0.011826235800981522,
-0.03813958540558815,
0.01700933277606964,
-0.03220931813120842,
0.030395271256566048,
0.02449098229408264,
0.041038695722818375,
-0.05683248117566109,
0.018888302147388458,
-0.030042164027690887,
0.004862415604293346,
0.009301570244133472,
-0.04186766967177391,
0.0031186905689537525,
0.02213362418115139,
-0.02321653440594673,
0.0005032945773564279,
-0.022676406428217888,
-0.003898379160091281,
-0.033292680978775024,
-0.005389594007283449,
0.05044155940413475,
0.03173133358359337,
-0.03349706530570984,
0.012513715773820877,
-0.003814051393419504,
0.04108384996652603,
-0.048453908413648605,
-0.021405303850769997,
-0.022182654589414597,
0.02053183875977993,
-0.029242578893899918,
-0.013358136638998985
] |
<p>A copy of <a href="http://math.stackexchange.com/questions/687534/are-continuous-mathematical-models-of-discrete-physical-phenomena-messy-because">my question on Mathematics</a>:</p>
<p>Examples from statistical mechanics and continuum mechanics abound: a discrete phenomenon (e.g. kinetic energy of molecules) is "averaged" out over the constituents of the system to which it applied (continuing the example: temperature, or pressure), and then calculations are simplified for certain special cases (e.g. ideal gases), at the cost of increasing "messiness" as increasingly general cases are considered (e.g. non-ideal gases).</p>
<p>I am not familiar with combinatorics and discrete mathematics, so please be gentle: are there trains of thought being explored in modern research that wonder if discrete physical phenomena might be better modelled by discrete mathematics?</p>
<p>If such a direction is not being seriously looked into because discrete math doesn't model discrete phenomenon in a neater way, why are discrete math models of discrete physical phenomena as messy as continuous math models of discrete physical phenomena?</p>
<p>P.S. What resources could I use to further read about related subjects?</p> | 38 | [
-0.028292976319789886,
-0.02438540942966938,
-0.008988391607999802,
-0.035504382103681564,
0.030111677944660187,
-0.0016247418243438005,
-0.012756017968058586,
0.005665270145982504,
0.012359616346657276,
0.002138985088095069,
0.039638884365558624,
0.005922484677284956,
0.03633800148963928,
-0.0037459617014974356,
0.025252513587474823,
0.00954239908605814,
-0.008887250907719135,
-0.02176148258149624,
0.01329648494720459,
0.01440484169870615,
0.020732121542096138,
0.013612695038318634,
0.04799129441380501,
0.013415098190307617,
-0.031654518097639084,
0.024616794660687447,
0.023831244558095932,
0.008227093145251274,
0.024506371468305588,
0.00007897301838966087,
-0.02517738938331604,
0.009680998511612415,
0.05088819935917854,
0.019310519099235535,
0.005790645722299814,
0.009477309882640839,
-0.024084456264972687,
-0.000957878481131047,
-0.014010263606905937,
0.007551146671175957,
-0.075908362865448,
-0.028077073395252228,
-0.008717745542526245,
0.02062973380088806,
-0.029342830181121826,
0.035321060568094254,
0.0015687234699726105,
-0.006636158097535372,
0.03563655540347099,
-0.06212873384356499,
0.07358132302761078,
-0.004721557721495628,
0.05713538080453873,
0.04230065643787384,
-0.005864191800355911,
0.014706235378980637,
0.07147398591041565,
0.07343225926160812,
-0.010757522657513618,
-0.04145488515496254,
0.008417359553277493,
-0.036667466163635254,
0.015806393697857857,
-0.011227237060666084,
-0.02745070308446884,
0.046147409826517105,
-0.019198179244995117,
-0.036965545266866684,
0.024908367544412613,
-0.0073659601621329784,
-0.01241725031286478,
0.009901673533022404,
0.044329237192869186,
0.0006770059699192643,
0.0594291053712368,
0.013664347119629383,
0.03805053234100342,
-0.017085757106542587,
0.04723575711250305,
0.04265385866165161,
-0.014810680411756039,
-0.004733630921691656,
0.01135232113301754,
0.02303069829940796,
-0.020207379013299942,
-0.07598403096199036,
0.061194874346256256,
-0.02453690767288208,
-0.011206967756152153,
0.0018848843174055219,
-0.004103987943381071,
-0.015760157257318497,
0.02711223065853119,
0.0019729482010006905,
-0.035652998834848404,
0.025494208559393883,
0.005988259334117174,
0.027464941143989563,
0.0021727208513766527,
-0.03460635989904404,
-0.0150443809106946,
-0.023028794676065445,
0.04895130172371864,
0.07658680528402328,
-0.04338570684194565,
-0.00935327261686325,
-0.031119652092456818,
0.016732871532440186,
-0.0020677740685641766,
-0.0051384917460381985,
-0.020190404728055,
0.0012250338913872838,
0.00679725781083107,
-0.010500703006982803,
-0.005647258833050728,
-0.009372160769999027,
0.0032080106902867556,
-0.037071261554956436,
0.029319491237401962,
0.09998694807291031,
0.027680078521370888,
-0.07652036100625992,
0.04594947397708893,
-0.03265019506216049,
-0.07448738068342209,
-0.013928225263953209,
0.02596338465809822,
-0.015272031538188457,
-0.021794982254505157,
0.006250245496630669,
0.0014557597460225224,
-0.004340396262705326,
0.03704827278852463,
0.019495686516165733,
0.03706347942352295,
-0.03630855306982994,
-0.06233527138829231,
-0.03634056821465492,
0.03397740423679352,
0.008711940608918667,
-0.04146851226687431,
-0.053410615772008896,
0.0048930649645626545,
-0.0050268834456801414,
0.04999424144625664,
0.0025634111370891333,
0.017927763983607292,
0.012170730158686638,
0.053979355841875076,
0.009063418954610825,
-0.023648684844374657,
0.008398052304983139,
0.012520911172032356,
-0.03345919027924538,
-0.0023204933386296034,
-0.06439768522977829,
0.049186669290065765,
0.028178412467241287,
0.01366205234080553,
-0.0259512010961771,
0.04755142703652382,
-0.01617584191262722,
-0.011703986674547195,
-0.003197493962943554,
0.024813896045088768,
-0.007373848930001259,
0.04240349680185318,
-0.004635904915630817,
0.04796396940946579,
0.031034670770168304,
0.03242756053805351,
-0.0009790409822016954,
0.02776433527469635,
0.03575249761343002,
0.037586111575365067,
-0.019170712679624557,
-0.0032999825198203325,
-0.010212455876171589,
-0.001405629562214017,
0.01306309923529625,
-0.03440544009208679,
-0.03134375065565109,
-0.005269703920930624,
0.007801850326359272,
-0.00086507189553231,
0.029780566692352295,
0.014765129424631596,
-0.023531002923846245,
0.020096996799111366,
-0.05256121978163719,
-0.0579322911798954,
-0.08624184876680374,
0.015472978353500366,
-0.03895863518118858,
0.005656814202666283,
0.05967482924461365,
-0.002083919011056423,
0.0338701456785202,
-0.024682635441422462,
-0.013989211991429329,
-0.007721840403974056,
-0.0024208740796893835,
0.018860792741179466,
-0.010120036080479622,
0.011805089190602303,
0.04801878333091736,
0.04036523401737213,
-0.009319349192082882,
0.009368451312184334,
0.006880051456391811,
-0.057853661477565765,
-0.016153549775481224,
-0.04753337427973747,
0.04459362477064133,
-0.017775798216462135,
-0.03114919364452362,
0.03163865581154823,
-0.015226899646222591,
-0.027406979352235794,
0.041414953768253326,
-0.03771499544382095,
0.03171101585030556,
0.05717846006155014,
0.037523053586483,
-0.005332264117896557,
0.05430944263935089,
0.0032833826262503862,
-0.02763632871210575,
0.037345416843891144,
-0.03997403755784035,
-0.031120464205741882,
0.023475226014852524,
0.07291434705257416,
0.06969811767339706,
-0.02593114785850048,
-0.01942247338593006,
0.015762221068143845,
0.06640612334012985,
0.04363197833299637,
0.022003261372447014,
-0.039426013827323914,
-0.020371219143271446,
0.05787421390414238,
0.014376454055309296,
0.02074579708278179,
-0.006748081650584936,
0.00024072120140772313,
-0.018895933404564857,
0.008640543557703495,
0.000283849542029202,
-0.03646837919950485,
0.04466038942337036,
-0.03031906858086586,
0.002405056729912758,
-0.010307958349585533,
-0.012729293666779995,
0.0484921932220459,
-0.032411545515060425,
-0.010191972367465496,
0.04338014870882034,
0.00943565834313631,
0.021526524797081947,
-0.00961923599243164,
-0.02926379069685936,
-0.007134512532502413,
0.028149884194135666,
-0.02444669045507908,
-0.022544270381331444,
0.01767744868993759,
-0.02692684717476368,
-0.0009911942761391401,
-0.025472421199083328,
-0.0032836291939020157,
-0.04394243285059929,
0.0185035839676857,
0.00419694185256958,
0.010759067721664906,
0.020078906789422035,
-0.044504500925540924,
-0.001525513012893498,
-0.007951033301651478,
-0.031548626720905304,
0.007489246316254139,
0.04051175341010094,
-0.04630948603153229,
-0.006257013883441687,
-0.04776403680443764,
-0.03080231323838234,
0.04228775575757027,
-0.04631279781460762,
0.013613092713057995,
-0.017845718190073967,
-0.025999411940574646,
-0.04471009597182274,
0.014047426171600819,
-0.02122829109430313,
0.035609371960163116,
-0.02615678869187832,
-0.011020083911716938,
0.028407733887434006,
-0.024693792685866356,
-0.0511593297123909,
0.008520176634192467,
-0.02570536360144615,
-0.03227933123707771,
-0.03561636805534363,
-0.033845171332359314,
0.04155280068516731,
-0.036832045763731,
0.0014549571787938476,
0.02837063930928707,
-0.037800516933202744,
0.00002825724550348241,
-0.05149945244193077,
-0.04435281828045845,
-0.004209098406136036,
-0.06610598415136337,
0.04649803414940834,
0.017215898260474205,
-0.011125718243420124,
0.05703829228878021,
-0.011562115512788296,
-0.048233576118946075,
0.005624592769891024,
-0.01746330037713051,
-0.02575855329632759,
-0.012831692583858967,
0.02148638479411602,
0.04107112064957619,
-0.0071739936247467995,
-0.01861889660358429,
0.040074534714221954,
0.038407713174819946,
0.026135575026273727,
-0.00949153583496809,
-0.024063795804977417,
0.01694243773818016,
0.002297538099810481,
0.012666651979088783,
0.026293452829122543,
-0.004079916980117559,
-0.025402596220374107,
0.02335960976779461,
-0.024142147973179817,
0.016914691776037216,
0.028768105432391167,
-0.060101982206106186,
0.0607023611664772,
0.024707525968551636,
0.017014306038618088,
-0.03417432680726051,
0.03944307938218117,
-0.0015389099717140198,
-0.0439005084335804,
0.0005520257400348783,
0.06335100531578064,
0.01952492445707321,
-0.04047487676143646,
0.018534895032644272,
0.05323103442788124,
0.065004862844944,
-0.03074808418750763,
0.013735318556427956,
0.006510405335575342,
0.004397139884531498,
0.05400504916906357,
-0.04089738056063652,
0.018711674958467484,
0.061868250370025635,
0.03223717212677002,
0.036298468708992004,
-0.021528469398617744,
-0.032003115862607956,
0.011301809921860695,
-0.07354399561882019,
-0.027085410431027412,
-0.03709544613957405,
0.06782861799001694,
-0.010517017915844917,
0.0393492616713047,
-0.009576335549354553,
0.00904887542128563,
0.0024106481578201056,
-0.014691470190882683,
-0.07298406213521957,
-0.004944575019180775,
0.0002592459786683321,
0.015091361477971077,
0.00022570831060875207,
0.012608344666659832,
0.03371691331267357,
-0.0035973640624433756,
-0.042535196989774704,
-0.015989776700735092,
0.029452668502926826,
-0.06056758761405945,
-0.017562376335263252,
-0.04295475035905838,
-0.03733852505683899,
-0.004502246621996164,
0.021902810782194138,
0.05908706411719322,
-0.04796571657061577,
0.028348593041300774,
0.01407876331359148,
-0.026932962238788605,
-0.01879013329744339,
-0.045134853571653366,
0.018038544803857803,
0.03564976155757904,
0.024021759629249573,
-0.009982326999306679,
0.030352501198649406,
0.012224984355270863,
0.023127080872654915,
0.027877148240804672,
0.05223787948489189,
-0.00897062849253416,
-0.008815694600343704,
-0.012462961487472057,
-0.06246595457196236,
-0.022417467087507248,
0.007003444246947765,
0.04918530955910683,
0.021542107686400414,
0.0321061834692955,
0.04448014497756958,
0.005472129676491022,
-0.013560798019170761,
0.022893717512488365,
0.029672659933567047,
-0.03819417953491211,
-0.036558687686920166,
-0.014011443592607975,
-0.020427817478775978,
-0.0370616652071476,
0.01010060589760542,
0.04750140383839607,
0.010646561160683632,
0.016581514850258827,
0.02231653407216072,
0.019437270238995552,
-0.004777031950652599,
-0.0262345839291811,
-0.01493077538907528,
0.023669932037591934,
0.013471655547618866,
-0.007073733024299145,
-0.03305672109127045,
0.005524029023945332,
0.04624444991350174,
0.022887105122208595,
-0.009760560467839241,
-0.01609862595796585,
-0.08620873838663101,
0.008501389995217323,
0.021382564678788185,
0.0035478342324495316,
-0.015143794938921928,
0.018538715317845345,
-0.05941016599535942,
-0.0003159544139634818,
0.040194328874349594,
-0.017274659126996994,
0.008939849212765694,
-0.03456610441207886,
0.008781866170465946,
-0.006349319592118263,
-0.009747428819537163,
-0.010826405137777328,
0.017482267692685127,
0.028731878846883774,
0.05115460604429245,
-0.007018819451332092,
-0.0031992404256016016,
-0.05474283918738365,
0.032610371708869934,
0.05377235263586044,
0.05222485959529877,
-0.017311161383986473,
-0.016642745584249496,
0.017310980707406998,
-0.007448764983564615,
-0.04007374495267868,
-0.07451152801513672,
0.004784320015460253,
0.018882136791944504,
-0.0033678621985018253,
0.036746423691511154,
-0.011971789412200451,
-0.04704158753156662,
-0.02104891650378704,
-0.011195442639291286,
-0.022154511883854866,
0.004640551749616861,
-0.01156425941735506,
0.06376554816961288,
0.018100924789905548,
-0.018161142244935036,
0.04466058686375618,
0.061293281614780426,
-0.011857324279844761,
-0.0024413412902504206,
-0.03415229171514511,
0.03225361555814743,
-0.010676476173102856,
0.000479939830256626,
-0.049696508795022964,
-0.033154793083667755,
-0.01917613111436367,
0.049200233072042465,
-0.00629424536600709,
-0.011842193081974983,
0.000969651504419744,
-0.03226100653409958,
0.005631276872009039,
0.03146728500723839,
0.015275918878614902,
-0.02149791270494461,
-0.025560257956385612,
0.029825160279870033,
0.014102336950600147,
-0.027173802256584167,
0.035725366324186325,
0.012619244866073132,
-0.02316596917808056,
0.014288878068327904,
-0.0362577922642231,
-0.006603070069104433,
-0.05935024842619896,
-0.003030613996088505,
0.012154968455433846,
-0.0010297675617039204,
0.02573569305241108,
-0.018872234970331192,
0.028647935017943382,
0.021279681473970413,
-0.0808320865035057,
-0.032972101122140884,
-0.02674783207476139,
0.010556448251008987,
0.010362211614847183,
-0.029004670679569244,
0.0117521146312356,
-0.007559528108686209,
-0.007225365843623877,
-0.06470570713281631,
-0.0749436616897583,
0.039798613637685776,
-0.01855822093784809,
-0.02571861818432808,
-0.060183484107255936,
0.02386666089296341,
-0.03164142370223999,
-0.028498437255620956,
0.031169189140200615,
0.050912968814373016,
-0.04316168278455734,
-0.008704321458935738,
0.018508760258555412,
0.018192654475569725,
0.06849835067987442,
0.009356554597616196,
-0.012863638810813427,
0.020891085267066956,
0.022481504827737808,
-0.024201540276408195,
-0.0009047121275216341,
0.032334208488464355,
-0.0376790389418602,
0.003024068661034107,
0.023200033232569695,
-0.016975920647382736,
0.05204832926392555,
-0.04763903468847275,
0.009764689020812511,
0.02371930330991745,
-0.01934029348194599,
0.017175517976284027,
-0.013479284010827541,
0.004644458647817373,
0.011237134225666523,
0.03507000952959061,
-0.0157626885920763,
0.01327491831034422,
0.007781126070767641,
-0.033010806888341904,
0.00468931021168828,
-0.0044549619778990746,
-0.021738369017839432,
0.05116788670420647,
0.012567095458507538,
-0.003279223805293441,
-0.00201107794418931,
0.022297551855444908,
-0.030967168509960175,
0.025969840586185455,
-0.03090406395494938,
0.00011231953976675868,
0.01615430787205696,
0.008392292074859142,
-0.01653434894979,
-0.06887511163949966,
-0.034332115203142166,
0.013514881022274494,
0.04767301678657532,
-0.026858629658818245,
0.039980608969926834,
0.014467179775238037,
-0.004211552441120148,
-0.005929852835834026,
-0.008668022230267525,
0.008198500610888004,
0.009881001897156239,
0.01542228739708662,
0.01722864806652069,
-0.017798271030187607,
-0.005039638839662075,
0.01785108633339405,
0.009862875565886497,
-0.0012392598437145352,
0.014857323840260506,
0.009518678300082684,
0.026164771988987923,
0.005187285598367453,
-0.02763456478714943,
-0.028875498101115227,
0.048861049115657806,
-0.0496610626578331,
0.00912543572485447,
-0.00011791175347752869,
-0.03115040622651577,
0.045028768479824066,
0.00362789211794734,
-0.006213081534951925,
-0.03489714860916138,
0.0035210363566875458,
-0.011095632798969746,
0.020227985456585884,
-0.0002448925224598497,
0.019047793000936508,
0.05304991826415062,
-0.017408521845936775,
0.020469820126891136,
0.009318763390183449,
-0.00893485452979803,
0.024147052317857742,
-0.05468364804983139,
-0.010173775255680084,
-0.01661146804690361,
-0.0606272928416729,
0.024986794218420982,
0.008025167509913445,
-0.0563485361635685,
0.002494567073881626,
-0.027877425774931908,
0.030202176421880722,
0.01252768561244011,
0.010373619385063648,
-0.03667221963405609,
0.053937625139951706,
-0.016664283350110054,
0.018978450447320938,
-0.05076771229505539,
0.010673404671251774,
0.10301689058542252,
0.03639451041817665,
0.0273224338889122,
-0.08907323330640793,
0.013671782799065113,
-0.009331092238426208,
0.005214672535657883,
-0.02860579639673233,
0.02157135121524334,
0.02531914785504341,
0.03175067901611328,
0.014304365031421185,
0.0717644914984703,
0.026882845908403397,
-0.0027309167198836803,
0.024095870554447174,
-0.028990555554628372,
-0.03222303092479706,
-0.002668343484401703,
-0.008072471246123314,
0.020772602409124374,
0.01600353978574276,
-0.04220164567232132,
0.03696257248520851,
-0.007368187885731459,
0.005732603836804628,
-0.032326407730579376,
0.00584556395187974,
0.009295826777815819,
0.029682720080018044,
-0.044504426419734955,
0.013778151012957096,
0.01752827689051628,
-0.028820626437664032,
-0.03253663331270218,
0.03392792493104935,
-0.00448873545974493,
-0.0034740325063467026,
0.02088320255279541,
0.013071385212242603,
0.005288294050842524,
0.005290056578814983,
0.01288254838436842,
0.020455654710531235,
-0.036547113209962845,
-0.023954613134264946,
-0.050045445561409,
0.02733982354402542,
-0.04152890667319298,
0.026578282937407494,
0.013222971931099892,
-0.003243647748604417,
-0.015637267380952835,
-0.042991913855075836,
-0.040394093841314316,
0.0008462632540613413,
0.03992895036935806,
-0.01972903497517109,
-0.03530231863260269,
-0.016992712393403053,
0.032113540917634964,
-0.025856930762529373,
0.043867453932762146,
0.0012235146714374423,
-0.06979238241910934,
-0.026037167757749557,
-0.0024435941595584154,
0.043312594294548035,
-0.015909254550933838,
-0.013086545281112194,
-0.06522644311189651,
0.009037663228809834,
-0.05143134668469429,
-0.030281566083431244,
0.012602919712662697,
-0.004520585294812918,
0.05394186079502106,
-0.011733912862837315,
-0.008252935484051704,
0.020096424967050552,
-0.028369998559355736,
0.013455596752464771,
0.003713298123329878,
0.0028656076174229383,
-0.027187634259462357,
-0.030268141999840736,
0.003658977337181568,
0.006412678398191929,
-0.020600788295269012,
0.01662939041852951,
-0.02633580006659031,
0.0141074750572443,
0.009055587463080883,
-0.025952642783522606,
-0.014682579785585403,
-0.0064452397637069225,
-0.023951224982738495,
0.024807563051581383,
0.03801337257027626,
0.06120241805911064,
0.027726322412490845,
-0.00236730114556849,
0.009099732153117657,
0.0655151829123497,
0.019541043788194656,
0.03199327364563942,
0.024701697751879692,
-0.044655002653598785,
0.006249436642974615,
0.007841154001653194,
0.014853515662252903,
-0.047293342649936676,
-0.06514821946620941,
-0.021919220685958862,
0.007458963897079229,
-0.011170868761837482,
-0.006239831913262606,
-0.033286161720752716,
-0.0015912706730887294,
-0.032115593552589417,
0.027417486533522606,
-0.04104624316096306,
-0.03588993474841118,
-0.07465340197086334,
-0.009397672489285469,
-0.018785148859024048,
-0.02479660138487816,
0.009967336431145668,
0.009308124892413616,
-0.003736187471076846,
-0.006693834438920021,
0.03794511780142784,
0.039585623890161514,
-0.00528815109282732,
-0.028806988149881363,
0.009235776029527187,
-0.010122348554432392,
0.053097281605005264,
-0.051170676946640015,
-0.05323672667145729,
0.054167285561561584,
0.002606712281703949,
-0.0639377012848854,
-0.004984388593584299,
-0.034665174782276154,
-0.016388680785894394,
0.031621646136045456,
-0.002896839054301381,
-0.02778586745262146,
0.05450277775526047,
-0.025769177824258804,
0.02277211658656597,
0.009902413934469223,
-0.0035945475101470947,
-0.037351418286561966,
-0.03595699369907379,
0.020418990403413773,
0.00843456108123064,
-0.018834548071026802,
0.030101647600531578,
0.061820097267627716,
0.016043050214648247,
-0.0026585746090859175,
0.04594598338007927,
-0.04358231648802757,
0.05539388582110405,
0.028064649552106857,
0.0466410368680954,
0.0038315204437822104,
0.0404290147125721,
-0.03648865967988968,
0.017155412584543228,
0.01751071773469448,
0.0176081582903862,
-0.09043760597705841,
-0.01512071955949068,
0.02639123611152172,
0.011221448890864849,
0.019338175654411316,
-0.054094213992357254,
-0.005699104629456997,
0.006923840846866369,
-0.06699605286121368,
-0.012941944412887096,
-0.026927437633275986,
-0.03584274277091026,
-0.03322373330593109,
-0.007758120074868202,
-0.05543653666973114,
0.02165781334042549,
0.02251555025577545,
0.04794049263000488,
0.0165930837392807,
0.013640603050589561,
-0.01851118728518486,
0.007038200739771128,
0.0003367680765222758,
0.02674177847802639,
-0.012065229937434196,
0.008825210854411125,
0.030331844463944435,
0.00416862778365612,
-0.032729268074035645,
0.002516681794077158,
-0.007965803146362305,
-0.002468047197908163,
0.016369031742215157,
-0.004038156941533089,
0.03168054670095444,
0.024949882179498672,
0.04371219128370285,
-0.035493746399879456,
0.007728428579866886,
0.016290364786982536,
0.02001006342470646,
0.011740531772375107,
0.021855689585208893,
0.020504940301179886,
0.043773092329502106,
-0.030457843095064163,
-0.017063159495592117,
0.015752457082271576,
0.009219503030180931,
-0.020324688404798508,
-0.00493900291621685,
0.016023239120841026,
0.03531891480088234,
-0.016199376434087753,
0.050438590347766876,
-0.03990808129310608,
0.005154710728675127,
0.03148472681641579,
0.03270783647894859,
0.02339722402393818,
-0.010209612548351288,
0.002001881366595626,
-0.03467125445604324,
-0.007868379354476929,
0.024073006585240364,
0.017207415774464607,
-0.0500776544213295,
-0.020412921905517578,
0.0066420817747712135,
0.00619300315156579,
0.013661009259521961,
-0.04917267709970474,
-0.04207947850227356,
0.060699302703142166,
-0.008307437412440777,
0.046770524233579636,
0.00015100873133633286,
-0.06101153418421745,
-0.02436928078532219,
-0.07225295901298523,
0.05875754728913307,
-0.024368857964873314,
0.02416149154305458,
-0.02489297091960907,
0.01733839511871338,
-0.00883494783192873,
0.004737487994134426,
0.07357528805732727,
0.02681012637913227,
-0.016363084316253662,
0.028706086799502373,
0.020633043721318245,
0.021922027692198753,
0.02069658599793911,
-0.02797478623688221,
-0.03092649020254612,
0.018640078604221344,
0.00021273328457027674,
-0.03898870199918747,
0.0032099843956530094,
0.04124556854367256,
0.040966808795928955,
0.0009791364427655935,
0.008958905003964901,
-0.0217520110309124,
-0.044232919812202454,
0.06176719442009926,
0.0011702991323545575,
-0.027472270652651787,
0.05729804188013077,
-0.01783464103937149,
0.04524096101522446,
0.011069505475461483,
0.0008717311429791152,
-0.003622500691562891,
0.019036225974559784,
-0.039914507418870926,
-0.013194110244512558,
-0.022817617282271385,
-0.0020294873975217342,
0.008649162016808987,
-0.036450427025556564,
0.01628108136355877,
0.015519432723522186,
-0.06696611642837524,
0.01316447276622057,
0.0063625723123550415,
0.037648141384124756,
0.05302819237112999,
-0.0033824979327619076,
-0.010172736831009388,
0.060134127736091614,
0.008156250230967999,
0.0026663898024708033,
0.043133966624736786,
0.05669798329472542,
0.009639445692300797,
-0.0032423825468868017,
0.024389013648033142,
-0.03326455503702164,
0.01703675091266632,
0.036344997584819794,
-0.0009246421977877617,
-0.004831683821976185,
-0.02438207156956196,
0.02344643324613571,
-0.010503536090254784,
-0.0007799160084687173,
0.013747029937803745,
0.004665382206439972,
0.08916940540075302,
0.008639579638838768,
0.023919450119137764,
-0.022695263847708702,
-0.019954830408096313,
-0.007819817401468754,
-0.02449147030711174,
-0.00689774751663208,
0.03948388993740082,
-0.003595757996663451,
-0.0012111352989450097,
-0.04197932407259941,
0.021543331444263458,
0.016324438154697418,
-0.038369640707969666,
0.016629844903945923,
-0.023382974788546562,
-0.020988168194890022,
0.0028093652799725533,
-0.029752518981695175,
-0.003353455336764455,
-0.04148083180189133,
0.048436105251312256,
0.07147722691297531,
0.044514600187540054,
0.030943632125854492,
-0.009362537413835526,
-0.022801868617534637,
0.07481134682893753,
-0.05557579919695854,
-0.03538816049695015,
-0.041258156299591064,
0.013485293835401535,
-0.02417634055018425,
-0.02819020114839077
] |
<p>I know ice floats in water because it's crystalline structure causes $H_20$ solid to be less dense than $H_20$ liquid. Is the same true for salt because it is crystalline? If not why?</p> | 2,050 | [
-0.05308263748884201,
0.015271399170160294,
-0.021906811743974686,
-0.022207681089639664,
0.04268418997526169,
0.014996787533164024,
-0.031359899789094925,
-0.012342586182057858,
0.007281806785613298,
-0.04706311970949173,
0.06809307634830475,
0.04197203367948532,
0.06404045969247818,
0.023161016404628754,
0.019776133820414543,
-0.010245981626212597,
-0.03084777109324932,
-0.02189796045422554,
0.015383441932499409,
-0.023217730224132538,
-0.022482097148895264,
0.031211169436573982,
0.0027877907268702984,
0.010801768861711025,
-0.015809068456292152,
0.03186831623315811,
0.008078138343989849,
0.0025640332605689764,
0.05827689170837402,
0.05661052092909813,
-0.012879735790193081,
-0.023845547810196877,
0.026917818933725357,
0.024670252576470375,
0.044401127845048904,
-0.03193579986691475,
-0.01817166432738304,
0.015028911642730236,
-0.032769739627838135,
0.0317930169403553,
-0.023047957569360733,
-0.0460050031542778,
0.0007188556483015418,
0.013955773785710335,
0.026172474026679993,
0.026280492544174194,
0.051570139825344086,
-0.027947166934609413,
0.02020234800875187,
-0.05555931106209755,
0.05522444471716881,
-0.005176142323762178,
0.0032767008524388075,
0.07496699690818787,
0.005585839040577412,
0.002482474083080888,
0.05061054229736328,
0.06488773971796036,
-0.021035218611359596,
-0.06176380813121796,
0.011425138451159,
-0.057026468217372894,
-0.013961267657577991,
-0.03555571287870407,
0.004265615250915289,
0.02625962160527706,
-0.017737528309226036,
-0.04629790410399437,
-0.00028554588789120317,
-0.01228922139853239,
-0.01654968038201332,
0.013672907836735249,
0.007803474087268114,
-0.022256670519709587,
-0.0034046631772071123,
-0.0019244349095970392,
0.013350083492696285,
0.020034557208418846,
0.004479576833546162,
0.021414564922451973,
0.012689344584941864,
-0.01200191956013441,
0.040817711502313614,
0.013413851149380207,
0.001048398669809103,
0.004905374720692635,
0.04704244062304497,
-0.014138796366751194,
0.024078693240880966,
0.0049600182101130486,
0.0053834677673876286,
0.004644577857106924,
0.02582772634923458,
0.02061678096652031,
-0.011339419521391392,
-0.020893754437565804,
0.004996259231120348,
0.03029538504779339,
0.013859357684850693,
-0.008354437537491322,
0.006888068281114101,
-0.02812827192246914,
0.04824518784880638,
0.10498393326997757,
-0.009990173391997814,
-0.038462456315755844,
-0.04143916070461273,
0.0053733643144369125,
-0.000669481756631285,
-0.01779676415026188,
0.030964719131588936,
0.03583206236362457,
-0.03417346253991127,
-0.055163782089948654,
0.006853348575532436,
-0.02094212919473648,
0.038956593722105026,
-0.026887770742177963,
0.0334944874048233,
0.0615151971578598,
0.022371994331479073,
-0.019024640321731567,
-0.00504692317917943,
-0.02233145758509636,
-0.054296113550662994,
0.0026479444932192564,
0.012375593185424805,
-0.019019657745957375,
-0.02292075753211975,
0.023182980716228485,
-0.005273485090583563,
0.02412131242454052,
0.02464303933084011,
-0.0255051851272583,
0.008318036794662476,
-0.02429836057126522,
-0.10508094727993011,
-0.041328758001327515,
0.046912264078855515,
-0.00662999926134944,
-0.018500935286283493,
-0.07476981729269028,
0.029456404969096184,
0.013742613606154919,
0.03763553500175476,
0.007582839112728834,
0.020391466096043587,
0.008589670993387699,
0.0638987198472023,
0.00361913675442338,
-0.0059154219925403595,
-0.02253412827849388,
0.00796964019536972,
-0.06649226695299149,
-0.015541809611022472,
-0.08997470885515213,
0.006419114302843809,
-0.005272329784929752,
0.013406186364591122,
-0.03405429795384407,
0.012912309728562832,
-0.03597356006503105,
0.01285025104880333,
0.0011303771752864122,
-0.007533053867518902,
-0.055471837520599365,
0.029141033068299294,
0.0068553658202290535,
0.020890172570943832,
0.048815228044986725,
0.02772882767021656,
0.019598158076405525,
0.005988462828099728,
0.03234885632991791,
0.028016366064548492,
0.0038524235133081675,
0.0061507271602749825,
-0.041949719190597534,
0.0049597881734371185,
0.008735135197639465,
-0.02657271735370159,
-0.010808070190250874,
0.026065004989504814,
-0.01234104111790657,
-0.02063046582043171,
0.016182467341423035,
0.01722249761223793,
-0.016016224399209023,
-0.015647821128368378,
-0.08566521108150482,
0.0043107206001877785,
-0.05822019279003143,
0.008827101439237595,
-0.028446638956665993,
0.01022060215473175,
0.035971470177173615,
0.05277981609106064,
0.01396643090993166,
-0.01353500410914421,
0.009532885625958443,
-0.027196701616048813,
0.0171725582331419,
0.010032499209046364,
-0.0320151150226593,
0.10586094111204147,
0.0161245446652174,
0.044461626559495926,
-0.006036374717950821,
0.007776705548167229,
-0.025516271591186523,
-0.006714508403092623,
-0.0035799620673060417,
-0.018156806007027626,
-0.008185151033103466,
-0.02052055113017559,
-0.0415429063141346,
0.03156420588493347,
0.021172527223825455,
-0.03449086472392082,
0.05508403480052948,
-0.006509849801659584,
0.0804222822189331,
0.04346378147602081,
0.013638160191476345,
0.02906523272395134,
0.02021198160946369,
0.02282821759581566,
0.024491487070918083,
0.005531469359993935,
-0.03822002559900284,
-0.04267474263906479,
-0.019214581698179245,
0.06123809888958931,
0.04832952097058296,
-0.0808098092675209,
0.025303354486823082,
0.02460028976202011,
0.02945595607161522,
0.03921828791499138,
0.010102654807269573,
-0.028692172840237617,
-0.028552135452628136,
0.022157106548547745,
0.018324656412005424,
0.021347537636756897,
-0.012698197737336159,
0.01602148823440075,
0.04419805482029915,
0.03820106014609337,
-0.04875926300883293,
-0.013982628472149372,
-0.007306697312742472,
-0.02141549438238144,
0.028979375958442688,
0.005512825679033995,
-0.040517255663871765,
0.03867394104599953,
-0.05105632543563843,
0.013031993061304092,
-0.0046695503406226635,
-0.00828047189861536,
0.011780771426856518,
-0.07461061328649521,
-0.018800858408212662,
0.022509032860398293,
0.026746179908514023,
-0.02952413819730282,
0.0014244246995076537,
0.026718292385339737,
-0.05177711322903633,
0.004059075843542814,
-0.006937085185199976,
0.02456655353307724,
-0.013377804309129715,
0.02923566848039627,
0.059190940111875534,
0.0013016301672905684,
0.028306711465120316,
-0.04856780171394348,
0.011091052554547787,
-0.029397210106253624,
-0.024196108803153038,
-0.038393277674913406,
-0.02349793165922165,
-0.007506886962801218,
0.006185438483953476,
-0.013808809220790863,
-0.018015345558524132,
0.018412254750728607,
-0.017158472910523415,
-0.029204875230789185,
-0.009526800364255905,
0.0024189918767660856,
-0.03997068479657173,
-0.024527033790946007,
-0.021325580775737762,
0.010682997293770313,
-0.06749739497900009,
-0.006349938455969095,
0.027665767818689346,
-0.01352072972804308,
-0.012072350829839706,
0.016677256673574448,
-0.035445161163806915,
-0.05883045122027397,
0.004371052607893944,
-0.014583075419068336,
-0.006425040774047375,
-0.036350298672914505,
0.03562811389565468,
0.03966813161969185,
-0.07526207715272903,
-0.0009764800197444856,
-0.04558468237519264,
-0.022227196022868156,
0.03607521206140518,
-0.01353748980909586,
0.04783391207456589,
-0.003002398880198598,
-0.021684816107153893,
0.056675609201192856,
0.038807548582553864,
-0.06675297766923904,
0.00882046204060316,
-0.013191232457756996,
-0.01901959255337715,
-0.008359048515558243,
0.026470856741070747,
0.030885275453329086,
0.016413968056440353,
-0.005355445202440023,
0.02672748640179634,
0.006087268237024546,
0.006495650392025709,
-0.0021568615920841694,
0.004963480401784182,
0.016718847677111626,
0.059215039014816284,
-0.0017098992830142379,
0.03858339414000511,
0.01821652427315712,
-0.04362712800502777,
-0.010063172318041325,
0.00617170799523592,
0.04585845768451691,
0.04374270886182785,
-0.03852658346295357,
0.06447386741638184,
-0.0156940259039402,
-0.0025791064836084843,
-0.04071817547082901,
0.02770032174885273,
-0.003668695455417037,
0.028067823499441147,
0.022205393761396408,
0.047798387706279755,
0.018710672855377197,
0.004348197486251593,
-0.017950767651200294,
0.02091199904680252,
0.058917976915836334,
-0.04928797855973244,
-0.03250065818428993,
-0.015797151252627373,
-0.018816974014043808,
0.0366782546043396,
0.033433690667152405,
-0.00689921947196126,
0.02675566077232361,
-0.0070551373064517975,
0.045107509940862656,
-0.019414329901337624,
-0.04164208099246025,
0.011659865267574787,
-0.06285669654607773,
0.006048091221600771,
-0.001477290061302483,
0.03150921314954758,
-0.019171763211488724,
0.04669351503252983,
0.007331294473260641,
0.02388441376388073,
0.014586344361305237,
0.031934190541505814,
-0.06133168190717697,
0.0019094719318673015,
-0.03435144200921059,
0.017690643668174744,
-0.01681073009967804,
-0.03287775442004204,
0.010310960002243519,
-0.02034815400838852,
-0.006737138610333204,
-0.020840808749198914,
-0.012773343361914158,
-0.028130337595939636,
0.025611823424696922,
0.006630131509155035,
-0.017229532822966576,
-0.007351472973823547,
0.014846482314169407,
0.007481378968805075,
-0.02991294302046299,
0.009915757924318314,
0.06615842133760452,
-0.027280952781438828,
0.028860745951533318,
-0.031033029779791832,
0.02441934309899807,
0.008910219185054302,
0.0037188308779150248,
0.013638032600283623,
-0.000576717488002032,
0.014073648490011692,
-0.016896337270736694,
0.002155059017241001,
0.054696425795555115,
-0.006582446396350861,
-0.007656347006559372,
-0.03835158795118332,
-0.041450172662734985,
0.0006919486331753433,
-0.005217207130044699,
0.005931191612035036,
-0.022944001480937004,
-0.0004332195094320923,
-0.023645495995879173,
-0.04210131615400314,
0.021953796967864037,
0.06936835497617722,
0.04962606355547905,
0.05456066504120827,
-0.011773866601288319,
-0.0741257444024086,
-0.05494796857237816,
-0.010277159512043,
-0.006732347421348095,
0.05506081134080887,
-0.004403834231197834,
-0.026977984234690666,
0.012149395421147346,
-0.014631145633757114,
0.012858182191848755,
0.013914080336689949,
-0.020156091079115868,
0.030310556292533875,
0.03284243494272232,
-0.03811292722821236,
0.010463787242770195,
0.007410475984215736,
0.02778794802725315,
0.03408432379364967,
-0.015315092168748379,
-0.014533154666423798,
-0.07945947349071503,
0.014336726628243923,
0.028340887278318405,
0.01764926314353943,
-0.02587168850004673,
0.006823384203016758,
-0.06589476019144058,
-0.006422314792871475,
0.05635490640997887,
-0.02344992198050022,
0.004570619203150272,
-0.03293009474873543,
0.0021571961697191,
-0.0054951817728579044,
0.004423567093908787,
-0.0016462423373013735,
-0.02587895840406418,
-0.015130195766687393,
0.021844010800123215,
-0.02649223431944847,
-0.025838246569037437,
-0.016977764666080475,
0.01732463575899601,
0.04725796729326248,
0.06523633003234863,
-0.011748643592000008,
0.015605964697897434,
-0.008213814347982407,
-0.037884876132011414,
-0.03941270709037781,
-0.06405386328697205,
-0.0030218851752579212,
-0.0010177791118621826,
0.014361708424985409,
0.015215129591524601,
-0.03509441390633583,
-0.06106691062450409,
0.03828902542591095,
0.010684349574148655,
-0.023230578750371933,
-0.001544175436720252,
-0.048209063708782196,
0.04104163870215416,
0.016579942777752876,
-0.007684472016990185,
0.02369089052081108,
0.04536684975028038,
0.007161552086472511,
-0.03783123567700386,
-0.03074660710990429,
0.04288913309574127,
-0.03736700862646103,
0.0034687945153564215,
-0.005558030679821968,
0.03951273113489151,
-0.04866909235715866,
0.04150819033384323,
-0.025086408481001854,
0.031028110533952713,
0.006926527246832848,
-0.00789600145071745,
0.029786206781864166,
0.029602164402604103,
0.01807490736246109,
-0.015170003287494183,
-0.009588823653757572,
0.01949726976454258,
-0.01424204558134079,
-0.005679091438651085,
0.012815069407224655,
-0.01555127464234829,
-0.013476990163326263,
0.017058731988072395,
-0.020650826394557953,
0.04104034602642059,
-0.02975289337337017,
-0.010784024372696877,
0.01578637957572937,
-0.03687489777803421,
0.04124368727207184,
-0.0465121790766716,
-0.028993036597967148,
0.0011241404572501779,
-0.08942519873380661,
0.010986054316163063,
0.029538163915276527,
0.018415363505482674,
0.0567777045071125,
-0.028533322736620903,
0.042946819216012955,
0.022258158773183823,
-0.011165895499289036,
-0.08148135244846344,
-0.034572236239910126,
0.03316212818026543,
0.07135315984487534,
-0.02458438277244568,
-0.05120828002691269,
0.03827923536300659,
-0.010568935424089432,
-0.030175840482115746,
-0.010842638090252876,
0.030644016340374947,
0.003370686899870634,
-0.05084088072180748,
0.03246254473924637,
0.026316840201616287,
0.07394877076148987,
0.010597115382552147,
-0.0605611652135849,
0.005347688216716051,
-0.007317612413316965,
-0.0311698317527771,
0.008206781931221485,
0.028494112193584442,
-0.019212301820516586,
-0.019798167049884796,
-0.0159225445240736,
-0.03180069848895073,
0.035787537693977356,
0.017949648201465607,
-0.010505331680178642,
0.006716660689562559,
0.018510006368160248,
-0.033317264169454575,
-0.051216721534729004,
0.00033174428972415626,
0.0033978286664932966,
0.03120226413011551,
-0.029626501724123955,
-0.01172679290175438,
-0.02674012817442417,
-0.038468409329652786,
0.008652572520077229,
-0.010652146302163601,
-0.014323463663458824,
-0.006509201135486364,
0.08576898276805878,
-0.011265363544225693,
0.003423146205022931,
0.015083794482052326,
-0.0063952188938856125,
0.028750859200954437,
0.016747474670410156,
0.015436502173542976,
0.01803692616522312,
0.04094008728861809,
-0.0026850930880755186,
-0.022173220291733742,
-0.030645374208688736,
0.024021245539188385,
0.07563392072916031,
-0.03344351425766945,
0.035370875149965286,
-0.007740105502307415,
-0.006648841314017773,
0.014758223667740822,
-0.014728441834449768,
0.009782706387341022,
0.0325838141143322,
0.008883636444807053,
0.04967605695128441,
-0.03119955211877823,
-0.0018448408227413893,
0.03137225657701492,
0.05976061522960663,
-0.0011229447554796934,
0.03019244782626629,
0.04654209315776825,
0.012078046798706055,
-0.035395894199609756,
-0.03365996479988098,
-0.05970179662108421,
0.03628672659397125,
-0.009512877091765404,
0.045081548392772675,
-0.012134513817727566,
-0.01196921244263649,
0.017559533938765526,
-0.008328191004693508,
0.034637853503227234,
-0.04813935607671738,
-0.02713368646800518,
0.0014682739274576306,
0.04646257683634758,
0.005481015890836716,
0.02589407190680504,
-0.000005240278369456064,
0.015127662569284439,
0.01987459510564804,
0.02430647984147072,
0.010752161964774132,
0.014316457323729992,
-0.08540192991495132,
-0.00012159823381807655,
0.0003769932663999498,
-0.030466770753264427,
0.028762435540556908,
0.011997975409030914,
-0.01860061101615429,
0.021217361092567444,
-0.016187680885195732,
0.033694300800561905,
0.025201814249157906,
-0.00871099904179573,
-0.020736873149871826,
0.03724552318453789,
0.029034579172730446,
0.01523549109697342,
0.009465469047427177,
0.009450491517782211,
0.10195817798376083,
0.05520718917250633,
0.04141252115368843,
-0.04910425841808319,
0.0012276433408260345,
-0.015888072550296783,
0.030547834932804108,
-0.055490631610155106,
-0.004490487277507782,
-0.018952561542391777,
0.0439557246863842,
0.0077481018379330635,
0.07274020463228226,
-0.008030533790588379,
0.01784646511077881,
0.04590808227658272,
-0.06087697669863701,
-0.032413773238658905,
-0.02748935855925083,
0.020135032013058662,
-0.020399056375026703,
0.02568967081606388,
-0.010943008586764336,
0.023519771173596382,
-0.015612180344760418,
-0.00818285159766674,
-0.05933976173400879,
-0.015218936838209629,
0.017712008208036423,
0.026315752416849136,
-0.06414185464382172,
-0.027242163196206093,
-0.01655438356101513,
-0.003244271967560053,
-0.060747336596250534,
0.0016540184151381254,
0.01298249140381813,
-0.03205006197094917,
-0.019008535891771317,
0.0025559416972100735,
0.011885365471243858,
0.02652783878147602,
0.012834141030907631,
0.026567401364445686,
-0.046359024941921234,
0.012124554254114628,
-0.0477769672870636,
-0.0004345329070929438,
-0.04339999705553055,
-0.03271135315299034,
0.0021200396586209536,
-0.0011053214548155665,
-0.010802358388900757,
-0.04814669117331505,
0.0036867992021143436,
-0.01465247105807066,
0.03751777485013008,
-0.001907645259052515,
-0.024321166798472404,
-0.03430475294589996,
0.026829326525330544,
-0.01377011276781559,
0.019374139606952667,
-0.0028590590227395296,
0.005604357924312353,
-0.003246350446715951,
0.03109297715127468,
-0.0019283154979348183,
-0.02317800559103489,
0.012482846155762672,
-0.02103910781443119,
-0.030013015493750572,
-0.05537765845656395,
-0.04847506433725357,
0.011382329277694225,
0.02763560228049755,
0.052163559943437576,
0.0024189020041376352,
0.03943543881177902,
-0.02007552608847618,
-0.05340880900621414,
0.037479646503925323,
-0.0081715052947402,
-0.017772536724805832,
-0.03276108577847481,
0.009524078108370304,
0.0059569100849330425,
0.05842586234211922,
-0.003193243406713009,
0.007558591663837433,
-0.003342488780617714,
-0.0066095395013689995,
0.019420523196458817,
-0.02416367270052433,
-0.027013173326849937,
0.0033107586205005646,
-0.0383831262588501,
0.03502722457051277,
0.009500844404101372,
0.002362453378736973,
0.055730607360601425,
0.02645324356853962,
0.010069254785776138,
-0.001126956776715815,
-0.023960696533322334,
0.004288783296942711,
-0.025591684505343437,
-0.021084725856781006,
0.014902749098837376,
0.040439389646053314,
-0.022331882268190384,
-0.01113036647439003,
-0.040135156363248825,
-0.015940921381115913,
-0.0007021705969236791,
0.014593539759516716,
0.027677547186613083,
-0.006787949241697788,
0.01229319628328085,
-0.015093532390892506,
0.01448134332895279,
-0.03210655227303505,
-0.015685252845287323,
-0.07873871922492981,
-0.015146316960453987,
0.02415218949317932,
-0.005628423299640417,
-0.03493321314454079,
0.008693300187587738,
-0.043422941118478775,
0.00790406670421362,
0.024873031303286552,
0.0056001110933721066,
0.04177486523985863,
-0.02052328549325466,
0.0314941368997097,
0.0009525535278953612,
0.052698828279972076,
-0.021428756415843964,
-0.03910931199789047,
0.032085079699754715,
-0.015706585720181465,
-0.027831250801682472,
0.006696008145809174,
-0.023562680929899216,
0.0030056973919272423,
0.017663482576608658,
0.028383685275912285,
0.01525176502764225,
0.07324917614459991,
-0.04341287538409233,
0.017916282638907433,
-0.012791338376700878,
-0.00870640017092228,
0.005912651773542166,
-0.00039863341953605413,
-0.00812063179910183,
0.0008554820669814944,
-0.024803971871733665,
0.06465829908847809,
0.03249359875917435,
0.007232483476400375,
-0.013602394610643387,
0.004364438354969025,
-0.012009560130536556,
-0.04937949776649475,
0.022761495783925056,
0.021750295534729958,
-0.001974351704120636,
0.01892707869410515,
-0.015818003565073013,
0.06639646738767624,
0.03554758056998253,
0.019374532625079155,
-0.08616092056035995,
-0.0023910498712211847,
0.02056286111474037,
0.026235323399305344,
0.03562323376536369,
-0.04454067721962929,
0.027014726772904396,
0.005561152473092079,
-0.07915990799665451,
0.007552840746939182,
-0.05935417115688324,
-0.04909517988562584,
-0.03102874383330345,
-0.03781437501311302,
-0.013583237305283546,
0.04989228770136833,
-0.010461177676916122,
0.03600858896970749,
0.033668845891952515,
0.0395151823759079,
-0.012874221429228783,
0.040811266750097275,
-0.01686602644622326,
0.027032705023884773,
0.013874874450266361,
-0.02117828279733658,
0.039033565670251846,
0.00008242659532697871,
-0.04447520524263382,
-0.006162742152810097,
-0.011233249679207802,
-0.010920688509941101,
0.012297382578253746,
0.009163890965282917,
-0.04404933750629425,
0.04919256642460823,
-0.00010610152094159275,
0.011406836099922657,
-0.005050288047641516,
0.023655518889427185,
-0.007881426252424717,
0.03182607144117355,
0.013304827734827995,
-0.019483350217342377,
0.0026548882015049458,
-0.043292708694934845,
-0.004657612647861242,
0.03556201234459877,
0.0009118814487010241,
0.015138804912567139,
-0.024942439049482346,
-0.00062683125725016,
0.054933637380599976,
-0.0020675878040492535,
0.012398604303598404,
-0.02445504441857338,
-0.020622776821255684,
0.059803564101457596,
-0.018327999860048294,
-0.03768320381641388,
0.02792791835963726,
0.040231216698884964,
-0.037900783121585846,
0.0027090932708233595,
0.011706879362463951,
-0.05040747672319412,
-0.024821124970912933,
-0.005312053021043539,
0.010310743935406208,
0.002645832719281316,
-0.02287636324763298,
-0.027471983805298805,
-0.05096781998872757,
0.05854067951440811,
0.016362536698579788,
0.027925316244363785,
0.03330120071768761,
-0.022581806406378746,
-0.06304056942462921,
-0.06290456652641296,
0.027555113658308983,
-0.014583743177354336,
-0.014584672637283802,
-0.011337758973240852,
0.01740265265107155,
-0.008646314963698387,
0.0292393546551466,
0.051464956253767014,
0.022685237228870392,
0.02093321643769741,
-0.030358068645000458,
-0.031776219606399536,
0.013560217805206776,
-0.051051121205091476,
0.01050269789993763,
0.020467067137360573,
-0.03946002572774887,
0.0405694805085659,
0.0009152507991530001,
-0.04047243297100067,
0.010606649331748486,
0.03456258028745651,
-0.01395376119762659,
0.015517538413405418,
-0.01775290071964264,
0.00451179314404726,
0.04119482636451721,
-0.004666301887482405,
-0.01851109229028225,
0.08170357346534729,
0.029028134420514107,
-0.008966967463493347,
0.027434194460511208,
-0.051239315420389175,
-0.04214996099472046,
0.0067005520686507225,
-0.038215093314647675,
0.0035402115900069475,
0.0026172653306275606,
-0.007129990961402655,
-0.017523912712931633,
-0.05276898294687271,
0.014833705499768257,
0.02521584741771221,
-0.009763523936271667,
0.00474374508485198,
0.03664441034197807,
0.049572769552469254,
0.05670030042529106,
0.012168715707957745,
0.009191807359457016,
-0.0072798896580934525,
-0.006754930131137371,
0.003370142076164484,
0.0615542009472847,
0.05670960992574692,
0.00015494566468987614,
0.0069258022122085094,
-0.004278914071619511,
0.0385005958378315,
-0.0222452525049448,
0.025989431887865067,
0.02704131416976452,
-0.03693963587284088,
-0.041023947298526764,
0.05460123345255852,
-0.004422752186655998,
0.02592231146991253,
-0.02569820173084736,
-0.015399796888232231,
0.06507755070924759,
-0.026264606043696404,
0.013734147883951664,
-0.029768822714686394,
-0.006220486480742693,
-0.018833862617611885,
0.023940742015838623,
0.024778977036476135,
0.031132763251662254,
-0.006097401957958937,
-0.015508139505982399,
-0.014689452014863491,
-0.04277339205145836,
0.010425357148051262,
-0.011446984484791756,
-0.02336914837360382,
-0.01694726012647152,
0.005168942268937826,
-0.015405137091875076,
0.031588438898324966,
-0.04307000711560249,
0.024923793971538544,
0.009452298283576965,
0.03684362396597862,
0.014036410488188267,
0.01895850896835327,
-0.015731479972600937,
0.00785269308835268,
0.05074184015393257,
-0.0663938969373703,
-0.011605973355472088,
-0.008402533829212189,
0.01853555627167225,
-0.020604068413376808,
-0.008903151378035545
] |
<p>In the popular culture the XIX-XX century competition between Thomas Edison and Nikola Tesla is well-known. The example could be the <a href="http://www.imdb.com/title/tt0482571/" rel="nofollow"><em>Prestige</em></a> movie, where there are some "Edison's agents" who sabotage Tesla's efforts. From electrical engineers' point of view the most known problem between them is whether to use DC or AC (the <a href="http://en.wikipedia.org/wiki/War_of_Currents" rel="nofollow">War of Currents</a>).</p>
<p>We can say that Edison is better known, because of the invention of a bulb or his first urban electricity system. Tesla is almost unknown, some people say about magic and so on. (That's why I recall the <em>Prestige</em> movie.)</p>
<p>In electricity it seems that Tesla has won, even if he's widely forgotten. We use AC mainly because of it's easy in transformers. We have an SI unit $\text{T}$ (tesla), which is for measuring magnetic induction.</p>
<p>But -- we can't forget Edison's impact on electricity. Even if he was mostly a great businessman, no-one can say he's done nothing but the bulb. <a href="http://en.wikipedia.org/wiki/List_of_Edison_patents" rel="nofollow">Here is some list of his patents</a>.</p>
<p>So why isn't he honored (like Tesla, Ampère, Volta, Siemens, Ohm, Faraday, ...) by his "own" unit in physics?</p> | 2,051 | [
-0.053553760051727295,
-0.023036211729049683,
-0.0018736054189503193,
-0.020711863413453102,
0.03282375633716583,
0.017414601519703865,
-0.04424622654914856,
-0.0074848392978310585,
-0.0017553010256960988,
-0.008541125804185867,
0.028730977326631546,
0.022523488849401474,
0.07778816670179367,
0.056793130934238434,
0.008438236080110073,
-0.03017866611480713,
0.0169418565928936,
0.00007921862561488524,
-0.012401982210576534,
-0.028418567031621933,
-0.036475084722042084,
-0.0005871477187611163,
-0.05261385813355446,
0.051886625587940216,
-0.015031587332487106,
0.04561951383948326,
0.00005631115709547885,
0.018263155594468117,
-0.028785554692149162,
0.017717404291033745,
-0.0006850808276794851,
-0.024458318948745728,
0.017811322584748268,
-0.035770416259765625,
0.0291086845099926,
-0.02066979557275772,
-0.018666841089725494,
-0.0403858944773674,
-0.011842130683362484,
0.03856176882982254,
-0.02735435776412487,
-0.005440243519842625,
-0.0020264084450900555,
0.024988757446408272,
-0.056423671543598175,
0.02767869457602501,
0.005156606435775757,
-0.03406583145260811,
0.0314108170568943,
-0.07868095487356186,
0.02717094123363495,
0.009864197112619877,
0.007681428454816341,
0.00370336277410388,
-0.032894380390644073,
0.004368619527667761,
0.052096739411354065,
0.017279570922255516,
-0.0037678671069443226,
-0.04966964200139046,
-0.013968231156468391,
-0.0012069991789758205,
-0.026515120640397072,
-0.0195169597864151,
-0.004283018875867128,
0.04897620528936386,
-0.008564256131649017,
-0.028918733820319176,
0.03719222545623779,
-0.053551770746707916,
0.0017711706459522247,
0.02663283608853817,
0.01183225680142641,
0.025959914550185204,
0.013329674489796162,
0.003711560508236289,
0.007069950923323631,
0.018990695476531982,
0.05240563675761223,
0.0023669167421758175,
-0.014165161177515984,
-0.014496334828436375,
0.02758214995265007,
0.010083450004458427,
-0.019024420529603958,
-0.015419302508234978,
0.03173438087105751,
-0.0332154706120491,
0.03302338346838951,
0.004598895087838173,
0.005139011889696121,
0.003596989205107093,
0.06678834557533264,
0.011947449296712875,
-0.00580170564353466,
0.026155805215239525,
-0.016756873577833176,
0.06176840886473656,
0.05704513564705849,
-0.0065779550932347775,
-0.0014616185799241066,
-0.0037862660828977823,
0.028679726645350456,
0.0785464271903038,
0.02472113072872162,
-0.03777354955673218,
0.008221876807510853,
-0.024757280945777893,
-0.012555206194519997,
0.005453367717564106,
-0.060503680258989334,
-0.005524516571313143,
0.01849273592233658,
0.023647697642445564,
-0.016412165015935898,
-0.008462181314826012,
0.013588854111731052,
0.00830268394201994,
0.10120577365159988,
0.06554491817951202,
0.047412727028131485,
-0.02926051616668701,
0.020045986399054527,
-0.0423000305891037,
-0.06810695677995682,
0.01451460923999548,
0.04281114786863327,
0.005125067662447691,
-0.011178389191627502,
0.06018397584557533,
0.0026421411894261837,
0.028942568227648735,
-0.02133377082645893,
-0.018971888348460197,
0.029743460938334465,
-0.02928008697926998,
-0.09317532926797867,
-0.04503535106778145,
0.02010457217693329,
0.004478536546230316,
-0.02696436271071434,
-0.05357642471790314,
-0.002919898135587573,
-0.02141069993376732,
0.08687946945428848,
0.0008693580166436732,
-0.025435209274291992,
0.0030349052976816893,
0.044433750212192535,
-0.007041607517749071,
-0.00980309210717678,
-0.010684631764888763,
0.06875278055667877,
-0.019263174384832382,
-0.024589983746409416,
-0.04240202531218529,
0.007303337100893259,
0.030162282288074493,
0.00652146153151989,
0.01255804579705,
0.049456704407930374,
0.033408381044864655,
-0.03857145458459854,
0.026598451659083366,
-0.020986320450901985,
-0.08551336824893951,
0.060014110058546066,
0.016456857323646545,
0.02738889306783676,
0.012741274200379848,
-0.010372373275458813,
0.0498306006193161,
0.04485064372420311,
0.009385456331074238,
0.05593070015311241,
-0.007637647911906242,
0.0010649490868672729,
-0.006777291186153889,
-0.008613861165940762,
0.009460038505494595,
-0.039642613381147385,
-0.06569342315196991,
0.018337208777666092,
0.007345263846218586,
0.006318993866443634,
0.07453690469264984,
-0.02788836508989334,
0.017342200502753258,
0.04875326156616211,
-0.04141194745898247,
-0.05682634189724922,
-0.04504891112446785,
0.01707211695611477,
0.026514336466789246,
-0.02534138597548008,
0.030147869139909744,
-0.0543227456510067,
-0.0058279442600905895,
0.0014763979706913233,
-0.037394680082798004,
0.0008220924064517021,
0.03307311609387398,
0.04371855780482292,
0.0026364752557128668,
0.028980150818824768,
0.0028247125446796417,
0.062236487865448,
-0.04600842297077179,
0.03249688446521759,
-0.018198838457465172,
-0.06996447592973709,
0.005345539655536413,
-0.03831973299384117,
0.050838325172662735,
0.0432434119284153,
-0.012818477116525173,
0.03563186898827553,
-0.036971986293792725,
-0.04045291244983673,
0.05343468487262726,
-0.02276674471795559,
0.04837332293391228,
0.03587810695171356,
0.011490407399833202,
-0.00970420055091381,
0.0677952915430069,
-0.00744106387719512,
0.012190151959657669,
0.022729452699422836,
0.002494147978723049,
-0.048555489629507065,
0.016140364110469818,
0.05575812608003616,
0.03011596016585827,
-0.029085973277688026,
0.014088623225688934,
0.018536798655986786,
0.05854107812047005,
0.0269489549100399,
-0.0035477974452078342,
-0.02285883016884327,
-0.039651330560445786,
0.010397279635071754,
0.020039351657032967,
-0.010910446755588055,
0.032589394599199295,
0.033319830894470215,
-0.0004993157344870269,
0.01563592068850994,
-0.02445199526846409,
0.02729390561580658,
0.05197183042764664,
-0.0102537265047431,
0.0011865745764225721,
0.016782961785793304,
0.000578533683437854,
0.008103284053504467,
-0.042340051382780075,
0.004873122554272413,
-0.002862397115677595,
-0.011919437907636166,
0.008613190613687038,
0.006356921512633562,
-0.007634336594492197,
-0.014149872586131096,
-0.03507198765873909,
-0.01963798888027668,
-0.0009102778858505189,
0.02350151166319847,
-0.04307295009493828,
0.014038004912436008,
-0.022126222029328346,
0.04189478978514671,
-0.0228237546980381,
-0.0177525095641613,
-0.018840335309505463,
0.013473731465637684,
0.048853158950805664,
0.008128543384373188,
-0.035939596593379974,
-0.0149993896484375,
-0.030106963589787483,
0.00827580876648426,
0.06309971958398819,
0.00209087785333395,
0.00920752715319395,
-0.041746508330106735,
-0.04275168851017952,
0.046872325241565704,
-0.004972269292920828,
0.012700337916612625,
-0.004805970937013626,
-0.015131539665162563,
-0.04057513549923897,
0.005783915985375643,
-0.01239598635584116,
0.00330363935790956,
-0.006838533096015453,
-0.02694784663617611,
0.05895235016942024,
-0.0017302784835919738,
-0.050479430705308914,
-0.006421109661459923,
-0.035716790705919266,
-0.03019946627318859,
-0.007104796357452869,
-0.013431084342300892,
0.01696772500872612,
-0.04342726245522499,
0.000013671975466422737,
0.028839316219091415,
-0.03667855262756348,
-0.019039610400795937,
-0.04792732372879982,
-0.03531505912542343,
-0.0012567306403070688,
-0.021591579541563988,
0.062250178307294846,
0.004940009210258722,
-0.008061758242547512,
0.010397221893072128,
0.04384228214621544,
-0.04099440947175026,
-0.03266950696706772,
-0.040608834475278854,
-0.006758945528417826,
-0.024106288328766823,
-0.0015044340398162603,
0.10154850780963898,
-0.023106327280402184,
0.010231303982436657,
0.014553365297615528,
0.006451159715652466,
0.022411614656448364,
0.00813218206167221,
-0.004227737430483103,
-0.0005153341335244477,
0.009899845346808434,
-0.011145888827741146,
0.06509356200695038,
0.02564566768705845,
-0.005500617902725935,
0.022790221497416496,
-0.017190145328640938,
0.03811078146100044,
0.04934073984622955,
-0.019544323906302452,
0.008795026689767838,
-0.031978923827409744,
-0.010391861200332642,
-0.025816896930336952,
-0.03751713037490845,
-0.011242211796343327,
0.008996575139462948,
0.0008011837489902973,
0.012675726786255836,
0.018909696489572525,
-0.03013727441430092,
-0.004094411619007587,
-0.002051870571449399,
0.062032636255025864,
-0.03592940419912338,
-0.020463336259126663,
-0.03026173636317253,
0.03687842935323715,
0.02048490196466446,
-0.017723601311445236,
-0.04493635520339012,
0.01563412696123123,
0.018048301339149475,
0.014228901825845242,
0.012324873358011246,
-0.01734328456223011,
-0.01004071719944477,
-0.05254339799284935,
-0.028429634869098663,
-0.02075590193271637,
0.06713060289621353,
-0.012298110872507095,
0.042745932936668396,
0.0019866274669766426,
0.010418600402772427,
-0.011606193147599697,
-0.02958909049630165,
-0.087937131524086,
-0.0042364876717329025,
-0.025900792330503464,
-0.01136152632534504,
-0.030892133712768555,
0.005823830142617226,
-0.010620846413075924,
0.023184554651379585,
0.021196359768509865,
-0.06233810633420944,
-0.0035158295650035143,
-0.043786097317934036,
0.013611973263323307,
-0.011719722300767899,
-0.048910290002822876,
-0.02939767949283123,
0.028362087905406952,
0.020759062841534615,
-0.03150707483291626,
0.03068690188229084,
-0.0035957973450422287,
-0.030742494389414787,
-0.009537744335830212,
-0.02990369126200676,
0.01557190902531147,
0.05771687626838684,
-0.01411363109946251,
0.016905441880226135,
0.017390811815857887,
-0.027204761281609535,
-0.002644216176122427,
0.07299411296844482,
0.031800348311662674,
0.012380908243358135,
-0.024588994681835175,
-0.04139450192451477,
-0.0007650530897080898,
-0.04622688144445419,
-0.018551262095570564,
0.050758473575115204,
-0.010299506597220898,
0.011637037619948387,
-0.003043606411665678,
0.023820141330361366,
0.018631968647241592,
0.032850317656993866,
0.014470922760665417,
-0.013171069324016571,
-0.013789455406367779,
-0.02225303463637829,
0.015725906938314438,
-0.021010318771004677,
-0.022517120465636253,
0.005663920659571886,
0.009353609755635262,
0.00818238127976656,
-0.05284203961491585,
0.0393737331032753,
0.014924086630344391,
-0.04408140480518341,
0.0484752357006073,
0.010243036784231663,
-0.012227929197251797,
-0.008392698131501675,
-0.0037477612495422363,
0.002226664684712887,
-0.000059370962844695896,
0.03813976049423218,
0.016513077542185783,
-0.008241797797381878,
-0.09074003994464874,
-0.01751643978059292,
0.03240196779370308,
0.06642558425664902,
-0.02519562654197216,
-0.029297202825546265,
-0.04612322896718979,
0.010665470734238625,
0.050872281193733215,
-0.030099131166934967,
0.013844367116689682,
-0.04663202539086342,
-0.00777469901368022,
-0.027657141909003258,
-0.025114143267273903,
-0.00662460969761014,
0.039735887199640274,
0.008074638433754444,
0.06485315412282944,
-0.013343487866222858,
-0.015527659095823765,
0.01519555039703846,
0.02294909581542015,
0.016188180074095726,
0.03703002631664276,
-0.01477560494095087,
-0.024850202724337578,
-0.0024736043997108936,
0.037532441318035126,
0.006667434237897396,
-0.07333915680646896,
-0.0002306937676621601,
-0.012612483464181423,
-0.027451949194073677,
0.04021719470620155,
-0.010004371404647827,
-0.06720086187124252,
0.030341947451233864,
0.019662074744701385,
0.0012331882026046515,
0.011264504864811897,
-0.014668626710772514,
0.0376412495970726,
0.026969874277710915,
-0.00831130426377058,
0.007264527026563883,
0.018864639103412628,
-0.024657299742102623,
0.019552458077669144,
0.006168560590595007,
0.006707106251269579,
-0.005913685541599989,
0.00290622073225677,
0.01985231786966324,
0.03719387948513031,
-0.047235943377017975,
0.025808658450841904,
-0.018969517201185226,
0.05213558301329613,
-0.06318482011556625,
-0.01725134812295437,
0.024050438776612282,
0.0028477951418608427,
-0.056245215237140656,
-0.014332395046949387,
-0.03209814056754112,
0.012435548938810825,
-0.007729025557637215,
-0.002388619352132082,
-0.0015325038693845272,
0.025436019524931908,
0.05292591080069542,
0.030192814767360687,
0.018735723569989204,
0.013357470743358135,
-0.030262989923357964,
-0.00645829364657402,
-0.008122861385345459,
-0.0421876423060894,
0.08240581303834915,
-0.001740672392770648,
0.0029410747811198235,
-0.010794488713145256,
-0.04341279715299606,
-0.08869579434394836,
0.002974718576297164,
-0.012535447254776955,
0.0445842482149601,
-0.0637759268283844,
0.026167957112193108,
0.005687812343239784,
-0.00938467402011156,
-0.029235368594527245,
-0.0202302448451519,
-0.02585979364812374,
0.03901762142777443,
0.021458443254232407,
0.02366340160369873,
0.004005121532827616,
0.018044130876660347,
-0.02453484572470188,
-0.03458765521645546,
0.011000972241163254,
-0.007224845699965954,
-0.006217482965439558,
0.013714614324271679,
0.024370552971959114,
0.07831161469221115,
-0.004260809626430273,
-0.031582463532686234,
-0.017193637788295746,
-0.012959343381226063,
-0.007224912755191326,
-0.01557972002774477,
0.05505388230085373,
-0.04016636312007904,
-0.028435854241251945,
0.021243806928396225,
-0.000020445339032448828,
0.0023105493746697903,
-0.004646772984415293,
0.00962783582508564,
0.04476139694452286,
0.01693422719836235,
-0.029514919966459274,
0.008486071601510048,
0.014691203832626343,
0.018821338191628456,
0.003062468720600009,
0.019760990515351295,
0.002575503895059228,
-0.016978533938527107,
-0.030149415135383606,
-0.002326466841623187,
0.011830819770693779,
-0.03706866502761841,
-0.034099429845809937,
0.01386340707540512,
-0.020333783701062202,
0.009425846859812737,
0.07441260665655136,
0.04361864551901817,
0.06365922093391418,
-0.007798935752362013,
0.0383819155395031,
0.006439600605517626,
0.026810841634869576,
-0.015638550743460655,
-0.00487459497526288,
-0.030773069709539413,
0.027320729568600655,
0.0026131633203476667,
-0.013201666995882988,
0.0565868616104126,
0.0035167881287634373,
-0.016211550682783127,
0.013435550965368748,
-0.010633259080350399,
-0.01655499078333378,
0.015632031485438347,
-0.020310986787080765,
0.005503155756741762,
0.0136265829205513,
0.050789229571819305,
0.04282201826572418,
0.01828639954328537,
0.0022832199465483427,
-0.028839662671089172,
-0.004831904545426369,
0.039244167506694794,
-0.009817946702241898,
-0.035397935658693314,
-0.026945393532514572,
0.05547352135181427,
-0.03345771133899689,
0.0149001469835639,
0.002804791321977973,
-0.0005888795130886137,
0.03124728612601757,
-0.01211926992982626,
-0.0013793192338198423,
-0.036267854273319244,
-0.06296377629041672,
-0.09173312038183212,
0.014212719164788723,
0.019776832312345505,
-0.003417662577703595,
-0.0022981001529842615,
-0.021252285689115524,
-0.0016520358622074127,
0.013200449757277966,
0.011116130277514458,
-0.02219972386956215,
-0.04120408371090889,
-0.010743499733507633,
-0.03233081474900246,
-0.031450845301151276,
0.05301981046795845,
-0.0009554253774695098,
-0.017691193148493767,
0.004305390641093254,
-0.02503465674817562,
0.0289936326444149,
0.046003106981515884,
0.018440376967191696,
0.0069588059559464455,
0.06438235938549042,
-0.029121018946170807,
0.038143061101436615,
-0.01833069883286953,
-0.011309471912682056,
0.14377200603485107,
0.011520043015480042,
0.03497441112995148,
-0.04889431595802307,
0.0076659321784973145,
-0.030543774366378784,
0.00844669621437788,
-0.05194918438792229,
0.004159898031502962,
-0.03522643446922302,
0.007454423233866692,
0.008551438339054585,
0.00716891884803772,
0.0392012745141983,
-0.0039248294197022915,
0.029473144561052322,
-0.0514625608921051,
-0.026498692110180855,
0.010723995044827461,
0.02599373087286949,
-0.011504008434712887,
-0.004906896036118269,
-0.05841855704784393,
0.0009533122647553682,
-0.0115024009719491,
0.04138661548495293,
-0.003324934048578143,
-0.042379919439554214,
0.029587522149086,
0.03190525248646736,
-0.008352421224117279,
0.024745747447013855,
0.04195515811443329,
0.014416723512113094,
-0.025271546095609665,
0.015791073441505432,
0.03127208724617958,
0.015583776868879795,
0.01883063092827797,
0.03656994551420212,
0.05417635291814804,
-0.03233514726161957,
-0.009152859449386597,
0.03190729022026062,
-0.057090479880571365,
0.0021749758161604404,
-0.05383588373661041,
0.017962757498025894,
0.0033864304423332214,
-0.0012196326861158013,
0.0062493025325238705,
0.020118720829486847,
-0.01677003875374794,
-0.024483926594257355,
-0.04624975100159645,
-0.022263256832957268,
0.05464500933885574,
-0.03755703195929527,
-0.017528677359223366,
-0.00521667068824172,
0.04393083229660988,
-0.04039432853460312,
0.03677411377429962,
0.004508471116423607,
-0.013263304717838764,
-0.008101367391645908,
-0.013318778946995735,
0.00558440200984478,
-0.014995615929365158,
-0.012991895899176598,
-0.04470132663846016,
-0.036950819194316864,
-0.04873337224125862,
-0.028662679716944695,
0.00028060117620043457,
0.02389465644955635,
0.029104236513376236,
-0.01510368101298809,
0.03240685164928436,
-0.01973622292280197,
-0.023237504065036774,
0.0343327671289444,
0.030963731929659843,
0.027430512011051178,
-0.018346698954701424,
0.01403229683637619,
0.009261777624487877,
-0.012054347433149815,
-0.01607416197657585,
-0.008605477400124073,
0.0327850803732872,
0.030079228803515434,
0.04885965585708618,
-0.022498583421111107,
-0.04640363156795502,
0.0035338897723704576,
-0.01397702470421791,
-0.003449587617069483,
0.008271962404251099,
0.019190000370144844,
0.019179461523890495,
-0.03455410525202751,
0.019974511116743088,
0.021071292459964752,
-0.005132089834660292,
-0.00442907540127635,
0.019012827426195145,
-0.06943244487047195,
-0.01255269069224596,
-0.03018937073647976,
0.016256947070360184,
0.019615940749645233,
-0.047374922782182693,
-0.04135895520448685,
0.05485812947154045,
0.019192932173609734,
0.02548471838235855,
0.00814735610038042,
-0.008588265627622604,
-0.01850736141204834,
0.036889031529426575,
-0.049116987735033035,
-0.016141628846526146,
-0.05019176006317139,
-0.007916773669421673,
-0.007833526469767094,
-0.011357683688402176,
0.009871859103441238,
0.06479451060295105,
-0.013949536718428135,
-0.012631713412702084,
0.0011965787271037698,
0.011419045738875866,
-0.06175171583890915,
-0.021450433880090714,
-0.05350730940699577,
-0.022264234721660614,
0.02802421897649765,
-0.042077045887708664,
-0.016379745677113533,
0.084966741502285,
0.008622203022241592,
-0.04078131541609764,
0.02438807301223278,
-0.024270035326480865,
-0.011721448041498661,
0.0295014139264822,
0.01928052492439747,
0.0009834656957536936,
0.04902447387576103,
-0.03582949936389923,
0.02149725891649723,
0.01886553131043911,
-0.009360934607684612,
0.012302267365157604,
0.020313218235969543,
-0.02550249919295311,
-0.011080170050263405,
0.006527028512209654,
0.0015704522375017405,
0.05169194936752319,
0.012490223161876202,
-0.008132094517350197,
-0.002885195193812251,
0.002607028465718031,
0.02126864530146122,
0.00781472772359848,
0.035817939788103104,
0.02267170138657093,
0.04218313843011856,
-0.06468743830919266,
0.009714514017105103,
0.03239375352859497,
0.02968999743461609,
-0.06703297048807144,
0.0062325214967131615,
0.01051503885537386,
0.010165732353925705,
0.017395751550793648,
-0.027837833389639854,
0.0006150380941107869,
-0.00056964170653373,
-0.09505926072597504,
0.017375091090798378,
0.014115771278738976,
-0.021203571930527687,
-0.020842280238866806,
-0.04249216243624687,
-0.0149937579408288,
0.04209725558757782,
0.008418135344982147,
0.04007392004132271,
0.03349711000919342,
0.020879339426755905,
0.01967654936015606,
-0.03068244829773903,
-0.04230528697371483,
0.01954076811671257,
0.001531067886389792,
0.010267606936395168,
0.06084630265831947,
-0.04213050752878189,
-0.03274931013584137,
0.0338522344827652,
0.010877911932766438,
0.010134266689419746,
-0.004438645672053099,
0.015737129375338554,
0.019188053905963898,
0.06324407458305359,
0.021057549864053726,
-0.015664365142583847,
-0.014259793795645237,
0.021544605493545532,
0.04867321252822876,
0.03293395787477493,
0.029132407158613205,
0.008929348550736904,
0.04993929713964462,
-0.017054781317710876,
-0.0197078175842762,
-0.004962863400578499,
0.010612702928483486,
-0.007906705141067505,
-0.006949456874281168,
0.04424953833222389,
0.042194921523332596,
0.015074826776981354,
-0.026272058486938477,
-0.019418107345700264,
-0.04728272557258606,
0.012916960753500462,
-0.016278084367513657,
0.05214868485927582,
-0.0070226420648396015,
-0.009052475914359093,
-0.06734170764684677,
0.06740060448646545,
0.012276962399482727,
-0.029192976653575897,
-0.03241221606731415,
-0.0013567206915467978,
0.010273356921970844,
0.008802165277302265,
0.00886103417724371,
-0.037108324468135834,
-0.03954959660768509,
0.01945674791932106,
0.016326909884810448,
0.012732097879052162,
-0.000427272985689342,
-0.09413770586252213,
-0.02026006579399109,
-0.08403854817152023,
0.045896466821432114,
-0.003030130872502923,
0.009898592717945576,
-0.016600744798779488,
-0.04541761055588722,
0.00002666765976755414,
0.026150602847337723,
0.04182182997465134,
-0.03812471032142639,
-0.02894449606537819,
0.004461842123419046,
-0.02906971611082554,
0.04319675266742706,
-0.042263664305210114,
0.03208094835281372,
0.045130323618650436,
0.0010950630530714989,
-0.002789152320474386,
0.032280150800943375,
-0.0017456421628594398,
0.022282162681221962,
0.021413784474134445,
0.025097165256738663,
-0.033577483147382736,
-0.051755595952272415,
-0.0302421972155571,
0.007546002510935068,
0.02284288965165615,
-0.02506188675761223,
0.06164681538939476,
0.008547504432499409,
0.029602233320474625,
-0.03809836879372597,
-0.022884156554937363,
-0.05313108116388321,
0.03296683728694916,
-0.007343463599681854,
-0.031129322946071625,
0.0029362100176513195,
-0.006048922892659903,
-0.0029158422257751226,
-0.02737596072256565,
-0.03756377100944519,
0.023213310167193413,
-0.0015197634929791093,
-0.021156301721930504,
0.034847360104322433,
0.02533581480383873,
-0.0005413222825154662,
0.02047002501785755,
-0.016218023374676704,
-0.016631754115223885,
0.027662862092256546,
-0.05639711767435074,
0.03182174265384674,
0.03940824419260025,
0.022503910586237907,
0.0067653898149728775,
0.024512644857168198,
0.02613414078950882,
0.003492694115266204,
0.0002588608185760677,
0.03196161985397339,
-0.015242130495607853,
-0.010620851069688797,
0.026589935645461082,
-0.013630779460072517,
-0.011420504190027714,
0.01074314583092928,
-0.011390137486159801,
0.06539543718099594,
-0.01699584163725376,
0.03049953654408455,
-0.012633630074560642,
0.014310633763670921,
-0.01341488491743803,
-0.029222333803772926,
0.0184153001755476,
0.0363641232252121,
-0.05256952345371246,
-0.0230998732149601,
-0.03494997322559357,
0.02037992514669895,
0.019492054358124733,
-0.039548616856336594,
0.005086093209683895,
-0.01680019311606884,
-0.004210657440125942,
0.001969575183466077,
0.0065551213920116425,
-0.015436512418091297,
-0.03691842406988144,
0.014006450772285461,
0.03527938947081566,
0.025049347430467606,
0.01315799355506897,
-0.015567547641694546,
-0.010511292144656181,
0.033372484147548676,
-0.04659659042954445,
-0.01900976523756981,
-0.033063482493162155,
0.030684586614370346,
0.02149568311870098,
-0.013260696083307266
] |
<p>The diagram in <a href="http://physics.stackexchange.com/questions/36092/why-are-l4-and-l5-lagrangian-points-stable">Why are L4 and L5 lagrangian points stable?</a> shows that the gravitational potential decreases outside the ring of Lagrange points — this image shows it even more clearly:
<img src="http://i.stack.imgur.com/JMnkQ.gif" alt="Potential surface"></p>
<p>If I understand correctly, using the rubber-sheet model analogy, an object placed in the field moves as if a marble rolls on the sheet with downward gravity. That's fine for objects inside the Lagrange ring: They move towards either mass.</p>
<p>But outside it, it implies that they move <strong>away</strong> from both masses. Is that really what happens? If so, why? If not, why does the surface slope downwards?</p> | 2,052 | [
-0.04507990553975105,
-0.010793423280119896,
-0.005027174949645996,
0.0027275963220745325,
-0.023518241941928864,
-0.0134139284491539,
0.02220488339662552,
-0.02684338577091694,
0.00912846252322197,
0.006205038633197546,
0.005684619769454002,
0.019052419811487198,
0.044328708201646805,
0.006529480218887329,
0.02535855397582054,
0.018001748248934746,
0.01601242832839489,
-0.005361212883144617,
0.010431723669171333,
-0.022569207474589348,
-0.018269307911396027,
0.021980883553624153,
0.018819212913513184,
-0.010768183507025242,
-0.03334464505314827,
-0.0007252166396938264,
0.014042890630662441,
-0.0201362706720829,
-0.004478346556425095,
0.09027385711669922,
-0.03457513824105263,
0.0015788666205480695,
0.0021543940529227257,
-0.004881083499640226,
0.020627673715353012,
0.013540959917008877,
-0.009755929931998253,
0.001292356289923191,
-0.027867162600159645,
0.02030913718044758,
-0.044255126267671585,
0.0027562188915908337,
-0.030615881085395813,
0.06705579906702042,
-0.0273406021296978,
-0.011677535250782967,
0.028637368232011795,
0.001264440594241023,
0.08388014137744904,
-0.03584935888648033,
0.03943272680044174,
0.020265331491827965,
0.00883875135332346,
0.04188016802072525,
-0.007603447884321213,
-0.026975683867931366,
0.0662168562412262,
0.06771185249090195,
-0.020492296665906906,
-0.060264237225055695,
-0.0589255690574646,
-0.053644467145204544,
-0.020716406404972076,
-0.03215523809194565,
-0.005473666358739138,
0.03169288486242294,
0.0026898798532783985,
0.036310646682977676,
0.04099125787615776,
-0.007878315635025501,
-0.021519631147384644,
0.05234790965914726,
0.02214818447828293,
-0.02968534454703331,
0.04282110184431076,
-0.008556531742215157,
0.028151830658316612,
-0.007705563213676214,
-0.005510355811566114,
0.01368276309221983,
0.004532552324235439,
0.02727522701025009,
0.02285783924162388,
0.04250641539692879,
0.01696041226387024,
-0.005191602744162083,
0.06189689412713051,
0.011573903262615204,
0.02919425070285797,
0.05483420938253403,
-0.018596867099404335,
-0.007973012514412403,
0.012641433626413345,
-0.02759407088160515,
-0.017311982810497284,
0.022827310487627983,
0.004598069470375776,
0.040726397186517715,
0.013464629650115967,
0.01709444634616375,
-0.03719603642821312,
-0.00477408105507493,
0.03783992677927017,
0.06465066969394684,
0.038012225180864334,
-0.030111435800790787,
-0.023493919521570206,
-0.001675893203355372,
0.02647719532251358,
-0.03329428657889366,
-0.026193538680672646,
0.021512974053621292,
0.002723423298448324,
-0.023414280265569687,
-0.00699507724493742,
-0.037519391626119614,
-0.004773512948304415,
-0.01563779078423977,
0.017154350876808167,
0.007522062864154577,
0.043546441942453384,
-0.03700941801071167,
0.021893177181482315,
-0.05359490215778351,
-0.02821892686188221,
0.0006563051138073206,
0.055267978459596634,
-0.032092735171318054,
-0.014277148991823196,
0.015864968299865723,
0.03637099266052246,
0.02202487178146839,
-0.012216714210808277,
0.016643045470118523,
0.029358545318245888,
0.005704384762793779,
-0.08372500538825989,
-0.05007244274020195,
0.07388191670179367,
0.04680885002017021,
-0.00805613398551941,
-0.06062103062868118,
-0.03808227926492691,
0.02373875118792057,
0.09290938824415207,
-0.00954918097704649,
0.007087492384016514,
0.01356093492358923,
0.016776660457253456,
-0.0014949494507163763,
0.02452673204243183,
0.002637820551171899,
-0.022256474941968918,
-0.05656846612691879,
-0.0214689951390028,
-0.10935976356267929,
-0.006622197572141886,
0.01921909675002098,
-0.020747113972902298,
-0.049231257289648056,
0.050990376621484756,
-0.04917127639055252,
0.04479050636291504,
-0.024560250341892242,
-0.03013341687619686,
0.011430269107222557,
0.05799310281872749,
-0.008603706955909729,
0.0040998379699885845,
0.039252229034900665,
0.0012681809021160007,
0.040265150368213654,
-0.013307105749845505,
0.030381426215171814,
0.028912166133522987,
-0.03327900171279907,
0.0036601179745048285,
-0.034833814948797226,
0.0010941715445369482,
-0.03122822381556034,
-0.0540277324616909,
-0.042007140815258026,
-0.0242094025015831,
-0.03557839244604111,
-0.020050641149282455,
0.04291588440537453,
-0.013116246089339256,
0.02503831312060356,
-0.01415864285081625,
-0.0313902385532856,
-0.018321247771382332,
-0.07288369536399841,
0.04404863715171814,
0.010861027985811234,
0.010528653860092163,
0.011377319693565369,
0.02588794007897377,
0.04377041757106781,
-0.027125105261802673,
0.018142936751246452,
-0.013969055376946926,
0.04392137750983238,
-0.04573861509561539,
0.01876910962164402,
0.00647529773414135,
0.05817973613739014,
0.013490411452949047,
0.023953134194016457,
-0.012236390262842178,
-0.0661691427230835,
-0.011692517437040806,
0.028654498979449272,
0.030620357021689415,
0.01851465366780758,
0.0001399018510710448,
-0.008735344745218754,
-0.01392788253724575,
0.015302215702831745,
-0.005178798455744982,
0.02815055102109909,
-0.047000445425510406,
0.04728955030441284,
0.02518807351589203,
0.007328056264668703,
-0.01640552654862404,
0.061551883816719055,
-0.005921696312725544,
0.030151112005114555,
0.023580243811011314,
-0.014432275667786598,
-0.05035921186208725,
0.018167782574892044,
0.008989635854959488,
0.05348610132932663,
-0.03820161148905754,
0.024740401655435562,
0.028832249343395233,
0.04751405864953995,
0.006728156004101038,
-0.002238416811451316,
-0.02543983981013298,
-0.022269614040851593,
0.0598493367433548,
0.013719246722757816,
-0.00047871272545307875,
0.012697573751211166,
0.026624735444784164,
0.029454397037625313,
0.0005484058638103306,
0.018657637760043144,
-0.023940861225128174,
0.04467778652906418,
-0.0017167208716273308,
0.021144669502973557,
-0.023811200633645058,
-0.02917628176510334,
0.04994989186525345,
-0.02413899078965187,
0.011213590390980244,
0.03355991095304489,
0.003836521180346608,
-0.008843054994940758,
-0.0680442675948143,
-0.0259795431047678,
0.04335085675120354,
0.014417503029108047,
0.0036491351202130318,
-0.030397504568099976,
0.006431497633457184,
-0.05375109985470772,
0.005703170318156481,
-0.020312964916229248,
-0.013296165503561497,
-0.022744743153452873,
0.0038989209569990635,
0.0019573220051825047,
0.00818621926009655,
-0.001712464028969407,
-0.040984123945236206,
-0.0017857651691883802,
0.004373654257506132,
-0.03994123637676239,
0.00985935889184475,
0.021252743899822235,
-0.04840574041008949,
-0.0004288727941457182,
-0.044595714658498764,
-0.010985284112393856,
0.06427782773971558,
0.029656175523996353,
-0.005166909191757441,
0.028990134596824646,
-0.002594403922557831,
-0.027023181319236755,
-0.016707245260477066,
0.001961059868335724,
0.015336626209318638,
-0.019681286066770554,
-0.008506485261023045,
0.06786736845970154,
-0.017644334584474564,
0.024497687816619873,
0.0232253298163414,
-0.045756228268146515,
-0.0183296836912632,
-0.012243818491697311,
0.036088284105062485,
-0.0072868880815804005,
0.012371142394840717,
-0.006505994126200676,
0.009915114380419254,
-0.004344501066952944,
0.006691370625048876,
-0.04655584692955017,
-0.03954322263598442,
-0.01906011998653412,
-0.019760042428970337,
0.017029104754328728,
-0.008453036658465862,
-0.007066722959280014,
0.10604935139417648,
0.04504196718335152,
-0.04121307656168938,
-0.028428003191947937,
-0.032864466309547424,
-0.04531151428818703,
-0.0032962309196591377,
0.0020231350790709257,
0.02687363140285015,
0.007770435884594917,
0.016646336764097214,
0.02600305713713169,
0.00914569292217493,
0.0006389201735146344,
-0.01566213369369507,
-0.017627010121941566,
-0.013691814616322517,
0.01662243902683258,
-0.034122150391340256,
0.027011744678020477,
-0.0011525736190378666,
-0.013033192604780197,
-0.011849935166537762,
-0.014476778917014599,
0.05413723364472389,
0.006291795056313276,
-0.05780414864420891,
0.06380224227905273,
-0.0044852388091385365,
-0.018997902050614357,
0.0023088871967047453,
0.043275557458400726,
0.011710097081959248,
-0.03380772843956947,
-0.004573326092213392,
-0.017857173457741737,
0.08014308661222458,
-0.02077394723892212,
-0.00847416091710329,
0.04667818918824196,
0.06432454288005829,
-0.04741869494318962,
-0.048413004726171494,
0.004417591728270054,
-0.015544390305876732,
0.05593087524175644,
-0.030261168256402016,
-0.007171357981860638,
0.011793440207839012,
0.008669007569551468,
-0.018511945381760597,
-0.00885604415088892,
-0.049985747784376144,
-0.031124968081712723,
-0.08715861290693283,
0.019986551254987717,
0.017276154831051826,
0.04675553739070892,
0.0052930619567632675,
0.035440586507320404,
0.022667545825242996,
0.005849038250744343,
0.014461045153439045,
0.017587369307875633,
-0.0875430479645729,
0.017477408051490784,
-0.04287083446979523,
-0.01328036468476057,
0.010078339837491512,
-0.014965792186558247,
0.0009458561544306576,
0.005814872682094574,
-0.025227481499314308,
-0.019095558673143387,
0.0021604453213512897,
-0.07334734499454498,
-0.01337508950382471,
-0.02391974627971649,
-0.022646958008408546,
-0.013645755127072334,
0.011595816351473331,
0.031063077971339226,
-0.011740139685571194,
0.0604417510330677,
0.03384383022785187,
-0.004471914377063513,
-0.021905312314629555,
-0.02295510284602642,
0.010432442650198936,
0.018544720485806465,
0.014040022157132626,
0.004471416585147381,
0.01774267479777336,
0.014453256502747536,
0.0038532728794962168,
0.0298615675419569,
0.06432074308395386,
0.013011586852371693,
-0.008602935820817947,
0.0004689862544182688,
-0.05359399691224098,
-0.02580917999148369,
-0.004542050417512655,
0.04434657841920853,
-0.011302965693175793,
-0.018316498026251793,
0.015507595613598824,
-0.005269543267786503,
0.008596943691372871,
0.0515911839902401,
0.04414128139615059,
0.025140590965747833,
-0.017586160451173782,
-0.05314263328909874,
-0.04863458499312401,
-0.017649533227086067,
-0.0008659237064421177,
0.04832804948091507,
-0.040841490030288696,
-0.014747030101716518,
0.014216371811926365,
0.02667928673326969,
0.01622539386153221,
-0.010554138571023941,
-0.0038214335218071938,
-0.006493016611784697,
0.04810059815645218,
-0.025740930810570717,
0.024602625519037247,
0.01919950731098652,
0.03759361058473587,
0.08190364390611649,
-0.009190893732011318,
0.003234763164073229,
-0.08560378104448318,
-0.03409687429666519,
0.016977844759821892,
0.027590032666921616,
-0.0024358872324228287,
-0.002126670442521572,
-0.051293130964040756,
-0.02215072140097618,
0.056169889867305756,
-0.014397509396076202,
0.04849753528833389,
-0.012735741212964058,
0.02922927774488926,
-0.03593216463923454,
-0.0052342708222568035,
-0.015303319320082664,
-0.01712789759039879,
-0.018097197636961937,
0.04182210564613342,
-0.027757231146097183,
0.01223725639283657,
-0.0197963397949934,
0.03194459155201912,
-0.0009685150580480695,
0.07226841896772385,
0.010196308605372906,
0.019856734201312065,
-0.032869257032871246,
-0.01882953941822052,
-0.0382508859038353,
-0.07141400128602982,
-0.0002859335800167173,
-0.005486993119120598,
-0.037420812994241714,
0.04490330442786217,
-0.04750460386276245,
-0.016300419345498085,
0.014336695894598961,
0.017080390825867653,
0.02132541872560978,
-0.022833622992038727,
-0.05489814653992653,
0.008897380903363228,
0.047010112553834915,
-0.0071380361914634705,
0.05776045471429825,
0.026099443435668945,
-0.017763778567314148,
-0.007729853503406048,
-0.01141153834760189,
0.042540472000837326,
-0.00967477262020111,
0.007477188482880592,
-0.03516453877091408,
-0.021589701995253563,
-0.038062307983636856,
0.026547718793153763,
0.021485311910510063,
0.004725436680018902,
-0.03560342267155647,
-0.049479834735393524,
-0.02843092754483223,
0.0001281899312743917,
0.015121827833354473,
0.006672783754765987,
0.015773747116327286,
0.011532203294336796,
0.006960588041692972,
-0.040188003331422806,
0.006606967654079199,
-0.0323299840092659,
-0.013064201921224594,
0.033489372581243515,
0.009080418385565281,
-0.0006408350891433656,
-0.009975036606192589,
-0.017001675441861153,
-0.017154255881905556,
-0.0563027523458004,
0.05314185097813606,
0.015515477396547794,
-0.018386028707027435,
0.061646245419979095,
-0.03515877574682236,
-0.00990641675889492,
-0.014194401912391186,
-0.012034828774631023,
-0.011775776743888855,
-0.05413084849715233,
0.022698771208524704,
0.0480409599840641,
0.025148434564471245,
-0.05967395007610321,
-0.05846566706895828,
0.021188125014305115,
-0.006918580271303654,
-0.016911203041672707,
-0.010861304588615894,
-0.012264196760952473,
-0.03208654746413231,
-0.02167150005698204,
-0.01570051722228527,
0.013220220804214478,
-0.0419975221157074,
0.0019737123511731625,
0.051629092544317245,
-0.018671130761504173,
0.07110925763845444,
-0.013486050069332123,
-0.003618081333115697,
0.023610981181263924,
0.036609552800655365,
-0.019932279363274574,
-0.016335343942046165,
0.07656534761190414,
-0.020519712939858437,
-0.022379323840141296,
-0.0009254809701815248,
0.004285232629626989,
0.0426187589764595,
-0.0036106305196881294,
-0.01516521442681551,
0.04510054737329483,
0.01869736798107624,
0.008901993744075298,
-0.02293756790459156,
0.01449668314307928,
-0.0045563713647425175,
0.03528730198740959,
0.014568392187356949,
0.015159279108047485,
0.022127337753772736,
-0.056950729340314865,
0.023012984544038773,
0.00968814268708229,
0.00926700234413147,
0.024800371378660202,
0.10504242777824402,
-0.030262822285294533,
-0.015094728209078312,
0.01733001321554184,
-0.009544365108013153,
0.06363540142774582,
0.02086135745048523,
-0.014457987621426582,
0.011387954466044903,
0.03452487289905548,
-0.021522609516978264,
-0.05689076706767082,
-0.012622496113181114,
0.007939718663692474,
0.05167049169540405,
-0.04326794296503067,
0.02063761278986931,
0.031612470746040344,
-0.03505571186542511,
-0.004716138821095228,
-0.025157524272799492,
-0.021548913791775703,
0.004938205238431692,
-0.009116909466683865,
0.008684869855642319,
-0.06387588381767273,
0.053931377828121185,
-0.028337586671113968,
0.027248822152614594,
-0.05280105397105217,
-0.014723138883709908,
0.04441886767745018,
0.03114323690533638,
0.013480310328304768,
0.006418977398425341,
-0.04256020113825798,
0.04093343764543533,
-0.024944616481661797,
0.0432078056037426,
0.009421898983418941,
-0.05272410809993744,
0.061058055609464645,
-0.007647315971553326,
0.008518755435943604,
-0.05005212873220444,
-0.033775027841329575,
-0.03138822689652443,
0.006024169735610485,
0.009851806797087193,
0.029969310387969017,
-0.005049176048487425,
0.007459144573658705,
0.02084525115787983,
0.026048656553030014,
-0.008675522170960903,
-0.02169901132583618,
-0.052972663193941116,
-0.052454378455877304,
-0.03866858407855034,
-0.054857026785612106,
0.044506363570690155,
0.010313407517969608,
-0.0059066959656775,
0.028903087601065636,
-0.04720275476574898,
0.010600288398563862,
-0.0025043445639312267,
0.03437289968132973,
-0.04257914051413536,
0.05925783887505531,
-0.01899183914065361,
0.03331087902188301,
-0.05750395730137825,
-0.014179364778101444,
0.1295333057641983,
0.05252153053879738,
-0.002582015935331583,
-0.048345841467380524,
0.011029834859073162,
-0.006383483298122883,
-0.010060104541480541,
-0.03847162798047066,
-0.008653810247778893,
-0.00775930006057024,
-0.000972550071310252,
-0.011837070807814598,
0.06114063784480095,
-0.012244193814694881,
0.028820091858506203,
0.05458729714155197,
-0.03850821778178215,
-0.0010188211454078555,
0.0014303820207715034,
0.030292438343167305,
-0.02167893759906292,
0.0404508039355278,
-0.03036336973309517,
0.03943873569369316,
-0.013493613339960575,
-0.03272571787238121,
-0.008665661327540874,
-0.04223889485001564,
0.02698214165866375,
0.004256926476955414,
-0.01804191805422306,
0.028559967875480652,
0.016566168516874313,
-0.037619784474372864,
-0.016112040728330612,
0.05802375450730324,
0.01981530338525772,
-0.012217863462865353,
0.04054057598114014,
0.027809539809823036,
-0.00547414505854249,
0.021860511973500252,
0.04324985668063164,
0.01653076522052288,
-0.027388250455260277,
-0.007638843264430761,
-0.04398413002490997,
0.03133886680006981,
-0.020323410630226135,
0.026651570573449135,
0.006288150325417519,
0.008674382232129574,
0.01223231852054596,
-0.011309122666716576,
-0.029767775908112526,
-0.004059209488332272,
0.0348362922668457,
0.02047308348119259,
-0.029447413980960846,
-0.014562120661139488,
0.02647167071700096,
0.009986075572669506,
0.0030564344488084316,
0.010771159082651138,
-0.012571298517286777,
-0.009016473777592182,
0.003891977248713374,
0.03288453817367554,
-0.029788333922624588,
0.009214334189891815,
-0.03279925882816315,
-0.00021030039351899177,
-0.03530401736497879,
-0.004892467521131039,
-0.0009591698762960732,
0.04649879410862923,
0.010570351034402847,
0.02221640944480896,
0.003051617881283164,
0.04899906367063522,
-0.06815794110298157,
0.030898885801434517,
-0.04142865911126137,
-0.022186793386936188,
-0.040160179138183594,
-0.034425921738147736,
0.00478548975661397,
-0.0010514436289668083,
0.008294454775750637,
0.01326338853687048,
-0.017192905768752098,
0.04383401200175285,
-0.03220725059509277,
-0.016669074073433876,
-0.04084347188472748,
0.03100905753672123,
-0.04353904351592064,
-0.0008039900567382574,
-0.014619841240346432,
0.04544474557042122,
-0.016421815380454063,
0.032131921499967575,
-0.0035327989608049393,
0.036296695470809937,
-0.01824009045958519,
0.0004988679429516196,
0.023062778636813164,
0.030620580539107323,
-0.030237877741456032,
0.036263540387153625,
-0.02379176765680313,
-0.03575943410396576,
-0.03277268260717392,
-0.00957518070936203,
-0.06110022962093353,
0.023881595581769943,
0.042235780507326126,
-0.034055378288030624,
0.01946420967578888,
-0.020757431164383888,
0.01865912415087223,
-0.0475541353225708,
-0.006961564067751169,
-0.0734637901186943,
-0.033752862364053726,
0.0072370488196611404,
-0.01463832426816225,
-0.029743818566203117,
0.01832697167992592,
-0.034147538244724274,
-0.018151042982935905,
0.009157262742519379,
-0.005308390129357576,
0.002527970587834716,
-0.006157503928989172,
0.041778843849897385,
0.004694134462624788,
0.01802796684205532,
0.003598029725253582,
-0.03489308804273605,
0.0290546678006649,
-0.023582104593515396,
-0.06351965665817261,
0.015648623928427696,
-0.0077452221885323524,
0.009936694987118244,
0.012324118055403233,
-0.021105237305164337,
0.019775981083512306,
0.05477770417928696,
-0.009622171521186829,
0.00947427935898304,
-0.011552444659173489,
-0.05274168774485588,
-0.006137106101959944,
0.017531247809529305,
-0.011279831640422344,
-0.03228260576725006,
0.008764068596065044,
-0.021873392164707184,
0.020863773301243782,
-0.031183255836367607,
-0.005021240096539259,
0.006647277623414993,
-0.010936767794191837,
0.014944660477340221,
-0.024108078330755234,
0.019482797011733055,
0.02323819324374199,
0.02286067046225071,
-0.011852073483169079,
-0.022820543497800827,
0.04946140944957733,
0.0019285967573523521,
-0.06718593835830688,
-0.02898230217397213,
-0.0003302899422124028,
-0.01765727996826172,
0.045097146183252335,
-0.06619299948215485,
0.003609076840803027,
0.050668541342020035,
-0.04949392378330231,
0.03182544931769371,
-0.03629513457417488,
-0.012196332216262817,
-0.041773274540901184,
-0.00947231613099575,
0.004345396533608437,
0.038983553647994995,
-0.0017974198563024402,
0.033904317766427994,
-0.021236896514892578,
0.01694612018764019,
-0.006803099997341633,
-0.011279704980552197,
-0.029264073818922043,
0.04573570936918259,
0.019602563232183456,
0.014531001448631287,
0.07600466907024384,
0.03149062767624855,
-0.03586077317595482,
0.02994394488632679,
-0.03369096666574478,
-0.02282932959496975,
0.015965472906827927,
-0.017328256741166115,
0.012781084515154362,
0.009911634959280491,
-0.002382681705057621,
-0.01754489168524742,
-0.017299596220254898,
0.03692572936415672,
0.03581859916448593,
0.03018442541360855,
-0.017159249633550644,
-0.005783999338746071,
0.01716521941125393,
-0.0378592349588871,
-0.03137020394206047,
0.015515466220676899,
-0.0324602909386158,
0.022839946672320366,
-0.031101055443286896,
0.011012307368218899,
0.03226189687848091,
-0.031517453491687775,
0.006903307978063822,
-0.025058329105377197,
0.007475713267922401,
0.048531871289014816,
-0.003445039503276348,
-0.0023276160936802626,
0.06595897674560547,
0.01138306874781847,
0.012212609872221947,
-0.0011511798948049545,
0.0019837329164147377,
0.0068184793926775455,
-0.050112951546907425,
0.015420963987708092,
-0.0020143233705312014,
-0.03991704061627388,
-0.03377687558531761,
-0.028510807082057,
-0.04241441935300827,
0.03936735913157463,
0.04043813422322273,
0.0203359667211771,
-0.027356669306755066,
-0.06102826073765755,
-0.035284098237752914,
-0.06851675361394882,
0.024739116430282593,
0.008774029091000557,
-0.06831950694322586,
-0.029555246233940125,
-0.042549628764390945,
0.008784170262515545,
0.019995786249637604,
0.014615965075790882,
-0.014658903703093529,
0.004557549487799406,
0.06828626245260239,
-0.007222212851047516,
0.029803110286593437,
0.023270266130566597,
-0.005315008573234081,
0.007762538269162178,
-0.0024764309637248516,
0.023000568151474,
0.007675970438867807,
-0.003171962685883045,
0.018317682668566704,
0.01125265471637249,
0.016372356563806534,
0.038006726652383804,
-0.006396924145519733,
-0.027963491156697273,
0.021986225619912148,
0.03409287706017494,
-0.03338230401277542,
0.08997787535190582,
-0.009221376851201057,
0.01629115827381611,
-0.014565936289727688,
-0.02730262093245983,
-0.015292074531316757,
0.037135157734155655,
-0.05255725607275963,
-0.00010908434342127293,
-0.028284238651394844,
-0.004117113072425127,
0.011144260875880718,
-0.0725979208946228,
0.0038758169393986464,
0.05631221458315849,
-0.02628914825618267,
-0.013895722106099129,
0.05294586345553398,
0.01969330385327339,
0.04062570258975029,
0.005528031382709742,
0.012297957204282284,
0.030231885612010956,
-0.003810014808550477,
0.011473705060780048,
0.012549878098070621,
0.04097389057278633,
0.01089291088283062,
0.0006739635136909783,
0.04754327982664108,
-0.022369148209691048,
0.04461369663476944,
0.013011296279728413,
0.041372429579496384,
0.007992936298251152,
-0.006172838620841503,
0.017373785376548767,
-0.008560621179640293,
-0.010254415683448315,
0.010476304218173027,
-0.016996989026665688,
0.04901193827390671,
-0.009636279195547104,
-0.0268377885222435,
-0.0006574540748260915,
0.012073012068867683,
0.017764069139957428,
0.004439299926161766,
0.017098046839237213,
0.023465042933821678,
0.01700606383383274,
-0.0002585359034128487,
-0.035916607826948166,
0.012195104733109474,
0.0013963949168100953,
0.005691305734217167,
-0.0009631554130464792,
-0.009316608309745789,
0.025008833035826683,
-0.018677975982427597,
-0.008614376187324524,
-0.03464021906256676,
0.009737945161759853,
0.021408941596746445,
0.025864167138934135,
0.044367462396621704,
-0.024456052109599113,
-0.011143438518047333,
-0.02110927365720272,
0.021634291857481003,
-0.06796383857727051,
-0.005158619023859501,
0.014540006406605244,
0.021478954702615738,
0.019559234380722046,
0.009373953565955162
] |
<p><img src="http://i.stack.imgur.com/sUvHk.png" alt="enter image description here"></p>
<p>As you see, this is the electric field generated by a point charge moving at constant speed v. I know that when $v$ -> 0, $E$ is just the Coloumb Law. But how do you interpret $E$ when $v$ -> $c$ ? </p>
<p>Can I just interpret it as the field of electromagnetic wave, because it moves at the speed of light?</p>
<p><img src="http://i.stack.imgur.com/LvWkF.png" alt="enter image description here"></p> | 2,053 | [
-0.026691190898418427,
-0.03148854151368141,
0.0011931293411180377,
-0.025622203946113586,
0.028976602479815483,
-0.0006772612687200308,
-0.016495903953909874,
-0.006805772893130779,
-0.015989985316991806,
-0.0251360684633255,
0.0505182147026062,
0.06118287146091461,
0.05179509520530701,
0.0009346658480353653,
0.03271111845970154,
0.01307476032525301,
-0.009054623544216156,
-0.010984616354107857,
-0.017841773107647896,
-0.04720894247293472,
0.00017188474885188043,
0.01666799560189247,
-0.008247295394539833,
0.04321496933698654,
-0.04623626545071602,
0.025333667173981667,
0.042433060705661774,
0.023357180878520012,
0.027267582714557648,
0.041009292006492615,
0.005314495414495468,
-0.053466301411390305,
-0.027055732905864716,
0.010929594747722149,
-0.011991285718977451,
0.007991181686520576,
-0.006157952826470137,
-0.04106851667165756,
0.010642589069902897,
0.010287683457136154,
0.003266955493018031,
-0.010912865400314331,
0.01059396006166935,
0.0706196278333664,
-0.02962506003677845,
-0.010762744583189487,
0.015025660395622253,
-0.007908908650279045,
0.060520730912685394,
-0.04272996634244919,
0.08608191460371017,
-0.0019540644716471434,
0.03455613553524017,
-0.00526199908927083,
0.014312869869172573,
0.015239541418850422,
0.07693265378475189,
0.045057035982608795,
-0.014496346935629845,
-0.036489102989435196,
-0.020074497908353806,
-0.017316175624728203,
-0.009557421319186687,
-0.025334760546684265,
-0.022499511018395424,
0.040246713906526566,
-0.015041004866361618,
-0.016238972544670105,
0.03886668011546135,
0.017681794241070747,
0.006909502204507589,
0.01931670866906643,
-0.00929408147931099,
-0.027361584827303886,
0.042371053248643875,
-0.05956081300973892,
0.013569163158535957,
0.001559792784973979,
0.029370184987783432,
0.030939117074012756,
-0.043659333139657974,
0.0023426800034940243,
0.014028330333530903,
0.0498870387673378,
0.009096772409975529,
0.005680512171238661,
0.0472983755171299,
-0.010937228798866272,
0.023835327476263046,
0.023528018966317177,
-0.02610386535525322,
0.024150017648935318,
-0.00451101316139102,
-0.022112099453806877,
-0.04000993072986603,
0.031105389818549156,
0.00030043587321415544,
0.03198524937033653,
0.025118963792920113,
-0.037295132875442505,
0.03132617101073265,
0.004742877557873726,
-0.008659033104777336,
0.051457833498716354,
0.004939225967973471,
0.00020619611314032227,
-0.047917235642671585,
0.04437737539410591,
-0.02742948941886425,
-0.019590415060520172,
-0.015739157795906067,
0.0488005094230175,
0.04688555747270584,
0.03383106365799904,
0.004044496454298496,
-0.0487341433763504,
0.044257793575525284,
-0.032944127917289734,
0.042897000908851624,
0.025280660018324852,
0.05929160490632057,
-0.062027458101511,
0.04745803028345108,
-0.004052991513162851,
-0.06385031342506409,
-0.015344533137977123,
0.009506884962320328,
0.006989887449890375,
-0.0009674394968897104,
0.008365249261260033,
-0.020008403807878494,
-0.02770145609974861,
-0.022494414821267128,
0.007928048260509968,
0.012155869975686073,
-0.024369891732931137,
-0.08181250840425491,
-0.0723787248134613,
0.011412255465984344,
-0.008348220027983189,
-0.018402067944407463,
-0.08256065100431442,
-0.025024695321917534,
0.010153090581297874,
0.059822920709848404,
-0.005560357589274645,
-0.00827194843441248,
-0.013385705649852753,
0.04580404609441757,
0.02334308624267578,
-0.0008176398114301264,
-0.015189050696790218,
-0.0327477753162384,
-0.03277253359556198,
0.03190549835562706,
-0.0637674331665039,
-0.0010114365722984076,
0.050693221390247345,
0.004092505667358637,
-0.0007359437877312303,
0.047472625970840454,
-0.027857383713126183,
-0.0272542592138052,
0.004071034956723452,
-0.021520650014281273,
-0.008062269538640976,
0.11501798778772354,
0.05067821964621544,
-0.002199094044044614,
0.06827245652675629,
0.03664823994040489,
0.06839561462402344,
0.026199597865343094,
0.017101241275668144,
0.060386043041944504,
-0.03378761559724808,
0.0058296010829508305,
-0.010524868965148926,
0.02534792758524418,
-0.003249538131058216,
-0.05238356813788414,
-0.05576023459434509,
0.0176315288990736,
0.012745818123221397,
-0.01303438562899828,
0.07137542963027954,
-0.02471678890287876,
0.01182731706649065,
-0.011290526017546654,
-0.018656667321920395,
-0.029438722878694534,
-0.056945618242025375,
0.044440872967243195,
0.029100017622113228,
-0.0014745808439329267,
0.01419160794466734,
-0.011990692466497421,
0.031591083854436874,
-0.04193499684333801,
-0.02199472300708294,
0.014681046828627586,
0.059460751712322235,
-0.028262821957468987,
-0.034499529749155045,
0.01727457158267498,
0.014957878738641739,
0.02936927042901516,
0.0452256053686142,
0.006940054707229137,
0.023656630888581276,
-0.035674042999744415,
0.027743803337216377,
-0.001053776009939611,
0.028442300856113434,
0.019571008160710335,
0.02928685024380684,
-0.011911186389625072,
0.009187694638967514,
-0.0011935994261875749,
0.04190392047166824,
-0.011326919309794903,
0.0627998635172844,
0.05455860123038292,
0.010546433739364147,
0.004708210006356239,
0.05211447551846504,
0.0025212427135556936,
-0.002275824313983321,
0.009682301431894302,
-0.05026240646839142,
-0.027781827375292778,
-0.017484650015830994,
0.019880205392837524,
0.0016701545100659132,
-0.029658118262887,
-0.006706688553094864,
0.017840642482042313,
0.015073138289153576,
0.04564938321709633,
0.038127005100250244,
-0.04559902846813202,
-0.025310082361102104,
0.026989882811903954,
0.00364434695802629,
-0.03459746390581131,
0.00217955163680017,
0.019973114132881165,
0.023847663775086403,
0.01674468442797661,
-0.02554968371987343,
-0.01758803427219391,
0.035357631742954254,
-0.01897241920232773,
-0.001914921565912664,
-0.002706929575651884,
-0.026144227012991905,
0.015375066548585892,
-0.04042700305581093,
0.026789989322423935,
0.011846663430333138,
-0.03964017331600189,
0.016192998737096786,
-0.045207321643829346,
0.01708962582051754,
0.02029140666127205,
0.004309657495468855,
-0.0331127904355526,
-0.03238874673843384,
0.016930995509028435,
-0.030370673164725304,
0.030140018090605736,
-0.02090398594737053,
-0.06485746055841446,
-0.024020714685320854,
-0.010584658943116665,
0.02512368932366371,
0.01835026778280735,
0.0328022837638855,
-0.0582285113632679,
-0.05144128203392029,
-0.009234648197889328,
-0.06632760912179947,
0.006613537669181824,
0.024765726178884506,
-0.013686118647456169,
0.02431892603635788,
-0.05574006214737892,
-0.04514244571328163,
0.06260734796524048,
0.010325645096600056,
0.019813071936368942,
0.05177628621459007,
-0.04415186494588852,
-0.043356798589229584,
-0.0019871287513524294,
-0.03364260122179985,
0.013471310026943684,
-0.02987656183540821,
-0.03287117928266525,
0.052357807755470276,
-0.04256085306406021,
-0.01650543138384819,
0.0034869106020778418,
-0.056231964379549026,
-0.04518745094537735,
0.006926285568624735,
-0.0161585733294487,
0.03500828891992569,
-0.061394065618515015,
0.06284818798303604,
-0.015266809612512589,
-0.04629630967974663,
0.022111637517809868,
-0.036969199776649475,
-0.02860746718943119,
0.035466860979795456,
-0.0035487255081534386,
0.02905508317053318,
-0.010873631574213505,
-0.0661146268248558,
0.0523187629878521,
0.05951651558279991,
-0.01552127581089735,
-0.0038956005591899157,
-0.021897662431001663,
-0.005739673972129822,
-0.007362490985542536,
-0.025028949603438377,
0.02234666608273983,
-0.02857070416212082,
-0.026898063719272614,
0.007796707563102245,
0.02851313352584839,
0.015357987955212593,
0.002614052966237068,
-0.002382738282904029,
-0.006152920424938202,
-0.02994026057422161,
0.024278081953525543,
0.05683212727308273,
0.008119750767946243,
-0.012931481003761292,
0.013896217569708824,
0.009851508773863316,
0.036517996340990067,
0.04361166059970856,
-0.012031422927975655,
0.033911023288965225,
0.022585280239582062,
0.02807421050965786,
-0.03993779793381691,
0.06495872139930725,
0.01578746922314167,
0.012611689046025276,
0.014710795134305954,
-0.012342956848442554,
0.02367602474987507,
-0.0364174023270607,
-0.00933255348354578,
0.024539045989513397,
0.017700739204883575,
-0.025943133980035782,
-0.0571482814848423,
-0.009306910447776318,
0.005463372450321913,
0.011551330797374249,
-0.004851489327847958,
-0.02221900410950184,
0.0401795469224453,
0.028899947181344032,
0.008117062039673328,
0.009800951927900314,
-0.025318065658211708,
0.006955093704164028,
-0.02002597227692604,
-0.013813376426696777,
0.030892781913280487,
0.015451359562575817,
0.03561750054359436,
0.08395902812480927,
0.010922448709607124,
0.019992414861917496,
0.04775725677609444,
0.017033379524946213,
-0.08688991516828537,
0.01561268325895071,
-0.037963155657052994,
-0.0011861755046993494,
-0.07930051535367966,
-0.018040234223008156,
-0.005760191008448601,
-0.007953391410410404,
-0.03785200044512749,
-0.005614437162876129,
0.005448916926980019,
-0.046777427196502686,
-0.004332733806222677,
-0.024411754682660103,
-0.005662206094712019,
-0.0433519147336483,
0.0075159864500164986,
0.01740151457488537,
-0.014101389795541763,
0.0037664559204131365,
0.046586669981479645,
-0.017078548669815063,
-0.0060610719956457615,
0.020964913070201874,
-0.03869718313217163,
0.018394960090517998,
0.0020144134759902954,
0.02854965440928936,
-0.02726706489920616,
-0.034448809921741486,
0.011058058589696884,
0.002623131964355707,
0.05334802716970444,
0.010149865411221981,
-0.00259074242785573,
-0.05583838000893593,
-0.05231030657887459,
-0.02391834743320942,
-0.04337413236498833,
0.06807738542556763,
0.028988506644964218,
0.016377300024032593,
0.04093393683433533,
-0.013176034204661846,
-0.003596584079787135,
0.04276527836918831,
0.06238468363881111,
0.030386725440621376,
-0.008491230197250843,
-0.0538305900990963,
0.029066016897559166,
-0.04047165438532829,
-0.015887407585978508,
0.004618406295776367,
-0.012546324171125889,
-0.004238403867930174,
-0.005434377118945122,
0.03407372906804085,
0.009225314483046532,
-0.009809867478907108,
0.0037498713936656713,
-0.009603233076632023,
-0.007735061459243298,
-0.01922934502363205,
-0.03415604680776596,
0.0015476037515327334,
0.03133084997534752,
0.05042571574449539,
-0.009217709302902222,
-0.03270921856164932,
-0.09317966550588608,
-0.03417730703949928,
0.03354507312178612,
0.012604694813489914,
-0.0026253859978169203,
-0.0006058329599909484,
-0.06685681641101837,
0.025034431368112564,
0.02170114777982235,
-0.05166085436940193,
-0.007416851352900267,
0.01474710088223219,
-0.014200975187122822,
-0.026632405817508698,
-0.011550952680408955,
-0.03238161280751228,
0.027484482154250145,
-0.02970113232731819,
0.011440994217991829,
-0.042649466544389725,
0.021078018471598625,
0.01503425557166338,
0.018647702410817146,
0.021333841606974602,
0.03963435813784599,
0.014727097004652023,
-0.004805999342352152,
0.0009169816039502621,
0.005711710546165705,
-0.026209574192762375,
-0.06283652782440186,
-0.005972196348011494,
-0.006371840834617615,
-0.006783458404242992,
0.04595228284597397,
-0.030742408707737923,
-0.0433567613363266,
0.02587716653943062,
-0.0014799797208979726,
0.020809315145015717,
0.0037650978192687035,
-0.05252237990498543,
0.04784911125898361,
-0.012230795808136463,
-0.009387148544192314,
0.022349704056978226,
0.0371796078979969,
0.005065033212304115,
-0.01584179699420929,
-0.006300546694546938,
0.04699564352631569,
-0.02137300930917263,
0.0023170269560068846,
-0.012454208917915821,
0.012342443689703941,
-0.047235675156116486,
0.047717154026031494,
-0.040298108011484146,
0.01058987807482481,
-0.0294832531362772,
-0.03684324771165848,
-0.008237228728830814,
0.007005629129707813,
0.01719038188457489,
0.002357215853407979,
-0.041134219616651535,
-0.00039908307371661067,
-0.022867558524012566,
-0.02401762083172798,
0.015851950272917747,
0.02429918758571148,
0.021908821538090706,
0.018816985189914703,
-0.0024654706940054893,
0.02271122857928276,
-0.011967189610004425,
-0.004092567600309849,
0.011401612311601639,
-0.0628485307097435,
0.02527122013270855,
0.00007049463602015749,
-0.023855850100517273,
-0.026883481070399284,
-0.05063706636428833,
-0.044336795806884766,
0.01875510811805725,
-0.003967787139117718,
0.02958565205335617,
-0.057007696479558945,
0.00996618065983057,
0.031896285712718964,
0.018671449273824692,
-0.05307609960436821,
-0.06897532939910889,
0.016088731586933136,
0.0188132394105196,
-0.0008771352586336434,
-0.016354568302631378,
-0.005647992715239525,
-0.025405555963516235,
-0.055720195174217224,
0.03584761172533035,
0.06286140531301498,
-0.003271535038948059,
-0.008468782529234886,
-0.000010921856301138178,
0.005561798345297575,
0.05670071393251419,
-0.008994387462735176,
-0.01595637947320938,
0.04520963877439499,
-0.025748172774910927,
-0.0028780512511730194,
0.005030377302318811,
0.06356801092624664,
0.0010797756258398294,
-0.02763979695737362,
-0.02329373173415661,
-0.002410704968497157,
0.02461973950266838,
-0.02740461938083172,
-0.006206313148140907,
0.02928982861340046,
0.036516860127449036,
-0.01841760240495205,
-0.0020363295916467905,
0.01937793381512165,
-0.005207303445786238,
0.010291170328855515,
-0.002590943593531847,
-0.0018022175645455718,
-0.04152168706059456,
-0.04128342494368553,
0.017047161236405373,
-0.004640732891857624,
0.04402483254671097,
-0.04159851372241974,
0.03075248934328556,
-0.025808462873101234,
0.00394478952512145,
-0.004689401015639305,
0.005834820214658976,
-0.006789133418351412,
0.00839851051568985,
-0.025327932089567184,
0.03491115942597389,
-0.011234696954488754,
-0.03252531960606575,
0.004299012012779713,
-0.06131095439195633,
-0.005030231084674597,
0.08966604620218277,
-0.019864117726683617,
0.06909707188606262,
0.0037221957463771105,
0.00020249739463906735,
0.0037575894966721535,
-0.021264808252453804,
-0.03188658133149147,
-0.00013930074055679142,
0.0205951277166605,
-0.03811274841427803,
-0.02677946910262108,
0.01524957362562418,
0.018713543191552162,
0.04841209575533867,
-0.020405329763889313,
0.024953484535217285,
0.06055160611867905,
0.048168547451496124,
0.03281480446457863,
0.018584763631224632,
-0.029625488445162773,
0.05686892569065094,
-0.008649535477161407,
0.025535713881254196,
0.006647666450589895,
-0.018996858969330788,
0.04762227460741997,
0.023525336757302284,
0.03089834935963154,
-0.02068527415394783,
-0.0122150257229805,
-0.037897322326898575,
0.006841803900897503,
0.013214515522122383,
0.00532909482717514,
-0.009044935926795006,
-0.005145126488059759,
-0.007601399905979633,
0.003318405942991376,
0.037167564034461975,
0.015596233308315277,
-0.05400443822145462,
-0.03271069377660751,
-0.03585781157016754,
-0.006356182973831892,
0.055881548672914505,
0.037973884493112564,
-0.005643534008413553,
0.009658601135015488,
-0.003609097097069025,
0.039534177631139755,
0.028302524238824844,
0.019327182322740555,
-0.008296731859445572,
0.05326072499155998,
0.007327253930270672,
-0.006311203818768263,
-0.009421700611710548,
0.015373190864920616,
0.1052565723657608,
0.06502292305231094,
-0.0066136084496974945,
-0.03228694573044777,
0.013253743760287762,
-0.035146936774253845,
0.01695423200726509,
-0.029507938772439957,
0.01077338308095932,
-0.06539486348628998,
0.030134156346321106,
0.012105167843401432,
0.04389924556016922,
0.016077319160103798,
0.028076810762286186,
0.037807561457157135,
-0.01820281334221363,
-0.031854577362537384,
-0.004330082330852747,
0.031131789088249207,
-0.012841884046792984,
0.03228648379445076,
-0.04061610996723175,
0.029149046167731285,
-0.04514307901263237,
-0.0028061429038643837,
-0.04661651328206062,
-0.023954488337039948,
0.017984982579946518,
-0.006051715463399887,
-0.04579058662056923,
-0.001516604796051979,
0.011661609634757042,
-0.014978945255279541,
-0.07303109019994736,
0.025311285629868507,
0.02804127149283886,
0.023197945207357407,
0.000015087745850905776,
0.009528026916086674,
-0.0007365471101365983,
0.013630617409944534,
0.026984062045812607,
0.016581201925873756,
-0.03481491655111313,
0.022110043093562126,
-0.0399395227432251,
0.0643848329782486,
0.013238484039902687,
0.030130524188280106,
-0.019733916968107224,
0.010353184305131435,
-0.010049269534647465,
-0.07122108340263367,
0.0011530190240591764,
-0.045082151889801025,
-0.006218650843948126,
0.028844496235251427,
-0.009080746211111546,
-0.06746366620063782,
0.000900415179785341,
-0.025368835777044296,
0.0035004233941435814,
0.012051925994455814,
-0.010453210212290287,
0.0024250750429928303,
-0.0042809536680579185,
0.04377599433064461,
-0.021648278459906578,
-0.044040095061063766,
0.028980538249015808,
-0.019841592758893967,
-0.044556524604558945,
0.009953162632882595,
0.015743831172585487,
0.03440658748149872,
0.01187598891556263,
-0.012823225930333138,
-0.02305043675005436,
-0.02238638885319233,
-0.1083083376288414,
0.03694683313369751,
0.004362870007753372,
-0.014081851579248905,
-0.02024851366877556,
0.023088926449418068,
0.010830877348780632,
0.05954683572053909,
-0.011575091630220413,
0.043020863085985184,
-0.004619109909981489,
0.01944061368703842,
0.0022850963287055492,
-0.021383704617619514,
-0.008009165525436401,
-0.01478428952395916,
-0.004649258218705654,
0.008745971135795116,
-0.008260868489742279,
0.029062818735837936,
0.026757201179862022,
0.023781871423125267,
-0.00774381123483181,
0.03489259257912636,
-0.027158010751008987,
-0.007136587519198656,
0.0038042855449020863,
-0.0285921860486269,
0.03733005002140999,
0.010517229326069355,
0.025659307837486267,
-0.025892332196235657,
0.0008201441960409284,
-0.004233409650623798,
0.009596073068678379,
-0.019943861290812492,
0.008843455463647842,
-0.017692729830741882,
0.0016699156258255243,
-0.009255560114979744,
0.010257687419652939,
-0.03289315849542618,
-0.029258782044053078,
-0.04229940474033356,
0.04718892648816109,
0.0120230782777071,
-0.012736575677990913,
-0.027085689827799797,
0.0499909408390522,
-0.036801259964704514,
-0.009812462143599987,
0.011386293917894363,
0.02437031827867031,
0.002868127077817917,
-0.005794161930680275,
0.033342164009809494,
-0.01654057949781418,
0.05935357138514519,
-0.012962421402335167,
-0.007507844362407923,
0.021025216206908226,
-0.03128639608621597,
-0.04985513910651207,
-0.004036685451865196,
0.0029205784667283297,
0.04009523615241051,
0.023423099890351295,
0.0018278437200933695,
0.00449435506016016,
0.04752986505627632,
-0.0051021696999669075,
0.031244389712810516,
-0.01698560081422329,
-0.07562749832868576,
-0.02215147763490677,
-0.006516816560178995,
0.007651066407561302,
0.02164832130074501,
-0.003165443195030093,
0.06440563499927521,
0.02064518630504608,
-0.016639096662402153,
-0.008456620387732983,
-0.0026695015840232372,
-0.005201689433306456,
-0.018538471311330795,
0.04490751028060913,
-0.01980871520936489,
0.020891010761260986,
0.05340796709060669,
-0.0011234980775043368,
0.025643182918429375,
-0.022170785814523697,
0.0029874707106500864,
-0.11356231570243835,
-0.01366786565631628,
0.023817677050828934,
0.02947891689836979,
0.0410180538892746,
-0.050718970596790314,
0.0023484027478843927,
0.04054511338472366,
-0.09235559403896332,
-0.010759617201983929,
-0.007215446326881647,
-0.0018757075304165483,
-0.011018085293471813,
-0.0031510975677520037,
0.001799708348698914,
0.05440600961446762,
0.02045433223247528,
0.038947947323322296,
0.02591094560921192,
0.006597085390239954,
-0.02677435800433159,
-0.044437386095523834,
-0.01605929248034954,
0.056675344705581665,
0.031304359436035156,
-0.0038496912457048893,
0.06928079575300217,
0.004193301312625408,
0.0029802266508340836,
0.029361028224229813,
0.014487999491393566,
0.02278045006096363,
-0.0034113461151719093,
0.012039665132761002,
0.03303274139761925,
0.024598052725195885,
-0.007523248437792063,
-0.046139419078826904,
-0.03689588978886604,
0.008244216442108154,
0.014618059620261192,
0.01663532666862011,
0.007558549288660288,
-0.00086380256107077,
0.016058851033449173,
-0.03630978614091873,
-0.046710070222616196,
0.03217872604727745,
-0.027277369052171707,
-0.04403551667928696,
0.00602892367169261,
0.012953917495906353,
0.0023987905588001013,
-0.02719756029546261,
0.04016885533928871,
-0.051647577434778214,
-0.00828129518777132,
0.02505945973098278,
0.005370286758989096,
-0.00507859792560339,
0.02209504321217537,
-0.004137909505516291,
-0.023995276540517807,
-0.005417789798229933,
0.02127533033490181,
-0.005117393098771572,
-0.07043811678886414,
0.0050806631334125996,
0.01782323606312275,
-0.02691313996911049,
0.01400479581207037,
-0.04473670572042465,
-0.05224200710654259,
0.012617822736501694,
0.030954955145716667,
0.023592285811901093,
0.010690007358789444,
-0.031408753246068954,
-0.03050990402698517,
-0.04568469151854515,
0.04351632297039032,
-0.0012467926135286689,
-0.017044516280293465,
-0.03762488812208176,
-0.048345815390348434,
-0.004443644545972347,
0.022798288613557816,
0.06464534252882004,
0.0024302739184349775,
-0.02513204514980316,
0.035648830235004425,
0.006333251018077135,
0.024445053189992905,
-0.07799138128757477,
-0.025177327916026115,
-0.0022128275595605373,
-0.024777991697192192,
0.015677984803915024,
0.022385351359844208,
-0.016231954097747803,
0.028323011472821236,
0.012288936413824558,
0.017756475135684013,
0.016696393489837646,
-0.032139744609594345,
-0.03747904673218727,
0.03658057004213333,
0.02386922389268875,
-0.03182326257228851,
0.06175070255994797,
-0.009974442422389984,
0.030921341851353645,
0.021581152454018593,
-0.017450805753469467,
-0.0006230983417481184,
0.012152469716966152,
-0.05881280079483986,
-0.010984311811625957,
-0.010679865255951881,
0.005141877569258213,
0.05347124859690666,
-0.059335798025131226,
0.024074940010905266,
0.04199055954813957,
-0.05834323912858963,
-0.0038956019561737776,
0.04723953828215599,
-0.027975793927907944,
0.02161049284040928,
0.017752353101968765,
0.011742507107555866,
-0.00195892620831728,
-0.0008326234528794885,
-0.02104542963206768,
0.007726875599473715,
0.018438275903463364,
-0.028420839458703995,
0.05001196265220642,
0.059214428067207336,
-0.00485845934599638,
-0.002433117013424635,
0.026389870792627335,
-0.0007651117048226297,
-0.012332276441156864,
-0.0024503429885953665,
-0.010663986206054688,
-0.01691683568060398,
0.0058827754110097885,
0.005467861425131559,
-0.0342898815870285,
0.08269301056861877,
-0.03248070925474167,
0.03269023820757866,
-0.01382199116051197,
-0.01193213276565075,
-0.010023705661296844,
0.015094591304659843,
0.0015558971790596843,
-0.004499453119933605,
0.012659371830523014,
0.004735635127872229,
-0.021499665454030037,
-0.018597448244690895,
0.02326289378106594,
-0.03971041738986969,
0.0298764705657959,
0.02075069025158882,
-0.05345473438501358,
0.008438927121460438,
-0.00028931390261277556,
-0.015231930650770664,
-0.0063760606572031975,
0.011394389905035496,
0.015755172818899155,
0.005668846890330315,
0.0038067547138780355,
0.004292048513889313,
0.0009190237615257502,
0.049020349979400635,
-0.05307250842452049,
0.0151663264259696,
-0.0023036145139485598,
-0.006460707169026136,
0.01036684401333332,
-0.017637144774198532
] |
<p>If while calculating a band gap, the band just below the Fermi level touches the Fermi level, can we say the material is semiconducting?</p> | 2,054 | [
0.005314727313816547,
-0.019792357459664345,
0.02022395469248295,
-0.02501639537513256,
0.008452313020825386,
0.011245613917708397,
-0.021015794947743416,
-0.010059753432869911,
0.019155848771333694,
-0.020754456520080566,
0.019638750702142715,
-0.01804185099899769,
0.027793724089860916,
0.013257556594908237,
0.010295066982507706,
0.041608382016420364,
-0.01580284722149372,
-0.010320065543055534,
-0.03139922022819519,
-0.03426658362150192,
0.004253987222909927,
0.026694927364587784,
-0.012151245959103107,
0.035855360329151154,
-0.012092689983546734,
-0.01033839862793684,
0.007521891500800848,
-0.02151658944785595,
0.013426561839878559,
0.012031689286231995,
-0.013489780016243458,
-0.0385986864566803,
0.03298565372824669,
0.004237851593643427,
0.04193554446101189,
-0.0024419655092060566,
-0.03633016720414162,
-0.04563497379422188,
-0.028052642941474915,
0.02930114045739174,
-0.0025757374241948128,
0.00586103368550539,
-0.0002990285283885896,
0.023763472214341164,
0.003626215737313032,
-0.0024989976081997156,
0.002825682982802391,
-0.02741946652531624,
0.012222113087773323,
-0.06734149903059006,
0.0308765210211277,
-0.016948258504271507,
0.06188109144568443,
0.034040991216897964,
-0.026345377787947655,
-0.0010109096765518188,
0.06973068416118622,
0.07954628020524979,
-0.02743876352906227,
-0.013101724907755852,
-0.03581024706363678,
-0.045432813465595245,
-0.01166587509214878,
-0.043903935700654984,
-0.050748031586408615,
0.04150477796792984,
-0.027449006214737892,
-0.040447719395160675,
0.008530551567673683,
-0.001113535719923675,
-0.009287280961871147,
0.006416823249310255,
-0.017973849549889565,
-0.05470619350671768,
0.002073588315397501,
-0.051271237432956696,
0.045788154006004333,
0.044748879969120026,
0.013859481550753117,
0.04220309853553772,
-0.033190105110406876,
0.01702752895653248,
0.037599481642246246,
0.009935669600963593,
0.013198061846196651,
-0.0258012767881155,
0.0565011240541935,
-0.03180050104856491,
-0.0008431038004346192,
0.022246360778808594,
-0.007769244257360697,
0.007970592938363552,
0.05175803229212761,
-0.020910007879137993,
-0.039090659469366074,
0.028027404099702835,
-0.016459209844470024,
0.048666052520275116,
-0.02712908387184143,
-0.039652980864048004,
0.04867389798164368,
0.019827546551823616,
0.09511949121952057,
0.07471675425767899,
0.02232837677001953,
-0.027961526066064835,
-0.010320967994630337,
0.022402448579669,
0.005299474112689495,
0.005593421868979931,
-0.03851645439863205,
0.020752793177962303,
-0.01105930469930172,
0.0033181575126945972,
0.03483672812581062,
0.00180276099126786,
-0.02489480935037136,
-0.029302384704351425,
-0.0046354844234883785,
0.03113606572151184,
-0.00043318496318534017,
-0.020349128171801567,
0.007751022931188345,
-0.014426279813051224,
-0.0731496587395668,
0.017374273389577866,
0.023708615452051163,
-0.029727932065725327,
-0.05683173984289169,
0.004933259449899197,
-0.005522791761904955,
-0.01875230483710766,
0.022885112091898918,
-0.05112001672387123,
0.046919167041778564,
-0.021160896867513657,
-0.057371705770492554,
-0.038829851895570755,
0.01151040755212307,
0.007919725961983204,
-0.016491487622261047,
-0.05783539265394211,
0.02818375639617443,
0.021423382684588432,
0.07196211814880371,
0.03923047333955765,
0.025679944083094597,
-0.000393014372093603,
0.0016315426910296082,
-0.007913815788924694,
0.00727652246132493,
-0.030347248539328575,
0.03559466451406479,
-0.03913453593850136,
0.04375234246253967,
-0.027310963720083237,
0.012636145576834679,
0.005370819941163063,
0.0022353280801326036,
-0.016673140227794647,
0.05382652208209038,
-0.04255320131778717,
-0.0077391681261360645,
-0.01677951216697693,
-0.024362195283174515,
-0.025712624192237854,
0.05541407689452171,
-0.004850954283028841,
0.027347583323717117,
0.045435830950737,
0.010325227864086628,
-0.009474286809563637,
0.014909782446920872,
0.04611577093601227,
0.05015552043914795,
-0.03376912698149681,
-0.032041147351264954,
-0.06546667963266373,
0.03621375933289528,
-0.0257672518491745,
-0.07429709285497665,
-0.020896362140774727,
0.004272856749594212,
0.04595799371600151,
0.035690583288669586,
0.03275936096906662,
0.01340632326900959,
-0.04568231850862503,
-0.009110117331147194,
-0.04702739790081978,
0.00018255820032209158,
-0.0355423241853714,
0.006118057761341333,
0.021824726834893227,
-0.004363029729574919,
0.015543362125754356,
0.003438908141106367,
0.019851526245474815,
-0.039722032845020294,
-0.016962114721536636,
-0.03263041004538536,
0.01791042648255825,
-0.006117104087024927,
-0.04055096209049225,
0.04993632063269615,
0.02081666886806488,
0.0665365606546402,
0.0007609387976117432,
0.04019347205758095,
-0.03366167098283768,
-0.04126400128006935,
0.01690887100994587,
-0.010618575848639011,
0.048263195902109146,
0.007725616917014122,
-0.0036931028589606285,
0.009191710501909256,
-0.03761954605579376,
-0.03176680952310562,
0.05287739261984825,
-0.00985955074429512,
0.08031398057937622,
0.02939988300204277,
0.01882927305996418,
-0.025216257199645042,
-0.01614045910537243,
0.005120398011058569,
0.02776254527270794,
-0.035516850650310516,
-0.03288724645972252,
-0.08284687250852585,
-0.00017623588792048395,
0.03280603885650635,
0.011488205753266811,
-0.021692322567105293,
0.023647751659154892,
0.016439925879240036,
0.016203712671995163,
0.02667183242738247,
0.012849337421357632,
-0.04095560684800148,
0.020037002861499786,
0.04101496934890747,
-0.005264362785965204,
0.021426163613796234,
-0.01768755167722702,
0.004109757952392101,
0.050383567810058594,
0.014204143546521664,
-0.01724233105778694,
0.005784094333648682,
0.03848441317677498,
0.016026994213461876,
-0.006030515767633915,
0.008164460770785809,
-0.05547359585762024,
0.0336185060441494,
-0.025365108624100685,
0.018634898588061333,
0.02600136213004589,
-0.03030383214354515,
0.02021668665111065,
-0.007471228949725628,
-0.024290990084409714,
0.011560965329408646,
0.0044157737866044044,
-0.03661522641777992,
-0.004314100835472345,
0.028102649375796318,
-0.05498823523521423,
0.004077782854437828,
-0.05824880674481392,
-0.0036378863733261824,
0.013999520801007748,
-0.036022111773490906,
0.038452621549367905,
-0.021250450983643532,
0.0704117864370346,
-0.04833375662565231,
0.0016189696034416556,
0.0019511841237545013,
-0.038412705063819885,
0.01483873650431633,
0.01708953268826008,
-0.03314930945634842,
0.014667907729744911,
-0.0031156339682638645,
-0.0630081295967102,
0.00895041972398758,
0.0029464061371982098,
-0.0033439781982451677,
0.016589917242527008,
-0.04115704819560051,
-0.0341571681201458,
0.014768365770578384,
-0.004678748082369566,
-0.0063077048398554325,
0.0030103609897196293,
-0.02324201539158821,
-0.00961423572152853,
0.007495061494410038,
-0.018754400312900543,
0.02277718298137188,
0.022661903873085976,
-0.045765433460474014,
-0.010193699039518833,
-0.05006808042526245,
0.010627257637679577,
-0.0344511903822422,
0.049893271178007126,
0.0060600098222494125,
-0.042144954204559326,
-0.001339202979579568,
-0.04560576006770134,
-0.0231434665620327,
0.05193862318992615,
-0.039201769977808,
-0.002950986847281456,
-0.019203057512640953,
-0.013263296335935593,
0.06943552196025848,
0.02601589262485504,
-0.013598035089671612,
0.001695775892585516,
-0.05094608664512634,
-0.019877493381500244,
0.014709124341607094,
0.0077582793310284615,
0.025307023897767067,
0.035145923495292664,
-0.003937679808586836,
-0.008317779749631882,
0.05416643247008324,
0.05741047486662865,
0.0001553602487547323,
-0.024423491209745407,
0.007859866134822369,
0.02215726114809513,
0.015152514912188053,
0.04252609610557556,
-0.009844767861068249,
-0.027843665331602097,
0.062450263649225235,
0.01253992598503828,
0.057998158037662506,
0.050987981259822845,
-0.012338013388216496,
0.05488528683781624,
-0.006154025439172983,
0.028495997190475464,
-0.058031510561704636,
0.05764812231063843,
0.047705937176942825,
0.01584012806415558,
0.011158033274114132,
0.03926396742463112,
0.016092682257294655,
-0.012735589407384396,
0.010215981863439083,
0.02317735366523266,
0.047760721296072006,
-0.01747187040746212,
-0.01389386598020792,
0.05285795032978058,
-0.013060812838375568,
0.0318087674677372,
-0.00514964759349823,
-0.03068014793097973,
0.02182837575674057,
0.04753921180963516,
0.0424497127532959,
0.009622209705412388,
-0.036297865211963654,
-0.010451557114720345,
-0.05679003521800041,
-0.004617801867425442,
0.010319599881768227,
0.046347927302122116,
-0.03540712967514992,
0.018437400460243225,
0.01718279905617237,
0.03229554742574692,
0.014460718259215355,
-0.013561648316681385,
-0.08660964667797089,
-0.010555986315011978,
-0.038853347301483154,
0.019346212968230247,
-0.026104621589183807,
-0.015674272552132607,
-0.029255524277687073,
0.0003467476926743984,
-0.013268493115901947,
-0.048837192356586456,
-0.009273393079638481,
-0.0035214582458138466,
0.02924835868179798,
0.006189311388880014,
0.0008102763094939291,
0.014610463753342628,
-0.022070225328207016,
0.009011388756334782,
-0.024190060794353485,
0.021808521822094917,
0.027741586789488792,
0.024896787479519844,
0.019070589914917946,
-0.017531612887978554,
0.016727227717638016,
0.006354596000164747,
0.0594438798725605,
0.031379133462905884,
0.030448870733380318,
-0.03896891325712204,
0.012439197860658169,
-0.010249204002320766,
0.06924117356538773,
-0.005264331586658955,
-0.052441731095314026,
-0.03664986789226532,
-0.03551933541893959,
-0.04807316139340401,
0.004334398545324802,
0.04001100733876228,
-0.02762904204428196,
0.03430880978703499,
0.05188125744462013,
0.00045756646431982517,
-0.04844583570957184,
0.04991854727268219,
0.03926629573106766,
0.018421214073896408,
-0.0325816348195076,
-0.03875588998198509,
-0.0362657867372036,
-0.05928177759051323,
0.0029729860834777355,
0.04388785362243652,
0.0029528678860515356,
-0.036709316074848175,
0.016902871429920197,
0.02430749125778675,
0.03333036229014397,
-0.03629905730485916,
0.005189297255128622,
0.005161091685295105,
-0.006697189528495073,
0.0029959259554743767,
-0.023977776989340782,
0.016121242195367813,
0.03779541701078415,
0.04123324528336525,
-0.02118690125644207,
0.015797941014170647,
-0.08502137660980225,
-0.009782170876860619,
0.054018277674913406,
0.02250230684876442,
-0.0029859349597245455,
-0.0005662425537593663,
-0.048548322170972824,
-0.003047936363145709,
0.02651270292699337,
0.004924551118165255,
0.03205350041389465,
-0.045592062175273895,
-0.00698964623734355,
-0.04937303066253662,
-0.029603485018014908,
0.012699760496616364,
0.0071053472347557545,
0.0183805450797081,
0.004912420641630888,
-0.025941791012883186,
-0.0563206672668457,
-0.04239852353930473,
-0.011415659449994564,
0.03467385098338127,
0.06747102737426758,
-0.010064889676868916,
0.022699609398841858,
0.022285105660557747,
-0.016103629022836685,
-0.010730046778917313,
-0.04271797835826874,
0.01386176235973835,
0.008791551925241947,
0.009226826950907707,
0.04258020594716072,
-0.008980505168437958,
-0.04435054212808609,
0.07371797412633896,
0.002697529038414359,
0.004352817311882973,
-0.01768202893435955,
0.010195638984441757,
0.08395520597696304,
0.030674483627080917,
-0.006255749613046646,
0.019329050555825233,
0.0030858961399644613,
-0.014958852902054787,
0.004982532933354378,
-0.030448321253061295,
0.030121270567178726,
-0.04868302121758461,
-0.007317684590816498,
0.005775923375040293,
-0.029145367443561554,
-0.02864779345691204,
0.024380771443247795,
-0.029723268002271652,
0.016626829281449318,
0.021839529275894165,
-0.0050667207688093185,
-0.009648451581597328,
-0.012947453185915947,
-0.03400344029068947,
0.019279509782791138,
-0.021035917103290558,
0.001437236787751317,
0.011667411774396896,
-0.037294868379831314,
0.005861924961209297,
0.0026945644058287144,
0.006397973746061325,
0.0009577811579219997,
-0.0063043334521353245,
0.01253703236579895,
-0.05626678094267845,
-0.009546840563416481,
-0.0029933247715234756,
-0.01986592635512352,
0.04849914088845253,
-0.027747832238674164,
0.010243793949484825,
-0.001381334150210023,
-0.05471194162964821,
-0.00945651438087225,
0.04240912199020386,
-0.019954433664679527,
-0.011332140304148197,
-0.05913623422384262,
0.046351153403520584,
0.043813977390527725,
-0.006494796834886074,
-0.0744488462805748,
-0.06306523829698563,
0.018320662900805473,
0.036554861813783646,
-0.023283353075385094,
-0.013716106303036213,
0.015183182433247566,
-0.023654190823435783,
-0.020465847104787827,
0.027547435835003853,
0.015764351934194565,
-0.0511065274477005,
-0.021088050678372383,
-0.009509560652077198,
-0.014967000111937523,
0.08444996178150177,
0.001912432606332004,
-0.045564569532871246,
-0.00802908930927515,
-0.03756425157189369,
0.00972008891403675,
-0.011324909515678883,
0.030077170580625534,
-0.024651939049363136,
-0.003848434891551733,
-0.009693153202533722,
-0.02320934273302555,
0.058328114449977875,
-0.021657245233654976,
-0.007757959421724081,
0.049672335386276245,
0.01194388885051012,
0.006239859387278557,
0.0005225194618105888,
0.057490214705467224,
-0.03196252882480621,
0.023366747424006462,
0.011188275180757046,
-0.011298185214400291,
-0.03941544517874718,
-0.018781602382659912,
0.05310767889022827,
-0.002354827942326665,
0.016681700944900513,
0.005421155598014593,
0.1033710166811943,
0.003629041835665703,
0.011357558891177177,
0.027292288839817047,
-0.03169573098421097,
0.012902322225272655,
-0.024545475840568542,
0.009222921915352345,
0.010225596837699413,
0.027813158929347992,
-0.01502953190356493,
-0.03901265561580658,
-0.015428043901920319,
-0.036464110016822815,
0.06675521284341812,
-0.04611485078930855,
0.01223873719573021,
0.008690571412444115,
-0.005464580841362476,
0.0216788649559021,
-0.04898446425795555,
-0.007726174313575029,
0.025038866326212883,
-0.023619208484888077,
0.035420406609773636,
-0.05205893889069557,
0.02216792106628418,
0.027947306632995605,
0.0353449285030365,
-0.026530658826231956,
0.04130706936120987,
0.042074985802173615,
0.021746644750237465,
0.03492702916264534,
0.00791716855019331,
-0.05051132291555405,
0.022078029811382294,
-0.05007589980959892,
0.021861055865883827,
0.011411873623728752,
-0.024038750678300858,
0.04991907626390457,
0.004787747748196125,
0.029888376593589783,
0.00791305210441351,
-0.01299569196999073,
-0.02370142936706543,
0.03325904533267021,
-0.00280592730268836,
0.021045910194516182,
0.0019364496693015099,
0.0009016545373015106,
0.005765608046203852,
0.007024272810667753,
-0.0006225454271771014,
-0.020583275705575943,
-0.05170473828911781,
-0.010755865834653378,
-0.042644526809453964,
0.01938641630113125,
0.00004167386214248836,
0.013534669764339924,
-0.03692401200532913,
0.01144728995859623,
-0.01686840131878853,
0.021062403917312622,
0.01691238209605217,
0.032547030597925186,
-0.013285082764923573,
0.03318874165415764,
-0.019042231142520905,
0.04417847841978073,
-0.0018201775383204222,
0.016175176948308945,
0.1203378289937973,
0.013014943338930607,
0.012607383541762829,
-0.03451915457844734,
0.02059047855436802,
-0.03280775249004364,
-0.002840321511030197,
0.0277194045484066,
-0.008128228597342968,
-0.03160563111305237,
0.004862118512392044,
-0.03600204363465309,
0.07939424365758896,
-0.037503428757190704,
0.03281343728303909,
0.0387885719537735,
-0.047052618116140366,
-0.0012531057000160217,
0.022084008902311325,
0.039600953459739685,
0.017353903502225876,
0.01138787716627121,
-0.0577579028904438,
-0.020177263766527176,
-0.02643023058772087,
0.00001090707792172907,
-0.01848023012280464,
0.005563987884670496,
0.06965918838977814,
0.0225276630371809,
-0.04899023473262787,
-0.009130651131272316,
0.021137110888957977,
0.0029400233179330826,
-0.03882666677236557,
0.030770480632781982,
0.03223409131169319,
-0.00038579548709094524,
0.019794730469584465,
0.03614247217774391,
0.027960725128650665,
0.008686235174536705,
0.005692198872566223,
0.0013951724395155907,
-0.03147733956575394,
0.01021222397685051,
-0.007421801798045635,
0.0061485655605793,
-0.003285946324467659,
-0.01373376790434122,
0.011021079495549202,
-0.001450565061531961,
0.0021795586217194796,
-0.01882796362042427,
-0.03144581988453865,
-0.011580359190702438,
0.02804173342883587,
0.015777312219142914,
0.004777882248163223,
0.002772070001810789,
0.0006552435224875808,
0.011986254714429379,
-0.018113214522600174,
-0.004034304525703192,
-0.0352567657828331,
0.027644922956824303,
0.03718401864171028,
0.020687349140644073,
-0.01414381992071867,
-0.022417748346924782,
0.0025228005833923817,
-0.00867349375039339,
-0.02428096905350685,
-0.053787119686603546,
0.00698957871645689,
0.027203548699617386,
0.04173614829778671,
-0.01016371138393879,
0.003916791174560785,
0.0004946946282871068,
-0.07943306118249893,
0.029199831187725067,
-0.01997787319123745,
-0.0020781871862709522,
-0.039680108428001404,
-0.032039083540439606,
0.0258207805454731,
0.06437496095895767,
-0.05616143345832825,
0.002674997551366687,
0.0016117205377668142,
0.037292975932359695,
0.014475950971245766,
-0.049708034843206406,
-0.02935675159096718,
-0.010097894817590714,
-0.007740989327430725,
0.05265967175364494,
-0.01857547089457512,
0.04653806984424591,
0.04370146989822388,
-0.010701564140617847,
-0.02129415050148964,
0.005085008218884468,
-0.034800320863723755,
0.001523211132735014,
0.004437228664755821,
-0.007093983702361584,
-0.03507159650325775,
-0.0042217327281832695,
0.0412716381251812,
-0.03482440859079361,
-0.016748568043112755,
-0.006388602312654257,
-0.011963596567511559,
0.0420638732612133,
0.017765145748853683,
-0.006890435703098774,
0.02177363447844982,
-0.019030174240469933,
0.0004897991311736405,
-0.04141218587756157,
-0.021130284294486046,
-0.035564862191677094,
-0.0008144130697473884,
0.03306230530142784,
-0.01017867960035801,
0.012188885360956192,
0.03669558838009834,
-0.04759153723716736,
0.029943285509943962,
0.06775548309087753,
0.024632925167679787,
-0.014999750070273876,
0.0341152660548687,
0.04109250754117966,
-0.017919916659593582,
0.011655112728476524,
-0.02000383846461773,
-0.0008000316447578371,
0.023691747337579727,
-0.03136513754725456,
-0.051097627729177475,
0.019064411520957947,
0.009253954514861107,
0.040177520364522934,
-0.010348176583647728,
-0.03173740208148956,
0.0016451010014861822,
0.020914560183882713,
-0.044649604707956314,
-0.012466127052903175,
0.010567683726549149,
-0.009076479822397232,
-0.008376827463507652,
-0.00970170646905899,
-0.006803741678595543,
0.00623535830527544,
-0.006832960527390242,
0.019886115565896034,
-0.009354081004858017,
0.004948668647557497,
-0.027990179136395454,
0.0006433908711187541,
-0.033690620213747025,
-0.0022652815096080303,
0.03130039572715759,
0.014636260457336903,
-0.01658717729151249,
0.04602900147438049,
-0.006496512331068516,
0.038195542991161346,
0.053215838968753815,
-0.002332253148779273,
-0.07576807588338852,
-0.027957206591963768,
0.003325955243781209,
-0.005934369284659624,
0.007878725416958332,
-0.03183050826191902,
0.046652499586343765,
-0.004526927601546049,
-0.10108432173728943,
0.0027832116466015577,
-0.017126107588410378,
-0.05749030411243439,
-0.0497090145945549,
0.005277454853057861,
-0.0403277724981308,
0.02743850089609623,
0.008254440501332283,
0.07546749711036682,
-0.00472309859469533,
0.025028185918927193,
-0.01443920936435461,
-0.004885868635028601,
-0.008650711737573147,
0.008744764141738415,
-0.0024227576795965433,
-0.02865787036716938,
0.03502765670418739,
-0.00311067420989275,
0.005369267892092466,
-0.01264580711722374,
0.019460469484329224,
-0.02862858586013317,
0.0029645280446857214,
-0.0009743652190081775,
-0.006598345469683409,
0.009675377048552036,
0.007416962180286646,
-0.013909785076975822,
-0.011696761474013329,
0.011144214309751987,
0.0018593344138935208,
0.06023465469479561,
-0.005948275327682495,
-0.002864941256120801,
0.02717815525829792,
-0.031107096001505852,
0.01891406625509262,
0.008736676536500454,
-0.00753650302067399,
-0.033877477049827576,
0.002863367786630988,
0.03949189558625221,
0.0014218370197340846,
-0.05811154469847679,
-0.003372838720679283,
-0.054215848445892334,
-0.06462439894676208,
0.018254760652780533,
0.041202906519174576,
-0.018032314255833626,
-0.03146616742014885,
0.005478295031934977,
-0.059087123721838,
0.04036032781004906,
0.022964539006352425,
-0.04799264669418335,
-0.041253816336393356,
-0.00797903910279274,
0.029946736991405487,
-0.028696024790406227,
0.025555895641446114,
-0.053304146975278854,
-0.03431488201022148,
0.04137778654694557,
-0.00031122227665036917,
0.02968672104179859,
-0.0015130797401070595,
-0.07543446123600006,
-0.01262683980166912,
-0.046113520860672,
0.054010309278964996,
-0.032245706766843796,
0.005293576046824455,
-0.018920905888080597,
-0.001596567570231855,
-0.020988991484045982,
0.024679070338606834,
0.10119616240262985,
0.01636030711233616,
0.006728620268404484,
-0.006502984091639519,
-0.04254484176635742,
0.018128179013729095,
0.001244327868334949,
0.027943020686507225,
0.008580195717513561,
-0.009592692367732525,
-0.018375352025032043,
0.01019876729696989,
-0.04645814746618271,
0.01766999438405037,
0.03730854392051697,
0.006003992166370153,
0.0016023938078433275,
-0.02070230059325695,
0.01884552650153637,
0.040633656084537506,
0.011763440445065498,
-0.01391120720654726,
0.08626340329647064,
-0.020253954455256462,
0.0007305730832740664,
0.033311452716588974,
0.016760792583227158,
-0.08629126846790314,
-0.007320938631892204,
-0.0122799351811409,
-0.0056143817491829395,
0.015971003100275993,
0.020558631047606468,
0.015015799552202225,
-0.023043278604745865,
-0.010810386389493942,
0.0434330552816391,
-0.014611451886594296,
-0.004016048740595579,
0.05118609219789505,
0.0026454541366547346,
0.01089394185692072,
-0.03540237620472908,
-0.014177476987242699,
0.027858106419444084,
0.0020559318363666534,
0.026397977024316788,
0.043609730899333954,
0.020557822659611702,
0.032659828662872314,
0.01909560151398182,
0.03419053182005882,
-0.007373107597231865,
-0.01627509668469429,
0.03021255135536194,
0.011651028878986835,
-0.016004636883735657,
-0.002073360839858651,
0.0457882434129715,
-0.009397509507834911,
0.017052670940756798,
0.025350626558065414,
-0.03110227920114994,
0.10843602567911148,
-0.032231442630290985,
0.02500813640654087,
-0.036636073142290115,
0.001663691597059369,
-0.0032324492931365967,
0.009426639415323734,
0.02412971295416355,
0.023206887766718864,
-0.017379363998770714,
-0.02829260379076004,
-0.056385595351457596,
0.010764526203274727,
0.04655850678682327,
-0.07511848956346512,
0.02726604975759983,
0.0040278322994709015,
-0.009097275324165821,
-0.010397369042038918,
-0.0023778353352099657,
0.010473409667611122,
0.005558690521866083,
0.0420663058757782,
0.0532674565911293,
0.007846969179809093,
0.002341704908758402,
0.0013600108213722706,
-0.01587953418493271,
0.05337262898683548,
-0.041433826088905334,
-0.001904069446027279,
-0.030442267656326294,
-0.007782874163240194,
-0.05101349949836731,
-0.03777686133980751
] |
<p>I'm currently reading the Seiberg-Witten paper on $N=2$ supersymmetric Yang Mills pure gauge theory (i.e. no hypermultiplets). I have the following question:</p>
<p>How does one understand that the metric on the moduli space of the full quantum theory is the same as the metric obtained from the Kahler potential for the scalar field (or in general the $N=1$ chiral superfield) in the low-energy effective theory? On the face of it, the two things seem quite different - while the moduli space is the space of all gauge-inequivalent vacua in the full theory, the Kahler metric is derived from the Kahler potential in the low energy theory. </p> | 2,055 | [
-0.006419059820473194,
0.007473130710422993,
0.005750144831836224,
-0.028772030025720596,
0.014512971043586731,
0.05044477432966232,
-0.0236639603972435,
-0.04886193946003914,
-0.015121370553970337,
-0.01753263920545578,
0.015504966489970684,
0.00038593460340052843,
0.09750261902809143,
0.017134441062808037,
0.012458142824470997,
-0.015237817540764809,
-0.012180131860077381,
-0.0073952823877334595,
0.006290983874350786,
-0.02403058111667633,
0.0034634126350283623,
0.010452155023813248,
0.011831867508590221,
-0.00933139119297266,
-0.008886532858014107,
0.007802535779774189,
-0.019174745306372643,
0.017112305387854576,
-0.0031074078287929296,
0.04282074421644211,
0.014697423204779625,
-0.05327088013291359,
0.023137610405683517,
0.0022062985226511955,
-0.03065141662955284,
-0.0084294518455863,
-0.046277955174446106,
-0.03597583249211311,
0.006338287610560656,
0.008294576779007912,
-0.04329809546470642,
-0.033547189086675644,
-0.046938456594944,
0.043987125158309937,
0.00008605708717368543,
0.012676781043410301,
-0.028393514454364777,
-0.01939062587916851,
0.031860221177339554,
-0.06352115422487259,
0.037174973636865616,
0.041599299758672714,
0.003068014979362488,
0.009077826514840126,
0.0036651839036494493,
-0.010376129299402237,
0.05451710894703865,
0.07950740307569504,
-0.026628980413079262,
-0.032194461673498154,
-0.10493173450231552,
-0.02319008857011795,
-0.00983422715216875,
-0.04695664346218109,
-0.012589627876877785,
0.03153664991259575,
0.027231380343437195,
-0.026534268632531166,
0.040726713836193085,
-0.005216340534389019,
-0.007818486541509628,
0.027082445099949837,
0.021085131913423538,
0.004671999718993902,
0.03573812171816826,
0.010288765653967857,
-0.004306759685277939,
-0.014129995368421078,
0.05860555171966553,
0.009357795119285583,
-0.014247842133045197,
0.017113495618104935,
0.03606383875012398,
0.043068934231996536,
-0.02537255547940731,
-0.005493554286658764,
0.0736769512295723,
0.03482550010085106,
-0.022508716210722923,
0.038328878581523895,
-0.020387468859553337,
-0.0037565799430012703,
0.030313003808259964,
-0.03709453344345093,
-0.027517784386873245,
0.03893803432583809,
0.011189576238393784,
0.06158631294965744,
-0.01430231798440218,
-0.013465098105370998,
-0.034367579966783524,
-0.014000470750033855,
0.009772051125764847,
0.05957980826497078,
0.01363187376409769,
-0.010324414819478989,
-0.020620819181203842,
0.03406291827559471,
-0.047417815774679184,
-0.013901048339903355,
-0.036163296550512314,
0.02624603733420372,
-0.027706125751137733,
-0.009243009611964226,
-0.004266421776264906,
-0.061400722712278366,
-0.0038504607509821653,
-0.03691085800528526,
0.049889665096998215,
0.0608331523835659,
0.05514200031757355,
-0.012156271375715733,
-0.011032133363187313,
-0.03365550562739372,
-0.043496835976839066,
0.01184224896132946,
0.03720710799098015,
-0.003465222893282771,
-0.03783530369400978,
-0.004681721795350313,
0.03332781046628952,
-0.007008376996964216,
0.011037379503250122,
0.022524258121848106,
0.038522616028785706,
-0.04294382780790329,
-0.0787677988409996,
-0.022160448133945465,
0.04946408420801163,
0.013640496879816055,
-0.008240515366196632,
-0.03431536257266998,
-0.0193775724619627,
0.03263804689049721,
0.08996693789958954,
-0.0005903523997403681,
0.026143694296479225,
0.021943511441349983,
-0.009079882875084877,
0.0130114471539855,
-0.009036446921527386,
-0.02558598481118679,
0.009883124381303787,
-0.015592217445373535,
-0.030752280727028847,
-0.04556060582399368,
0.026486843824386597,
0.030365541577339172,
-0.00837321113795042,
-0.015955248847603798,
0.07241716235876083,
0.011521579697728157,
0.02825309708714485,
0.02319585159420967,
0.026857594028115273,
-0.011359856463968754,
0.05680772662162781,
0.0051478068344295025,
-0.0008475349750369787,
0.019785217940807343,
-0.03166385367512703,
-0.001291208085604012,
0.026530373841524124,
0.04728014022111893,
0.03787258639931679,
-0.009248281829059124,
0.0032710868399590254,
-0.0035658879205584526,
0.031278423964977264,
0.011397828347980976,
-0.028770573437213898,
-0.0287790410220623,
-0.0203385092318058,
0.006910067517310381,
0.017157943919301033,
0.019642548635601997,
-0.02499336004257202,
-0.042340826243162155,
0.02494760788977146,
-0.049337852746248245,
-0.005770563613623381,
-0.042097512632608414,
-0.004226097837090492,
0.0007917092298157513,
-0.005828580819070339,
0.03460705652832985,
0.022730965167284012,
-0.008394175209105015,
0.0006065925699658692,
-0.0298625398427248,
0.004747759085148573,
0.029077401384711266,
-0.027420207858085632,
0.021786117926239967,
0.03504220023751259,
0.008565325289964676,
0.011829439550638199,
-0.0020053198095411062,
0.05808563530445099,
-0.0000624924578005448,
-0.03023098222911358,
0.01026134006679058,
0.01801508478820324,
0.032488804310560226,
-0.0055512976832687855,
-0.008544376119971275,
-0.03231653943657875,
0.018413491547107697,
-0.01170254498720169,
0.048413701355457306,
-0.07123593240976334,
0.05911614000797272,
0.02488809823989868,
0.019915034994482994,
-0.0235343798995018,
0.019122770056128502,
-0.03525790944695473,
0.05598103255033493,
0.025540703907608986,
-0.025736374780535698,
-0.03577331081032753,
-0.01737956516444683,
0.05437988042831421,
0.024977611377835274,
-0.021258685737848282,
0.013389283791184425,
0.026932628825306892,
-0.014119317755103111,
0.026351522654294968,
-0.010822379030287266,
0.0023817301262170076,
-0.03132317587733269,
0.04611383005976677,
0.0030498586129397154,
-0.020760977640748024,
-0.014265699312090874,
0.029159141704440117,
0.0004859435430262238,
-0.00318146008066833,
-0.0014288140228018165,
-0.01911761239171028,
0.04335686191916466,
-0.023424146696925163,
-0.0017927080625668168,
-0.001785910688340664,
-0.013198384083807468,
0.03990159183740616,
0.027739737182855606,
0.05189123749732971,
0.06138354539871216,
0.007691515609622002,
-0.0025484629441052675,
-0.0009956363355740905,
-0.01766662858426571,
0.05563276261091232,
0.020313439890742302,
-0.010564315132796764,
-0.015633558854460716,
0.010425630025565624,
-0.033944256603717804,
0.015269074589014053,
-0.024442650377750397,
-0.023726528510451317,
-0.009206250309944153,
0.00658392533659935,
0.01022745855152607,
-0.036999814212322235,
0.015141332522034645,
-0.030152328312397003,
-0.05667757987976074,
0.056151486933231354,
-0.005995772313326597,
0.035278383642435074,
0.029476583003997803,
-0.001318817725405097,
0.010854116640985012,
-0.05827239900827408,
0.0041608065366744995,
0.03957298770546913,
0.01413700170814991,
0.05651799216866493,
-0.03342659771442413,
-0.035570885986089706,
-0.02116621658205986,
-0.008914516307413578,
-0.012670302763581276,
0.03633195906877518,
0.006402895785868168,
0.007450873032212257,
0.04095912352204323,
0.02564101293683052,
-0.03479127585887909,
-0.0111157838255167,
0.018392052501440048,
-0.038253121078014374,
-0.03340062499046326,
0.003230182221159339,
0.04123835638165474,
-0.05105118826031685,
0.04212604835629463,
0.047352131456136703,
-0.04518952593207359,
0.0017985041486099362,
-0.052822522819042206,
-0.0661512017250061,
0.030402645468711853,
-0.008096878416836262,
0.0031028189696371555,
0.01670389249920845,
-0.061946477741003036,
0.12415601313114166,
0.015016504563391209,
-0.02791278250515461,
-0.028765050694346428,
-0.006322863046079874,
-0.015944108366966248,
-0.0008594683022238314,
0.0014775301096960902,
0.02626478299498558,
0.009806610643863678,
0.03850903734564781,
0.049256473779678345,
0.0659831315279007,
0.04555385932326317,
-0.01085827499628067,
-0.03558450564742088,
-0.009701507166028023,
0.026330599561333656,
-0.002639040583744645,
0.024493861943483353,
-0.003109243931248784,
-0.03866451606154442,
-0.0068078176118433475,
0.01845918782055378,
0.014089521020650864,
0.03379946947097778,
-0.016159195452928543,
0.03356167674064636,
-0.009068348444998264,
0.019007209688425064,
-0.02455570176243782,
0.050111621618270874,
-0.009457595646381378,
-0.06949927657842636,
0.008153458125889301,
0.008947680704295635,
0.025691095739603043,
-0.03734573721885681,
-0.0015697212656959891,
0.01431269384920597,
-0.005106777884066105,
-0.07331569492816925,
-0.030715661123394966,
-0.007580577861517668,
-0.01997905783355236,
0.012614850886166096,
-0.002623822772875428,
-0.022115642204880714,
0.021138986572623253,
0.024604972451925278,
0.0020049666054546833,
-0.00627957284450531,
-0.031155407428741455,
0.012846434488892555,
-0.04462563246488571,
-0.008828493766486645,
0.0425889678299427,
0.032996825873851776,
-0.01926935464143753,
0.031740013509988785,
-0.0029855910688638687,
0.033528562635183334,
-0.02201463095843792,
0.015078309923410416,
-0.05738326907157898,
-0.02169618383049965,
-0.05173252522945404,
-0.014270000159740448,
-0.02789861336350441,
-0.04624248668551445,
0.012094161473214626,
-0.02247072011232376,
-0.09049037098884583,
-0.026442360132932663,
-0.019518498331308365,
-0.053969383239746094,
0.03987208008766174,
-0.06189567223191261,
-0.013452848419547081,
-0.0421978123486042,
0.059256307780742645,
0.05439753457903862,
-0.026256533339619637,
0.0003327124868519604,
0.02973451092839241,
-0.021527627483010292,
-0.012495456263422966,
0.005528464447706938,
0.029038555920124054,
0.0006273330072872341,
0.02240079827606678,
0.009289218112826347,
0.016648072749376297,
-0.01727565936744213,
0.03736371174454689,
0.020113293081521988,
0.05033041536808014,
-0.013068103231489658,
-0.008744021877646446,
0.01280028373003006,
-0.055288802832365036,
0.000552730867639184,
0.0028088416438549757,
0.07359220832586288,
0.02806173637509346,
-0.007915589958429337,
0.038540031760931015,
0.02217496559023857,
0.0004477993643376976,
-0.0019476906163617969,
0.04954696074128151,
-0.03840287774801254,
-0.03312484920024872,
-0.060143254697322845,
0.01791163720190525,
-0.013783303089439869,
0.0072718532755970955,
0.006601950153708458,
-0.0334329791367054,
-0.026525234803557396,
0.01222286093980074,
0.017248308286070824,
0.004814958665519953,
-0.05264701321721077,
-0.03139368072152138,
0.00866696797311306,
0.010703318752348423,
-0.026398908346891403,
-0.007445111405104399,
0.02532946690917015,
0.0538543201982975,
0.05914704129099846,
-0.019619787111878395,
-0.008959040977060795,
-0.06794805824756622,
-0.011027335189282894,
0.01715198904275894,
0.023048749193549156,
0.0208695400506258,
-0.009739390574395657,
-0.06896032392978668,
-0.017492303624749184,
0.04046568647027016,
-0.002030986361205578,
0.008241222240030766,
0.03160268813371658,
-0.003050899598747492,
-0.016132164746522903,
0.014349198900163174,
0.02593797631561756,
0.03827444463968277,
0.012689558789134026,
-0.007794390898197889,
0.01779448427259922,
0.004135922063142061,
-0.019626036286354065,
0.04871432110667229,
0.03180285543203354,
0.03942287340760231,
0.06223737448453903,
0.026599738746881485,
-0.003926778677850962,
0.02648072876036167,
-0.031134024262428284,
-0.08236493170261383,
0.019316621124744415,
0.01598421111702919,
-0.023947129026055336,
0.028577765449881554,
-0.026222223415970802,
-0.010518435388803482,
0.01282841432839632,
-0.014498851262032986,
-0.008894957602024078,
0.02571246773004532,
-0.044347722083330154,
0.011092385277152061,
0.02894984558224678,
-0.004095630720257759,
0.04024073854088783,
0.01782204955816269,
-0.02523886226117611,
-0.007747148163616657,
-0.04034881666302681,
0.044191163033246994,
-0.04259766638278961,
-0.025992680341005325,
-0.05569274351000786,
-0.02066182717680931,
-0.032059673219919205,
0.021411580964922905,
-0.017610790207982063,
0.01844787783920765,
-0.044435955584049225,
-0.051313284784555435,
-0.049026235938072205,
0.025881566107273102,
0.04748816415667534,
-0.0012074328260496259,
-0.001298933639191091,
0.04946870729327202,
0.009291407652199268,
-0.002780953887850046,
0.006953151430934668,
-0.008818844333291054,
-0.01169447973370552,
0.013079069554805756,
0.00654700817540288,
0.0473770909011364,
-0.023133868351578712,
-0.007959365844726562,
0.05608909949660301,
-0.013133911415934563,
0.015063423663377762,
-0.01196093950420618,
-0.04238049313426018,
-0.022778399288654327,
-0.029512597247958183,
-0.0010683567961677909,
-0.020421501249074936,
-0.007538600359112024,
0.022248050197958946,
-0.018459470942616463,
0.043807610869407654,
0.04292535036802292,
-0.013648630119860172,
-0.07941979914903641,
-0.03350403532385826,
-0.017360052093863487,
0.0007373082335107028,
-0.030141113325953484,
-0.025989342480897903,
-0.007453751750290394,
-0.008419374004006386,
-0.035854876041412354,
-0.019063064828515053,
0.04460190609097481,
-0.03922625258564949,
0.0064421058632433414,
0.017692292109131813,
0.07920119911432266,
0.01019778661429882,
0.014348001219332218,
0.011415600776672363,
0.015809042379260063,
0.005848543718457222,
-0.0024785140994936228,
0.003884986974298954,
0.050158560276031494,
-0.00439058942720294,
0.004900021944195032,
-0.03727692365646362,
-0.03969860076904297,
0.03156469017267227,
-0.018653709441423416,
0.03139191120862961,
0.0041801221668720245,
0.03347298502922058,
0.01933245174586773,
-0.02705317921936512,
-0.030318794772028923,
-0.007169580552726984,
0.030125614255666733,
-0.022842537611722946,
0.015395750291645527,
0.007980989292263985,
-0.02593756839632988,
0.062074124813079834,
-0.01787465810775757,
0.00926391500979662,
-0.010844076052308083,
0.052615515887737274,
-0.00913879182189703,
-0.05832832679152489,
0.018355336040258408,
-0.06325796246528625,
-0.01875379867851734,
0.0297476127743721,
0.028938010334968567,
0.02422916889190674,
0.01884664222598076,
0.007368872407823801,
-0.05077054351568222,
-0.030355121940374374,
0.005682508926838636,
0.06602682173252106,
-0.0022987499833106995,
0.014117555692791939,
-0.028344029560685158,
-0.04216723144054413,
0.028042078018188477,
-0.035062745213508606,
-0.018169665709137917,
-0.002014121040701866,
0.0027637332677841187,
0.02485567517578602,
-0.030181214213371277,
-0.010952540673315525,
0.010349048301577568,
0.04121904820203781,
-0.03417427837848663,
0.027103062719106674,
0.03601111099123955,
0.03730274364352226,
0.0156081048771739,
-0.01015050895512104,
-0.03472018986940384,
0.05513206124305725,
0.02227933518588543,
0.028448011726140976,
0.014321573078632355,
0.0022690061014145613,
0.028851207345724106,
0.018525607883930206,
-0.00118952093180269,
-0.012499898672103882,
0.0041664354503154755,
-0.058892250061035156,
0.03560340404510498,
0.008933750912547112,
0.03360209986567497,
0.012043490074574947,
0.02598523162305355,
0.024943536147475243,
0.004389608278870583,
-0.006647048052400351,
-0.017867282032966614,
-0.03164983168244362,
-0.0445338599383831,
-0.0261465422809124,
-0.03714282438158989,
0.026238132268190384,
-0.0061774174682796,
-0.06437882035970688,
0.0017364394152536988,
-0.032446976751089096,
0.02606029622256756,
-0.023564735427498817,
0.031928304582834244,
-0.007567272987216711,
0.07097053527832031,
-0.010396119207143784,
0.039131298661231995,
-0.015499035827815533,
0.0076550208032131195,
0.11008752137422562,
0.06298535317182541,
-0.022813336923718452,
-0.11708397418260574,
0.024692581966519356,
-0.0060916743241250515,
-0.0049041034653782845,
-0.04869767278432846,
0.028138935565948486,
0.010999810881912708,
-0.01786043867468834,
0.03055790811777115,
0.07770224660634995,
0.03312700614333153,
0.006300781387835741,
0.04723653569817543,
-0.008773107081651688,
-0.05285737290978432,
0.0018584909848868847,
-0.0017845298862084746,
-0.046942178159952164,
0.002302770037204027,
-0.029386000707745552,
0.015616776421666145,
0.031244637444615364,
0.04652590677142143,
-0.013242986053228378,
-0.029553627595305443,
0.019844813272356987,
0.008275308646261692,
-0.03182545304298401,
0.019673027098178864,
-0.011564914137125015,
0.01381456758826971,
-0.032550983130931854,
-0.009360349737107754,
0.0048079900443553925,
0.011108774691820145,
0.016241293400526047,
0.03696779906749725,
0.024152254685759544,
-0.011586432345211506,
0.0002718166506383568,
0.013813079334795475,
-0.04685025289654732,
-0.037614140659570694,
-0.04021987318992615,
0.012495411559939384,
-0.035640399903059006,
-0.01778453402221203,
-0.014671502634882927,
-0.013630921952426434,
0.001534519251435995,
-0.012897706590592861,
-0.0036678349133580923,
-0.021918071433901787,
0.01667560264468193,
-0.032012831419706345,
-0.0004427467647474259,
-0.017557308077812195,
0.03803218528628349,
0.013265042565762997,
0.010466928593814373,
-0.037597279995679855,
-0.004390322137624025,
0.017003078013658524,
0.006022240500897169,
-0.004558762069791555,
0.02819969318807125,
-0.02650528959929943,
-0.002665113192051649,
-0.007075903937220573,
-0.0307538490742445,
-0.04689333215355873,
0.005003654398024082,
-0.006983000319451094,
0.06215778738260269,
-0.005138506181538105,
0.022036660462617874,
0.00523015670478344,
-0.055398549884557724,
0.02479369193315506,
0.0060755605809390545,
-0.030956635251641273,
-0.018515942618250847,
-0.003116446081548929,
0.0002231300313724205,
0.023118866607546806,
-0.010729054920375347,
0.013383769430220127,
0.0013175979256629944,
0.009037688374519348,
0.004983956925570965,
-0.03656983748078346,
0.00954396091401577,
-0.0025976437609642744,
-0.029326843097805977,
-0.010934149846434593,
-0.008970994502305984,
0.016308115795254707,
0.011057287454605103,
0.025716567412018776,
0.012266532517969608,
0.049508120864629745,
-0.02100750245153904,
0.0011046030558645725,
-0.0032440228387713432,
-0.011905243620276451,
-0.004994234535843134,
0.01590225286781788,
0.014979389496147633,
-0.01690404675900936,
-0.05358919873833656,
-0.03576943650841713,
0.002465026918798685,
-0.007328411564230919,
0.01784426160156727,
-0.06699689477682114,
-0.013008201494812965,
-0.019989099353551865,
-0.016372866928577423,
-0.050893109291791916,
-0.03329461067914963,
-0.009912746958434582,
0.07055576145648956,
0.012660752981901169,
0.010947727598249912,
0.04280506446957588,
0.011271988973021507,
-0.040373630821704865,
-0.03624780476093292,
0.0061493609100580215,
-0.007796806748956442,
-0.06175214797258377,
0.0066566262394189835,
0.03345644846558571,
-0.011743064038455486,
0.04079492762684822,
-0.043912287801504135,
-0.0308567862957716,
0.04273008555173874,
-0.06083201244473457,
-0.07639797031879425,
0.009283624589443207,
-0.011682617478072643,
0.021534178406000137,
0.05310584977269173,
-0.012091638520359993,
-0.015610781498253345,
0.01775265671312809,
-0.014928050339221954,
-0.004721375647932291,
-0.004086114000529051,
-0.025912709534168243,
0.0020313127897679806,
-0.01754169538617134,
0.012981356121599674,
-0.016004124656319618,
0.02423137053847313,
0.052353933453559875,
0.008724248968064785,
-0.008650588802993298,
-0.04048458859324455,
-0.00158510182518512,
-0.02410118840634823,
0.054871249943971634,
-0.004356876481324434,
-0.007556322496384382,
-0.010863222181797028,
0.039446957409381866,
-0.0629252940416336,
-0.0019932121504098177,
-0.011832662858068943,
-0.0006530514219775796,
-0.06708475947380066,
-0.029345236718654633,
0.010069872252643108,
0.03461258113384247,
0.04696088656783104,
-0.06778647005558014,
0.022730013355612755,
0.04114126041531563,
-0.04850444942712784,
0.03742827847599983,
-0.002528890734538436,
-0.008103911764919758,
-0.02207324653863907,
0.015183837153017521,
-0.032485589385032654,
0.05032336339354515,
0.06005769968032837,
0.02829883247613907,
0.017159370705485344,
-0.032796092331409454,
0.005435867700725794,
0.005940007511526346,
-0.0377948172390461,
-0.006254842504858971,
0.02154703624546528,
-0.06050042062997818,
0.11960450559854507,
-0.0037718876264989376,
-0.046923793852329254,
0.050060294568538666,
0.00842017587274313,
-0.0047066728584468365,
0.004187119659036398,
0.007397320121526718,
-0.001428181305527687,
0.041328005492687225,
0.053780004382133484,
-0.004844279028475285,
-0.009603629820048809,
0.006642188876867294,
0.018192077055573463,
0.03997452184557915,
-0.009449262171983719,
0.009161979891359806,
0.007096935994923115,
-0.035475388169288635,
-0.017113706097006798,
0.013227712363004684,
-0.015154486522078514,
-0.04470420628786087,
-0.01470967661589384,
-0.023634765297174454,
0.023780493065714836,
-0.0005970047204755247,
0.021065719425678253,
-0.02865288034081459,
0.016762923449277878,
0.0771399661898613,
0.0018523072358220816,
0.0030791773460805416,
0.0459725521504879,
-0.0019363455940037966,
-0.030193855985999107,
0.015965251252055168,
0.05575008690357208,
-0.0078040421940386295,
-0.016272881999611855,
-0.035029344260692596,
-0.004012880846858025,
0.011202141642570496,
0.0003505137574393302,
-0.03525848314166069,
-0.014910707250237465,
0.05172877758741379,
0.0021553460974246264,
0.04693632945418358,
-0.03491930291056633,
-0.00222216360270977,
-0.04246344044804573,
-0.06811664998531342,
0.020766248926520348,
-0.00774361053481698,
0.00352937588468194,
-0.010940336622297764,
0.03669329732656479,
-0.007848740555346012,
-0.015026911161839962,
0.01838734745979309,
-0.019375013187527657,
-0.029852913692593575,
0.0005422187969088554,
0.01498627383261919,
0.03624199703335762,
0.006768367253243923,
-0.012561176903545856,
0.0015379831893369555,
-0.031996678560972214,
0.01767776720225811,
0.00280283042229712,
-0.028503667563199997,
0.03887104243040085,
0.021134819835424423,
-0.006380102597177029,
0.029716214165091515,
-0.014499878510832787,
-0.009598306380212307,
0.05963318049907684,
0.0018407905008643866,
-0.017351819202303886,
0.04417802393436432,
-0.01205530483275652,
0.042904943227767944,
0.040899187326431274,
-0.02528247982263565,
-0.002469488885253668,
0.0085509167984128,
-0.03517547622323036,
-0.007370227016508579,
0.01516902819275856,
-0.0001358261943096295,
0.023706398904323578,
-0.03343343734741211,
-0.008167574182152748,
0.04094851762056351,
-0.02832399308681488,
-0.04150371253490448,
0.04021892324090004,
-0.003043434815481305,
0.01687254197895527,
0.05270044133067131,
0.012391838245093822,
0.0045950450003147125,
0.038405437022447586,
0.035260602831840515,
0.05553716421127319,
0.04163826256990433,
-0.018090078607201576,
-0.034147195518016815,
0.014507412910461426,
-0.020721672102808952,
0.01080235093832016,
0.004892364609986544,
0.057385724037885666,
-0.04538040980696678,
-0.04453650489449501,
0.02791970781981945,
-0.02222667820751667,
0.014570510946214199,
0.017171500250697136,
-0.05238167196512222,
0.09942557662725449,
-0.025659611448645592,
0.027581140398979187,
-0.028516700491309166,
-0.005986544769257307,
-0.017562570050358772,
0.01351703330874443,
-0.0017652199603617191,
0.06614015996456146,
0.0037995793391019106,
-0.0019132612505927682,
-0.006345043890178204,
-0.008607896976172924,
-0.007948705926537514,
-0.056172486394643784,
0.003578153206035495,
-0.0347239151597023,
-0.02110723964869976,
-0.02407102845609188,
-0.022375132888555527,
0.00005088599573355168,
0.001839025761000812,
0.004557449836283922,
0.030605167150497437,
0.058551084250211716,
0.0024350867606699467,
-0.010399025864899158,
-0.01374917570501566,
0.0317961722612381,
-0.04169025644659996,
0.006511100102216005,
-0.02100388891994953,
-0.010688479989767075,
0.007507968693971634,
-0.02917660027742386
] |
<p>I'm swimming in the ocean and there's a thunderstorm. Lightning bolts hit ships around me. Should I get out of the water?</p> | 2,056 | [
-0.026308676227927208,
-0.035684358328580856,
-0.023549295961856842,
-0.0000172117943293415,
0.008155161514878273,
0.003474727738648653,
-0.030467700213193893,
-0.009268078953027725,
0.04163121059536934,
-0.018578270450234413,
0.07110492885112762,
0.08896584063768387,
0.021083323284983635,
0.03360268473625183,
-0.021434301510453224,
0.018400097265839577,
0.019310811534523964,
-0.019558468833565712,
0.011388245038688183,
-0.027687083929777145,
-0.023761097341775894,
0.004617332015186548,
-0.03324049338698387,
0.0037937129382044077,
-0.04663412272930145,
0.012776940129697323,
0.02888263761997223,
-0.012608502991497517,
0.034437067806720734,
0.018132802098989487,
-0.05024385079741478,
-0.04550713300704956,
0.045911069959402084,
0.016095533967018127,
0.04807577282190323,
0.02516982890665531,
-0.007533954456448555,
0.008665724657475948,
-0.04101775214076042,
-0.021556846797466278,
0.03422684594988823,
-0.04820861667394638,
0.005274403374642134,
0.026321018114686012,
-0.031821977347135544,
-0.0013858999591320753,
-0.002751260995864868,
-0.03865703567862511,
0.0027050587814301252,
-0.06395019590854645,
0.0458797924220562,
-0.008378110826015472,
0.004261319059878588,
0.02377074584364891,
0.015532687306404114,
0.05232471227645874,
0.05667605251073837,
0.08169515430927277,
-0.019770948216319084,
-0.022236039862036705,
0.025338511914014816,
-0.01781380921602249,
0.004611610434949398,
-0.01149939838796854,
-0.021226324141025543,
0.03805729001760483,
0.020302388817071915,
-0.03243355080485344,
0.04618598148226738,
0.002281567780300975,
-0.04757248982787132,
-0.003765304572880268,
0.016958478838205338,
-0.021808195859193802,
0.0034169608261436224,
-0.05095691978931427,
0.0072239357978105545,
0.027088521048426628,
0.03141635283827782,
0.032322563230991364,
0.0072211469523608685,
0.00512802554294467,
0.010896335355937481,
0.006532550323754549,
0.04976026341319084,
-0.031395941972732544,
0.08954937011003494,
0.004020241089165211,
0.0007153917104005814,
-0.0016631106846034527,
-0.026065614074468613,
-0.022687336429953575,
-0.03188901022076607,
0.0325169563293457,
-0.014408983290195465,
0.027643563225865364,
-0.007020097691565752,
0.02073458582162857,
0.027637002989649773,
-0.02107071690261364,
-0.024714643135666847,
-0.008596588857471943,
0.03547510504722595,
0.008592263795435429,
0.012194175273180008,
-0.0043009803630411625,
-0.06647608429193497,
0.0057735322043299675,
-0.004580240696668625,
-0.038534559309482574,
-0.030802031978964806,
-0.00008814434113446623,
-0.024629810824990273,
-0.045048873871564865,
0.005880296230316162,
-0.019922414794564247,
0.016939999535679817,
-0.024386463686823845,
0.03159084916114807,
0.05716868117451668,
0.026589341461658478,
-0.002497689099982381,
0.04301821440458298,
-0.017176887020468712,
-0.06618677824735641,
0.025631938129663467,
0.02410196326673031,
-0.05062348395586014,
-0.01604791171848774,
0.03947371989488602,
-0.028765883296728134,
-0.005649281665682793,
-0.011190418154001236,
-0.02155185118317604,
0.05434245243668556,
0.01791076362133026,
-0.09446336328983307,
-0.06652066111564636,
0.04839491844177246,
0.006211202125996351,
-0.013869065791368484,
-0.06830747425556183,
-0.0013615423813462257,
0.03396623581647873,
0.04370184242725372,
0.01678711175918579,
0.01957777887582779,
0.005013781134039164,
0.046604305505752563,
-0.0000938489320105873,
-0.017682762816548347,
-0.006502050906419754,
-0.038037728518247604,
-0.022642306983470917,
0.04284404590725899,
-0.10090984404087067,
0.00014778751938138157,
0.016310591250658035,
0.03564785420894623,
0.008332920260727406,
0.024185145273804665,
-0.007737798150628805,
-0.019730929285287857,
0.009758368134498596,
-0.0297671090811491,
-0.007627747021615505,
0.09427672624588013,
-0.010970479808747768,
0.007241245824843645,
0.009761976078152657,
0.04308343306183815,
0.0225463155657053,
-0.008311768993735313,
0.0200788751244545,
0.05820506811141968,
-0.011402939446270466,
0.06503999978303909,
-0.010821683332324028,
0.023734362795948982,
-0.016089104115962982,
-0.029293932020664215,
-0.016945943236351013,
0.016171259805560112,
-0.02268930897116661,
0.027371829375624657,
0.05086309462785721,
-0.014711940661072731,
-0.020982317626476288,
-0.012080386281013489,
0.004776393994688988,
-0.020572979003190994,
-0.03139113262295723,
0.046998392790555954,
-0.02105829119682312,
0.05400589480996132,
0.005629281047731638,
-0.00656911451369524,
0.058041274547576904,
-0.08116088807582855,
0.010567347519099712,
-0.01637757383286953,
0.021165475249290466,
0.036393120884895325,
-0.043283961713314056,
0.015385258011519909,
0.031995635479688644,
0.008599717170000076,
0.01699088141322136,
0.00985768437385559,
0.005806631408631802,
-0.013505020178854465,
-0.0012641873909160495,
-0.019020484760403633,
0.0018794237403199077,
0.0325855053961277,
-0.016378942877054214,
0.05415487661957741,
-0.008738216944038868,
0.00831674411892891,
0.00441373698413372,
-0.009913777001202106,
0.07225983589887619,
-0.0021255649626255035,
-0.021230556070804596,
-0.0020846822299063206,
0.02685183845460415,
0.019078053534030914,
-0.03339042514562607,
0.02197284996509552,
0.017771469429135323,
-0.026134205982089043,
0.024916106835007668,
0.04688407480716705,
-0.008740395307540894,
0.004783071111887693,
0.012015377171337605,
0.03140652924776077,
0.013416612520813942,
0.016785336658358574,
0.0057005505077540874,
-0.011427566409111023,
-0.04794158786535263,
0.014311625622212887,
0.013619081117212772,
-0.010794704779982567,
0.006524545140564442,
0.07085146754980087,
-0.010230820626020432,
-0.011526600457727909,
-0.041794564574956894,
0.014084059745073318,
0.0038632818032056093,
-0.0003769224276766181,
0.04250863566994667,
-0.010640016756951809,
-0.06487178057432175,
0.017491642385721207,
-0.020818954333662987,
0.010723189450800419,
-0.005942862015217543,
0.03186162933707237,
0.0004481250362005085,
0.003496067365631461,
0.01779688149690628,
-0.01935349404811859,
0.002689455635845661,
-0.029956910759210587,
-0.011502155102789402,
0.0670294538140297,
-0.06066696718335152,
-0.01237416174262762,
0.00707905413582921,
0.006404468789696693,
-0.008502043783664703,
-0.011741023510694504,
0.015141665935516357,
0.021350324153900146,
0.023948177695274353,
-0.017513278871774673,
-0.04881893843412399,
-0.00506247254088521,
0.023047201335430145,
-0.015069774352014065,
0.016211574897170067,
-0.06512451171875,
0.022900689393281937,
-0.03199610859155655,
-0.02962266281247139,
0.030870649963617325,
-0.006354761775583029,
0.01857997290790081,
0.02811978943645954,
0.00627015670761466,
-0.014450883492827415,
0.012383222579956055,
-0.027821995317935944,
-0.018298150971531868,
-0.005006648600101471,
-0.05060518905520439,
0.04909543693065643,
-0.014947948977351189,
-0.04129253700375557,
-0.00037430820520967245,
-0.041490260511636734,
-0.06528684496879578,
0.00027019274421036243,
0.006153204012662172,
0.023163778707385063,
0.0023885592818260193,
-0.005726830568164587,
-0.0075283898040652275,
-0.04972749203443527,
0.01751052401959896,
-0.03051917441189289,
-0.07953372597694397,
0.002355727832764387,
0.040223896503448486,
0.04182812571525574,
-0.014147039502859116,
-0.04814279079437256,
0.03110259212553501,
0.023340944200754166,
-0.03255568444728851,
0.02679787389934063,
-0.017872927710413933,
-0.06176238879561424,
-0.0017187661724165082,
-0.04814505949616432,
0.04367538169026375,
-0.01956997811794281,
0.0005460731917992234,
0.01060275174677372,
0.04118697717785835,
0.004728312604129314,
-0.011933824978768826,
-0.010689393617212772,
-0.008445875719189644,
0.0012696629855781794,
-0.0013302909210324287,
0.024837568402290344,
0.03226418048143387,
-0.018938470631837845,
0.03395463526248932,
-0.013450548984110355,
0.008955474011600018,
0.05025855824351311,
0.009417910128831863,
0.05895773321390152,
-0.0042261541821062565,
-0.0022543028462678194,
0.0005446191062219441,
0.06001938134431839,
-0.004473942797631025,
-0.014329438097774982,
-0.010623771697282791,
-0.00015839701518416405,
0.06235972046852112,
-0.02358509786427021,
0.01436595618724823,
0.02275882475078106,
0.05031753331422806,
-0.008707751519978046,
-0.01230678241699934,
0.014213364571332932,
0.045670926570892334,
0.029362814500927925,
-0.0033784646075218916,
0.019054152071475983,
0.02684224583208561,
-0.002887133276090026,
0.03446214273571968,
-0.009025129489600658,
-0.024121278896927834,
0.008826387114822865,
-0.07658477872610092,
0.01609642803668976,
-0.010050336830317974,
0.046710819005966187,
0.0080482829362154,
0.06757297366857529,
0.004770385567098856,
0.022582808509469032,
0.02192096598446369,
0.04843892529606819,
-0.04304632171988487,
0.03362609073519707,
-0.007140649016946554,
0.03066621907055378,
-0.037038929760456085,
0.016067134216427803,
-0.03260595351457596,
-0.005123061127960682,
-0.013440579175949097,
-0.021604392677545547,
-0.03180290386080742,
-0.049409419298172,
0.011375105939805508,
-0.007937220856547356,
-0.019973084330558777,
0.003986249677836895,
-0.031482450664043427,
0.030130010098218918,
-1.7641166039084055e-7,
0.009830339811742306,
0.038930948823690414,
-0.018396662548184395,
0.00026006027474068105,
0.018570227548480034,
-0.02064676396548748,
0.0014227653155103326,
0.019811531528830528,
0.011876087635755539,
-0.020078498870134354,
-0.03928902745246887,
-0.02197573333978653,
-0.02881561778485775,
-0.024656273424625397,
-0.03702297434210777,
0.013116945512592793,
-0.04493550956249237,
-0.02201905846595764,
-0.016938596963882446,
0.002945913700386882,
0.03908981382846832,
-0.027276646345853806,
-0.01590183563530445,
0.027610735967755318,
-0.02100130170583725,
0.0014199313009157777,
0.03943832218647003,
0.037852466106414795,
0.012231825850903988,
0.0029026640113443136,
-0.017594946548342705,
0.0328272208571434,
-0.016671765595674515,
-0.02215314470231533,
-0.0026445069815963507,
-0.005628564395010471,
0.00011716908193193376,
0.0047695329412817955,
0.009799468331038952,
-0.010469491593539715,
-0.018633747473359108,
0.005693384446203709,
-0.009629935026168823,
0.014317930676043034,
0.01144514698535204,
0.0016956647159531713,
0.0267974603921175,
0.01868456043303013,
0.04074971005320549,
-0.039226725697517395,
-0.05614514276385307,
-0.07355763018131256,
0.010579179972410202,
0.03872636333107948,
0.03362248092889786,
-0.018593676388263702,
0.019258106127381325,
-0.06245802342891693,
-0.01027665939182043,
0.05871647596359253,
-0.016320575028657913,
-0.02079036831855774,
-0.003943190444260836,
-0.019477011635899544,
-0.023880362510681152,
-0.03440673649311066,
-0.0392858050763607,
-0.02471705712378025,
0.017414217814803123,
0.028383731842041016,
0.0014766467502340674,
-0.012655232101678848,
0.014507320709526539,
0.05754510313272476,
0.0213011521846056,
0.06737275421619415,
-0.027442513033747673,
-0.010103627108037472,
-0.018338125199079514,
-0.034021127969026566,
-0.04783130809664726,
-0.023075005039572716,
0.0016110817668959498,
-0.0026212637312710285,
-0.05297568067908287,
0.05939885228872299,
0.0042226966470479965,
-0.07853394001722336,
0.020315589383244514,
-0.002490016631782055,
0.0077766431495547295,
-0.005007977597415447,
-0.07147827744483948,
0.01423319149762392,
0.021801356226205826,
0.017958028241991997,
0.034981779754161835,
0.03126806020736694,
-0.06886222958564758,
0.0020377112086862326,
-0.007733483333140612,
0.030433816835284233,
-0.005123800132423639,
-0.030344264581799507,
0.016789400950074196,
-0.0256198700517416,
-0.02355353906750679,
0.09151832014322281,
-0.03718188777565956,
0.016717107966542244,
-0.00877191312611103,
-0.008779782801866531,
-0.013105418533086777,
0.019251542165875435,
0.0335204191505909,
-0.04232953116297722,
-0.02649630419909954,
-0.033504560589790344,
-0.028608577325940132,
-0.02963612787425518,
0.005926181096583605,
-0.02275051549077034,
0.030852757394313812,
0.01925382763147354,
-0.017087744548916817,
-0.00030649927794001997,
-0.04011823236942291,
-0.037501998245716095,
-0.0065323286689817905,
-0.05214259400963783,
0.03860744833946228,
-0.007596950046718121,
-0.05398170277476311,
0.03211893141269684,
-0.046662382781505585,
0.00796489231288433,
0.01504100114107132,
-0.01793820597231388,
0.024615628644824028,
-0.028050759807229042,
0.06444074213504791,
0.03699969872832298,
0.01073203794658184,
-0.07208552956581116,
-0.05623384192585945,
0.015226132236421108,
0.023973632603883743,
-0.012777489610016346,
-0.044896986335515976,
0.023442178964614868,
-0.04771670326590538,
-0.026858031749725342,
-0.03884511440992355,
0.005906200036406517,
-0.01712799444794655,
0.015039670281112194,
-0.006083040032535791,
-0.04855520278215408,
0.09492793679237366,
-0.007583312690258026,
-0.021043943241238594,
0.026881247758865356,
-0.056650303304195404,
-0.020729606971144676,
-0.034502558410167694,
0.025950979441404343,
-0.0019515147432684898,
-0.028389213606715202,
0.0038372045382857323,
0.005028707440942526,
0.00938277505338192,
0.009587883949279785,
0.02155851572751999,
0.027161825448274612,
0.0006832614308223128,
-0.02453923039138317,
-0.012994486838579178,
0.01718028448522091,
0.0023390622809529305,
0.001718113082461059,
-0.007455183658748865,
0.0367245078086853,
0.007604385260492563,
-0.025681596249341965,
0.016240905970335007,
0.0026358223985880613,
0.004631416872143745,
0.012409165501594543,
0.04821987450122833,
-0.031336721032857895,
0.011644335463643074,
0.03468666225671768,
-0.022364608943462372,
0.03956534340977669,
-0.017008211463689804,
-0.056759461760520935,
0.008049318566918373,
0.018997058272361755,
-0.024350568652153015,
-0.037823569029569626,
0.020465590059757233,
0.014897788874804974,
0.041830338537693024,
-0.05109575390815735,
0.03767805173993111,
0.0032189383637160063,
0.033265620470047,
0.06023029983043671,
0.015962941572070122,
0.017173537984490395,
0.016246968880295753,
-0.022191209718585014,
-0.007821579463779926,
-0.019415833055973053,
0.029763123020529747,
-0.00921054556965828,
0.04415862634778023,
0.015114715322852135,
0.009836869314312935,
0.024235930293798447,
0.04695074260234833,
0.002212234539911151,
0.0025255996733903885,
-0.03932797163724899,
-0.002066020155325532,
-0.09367262572050095,
0.02532024309039116,
0.0017848340794444084,
-0.00096210214542225,
0.038534458726644516,
-0.003066389122977853,
-0.014104361645877361,
-0.004990134388208389,
-0.010525686666369438,
0.024159617722034454,
-0.018312692642211914,
-0.04306170344352722,
0.012395710684359074,
-0.02601168118417263,
0.027742743492126465,
0.006255961488932371,
-0.02007908932864666,
0.001067431061528623,
-0.011528135277330875,
-0.08611078560352325,
-0.04786663502454758,
-0.025258494541049004,
-0.012307708151638508,
0.04187652841210365,
0.01615600287914276,
-0.002203991636633873,
0.03941929340362549,
-0.022770587354898453,
0.05128970742225647,
-0.013737499713897705,
0.03847776725888252,
-0.026955893263220787,
0.04440121725201607,
-0.02508450299501419,
-0.0052629075944423676,
0.003345469245687127,
-0.0022506702225655317,
0.10938677936792374,
0.0434151254594326,
0.03497474640607834,
-0.03243222460150719,
0.007955147884786129,
-0.059868223965168,
-0.0023747682571411133,
-0.01972799003124237,
-0.017062652856111526,
-0.007485694717615843,
0.03618765249848366,
0.02646070159971714,
0.04097790643572807,
0.02201911248266697,
0.010298599489033222,
0.03597019612789154,
-0.037728194147348404,
-0.0001800485624698922,
0.019681677222251892,
0.006293646991252899,
-0.024241352453827858,
0.042060017585754395,
-0.053530965000391006,
0.02108173258602619,
-0.02288382314145565,
0.01848388835787773,
-0.023016812279820442,
-0.030465219169855118,
0.045847244560718536,
0.02850874699652195,
-0.027908526360988617,
-0.011658667586743832,
0.019728612154722214,
-0.0009874374372884631,
-0.007056842092424631,
0.03488829731941223,
0.04279494658112526,
0.009522823616862297,
0.004010112024843693,
0.0047140223905444145,
0.03159221634268761,
0.01983390562236309,
0.019458042457699776,
0.02429068274796009,
-0.04622914642095566,
0.002354994649067521,
-0.026233498007059097,
0.01819414645433426,
0.03291342779994011,
0.03760189563035965,
-0.0013254090445116162,
0.03926141560077667,
0.02484678477048874,
-0.04500165581703186,
-0.060913823544979095,
0.021342825144529343,
0.01999911665916443,
0.02086242474615574,
-0.011571332812309265,
-0.06414733082056046,
0.009588946588337421,
0.01461489126086235,
0.010859052650630474,
0.006719429511576891,
0.016437852755188942,
-0.052521441131830215,
0.006070213858038187,
0.0047052279114723206,
-0.014924535527825356,
-0.007823919877409935,
-0.017739305272698402,
0.02541789785027504,
-0.03851470351219177,
-0.0475727878510952,
0.00910366140305996,
0.01915464922785759,
0.02193666435778141,
0.04540079087018967,
-0.01459946297109127,
-0.05120282247662544,
-0.04281642660498619,
0.044690508395433426,
-0.03733750060200691,
-0.001851304667070508,
-0.03824514523148537,
0.009512128308415413,
0.0007452851277776062,
-0.02476186491549015,
-0.012782636098563671,
0.018940862268209457,
0.007077771704643965,
0.08088713139295578,
0.012897472828626633,
-0.017236799001693726,
-0.0029397739563137293,
-0.029335491359233856,
-0.01783449575304985,
0.04217604920268059,
-0.004696771968156099,
0.03785110265016556,
0.0037656263448297977,
-0.00920502282679081,
0.060804788023233414,
0.014771191403269768,
-0.007088738959282637,
-0.006074906792491674,
0.05483931675553322,
-0.03564833849668503,
-0.051430389285087585,
0.05628533661365509,
0.027373449876904488,
0.007075774483382702,
-0.007818616926670074,
-0.03955799341201782,
-0.005009273998439312,
-0.014331115409731865,
0.0021648979745805264,
-0.039286382496356964,
0.023973284289240837,
0.0017112743807956576,
0.03614073246717453,
-0.02427484840154648,
-0.04178975149989128,
-0.07000740617513657,
-0.03493868187069893,
-0.033675599843263626,
-0.02518966607749462,
-0.02613108791410923,
0.021084921434521675,
-0.07804860919713974,
0.027819663286209106,
0.030705498531460762,
-0.04271862655878067,
-0.0028959237970411777,
0.0018642483046278358,
0.03402749076485634,
-0.02472499944269657,
0.05324168503284454,
-0.04110875725746155,
-0.05054343491792679,
0.07755044847726822,
-0.015483610332012177,
-0.019486097618937492,
0.04296179115772247,
-0.03732777014374733,
0.08018148690462112,
0.04335286095738411,
0.019082091748714447,
-0.025156334042549133,
0.09302281588315964,
-0.011248094029724598,
0.011871600523591042,
-0.00204667542129755,
-0.0009596477611921728,
0.034895434975624084,
0.021572405472397804,
0.017600635066628456,
-0.01651879772543907,
-0.046638861298561096,
0.043426577001810074,
0.0706084668636322,
0.026916498318314552,
0.022456275299191475,
-0.00373904244042933,
0.0017864638939499855,
-0.006755953188985586,
-0.0009082850883714855,
0.006287622731178999,
-0.00161552254576236,
0.05947594717144966,
0.021541940048336983,
0.03631216287612915,
-0.018494250252842903,
-0.013257086277008057,
-0.10591518878936768,
-0.021563200280070305,
-0.01985837332904339,
0.017252052202820778,
0.05377849563956261,
-0.012577101588249207,
0.01614152081310749,
0.034525565803050995,
-0.058678772300481796,
0.005848371423780918,
0.021506033837795258,
-0.03444763273000717,
-0.01711542159318924,
0.022584518417716026,
-0.01758408360183239,
0.018682943657040596,
-0.005566603038460016,
0.009007653221487999,
0.0409538559615612,
0.048911310732364655,
0.013988088816404343,
-0.015552692115306854,
0.006347444839775562,
0.06635897606611252,
0.04079074785113335,
0.002319681691005826,
0.06008102372288704,
-0.03217634558677673,
-0.018711507320404053,
0.01899491623044014,
-0.018035216256976128,
0.02449091710150242,
0.02307010255753994,
0.008141163736581802,
0.007545258849859238,
0.021529866382479668,
0.0045719207264482975,
0.02072865329682827,
-0.030218878760933876,
0.016923688352108,
0.02748054265975952,
-0.004329477436840534,
-0.010084070265293121,
-0.017977191135287285,
0.0177913885563612,
-0.01597202941775322,
-0.06238637864589691,
0.019796976819634438,
-0.009753444232046604,
0.047887980937957764,
-0.01433387491852045,
0.03995124250650406,
-0.029475819319486618,
-0.02404284104704857,
-0.06509559601545334,
-0.02269461192190647,
0.03851252421736717,
0.007142529357224703,
0.013575436547398567,
0.00768033554777503,
0.024709410965442657,
0.014591515064239502,
-0.0624338760972023,
-0.043384745717048645,
-0.011734893545508385,
-0.03486378490924835,
-0.048885494470596313,
-0.021326664835214615,
0.016720373183488846,
0.02568431757390499,
-0.02180464379489422,
0.003664460266008973,
-0.017550447955727577,
0.01226264238357544,
0.024821413680911064,
0.03499651327729225,
0.04824148491024971,
-0.06400063633918762,
-0.030412739142775536,
-0.06534546613693237,
0.031987324357032776,
0.0008502244600094855,
-0.02148616686463356,
-0.053426582366228104,
-0.03278530389070511,
0.0032779278699308634,
0.027222203090786934,
0.04126143455505371,
-0.02066010609269142,
-0.011424025520682335,
0.013497225940227509,
-0.012766066007316113,
-0.012066422030329704,
-0.024794818833470345,
-0.04055498540401459,
0.027225011959671974,
-0.021330183371901512,
0.010350855998694897,
0.007306534796953201,
-0.009746232070028782,
-0.013389280065894127,
0.033850375562906265,
0.02246467024087906,
0.051090680062770844,
0.02733919955790043,
0.00526948319748044,
0.014966944232583046,
0.003645392367616296,
0.017074985429644585,
0.034358199685811996,
-0.0297330841422081,
0.0014824096579104662,
0.03524145111441612,
-0.06651752442121506,
-0.051618315279483795,
0.05425171181559563,
-0.026039596647024155,
0.023689202964305878,
0.03925323858857155,
-0.046300772577524185,
0.03674645721912384,
-0.05441159009933472,
0.04176301509141922,
0.014151846058666706,
-0.013382834382355213,
0.020317357033491135,
0.03639267012476921,
-0.0006167940446175635,
0.014806879684329033,
-0.04138122498989105,
0.028395118191838264,
0.012635930441319942,
-0.01855454407632351,
-0.003803943982347846,
0.023805128410458565,
0.036368999630212784,
-0.001043285010382533,
0.02845790795981884,
0.013496647588908672,
0.017003575339913368,
0.039780158549547195,
-0.003060764167457819,
0.006111820228397846,
-0.004160895477980375,
-0.016462307423353195,
0.024936256930232048,
-0.025429191067814827,
-0.018962141126394272,
-0.00023666858032811433,
-0.0008868908626027405,
0.049624066799879074,
-0.0005868022562935948,
0.005794641561806202,
-0.00330137531273067,
-0.022908790037035942,
-0.013781865127384663,
0.003962618298828602,
-0.0023638152051717043,
0.0039015444926917553,
-0.023021817207336426,
-0.025240708142518997,
-0.034295834600925446,
0.002646840177476406,
0.04816870391368866,
-0.024820230901241302,
0.029304105788469315,
-0.024197455495595932,
0.03472999110817909,
-0.03215382620692253,
0.017438288778066635,
-0.035631872713565826,
-0.008913015946745872,
0.020211236551404,
-0.03238559514284134,
-0.001891127321869135,
0.011938747018575668,
-0.001104439957998693,
-0.023850131779909134,
0.014336816966533661,
-0.050618287175893784,
0.008525043725967407,
-0.0038288715295493603,
0.000005194041023059981,
-0.007082213182002306,
-0.03383658081293106
] |
<h1>Problem</h1>
<p>If you had a long bar floating in space, what would be the compressive force at the centre of the bar, due to the self-weight of both ends?</p>
<p>Diagram - what is the force at point X in the middle of the bar?:</p>
<pre><code><----------------------L--------------------->, total mass M
=======================X====================== <- the bar
F---> X <---F
</code></pre>
<h1>Summary</h1>
<p>You should be able to simplify by cutting the bar into pieces, but that gives a different answer depending on how many pieces you use (see below). So the simplification must be wrong - but why?</p>
<h1>My approach</h1>
<h3>Split bar in two</h3>
<p>So, one approximation would be to cut the bar in half - two pieces of length L/2, mass M/2:</p>
<pre><code> (M/2)<-------L/2------->(M/2)
#1 X #2 <- bar approximated as blobs #1 and #2
</code></pre>
<p>Force at X is G(M1.M2)/(R^2) = G (M/2)^2 / (L/2)^2 = G M^2 / L^2</p>
<p>Or Fx / (G. M^2 / L^2) = <strong>1</strong></p>
<p>But is that really valid? If so, shouldn't you get the same answer if you split the bar into four pieces?</p>
<h3>Split bar into four</h3>
<pre><code> (M/4)<-L/4->(M/4)<-L/4->(M/4)<-L/4->(M/4)
#1 #2 X #3 #4
</code></pre>
<p>My assumption is that the force at X is the sum of the attractions of each blob on the left to every blob on the right.</p>
<p>Force at X = #1<>#3 + #1<>#4 + #2<>#3 + #2<>#4</p>
<p>('<>' being force between blobs #x and #y).</p>
<p>Fx / (G.M^2 / L^2) = (2/4)^-2 + (3/4)^-2 + (1/4)^-2 + (2/4)^-2 = <strong>1.61</strong></p>
<p>This is bigger than the previous result (1.61 vs 1).</p>
<h3>Split bar into six</h3>
<p>Similarly, if you split into 6 blobs, the total force comes out as:</p>
<p>Fx / (G.M^2 / L^2) = (3/6)^-2+(4/6)^-2+(5/6)^-2 + (2/6)^-2+(3/6)^-2+(4/6)^-2 + (1/6)^-2+(2/6)^-2+(3/6)^-2</p>
<p>Fx / (G.M^2 / L^2) = <strong>2.00</strong></p>
<h3>So what's wrong with my approach? And what is the real answer?</h3>
<p>So it seems the more pieces we split the bar into, the larger the result gets. There's clearly something wrong with my assumptions! - but what?</p>
<p>I'd be very glad if someone here could explain this. Thanks!</p>
<p><strong>EDIT</strong>
As Peter Shor pointed out, my calculations had some dodgy algebra and I'd calculated $$L^2/M^2$$ values rather than $$M^2/L^2$$. I've now corrected that - the value still increases as you divide into more masses.</p>
<p>I'll do a bit more work with more divisions and see if this leads to convergence or not.</p> | 2,057 | [
-0.012479310855269432,
0.018444983288645744,
-0.012292738072574139,
-0.006860875524580479,
0.04049456864595413,
0.003127970267087221,
-0.01134730689227581,
-0.03337346389889717,
0.022920770570635796,
-0.0010041582863777876,
0.018255159258842468,
0.02652803622186184,
0.07274430990219116,
0.02373296394944191,
0.028179438784718513,
-0.012340685352683067,
-0.0060607013292610645,
-0.024354280903935432,
0.04493381828069687,
0.00261239823885262,
-0.02196519821882248,
-0.03415117785334587,
0.016739150509238243,
-0.0014455945929512382,
-0.01429244875907898,
0.021229514852166176,
0.052774298936128616,
-0.0053709871135652065,
0.009747934527695179,
0.06796524673700333,
-0.049495991319417953,
-0.019916541874408722,
0.005917675327509642,
0.019776402041316032,
0.04730224609375,
0.028536083176732063,
-0.025440741330385208,
-0.0262319166213274,
-0.009502705186605453,
0.03374699875712395,
0.0017498930683359504,
0.02702535130083561,
-0.030483542010188103,
0.025920361280441284,
-0.020742641761898994,
0.06889425963163376,
-0.019007548689842224,
-0.014677690342068672,
0.05867723003029823,
-0.01829470321536064,
0.08123888075351715,
-0.0010393850971013308,
0.07709072530269623,
0.04885917901992798,
-0.032134443521499634,
-0.05148719251155853,
0.04019596800208092,
0.03678948059678078,
-0.008438638411462307,
-0.03868450969457626,
-0.008368833921849728,
0.011537561193108559,
-0.019773980602622032,
-0.006777623202651739,
0.020848959684371948,
0.00921925064176321,
-0.026722265407443047,
0.014512400142848492,
0.04311659559607506,
-0.016399262472987175,
-0.0076591623947024345,
0.02680084854364395,
0.03552872687578201,
-0.010496879927814007,
0.03232698515057564,
-0.0010145691921934485,
-0.018739378079771996,
-0.0068476502783596516,
0.037273865193128586,
0.03011174127459526,
-0.05269048735499382,
-0.006885586306452751,
0.026266472414135933,
0.04039441794157028,
0.01638309471309185,
-0.028448054566979408,
0.051184073090553284,
0.01049302238970995,
-0.011001264676451683,
0.011123985052108765,
0.04489675909280777,
0.0010026328964158893,
0.05485571548342705,
0.03235803544521332,
0.013880608603358269,
0.0554814450442791,
0.005062914919108152,
-0.0029699685983359814,
0.006195018067955971,
0.022831261157989502,
-0.03810533136129379,
-0.0507136769592762,
0.0075548370368778706,
0.07889660447835922,
-0.024738214910030365,
-0.03563709557056427,
-0.012983327731490135,
0.006482235621660948,
0.006956411525607109,
-0.010959326289594173,
-0.014981532469391823,
0.013690977357327938,
0.010600549168884754,
-0.022211378440260887,
-0.0012929602526128292,
-0.05638160929083824,
0.012249994091689587,
-0.009067468345165253,
0.008336159400641918,
0.023961352184414864,
0.0492529422044754,
-0.013857227750122547,
0.033897291868925095,
-0.03037736564874649,
-0.056626882404088974,
0.01225672010332346,
0.013585645705461502,
-0.022188011556863785,
0.005606285762041807,
0.05219007655978203,
-0.01713847927749157,
0.007905016653239727,
0.001188920228742063,
-0.008912725374102592,
0.02302384190261364,
0.004799800459295511,
-0.10896186530590057,
-0.048492588102817535,
0.03160766139626503,
0.009074773639440536,
-0.02503122016787529,
-0.04994302988052368,
0.0022604744881391525,
0.03363846242427826,
0.07681712508201599,
0.0158077422529459,
0.02428179606795311,
-0.001504045445472002,
0.0054644811898469925,
0.0008782026125118136,
0.0019488631514832377,
0.0015292466850951314,
-0.02435031719505787,
0.014124368317425251,
-0.03373591974377632,
-0.039413854479789734,
-0.02130015939474106,
0.031422629952430725,
-0.013410250656306744,
-0.027232738211750984,
0.023652857169508934,
-0.028277648612856865,
0.006828719284385443,
-0.006244361400604248,
-0.04234914109110832,
-0.028599191457033157,
0.0654260590672493,
0.011315341107547283,
0.001323055475950241,
0.07464238256216049,
-0.010592125356197357,
-0.02418847568333149,
-0.031606607139110565,
-0.043594375252723694,
0.023643329739570618,
-0.019449507817626,
-0.015696045011281967,
-0.034318216145038605,
-0.0009759137174114585,
0.024453621357679367,
-0.04751604422926903,
-0.0728447437286377,
-0.02624736726284027,
-0.015955142676830292,
0.03984096273779869,
0.06387543678283691,
0.03503013402223587,
-0.0365133099257946,
0.033916670829057693,
-0.0384843535721302,
-0.03823345527052879,
-0.05041806772351265,
0.05447917431592941,
0.009089197032153606,
-0.005671722814440727,
-0.01514922734349966,
-0.003987088333815336,
-0.012738330289721489,
0.027918193489313126,
0.008380628190934658,
0.0059437742456793785,
0.020437458530068398,
0.008657300844788551,
-0.00018973842088598758,
-0.013299280777573586,
0.07951697707176208,
0.005319541320204735,
-0.015813201665878296,
0.030264457687735558,
-0.0243490282446146,
-0.03202148154377937,
0.02000482752919197,
-0.020636027678847313,
0.0023814302403479815,
-0.015116331167519093,
-0.02758626826107502,
0.03156633675098419,
-0.024220725521445274,
-0.015315388329327106,
0.02901921235024929,
-0.028385553508996964,
0.06366503983736038,
0.059826772660017014,
-0.017203079536557198,
0.013937829062342644,
-0.0035059978254139423,
-0.008536696434020996,
0.048160772770643234,
0.002147009829059243,
-0.003153800731524825,
-0.05758567154407501,
-0.012420948594808578,
0.022141488268971443,
0.030856601893901825,
-0.025380495935678482,
0.0018634191947057843,
0.039837803691625595,
-0.01879849098622799,
0.005244061350822449,
0.007495727390050888,
-0.014758761040866375,
-0.01585506647825241,
0.05823610723018646,
0.027974294498562813,
0.01626334898173809,
-0.005141166970133781,
0.004413777496665716,
0.03857417032122612,
0.01456319261342287,
-0.004075522068887949,
0.008692603558301926,
0.026160966604948044,
-0.020343206822872162,
-0.019735967740416527,
-0.014221585355699062,
-0.03151097148656845,
0.043053556233644485,
-0.010425218380987644,
0.009714431129395962,
0.07035284489393234,
0.01546064205467701,
-0.012129450216889381,
-0.06262939423322678,
-0.019334392622113228,
-0.023492632433772087,
0.024858085438609123,
0.006735441740602255,
-0.010023553855717182,
0.03020968846976757,
0.007945540361106396,
0.009760972112417221,
-0.05111035332083702,
-0.04326852783560753,
-0.05016792193055153,
0.003336549736559391,
0.0027083209715783596,
0.004528622608631849,
0.021340997889637947,
-0.011212700977921486,
0.012752442620694637,
-0.02343679964542389,
0.006188950035721064,
0.0015245211543515325,
-0.049298420548439026,
-0.034999772906303406,
-0.0024482239969074726,
-0.021381139755249023,
-0.010701733641326427,
0.050858501344919205,
0.0196846853941679,
-0.030951520428061485,
-0.014774806797504425,
0.015705252066254616,
-0.03822491317987442,
-0.0064398921094834805,
-0.018854662775993347,
0.007200208958238363,
-0.026270875707268715,
0.015912272036075592,
0.07727470248937607,
-0.00015683022502344102,
-0.02395814284682274,
0.045645277947187424,
0.0010055978782474995,
-0.017743173986673355,
-0.030884595587849617,
-0.006746892351657152,
0.00865634810179472,
0.004423569887876511,
-0.0018489555222913623,
0.042271364480257034,
0.018349729478359222,
-0.0009572940762154758,
-0.05170225724577904,
-0.01612924411892891,
-0.01267983391880989,
0.0017583672888576984,
0.07291678339242935,
0.029006561264395714,
-0.0340680368244648,
0.10948912054300308,
-0.006468582432717085,
-0.031403761357069016,
-0.051347050815820694,
-0.009931479580700397,
0.01384181622415781,
-0.05033668503165245,
0.029217034578323364,
0.012353629805147648,
-0.023073898628354073,
-0.010323496535420418,
-0.003493164898827672,
0.0063431113958358765,
0.0039509497582912445,
0.015446897596120834,
0.025936752557754517,
0.02544867806136608,
0.02804156392812729,
-0.04611087590456009,
0.06172122061252594,
0.024807775393128395,
-0.006057551130652428,
0.017332516610622406,
0.0023124446161091328,
0.009761911816895008,
0.00988026987761259,
-0.08171699196100235,
0.009003561921417713,
-0.015546519309282303,
0.016392264515161514,
-0.024847526103258133,
0.04003772512078285,
-0.011747704818844795,
-0.06724893301725388,
0.007793201133608818,
-0.019197041168808937,
0.055528122931718826,
0.014761884696781635,
-0.02194048836827278,
0.07087879627943039,
0.06949127465486526,
-0.025474045425653458,
-0.017352180555462837,
0.02339746616780758,
0.0004710339126177132,
0.014382493682205677,
-0.025267986580729485,
-0.014847787097096443,
0.03552648052573204,
0.04799835756421089,
0.027254905551671982,
-0.00007607097359141335,
0.01721988059580326,
-0.011607981286942959,
-0.0806213989853859,
0.005558003671467304,
-0.011184443719685078,
0.04957248643040657,
-0.0015872654039412737,
0.061809223145246506,
0.008345717564225197,
0.005140332505106926,
-0.012705635279417038,
0.034373775124549866,
-0.11257486790418625,
0.014108906500041485,
-0.006337798200547695,
-0.007232138887047768,
0.036307092756032944,
-0.008791584521532059,
-0.026408901438117027,
-0.03572800010442734,
-0.006147963460534811,
-0.031586531549692154,
-0.0118826599791646,
-0.06189257279038429,
0.014437682926654816,
-0.00271808635443449,
0.010163692757487297,
0.012967325747013092,
0.008026961237192154,
0.06816145777702332,
0.02223867177963257,
0.03359277546405792,
0.04494868591427803,
-0.048306748270988464,
-0.0007629446918144822,
-0.027458488941192627,
-0.01541411317884922,
0.0033494119998067617,
0.02568366378545761,
-0.004668854642659426,
0.019096875563263893,
0.00690602557733655,
-0.040356867015361786,
0.04049631208181381,
0.02823805809020996,
-0.018803704530000687,
-0.013930456712841988,
0.026589805260300636,
-0.01852637715637684,
0.00041258943383581936,
0.006511169020086527,
0.0461660772562027,
-0.02357659861445427,
-0.011349201202392578,
-0.007466691080480814,
0.014814924448728561,
-0.0003603426448535174,
0.04370793700218201,
0.09018941968679428,
0.019399099051952362,
-0.04966145008802414,
-0.07055194675922394,
-0.014489921741187572,
-0.02755253203213215,
-0.013205008581280708,
-0.0016660533146932721,
0.0398816242814064,
-0.01970037817955017,
0.033745866268873215,
0.022578565403819084,
0.029221300035715103,
-0.019677387550473213,
0.05796756222844124,
0.0033872390631586313,
-0.026644332334399223,
-0.017699480056762695,
0.017715349793434143,
-0.0017471086466684937,
0.014219945296645164,
0.0474698431789875,
0.015608411282300949,
-0.026991121470928192,
-0.06447850167751312,
-0.014582178555428982,
0.023157687857747078,
0.03740668296813965,
0.0007187024457380176,
0.017573930323123932,
-0.03707600012421608,
-0.04132533818483353,
0.0145883122459054,
-0.021008851006627083,
0.024377286434173584,
-0.044098544865846634,
0.07191057503223419,
-0.009911920875310898,
-0.03745168820023537,
-0.05772215500473976,
0.010588559322059155,
-0.05489787459373474,
0.03211512789130211,
-0.008855979889631271,
-0.003903648117557168,
0.021374590694904327,
0.04017435014247894,
0.030908118933439255,
0.03136040270328522,
-0.019519194960594177,
-0.045167386531829834,
-0.05367354303598404,
0.0455910786986351,
-0.04656777158379555,
-0.061467450112104416,
-0.010487580671906471,
-0.037438999861478806,
-0.031000591814517975,
0.049070294946432114,
-0.014147467911243439,
-0.055871669203042984,
0.05248793214559555,
0.029736949130892754,
0.03896540775895119,
-0.0028558799531310797,
-0.007397807668894529,
0.040536653250455856,
0.05907466262578964,
-0.004934343509376049,
0.030050048604607582,
0.0518919974565506,
-0.03855712711811066,
-0.0020508940797299147,
-0.010352636687457561,
-0.010114159435033798,
-0.000880685169249773,
0.0016764821484684944,
-0.07640215754508972,
-0.013692876324057579,
-0.0189067292958498,
-0.004558608401566744,
-0.031355004757642746,
0.03969605267047882,
-0.047854386270046234,
-0.060993146151304245,
0.022649608552455902,
0.023016005754470825,
0.024179454892873764,
0.01855572685599327,
-0.026784401386976242,
0.03792433440685272,
0.009833731688559055,
-0.0029084845446050167,
0.00979654211550951,
0.02102787420153618,
0.006265989504754543,
0.027020934969186783,
-0.021614549681544304,
0.005474218167364597,
-0.054716773331165314,
-0.027600456029176712,
0.01890285313129425,
-0.06693986058235168,
0.029964501038193703,
-0.014993165619671345,
0.03999042883515358,
0.01929664984345436,
0.0033224811777472496,
-0.01704195886850357,
0.042565543204545975,
-0.006147865671664476,
-0.01890162006020546,
-0.003123838221654296,
0.014133508317172527,
0.0196804478764534,
-0.009844556450843811,
-0.01405123621225357,
-0.03151480853557587,
0.016548948362469673,
-0.00003263610778958537,
-0.011352415196597576,
-0.0239787045866251,
-0.04538806900382042,
0.00027249252889305353,
-0.025641383603215218,
-0.023091914132237434,
0.05274012312293053,
-0.03618820384144783,
0.024827010929584503,
0.02102559246122837,
-0.04070458933711052,
0.047604918479919434,
0.015615700744092464,
0.008292768150568008,
-0.003954516723752022,
-0.01645609363913536,
-0.007237321697175503,
-0.016420230269432068,
0.0011356534669175744,
-0.052140142768621445,
-0.0601898729801178,
-0.015488209202885628,
0.023327626287937164,
0.06784170866012573,
-0.00716374022886157,
0.010843822732567787,
0.009528948925435543,
0.02994166687130928,
-0.029541632160544395,
-0.02505268156528473,
0.012579500675201416,
0.01625923439860344,
0.012930664233863354,
-0.014565284363925457,
-0.0064874025993049145,
-0.04728757217526436,
-0.032296981662511826,
0.018695244565606117,
-0.022710032761096954,
-0.020838715136051178,
0.004546446725726128,
0.06739898025989532,
-0.01514457818120718,
0.020246321335434914,
0.008670628070831299,
-0.05377452075481415,
0.05441269651055336,
0.0013058613985776901,
-0.0338115468621254,
0.035879459232091904,
0.030110681429505348,
-0.03355064243078232,
-0.01624971069395542,
-0.011947782710194588,
0.010787242092192173,
0.02637193724513054,
-0.005678205750882626,
0.039039790630340576,
0.021813444793224335,
-0.027844972908496857,
0.014803451485931873,
-0.006139123346656561,
-0.028613993898034096,
-0.013401712290942669,
0.016058800742030144,
0.07431610673666,
-0.030701255425810814,
-0.0519804023206234,
0.04595128446817398,
-0.006375381723046303,
-0.022527407854795456,
-0.05985033139586449,
0.028809070587158203,
-0.02984478324651718,
0.019356679171323776,
-0.0526154451072216,
0.00411752937361598,
0.054918792098760605,
-0.019276916980743408,
0.029314721003174782,
-0.02360805682837963,
-0.0026428280398249626,
0.02162923477590084,
-0.004623416345566511,
-0.019171470776200294,
-0.043600741773843765,
0.008909940719604492,
-0.0229241494089365,
0.01963687315583229,
0.030776195228099823,
-0.0231917817145586,
-0.0001722178130876273,
-0.004977791104465723,
0.0195651613175869,
0.009339869022369385,
0.027913503348827362,
0.0024616981390863657,
-0.06312339752912521,
-0.02382972277700901,
0.017625220119953156,
-0.03308326005935669,
0.05335291847586632,
0.0222279354929924,
-0.061230361461639404,
0.06033453717827797,
-0.03417400270700455,
0.08211664110422134,
0.006028987001627684,
-0.0032920720987021923,
-0.027480794116854668,
0.052274368703365326,
-0.0204082652926445,
-0.000769750855397433,
-0.02948005497455597,
-0.010494774207472801,
0.15240158140659332,
0.03116048313677311,
0.027136147022247314,
-0.026168344542384148,
0.02461458370089531,
0.022122154012322426,
-0.015562632121145725,
0.016642501577734947,
-0.0319044403731823,
0.0038045605178922415,
0.011141007766127586,
0.025984345003962517,
0.0320759117603302,
-0.047484517097473145,
-0.0018764117266982794,
0.0326719731092453,
-0.039405833929777145,
-0.011985077522695065,
-0.015357956290245056,
0.038053933531045914,
-0.021362314000725746,
-0.016337741166353226,
-0.06855176389217377,
0.0205061212182045,
0.006664161570370197,
-0.009741037152707577,
-0.05192067474126816,
-0.037193335592746735,
0.030451403930783272,
-0.00585567532107234,
-0.024487309157848358,
0.031822144985198975,
-0.0029978130478411913,
-0.05165674909949303,
0.016855301335453987,
0.01735587976872921,
0.01989053189754486,
-0.036269329488277435,
0.014306146651506424,
0.04246509447693825,
-0.007433258928358555,
0.00521859060972929,
-0.0022615089546889067,
0.03751559928059578,
-0.04433734714984894,
-0.012247847393155098,
-0.046075377613306046,
0.029629575088620186,
0.006522960029542446,
-0.021048275753855705,
0.023178694769740105,
0.0019988969434052706,
0.018339699134230614,
-0.007855100557208061,
0.006075041834264994,
0.045566849410533905,
0.03342171758413315,
0.025361329317092896,
-0.016453726217150688,
0.004503158386796713,
0.01940632425248623,
-0.01624629832804203,
-0.029992306604981422,
-0.0054498882964253426,
-0.01586567796766758,
0.0007888730033300817,
-0.003933997824788094,
0.04712127894163132,
-0.01167388167232275,
-0.001591264852322638,
0.003481837920844555,
-0.02802908606827259,
0.005172139964997768,
-0.033039964735507965,
-0.005578207783401012,
0.04946522414684296,
0.006325142458081245,
0.002255209255963564,
-0.0016113122692331672,
-0.0303569994866848,
0.010711006820201874,
0.0639101043343544,
-0.018904097378253937,
-0.03449804335832596,
-0.0193231999874115,
-0.013178767636418343,
-0.018615245819091797,
0.04090191423892975,
0.02918144501745701,
0.02552078291773796,
0.0028596334159374237,
0.040748752653598785,
-0.025384554639458656,
-0.044001225382089615,
-0.05476084351539612,
0.03535797446966171,
-0.011031059548258781,
0.016096901148557663,
0.0224586371332407,
0.01181941106915474,
-0.006864211056381464,
0.022369729354977608,
0.008811389096081257,
0.01777605339884758,
0.02030319534242153,
-0.038207896053791046,
0.02256922610104084,
-0.03551197424530983,
0.005408931989222765,
0.006654865108430386,
-0.015746766701340675,
-0.06356864422559738,
0.020058846101164818,
-0.03175690770149231,
-0.04645552858710289,
-0.05901235714554787,
0.057837821543216705,
-0.03780490905046463,
0.025306986644864082,
-0.011108669452369213,
-0.00020234864496160299,
-0.027337856590747833,
0.0008268828969448805,
-0.01820489764213562,
-0.03563325107097626,
-0.023102596402168274,
-0.032917194068431854,
-0.03730127960443497,
0.01617884449660778,
-0.01843571476638317,
0.024544360116124153,
0.00351037853397429,
-0.010153863579034805,
-0.015909409150481224,
0.0016522801015526056,
0.024003105238080025,
0.012447274290025234,
-0.010607988573610783,
0.006758254021406174,
-0.01834440790116787,
0.008660039864480495,
-0.037691887468099594,
-0.0620674304664135,
0.025315063074231148,
0.009311139583587646,
0.044384539127349854,
0.005532665643841028,
0.0011171926744282246,
-0.010923468507826328,
0.06978876888751984,
-0.02359863743185997,
-0.018886668607592583,
-0.022105101495981216,
-0.03506562486290932,
0.01971917599439621,
-0.029029926285147667,
-0.034054990857839584,
-0.027654992416501045,
0.002868628827854991,
0.023591576144099236,
0.017602713778614998,
0.002692679176107049,
-0.009858723729848862,
0.016225414350628853,
-0.004863122012466192,
0.020798159763216972,
-0.009211881086230278,
0.0218159481883049,
0.03583609312772751,
0.019700856879353523,
0.004679975099861622,
-0.0016657286323606968,
-0.021502988412976265,
0.03107381798326969,
-0.10979720950126648,
-0.03586932644248009,
0.005321396514773369,
-0.007456593215465546,
0.04503965377807617,
-0.025495151057839394,
0.01589619740843773,
0.020256193354725838,
-0.06278561055660248,
0.011332619935274124,
-0.05016341805458069,
-0.01794879138469696,
-0.041723478585481644,
-0.00657461816444993,
-0.03996335715055466,
0.057358838617801666,
-0.0041073523461818695,
0.03190553933382034,
0.0174876656383276,
0.035172853618860245,
-0.025322118774056435,
-0.030541805550456047,
-0.014493100345134735,
-0.005150467157363892,
-0.04893557354807854,
-0.012173772789537907,
0.04894476756453514,
-0.014101498760282993,
0.0033608025405555964,
0.014137630350887775,
-0.07799545675516129,
0.04051288589835167,
0.013998267240822315,
-0.0030105647165328264,
0.025962209329009056,
0.0433911569416523,
0.029322989284992218,
0.016861919313669205,
-0.024372491985559464,
0.015124938450753689,
-0.015952736139297485,
-0.0012561120092868805,
-0.013536566868424416,
0.015624988824129105,
0.011414460837841034,
-0.045794546604156494,
-0.012812115252017975,
0.024926014244556427,
-0.017094071954488754,
0.017103685066103935,
-0.02461666241288185,
0.02642444148659706,
0.001660780981183052,
-0.04036686196923256,
-0.005196060985326767,
-0.04590912163257599,
0.03268842026591301,
0.06361331045627594,
-0.02299928292632103,
-0.029448358342051506,
0.052269648760557175,
0.012596813030540943,
0.01072241086512804,
-0.03322776034474373,
0.0029456799384206533,
-0.0033099742140620947,
-0.03201191499829292,
-0.023619147017598152,
0.02771940268576145,
0.01329656969755888,
-0.0027091579977422953,
-0.012071938253939152,
-0.0004241682472638786,
0.0158340185880661,
0.018724795430898666,
0.02938331663608551,
-0.015243890695273876,
0.008634023368358612,
0.017961468547582626,
-0.09671474248170853,
0.026780767366290092,
0.02606692723929882,
-0.05481100082397461,
-0.04056832194328308,
-0.029981302097439766,
-0.007232215255498886,
0.03755674511194229,
0.06817509979009628,
0.011907379142940044,
-0.0015713914763182402,
0.006407498382031918,
0.0024522896856069565,
-0.0008582354057580233,
-0.0387435108423233,
-0.017402037978172302,
0.0031742400024086237,
-0.005561480298638344,
0.008057848550379276,
-0.002337156794965267,
-0.004475893918424845,
-0.010526387020945549,
0.019697267562150955,
0.01004712376743555,
-0.014970580115914345,
-0.014073903672397137,
-0.020942898467183113,
0.0007716748514212668,
-0.005011170171201229,
-0.010367368347942829,
0.06964365392923355,
-0.0018661690410226583,
0.05420156940817833,
0.04250993952155113,
-0.03686535358428955,
-0.047102123498916626,
0.016369560733437538,
-0.0391031876206398,
-0.002630275906994939,
0.011711299419403076,
-0.016082707792520523,
0.03712785989046097,
-0.06846623867750168,
-0.028238624334335327,
0.009893934242427349,
-0.016698729246854782,
-0.03355700150132179,
0.0163721926510334,
0.05285055190324783,
0.0433550588786602,
-0.02505735494196415,
-0.007099218666553497,
0.011563400737941265,
-0.005162922665476799,
0.04334012046456337,
0.003983267117291689,
0.019829977303743362,
0.028931887820363045,
-0.0017140833660960197,
0.06014247611165047,
-0.03281265124678612,
-0.007352204993367195,
0.019641002640128136,
0.029125789180397987,
-0.026795409619808197,
-0.02363778091967106,
0.0020855474285781384,
0.0003607303078752011,
0.006550105754286051,
0.030329978093504906,
-0.03211741894483566,
0.06203185021877289,
-0.001019705319777131,
0.011073396541178226,
-0.032618146389722824,
0.012792525812983513,
0.0053478810004889965,
0.018797438591718674,
-0.007596972864121199,
0.0222525205463171,
0.008899827487766743,
0.022159233689308167,
-0.014081951230764389,
-0.00706903263926506,
0.018522782251238823,
0.019543930888175964,
0.024876656010746956,
-0.014554438181221485,
0.013145900331437588,
-0.003187872003763914,
-0.007050172425806522,
-0.03872526437044144,
-0.031708430498838425,
0.05949500948190689,
0.02305569499731064,
-0.0037398082204163074,
-0.01720401644706726,
0.004942147992551327,
-0.020914437249302864,
0.029394114390015602,
-0.025106631219387054,
-0.015771355479955673,
0.01001817174255848,
0.029952358454465866,
0.0004030675918329507,
0.001230543595738709
] |
<p>The Lippmann-Schwinger equation in the first Born approximation, in the far field, is the Fourier transform of the potential. The scattering potential for an electron beam incident on a crystal is by the Coulomb potential which can be recast as crystal electron density by the Poisson equation. The scattering field is then the Fourier transform of the charge density.</p>
<p>Far field x-ray scattering in a crystal is the Fourier transform of the charge density. But the x-rays are not scattered off of the Coulomb potential. So, how does one go from the Lippmann-Schwinger to the Fourier transform of the charge density for x-ray scattering?</p> | 2,058 | [
0.005516829434782267,
-0.00725857587531209,
0.06281237304210663,
-0.04117223620414734,
0.022626670077443123,
0.007484568748623133,
-0.026902230456471443,
-0.0051595368422567844,
0.029255958274006844,
0.00884460099041462,
0.03925618156790733,
0.01686256006360054,
0.06572531908750534,
0.045641954988241196,
0.021315816789865494,
0.023671861737966537,
-0.01195999514311552,
0.0020383887458592653,
-0.03387582302093506,
-0.016545366495847702,
-0.009409290738403797,
0.03100501373410225,
-0.0006463110912591219,
0.015133200213313103,
-0.017861725762486458,
0.02312537468969822,
-0.0293415617197752,
-0.0004649549664463848,
0.028708361089229584,
0.04049365222454071,
0.03273223340511322,
-0.016053713858127594,
0.02289135381579399,
-0.00532888900488615,
0.026197606697678566,
0.002219862537458539,
-0.005044037010520697,
-0.009242621250450611,
-0.012907624244689941,
0.013377035968005657,
0.007114398758858442,
-0.02873031236231327,
0.009938434697687626,
0.036383237689733505,
0.025715844705700874,
0.012546899728477001,
-0.003566734492778778,
-0.02021106518805027,
0.03636029735207558,
-0.04518474265933037,
0.03385184705257416,
-0.015413109213113785,
0.0013984744437038898,
0.005226085428148508,
-0.015307446010410786,
-0.028686560690402985,
0.043223049491643906,
0.06470263004302979,
0.030656933784484863,
-0.04395051300525665,
-0.026182672008872032,
0.005739153362810612,
-0.04447738081216812,
-0.004290252923965454,
-0.0031394721008837223,
0.012446087785065174,
-0.002034632256254554,
-0.038789767771959305,
0.005209974013268948,
-0.04786553978919983,
0.011146171018481255,
0.03591118007898331,
0.006002406589686871,
-0.05234150588512421,
0.018034476786851883,
0.009143541567027569,
0.028219478204846382,
-0.013446792960166931,
0.013870938681066036,
0.01631929539144039,
-0.0230302382260561,
0.023941652849316597,
0.015729553997516632,
0.030785435810685158,
-0.024068178609013557,
-0.012216196395456791,
0.0718759149312973,
-0.011862081475555897,
-0.04336810111999512,
0.0627259761095047,
0.011283909901976585,
0.009135470725595951,
0.04622015357017517,
0.008206360973417759,
-0.027244746685028076,
0.023853525519371033,
-0.014559791423380375,
0.06499898433685303,
0.013174773193895817,
-0.05096692591905594,
0.012646570801734924,
-0.025373587384819984,
0.0239592045545578,
0.0528174452483654,
-0.014881739392876625,
-0.005115786101669073,
-0.009848357178270817,
0.0031729373149573803,
-0.004650941584259272,
-0.028522970154881477,
-0.008773064240813255,
0.044115472584962845,
0.003808367997407913,
0.021842049434781075,
0.01859886571764946,
-0.015721650794148445,
0.013567626476287842,
0.0025529584381729364,
0.04350234568119049,
0.0991809219121933,
0.032630838453769684,
0.0028233053162693977,
0.04882711544632912,
-0.025062665343284607,
-0.07522910833358765,
0.0033078573178499937,
0.0311135221272707,
0.0015303734689950943,
-0.019692204892635345,
0.04086616635322571,
0.012619745917618275,
0.0028910981491208076,
-0.0004409070825204253,
-0.011998755857348442,
0.01704769767820835,
0.005565440282225609,
-0.09155403077602386,
-0.04621647298336029,
0.022259844467043877,
0.004403093829751015,
0.0017675303388386965,
-0.08143065124750137,
-0.017139915376901627,
0.017749136313796043,
0.0671936497092247,
0.02445482648909092,
0.006411303766071796,
-0.019904812797904015,
0.04419197514653206,
-0.013656795024871826,
0.01719449833035469,
-0.020776810124516487,
-0.02295808307826519,
0.012747603468596935,
-0.009162111207842827,
-0.02900271862745285,
0.03389470651745796,
0.021169833838939667,
-0.023794176056981087,
-0.01869748905301094,
0.061570778489112854,
0.0006943032494746149,
-0.052682098001241684,
-0.01124168187379837,
-0.04002324119210243,
-0.045394208282232285,
0.04206174612045288,
0.038557909429073334,
-0.014904746785759926,
0.04177957400679588,
0.002966582775115967,
0.0034142187796533108,
-0.019914545118808746,
-0.0032609079498797655,
0.004563469905406237,
-0.02172534540295601,
0.005193089600652456,
-0.018748799338936806,
0.013854091055691242,
0.012782789766788483,
-0.018461136147379875,
0.0006295070634223521,
-0.010258345864713192,
0.03434489667415619,
0.03849140927195549,
0.037257835268974304,
-0.010715904645621777,
-0.02562575787305832,
-0.013481899164617062,
-0.03404949977993965,
-0.03533544763922691,
-0.03757479786872864,
0.02870906889438629,
-0.030234619975090027,
-0.00751187140122056,
0.04819970950484276,
0.0293862484395504,
0.0024645214434713125,
-0.012127651832997799,
-0.01609126292169094,
-0.019412444904446602,
0.032794881612062454,
-0.007875488139688969,
0.004217110108584166,
0.030077319592237473,
0.044024527072906494,
0.042644839733839035,
0.004874183796346188,
0.03137652948498726,
-0.019398100674152374,
0.002079959260299802,
-0.022537967190146446,
-0.039052046835422516,
0.01600920967757702,
0.027583889663219452,
0.006022341083735228,
-0.008626032620668411,
0.013948005624115467,
-0.021604401990771294,
-0.00034935656003654003,
0.013363871723413467,
0.018631674349308014,
0.05706917494535446,
0.03803931921720505,
0.023946406319737434,
0.035775717347860336,
0.012051265686750412,
0.0521765798330307,
0.04959838464856148,
-0.04207615554332733,
-0.04350629076361656,
-0.029617244377732277,
0.0414552167057991,
0.032512884587049484,
-0.04362461715936661,
0.03032160922884941,
0.04186994954943657,
-0.0034622736275196075,
0.02764400839805603,
0.025940727442502975,
-0.04922495782375336,
-0.026569712907075882,
0.022424163296818733,
0.004866465460509062,
-0.03174687922000885,
-0.01532664056867361,
0.01045226026326418,
-0.03627772256731987,
-0.006306108087301254,
-0.0028494002763181925,
-0.04309524595737457,
0.015159830451011658,
-0.016999997198581696,
0.0033522865269333124,
0.013886717148125172,
-0.06670331954956055,
0.010809890925884247,
0.0181230828166008,
0.029561452567577362,
-0.008760589174926281,
-0.06083756312727928,
-0.0028814661782234907,
-0.021242136135697365,
-0.0023825180251151323,
0.020775364711880684,
-0.02900523878633976,
-0.014432315714657307,
-0.0018044929020106792,
0.022930169478058815,
-0.08563388884067535,
-0.024257343262434006,
0.005899031180888414,
-0.03183484077453613,
-0.021544303745031357,
0.024654271081089973,
0.04975573346018791,
0.02084789052605629,
0.02059727907180786,
-0.005011958070099354,
-0.05388427898287773,
0.014776996336877346,
-0.03993641212582588,
0.04517645388841629,
0.02067621424794197,
-0.05018536001443863,
0.007514685858041048,
-0.04626743122935295,
-0.03763251006603241,
0.03070756047964096,
0.0031044152565300465,
0.023772399872541428,
-0.020696092396974564,
0.020341375842690468,
-0.031493209302425385,
-0.0022626265417784452,
-0.015616794116795063,
0.016741560772061348,
0.014054025523364544,
0.030248714610934258,
0.004614574369043112,
-0.019854383543133736,
-0.02012462727725506,
0.02528316341340542,
0.006149211432784796,
-0.03427179902791977,
-0.002458258531987667,
-0.010691527277231216,
-0.003804465988650918,
-0.01747320219874382,
0.0243981946259737,
0.040162816643714905,
-0.05840548500418663,
0.009087967686355114,
-0.06887772679328918,
-0.007025338243693113,
0.025373287498950958,
-0.012203182093799114,
0.007091067731380463,
-0.019009793177247047,
-0.04167021065950394,
0.07726264744997025,
0.028169849887490273,
-0.0392901711165905,
-0.029942385852336884,
0.0032935612834990025,
-0.0005522409919649363,
-0.013386614620685577,
0.004858346190303564,
0.016579220071434975,
-0.008824589662253857,
0.04147345945239067,
-0.016822058707475662,
0.058944229036569595,
0.06061762571334839,
0.007060689851641655,
0.0011306321248412132,
0.0015067276544868946,
0.00530433002859354,
0.026293540373444557,
0.020619383081793785,
-0.012945832684636116,
-0.027948057278990746,
0.02032984234392643,
0.002234827494248748,
-0.022485142573714256,
0.013160445727407932,
-0.05129120126366615,
-0.009805715642869473,
-0.004969750996679068,
0.003407874144613743,
-0.05363902077078819,
0.044444236904382706,
-0.00003293706686235964,
0.019533658400177956,
0.013156353496015072,
0.049710653722286224,
0.048940930515527725,
-0.003262642305344343,
-0.03859904408454895,
0.01455269567668438,
0.05719976872205734,
-0.01780102215707302,
-0.04059455543756485,
0.001303192344494164,
-0.02149200811982155,
0.014825952239334583,
0.007926148362457752,
-0.019675293937325478,
0.017902608960866928,
0.01489650271832943,
0.04085271432995796,
-0.00980396755039692,
-0.0026451442390680313,
0.0016225102590397,
-0.049695536494255066,
0.02690080925822258,
0.03536342829465866,
0.07177843153476715,
0.03427659347653389,
0.059377554804086685,
0.05163371562957764,
-0.010513716377317905,
-0.000601941195782274,
0.03079291433095932,
-0.06624387949705124,
0.03157391771674156,
0.012671064585447311,
0.03153613209724426,
-0.02919834665954113,
-0.02455611526966095,
-0.015046102926135063,
-0.013729244470596313,
-0.02619962953031063,
-0.013187019154429436,
-0.019193612039089203,
-0.049010951071977615,
-0.004000429064035416,
-0.022666526958346367,
-0.011981405317783356,
-0.05120983347296715,
0.05732196941971779,
0.03396323695778847,
-0.022011781111359596,
0.0017807153053581715,
0.04484303668141365,
-0.015449062921106815,
-0.00900906603783369,
-0.031103193759918213,
0.018902001902461052,
0.0010677982354536653,
0.06866711378097534,
0.015519309788942337,
-0.014774162322282791,
-0.022196251899003983,
0.008233997039496899,
0.010058321990072727,
0.04776887595653534,
0.03952807933092117,
-0.01893800124526024,
0.017795581370592117,
-0.05685604363679886,
0.003762907115742564,
-0.012347341515123844,
0.06157827749848366,
-0.020828453823924065,
0.0023141622077673674,
0.04001760482788086,
-0.008025502786040306,
0.0001341612805845216,
0.06677331030368805,
0.05540908873081207,
0.004052154254168272,
-0.017279313877224922,
-0.055012304335832596,
-0.004732164554297924,
-0.01007877103984356,
-0.011654224246740341,
0.03484535962343216,
0.006460527889430523,
0.008478857576847076,
0.02622857131063938,
0.03193335980176926,
0.032372478395700455,
-0.032361745834350586,
-0.02249683253467083,
0.005179105792194605,
0.013596374541521072,
-0.011421781033277512,
0.0021888562478125095,
-0.01620880514383316,
0.02995416522026062,
0.05934561789035797,
0.009649147279560566,
0.036409590393304825,
-0.07557328790426254,
-0.0316915437579155,
0.007974999025464058,
0.048938363790512085,
-0.030498234555125237,
-0.0013458443572744727,
-0.0578986294567585,
-0.02275591529905796,
0.05925099551677704,
-0.005787982139736414,
0.008842963725328445,
-0.04087948426604271,
-0.005261912010610104,
-0.02380175143480301,
-0.012524879537522793,
-0.06107117980718613,
-0.006017864216119051,
-0.024394523352384567,
-0.012977170757949352,
-0.03745415434241295,
0.009067408740520477,
-0.002498446963727474,
0.04839376360177994,
-0.03310908004641533,
0.057911381125450134,
0.02566739171743393,
0.014942781999707222,
-0.022647161036729813,
0.024966619908809662,
-0.018865540623664856,
-0.075008325278759,
0.020146330818533897,
-0.007904281839728355,
0.04241594672203064,
0.03972455486655235,
-0.017310749739408493,
-0.06168727949261665,
0.021450085565447807,
-0.016227448359131813,
-0.00938760582357645,
-0.001995868980884552,
-0.03938072547316551,
0.029632950201630592,
0.0011983265867456794,
-0.010857108049094677,
0.06182368844747543,
0.037610989063978195,
-0.02700759656727314,
0.0072996895760297775,
-0.014374963939189911,
0.044563598930835724,
-0.004155014641582966,
0.042739782482385635,
-0.036906056106090546,
0.029192758724093437,
-0.024222970008850098,
0.045198842883110046,
-0.039924897253513336,
0.035275232046842575,
0.01260545663535595,
0.0038135754875838757,
0.015251142904162407,
0.015521945431828499,
-0.04840736836194992,
0.013176625594496727,
0.008673501200973988,
0.022717410698533058,
-0.007600379642099142,
-0.019164474681019783,
0.012315107509493828,
-0.0009846738539636135,
0.002551639685407281,
-0.007638873532414436,
0.013508246280252934,
0.035627178847789764,
-0.009095937944948673,
0.01253176387399435,
0.03432060778141022,
-0.05134717747569084,
0.045571282505989075,
0.01336720585823059,
0.002501302631571889,
0.012197978794574738,
-0.0705500915646553,
-0.014586635865271091,
0.034097809344530106,
-0.0018438959959894419,
0.07317183911800385,
-0.034976694732904434,
-0.001776787918061018,
0.01673537865281105,
-0.012351425364613533,
-0.07431551814079285,
-0.03357190638780594,
0.0035453476011753082,
0.015836356207728386,
-0.03415868431329727,
-0.002768127480521798,
-0.024004561826586723,
0.02274727076292038,
-0.0030958554707467556,
0.030917877331376076,
0.018152255564928055,
0.0007537190685980022,
-0.02172505110502243,
0.012938165105879307,
0.009950830601155758,
0.04571967199444771,
0.014998630620539188,
-0.021314119920134544,
0.029333040118217468,
-0.014881209470331669,
-0.014884973876178265,
0.029886368662118912,
0.016405317932367325,
0.0005530405323952436,
-0.020195525139570236,
-0.057739563286304474,
-0.0002106671454384923,
0.04632347822189331,
-0.036294762045145035,
-0.04621349275112152,
0.0011138407280668616,
0.004351103212684393,
-0.008163214661180973,
-0.0338805690407753,
-0.009668072685599327,
0.0008054347708821297,
0.04675332456827164,
-0.02557622268795967,
-0.00017328045214526355,
-0.054823555052280426,
-0.023837825283408165,
-0.003875595284625888,
0.01964694820344448,
0.04335743561387062,
0.023940308019518852,
0.04446147009730339,
-0.005200840998440981,
-0.003961607348173857,
0.040429577231407166,
0.02702849730849266,
-0.00022476051526609808,
-0.042302876710891724,
0.0369892492890358,
0.0350157767534256,
0.04379046708345413,
-0.018062938004732132,
-0.003832124872133136,
-0.021753478795289993,
-0.011109030805528164,
0.06188558414578438,
0.0014916674699634314,
0.02911793254315853,
0.011682671494781971,
0.0005269603570923209,
-0.02855159342288971,
-0.014402857050299644,
-0.0135421147570014,
-0.007690285332500935,
-0.02868967317044735,
0.04194185137748718,
-0.05896613001823425,
-0.039570402354002,
0.0277607012540102,
0.061569612473249435,
-0.050886765122413635,
0.020269952714443207,
-0.003913670778274536,
0.00564941531047225,
-0.0013865906512364745,
-0.004466576036065817,
-0.03992567956447601,
0.057676125317811966,
-0.005573772359639406,
0.02427751198410988,
0.007038705516606569,
-0.018758751451969147,
0.03297659009695053,
0.04382910951972008,
0.010202059522271156,
-0.01202722080051899,
-0.06785692274570465,
-0.018197789788246155,
0.02775629796087742,
-0.0012617779430001974,
0.04907412827014923,
-0.008787315338850021,
-0.01013985089957714,
0.04775778949260712,
0.016495050862431526,
0.015606455504894257,
0.0050092884339392185,
-0.04975011199712753,
-0.019934752956032753,
-0.06229826807975769,
-0.029940782114863396,
0.04215642809867859,
-0.03659701719880104,
-0.010302864946424961,
0.041893888264894485,
-0.0366392582654953,
0.04866492375731468,
0.030185364186763763,
-0.006305122748017311,
-0.00906294398009777,
0.06436574459075928,
-0.01539879571646452,
0.003999907989054918,
-0.011413773521780968,
-0.003279038006439805,
0.1293998807668686,
0.05575265362858772,
0.044820163398981094,
-0.08891390264034271,
-0.01400291733443737,
-0.025522544980049133,
0.016442934051156044,
-0.01562083326280117,
0.031084595248103142,
-0.039061032235622406,
-0.004731622990220785,
-0.02897828444838524,
0.0561053603887558,
-0.008999809622764587,
0.039641886949539185,
0.04015231877565384,
-0.03607778623700142,
-0.013963805511593819,
0.055518049746751785,
-0.010453509166836739,
0.045405108481645584,
0.016054173931479454,
-0.05588196590542793,
0.018422875553369522,
-0.02557278424501419,
-0.004946412984281778,
-0.04715469479560852,
-0.04923219606280327,
0.011935225687921047,
-0.03831556811928749,
-0.07483146339654922,
0.013102754019200802,
0.014709669165313244,
-0.0005902915145270526,
-0.03574881702661514,
0.012398520484566689,
-0.009634406305849552,
-0.028480010107159615,
0.018327245488762856,
0.03384999558329582,
0.01935097761452198,
-0.003091350896283984,
0.005667663644999266,
0.0132483234629035,
-0.008696358650922775,
-0.020814601331949234,
-0.013818690553307533,
0.017412137240171432,
-0.014869239181280136,
-0.0447719544172287,
-0.0070608449168503284,
-0.010692032054066658,
0.028750354424118996,
-0.04982179030776024,
-0.014883656054735184,
0.012237999588251114,
0.03898139297962189,
0.008530642837285995,
-0.03533536195755005,
0.004811047110706568,
0.04752655327320099,
-0.0133696673437953,
0.0020125280134379864,
-0.01967906765639782,
-0.0005376031622290611,
-0.0041014584712684155,
-0.009109889157116413,
0.04424625635147095,
-0.004737550392746925,
-0.02291431836783886,
-0.06105540320277214,
0.0020788598340004683,
-0.03912223130464554,
-0.046770114451646805,
0.010713255032896996,
0.024820588529109955,
0.06176302582025528,
-0.046676475554704666,
-0.014959513209760189,
-0.019147660583257675,
-0.06409543752670288,
-0.0049062371253967285,
-0.008193780668079853,
0.012555954977869987,
-0.01394696719944477,
0.027474086731672287,
-0.009247231297194958,
0.06869193911552429,
-0.04233139008283615,
-0.014434384182095528,
0.01284140907227993,
-0.01721135340631008,
0.006410968955606222,
-0.0536385104060173,
-0.043750062584877014,
0.031360846012830734,
0.01883482187986374,
-0.009454629383981228,
0.006216614972800016,
-0.005931757390499115,
0.03834444284439087,
0.013712936080992222,
0.004879307001829147,
0.03266847878694534,
-0.039290666580200195,
0.013979833573102951,
-0.01917364075779915,
-0.0013315773103386164,
-0.016513681039214134,
0.005758125334978104,
0.0016372130485251546,
-0.05884715914726257,
-0.028318369761109352,
-0.034102171659469604,
-0.025029586628079414,
0.038921382278203964,
0.055777810513973236,
-0.030500071123242378,
-0.004519080277532339,
-0.01984865963459015,
0.015123249962925911,
-0.006194199435412884,
-0.0013612540205940604,
-0.038570042699575424,
0.043911200016736984,
-0.00794162042438984,
-0.012243437580764294,
-0.027016656473279,
0.054160770028829575,
-0.04780500754714012,
-0.03231373056769371,
0.019137252122163773,
0.023711849004030228,
-0.0025245952419936657,
0.007023364305496216,
0.0020086998119950294,
-0.0006742732366546988,
-0.006658521480858326,
-0.018838489428162575,
0.017505059018731117,
0.0186956487596035,
-0.07350112497806549,
-0.049507636576890945,
0.012638728134334087,
-0.008163195103406906,
0.004889059346169233,
0.04340300336480141,
0.05098573490977287,
-0.005302799865603447,
0.008834026753902435,
-0.013414843939244747,
0.00466076098382473,
-0.027688199654221535,
-0.01830766163766384,
0.023972077295184135,
-0.016736425459384918,
0.026783950626850128,
-0.02789360098540783,
-0.012348988093435764,
0.059593137353658676,
-0.002600327366963029,
-0.00963175855576992,
0.0008199362782761455,
0.0028706148732453585,
-0.03288771212100983,
-0.020785750821232796,
0.03175487741827965,
0.011031117290258408,
0.0014016763307154179,
0.04877925291657448,
0.02886437065899372,
0.020544692873954773,
0.027489658445119858,
-0.00018010461644735187,
-0.1065773218870163,
-0.007116454187780619,
-0.008181476034224033,
0.0042667081579566,
0.050985075533390045,
-0.04868527874350548,
-0.005918401759117842,
-0.000530294724740088,
-0.11371540278196335,
0.0482974648475647,
0.008073178119957447,
-0.022379623726010323,
-0.03248671814799309,
0.05197329446673393,
-0.03318459913134575,
0.03929145261645317,
0.05315164104104042,
0.04140492528676987,
0.004191289655864239,
0.005101711954921484,
-0.010090015828609467,
0.01200682483613491,
-0.02051282301545143,
-0.009833339601755142,
0.02005407214164734,
-0.033705420792102814,
0.06631046533584595,
-0.030182281509041786,
0.0036658551543951035,
0.010310724377632141,
-0.022534102201461792,
-0.0009450875222682953,
0.002191664185374975,
0.004502799827605486,
0.00620991550385952,
-0.0021081704180687666,
-0.01723533496260643,
-0.03515248000621796,
0.012734279967844486,
0.027507144957780838,
0.039226580411195755,
0.012318658642470837,
-0.005088855046778917,
-0.002339169615879655,
-0.006757746450603008,
-0.03047746606171131,
-0.041573673486709595,
0.04996127635240555,
0.023606402799487114,
0.001667342963628471,
-0.0012847279431298375,
0.017982667312026024,
0.038270995020866394,
-0.005439430940896273,
0.0019553913734853268,
-0.059159353375434875,
-0.03944278508424759,
0.0038707954809069633,
0.0004179028910584748,
-0.012653704732656479,
0.04240822419524193,
-0.06686850637197495,
-0.029100919142365456,
0.02681506611406803,
0.0050995685160160065,
-0.048696909099817276,
-0.03156637027859688,
-0.028344595804810524,
0.012415534816682339,
-0.011645736172795296,
-0.01754903234541416,
-0.0037866029888391495,
-0.03597886860370636,
0.08091825246810913,
-0.008366203866899014,
0.0569397434592247,
-0.043526582419872284,
-0.0180658046156168,
-0.017057020217180252,
-0.04245390370488167,
0.005937664769589901,
-0.004381258971989155,
-0.014757114462554455,
-0.0031231087632477283,
-0.02361951395869255,
0.032027389854192734,
0.019055496901273727,
0.04205358773469925,
0.013081105425953865,
-0.008059031330049038,
-0.04282916337251663,
-0.054398879408836365,
-0.0016467836685478687,
-0.03091512992978096,
-0.025866633281111717,
-0.0005418734508566558,
-0.02662971429526806,
-0.0035009761340916157,
-0.015538893640041351,
-0.028845248743891716,
0.05049210786819458,
0.01751633919775486,
0.010008606128394604,
-0.0003977866726927459,
-0.018159965053200722,
-0.06680961698293686,
0.045931555330753326,
0.008096221834421158,
-0.03514321148395538,
0.02057846635580063,
-0.015064174309372902,
0.009594972245395184,
0.018719227984547615,
-0.04250100627541542,
-0.0442795604467392,
0.006479141768068075,
-0.07869378477334976,
-0.02194194309413433,
-0.024793505668640137,
0.017108185216784477,
0.005240610800683498,
-0.0013421118492260575,
0.005852019414305687,
0.0333956740796566,
-0.016925599426031113,
-0.011534788645803928,
0.06215175241231918,
0.012417210265994072,
0.0457361564040184,
0.04740361496806145,
-0.009778846986591816,
-0.024557137861847878,
0.011588367633521557,
-0.005412224214524031,
0.02299928106367588,
0.03135119378566742,
-0.016826895996928215,
0.02385801076889038,
0.034422218799591064,
0.026860440149903297,
-0.051700253039598465,
0.04039188101887703,
0.07453375309705734,
-0.05737921595573425,
-0.007858248427510262,
0.03036106377840042,
-0.0335010290145874,
-0.0024124609772115946,
0.0037517682649195194,
-0.026226649060845375,
0.07415862381458282,
-0.020238783210515976,
0.0017440803349018097,
0.002874650526791811,
-0.022762853652238846,
0.006896413862705231,
0.03852422535419464,
0.03955141827464104,
0.033348072320222855,
-0.021170198917388916,
-0.05554879829287529,
-0.044553712010383606,
-0.004149992950260639,
0.023648357018828392,
-0.04988129809498787,
-0.035463083535432816,
-0.027992408722639084,
-0.038885463029146194,
0.01620759628713131,
0.016618382185697556,
-0.06488876789808273,
-0.004371204413473606,
0.0024072383530437946,
0.04907207936048508,
0.017928335815668106,
0.016324443742632866,
0.011877872049808502,
-0.007041175849735737,
0.030473174527287483,
-0.060731079429388046,
0.01382539514452219,
-0.016941916197538376,
0.016852933913469315,
0.015429157763719559,
0.02911059744656086
] |
<p>Does the nature of the assortment of virtual particles depend upon the warping of spacetime in a direct manner ?</p> | 2,059 | [
-0.014678950421512127,
-0.03331553190946579,
-0.00047603331040591,
-0.053142815828323364,
0.03364656865596771,
0.0081804683431983,
-0.051035210490226746,
-0.03598781302571297,
-0.0341816209256649,
-0.025060558691620827,
0.02698482945561409,
0.0051871053874492645,
0.034659095108509064,
0.011636404320597649,
-0.01864047534763813,
-0.004171491134911776,
0.002501213923096657,
-0.0012702327221632004,
-0.00833059661090374,
-0.04336157068610191,
0.02054988034069538,
0.03480836749076843,
0.013894419185817242,
-0.025652749463915825,
-0.009806969203054905,
0.02163817174732685,
0.03566286340355873,
0.01292385719716549,
0.013772658072412014,
0.057056717574596405,
-0.003344598226249218,
-0.01228505652397871,
0.025912346318364143,
0.044026389718055725,
-0.015601418912410736,
-0.05337543040513992,
-0.04497348889708519,
-0.04249664396047592,
0.028444254770874977,
-0.024095697328448296,
-0.03328223153948784,
-0.026867670938372612,
-0.03515791520476341,
0.089616559445858,
0.006918467581272125,
0.011209576390683651,
-0.004802349489182234,
0.005712462589144707,
0.04495522379875183,
-0.030629528686404228,
0.10055417567491531,
0.04137735813856125,
0.00440552132204175,
-0.004225840792059898,
-0.02498008869588375,
0.02715478278696537,
0.08036229759454727,
0.05238186568021774,
-0.013467799872159958,
-0.03712001070380211,
0.002250210614874959,
-0.009420366026461124,
-0.014591412618756294,
-0.034801874309778214,
-0.027184581384062767,
0.031840838491916656,
-0.012479024939239025,
-0.010393167845904827,
-0.0011907679727301002,
-0.014708091504871845,
0.00414892565459013,
0.00009899392171064392,
0.031070636585354805,
-0.009697314351797104,
0.01909959875047207,
0.013979209586977959,
0.030593639239668846,
0.010874928906559944,
0.03802613914012909,
0.03752594068646431,
0.023455502465367317,
0.008592300117015839,
0.044279471039772034,
-0.012385101988911629,
0.015781808644533157,
-0.008106667548418045,
0.06179998070001602,
-0.02817927673459053,
0.004195369314402342,
0.08385643362998962,
-0.02191912569105625,
-0.013889916241168976,
0.05923362448811531,
-0.022624142467975616,
-0.03429142013192177,
0.0024756374768912792,
0.008951623924076557,
0.03642479330301285,
0.011025807820260525,
-0.023801585659384727,
-0.022408798336982727,
0.009594021365046501,
-0.0004167863808106631,
0.05813916027545929,
0.009010378271341324,
-0.019337525591254234,
-0.05680965259671211,
0.029153523966670036,
-0.004947217646986246,
-0.027658546343445778,
-0.01872444525361061,
0.009505950845777988,
-0.021868757903575897,
0.024191131815314293,
0.03059765137732029,
-0.043261632323265076,
0.0072296117432415485,
-0.0414760448038578,
0.06798111647367477,
0.06037561595439911,
0.041733864694833755,
-0.04842419922351837,
0.0024274326860904694,
0.0033146331552416086,
-0.03247198835015297,
0.023795144632458687,
0.042669110000133514,
-0.011675295419991016,
-0.03275003656744957,
0.012782713398337364,
0.0015111847314983606,
-0.01592249609529972,
0.03148455172777176,
0.00695294514298439,
0.013480370864272118,
0.025616684928536415,
-0.10345575213432312,
-0.03892127424478531,
0.05285492539405823,
-0.00710189389064908,
-0.010779179632663727,
-0.03813212364912033,
0.00368952052667737,
0.03214041516184807,
0.09074980765581131,
-0.01377190463244915,
0.0009241478983312845,
0.020947515964508057,
0.04165499284863472,
0.009373794309794903,
-0.028126804158091545,
0.004416005685925484,
-0.02129708230495453,
-0.048558108508586884,
0.011358487419784069,
-0.056366655975580215,
0.006418196950107813,
0.09079602360725403,
0.004996416158974171,
0.00702471099793911,
0.0847514420747757,
-0.010489710606634617,
-0.00045992626110091805,
0.028056081384420395,
-0.008153720758855343,
-0.02791663073003292,
0.01905696839094162,
-0.023219484835863113,
0.00675099017098546,
0.02868795022368431,
0.010418311692774296,
0.034530460834503174,
0.01800403743982315,
0.02889375016093254,
0.03159328177571297,
-0.02743765525519848,
-0.01087826769798994,
0.024327250197529793,
0.007480920758098364,
-0.028875477612018585,
-0.045563098043203354,
-0.03341330960392952,
-0.011159250512719154,
-0.0025143660604953766,
-0.016401134431362152,
0.053357865661382675,
0.0024806626606732607,
0.0028329233173280954,
-0.02531254105269909,
-0.05414043739438057,
-0.029086964204907417,
-0.07738965004682541,
0.01289477851241827,
0.005545719526708126,
-0.008744874969124794,
0.048204198479652405,
0.04040900245308876,
0.016693100333213806,
0.00008591898222221062,
-0.0358746200799942,
-0.017365712672472,
0.03609006851911545,
0.010792361572384834,
0.00297933304682374,
0.010171674191951752,
0.0630115270614624,
0.024477368220686913,
-0.010902070440351963,
-0.018365612253546715,
-0.0023149859625846148,
-0.05707070976495743,
0.016684936359524727,
-0.003958825953304768,
0.04586722329258919,
-0.030960042029619217,
0.002753886627033353,
0.0066518415696918964,
0.013159723952412605,
-0.024951115250587463,
0.058690235018730164,
-0.02430398017168045,
0.04858272150158882,
0.018773769959807396,
0.003924282267689705,
-0.018381714820861816,
0.06269636005163193,
0.009122044779360294,
-0.006660285871475935,
0.009025320410728455,
-0.005718977190554142,
-0.041808005422353745,
-0.018126288428902626,
0.03617420420050621,
0.0676039606332779,
-0.005843388382345438,
0.034222789108753204,
0.006000471767038107,
0.04547567665576935,
0.00028796971309930086,
0.011851620860397816,
-0.0343768335878849,
-0.053330253809690475,
0.004397002514451742,
0.004264000337570906,
0.06724808365106583,
-0.02620353177189827,
0.010287297889590263,
0.01590035669505596,
-0.03455052152276039,
-0.0010504175443202257,
-0.0183100588619709,
0.012668418698012829,
0.013135945424437523,
-0.015142851509153843,
0.000010500742064323276,
-0.056941453367471695,
-0.0073197754099965096,
0.0016598666552454233,
0.007212921045720577,
0.017796432599425316,
0.0017272821860387921,
-0.05619777366518974,
-0.03768771514296532,
-0.013454730622470379,
0.03625474497675896,
0.035605110228061676,
-0.02149144373834133,
-0.014433430507779121,
0.040832698345184326,
-0.031126223504543304,
0.03058544546365738,
0.0014703579945489764,
-0.023803096264600754,
0.012323345057666302,
-0.004475774709135294,
0.004649808630347252,
0.019710591062903404,
0.023401722311973572,
-0.03448210656642914,
-0.03171641752123833,
0.029693765565752983,
-0.02477901428937912,
-0.01550340373069048,
0.04448115825653076,
-0.07958030700683594,
0.034991305321455,
-0.047935597598552704,
-0.07009390741586685,
0.004087789449840784,
-0.021853439509868622,
0.022652266547083855,
0.03073141723871231,
-0.014724849723279476,
-0.054671164602041245,
0.000543059257324785,
-0.004168272949755192,
0.001922018826007843,
-0.05131620541214943,
0.027842488139867783,
0.03717122972011566,
-0.00705323088914156,
-0.0579465813934803,
-0.004341015592217445,
-0.010845733806490898,
-0.05450432002544403,
-0.004629387520253658,
-0.020326847210526466,
0.025201858952641487,
-0.023845482617616653,
-0.003260323777794838,
0.0411815345287323,
-0.05336933210492134,
0.039185088127851486,
-0.024919992312788963,
-0.06429650634527206,
0.03026316687464714,
-0.03604520484805107,
0.04170792177319527,
-0.01436841394752264,
-0.010814391076564789,
0.06948646157979965,
0.0344415083527565,
-0.027139661833643913,
-0.012367666698992252,
-0.026216289028525352,
0.019342472776770592,
0.013119331561028957,
0.02773961052298546,
0.020474428310990334,
-0.011836444959044456,
0.0416967049241066,
0.08969078212976456,
0.043003492057323456,
0.015649162232875824,
0.011193016543984413,
-0.0438290499150753,
-0.013050408102571964,
0.0027820731047540903,
-0.019539710134267807,
0.010442733764648438,
0.02032211795449257,
-0.022175369784235954,
0.0056751687079668045,
0.006998486816883087,
0.021111801266670227,
0.004341256804764271,
-0.04262036830186844,
0.06229112297296524,
0.029320072382688522,
0.037125881761312485,
0.017399711534380913,
0.024983244016766548,
0.0016024330398067832,
-0.018156779929995537,
-0.01443177554756403,
0.01680830307304859,
0.018627721816301346,
-0.020883768796920776,
0.000762571522500366,
0.03124493733048439,
0.022308025509119034,
-0.015375111252069473,
-0.027257945388555527,
-0.005249036476016045,
-0.02108611725270748,
0.01938638836145401,
-0.00635913573205471,
-0.021815525367856026,
0.0647687092423439,
0.029147595167160034,
0.04328904300928116,
0.01793992519378662,
-0.05122499167919159,
-0.0047435699962079525,
-0.03247927501797676,
0.007606441620737314,
0.004564736504107714,
-0.007396715227514505,
-0.0013464094372466207,
0.0311298631131649,
0.011736416257917881,
0.01639418862760067,
-0.020194189622998238,
0.0021020909771323204,
-0.07183604687452316,
-0.0006705595296807587,
-0.043148864060640335,
0.02762690745294094,
-0.02742902562022209,
-0.010789073072373867,
0.010034903883934021,
-0.0378929004073143,
-0.0005617047427222133,
-0.02815495990216732,
-0.014912992715835571,
-0.051184430718421936,
0.007399060297757387,
-0.017797455191612244,
-0.030778953805565834,
-0.010792592540383339,
0.033804647624492645,
0.03910791501402855,
-0.011972635984420776,
0.0456354096531868,
0.04301844909787178,
-0.051913172006607056,
0.0014272903790697455,
-0.015130479820072651,
0.06557353585958481,
-0.02273988351225853,
0.035475973039865494,
0.008654228411614895,
-0.002010518219321966,
-0.07044969499111176,
-0.015852291136980057,
-0.000504674855619669,
0.028299998492002487,
-0.009206007234752178,
0.001222017570398748,
-0.033945243805646896,
-0.0513562448322773,
-0.03268434852361679,
-0.00440817279741168,
0.06394588202238083,
0.012484349310398102,
-0.000377499993192032,
0.06909060478210449,
0.008095619268715382,
-0.0147023256868124,
0.043380238115787506,
0.050162073224782944,
-0.006897889077663422,
-0.03986765816807747,
-0.021735500544309616,
0.014045760966837406,
0.01701441779732704,
0.004902958869934082,
-0.004267573356628418,
-0.0168745256960392,
-0.024013839662075043,
0.046475861221551895,
0.0020299491006881,
-0.01005557831376791,
-0.0442083440721035,
-0.02428850531578064,
-0.02947896532714367,
-0.006420860532671213,
-0.017754508182406425,
0.008031146600842476,
0.0015963176265358925,
0.04580140858888626,
0.04136631265282631,
0.021906526759266853,
-0.05450105294585228,
-0.10679146647453308,
-0.019639145582914352,
0.05996553599834442,
0.03416847437620163,
-0.0029025471303611994,
-0.014289562590420246,
-0.03412286192178726,
-0.016789300367236137,
0.057472676038742065,
-0.02561577595770359,
-0.024725809693336487,
-0.011195658706128597,
-0.01614687219262123,
-0.04839339479804039,
-0.007997534237802029,
-0.022980112582445145,
0.024790823459625244,
-0.042705509811639786,
-0.010438134893774986,
-0.0503753125667572,
0.010466651991009712,
-0.0077528515830636024,
0.04639406129717827,
0.008176193572580814,
0.038441963493824005,
0.044933218508958817,
0.03219713270664215,
-0.010249603539705276,
0.020150402560830116,
-0.07142246514558792,
-0.04763336479663849,
0.017198851332068443,
0.04559646174311638,
-0.011061467230319977,
0.054206591099500656,
-0.0198528952896595,
-0.035979390144348145,
0.010524319484829903,
-0.03014872595667839,
0.02767045423388481,
0.009051303379237652,
-0.04859122261404991,
0.048425886780023575,
-0.006138387601822615,
0.016013098880648613,
0.034928228706121445,
0.02979755774140358,
-0.025017675012350082,
-0.031924474984407425,
-0.031274400651454926,
0.046929944306612015,
-0.053040727972984314,
0.02393532358109951,
0.005399324931204319,
-0.029283011332154274,
-0.005985408555716276,
0.037933699786663055,
0.016795743256807327,
0.0037905233912169933,
0.018752941861748695,
-0.04191581904888153,
-0.033355746418237686,
-0.0029181542340666056,
0.032332275062799454,
0.02021956816315651,
0.006375591270625591,
-0.001140131033025682,
0.0005212037940509617,
-0.000884972745552659,
0.03926507383584976,
0.026248669251799583,
-0.01209375262260437,
0.025575747713446617,
-0.007921380922198296,
0.011671625077724457,
-0.01062482874840498,
0.008641371503472328,
0.02162862941622734,
-0.04969094693660736,
0.030671555548906326,
0.02749444730579853,
-0.010064489208161831,
0.04688428342342377,
-0.07373647391796112,
-0.011891481466591358,
-0.013881603255867958,
-0.05778549239039421,
0.014422453008592129,
-0.032891884446144104,
0.016501205042004585,
-0.0005435874336399138,
0.048264116048812866,
-0.08310998976230621,
-0.04115467146039009,
0.009711354039609432,
-0.008829142898321152,
0.018099462613463402,
-0.03212541341781616,
0.02453554794192314,
-0.06313479691743851,
-0.009294030256569386,
-0.00313576334156096,
0.06025766581296921,
-0.016643648967146873,
0.01287929993122816,
0.0018661192152649164,
0.025820299983024597,
0.04464863985776901,
-0.026743866503238678,
-0.01748502627015114,
-0.007247935514897108,
0.019361907616257668,
0.025278571993112564,
0.01731954887509346,
0.05529484897851944,
-0.040393367409706116,
-0.0225361455231905,
0.015034300275146961,
-0.024951249361038208,
0.012971756048500538,
-0.03818652033805847,
0.01631183922290802,
0.038738399744033813,
-0.003248773515224457,
-0.006913607474416494,
-0.019170304760336876,
0.01445826981216669,
-0.023430235683918,
-0.0005356147885322571,
-0.0038532500620931387,
0.0013450825354084373,
0.01038345880806446,
-0.020526444539427757,
0.052953775972127914,
0.031512051820755005,
-0.010426702909171581,
0.03398437425494194,
0.023993203416466713,
0.0036806114949285984,
-0.017700541764497757,
0.005064007826149464,
-0.06658808141946793,
0.00654861144721508,
-0.021591177210211754,
0.004268672317266464,
0.01062597893178463,
-0.012712482362985611,
-0.011382444761693478,
-0.01125318743288517,
-0.03392372652888298,
0.002290416043251753,
0.029846029356122017,
-0.009292910806834698,
0.03520010784268379,
0.008982128463685513,
-0.02848181128501892,
-0.013386992737650871,
-0.024689173325896263,
0.0074393353424966335,
0.011798769235610962,
-0.01528691966086626,
0.021276993677020073,
-0.02909942716360092,
0.01406160183250904,
-0.0017206083284690976,
0.03387168422341347,
-0.023673394694924355,
0.01457672193646431,
0.007687919773161411,
-0.014811122789978981,
0.008731602691113949,
-0.012357894331216812,
-0.030886277556419373,
0.009802786633372307,
-0.04181133210659027,
-0.006504186429083347,
-0.02403024397790432,
0.017110610380768776,
0.021484557539224625,
0.001915032509714365,
0.05827365070581436,
0.01515677198767662,
-0.03807579725980759,
-0.031059682369232178,
0.003050056751817465,
0.0008766414248384535,
0.0507618673145771,
0.024523133412003517,
0.007965633645653725,
0.06126245856285095,
0.014958184212446213,
-0.0015187410172075033,
-0.021547261625528336,
-0.09566608816385269,
-0.051165856420993805,
-0.02954053319990635,
-0.020933620631694794,
0.03127172589302063,
0.021762093529105186,
-0.021080786362290382,
0.009712434373795986,
-0.021491732448339462,
0.05607539415359497,
-0.007657746318727732,
0.061032168567180634,
-0.018109848722815514,
0.07217186689376831,
-0.0060010324232280254,
0.014376234263181686,
-0.04495428502559662,
-0.010846170596778393,
0.12419263273477554,
0.0450231097638607,
0.01666867546737194,
-0.05630311369895935,
0.024920005351305008,
-0.023857856169342995,
-0.0003102249756921083,
-0.016670722514390945,
-0.011111856438219547,
-0.013657459989190102,
0.013208636082708836,
-0.038557130843400955,
0.058531928807497025,
0.00494200736284256,
-0.02713189087808132,
0.0503167100250721,
-0.0635514110326767,
-0.059214286506175995,
-0.032396890223026276,
-0.005048337858170271,
0.00923848431557417,
0.010683954693377018,
-0.0665186196565628,
0.015441584400832653,
-0.03657761961221695,
0.005959426984190941,
-0.01667059399187565,
-0.023858727887272835,
0.007912436500191689,
-0.02709885872900486,
-0.042201604694128036,
0.017301075160503387,
0.021884368732571602,
-0.03153325989842415,
-0.06145450472831726,
-0.01983318105340004,
-0.005329005885869265,
-0.019941112026572227,
0.0694579929113388,
0.04211778566241264,
-0.0071793473325669765,
0.02651716209948063,
-0.004774064756929874,
0.009006328880786896,
-0.04248049482703209,
-0.007482662331312895,
-0.020670969039201736,
0.04003819823265076,
0.001022685901261866,
0.007336493581533432,
0.017598947510123253,
-0.014733892865478992,
-0.01219856832176447,
-0.0877876803278923,
-0.007788448594510555,
-0.02109098806977272,
0.012798940762877464,
0.0059920409694314,
-0.0169687420129776,
-0.02060760371387005,
0.017952824011445045,
-0.030285140499472618,
0.021499136462807655,
-0.030029626563191414,
0.03716588392853737,
0.001736856414936483,
0.0019047986716032028,
0.042546454817056656,
-0.006682044826447964,
-0.016399390995502472,
-0.0458393432199955,
-0.012868301942944527,
-0.021008707582950592,
-0.000442638760432601,
0.02947547473013401,
0.02814585343003273,
0.05581284314393997,
0.0021142675541341305,
0.005957559682428837,
-0.016223672777414322,
-0.03925192356109619,
0.012190395966172218,
-0.03630245104432106,
-0.019383734092116356,
-0.03115076757967472,
0.05823132395744324,
0.03091820515692234,
0.03859415650367737,
-0.012479414232075214,
0.02218431979417801,
-0.0227910615503788,
0.023412149399518967,
0.003023625584319234,
-0.0047708242200315,
0.014707296155393124,
-0.01620241068303585,
-0.029299944639205933,
-0.023299168795347214,
-0.03554359823465347,
0.026702212169766426,
-0.006109397858381271,
-0.031245509162545204,
-0.0010273315710946918,
0.04569815844297409,
0.0024853369686752558,
0.0029102510306984186,
0.03954077884554863,
-0.004312919918447733,
0.005718715488910675,
0.025710904970765114,
-0.0055450983345508575,
-0.033631276339292526,
-0.03705891594290733,
-0.013627219013869762,
-0.025499654933810234,
-0.006901456508785486,
0.010839554481208324,
-0.007482440676540136,
0.04299715906381607,
-0.008639669045805931,
0.012727751396596432,
-0.03892013803124428,
-0.02100585773587227,
-0.02218696102499962,
0.024739494547247887,
-0.02852553501725197,
-0.02752811089158058,
0.010400870814919472,
0.04003923758864403,
-0.037508513778448105,
-0.008091268129646778,
0.0385444276034832,
0.0323503278195858,
-0.030393052846193314,
-0.022386688739061356,
0.04849997162818909,
-0.008883623406291008,
0.034504376351833344,
0.0059630717150866985,
-0.07330256700515747,
0.02941584214568138,
-0.036758702248334885,
-0.05230378359556198,
0.02930459752678871,
-0.046247635036706924,
0.035892635583877563,
0.02153886668384075,
-0.015797177329659462,
-0.020579952746629715,
0.054441552609205246,
-0.03775859624147415,
0.00027498090639710426,
0.014416557736694813,
-0.044662412256002426,
0.00003498229489196092,
-0.011541127227246761,
0.012934338301420212,
0.015320846810936928,
-0.0379900299012661,
0.032754335552453995,
0.030247515067458153,
-0.01199046615511179,
-0.007505827117711306,
0.008921747095882893,
0.0000632237788522616,
0.05233897268772125,
-0.00018917869601864368,
0.029994329437613487,
0.019320668652653694,
0.04876365140080452,
-0.02136993035674095,
0.032784603536129,
0.03284807503223419,
-0.0033279506023973227,
-0.10763431340456009,
-0.01206462737172842,
0.011739740148186684,
0.02804931253194809,
0.03325153887271881,
-0.02681286819279194,
0.018724052235484123,
0.015730082988739014,
-0.06069051846861839,
0.03920469433069229,
-0.01625281572341919,
-0.004896633327007294,
-0.02893596887588501,
0.0020520202815532684,
-0.03313826397061348,
0.05670851096510887,
0.06597112119197845,
0.052550021559000015,
0.016241149976849556,
0.009050464257597923,
-0.035819850862026215,
-0.04184458404779434,
-0.009476082399487495,
0.015020333230495453,
-0.005414281971752644,
-0.02958073653280735,
0.08874517679214478,
0.0290976669639349,
-0.04132404550909996,
0.016730019822716713,
0.05043358728289604,
0.008168255910277367,
0.004024365451186895,
0.014725642278790474,
0.04542805626988411,
0.018540389835834503,
0.0009542369516566396,
0.0144890658557415,
0.02540343441069126,
0.03275374323129654,
-0.0035106928553432226,
0.01837303675711155,
0.0022847552318125963,
-0.012555870227515697,
-0.014406278729438782,
-0.020707780495285988,
0.005734576378017664,
0.0005962703144177794,
-0.013353393413126469,
-0.038171663880348206,
-0.03260526433587074,
0.033918820321559906,
-0.002883386565372348,
0.017988640815019608,
0.025441396981477737,
-0.04883044585585594,
-0.0031444744672626257,
0.04362829774618149,
-0.012206974439322948,
-0.013686149381101131,
0.04205421730875969,
-0.010694948025047779,
-0.01293062511831522,
-0.016942046582698822,
0.014216843992471695,
-0.01718302257359028,
-0.009715253487229347,
0.02354731783270836,
0.00859228614717722,
0.03792678937315941,
0.020194992423057556,
-0.038994111120700836,
-0.00869077816605568,
0.029141714796423912,
0.005401282571256161,
0.033165767788887024,
0.006201277486979961,
-0.031940724700689316,
-0.027020124718546867,
-0.03289191797375679,
0.026732681319117546,
0.007888524793088436,
-0.009159338660538197,
-0.03161423280835152,
-0.008882388472557068,
-0.016171833500266075,
0.04293425381183624,
0.052258461713790894,
-0.020137745887041092,
0.007318713702261448,
0.0030251597054302692,
0.01587214134633541,
0.021251413971185684,
-0.03718509525060654,
-0.028464075177907944,
0.002854045480489731,
-0.022401539608836174,
0.0040620435029268265,
-0.003853704547509551,
-0.01803615503013134,
0.025128880515694618,
0.024607103317975998,
-0.00682493532076478,
0.03459114208817482,
0.028929200023412704,
-0.039095062762498856,
0.037710096687078476,
0.015173389576375484,
0.0072141229175031185,
0.044711172580718994,
0.000661994970869273,
0.040437810122966766,
0.00959162786602974,
-0.003988310694694519,
-0.011976819485425949,
-0.03560728579759598,
-0.021261043846607208,
-0.03257010504603386,
-0.014487112872302532,
0.01122930459678173,
0.001002736040391028,
-0.032152239233255386,
-0.030912460759282112,
0.0458386167883873,
-0.031073305755853653,
-0.011033589951694012,
0.05943808704614639,
0.00483453506603837,
0.03191572427749634,
0.021746568381786346,
0.014185745269060135,
0.01975826546549797,
-0.0077931247651577,
0.013000118546187878,
0.05765299126505852,
0.03896148130297661,
0.00013233561185188591,
-0.011286378838121891,
0.039442021399736404,
-0.01615457609295845,
0.030372710898518562,
0.013702447526156902,
0.03636544942855835,
-0.05777966231107712,
-0.01072941068559885,
0.014182716608047485,
-0.013120414689183235,
-0.0022307191975414753,
0.021034497767686844,
-0.022968392819166183,
0.10476554930210114,
-0.02076735347509384,
0.015172535553574562,
-0.041954901069402695,
-0.006654561497271061,
0.007848978042602539,
0.028697216883301735,
-0.003799246158450842,
0.014654740691184998,
-0.003095838939771056,
-0.016939114779233932,
-0.016495678573846817,
0.01650426536798477,
0.020878681913018227,
-0.05039088800549507,
-0.011313042603433132,
-0.01589473895728588,
-0.012378973886370659,
0.03318121284246445,
-0.006026681046932936,
-0.024795589968562126,
-0.023157663643360138,
0.009289472363889217,
0.02083975449204445,
0.030307399109005928,
-0.04135629162192345,
0.006561154033988714,
-0.05722483620047569,
0.00972742773592472,
-0.020247723907232285,
-0.03372000902891159,
-0.02004961110651493,
0.023938190191984177,
-0.028447259217500687,
-0.01653410866856575
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.