question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
sequencelengths 1.02k
1.02k
|
|---|---|---|
<p>If two identical masses are somehow "released" into deep space (that is, they're subject to no other gravitation forces but their own, and are initially at rest to each other). What decides whether they collide or orbit each other? I'm imagining for example two 1 kg masses initially at rest, say 10 m apart. What happens next?</p> | 1,495 | [
-0.003791081253439188,
-0.03352634608745575,
-0.05357916280627251,
-0.017989585176110268,
0.0004724144528154284,
-0.008761737495660782,
-0.019177118316292763,
-0.011016249656677246,
0.03881596401333809,
-0.035400111228227615,
0.004593444522470236,
0.03782931715250015,
0.036369699984788895,
-0.00756047060713172,
0.02089131809771061,
0.006407053675502539,
-0.011629709973931313,
-0.023057257756590843,
0.008055122569203377,
-0.024783793836832047,
0.003038850612938404,
-0.004331083502620459,
0.04905019327998161,
0.008234546519815922,
-0.050030771642923355,
0.0176046434789896,
0.027820127084851265,
-0.04755169898271561,
0.02492552250623703,
0.047739967703819275,
-0.019908186048269272,
-0.02926049567759037,
-0.006666271947324276,
0.04507738724350929,
-0.007990810088813305,
0.005458480678498745,
-0.03946346044540405,
-0.032074786722660065,
-0.0205422043800354,
0.011948742903769016,
-0.08212994039058685,
-0.06061490625143051,
-0.04717717319726944,
0.037581540644168854,
-0.03224930167198181,
-0.01814376562833786,
0.021925773471593857,
-0.002948538400232792,
0.06887484341859818,
-0.048024073243141174,
0.04482860490679741,
0.018985193222761154,
0.04616926982998848,
0.03856043517589569,
0.006894586607813835,
-0.006924005690962076,
0.03379683196544647,
0.06331970542669296,
0.002698608674108982,
-0.02972329966723919,
-0.059233684092760086,
0.002748593920841813,
-0.01584363728761673,
-0.022859999909996986,
-0.03556611388921738,
0.06237286329269409,
-0.030158884823322296,
0.003612381871789694,
0.021273482590913773,
0.03670714423060417,
0.024420825764536858,
0.03322948142886162,
0.041553448885679245,
-0.031718187034130096,
0.018885375931859016,
-0.007133261766284704,
0.03262094408273697,
-0.004770745523273945,
0.03620533645153046,
0.022925101220607758,
-0.04992010071873665,
-0.005789386108517647,
0.03779465705156326,
0.033245254307985306,
0.0055616553872823715,
0.0012644657399505377,
0.04088389500975609,
0.0011559491977095604,
-0.003968013916164637,
0.04406038299202919,
-0.007027416490018368,
0.024532757699489594,
0.025036482140421867,
-0.016278259456157684,
-0.0025771865621209145,
0.033215489238500595,
0.009820804931223392,
0.07058846205472946,
-0.013108838349580765,
-0.03747296333312988,
0.026524333283305168,
-0.0002030205650953576,
0.010289414785802364,
0.06940951198339462,
0.023053564131259918,
-0.038758352398872375,
-0.04760492965579033,
0.043444979935884476,
-0.04057132080197334,
-0.03099432773888111,
-0.013028363697230816,
0.005555958021432161,
-0.004846277181059122,
-0.012125708162784576,
0.06968578696250916,
-0.017552021890878677,
0.0062194750644266605,
-0.01664021983742714,
0.04846649989485741,
0.029485506936907768,
0.07362964749336243,
-0.02270536497235298,
0.03545650094747543,
-0.04055527597665787,
-0.016413869336247444,
0.001207094406709075,
0.054637424647808075,
-0.002354678465053439,
-0.011959684081375599,
0.011707346886396408,
-0.021282460540533066,
-0.026292217895388603,
-0.03421293571591377,
-0.02961304597556591,
0.034912243485450745,
-0.01367286965250969,
-0.07531808316707611,
-0.04826796054840088,
0.04162123426795006,
-0.019100897014141083,
-0.017653973773121834,
-0.06780634075403214,
0.012431701645255089,
0.03302842006087303,
0.060777697712183,
0.0006459591677412391,
-0.026945581659674644,
0.0015897254925221205,
0.056748662143945694,
0.017216606065630913,
-0.011637826450169086,
-0.030288033187389374,
-0.023957213386893272,
-0.037112534046173096,
0.007370714098215103,
-0.06769003719091415,
-0.014503750018775463,
0.02440270595252514,
0.00419978704303503,
-0.037206947803497314,
0.025259435176849365,
-0.04640159010887146,
0.018818970769643784,
0.006402696017175913,
0.029895631596446037,
-0.030339635908603668,
0.07479779422283173,
0.016844457015395164,
-0.016217119991779327,
0.07035347819328308,
0.06297008693218231,
0.03248470276594162,
0.03501802310347557,
0.055699482560157776,
0.014858989045023918,
-0.02830115333199501,
0.005738648120313883,
-0.019162790849804878,
-0.01130373403429985,
-0.03904275968670845,
-0.0038702834863215685,
-0.055838316679000854,
-0.015240675769746304,
-0.020978184416890144,
-0.006136102601885796,
0.027638647705316544,
-0.022906528785824776,
-0.002232654020190239,
-0.017306454479694366,
-0.008327527903020382,
-0.02392655983567238,
-0.061929404735565186,
0.02875501476228237,
0.0049351416528224945,
0.003044284414499998,
0.03411327674984932,
0.03415559232234955,
0.04051314294338226,
-0.015022235922515392,
-0.027508795261383057,
-0.017246142029762268,
0.028771596029400826,
-0.02751859277486801,
0.00792583916336298,
-0.0022464378271251917,
0.039077769964933395,
0.03582896292209625,
0.013645147904753685,
0.01190404687076807,
0.006274475250393152,
-0.054406825453042984,
0.003859810996800661,
0.01700727641582489,
0.0022427525836974382,
-0.02260666713118553,
0.030376357957720757,
0.02138517051935196,
-0.0412861630320549,
0.014039382338523865,
0.028801990672945976,
-0.018735093995928764,
0.11109334975481033,
0.016746092587709427,
0.026972731575369835,
0.0030643825884908438,
0.03331383690237999,
0.045335572212934494,
-0.001495121163316071,
-0.01585116796195507,
-0.05159063637256622,
-0.03585037589073181,
-0.01679890602827072,
-0.0044363560155034065,
0.04265787452459335,
-0.005198488011956215,
0.0258766021579504,
0.03096308931708336,
0.06025533750653267,
0.027854399755597115,
0.009076441638171673,
-0.04255066066980362,
-0.011040924116969109,
0.01852043718099594,
0.01370725966989994,
0.008197100833058357,
-0.010185282677412033,
0.028440069407224655,
0.052742850035429,
-0.02332353964447975,
0.003418698674067855,
-0.04701636731624603,
0.026397719979286194,
-0.010319904424250126,
0.010292168706655502,
-0.024198541417717934,
-0.055004462599754333,
0.04141511395573616,
-0.00399848772212863,
0.015319479629397392,
0.03658169507980347,
0.008709797635674477,
-0.028014859184622765,
-0.046650081872940063,
0.017400497570633888,
0.002710422035306692,
0.009534388780593872,
-0.011112459935247898,
-0.009985169395804405,
0.018547575920820236,
-0.0561232753098011,
0.03972743824124336,
0.00761713832616806,
-0.01644742488861084,
-0.019209839403629303,
0.017977366223931313,
0.0011739764595404267,
0.009895683266222477,
0.021638276055455208,
-0.027605922892689705,
-0.05911635234951973,
-0.029187655076384544,
-0.03832444176077843,
-0.014653741382062435,
0.03816041350364685,
-0.06352026015520096,
0.050790879875421524,
-0.018208744004368782,
-0.05967823415994644,
0.08042865991592407,
-0.0014344932278618217,
0.0417390838265419,
0.041233789175748825,
-0.015719590708613396,
-0.04671654850244522,
-0.03452472761273384,
-0.025746092200279236,
-0.02366136573255062,
-0.02341468073427677,
0.04954060539603233,
0.0775560513138771,
-0.011193902231752872,
-0.0505240373313427,
0.02030491642653942,
-0.061979785561561584,
-0.036071863025426865,
-0.015693845227360725,
0.00953314732760191,
0.009625129401683807,
-0.04693989455699921,
0.025773612782359123,
-0.007465756498277187,
-0.01954018883407116,
-0.004270358011126518,
-0.04996952787041664,
-0.037323955446481705,
0.025071006268262863,
-0.01896226964890957,
0.015797749161720276,
-0.012099034152925014,
-0.04220910370349884,
0.07758647203445435,
0.007012493908405304,
0.030893076211214066,
-0.006467059254646301,
0.0006815872038714588,
0.009302791208028793,
0.006092039402574301,
0.03270008787512779,
-0.01640171743929386,
0.010097808204591274,
-0.011075933463871479,
0.07391846925020218,
0.00222968403249979,
0.020624980330467224,
-0.021126724779605865,
-0.006199537310749292,
0.010748004540801048,
0.033093955367803574,
-0.003577485214918852,
0.0034681919496506453,
0.01247799675911665,
-0.0218393225222826,
0.00795771460980177,
0.020062148571014404,
0.030351797118782997,
0.007160603068768978,
-0.05106234923005104,
0.039239730685949326,
0.009335851296782494,
0.01486173179000616,
0.011892258189618587,
0.02651451714336872,
-0.016488999128341675,
-0.004951030481606722,
0.022836992517113686,
0.005320763681083918,
0.07612217217683792,
-0.016773877665400505,
-0.029902752488851547,
0.023931680247187614,
0.04636041820049286,
-0.028857341036200523,
-0.02994484081864357,
0.0025744761805981398,
-0.009855798445641994,
0.029740482568740845,
-0.005648099351674318,
-0.0019170362502336502,
0.036820169538259506,
-0.007358691189438105,
0.030482051894068718,
-0.0042813438922166824,
-0.011410466395318508,
-0.008787783794105053,
-0.07856433838605881,
-0.020707562565803528,
0.022420620545744896,
0.0250028558075428,
-0.006420515011996031,
0.06818946450948715,
0.03223922848701477,
0.0118333138525486,
0.02181202918291092,
0.010309162549674511,
-0.08666541427373886,
0.029621152207255363,
-0.05835442990064621,
-0.046398814767599106,
0.028631458058953285,
-0.014177216216921806,
-0.03570473939180374,
-0.011853926815092564,
-0.0042811548337340355,
-0.030750690028071404,
-0.0009317639633081853,
-0.07226331532001495,
-0.015117054805159569,
-0.06069754436612129,
-0.04465524107217789,
-0.01029578223824501,
0.026288531720638275,
0.0015791348414495587,
-0.0011999874841421843,
0.04202721640467644,
0.02517608366906643,
-0.03133596107363701,
-0.013256591744720936,
-0.03541688993573189,
0.0016283803852275014,
-0.01290388498455286,
0.02007213607430458,
0.0333264023065567,
0.02367583103477955,
-0.013602091930806637,
-0.002031766576692462,
0.017269771546125412,
0.04331135377287865,
-0.011068540625274181,
-0.0025899081956595182,
-0.003307867795228958,
-0.05401681363582611,
-0.01292656920850277,
0.0032895226031541824,
0.023498542606830597,
-0.01737617515027523,
0.011507809162139893,
0.03078460320830345,
0.004988564644008875,
0.03479520604014397,
0.06150570139288902,
0.055366095155477524,
0.032658886164426804,
-0.027304284274578094,
0.002799299778416753,
-0.015609439462423325,
-0.027648836374282837,
0.00505524966865778,
0.043194063007831573,
-0.014466864056885242,
-0.028644604608416557,
0.012138407677412033,
0.0008868534350767732,
0.0407964326441288,
-0.030027760192751884,
-0.019765831530094147,
-0.01487105991691351,
0.04091706499457359,
-0.042194802314043045,
-0.01608036458492279,
-0.00852507445961237,
0.021836865693330765,
0.052629321813583374,
-0.0015779088716953993,
0.022951778024435043,
-0.07310129702091217,
-0.006334621459245682,
0.03498486429452896,
0.00025764419115148485,
-0.02440410852432251,
-0.031459081918001175,
-0.049846287816762924,
-0.018663236871361732,
0.02979467622935772,
-0.044949304312467575,
-0.0024743457324802876,
0.019064122810959816,
0.03209976106882095,
0.02226286567747593,
0.008616660721600056,
-0.0019241055706515908,
0.06205187365412712,
0.02137918956577778,
0.004097518976777792,
0.004468416329473257,
-0.008308018557727337,
0.008569486439228058,
0.0479469820857048,
0.049499932676553726,
0.03663138672709465,
0.011887850239872932,
-0.0026615094393491745,
-0.022184887900948524,
0.009970657527446747,
-0.016094500198960304,
-0.05690779909491539,
-0.014171043410897255,
-0.01080036349594593,
-0.03380358964204788,
0.05710143595933914,
-0.04330166429281235,
-0.0623946376144886,
0.014447370544075966,
0.0011210337979719043,
0.01788575015962124,
0.012439828366041183,
0.002461155643686652,
0.027521975338459015,
0.04559079557657242,
-0.006964479573071003,
0.0276186540722847,
-0.0028181339148432016,
-0.018798133358359337,
-0.03383288159966469,
-0.005051298998296261,
0.06156039983034134,
-0.04897637292742729,
-0.0025696197990328074,
-0.012380402535200119,
0.012462666258215904,
-0.05122361332178116,
0.04479147493839264,
-0.0207744762301445,
0.0026155796367675066,
0.01661822758615017,
-0.05401413142681122,
0.0051515656523406506,
0.05664489418268204,
0.02166685461997986,
0.027934303507208824,
0.024775121361017227,
0.01874365471303463,
-0.03364875540137291,
-0.018059812486171722,
0.028122609481215477,
0.0072637442499399185,
0.007566860411316156,
-0.013496523723006248,
-0.05546979606151581,
0.02620188146829605,
-0.013943275436758995,
-0.01672735996544361,
0.030291439965367317,
-0.04495096206665039,
0.07078991830348969,
-0.0069267284125089645,
-0.0009070329833775759,
0.0453471913933754,
-0.06127481162548065,
-0.025599461048841476,
-0.00521517638117075,
0.002535468665882945,
0.05001531168818474,
-0.04949980601668358,
0.030247144401073456,
0.018450265750288963,
0.0022537868935614824,
-0.07134945690631866,
-0.025938788428902626,
0.022614262998104095,
0.008274196647107601,
0.014744176529347897,
-0.047014281153678894,
0.035684555768966675,
-0.036772534251213074,
-0.010487619787454605,
-0.03584955260157585,
0.07539074867963791,
-0.023844540119171143,
0.008535942062735558,
0.0050376541912555695,
-0.006258278153836727,
0.03420887514948845,
0.02380838245153427,
-0.01342784147709608,
-0.015783775597810745,
-0.011699053458869457,
0.012694335542619228,
0.011295046657323837,
0.0737905502319336,
-0.02244197577238083,
-0.07223052531480789,
-0.042573653161525726,
-0.043169815093278885,
0.03848213702440262,
-0.05701290816068649,
0.02794107422232628,
0.04400455951690674,
0.005950749386101961,
0.038951385766267776,
0.012623331509530544,
0.03156028687953949,
-0.029852278530597687,
0.03289205953478813,
0.015248151496052742,
-0.035730939358472824,
0.02412598207592964,
-0.062006011605262756,
0.043677739799022675,
-0.012343142181634903,
0.011269810609519482,
-0.0019460829207673669,
0.04722107946872711,
0.032291293144226074,
-0.023541640490293503,
-0.007731236983090639,
0.033328235149383545,
0.026522362604737282,
-0.06180436164140701,
-0.01209294144064188,
0.04746965691447258,
0.007725478615611792,
-0.028189651668071747,
-0.030336642637848854,
-0.03892612084746361,
-0.0008765782113187015,
0.08666694909334183,
-0.07125668972730637,
0.06428224593400955,
0.029932944104075432,
0.0029002740047872066,
-0.0030469221528619528,
-0.03114176169037819,
0.021671965718269348,
0.006151064299046993,
0.009202160872519016,
-0.00021897722035646439,
-0.0117871118709445,
-0.0032086786814033985,
0.03634564206004143,
0.062252357602119446,
0.012736361473798752,
0.008026344701647758,
0.01865360513329506,
0.015973586589097977,
0.03191673010587692,
0.004127098247408867,
-0.024037377908825874,
0.011332029476761818,
-0.0389806367456913,
-0.0025525123346596956,
-0.0024041763972491026,
0.007147339638322592,
0.018006030470132828,
0.030774885788559914,
-0.0032487043645232916,
-0.029245132580399513,
-0.04684053361415863,
-0.03463027998805046,
0.04730158671736717,
0.046204064041376114,
0.006836512126028538,
0.007588136475533247,
0.03891189023852348,
0.005717704072594643,
0.022691912949085236,
-0.004814955871552229,
-0.015623845160007477,
-0.07023042440414429,
-0.0303818192332983,
-0.02135341800749302,
-0.046279944479465485,
0.04122886434197426,
0.015244171023368835,
-0.018653126433491707,
0.012188124470412731,
-0.020656654611229897,
0.013441167771816254,
0.0325394831597805,
0.0009460761793889105,
-0.01623169705271721,
0.08795057982206345,
-0.003912832122296095,
0.005278530530631542,
-0.04135731980204582,
0.01550440862774849,
0.09022850543260574,
0.008351035416126251,
0.03239845857024193,
-0.05394744500517845,
0.006419149227440357,
0.016044046729803085,
-0.009876229800283909,
-0.02757260762155056,
0.0276817437261343,
0.04639901593327522,
0.019557978957891464,
0.024871541187167168,
0.032825715839862823,
-0.011234479025006294,
-0.04507880285382271,
0.05877622216939926,
-0.015107987448573112,
-0.03378983959555626,
-0.04580480605363846,
0.009207839146256447,
0.012604857794940472,
0.007446486037224531,
-0.03180338814854622,
0.029529308900237083,
-0.021656205877661705,
0.028918055817484856,
-0.06386896967887878,
-0.021892890334129333,
0.02527635730803013,
0.00919532310217619,
-0.05292074754834175,
0.021095460280776024,
0.0024638038594275713,
-0.04852336272597313,
-0.032217010855674744,
0.055252451449632645,
0.01011042669415474,
-0.018228888511657715,
0.0201924629509449,
-0.005667520686984062,
-0.006449589040130377,
0.014075755141675472,
-0.0017560541164129972,
-0.012846145778894424,
-0.030463431030511856,
0.0027103591710329056,
-0.009018361568450928,
0.07915806770324707,
-0.03928158059716225,
-0.026425456628203392,
0.014010697603225708,
0.010731106624007225,
0.003103586845099926,
-0.020402610301971436,
-0.022311044856905937,
-0.03755345568060875,
0.011252106167376041,
0.003989936783909798,
0.006190781947225332,
-0.008296108804643154,
0.03519304096698761,
-0.006624139845371246,
0.044427089393138885,
-0.024761123582720757,
0.009907403029501438,
0.02210957184433937,
-0.047112010419368744,
0.04936771094799042,
-0.01415218785405159,
-0.0022801326122134924,
-0.04489722475409508,
-0.009145361371338367,
-0.038655348122119904,
-0.014059756882488728,
-0.001628764788620174,
0.0603829063475132,
-0.0018465149914845824,
0.016143271699547768,
-0.009930017404258251,
-0.02179773338139057,
-0.025462644174695015,
0.034183893352746964,
-0.017888875678181648,
-0.01946287415921688,
-0.02799232117831707,
-0.009055783040821552,
0.019793692976236343,
0.028837239369750023,
-0.024923522025346756,
0.001651077182032168,
-0.01689884252846241,
0.03446879982948303,
-0.018898747861385345,
-0.018846610561013222,
0.011986962519586086,
0.007093702908605337,
-0.01397072896361351,
-0.006754942703992128,
-0.023836463689804077,
0.0151047483086586,
0.026672549545764923,
-0.025087883695960045,
0.007675778120756149,
0.022728469222784042,
-0.010661687701940536,
0.03674697503447533,
0.026323234662413597,
-0.03527817130088806,
-0.012565048411488533,
0.006706655491143465,
0.010133280418813229,
-0.019313162192702293,
-0.008693279698491096,
-0.016080455854535103,
-0.036734554916620255,
-0.015945246443152428,
0.031371910125017166,
-0.024622667580842972,
0.06104651838541031,
-0.006930338218808174,
0.031560614705085754,
-0.04319118335843086,
0.0035422644577920437,
-0.05175958573818207,
0.014872652478516102,
0.020031047984957695,
-0.008268286474049091,
-0.038210172206163406,
0.015367705374956131,
-0.010625742375850677,
-0.04576374217867851,
0.0037723251152783632,
-0.02330132946372032,
-0.0016174757620319724,
0.016054905951023102,
0.029031796380877495,
-0.03909383341670036,
0.04929735139012337,
0.01765715330839157,
-0.008372130803763866,
0.011066744104027748,
-0.015232544392347336,
-0.05006364732980728,
0.04931386932730675,
-0.021065041422843933,
0.036513835191726685,
0.040929097682237625,
-0.05710431933403015,
-0.03517910838127136,
0.09516593813896179,
-0.016613593325018883,
-0.022410359233617783,
0.02118067629635334,
-0.013722244650125504,
-0.05683373659849167,
0.032275836914777756,
0.01371755450963974,
-0.04950316995382309,
-0.011759337969124317,
0.00434570387005806,
0.03164028748869896,
-0.029660921543836594,
-0.008990269154310226,
-0.02213350124657154,
0.015415363013744354,
0.004249172750860453,
-0.000718176830559969,
0.000622809398919344,
0.01583550125360489,
0.06876686215400696,
-0.03453095257282257,
0.01271825935691595,
0.04365209490060806,
0.0029599315021187067,
-0.08078987896442413,
-0.02534698136150837,
0.007325663696974516,
-0.0072688874788582325,
0.021742111071944237,
-0.03613177686929703,
0.0025896732695400715,
0.02155347727239132,
-0.04299987107515335,
0.0030893769580870867,
-0.05476346239447594,
-0.01857408881187439,
-0.011693139560520649,
-0.012194114737212658,
0.012361614033579826,
0.07701872289180756,
0.024401050060987473,
0.0032260739244520664,
-0.009151041507720947,
-0.011079450137913227,
-0.024468692019581795,
0.013095591217279434,
-0.014245931059122086,
-0.018574971705675125,
-0.01525217667222023,
0.026804853230714798,
0.04504229873418808,
-0.012955506332218647,
-0.033101245760917664,
0.04577602446079254,
-0.012095354497432709,
-0.015215815044939518,
-0.007073527202010155,
-0.009077101945877075,
-0.0008545873570255935,
-0.00508784269914031,
-0.02190946415066719,
0.002731428248807788,
-0.0011983690783381462,
0.03516117110848427,
0.009970593266189098,
-0.011382415890693665,
-0.010092169977724552,
0.0091004129499197,
0.028819991275668144,
-0.03766392916440964,
-0.02021738514304161,
0.006135548464953899,
-0.009011597372591496,
0.004553833045065403,
-0.01113118976354599,
0.011601265519857407,
0.006924378219991922,
-0.01639917865395546,
-0.018929410725831985,
-0.04257065802812576,
0.011016436852514744,
0.02308477833867073,
0.014463978819549084,
0.002019003266468644,
0.030005279928445816,
-0.014208465814590454,
0.004919890314340591,
-0.015622851438820362,
0.020934278145432472,
-0.00927054975181818,
-0.047726839780807495,
-0.023407647386193275,
-0.022648874670267105,
0.004936258774250746,
0.005266469903290272,
-0.08376150578260422,
-0.021463394165039062,
0.07658933848142624,
-0.006850694306194782,
0.020850233733654022,
-0.026680583134293556,
-0.06739742308855057,
-0.0008113306830637157,
-0.03500894829630852,
-0.0008163208840414882,
-0.016081565991044044,
-0.001868138904683292,
-0.04982098191976547,
-0.015351172536611557,
-0.024065272882580757,
-0.021339749917387962,
0.012823348864912987,
0.02804482728242874,
0.008918875828385353,
0.039310336112976074,
0.0015078982105478644,
-0.011255430988967419,
-0.015493707731366158,
-0.017693882808089256,
-0.016750572249293327,
-0.019472820684313774,
0.009401720948517323,
-0.019863687455654144,
0.005458950996398926,
0.017156219109892845,
-0.0002971198409795761,
-0.015979377552866936,
0.02020605094730854,
0.015285006724298,
-0.020770741626620293,
0.06484103947877884,
0.012382004410028458,
0.04271427169442177,
0.06710471957921982,
-0.019703177735209465,
0.03473672270774841,
0.022107278928160667,
-0.024140331894159317,
-0.028623228892683983,
0.036513615399599075,
-0.041395723819732666,
0.020197629928588867,
-0.02619958110153675,
0.016766708344221115,
-0.020987343043088913,
-0.03533140569925308,
0.005087923724204302,
0.013155480846762657,
-0.009266670793294907,
-0.0046573542058467865,
0.025913426652550697,
0.010427668690681458,
0.04550134018063545,
0.003780719358474016,
0.015461494214832783,
0.012081201188266277,
-0.0023977700620889664,
0.0031246126163750887,
0.005304854828864336,
0.03727234899997711,
0.019198618829250336,
0.004708901047706604,
0.011801362968981266,
0.016070805490016937,
0.011208080686628819,
0.005570529960095882,
0.049391020089387894,
-0.007496775593608618,
-0.0347234345972538,
-0.002811393002048135,
-0.021803012117743492,
0.0071791126392781734,
-0.007788015995174646,
-0.000598305428866297,
0.07445301860570908,
-0.043387215584516525,
0.01385662890970707,
0.003414840903133154,
-0.006182133220136166,
0.017126239836215973,
0.025383235886693,
-0.01342077273875475,
0.03262244537472725,
-0.013839533552527428,
-0.007966681383550167,
-0.03422112762928009,
-0.007980636321008205,
0.024969613179564476,
0.02054610848426819,
0.012607287615537643,
0.026734821498394012,
0.0004427667590789497,
-0.0021618816535919905,
-0.005931362509727478,
-0.03713458776473999,
-0.05203317478299141,
0.05219276249408722,
0.0515117272734642,
0.02648787945508957,
-0.022520579397678375,
0.005098673049360514,
-0.02247253991663456,
0.026157010346651077,
-0.037200428545475006,
-0.05334635451436043,
-0.020581718534231186,
0.04218555986881256,
-0.008998171426355839,
0.025427792221307755
] |
<p>we vistited yesterday a fun park and saw a ride which was a big centrifuge only in vertical.
this one had a speed meter but it was broken and i also wanted to know how much g-force is on there...</p>
<p>so my first thought was to calculate this with the centrifugal-accerleration. I have $\omega = \frac {0.5*2\pi} 1 [\frac {rad} s]$ and $r= 25[m]$, so the accerleration is $a_z = \omega^2r = \pi^2*25 = ~246$</p>
<p>then i can calculate the g force with $g_{force} = \frac {a_z} g$ which gives me about $24g$ that seems fairly too high! </p>
<p>what am i missing?</p> | 1,496 | [
-0.028978273272514343,
-0.02178516797721386,
-0.033092714846134186,
0.004656763281673193,
0.0812862291932106,
-0.03964453563094139,
-0.02793746627867222,
-0.02169962041079998,
-0.011345078237354755,
-0.004277155734598637,
0.025912368670105934,
0.06075714901089668,
0.047187451273202896,
0.04341878369450569,
0.04657773673534393,
-0.029440991580486298,
-0.004855529870837927,
-0.008197654969990253,
0.03924822807312012,
-0.015664968639612198,
-0.039328500628471375,
0.003836297430098057,
0.012026624754071236,
-0.04065670445561409,
-0.005642302799969912,
-0.015942031517624855,
0.06662184745073318,
-0.015312540344893932,
-0.040807437151670456,
0.016056664288043976,
-0.020101670175790787,
0.0010936931939795613,
0.0209281574934721,
0.03392258286476135,
0.017803287133574486,
0.010027177631855011,
-0.05435441806912422,
-0.0038177589885890484,
0.007139332126826048,
0.053843799978494644,
-0.04071219637989998,
-0.03179483115673065,
-0.006621816195547581,
0.05682636424899101,
-0.007052114233374596,
0.026448624208569527,
-0.023057466372847557,
0.016034644097089767,
0.0803946927189827,
-0.04789144918322563,
0.04510580748319626,
0.013021625578403473,
0.022842343896627426,
-0.001905148266814649,
-0.00823977217078209,
-0.014126753434538841,
0.06428791582584381,
0.03808245435357094,
0.00518773403018713,
-0.01681896299123764,
0.001778156729415059,
-0.0306262020021677,
-0.051126208156347275,
-0.030408380553126335,
0.029423372820019722,
0.010846028104424477,
-0.04686306416988373,
-0.021722083911299706,
0.040333282202482224,
-0.010094630531966686,
0.017427116632461548,
0.018826350569725037,
0.02485898695886135,
-0.02789219096302986,
-0.006253382656723261,
-0.023723572492599487,
0.006733562797307968,
0.022851482033729553,
0.017543459311127663,
0.0245071928948164,
-0.02925742231309414,
0.006354297511279583,
0.03629985824227333,
0.04920123144984245,
0.010478810407221317,
-0.0490846112370491,
0.048759397119283676,
0.0130009725689888,
-0.021508829668164253,
-0.0073404801078140736,
-0.019849998876452446,
-0.006947031244635582,
-0.0036737972404807806,
-0.017144234851002693,
-0.02611817978322506,
0.014824400655925274,
-0.015075934119522572,
0.061752382665872574,
0.0043061599135398865,
-0.0031473052222281694,
-0.0072420137003064156,
-0.013374794274568558,
0.0014488823944702744,
0.09478266537189484,
-0.014263255521655083,
0.0017118125688284636,
-0.019264167174696922,
-0.013235259801149368,
-0.007926874794065952,
-0.026718318462371826,
-0.07479701936244965,
0.015123304910957813,
-0.01170979905873537,
-0.05457308515906334,
-0.0038807280361652374,
0.02097477950155735,
-0.01742376573383808,
-0.015243708156049252,
0.06322209537029266,
0.04384654015302658,
0.058467619121074677,
-0.03018193691968918,
-0.027434440329670906,
-0.03210253268480301,
-0.03489592671394348,
-0.0018381393747404218,
0.04625854641199112,
-0.014230532571673393,
-0.05054748058319092,
0.029346665367484093,
0.022589493542909622,
-0.01923881657421589,
-0.024404125288128853,
-0.006687479093670845,
0.008464731276035309,
-0.012814893387258053,
-0.09320347011089325,
-0.06610888987779617,
0.0745706558227539,
-0.02679174393415451,
0.0010747706983238459,
-0.11577606946229935,
-0.0027652368880808353,
0.002367923269048333,
0.05338414013385773,
0.025159569457173347,
0.003998874220997095,
-0.01452830620110035,
0.04266165569424629,
0.005321001634001732,
-0.010002965107560158,
-0.009121150709688663,
0.0013214180944487453,
-0.020660610869526863,
-0.022112170234322548,
-0.04315841943025589,
0.027698561549186707,
0.01947912387549877,
0.0053239320404827595,
-0.013868516311049461,
0.029070625081658363,
0.000042544546886347234,
0.012910803779959679,
0.02291705459356308,
0.008915882557630539,
-0.03423752635717392,
0.04987557977437973,
-0.0018251299625262618,
0.004455715883523226,
0.04662134870886803,
-0.014212577603757381,
0.011254943907260895,
0.02277798019349575,
-0.043861184269189835,
0.09161600470542908,
-0.01914145052433014,
0.004579091444611549,
-0.03827080875635147,
0.029066065326333046,
0.005299726966768503,
-0.03100692853331566,
-0.05538706108927727,
-0.016838444396853447,
0.036829136312007904,
0.03014553152024746,
0.03422541916370392,
0.004509965423494577,
-0.018462130799889565,
0.03453126922249794,
-0.041888024657964706,
0.023641351610422134,
-0.03806142881512642,
0.03331906348466873,
-0.00954625103622675,
0.008580179885029793,
-0.01860613003373146,
0.023732688277959824,
0.029947560280561447,
-0.01453704945743084,
-0.009464932605624199,
0.0253149401396513,
0.01693875528872013,
-0.010993670672178268,
-0.008057600818574429,
0.004268985707312822,
-0.006822946947067976,
0.025278721004724503,
0.006002706475555897,
0.04054689034819603,
0.005907050333917141,
-0.015905553475022316,
-0.03006744384765625,
-0.01809937320649624,
0.01245060283690691,
-0.028074927628040314,
-0.004532682243734598,
0.030726494267582893,
-0.0052912537939846516,
0.0017364067025482655,
0.04023418575525284,
-0.024729900062084198,
0.07351157069206238,
0.06279245018959045,
0.0047543845139443874,
0.052298665046691895,
0.037135567516088486,
-0.005994003266096115,
0.019582560285925865,
0.009188327006995678,
-0.0054609812796115875,
-0.0749230906367302,
-0.024720437824726105,
0.05082210525870323,
0.023257087916135788,
-0.034085962921381,
0.010819532908499241,
0.06610094010829926,
0.01958272233605385,
0.006320414133369923,
0.008504562079906464,
0.004409159068018198,
-0.07083822786808014,
0.02933185175061226,
0.07477172464132309,
-0.017628418281674385,
-0.02368941344320774,
-0.00862192828208208,
0.048108432441949844,
-0.014721314422786236,
0.0011660560267046094,
0.021418776363134384,
0.01558021828532219,
-0.019951751455664635,
0.02234489656984806,
0.02219489961862564,
-0.006922219414263964,
0.049417395144701004,
-0.009929999709129333,
0.0237802192568779,
0.03964086249470711,
-0.012051892466843128,
0.01570785790681839,
-0.006997930351644754,
-0.019183186814188957,
0.027179153636097908,
0.0027174947317689657,
-0.023631568998098373,
-0.03736245632171631,
0.02586098201572895,
-0.03407185152173042,
0.004099223297089338,
-0.011838396079838276,
-0.020134398713707924,
-0.015125560574233532,
-0.012467757798731327,
0.008823500946164131,
-0.015112130902707577,
0.032123930752277374,
-0.02052287943661213,
0.002869050018489361,
0.015858571976423264,
-0.005801288411021233,
0.008808296173810959,
0.022324346005916595,
-0.039734698832035065,
0.0220126174390316,
-0.020886320620775223,
-0.04913592338562012,
0.027221083641052246,
0.012792568653821945,
-0.029450999572873116,
-0.008287338539958,
0.005448363721370697,
-0.04770629107952118,
0.030384834855794907,
-0.004691998939961195,
-0.007237233687192202,
-0.04898954927921295,
-0.031565845012664795,
0.04499407485127449,
-0.010692575015127659,
-0.007843153551220894,
0.0103980777785182,
-0.054783131927251816,
-0.022361215204000473,
0.019392065703868866,
0.04115505516529083,
0.014580581337213516,
-0.045008283108472824,
-0.026696430519223213,
0.01598159223794937,
-0.025244394317269325,
0.0008532690699212253,
-0.0405210517346859,
-0.044787779450416565,
0.008681908249855042,
0.008302194997668266,
0.056220050901174545,
0.010761724784970284,
-0.02095838636159897,
0.0707864761352539,
0.013818050734698772,
-0.030003836378455162,
-0.0023538556415587664,
-0.004753893241286278,
0.011838987469673157,
-0.02814830094575882,
-0.02602388709783554,
0.03576446697115898,
0.003961481619626284,
0.02353973500430584,
0.03459586575627327,
-0.0017952399794012308,
0.02523236908018589,
-0.009328576736152172,
0.015629468485713005,
-0.00326702743768692,
0.02544371597468853,
0.037533748894929886,
0.05968805402517319,
0.0053565832786262035,
-0.040011513978242874,
0.0031976301688700914,
-0.01777839846909046,
0.020675409585237503,
-0.004932980984449387,
-0.06402753293514252,
0.06729365140199661,
0.020647887140512466,
0.007920611649751663,
0.01378589402884245,
-0.01207367517054081,
0.03154546022415161,
-0.03279491886496544,
0.0009297151118516922,
0.0293201245367527,
0.05013514310121536,
-0.01909741759300232,
-0.000616285135038197,
0.049640506505966187,
0.015706561505794525,
-0.05156160145998001,
-0.020105723291635513,
0.00017450902669224888,
0.0019437852315604687,
-0.009834337048232555,
-0.012688846327364445,
-0.02510436624288559,
0.027314839884638786,
0.02024761587381363,
0.013326562009751797,
0.0049866363406181335,
-0.03404805809259415,
0.024671129882335663,
-0.06884152442216873,
-0.035877350717782974,
-0.015344462357461452,
0.02420065365731716,
-0.00733668077737093,
0.03865206986665726,
0.01863316260278225,
0.004740049596875906,
0.021627122536301613,
-0.0023189601488411427,
-0.07548494637012482,
0.02862628921866417,
-0.07499419152736664,
0.011322722770273685,
0.012296236120164394,
-0.022967150434851646,
0.03457235172390938,
-0.039381299167871475,
0.005712432321161032,
-0.029289208352565765,
-0.010621696710586548,
-0.036692578345537186,
-0.0070672002620995045,
-0.001108482712879777,
-0.030580995604395866,
-0.01839206926524639,
0.03422148525714874,
-0.008009470999240875,
-0.03700369969010353,
0.0019160094670951366,
0.03500177711248398,
-0.0055214534513652325,
-0.007028935942798853,
0.01855091191828251,
-0.030575856566429138,
-0.018457967787981033,
0.0002982319856528193,
0.02464001253247261,
0.006605159025639296,
-0.01423220057040453,
-0.041417527943849564,
-0.010719059035182,
0.02734271064400673,
0.02889777347445488,
-0.014390205033123493,
-0.011511074379086494,
-0.06401203572750092,
-0.023913918063044548,
0.007562094833701849,
0.013948837295174599,
-0.005823878571391106,
0.004675563424825668,
0.02080664411187172,
-0.015799537301063538,
0.01463261991739273,
0.02402646839618683,
0.023567115887999535,
-0.003169413423165679,
0.0032645990140736103,
-0.0560808926820755,
-0.0038211271166801453,
-0.03456879034638405,
-0.0273074209690094,
0.014364514499902725,
0.028815889731049538,
-0.036716751754283905,
-0.004259754903614521,
0.05981704592704773,
0.020415155217051506,
-0.0166877880692482,
0.030765244737267494,
-0.0017719062743708491,
0.035413723438978195,
0.014758354984223843,
-0.007952772080898285,
-0.03504505753517151,
0.04449271783232689,
0.02535105124115944,
-0.024433784186840057,
-0.011506197042763233,
-0.06077396497130394,
-0.03620864823460579,
0.014249220490455627,
0.025253107771277428,
-0.019463788717985153,
-0.004498313646763563,
-0.06532686203718185,
-0.01911046914756298,
0.03673213720321655,
-0.02864942140877247,
0.03815244138240814,
-0.0035221162252128124,
0.036398280411958694,
-0.010662493295967579,
-0.019125113263726234,
-0.03789569064974785,
0.030087372288107872,
-0.006395427044481039,
-0.03185223788022995,
-0.06426387280225754,
0.0011161417933180928,
0.022606752812862396,
-0.0026960065588355064,
0.05415835604071617,
0.02100900001823902,
0.04786750301718712,
-0.009309744462370872,
-0.004670523572713137,
0.014263324439525604,
-0.03742993623018265,
-0.04205261543393135,
-0.03329829126596451,
-0.017070328816771507,
0.01653147116303444,
0.03657867759466171,
-0.04198707267642021,
-0.04981161653995514,
0.029685255140066147,
0.008393026888370514,
0.04161724075675011,
0.015702174976468086,
-0.07128570973873138,
0.030209247022867203,
0.05411313474178314,
0.03158446401357651,
0.029506420716643333,
0.0192538071423769,
0.000685522856656462,
0.02890249341726303,
0.012731018476188183,
-0.007864000275731087,
-0.03058929741382599,
-0.00756160169839859,
-0.008485154248774052,
0.019251994788646698,
-0.03909880295395851,
0.029333598911762238,
-0.007535458542406559,
0.044524241238832474,
-0.03651299327611923,
-0.051526930183172226,
0.0227854885160923,
0.015249660238623619,
0.017725281417369843,
-0.003476466052234173,
0.03142441809177399,
-0.0006695683696307242,
0.0211147703230381,
-0.03903523087501526,
-0.00769578805193305,
0.010695590637624264,
-0.003776920959353447,
0.009190409444272518,
-0.014613132923841476,
-0.023260556161403656,
-0.01719840243458748,
-0.02642631158232689,
0.003777621779590845,
-0.06407535821199417,
0.09517791867256165,
-0.05428626760840416,
0.0014170043868944049,
-0.021728968247771263,
-0.02484554797410965,
-0.037077758461236954,
0.00645452132448554,
0.00796524714678526,
0.011680510826408863,
-0.045004770159721375,
-0.023650117218494415,
0.0036881829146295786,
0.030201291665434837,
-0.023935360834002495,
-0.018339762464165688,
0.06127341091632843,
0.0011053566122427583,
-0.006959536578506231,
-0.05554657429456711,
0.01422236766666174,
-0.022971443831920624,
-0.060037657618522644,
-0.026724277064204216,
0.03097604028880596,
-0.018147574737668037,
0.007148073986172676,
-0.003051847219467163,
0.0076590185053646564,
0.04869583621621132,
-0.003426477313041687,
-0.015270897187292576,
0.02612796239554882,
0.01162703800946474,
-0.004357530735433102,
-0.004109395667910576,
0.043913934379816055,
-0.03878962621092796,
-0.0006296884384937584,
0.013181077316403389,
-0.004897014703601599,
0.02255326509475708,
-0.0051575624383986,
0.03385598212480545,
0.01921108178794384,
-0.015596127137541771,
-0.02441110834479332,
-0.018109021708369255,
0.03091614879667759,
-0.009231720119714737,
0.017993053421378136,
-0.04377704858779907,
-0.024413837119936943,
-0.030064795166254044,
0.005137759260833263,
0.03907482698559761,
0.03614859655499458,
-0.006468366365879774,
-0.0013791010715067387,
0.08889815211296082,
-0.016519343480467796,
-0.04760712757706642,
-0.016722138971090317,
-0.0205522570759058,
0.02402378059923649,
0.0028893614653497934,
-0.005046718288213015,
0.02366446889936924,
-0.013668417930603027,
0.012541302479803562,
-0.021221701055765152,
-0.036968305706977844,
-0.009606045670807362,
0.08630456775426865,
-0.006689349189400673,
0.04185217246413231,
-0.006983951665461063,
-0.01652003452181816,
-0.013472594320774078,
0.011020906269550323,
-0.00902771670371294,
0.02588515542447567,
0.01151047833263874,
0.030083242803812027,
-0.014029172249138355,
0.007170477882027626,
0.019907427951693535,
0.05701699107885361,
-0.017387470230460167,
-0.0036223349161446095,
0.06315359473228455,
0.018276439979672432,
-0.017070431262254715,
-0.024815507233142853,
-0.036138810217380524,
0.030809132382273674,
-0.006567622534930706,
0.109330914914608,
-0.028779860585927963,
0.0235263891518116,
0.060822706669569016,
0.01924790069460869,
0.004447293467819691,
-0.04627952724695206,
0.034773483872413635,
-0.029681280255317688,
-0.00827915221452713,
0.029820304363965988,
-0.01622105948626995,
0.0010336708510294557,
-0.004412887617945671,
0.049180783331394196,
0.006651405245065689,
0.02874922566115856,
-0.005070282146334648,
-0.0116198118776083,
0.04451336711645126,
-0.009989357553422451,
-0.07335425913333893,
0.04299233853816986,
0.024149879813194275,
-0.04713592305779457,
0.014125225134193897,
-0.0265002753585577,
0.02926834113895893,
0.011756635271012783,
0.019256798550486565,
-0.030608413740992546,
0.08772780001163483,
-0.043270185589790344,
0.008476927876472473,
0.005064138676971197,
0.003995382692664862,
0.1225249320268631,
0.04936325550079346,
0.014861339703202248,
0.0009113785927183926,
-0.015099238604307175,
-0.05594503507018089,
-0.000047164910938590765,
-0.03449268266558647,
0.019171787425875664,
-0.025704318657517433,
-0.018366677686572075,
0.01308523304760456,
0.06795370578765869,
-0.02073647826910019,
-0.0347566083073616,
0.024676786735653877,
-0.014696098864078522,
0.00744943181052804,
-0.010781511664390564,
0.01645054668188095,
-0.02802465483546257,
-0.027290821075439453,
-0.000654274073895067,
0.05039020627737045,
-0.03973748907446861,
-0.0015553649282082915,
-0.06855305284261703,
-0.008468360640108585,
-0.007515246514230967,
-0.006548262666910887,
-0.059725187718868256,
0.022130966186523438,
-0.031197672709822655,
-0.04234446957707405,
-0.07453019917011261,
-0.003913795109838247,
0.013930534943938255,
0.0035045661497861147,
0.023981807753443718,
0.04436817392706871,
-0.035970862954854965,
0.0368756540119648,
-0.0009042905294336379,
0.008321425877511501,
-0.04153160750865936,
0.005830602720379829,
-0.016971757635474205,
0.04392305761575699,
-0.01658935472369194,
0.027019169181585312,
0.004559413529932499,
0.015153331682085991,
-0.0006837237742729485,
-0.028926262632012367,
0.020712625235319138,
0.0061715892516076565,
0.007668185979127884,
-0.049923382699489594,
-0.018247412517666817,
-0.01554257981479168,
0.023551572114229202,
0.024053141474723816,
-0.0016698881518095732,
0.012794085778295994,
0.006384436506778002,
0.019196242094039917,
0.004205777775496244,
0.07103082537651062,
-0.01019089575856924,
-0.04889762029051781,
-0.0029057476203888655,
0.015247738920152187,
-0.034946318715810776,
0.040253646671772,
0.0076785762794315815,
0.015808170661330223,
0.04018869996070862,
0.007546094246208668,
-0.054903581738471985,
-0.061210211366415024,
-0.03562376648187637,
0.06078096479177475,
-0.013858076184988022,
-0.0483064129948616,
-0.014079502783715725,
-0.05589429289102554,
-0.02825920470058918,
0.04980705678462982,
-0.000794199004303664,
0.04546857252717018,
-0.0012058785650879145,
0.05640530586242676,
0.003334339475259185,
-0.020676294341683388,
0.00981768686324358,
0.014244530349969864,
-0.05579403042793274,
0.000028614624170586467,
-0.0002809736179187894,
0.036511845886707306,
0.04598158970475197,
0.0026085975114256144,
0.029648233205080032,
-0.004149333108216524,
-0.032466523349285126,
0.009905610233545303,
0.03346734121441841,
0.005004297476261854,
0.002914795419201255,
0.002311455551534891,
0.02373421937227249,
-0.05091719701886177,
-0.019065678119659424,
-0.0038345647044479847,
-0.0015663508092984557,
-0.01790486089885235,
0.007265246473252773,
0.01553256530314684,
-0.010491598397493362,
-0.026067327708005905,
0.006647591479122639,
-0.012785151600837708,
0.018959123641252518,
-0.04814722761511803,
0.021809721365571022,
0.008366882801055908,
-0.003407592885196209,
-0.06571891158819199,
0.04764070361852646,
-0.02990100160241127,
0.00009198372572427616,
0.017006289213895798,
0.01406580675393343,
-0.010100136511027813,
-0.02580823190510273,
0.011596034280955791,
-0.02379046380519867,
0.05191279575228691,
0.0007026339881122112,
-0.0017939661629498005,
0.0538017600774765,
-0.03562546148896217,
-0.05633711814880371,
0.044414956122636795,
0.007432456128299236,
0.014142933301627636,
0.013409631326794624,
-0.010501742362976074,
-0.00655505433678627,
0.020331522449851036,
-0.020922256633639336,
-0.009405224584043026,
-0.03128666803240776,
0.008413843810558319,
-0.008074796758592129,
-0.0023345069494098425,
0.03280895948410034,
-0.03132864832878113,
0.004637819714844227,
0.022277506068348885,
0.003678814508020878,
-0.03741687163710594,
0.041362788528203964,
0.004134170711040497,
-0.011494556441903114,
-0.035449571907520294,
0.025736112147569656,
0.00982614979147911,
0.034127213060855865,
0.05198404937982559,
-0.031524620950222015,
-0.023417145013809204,
-0.0035854522138834,
0.036698196083307266,
-0.0875348150730133,
-0.03713148832321167,
0.013239331543445587,
0.03303779289126396,
0.04422405734658241,
-0.06298774480819702,
0.006404653657227755,
0.01795109547674656,
-0.08271218091249466,
-0.02491094172000885,
-0.030836626887321472,
-0.014500747434794903,
-0.0498800128698349,
-0.026879625394940376,
0.012443001382052898,
-0.0005962026189081371,
-0.007225106470286846,
0.038966454565525055,
0.01969166100025177,
-0.003522205166518688,
-0.04240214452147484,
-0.044835641980171204,
0.024406660348176956,
0.04275146499276161,
-0.0007398542948067188,
-0.0007529412396252155,
0.06341065466403961,
-0.01246766746044159,
-0.029591530561447144,
-0.001250535948202014,
0.002894002478569746,
0.044997502118349075,
-0.02277015894651413,
0.00039511139038950205,
-0.011315842159092426,
0.06639183312654495,
0.03797817975282669,
-0.015632260590791702,
-0.03311322629451752,
0.024941110983490944,
0.006750991567969322,
0.057165224105119705,
-0.034962136298418045,
0.008458653464913368,
0.0403275229036808,
-0.004087630193680525,
-0.02665475197136402,
0.028303148224949837,
-0.030933136120438576,
0.012743228115141392,
0.01596684940159321,
-0.011719008907675743,
-0.01227609720081091,
-0.047216568142175674,
-0.009361574426293373,
-0.01884893700480461,
0.02511724829673767,
0.0287470705807209,
-0.040255554020404816,
-0.008471298031508923,
-0.011459254659712315,
0.01589333824813366,
-0.0010483874939382076,
-0.014815662056207657,
-0.03278869763016701,
-0.03922395408153534,
-0.015614883974194527,
-0.029107702895998955,
-0.019821245223283768,
0.0027656727470457554,
0.025516528636217117,
-0.01565357856452465,
0.011423993855714798,
0.037863411009311676,
0.03765980899333954,
0.00954124890267849,
0.011978263035416603,
-0.007135051768273115,
0.013268745504319668,
-0.0480559840798378,
0.006952257826924324,
0.026316871866583824,
-0.026940422132611275,
0.00747125456109643,
-0.006125129293650389,
0.008749982342123985,
-0.029836373403668404,
0.07149291038513184,
0.005023999605327845,
-0.01908666081726551,
0.044944845139980316,
0.03151442110538483,
0.014168542809784412,
-0.04448075219988823,
0.03095017746090889,
-0.010665412992238998,
-0.011457758955657482,
0.002311169635504484,
-0.008955124765634537,
-0.008803046308457851,
-0.012660343199968338,
0.04049132019281387,
0.009669341146945953,
0.03824387863278389,
-0.039034850895404816,
-0.01043786946684122,
0.07852645218372345,
0.01284227054566145,
0.012136504054069519,
0.06090159714221954,
-0.0032287740614265203,
0.024050455540418625,
0.029980206862092018,
-0.029804101213812828,
-0.07109536230564117,
0.052891965955495834,
-0.01937139965593815,
-0.007207788061350584,
-0.026229454204440117,
-0.025479314848780632,
-0.0052059972658753395,
-0.026721710339188576,
0.02599354274570942,
0.047042377293109894,
-0.03469689190387726,
-0.01572611555457115,
0.010952589102089405,
0.02144051156938076,
0.006538026966154575,
0.007059968542307615,
0.02369079738855362,
0.03438230976462364,
-0.04812861979007721,
-0.0008052613702602684,
0.055376917123794556,
0.017369654029607773,
-0.01138073019683361,
0.012731540016829967,
0.06689771264791489,
0.010834703221917152,
0.011910232715308666,
0.047388315200805664,
0.006729435175657272,
-0.013242365792393684,
-0.023515941575169563,
-0.039694659411907196,
-0.005898266099393368,
0.02461099997162819,
0.06216031685471535,
-0.01743626967072487,
0.07582010328769684,
-0.015072106383740902,
-0.031259018927812576,
-0.010888339951634407,
-0.030224675312638283,
-0.031369175761938095,
-0.002922635991126299,
0.0015245581744238734,
0.021905770525336266,
-0.00031270444742403924,
0.01754707098007202,
-0.0005250349058769643,
-0.012444926425814629,
0.01782577857375145,
0.012300081551074982,
0.028483150526881218,
0.022172939032316208,
0.019685888662934303,
0.01238847803324461,
-0.05872362107038498,
-0.0075440132059156895,
-0.06209934502840042,
0.05808209627866745,
0.00933723896741867,
0.008816046640276909,
-0.01725362241268158,
0.013306183740496635,
-0.03431393578648567,
0.07250241190195084,
-0.07278206199407578,
-0.017106154933571815,
-0.001047629746608436,
0.012112206779420376,
-0.002810993231832981,
-0.01747961714863777
] |
<p>Not having studied General Relativity, I have sometimes been puzzled by references to the behaviour for "classic" black holes — as they are popularly portrayed — as being true for black holes which are not rotating and which have no charge. I don't understand the role rotation <em>does</em> play, but at least because it has to do with the motion of massive bodies, I can understand why it <em>could</em> play an important role. But I have no such intuition for electrical charge.</p>
<p>How does <em>charge</em> change the behaviour of a black hole, aside from the obvious role of electrostatic force? (It will preferentially attract particles of the opposite charge, obviously.) But it would seem that charge plays a more intriguing role than just this.</p>
<p>The current status of the <a href="http://en.wikipedia.org/wiki/Black_hole#Singularity" rel="nofollow">Wikipedia page on black holes</a> claims that you can theoretically avoid the singularity of a charged black hole. It also describes there that there is a theoretical upper bound on the charge/mass ratio of a black hole: that any would-be black hole exceeding it (which is generally thought to be impossible — see <a href="http://physics.stackexchange.com/q/6650/4976">this related question on trying to force saturation of the charge/mass ratio or black holes</a>) would lack an event horizon (and therefore presumably not be a black hole). Why should that be? Furthermore: from <a href="http://physics.stackexchange.com/q/9516/4976">this other related question on repulsion of pairs of charged black holes</a> (and from Willie Wong's comment, below), ir seems that the size of the event horizon may change depending on how close it is to being extremal! Why would the event horizon of a <em>highly charged</em> black hole be different than the event horizon of a <em>neutral</em> black hole, of similar mass?</p>
<p>Is there a clear reason for such an interplay is there between electrodynamics (aside from local Lorentz invariance) and general relativity that bring these things about?</p> | 1,497 | [
-0.030237330123782158,
-0.02950930781662464,
0.033623725175857544,
-0.03431355208158493,
0.023659754544496536,
0.002447011647745967,
-0.04660908505320549,
-0.03809567168354988,
-0.03919478505849838,
-0.03193296492099762,
0.03371495380997658,
0.027900410816073418,
0.05578819662332535,
0.03807184845209122,
-0.019731417298316956,
-0.008544097654521465,
-0.009958452545106411,
-0.012233750894665718,
0.013418295420706272,
-0.01681055873632431,
0.014368830248713493,
0.049607548862695694,
0.012753943912684917,
0.013868482783436775,
-0.018681352958083153,
-0.006503198761492968,
0.03063616156578064,
-0.0006323222769424319,
0.016525782644748688,
0.06297937780618668,
-0.03892838582396507,
-0.040704239159822464,
0.02035718970000744,
0.01307159848511219,
0.005805969703942537,
-0.002908414462581277,
0.016336577013134956,
-0.03643172234296799,
-0.019208040088415146,
0.007890285924077034,
-0.025462981313467026,
-0.008339273743331432,
0.015800785273313522,
0.031702201813459396,
-0.044659316539764404,
0.019100261852145195,
-0.0005622407770715654,
-0.021877603605389595,
0.028709765523672104,
-0.07548180222511292,
0.04654264077544212,
0.012851948849856853,
0.04227686673402786,
0.021641846746206284,
0.02760227397084236,
-0.019633254036307335,
0.08429370820522308,
0.052014824002981186,
-0.022689390927553177,
-0.04214343801140785,
-0.008790466003119946,
-0.015133386477828026,
-0.01973956637084484,
-0.006233208812773228,
0.009714440442621708,
0.05296929553151131,
0.00960372481495142,
-0.008065789937973022,
0.024230683222413063,
-0.016227582469582558,
0.025872768834233284,
-0.000527863681782037,
-0.041338417679071426,
0.0013103237142786384,
-0.005394886713474989,
-0.02710708975791931,
0.0013758490094915032,
-0.006872102618217468,
0.035429421812295914,
0.07236472517251968,
-0.027474042028188705,
-0.00535282026976347,
0.052797261625528336,
0.011876429431140423,
0.018970731645822525,
0.004421983379870653,
0.0765390619635582,
-0.02492396906018257,
-0.008556381799280643,
0.007545715197920799,
-0.02576669678092003,
-0.01415727287530899,
0.0037731060292571783,
-0.04293103516101837,
-0.020946526899933815,
0.0036395685747265816,
0.022097725421190262,
0.05713126063346863,
-0.03771403804421425,
0.012632925994694233,
-0.026181001216173172,
0.011230286210775375,
-0.013677393086254597,
0.07123252749443054,
0.024009685963392258,
-0.036090973764657974,
-0.06314464658498764,
0.030439764261245728,
-0.02934238128364086,
-0.03171781450510025,
-0.02814568392932415,
-0.002831471851095557,
-0.020502999424934387,
-0.04455425962805748,
-0.0004606887814588845,
-0.03694992512464523,
0.03365638852119446,
-0.03066958487033844,
0.055508844554424286,
0.06101624667644501,
0.03146570920944214,
-0.03286338597536087,
0.009838548488914967,
-0.029035771265625954,
-0.041522275656461716,
-0.0044876751489937305,
0.0669046938419342,
0.008528409525752068,
-0.009843170642852783,
0.003613761393353343,
-0.02056686207652092,
0.009366463869810104,
0.006773880682885647,
0.008410202339291573,
0.03596656024456024,
-0.0127799641340971,
-0.08649203926324844,
-0.03381144627928734,
0.04372984543442726,
0.0028860545717179775,
-0.027409439906477928,
-0.08028504997491837,
-0.013093256391584873,
0.034244783222675323,
0.08568421006202698,
-0.00061174196889624,
-0.00681345583871007,
0.017056507989764214,
0.035131435841321945,
0.031768180429935455,
-0.02153180167078972,
0.027303744107484818,
0.00802728533744812,
-0.005530001129955053,
-0.019243991002440453,
-0.0747864842414856,
0.01030774600803852,
0.007136508356779814,
0.024164503440260887,
-0.013948801904916763,
0.0652918592095375,
-0.012925028800964355,
-0.008336029015481472,
0.017127757892012596,
-0.0015962517354637384,
-0.0032528711017221212,
0.08819051831960678,
-0.0017293724231421947,
-0.0059585548005998135,
0.06137055158615112,
-0.012661641463637352,
0.05817762017250061,
0.026150763034820557,
0.02010674774646759,
0.021989978849887848,
-0.03267986327409744,
-0.013155451975762844,
-0.05625447258353233,
-0.012718701735138893,
0.002804987831041217,
-0.02034868113696575,
-0.03861089050769806,
-0.021446235477924347,
-0.007909201085567474,
0.009489830583333969,
0.024700084701180458,
-0.018479064106941223,
-0.01986662484705448,
-0.0018946874188259244,
-0.05872398614883423,
-0.02269178442656994,
-0.045971956104040146,
0.008134319446980953,
0.017092520371079445,
-0.00521843321621418,
0.03522702679038048,
-0.00414581224322319,
0.006235925480723381,
-0.05090916529297829,
-0.0042382339015603065,
0.01494868565350771,
0.05014658346772194,
-0.009764539077877998,
0.003244994906708598,
0.0026891306042671204,
0.029709691181778908,
0.028521541506052017,
-0.019980616867542267,
-0.01999741606414318,
0.018456125631928444,
-0.03860253095626831,
-0.01817774400115013,
-0.00034310712362639606,
0.03423386812210083,
-0.022980421781539917,
0.005327177699655294,
0.028790587559342384,
0.030719757080078125,
0.018562084063887596,
0.05061081796884537,
-0.0168878473341465,
0.07959087938070297,
0.006929345428943634,
0.008770967833697796,
-0.00675944471731782,
0.06729355454444885,
0.015983087942004204,
-0.0023220949806272984,
-0.013953637331724167,
0.019386226311326027,
-0.05737213045358658,
0.020402692258358,
0.03489421680569649,
0.0454937182366848,
-0.0460037961602211,
0.028242696076631546,
0.03810896724462509,
0.044493287801742554,
0.011381490156054497,
0.020861279219388962,
0.0033037851098924875,
-0.0446811206638813,
0.017409048974514008,
-0.02727811224758625,
0.02177593484520912,
0.007740779779851437,
0.03869536891579628,
0.0026504090055823326,
0.020608266815543175,
-0.02632402814924717,
-0.005065372213721275,
0.022284699603915215,
-0.004492598585784435,
0.02043449878692627,
0.016569217666983604,
-0.003148098010569811,
0.022584833204746246,
-0.00847945362329483,
0.0184548981487751,
-0.0037714182399213314,
0.005154715385288,
0.01587807387113571,
-0.06776547431945801,
0.0206759013235569,
-0.009357484057545662,
0.010109519585967064,
0.03508388623595238,
0.01603616774082184,
-0.0024144684430211782,
-0.07378211617469788,
0.018623556941747665,
-0.010972674936056137,
-0.03428134322166443,
-0.03859270364046097,
0.0047971755266189575,
-0.003548082197085023,
0.017764952033758163,
0.04380228370428085,
0.001193295349366963,
-0.008814863860607147,
0.022819118574261665,
-0.017137257382273674,
-0.009292823262512684,
0.013803808949887753,
-0.03251282870769501,
-0.010800883173942566,
-0.03483371436595917,
-0.01472966093569994,
0.04721389338374138,
0.008668176829814911,
0.024326372891664505,
0.019585419446229935,
-0.001279097399674356,
-0.01741669699549675,
0.015511302277445793,
-0.04026049003005028,
0.010667944326996803,
-0.055996641516685486,
-0.018117113038897514,
0.07063103467226028,
0.02111825719475746,
-0.04576371982693672,
0.03412315621972084,
-0.015847723931074142,
-0.040169671177864075,
0.0015869889175519347,
-0.004379946272820234,
-0.004583308007568121,
-0.034732021391391754,
0.009325862862169743,
0.020116068422794342,
-0.021267160773277283,
-0.012584008276462555,
-0.044800758361816406,
-0.016191184520721436,
0.032539136707782745,
-0.03689601272344589,
0.044321209192276,
-0.009474695660173893,
-0.044694121927022934,
0.05897060036659241,
-0.002736772643402219,
-0.0013643893180415034,
-0.01950199343264103,
-0.026561832055449486,
-0.015848316252231598,
0.005556051153689623,
-0.009567677974700928,
0.0711999163031578,
0.00047192355850711465,
-0.018141774460673332,
0.025764357298612595,
0.03760295361280441,
-0.008691476657986641,
0.015337735414505005,
0.01662994921207428,
-0.008051554672420025,
0.016958758234977722,
0.004728260450065136,
0.06988570094108582,
0.008175722323358059,
-0.03485583886504173,
0.024065282195806503,
0.004238927736878395,
0.03788066282868385,
0.009224704466760159,
-0.039715345948934555,
0.04153566434979439,
-0.003156575607135892,
0.027387451380491257,
0.011414839886128902,
0.021617837250232697,
-0.025064120069146156,
-0.05455255135893822,
0.01926013082265854,
-0.0007643283461220562,
0.04757137596607208,
-0.011009112931787968,
-0.013269315473735332,
0.029147980734705925,
0.0805078074336052,
-0.05983347445726395,
-0.008406233973801136,
-0.0061855013482272625,
-0.045913998037576675,
0.026593100279569626,
-0.05184599384665489,
-0.024891750887036324,
0.0464603416621685,
0.007034762762486935,
0.022990569472312927,
0.019857367500662804,
-0.004708476830273867,
-0.012862203642725945,
-0.08796990662813187,
-0.008655809797346592,
-0.026892997324466705,
0.05561968311667442,
-0.016068559139966965,
0.03980061039328575,
0.01963205821812153,
0.0009181147324852645,
-0.02788129635155201,
-0.006546272896230221,
-0.11071177572011948,
-0.001658105873502791,
-0.06811368465423584,
-0.02524927444756031,
0.006458109710365534,
-0.006305940914899111,
-0.00652265502139926,
0.0016477002063766122,
-0.016166144981980324,
-0.031049352139234543,
0.03709351643919945,
-0.052122246474027634,
0.018291037529706955,
-0.04823103919625282,
-0.031994957476854324,
0.010005379095673561,
0.04510662704706192,
0.029215194284915924,
-0.027602436020970345,
-0.02050700969994068,
0.0050467224791646,
-0.04322575032711029,
-0.0066663483157753944,
0.02110956236720085,
0.02876402623951435,
0.016077756881713867,
0.04063016548752785,
-0.0060824002139270306,
-0.0034388466738164425,
-0.030369415879249573,
-0.024971438571810722,
0.04033994674682617,
0.03450419753789902,
0.0038736213464289904,
-0.023671647533774376,
-0.04025224596261978,
-0.0461789108812809,
-0.012108566239476204,
-0.027823323383927345,
0.09297896921634674,
-0.009249699302017689,
-0.015687482431530952,
0.019571920856833458,
-0.03776368498802185,
0.04265064373612404,
0.013264240697026253,
0.030334407463669777,
0.035234250128269196,
-0.02124185673892498,
-0.038884371519088745,
-0.031575191766023636,
-0.01360570639371872,
0.04025641456246376,
0.01869773492217064,
-0.006987399887293577,
-0.05406373739242554,
-0.025200720876455307,
0.013071215711534023,
-0.0034965688828378916,
-0.03530195727944374,
-0.032119955867528915,
0.013898971490561962,
0.03407759964466095,
-0.028406985104084015,
0.040274787694215775,
0.0195954330265522,
0.006658685393631458,
0.08699354529380798,
0.01083238422870636,
-0.0029089543968439102,
-0.06716734170913696,
-0.044477928429841995,
0.04882192239165306,
0.06323182582855225,
0.0027759314980357885,
-0.03391413763165474,
-0.0601319894194603,
0.04677155241370201,
0.030872361734509468,
-0.059668220579624176,
0.023040076717734337,
-0.0019006128422915936,
0.043464574962854385,
-0.030306881293654442,
-0.018781810998916626,
0.007869510911405087,
0.024042123928666115,
-0.015378807671368122,
-0.004142485558986664,
-0.018293101340532303,
0.02117462456226349,
-0.005849551409482956,
0.008866152726113796,
0.007770337164402008,
0.05663541331887245,
0.001138403662480414,
-0.0059157973155379295,
0.027424685657024384,
-0.03278438374400139,
-0.034919947385787964,
-0.11139987409114838,
-0.009199991822242737,
0.0023172919172793627,
-0.026136288419365883,
0.01113155484199524,
-0.042814429849386215,
0.008018124848604202,
0.01230385061353445,
-0.006071122363209724,
-0.02921382524073124,
0.03339555114507675,
-0.07058592885732651,
0.00925934687256813,
0.02066449075937271,
-0.019766483455896378,
0.03004237450659275,
0.0011892789043486118,
-0.025086114183068275,
-0.011117573827505112,
-0.05743328481912613,
0.026454424485564232,
-0.0470147468149662,
-0.03056429885327816,
-0.0064902519807219505,
0.008751667104661465,
-0.06122118979692459,
0.06504172086715698,
-0.009023020975291729,
0.017980501055717468,
0.0054807779379189014,
-0.03873487934470177,
-0.023575467988848686,
0.012381158769130707,
-0.016339490190148354,
-0.0020778768230229616,
-0.0022534343879669905,
0.03157892823219299,
0.02710549719631672,
-0.01657322607934475,
0.029747581109404564,
0.010117555037140846,
0.005510563962161541,
0.06225981563329697,
-0.031425874680280685,
-0.008203096687793732,
-0.011864657513797283,
0.017406679689884186,
0.027586670592427254,
-0.0356704406440258,
0.08581375330686569,
-0.015141274780035019,
-0.030124638229608536,
0.03413389250636101,
-0.018836673349142075,
-0.01735687628388405,
0.022042613476514816,
0.017713036388158798,
0.03631358593702316,
-0.04210427403450012,
0.015308888629078865,
0.04341815039515495,
0.01389383990317583,
-0.06992262601852417,
-0.036895208060741425,
0.05504796281456947,
0.02483914978802204,
-0.018110424280166626,
-0.015179747715592384,
0.009719065390527248,
-0.048279087990522385,
-0.04280240461230278,
-0.020121095702052116,
0.06187072768807411,
-0.04941793158650398,
0.008818288333714008,
0.013611257076263428,
0.02403777465224266,
0.03681395947933197,
-0.011109002865850925,
-0.017833586782217026,
0.022501787170767784,
-0.0066168783232569695,
0.032257501035928726,
-0.010489349253475666,
0.03634173050522804,
-0.013627666980028152,
-0.05586428940296173,
-0.027790836989879608,
-0.01767851784825325,
0.018464017659425735,
-0.0013603910338133574,
0.015102086588740349,
0.043954040855169296,
-0.008214592933654785,
-0.00948916282504797,
-0.004909423179924488,
0.02387554943561554,
-0.009540878236293793,
0.04194130748510361,
-0.03164411708712578,
-0.00650382786989212,
-0.010830448009073734,
-0.05797716975212097,
0.03983409330248833,
0.009429726749658585,
-0.02517790161073208,
-0.01019352301955223,
0.03903141990303993,
-0.007050978485494852,
-0.03686821088194847,
-0.020364386960864067,
-0.04336708411574364,
0.029867516830563545,
0.005276199895888567,
0.0018364661373198032,
0.002947890432551503,
0.011526684276759624,
0.0019349406938999891,
-0.036046672612428665,
-0.016657469794154167,
0.01860598661005497,
0.0858817771077156,
0.033109284937381744,
0.026418112218379974,
0.024406250566244125,
-0.03287343680858612,
-0.029427845031023026,
-0.03937719017267227,
0.006038337480276823,
0.015569816343486309,
0.008936766535043716,
-0.006989157292991877,
0.0014168379129841924,
0.007344485726207495,
0.04271181672811508,
0.04987015202641487,
-0.01420742180198431,
0.013376038521528244,
0.03831160068511963,
0.010130899026989937,
0.0032804093789309263,
-0.016909616068005562,
-0.03284404054284096,
0.052673324942588806,
-0.03331470862030983,
0.04350914806127548,
0.007435150910168886,
-0.00018612742132972926,
0.013386642560362816,
-0.004917580168694258,
0.04636741057038307,
-0.03527074679732323,
-0.03789067268371582,
-0.04218230023980141,
0.0018404655857011676,
-0.0018424809677526355,
-0.0068794661201536655,
-0.011380577459931374,
0.01585236005485058,
-0.006194118410348892,
-0.004722095560282469,
0.0043601589277386665,
0.0028185707051306963,
-0.05393318459391594,
-0.003983920905739069,
-0.02977054752409458,
-0.06936071068048477,
0.04360261186957359,
0.04248921200633049,
-0.030931608751416206,
0.027982519939541817,
-0.053950436413288116,
0.03647967427968979,
0.038757529109716415,
0.019576946273446083,
-0.011796430684626102,
0.02512868493795395,
-0.021580394357442856,
0.006936741527169943,
-0.06308065354824066,
0.007833088748157024,
0.12972861528396606,
0.042985666543245316,
0.0336083248257637,
-0.04430945962667465,
0.028339074924588203,
-0.008588438853621483,
-0.003641560673713684,
-0.05182261019945145,
0.005730894394218922,
-0.034800250083208084,
0.0020364888478070498,
0.012493734247982502,
0.04061705246567726,
0.009535794146358967,
-0.04834585264325142,
0.04324159398674965,
-0.024741698056459427,
-0.031228436157107353,
0.00384226581081748,
0.03845345601439476,
0.0072847576811909676,
0.043581683188676834,
-0.029771240428090096,
0.03158869221806526,
-0.03720153868198395,
0.011919836513698101,
-0.06387508660554886,
-0.006504775024950504,
0.0021379373501986265,
-0.031991735100746155,
-0.05345592275261879,
-0.017845232039690018,
-0.0037173782475292683,
-0.04586486145853996,
-0.02933955378830433,
0.016600970178842545,
0.022896626964211464,
-0.010670920833945274,
-0.008032793179154396,
0.03215397149324417,
-0.0022052652202546597,
0.018050339072942734,
0.014931675046682358,
0.027011580765247345,
-0.05654415488243103,
0.023956863209605217,
-0.018129145726561546,
0.027891671285033226,
-0.032760802656412125,
0.01555404532700777,
0.0022334314417093992,
-0.003832833841443062,
0.008641562424600124,
-0.04658892750740051,
-0.02992180548608303,
-0.025238826870918274,
-0.00844589713960886,
0.015381019562482834,
-0.03212648257613182,
-0.0039206501096487045,
0.056960854679346085,
0.02563362568616867,
0.038116972893476486,
-0.007793441414833069,
0.00791136734187603,
-0.0019448796520009637,
-0.013886637054383755,
0.00421585887670517,
-0.006719775497913361,
0.012786922045052052,
0.0030699786730110645,
0.004648477770388126,
-0.05121120810508728,
-0.03751365467905998,
0.005613283254206181,
0.031388405710458755,
0.02063622511923313,
0.03724883496761322,
0.007139083929359913,
-0.009847588837146759,
-0.0669790580868721,
0.02841421589255333,
-0.00925679225474596,
-0.021482182666659355,
-0.029628120362758636,
0.02896219491958618,
-0.009867822751402855,
0.022455131635069847,
0.0004990427405573428,
-0.007336280774325132,
0.017401231452822685,
0.03544711321592331,
-0.027996907010674477,
-0.0031600536312907934,
-0.015059596858918667,
0.0026677753776311874,
-0.041237667202949524,
-0.007373452186584473,
0.0026206220500171185,
0.007066650781780481,
0.00947319995611906,
-0.010282850824296474,
0.04093804210424423,
0.025268027558922768,
-0.01941036619246006,
-0.015126161277294159,
0.05173367261886597,
-0.002160286298021674,
-0.00824148952960968,
0.011699262075126171,
0.02765401266515255,
-0.04128752648830414,
-0.03646603226661682,
0.0020670138765126467,
-0.000665137660689652,
-0.03189217299222946,
0.038475412875413895,
-0.015600205399096012,
-0.0037387809716165066,
-0.009677388705313206,
0.015468772500753403,
-0.05139555409550667,
-0.06488052010536194,
-0.040446165949106216,
0.02307330258190632,
-0.03894165903329849,
0.006493774708360434,
0.004956704098731279,
-0.008839837275445461,
-0.00629980256780982,
-0.018283989280462265,
-0.002457019640132785,
0.010609034448862076,
-0.03842046111822128,
-0.004290532786399126,
0.022767124697566032,
-0.015839653089642525,
0.030665958300232887,
-0.006442831363528967,
-0.019216904416680336,
0.030871858820319176,
-0.02876978926360607,
-0.05454746633768082,
0.008835668675601482,
-0.018463680520653725,
0.016576670110225677,
0.024358397349715233,
-0.014556330628693104,
-0.009692351333796978,
0.06089671701192856,
-0.010886572301387787,
-0.013743082992732525,
-0.011560965329408646,
-0.013290000148117542,
0.0005051076877862215,
-0.003428548574447632,
0.028952831402420998,
-0.017180772498250008,
0.016585370525717735,
0.027297964319586754,
0.008058774285018444,
-0.0442679300904274,
-0.03324056789278984,
0.009601430967450142,
0.014433113858103752,
0.017557216808199883,
0.007364765740931034,
0.01389806717634201,
0.018819261342287064,
0.04598550125956535,
-0.047699183225631714,
0.046139203011989594,
0.04849109798669815,
0.024528268724679947,
-0.08518519997596741,
-0.0254843570291996,
0.02413942664861679,
0.03489771485328674,
0.045813318341970444,
-0.018616177141666412,
-0.001482682884670794,
-0.006688857916742563,
-0.06675437092781067,
0.0032423855736851692,
-0.029461907222867012,
-0.01797144114971161,
-0.002486723242327571,
-0.029042357578873634,
-0.010070704855024815,
0.005395337473601103,
0.04529305174946785,
0.03851074352860451,
0.004076056182384491,
-0.003367515979334712,
-0.013496870175004005,
-0.044213902205228806,
-0.013864683918654919,
0.038135331124067307,
-0.01871439442038536,
-0.012010590173304081,
0.06001392379403114,
-0.002790785161778331,
-0.004372583702206612,
0.032024580985307693,
0.041534535586833954,
-0.008652789518237114,
0.009586415253579617,
0.013329497538506985,
0.025761693716049194,
0.036236297339200974,
0.0403817780315876,
0.010903200134634972,
-0.02362115867435932,
0.003669960191473365,
0.0005811069277115166,
0.03412316367030144,
-0.018358048051595688,
-0.012455698102712631,
0.024859337136149406,
-0.027236249297857285,
0.014138052240014076,
0.015551045536994934,
-0.040977198630571365,
-0.03469105064868927,
-0.018499890342354774,
0.031817931681871414,
-0.005884242709726095,
-0.009524251334369183,
0.00941372849047184,
-0.02868080511689186,
-0.009699909016489983,
0.02284254878759384,
0.007215564139187336,
0.05254735052585602,
0.052346453070640564,
0.013032397255301476,
0.005876949056982994,
0.010417508892714977,
-0.01924263685941696,
0.03160778805613518,
-0.06165040656924248,
0.0036120107397437096,
-0.0020617786794900894,
0.029686104506254196,
0.03127552196383476,
-0.05198924243450165,
-0.02328440546989441,
0.03523954376578331,
0.003387793665751815,
0.01778028905391693,
-0.0012034024111926556,
-0.050295669585466385,
-0.004119579214602709,
-0.07503154873847961,
-0.007052927277982235,
-0.01783039979636669,
0.010705404914915562,
-0.03566696122288704,
-0.0742262452840805,
0.020086243748664856,
0.021759405732154846,
0.06642928719520569,
-0.0021942679304629564,
-0.022341858595609665,
0.03840562328696251,
-0.02301105484366417,
-0.0003825098101515323,
-0.03130076080560684,
-0.0024946818593889475,
0.014541860669851303,
-0.028756098821759224,
0.018210947513580322,
0.004301724024116993,
-0.015957126393914223,
0.031356602907180786,
0.04095727950334549,
-0.02363000437617302,
0.06537124514579773,
-0.011801560409367085,
-0.0037410182412713766,
0.0634273961186409,
0.040795933455228806,
0.021353695541620255,
0.06381744146347046,
0.006627122405916452,
0.037751205265522,
-0.0014202637830749154,
-0.010728475637733936,
0.0010308033088222146,
-0.00021724931139033288,
-0.021524475887417793,
-0.00699639692902565,
-0.007674265652894974,
-0.017346128821372986,
0.031202316284179688,
-0.026152530685067177,
-0.0007779044099152088,
0.05612489953637123,
-0.03022913634777069,
-0.024101780727505684,
0.054020728915929794,
0.032525405287742615,
0.02795322984457016,
-0.02306368574500084,
0.018406158313155174,
-0.0328313484787941,
-0.010749808512628078,
-0.00366775831207633,
0.014426029287278652,
0.07846950739622116,
0.017679892480373383,
-0.01121611800044775,
0.03369516879320145,
0.020893430337309837,
-0.0013875274453312159,
-0.01755574531853199,
0.04192427173256874,
-0.017028462141752243,
-0.04559364169836044,
0.0224522203207016,
-0.0097634457051754,
0.041536685079336166,
0.03130456060171127,
-0.02668032981455326,
0.08102265745401382,
0.0012401295825839043,
0.018625734373927116,
0.01857736147940159,
0.007996750995516777,
0.015580019913613796,
0.0598522424697876,
-0.0061618871986866,
0.07424002885818481,
-0.015219958499073982,
-0.021252034232020378,
0.0016315393149852753,
-0.0007499459316022694,
0.004102328326553106,
-0.009020416997373104,
-0.008030307479202747,
0.0396515429019928,
0.013113191351294518,
-0.010454786010086536,
-0.01595904864370823,
-0.012632585130631924,
-0.0003996101440861821,
0.017555788159370422,
0.0031182444654405117,
0.03070712648332119,
-0.0004056063771713525,
-0.026085712015628815,
-0.025976166129112244,
0.032912466675043106,
-0.049069564789533615,
-0.04250955209136009,
-0.0032219865825027227,
0.008020282723009586,
-0.034871358424425125,
-0.003040663432329893
] |
<p>I am reading up on the Schrödinger equation and I quote:</p>
<blockquote>
<p><em>Because the potential is symmetric under $x\to-x$, we expect that there will be solutions of definite parity.</em></p>
</blockquote>
<p>Could someone kindly explain why this is true? And perhaps also what it means physically?</p> | 1,498 | [
-0.011492090299725533,
-0.03541705757379532,
-0.012397663667798042,
-0.0342303141951561,
0.010307034477591515,
0.01156963687390089,
-0.033290788531303406,
0.018296431750059128,
0.05047570541501045,
-0.03163297101855278,
0.01532670110464096,
0.02005130611360073,
0.018655424937605858,
-0.01987607032060623,
0.015953857451677322,
0.05371161177754402,
0.004428519401699305,
-0.008778082206845284,
-0.001366998883895576,
-0.001961949048563838,
0.010818763636052608,
0.011625031940639019,
0.040552422404289246,
0.02898431569337845,
-0.021406468003988266,
0.027518944814801216,
-0.02309713512659073,
0.01703271083533764,
0.015372092835605145,
0.085175059735775,
0.005800270009785891,
-0.004859577398747206,
0.04465286433696747,
0.04990776628255844,
0.030803201720118523,
0.010434729047119617,
0.005088642705231905,
-0.030944112688302994,
0.010815944522619247,
0.020247409120202065,
-0.03128283843398094,
-0.03845396265387535,
-0.005108292680233717,
0.0543048121035099,
-0.03931054845452309,
0.0054144603200256824,
0.00341879203915596,
-0.047038473188877106,
0.043507225811481476,
-0.03291274607181549,
0.07456730306148529,
-0.005491148680448532,
0.061770323663949966,
-0.003457407932728529,
-0.004572601057589054,
-0.017790772020816803,
0.06765308976173401,
0.0661538690328598,
-0.009099277667701244,
-0.06047622114419937,
-0.007089795079082251,
-0.07002443075180054,
0.006104445084929466,
-0.008638241328299046,
-0.03326401859521866,
-0.010540025308728218,
0.02620626613497734,
-0.0732298418879509,
-0.007414745166897774,
-0.03499140962958336,
0.007561508100479841,
0.03901476785540581,
0.014122438617050648,
-0.026796601712703705,
-0.007135176565498114,
-0.03491070866584778,
0.006162174511700869,
-0.001639504567719996,
0.008157897740602493,
-0.012628848664462566,
-0.009407485835254192,
0.018733320757746696,
-0.02333538420498371,
0.03698624670505524,
-0.03637123480439186,
-0.004746478982269764,
0.04998193681240082,
0.0006918268045410514,
0.018732529133558273,
0.020174184814095497,
0.028787536546587944,
0.02674677036702633,
0.02859547547996044,
-0.05118205398321152,
-0.02237635664641857,
0.028789738193154335,
0.014226370491087437,
0.030299663543701172,
-0.004039752297103405,
-0.05333567038178444,
-0.008002410642802715,
-0.013922438025474548,
-0.002471745712682605,
0.06741496920585632,
-0.0027244926895946264,
-0.017903875559568405,
-0.04194066673517227,
0.033444736152887344,
0.015620340593159199,
0.02072039060294628,
-0.011557217687368393,
0.008384447544813156,
-0.013576371595263481,
-0.008112655021250248,
-0.011094335466623306,
-0.023071419447660446,
-0.015800194814801216,
-0.013020774349570274,
0.041761066764593124,
0.056026391685009,
0.02675003372132778,
-0.030141860246658325,
0.06827346980571747,
-0.05263560637831688,
-0.08454892784357071,
0.006603369954973459,
0.040372394025325775,
0.015354457311332226,
-0.04523169994354248,
0.01787107065320015,
0.04162547364830971,
-0.010312683880329132,
-0.01399457547813654,
0.011409142054617405,
0.041980549693107605,
-0.03410792350769043,
-0.10298562049865723,
-0.08439034968614578,
0.005984626244753599,
-0.011815018951892853,
-0.01947593130171299,
-0.07377995550632477,
-0.004889632575213909,
0.0486038438975811,
0.09496862441301346,
-0.029253074899315834,
0.036480531096458435,
0.025571560487151146,
-0.021330146118998528,
0.0200504083186388,
-0.002633357420563698,
-0.039838675409555435,
-0.01527931448072195,
-0.03447752818465233,
-0.021901020780205727,
-0.059527669101953506,
0.00508303614333272,
0.0019332164665684104,
0.03258708119392395,
-0.031140994280576706,
0.04610513523221016,
-0.05597265064716339,
0.007715770974755287,
0.011471104808151722,
-0.02693217247724533,
-0.0338674820959568,
0.10912009328603745,
0.04765145853161812,
-0.0191320963203907,
0.05153479054570198,
-0.009831310249865055,
0.05678640305995941,
-0.016521058976650238,
0.03871807083487511,
0.006621151231229305,
-0.025297198444604874,
0.0023264631163328886,
-0.0357501357793808,
0.01715184934437275,
-0.011901330202817917,
-0.020346786826848984,
-0.015846505761146545,
-0.035761117935180664,
0.02803526073694229,
-0.00181725830771029,
0.03856905922293663,
-0.016831092536449432,
0.009284951724112034,
0.01370315533131361,
-0.0484381839632988,
-0.016123417764902115,
-0.03926899656653404,
0.030116919428110123,
0.02120121754705906,
-0.02846713177859783,
0.04432416707277298,
0.05163954198360443,
0.01132899709045887,
-0.012690928764641285,
-0.027352355420589447,
-0.014983925968408585,
0.006617114879190922,
0.008006984367966652,
-0.012054439634084702,
0.028458427637815475,
0.07227182388305664,
0.041104674339294434,
0.0026729977689683437,
0.03398614004254341,
-0.027938539162278175,
0.01090551633387804,
-0.006314076948910952,
-0.010465407744050026,
0.04355500265955925,
0.018550202250480652,
-0.02976592443883419,
-0.035681918263435364,
-0.008413635194301605,
0.0038291995879262686,
0.04120935872197151,
-0.050952453166246414,
0.05487566813826561,
0.028790956363081932,
0.007825149223208427,
-0.006655923556536436,
0.022238967940211296,
0.045238200575113297,
0.019170396029949188,
0.03554794192314148,
-0.03806651756167412,
-0.03285307437181473,
0.011488083750009537,
0.007253237068653107,
0.019884416833519936,
-0.034576497972011566,
-0.0023727291263639927,
0.016055170446634293,
0.024560637772083282,
0.02443716488778591,
0.01690477319061756,
-0.04097979888319969,
-0.0427425242960453,
0.03188055381178856,
-0.00647671427577734,
0.02306823991239071,
0.033084381371736526,
0.06541960686445236,
0.015901900827884674,
0.025418361648917198,
-0.02259877324104309,
-0.01213528960943222,
0.03391796723008156,
0.00849526934325695,
0.03895307332277298,
0.037712059915065765,
-0.024053584784269333,
0.015393088571727276,
0.004054658580571413,
0.007596045732498169,
-0.0006082098698243499,
-0.037549424916505814,
0.020177314057946205,
-0.04403394088149071,
-0.017375575378537178,
-0.006853960920125246,
-0.008337479084730148,
-0.05231538042426109,
-0.018548959866166115,
0.02583000622689724,
-0.027527017518877983,
-0.007063050288707018,
-0.004074789118021727,
-0.03308394178748131,
-0.024622458964586258,
-0.05679730325937271,
0.08448094129562378,
0.022816624492406845,
0.0421886146068573,
-0.008844608440995216,
-0.0266600139439106,
0.010908139869570732,
-0.02235201746225357,
-0.013475858606398106,
0.026917627081274986,
-0.04730650782585144,
0.0347033329308033,
-0.06369215250015259,
-0.03953896835446358,
0.023306306451559067,
0.031153244897723198,
0.017850719392299652,
0.0034356035757809877,
-0.012213500216603279,
-0.04390677809715271,
-0.023945776745676994,
-0.04799880087375641,
0.007344905287027359,
-0.062357187271118164,
0.02145223133265972,
0.04760967940092087,
0.011159112676978111,
0.0030888239853084087,
0.008479278534650803,
-0.05126693844795227,
-0.027503058314323425,
-0.03835836797952652,
-0.028553541749715805,
0.05795660614967346,
0.005767291411757469,
0.017475144937634468,
0.005194215103983879,
-0.041348960250616074,
0.0028987289406359196,
-0.0536053404211998,
-0.04002632945775986,
0.011910014785826206,
0.0021160689648240805,
0.021057844161987305,
0.011911144480109215,
-0.020097045227885246,
0.10451134294271469,
0.01059982180595398,
-0.0016253275098279119,
-0.004788425751030445,
-0.01928495429456234,
-0.031254854053258896,
-0.014438388869166374,
0.03243749588727951,
0.05144834518432617,
0.017758289352059364,
0.06562861800193787,
0.017338290810585022,
0.06927724182605743,
-0.007246897090226412,
-0.00010997160279657692,
-0.06709856539964676,
0.0016861469484865665,
-0.009544849395751953,
-0.010994142852723598,
0.0184333436191082,
0.002600498264655471,
-0.05012507736682892,
0.022134140133857727,
-0.002873979974538088,
-0.005724008195102215,
0.020991157740354538,
-0.01974557712674141,
0.06812363117933273,
-0.010947034694254398,
0.015787120908498764,
-0.004778007976710796,
0.06235438212752342,
-0.027314312756061554,
0.0033838669769465923,
-0.0017468780279159546,
0.0033293331507593393,
0.06723638623952866,
-0.0488891676068306,
-0.009395595639944077,
0.011623091995716095,
0.025714505463838577,
-0.02589254640042782,
0.022746248170733452,
0.021005308255553246,
-0.0001471971336286515,
0.0239640511572361,
-0.012735866941511631,
-0.03979340195655823,
0.035974014550447464,
0.001659576315432787,
0.009392841719090939,
-0.027375932782888412,
-0.03293187916278839,
-0.0190045814961195,
-0.028710544109344482,
0.036491960287094116,
-0.020908761769533157,
0.04028615355491638,
-0.005228637717664242,
0.06037916615605354,
0.027139130979776382,
0.03501788154244423,
0.010994433425366879,
-0.010393002070486546,
-0.029900744557380676,
0.011034989729523659,
-0.020806727930903435,
0.037431757897138596,
-0.03622495010495186,
-0.0017785921227186918,
-0.016121404245495796,
-0.05327359214425087,
-0.012004180811345577,
0.006223894190043211,
-0.003459757659584284,
-0.05376103147864342,
-0.006549311801791191,
-0.018304774537682533,
-0.021765142679214478,
-0.037688933312892914,
0.05559554696083069,
0.042858727276325226,
-0.015530425123870373,
0.037460390478372574,
0.01374093722552061,
-0.021916473284363747,
-0.01950090564787388,
-0.02338137850165367,
0.017918676137924194,
0.04897712543606758,
0.02817912958562374,
0.029618902131915092,
0.004388889297842979,
-0.016436802223324776,
0.012159908190369606,
-0.0010244313161820173,
0.08430752158164978,
0.009012987837195396,
-0.013566560111939907,
0.012009920552372932,
-0.019631417468190193,
-0.007868357002735138,
-0.012680338695645332,
0.023848174139857292,
0.01176154799759388,
0.04910461977124214,
0.015937961637973785,
0.00017917553486768156,
-0.01339707337319851,
0.014103872701525688,
0.038746122270822525,
0.013249426148831844,
0.01601189747452736,
-0.04520224779844284,
0.017607107758522034,
-0.030785465613007545,
0.01135033369064331,
-0.015080412849783897,
-0.034085385501384735,
-0.02087213471531868,
0.009960219264030457,
0.01625918783247471,
0.028856566175818443,
-0.020715106278657913,
-0.02487189508974552,
-0.04987498000264168,
0.01315582636743784,
-0.012875298038125038,
-0.013699570670723915,
0.01998552307486534,
0.018612103536725044,
0.03671686351299286,
0.013308447785675526,
0.011374392546713352,
-0.08858314901590347,
-0.001827115542255342,
0.04101403430104256,
0.03317231312394142,
0.002657943405210972,
-0.006498139817267656,
-0.05588309466838837,
0.015382753685116768,
0.06068383902311325,
-0.022451121360063553,
0.03141919523477554,
-0.03293062001466751,
-0.02390359528362751,
-0.02407778613269329,
-0.06485940515995026,
-0.023176226764917374,
0.023746879771351814,
0.0262078195810318,
0.0015256318729370832,
-0.029002083465456963,
0.00367149175144732,
-0.0442194826900959,
0.010880418121814728,
-0.027521714568138123,
0.06589902937412262,
-0.0024734472390264273,
0.002717915689572692,
-0.01990467868745327,
0.03801259025931358,
0.004016297869384289,
-0.0799969881772995,
0.020186392590403557,
0.01961006596684456,
0.010527480393648148,
0.05277950316667557,
-0.03319128230214119,
-0.038955364376306534,
0.05338340625166893,
-0.02115580439567566,
-0.03265482559800148,
0.003647171426564455,
-0.043465666472911835,
0.005281758029013872,
0.04376031458377838,
-0.007916849106550217,
0.054481517523527145,
0.0157795213162899,
-0.011694191955029964,
-0.026501387357711792,
-0.017152028158307076,
0.05705792456865311,
-0.035108935087919235,
-0.013798635452985764,
-0.05292089283466339,
0.0028894527349621058,
-0.018263086676597595,
0.04013305902481079,
-0.02222430892288685,
0.011238791048526764,
-0.010660117492079735,
-0.010004107840359211,
-0.02395070530474186,
0.03430155664682388,
0.02009684406220913,
-0.008203833363950253,
-0.0005512294010259211,
0.00855017825961113,
0.016547275707125664,
-0.03682404384016991,
-0.017964383587241173,
-0.037691667675971985,
-0.025953609496355057,
0.022745441645383835,
-0.02758309431374073,
0.009465773589909077,
-0.013436302542686462,
-0.04152616858482361,
-0.005838887766003609,
-0.047576602548360825,
-0.013653306290507317,
-0.030498052015900612,
-0.014588124118745327,
0.06340818107128143,
-0.0632200762629509,
-0.024108657613396645,
0.04432845860719681,
0.0011143733281642199,
0.004184373654425144,
-0.035390857607126236,
0.029919346794486046,
0.01920166052877903,
0.022354591637849808,
-0.08594183623790741,
-0.046658556908369064,
0.03628489002585411,
-0.025602132081985474,
-0.03133225440979004,
-0.011192498728632927,
-0.037357352674007416,
0.015816861763596535,
-0.022982431575655937,
0.025118300691246986,
0.006132768467068672,
-0.0014402803499251604,
-0.03603475168347359,
0.000902823987416923,
0.009630538523197174,
0.02075617015361786,
-0.03891046717762947,
0.007606265135109425,
-0.0035053016617894173,
-0.008435986936092377,
-0.013211662881076336,
-0.013810593634843826,
0.06500563770532608,
-0.014674217440187931,
-0.03563087433576584,
-0.005973146762698889,
-0.04765348136425018,
0.027079742401838303,
-0.02167161926627159,
-0.025454893708229065,
-0.02458997070789337,
-0.00595840672031045,
0.01877555064857006,
-0.02490447461605072,
-0.018758049234747887,
-0.00004392787013784982,
0.01999974064528942,
0.04710840806365013,
0.00006539696187246591,
-0.03757752850651741,
-0.012756346724927425,
0.020183075219392776,
0.0024937011767178774,
-0.00028829704388044775,
0.028512515127658844,
0.08022913336753845,
0.000686462561134249,
0.021244123578071594,
0.024862727150321007,
0.02557310461997986,
0.028321001678705215,
-0.004019817803055048,
-0.009006903506815434,
-0.009601082652807236,
0.02440006285905838,
-0.02848724089562893,
-0.03227001801133156,
-0.02588360384106636,
0.04194044694304466,
0.022466691210865974,
-0.010877903550863266,
0.038012027740478516,
0.014276959002017975,
-0.018458489328622818,
-0.022179769352078438,
-0.00583940465003252,
0.0013670583721250296,
0.014739850535988808,
0.0064306617714464664,
0.04151947423815727,
-0.07052792608737946,
0.02151615545153618,
0.01107444241642952,
0.07281523197889328,
-0.01552154216915369,
-0.0324866808950901,
0.02590138092637062,
0.0077993315644562244,
0.02164134383201599,
0.008355949074029922,
-0.03918033465743065,
0.048956166952848434,
-0.025768879801034927,
0.05155107006430626,
0.0167632307857275,
-0.010640795342624187,
0.039187729358673096,
-0.028814228251576424,
0.009311315603554249,
-0.060007549822330475,
-0.028595730662345886,
-0.01982482522726059,
-0.010675002820789814,
0.01286361739039421,
0.0006239863578230143,
0.008979454636573792,
0.05465419963002205,
0.016763418912887573,
0.02521309070289135,
0.013223777525126934,
-0.016148263588547707,
-0.04510042071342468,
-0.03441620618104935,
-0.04162626713514328,
-0.06522262096405029,
0.017595624551177025,
-0.021309485659003258,
0.010088128969073296,
-0.027937090024352074,
-0.031218457967042923,
0.0009053749381564558,
0.005447110626846552,
0.023244772106409073,
-0.04105206951498985,
0.05536026507616043,
0.02887505292892456,
0.04749392718076706,
-0.0022831137757748365,
0.03142567723989487,
0.09503626823425293,
0.032965898513793945,
0.032077230513095856,
-0.02425229735672474,
0.021011140197515488,
-0.016999604180455208,
-0.024769434705376625,
-0.00891353003680706,
0.02119327150285244,
0.021885329857468605,
-0.021544350311160088,
-0.005327902268618345,
0.04508798569440842,
0.01718633621931076,
0.016448933631181717,
0.04308425635099411,
-0.05273270979523659,
-0.04854367673397064,
-0.013084216974675655,
0.01828181743621826,
-0.0018322551622986794,
0.017861250787973404,
0.008579056710004807,
0.010474440641701221,
-0.03509612753987312,
0.005822897423058748,
-0.014687311835587025,
-0.02462339773774147,
0.020721517503261566,
0.040704287588596344,
-0.00835941731929779,
-0.017116308212280273,
0.02541407383978367,
0.01106587890535593,
-0.06155623868107796,
-0.0007668890757486224,
0.01783684641122818,
-0.03516920283436775,
0.03919012472033501,
0.020354177802801132,
-0.01025757472962141,
0.011767202988266945,
0.01628681644797325,
0.031647779047489166,
-0.05995415896177292,
0.002714145230129361,
-0.011083336547017097,
0.01030336506664753,
-0.00361465523019433,
-0.009598434902727604,
-0.00896729901432991,
0.030532756820321083,
0.025433344766497612,
-0.04802929610013962,
-0.039570633322000504,
0.0070135993883013725,
0.014689631760120392,
-0.02623593993484974,
-0.027229193598031998,
-0.005654043052345514,
-0.03365745395421982,
0.012075710110366344,
0.018439609557390213,
0.0031326287426054478,
-0.01702216826379299,
0.012613021768629551,
-0.03213849663734436,
0.03555835783481598,
-0.028605416417121887,
0.00013641815166920424,
-0.028420405462384224,
-0.01890462450683117,
-0.040185119956731796,
-0.03468818590044975,
0.03542854264378548,
-0.0004282336449250579,
0.05525241419672966,
-0.0008696954464539886,
0.004900735802948475,
-0.005340876989066601,
-0.03461182117462158,
0.04740316420793533,
-0.036880046129226685,
-0.01911233365535736,
-0.00266676745377481,
0.03202377259731293,
-0.02358761802315712,
0.04622314125299454,
-0.05180882662534714,
0.025344904512166977,
-0.00765182776376605,
0.03513532504439354,
0.024534421041607857,
-0.01772119477391243,
-0.040414780378341675,
0.04317478835582733,
-0.049814123660326004,
-0.0013836005236953497,
0.0037758266553282738,
0.008481591939926147,
0.005503445863723755,
0.03220037743449211,
-0.005960959475487471,
0.03069203346967697,
-0.05386269465088844,
-0.0025137795601040125,
-0.003975340165197849,
-0.018016871064901352,
-0.019469134509563446,
0.018798504024744034,
0.012321255169808865,
-0.018555117771029472,
-0.04195087030529976,
-0.0028692560736089945,
-0.002889065071940422,
0.04955257475376129,
0.038119226694107056,
0.011043399572372437,
-0.01719614490866661,
-0.02589704655110836,
0.040137842297554016,
-0.03678129240870476,
-0.03748318925499916,
-0.025483908131718636,
0.03487589955329895,
0.03460860624909401,
0.00041585779399611056,
0.008182693272829056,
-0.0007042006473056972,
0.002012554556131363,
-0.04692911356687546,
0.0554528646171093,
-0.007838740944862366,
-0.0035742023028433323,
-0.010621040128171444,
0.06670874357223511,
0.0026839023921638727,
0.041837409138679504,
0.0052145314402878284,
-0.009814482182264328,
0.05234384536743164,
-0.04928765445947647,
-0.03128381446003914,
0.026739805936813354,
-0.02106805518269539,
0.038660574704408646,
0.004513761028647423,
0.009246811270713806,
-0.00218697520904243,
0.025916332378983498,
-0.03788626566529274,
-0.018008362501859665,
-0.006887529511004686,
-0.013133752159774303,
0.019479388371109962,
-0.013787870295345783,
-0.012807687744498253,
-0.028756998479366302,
-0.0240289568901062,
0.013540043495595455,
0.017127692699432373,
-0.019985035061836243,
-0.033727001398801804,
-0.0071024214848876,
0.01416983176022768,
0.015318704769015312,
0.007075943518429995,
0.002283073728904128,
0.008442504331469536,
0.014577728696167469,
-0.03419164568185806,
0.05669939145445824,
0.04852212220430374,
0.01079601887613535,
-0.055827546864748,
0.013747538439929485,
0.008588237687945366,
-0.01908128894865513,
0.0508076436817646,
-0.07059605419635773,
-0.008249219506978989,
0.021634962409734726,
-0.05383948236703873,
0.046520497649908066,
-0.01923808641731739,
-0.0031860608141869307,
-0.020089592784643173,
0.02672399766743183,
-0.033837661147117615,
0.07038263231515884,
0.030470995232462883,
0.05030374228954315,
0.025079021230340004,
0.017281267791986465,
0.00600053695961833,
-0.03857196122407913,
0.005380474962294102,
0.03254414349794388,
-0.03845542296767235,
-0.0061415499076247215,
0.07122647017240524,
-0.031013356521725655,
-0.027576744556427002,
0.03614875301718712,
-0.03025791235268116,
-0.054714370518922806,
0.020326927304267883,
0.026114637032151222,
-0.0022688722237944603,
0.004269453231245279,
0.03933979570865631,
0.04527461528778076,
-0.006902805995196104,
0.014613856561481953,
0.027661098167300224,
0.023438094183802605,
-0.008277403190732002,
-0.0063796634785830975,
0.0012416148092597723,
-0.026443704962730408,
-0.047865305095911026,
0.055179763585329056,
-0.008137143217027187,
-0.010384613648056984,
0.007379818242043257,
0.0053664701990783215,
0.005077273119240999,
-0.014633194543421268,
0.03135788068175316,
0.0021797586232423782,
-0.01754424348473549,
0.0006308022420853376,
0.028376981616020203,
0.013353650458157063,
0.04729790613055229,
-0.01899111270904541,
-0.06512225419282913,
0.06035666540265083,
0.01719231717288494,
0.009326511062681675,
-0.03774586692452431,
-0.013264717534184456,
0.01924293115735054,
-0.018862320110201836,
-0.01724136807024479,
-0.014398021623492241,
-0.04816707968711853,
0.02773064188659191,
0.021590301766991615,
0.0034798006527125835,
-0.021338067948818207,
-0.04493154585361481,
-0.05791544169187546,
-0.06097111850976944,
0.015898410230875015,
0.01443933043628931,
0.0118784224614501,
-0.018268706277012825,
0.004002900328487158,
-0.028107238933444023,
0.004147921688854694,
0.027951320633292198,
-0.005162939894944429,
0.0020250387024134398,
0.02547796070575714,
-0.04809047654271126,
-0.00008051336044445634,
-0.020639637485146523,
-0.025726377964019775,
-0.010205796919763088,
-0.01843547448515892,
0.016392935067415237,
0.01601116545498371,
-0.003961830399930477,
0.031027918681502342,
-0.020873630419373512,
-0.009779694490134716,
0.02164851687848568,
-0.020771661773324013,
-0.05707938224077225,
0.055952973663806915,
0.04870908334851265,
0.002047294983640313,
0.0841841921210289,
0.003532370086759329,
0.017160626128315926,
-0.016530802473425865,
-0.007648910395801067,
-0.03545352444052696,
-0.00026592210633680224,
-0.05338536575436592,
0.00505451112985611,
0.02528063952922821,
-0.009562632068991661,
0.041876308619976044,
-0.0037992855068296194,
-0.005813607480376959,
0.020653454586863518,
-0.0505639985203743,
-0.04799918830394745,
0.06088743731379509,
0.04861461743712425,
0.022307556122541428,
0.0065453071147203445,
-0.0003561370831448585,
0.020303118973970413,
0.019921528175473213,
0.007745412643998861,
0.0514148585498333,
0.02404652163386345,
-0.0028712009079754353,
0.014270556159317493,
-0.008956527337431908,
0.008470725268125534,
0.04395680129528046,
0.016469456255435944,
0.06634639203548431,
-0.026285845786333084,
0.009896823205053806,
0.02914573810994625,
0.025262488052248955,
0.007336879149079323,
-0.025116508826613426,
-0.007077000569552183,
0.07498444616794586,
-0.01619068719446659,
0.0025157160125672817,
-0.03165433183312416,
0.008347894996404648,
-0.0012680281652137637,
-0.0031864861957728863,
0.026472901925444603,
0.027697689831256866,
-0.02000003680586815,
-0.014351865276694298,
-0.0238744355738163,
0.0276967640966177,
-0.024167370051145554,
-0.05169079452753067,
-0.0008897811640053988,
-0.007267361972481012,
-0.010031130164861679,
-0.030301768332719803,
0.00004649937909562141,
0.02523980662226677,
0.013282445259392262,
0.004810159094631672,
0.02778191864490509,
0.024864928796887398,
0.018523123115301132,
-0.009454239159822464,
-0.016792820766568184,
0.032338473945856094,
-0.034716833382844925,
-0.06282105296850204,
-0.0455162450671196,
-0.000914973032195121,
-0.02893366850912571,
0.009504256770014763
] |
<p>when firing a proton (for example) to an atomic nucleus, from a distance $D$, the deflection angle of the proton $\alpha $ to the type of changes atomic nuclei? or always constant?</p> | 1,499 | [
-0.04879254475235939,
0.01120203547179699,
-0.002791063627228141,
-0.009637813083827496,
0.044985249638557434,
0.07568345218896866,
-0.04044867306947708,
-0.024942390620708466,
-0.002620578045025468,
-0.060853853821754456,
0.024145491421222687,
0.007507306523621082,
0.05812254920601845,
0.0011607498163357377,
0.022437985986471176,
0.019747937098145485,
0.0021485979668796062,
0.010628024116158485,
-0.001392242033034563,
-0.004202462732791901,
0.030410103499889374,
0.0162093173712492,
-0.039044417440891266,
-0.012732226401567459,
0.016706647351384163,
0.058433786034584045,
-0.0056258151307702065,
0.00872250460088253,
0.02662825770676136,
0.030569110065698624,
0.032048992812633514,
-0.017287125810980797,
0.036401454359292984,
0.04133160039782524,
0.012871109880506992,
-0.001830848166719079,
0.022993842139840126,
-0.02709149196743965,
-0.04793715104460716,
0.05116773024201393,
-0.06182945892214775,
-0.04315462335944176,
-0.020728016272187233,
0.06531374156475067,
-0.008541414514183998,
0.013382390141487122,
-0.0037866232451051474,
-0.020910140126943588,
0.07008760422468185,
-0.026812370866537094,
0.06002982705831528,
-0.01371847279369831,
0.009887109510600567,
0.022365421056747437,
-0.0345427542924881,
-0.023315897211432457,
0.06552032381296158,
0.028394002467393875,
-0.03492644429206848,
-0.042710401117801666,
-0.01370385941118002,
-0.051178183406591415,
0.018574053421616554,
0.018911316990852356,
-0.019412811845541,
0.009408046491444111,
-0.011341112665832043,
-0.043919019401073456,
0.00008620017615612596,
-0.00682475883513689,
0.022684292867779732,
0.01392399612814188,
-0.01398280169814825,
-0.05917641147971153,
0.0040672579780220985,
-0.03974835202097893,
0.028403421863913536,
0.05567973107099533,
0.036025870591402054,
0.025286639109253883,
-0.028606876730918884,
-0.023707663640379906,
0.07574266195297241,
-0.016808945685625076,
-0.01801207847893238,
-0.010870831087231636,
0.052512720227241516,
-0.011131763458251953,
-0.004352575168013573,
0.05821691453456879,
0.0011330483248457313,
0.03468737006187439,
0.022102627903223038,
-0.010545383207499981,
0.006964367348700762,
0.05361215025186539,
0.006593435537070036,
0.06602954119443893,
-0.0073797861114144325,
-0.02839047461748123,
0.04676467180252075,
-0.0184532068669796,
-0.0026142296846956015,
0.06925619393587112,
0.027747521176934242,
-0.020073099061846733,
-0.030564075335860252,
-0.005079446826130152,
-0.06070144847035408,
0.0020223846659064293,
-0.03276457637548447,
0.01004775706678629,
-0.014771114103496075,
-0.015544447116553783,
0.05034413933753967,
-0.018666617572307587,
0.016685958951711655,
-0.009881745092570782,
0.07198908179998398,
0.06890993565320969,
0.04409464821219444,
-0.03810558840632439,
0.028239410370588303,
-0.032811976969242096,
-0.0469885990023613,
0.0004236343957018107,
0.059138428419828415,
0.00310680759139359,
-0.04505280405282974,
0.007223418448120356,
-0.022442789748311043,
-0.00391758419573307,
-0.02042313665151596,
-0.022445132955908775,
-0.001852253801189363,
0.019035406410694122,
-0.09883949905633926,
-0.054448094218969345,
0.006453255191445351,
0.025917774066329002,
-0.030623776838183403,
-0.10281666368246078,
0.010591953061521053,
0.031642846763134,
0.042981263250112534,
-0.013087986037135124,
-0.01717653125524521,
0.0028689841274172068,
0.032620422542095184,
-0.0018126842333003879,
0.008258596993982792,
0.0019294628873467445,
0.007741076871752739,
-0.02357233688235283,
-0.0195799358189106,
-0.04181103780865669,
0.02473588101565838,
0.03603672236204147,
0.004407359287142754,
0.006621975917369127,
0.05089923366904259,
-0.0259025190025568,
0.009435232728719711,
0.026067977771162987,
0.018560990691184998,
-0.01637621596455574,
0.0744909718632698,
0.04178381711244583,
-0.01869666948914528,
0.015556533820927143,
0.0068984199315309525,
0.03722545504570007,
0.005486638750880957,
0.01354983076453209,
0.060243550688028336,
-0.04475279897451401,
-0.0335313156247139,
-0.0300228763371706,
0.0018323768163099885,
0.007487085182219744,
-0.030725110322237015,
-0.02475796826183796,
0.0053595807403326035,
0.015886874869465828,
-0.037657447159290314,
0.04063922539353371,
0.005700245965272188,
0.040948498994112015,
0.007891464978456497,
-0.019427059218287468,
-0.013770757243037224,
-0.0656905397772789,
0.06746551394462585,
-0.041816405951976776,
-0.017233744263648987,
0.03690016642212868,
0.03430267795920372,
-0.043006278574466705,
0.02473759651184082,
-0.05156450346112251,
0.004937677178531885,
0.012818845920264721,
-0.006265026517212391,
-0.04958628490567207,
0.011841883882880211,
0.046331051737070084,
-0.007913927547633648,
0.022744949907064438,
0.03404868394136429,
-0.0036583461333066225,
-0.028937024995684624,
-0.0002956438693217933,
-0.04398718476295471,
0.008909898810088634,
0.0020881446544080973,
0.03301301226019859,
-0.015009316615760326,
-0.009552521631121635,
0.004910365678369999,
0.03502661734819412,
-0.037917908281087875,
0.0928192064166069,
0.013624001294374466,
-0.029260385781526566,
0.029963763430714607,
0.06977225840091705,
0.012226266786456108,
0.010064749047160149,
-0.014912745915353298,
-0.051638584583997726,
-0.04849294200539589,
-0.01944626308977604,
0.006398375611752272,
0.01051576528698206,
-0.058941226452589035,
0.026556117460131645,
-0.018468501046299934,
0.04456904157996178,
0.002782269148156047,
0.023990198969841003,
-0.02357439137995243,
-0.08398081362247467,
0.012611934915184975,
0.030348148196935654,
-0.02883050963282585,
0.002836418803781271,
0.010378004051744938,
-0.00865601934492588,
-0.009395970962941647,
-0.0030509254429489374,
0.00704623106867075,
0.03527342528104782,
-0.012095192447304726,
0.004905333276838064,
0.017220502719283104,
-0.04814866930246353,
0.038592878729104996,
0.013608410023152828,
0.02626221626996994,
0.021985957399010658,
-0.042701587080955505,
-0.019855830818414688,
-0.006536131724715233,
0.011222921311855316,
0.02773316204547882,
0.033755358308553696,
-0.00881163589656353,
-0.03761504590511322,
0.038116082549095154,
-0.03409988805651665,
0.009603028185665607,
-0.03489521145820618,
0.007319142110645771,
0.020226389169692993,
-0.03212854266166687,
0.04039885103702545,
0.04191803187131882,
0.012492278590798378,
-0.02738189324736595,
-0.01807687059044838,
0.009699143469333649,
-0.018893053755164146,
0.004415540490299463,
0.02853664755821228,
-0.023198723793029785,
0.018303362652659416,
-0.0306082833558321,
-0.004549076780676842,
0.027386363595724106,
-0.019243448972702026,
0.030990220606327057,
0.04437484219670296,
-0.004975032992660999,
-0.056796595454216,
-0.025052808225154877,
-0.012757154181599617,
-0.0067652752622962,
-0.02417980134487152,
0.011515872552990913,
0.015553165227174759,
0.005868909880518913,
0.01367274858057499,
0.0013026715023443103,
-0.057332877069711685,
-0.007512474432587624,
-0.026339752599596977,
-0.03909197449684143,
0.0318877175450325,
-0.0005762879154644907,
0.008438381366431713,
0.04649707302451134,
-0.06684787571430206,
0.022829417139291763,
-0.02514634281396866,
-0.0369882769882679,
0.029497014358639717,
-0.015915557742118835,
0.01703813672065735,
-0.01436860952526331,
-0.026683788746595383,
0.05963898077607155,
0.025244206190109253,
-0.05526908487081528,
-0.003838529344648123,
0.006464596837759018,
-0.013332979753613472,
-0.03854886069893837,
-0.010408845730125904,
0.03755061700940132,
0.010607902891933918,
0.030781416222453117,
-0.005631045438349247,
0.05288132652640343,
0.018910299986600876,
0.032117705792188644,
-0.014498493634164333,
0.033427510410547256,
0.006303817965090275,
0.011868394911289215,
0.03693093731999397,
0.026385966688394547,
-0.04364382103085518,
-0.015584813430905342,
0.012888691388070583,
0.039137810468673706,
-0.0023552007041871548,
-0.06358414143323898,
0.04144437238574028,
-0.016220716759562492,
-0.022181568667292595,
-0.0038584875874221325,
0.05708012729883194,
-0.020197167992591858,
-0.016450224444270134,
-0.002056434052065015,
0.03809117525815964,
0.04941286891698837,
-0.0071298591792583466,
-0.015281647443771362,
0.01727267913520336,
0.014467009343206882,
-0.012488989159464836,
-0.03107517771422863,
0.0046999286860227585,
-0.001252614427357912,
0.031188197433948517,
-0.01898675598204136,
-0.03373251482844353,
-0.0028287251479923725,
0.002937051933258772,
0.0300291758030653,
0.0005432001198641956,
-0.056278400123119354,
0.02122616022825241,
-0.04771054536104202,
0.00439880695194006,
0.011592650786042213,
0.013939869590103626,
0.005525008775293827,
0.0655331164598465,
0.05242612957954407,
0.048437971621751785,
0.007030501030385494,
-0.024858810007572174,
-0.06025102362036705,
0.02951478213071823,
-0.08279963582754135,
-0.013076492585241795,
-0.018403153866529465,
-0.009009629487991333,
-0.027483440935611725,
-0.034180182963609695,
0.01956624910235405,
-0.03219646215438843,
-0.01894271746277809,
-0.023173747584223747,
0.02056383155286312,
-0.03242218494415283,
-0.07482391595840454,
-0.02965249866247177,
0.09122574329376221,
0.023171372711658478,
-0.021442584693431854,
0.053466856479644775,
0.0046974653378129005,
-0.019006554037332535,
-0.020966436713933945,
-0.0014207945205271244,
0.027384765446186066,
-0.031611934304237366,
0.03614039346575737,
0.042353831231594086,
0.014787322841584682,
-0.00844306405633688,
0.002997966716066003,
0.021491892635822296,
0.035381533205509186,
0.011935411021113396,
-0.02444867230951786,
0.0005420566885732114,
-0.06513071060180664,
-0.01663706637918949,
-0.023500753566622734,
0.04402613267302513,
-0.004455713089555502,
0.009745136834681034,
0.01094623189419508,
0.013359344564378262,
-0.030976518988609314,
0.024305203929543495,
0.010014975443482399,
0.05054366588592529,
-0.04083865508437157,
-0.06025586649775505,
0.023360198363661766,
0.009448761120438576,
-0.002350572030991316,
-0.009874467737972736,
-0.04597289860248566,
-0.012367093935608864,
0.02005877159535885,
-0.0006292971083894372,
-0.005373483989387751,
-0.021851446479558945,
0.014878308400511742,
-0.005254060495644808,
-0.006725627928972244,
0.011757553555071354,
0.010750065557658672,
0.035305898636579514,
0.021818529814481735,
0.051847636699676514,
-0.005190699826925993,
0.005615490488708019,
-0.08607473969459534,
0.006029061507433653,
0.03708316758275032,
0.07157378643751144,
-0.05054822564125061,
-0.005668900441378355,
-0.026681259274482727,
-0.02056371234357357,
0.06773622334003448,
0.007822372950613499,
0.05117608606815338,
-0.02085389383137226,
-0.016395756974816322,
0.011739498935639858,
0.0011795518221333623,
-0.053100522607564926,
0.020368194207549095,
0.025361595675349236,
-0.009532065130770206,
-0.05087921395897865,
-0.0168421920388937,
0.02537526562809944,
-0.0030718545895069838,
0.04543698951601982,
0.014026635326445103,
0.009829807095229626,
-0.0063102226704359055,
-0.006992262788116932,
0.024965204298496246,
0.015223431400954723,
-0.06766451150178909,
0.031822867691516876,
0.015610950067639351,
0.017389561980962753,
0.02094276435673237,
-0.015016205608844757,
-0.0584692507982254,
0.03927244991064072,
0.0021244597155600786,
0.025923224166035652,
-0.014719516038894653,
-0.029686307534575462,
0.024518396705389023,
0.04001406952738762,
-0.011050896719098091,
0.030788976699113846,
0.03784329071640968,
-0.024706082418560982,
-0.019887534901499748,
-0.0039879209361970425,
0.05743354558944702,
-0.029296059161424637,
-0.02732256054878235,
-0.04824453592300415,
0.032975923269987106,
0.005721930880099535,
0.01924017444252968,
-0.0025390854571014643,
0.024846237152814865,
0.027366578578948975,
-0.04313761740922928,
-0.023021770641207695,
0.031501226127147675,
-0.032597728073596954,
-0.00018395688675809652,
0.007886202074587345,
0.03976566717028618,
-0.012585695832967758,
-0.02276458591222763,
-0.017955901101231575,
-0.003246691543608904,
0.013805180788040161,
0.0022493621800094843,
-0.014354607090353966,
-0.002364818239584565,
-0.006324008107185364,
-0.036378566175699234,
0.03441450372338295,
-0.05117778480052948,
0.038840096443891525,
-0.004139434080570936,
-0.032294753938913345,
0.033427465707063675,
-0.07527661323547363,
-0.02469136193394661,
0.018872739747166634,
-0.04592860862612724,
0.06939603388309479,
-0.049439117312431335,
0.003714798716828227,
-0.020381690934300423,
0.0320885144174099,
-0.06289629638195038,
-0.023132486268877983,
0.020090661942958832,
0.005345719400793314,
-0.03335149213671684,
-0.0034689470194280148,
-0.00869709812104702,
0.004402083810418844,
-0.03743218258023262,
0.0035820326302200556,
0.02986014261841774,
-0.047070328146219254,
0.0018523848848417401,
-0.00479657668620348,
0.009888485074043274,
0.032253164798021317,
-0.00894824881106615,
-0.007508664391934872,
-0.02199949510395527,
-0.037912242114543915,
0.01701299287378788,
-0.01762046478688717,
0.08859184384346008,
-0.025218503549695015,
-0.023877661675214767,
0.007784175220876932,
-0.008165648207068443,
0.021383104845881462,
-0.025439972057938576,
-0.01010189950466156,
0.007751769851893187,
0.008491219952702522,
-0.004056068602949381,
0.03899586573243141,
-0.01084413193166256,
-0.016890868544578552,
0.03296646475791931,
-0.013212417252361774,
0.0038045207038521767,
-0.007166061084717512,
-0.04076126962900162,
0.013659156858921051,
0.024585217237472534,
0.046501632779836655,
0.034866541624069214,
0.036258019506931305,
-0.03996474668383598,
-0.017977021634578705,
0.023959273472428322,
0.007055805064737797,
0.050044018775224686,
-0.022902773693203926,
0.01568393036723137,
0.01882890984416008,
-0.013315915130078793,
-0.00702088326215744,
-0.015911128371953964,
-0.03291746601462364,
0.013909347355365753,
0.07024873048067093,
-0.003050816711038351,
0.06684263050556183,
-0.0016924880910664797,
0.03834459185600281,
-0.008938383311033249,
-0.02746453322470188,
-0.03063395619392395,
-0.02674221619963646,
0.011221228167414665,
0.028528783470392227,
-0.02245229296386242,
-0.013707559555768967,
0.003902426455169916,
0.044211357831954956,
-0.04724685847759247,
-0.010669839568436146,
0.030791305005550385,
0.04311152920126915,
0.007617826107889414,
-0.01888349838554859,
-0.07787643373012543,
0.01886659860610962,
-0.023746689781546593,
0.037110038101673126,
0.01797492429614067,
-0.0417088083922863,
0.042868904769420624,
-0.002511906437575817,
0.05199890211224556,
-0.028298480436205864,
-0.01570609211921692,
-0.040936436504125595,
0.015500749461352825,
0.018499089404940605,
0.03816689923405647,
-0.03200770914554596,
0.044210147112607956,
0.06249236315488815,
-0.026492146775126457,
-0.008833378553390503,
-0.005786395166069269,
-0.04160713404417038,
-0.014326619915664196,
-0.016577551141381264,
-0.036701545119285583,
0.05287681147456169,
-0.04864361882209778,
-0.037491850554943085,
0.00646821828559041,
-0.006281926762312651,
0.02169298753142357,
0.05183349922299385,
0.009842881932854652,
-0.007118396461009979,
0.04624100401997566,
0.003113559214398265,
0.010541031137108803,
-0.022068621590733528,
-0.012267811223864555,
0.11041414737701416,
0.056785162538290024,
0.024715032428503036,
-0.022644467651844025,
0.01693149283528328,
-0.052210353314876556,
0.004357765894383192,
-0.002467314712703228,
-0.008930351585149765,
-0.002287266543135047,
-0.0074078054167330265,
-0.011949017643928528,
0.033607836812734604,
0.02947421930730343,
0.010707887820899487,
0.0694483071565628,
-0.026778453961014748,
-0.018362030386924744,
0.005639251321554184,
0.014906265772879124,
0.005298924632370472,
0.010229131206870079,
0.005092998500913382,
-0.007496777921915054,
-0.0028390358202159405,
0.019890490919351578,
-0.038915928453207016,
-0.0485689602792263,
0.006887797731906176,
0.004599699750542641,
-0.05198359116911888,
-0.012459119781851768,
0.007767368573695421,
-0.008719359524548054,
-0.06608246266841888,
0.024560648947954178,
-0.004449596628546715,
-0.020629707723855972,
-0.031243013218045235,
0.025499911978840828,
0.017855755984783173,
-0.004114015493541956,
0.005509031005203724,
-0.007431798614561558,
-0.024344904348254204,
-0.00979918334633112,
-0.0375467948615551,
0.03134681656956673,
-0.010499599389731884,
0.023433398455381393,
-0.02291438914835453,
0.04682374373078346,
-0.003790369024500251,
-0.061566952615976334,
-0.001625950913876295,
0.01996782422065735,
-0.014144708402454853,
-0.0017355023883283138,
0.006380916107445955,
0.018556538969278336,
0.05878879874944687,
-0.017629841342568398,
-0.0066243745386600494,
0.0037255154456943274,
0.02202337235212326,
0.007252722512930632,
0.02618805319070816,
0.06387998163700104,
-0.012733072973787785,
-0.03203430399298668,
-0.04377942904829979,
0.026856306940317154,
-0.05585102364420891,
-0.009968656115233898,
0.041974496096372604,
0.03231712803244591,
0.0478619709610939,
0.006563217379152775,
-0.009837307967245579,
0.002357404911890626,
-0.0851491242647171,
0.02625289000570774,
0.006757387425750494,
0.004783590789884329,
-0.0522051639854908,
0.012660334818065166,
0.015927307307720184,
0.00572538236156106,
-0.007925503887236118,
0.005993782542645931,
-0.02314077690243721,
0.013192682527005672,
0.026922764256596565,
-0.022990142926573753,
-0.014260150492191315,
0.021856343373656273,
-0.03719869628548622,
0.015095321461558342,
-0.013180862180888653,
0.009406122379004955,
0.0290033221244812,
0.005109390243887901,
0.013754770159721375,
-0.0011093514040112495,
-0.03498128429055214,
0.03528297692537308,
0.00901082344353199,
-0.03105941414833069,
0.001276983181014657,
0.01071775984019041,
-0.05083887279033661,
-0.0748356506228447,
0.015926947817206383,
-0.027729878202080727,
-0.01298090722411871,
0.02436872571706772,
0.012992850504815578,
0.016437601298093796,
0.01006547175347805,
-0.03084508143365383,
0.006474840920418501,
0.004252148792147636,
-0.011337772011756897,
-0.0357159748673439,
0.0018378841923549771,
0.0024437604006379843,
0.006663985550403595,
-0.02067800983786583,
0.05332488939166069,
-0.015415963716804981,
-0.03879517689347267,
0.018156906589865685,
0.011831110343337059,
-0.0013379454612731934,
0.001959724584594369,
0.03095025010406971,
-0.0038120902609080076,
0.037069931626319885,
-0.02604605257511139,
-0.02072618342936039,
0.01269484218209982,
-0.03195928409695625,
-0.052680447697639465,
0.04605448618531227,
-0.02515595592558384,
0.014174827374517918,
0.0011322031496092677,
0.009489272721111774,
0.009262332692742348,
0.08519142866134644,
-0.04135233536362648,
-0.009156572632491589,
0.008493800647556782,
0.015427459962666035,
0.011014335788786411,
-0.01973525434732437,
-0.00485891941934824,
0.0018911277875304222,
0.005192975513637066,
0.046706754714250565,
0.005456971470266581,
-0.030630744993686676,
0.01984190195798874,
-0.007369200699031353,
-0.012723881751298904,
-0.00862978771328926,
0.010391131043434143,
0.046623945236206055,
0.009887154214084148,
0.03012765944004059,
0.011791636236011982,
0.029863590374588966,
0.026261981576681137,
-0.00922897644340992,
-0.08509296923875809,
-0.004001490771770477,
0.02236136607825756,
0.0035507511347532272,
0.03342723101377487,
-0.05919063091278076,
0.033555030822753906,
0.01741880737245083,
-0.11390005052089691,
0.01112366747111082,
-0.05050935968756676,
0.007690360303968191,
-0.029419226571917534,
-0.03898564726114273,
-0.0015029695350676775,
0.05373626947402954,
0.0155878197401762,
0.025334322825074196,
0.03018667735159397,
-0.01597001776099205,
-0.02673107199370861,
-0.0022064566146582365,
-0.026060068979859352,
0.03531099855899811,
0.041118502616882324,
-0.023332204669713974,
0.06132036820054054,
0.022302914410829544,
-0.03432618826627731,
0.014991645701229572,
0.01283703837543726,
0.020979000255465508,
-0.03127144277095795,
0.003760106861591339,
0.042758964002132416,
0.03598660230636597,
-0.013749297708272934,
0.011191906407475471,
-0.02023468352854252,
0.02207048237323761,
-0.008742718026041985,
0.016200335696339607,
-0.02614922821521759,
0.008597450330853462,
-0.007807652931660414,
-0.06555024534463882,
-0.04764444753527641,
-0.024948712438344955,
0.0028895463328808546,
-0.026072850450873375,
0.020388785749673843,
0.023910515010356903,
0.010807525366544724,
-0.019770585000514984,
-0.006595128681510687,
-0.03705066442489624,
0.014955421909689903,
0.03141510859131813,
0.0009943863842636347,
0.008770665153861046,
0.03332081064581871,
-0.024465639144182205,
-0.02096771076321602,
0.016283327713608742,
0.009098397567868233,
-0.05488622561097145,
-0.0344240665435791,
0.009585557505488396,
0.011000409722328186,
0.009304221719503403,
0.028165128082036972,
-0.02439848519861698,
-0.03365803882479668,
0.03899766132235527,
-0.003741342108696699,
0.030123354867100716,
-0.008709113113582134,
-0.035109102725982666,
-0.034815143793821335,
-0.05742133781313896,
0.054582979530096054,
-0.019435139372944832,
-0.01987309195101261,
-0.03171816095709801,
-0.05121629312634468,
-0.03920464217662811,
0.017678670585155487,
0.030032334849238396,
0.007661796174943447,
-0.03196517750620842,
0.007396303117275238,
-0.030888350680470467,
0.000935751071665436,
-0.026894792914390564,
0.006293863523751497,
0.0096910260617733,
-0.008433137089014053,
0.013820800930261612,
0.003657558234408498,
-0.004511856008321047,
0.03184489160776138,
-0.02652919478714466,
-0.0016841478645801544,
0.007173146121203899,
0.030531154945492744,
-0.04071519896388054,
0.024714719504117966,
0.008365382440388203,
-0.004546120297163725,
0.05980117619037628,
0.029066789895296097,
-0.01184878870844841,
0.018225258216261864,
-0.037505727261304855,
-0.04875677451491356,
-0.0035511343739926815,
-0.012458640150725842,
-0.0006704055122099817,
-0.041928984224796295,
-0.008342762477695942,
0.05315743386745453,
-0.02347741276025772,
-0.002562888665124774,
0.06799051910638809,
-0.06379232555627823,
0.00012243131641298532,
0.01843656599521637,
0.027270615100860596,
0.0208690594881773,
0.033825989812612534,
0.03917759284377098,
0.02850160002708435,
0.0013952833833172917,
-0.005456050857901573,
0.02547420747578144,
0.04743613675236702,
0.019481999799609184,
0.00843057967722416,
0.03241453692317009,
0.020193303003907204,
-0.002136645605787635,
0.016833672299981117,
0.03059883788228035,
-0.023740701377391815,
-0.022765055298805237,
0.02289428561925888,
-0.014091454446315765,
-0.015336590819060802,
0.036489296704530716,
-0.01733211800456047,
0.046212367713451385,
-0.02235499396920204,
0.00342617928981781,
-0.02452920936048031,
-0.016395103186368942,
0.017187125980854034,
0.01235493179410696,
0.007638539187610149,
0.02502565085887909,
-0.0017410976579412818,
-0.030725622549653053,
-0.0050365012139081955,
-0.0048945993185043335,
0.03931339457631111,
-0.05454014614224434,
0.005307098384946585,
-0.019383182749152184,
-0.005366938654333353,
-0.012567478232085705,
0.008361331187188625,
-0.06418382376432419,
-0.04018062725663185,
0.024969398975372314,
0.04098566994071007,
0.06032542139291763,
0.01119215413928032,
0.0022588432766497135,
-0.05231200531125069,
0.024300485849380493,
-0.046472907066345215,
-0.04517766833305359,
-0.03739558532834053,
0.007613320369273424,
0.015314626507461071,
0.02914706990122795
] |
<p>It's actually a teaching conflict at my school. They said that $$\text{Flux}=\frac{q}{\varepsilon_0}.$$ Say for a point charge at the centre of the sphere and let's say we not put water into the sphere, so now $E/ \varepsilon_0=K$. Thus $E= \varepsilon_0 K$.
So flux becomes $q/\varepsilon_0 K$. That means that any change in medium changes the flux.</p>
<p>However, in FIITJEE I was told that the addition of a medium won't change the flux since the number of electric field lines remains constant for any medium. So changing medium won't change the formula, $\text{flux}=q/\varepsilon_0$.</p>
<p>So, does flux actually change with change in medium or not? </p>
<p>$K$ is the dielectric constant.</p> | 1,500 | [
-0.016215993091464043,
0.0006561928312294185,
-0.005520537029951811,
-0.005121962632983923,
0.03377121686935425,
0.013003501109778881,
-0.027090800926089287,
0.002880146261304617,
0.006660104263573885,
-0.026834538206458092,
0.03284898400306702,
0.016314411535859108,
0.08028066903352737,
0.013214685954153538,
0.03712864965200424,
-0.004238518420606852,
-0.008312405087053776,
0.007704513613134623,
-0.015787171199917793,
0.00011222529428778216,
0.0011983260046690702,
0.032260119915008545,
0.013226412236690521,
0.007089232560247183,
-0.001099742716178298,
0.04688267782330513,
0.002884906018152833,
-0.016763469204306602,
0.029556039720773697,
0.042267173528671265,
0.034214552491903305,
-0.03946181759238243,
0.027771487832069397,
-0.006410629488527775,
0.020059634000062943,
0.0017149938503280282,
-0.006251745857298374,
-0.056817084550857544,
-0.008176068775355816,
0.017370061948895454,
-0.0017260578460991383,
0.004326265305280685,
0.019756916910409927,
0.040993593633174896,
-0.015388154424726963,
0.02637500688433647,
0.023399822413921356,
-0.019064096733927727,
0.05117597430944443,
-0.04623158276081085,
0.029607990756630898,
0.024566469714045525,
0.04361189901828766,
0.06982088834047318,
-0.028776898980140686,
-0.006528261583298445,
0.08876383304595947,
0.058595120906829834,
-0.003855321556329727,
-0.005026732571423054,
-0.014559837058186531,
-0.019216908141970634,
-0.013240744359791279,
-0.05350317433476448,
-0.03012397512793541,
0.02937879040837288,
0.006094598677009344,
-0.008068939670920372,
0.05302577093243599,
-0.0017573053482919931,
0.005567572079598904,
0.011465590447187424,
0.009794031269848347,
0.0018086832715198398,
0.0051245610229671,
-0.031771156936883926,
0.020573485642671585,
0.03650816157460213,
0.015029040165245533,
0.05893699452280998,
-0.00756500568240881,
0.008134446106851101,
0.023665042594075203,
0.021307338029146194,
0.032084088772535324,
-0.006033786106854677,
0.0281844362616539,
0.00808035023510456,
0.018886074423789978,
0.0410492867231369,
-0.017649810761213303,
0.017203522846102715,
0.02196401171386242,
-0.01951269619166851,
-0.00822649896144867,
0.010267132893204689,
-0.004422733560204506,
0.022682996466755867,
0.008673508651554585,
-0.024251330643892288,
0.025530992075800896,
0.016644775867462158,
0.05599140748381615,
0.06892995536327362,
0.0292472243309021,
-0.0450051948428154,
-0.04104118421673775,
-0.006545132026076317,
-0.03035011887550354,
-0.03407755866646767,
-0.03922756388783455,
0.010009084828197956,
-0.020074661821126938,
0.028502466157078743,
-0.021306578069925308,
-0.04061419889330864,
0.01715315319597721,
-0.028165966272354126,
0.08895934373140335,
0.03113574907183647,
0.04560714215040207,
-0.05177396163344383,
-0.005640444811433554,
-0.014919718727469444,
-0.06514357775449753,
0.020295174792408943,
0.008110825903713703,
-0.008621059358119965,
-0.024592380970716476,
0.013225767761468887,
-0.0030294922180473804,
0.00611743051558733,
0.004327320959419012,
0.009104868397116661,
0.00943843461573124,
0.005707004573196173,
-0.08538476377725601,
-0.05044732615351677,
0.024570228531956673,
-0.0347190760076046,
0.005161755718290806,
-0.08152586966753006,
-0.010218484327197075,
0.012281510047614574,
0.0598130039870739,
-0.015461880713701248,
-0.00040540978079661727,
0.011135545559227467,
0.06236062943935394,
-0.001009453204460442,
-0.010132485069334507,
-0.027705157175660133,
0.01655728928744793,
-0.058627448976039886,
0.02750660851597786,
-0.04799364134669304,
0.013737733475863934,
0.04525895044207573,
0.011353039182722569,
0.001624301541596651,
0.07016608119010925,
-0.02469570003449917,
-0.0065211099572479725,
0.027557816356420517,
-0.041421663016080856,
-0.048833999782800674,
0.057828351855278015,
-0.0026398608461022377,
0.054952219128608704,
0.01421489380300045,
0.022367103025317192,
0.00467979721724987,
0.005606523714959621,
0.03948051109910011,
0.052276287227869034,
-0.03010321408510208,
-0.002812671009451151,
-0.07517611235380173,
0.027202412486076355,
0.0056204162538051605,
-0.0652003213763237,
-0.01815570518374443,
0.01859993115067482,
0.04551234841346741,
-0.002440584823489189,
0.05509179085493088,
-0.00257619540207088,
0.002268868265673518,
-0.02216179668903351,
-0.04629968851804733,
-0.022863060235977173,
-0.016033118590712547,
0.04015449434518814,
-0.004878700245171785,
-0.02789725363254547,
-0.008232719264924526,
-0.025091275572776794,
-0.0027433058712631464,
-0.04402626305818558,
-0.04778452217578888,
0.011777151376008987,
0.02077740803360939,
-0.010841681621968746,
-0.02796589583158493,
0.015475223772227764,
0.03227216377854347,
0.021762510761618614,
0.0078279385343194,
0.023944826796650887,
-0.04325925558805466,
0.0023559005931019783,
-0.0038510134909301996,
-0.021689429879188538,
0.04754337668418884,
-0.005884724669158459,
-0.05101264640688896,
0.007162222173064947,
0.02679523453116417,
0.000535248254891485,
0.024045271798968315,
-0.03502201288938522,
0.04001356661319733,
0.05920371413230896,
0.003612571395933628,
-0.010022608563303947,
0.021871892735362053,
-0.010085606016218662,
0.009993021376430988,
-0.03188268095254898,
-0.047808945178985596,
-0.04487462341785431,
0.024152623489499092,
0.04394149035215378,
-0.0007422369089908898,
0.01274163369089365,
0.008887258358299732,
-0.006941827479749918,
0.026195963844656944,
0.022450771182775497,
-0.004839785862714052,
0.012306739576160908,
-0.07687938213348389,
0.02345186099410057,
0.008590660989284515,
0.0011228066869080067,
0.030819838866591454,
0.020659195259213448,
-0.0022776583209633827,
0.017679329961538315,
-0.029472993686795235,
0.010801883414387703,
-0.010275308042764664,
0.003130385186523199,
0.034105028957128525,
0.013801340013742447,
-0.006942403968423605,
-0.02301642671227455,
-0.05194792151451111,
0.03838934749364853,
0.024642979726195335,
0.019674716517329216,
0.0009653690503910184,
-0.03318491950631142,
0.004922965541481972,
0.017215179279446602,
-0.025220949202775955,
-0.01717127487063408,
-0.013190052472054958,
0.012598558329045773,
-0.04569181799888611,
0.010606179013848305,
0.02596300095319748,
0.012770404107868671,
-0.003590429201722145,
-0.033858854323625565,
-0.0024593151174485683,
0.014840412884950638,
0.055798739194869995,
-0.031379204243421555,
0.0011093545472249389,
0.005258465651422739,
-0.029404373839497566,
0.0014697856968268752,
0.026228323578834534,
-0.02288849838078022,
0.013755852356553078,
-0.004084357991814613,
-0.0353984460234642,
0.028068698942661285,
-0.013956871815025806,
-0.01957562007009983,
0.04819224402308464,
-0.016710758209228516,
-0.057309340685606,
0.01574535109102726,
-0.005336133763194084,
-0.00221286341547966,
-0.005677920300513506,
0.011569625698029995,
0.012539731338620186,
-0.02471192739903927,
-0.03914964944124222,
-0.019457882270216942,
-0.05186649411916733,
-0.056503698229789734,
-0.04189695790410042,
-0.04089634492993355,
0.03779895603656769,
-0.009771221317350864,
0.021667081862688065,
0.010582111775875092,
-0.05627327039837837,
-0.010561740957200527,
-0.03082227148115635,
-0.04813531041145325,
0.026051290333271027,
-0.04279114678502083,
0.06756173074245453,
-0.03354434669017792,
-0.08501330763101578,
0.05787897855043411,
0.05927348509430885,
-0.04838961362838745,
-0.009125923737883568,
0.009207731112837791,
0.004963276907801628,
-0.07857910543680191,
0.0014150784118101,
0.031777456402778625,
-0.044996194541454315,
0.02198445424437523,
0.01204622257500887,
0.025017090141773224,
0.005725207272917032,
0.02433045767247677,
-0.004059168975800276,
-0.01241367682814598,
0.017932409420609474,
0.0051012905314564705,
0.07699379324913025,
0.024142319336533546,
0.01576817035675049,
-0.013252431526780128,
-0.03275483846664429,
0.060824137181043625,
0.04912814870476723,
0.010297105647623539,
0.039800673723220825,
-0.00985001027584076,
0.026843877509236336,
-0.032850198447704315,
0.07011876255273819,
0.002471271436661482,
-0.016381902620196342,
0.021253427490592003,
0.0038199087139219046,
0.022113941609859467,
-0.03241574391722679,
0.008885716088116169,
0.009386362507939339,
0.04026787728071213,
-0.0351138636469841,
-0.007506635971367359,
0.0021974702831357718,
0.006244373973459005,
0.025696253404021263,
-0.04155201092362404,
-0.01837739534676075,
0.024930763989686966,
0.014096754603087902,
0.030009979382157326,
-0.014550679363310337,
-0.04775385186076164,
-0.023491665720939636,
-0.030017586424946785,
-0.028674008324742317,
0.0023066834546625614,
0.016306554898619652,
0.014437662437558174,
0.052656810730695724,
-0.0038871269207447767,
0.004433176014572382,
0.004515488166362047,
0.0075250412337481976,
-0.06548706442117691,
0.0018822102574631572,
-0.01639239862561226,
-0.0184995848685503,
-0.06464753299951553,
-0.020946132019162178,
-0.02894766442477703,
-0.0013853225391358137,
-0.018606865778565407,
-0.034043777734041214,
-0.015959369018673897,
-0.051223378628492355,
0.045464809983968735,
-0.04570486769080162,
-0.02002648636698723,
-0.027547547593712807,
0.07036382704973221,
0.033685557544231415,
-0.05064627528190613,
-0.014745798893272877,
-0.00626935251057148,
-0.04230522736907005,
0.0009952927939593792,
-0.006654735188931227,
-0.010796699672937393,
0.03380176052451134,
0.018979908898472786,
0.0214619729667902,
0.003555950475856662,
-0.008844687603414059,
0.04864107817411423,
0.020210079848766327,
0.04192591458559036,
-0.01480052713304758,
-0.041470568627119064,
-0.05389149487018585,
-0.051679786294698715,
-0.03874946013092995,
-0.03986209258437157,
0.07522913813591003,
-0.013972102664411068,
-0.021178195253014565,
0.01312701404094696,
-0.01015775091946125,
-0.019642675295472145,
0.027191417291760445,
0.03360382467508316,
0.009344863705337048,
-0.005839501041918993,
-0.05291397497057915,
0.009305445477366447,
-0.026340536773204803,
-0.006815684027969837,
0.0098738893866539,
0.02349131368100643,
-0.004508398473262787,
-0.02444293536245823,
0.007155767176300287,
0.010206307284533978,
0.02725904807448387,
0.0173138827085495,
0.0015367441810667515,
-0.02063021808862686,
0.0025358928833156824,
-0.03220932558178902,
0.0009867765475064516,
0.02662658877670765,
0.018467411398887634,
-0.006207985803484917,
-0.023375866934657097,
-0.10677430778741837,
-0.015595385804772377,
0.02223525010049343,
0.021979324519634247,
-0.03439593315124512,
0.028589993715286255,
-0.05578777939081192,
-0.02016284316778183,
0.02450437843799591,
-0.03583472594618797,
0.01977081410586834,
-0.002534102415665984,
0.011024551466107368,
-0.011717889457941055,
-0.03237544372677803,
-0.027066083624958992,
0.03409787267446518,
0.007250568363815546,
0.03977872431278229,
-0.008018787950277328,
0.024527350440621376,
0.0003976988955400884,
0.031742315739393234,
0.02544233947992325,
0.05593553185462952,
0.002834363840520382,
-0.009391584433615208,
0.016226796433329582,
-0.0028940828051418066,
-0.017166050150990486,
-0.06294858455657959,
0.041195567697286606,
0.00550355389714241,
0.03669079393148422,
0.01425759494304657,
-0.02009502425789833,
-0.06433892995119095,
0.012802723795175552,
0.0328674353659153,
-0.007823895663022995,
0.014823799952864647,
0.0010862924391403794,
0.049738746136426926,
0.01886659860610962,
-0.0012538500595837831,
0.069144606590271,
0.000036135854315944016,
-0.020288478583097458,
-0.012608819641172886,
-0.044853199273347855,
0.021000349894165993,
-0.026754237711429596,
-0.023811841383576393,
0.02862360142171383,
0.02504033036530018,
-0.023097703233361244,
0.03962733969092369,
0.00047961954260244966,
0.015584391541779041,
-0.01092110201716423,
-0.026329955086112022,
-0.011332984082400799,
-0.022181246429681778,
0.0020023479592055082,
0.012465539388358593,
-0.012604890391230583,
0.018916182219982147,
0.01639171689748764,
-0.03597214072942734,
0.019232381135225296,
0.016291169449687004,
0.0024961167946457863,
0.022227298468351364,
0.006702366750687361,
0.03176778182387352,
-0.005453519988805056,
-0.036482494324445724,
-0.007746156770735979,
-0.04054689034819603,
0.04032701626420021,
-0.004705799277871847,
0.00009745674469741061,
-0.0019502646755427122,
-0.06551852822303772,
-0.05359086021780968,
0.005711725447326899,
-0.042931441217660904,
0.009325799532234669,
-0.055415570735931396,
0.00041181640699505806,
0.026445506140589714,
0.04105532169342041,
-0.06096149608492851,
-0.07255816459655762,
0.017009597271680832,
0.021764684468507767,
-0.0009627505787648261,
-0.004031503107398748,
0.005821566097438335,
-0.029746590182185173,
-0.065587118268013,
0.00911750365048647,
0.04002169519662857,
-0.05841238051652908,
-0.02040966972708702,
0.016162151470780373,
0.02752077952027321,
0.06075267866253853,
-0.011942262761294842,
0.008329275995492935,
0.0003789779730141163,
-0.02907499298453331,
-0.00890892744064331,
-0.010890359058976173,
0.034955453127622604,
-0.00960619654506445,
-0.019550150260329247,
-0.008098595775663853,
-0.01018571574240923,
0.024645989760756493,
0.006003191694617271,
-0.023983296006917953,
0.029789645224809647,
-0.014721130952239037,
0.0013646312290802598,
-0.022490376606583595,
0.0028903011698275805,
0.030493352562189102,
0.03889834135770798,
-0.027894284576177597,
0.008399062789976597,
-0.054096948355436325,
-0.02411891520023346,
0.013321914710104465,
-0.00891411118209362,
0.041010722517967224,
-0.013957204297184944,
0.08692710846662521,
-0.023266740143299103,
-0.03152043744921684,
0.0010759031865745783,
-0.016376608982682228,
0.0027547047939151525,
0.016181504353880882,
-0.03892409801483154,
0.02121022529900074,
0.030186228454113007,
-0.02445274405181408,
-0.014555378817021847,
-0.03565653786063194,
0.013885186053812504,
0.03417087346315384,
-0.031228620558977127,
0.008920196443796158,
0.03474111109972,
0.0014163872692734003,
0.02351999655365944,
-0.02262737974524498,
-0.04155567288398743,
0.02933412417769432,
-0.029232481494545937,
0.022880759090185165,
-0.013586822897195816,
0.006882118061184883,
0.00526386359706521,
0.040606990456581116,
-0.0095085259526968,
0.011588862165808678,
0.02253122068941593,
0.03937476500868797,
0.0066323732025921345,
-0.016198834404349327,
-0.07385095208883286,
0.044708192348480225,
-0.05650384724140167,
0.05140584707260132,
-0.0021192205604165792,
-0.0043975599110126495,
0.08242999762296677,
-0.005842663813382387,
0.002698836848139763,
-0.058627840131521225,
-0.021844474598765373,
-0.05119473487138748,
0.016546662896871567,
-0.019660791382193565,
0.019714882597327232,
-0.025731921195983887,
-0.001309691579081118,
0.021590275689959526,
0.021279113367199898,
0.003793940646573901,
-0.012330472469329834,
-0.07678905129432678,
-0.02125578187406063,
-0.009939874522387981,
-0.020064372569322586,
0.04093889892101288,
-0.012330466881394386,
-0.040751371532678604,
0.011694392189383507,
-0.042280927300453186,
0.07053784281015396,
0.01965220645070076,
0.014508506283164024,
-0.018832890316843987,
0.03184642270207405,
-0.041714925318956375,
0.0347922220826149,
-0.0052853794768452644,
0.027220336720347404,
0.13046860694885254,
0.04251641035079956,
0.020434612408280373,
-0.03959718346595764,
0.01337040588259697,
-0.027556268498301506,
0.016331393271684647,
-0.02861611731350422,
0.009551682509481907,
-0.05623507499694824,
0.029882259666919708,
0.026336532086133957,
0.045029498636722565,
0.007068602368235588,
0.0016355167608708143,
0.027598470449447632,
-0.028498733416199684,
-0.016229821369051933,
-0.03322432562708855,
0.020395435392856598,
-0.029196957126259804,
0.05457065999507904,
-0.05241817981004715,
0.019129542633891106,
-0.04303901642560959,
0.011285177432000637,
-0.018847065046429634,
0.013609406538307667,
0.015890106558799744,
0.016368318349123,
-0.06235291436314583,
0.011793541721999645,
-0.0004890355630777776,
-0.013261264190077782,
-0.05231016129255295,
0.00830861832946539,
0.053209204226732254,
-0.0013532997108995914,
-0.02898561581969261,
0.025301463901996613,
-0.0024539155419915915,
0.01298325415700674,
0.004830795340240002,
0.03993428125977516,
-0.03786865249276161,
0.013907342217862606,
-0.05494394153356552,
0.048368409276008606,
-0.004316005390137434,
0.033098407089710236,
0.01696573570370674,
-0.023590976372361183,
0.006733452435582876,
-0.036906760185956955,
-0.024712076410651207,
0.0037552218418568373,
0.012737590819597244,
-0.015525829046964645,
0.018992099910974503,
-0.04138534143567085,
0.05150487273931503,
0.007408465724438429,
0.008290042169392109,
0.05887417867779732,
-0.0012430684873834252,
-0.005622717086225748,
0.032905641943216324,
0.0387585274875164,
-0.027202006429433823,
-0.015608350746333599,
0.009431361220777035,
0.015874383971095085,
-0.02606736496090889,
-0.033882249146699905,
-0.001811290392652154,
0.04018624871969223,
0.06388768553733826,
-0.04751460999250412,
-0.014966144226491451,
0.021564187481999397,
-0.06251326203346252,
-0.001143792411312461,
0.0075260428711771965,
0.023843994364142418,
-0.03465640917420387,
0.016933400183916092,
0.012500738725066185,
0.05020331218838692,
-0.043252140283584595,
-0.008556293323636055,
0.020705321803689003,
-0.004580432549118996,
0.012351864017546177,
-0.029025360941886902,
-0.028453903272747993,
-0.0045305402018129826,
-0.039349593222141266,
0.004071338567882776,
-0.04162118211388588,
0.03464088588953018,
0.0393994115293026,
0.003909807652235031,
0.018996387720108032,
0.04278663173317909,
-0.002543550916016102,
0.009178138338029385,
-0.014005444012582302,
0.003048910293728113,
0.014819959178566933,
0.005467122420668602,
-0.012257273308932781,
0.007078593596816063,
0.004719567485153675,
-0.02647537551820278,
0.017492758110165596,
0.012222995981574059,
0.009099604561924934,
-0.01064333226531744,
-0.015626000240445137,
-0.036290306597948074,
0.00999319739639759,
-0.03300536796450615,
-0.023495467379689217,
-0.03335344418883324,
-0.019778281450271606,
0.05147838965058327,
0.037463802844285965,
0.02078309841454029,
0.010079788975417614,
-0.048961520195007324,
-0.02579602226614952,
0.041335251182317734,
-0.01584748923778534,
0.016047043725848198,
-0.042367879301309586,
0.010106815956532955,
0.01296930480748415,
0.0644511952996254,
-0.0450998991727829,
-0.07100998610258102,
0.0598285049200058,
-0.008047833107411861,
-0.042499441653490067,
0.02138320356607437,
0.0323479101061821,
0.023709207773208618,
0.05287808179855347,
0.009102723561227322,
0.014138566330075264,
0.06617268174886703,
-0.012295985594391823,
0.03296980634331703,
-0.03778963163495064,
-0.04003429785370827,
-0.0036771136801689863,
-0.05531913787126541,
0.012990308925509453,
0.04070284217596054,
0.01587267406284809,
0.049063216894865036,
0.011855289340019226,
-0.016289368271827698,
-0.01961412839591503,
0.0069083478301763535,
0.0018101674504578114,
-0.035605888813734055,
0.05599961057305336,
0.02744384855031967,
0.0014841749798506498,
0.046208519488573074,
-0.010035368613898754,
0.007478322833776474,
0.027633192017674446,
0.0015559546882286668,
-0.09355644881725311,
-0.03216930106282234,
0.020282955840229988,
0.028655383735895157,
0.018994959071278572,
-0.05634979531168938,
0.026315055787563324,
0.049614135175943375,
-0.08761516958475113,
-0.023726213723421097,
-0.019856849685311317,
-0.013915660791099072,
-0.03710440173745155,
-0.00753296073526144,
-0.005490499082952738,
0.011413023807108402,
0.022838521748781204,
0.03643054515123367,
0.00930007640272379,
0.031799666583538055,
0.010745584033429623,
-0.00585296843200922,
-0.04190630838274956,
0.03681930899620056,
-0.01831631176173687,
-0.04339604452252388,
0.033392928540706635,
-0.015246336348354816,
-0.011422314681112766,
0.01215176098048687,
0.009390660561621189,
0.003510242560878396,
-0.00021492820815183222,
0.045802224427461624,
0.04887242987751961,
0.04157775267958641,
-0.03308399021625519,
-0.004675775766372681,
-0.020343171432614326,
0.04090242460370064,
0.03260468319058418,
-0.017519595101475716,
-0.016916558146476746,
-0.013481579720973969,
0.07696777582168579,
-0.04170158505439758,
0.008402555249631405,
0.0014870770974084735,
-0.05199309065937996,
-0.004509240388870239,
0.0037368773482739925,
0.01962202787399292,
0.012717247940599918,
-0.0015078531578183174,
-0.024079985916614532,
-0.07827134430408478,
-0.023865772411227226,
0.037084173411130905,
0.016322240233421326,
0.010211206041276455,
-0.005448747891932726,
0.009349426254630089,
-0.004543603863567114,
0.042934734374284744,
0.013661571778357029,
0.02261693961918354,
-0.024176599457859993,
-0.018776966258883476,
0.014602115377783775,
0.018342027440667152,
0.026527514681220055,
-0.022198274731636047,
-0.05597281455993652,
0.007388782687485218,
0.014868649654090405,
0.002774476073682308,
-0.02054128237068653,
-0.06665153056383133,
-0.021912813186645508,
-0.0481252484023571,
0.03983430936932564,
0.01591806858778,
-0.01584794744849205,
-0.03612335026264191,
-0.005736768711358309,
-0.04513699561357498,
0.04416552186012268,
0.0665031373500824,
0.0011722875060513616,
-0.008859440684318542,
0.003331445623189211,
0.006679545622318983,
0.06185207515954971,
-0.07249060273170471,
0.011950241401791573,
0.03519883006811142,
-0.01839519292116165,
0.056497883051633835,
0.038212377578020096,
-0.01863403432071209,
0.02529323659837246,
0.00012732345203403383,
-0.016788695007562637,
0.017480777576565742,
-0.013971884734928608,
-0.031214788556098938,
0.011850782670080662,
0.011351540684700012,
-0.010470288805663586,
0.05537562817335129,
-0.019471144303679466,
0.04713775962591171,
0.010012075304985046,
-0.020837711170315742,
-0.026293940842151642,
-0.01509933266788721,
-0.03865363448858261,
0.03149997442960739,
-0.03211944177746773,
0.015560227446258068,
0.037913717329502106,
-0.030660366639494896,
-0.001089548459276557,
0.029323168098926544,
-0.04054771736264229,
-0.010440130718052387,
0.06415694952011108,
-0.003685969626531005,
0.0396031029522419,
-0.008237197063863277,
0.011333287693560123,
-0.0002663139603100717,
-0.00969495065510273,
-0.010060586966574192,
0.029926350340247154,
0.05030479282140732,
0.005564036313444376,
-0.004562883172184229,
0.0432882159948349,
0.009768555872142315,
0.009759090840816498,
-0.026592448353767395,
0.00678049772977829,
-0.003656896995380521,
-0.014407308772206306,
0.012845126911997795,
-0.006499931216239929,
-0.024956950917840004,
0.030389223247766495,
0.01991621032357216,
0.05421219766139984,
-0.04153664782643318,
0.0076507339254021645,
-0.0044906469993293285,
0.023356877267360687,
0.02600674144923687,
0.05194505304098129,
0.00774012366309762,
0.039532896131277084,
0.006565132178366184,
-0.049505170434713364,
-0.022882159799337387,
-0.0276810172945261,
0.007388182915747166,
-0.06038589030504227,
0.01047083456069231,
-0.0027177101001143456,
0.0029012393206357956,
-0.025503065437078476,
-0.000505227770190686,
-0.0060157375410199165,
-0.003394448896870017,
0.054706696420907974,
0.004905032925307751,
-0.008329818956553936,
0.010369534604251385,
-0.05084451287984848,
-0.021809184923768044,
0.05365613102912903,
-0.026446767151355743,
0.008094250224530697,
-0.017794201150536537,
0.028708565980196,
0.027587253600358963,
-0.02170909196138382
] |
<p>Suppose we have a parallelepiped shaped box full of water on the surface of the sea. Suddenly the box disappears. What is the shape of the waves vs. time caused by the fall of the water contained in the box?</p> | 1,501 | [
-0.018092675134539604,
-0.05291178449988365,
-0.005099270027130842,
-0.014001280069351196,
0.020757487043738365,
0.0051034134812653065,
-0.026870576664805412,
-0.006513801869004965,
0.03014354221522808,
0.0034418317954987288,
0.0331609882414341,
0.08275388181209564,
0.014440089464187622,
-0.011143994517624378,
0.026248667389154434,
0.04269044101238251,
-0.030940748751163483,
-0.018051235005259514,
-0.0056980932131409645,
-0.0374104268848896,
0.03795185685157776,
0.011708008125424385,
0.0021991385146975517,
-0.006655145436525345,
-0.04062396660447121,
0.017408346757292747,
0.05557675659656525,
-0.013911274261772633,
0.042803410440683365,
0.05228511244058609,
-0.006155380047857761,
-0.038169052451848984,
0.0035428544506430626,
0.04293166473507881,
0.0076120574958622456,
0.008660790510475636,
-0.04159088805317879,
-0.029447972774505615,
-0.03718670830130577,
0.043195534497499466,
0.047764088958501816,
-0.025189878419041634,
-0.009837799705564976,
0.04532233625650406,
-0.019893212243914604,
0.02387457899749279,
0.01960652694106102,
-0.048639919608831406,
0.032135479152202606,
-0.03822675347328186,
0.0767984464764595,
-0.01699735037982464,
0.03726891800761223,
-0.00725448178127408,
-0.015173275955021381,
-0.0028763881418854,
0.06849677860736847,
0.056252699345350266,
-0.024335961788892746,
-0.08324659615755081,
0.01575288362801075,
0.007195298559963703,
-0.007408273406326771,
-0.035310812294483185,
-0.029388142749667168,
0.0025723527651280165,
-0.032408423721790314,
-0.0078017269261181355,
0.0122605599462986,
-0.031901754438877106,
-0.00798620656132698,
0.011994103901088238,
0.04134012386202812,
-0.03581341728568077,
0.01896529644727707,
-0.031092867255210876,
-0.005504014436155558,
0.051504191011190414,
0.02157127857208252,
0.031658221036195755,
0.0023365216329693794,
-0.011853979900479317,
0.021155694499611855,
0.01530460175126791,
0.03121579810976982,
-0.01314596924930811,
0.06083188205957413,
-0.007539564743638039,
-0.0087283318862319,
0.027270274236798286,
-0.02068316377699375,
-0.0029561950359493494,
-0.003829509951174259,
-0.009001604281365871,
0.0011269181268289685,
0.03767776116728783,
-0.0020949996542185545,
0.06659449636936188,
0.05318862572312355,
-0.049823563545942307,
0.015665268525481224,
-0.07567709684371948,
-0.01075103972107172,
0.10227660834789276,
0.043647054582834244,
0.0158148892223835,
-0.04439092054963112,
0.028179693967103958,
-0.03886546567082405,
-0.018865084275603294,
0.004864918999373913,
0.003936382941901684,
-0.013743475079536438,
-0.00716140354052186,
0.017780786380171776,
-0.008284310810267925,
0.01352112740278244,
-0.02649719826877117,
0.05084561929106712,
0.0488017275929451,
0.04928058758378029,
-0.020277252420783043,
0.01945185288786888,
-0.018792597576975822,
-0.08108089864253998,
-0.002081455895677209,
0.024371357634663582,
-0.03382442519068718,
-0.040714144706726074,
0.011396046727895737,
0.002212769351899624,
-0.01856827549636364,
0.02367667481303215,
-0.03217652440071106,
0.0407756082713604,
-0.012107249349355698,
-0.07925460487604141,
-0.05295507237315178,
0.014335372485220432,
-0.017253762111067772,
-0.06719191372394562,
-0.04325127229094505,
0.0018756313947960734,
0.014807654544711113,
0.05448602885007858,
-0.017806870862841606,
0.0066755106672644615,
0.02676914446055889,
0.0310271754860878,
-0.028976138681173325,
-0.021872637793421745,
0.0212709978222847,
0.009408140555024147,
-0.03271190822124481,
0.017375217750668526,
-0.03660276159644127,
-0.01985696516931057,
0.05132421851158142,
0.0064622568897902966,
0.0007226322195492685,
0.0235005933791399,
-0.03689514100551605,
-0.02651374787092209,
0.020312344655394554,
-0.023207662627100945,
-0.04883836209774017,
0.06815864890813828,
0.005107590463012457,
-0.009680417366325855,
-0.0028988816775381565,
0.009551992639899254,
0.029636012390255928,
0.0035457287449389696,
-0.002736358903348446,
0.03185421973466873,
-0.027103552594780922,
0.0012341947294771671,
0.0211003627628088,
-0.007009436842054129,
0.03809676691889763,
-0.017917891964316368,
-0.02160138078033924,
-0.006916604470461607,
-0.00621948903426528,
0.013268153183162212,
0.036918219178915024,
0.004759995732456446,
-0.0264736320823431,
-0.03587797284126282,
-0.046605661511421204,
0.007832777686417103,
-0.07320336252450943,
0.05604328215122223,
0.007405912037938833,
0.028286699205636978,
-0.022848840802907944,
0.002832970814779401,
0.01822987198829651,
-0.047502145171165466,
-0.03292256221175194,
-0.031056813895702362,
0.02853449620306492,
-0.015894625335931778,
-0.016373829916119576,
-0.011949636042118073,
0.03465099632740021,
0.050350721925497055,
-0.03151159733533859,
0.02602451480925083,
-0.04008125141263008,
-0.002185340039432049,
-0.014316700398921967,
-0.013214793056249619,
0.01203884743154049,
-0.013380054384469986,
-0.0006128206150606275,
0.016914142295718193,
0.0006652759620919824,
0.009288862347602844,
0.0031555150635540485,
-0.03401639685034752,
0.04936164990067482,
0.0994034931063652,
0.007236763834953308,
0.03603820875287056,
-0.006807583384215832,
0.01264948956668377,
0.003365165088325739,
0.011062722653150558,
-0.025274626910686493,
-0.023114828392863274,
-0.016995493322610855,
0.0024675268214195967,
0.030242033302783966,
0.006436352618038654,
0.015242044813930988,
-0.0009521249448880553,
0.011637081392109394,
0.07165162265300751,
0.007031269371509552,
0.015279186889529228,
-0.008768648840487003,
0.010094978846609592,
0.016909576952457428,
0.01373384241014719,
0.0068502104841172695,
0.03419424965977669,
0.0265149287879467,
-0.015081229619681835,
-0.03439194709062576,
-0.033069003373384476,
0.018467238172888756,
0.010759981349110603,
0.0076610553078353405,
-0.015172207728028297,
-0.014011339284479618,
0.0247325636446476,
-0.03895663470029831,
-0.014081349596381187,
-0.00802544690668583,
0.00237994734197855,
0.025398243218660355,
-0.04531168192625046,
0.007499624975025654,
0.04595121741294861,
-0.005905776284635067,
-0.015100191347301006,
-0.03560705855488777,
0.0359281487762928,
-0.013469455763697624,
-0.0029301815666258335,
-0.0037813386879861355,
-0.026286467909812927,
0.0023873322643339634,
-0.0027817434165626764,
0.05363902822136879,
0.03195163607597351,
0.05290701240301132,
0.01171832624822855,
-0.013266355730593204,
0.019354356452822685,
-0.01426159031689167,
-0.02945266105234623,
-0.0034029469825327396,
-0.08042267709970474,
0.038626790046691895,
-0.04509369283914566,
-0.026582036167383194,
0.06126805767416954,
-0.011749090626835823,
-0.00040480721509084105,
0.0481162890791893,
0.0024910683277994394,
-0.0231232400983572,
-0.028604986146092415,
-0.04745279252529144,
0.012488131411373615,
-0.021712323650717735,
0.026179078966379166,
0.06930799037218094,
-0.015389658510684967,
-0.033160801976919174,
0.03498869016766548,
-0.032398175448179245,
-0.06686485558748245,
-0.04713447391986847,
-0.015316859818994999,
0.02255253680050373,
-0.023371588438749313,
-0.013478264212608337,
-0.02600897289812565,
-0.03103964775800705,
0.027021419256925583,
-0.023163259029388428,
-0.0858641192317009,
0.010240808129310608,
-0.031620778143405914,
0.03523794561624527,
-0.013844487257301807,
-0.021642589941620827,
0.0741720199584961,
0.0015376022784039378,
-0.010219602845609188,
0.006331764627248049,
0.006102296989411116,
0.009739847853779793,
0.001063376315869391,
0.004875957500189543,
0.026053328067064285,
-0.027481401339173317,
0.044027864933013916,
-0.003867045510560274,
-0.006430741399526596,
0.035045426338911057,
0.01220870204269886,
-0.009320957586169243,
0.007818048819899559,
0.023034216836094856,
0.02593429945409298,
0.015975190326571465,
0.02194533683359623,
-0.02814040519297123,
0.018871089443564415,
-0.028695425018668175,
0.018194682896137238,
0.03419974818825722,
-0.07473421096801758,
0.03991292789578438,
-0.004220838658511639,
-0.014528156258165836,
0.02528565376996994,
0.035384293645620346,
-0.05248434841632843,
0.027164757251739502,
-0.0286570955067873,
0.017267437651753426,
0.06563452631235123,
0.00829365011304617,
-0.006968588102608919,
0.03640122711658478,
0.06121215969324112,
-0.009835563600063324,
-0.05558457598090172,
-0.014816263690590858,
0.0189952552318573,
0.05881704017519951,
0.00794058945029974,
-0.046201884746551514,
0.04669315367937088,
0.015128630213439465,
0.028040893375873566,
0.01910153403878212,
-0.022513506934046745,
-0.028721559792757034,
-0.05517600104212761,
-0.025380922481417656,
0.02094596065580845,
0.04086815565824509,
0.01333079393953085,
0.040450409054756165,
0.018341733142733574,
0.0002887417213059962,
0.030506977811455727,
0.013577126897871494,
-0.048419877886772156,
0.005397476255893707,
-0.018534664064645767,
0.00570865161716938,
-0.039637982845306396,
0.041016221046447754,
0.018595026805996895,
0.001136447535827756,
-0.009931119158864021,
-0.009651840664446354,
-0.03132479265332222,
-0.08631572127342224,
0.017473511397838593,
0.01069294847548008,
-0.0312994085252285,
0.015189027413725853,
0.026428060606122017,
0.037040021270513535,
0.02070370875298977,
0.023001778870821,
0.0339408814907074,
-0.029317757114768028,
0.02162935771048069,
0.028056766837835312,
-0.006677957251667976,
0.022418225184082985,
0.009094751439988613,
0.04006756469607353,
0.015513072721660137,
-0.005684587173163891,
0.013212557882070541,
0.021286139264702797,
0.027450811117887497,
-0.025634216144680977,
0.003297362243756652,
-0.006571292877197266,
-0.056008655577898026,
0.030756257474422455,
0.010285685770213604,
0.033465880900621414,
0.006060480140149593,
-0.02610248327255249,
0.009300298988819122,
0.037547770887613297,
0.004454430192708969,
0.04907216131687164,
0.050662051886320114,
0.007888894528150558,
-0.008731885813176632,
-0.04145125299692154,
0.021708548069000244,
-0.0446857288479805,
-0.029589900746941566,
-0.014153189025819302,
-0.009156796149909496,
-0.02328546904027462,
0.01677129976451397,
0.0049848114140331745,
-0.00911071989685297,
0.00655654352158308,
0.007891112938523293,
0.0169584508985281,
-0.029793918132781982,
-0.02535845711827278,
0.009206482209265232,
0.02096446417272091,
0.0658273845911026,
0.04537269100546837,
-0.014937309548258781,
-0.015209979377686977,
-0.03888343274593353,
-0.03633100911974907,
0.022080235183238983,
0.0076719303615391254,
0.013638616539537907,
0.01319140288978815,
-0.0800057202577591,
-0.05750928446650505,
0.09331860393285751,
-0.025518957525491714,
-0.008499342016875744,
0.0036048286128789186,
0.0016483222134411335,
-0.003997349180281162,
-0.011926863342523575,
-0.011883286759257317,
0.02227996662259102,
0.004568665754050016,
0.04078085348010063,
-0.00492908526211977,
-0.018047219142317772,
0.031211471185088158,
0.03952086344361305,
0.05133158713579178,
0.04649629816412926,
0.027015717700123787,
0.020661352202296257,
-0.015947125852108,
-0.023331528529524803,
-0.04383905977010727,
-0.02445177547633648,
0.00841093435883522,
-0.011315670795738697,
-0.026648910716176033,
0.03807995840907097,
-0.016652550548315048,
-0.04692927002906799,
0.03230739012360573,
0.012864024378359318,
-0.00670641427859664,
0.024079198017716408,
-0.05069161206483841,
0.031226519495248795,
0.02761946991086006,
0.014373842626810074,
-0.011606178246438503,
0.039917390793561935,
-0.03339076042175293,
-0.05110888555645943,
-0.021083815023303032,
0.01025256235152483,
-0.02035420574247837,
-0.011803288012742996,
-0.022831862792372704,
-0.022807197645306587,
-0.03671601414680481,
0.03535415232181549,
-0.006217708811163902,
-0.011703329160809517,
0.01644844561815262,
-0.029451852664351463,
-0.004379567224532366,
0.025948161259293556,
0.011266008019447327,
-0.012182559818029404,
0.011613930575549603,
-0.0380481518805027,
0.034307464957237244,
-0.04273851215839386,
-0.01812565326690674,
-0.0030700962524861097,
0.011952128261327744,
0.022360743954777718,
0.01831061765551567,
0.03605549409985542,
-0.00187765306327492,
-0.007378234528005123,
-0.0054558077827095985,
-0.05210883915424347,
0.02115604095160961,
-0.01622900180518627,
-0.006731792818754911,
0.07883180677890778,
-0.05814535543322563,
-0.0004343751061242074,
-0.005390295293182135,
-0.0015036908444017172,
0.03154094144701958,
-0.07571858912706375,
0.02627210132777691,
0.0556894987821579,
0.015307176858186722,
-0.08538291603326797,
-0.02782326005399227,
0.06092929467558861,
0.001625247299671173,
-0.024186713621020317,
-0.023002514615654945,
0.036968592554330826,
-0.03807429224252701,
-0.01887587644159794,
-0.024243921041488647,
0.04816002398729324,
-0.02033035270869732,
-0.0365736223757267,
-0.020977158099412918,
0.022716058418154716,
0.07250001281499863,
0.0003107238153461367,
0.0029898665379732847,
-0.01913469284772873,
-0.031051291152834892,
-0.010972586460411549,
-0.022747119888663292,
0.08367601037025452,
-0.021253004670143127,
-0.0191178098320961,
0.0026596698444336653,
-0.04190706089138985,
0.01974351704120636,
-0.025050345808267593,
0.019865170121192932,
0.045385122299194336,
0.050416961312294006,
-0.024978674948215485,
0.00024166860384866595,
0.021824322640895844,
-0.006011781748384237,
0.00904029794037342,
0.029499992728233337,
-0.030793428421020508,
-0.03986102342605591,
-0.048147257417440414,
0.0018604341894388199,
-0.025829710066318512,
-0.0043637980706989765,
-0.02647021785378456,
0.05115823447704315,
-0.054536834359169006,
-0.010891339741647243,
0.02826169691979885,
-0.011906440369784832,
0.013626989908516407,
0.019544735550880432,
-0.05477570742368698,
0.001934730913490057,
0.02999778650701046,
-0.007009567692875862,
0.0001958885695785284,
-0.04986145719885826,
0.020191486924886703,
0.06801752746105194,
-0.024805089458823204,
0.03571946918964386,
0.0009505947818979621,
0.046308767050504684,
0.00021699347416870296,
-0.0075155263766646385,
0.012411626987159252,
0.013713079504668713,
0.0010616754880174994,
0.06705692410469055,
-0.04507926478981972,
0.012912419624626637,
0.0017622067825868726,
0.03469493240118027,
-0.013181230053305626,
0.05614244192838669,
0.0021576909348368645,
-0.0051991380751132965,
0.018492603674530983,
0.021133694797754288,
-0.04999775439500809,
0.016407456248998642,
-0.021537339314818382,
0.026843637228012085,
-0.016828952357172966,
-0.012177636846899986,
0.02989465557038784,
0.006402216386049986,
-0.02587985061109066,
-0.024889057502150536,
-0.003456918289884925,
-0.013262161053717136,
0.007810274139046669,
0.010575693100690842,
0.057172831147909164,
-0.010475815273821354,
0.03584820777177811,
0.05180324241518974,
-0.0016028365353122354,
0.037856630980968475,
0.008267323486506939,
-0.06303006410598755,
-0.01578407920897007,
-0.019190773367881775,
-0.04593340680003166,
0.06248747184872627,
0.019156016409397125,
0.014514097943902016,
-0.0003758894745260477,
-0.02254844456911087,
-0.016160525381565094,
0.009635059162974358,
0.016332224011421204,
-0.03138023987412453,
0.06688536703586578,
-0.00011151854414492846,
-0.005030353553593159,
-0.041661351919174194,
-0.018067970871925354,
0.11563313752412796,
0.060125481337308884,
0.031962811946868896,
-0.055482666939496994,
0.01868297904729843,
-0.023454608395695686,
0.007735613267868757,
-0.04551347345113754,
-0.009477188810706139,
0.003894347231835127,
0.024083472788333893,
0.01968003436923027,
0.0426250584423542,
-0.0016401000320911407,
-0.013778927735984325,
-0.008734139613807201,
-0.0667317658662796,
-0.04443136230111122,
-0.023343147709965706,
0.02057539112865925,
-0.008595837280154228,
0.027810264378786087,
-0.06181944161653519,
0.05318323150277138,
-0.05405457690358162,
-0.014783360064029694,
-0.04251684248447418,
-0.04818958789110184,
0.05215756595134735,
-0.01671656034886837,
-0.05378144979476929,
0.027842825278639793,
0.018267948180437088,
-0.017115678638219833,
-0.045889198780059814,
0.045789387077093124,
0.00837824959307909,
-0.020233381539583206,
0.009761422872543335,
0.010412604548037052,
0.05597195401787758,
-0.008275918662548065,
0.0094072250649333,
0.01638066954910755,
-0.039164528250694275,
0.0055512189865112305,
-0.03955268859863281,
0.045997850596904755,
0.008278194814920425,
-0.004759859759360552,
0.00456936564296484,
-0.007434031460434198,
-0.012841942720115185,
-0.06505841016769409,
0.001401543035171926,
0.0036165323108434677,
0.04548410698771477,
0.003436736296862364,
0.004446517210453749,
0.028683722019195557,
0.03633136302232742,
-0.0023911905009299517,
0.017166197299957275,
0.012420403771102428,
0.004552817437797785,
-0.013376688584685326,
0.01871415227651596,
0.03941236063838005,
-0.03931162506341934,
0.0029776168521493673,
-0.043566539883613586,
-0.007709541358053684,
-0.0377599373459816,
0.007792470511049032,
0.02437490224838257,
0.03531879931688309,
0.010671429336071014,
0.010867515578866005,
-0.0021571386605501175,
-0.007340533658862114,
-0.08019081503152847,
0.050763942301273346,
-0.014444475993514061,
-0.019773995503783226,
-0.03787112981081009,
0.012747588567435741,
0.04138500243425369,
0.04119788110256195,
-0.02728181891143322,
0.011591298505663872,
-0.002691658679395914,
0.03910832479596138,
0.015678811818361282,
-0.013782523572444916,
0.011666259728372097,
0.010231410153210163,
0.017518792301416397,
0.000010236514754069503,
-0.01925891451537609,
0.04215645790100098,
0.024570517241954803,
-0.006061948370188475,
-0.014359476044774055,
0.022463740780949593,
-0.02787269838154316,
-0.025632532313466072,
0.005802162457257509,
-0.05726300925016403,
-0.00004329827061155811,
0.011925033293664455,
0.03386519104242325,
-0.0374164804816246,
-0.005829355679452419,
-0.009624447673559189,
-0.0018701555673033,
0.0076258061453700066,
0.016160309314727783,
-0.048324696719646454,
0.027308525517582893,
-0.016633495688438416,
0.028558257967233658,
-0.011992557905614376,
-0.003470411989837885,
-0.04908662289381027,
-0.013115492649376392,
0.01676301844418049,
-0.03400878608226776,
-0.029138876125216484,
0.022834205999970436,
-0.033247269690036774,
-0.03961946442723274,
-0.009585663676261902,
0.009811692871153355,
-0.0017020900268107653,
-0.0012887849006801844,
0.02700023725628853,
0.024749385192990303,
0.046110447496175766,
-0.007836584933102131,
-0.05993148311972618,
0.01983252540230751,
-0.04758772253990173,
-0.01972612924873829,
0.04808848723769188,
-0.010274815373122692,
0.0429561622440815,
-0.0012336511863395572,
0.02407068759202957,
-0.003951534163206816,
0.06259825825691223,
-0.022403886541724205,
0.019206412136554718,
0.008423454128205776,
-0.05590848624706268,
0.006814948748797178,
-0.010616419836878777,
0.02420472912490368,
-0.001545202569104731,
-0.05964726209640503,
-0.005258732941001654,
0.03391499072313309,
0.015807228162884712,
-0.010940823704004288,
-0.013762788847088814,
-0.03269241005182266,
0.01232929527759552,
-0.013454233296215534,
-0.012829044833779335,
0.01919623464345932,
0.041797444224357605,
-0.03287205472588539,
-0.007363316603004932,
-0.019006846472620964,
-0.0409046933054924,
-0.11079540848731995,
0.015524417161941528,
0.011863728053867817,
0.037886593490839005,
0.0453156940639019,
-0.04341719299554825,
0.010919027961790562,
0.04326075315475464,
-0.05549003928899765,
0.04609140381217003,
-0.03516635671257973,
0.031640999019145966,
-0.00465708551928401,
-0.005317149683833122,
-0.00638235779479146,
0.061716169118881226,
0.03038625977933407,
0.017428439110517502,
0.03655929118394852,
0.00918390229344368,
-0.014795858412981033,
-0.041127562522888184,
-0.007332988549023867,
0.038054242730140686,
0.013428160920739174,
0.012065213173627853,
0.038112662732601166,
-0.003799817990511656,
-0.004647060297429562,
0.02228160947561264,
-0.02932579629123211,
0.024007443338632584,
-0.012940985150635242,
-0.024071883410215378,
-0.005554247181862593,
-0.00012843972945120186,
0.029884766787290573,
0.022303957492113113,
-0.0031926394440233707,
0.023650141432881355,
0.026123037561774254,
-0.0035823213402181864,
0.00400588707998395,
0.007983165793120861,
0.003362172981724143,
-0.044983405619859695,
-0.028541574254631996,
0.007734932471066713,
0.015482422895729542,
0.014753256924450397,
0.00864845234900713,
-0.02184804156422615,
0.05735347419977188,
0.0033347741700708866,
-0.01179168839007616,
-0.031190207228064537,
-0.006525438744574785,
0.037210315465927124,
0.00019205162243451923,
-0.05639929324388504,
0.017396366223692894,
-0.008243203163146973,
-0.06461762636899948,
-0.01185026578605175,
0.0003752498887479305,
0.00012796946975868195,
-0.032705459743738174,
-0.03129410371184349,
-0.0012253888417035341,
-0.00687674293294549,
-0.0014024102129042149,
-0.04707338288426399,
-0.02425987273454666,
0.007491961121559143,
0.04383651167154312,
0.010501410812139511,
-0.0031051503028720617,
-0.004972976632416248,
-0.035792551934719086,
-0.07502217590808868,
0.04959579184651375,
-0.011982802301645279,
-0.03862742334604263,
-0.026969555765390396,
0.011819694191217422,
0.006723884027451277,
0.01721733994781971,
0.055721789598464966,
-0.020938578993082047,
-0.039343029260635376,
0.008520313538610935,
-0.05322476476430893,
0.014627874828875065,
-0.011456737294793129,
-0.011519002728164196,
0.009105869568884373,
-0.05238436162471771,
0.0172408539801836,
0.0037706131115555763,
0.017727011814713478,
-0.02312183752655983,
0.004691286478191614,
0.019476614892482758,
0.005835158750414848,
-0.002261590911075473,
-0.0032941116951406,
0.022956587374210358,
-0.007031712681055069,
-0.023497190326452255,
0.0773623138666153,
0.025276703760027885,
0.00038302180473692715,
0.020609896630048752,
-0.04953581839799881,
-0.06275743246078491,
-0.017864953726530075,
-0.051354967057704926,
0.007666529156267643,
-0.013985048048198223,
-0.023496590554714203,
0.03696424514055252,
-0.046590931713581085,
-0.015083592385053635,
0.025442304089665413,
-0.0210186168551445,
-0.02676377259194851,
0.05087900161743164,
0.0023653660900890827,
-0.005541941616684198,
-0.046805791556835175,
0.01997770369052887,
0.025861967355012894,
-0.01741584576666355,
0.04246121272444725,
0.02415328472852707,
0.03547943755984306,
0.011857402510941029,
0.03577946126461029,
0.02336563728749752,
0.0025227167643606663,
0.016099102795124054,
0.010626583360135555,
-0.0006932219257578254,
-0.0212901271879673,
-0.0300569087266922,
0.03708256781101227,
-0.01376559678465128,
-0.06184989586472511,
0.024183085188269615,
-0.0077950782142579556,
0.05304274708032608,
0.026407115161418915,
0.006651077885180712,
-0.02513096109032631,
-0.03502761572599411,
-0.022117557004094124,
0.03209156543016434,
0.03290325403213501,
0.015555194579064846,
-0.023332295939326286,
0.0125211076810956,
0.0012148581445217133,
-0.012908008880913258,
0.02317456342279911,
-0.023267369717359543,
0.003460625186562538,
-0.031038252636790276,
0.002779334085062146,
-0.012875944375991821,
-0.00960421934723854,
-0.035045325756073,
-0.009457557462155819,
0.028877079486846924,
0.029683494940400124,
0.022679349407553673,
0.014662472531199455,
0.027041181921958923,
-0.012337545864284039,
0.08044137060642242,
-0.08785422146320343,
0.013287443667650223,
0.0038611579220741987,
0.02691102959215641,
0.0073768929578363895,
-0.021314259618520737
] |
<p>One of the most famous experiments in quantum mechanics in the context of wave-particle duality is certainly passing a beam of electrons through two slits, which results in an interference pattern being formed on a screen positioned after them.</p>
<p>Now, <strong>starting from the Schrödinger equation</strong> (which we know is obeyed by electrons), how can we derive the formula describing the interference pattern?</p>
<p>I am pretty sure we already know the answer, i.e. it is the same pattern generated by light going through two slits (so a sine squared modulated by a sinc envelope), but how do we get it <strong><em>from quantum mechanics</em></strong> ?</p> | 1,502 | [
-0.026779159903526306,
-0.019057350233197212,
0.019382959231734276,
-0.03744940459728241,
0.01443360187113285,
0.0122173260897398,
0.0021150275133550167,
-0.025116372853517532,
0.010104021988809109,
0.01190586481243372,
0.050608545541763306,
0.03202226012945175,
0.038963839411735535,
0.007215357851237059,
0.014645522460341454,
0.020716987550258636,
0.008567719720304012,
-0.022981559857726097,
-0.04007943719625473,
-0.05368062108755112,
-0.04436294734477997,
0.001841177698224783,
0.01176395546644926,
0.022173937410116196,
-0.0114477863535285,
0.044212706387043,
0.0491618812084198,
0.01570996083319187,
0.02708378992974758,
0.04273068904876709,
0.01808933913707733,
-0.004868112504482269,
0.04307674616575241,
0.019036278128623962,
0.01302830409258604,
-0.00462398212403059,
-0.020337700843811035,
-0.02156519889831543,
0.01824965327978134,
0.002875725971534848,
-0.013635236769914627,
0.004922026302665472,
-0.019148273393511772,
0.047522153705358505,
-0.0319347083568573,
-0.006104671861976385,
-0.01939166896045208,
-0.041721608489751816,
0.026609865948557854,
-0.0836775153875351,
0.07410819828510284,
-0.00842426810413599,
0.053321149200201035,
0.017568720504641533,
-0.028843116015195847,
-0.017521092668175697,
0.11653287708759308,
0.03972944617271423,
-0.011804027482867241,
-0.0358281135559082,
-0.01122995000332594,
-0.023731162771582603,
-0.012878748588263988,
-0.021028177812695503,
-0.02021450735628605,
0.023060046136379242,
-0.006577248685061932,
-0.03745210915803909,
0.01754494197666645,
-0.03162423148751259,
-0.005921846255660057,
0.02571192942559719,
0.07310660928487778,
-0.018056543543934822,
0.005497737787663937,
-0.017734650522470474,
0.011011224240064621,
0.016703350469470024,
0.025520671159029007,
0.045397400856018066,
-0.0047583323903381824,
0.032008085399866104,
0.03345393389463425,
0.046578843146562576,
-0.0066049001179635525,
-0.031622521579265594,
0.08074653893709183,
-0.017396878451108932,
-0.0018776810029521585,
0.024996213614940643,
-0.0408768504858017,
0.037796568125486374,
0.03826962411403656,
0.009510267525911331,
-0.02463262900710106,
0.019619036465883255,
-0.006891945842653513,
0.054827939718961716,
0.046530626714229584,
-0.020155781880021095,
0.018656903877854347,
0.000018646464013727382,
-0.009377519600093365,
0.06399155408143997,
-0.009892350994050503,
-0.003605080069974065,
-0.01744084246456623,
0.05633143335580826,
-0.0040560271590948105,
-0.0027232046704739332,
0.0013280801940709352,
0.04229530692100525,
0.03234146162867546,
0.054814744740724564,
-0.010708958841860294,
-0.0051286169327795506,
0.005580071825534105,
-0.03184729442000389,
0.03534223139286041,
0.08391035348176956,
0.022782187908887863,
-0.022449200972914696,
0.022566571831703186,
-0.034166812896728516,
-0.0679064393043518,
-0.013712464831769466,
0.021864699199795723,
-0.0084996884688735,
-0.007325492333620787,
0.03723972663283348,
0.007951192557811737,
-0.025027621537446976,
-0.0002341012004762888,
0.007941434159874916,
-0.007969294674694538,
0.005306310951709747,
-0.13080185651779175,
-0.05650640279054642,
0.02647332288324833,
-0.014925019815564156,
-0.06378224492073059,
-0.04746491461992264,
0.02122318372130394,
0.04475751891732216,
0.10303112119436264,
-0.01718161813914776,
0.004743995610624552,
-0.00840885378420353,
-0.021703355014324188,
0.00913128163665533,
0.010767601430416107,
-0.002169637940824032,
0.015505672432482243,
-0.028283238410949707,
-0.0015288364375010133,
-0.010205001570284367,
0.015084180049598217,
0.016992822289466858,
-0.02498968318104744,
-0.019930372014641762,
0.060429833829402924,
-0.009319095872342587,
-0.03234477713704109,
0.009710955433547497,
-0.008374708704650402,
-0.06232047453522682,
0.11150017380714417,
0.032325562089681625,
-0.011755818501114845,
0.033737607300281525,
-0.025553807616233826,
0.005603238474577665,
-0.01923999935388565,
-0.007873330265283585,
-0.01414367463439703,
-0.003456388134509325,
0.004084394313395023,
-0.011684291996061802,
0.008581959642469883,
-0.004888888914138079,
-0.0021380295511335135,
-0.02939872443675995,
0.0001423152134520933,
0.028470013290643692,
0.008649813011288643,
0.035142552107572556,
-0.02785664238035679,
-0.03555377200245857,
-0.027913909405469894,
-0.03620068356394768,
-0.01730242371559143,
-0.08176174014806747,
0.011541825719177723,
0.012354793958365917,
-0.01674739085137844,
0.04319722577929497,
0.0026381509378552437,
-0.016307085752487183,
0.023749230429530144,
-0.04639022424817085,
-0.02661721408367157,
0.033110249787569046,
-0.00918740313500166,
0.007949505932629108,
0.019510168582201004,
0.050748057663440704,
0.04001561552286148,
-0.033342331647872925,
0.03445377200841904,
-0.028526095673441887,
-0.042581379413604736,
-0.0013916748575866222,
-0.04308650642633438,
0.030440635979175568,
0.003914402797818184,
0.021070176735520363,
0.026142973452806473,
0.01081804558634758,
-0.01858999766409397,
0.018843915313482285,
-0.039162881672382355,
0.03610433265566826,
0.024898666888475418,
0.03811667487025261,
-0.013920594938099384,
0.044237375259399414,
0.005731414537876844,
0.00954216718673706,
0.034612420946359634,
-0.0596446618437767,
-0.025740869343280792,
-0.01421148981899023,
0.025125276297330856,
0.014749398455023766,
-0.011570140719413757,
0.016063202172517776,
-0.01660132221877575,
0.016350707039237022,
0.023498021066188812,
0.03881502151489258,
-0.016573667526245117,
0.00628972053527832,
-0.0045813582837581635,
-0.011869622394442558,
-0.0209786519408226,
0.011054347269237041,
0.013749048113822937,
0.025518028065562248,
-0.0631965920329094,
0.005208393093198538,
-0.04787001386284828,
0.009695333428680897,
-0.024830639362335205,
0.009727870114147663,
-0.017814844846725464,
-0.044505976140499115,
0.021034885197877884,
-0.019598443061113358,
-0.004990128800272942,
0.01508027408272028,
-0.008501488715410233,
-0.009530208073556423,
-0.045494016259908676,
0.017489362508058548,
0.02165113016963005,
-0.02340022474527359,
-0.03310750052332878,
0.02781277894973755,
0.038800884038209915,
-0.039878297597169876,
0.041286684572696686,
-0.017363471910357475,
-0.0194656103849411,
-0.022420629858970642,
0.009209124371409416,
0.020875999704003334,
0.02871430292725563,
0.02984878607094288,
-0.038092926144599915,
-0.06464190781116486,
0.022592321038246155,
-0.03355751186609268,
0.045228783041238785,
0.04247834533452988,
-0.017682932317256927,
0.021690648049116135,
-0.04467727988958359,
-0.01954592391848564,
0.052378762513399124,
-0.014058028347790241,
0.01413670927286148,
-0.024178819730877876,
-0.03846209496259689,
-0.0493694506585598,
-0.01574517786502838,
-0.010699824430048466,
0.004699036944657564,
-0.01162040326744318,
0.009263397194445133,
0.03183542937040329,
-0.01878124102950096,
-0.03890422359108925,
0.01202908530831337,
-0.012585372664034367,
-0.027207665145397186,
-0.02567616105079651,
-0.0007095893961377442,
0.02186541259288788,
-0.009982571937143803,
0.012878695502877235,
0.025890665128827095,
-0.040259215980768204,
-0.00027272666920907795,
-0.054936956614255905,
-0.04124753549695015,
0.00649980828166008,
-0.031761232763528824,
0.029513057321310043,
-0.017035208642482758,
-0.009298223070800304,
0.07817459851503372,
-0.007433853577822447,
-0.02304251119494438,
-0.026872342452406883,
0.0011030933819711208,
0.013501681387424469,
-0.02135181985795498,
0.022771494463086128,
0.05483030527830124,
0.015113954432308674,
0.04520468786358833,
0.007917269133031368,
0.003286423161625862,
0.05405865237116814,
0.05713951587677002,
0.001093102153390646,
0.003640945302322507,
-0.029450396075844765,
-0.010102085769176483,
0.010649451054632664,
-0.003933225758373737,
-0.02737092226743698,
0.005437904968857765,
0.02980017475783825,
-0.005070422776043415,
0.018126314505934715,
-0.046066779643297195,
0.0138754453510046,
-0.014409821480512619,
0.01595432683825493,
-0.028019456192851067,
0.05080008879303932,
-0.0013589489972218871,
0.01706043630838394,
0.005639664363116026,
0.00025627866853028536,
0.02308127097785473,
0.0013752315426245332,
-0.008721026591956615,
0.05866304412484169,
0.018395528197288513,
0.007844842039048672,
-0.04783323407173157,
0.008734125643968582,
-0.018441058695316315,
0.02551862969994545,
-0.055822212249040604,
-0.04489174485206604,
0.027768727391958237,
0.02011372335255146,
0.04191594570875168,
-0.02528669312596321,
-0.043574199080467224,
-0.020847508683800697,
-0.030200080946087837,
-0.009685252793133259,
-0.010907500050961971,
0.047152046114206314,
0.02015405148267746,
0.08275984227657318,
0.02526470646262169,
0.017299244180321693,
0.019833272323012352,
-0.00837617740035057,
-0.05637294799089432,
0.01697358302772045,
0.001977094216272235,
-0.014178288169205189,
-0.044294919818639755,
-0.015276669524610043,
0.02269214764237404,
-0.027939319610595703,
-0.03512199968099594,
-0.03397895395755768,
-0.039865195751190186,
-0.02852724865078926,
-0.01642647571861744,
-0.035115499049425125,
-0.04875768721103668,
-0.026961473748087883,
0.05898594856262207,
0.037937235087156296,
-0.016985325142741203,
0.0009288594010286033,
0.036962080746889114,
-0.045726679265499115,
-0.002263674745336175,
-0.007722171489149332,
0.022800924256443977,
-0.013181723654270172,
0.046322017908096313,
0.027100978419184685,
0.022329535335302353,
0.011554835364222527,
-0.009507945738732815,
0.008467680774629116,
0.07059884816408157,
-0.0036365657579153776,
-0.009610815905034542,
-0.007741350214928389,
0.015648625791072845,
0.010348877869546413,
-0.0224644523113966,
0.07403495907783508,
-0.018373973667621613,
0.000683383084833622,
0.036963123828172684,
0.04192068800330162,
-0.056686434894800186,
0.04804281145334244,
0.04507936164736748,
0.048609569668769836,
-0.02256396971642971,
-0.03554544597864151,
0.019120389595627785,
-0.04170258343219757,
0.016710370779037476,
-0.011132984422147274,
-0.003923350013792515,
0.016014253720641136,
0.034111905843019485,
0.04533151164650917,
0.018382536247372627,
-0.010385319590568542,
-0.014524971134960651,
-0.0693744644522667,
-0.020096221938729286,
-0.007484209258109331,
0.023968243971467018,
-0.03738228604197502,
0.021393349394202232,
0.02137218788266182,
0.02326015755534172,
-0.015371082350611687,
-0.05625951662659645,
-0.010544706135988235,
0.011331064626574516,
0.03133634477853775,
0.007114018779247999,
-0.022870371118187904,
-0.06648028641939163,
-0.031987570226192474,
0.0684291273355484,
0.005389912985265255,
0.023403353989124298,
-0.024810126051306725,
-0.011334855109453201,
-0.05603344365954399,
0.011593557894229889,
-0.03235943615436554,
0.0324162095785141,
0.007535990327596664,
0.038017142564058304,
-0.009639712050557137,
-0.03737891837954521,
-0.02271459810435772,
0.03942647948861122,
0.014535791240632534,
0.04052000865340233,
0.01300852932035923,
-0.013438763096928596,
-0.04759252816438675,
0.006911749951541424,
-0.02805940806865692,
-0.06436040997505188,
0.02077782154083252,
0.014354809187352657,
0.00520910881459713,
0.03976229578256607,
-0.05353797227144241,
-0.02963058464229107,
-0.023583028465509415,
-0.019899649545550346,
0.00971605908125639,
0.026566486805677414,
-0.02452044188976288,
0.046585600823163986,
0.026715794578194618,
0.01108289510011673,
0.060320429503917694,
0.014028873294591904,
-0.030737044289708138,
0.015358363278210163,
-0.0009231733856722713,
0.05851361155509949,
-0.0018766606226563454,
-0.009822333231568336,
-0.023173648864030838,
-0.014328354969620705,
-0.05177459120750427,
0.04582328721880913,
0.006163244601339102,
0.042292237281799316,
0.002017791150137782,
-0.041710179299116135,
-0.020134665071964264,
-0.007543832529336214,
-0.02724451944231987,
0.013376004062592983,
-0.010332217440009117,
0.02076624520123005,
0.03252745419740677,
-0.04652467370033264,
0.0014200243167579174,
-0.013540754094719887,
0.018317613750696182,
0.012042781338095665,
-0.007377585396170616,
0.04373812675476074,
-0.04471603035926819,
-0.00005726273593609221,
0.019761746749281883,
-0.03921641409397125,
0.016590485349297523,
-0.04854820668697357,
0.013889653608202934,
-0.0007705366588197649,
-0.05794442072510719,
-0.047981228679418564,
0.007166699972003698,
-0.010144897736608982,
0.01940876618027687,
-0.022877587005496025,
0.027590489014983177,
0.02109489217400551,
-0.012291546911001205,
-0.06922715902328491,
-0.05410804599523544,
0.01500589307397604,
0.003936328459531069,
-0.018610402941703796,
-0.02035360597074032,
0.015132720582187176,
0.015223181806504726,
-0.04242437332868576,
0.00794572290033102,
0.010756419040262699,
-0.026867320761084557,
-0.014879968017339706,
0.0034039244055747986,
-0.0032591873314231634,
0.04934157058596611,
-0.002315080724656582,
-0.022216489538550377,
0.006533279549330473,
-0.040735550224781036,
0.008078663609921932,
0.024572232738137245,
0.017974263057112694,
-0.012046277523040771,
-0.046933144330978394,
-0.03567790612578392,
-0.014016522094607353,
-0.010708027519285679,
-0.05421675741672516,
0.011690518818795681,
0.037795230746269226,
0.04755125939846039,
-0.00400577625259757,
-0.017912747338414192,
-0.020041098818182945,
0.014490317553281784,
0.03695046156644821,
0.02814922295510769,
0.005367355886846781,
-0.0369279719889164,
-0.02832828275859356,
0.037484265863895416,
0.008209003135561943,
0.00865045003592968,
-0.027882220223546028,
0.01009801123291254,
0.007573048584163189,
-0.039451614022254944,
0.03975475952029228,
-0.018193848431110382,
0.019818587228655815,
-0.012747153639793396,
0.02338125929236412,
0.007930471561849117,
0.011455871164798737,
-0.050838325172662735,
-0.06241312623023987,
-0.032257962971925735,
0.008051717653870583,
0.04470148682594299,
-0.034458473324775696,
0.06945890933275223,
-0.007162322755903006,
-0.040150873363018036,
-0.022403456270694733,
0.016407236456871033,
0.008119733072817326,
0.010856895707547665,
-0.006990435998886824,
0.026840781792998314,
-0.041097018867731094,
0.02512151561677456,
0.021142760291695595,
0.041915200650691986,
-0.01484620850533247,
0.03463396057486534,
0.01746446266770363,
0.025973360985517502,
0.047858793288469315,
-0.01930859684944153,
-0.03137413412332535,
0.04846538230776787,
-0.02875031717121601,
0.01914346218109131,
-0.0032387550454586744,
0.002174076158553362,
0.030095838010311127,
-0.008275392465293407,
-0.005651870276778936,
-0.008906631730496883,
-0.01003843080252409,
-0.03049534559249878,
0.005114047322422266,
0.01776020973920822,
0.022166838869452477,
0.012264383025467396,
0.02449919283390045,
0.00715560233220458,
0.022590160369873047,
-0.004694294184446335,
-0.015267806127667427,
-0.06283137202262878,
-0.028400074690580368,
-0.038006167858839035,
-0.00846656784415245,
0.06923525035381317,
0.024361824616789818,
0.00008549803169444203,
0.011598926968872547,
-0.024797646328806877,
0.006344773806631565,
0.04457594454288483,
0.030077001079916954,
-0.04832451418042183,
0.035061467438936234,
-0.020279696211218834,
0.02354792319238186,
-0.04988614097237587,
-0.010963253676891327,
0.0870627909898758,
0.046826306730508804,
0.03399462625384331,
-0.09152422100305557,
0.01646222174167633,
-0.02187059260904789,
-0.003434703452512622,
-0.013406125828623772,
0.03883678466081619,
-0.01422126591205597,
0.018095659092068672,
0.0059242877177894115,
0.05499054491519928,
0.05343342572450638,
0.03264550492167473,
0.03808200731873512,
-0.05541767552495003,
-0.03641173616051674,
0.02271013893187046,
0.003644982585683465,
0.03291158378124237,
0.005905714351683855,
-0.0288980882614851,
0.012615606188774109,
-0.028885476291179657,
-0.028405936434864998,
-0.005581658333539963,
-0.016318799927830696,
0.0224944818764925,
-0.005343739874660969,
-0.020225798711180687,
0.010594838298857212,
0.010288572870194912,
-0.023805536329746246,
-0.031430501490831375,
0.014956996776163578,
0.024614712223410606,
0.00659796642139554,
0.05106348171830177,
0.025765758007764816,
0.020174607634544373,
-0.010819345712661743,
-0.023108845576643944,
0.001407078467309475,
-0.018660953268408775,
-0.02480173669755459,
-0.018154358491301537,
0.0343334935605526,
-0.006966286804527044,
-0.034295037388801575,
-0.004156075417995453,
-0.02014145813882351,
0.000576508289668709,
-0.03796755149960518,
-0.011059797368943691,
-0.008919907733798027,
0.037215299904346466,
-0.05374281108379364,
-0.010551401413977146,
0.006326809525489807,
0.024251246824860573,
-0.034122105687856674,
-0.005876511335372925,
0.002426643157377839,
-0.015020022168755531,
-0.04155156388878822,
0.005562117323279381,
0.04681878909468651,
0.025081949308514595,
-0.05717137083411217,
-0.02291836030781269,
-0.03273038566112518,
-0.020560286939144135,
-0.028582051396369934,
0.008175223134458065,
0.020048007369041443,
0.026901764795184135,
-0.02127627469599247,
0.0012085763737559319,
0.013098816387355328,
-0.07656548917293549,
0.02497621439397335,
-0.049554429948329926,
-0.0002819621586240828,
0.01878334954380989,
-0.015588056296110153,
0.06457214057445526,
0.07356695085763931,
-0.02181077003479004,
0.010407846421003342,
0.03410852327942848,
0.02632768079638481,
0.061422448605298996,
-0.05848224088549614,
-0.021226173266768456,
0.023516379296779633,
0.01883595436811447,
-0.011372081935405731,
-0.018363894894719124,
0.019297728314995766,
0.01258812379091978,
0.03817472606897354,
0.012165040709078312,
0.05024164170026779,
-0.03309917077422142,
-0.015675285831093788,
-0.04970529302954674,
-0.023698408156633377,
-0.011842749081552029,
0.006849589291960001,
0.06330776959657669,
-0.031914714723825455,
-0.019601279869675636,
-0.022585975006222725,
-0.0025600017979741096,
0.00797200109809637,
0.0169094055891037,
-0.02146672084927559,
-0.00036827963776886463,
0.013524615205824375,
0.011628726497292519,
-0.020818792283535004,
-0.012735594995319843,
-0.01152824703603983,
0.02861892059445381,
0.007946552708745003,
-0.024194922298192978,
-0.030672650784254074,
0.0549909733235836,
0.005937266629189253,
-0.0553288608789444,
0.00952005572617054,
0.03365553915500641,
-0.00477447547018528,
0.024263570085167885,
0.011672473512589931,
-0.022267187014222145,
0.00797255802899599,
0.013811055570840836,
-0.053999364376068115,
0.004015774000436068,
-0.06574893742799759,
-0.03769786283373833,
0.015267632901668549,
-0.02193593978881836,
0.027243318036198616,
0.02836225926876068,
0.0019385031191632152,
0.03503118455410004,
0.008644931949675083,
-0.01009034737944603,
-0.025840628892183304,
0.030213363468647003,
-0.0031376031693071127,
0.00021857416140846908,
-0.027793340384960175,
0.024307366460561752,
-0.013999873772263527,
-0.00416951160877943,
0.03450591862201691,
-0.0019133271416649222,
0.023762183263897896,
0.018736183643341064,
0.022843752056360245,
-0.028222747147083282,
0.04326731339097023,
-0.0034005327615886927,
-0.00965756457298994,
-0.015250198543071747,
0.037386443465948105,
0.011253084987401962,
0.02926049940288067,
0.009683318436145782,
0.019541077315807343,
-0.08236239105463028,
0.0067757973447442055,
0.020974475890398026,
0.0055738831870257854,
0.05488479882478714,
-0.0328444205224514,
0.02534191869199276,
0.04618578031659126,
-0.0807424858212471,
-0.0017689132364466786,
0.012126674875617027,
0.009371806867420673,
-0.01547480933368206,
0.020003287121653557,
-0.045599937438964844,
0.0267022717744112,
0.006858008913695812,
0.03425460681319237,
0.009128694422543049,
0.04493781179189682,
-0.009280053898692131,
-0.03138936311006546,
-0.0210335161536932,
-0.012714001350104809,
0.020287128165364265,
-0.00018086250929627568,
0.08281455188989639,
-0.018367409706115723,
-0.002177651971578598,
0.031645916402339935,
-0.011893433518707752,
-0.0008529933402314782,
-0.04034776985645294,
-0.002301301108673215,
-0.005916025955229998,
0.026160944253206253,
-0.030959350988268852,
-0.012320594862103462,
0.008720413781702518,
-0.00455777533352375,
0.030649660155177116,
-0.0017916550859808922,
0.013725662603974342,
-0.04831944778561592,
0.008678870275616646,
-0.01667822152376175,
-0.016469357535243034,
0.031685732305049896,
0.04887262359261513,
-0.010032068006694317,
-0.0007096159388311207,
0.03361817076802254,
0.05558381602168083,
-0.0006436810945160687,
-0.0029784650541841984,
-0.073609359562397,
-0.0009349404135718942,
0.007531570736318827,
0.020068859681487083,
-0.018465671688318253,
0.007943953387439251,
-0.05355681851506233,
-0.03303247690200806,
0.07438652962446213,
0.02993645705282688,
-0.008877434767782688,
-0.04691840335726738,
-0.021095717325806618,
0.021803036332130432,
0.007915963418781757,
0.055211391299963,
-0.01901310682296753,
-0.008087782189249992,
-0.0010195317445322871,
-0.022252298891544342,
0.016601722687482834,
-0.0215603057295084,
-0.06411118060350418,
-0.0016666317824274302,
-0.020107828080654144,
0.03097098506987095,
0.036205071955919266,
-0.0071675763465464115,
-0.03381903097033501,
-0.024353651329874992,
-0.003513565519824624,
0.04195408895611763,
0.07202968001365662,
0.0008430665475316346,
-0.014461892656981945,
-0.008724130690097809,
-0.0046043009497225285,
0.039178501814603806,
-0.03388126567006111,
-0.0035761187318712473,
-0.017931446433067322,
-0.0014869043370708823,
-0.023065052926540375,
0.013502012006938457,
0.025805246084928513,
0.024564411491155624,
-0.008563763462007046,
0.010215913876891136,
0.007022039499133825,
-0.020357048138976097,
-0.05857721343636513,
0.0276808999478817,
0.013283725827932358,
-0.010215960443019867,
0.07590481638908386,
-0.018890047445893288,
0.01875123754143715,
-0.00175370741635561,
-0.006971354130655527,
-0.05863538756966591,
-0.011058527044951916,
-0.05340107902884483,
-0.015926720574498177,
0.019545482471585274,
0.0575413778424263,
0.026124903932213783,
-0.04002057760953903,
-0.041193775832653046,
0.01626569963991642,
-0.010470014996826649,
-0.026148952543735504,
0.080248162150383,
-0.01341241504997015,
0.01826312020421028,
0.004638227168470621,
0.021672382950782776,
0.030790550634264946,
0.03125034272670746,
-0.009526706300675869,
0.05138199403882027,
0.08071590214967728,
-0.02513016201555729,
0.036015529185533524,
0.052584778517484665,
0.019111603498458862,
-0.012223895639181137,
-0.007100091781467199,
0.033617593348026276,
0.01211674977093935,
0.014359596185386181,
-0.024648966267704964,
-0.04262808337807655,
-0.0391828790307045,
0.018212275579571724,
-0.03870070353150368,
0.08903824537992477,
0.0005577336996793747,
0.022958623245358467,
0.005196255631744862,
0.02063746191561222,
-0.040094051510095596,
0.01617107167840004,
0.05942625179886818,
0.017664626240730286,
-0.0046591185964643955,
0.0074024684727191925,
-0.01917026937007904,
0.024411719292402267,
-0.0035316161811351776,
-0.057210855185985565,
-0.013190247118473053,
0.005501355975866318,
-0.02336488664150238,
-0.011868761852383614,
-0.0022962342482060194,
-0.02085849456489086,
-0.03919459134340286,
0.033083103597164154,
-0.003911864943802357,
-0.014183400198817253,
0.006834360770881176,
-0.004791873507201672,
-0.03743944317102432,
0.06036600470542908,
-0.07222330570220947,
-0.021433167159557343,
-0.015513608232140541,
0.04044264927506447,
-0.04910619556903839,
-0.03517967835068703
] |
<p>This is a historical question partly, and maybe too broad for this site, but would require some familiarity with modern physics research practice so hopefully appropriate here. </p>
<p>Einstein's later years, after general relativity, were (as I understand it) taken up predominantly by his effort to find a unified theory that explains both gravitation and electromagnetism and their interrelation. </p>
<p>And from what I understand his approach was mainly mathematical, trying variations of functions and so forth, looking for something that fit - and doing his work predominantly on paper. </p>
<p>Had he access to modern computers - programming languages, mathematica, etc. - how might that have changed his progress, and willingness to give up perhaps? And in what ways have computers in general changed / revolutionized theoretical & mathematical physics?</p> | 1,503 | [
-0.008979929611086845,
-0.04765675961971283,
-0.022960156202316284,
-0.05849819257855415,
0.05836925655603409,
0.007815954275429249,
-0.01771700382232666,
-0.010664587840437889,
-0.04226287081837654,
-0.007460778579115868,
0.019986094906926155,
0.006582033820450306,
0.07725708186626434,
-0.0018998178420588374,
0.027330974116921425,
-0.014867979101836681,
0.03860682621598244,
-0.024872280657291412,
-0.0126196825876832,
-0.01260133646428585,
0.02100379578769207,
0.024426676332950592,
-0.013633613474667072,
0.027604389935731888,
-0.03101947531104088,
0.02690553292632103,
0.005194385536015034,
-0.020481763407588005,
0.016335587948560715,
0.05579107627272606,
-0.025689702481031418,
-0.0020663044415414333,
0.007226144894957542,
0.02793315425515175,
0.027869753539562225,
-0.021733302623033524,
-0.05016784742474556,
-0.05027054622769356,
0.01264957431703806,
0.004510965663939714,
-0.03904075548052788,
0.0009499030420556664,
-0.0316663533449173,
0.012967681512236595,
0.002832792466506362,
0.03455674648284912,
-0.009415333159267902,
-0.011473841965198517,
0.029872551560401917,
-0.043894603848457336,
0.06751533597707748,
0.01301011722534895,
0.018518885597586632,
0.009532665833830833,
-0.015406358987092972,
0.009116770699620247,
0.06784902513027191,
0.0735340267419815,
-0.0010239571565762162,
-0.050063859671354294,
-0.04297545924782753,
-0.011952736414968967,
-0.016381893306970596,
0.0006208422710187733,
-0.025061363354325294,
0.05085330083966255,
-0.02998100221157074,
-0.014131538569927216,
0.022929100319743156,
-0.047913238406181335,
-0.04102310910820961,
0.029163403436541557,
0.0358002707362175,
0.0016075694002211094,
0.016993537545204163,
-0.017456039786338806,
0.006061859428882599,
-0.043444301933050156,
-0.011638079769909382,
0.016315989196300507,
-0.018339425325393677,
-0.012817281298339367,
0.04881289601325989,
0.0600639171898365,
0.02062544785439968,
-0.003657239954918623,
0.07367595285177231,
-0.05699360370635986,
-0.012531002052128315,
0.007762988563627005,
-0.03067152202129364,
0.0027888452168554068,
0.046140555292367935,
-0.018089547753334045,
-0.06927572935819626,
-0.015176985412836075,
0.03256627917289734,
0.03165170177817345,
0.03063589707016945,
-0.035574499517679214,
0.021757137030363083,
-0.023922597989439964,
-0.0015342362457886338,
0.07526526600122452,
0.04444211348891258,
-0.014236144721508026,
-0.027895823121070862,
0.004322177730500698,
-0.0323309563100338,
-0.03681826591491699,
-0.0069801658391952515,
0.02810933068394661,
0.020566487684845924,
-0.03662072494626045,
0.028597792610526085,
-0.03549748286604881,
-0.0034271369222551584,
-0.05449878051877022,
0.0740223228931427,
0.05868757143616676,
0.04368727281689644,
-0.037530552595853806,
0.043897341936826706,
-0.02794385328888893,
-0.04601548984646797,
-0.02792249247431755,
0.055870167911052704,
-0.01299650315195322,
-0.0312652513384819,
0.032216936349868774,
-0.006668920163065195,
0.0285894013941288,
0.025894850492477417,
0.037699729204177856,
0.012858700938522816,
-0.018189869821071625,
-0.09156771004199982,
-0.04696468636393547,
0.03702739253640175,
-0.006588123273104429,
-0.024780485779047012,
-0.050057630985975266,
0.009499533101916313,
0.005490630865097046,
0.08717752993106842,
0.012250632978975773,
-0.018292509019374847,
0.006773538421839476,
0.07246086746454239,
-0.001292013330385089,
-0.02678242139518261,
0.0074892351403832436,
-0.008498107083141804,
-0.020899372175335884,
-0.017423346638679504,
-0.09385617077350616,
-0.013487751595675945,
0.01575464941561222,
-0.010725813917815685,
-0.0512549988925457,
0.11330462247133255,
0.00965909007936716,
-0.00010931789438473061,
-0.006160642486065626,
-0.0038571348413825035,
-0.00651679839938879,
0.05099140480160713,
0.029763169586658478,
0.0165675301104784,
0.028349006548523903,
0.0013841585023328662,
0.05915580689907074,
0.01748812012374401,
-0.00654151476919651,
0.06889904290437698,
-0.055176280438899994,
0.007442655973136425,
0.02852902002632618,
-0.049838095903396606,
-0.00991462729871273,
0.003111262572929263,
-0.08388116955757141,
0.024803558364510536,
-0.006192583125084639,
0.01281864196062088,
0.06728461384773254,
-0.0016209062887355685,
0.013709931634366512,
0.015985911712050438,
-0.020327189937233925,
-0.00794261321425438,
-0.0711025819182396,
0.013490178622305393,
0.0031794116366654634,
0.02166154980659485,
0.03697120398283005,
0.00217456859536469,
0.0017798636108636856,
0.014726504683494568,
-0.05497274920344353,
0.01743166521191597,
0.053050849586725235,
0.018092023208737373,
0.020646385848522186,
-0.011157612316310406,
0.04036388918757439,
0.025067823007702827,
0.004370846785604954,
0.0009286417625844479,
-0.009588297456502914,
-0.02296086587011814,
0.024609152227640152,
-0.01576249487698078,
0.025652432814240456,
0.004954606760293245,
0.005289838649332523,
-0.028109900653362274,
-0.018552470952272415,
-0.026089109480381012,
0.016408558934926987,
-0.010799707844853401,
0.06433339416980743,
0.019601229578256607,
-0.009447556920349598,
0.0065183271653950214,
0.0738835334777832,
-0.002722000004723668,
0.012731817550957203,
0.05196678638458252,
-0.040185946971178055,
-0.03578469157218933,
0.009990083985030651,
0.05357780680060387,
0.047892313450574875,
-0.0513322651386261,
0.053096089512109756,
0.016881730407476425,
0.03982177749276161,
0.0007819784223102033,
0.008286216296255589,
-0.058138638734817505,
-0.019303137436509132,
0.028662124648690224,
0.015646452084183693,
0.001981075620278716,
0.018037769943475723,
0.005480461288243532,
0.0319194421172142,
-0.03522307425737381,
-0.0009193033329211175,
-0.024236198514699936,
-0.0038414353039115667,
0.00722468551248312,
0.003799122292548418,
-0.0219331756234169,
-0.011586034670472145,
0.009293550625443459,
-0.02999712899327278,
-0.012726282700896263,
0.028590716421604156,
0.01186201348900795,
-0.009895287454128265,
-0.03647862374782562,
-0.03377867490053177,
0.03350231051445007,
0.010902870446443558,
-0.011495866812765598,
-0.019082263112068176,
0.018566733226180077,
-0.03948906436562538,
0.032929472625255585,
-0.0053015537559986115,
0.017667362466454506,
-0.04216121882200241,
0.0368601493537426,
-0.0030594991985708475,
0.01897803694009781,
0.03713708370923996,
-0.008628950454294682,
-0.01849188655614853,
0.024245886132121086,
-0.04435236006975174,
0.0050933146849274635,
0.024332433938980103,
-0.031632162630558014,
-0.015008357353508472,
-0.0400325171649456,
0.002919215941801667,
0.023539965972304344,
-0.044757209718227386,
0.012192507274448872,
0.017937375232577324,
0.0040909964591264725,
-0.053931258618831635,
-0.02491677552461624,
-0.02498759515583515,
0.01763463020324707,
-0.015206540003418922,
-0.021694760769605637,
0.03436901420354843,
-0.008034796454012394,
-0.006369659677147865,
0.024000469595193863,
-0.022011812776327133,
-0.06764918565750122,
-0.022061465308070183,
-0.0038523327093571424,
0.008732294663786888,
-0.0425458624958992,
0.024737361818552017,
0.017496326938271523,
-0.0416429229080677,
-0.011128216981887817,
-0.0814862921833992,
-0.05083199217915535,
0.023225106298923492,
-0.010517699643969536,
0.04283783584833145,
0.0032475567422807217,
-0.00013525968824978918,
0.04281213879585266,
0.013624203391373158,
-0.04397149756550789,
-0.03127695620059967,
0.005870081949979067,
0.010034178383648396,
0.009340636432170868,
0.00911833718419075,
0.0010785473277792335,
-0.00011435079795774072,
0.0030864651780575514,
0.012808015570044518,
0.01859692670404911,
0.013772757723927498,
0.01379290409386158,
0.006284988950937986,
0.01812903769314289,
-0.018544241786003113,
0.004279679153114557,
0.013118578121066093,
0.004016874823719263,
-0.0238825511187315,
-0.011362064629793167,
-0.0004425796214491129,
-0.008735653012990952,
0.023402158170938492,
-0.030976692214608192,
0.053621161729097366,
0.010822120122611523,
0.034460991621017456,
0.00023314110876526684,
0.005544878076761961,
-0.00918411836028099,
-0.037080589681863785,
0.028618842363357544,
0.026637835428118706,
0.022853486239910126,
-0.01695943996310234,
-0.01068339217454195,
0.009337452240288258,
0.0541871152818203,
-0.06829706579446793,
0.008256588131189346,
-0.006796969100832939,
0.0011120951967313886,
0.0249234139919281,
-0.02123376913368702,
-0.003687188494950533,
0.04415521025657654,
0.021245822310447693,
0.01781976781785488,
0.01310169417411089,
-0.01881246827542782,
-0.031712599098682404,
-0.058280158787965775,
-0.009270936250686646,
0.00918340403586626,
0.09037370979785919,
-0.012670962139964104,
0.03322925791144371,
0.03792641684412956,
-0.0082024484872818,
0.0038640585262328386,
-0.0004791739920619875,
-0.11269327253103256,
-0.006264294032007456,
-0.05672326683998108,
-0.016934024170041084,
-0.0072109694592654705,
0.008045149967074394,
0.023568546399474144,
-0.0005573430680669844,
-0.03073723055422306,
-0.02903570793569088,
0.019775839522480965,
-0.06541088968515396,
0.04689520597457886,
-0.046651069074869156,
-0.0377814881503582,
0.008635072968900204,
0.020535869523882866,
0.014100554399192333,
-0.01798720844089985,
-0.010198147967457771,
0.047933127731084824,
-0.015416133217513561,
-0.03912204131484032,
-0.009664153680205345,
0.03212578594684601,
-0.001144744805060327,
-0.003534255549311638,
0.00647836085408926,
0.03759697824716568,
-0.00701804319396615,
0.014686130918562412,
0.030474156141281128,
0.06695732474327087,
0.0269660372287035,
-0.007343763951212168,
-0.019711660221219063,
-0.05556085333228111,
-0.006907270755618811,
0.008322913199663162,
0.05545005574822426,
-0.0031066087540239096,
0.008866983465850353,
0.015043879859149456,
0.02390574850142002,
0.01906431093811989,
0.02733585424721241,
0.09966414421796799,
-0.008051978424191475,
-0.02783653512597084,
-0.023890649899840355,
-0.023262297734618187,
-0.029780598357319832,
-0.009570233523845673,
0.04044153168797493,
0.02069046162068844,
-0.02102246694266796,
0.0062964484095573425,
0.02982761338353157,
-0.003936522640287876,
-0.05603855103254318,
-0.017665881663560867,
0.008268831297755241,
0.021275866776704788,
0.020533058792352676,
0.01850626803934574,
-0.012439511716365814,
0.015050468035042286,
0.06844811886548996,
-0.009813821874558926,
0.017428314313292503,
-0.07945463806390762,
-0.01903676614165306,
0.060150615870952606,
0.031933970749378204,
-0.02144630067050457,
0.0043650101870298386,
-0.07272468507289886,
0.01304082665592432,
0.04355724900960922,
-0.005499501246958971,
-0.008008703589439392,
-0.0034024508204311132,
-0.008567729964852333,
-0.00216676271520555,
-0.03443705290555954,
-0.0034055705182254314,
0.008412381634116173,
-0.01457912102341652,
0.0295402891933918,
-0.022038299590349197,
0.007717595901340246,
-0.03646933287382126,
0.004357998725026846,
0.03060331754386425,
0.033234603703022,
0.019905665889382362,
0.01555083692073822,
-0.007278334349393845,
-0.004617316648364067,
-0.04238017275929451,
-0.09384188055992126,
-0.013642653822898865,
0.007044154219329357,
-0.03157752379775047,
0.02836010977625847,
-0.024281051009893417,
-0.027262302115559578,
0.026179051026701927,
-0.004670323804020882,
-0.00854155421257019,
0.01554555632174015,
-0.0173417329788208,
0.017864875495433807,
0.023370850831270218,
-0.012600780464708805,
0.027913842350244522,
0.041382163763046265,
-0.04751639440655708,
0.007708822842687368,
-0.020147565752267838,
0.00021799132809974253,
0.0005255434080027044,
0.00978785753250122,
-0.02331778034567833,
-0.011462136171758175,
-0.04112422466278076,
0.03185643255710602,
-0.008447944186627865,
0.013199102133512497,
-0.02798089012503624,
-0.0405256450176239,
-0.0176544189453125,
0.02066866308450699,
-0.022720610722899437,
-0.0359458401799202,
-0.02492559142410755,
0.014948440715670586,
-0.025700611993670464,
-0.014959639869630337,
0.020983288064599037,
-0.004053120967000723,
-0.00023926343419589102,
0.0032999722752720118,
-0.016666065901517868,
-0.007391597609966993,
-0.024383926764130592,
0.0023163212463259697,
0.006595299579203129,
-0.008471144363284111,
0.06337762624025345,
0.006358148064464331,
-0.0033053045626729727,
0.0546611025929451,
-0.05198541656136513,
-0.024858882650732994,
-0.01400151289999485,
0.018759341910481453,
-0.00220158277079463,
-0.023413414135575294,
-0.004816554021090269,
-0.03776556998491287,
0.0029095944482833147,
-0.06163812056183815,
-0.04120151698589325,
0.05708163231611252,
0.004714838229119778,
0.004926619119942188,
-0.0023895534686744213,
0.0014581895666196942,
-0.053308676928281784,
0.025793859735131264,
-0.009030789136886597,
0.030520295724272728,
-0.016801461577415466,
0.0027367710135877132,
0.0414322093129158,
0.006067218258976936,
0.024956392124295235,
-0.050093986093997955,
0.009058483876287937,
0.03939495235681534,
0.012656301259994507,
0.01825498417019844,
0.019001217558979988,
0.05932442843914032,
-0.009917260147631168,
-0.018902581185102463,
-0.008474673144519329,
0.014529174193739891,
0.03185749426484108,
-0.030425207689404488,
0.0010770641965791583,
0.058146700263023376,
-0.029257697984576225,
0.0015061467420309782,
0.015238531865179539,
-0.02547270432114601,
-0.0258809644728899,
0.026962362229824066,
-0.007526880595833063,
-0.005269916262477636,
0.04529774934053421,
-0.02617393061518669,
0.04613102972507477,
0.013157899491488934,
-0.010489977896213531,
0.020405510440468788,
0.032234076410532,
0.02080087549984455,
-0.033157072961330414,
0.008930849842727184,
-0.02777961827814579,
0.011463186703622341,
0.00015743541007395834,
0.03207191824913025,
0.00622963160276413,
0.017386171966791153,
0.0017108583124354482,
-0.031122392043471336,
-0.007995028980076313,
-0.03873563930392265,
0.07372346520423889,
0.008706372231245041,
0.013268663547933102,
0.05750807374715805,
-0.01105011161416769,
-0.021057121455669403,
-0.008065485395491123,
-0.018318578600883484,
-0.00007800644380040467,
0.009558316320180893,
0.039396028965711594,
0.007142264861613512,
-0.019610954448580742,
0.05897260829806328,
0.009351066313683987,
-0.0020152637735009193,
0.00322516611777246,
0.004368665628135204,
0.03629253804683685,
0.01826285943388939,
-0.06011659651994705,
-0.04109897091984749,
0.010094753466546535,
-0.024465007707476616,
0.03730176389217377,
0.005006303079426289,
-0.019505135715007782,
0.03495624661445618,
0.01237087044864893,
0.014244643971323967,
-0.0255313441157341,
-0.00877293013036251,
-0.061207376420497894,
-0.009068979881703854,
0.010416931472718716,
0.029078641906380653,
0.023101136088371277,
0.01964571326971054,
0.03192424401640892,
0.017791427671909332,
-0.0031719557009637356,
0.002102235797792673,
-0.08280495554208755,
-0.06103585660457611,
-0.045777175575494766,
-0.05364038422703743,
0.03243614360690117,
0.03250253573060036,
-0.03275582566857338,
-0.0018553715199232101,
-0.005865806248039007,
0.028882857412099838,
0.0191971268504858,
0.04146856069564819,
-0.0519939549267292,
0.05772456154227257,
-0.0348227433860302,
0.013177112676203251,
-0.036049749702215195,
-0.012872531078755856,
0.11499757319688797,
0.07414308190345764,
0.026977473869919777,
-0.07688542455434799,
0.03555309399962425,
-0.0329640656709671,
-0.019057193771004677,
-0.05577675625681877,
0.0449678860604763,
-0.01120800618082285,
0.017375530675053596,
0.00846171099692583,
0.03195223584771156,
-0.007939653471112251,
0.0030162734910845757,
0.0681132897734642,
-0.041676115244627,
-0.05645044147968292,
-0.001031449413858354,
0.011178644374012947,
0.0065543693490326405,
0.030353553593158722,
-0.0060006375424563885,
0.03481772169470787,
-0.05457046255469322,
0.023790379986166954,
-0.030972454696893692,
-0.046612292528152466,
0.03633713722229004,
0.02334154210984707,
-0.06161893904209137,
0.03379770740866661,
0.012548837810754776,
-0.0033058219123631716,
-0.04677914083003998,
0.008198380470275879,
0.036853939294815063,
0.014972072094678879,
-0.005013014655560255,
0.05768856406211853,
0.022619856521487236,
-0.008397995494306087,
-0.029086487367749214,
-0.02031560242176056,
-0.037819262593984604,
-0.024158868938684464,
-0.027142666280269623,
0.06103544309735298,
-0.017420992255210876,
0.004369371570646763,
0.015205156989395618,
-0.02202468179166317,
0.004361683968454599,
-0.007829731330275536,
-0.02216544933617115,
-0.00092481286264956,
0.016613531857728958,
0.007756425067782402,
0.0066229477524757385,
0.023528045043349266,
0.03313600271940231,
-0.0034701337572187185,
0.024859536439180374,
-0.005202350672334433,
-0.041536007076501846,
-0.007768685929477215,
-0.008637214079499245,
0.005301903933286667,
0.01260033342987299,
-0.020121967419981956,
-0.024314485490322113,
-0.00774198304861784,
-0.02363237924873829,
-0.009333622641861439,
0.030740557238459587,
0.0402919165790081,
0.019432738423347473,
-0.02810097299516201,
0.007739751599729061,
-0.001631295308470726,
-0.05840618908405304,
0.029361166059970856,
-0.0077140675857663155,
0.02824658900499344,
-0.01873805932700634,
-0.02110324241220951,
0.006237136200070381,
0.02205219306051731,
-0.009499148465692997,
-0.035405661910772324,
-0.0297844335436821,
-0.00034035657881759107,
-0.004581317771226168,
0.0031885879579931498,
-0.014594261534512043,
-0.012901498936116695,
-0.040336787700653076,
0.006479235365986824,
-0.05541795864701271,
0.011587131768465042,
0.01841910555958748,
0.00646132742986083,
0.005823695566505194,
0.049161575734615326,
-0.009727424941956997,
0.008636156097054482,
0.015614340081810951,
-0.025215324014425278,
-0.033153314143419266,
-0.0021523325704038143,
0.03978579118847847,
-0.052881136536598206,
-0.02300184965133667,
-0.022051552310585976,
0.016471590846776962,
0.011672217398881912,
0.017622187733650208,
0.036079324781894684,
0.04648912325501442,
-0.012493387795984745,
0.009844332002103329,
-0.019558321684598923,
0.024666637182235718,
-0.0343422070145607,
0.0041230120696127415,
0.025260791182518005,
-0.017942575737833977,
0.034201495349407196,
0.01777486689388752,
0.006703634280711412,
-0.04272416979074478,
0.009131680242717266,
0.03269711136817932,
-0.019907645881175995,
-0.005680235568434,
-0.021768098697066307,
0.023951208218932152,
0.04933604970574379,
-0.01432019006460905,
-0.04121142998337746,
0.028025787323713303,
-0.025614235550165176,
-0.04980994015932083,
0.03498869761824608,
-0.046204574406147,
-0.010456915013492107,
0.052899230271577835,
-0.02855239436030388,
-0.02234572544693947,
0.06803074479103088,
-0.027894264087080956,
0.011481099762022495,
0.00811410415917635,
-0.018371770158410072,
0.0028807525523006916,
0.012097634375095367,
0.023613309487700462,
-0.016331641003489494,
-0.05779775232076645,
0.029310377314686775,
0.046911582350730896,
-0.029368434101343155,
0.007006517145782709,
0.012125277891755104,
-0.0037382664158940315,
-0.007102983072400093,
0.02276250720024109,
0.0025531488936394453,
0.06206560134887695,
0.052160196006298065,
-0.047475576400756836,
0.021467529237270355,
0.03083123452961445,
0.011457288637757301,
-0.10480320453643799,
0.0099329287186265,
-0.002584443660452962,
0.011890232563018799,
0.047051433473825455,
-0.048603739589452744,
0.02371150068938732,
-0.00427072262391448,
-0.04568706825375557,
0.028588097542524338,
-0.036161869764328,
-0.03430743142962456,
-0.02208474464714527,
-0.04035600647330284,
-0.018720785155892372,
0.03920011594891548,
0.025127490982413292,
0.02887270227074623,
0.0571286678314209,
-0.013709069229662418,
0.014896586537361145,
0.0055818879045546055,
-0.01317751407623291,
0.008351151831448078,
-0.008724099956452847,
0.003720698179677129,
0.014103722758591175,
-0.02493363618850708,
-0.05842526629567146,
0.013097438961267471,
0.010823794640600681,
0.017413504421710968,
-0.066490039229393,
-0.016907252371311188,
0.02971850521862507,
0.01869194582104683,
0.0019108254928141832,
-0.025911273434758186,
-0.0025127523113042116,
0.047978587448596954,
-0.01572439819574356,
0.02413124591112137,
0.019833961501717567,
0.03919576480984688,
-0.003247001441195607,
-0.03615780919790268,
-0.039424456655979156,
0.017174072563648224,
-0.019442345947027206,
-0.01915663853287697,
-0.005391617771238089,
0.025321831926703453,
0.00394941633567214,
-0.002509540179744363,
-0.0023162129800766706,
-0.046568527817726135,
-0.03792658448219299,
0.004282990004867315,
0.022825177758932114,
0.02078351378440857,
0.03858460113406181,
-0.019939372316002846,
-0.021180886775255203,
-0.004679708741605282,
-0.01801130920648575,
0.0156041095033288,
-0.05851906165480614,
0.0039471108466386795,
0.015616736374795437,
0.0071179624646902084,
0.023927006870508194,
-0.026965824887156487,
-0.008061899803578854,
0.018850617110729218,
0.012586944736540318,
0.0029605648014694452,
0.0034084252547472715,
-0.043946608901023865,
-0.021853560581803322,
-0.061843693256378174,
0.002304546069353819,
-0.03099360503256321,
0.028341108933091164,
-0.005067784339189529,
0.017905300483107567,
-0.02369554154574871,
0.002936858916655183,
0.016500970348715782,
-0.041374508291482925,
-0.00946637149900198,
-0.01571159064769745,
-0.015116208232939243,
0.027291467413306236,
-0.045858751982450485,
0.02436007931828499,
-0.02603243477642536,
-0.009026606567203999,
-0.022378897294402122,
-0.026353739202022552,
-0.012129152193665504,
0.023683270439505577,
0.028080331161618233,
0.010792738758027554,
0.010695362463593483,
-0.01624394580721855,
-0.055840980261564255,
0.025620680302381516,
0.0637890174984932,
-0.024471480399370193,
0.034007154405117035,
0.0028540375642478466,
0.01843789964914322,
0.04014468193054199,
-0.015174364671111107,
-0.03281706944108009,
0.08078692108392715,
-0.01888132467865944,
-0.03759384900331497,
-0.02120308205485344,
-0.021001754328608513,
-0.020351402461528778,
-0.05440610647201538,
0.026328761130571365,
0.052680984139442444,
0.022783620283007622,
0.01597669906914234,
0.05179307982325554,
0.0074636987410485744,
0.0028916606679558754,
0.03960464894771576,
-0.03931284323334694,
0.05204837769269943,
0.00932408683001995,
-0.03373896703124046,
0.031165074557065964,
0.060266781598329544,
0.03485386446118355,
0.013116459362208843,
0.012814759276807308,
0.022259032353758812,
0.014089169912040234,
0.002604580717161298,
0.023185068741440773,
-0.04718425124883652,
-0.03497127443552017,
0.05205599218606949,
0.0169669296592474,
-0.012153539806604385,
-0.004620693624019623,
-0.009063302539288998,
0.0816950798034668,
-0.029590092599391937,
0.014332332648336887,
0.006092395167797804,
-0.02524583600461483,
-0.01930488832294941,
-0.0002749391715042293,
0.018415585160255432,
0.057957809418439865,
-0.019382549449801445,
-0.029281621798872948,
-0.021470582112669945,
0.024720028042793274,
0.05266579985618591,
-0.002096976153552532,
0.025857077911496162,
0.036307159811258316,
-0.0243954099714756,
-0.003929424099624157,
0.007703392766416073,
-0.04339446499943733,
0.003331793937832117,
0.013264725916087627,
0.03223775327205658,
0.04879208654165268,
-0.02180112712085247,
-0.007676144130527973,
-0.018866170197725296,
0.08238211274147034,
-0.011835909448564053,
-0.006606126669794321,
-0.016314635053277016,
0.0009115039720200002,
-0.01626777835190296,
0.006800270639359951
] |
<p>In QFT the principle of stationary action states that we choose fields that will make the action stationary but what if the action has many stationary points? What's the significance of these other solutions?</p> | 1,504 | [
0.015652786940336227,
0.006787712220102549,
-0.010415541008114815,
-0.02789659984409809,
0.04416913166642189,
-0.0028519751504063606,
-0.04703132063150406,
-0.008503570221364498,
-0.02958878129720688,
-0.043743256479501724,
0.0017367247492074966,
-0.009187832474708557,
0.005690831691026688,
-0.010465572588145733,
0.013557840138673782,
-0.0059600938111543655,
0.02606537751853466,
-0.003607270773500204,
-0.016400154680013657,
-0.014152522198855877,
-0.009082276374101639,
0.05144541338086128,
0.02351231500506401,
-0.011538635939359665,
-0.016709087416529655,
0.00944259949028492,
-0.010133098810911179,
0.04994923621416092,
0.0199111495167017,
0.057860117405653,
-0.03880694508552551,
-0.03917783126235008,
-0.015781907364726067,
0.07448399811983109,
0.017140015959739685,
0.006257504224777222,
-0.004624712280929089,
-0.034840356558561325,
-0.002758145099505782,
0.0009412649087607861,
-0.043766625225543976,
-0.02788023091852665,
-0.016878942027688026,
0.025879330933094025,
-0.027633696794509888,
0.013671600259840488,
0.0295767392963171,
-0.021197805181145668,
0.07739853113889694,
-0.028365017846226692,
0.054166849702596664,
0.016110965982079506,
0.011347955092787743,
-0.004271858837455511,
-0.028737440705299377,
-0.01955096237361431,
0.07093246281147003,
0.02793600969016552,
-0.031797654926776886,
-0.05870939791202545,
-0.058353643864393234,
0.010504569858312607,
0.004189696162939072,
-0.03500351309776306,
0.007591032888740301,
0.05119587853550911,
0.02874278835952282,
0.02896767109632492,
0.02427525445818901,
-0.023008467629551888,
-0.0005307067767716944,
0.015408556908369064,
0.034452736377716064,
-0.012352454476058483,
0.020551037043333054,
-0.00920165330171585,
0.027592070400714874,
-0.005058291368186474,
0.03477514162659645,
0.018571846187114716,
-0.020673787221312523,
0.014431759715080261,
0.029658988118171692,
0.012352527119219303,
0.012580008246004581,
-0.00510913971811533,
0.03279951959848404,
-0.00019146011618431658,
0.01103635411709547,
0.035108815878629684,
-0.015536325052380562,
0.004185395780950785,
0.037116825580596924,
-0.021199023351073265,
-0.023001695051789284,
0.025867106392979622,
0.009478216990828514,
0.019271960482001305,
0.027105296030640602,
0.02019537426531315,
0.007506664376705885,
-0.029544958844780922,
-0.0007253667572513223,
0.06060267239809036,
0.007479405030608177,
-0.0021255589090287685,
-0.05829479917883873,
0.015392984263598919,
-0.015096364542841911,
0.0035728965885937214,
-0.05125144124031067,
-0.013598524034023285,
-0.004403978586196899,
0.012958494015038013,
0.011833728291094303,
-0.009629654698073864,
0.003314322093501687,
-0.03797440603375435,
0.05001173913478851,
0.07385311275720596,
0.03121008537709713,
-0.03793977573513985,
0.014851064421236515,
0.014041092246770859,
-0.06700152903795242,
-0.018516292795538902,
0.027151968330144882,
0.0008172733359970152,
-0.03545183315873146,
-0.006393711548298597,
0.006599872373044491,
-0.027339676395058632,
-0.01074229460209608,
0.03910183534026146,
0.04405686631798744,
-0.021305343136191368,
-0.10618344694375992,
-0.05992955341935158,
0.04496081545948982,
-0.037013061344623566,
-0.02584637887775898,
-0.042463742196559906,
-0.006418229080736637,
0.02859950251877308,
0.07354498654603958,
-0.030460607260465622,
-0.01862601563334465,
0.023638945072889328,
0.05684986710548401,
0.007205507718026638,
-0.01869058609008789,
0.020403867587447166,
-0.026363497599959373,
-0.0461987741291523,
-0.000972715497482568,
-0.057667385786771774,
0.010733441449701786,
0.025471942499279976,
0.007444760762155056,
-0.02216840721666813,
0.051821935921907425,
-0.02659127302467823,
-0.0009050553780980408,
-0.008990135043859482,
-0.01933363452553749,
-0.005678658373653889,
0.054947856813669205,
-0.0033482681028544903,
0.0242837592959404,
0.03536713495850563,
-0.013153175823390484,
0.05808812379837036,
0.003567479085177183,
0.04214807227253914,
-0.004439002368599176,
-0.0018794311909005046,
-0.0029677601996809244,
-0.016609322279691696,
0.02322068065404892,
0.02810084819793701,
-0.05102227255702019,
-0.037479449063539505,
-0.0012358392123132944,
0.0020824470557272434,
-0.045351818203926086,
0.052113454788923264,
-0.035528551787137985,
0.015258613973855972,
-0.001517957542091608,
-0.05969341844320297,
-0.004057727288454771,
-0.0753219947218895,
0.026358487084507942,
0.018474452197551727,
0.0013281491119414568,
0.031178871169686317,
0.0876953974366188,
0.03881095349788666,
-0.05403278395533562,
-0.04162733256816864,
-0.013674089685082436,
0.024960851296782494,
-0.00392516003921628,
0.012928221374750137,
0.030138827860355377,
0.0455031581223011,
0.02091224677860737,
0.005046159494668245,
0.05065486580133438,
-0.02984894998371601,
0.0008248144295066595,
0.019709207117557526,
-0.018018100410699844,
0.024861672893166542,
-0.014266416430473328,
-0.007673775777220726,
-0.03037012368440628,
-0.0009467320051044226,
0.0004641120322048664,
0.0489921011030674,
-0.06583961844444275,
0.08428527414798737,
0.054614387452602386,
-0.013960199430584908,
-0.015808667987585068,
0.0508694089949131,
-0.016213707625865936,
-0.0025988605339080095,
-0.003372719744220376,
-0.043008461594581604,
-0.04106762260198593,
-0.026193983852863312,
0.04870836064219475,
0.04051179438829422,
-0.0665508434176445,
0.006659924518316984,
0.017277274280786514,
0.030153175815939903,
0.035841893404722214,
0.019390486180782318,
0.008384369313716888,
-0.028398124501109123,
0.03245515376329422,
0.015914229676127434,
0.0005839162040501833,
0.005577920936048031,
0.06126910820603371,
-0.009823841042816639,
-0.004078539554029703,
0.01009729877114296,
-0.04495887830853462,
0.031093334779143333,
-0.00868319720029831,
0.0035785872023552656,
-0.007583098951727152,
-0.037702709436416626,
-0.0031070527620613575,
0.008136733435094357,
0.06455834954977036,
0.010602971538901329,
0.012505121529102325,
0.021997520700097084,
-0.008000833913683891,
-0.015838706865906715,
0.02378436177968979,
-0.009482156485319138,
-0.013000444509088993,
-0.04364366456866264,
0.0370350256562233,
-0.06860338896512985,
0.002889842027798295,
-0.032181266695261,
-0.010930313728749752,
-0.00425123143941164,
-0.04008335992693901,
0.034639954566955566,
-0.013112890534102917,
0.03607110679149628,
-0.023149048909544945,
-0.039150089025497437,
-0.0015192165737971663,
-0.03623862564563751,
0.02370362915098667,
0.04388251155614853,
-0.05627133324742317,
0.0009555943543091416,
-0.0620773583650589,
-0.05719439685344696,
0.05143847316503525,
-0.012038901448249817,
0.011288086883723736,
0.021785924211144447,
-0.026616228744387627,
-0.012649659998714924,
-0.009295642375946045,
-0.048176009207963943,
0.04929462447762489,
-0.03980837017297745,
0.016565827652812004,
0.07872190326452255,
-0.023124247789382935,
-0.051233939826488495,
-0.0021325789857655764,
-0.01579998806118965,
-0.04800870269536972,
-0.005344871431589127,
-0.002861007582396269,
0.014883044175803661,
-0.051654696464538574,
0.01895926333963871,
0.019234230741858482,
-0.04127684608101845,
-0.024175923317670822,
-0.038158901035785675,
-0.029424943029880524,
-0.0016575843328610063,
-0.014724357053637505,
0.04614699259400368,
-0.019781671464443207,
-0.03261171653866768,
0.08519607782363892,
0.06885355710983276,
-0.03286677226424217,
0.018273083493113518,
-0.02282792143523693,
-0.04719670116901398,
-0.007861681282520294,
0.008856348693370819,
0.033791735768318176,
-0.0029069276060909033,
0.06491417437791824,
0.05692623183131218,
0.032813139259815216,
0.061554498970508575,
-0.00014984500012360513,
-0.02685481868684292,
0.009208917617797852,
-0.00475816847756505,
-0.00026872113812714815,
0.038004789501428604,
-0.00827827863395214,
-0.017977437004446983,
-0.00020314397988840938,
0.046493951231241226,
0.023604247719049454,
0.02449323609471321,
-0.011929688975214958,
0.07023400813341141,
0.0001972697937162593,
0.04752722010016441,
-0.028346959501504898,
0.023797722533345222,
-0.0020482062827795744,
-0.03113904967904091,
-0.03894577920436859,
-0.004223545081913471,
0.0297095887362957,
-0.03831115737557411,
0.011886319145560265,
0.0021991096436977386,
0.037782758474349976,
-0.057711418718099594,
-0.027988824993371964,
-0.017748776823282242,
-0.029930150136351585,
0.020493190735578537,
0.0005595121765509248,
-0.04944085702300072,
0.041499603539705276,
-0.0032713119871914387,
-0.004875573795288801,
0.011414487846195698,
-0.0481276698410511,
-0.020697101950645447,
-0.05570259690284729,
0.013936292380094528,
0.00741575239226222,
0.0484844408929348,
0.012525464408099651,
0.02757735550403595,
0.01041217427700758,
-0.008728333748877048,
0.00811944529414177,
0.02319713681936264,
-0.06559022516012192,
0.05099330469965935,
-0.016912823542952538,
0.013099594973027706,
-0.013975894078612328,
-0.023616202175617218,
-0.0009991409024223685,
-0.0179459098726511,
-0.011552918702363968,
-0.014942404814064503,
-0.01742824912071228,
-0.05332830548286438,
-0.008530066348612309,
-0.037586141377687454,
-0.0356782041490078,
-0.03678714483976364,
0.046885717660188675,
0.06185011938214302,
-0.03465161845088005,
-0.005331610795110464,
0.03571981191635132,
-0.039213649928569794,
-0.013165248557925224,
-0.00646314537152648,
0.006034486927092075,
-0.001018990995362401,
0.007021448574960232,
0.020783143118023872,
0.017353545874357224,
-0.008852907456457615,
0.0032217891421169043,
0.0013717975234612823,
0.036736924201250076,
0.012596188113093376,
-0.03346803039312363,
-0.006577455438673496,
-0.063736192882061,
0.013421040028333664,
-0.00925962533801794,
0.04321116954088211,
0.018723268061876297,
-0.0019415304996073246,
0.037019021809101105,
0.024207524955272675,
-0.02743670903146267,
0.015757426619529724,
0.049991264939308167,
0.02071431279182434,
-0.04214495047926903,
-0.01466051023453474,
-0.0014056226937100291,
0.0037631129380315542,
0.02623998560011387,
-0.0020748325623571873,
-0.034983351826667786,
-0.05245627835392952,
0.0192138459533453,
-0.011478528380393982,
0.01616962067782879,
-0.02523108758032322,
-0.023523395881056786,
-0.010321873240172863,
0.015272793360054493,
-0.006032728124409914,
-0.031473558396101,
0.005680443719029427,
0.03929153457283974,
0.04036182165145874,
0.01255366113036871,
0.009039868600666523,
-0.0705251470208168,
0.023564361035823822,
0.03584101423621178,
-0.007619909476488829,
0.009367021732032299,
0.013248326256871223,
-0.06873083114624023,
-0.00042607003706507385,
0.05863136798143387,
-0.047772131860256195,
0.032766375690698624,
0.017011335119605064,
-0.01720653846859932,
-0.02969675324857235,
-0.02475855126976967,
-0.05711779370903969,
0.03853334113955498,
-0.01226054597645998,
-0.007497955579310656,
-0.009650553576648235,
0.002254089806228876,
0.0011378764174878597,
0.027272216975688934,
-0.015154117718338966,
0.029016368091106415,
0.04076904058456421,
0.03145669400691986,
0.0209147147834301,
0.04004694148898125,
0.011597808450460434,
-0.08148380368947983,
-0.0008480946999043226,
0.03399474546313286,
-0.030131174251437187,
0.041880324482917786,
-0.024677665904164314,
-0.05053151771426201,
0.004275514744222164,
-0.0005698612076230347,
-0.04267554730176926,
0.026408258825540543,
-0.07032959163188934,
0.010112699121236801,
0.04546256735920906,
0.02277933433651924,
0.05418248847126961,
0.0015048608183860779,
-0.039494555443525314,
-0.023074617609381676,
-0.0014771270798519254,
0.030459893867373466,
0.009196726605296135,
0.012692964635789394,
-0.011879123747348785,
-0.022648893296718597,
-0.05148961767554283,
0.05719330161809921,
-0.02284019999206066,
0.004795880056917667,
0.010381198488175869,
-0.005075742490589619,
-0.04682254046201706,
0.022782329469919205,
0.035789553076028824,
-0.012416231445968151,
0.011851571500301361,
0.018947793170809746,
0.0009822280844673514,
-0.0371142141520977,
-0.004411477129906416,
-0.0037138231564313173,
0.01872088573873043,
0.024003375321626663,
0.00032798704341985285,
0.0053283702582120895,
-0.03454781323671341,
-0.008905154652893543,
0.0016459848266094923,
-0.027349097654223442,
0.048924531787633896,
0.03466317057609558,
-0.0065926150418818,
0.02452286332845688,
-0.06827285140752792,
-0.032942987978458405,
-0.014448320493102074,
-0.014497581869363785,
0.010696982964873314,
-0.009350784122943878,
0.04415885731577873,
0.009172516874969006,
0.00981145165860653,
-0.10553881525993347,
-0.04524759575724602,
-0.0009243276435881853,
0.03273891285061836,
-0.007353614084422588,
-0.006551358848810196,
0.017329689115285873,
-0.027817297726869583,
-0.0483323372900486,
0.020240431651473045,
0.04977193474769592,
-0.02295037917792797,
-0.029960505664348602,
0.009167431853711605,
0.03826651722192764,
0.016535434871912003,
-0.01245757844299078,
-0.0209041777998209,
0.03378898277878761,
-0.009742982685565948,
-0.02782314643263817,
-0.014340891502797604,
0.05909257382154465,
-0.01922367326915264,
-0.03680642321705818,
-0.007518593221902847,
0.0030464339070022106,
-0.0006774032954126596,
-0.012195113115012646,
-0.005354769993573427,
0.02779734507203102,
0.008213642984628677,
-0.01763467863202095,
-0.03002338856458664,
0.0022690538316965103,
0.02390991523861885,
0.027402307838201523,
0.0037837428972125053,
0.010890777222812176,
0.038718197494745255,
-0.06968148797750473,
0.031389690935611725,
0.008050655946135521,
-0.027839988470077515,
0.026263879612088203,
0.06978857517242432,
-0.0023156560491770506,
-0.010849402286112309,
-0.011854843236505985,
-0.00269228289835155,
0.0290440134704113,
-0.013401532545685768,
0.005029764492064714,
-0.002753075212240219,
0.011479990556836128,
-0.03195585310459137,
-0.03207772597670555,
-0.0018585249781608582,
0.03420543298125267,
0.05441778898239136,
0.01664881221950054,
0.04154553264379501,
0.05524427816271782,
-0.003977913409471512,
-0.014016394503414631,
-0.006090275943279266,
-0.00874926708638668,
0.012138246558606625,
0.0018576716538518667,
0.025834528729319572,
-0.023564130067825317,
0.012868843972682953,
0.030236506834626198,
0.04244886711239815,
0.0047757686115801334,
0.016956033185124397,
0.01699184998869896,
0.019148748368024826,
0.03368910402059555,
0.018505554646253586,
-0.05033364146947861,
0.03783315420150757,
-0.0445377379655838,
0.02351565845310688,
0.03142793849110603,
-0.006528195459395647,
0.02377973310649395,
-0.005280336365103722,
0.015224079601466656,
-0.0038079849909991026,
-0.017336873337626457,
-0.04063104838132858,
0.000241546644247137,
-0.009196854196488857,
0.04135188087821007,
0.03414709493517876,
0.027187718078494072,
0.026162846013903618,
-0.007343466859310865,
0.007404077332466841,
0.014631764963269234,
-0.027818970382213593,
-0.04458659887313843,
-0.05973275005817413,
-0.03607901930809021,
0.046445347368717194,
-0.007130514830350876,
-0.030046578496694565,
-0.033521853387355804,
-0.04043653607368469,
-0.0022149805445224047,
-0.001393767073750496,
0.027500968426465988,
-0.020675428211688995,
0.08633503317832947,
0.020288139581680298,
0.013786054216325283,
-0.014969049952924252,
0.009891949594020844,
0.1126379519701004,
0.08965756744146347,
0.012891455553472042,
-0.09499181061983109,
0.026569528505206108,
-0.018407858908176422,
-0.0086727449670434,
-0.025905197486281395,
0.031279683113098145,
0.009839161299169064,
0.023313118144869804,
0.013805299997329712,
0.02280549332499504,
0.00892642606049776,
-0.005977665539830923,
0.04983137920498848,
-0.04771765321493149,
-0.06011349707841873,
-0.008382807485759258,
0.03597892448306084,
-0.0013325718464329839,
0.01903986558318138,
-0.02260979264974594,
0.010956775397062302,
-0.033039163798093796,
0.009697500616312027,
0.030278779566287994,
-0.06291098892688751,
0.036223653703927994,
0.013768372125923634,
-0.001190577051602304,
-0.02499290369451046,
-0.007905361242592335,
-0.005024539306759834,
-0.05379698425531387,
0.046607986092567444,
-0.0023188325576484203,
-0.005296375136822462,
0.05290855094790459,
0.028726851567626,
0.007654072716832161,
0.003414527978748083,
0.0029893890023231506,
0.009066366590559483,
-0.02281404286623001,
-0.013304833322763443,
-0.04609343782067299,
0.02548985555768013,
-0.002144123427569866,
-0.006614771205931902,
-0.007771757431328297,
0.011799350380897522,
0.005335924215614796,
-0.021994179114699364,
-0.03235935419797897,
-0.012374685145914555,
0.013566645793616772,
-0.0120773920789361,
-0.02367210015654564,
-0.033167511224746704,
0.012226922437548637,
0.020344004034996033,
0.00041637971298769116,
-0.016418740153312683,
-0.0006713294424116611,
0.014130189083516598,
-0.017401933670043945,
0.046056948602199554,
0.008982173167169094,
-0.019064784049987793,
-0.02372031845152378,
-0.014268526807427406,
-0.0053160181269049644,
0.0009169464465230703,
-0.009072222746908665,
0.008431761525571346,
0.017699917778372765,
-0.002738672774285078,
0.0121108777821064,
-0.007470958400517702,
-0.05006401985883713,
0.020192593336105347,
-0.04401295632123947,
0.0003599313204176724,
0.005507988389581442,
-0.005953052081167698,
-0.023374950513243675,
0.05797338858246803,
0.010867610573768616,
-0.015897046774625778,
-0.03196590766310692,
0.04774855077266693,
0.003691652324050665,
-0.014411893673241138,
-0.0035667945630848408,
-0.02079249545931816,
-0.03268356993794441,
-0.018313147127628326,
-0.011967328377068043,
0.03898830711841583,
0.022922519594430923,
0.007120661903172731,
0.0300492811948061,
0.032499004155397415,
-0.017878394573926926,
-0.013486597687005997,
0.02198544144630432,
-0.041721563786268234,
0.010018629021942616,
0.04207674786448479,
-0.021782532334327698,
-0.05188494175672531,
-0.0506022647023201,
-0.00018157530575990677,
0.0127125708386302,
0.0152351763099432,
0.04033586010336876,
-0.04089510440826416,
0.014527047984302044,
-0.014080682769417763,
0.029156945645809174,
-0.06294067949056625,
-0.001263433019630611,
-0.07145490497350693,
0.035703469067811966,
-0.01360615435987711,
-0.025344884023070335,
0.0014899397501721978,
0.003110883990302682,
0.0039052192587405443,
-0.03240342065691948,
-0.019996097311377525,
0.01030661165714264,
-0.007862232625484467,
0.014421527273952961,
0.039145972579717636,
0.005317990202456713,
0.032588254660367966,
0.0032301878090947866,
-0.019748451188206673,
-0.020182281732559204,
-0.04756678268313408,
-0.03598971292376518,
0.036578163504600525,
-0.001024163793772459,
0.04267782345414162,
0.03368515148758888,
0.0038445095997303724,
-0.011659838259220123,
0.01893618330359459,
-0.03079262189567089,
-0.028465475887060165,
0.018879422917962074,
-0.03206191211938858,
0.0009626291575841606,
-0.03203188255429268,
0.04664617031812668,
0.015721244737505913,
-0.03306422755122185,
0.01499124150723219,
0.02980102226138115,
-0.013133631087839603,
-0.025907278060913086,
0.01073242723941803,
-0.04536845162510872,
0.06145220622420311,
0.022905658930540085,
0.019203007221221924,
0.025836465880274773,
0.05983789637684822,
-0.024161670356988907,
0.011822475120425224,
0.010682198219001293,
0.04712873324751854,
-0.0797448381781578,
-0.014419217593967915,
0.02373138628900051,
-0.01454224344342947,
0.05389507859945297,
-0.007773425430059433,
0.018922938033938408,
0.06907407194375992,
-0.050194717943668365,
0.030671028420329094,
-0.023761285468935966,
-0.0009659981587901711,
-0.02023187279701233,
0.005075412802398205,
-0.025048891082406044,
0.06278359889984131,
0.06573093682527542,
0.02798079326748848,
0.025732921436429024,
0.008015228435397148,
-0.0006374249351210892,
-0.02492331527173519,
-0.005171650554984808,
0.027495309710502625,
-0.024476148188114166,
0.008990870788693428,
0.074823759496212,
0.00048236583825200796,
-0.060641732066869736,
0.007401753216981888,
-0.022416366264224052,
-0.03366271033883095,
-0.011345885694026947,
0.003747606882825494,
0.005693305749446154,
0.024027328938245773,
0.029669227078557014,
-0.0132020004093647,
-0.007295277900993824,
-0.021292150020599365,
0.04949784651398659,
0.012349341996014118,
-0.008730465546250343,
0.018010122701525688,
0.017874281853437424,
-0.0402190126478672,
-0.02856629714369774,
0.02884184569120407,
0.0066282544285058975,
-0.046298809349536896,
-0.00847743358463049,
-0.00034868830698542297,
0.016508428379893303,
-0.013543295674026012,
-0.019960539415478706,
-0.02648577280342579,
-0.020141849294304848,
0.031945280730724335,
0.009961554780602455,
0.007409465499222279,
0.006814553402364254,
-0.021965352818369865,
-0.02731410413980484,
0.003922660369426012,
0.0361669547855854,
0.007381935603916645,
-0.08625848591327667,
-0.02022835798561573,
0.015364582650363445,
-0.04855821281671524,
-0.04179660230875015,
-0.013380330987274647,
-0.032366421073675156,
-0.008465364575386047,
0.02606082707643509,
0.022498533129692078,
-0.033044468611478806,
-0.046589210629463196,
-0.019701985642313957,
-0.0842680037021637,
0.04308392480015755,
-0.004638290964066982,
0.02231370285153389,
-0.042670100927352905,
-0.03543451055884361,
-0.00785788707435131,
-0.0012156983138993382,
0.028206201270222664,
-0.02168409340083599,
-0.01353750191628933,
0.024412531405687332,
-0.01619144342839718,
0.009435649961233139,
-0.009923703968524933,
-0.03673671558499336,
0.012696257792413235,
0.020980441942811012,
-0.03365401551127434,
-0.0029767309315502644,
0.01970415748655796,
0.00613552238792181,
0.024692628532648087,
-0.010764171369373798,
0.04005216434597969,
0.009855508804321289,
-0.02805650234222412,
0.06486860662698746,
0.016884010285139084,
0.006261945236474276,
0.024202732369303703,
-0.029136333614587784,
0.020648464560508728,
0.022401966154575348,
-0.05629946291446686,
-0.029329674318432808,
0.012636889703571796,
-0.03750867024064064,
0.009621290490031242,
0.017465993762016296,
-0.0033097141422331333,
0.015403755940496922,
-0.05069383978843689,
-0.024095851927995682,
0.07305742800235748,
-0.03566598892211914,
-0.01395275816321373,
0.039994977414608,
0.012803440913558006,
0.04785297438502312,
-0.005217649042606354,
-0.01735430397093296,
0.019336825236678123,
0.047095462679862976,
0.01398561242967844,
0.0439438559114933,
0.026421314105391502,
0.01381401252001524,
0.005397439002990723,
0.0001677867112448439,
-0.025320330634713173,
0.014901245012879372,
0.02017754316329956,
0.056849051266908646,
-0.05616169050335884,
-0.002092337002977729,
-0.005318657029420137,
0.0018538240110501647,
0.04797185957431793,
0.01594504341483116,
-0.0033520804718136787,
0.08164327591657639,
-0.03466598317027092,
0.0022510120179504156,
-0.023579733446240425,
0.0024036846589297056,
-0.006678668316453695,
-0.01550722774118185,
-0.011041400954127312,
0.08845309168100357,
0.005231514573097229,
0.01449301466345787,
0.01977904513478279,
0.037393536418676376,
-0.004255320411175489,
-0.05832507833838463,
0.008795446716248989,
0.019179200753569603,
-0.0016287757316604257,
0.02445087395608425,
-0.007012722548097372,
-0.006267738528549671,
-0.009179421700537205,
0.02686115726828575,
0.04721218720078468,
0.025120945647358894,
0.012259026058018208,
-0.020823752507567406,
-0.0705961138010025,
0.03848077356815338,
-0.042619310319423676,
-0.025382867082953453,
-0.0058343973942101,
0.01069751288741827,
-0.00432424945756793,
0.00587672833353281
] |
<p>Through a bit calculation we can derive that in a cavity, the energy density $$u(f,T)=\overline{E(f)}\times G(f)=\frac{8\pi h}{c^3}\frac{f^3}{e^{h\nu /kT}-1}$$
If we take the integral over all frequency, we get
$$U(T)=\frac{8πh}{c^3}\frac{(kT)^4}{h^3}{\frac{π^4}{15}}=C_{onst}T^4$$
And Stefan-Boltzmann Law claims that for a perfect black-body
$$j^*=\sigma T^4$$
where $j^*$ is the radiant exitance, which is defined as the total energy radiated per unit surface area of a black body across all wavelengths per unit time.</p>
<p>And it just so happens that $\frac{\sigma}{C_{onst}}=\frac{c}{4}$, why is that?</p>
<p>P.S. The professor told me to refer to some thermodynamics book, where a more general case is discussed. But we don't have that book in our library and the professor's now out of town xD.</p> | 1,505 | [
-0.011533287353813648,
-0.05230472609400749,
0.024471914395689964,
-0.021493468433618546,
0.04164896905422211,
0.029931602999567986,
-0.012195402756333351,
-0.011235199868679047,
-0.010641724802553654,
0.017995409667491913,
0.044380784034729004,
0.03088967688381672,
0.07067737728357315,
0.016341039910912514,
0.015297519974410534,
-0.028545241802930832,
-0.029652824625372887,
-0.01079160999506712,
-0.026201847940683365,
-0.046707529574632645,
0.039063192903995514,
0.043482109904289246,
-0.054291632026433945,
-0.03449971601366997,
-0.04516815394163132,
0.03383736312389374,
-0.01966021955013275,
-0.021839162334799767,
0.02567998506128788,
0.029682086780667305,
-0.04245620220899582,
-0.0028068446554243565,
0.027627907693386078,
0.014527535997331142,
0.04388781636953354,
-0.002297978848218918,
-0.05138355866074562,
0.004362902138382196,
-0.03824395686388016,
0.04851919040083885,
-0.04401190206408501,
-0.011640026234090328,
-0.01794123835861683,
0.024530895054340363,
0.030276646837592125,
-0.01749737374484539,
0.005321807693690062,
-0.023404721170663834,
0.021036073565483093,
-0.10652758926153183,
0.05122434347867966,
0.0041299844160676,
0.03948831558227539,
0.004874792881309986,
0.012131212279200554,
0.004327615723013878,
0.07204369455575943,
0.08516993373632431,
0.02253485657274723,
-0.02671811915934086,
-0.007204060908406973,
-0.00531400553882122,
-0.04282672703266144,
0.012110340408980846,
0.004610483534634113,
0.004429149441421032,
-0.00811463687568903,
-0.07941893488168716,
0.05512404441833496,
-0.027557844296097755,
0.01038295030593872,
0.0006239295471459627,
0.03286459669470787,
-0.010848918929696083,
0.049408525228500366,
0.003130438504740596,
0.008672227151691914,
0.05505954846739769,
0.014842069707810879,
0.04382028430700302,
-0.02864866517484188,
-0.0006692492752335966,
0.027164926752448082,
0.06188496947288513,
-0.01299367193132639,
0.030586283653974533,
0.07180273532867432,
0.008154383860528469,
0.0334625281393528,
0.03107038512825966,
0.009966930374503136,
-0.012507239356637001,
0.04807424172759056,
0.026780160143971443,
-0.03423476591706276,
0.016932934522628784,
0.011701073497533798,
0.04820515587925911,
-0.0047478084452450275,
-0.04793122038245201,
0.005975441541522741,
-0.013347780331969261,
0.03135490044951439,
0.07315164059400558,
0.019830282777547836,
-0.026984529569745064,
-0.055338505655527115,
0.01744885742664337,
-0.023779291659593582,
-0.020451422780752182,
-0.046621065586805344,
0.0074843754991889,
-0.018889473751187325,
-0.0210121963173151,
-0.020008083432912827,
-0.0004727349733002484,
-0.003964596893638372,
-0.00405923742800951,
0.03864267095923424,
0.045262549072504044,
0.04201526939868927,
0.022623350843787193,
0.017830586060881615,
-0.03103778511285782,
-0.05077279731631279,
0.0403086356818676,
0.033541422337293625,
-0.002029621507972479,
-0.04935546964406967,
0.014228331856429577,
0.002023984445258975,
0.015734249725937843,
0.011745373718440533,
0.01889430731534958,
-0.010699218139052391,
-0.0424189418554306,
-0.08541104197502136,
-0.03791787102818489,
0.05855906382203102,
-0.03976771980524063,
-0.03895708918571472,
-0.08857648074626923,
-0.007271899841725826,
0.025047481060028076,
0.0762808695435524,
-0.026247229427099228,
-0.03166240453720093,
-0.05695069953799248,
0.02980859950184822,
0.0006160682532936335,
0.00869144219905138,
0.0028608872089535,
-0.017162643373012543,
-0.017755325883626938,
0.0038600468542426825,
-0.038174599409103394,
0.03978130593895912,
0.05045690760016441,
0.02961716055870056,
-0.019837988540530205,
0.08726904541254044,
0.0033763472456485033,
-0.01840546540915966,
0.0004181111871730536,
0.013290509581565857,
-0.023059960454702377,
0.05883420631289482,
0.025945620611310005,
-0.02407120354473591,
-0.007163238245993853,
0.06359408795833588,
-0.022009508684277534,
-0.0041149393655359745,
0.027118587866425514,
-0.006843819748610258,
-0.029477981850504875,
0.028464969247579575,
-0.07048564404249191,
0.011068128980696201,
0.032605431973934174,
-0.017323289066553116,
-0.03173650801181793,
0.013578912243247032,
-0.017987430095672607,
-0.0039223721250891685,
0.04122304916381836,
-0.016498498618602753,
-0.006236909423023462,
-0.00216407747939229,
-0.05024319142103195,
-0.018754547461867332,
-0.05357125401496887,
0.04188695549964905,
0.017311986535787582,
0.012895344756543636,
0.02837427519261837,
0.014899282716214657,
0.014096188358962536,
0.011804071255028248,
-0.03703556954860687,
0.011572632007300854,
0.02876165322959423,
0.0018490294460207224,
-0.02093338966369629,
0.031039472669363022,
0.01909278705716133,
0.03984881564974785,
-0.01952037215232849,
0.036965299397706985,
-0.038391802459955215,
-0.051095664501190186,
-0.029032612219452858,
-0.01132551021873951,
0.043900828808546066,
-0.03170643001794815,
-0.025559136644005775,
0.003873456735163927,
-0.015940368175506592,
0.02225303463637829,
0.02796434424817562,
-0.02150266245007515,
0.017267638817429543,
0.030867820605635643,
0.01810947060585022,
0.034692298620939255,
0.049822159111499786,
0.004189647268503904,
0.030860956758260727,
-0.012127373367547989,
-0.04817354306578636,
-0.0342232920229435,
0.012424980290234089,
0.03404766693711281,
0.007532278075814247,
-0.02810593508183956,
0.009747846983373165,
0.06360062956809998,
0.010207048617303371,
0.05772271007299423,
0.011218602769076824,
-0.015778981149196625,
-0.020261745899915695,
0.057777516543865204,
0.015807434916496277,
0.023528942838311195,
0.005619090050458908,
-0.00870378315448761,
0.010641946457326412,
-0.014739354141056538,
-0.001719622639939189,
0.008935416117310524,
0.008275389671325684,
0.0005511519848369062,
0.03287235647439957,
-0.032552774995565414,
0.008200814947485924,
0.05025876313447952,
-0.04710948094725609,
0.017028698697686195,
0.02168278954923153,
-0.008039724081754684,
0.021121736615896225,
-0.057159002870321274,
-0.015577573329210281,
0.01833329163491726,
-0.001967039192095399,
0.0012302069226279855,
0.016493480652570724,
0.023176081478595734,
-0.03642996400594711,
0.01145201362669468,
0.012288166210055351,
0.029533730819821358,
0.0012283619726076722,
0.020800014957785606,
0.03624435514211655,
0.025683369487524033,
0.022270087152719498,
-0.05634688213467598,
-0.04616172984242439,
-0.011777958832681179,
-0.021834228187799454,
0.009017190895974636,
0.02423415146768093,
-0.018811360001564026,
-0.029123028740286827,
-0.00847336370497942,
-0.02488737367093563,
0.018271658569574356,
-0.02289655990898609,
0.01121495757251978,
0.03579157963395119,
-0.0225253663957119,
-0.014732754789292812,
-0.029628297314047813,
0.011454719118773937,
0.0076932404190301895,
-0.03000669553875923,
0.010780548676848412,
0.03465202823281288,
-0.06100624054670334,
-0.047469910234212875,
0.007400139234960079,
-0.04252111539244652,
-0.07217994332313538,
0.009215041995048523,
-0.03434840962290764,
0.028966018930077553,
-0.018702445551753044,
0.02968052588403225,
0.022539252415299416,
-0.029680326581001282,
-0.034986961632966995,
-0.03751042112708092,
-0.04120916873216629,
0.06899245083332062,
-0.007087388075888157,
0.04221765324473381,
-0.014962238259613514,
-0.01679440215229988,
0.04888634756207466,
0.024068670347332954,
-0.006993334274739027,
0.0008246673387475312,
-0.017256133258342743,
-0.016865408048033714,
-0.03323173150420189,
-0.027909044176340103,
0.03210347890853882,
-0.041014302521944046,
-0.011984609067440033,
-0.0073194499127566814,
0.033825263381004333,
0.05084648355841637,
0.009897063486278057,
-0.010293183848261833,
0.009268314577639103,
-0.03157392144203186,
0.020498251542448997,
0.0660080760717392,
-0.008534923195838928,
0.013619720004498959,
0.0029242776799947023,
-0.01828685589134693,
0.04073980823159218,
0.06531505286693573,
-0.08576743304729462,
0.013734945096075535,
0.022841161116957664,
0.0069366153329610825,
-0.062223169952631,
0.0313386507332325,
-0.014500546269118786,
-0.054317690432071686,
0.0074410224333405495,
0.04544614627957344,
0.05364088714122772,
-0.021304795518517494,
-0.01540497224777937,
0.004887844901531935,
0.019938793033361435,
0.009276650846004486,
-0.03261818364262581,
0.010213656350970268,
-0.003182612359523773,
0.01227583084255457,
-0.016511613503098488,
0.003690806683152914,
0.024980515241622925,
0.06848607212305069,
0.03221800550818443,
-0.024470336735248566,
-0.038967911154031754,
-0.026821693405508995,
-0.0337776355445385,
-0.047552820295095444,
-0.04366031661629677,
0.0749220922589302,
0.030569521710276604,
0.03988374397158623,
0.02175585925579071,
0.027307501062750816,
0.0697103813290596,
-0.01453206967562437,
-0.08320875465869904,
-0.005671605467796326,
-0.0032984698191285133,
0.00018496483971830457,
-0.011559666134417057,
-0.008573957718908787,
0.014963124878704548,
-0.039285097271203995,
-0.057320479303598404,
0.015824707224965096,
-0.007083574775606394,
-0.05957460403442383,
-0.005912189371883869,
-0.031266793608665466,
-0.06429215520620346,
-0.021268105134367943,
0.04073468595743179,
0.04427627474069595,
-0.027960116043686867,
0.00012881390284746885,
0.061724383383989334,
-0.02918528951704502,
-0.00715899420902133,
-0.019302472472190857,
0.004927870351821184,
0.0030705935787409544,
0.02208908647298813,
0.04471731185913086,
0.0028331882786005735,
-0.016207166016101837,
0.013960829935967922,
0.06307727098464966,
0.005253797862678766,
-0.002146907150745392,
-0.026764264330267906,
-0.016967078670859337,
-0.02123296447098255,
0.021488171070814133,
0.031016994267702103,
0.05940737947821617,
0.010034036822617054,
0.01449307519942522,
0.012794272974133492,
0.005820896942168474,
0.0038487149868160486,
0.039214104413986206,
0.024184249341487885,
-0.02998702973127365,
-0.013951875269412994,
-0.04519645497202873,
0.006266512908041477,
-0.007275415118783712,
-0.0009231985313817859,
0.0025319294072687626,
0.029192360118031502,
-0.025222091004252434,
-0.0006591932033188641,
-0.007932092063128948,
0.018982980400323868,
0.011827277950942516,
-0.007754630409181118,
-0.00854276493191719,
0.008483784273266792,
-0.03769773617386818,
-0.005731592420488596,
-0.029421942308545113,
0.006653625518083572,
0.0556107833981514,
-0.0069972192868590355,
-0.01677626371383667,
-0.05603000894188881,
-0.03745800256729126,
0.02165052480995655,
0.039703644812107086,
0.00971095822751522,
-0.011078153736889362,
-0.04596463218331337,
0.0017287911614403129,
0.019287750124931335,
0.02826729416847229,
0.04710707068443298,
0.014237985014915466,
0.008158599957823753,
0.011666025035083294,
-0.07225312292575836,
-0.011883087456226349,
-0.005601242650300264,
-0.010610497556626797,
0.03084644302725792,
-0.028759602457284927,
-0.03901307284832001,
0.03143707662820816,
0.02950803004205227,
0.03650270402431488,
0.019208362326025963,
-0.030972162261605263,
-0.029906805604696274,
0.02980940230190754,
0.006356178782880306,
-0.035196688026189804,
-0.053152021020650864,
-0.03084564581513405,
-0.02568928338587284,
0.018789783120155334,
0.02602762170135975,
-0.05124291777610779,
-0.014932316727936268,
0.02255159057676792,
0.03692574426531792,
-0.019010433927178383,
0.0015290578594431281,
-0.033665839582681656,
0.06995398551225662,
-0.021007945761084557,
-0.02155713178217411,
0.04529405012726784,
0.01970963180065155,
0.012200509198009968,
0.024229498580098152,
-0.04928097873926163,
0.04568960517644882,
-0.015806663781404495,
-0.013213553465902805,
-0.020901557058095932,
0.006825832184404135,
-0.02764732763171196,
0.03830989450216293,
0.0009993353160098195,
0.02782403863966465,
0.003918349277228117,
-0.04748620465397835,
0.03543481230735779,
-0.012902460992336273,
-0.016941865906119347,
0.025280283764004707,
-0.011043502949178219,
-0.015618919394910336,
0.022740203887224197,
-0.02816806361079216,
-0.00469649164006114,
-0.026710495352745056,
0.00224719918332994,
0.0262460857629776,
0.01879877969622612,
0.0508001334965229,
-0.02894364669919014,
-0.021848164498806,
0.0339578315615654,
-0.04607643932104111,
0.026270978152751923,
-0.02184705063700676,
0.041488464921712875,
0.014764356426894665,
-0.013307297602295876,
0.0013210591860115528,
-0.030279314145445824,
-0.009966579265892506,
0.025004204362630844,
-0.05207861214876175,
0.020138097926974297,
-0.00253405817784369,
0.02442285791039467,
-0.06818509101867676,
0.015140142291784286,
0.02497369982302189,
0.02343505620956421,
-0.043314993381500244,
-0.039011843502521515,
-0.0044294437393546104,
-0.020854948088526726,
-0.040835123509168625,
0.02633844129741192,
0.026564059779047966,
-0.007973240688443184,
0.0027656310703605413,
0.005287403706461191,
0.048680782318115234,
0.020327173173427582,
0.0010618172818794847,
-0.013040721416473389,
-0.006746630184352398,
0.02024848200380802,
-0.027082376182079315,
0.011644943617284298,
0.08173713088035583,
-0.0076626879163086414,
-0.026167694479227066,
0.010383481159806252,
0.0030129062943160534,
0.047670960426330566,
-0.022061020135879517,
0.006084157153964043,
0.0022070249542593956,
0.037025123834609985,
-0.021310700103640556,
0.02645648829638958,
0.013437771238386631,
0.00042279844637960196,
0.03695128113031387,
-0.029661934822797775,
0.000884378096088767,
-0.034058284014463425,
-0.018478935584425926,
0.0003550700203049928,
-0.007710556033998728,
0.02994900941848755,
-0.024877887219190598,
0.09908267855644226,
0.009009642526507378,
-0.02348272129893303,
0.00002630427297845017,
0.005662910640239716,
0.011056757532060146,
0.0026700966991484165,
0.029245411977171898,
0.001823434024117887,
0.031086111441254616,
0.0074832383543252945,
-0.028727538883686066,
-0.09187085926532745,
0.0137784443795681,
0.03287706524133682,
-0.04107005149126053,
0.037498604506254196,
0.0032848294358700514,
0.015517239458858967,
0.03891903907060623,
-0.0217887032777071,
-0.01494640950113535,
0.050689369440078735,
-0.024098213762044907,
0.03698963299393654,
-0.008705787360668182,
-0.0153932711109519,
0.022815221920609474,
0.0338723361492157,
-0.03347598761320114,
0.034533120691776276,
0.002739864867180586,
0.031230000779032707,
-0.019077971577644348,
-0.02841286174952984,
-0.02983003295958042,
0.07039634883403778,
-0.033105697482824326,
0.030489422380924225,
0.009429537691175938,
0.04260178655385971,
0.013436042703688145,
0.026478519663214684,
0.009754585102200508,
-0.07280775904655457,
-0.007906541228294373,
-0.030923547223210335,
0.017394963651895523,
0.027137722820043564,
-0.005258843768388033,
0.00022404752962756902,
0.007075571455061436,
0.04620935395359993,
0.004793578293174505,
0.0029055075719952583,
0.015735477209091187,
-0.052274998277425766,
0.0014341372298076749,
-0.02620665356516838,
-0.043847765773534775,
0.01596793904900551,
-0.018352482467889786,
-0.02396024391055107,
0.043450627475976944,
-0.013073013164103031,
0.018993893638253212,
0.028663409873843193,
0.03230353817343712,
0.03616366535425186,
0.06257392466068268,
0.008366438560187817,
0.0123082110658288,
-0.019056931138038635,
0.029393469914793968,
0.12679636478424072,
0.030425934121012688,
0.013555319048464298,
-0.02794758975505829,
0.011149208061397076,
-0.024401938542723656,
0.022512130439281464,
-0.04190513491630554,
0.01673470437526703,
-0.015001215972006321,
0.010703767649829388,
0.020030926913022995,
0.06307220458984375,
0.02184799686074257,
-0.030174588784575462,
-0.022314535453915596,
-0.030143043026328087,
0.00010924584785243496,
0.03800952807068825,
0.02085402049124241,
-0.025184107944369316,
-0.022736046463251114,
-0.021548975259065628,
-0.010179958306252956,
-0.0075523741543293,
0.0017368615372106433,
-0.02158363163471222,
-0.03204694017767906,
0.014996694400906563,
-0.01609516143798828,
-0.05163121595978737,
0.0343838669359684,
-0.033085212111473083,
-0.02992754615843296,
-0.016221879050135612,
0.015093561261892319,
0.02387925796210766,
-0.0033115416299551725,
0.005884845741093159,
0.06235961243510246,
0.015804985538125038,
0.004820496775209904,
0.02551293559372425,
0.06515136361122131,
-0.0024524054024368525,
-0.004593807738274336,
-0.052217643707990646,
0.04817734658718109,
-0.03461603820323944,
-0.002430507680401206,
-0.00882683414965868,
0.02089015766978264,
0.01527049858123064,
-0.052967626601457596,
0.007494270335882902,
-0.048974763602018356,
0.023885861039161682,
-0.03521909937262535,
-0.03443589061498642,
-0.000157003611093387,
0.0032724894117563963,
0.022107381373643875,
-0.010731348767876625,
0.017857801169157028,
0.0014806040562689304,
0.00961378775537014,
0.0007204092107713223,
0.05387935787439346,
-0.006253579631447792,
-0.020312264561653137,
-0.019202839583158493,
-0.028531331568956375,
-0.04087064042687416,
-0.017368044704198837,
-0.00828191451728344,
0.01860787905752659,
0.030057720839977264,
-0.00924789160490036,
-0.010316421277821064,
-0.06886066496372223,
-0.06958956271409988,
0.0039770640432834625,
-0.02108604647219181,
-0.02327326126396656,
-0.007942073047161102,
-0.052573420107364655,
-0.019091295078396797,
0.025280345231294632,
-0.01713564060628414,
0.0032207765616476536,
0.02910420298576355,
0.02474079094827175,
0.01540190726518631,
-0.009471115656197071,
-0.01172429695725441,
-0.002745185513049364,
-0.015714062377810478,
0.03360642120242119,
0.011852982454001904,
0.022786879912018776,
0.02446652017533779,
0.004048272036015987,
0.03042934462428093,
0.030673479661345482,
-0.03998982533812523,
0.010386748239398003,
0.01775909774005413,
-0.043480657041072845,
-0.01697186939418316,
0.01991311088204384,
-0.010076269507408142,
-0.03028951585292816,
-0.06421957165002823,
-0.02596469037234783,
0.009803756140172482,
-0.005641331430524588,
0.008344086818397045,
-0.015640802681446075,
0.0027328222058713436,
-0.0004494432359933853,
0.004429950844496489,
-0.0549476183950901,
-0.01376678142696619,
-0.03854406625032425,
0.013063967227935791,
0.02515539899468422,
0.0019335472024977207,
-0.035709746181964874,
0.014410572126507759,
-0.03619041666388512,
-0.027008486911654472,
0.017213184386491776,
0.02255701832473278,
-0.02096610702574253,
-0.06078742817044258,
-0.02048494666814804,
-0.002305098343640566,
0.04012064263224602,
0.01607234589755535,
-0.002377357566729188,
0.0646812841296196,
-0.02960168942809105,
-0.06495387107133865,
0.025578901171684265,
0.024348655715584755,
0.00888135377317667,
0.005910270381718874,
0.03380937874317169,
0.005005085840821266,
0.061547961086034775,
-0.007513570133596659,
0.005868695210665464,
-0.007948605343699455,
-0.0077365911565721035,
0.0018664197996258736,
-0.008238844573497772,
0.018106229603290558,
-0.010917402803897858,
0.024270888417959213,
0.012818685732781887,
0.023573867976665497,
-0.019116630777716637,
0.024483663961291313,
0.0047820862382650375,
-0.04266234487295151,
-0.023037828505039215,
0.016902685165405273,
0.038717519491910934,
0.009505926631391048,
0.05384937301278114,
0.013005617074668407,
0.030949877575039864,
0.014305799268186092,
0.01628689095377922,
-0.06217047572135925,
-0.024708500131964684,
-0.019031573086977005,
-0.0028693615458905697,
-0.002893715864047408,
-0.06964165717363358,
0.02395467832684517,
0.019224124029278755,
-0.06823404878377914,
0.03833431378006935,
-0.020250845700502396,
-0.01657269150018692,
-0.049657512456178665,
-0.0002449772146064788,
-0.0429094024002552,
-0.00938496459275484,
0.01649848371744156,
-0.004494315478950739,
-0.02303047850728035,
0.04502461105585098,
-0.013921673409640789,
-0.03009592369198799,
0.012521774508059025,
0.029282165691256523,
0.01776832900941372,
-0.009412079118192196,
0.05780209228396416,
0.0024021663703024387,
-0.013417587615549564,
0.005243798717856407,
-0.030786626040935516,
-0.01812474988400936,
-0.04274369031190872,
0.009822218678891659,
-0.01904972456395626,
0.01742914877831936,
0.032463472336530685,
-0.01689651980996132,
0.008760761469602585,
0.020973749458789825,
0.03088037669658661,
-0.010631734505295753,
0.006198846735060215,
0.021224791184067726,
0.03706597164273262,
-0.02848975546658039,
-0.026289476081728935,
0.030842704698443413,
-0.014836806803941727,
-0.006458056624978781,
0.03884870931506157,
-0.0028945866506546736,
-0.0011197510175406933,
-0.02517648972570896,
0.007170664146542549,
-0.07315831631422043,
-0.0031511709094047546,
0.001787835150025785,
0.03438262641429901,
0.03787754848599434,
-0.027081644162535667,
-0.005885610356926918,
-0.019297070801258087,
0.008316528983414173,
0.022499175742268562,
-0.044587697833776474,
-0.015424595214426517,
-0.027975330129265785,
-0.01812281273305416,
0.0016377079300582409,
-0.006046231836080551,
-0.056652046740055084,
-0.06709353625774384,
0.0026416906621307135,
0.02162441611289978,
0.003668274497613311,
-0.015953751280903816,
-0.037088967859745026,
-0.02861061878502369,
-0.06815695017576218,
0.004387410823255777,
-0.015993749722838402,
0.021568192169070244,
-0.029755596071481705,
-0.023163676261901855,
-0.012468162924051285,
0.02471156045794487,
0.05289900675415993,
-0.0014439447550103068,
-0.038495201617479324,
0.0008117724792100489,
-0.03546962887048721,
0.00032149124308489263,
-0.06450928747653961,
0.0023376098833978176,
0.002963281935080886,
0.0027426250744611025,
-0.010115141980350018,
0.039912451058626175,
-0.0027799869421869516,
-0.0148190688341856,
0.02333149127662182,
-0.028225954622030258,
0.011300383135676384,
-0.028961224481463432,
-0.023897891864180565,
0.035067155957221985,
0.005715633276849985,
-0.020802175626158714,
0.04522942379117012,
0.016543790698051453,
0.0351543091237545,
0.04653841257095337,
-0.03218027949333191,
-0.015309435315430164,
0.027087830007076263,
0.005262375809252262,
0.007565070874989033,
-0.0555107407271862,
-0.007090605795383453,
0.027877040207386017,
-0.04820863530039787,
-0.01028585433959961,
0.04725639522075653,
-0.0718027800321579,
-0.02746061235666275,
0.00411094818264246,
0.015442624688148499,
0.020820587873458862,
-0.013221313245594501,
0.020241599529981613,
-0.009864114224910736,
-0.0063520027324557304,
-0.051059599965810776,
0.06656437367200851,
0.0022883820347487926,
-0.014204027131199837,
0.0394996702671051,
0.03707098960876465,
-0.03677140921354294,
-0.0110703743994236,
0.0029388396069407463,
0.03206193819642067,
-0.015377488918602467,
-0.03081965260207653,
0.018612833693623543,
0.022423982620239258,
-0.009017403237521648,
0.026245560497045517,
-0.028615284711122513,
0.08210839331150055,
0.015912655740976334,
0.02507081814110279,
-0.03723575174808502,
-0.03614410012960434,
-0.025340301916003227,
0.04872286692261696,
0.029088247567415237,
0.06442956626415253,
-0.03732343390583992,
-0.005340917035937309,
-0.03138938173651695,
0.0038689696229994297,
0.023844148963689804,
-0.053527720272541046,
-0.02266274392604828,
0.013217026367783546,
0.0026144739240407944,
-0.021418103948235512,
0.02324969880282879,
0.03565243259072304,
-0.01844005659222603,
0.014055591076612473,
0.040554437786340714,
0.007037392817437649,
0.03083174116909504,
-0.0032413427252322435,
0.02825316973030567,
0.06910591572523117,
-0.029197175055742264,
-0.0029953522607684135,
0.019660931080579758,
0.05736134946346283,
-0.0019969891291111708,
-0.019868629053235054
] |
<p>I have known the reason why skate can slide over ice is that water's melting curve in terms of pressure and temperature has a negative slope. If the pressure due to our mass increases sufficiently high, the ice starts to melt.</p>
<p>But someone says, according to latest research, it is not true because the time for which we pressure the ice is too short so the ice can't has enough time to melt.</p>
<p>Which is more reasonable between the two arguments?</p> | 22 | [
-0.015049183741211891,
-0.06497413665056229,
-0.016416111961007118,
-0.03988192230463028,
0.023263800889253616,
-0.011931735090911388,
-0.034740544855594635,
0.002653595292940736,
-0.01540753711014986,
0.017778245732188225,
0.01787451095879078,
0.0443013533949852,
0.00773715740069747,
0.021472275257110596,
-0.011721705086529255,
0.05073986202478409,
-0.015300440602004528,
-0.035574931651353836,
0.018078869208693504,
-0.016707463189959526,
-0.011534254066646099,
-0.01545094046741724,
-0.020604336634278297,
0.0478086918592453,
-0.028893833979964256,
-0.015368408523499966,
0.05278531834483147,
0.0021299864165484905,
0.016010910272598267,
0.04753568023443222,
0.008254866115748882,
-0.013558794744312763,
0.03784143179655075,
0.0024405233561992645,
0.049604155123233795,
0.017836131155490875,
-0.038233980536460876,
0.0024988336954265833,
-0.010289824567735195,
0.02651757188141346,
0.003935068380087614,
-0.0013261997373774648,
0.020821353420615196,
0.03741233050823212,
-0.05050409212708473,
0.060124896466732025,
0.016431815922260284,
-0.04656600579619408,
0.018498098477721214,
-0.06862346827983856,
0.018277134746313095,
0.002029797760769725,
0.04916976019740105,
0.029230264946818352,
0.008701861836016178,
-0.0043380241841077805,
0.08141916245222092,
0.06720540672540665,
-0.02303316816687584,
-0.06541214138269424,
0.014557192102074623,
-0.010165462270379066,
-0.034145843237638474,
0.05177988484501839,
-0.005933616776019335,
0.027253534644842148,
-0.017090287059545517,
-0.018883230164647102,
0.008120515383780003,
0.0012981046456843615,
0.005758160725235939,
-0.025510752573609352,
0.03900548443198204,
0.02696879394352436,
0.043754611164331436,
-0.0161898173391819,
-0.002203558571636677,
0.058499984443187714,
0.0176030695438385,
0.06217814236879349,
-0.00460949819535017,
0.02526143752038479,
0.05129707604646683,
0.05929892137646675,
0.011741108261048794,
-0.0327235572040081,
0.06548179686069489,
0.005830464418977499,
0.017887379974126816,
0.047900184988975525,
0.014621646143496037,
0.016281304880976677,
0.011649874038994312,
-0.01985103450715542,
0.040516603738069534,
-0.021876614540815353,
0.02779652178287506,
0.0535956509411335,
0.013577605597674847,
0.01083312463015318,
0.009035021997988224,
-0.02121352218091488,
0.008858300745487213,
0.05462522804737091,
0.04150572419166565,
-0.00019453010463621467,
-0.038202788680791855,
0.0305305365473032,
-0.009372923523187637,
-0.03382134065032005,
-0.014024881646037102,
0.008394701406359673,
-0.021951790899038315,
-0.021221822127699852,
-0.030427180230617523,
-0.012829176150262356,
0.02013753168284893,
-0.007650365121662617,
0.07004162669181824,
0.03638806939125061,
-0.0020313782151788473,
-0.008946975693106651,
-0.005532521288841963,
-0.03022967092692852,
-0.07276392728090286,
0.02496628277003765,
0.02614304982125759,
-0.0062856525182724,
-0.016467547044157982,
0.008148221299052238,
0.027877401560544968,
0.03773486241698265,
0.020792648196220398,
-0.014833820052444935,
0.044275250285863876,
0.009180732071399689,
-0.09147704392671585,
-0.04338495060801506,
0.06101689487695694,
0.020091332495212555,
-0.02551225572824478,
-0.07502453029155731,
0.013169229961931705,
-0.0075583430007100105,
0.07693944871425629,
0.004907979164272547,
0.04428090527653694,
-0.0031332755461335182,
0.009163334965705872,
-0.03204423934221268,
0.010628857649862766,
-0.022207792848348618,
-0.005167950410395861,
-0.03808886185288429,
-0.010627251118421555,
-0.08072081208229065,
0.016477230936288834,
0.057909589260816574,
-0.012282752431929111,
0.0031729608308523893,
0.005364552140235901,
-0.04800168424844742,
0.007286919746547937,
-0.019899720326066017,
0.012528233230113983,
-0.04279087483882904,
0.041129350662231445,
-0.011284391395747662,
0.014550258405506611,
0.03371034935116768,
0.024169767275452614,
0.03589342162013054,
0.0011524306610226631,
0.035727694630622864,
0.056238822638988495,
-0.054483089596033096,
0.0023779349867254496,
-0.025589484721422195,
-0.02619551494717598,
-0.016285978257656097,
-0.053375229239463806,
-0.009696334600448608,
0.011501294560730457,
0.018129082396626472,
0.01579003408551216,
0.04282945394515991,
0.014668968506157398,
0.039045482873916626,
0.02001243643462658,
-0.07960119843482971,
-0.04795662686228752,
-0.0651388019323349,
0.03502197191119194,
-0.0242998655885458,
-0.000992880668491125,
0.021786438301205635,
0.004398147575557232,
0.015761487185955048,
-0.05048404633998871,
-0.01006824430078268,
0.0005533148651011288,
0.0527474619448185,
0.0448598749935627,
-0.007346314378082752,
0.008355721831321716,
0.05485027655959129,
0.00008190839434973896,
-0.026579691097140312,
-0.014198084361851215,
-0.00787423923611641,
-0.03664158284664154,
0.04665408656001091,
-0.024402717128396034,
0.020024986937642097,
0.0024467986077070236,
0.005726136267185211,
0.029735762625932693,
0.030341142788529396,
-0.03865545243024826,
0.03919084742665291,
-0.022208351641893387,
0.09685665369033813,
0.04055912792682648,
0.028389208018779755,
-0.016086788848042488,
0.019407503306865692,
0.03759344294667244,
-0.035820428282022476,
0.0339089073240757,
-0.020775439217686653,
-0.04581664502620697,
-0.010710724629461765,
0.005627998150885105,
0.03245651349425316,
-0.04286549240350723,
0.001737383077852428,
0.028003903105854988,
0.007125531788915396,
0.0187369417399168,
0.036001142114400864,
0.00001086372049030615,
-0.03532757982611656,
0.024237357079982758,
0.02947956882417202,
0.032518770545721054,
0.009765367023646832,
0.03506893664598465,
0.024125682190060616,
0.022401118651032448,
-0.04854702204465866,
-0.056063614785671234,
0.004597838502377272,
0.03111315704882145,
0.04617522284388542,
0.023458922281861305,
0.007113804575055838,
0.03315705806016922,
-0.05580631643533707,
0.00582484807819128,
0.007323388010263443,
0.024760112166404724,
0.02103511616587639,
-0.07982224225997925,
0.004076894372701645,
0.01772945001721382,
0.0017184298485517502,
0.014899366535246372,
-0.00987938977777958,
0.04040912911295891,
-0.02683083526790142,
-0.017378875985741615,
-0.011107263155281544,
-0.04001376032829285,
-0.024225376546382904,
0.021798040717840195,
0.027314238250255585,
-0.007934993132948875,
0.03458313271403313,
-0.03399527445435524,
-0.03577445074915886,
-0.009433473460376263,
-0.04874106124043465,
-0.035551682114601135,
0.008474796079099178,
-0.04346081241965294,
0.008930719457566738,
-0.029471106827259064,
-0.05773921310901642,
0.026730043813586235,
-0.009452424943447113,
0.019087975844740868,
0.025288963690400124,
-0.007964636199176311,
-0.026501348242163658,
-0.047098129987716675,
-0.015055086463689804,
-0.001969957957044244,
-0.026168866083025932,
-0.009770129807293415,
0.06484408676624298,
-0.0021967582870274782,
-0.04521435126662254,
0.04083872586488724,
-0.02936869114637375,
-0.049843572080135345,
0.016983065754175186,
-0.015485957264900208,
0.024485651403665543,
-0.017096607014536858,
0.0009941025637090206,
-0.003777693957090378,
-0.04613929241895676,
-0.015053263865411282,
-0.012197711504995823,
-0.05020783469080925,
0.05449240282177925,
-0.048142820596694946,
0.033176496624946594,
-0.028378602117300034,
-0.02227216586470604,
0.057668935507535934,
-0.0004957783385179937,
-0.005569480359554291,
-0.033436425030231476,
-0.021516554057598114,
-0.018611105158925056,
-0.012439803220331669,
0.00024949354701675475,
0.05755900591611862,
-0.026764845475554466,
-0.021201740950345993,
0.0003072301915381104,
0.04113932326436043,
0.015171688050031662,
0.01874746009707451,
-0.010301237925887108,
-0.013047485612332821,
0.04031173512339592,
0.0014459699159488082,
0.013492227531969547,
-0.005913061089813709,
-0.024089539423584938,
0.00808623619377613,
-0.05012349784374237,
0.06493102759122849,
0.01615397445857525,
-0.04593461751937866,
0.04828070104122162,
-0.031220972537994385,
-0.014961499720811844,
-0.011730826459825039,
0.009054617956280708,
0.004953368566930294,
-0.001012109685689211,
0.02740756794810295,
0.04209233075380325,
0.01827041618525982,
0.003004408208653331,
-0.00022039942268747836,
-0.002115963725373149,
0.03798171132802963,
-0.029964003711938858,
-0.04276822507381439,
-0.03146829456090927,
0.008616354316473007,
0.05198703706264496,
-0.010293267667293549,
0.019865551963448524,
0.032325614243745804,
0.020682213827967644,
0.0022202697582542896,
0.01952134631574154,
-0.026200490072369576,
-0.014998724684119225,
-0.07939717918634415,
0.01693222112953663,
0.01339747291058302,
0.04832734167575836,
0.01599050685763359,
0.01185025367885828,
0.024187786504626274,
0.0122395483776927,
0.02552374266088009,
-0.021507587283849716,
-0.08907853066921234,
-0.0033554104156792164,
-0.04140628129243851,
-0.018380198627710342,
-0.007045895326882601,
-0.028125274926424026,
0.001650687656365335,
-0.06865482777357101,
-0.011128236539661884,
-0.013447420671582222,
0.016473736613988876,
-0.049720291048288345,
0.0046889386139810085,
-0.008489050902426243,
-0.05813267081975937,
-0.008317596279084682,
-0.005751166958361864,
0.052146293222904205,
-0.026160599663853645,
0.05358361080288887,
0.041299134492874146,
-0.022195052355527878,
-0.02314462885260582,
0.005286875646561384,
0.011542565189301968,
0.032217513769865036,
0.05294918268918991,
-0.034211087971925735,
0.019017796963453293,
-0.001901760813780129,
0.01610092632472515,
-0.0074252234771847725,
0.028122423216700554,
0.014365487731993198,
-0.026071729138493538,
-0.05466042831540108,
-0.06990082561969757,
0.011566861532628536,
0.030680691823363304,
0.05609403923153877,
0.012268617749214172,
-0.01327804010361433,
-0.04410286992788315,
0.006969623267650604,
0.025802932679653168,
0.042650312185287476,
0.05554768815636635,
0.015906695276498795,
0.038742903620004654,
-0.06726515293121338,
-0.03352821618318558,
-0.060291837900877,
0.007818012498319149,
0.033419135957956314,
0.00965779460966587,
-0.002576395170763135,
-0.008529266342520714,
0.02583354525268078,
0.01880086027085781,
0.009529640898108482,
0.019710518419742584,
-0.006406316999346018,
-0.00335685140453279,
-0.04876773804426193,
-0.0010288308840245008,
0.026454834267497063,
0.013823586516082287,
0.03546971082687378,
-0.007884882390499115,
-0.007765784393996,
-0.05418577790260315,
-0.05002255365252495,
0.05675967410206795,
0.021209048107266426,
-0.02564321458339691,
0.00519568519666791,
-0.063839390873909,
0.0008036216604523361,
-0.008993569761514664,
0.0022612817119807005,
0.0012984548229724169,
-0.027962766587734222,
0.03605631738901138,
-0.06705842167139053,
-0.024838536977767944,
0.028629016131162643,
0.007962954230606556,
-0.007596774026751518,
0.020846430212259293,
-0.015266770496964455,
-0.025269722566008568,
0.03389289975166321,
-0.013146398589015007,
0.044761255383491516,
0.044565871357917786,
0.000151552987517789,
-0.005556182470172644,
-0.009841522201895714,
-0.011236998252570629,
-0.06666076928377151,
-0.06374767422676086,
0.0005304223741404712,
-0.016782863065600395,
0.008433573879301548,
0.00752433855086565,
-0.021027246490120888,
-0.08645829558372498,
0.03239971399307251,
0.009495087899267673,
0.0019072177819907665,
-0.02247363142669201,
-0.04907653108239174,
0.031106073409318924,
0.04374506697058678,
-0.034045781940221786,
0.013315857388079166,
0.039977945387363434,
-0.04368103668093681,
-0.042935047298669815,
-0.0191231407225132,
0.04283049330115318,
-0.019972147420048714,
0.013621299527585506,
0.021261610090732574,
-0.012616400606930256,
-0.04889784753322601,
0.005918348208069801,
0.00336832064203918,
0.02246836945414543,
-0.03405621275305748,
-0.02088988944888115,
-0.008243272081017494,
-0.01662888564169407,
0.00555621599778533,
-0.00548062426969409,
0.004975359421223402,
0.003294992260634899,
0.026403969153761864,
0.027845682576298714,
0.039464518427848816,
-0.02199328877031803,
0.021844053640961647,
0.04880823194980621,
-0.01939106360077858,
0.012516411952674389,
-0.015239348635077477,
-0.041396960616111755,
-0.01653227023780346,
-0.023304814472794533,
0.019066626206040382,
-0.01610858552157879,
-0.016853060573339462,
0.044675786048173904,
-0.02050243690609932,
0.013009406626224518,
0.018849249929189682,
0.02334928885102272,
0.0076741850934922695,
-0.05482402816414833,
0.021654412150382996,
0.031190726906061172,
0.026154348626732826,
-0.04030643403530121,
-0.04285037890076637,
0.020997708663344383,
-0.010717750526964664,
-0.021196654066443443,
-0.04497433826327324,
-0.005702113267034292,
-0.0335707813501358,
-0.027723241597414017,
0.029583118855953217,
0.028537042438983917,
-0.009600983932614326,
-0.018616264685988426,
0.04083702340722084,
-0.00311508821323514,
0.050741273909807205,
-0.017111750319600105,
-0.0035706597846001387,
-0.017722876742482185,
-0.03384166210889816,
-0.025636807084083557,
0.013435994274914265,
0.05215667188167572,
-0.01718148961663246,
-0.002387709217146039,
0.006700202357023954,
-0.031132103875279427,
0.026425227522850037,
0.022884787991642952,
0.01691717468202114,
0.025421595200896263,
0.03006533719599247,
-0.007824006490409374,
-0.050627291202545166,
0.033180538564920425,
0.019137583673000336,
0.015454281121492386,
0.013545364141464233,
-0.008892224170267582,
-0.026900576427578926,
-0.028184475377202034,
-0.0016819079173728824,
0.0008497267845086753,
-0.01261367741972208,
-0.015680715441703796,
0.037101954221725464,
-0.05506984516978264,
-0.02695237472653389,
-0.006666055880486965,
-0.04857299476861954,
0.05833351984620094,
0.014471907168626785,
0.000898718077223748,
0.018904125317931175,
0.011464289389550686,
-0.01774422824382782,
-0.03339720889925957,
-0.026270899921655655,
-0.002507949946448207,
0.015013741329312325,
-0.011297222226858139,
0.06203237175941467,
-0.000203985400730744,
-0.008096808567643166,
-0.0474056750535965,
-0.02125215344130993,
0.005168628413230181,
0.022492460906505585,
-0.018485812470316887,
0.0059868269599974155,
-0.027912333607673645,
0.027824025601148605,
0.022839128971099854,
0.022394422441720963,
0.00010181625111727044,
0.003976194653660059,
0.046803027391433716,
0.002288144314661622,
0.013157530687749386,
-0.01392760593444109,
-0.025958681479096413,
0.06029793247580528,
-0.03665190935134888,
0.04120924323797226,
-0.03363041952252388,
0.03621656447649002,
0.020054541528224945,
-0.00900256261229515,
0.028732402250170708,
-0.08177973330020905,
0.02505735121667385,
-0.03425685316324234,
0.000053767264034831896,
0.009012454189360142,
0.0030543627217411995,
0.006736347451806068,
0.02383437193930149,
0.018588392063975334,
0.050257474184036255,
0.01868371106684208,
-0.014208046719431877,
-0.07642040401697159,
-0.01959136500954628,
-0.006884040776640177,
-0.026554157957434654,
0.01567676104605198,
-0.008003531023859978,
-0.011680295690894127,
0.025394652038812637,
-0.05160707235336304,
-0.0005580734577961266,
0.023938698694109917,
0.04562991112470627,
-0.04264675825834274,
0.08099433034658432,
-0.014396969228982925,
0.024993501603603363,
0.00032391180866397917,
0.03252862021327019,
0.11976087093353271,
0.029549073427915573,
0.015157966874539852,
-0.03869108483195305,
0.026423577219247818,
0.0071233175694942474,
-0.019829396158456802,
-0.04345441237092018,
-0.009664865210652351,
0.01167087908834219,
-0.0017780313501134515,
0.009276923723518848,
0.021849943324923515,
-0.002526698401197791,
-0.017864065244793892,
-0.012036433443427086,
-0.0625714510679245,
-0.0033512345980852842,
-0.011463194154202938,
0.019411658868193626,
-0.02951326221227646,
0.017703140154480934,
0.0285133495926857,
0.01597100868821144,
-0.02608245424926281,
-0.027056274935603142,
0.006810827646404505,
-0.018037794157862663,
0.01730506494641304,
0.018717989325523376,
-0.06062379479408264,
0.04541593790054321,
0.02642500400543213,
-0.025500336661934853,
-0.04731617122888565,
0.02546822652220726,
-0.030359117314219475,
-0.03287585824728012,
-0.00898783840239048,
0.03512955456972122,
0.036870039999485016,
-0.0072435955516994,
0.0035169741604477167,
0.025338906794786453,
-0.0662989690899849,
0.0023980478290468454,
-0.05685975030064583,
0.0160916019231081,
0.003323747543618083,
-0.01253218948841095,
0.04935640096664429,
-0.010259857401251793,
-0.0036181474570184946,
-0.04552609845995903,
-0.04310432821512222,
-0.017849909141659737,
0.03872821107506752,
-0.01628204993903637,
-0.03519919142127037,
-0.03952575847506523,
0.020101582631468773,
-0.03282817080616951,
-0.012769260443747044,
0.03837636485695839,
0.007173454854637384,
-0.007867648266255856,
0.03902239352464676,
0.026288095861673355,
-0.023435577750205994,
0.012985745444893837,
-0.004157111048698425,
0.012555218301713467,
-0.07020968198776245,
0.0075399018824100494,
-0.003805184969678521,
-0.006445720791816711,
0.006265581119805574,
0.010659768246114254,
-0.021655654534697533,
-0.03973875939846039,
-0.024240318685770035,
0.05405336618423462,
-0.017021475359797478,
-0.013077683746814728,
-0.049325864762067795,
-0.01468947809189558,
-0.0018995776772499084,
0.05810720473527908,
-0.03947531431913376,
0.006411573383957148,
0.015697281807661057,
0.04901602864265442,
0.020438281819224358,
-0.012517521157860756,
-0.02773020789027214,
-0.025021571666002274,
-0.041441578418016434,
0.016721706837415695,
0.009247525595128536,
0.06108465790748596,
0.001756591023877263,
-0.002436624374240637,
0.03628838434815407,
-0.0022621836978942156,
-0.0038380168844014406,
0.012193451635539532,
-0.010205885395407677,
0.006018576677888632,
-0.005299155600368977,
-0.004019280429929495,
-0.02728174440562725,
-0.0024547800421714783,
-0.03029657155275345,
-0.006443175487220287,
0.029458466917276382,
0.015081132762134075,
0.010044886730611324,
-0.024196943268179893,
0.0525907538831234,
0.00787402968853712,
0.03456703945994377,
-0.03282171115279198,
-0.004374661482870579,
-0.03254612535238266,
-0.0004543798859231174,
0.002957176649942994,
0.0006721499958075583,
-0.03387591615319252,
0.03112560324370861,
0.0031218579970300198,
0.01031547598540783,
0.013424997217953205,
0.02101171389222145,
-0.033895742148160934,
-0.010167640633881092,
0.06624004989862442,
0.0003932348045054823,
0.05389159545302391,
-0.012063429690897465,
-0.04710445553064346,
0.029894014820456505,
-0.04411883279681206,
-0.05133983492851257,
0.007181947119534016,
-0.011966049671173096,
-0.022008484229445457,
-0.027777869254350662,
0.023273654282093048,
-0.006532003171741962,
0.06326410919427872,
-0.026829492300748825,
-0.009182569570839405,
-0.009864105843007565,
-0.010403668507933617,
-0.057637132704257965,
0.018270179629325867,
0.020296040922403336,
-0.06048424541950226,
0.006020066794008017,
0.04472794383764267,
0.009850412607192993,
-0.04959418624639511,
-0.0202656127512455,
-0.04161730036139488,
-0.01813202165067196,
0.03774884343147278,
0.02393145114183426,
-0.036300718784332275,
0.02628200873732567,
0.036893330514431,
0.00999437551945448,
0.004632227122783661,
-0.030437937006354332,
-0.013389382511377335,
-0.09043586999177933,
-0.012189274653792381,
0.003838659729808569,
-0.020442571491003036,
0.0279160775244236,
-0.016745498403906822,
0.00819928478449583,
0.015288903377950191,
-0.07121221721172333,
-0.005208594724535942,
-0.01623155176639557,
-0.021893173456192017,
-0.04011192545294762,
-0.035143595188856125,
0.0029839484486728907,
0.05314693599939346,
0.03061845898628235,
0.04128332808613777,
0.03285781294107437,
0.018307175487279892,
-0.006629178300499916,
-0.014942756853997707,
0.011567464098334312,
0.038692016154527664,
0.001354330568574369,
-0.030712487176060677,
0.04918692633509636,
-0.016304247081279755,
-0.0007704998715780675,
0.012169774621725082,
-0.022498279809951782,
0.014871924184262753,
0.043841611593961716,
0.06947217881679535,
0.0016203628620132804,
-0.0009215163881890476,
0.018893906846642494,
-0.033477719873189926,
0.013902909122407436,
0.03658447787165642,
-0.019618723541498184,
0.01854780502617359,
0.021907614544034004,
0.040053319185972214,
0.002764576580375433,
-0.030899615958333015,
-0.0067412047646939754,
0.017335129901766777,
-0.029049938544631004,
-0.014003042131662369,
0.011314871720969677,
0.02152274176478386,
0.031073417514562607,
0.0026116168592125177,
-0.03724216669797897,
-0.007403641939163208,
-0.010894577950239182,
-0.0030065954197198153,
-0.0002728617109823972,
-0.03636518120765686,
0.024147571995854378,
-0.02397351711988449,
-0.005064793862402439,
-0.0007792533724568784,
-0.019145645201206207,
-0.0182897187769413,
-0.005483344662934542,
-0.012253692373633385,
-0.0001193877833429724,
0.005205764900892973,
-0.04935738071799278,
-0.013255803845822811,
-0.031756069511175156,
0.03953782841563225,
0.05345308780670166,
0.05327307805418968,
0.024495216086506844,
-0.03129999339580536,
0.00038677750853821635,
-0.049411896616220474,
0.06329520791769028,
-0.04381556436419487,
0.03316068649291992,
-0.04095608368515968,
-0.020777607336640358,
-0.004880511201918125,
0.0028919458854943514,
0.056915562599897385,
-0.023650016635656357,
0.004319067113101482,
0.00532089127227664,
-0.002971602138131857,
0.02882964164018631,
0.005872387904673815,
-0.015845073387026787,
0.0018512114183977246,
0.0027494803071022034,
0.04369710758328438,
-0.00651529710739851,
-0.0005523517611436546,
0.013365794904530048,
0.017407728359103203,
-0.01926025003194809,
0.05495677515864372,
0.035794634371995926,
0.0023250486701726913,
0.022296782582998276,
0.00977715477347374,
-0.02811492793262005,
0.08980533480644226,
-0.04485158249735832,
0.01665135845541954,
-0.018601438030600548,
-0.017147250473499298,
-0.06982418894767761,
0.03748588636517525,
-0.026350557804107666,
0.04600755497813225,
-0.018979281187057495,
-0.058582235127687454,
0.013540073297917843,
-0.04002660885453224,
0.007608360145241022,
-0.020658856257796288,
-0.039840470999479294,
0.004811894614249468,
0.02233758568763733,
0.01760418526828289,
0.04349224269390106,
-0.04240252077579498,
-0.012005919590592384,
-0.03167536109685898,
0.01492678839713335,
-0.014536164700984955,
0.04633716866374016,
0.04278935119509697,
0.006491725333034992,
0.009924930520355701,
0.020658964291214943,
0.04282403364777565,
0.05761462822556496,
0.03588644415140152,
0.057019755244255066,
0.011301864869892597,
-0.03032749705016613,
0.03945375978946686,
0.01620832458138466,
-0.003566408297047019,
0.04490220174193382,
-0.0026393781881779432,
0.06478210538625717,
0.002422265475615859,
0.013682299293577671,
-0.029719209298491478,
-0.02631407603621483,
-0.02905355580151081,
0.018905390053987503,
0.006517738103866577,
-0.003243747167289257,
-0.002215199638158083,
-0.02504716068506241,
0.013428773730993271,
0.013446174561977386,
0.009918631985783577,
0.005694430787116289,
0.007945409044623375,
-0.009882076643407345,
0.028389444574713707,
0.004754186607897282,
0.0002893483324442059,
-0.029431935399770737,
0.0049175117164850235,
0.04750671610236168,
0.028607985004782677,
-0.005500410683453083,
0.008468935266137123,
-0.0029269701335579157,
-0.0168097335845232,
0.027081534266471863,
-0.08663821220397949,
-0.02125106193125248,
-0.019580936059355736,
0.04715882986783981,
0.014100244268774986,
-0.01411969494074583
] |
<p>The articles I found on radiation in the solar system mostly dealt with solar wind, I wonder about other types. Is there a breakdown that tells me, withhin an order of magnitude, at least what intensity I can expect for a the different spectra - hard gamma through to radio frequencies, and chargede particles - and how this varies depending on my position?</p> | 1,506 | [
-0.0053937421180307865,
-0.03728111460804939,
0.0063596684485673904,
-0.016055090352892876,
0.06252402067184448,
0.06529208272695541,
0.018361428752541542,
-0.044107791036367416,
0.02009567618370056,
-0.08738422393798828,
0.03894304484128952,
0.028438368812203407,
0.034641191363334656,
0.02347828634083271,
0.014287433587014675,
-0.028354404494166374,
-0.02690652199089527,
-0.03731919825077057,
-0.009637929499149323,
-0.0032926977146416903,
0.011779769323766232,
-0.02112254500389099,
-0.020656172186136246,
0.02554457262158394,
-0.06906607002019882,
0.020475247874855995,
0.028027115389704704,
0.02618187665939331,
0.02035352773964405,
0.022141048684716225,
-0.004583883564919233,
-0.009281249716877937,
0.020441142842173576,
0.003201698185876012,
0.04259435459971428,
0.003371433587744832,
-0.023652400821447372,
-0.053430672734975815,
-0.02087228186428547,
0.01906442642211914,
-0.03648863360285759,
-0.07172279059886932,
-0.00604079058393836,
0.026988867670297623,
-0.06149052083492279,
-0.008043537847697735,
0.020128192380070686,
-0.03497055917978287,
0.03589463233947754,
-0.0864507406949997,
0.08507250249385834,
-0.005020776763558388,
0.07440294325351715,
0.014382297173142433,
0.00009341666009277105,
0.03554568439722061,
0.0936051532626152,
0.04396679624915123,
0.010970251634716988,
-0.0539337657392025,
-0.02757374756038189,
-0.027384916320443153,
-0.0198989100754261,
-0.019195036962628365,
-0.021635420620441437,
0.02223360911011696,
-0.040404077619314194,
-0.0360199511051178,
0.04771633446216583,
0.068776436150074,
0.039648719131946564,
0.03194611892104149,
0.01951722614467144,
-0.011469576507806778,
0.015365533530712128,
0.00225357455201447,
0.05454815924167633,
0.02083076536655426,
0.03880792111158371,
0.017790233716368675,
0.00317961722612381,
-0.013112954795360565,
-0.003300602314993739,
0.03865182399749756,
0.029290195554494858,
0.02455945312976837,
0.07402829080820084,
-0.034132782369852066,
-0.0013038725592195988,
-0.005391739308834076,
0.012780504301190376,
0.02271847240626812,
0.011575625278055668,
0.010833283886313438,
-0.04808083921670914,
0.033295370638370514,
-0.024991704151034355,
0.02909468673169613,
-0.007589680142700672,
-0.0009088135557249188,
0.05845014750957489,
0.01746966689825058,
0.016807934269309044,
0.061657875776290894,
0.014147327281534672,
-0.034523189067840576,
-0.04919237643480301,
-0.009783469140529633,
-0.01682445779442787,
-0.02626658044755459,
-0.023204021155834198,
0.04039483889937401,
-0.000035830373235512525,
-0.0039714970625936985,
0.017861340194940567,
-0.0028582883533090353,
0.0097292959690094,
-0.03312717005610466,
0.05583037808537483,
0.08467257022857666,
0.05772719159722328,
-0.016432205215096474,
0.04593438282608986,
-0.024112649261951447,
-0.03580614924430847,
0.02080833725631237,
0.04593364894390106,
-0.01765606179833412,
-0.06258420646190643,
0.006969812326133251,
-0.017009520903229713,
-0.01960732974112034,
0.021743835881352425,
-0.05399765074253082,
0.052084580063819885,
-0.0004980000085197389,
-0.049549367278814316,
-0.06184595450758934,
-0.0002807880227919668,
0.0012344563147053123,
-0.0026437442284077406,
-0.018865659832954407,
-0.01694580167531967,
0.030482502654194832,
0.05978615581989288,
0.015021730214357376,
0.01305162813514471,
-0.010083978064358234,
0.04572758451104164,
0.0011156665859743953,
-0.0711245909333229,
0.023952610790729523,
-0.006798905320465565,
-0.03601495176553726,
0.01306552067399025,
-0.06847570091485977,
0.049648772925138474,
0.047846902161836624,
0.04378505051136017,
-0.007469679228961468,
0.07492202520370483,
-0.01992848888039589,
0.012165413238108158,
-0.007259609177708626,
0.006832585670053959,
0.004458514042198658,
0.07557902485132217,
0.023144511505961418,
0.0038542328402400017,
0.02262881025671959,
0.03153705969452858,
0.007948973216116428,
0.030263112857937813,
0.019355785101652145,
0.08543619513511658,
-0.08379939943552017,
-0.0349133238196373,
-0.04105464741587639,
0.007799571845680475,
-0.014328817836940289,
-0.05916835367679596,
0.0031176346819847822,
0.03194836154580116,
0.018583765253424644,
-0.006103754974901676,
0.026465363800525665,
0.0165620818734169,
-0.042939335107803345,
0.0057337163016200066,
-0.023359941318631172,
0.007250649388879538,
0.003803240368142724,
0.023766597732901573,
-0.028521956875920296,
-0.027678241953253746,
0.028058409690856934,
0.030124293640255928,
0.009413323365151882,
-0.030199553817510605,
-0.06177787482738495,
0.028500506654381752,
0.05805087089538574,
0.006915545556694269,
0.00271597714163363,
-0.00006905686313984916,
0.039626073092222214,
0.0028709156904369593,
0.018556086346507072,
0.018193762749433517,
0.009438677690923214,
-0.03999054804444313,
-0.02226363867521286,
-0.06812555342912674,
0.02213270030915737,
0.030251754447817802,
-0.011392995715141296,
-0.016085024923086166,
-0.04997972771525383,
-0.007023773156106472,
0.027626484632492065,
-0.0033959064166992903,
0.06555386632680893,
0.010164167732000351,
0.03550885245203972,
0.005152497440576553,
0.017578821629285812,
0.01808536797761917,
-0.019684789702296257,
-0.03503330424427986,
-0.04606972634792328,
-0.061824847012758255,
-0.019297078251838684,
0.035452671349048615,
-0.007950697094202042,
-0.03790167719125748,
-0.0007396549335680902,
0.03443142771720886,
0.019682714715600014,
0.030564529821276665,
0.03828668221831322,
-0.024971090257167816,
-0.03456166014075279,
0.0001995427446672693,
0.03585829958319664,
0.004680600017309189,
-0.01010843738913536,
0.031842611730098724,
0.02162204124033451,
-0.006196973845362663,
-0.018274137750267982,
-0.005722947884351015,
0.02078939601778984,
-0.030672501772642136,
0.011297560296952724,
-0.018706485629081726,
-0.03998890519142151,
0.053196582943201065,
-0.04793402552604675,
0.005237104836851358,
-0.005304067395627499,
-0.025785911828279495,
-0.02588697336614132,
-0.001448828843422234,
-0.00441752327606082,
0.016909155994653702,
-0.020520299673080444,
-0.013120103627443314,
0.018011676147580147,
0.052352044731378555,
-0.04229641705751419,
0.04442106559872627,
0.007131866179406643,
-0.018775450065732002,
-0.022975442931056023,
-0.0002707900130189955,
0.02777204103767872,
0.010651311837136745,
0.02133367210626602,
-0.023543324321508408,
-0.04087992385029793,
-0.017523324117064476,
-0.03675850108265877,
-0.007710800971835852,
0.013166991993784904,
-0.04017208144068718,
0.013236663304269314,
-0.0368054024875164,
-0.025735272094607353,
0.040985170751810074,
-0.01996663026511669,
-0.024941064417362213,
0.0400400385260582,
-0.019637465476989746,
-0.025954172015190125,
0.019759854301810265,
0.010204044170677662,
0.016285870224237442,
-0.04399312660098076,
-0.008981333114206791,
0.0379580594599247,
-0.03320503607392311,
-0.017436178401112556,
0.020483048632740974,
-0.04343562573194504,
-0.0026429740246385336,
-0.03160746768116951,
0.024425838142633438,
0.01755882427096367,
-0.025044847279787064,
-0.0011498242383822799,
0.03896109387278557,
-0.0647960975766182,
0.0008575376123189926,
-0.011368226259946823,
-0.019383002072572708,
0.02596074528992176,
0.005532015580683947,
0.0326281413435936,
-0.037477388978004456,
-0.056109651923179626,
0.04127046838402748,
0.05111338198184967,
0.009933392517268658,
-0.002512306207790971,
0.0057452162727713585,
-0.03594870865345001,
0.008831238374114037,
0.008059671148657799,
0.002120417542755604,
0.01790640875697136,
0.007249606307595968,
0.003856102004647255,
0.01568799465894699,
-0.004278447013348341,
0.02093411423265934,
-0.01058890949934721,
0.007984364405274391,
0.02508099563419819,
-0.002496107015758753,
0.04610653966665268,
0.02346249669790268,
-0.036732982844114304,
0.026601683348417282,
0.0014802436344325542,
0.024792656302452087,
0.03539087623357773,
0.0006527143414132297,
0.035300008952617645,
0.037513263523578644,
0.01419881172478199,
-0.01623825915157795,
0.020600171759724617,
0.028974568471312523,
0.005137521307915449,
0.006642297841608524,
0.00707654282450676,
0.028386035934090614,
-0.008574442937970161,
-0.005782862659543753,
0.017971619963645935,
0.06666434556245804,
0.002675029681995511,
-0.03953078016638756,
0.0020236573182046413,
0.012987091206014156,
-0.015600582584738731,
-0.01815953105688095,
0.0037781500723212957,
0.05348370224237442,
0.0027358285151422024,
0.039111897349357605,
0.004219611641019583,
-0.037260670214891434,
0.0121332798153162,
-0.045078907161951065,
-0.00781466718763113,
-0.035331401973962784,
0.031494248658418655,
0.02874322049319744,
0.03063145838677883,
0.005601210054010153,
-0.02153964154422283,
0.055253610014915466,
-0.0009891598019748926,
-0.06520050764083862,
0.03412534296512604,
-0.007953048683702946,
-0.027958614751696587,
-0.005578265991061926,
0.002202748553827405,
-0.04687461256980896,
0.01417701505124569,
-0.015062958002090454,
-0.01980758085846901,
-0.0012733133044093847,
-0.03556474298238754,
0.05603305622935295,
-0.018805846571922302,
-0.06354017555713654,
-0.05860264599323273,
0.049355361610651016,
0.04025102034211159,
0.0018734654877334833,
-0.016245923936367035,
0.014293339103460312,
-0.03046760894358158,
0.0011150898644700646,
-0.004823679104447365,
0.024205559864640236,
-0.03088415414094925,
0.045160748064517975,
0.030945871025323868,
-0.009777064435184002,
-0.041150979697704315,
-0.018932433798909187,
0.0034014189150184393,
0.018076637759804726,
0.0214063823223114,
-0.016821004450321198,
-0.0074666207656264305,
-0.03891109675168991,
-0.018278568983078003,
-0.0028513760771602392,
0.00844736211001873,
-0.0071317050606012344,
0.0195617638528347,
0.04418236389756203,
-0.014302407391369343,
-0.046263307332992554,
0.02367481403052807,
0.025484390556812286,
-0.011641569435596466,
-0.009522620588541031,
0.009156841784715652,
0.0001159482344519347,
0.005420236382633448,
-0.010356146842241287,
-0.012200256809592247,
-0.0029734063427895308,
-0.03875156119465828,
0.012446509674191475,
0.01067566592246294,
-0.02769693359732628,
-0.017764991149306297,
-0.029900869354605675,
-0.001149290706962347,
0.005216145422309637,
-0.03701132535934448,
-0.060262929648160934,
0.018309397622942924,
0.018668178468942642,
0.05234161764383316,
0.006713970098644495,
-0.02056138403713703,
-0.0738605335354805,
-0.0030446466989815235,
0.04618479683995247,
0.038439564406871796,
0.019199764356017113,
-0.01637929491698742,
-0.02202746830880642,
0.005026397295296192,
0.04396316036581993,
-0.00857685599476099,
-0.004469225648790598,
-0.00565191637724638,
0.00042777028284035623,
-0.02056499943137169,
-0.015970230102539062,
-0.046349797397851944,
0.039320170879364014,
0.020754439756274223,
0.014551310800015926,
-0.034052371978759766,
0.008296018466353416,
-0.029517652466893196,
0.033367820084095,
0.03149210289120674,
0.039146751165390015,
0.028492672368884087,
-0.0027209515683352947,
-0.013256656005978584,
0.01814018189907074,
0.010774925351142883,
-0.021533826366066933,
-0.011471381410956383,
0.004129716660827398,
-0.05039632320404053,
0.0512872189283371,
-0.028649641200900078,
-0.03203374147415161,
-0.0028756698593497276,
0.02605767361819744,
0.02844523824751377,
-0.024198481813073158,
-0.07717471569776535,
0.05690675973892212,
0.029782194644212723,
0.03410275653004646,
0.08620632439851761,
0.010023118928074837,
-0.040595803409814835,
0.007326677907258272,
-0.02798762544989586,
0.0533607080578804,
-0.04204278439283371,
-0.0071566482074558735,
0.018984820693731308,
-0.025521600618958473,
-0.022077171131968498,
0.04512060061097145,
-0.01501194667071104,
0.0006509680533781648,
0.021217448636889458,
-0.019051650539040565,
-0.025087321177124977,
0.025721650570631027,
-0.035234879702329636,
-0.0198229793459177,
-0.011220029555261135,
0.039625134319067,
-0.038565438240766525,
-0.0156254805624485,
0.027845894917845726,
-0.014304658398032188,
-0.024186041206121445,
0.02494792267680168,
-0.013163978233933449,
-0.0013433375861495733,
-0.03910578787326813,
0.0020659188739955425,
0.02885322831571102,
-0.036340802907943726,
0.04995514452457428,
-0.011885745450854301,
-0.02859135903418064,
-0.003765840781852603,
-0.060714609920978546,
-0.009976131841540337,
0.006198960822075605,
-0.025366079062223434,
0.06747307628393173,
-0.011406546458601952,
0.026596009731292725,
-0.02509966865181923,
0.01939583383500576,
-0.0852842628955841,
-0.018401090055704117,
0.014320900663733482,
0.03154489025473595,
0.0021991829853504896,
-0.05141181871294975,
0.0213288813829422,
-0.053868599236011505,
-0.05231425538659096,
0.007809150964021683,
0.02557993493974209,
-0.03713560476899147,
0.01226679515093565,
0.0047750030644237995,
0.005869523622095585,
0.05046706646680832,
-0.022967377677559853,
-0.01595018245279789,
0.03491325303912163,
0.011550995521247387,
0.0033485079184174538,
-0.047649551182985306,
0.023673100396990776,
-0.02899010479450226,
-0.0016765506006777287,
-0.021774811670184135,
-0.02178892120718956,
0.017416609451174736,
-0.05509008839726448,
-0.04152989387512207,
0.0815104991197586,
0.013003944419324398,
-0.010342336259782314,
-0.004149473737925291,
0.009357021190226078,
-0.04415067285299301,
0.026258330792188644,
-0.035647761076688766,
-0.0378083661198616,
-0.03389192745089531,
-0.03252485394477844,
0.0032504622358828783,
-0.0046386998146772385,
0.06156734377145767,
0.01584439165890217,
0.0360666885972023,
0.00638970360159874,
0.013798202387988567,
0.0047336723655462265,
-0.00284149800427258,
0.009736502543091774,
-0.05240510031580925,
0.013467845506966114,
0.04073375090956688,
0.006825179327279329,
-0.029568471014499664,
-0.04537970945239067,
-0.06453324854373932,
-0.021998142823576927,
0.04774472117424011,
-0.031033366918563843,
0.026829050853848457,
0.02445308305323124,
0.005579160526394844,
-0.0016249690670520067,
-0.03001522272825241,
-0.017071271315217018,
-0.015627892687916756,
-0.008317739702761173,
-0.01015243399888277,
0.003591798944398761,
-0.012237156741321087,
0.033581189811229706,
0.06086450815200806,
-0.0074937366880476475,
0.06693243980407715,
0.012782848440110683,
0.02137669362127781,
0.020090380683541298,
-0.027182025834918022,
-0.06298186630010605,
0.011674712412059307,
-0.04544685408473015,
0.019515465945005417,
0.024394193664193153,
-0.01429557055234909,
0.06462707370519638,
0.0178466085344553,
0.011171042919158936,
-0.04652882367372513,
-0.024334339424967766,
-0.041184116154909134,
0.013823622837662697,
0.03383497893810272,
-0.0006425840547308326,
-0.03236698359251022,
0.02232316881418228,
0.03223958611488342,
-0.00989889819175005,
-0.010965358465909958,
0.030741974711418152,
-0.08394893258810043,
-0.04393885284662247,
-0.033855002373456955,
-0.06898309290409088,
0.04976887255907059,
-0.008529609069228172,
-0.05786166712641716,
0.014264171943068504,
-0.023385891690850258,
0.040219973772764206,
0.009540615603327751,
0.021709447726607323,
0.018233884125947952,
0.05632913485169411,
-0.040578581392765045,
-0.044625479727983475,
-0.016159091144800186,
0.026773009449243546,
0.10495360940694809,
0.08784230798482895,
-0.013463224284350872,
-0.030854210257530212,
-0.020623276010155678,
-0.02867220714688301,
0.028753485530614853,
0.012848463840782642,
0.0020780207123607397,
0.004877717234194279,
0.01509203389286995,
0.023895468562841415,
0.03542323037981987,
-0.03160714730620384,
0.021514924243092537,
0.059397269040346146,
-0.016157077625393867,
-0.015862876549363136,
0.016849787905812263,
0.04494233801960945,
0.008381830528378487,
0.031476203352212906,
-0.04142013192176819,
0.016118958592414856,
-0.030473511666059494,
0.038461267948150635,
-0.020495206117630005,
-0.034559886902570724,
0.03411311283707619,
-0.01768619194626808,
-0.06487420946359634,
-0.03871830925345421,
-0.020601347088813782,
0.017442988231778145,
-0.0053556752391159534,
0.021719269454479218,
0.04957801476120949,
-0.010949640534818172,
-0.030637968331575394,
-0.025158260017633438,
-0.028436167165637016,
0.01278884056955576,
0.005764239467680454,
0.020121272653341293,
-0.017553437501192093,
0.011395738460123539,
-0.01245252788066864,
0.030526507645845413,
0.007082946132868528,
0.02637273073196411,
-0.0007134819170460105,
0.0678180530667305,
0.0018242108635604382,
-0.02096591517329216,
-0.007087001111358404,
0.0024478102568536997,
0.016495907679200172,
-0.061172887682914734,
-0.006198248825967312,
-0.02839946746826172,
0.01978212594985962,
-0.013285988010466099,
0.03606956824660301,
0.01842118799686432,
-0.025599824264645576,
-0.007984176278114319,
-0.03167225047945976,
0.013223269023001194,
-0.00407060282304883,
-0.017482340335845947,
-0.04008815437555313,
-0.04501033201813698,
-0.02980544976890087,
-0.005420219618827105,
0.02113940194249153,
0.02680218778550625,
0.03967960923910141,
0.04569081962108612,
-0.04876253753900528,
-0.01246477011591196,
-0.031516190618276596,
0.03741247206926346,
-0.007651476189494133,
-0.010550073347985744,
-0.010699344798922539,
0.001365591655485332,
0.023457972332835197,
0.012869607657194138,
0.012906557880342007,
0.0408928208053112,
-0.03477274253964424,
0.014278659597039223,
0.034800898283720016,
-0.04557119309902191,
-0.001362260547466576,
0.024790562689304352,
-0.0016125262482091784,
0.013031868264079094,
-0.014999312348663807,
0.033742256462574005,
0.0019807755015790462,
-0.018772274255752563,
0.009867153130471706,
0.020599933341145515,
-0.0354306623339653,
-0.030340489000082016,
-0.010824269615113735,
-0.042808979749679565,
-0.010974555276334286,
-0.011856571771204472,
-0.012184545397758484,
-0.015550492331385612,
-0.0007145254057832062,
-0.04486465826630592,
0.014466524124145508,
-0.012300745584070683,
0.016961801797151566,
0.0011975351953878999,
0.05280136317014694,
-0.004108707886189222,
0.0033181735780090094,
0.0039909458719193935,
-0.01663951762020588,
-0.01951437070965767,
0.037063345313072205,
0.012247302569448948,
-0.018262052908539772,
0.00047759086010046303,
0.024950992316007614,
-0.020062709227204323,
-0.020764250308275223,
0.03621251881122589,
-0.015005577355623245,
0.01226694043725729,
0.005999297834932804,
0.004656363744288683,
-0.04525641351938248,
0.06983724236488342,
-0.01485445536673069,
-0.018668552860617638,
0.013702954165637493,
-0.04037892445921898,
-0.07634275406599045,
0.05887196213006973,
-0.018973205238580704,
0.025488315150141716,
0.03755204379558563,
0.006771690212190151,
-0.02807714231312275,
0.07952253520488739,
0.008322320878505707,
-0.003279014490544796,
-0.015263451263308525,
0.027615532279014587,
-0.018730297684669495,
-0.011577838100492954,
0.037977054715156555,
0.007006867788732052,
-0.0008888292359188199,
0.040854405611753464,
0.008682665415108204,
0.010837406851351261,
0.03980385884642601,
-0.01944861374795437,
-0.04599196836352348,
-0.020816663280129433,
-0.003970643039792776,
-0.009202860295772552,
0.03645552694797516,
0.028630662709474564,
-0.05227268859744072,
0.047644563019275665,
0.030467912554740906,
0.0034900428727269173,
-0.07088524103164673,
-0.012886373326182365,
0.005495293065905571,
0.00516399834305048,
0.013422832824289799,
-0.07313608378171921,
0.037215858697891235,
0.042577050626277924,
-0.08235032856464386,
-0.016597440466284752,
0.0050957174971699715,
0.016323335468769073,
-0.00910776387900114,
0.0012695243349298835,
-0.014017172157764435,
-0.008290709927678108,
0.01965857483446598,
0.06277412921190262,
0.02730230800807476,
0.023014482110738754,
-0.026580089703202248,
-0.035263463854789734,
-0.013895568437874317,
0.03586852550506592,
0.0017354256706312299,
-0.018892740830779076,
0.08403677493333817,
-0.010826876387000084,
-0.01662396267056465,
0.012380440719425678,
0.0010690513299778104,
0.004886019043624401,
-0.008298829197883606,
0.04305915907025337,
0.021422317251563072,
0.03713909536600113,
-0.007764190435409546,
-0.03311261534690857,
0.002736035967245698,
-0.009764165617525578,
0.008226818405091763,
0.024748094379901886,
0.008334300480782986,
0.044050224125385284,
0.043688736855983734,
-0.025472518056631088,
-0.021310338750481606,
0.024732837453484535,
0.01177067868411541,
-0.01783856935799122,
-0.0036332481540739536,
0.005972546990960836,
0.040581781417131424,
0.002771689323708415,
0.048543915152549744,
-0.06937205791473389,
0.006563015282154083,
-0.020554209128022194,
0.002003537490963936,
0.020472969859838486,
0.021049344912171364,
-0.010065322741866112,
-0.017633097246289253,
0.01528131403028965,
-0.00003723524059751071,
-0.036346934735774994,
-0.013031280599534512,
0.011068343184888363,
0.013318696990609169,
0.03316598758101463,
-0.005373368505388498,
-0.022687962278723717,
-0.05634327977895737,
0.010574620217084885,
-0.011061170138418674,
0.005526368506252766,
0.01741037517786026,
-0.043318018317222595,
0.008300184272229671,
-0.045273080468177795,
0.041078560054302216,
-0.004245872609317303,
-0.016355784609913826,
-0.06147555261850357,
-0.028392253443598747,
-0.00720266904681921,
0.016174867749214172,
0.03667835891246796,
-0.004330878145992756,
-0.006757532712072134,
0.016444474458694458,
0.019460264593362808,
0.0059145851992070675,
-0.09368396550416946,
-0.007340643554925919,
0.006369911599904299,
-0.06930197775363922,
-0.01608378440141678,
-0.010364758782088757,
-0.0054544731974601746,
0.01836373098194599,
0.025035828351974487,
0.0065773287788033485,
0.012730592861771584,
-0.008280077949166298,
0.005343342199921608,
0.052161235362291336,
0.036992426961660385,
-0.03465896472334862,
0.045405950397253036,
-0.008065428584814072,
0.015411553904414177,
0.05039571598172188,
-0.010750588960945606,
-0.005528553854674101,
0.02608311176300049,
-0.0014250647509470582,
0.008098626509308815,
0.017683248966932297,
-0.0033710517454892397,
0.009983817115426064,
-0.04396817833185196,
0.00018371045007370412,
0.04535863921046257,
-0.03158474713563919,
0.010108155198395252,
0.030332978814840317,
0.010312951169908047,
0.0059320940636098385,
0.021835053339600563,
0.03616036847233772,
0.03198321536183357,
-0.01565559208393097,
-0.0585717037320137,
0.03217384219169617,
0.008999831974506378,
-0.00562466261908412,
0.030765656381845474,
0.00492987921461463,
-0.0012918129796162248,
0.04160631075501442,
0.001765238237567246,
0.011961917392909527,
-0.03947456181049347,
-0.00562285166233778,
0.00213062996044755,
0.0014148810878396034,
-0.0035161240957677364,
0.02155688777565956,
-0.009363795630633831,
0.04607319086790085,
-0.006283394061028957,
-0.019751761108636856,
-0.021610865369439125,
-0.02666623145341873,
-0.004626805428415537,
-0.006296904291957617,
-0.004442157223820686,
0.02569073624908924,
0.002095281844958663,
0.0025882157497107983,
-0.014305354095995426,
0.0026884153485298157,
0.06164725124835968,
-0.07067564874887466,
0.038782697170972824,
0.0028092970605939627,
-0.005582672543823719,
-0.03027348406612873,
-0.006124142557382584,
-0.03343697264790535,
-0.02796376310288906,
0.0022332987282425165,
0.023287445306777954,
-0.0069069028832018375,
0.0017881336389109492,
-0.04335297644138336,
-0.013242763467133045,
0.02840684913098812,
-0.058282941579818726,
0.03675290197134018,
-0.008181100711226463,
0.034240953624248505,
-0.015245785005390644,
0.007261012680828571
] |
<p>I've been reading up on nuclear reactors, and understand explanations of how it works, how water is heated to steam, which turns the turbines, etc.. I understand all of the safety features, and how control rods are used, and what they do with spent fuel.</p>
<p>However, what I can't figure out (after lookin at many websites and videos) is where the reaction actually starts. The fuel rods contain Uranium pellets, and then they're put in the reactor, where the reaction starts and neutrons start hitting each other to create heat? So is this happening all over the reactor, or just in each fuel rod assembly?</p>
<p>Also, you can hold a Uranium pellet in your hand (ideally wearing a glove) and it's not dangerous, so what <em>starts</em> a reaction? A lot of people say the reaction can start by itself, so why do uranium pellets not suddenly heat up and start spreading radiation by themselves? Is it because they haven't been <em>enriched</em>?</p>
<p>What if you dropped a Uranium pellet on the floor?</p> | 1,507 | [
0.0172870010137558,
-0.0880509540438652,
0.01708412729203701,
-0.022545384243130684,
-0.035701196640729904,
-0.01011093333363533,
-0.02746099792420864,
-0.030338797718286514,
0.011717751622200012,
-0.06845756620168686,
0.03421971574425697,
0.03214332461357117,
0.04632473737001419,
-0.024138562381267548,
0.007391168735921383,
0.02247004769742489,
0.014413110911846161,
-0.052512288093566895,
-0.011587054468691349,
-0.026954352855682373,
0.0008030253811739385,
-0.04911135137081146,
-0.009138011373579502,
-0.011835074052214622,
-0.028200829401612282,
0.03187645971775055,
0.007974827662110329,
0.01620374619960785,
0.05011862516403198,
0.036151666194200516,
0.02821802720427513,
-0.02916828915476799,
-0.0037970812991261482,
0.00040667623397894204,
0.02686901018023491,
0.0014642832102254033,
-0.02945818193256855,
-0.008983953855931759,
-0.03391260281205177,
-0.007544591557234526,
0.013613644987344742,
-0.016737334430217743,
0.014656816609203815,
0.0126594677567482,
-0.029421554878354073,
0.005235554650425911,
-0.013366197235882282,
0.029726658016443253,
0.06066124141216278,
-0.05633377283811569,
0.006850570440292358,
0.010276656597852707,
0.03252546861767769,
0.034966692328453064,
0.037988804280757904,
0.004475330002605915,
0.06476646661758423,
0.037472862750291824,
-0.015660282224416733,
-0.01998210698366165,
-0.015495874918997288,
0.01629040203988552,
-0.04339325800538063,
-0.02539929375052452,
0.028976628556847572,
0.03676140308380127,
-0.01941045932471752,
-0.004002740141004324,
-0.02008620649576187,
0.027362992987036705,
0.042313072830438614,
0.00986013375222683,
-0.0029457604978233576,
0.010005068965256214,
0.0011725686490535736,
-0.016305208206176758,
0.03979318588972092,
-0.007270279806107283,
0.024179913103580475,
0.04872928187251091,
-0.02528841234743595,
0.04692995548248291,
0.009557108394801617,
0.03625679016113281,
0.01736181415617466,
-0.008305422961711884,
0.08497276157140732,
0.015421471558511257,
0.030172904953360558,
0.014561493881046772,
0.00013580668019130826,
0.01300270576030016,
0.012631682679057121,
0.02881527878344059,
0.001160968909971416,
-0.0021135404240339994,
0.01709076762199402,
0.07782885432243347,
0.025223035365343094,
-0.0002529851335566491,
0.06849536299705505,
0.022854788228869438,
0.05036201328039169,
0.0781211107969284,
-0.007690390106290579,
-0.05195668339729309,
-0.05778122693300247,
0.01759308949112892,
0.00017805690004024655,
-0.03280337527394295,
-0.07816275209188461,
0.02642681449651718,
-0.021549943834543228,
-0.011351145803928375,
0.02637173980474472,
-0.011556991375982761,
0.015798423439264297,
-0.03571835905313492,
0.06459386646747589,
0.011904306709766388,
0.04440854862332344,
0.0008370744762942195,
0.0019011053955182433,
-0.04354500398039818,
-0.07079769670963287,
0.01784423179924488,
0.027288760989904404,
-0.01147241611033678,
-0.037731416523456573,
0.05147663131356239,
-0.02879946306347847,
-0.014507247135043144,
-0.00029431970324367285,
0.020527474582195282,
0.03278825432062149,
0.016416098922491074,
-0.10507635772228241,
-0.05861204117536545,
0.04566747322678566,
-0.001423114212229848,
-0.028077946975827217,
-0.09361889958381653,
-0.015358183532953262,
0.024122139438986778,
0.01641410030424595,
-0.025460749864578247,
-0.0278487466275692,
0.008451366797089577,
0.007225130219012499,
-0.025740912184119225,
-0.012159017845988274,
-0.047348108142614365,
0.006239061243832111,
-0.02868802472949028,
0.021845974028110504,
-0.06329015642404556,
0.05065448582172394,
0.03530454635620117,
-0.007255891803652048,
-0.043884389102458954,
0.03764794394373894,
-0.03457838296890259,
0.012322217226028442,
0.015115497633814812,
-0.03057091310620308,
-0.020134499296545982,
0.08990153670310974,
0.0325004905462265,
-0.018801189959049225,
0.06158417463302612,
0.035157252103090286,
0.047394029796123505,
-0.02109629288315773,
0.051396291702985764,
0.026923533529043198,
-0.04045912250876427,
-0.02032519318163395,
-0.019748149439692497,
0.001836968120187521,
0.011204001493752003,
-0.04852738603949547,
-0.005581265781074762,
0.0065031517297029495,
0.005028421990573406,
0.003669645171612501,
0.02620006911456585,
0.03560566529631615,
-0.02790527045726776,
-0.03423158824443817,
-0.010882426053285599,
-0.04421693831682205,
-0.054798103868961334,
-0.0019310961943119764,
-0.054581865668296814,
-0.031602948904037476,
-0.014562813565135002,
0.0013544167159125209,
0.018242770805954933,
-0.05855222046375275,
-0.05083481967449188,
0.0003816639364231378,
0.0057161226868629456,
0.014647753909230232,
0.008477485738694668,
-0.006685471627861261,
0.03114929236471653,
-0.020565159618854523,
-0.005909020081162453,
0.022036781534552574,
-0.044514838606119156,
0.016725357621908188,
-0.03551092743873596,
-0.011344805359840393,
-0.020040683448314667,
0.03160126879811287,
-0.07490707188844681,
-0.01583936996757984,
-0.031905751675367355,
0.014516053721308708,
0.03506620600819588,
0.001894188579171896,
0.09413950145244598,
0.004934839438647032,
0.01613110676407814,
-0.021099446341395378,
0.005505036562681198,
0.006201677490025759,
-0.02038290910422802,
-0.0015706458361819386,
-0.053189001977443695,
-0.08751960098743439,
-0.029430726543068886,
0.03297138959169388,
-0.003968419972807169,
-0.013917612843215466,
0.01252000406384468,
-0.01615316979587078,
0.047808025032281876,
0.005306335166096687,
0.004219510592520237,
-0.023765655234456062,
0.018877388909459114,
0.0098065584897995,
0.03718828782439232,
-0.024662980809807777,
0.006643771193921566,
-0.0013186181895434856,
0.04743529483675957,
0.023588385432958603,
-0.012915504164993763,
-0.03270255774259567,
0.04692181944847107,
-0.00390224764123559,
0.0050659202970564365,
-0.004558568354696035,
-0.027370980009436607,
0.04465460404753685,
-0.01606605015695095,
0.014559282921254635,
-0.006353780161589384,
0.013363559730350971,
-0.02722887508571148,
0.011404817923903465,
-0.029119715094566345,
-0.01626320369541645,
0.04327342286705971,
-0.024797819554805756,
-0.025123782455921173,
0.027637364342808723,
-0.02505333721637726,
0.01635800302028656,
-0.005006634630262852,
-0.0034761535935103893,
-0.0034523122012615204,
0.013739973306655884,
0.0027257008478045464,
0.0007465871167369187,
0.007644988596439362,
-0.05054015666246414,
-0.05445495620369911,
-0.03626973181962967,
-0.06276437640190125,
0.01831958256661892,
0.032042670994997025,
-0.05517225340008736,
0.04463576897978783,
-0.022720854729413986,
0.012752923183143139,
0.043243952095508575,
0.016116274520754814,
-0.0006561262998729944,
0.007385989185422659,
-0.01080506481230259,
-0.07126392424106598,
-0.0249856635928154,
0.009522061794996262,
-0.0017198778223246336,
0.019128240644931793,
0.019227169454097748,
0.06973730027675629,
-0.032801516354084015,
-0.01705084927380085,
0.026850733906030655,
-0.04464073106646538,
0.008770191110670567,
-0.006066944450139999,
0.012951665557920933,
0.0019373527029529214,
-0.007539067417383194,
-0.01317715272307396,
0.030077802017331123,
-0.07757570594549179,
-0.0023399507626891136,
-0.021420177072286606,
-0.01453414186835289,
0.015782050788402557,
-0.012498215772211552,
0.04600102826952934,
0.019347649067640305,
0.0014176771510392427,
0.06411706656217575,
0.008485307916998863,
-0.002044602995738387,
0.0013337203999981284,
-0.0014901809627190232,
-0.005494497716426849,
-0.02251577004790306,
0.03553708270192146,
0.039180491119623184,
0.02425411157310009,
0.010017727501690388,
-0.0031482530757784843,
0.04882211983203888,
0.012437009252607822,
0.008370335213840008,
0.008082916960120201,
-0.016446659341454506,
0.010395017452538013,
0.011155850253999233,
-0.006086003500968218,
-0.0006421800935640931,
0.0027083021122962236,
0.016961004585027695,
-0.0038326347712427378,
0.04774131253361702,
0.0252414308488369,
-0.040604542940855026,
0.03846735879778862,
0.02313455380499363,
-0.017275627702474594,
-0.0648287832736969,
0.04119032621383667,
-0.027802808210253716,
-0.010106646455824375,
-0.0009328022715635598,
0.024063248187303543,
0.07220019400119781,
-0.03159058466553688,
0.03047921694815159,
0.0037444550544023514,
0.056824930012226105,
-0.007422718219459057,
-0.03019949048757553,
-0.021888628602027893,
-0.029744913801550865,
-0.002271247562021017,
0.03327704966068268,
0.04553403705358505,
0.052611712366342545,
0.014125188812613487,
0.029264573007822037,
-0.0062436857260763645,
-0.023837102577090263,
-0.003328198567032814,
-0.0709407851099968,
-0.030029891058802605,
0.021933933719992638,
0.04821569845080376,
0.00782416108995676,
0.051089391112327576,
0.00004260479545337148,
0.00587455602362752,
-0.012773172929883003,
-0.03212999925017357,
-0.05909685790538788,
0.01595611497759819,
-0.046444300562143326,
-0.03120117075741291,
-0.0048553659580647945,
-0.012457913719117641,
-0.0418187640607357,
-0.00030767673160880804,
-0.06654207408428192,
0.005966800265014172,
-0.04285070672631264,
-0.04158922657370567,
0.051229942589998245,
-0.029510440304875374,
-0.01583773083984852,
-0.011471496894955635,
0.008997871540486813,
0.03530043363571167,
-0.001427353243343532,
-0.0009122855262830853,
0.004067810717970133,
-0.0316275954246521,
0.02697930485010147,
-0.019224906340241432,
0.01187088806182146,
0.019272329285740852,
0.05646107345819473,
0.009254938922822475,
0.0196211114525795,
-0.025742655619978905,
0.014394005760550499,
0.01303072739392519,
0.04013674333691597,
0.012107216753065586,
-0.03711121156811714,
-0.029712118208408356,
-0.042788516730070114,
-0.001614199485629797,
0.02382194809615612,
0.0068175336346030235,
-0.019231297075748444,
0.04445432126522064,
0.0013877012534067035,
-0.0000882007007021457,
-0.037633396685123444,
0.008614527061581612,
0.02900560200214386,
-0.008610756136476994,
-0.0004630048933904618,
-0.035287849605083466,
-0.013322658836841583,
-0.02512647584080696,
-0.006960495375096798,
0.013400589115917683,
0.0025095881428569555,
-0.03060479275882244,
0.0031625342089682817,
0.06030209735035896,
-0.002941989805549383,
-0.023480728268623352,
0.030348852276802063,
-0.010043985210359097,
0.01620541512966156,
0.03042084351181984,
-0.006274436134845018,
0.04762993007898331,
0.007509677205234766,
0.028636973351240158,
-0.013620905578136444,
0.009600120596587658,
-0.04822360351681709,
0.008437386713922024,
0.0678430125117302,
0.03703191503882408,
-0.022974800318479538,
0.012003294192254543,
-0.0313875712454319,
-0.03931507468223572,
0.07580246776342392,
-0.03054601140320301,
0.023083213716745377,
-0.056516923010349274,
-0.016601577401161194,
-0.0035681845620274544,
-0.032712455838918686,
-0.02681896463036537,
0.003752808552235365,
-0.01975208707153797,
0.015027658082544804,
-0.020643170922994614,
-0.03730594739317894,
-0.024101538583636284,
0.03709918633103371,
0.056509315967559814,
0.018337426707148552,
-0.0010669756447896361,
0.032674308866262436,
-0.0160141009837389,
0.03131585195660591,
-0.009937997907400131,
-0.07697582989931107,
0.0011868575820699334,
0.000043237145291641355,
-0.007708478718996048,
0.05249444395303726,
-0.030893053859472275,
-0.06249411031603813,
0.042068760842084885,
0.05668920651078224,
0.008323544636368752,
-0.04215523228049278,
-0.04301467910408974,
0.029118487611413002,
0.07046730071306229,
-0.024790436029434204,
0.036246951669454575,
0.04010718688368797,
-0.031550779938697815,
0.011370670981705189,
-0.055351175367832184,
0.010349718853831291,
-0.030190667137503624,
0.011033914983272552,
0.0007194129866547883,
0.033257558941841125,
0.011877404525876045,
0.05211689695715904,
-0.0000047596822696505114,
-0.014580557122826576,
0.004407841712236404,
-0.002663201652467251,
-0.0004113264731131494,
-0.026247607544064522,
0.005852732341736555,
0.0012727034045383334,
-0.007512026932090521,
0.01226239837706089,
0.0018302957760170102,
-0.04615003988146782,
0.02143433317542076,
-0.02185831405222416,
0.02962285466492176,
0.0054665254428982735,
-0.014449013397097588,
-0.005487748421728611,
-0.019363941624760628,
-0.02142154611647129,
0.044162120670080185,
-0.02395712584257126,
0.06753627955913544,
0.009356144815683365,
0.0034566065296530724,
0.025234730914235115,
-0.031044460833072662,
-0.024004660546779633,
0.021656453609466553,
-0.0028852771501988173,
0.02757866308093071,
-0.020482996478676796,
0.0711112841963768,
-0.006388620473444462,
0.02000785805284977,
-0.053286511451005936,
-0.07164310663938522,
0.044137440621852875,
-0.01853545755147934,
-0.03499127924442291,
-0.06360720843076706,
0.006531920749694109,
-0.017957981675863266,
-0.03150278702378273,
-0.01926049217581749,
0.025609437376260757,
-0.032241664826869965,
0.007713587023317814,
0.035357967019081116,
0.012111576274037361,
0.0811103954911232,
-0.010492180474102497,
-0.04324780032038689,
0.0115552619099617,
-0.01329185999929905,
-0.0008293247083202004,
-0.03494908660650253,
0.06137505918741226,
-0.013808699324727058,
-0.020973555743694305,
0.013584757223725319,
0.0021665317472070456,
0.05697958916425705,
-0.02984776720404625,
0.016076603904366493,
0.04796595498919487,
0.021681873127818108,
0.019785799086093903,
-0.020857835188508034,
0.020905347540974617,
0.0410868301987648,
0.030056452378630638,
0.010816771537065506,
-0.03745834529399872,
0.01186979841440916,
-0.004203328397125006,
0.036828361451625824,
-0.003690788522362709,
0.020353855565190315,
0.03757529333233833,
0.035957615822553635,
-0.005966827739030123,
0.01727558858692646,
0.01858372986316681,
-0.02520274929702282,
0.010159277357161045,
-0.04076259955763817,
0.0022154117468744516,
0.02470502071082592,
-0.038835927844047546,
-0.03427784517407417,
-0.048846255987882614,
-0.03392476215958595,
0.019855746999382973,
0.03434949368238449,
-0.02233433537185192,
0.02637944184243679,
-0.00839215237647295,
0.004396889358758926,
0.023766182363033295,
0.016362501308321953,
-0.05407983437180519,
-0.011357562616467476,
-0.03168705478310585,
0.027163956314325333,
0.014342520385980606,
-0.011913244612514973,
-0.00796964205801487,
0.04225838556885719,
0.038359563797712326,
0.04985887557268143,
0.01393795758485794,
-0.01409560814499855,
0.03548916429281235,
0.02756362408399582,
-0.039078760892152786,
0.020357048138976097,
-0.03417199105024338,
0.022204618901014328,
0.005267992150038481,
-0.02897605299949646,
0.04665742069482803,
-0.01550300046801567,
0.0024882834404706955,
-0.02110961638391018,
-0.005125719588249922,
-0.03340258449316025,
0.015637237578630447,
-0.02089909464120865,
0.027651628479361534,
-0.04316897317767143,
-0.002871366683393717,
0.044958990067243576,
-0.03238578513264656,
-0.029317496344447136,
0.011216489598155022,
-0.06700542569160461,
-0.01162505242973566,
-0.027410838752985,
-0.04796930402517319,
0.05594011768698692,
-0.02343561500310898,
-0.029842309653759003,
-0.021571040153503418,
-0.04719043895602226,
0.02945316582918167,
0.0033104647882282734,
0.07511575520038605,
0.005736664403229952,
0.05374113842844963,
0.01580370031297207,
0.01994023099541664,
-0.02391999028623104,
0.029529785737395287,
0.12841281294822693,
-0.007726606912910938,
-0.033123679459095,
-0.0547214038670063,
-0.05050695315003395,
-0.02043912373483181,
0.019352545961737633,
0.017529340460896492,
-0.0072871726006269455,
-0.001262332429178059,
0.05389120429754257,
0.06151309609413147,
0.03193866088986397,
0.01633637212216854,
0.027906520292162895,
0.040274959057569504,
-0.030882244929671288,
-0.038228604942560196,
0.010447471402585506,
-0.018939903005957603,
-0.027846477925777435,
0.019106008112430573,
-0.059827547520399094,
0.0025314735248684883,
0.011366053484380245,
-0.0070603638887405396,
-0.04012313485145569,
-0.03034801036119461,
0.04621652141213417,
0.0293166134506464,
-0.035881590098142624,
-0.01812472939491272,
-0.033057957887649536,
-0.0278963353484869,
0.013698709197342396,
0.03637973591685295,
0.001502004568465054,
-0.039659470319747925,
0.024084432050585747,
-0.019456516951322556,
0.01648201048374176,
-0.0010970983421429992,
0.010099098086357117,
0.005273244809359312,
-0.009702189825475216,
-0.00024853431386873126,
0.00546247698366642,
0.024137480184435844,
-0.045117367058992386,
-0.001868624472990632,
-0.01944916509091854,
-0.0001605716533958912,
0.02454361505806446,
-0.012632009573280811,
-0.037103187292814255,
0.007750937715172768,
0.027043970301747322,
-0.019239213317632675,
-0.002139495685696602,
-0.04653865844011307,
0.010952163487672806,
-0.051676809787750244,
0.03646547719836235,
0.03970835730433464,
0.024952026084065437,
0.00889692734926939,
-0.04133248329162598,
0.005277992691844702,
-0.02135545201599598,
0.002192155225202441,
-0.059528544545173645,
0.01957826316356659,
-0.034474294632673264,
0.0008657849975861609,
0.03169466182589531,
0.026526382192969322,
0.035081855952739716,
0.023504607379436493,
-0.019795773550868034,
0.02226453647017479,
-0.03477177768945694,
0.06629777699708939,
-0.014578597620129585,
-0.03158089146018028,
-0.04424113407731056,
-0.01650182716548443,
-0.004884340800344944,
0.05291257053613663,
0.00004418512980919331,
-0.008859008550643921,
-0.009919749572873116,
0.007618448697030544,
0.023661527782678604,
-0.01949376054108143,
-0.018326200544834137,
0.048180315643548965,
-0.01898525096476078,
-0.010282430797815323,
-0.010366234928369522,
0.02661239542067051,
0.031966861337423325,
-0.007012302055954933,
0.024576518684625626,
0.011180710978806019,
-0.03461604565382004,
-0.004070132505148649,
0.015266050584614277,
-0.007929178886115551,
-0.005697624757885933,
-0.008710508234798908,
-0.003643953474238515,
-0.013411357998847961,
-0.03142883628606796,
-0.01750827580690384,
-0.026657389476895332,
-0.002289585303515196,
0.053073108196258545,
0.004016665276139975,
0.024686455726623535,
-0.056380756199359894,
0.0371265672147274,
0.01768505573272705,
0.003999271895736456,
-0.06450142711400986,
-0.0020248377695679665,
0.044721901416778564,
0.01378664094954729,
-0.024585308507084846,
0.017042163759469986,
0.01806100644171238,
0.009808937087655067,
0.010077351704239845,
0.004825667478144169,
-0.012939020991325378,
0.015277487225830555,
-0.007343180011957884,
-0.00961721409112215,
0.030321763828396797,
0.008066154085099697,
0.012099226005375385,
0.029852092266082764,
-0.0275606457144022,
-0.04127524793148041,
0.022133270278573036,
-0.009342978708446026,
0.008620101027190685,
0.031730495393276215,
-0.021326635032892227,
0.009243296459317207,
0.08832288533449173,
-0.005208802409470081,
-0.016363313421607018,
0.0021562364418059587,
0.001179519109427929,
0.009223274886608124,
0.017034772783517838,
0.0196069348603487,
-0.033711113035678864,
-0.011730164289474487,
0.03584684804081917,
0.01827993430197239,
-0.009140213951468468,
0.019007040187716484,
-0.03499731421470642,
-0.006661540362983942,
0.007937407121062279,
0.014151534996926785,
0.027340207248926163,
-0.011386035941541195,
0.05278958007693291,
-0.03272077441215515,
0.07124313712120056,
-0.0060541643761098385,
-0.013662301003932953,
-0.06855731457471848,
-0.022257041186094284,
-0.012907485477626324,
-0.02958366461098194,
0.0026757840532809496,
-0.04532763361930847,
-0.010192903690040112,
0.059872452169656754,
-0.05639301612973213,
-0.003908200189471245,
-0.04054209217429161,
-0.060481779277324677,
-0.019796492531895638,
-0.007606916129589081,
0.006449404172599316,
0.03331761434674263,
0.03986196964979172,
0.060503389686346054,
0.01446140930056572,
0.011505929753184319,
-0.01862071454524994,
0.038476262241601944,
0.018467571586370468,
0.03528213873505592,
-0.033962637186050415,
-0.01793775148689747,
0.07456810772418976,
-0.013858850114047527,
0.025308450683951378,
0.007771738804876804,
-0.011854407377541065,
-0.008091816678643227,
0.007896952331066132,
0.017297999933362007,
-0.010749352164566517,
0.04241548106074333,
-0.006057797931134701,
-0.01695060171186924,
-0.009383335709571838,
0.06500383466482162,
0.05320345237851143,
0.023617122322320938,
-0.01752042956650257,
0.006521317176520824,
0.019350998103618622,
-0.028236959129571915,
-0.010342210531234741,
0.043870363384485245,
0.017848830670118332,
-0.01997251994907856,
0.007329266052693129,
0.015563341788947582,
0.04865747690200806,
-0.0412137545645237,
0.009675540961325169,
-0.04105951264500618,
0.0013792975805699825,
-0.012216917239129543,
0.010562344454228878,
0.025184273719787598,
0.031438082456588745,
-0.01561333891004324,
0.0386805385351181,
-0.02102152444422245,
-0.0101370420306921,
-0.012287833727896214,
-0.005324793979525566,
0.020217498764395714,
0.010710787028074265,
-0.007118235807865858,
0.0027413899078965187,
-0.022481070831418037,
-0.036706794053316116,
0.04468557983636856,
0.046382322907447815,
0.011279698461294174,
0.0276530422270298,
-0.05235651880502701,
-0.01470966823399067,
-0.02975601702928543,
0.04117952287197113,
0.014847391285002232,
-0.028891541063785553,
-0.03897824138402939,
-0.006485118065029383,
0.012748882174491882,
0.012175355106592178,
0.024331042543053627,
0.042964354157447815,
-0.017277872189879417,
0.005186996888369322,
-0.01755228266119957,
0.038720741868019104,
-0.025894775986671448,
0.03298487514257431,
-0.00034988304832950234,
-0.02657984383404255,
-0.02352045476436615,
0.0014053370105102658,
-0.0295797660946846,
0.02586289308965206,
0.01942732371389866,
-0.02094116248190403,
-0.034846946597099304,
-0.03947467356920242,
-0.010163569822907448,
0.05023820325732231,
0.0201107170432806,
0.022131675854325294,
0.056759048253297806,
-0.031130539253354073,
0.015626095235347748,
0.01957806572318077,
-0.012619895860552788,
-0.024813063442707062,
0.04938279092311859,
-0.014373067766427994,
0.02469763718545437,
0.007207673974335194,
-0.04913809150457382,
0.03714204579591751,
-0.03368561342358589,
0.030732089653611183,
0.00754034798592329,
-0.04832801595330238,
-0.0061634802259504795,
-0.006258670706301928,
0.00087622000137344,
0.042667143046855927,
0.013155216351151466,
-0.014805402606725693,
0.019678257405757904,
-0.005930609535425901,
0.020925505086779594,
0.037420377135276794,
-0.0003959020250476897,
-0.0147751709446311,
0.018165677785873413,
-0.008295165374875069,
-0.028640415519475937,
0.007424947340041399,
-0.005952210631221533,
0.011341230943799019,
-0.028853069990873337,
-0.020995046943426132,
0.025798773393034935,
-0.06617724150419235,
-0.029471948742866516,
0.011683154851198196,
-0.03356068953871727,
0.0725334882736206,
-0.006224042735993862,
0.014449086971580982,
-0.020972324535250664,
0.018386295065283775,
0.02869275212287903,
0.009117554873228073,
0.0035369358956813812,
0.023771507665514946,
-0.03514435514807701,
-0.00177786685526371,
-0.018940916284918785,
0.01406631339341402,
0.0658378154039383,
-0.002074456075206399,
0.040827058255672455,
-0.025913091376423836,
-0.007189239375293255,
-0.024199487641453743,
-0.05824077129364014,
-0.016035988926887512,
-0.05163132771849632,
0.06059630960226059,
0.032682329416275024,
-0.0034625667612999678,
0.014077938161790371,
-0.03960471600294113,
-0.05520987883210182,
0.04347442835569382,
-0.0556165911257267,
-0.001036300091072917,
-0.05293867364525795,
0.004849375691264868,
-0.009064063429832458,
-0.004726276732981205
] |
<p>We know that a piece of ferromagnet, such as iron, can be magnetized by putting in a strong magnetic field to get domains parallel to the field grow. </p>
<p>I also remember from pop. culture and MacGyver old tv series that you can magnetize a piece of iron by hitting it hard, with a hammer say, along the same direction.</p>
<p>1-Is this way of magnetizing iron scientific? or is it pseudoscience?</p>
<p>and if it is scientific then:</p>
<p>2-what is the physical principle that will allow iron to get magnetized by hitting? and </p>
<p>3-how about nonferromagnetic materials?</p> | 1,508 | [
-0.0571361668407917,
-0.03037257492542267,
-0.018455281853675842,
-0.08947513997554779,
0.02767464518547058,
0.0020398139022290707,
-0.062336210161447525,
0.015765441581606865,
0.016571082174777985,
0.0042166318744421005,
0.03405500948429108,
0.047328267246484756,
0.03360937163233757,
0.027723146602511406,
0.03208848834037781,
0.005385508760809898,
0.03293338790535927,
-0.033252838999032974,
-0.006068918388336897,
-0.03174062818288803,
0.055858563631772995,
-0.01976657658815384,
-0.015743618831038475,
0.01333321537822485,
-0.022059142589569092,
-0.015122868120670319,
0.006209199316799641,
0.020517295226454735,
0.013445726595818996,
-0.01578598842024803,
0.01615760661661625,
-0.025990383699536324,
0.030257880687713623,
-0.018488755449652672,
0.0338994525372982,
-0.005507930181920528,
-0.03187490254640579,
-0.03444276750087738,
-0.0019249594770371914,
0.032220203429460526,
-0.051271703094244,
-0.01432983297854662,
-0.010742558166384697,
0.043555572628974915,
-0.04679558053612709,
-0.0037022873293608427,
-0.003740377491340041,
-0.030693676322698593,
0.057875316590070724,
-0.05438288301229477,
0.04667407274246216,
-0.03235596418380737,
0.03674497827887535,
0.014318164438009262,
-0.00234910286962986,
-0.03797890990972519,
0.08452852815389633,
0.044709865003824234,
-0.0058517782017588615,
-0.060903504490852356,
-0.014769315719604492,
-0.0014366586692631245,
-0.006438035983592272,
-0.03725568577647209,
-0.04467913508415222,
0.08649681508541107,
0.0027479655109345913,
0.0015648769913241267,
0.03880036249756813,
-0.009726169519126415,
0.013348033651709557,
0.027045289054512978,
0.048139069229364395,
-0.0024369871243834496,
0.026905756443738937,
-0.03409426659345627,
0.033414363861083984,
-0.0034397889394313097,
0.04229510575532913,
0.021228093653917313,
-0.008538582362234592,
0.018063602969050407,
0.028904547914862633,
0.0713571161031723,
0.013186789117753506,
-0.021232476457953453,
0.07844764739274979,
0.01702308841049671,
0.03425779938697815,
0.05158057436347008,
0.02056494541466236,
0.0009517016005702317,
0.048207931220531464,
-0.03595208004117012,
-0.029840964823961258,
0.03788813203573227,
0.023610278964042664,
0.06304197013378143,
0.008585678413510323,
-0.021439721807837486,
-0.005825866013765335,
-0.004503240343183279,
0.024172641336917877,
0.04686615616083145,
0.04095020517706871,
-0.03866840526461601,
-0.001806807704269886,
0.03815312311053276,
-0.03683418780565262,
0.009573161602020264,
0.007005230523645878,
0.043490853160619736,
-0.0016917450120672584,
-0.02493336796760559,
0.05923519283533096,
0.022440539672970772,
0.012488803826272488,
-0.03521942347288132,
0.006802245508879423,
0.05989685654640198,
-0.03471245616674423,
-0.034160614013671875,
0.024306179955601692,
-0.04272235184907913,
-0.05678781121969223,
0.003316963091492653,
0.033882204443216324,
-0.015131953172385693,
-0.013855797238647938,
0.005471875891089439,
0.005846476182341576,
-0.016160480678081512,
-0.0220341794192791,
0.025928523391485214,
0.015697704628109932,
-0.015872107818722725,
-0.12051690369844437,
-0.036809369921684265,
0.07921195775270462,
0.010079216212034225,
-0.012505649589002132,
-0.07540290057659149,
0.005355591420084238,
0.014211676083505154,
0.07232923060655594,
0.026212545111775398,
-0.004697252996265888,
-0.027482636272907257,
0.03918994218111038,
-0.014091492630541325,
-0.014317295514047146,
-0.024389950558543205,
0.005246172193437815,
-0.04275631904602051,
-0.015036032535135746,
-0.06248168274760246,
0.020713774487376213,
-0.007929537445306778,
-0.006643197033554316,
-0.03787291795015335,
0.05889870971441269,
-0.05338240787386894,
0.0019894421566277742,
0.01584492065012455,
-0.0342022068798542,
0.00032876545446924865,
0.07250682264566422,
0.008137129247188568,
0.03191884979605675,
0.034276798367500305,
-0.0007086066761985421,
0.014330748468637466,
0.02290903590619564,
0.046455055475234985,
0.02718283236026764,
-0.07738593220710754,
-0.02259063348174095,
-0.02126369997859001,
0.03870139643549919,
-0.018641486763954163,
-0.043191779404878616,
-0.005398143082857132,
-0.007530315779149532,
0.029318226501345634,
0.007391530554741621,
0.052173636853694916,
0.0019625085406005383,
-0.019610118120908737,
-0.01457812450826168,
-0.030269265174865723,
-0.010299033485352993,
-0.05478008836507797,
0.009754618629813194,
-0.041641443967819214,
-0.028310293331742287,
0.05213433504104614,
-0.016950169578194618,
0.029158199205994606,
-0.026636233553290367,
-0.02846331149339676,
0.016599630936980247,
0.015475602820515633,
0.028270214796066284,
0.0059164282865822315,
-0.007396718021482229,
0.06463012844324112,
-0.0007756940321996808,
-0.030547209084033966,
0.04720800369977951,
-0.023650968447327614,
-0.03129967674612999,
-0.0029984840657562017,
0.007072799373418093,
0.015366077423095703,
0.021739298477768898,
-0.008504717610776424,
0.028905507177114487,
-0.004599994048476219,
-0.027540724724531174,
0.00951074343174696,
-0.007087433245033026,
0.07370446622371674,
0.032281532883644104,
-0.020259134471416473,
0.03339538723230362,
0.006827131379395723,
-0.023622632026672363,
0.012525150552392006,
0.0343589186668396,
-0.049538157880306244,
-0.07586158066987991,
-0.008308318443596363,
0.023360829800367355,
0.012118667364120483,
-0.021302662789821625,
0.03786458447575569,
-0.006867712363600731,
0.05471929535269737,
0.014391951262950897,
0.023875538259744644,
-0.02217138186097145,
-0.023177357390522957,
-0.006883147172629833,
0.012275843881070614,
0.01877250149846077,
0.02253837138414383,
0.02492397092282772,
0.0023936580400913954,
0.0019832635298371315,
0.03445810079574585,
-0.03623057156801224,
0.03172861412167549,
0.018658820539712906,
-0.02015170268714428,
0.02135469950735569,
-0.04654950276017189,
0.0365375392138958,
0.004434504546225071,
-0.007409558165818453,
0.00330575043335557,
-0.0010948673589155078,
-0.000008707560482434928,
-0.031964290887117386,
-0.0049855588003993034,
-0.031139858067035675,
0.014967849478125572,
0.02168116346001625,
-0.011796923354268074,
0.025967629626393318,
-0.01328347995877266,
-0.02812747284770012,
-0.004651688504964113,
0.013179708272218704,
-0.010673711076378822,
0.004061155486851931,
0.026322824880480766,
0.008884024806320667,
0.05204946547746658,
-0.0304065253585577,
-0.022222910076379776,
0.007073864806443453,
-0.04080786928534508,
0.007440478075295687,
0.018847867846488953,
-0.051166269928216934,
0.027180934324860573,
-0.06253953278064728,
0.015353280119597912,
0.03977145254611969,
0.004096644464880228,
-0.00879910122603178,
0.01640302687883377,
0.028690379112958908,
-0.06494015455245972,
-0.024203503504395485,
-0.007473207078874111,
0.017774414271116257,
-0.0035587141755968332,
0.018106816336512566,
0.02477351576089859,
0.004242510534822941,
-0.017565486952662468,
0.010409372858703136,
-0.0005458795931190252,
-0.020605536177754402,
-0.03247527778148651,
-0.0324774831533432,
0.011385651305317879,
-0.017885304987430573,
0.03062383458018303,
0.031813185662031174,
-0.043056100606918335,
-0.004423788748681545,
-0.030092258006334305,
0.003420792752876878,
0.008537465706467628,
-0.032966263592243195,
0.02087984047830105,
0.00012736127246171236,
-0.011524873785674572,
0.05049567297101021,
0.01594618521630764,
-0.07091774046421051,
-0.01767069473862648,
-0.02650156430900097,
0.019604653120040894,
-0.026461927220225334,
0.026656677946448326,
0.05048414319753647,
-0.029313180595636368,
-0.001403014874085784,
0.019685819745063782,
0.017897330224514008,
0.019602544605731964,
0.019450955092906952,
-0.029651908203959465,
0.02385365590453148,
0.0172945037484169,
0.003229606430977583,
0.009228511713445187,
0.020481126382946968,
-0.055016886442899704,
0.050387658178806305,
-0.005441039800643921,
0.026089143007993698,
0.047162748873233795,
-0.04151228442788124,
0.049819838255643845,
0.009908303618431091,
0.010464745573699474,
-0.0510256327688694,
0.03156916797161102,
-0.004707631189376116,
-0.025323299691081047,
0.024198416620492935,
0.03699393570423126,
0.021481728181242943,
-0.010236751288175583,
-0.007694399915635586,
0.016269788146018982,
0.020757034420967102,
-0.03596024215221405,
0.010308225639164448,
-0.03590371459722519,
-0.008199489675462246,
0.014937304891645908,
-0.03805418685078621,
0.03207182511687279,
0.013002709485590458,
0.023298202082514763,
0.02764318138360977,
0.022738028317689896,
-0.002780902897939086,
-0.032420724630355835,
-0.07423016428947449,
0.01443809736520052,
-0.0035525390412658453,
0.020113449543714523,
0.019505048170685768,
0.023075668141245842,
0.024924131110310555,
0.011815532110631466,
0.03338286280632019,
-0.023547451943159103,
-0.09352558851242065,
0.040406398475170135,
-0.02436048537492752,
-0.01855790801346302,
-0.0028780424036085606,
-0.021820642054080963,
-0.009490088559687138,
-0.01220688410103321,
0.0025422791950404644,
-0.024437952786684036,
-0.03226052224636078,
-0.04300382733345032,
0.0187070369720459,
-0.01256738044321537,
-0.05857506021857262,
-0.001902941963635385,
0.02769392728805542,
0.02537526749074459,
-0.03490760549902916,
0.012414081953465939,
-0.014468733221292496,
-0.012477440759539604,
0.022117385640740395,
-0.025352729484438896,
0.02497546561062336,
0.010770434513688087,
0.03168211877346039,
0.0055669136345386505,
-0.01802108623087406,
-0.012573960237205029,
0.019006481394171715,
0.029013218358159065,
0.05627663433551788,
0.03136882930994034,
-0.014452369883656502,
-0.08895084261894226,
-0.04401353746652603,
-0.0003579951007850468,
-0.00813633855432272,
0.04164901375770569,
0.016041213646531105,
0.01998623088002205,
0.006110251881182194,
0.021865228191018105,
-0.0047255950048565865,
0.017203666269779205,
0.06340152025222778,
0.007590159308165312,
-0.005874770227819681,
-0.062499869614839554,
-0.03424450010061264,
-0.0305535439401865,
0.008449260145425797,
0.03242729231715202,
-0.018512574955821037,
-0.015399834141135216,
0.013910937123000622,
0.005387774668633938,
0.006704432424157858,
0.0056967176496982574,
0.021717142313718796,
-0.005377916619181633,
-0.002604020293802023,
-0.005304987542331219,
-0.010855371132493019,
-0.021349914371967316,
0.040667641907930374,
0.09773916006088257,
-0.006573570426553488,
-0.06296985596418381,
-0.07280240207910538,
0.015884466469287872,
0.002850840799510479,
0.019043052569031715,
-0.03417227044701576,
0.005928435828536749,
-0.009632423520088196,
-0.016293704509735107,
0.0030417032539844513,
-0.07304629683494568,
0.012837007641792297,
-0.057796623557806015,
0.007916895672678947,
-0.061512187123298645,
-0.008529303595423698,
-0.03443038836121559,
0.014309210702776909,
-0.00930854119360447,
0.016393490135669708,
-0.015750037506222725,
-0.033016037195920944,
-0.030749129131436348,
-0.0015837436076253653,
0.03048788011074066,
0.02988516353070736,
-0.01511477679014206,
0.043969642370939255,
-0.02039218135178089,
0.043624844402074814,
-0.01867591217160225,
-0.09023865312337875,
-0.0003163048531860113,
0.02040657214820385,
-0.027429869398474693,
0.040425196290016174,
-0.017518816515803337,
-0.07648135721683502,
0.03371933847665787,
-0.0011957298265770078,
-0.007120256312191486,
0.006872514262795448,
-0.016041230410337448,
0.04319878667593002,
0.042917992919683456,
0.0005335599998943508,
0.02193637192249298,
0.044593486934900284,
-0.039398111402988434,
-0.009205332025885582,
-0.03151741251349449,
0.0353713184595108,
-0.008208399638533592,
0.04511651396751404,
-0.026387831196188927,
0.033770449459552765,
-0.005176982842385769,
0.03615780919790268,
0.010852782055735588,
-0.009582164697349072,
-0.013522974215447903,
-0.028420114889740944,
-0.02428969368338585,
0.0035418260376900434,
0.0161735936999321,
-0.038509566336870193,
-0.005805466324090958,
0.023381076753139496,
-0.0057138362899422646,
0.004685112740844488,
0.009925554506480694,
0.006812411826103926,
0.0089180339127779,
0.023629015311598778,
-0.02860388718545437,
-0.004264976363629103,
-0.06768861413002014,
0.0191749669611454,
0.0031953537836670876,
-0.06171362102031708,
0.06287864595651627,
0.014631081372499466,
-0.0030227655079215765,
-0.012061605229973793,
-0.024871500208973885,
0.010191719979047775,
-0.010118681937456131,
0.014348337426781654,
0.03630179911851883,
-0.030248261988162994,
0.01680584065616131,
-0.017391951754689217,
0.02576221153140068,
-0.02244654856622219,
-0.0783960372209549,
0.010049882344901562,
-0.004300504457205534,
-0.0016492314171046019,
0.00007921450742287561,
-0.000683514925185591,
-0.01723330467939377,
-0.043547481298446655,
0.0061290268786251545,
0.025462932884693146,
-0.03374296799302101,
-0.01841544359922409,
0.05548551306128502,
-0.0305622648447752,
0.055956289172172546,
0.00601272052153945,
-0.06028866395354271,
0.02795129083096981,
0.008818117901682854,
-0.0007147993892431259,
-0.00885285809636116,
0.020941922441124916,
-0.03425319865345955,
-0.025359610095620155,
-0.015292665921151638,
0.02775896154344082,
0.030799712985754013,
0.00020051088358741254,
0.006571558304131031,
0.026875276118516922,
0.018017582595348358,
-0.007318676449358463,
-0.055882081389427185,
0.017908167093992233,
0.057131096720695496,
0.02403886243700981,
-0.011937610805034637,
0.007930916734039783,
-0.04093824699521065,
-0.03353305160999298,
0.04812692850828171,
-0.0018756092758849263,
0.0378216989338398,
0.01322876662015915,
0.04833588749170303,
-0.006900959648191929,
0.01491494569927454,
0.04439309239387512,
-0.04806862398982048,
0.033703092485666275,
-0.021313423290848732,
0.027695437893271446,
-0.004760584328323603,
0.006686895154416561,
-0.016275830566883087,
-0.0201534703373909,
-0.01294437050819397,
0.03591378405690193,
0.04644961655139923,
-0.04339050129055977,
0.07235191017389297,
0.022108137607574463,
-0.018627267330884933,
-0.04898117855191231,
-0.00704661849886179,
-0.0014805351383984089,
-0.01593809202313423,
0.003455030731856823,
0.05404889956116676,
-0.018269743770360947,
0.022565588355064392,
0.03603358194231987,
0.02934635803103447,
-0.03035370633006096,
0.007996964268386364,
0.0359608419239521,
0.027950607240200043,
0.05628713592886925,
0.001094728009775281,
-0.02192796766757965,
0.0766594186425209,
-0.04148462414741516,
0.008032064884901047,
0.025284092873334885,
0.003645353950560093,
0.0404873862862587,
-0.003711427329108119,
0.007673437241464853,
-0.03734975308179855,
-0.022957729175686836,
-0.017237387597560883,
0.006073313765227795,
0.002890488365665078,
0.02496219053864479,
0.014575496315956116,
-0.0038301791064441204,
0.018802333623170853,
0.011035691946744919,
-0.009737346321344376,
0.006229996681213379,
-0.07750611007213593,
0.014044275507330894,
-0.047897811979055405,
-0.058334410190582275,
0.017050301656126976,
0.0226530022919178,
-0.02602759189903736,
0.03523745760321617,
-0.05012930929660797,
0.02813919447362423,
0.010636692866683006,
0.0347779244184494,
-0.03456166759133339,
0.04747897759079933,
-0.01851038634777069,
0.01990083046257496,
0.0053150164894759655,
0.019956527277827263,
0.11844170093536377,
0.022094324231147766,
0.04566472768783569,
-0.05167311057448387,
0.008004707284271717,
-0.04874409735202789,
-0.008790295571088791,
-0.007444897200912237,
0.0010288771009072661,
-0.04179392009973526,
0.02240067720413208,
-0.006406319793313742,
0.0868067517876625,
0.002157142385840416,
0.03383363410830498,
0.049132637679576874,
-0.019822759553790092,
-0.003579067764803767,
-0.014919281005859375,
0.0002007536677410826,
-0.018302028998732567,
-0.00024996939464472234,
-0.041198909282684326,
0.012343086302280426,
-0.05384976789355278,
-0.02898193523287773,
0.02956974320113659,
-0.05118335783481598,
0.0374656617641449,
0.0394558347761631,
-0.015338282100856304,
0.013914315961301327,
0.0035530701279640198,
-0.022805703803896904,
-0.032387133687734604,
0.020322168245911598,
0.037001583725214005,
-0.0017035114578902721,
0.01443040557205677,
0.0149436816573143,
0.02923191897571087,
0.016001634299755096,
-0.002156229689717293,
0.05079580843448639,
-0.0414811372756958,
0.004523438401520252,
-0.04818139970302582,
0.016260989010334015,
-0.03502930700778961,
0.010806087404489517,
0.0137383583933115,
0.0018068284261971712,
0.033073265105485916,
-0.012895283289253712,
-0.05791586637496948,
0.019331034272909164,
0.004945393651723862,
-0.00975334458053112,
0.008731955662369728,
-0.029394282028079033,
0.058255791664123535,
0.012244015000760555,
0.008625752292573452,
-0.0081861587241292,
-0.009740954264998436,
0.03942984715104103,
0.02702803537249565,
0.04161231592297554,
0.025530358776450157,
-0.024511050432920456,
-0.06190752983093262,
0.011742699891328812,
-0.054429467767477036,
0.050470441579818726,
-0.01438347902148962,
-0.004759515635669231,
0.010443870909512043,
-0.03695815056562424,
-0.018105098977684975,
0.012705442495644093,
-0.001896261121146381,
0.03998379781842232,
-0.03934766352176666,
0.005834781099110842,
-0.04273619502782822,
-0.02531055361032486,
0.012146185152232647,
0.03601245954632759,
-0.024515938013792038,
0.0026733821723610163,
-0.004596022889018059,
-0.03739996626973152,
0.021558286622166634,
-0.031723588705062866,
-0.046530939638614655,
-0.0349385142326355,
-0.022733408957719803,
0.014185280539095402,
0.009305166080594063,
0.04938396066427231,
0.034556686878204346,
-0.04416854307055473,
0.02973363921046257,
0.009633280336856842,
-0.02196752093732357,
-0.011042425408959389,
0.03591584786772728,
-0.028775326907634735,
-0.007660266477614641,
-0.017459634691476822,
-0.01504572480916977,
-0.051967475563287735,
-0.034364428371191025,
-0.024559030309319496,
-0.017442723736166954,
-0.0007520264480262995,
0.06855615973472595,
-0.02339072711765766,
0.01607668027281761,
-0.018230261281132698,
0.049344755709171295,
-0.05879465490579605,
-0.017087260261178017,
-0.03013686276972294,
0.0058204359374940395,
0.014502088539302349,
-0.010815824382007122,
0.013066933490335941,
0.04228384047746658,
-0.005496039520949125,
0.014871210791170597,
0.01748463325202465,
0.010259541682898998,
0.0038287946954369545,
0.044589731842279434,
0.007785256952047348,
0.007138146553188562,
0.008519048802554607,
0.001630872953683138,
-0.021237259730696678,
0.01748526655137539,
-0.026193778961896896,
-0.0598735511302948,
0.01673930324614048,
-0.04791482165455818,
0.004215872380882502,
-0.00425821403041482,
-0.0005330445128493011,
-0.014391981065273285,
0.031498443335294724,
-0.023607173934578896,
0.003816581331193447,
0.00297292391769588,
-0.007565291132777929,
-0.007177865132689476,
0.02091771736741066,
0.02267410047352314,
-0.016392892226576805,
-0.0038311113603413105,
0.025874856859445572,
0.013049567118287086,
0.05725634843111038,
-0.005490731913596392,
-0.004628812428563833,
0.0003772615164052695,
-0.04333890974521637,
0.029317785054445267,
-0.013268405571579933,
0.005583064164966345,
0.0619785450398922,
-0.022102100774645805,
0.031039102002978325,
-0.0032643424347043037,
-0.0057666185311973095,
-0.08731930702924728,
-0.004715263843536377,
0.011507028713822365,
-0.04929511994123459,
0.026236750185489655,
-0.034225743263959885,
0.000763851625379175,
-0.0028379715513437986,
-0.10507116466760635,
0.015637269243597984,
-0.028579141944646835,
-0.0576421283185482,
-0.035272952169179916,
0.008554171770811081,
0.006937150843441486,
0.030060337856411934,
0.010550913400948048,
0.0467943511903286,
0.00859486311674118,
0.03548411279916763,
-0.027102146297693253,
0.037409622222185135,
-0.005575938615947962,
0.0035167455207556486,
0.005062267184257507,
0.0018718031933531165,
0.06384648382663727,
-0.04137503355741501,
-0.04321370646357536,
0.05590329319238663,
-0.03872058540582657,
0.011508098803460598,
0.032429881393909454,
-0.0008237016736529768,
-0.025543536990880966,
-0.02251775935292244,
0.03752553462982178,
0.005661380477249622,
0.013145135715603828,
0.03318748623132706,
0.026649903506040573,
0.05663246288895607,
0.0023379891645163298,
0.00057850347366184,
0.010748804546892643,
-0.018554477021098137,
0.02375100366771221,
0.020312100648880005,
-0.0366513766348362,
-0.043642573058605194,
0.007457054685801268,
0.023265641182661057,
0.0007655243971385062,
0.028026290237903595,
0.018270350992679596,
-0.04298956319689751,
-0.021347928792238235,
0.005122434813529253,
-0.016651442274451256,
0.005635212641209364,
0.042542025446891785,
-0.04290938749909401,
-0.006434091366827488,
-0.0075216530822217464,
-0.018035147339105606,
-0.03507235646247864,
-0.04059753566980362,
0.002860673703253269,
0.041425202041864395,
0.02512587234377861,
-0.010214368812739849,
-0.04257456213235855,
-0.009906821884214878,
0.03606066107749939,
0.0159439817070961,
0.028831709176301956,
0.012803788296878338,
-0.01649877429008484,
-0.01637684740126133,
-0.0560469850897789,
0.04284411668777466,
-0.04628162086009979,
-0.0199204683303833,
-0.058834657073020935,
-0.01747267320752144,
0.02011268213391304,
0.010581471025943756,
0.04908251389861107,
-0.021041149273514748,
0.007239930797368288,
-0.00694664241746068,
-0.024832868948578835,
0.030342034995555878,
-0.012708728201687336,
-0.016718370839953423,
0.006715315859764814,
0.004556505009531975,
0.00474820239469409,
0.003038637340068817,
-0.010363928973674774,
0.020973827689886093,
0.01580953225493431,
0.04019193723797798,
0.003399765118956566,
-0.00017726597434375435,
-0.0547320693731308,
0.00828934833407402,
-0.019214577972888947,
0.013731760904192924,
0.052239466458559036,
-0.022948050871491432,
0.010938474908471107,
-0.03168430179357529,
-0.04527789726853371,
-0.025621995329856873,
0.01803736574947834,
-0.040063563734292984,
0.0172496996819973,
-0.034178052097558975,
-0.025978991761803627,
0.0554807148873806,
-0.04046805948019028,
0.004411671776324511,
0.02714839205145836,
0.016088737174868584,
0.022946111857891083,
0.026137661188840866,
0.013265104033052921,
0.022775642573833466,
-0.0468783937394619,
0.014544514939188957,
0.005385567434132099,
-0.015383151359856129,
-0.019732369109988213,
0.05549819394946098,
0.019790714606642723,
0.007360931020230055,
0.004345294088125229,
0.021837754175066948,
-0.021739760413765907,
-0.0012943731853738427,
0.05617474392056465,
0.06293544173240662,
0.019746888428926468,
-0.020239507779479027,
0.02211112342774868,
-0.025929147377610207,
0.02588352933526039,
0.023525381460785866,
0.0032742596231400967,
0.07452508062124252,
-0.020266935229301453,
-0.017598392441868782,
-0.015501581132411957,
0.010825157165527344,
-0.004807048477232456,
0.0009368765167891979,
0.00005118806802784093,
0.05468345060944557,
0.018158184364438057,
-0.030668357387185097,
-0.010333655402064323,
0.03715057298541069,
0.0511443167924881,
-0.015768712386488914,
0.03748461976647377,
-0.03513960912823677,
-0.0033111791126430035,
-0.00414433516561985,
-0.022454535588622093,
-0.03957768529653549,
-0.027234414592385292,
0.024223312735557556,
0.0004365644126664847,
0.018818410113453865,
0.005420387722551823,
-0.008272724226117134,
-0.026526225730776787,
0.018682952970266342,
-0.07277426868677139,
0.0037479810416698456,
-0.060385171324014664,
0.026503341272473335,
-0.02087298035621643,
-0.006527085322886705
] |
<p>We all know the effects of speed on time, and we have a formula for that, but I have a hunch, that time also is relative to pressure, and that by increasing the pressure on matter, in fact time will speed up for that matter. </p>
<p>I am not a physics expert ( I have a Masters Degree in Computer Engineering, and have hence taken several physics, math and chemistry classes ) so don't slaughter me, I would appreciate a talkative tone. </p>
<p>So I will say some "ideas" in my head that might be stupid, or assumptions from my understanding of how things are that are in fact wrong from an expert view, but please try to understand my <strong>intention</strong> or follow my idea of what I am thinking instead of focusing on details.</p>
<p>So, my thinking is that once something starts travelling near the speed of light, or the speed of light, it will start to dissolve, before turning into energy and becoming the lightest of all while dissolving = light, and hence is why it can travel at the speed of light. So if something is to travel at the speed of light, it actually have to be dissolved into energy.</p>
<p>The idea I have with pressure, is that if matter, in a pressure chamber, where pressure is turned up, the matter will eventually turn into pure energy as well = light. </p>
<p>I also have this thought, that once pressure is applied to matter, the atoms starts to vibrate, move faster, and a reaction that would normally take hundreds of years, can be achieved with quicker results in a pressure chamber because time for all that materia increases, not because of the pressure, but because time is happening faster, which supports my idea of time actually speeding up for those particles. </p>
<p>What happens with used reactor fuel in a pressure chamber today? How much can we speed up the halftime?</p>
<p>It appears to me that if this was true, it will be the contradiction to speed. A twin X travelling near the speed of light, will come back to visit an older twin Y on earth. </p>
<p>However, with pressure, it might just be the opposite, that twin X in the pressure chamber will in fact be older than twin Y outside.</p>
<p>Surely turning up pressure on a twin might not be so healthy, but neither is acceleration from 0 to the speed of light in 1s. So pressure is probably not a healthy way to speed up time for matter, it will probably destroy certain things in it. </p>
<p>Am I on something here? No?</p> | 1,509 | [
-0.004274170845746994,
-0.0597359761595726,
-0.02057720720767975,
-0.08823325484991074,
0.03326546773314476,
-0.04219427332282066,
-0.05134527012705803,
-0.008407853543758392,
0.0038100266829133034,
-0.026089033111929893,
0.045926835387945175,
0.057873595505952835,
0.02204114757478237,
-0.014036043547093868,
-0.020391980186104774,
0.035249460488557816,
0.036230478435754776,
-0.022374242544174194,
-0.006898056715726852,
-0.059382278472185135,
0.029359837993979454,
-0.046087127178907394,
-0.011234714649617672,
0.015350143425166607,
-0.02514784410595894,
0.04004853591322899,
0.004965726286172867,
-0.013011910952627659,
-0.003302555065602064,
0.05655631795525551,
0.020541245117783546,
-0.03314109519124031,
0.009850780479609966,
0.007153763435781002,
0.02416038140654564,
-0.002902477979660034,
-0.03312988579273224,
-0.033586420118808746,
0.008327786810696125,
0.05414256453514099,
-0.004308357369154692,
0.024099096655845642,
-0.01982254534959793,
0.0024881279096007347,
-0.0024465376045554876,
0.05418899655342102,
-0.0035752763506025076,
-0.025105677545070648,
0.05745858699083328,
-0.03635255992412567,
0.030557038262486458,
-0.007174968719482422,
0.011237173341214657,
0.012836345471441746,
0.0014527988387271762,
-0.026452509686350822,
0.07632621377706528,
0.06671670079231262,
0.008931380696594715,
-0.026546873152256012,
0.021108323708176613,
0.05844125896692276,
-0.006456469185650349,
-0.006125807296484709,
-0.009830842725932598,
-0.01706361584365368,
-0.03304651752114296,
-0.007148792967200279,
-0.002217699307948351,
-0.0017495673382654786,
0.03502076491713524,
-0.007546051871031523,
0.046853695064783096,
0.01402533520013094,
-0.0018852383363991976,
-0.0337199941277504,
-0.003766776295378804,
0.002361942082643509,
0.026039034128189087,
0.06497987359762192,
-0.026472508907318115,
0.01102379709482193,
-0.005312029737979174,
0.030105264857411385,
-0.017614079639315605,
0.01546138059347868,
0.048264335840940475,
-0.015191642567515373,
-0.034811560064554214,
0.05477051064372063,
-0.0012796197552233934,
0.008023868314921856,
0.03030065819621086,
0.012413647957146168,
0.018083861097693443,
0.014364748261868954,
-0.01626196689903736,
0.06604525446891785,
0.01710483804345131,
0.015785997733473778,
0.02087884023785591,
-0.012018543668091297,
0.007540089078247547,
0.039846405386924744,
0.014506618492305279,
-0.055456001311540604,
-0.04025563225150108,
0.010178832337260246,
0.004542147740721703,
-0.0069098942913115025,
-0.04189098998904228,
-0.028014544397592545,
-0.009481837972998619,
0.01885811798274517,
0.003906102618202567,
-0.030419152230024338,
0.005428748205304146,
-0.03933240473270416,
0.11102934926748276,
0.021892279386520386,
0.02563348226249218,
-0.016793783754110336,
0.013342943042516708,
0.001297110109589994,
-0.05011926218867302,
-0.0048807961866259575,
0.012595460750162601,
-0.016176585108041763,
-0.020945800468325615,
0.006455664057284594,
-0.006850667763501406,
-0.0358310267329216,
0.03885048255324364,
-0.025331664830446243,
0.03903207182884216,
0.010531468316912651,
-0.09260426461696625,
-0.06053364649415016,
0.03809804469347,
0.01842944324016571,
-0.040234893560409546,
-0.0820213034749031,
0.02938777580857277,
-0.017133474349975586,
0.088141068816185,
0.008655808866024017,
-0.03352891281247139,
-0.0029192783404141665,
0.05306126922369003,
0.017711862921714783,
-0.015865284949541092,
-0.010215758346021175,
0.026744620874524117,
-0.016232190653681755,
-0.004558345302939415,
-0.05952845513820648,
-0.009903804399073124,
0.052049633115530014,
-0.01853850670158863,
0.006863648537546396,
0.03891874477267265,
-0.06689896434545517,
0.004696924705058336,
0.004466402344405651,
0.0026113272178918123,
-0.056008920073509216,
0.07672914117574692,
0.010892774909734726,
-0.022644149139523506,
0.016368979588150978,
0.05139109864830971,
0.03354714438319206,
-0.015100599266588688,
-0.029689181596040726,
0.005668708123266697,
-0.02706187218427658,
0.006576496176421642,
-0.006862794514745474,
-0.04001573100686073,
-0.026319120079278946,
-0.044267576187849045,
-0.04632813110947609,
-0.023745158687233925,
-0.0054819583892822266,
0.028007594868540764,
0.03935493901371956,
0.0016641782131046057,
-0.006529319100081921,
-0.0009418830159120262,
-0.029944950714707375,
0.0008587610791437328,
-0.07790658622980118,
-0.0019221148686483502,
-0.00005795903052785434,
0.004931364208459854,
-0.008751329965889454,
0.003165917005389929,
0.043633993715047836,
-0.03360249474644661,
-0.040676653385162354,
-0.015832245349884033,
0.04441298544406891,
0.017331134527921677,
-0.010805782862007618,
0.003983544651418924,
0.056799035519361496,
0.006724607199430466,
-0.02721860259771347,
-0.04473056271672249,
0.02558077871799469,
-0.0032936648931354284,
0.028946509584784508,
-0.010212911292910576,
0.012202058918774128,
0.028449086472392082,
-0.0343049019575119,
0.032509345561265945,
-0.012027140706777573,
0.003998202737420797,
-0.009439365938305855,
0.001421976718120277,
0.1167261004447937,
0.012257332913577557,
-0.01596769690513611,
-0.015148463658988476,
0.04688430577516556,
0.0009315690258517861,
0.02861637808382511,
-0.023332655429840088,
-0.029941389337182045,
-0.03579462692141533,
-0.05450883135199547,
0.01915227808058262,
0.02982921153306961,
-0.02758573740720749,
0.03440431132912636,
0.0052634552121162415,
0.023180609568953514,
0.04181584343314171,
-0.023585017770528793,
0.0028215202037245035,
-0.022026490420103073,
0.0199296697974205,
0.014848175458610058,
0.009093165397644043,
0.023676827549934387,
0.018160175532102585,
0.01814332790672779,
0.01646541617810726,
-0.057637572288513184,
0.021138418465852737,
-0.005321442149579525,
0.03643910214304924,
-0.013202599249780178,
0.0255410335958004,
-0.019613323733210564,
0.011828123591840267,
0.020318729802966118,
0.02722499519586563,
0.0025605654809623957,
0.0320495069026947,
0.01719198375940323,
-0.06377977877855301,
0.0029583023861050606,
-0.02448505163192749,
0.028436951339244843,
0.0025078433100134134,
0.0038589080795645714,
0.03226109966635704,
-0.018205879256129265,
0.016028068959712982,
0.0058375210501253605,
-0.00966564379632473,
-0.01585550606250763,
-0.0505024753510952,
-0.04269201308488846,
0.032680314034223557,
0.049955133348703384,
-0.03229575604200363,
-0.025535425171256065,
-0.0007540611550211906,
-0.03667008504271507,
-0.009867632761597633,
-0.025846192613244057,
-0.039122145622968674,
0.0469173938035965,
-0.02444346249103546,
-0.044959597289562225,
0.013638133183121681,
-0.00226198579184711,
0.00894339382648468,
0.02511763386428356,
-0.03277764841914177,
-0.10532817989587784,
-0.027986403554677963,
-0.027219537645578384,
-0.03140128776431084,
-0.012232243083417416,
0.02147536538541317,
0.06986909359693527,
-0.019851388409733772,
-0.07580966502428055,
-0.014999245293438435,
-0.045714981853961945,
-0.008603655733168125,
-0.026629677042365074,
-0.02406858466565609,
-0.028614096343517303,
-0.03201345354318619,
0.017874490469694138,
0.03542115166783333,
-0.07409211993217468,
-0.019412370398640633,
-0.019144373014569283,
0.00132551952265203,
0.0542038194835186,
0.0006515370914712548,
0.07208205759525299,
-0.018583539873361588,
-0.03165777772665024,
0.07793086022138596,
0.018152901902794838,
0.023140359669923782,
-0.03464497625827789,
0.012658484280109406,
0.018277376890182495,
-0.003229008289054036,
0.062143776565790176,
0.026688728481531143,
-0.03169659152626991,
-0.01555794756859541,
0.018767450004816055,
0.07308967411518097,
0.019636929035186768,
0.027850491926074028,
-0.015691911801695824,
0.008161795325577259,
0.017414765432476997,
0.031876660883426666,
0.04442305117845535,
0.0400615856051445,
-0.03009612113237381,
0.047895919531583786,
-0.04372946172952652,
0.042109474539756775,
0.02674831822514534,
-0.087485671043396,
0.0488312765955925,
0.051205866038799286,
0.010158020071685314,
-0.010558030568063259,
0.0075267404317855835,
-0.012072918005287647,
-0.05120730400085449,
0.004604582209140062,
0.03142910450696945,
0.040412161499261856,
0.020367398858070374,
-0.017459165304899216,
0.00526268919929862,
0.05228428170084953,
0.012668841518461704,
-0.03107963502407074,
0.014443560503423214,
-0.02514563500881195,
0.017711151391267776,
-0.01047172024846077,
0.007048687897622585,
0.04633777588605881,
0.012680615298449993,
-0.0007810914539732039,
-0.006952524185180664,
-0.009882243350148201,
-0.012827932834625244,
-0.0730874165892601,
-0.0336671844124794,
0.003063339041545987,
0.04288553446531296,
0.025462042540311813,
0.07783464342355728,
0.020112760365009308,
-0.010061666369438171,
0.024574844166636467,
-0.02765233814716339,
-0.09011813253164291,
-0.010563725605607033,
-0.019014529883861542,
-0.013955268077552319,
-0.007403014227747917,
0.01086156815290451,
-0.045004703104496,
-0.03950481116771698,
-0.01529600378125906,
-0.018403474241495132,
0.011226171627640724,
-0.09028900414705276,
0.036021821200847626,
-0.02502814494073391,
-0.04945102706551552,
-0.010166246443986893,
0.04014112427830696,
0.05626978352665901,
0.02731909416615963,
0.03389889374375343,
0.020347539335489273,
-0.05549831688404083,
-0.028159644454717636,
0.00513920234516263,
-0.01169363223016262,
0.050297874957323074,
0.02427779696881771,
0.008700771257281303,
0.008979560807347298,
-0.04144318029284477,
0.0234193354845047,
0.028127066791057587,
0.006744197104126215,
-0.009875555522739887,
-0.013489545322954655,
-0.029901646077632904,
-0.007816768251359463,
-0.031937990337610245,
0.031160347163677216,
0.03440555930137634,
-0.00010917822510236874,
0.017310665920376778,
-0.025621477514505386,
0.00247120950371027,
0.0035393917933106422,
0.010140771977603436,
0.037740275263786316,
-0.027004424482584,
-0.030217627063393593,
-0.02786337584257126,
-0.005668747704476118,
-0.020687341690063477,
-0.006357183679938316,
-0.0383894182741642,
0.023701852187514305,
-0.0346226803958416,
-0.009354455396533012,
-0.018792377784848213,
0.027762020006775856,
-0.03121361881494522,
0.019094951450824738,
-0.022754715755581856,
-0.019427653402090073,
0.011933495290577412,
0.016249993816018105,
0.01776178739964962,
0.006650126073509455,
0.01618548110127449,
0.0032400195486843586,
0.03430045396089554,
-0.06944721937179565,
-0.020155904814600945,
0.04309200495481491,
0.0695008859038353,
-0.018455658107995987,
0.01598900556564331,
-0.021672530099749565,
-0.05923980847001076,
0.02264070324599743,
-0.031046060845255852,
0.005364576820284128,
-0.011036654002964497,
-0.025176815688610077,
-0.012668892741203308,
-0.04680371657013893,
-0.013391267508268356,
0.017731765285134315,
-0.031524427235126495,
0.008315018378198147,
0.0077582187950611115,
-0.012553141452372074,
0.00413946807384491,
-0.002513085724785924,
0.0104927783831954,
0.006406873464584351,
-0.00005921405318076722,
-0.021125776693224907,
-0.032066140323877335,
0.0023188770283013582,
-0.02903900295495987,
-0.07076967507600784,
0.019999602809548378,
-0.008857821114361286,
-0.011623426340520382,
0.055342897772789,
-0.011967497877776623,
-0.06647744029760361,
0.06536240875720978,
0.009699024260044098,
-0.022957485169172287,
-0.008704538457095623,
-0.0522892139852047,
0.05742776766419411,
0.0296485498547554,
-0.009651304222643375,
0.001401598216034472,
0.047625619918107986,
-0.05671779811382294,
0.011457249522209167,
-0.006474955007433891,
0.021774882450699806,
-0.025021394714713097,
0.05516078323125839,
0.0001944301329785958,
0.015520971268415451,
-0.026080334559082985,
0.020770695060491562,
0.0010563170071691275,
-0.025000615045428276,
0.013847848400473595,
-0.022218044847249985,
0.04017890989780426,
-0.0022915732115507126,
0.035926368087530136,
0.011988965794444084,
-0.04958038032054901,
0.0006439630524255335,
-0.013313463889062405,
-0.023066502064466476,
0.006174193695187569,
0.017700951546430588,
0.008295667357742786,
0.02908148616552353,
-0.01322856917977333,
0.012899087741971016,
-0.01722441241145134,
-0.03004026599228382,
0.04734455421566963,
-0.018901998177170753,
0.06350364536046982,
-0.03550753742456436,
0.03457380831241608,
0.052558090537786484,
-0.016078293323516846,
-0.01982639729976654,
0.006724299397319555,
-0.051013123244047165,
-0.0022557664196938276,
-0.042323123663663864,
-0.003079949878156185,
0.0050872135907411575,
-0.008938705548644066,
-0.05080970376729965,
-0.036141470074653625,
0.03092837706208229,
-0.03587016835808754,
-0.04852183535695076,
-0.03586852177977562,
0.004737247247248888,
-0.02503623068332672,
-0.04311961680650711,
-0.010206900537014008,
0.059746358543634415,
-0.009179675951600075,
-0.014953715726733208,
0.027280287817120552,
0.023565934970974922,
0.03780711442232132,
-0.010507647879421711,
-0.012050625868141651,
-0.03285631164908409,
-0.0054638017900288105,
0.011998414061963558,
-0.019789084792137146,
0.010989755392074585,
-0.043221138417720795,
0.0003218858619220555,
0.006474851164966822,
-0.022821690887212753,
0.03384203091263771,
-0.03634785860776901,
0.05288958176970482,
0.03703983128070831,
-0.007311241701245308,
-0.010622521862387657,
0.01028873398900032,
0.028573747724294662,
0.02968699298799038,
0.011181208305060863,
0.01495154295116663,
0.004125448875129223,
-0.020872652530670166,
-0.04504643380641937,
0.02307487279176712,
0.009349527768790722,
0.015060367062687874,
-0.022326581180095673,
0.051200982183218,
0.02034219168126583,
-0.005850093439221382,
0.01412491500377655,
-0.05050283297896385,
-0.017547452822327614,
0.0028062057681381702,
-0.018001779913902283,
0.016872309148311615,
-0.041892100125551224,
-0.017775388434529305,
-0.015332593582570553,
-0.012804537080228329,
-0.014398917555809021,
0.027484159916639328,
-0.021148644387722015,
0.05184176564216614,
-0.010406781919300556,
-0.0172532070428133,
-0.02008318342268467,
-0.0341322086751461,
-0.017566241323947906,
0.00891084410250187,
-0.016001107171177864,
0.029866892844438553,
-0.020351406186819077,
-0.05224519222974777,
0.03608965501189232,
0.03635510429739952,
-0.025564182549715042,
0.008781271986663342,
0.03506352752447128,
-0.014122613705694675,
0.020695658400654793,
-0.025953693315386772,
-0.018677378073334694,
0.0022658442612737417,
-0.034245096147060394,
0.016098158434033394,
0.011399435810744762,
0.043115533888339996,
0.023002363741397858,
0.05133088678121567,
-0.0038403093349188566,
-0.07200649380683899,
-0.02806323952972889,
-0.06864012777805328,
-0.01394813135266304,
0.0027511476073414087,
-0.007112626451998949,
0.009959524497389793,
0.012946557253599167,
0.02822186052799225,
0.044273849576711655,
-0.0004706566978711635,
-0.013525743037462234,
-0.03334236145019531,
-0.026752665638923645,
-0.018801972270011902,
-0.036714036017656326,
0.03511400893330574,
-0.029224442318081856,
-0.007860417477786541,
-0.013641389086842537,
-0.02593698352575302,
0.027541153132915497,
-0.005515617318451405,
0.02178996428847313,
-0.01458652876317501,
0.06709843128919601,
0.013798481784760952,
0.023530391976237297,
-0.0070919315330684185,
0.04441358521580696,
0.1472475379705429,
0.012627183459699154,
0.01028553768992424,
-0.021469933912158012,
0.02297772839665413,
-0.003979703411459923,
0.03299449011683464,
-0.004892630502581596,
-0.01592341437935829,
0.010309610515832901,
0.005658051930367947,
0.04068314656615257,
0.051109060645103455,
-0.011034216731786728,
-0.011797544546425343,
0.03821921348571777,
-0.033203478902578354,
-0.017385415732860565,
-0.011772355996072292,
0.01702188141644001,
-0.026493707671761513,
0.015326007269322872,
-0.002356473822146654,
0.0256793275475502,
-0.02998855710029602,
0.004452674183994532,
-0.034085340797901154,
-0.03329160064458847,
0.03179321810603142,
-0.00647912360727787,
-0.03921552374958992,
0.028842145577073097,
-0.01797458529472351,
-0.059466272592544556,
-0.010562179610133171,
0.04819735139608383,
0.026383303105831146,
-0.009935273788869381,
-0.009495798498392105,
0.03129660338163376,
0.005923104472458363,
0.012280798517167568,
0.006719514261931181,
-0.0017167122568935156,
-0.04784757271409035,
0.014522137120366096,
-0.010859895497560501,
0.03558514639735222,
-0.04495113343000412,
-0.024787411093711853,
0.028137411922216415,
-0.007775835692882538,
0.031785305589437485,
-0.031857505440711975,
-0.00625036284327507,
0.01321005541831255,
0.0038143580313771963,
0.022369785234332085,
0.001118220272473991,
0.01616545580327511,
0.01459310669451952,
0.005476236343383789,
0.016078755259513855,
0.004715288057923317,
0.01380494050681591,
-0.007570482324808836,
-0.003439502790570259,
0.026220612227916718,
-0.01436119619756937,
-0.00538735231384635,
-0.056056875735521317,
0.03168664127588272,
-0.0523109957575798,
-0.003809157758951187,
0.038565993309020996,
0.055739566683769226,
0.030499795451760292,
-0.0026868991553783417,
-0.024852709844708443,
-0.04385857284069061,
-0.03253015875816345,
0.05738745257258415,
-0.026476513594388962,
-0.030452487990260124,
-0.041828107088804245,
0.037915896624326706,
0.022551562637090683,
0.06598800420761108,
-0.048924535512924194,
0.000720980460755527,
-0.02450665459036827,
0.07058412581682205,
0.04368351027369499,
-0.02441910095512867,
-0.030252858996391296,
0.0011647273786365986,
-0.008179360069334507,
0.012592812068760395,
0.012849339284002781,
0.03509511798620224,
0.02597844786942005,
-0.034063003957271576,
0.044481825083494186,
-0.0025558331981301308,
0.0143049331381917,
0.004909723065793514,
0.015264539048075676,
-0.00358117138966918,
-0.0021612232085317373,
-0.007866348139941692,
0.04694204032421112,
0.02408614009618759,
0.004088567104190588,
-0.03458135202527046,
-0.01149819977581501,
-0.003089937148615718,
0.005659522954374552,
-0.00004553707913146354,
0.056116849184036255,
-0.001955687766894698,
0.010989829897880554,
-0.014160492457449436,
0.046400703489780426,
-0.010473191738128662,
0.021474771201610565,
0.012511789798736572,
-0.009049007669091225,
-0.018360793590545654,
0.037199415266513824,
-0.02310883067548275,
-0.0007518717902712524,
0.029771873727440834,
0.014910043217241764,
-0.02512103132903576,
-0.002500501461327076,
0.05140034481883049,
-0.0009418593836016953,
0.01827245019376278,
-0.017317239195108414,
-0.01257001981139183,
0.002339739818125963,
-0.0019223589915782213,
-0.07039107382297516,
0.024344228208065033,
-0.02295890636742115,
0.012885610572993755,
0.02380126155912876,
0.03023310750722885,
-0.028134707361459732,
0.04918482527136803,
-0.0029924195259809494,
-0.014076842926442623,
0.002036035293713212,
-0.023445917293429375,
-0.02015645243227482,
-0.0073045543394982815,
0.06127319857478142,
-0.026297029107809067,
-0.01614833064377308,
0.01728580892086029,
0.0017564889276400208,
-0.006478230934590101,
0.04081960394978523,
-0.04565151035785675,
-0.01632344350218773,
0.016537711024284363,
0.015333483926951885,
-0.018977122381329536,
0.03298230841755867,
0.04916469007730484,
-0.03701051324605942,
0.019499221816658974,
0.015282737091183662,
-0.03660086542367935,
-0.07122674584388733,
0.003202705644071102,
-0.012627056799829006,
0.0004058651684317738,
0.04974212124943733,
-0.0006791848572902381,
0.015949804335832596,
0.04335961490869522,
-0.07453614473342896,
-0.003385870484635234,
-0.010372872464358807,
-0.014980114065110683,
-0.0437527559697628,
-0.004012376070022583,
-0.03359520435333252,
0.05726543068885803,
0.03410065546631813,
0.06704214215278625,
0.016125263646245003,
0.055263079702854156,
-0.020716873928904533,
-0.0432777926325798,
0.01502729021012783,
0.01558922603726387,
-0.04214376583695412,
0.06911534070968628,
0.07298963516950607,
-0.03723930940032005,
0.02265087328851223,
0.018828071653842926,
0.02938622608780861,
0.06044010445475578,
-0.0518476776778698,
0.027973372489213943,
-0.015639331191778183,
0.025011230260133743,
-0.020222490653395653,
0.001931474544107914,
0.03330554440617561,
0.04126837104558945,
-0.02578977681696415,
0.016865303739905357,
-0.006817189510911703,
-0.019808027893304825,
0.009926928207278252,
-0.022249281406402588,
0.015522096306085587,
0.0282419566065073,
0.010278182104229927,
-0.0011804763926193118,
0.03582140803337097,
0.03975200280547142,
-0.0004517418274190277,
-0.013479430228471756,
-0.029595008119940758,
-0.03432527557015419,
-0.0017531306948512793,
0.020121581852436066,
0.037853583693504333,
-0.02524631842970848,
0.018203886225819588,
-0.006075853016227484,
-0.013225071132183075,
0.014525391161441803,
-0.0100626889616251,
-0.005278534255921841,
0.009607766754925251,
-0.018279695883393288,
0.01504979096353054,
0.013388263061642647,
-0.0004478542832657695,
-0.023882193490862846,
-0.04206133633852005,
0.028125282377004623,
0.04590035602450371,
0.009588557295501232,
-0.023484187200665474,
-0.021253379061818123,
-0.0067764450795948505,
-0.046944115310907364,
0.021422840654850006,
-0.017948269844055176,
0.04203973710536957,
-0.05937288701534271,
-0.02625208906829357,
-0.011355881579220295,
0.022233597934246063,
0.07070428133010864,
0.015754614025354385,
-0.008091744035482407,
0.02588258497416973,
-0.013417704030871391,
0.012954832054674625,
-0.035438571125268936,
0.011433550156652927,
0.00924562569707632,
-0.01393223088234663,
-0.012123873457312584,
0.008931278251111507,
-0.015701420605182648,
0.015191889367997646,
0.05346475914120674,
-0.03941043093800545,
-0.007455775979906321,
-0.0051356893964111805,
-0.02883131615817547,
0.03451097011566162,
-0.0001474499877076596,
0.013266636058688164,
0.05112738534808159,
-0.016986239701509476,
0.016863279044628143,
0.039138805121183395,
-0.022852955386042595,
-0.07953006029129028,
-0.006566237658262253,
-0.04211210459470749,
0.033666688948869705,
-0.019569646567106247,
-0.03467823192477226,
0.017553379759192467,
-0.03601617366075516,
0.02342335321009159,
0.0235064048320055,
-0.04065374284982681,
-0.0042610764503479,
0.05077749863266945,
0.007734307553619146,
0.034926798194646835,
-0.023654919117689133,
0.02684919163584709,
-0.005322656594216824,
0.008318068459630013,
-0.010976936668157578,
0.03848957270383835,
0.01566886156797409,
0.01798582449555397,
0.015825770795345306,
0.030860619619488716,
0.027526138350367546,
0.015180692076683044,
0.0012591915437951684,
0.02430867962539196,
-0.0411858931183815,
-0.016242466866970062,
0.004513380583375692,
-0.016245214268565178,
0.017230601981282234,
0.04553598538041115,
0.004824731964617968,
0.07699163258075714,
-0.030158694833517075,
0.004333333112299442,
-0.01097613014280796,
0.009053073823451996,
-0.024580875411629677,
-0.010779613628983498,
0.00777472835034132,
0.01659434475004673,
-0.04305339977145195,
-0.0036338414065539837,
-0.00915758777409792,
-0.0003851126239169389,
0.042728178203105927,
-0.03759605810046196,
-0.0029578327666968107,
-0.0195161160081625,
-0.016294224187731743,
0.0015181024791672826,
-0.03581692650914192,
-0.023162925615906715,
-0.03681124001741409,
0.019093262031674385,
-0.00030037283431738615,
-0.008671417832374573,
0.02124026045203209,
0.0012019420973956585,
0.0000963109778240323,
0.05964670330286026,
-0.027223171666264534,
0.005909499246627092,
0.00717173283919692,
0.044113047420978546,
-0.020789412781596184,
-0.033068735152482986
] |
<p>I read about Goodwin's "proof" that $\pi = 3.20$, it's BS and I know that. What I am wondering is whether his technique may have stumbled on something ( a warped space) years before Einstein. So I guess my question is this: </p>
<p>Is it possible that somewhere in the universe (say the vicinity of a neutron star) where (due to the warped space) the ratio of the circumference to the radius is measured as something other than 3.14...? </p>
<p>Following from that, is it possible that we only measure $\pi$ as 3.14... because of the way <em>our</em> local space time is curved by the earth?</p> | 1,510 | [
0.013260281644761562,
-0.024158604443073273,
0.00907430611550808,
-0.0392765998840332,
0.042426031082868576,
0.03431408852338791,
-0.05907903611660004,
-0.03237514570355415,
-0.012241698801517487,
0.00022716863895766437,
-0.017788460478186607,
0.021918583661317825,
0.0474974662065506,
0.03131314367055893,
0.015327933244407177,
0.02455946058034897,
-0.04124072939157486,
0.030069289728999138,
-0.016610611230134964,
-0.05102551728487015,
0.07419853657484055,
0.008913966827094555,
-0.026017719879746437,
-0.017185643315315247,
-0.011698208749294281,
-0.0009098354494199157,
0.030097655951976776,
0.005408210679888725,
0.007298843469470739,
0.058164000511169434,
0.03047160618007183,
-0.01307889074087143,
0.009801625274121761,
0.024344824254512787,
0.050249770283699036,
-0.0007376967114396393,
-0.009109115228056908,
0.008246418088674545,
0.020595015957951546,
0.06516864895820618,
-0.06671115010976791,
-0.026201650500297546,
0.0061380015686154366,
0.042721666395664215,
-0.025046300143003464,
0.036758895963430405,
-0.0042942482978105545,
-0.00931515172123909,
0.06852198392152786,
-0.03466631472110748,
0.06706111878156662,
0.0035511197056621313,
-0.018941562622785568,
0.04489338397979736,
-0.00710453512147069,
0.01557480450719595,
0.07977397739887238,
0.04017725959420204,
-0.03941027447581291,
-0.025277718901634216,
-0.028636986389756203,
-0.019010258838534355,
-0.019297059625387192,
0.005855929106473923,
-0.010931163094937801,
-0.0008789612911641598,
-0.05614791810512543,
-0.020769625902175903,
-0.023919591680169106,
-0.037763528525829315,
-0.03214534744620323,
0.02796022966504097,
0.019003968685865402,
0.00018101659952662885,
-0.0028039535973221064,
0.002986256731674075,
-0.01358645036816597,
-0.03621571138501167,
0.02645414136350155,
0.0053070541471242905,
-0.009932231158018112,
0.008624632842838764,
0.06700035184621811,
0.03138934075832367,
0.013400914147496223,
0.02062860131263733,
0.04934774711728096,
-0.032618165016174316,
0.004444670397788286,
0.058500781655311584,
0.0003169990668538958,
-0.015549317933619022,
0.01744200475513935,
-0.05509436875581741,
0.002131369663402438,
0.05694705992937088,
0.0011868198635056615,
0.028329690918326378,
-0.02303357981145382,
-0.013861133717000484,
0.017704980447888374,
-0.02147960662841797,
-0.02348311059176922,
0.079441137611866,
0.01634666882455349,
-0.05788453668355942,
-0.05326234921813011,
0.03683394566178322,
-0.008053929544985294,
-0.011290343478322029,
-0.03932054340839386,
0.010023577138781548,
-0.012650825083255768,
0.006105094216763973,
-0.0005229183589108288,
-0.031046835705637932,
-0.01427097711712122,
-0.03965011239051819,
0.06216929852962494,
0.03274276480078697,
0.0487421415746212,
-0.013826923444867134,
0.004173470661044121,
-0.0500660315155983,
-0.053217872977256775,
0.05660834163427353,
0.05204964801669121,
-0.0028102556243538857,
-0.015159823931753635,
0.028818404302001,
0.021720031276345253,
0.0008345859823748469,
0.024006839841604233,
0.01667316071689129,
0.042514633387327194,
0.011653969995677471,
-0.11752089858055115,
-0.04818262159824371,
0.05245498940348625,
0.013536888174712658,
-0.03726464882493019,
-0.04370613768696785,
0.04997175559401512,
0.005486141424626112,
0.0851779654622078,
0.014962086454033852,
0.0026419805362820625,
-0.004691039677709341,
0.03515975549817085,
0.011145105585455894,
-0.03078453242778778,
-0.022156957536935806,
0.01621963642537594,
-0.04937036707997322,
-0.005222045350819826,
-0.0575314424932003,
-0.026154976338148117,
0.016473472118377686,
0.017255811020731926,
-0.05097328871488571,
0.08859449625015259,
-0.02226749062538147,
-0.009862391278147697,
0.02582845836877823,
-0.03820417448878288,
-0.04394223541021347,
0.10105592012405396,
0.0528181716799736,
-0.05570188909769058,
0.037683166563510895,
0.029955865815281868,
0.029052259400486946,
0.008995692245662212,
-0.0006905384361743927,
0.038285993039608,
-0.022933803498744965,
-0.016962504014372826,
-0.007350259460508823,
-0.004380216356366873,
0.0078054433688521385,
-0.025102822110056877,
0.0024955994449555874,
0.015923909842967987,
0.0062444922514259815,
-0.006670766975730658,
0.05284246802330017,
0.0063874912448227406,
0.013390984386205673,
0.02729453146457672,
-0.04581268131732941,
0.007623239420354366,
-0.05148288235068321,
-0.025490228086709976,
0.029130395501852036,
-0.0005275533767417073,
0.021559085696935654,
0.04542100057005882,
0.02723972126841545,
-0.036250170320272446,
-0.06756608933210373,
-0.01128358580172062,
0.04916016384959221,
0.023630116134881973,
-0.021701686084270477,
0.029602233320474625,
0.03094395250082016,
0.01621624268591404,
-0.04416388273239136,
-0.01771758683025837,
0.014795907773077488,
-0.017294567078351974,
0.019680770114064217,
-0.022546371445059776,
0.013599925674498081,
-0.018541710451245308,
0.011368243023753166,
0.011351963505148888,
0.010439095087349415,
-0.027127811685204506,
0.05946524813771248,
-0.011865266598761082,
0.07249263674020767,
-0.009520305320620537,
-0.017223535105586052,
0.002288330579176545,
0.018958691507577896,
0.018652424216270447,
0.008307195268571377,
-0.010419285856187344,
-0.04461069405078888,
-0.06214743107557297,
-0.03861469775438309,
0.027106590569019318,
0.03179781883955002,
-0.019356179982423782,
0.013930276967585087,
0.049439020454883575,
0.05385696887969971,
0.0033788869623094797,
0.0002129450294887647,
-0.006942530162632465,
-0.037516720592975616,
-0.007307137828320265,
0.03404711186885834,
0.016360832378268242,
0.031522300094366074,
0.011723197996616364,
0.010655064135789871,
-0.012441297993063927,
-0.014299312606453896,
-0.009539462625980377,
-0.01738675870001316,
-0.03074747882783413,
0.011019385419785976,
0.02288888767361641,
-0.0032349443063139915,
0.0368947871029377,
-0.03654360771179199,
0.03259454667568207,
0.013327267952263355,
-0.013537525199353695,
0.008419184014201164,
-0.050776317715644836,
0.0023266952484846115,
0.018400605767965317,
0.012007382698357105,
-0.04841801896691322,
-0.004179392475634813,
0.017142899334430695,
-0.045108675956726074,
0.0022650668397545815,
-0.015060302801430225,
0.019073838368058205,
-0.04060399904847145,
-0.0225983839482069,
0.020559262484312057,
0.005481929983943701,
0.015857886523008347,
-0.019237229600548744,
-0.03486739471554756,
0.023235371336340904,
-0.023016445338726044,
-0.02789052203297615,
0.010823107324540615,
-0.04814327135682106,
0.03532938286662102,
-0.002432477194815874,
-0.03245855122804642,
0.020152058452367783,
0.004561447072774172,
0.08310717344284058,
0.017683083191514015,
-0.02752840146422386,
-0.02241695299744606,
-0.008226164616644382,
-0.012831623665988445,
-0.01493006944656372,
-0.00999809242784977,
-0.005151728168129921,
0.03989256173372269,
0.019433066248893738,
-0.030246907845139503,
0.0008156865951605141,
-0.057607557624578476,
-0.014247884973883629,
-0.02732817642390728,
-0.009771060198545456,
0.015844125300645828,
-0.049809545278549194,
0.036766164004802704,
0.02512814849615097,
-0.0373530313372612,
-0.0047106570564210415,
-0.036567945033311844,
-0.035954732447862625,
0.050611063838005066,
0.016440220177173615,
0.04487673193216324,
-0.017326196655631065,
-0.005512360017746687,
0.0695304349064827,
0.03374683856964111,
-0.04263170436024666,
-0.03874647617340088,
0.02130717970430851,
0.024571316316723824,
-0.009283951483666897,
-0.010669583454728127,
0.0012882626615464687,
-0.021434446796774864,
0.02791021019220352,
0.02916843630373478,
0.03872400149703026,
0.023088254034519196,
0.024160439148545265,
-0.00023836083710193634,
-0.016701675951480865,
-0.029819071292877197,
0.002608680631965399,
0.050097182393074036,
0.028934309259057045,
-0.006005014292895794,
-0.026950638741254807,
0.006265886593610048,
0.03548929840326309,
0.006501405034214258,
-0.05292171239852905,
0.03723885118961334,
0.004546714946627617,
0.037457216531038284,
0.0037100855261087418,
-0.0025785514153540134,
-0.020199671387672424,
0.029367614537477493,
0.028527304530143738,
0.020642006769776344,
0.042342934757471085,
0.012094146572053432,
0.0020332951098680496,
0.013458753004670143,
-0.008870402351021767,
-0.0031347181648015976,
-0.012989317066967487,
-0.012765496037900448,
-0.011112986132502556,
0.03665132448077202,
-0.016115866601467133,
-0.023987019434571266,
0.059259526431560516,
0.05943556874990463,
0.03227224573493004,
-0.027760948985815048,
-0.02122102677822113,
0.032973937690258026,
-0.07221056520938873,
-0.014704371802508831,
0.005086901132017374,
0.03625636175274849,
-0.004365829285234213,
0.012665610760450363,
0.045871805399656296,
0.023496707901358604,
0.015863796696066856,
-0.029623327776789665,
-0.07621844857931137,
0.01675643026828766,
-0.03704492375254631,
0.007656259462237358,
-0.01547505147755146,
-0.032015252858400345,
-0.006750337313860655,
-0.007817111909389496,
0.020556317642331123,
0.001723067369312048,
-0.03064829111099243,
-0.05193931609392166,
0.015072577632963657,
-0.008944730274379253,
-0.031843334436416626,
-0.02502518519759178,
0.08032072335481644,
0.06845279783010483,
-0.01687960885465145,
0.00677989237010479,
0.02477329410612583,
-0.03333134204149246,
-0.0404614619910717,
-0.01038652379065752,
0.02438415214419365,
0.0016594516346231103,
0.02840832620859146,
0.03401635214686394,
0.009862326085567474,
0.00044972807518206537,
0.01120713260024786,
0.02472579851746559,
0.027153488248586655,
0.01977294683456421,
-0.02424166537821293,
-0.05284528806805611,
-0.01250384096056223,
-0.02492396906018257,
0.008159969933331013,
0.06322020292282104,
0.006774612702429295,
0.005376716144382954,
0.015432829037308693,
0.005627599079161882,
-0.022779539227485657,
-0.0011360133066773415,
0.08255942910909653,
-0.05179031193256378,
-0.055898167192935944,
-0.04245755448937416,
-0.05950098857283592,
-0.002330210991203785,
-0.013652035035192966,
0.009552250616252422,
-0.00493591045960784,
-0.011622551828622818,
0.020594539120793343,
0.04210089147090912,
-0.002142665209248662,
-0.01724199578166008,
0.024519890546798706,
-0.008313680067658424,
-0.0005239595775492489,
-0.019617894664406776,
0.022492801770567894,
-0.000043998028559144586,
0.019227227196097374,
0.0628076046705246,
0.012336023151874542,
-0.0018318642396479845,
-0.09685124456882477,
-0.015218821354210377,
0.03550779074430466,
0.02692657895386219,
-0.02868187427520752,
0.0022198869846761227,
-0.08115947991609573,
0.001374696264974773,
0.06647014617919922,
-0.015598859637975693,
-0.002280043438076973,
-0.014138131402432919,
-0.02876731939613819,
-0.030810469761490822,
-0.01533106155693531,
0.0031385926995426416,
0.01445663720369339,
-0.009646644815802574,
0.0013646448496729136,
-0.0328017883002758,
0.013407011516392231,
0.00014151369396131486,
0.0034036661963909864,
0.017475299537181854,
0.043105632066726685,
0.06481154263019562,
0.00841501634567976,
-0.0019152805907651782,
0.02393759973347187,
-0.018674956634640694,
-0.03604291379451752,
0.021223710849881172,
0.015096554532647133,
0.0035980348475277424,
0.036320991814136505,
-0.025303799659013748,
-0.07631850987672806,
0.03929673135280609,
-0.017421163618564606,
-0.004930119030177593,
0.026849692687392235,
-0.05175558105111122,
0.008893953636288643,
0.0016734657110646367,
-0.009708606638014317,
0.02535841427743435,
0.0361894927918911,
0.005710949655622244,
-0.008560019545257092,
-0.040437739342451096,
0.032483890652656555,
-0.036228105425834656,
0.00169735262170434,
-0.02112700417637825,
0.006969574373215437,
-0.042657140642404556,
0.03841709345579147,
0.013992419466376305,
0.0009844624437391758,
0.031119130551815033,
-0.0344260148704052,
0.008864965289831161,
0.00010576975182630122,
0.005685742013156414,
0.002918080659583211,
-0.008057588711380959,
0.0075066424906253815,
0.033948078751564026,
-0.031451720744371414,
0.01859304867684841,
0.02784387208521366,
0.002679905155673623,
0.034675613045692444,
-0.009733474813401699,
-0.0002697703894227743,
0.03145522624254227,
-0.0127092394977808,
0.04340720549225807,
-0.013160639442503452,
0.041128259152173996,
-0.0042024399153888226,
-0.013294360600411892,
0.019194573163986206,
-0.04217694327235222,
-0.008782630786299706,
-0.02395504154264927,
-0.04131830856204033,
0.043106984347105026,
-0.0529802180826664,
-0.005441196262836456,
-0.0006200061761774123,
0.03844695910811424,
-0.09573236852884293,
-0.011534414254128933,
0.046483732759952545,
-0.001114245387725532,
-0.017756903544068336,
-0.012226016260683537,
-0.03474648296833038,
-0.034677550196647644,
-0.004253724589943886,
0.009338410571217537,
0.0576014444231987,
0.007417564745992422,
-0.021584149450063705,
-0.02167585678398609,
0.039329644292593,
0.08840487152338028,
-0.03311081975698471,
-0.007608944084495306,
-0.001744682784192264,
0.007105331867933273,
-0.00010094482422573492,
0.013061785139143467,
0.06659237295389175,
-0.03321504220366478,
-0.03652887046337128,
-0.03925727307796478,
-0.029104281216859818,
-0.01900426484644413,
-0.020895713940262794,
-0.028924448415637016,
0.04610802233219147,
-0.00822732225060463,
0.01894349232316017,
-0.013643339276313782,
0.031706444919109344,
0.0009199560154229403,
-0.024917572736740112,
-0.04375753551721573,
0.0042939805425703526,
-0.024996545165777206,
-0.020517531782388687,
0.03926999866962433,
0.022688116878271103,
0.0013004242209717631,
-0.008681358769536018,
0.02169922925531864,
0.021523399278521538,
-0.06308817118406296,
0.03283500298857689,
-0.031359270215034485,
0.02222495526075363,
-0.020067518576979637,
0.023184023797512054,
0.019622689113020897,
0.009224108420312405,
-0.05375354364514351,
-0.024613825604319572,
-0.014633312821388245,
0.007624109275639057,
0.07537493854761124,
-0.0016102842055261135,
0.06850798428058624,
0.034041281789541245,
-0.046427011489868164,
0.0013412288390100002,
-0.001292465953156352,
-0.02004174143075943,
0.006709263660013676,
-0.026115180924534798,
0.05897589772939682,
-0.032419342547655106,
0.017509853467345238,
-0.0034347856417298317,
0.026354987174272537,
-0.02557685784995556,
0.011580157093703747,
-0.014431406743824482,
0.021697688847780228,
0.024603979662060738,
-0.008409302681684494,
-0.030306177213788033,
0.02974824421107769,
0.010425734333693981,
0.020145392045378685,
-0.007347990293055773,
-0.0064817555248737335,
0.024841690436005592,
0.012328880839049816,
0.05426323786377907,
-0.01828649826347828,
-0.035688165575265884,
-0.035593289881944656,
-0.03869089111685753,
-0.004296126309782267,
0.0063041518442332745,
0.026959404349327087,
0.017656533047556877,
0.0350213423371315,
0.028388330712914467,
0.01756426878273487,
-0.013462958857417107,
-0.09772123396396637,
-0.03903820365667343,
-0.05529516562819481,
-0.0034774625673890114,
0.03965982422232628,
0.0178496353328228,
-0.050751909613609314,
0.01950308308005333,
-0.0033698673360049725,
0.033993083983659744,
0.04427305981516838,
0.038307398557662964,
-0.0601971298456192,
0.0612199567258358,
-0.033322516828775406,
0.007590698078274727,
-0.037873249500989914,
-0.0067689609713852406,
0.09911444038152695,
0.05339161679148674,
-0.0146830715239048,
-0.07496248930692673,
0.03996267169713974,
-0.02646302804350853,
-0.002112682443112135,
-0.03593798354268074,
0.013837053440511227,
-0.04929307475686073,
-0.029325097799301147,
0.03218081220984459,
0.05200037732720375,
-0.0029497782234102488,
-0.0410192534327507,
0.055574387311935425,
-0.015392721630632877,
-0.04262882098555565,
0.009509287774562836,
0.029068881645798683,
0.030444500967860222,
-0.01816079393029213,
-0.03290913626551628,
0.06341280788183212,
-0.033323708921670914,
0.031170206144452095,
0.0026633793022483587,
-0.01805238611996174,
-0.0219865869730711,
-0.004915733356028795,
-0.04758666455745697,
0.02649640664458275,
0.01798434741795063,
-0.03361474350094795,
-0.04431508481502533,
-0.021110735833644867,
-0.02104041539132595,
-0.019531065598130226,
0.02478005737066269,
0.04840924218297005,
-0.006672582123428583,
0.008452855050563812,
-0.018642250448465347,
0.015010597184300423,
-0.04123609885573387,
-0.009447804652154446,
-0.024021513760089874,
0.04342411831021309,
-0.010768386535346508,
-0.008535545319318771,
0.011171470396220684,
-0.001473334850743413,
-0.0024045349564403296,
-0.03795452043414116,
0.0239417664706707,
-0.03576524183154106,
0.009140650741755962,
-0.01881369948387146,
-0.07937860488891602,
-0.011863425374031067,
0.02575274556875229,
-0.02535145729780197,
0.06319286674261093,
0.00042954302625730634,
-0.0018565079662948847,
0.03249851614236832,
-0.02174699306488037,
0.03530603647232056,
0.01995627023279667,
-0.00487854890525341,
-0.014925540424883366,
0.004956529010087252,
-0.006617836654186249,
-0.004477312788367271,
0.017466844990849495,
-0.005599537398666143,
0.01933804154396057,
-0.01741555891931057,
-0.0050376844592392445,
-0.032082706689834595,
-0.03542531281709671,
0.03443388268351555,
-0.04843056574463844,
-0.012129179202020168,
-0.050727684050798416,
-0.006060073152184486,
0.013381721451878548,
0.053614214062690735,
-0.012025419622659683,
-0.023383188992738724,
-0.017000945284962654,
0.015672914683818817,
0.02609504573047161,
-0.02906751073896885,
0.011212586425244808,
-0.00964419636875391,
-0.06053518131375313,
0.010704085230827332,
-0.042561233043670654,
0.0442192368209362,
0.03073832206428051,
-0.004022444132715464,
0.029522579163312912,
0.024549735710024834,
-0.024623673409223557,
-0.022251464426517487,
0.006073766387999058,
-0.020050331950187683,
0.013255173340439796,
-0.013329100795090199,
0.0021939422003924847,
-0.039040468633174896,
-0.026077838614583015,
-0.041063323616981506,
0.0013384281191974878,
-0.03242787718772888,
0.0024978849105536938,
-0.01443724986165762,
0.025334369391202927,
-0.005897251423448324,
-0.00041011039866134524,
-0.04924652352929115,
0.011330229230225086,
-0.031118642538785934,
-0.008637122809886932,
-0.0006160373450256884,
0.00007474149606423452,
0.022073330357670784,
0.06839373707771301,
-0.02562919817864895,
-0.05733049660921097,
0.02131224237382412,
0.00608154758810997,
-0.04667581990361214,
0.014712601900100708,
0.025675153359770775,
0.03148707002401352,
0.03313145413994789,
-0.05061290040612221,
-0.03347334265708923,
0.02818874642252922,
-0.06245102360844612,
-0.08112486451864243,
0.044406019151210785,
-0.023594144731760025,
0.014922170899808407,
0.019091680645942688,
0.008148031309247017,
-0.014044960029423237,
0.07094574719667435,
-0.000628563342615962,
0.019823988899588585,
0.012046538293361664,
0.011723650619387627,
0.015146452933549881,
0.002727833343669772,
0.018771063536405563,
-0.03081047721207142,
-0.01618359424173832,
0.03294803202152252,
-0.010687313042581081,
0.002924947766587138,
0.015299987979233265,
0.0006973654963076115,
-0.019887739792466164,
0.00455863680690527,
0.00006127500819275156,
-0.0024944308679550886,
0.01823933981359005,
0.04584150016307831,
-0.06444034725427628,
0.011651400476694107,
0.04926535487174988,
0.018390614539384842,
-0.08036256581544876,
0.0281062014400959,
0.0029397637117654085,
0.005606414750218391,
-0.0030614077113568783,
-0.04679029434919357,
0.004102999810129404,
0.007637587375938892,
-0.06005321443080902,
0.037148553878068924,
-0.01735466904938221,
-0.013068059459328651,
-0.04101797193288803,
-0.039416130632162094,
0.008596763014793396,
0.0330624096095562,
0.05981255695223808,
0.04033985361456871,
-0.010691504925489426,
0.009590644389390945,
-0.008616453036665916,
-0.01680307276546955,
-0.008796884678304195,
-0.0070067341439425945,
0.020552849397063255,
-0.018528588116168976,
0.05450352653861046,
-0.033020973205566406,
-0.029890358448028564,
0.017582735046744347,
-0.006078428588807583,
-0.010512186214327812,
-0.012023821473121643,
-0.023767881095409393,
-0.007830432616174221,
-0.005090523976832628,
0.03264010325074196,
-0.02094101719558239,
0.007195548620074987,
0.034709807485342026,
-0.015196123160421848,
0.028182106092572212,
0.018830548971891403,
-0.019025102257728577,
0.003179582767188549,
-0.02991134114563465,
-0.006015651393681765,
-0.008996550925076008,
0.004570458550006151,
-0.014910529367625713,
0.02007167786359787,
0.03242234140634537,
0.01986725442111492,
-0.03824260085821152,
0.04025520756840706,
-0.020026355981826782,
-0.007319079712033272,
0.029031185433268547,
0.014881597831845284,
-0.023706354200839996,
0.05521364137530327,
-0.03195710480213165,
-0.0030811545439064503,
0.012337366119027138,
0.0009691803134046495,
-0.013574512675404549,
-0.01572604849934578,
0.0028139667119830847,
0.016999952495098114,
-0.012560838833451271,
0.02599257603287697,
-0.017282836139202118,
-0.026103513315320015,
0.018511688336730003,
0.0182730071246624,
0.02378471940755844,
0.010931992903351784,
0.01349994819611311,
-0.021541394293308258,
-0.05686301738023758,
0.028377842158079147,
0.007672939915210009,
0.019799506291747093,
-0.016578519716858864,
0.008141724392771721,
-0.005153266247361898,
0.004538348875939846,
0.03501954302191734,
-0.016096366569399834,
0.016607001423835754,
0.017668331041932106,
-0.024023400619626045,
-0.0053249867632985115,
-0.06641358137130737,
-0.006693425588309765,
0.008077843114733696,
-0.018414616584777832,
0.006844496354460716,
0.0033294844906777143,
-0.025505902245640755,
-0.033921997994184494,
0.004228936042636633,
0.014954223297536373,
0.018570847809314728,
0.0022673411294817924,
-0.0228740144520998,
0.015501093119382858,
-0.001861297176219523,
0.027920173481106758,
0.05297332629561424,
0.01051998045295477,
0.005082361400127411,
0.03710910677909851,
-0.01422422006726265,
-0.05130777135491371,
0.017745669931173325,
-0.0001713700039545074,
-0.019571272656321526,
-0.03417003154754639,
-0.001169546158052981,
-0.018540585413575172,
-0.004568297881633043,
-0.027559513226151466,
0.04980603605508804,
-0.025985857471823692,
-0.0042461371049284935,
0.020950954407453537,
-0.014230648055672646,
0.022982992231845856,
0.01484417449682951,
-0.013863688334822655,
0.009684556163847446,
0.012361054308712482,
0.014074119739234447,
0.043755173683166504,
0.06705265492200851,
0.0026393779553472996,
-0.0004635062941815704,
0.024316348135471344,
0.01630408503115177,
0.012923536822199821,
-0.015110425651073456,
0.1114891767501831,
-0.03658230975270271,
-0.0045327492989599705,
-0.0074816374108195305,
-0.004101778380572796,
0.00014204859326127917,
0.030830124393105507,
-0.03653934597969055,
0.09640804678201675,
0.014859163202345371,
0.004109680186957121,
-0.0045885927975177765,
-0.028516598045825958,
-0.006681353319436312,
0.04942261800169945,
0.018225539475679398,
0.022549904882907867,
-0.019251439720392227,
-0.016149437054991722,
-0.012916400097310543,
0.0048312717117369175,
0.03666851297020912,
-0.02579139731824398,
-0.0011868791189044714,
0.00971859972923994,
-0.007478058338165283,
0.037833187729120255,
-0.0320093110203743,
-0.0009131925762630999,
-0.022999169304966927,
0.016663221642374992,
0.025959329679608345,
0.05064310505986214,
-0.021246807649731636,
-0.009665273129940033,
0.002973852213472128,
0.030341636389493942,
-0.0764673724770546,
-0.034127239137887955,
-0.015387419611215591,
0.01126842200756073,
-0.004259830340743065,
-0.01890154369175434
] |
<p>How can I recognize clearly when I deal with capacitors in parallel or capacitors in series? Can follow a "rule" or a intuitive method?
I have to do difficult exercises regarding system of capacitors so I must understand when I have capacitors in parallel or in series. Can you explain me in a simple way?</p> | 1,511 | [
-0.012794229201972485,
-0.027928872033953667,
-0.02367217279970646,
0.023964188992977142,
0.019725870341062546,
0.000009938133189280052,
0.00712192477658391,
0.0027368594892323017,
0.02259240858256817,
-0.004927839618176222,
0.04006391018629074,
0.01993047073483467,
0.03516295179724693,
0.019644543528556824,
0.016997169703245163,
-0.018711870536208153,
-0.0145268514752388,
-0.020643245428800583,
-0.002883340697735548,
0.002862640656530857,
-0.0017737190937623382,
0.022180069237947464,
0.023802269250154495,
0.00033897781395353377,
0.004906811751425266,
0.038185812532901764,
0.023912463337183,
0.007479133550077677,
0.021368365734815598,
-0.0002983104786835611,
-0.0215911902487278,
-0.048291221261024475,
-0.007597926072776318,
0.033707164227962494,
0.01821613684296608,
-0.01721700094640255,
0.01709146238863468,
-0.04928237572312355,
0.003493549535050988,
0.021495429798960686,
-0.024785859510302544,
-0.024184612557291985,
-0.00230286899022758,
0.03180624172091484,
-0.043289363384246826,
-0.010324119590222836,
0.01898219995200634,
-0.011488018557429314,
0.002891069045290351,
-0.08836568146944046,
0.0888480618596077,
-0.0038469790015369654,
0.0668981671333313,
0.05025094375014305,
-0.0007485700771212578,
0.018415769562125206,
0.02457447350025177,
0.05619880557060242,
-0.04068371653556824,
-0.025951746851205826,
0.0026606759056448936,
-0.002877430524677038,
0.0055343820713460445,
-0.037874314934015274,
-0.03845746070146561,
0.06618908792734146,
0.013958565890789032,
-0.008731218986213207,
-0.011207775212824345,
-0.007180155720561743,
0.012953139841556549,
0.018290335312485695,
0.04678531363606453,
-0.03917090222239494,
-0.006077914964407682,
-0.023590965196490288,
0.002437045332044363,
0.022117629647254944,
0.052439797669649124,
0.05398029088973999,
0.008284753188490868,
0.04389446973800659,
0.03877361863851547,
0.017650945112109184,
0.028589900583028793,
-0.06898341327905655,
0.050794169306755066,
0.01484412420541048,
0.021745335310697556,
-0.018554560840129852,
-0.002006542170420289,
0.0013342422898858786,
0.058245014399290085,
-0.00044283911120146513,
-0.03911419212818146,
0.025198645889759064,
-0.008472776040434837,
0.025311050936579704,
0.005841047503054142,
-0.013576572760939598,
0.04574208706617355,
-0.02511170506477356,
0.03353283926844597,
0.04922019690275192,
0.007808657828718424,
0.010858534835278988,
-0.029458893463015556,
0.02571900002658367,
0.010429850779473782,
-0.01849452406167984,
-0.03745351731777191,
0.04782593995332718,
0.04162027686834335,
0.04147367551922798,
-0.0026997672393918037,
0.03652486205101013,
0.023835759609937668,
0.013601172715425491,
0.05182778090238571,
0.05007995292544365,
0.05798281356692314,
-0.03887181356549263,
0.03388398513197899,
-0.01777523010969162,
-0.07969177514314651,
0.009287472814321518,
-0.0068551949225366116,
-0.006990703288465738,
-0.010714218020439148,
0.04495393857359886,
-0.007324822712689638,
-0.016376832500100136,
-0.021346958354115486,
-0.01808222383260727,
0.056800246238708496,
0.004961618687957525,
-0.06600025296211243,
-0.026320379227399826,
0.02428615465760231,
-0.04331139102578163,
-0.008253244683146477,
-0.0669383555650711,
0.045213017612695694,
0.019067581743001938,
0.06205679848790169,
-0.00479256734251976,
-0.009876815602183342,
0.01737469621002674,
0.02934711053967476,
0.0024013419169932604,
-0.01769043318927288,
-0.04335028678178787,
0.004588610492646694,
-0.012891408056020737,
0.022445131093263626,
-0.0495213158428669,
0.01230738963931799,
0.06399606168270111,
0.016442596912384033,
-0.021617906168103218,
0.05355941504240036,
0.014380179345607758,
-0.026480253785848618,
0.013789338991045952,
-0.03691632300615311,
-0.032406777143478394,
0.055848393589258194,
-0.03677871450781822,
0.028808798640966415,
0.04409874603152275,
0.0336395688354969,
0.018351035192608833,
-0.002477531787008047,
0.031563978642225266,
0.0561591275036335,
0.00205318839289248,
-0.013438668102025986,
-0.009160887449979782,
-0.00604172283783555,
-0.016118574887514114,
-0.05976458638906479,
-0.03190493956208229,
0.007929426617920399,
0.02627665176987648,
0.011988626793026924,
0.028211381286382675,
0.013371795415878296,
-0.043457187712192535,
-0.01437284704297781,
-0.021432099863886833,
-0.026767423376441002,
-0.07103178650140762,
0.03312230110168457,
-0.01986372098326683,
-0.026024628430604935,
0.02687481790781021,
0.00005771591895609163,
-0.003677520202472806,
-0.03771517053246498,
-0.008040002547204494,
-0.01891622319817543,
0.02108331210911274,
-0.0408538356423378,
-0.017212795093655586,
0.03977733105421066,
0.02499988116323948,
0.028838124126195908,
0.030329369008541107,
0.046410754323005676,
-0.0571662075817585,
0.009529819712042809,
0.03368096053600311,
-0.008465384133160114,
0.015002910979092121,
0.0188047606498003,
0.00294100190512836,
0.0006297806976363063,
-0.0001482368679717183,
-0.008810712024569511,
0.038924701511859894,
-0.03107636794447899,
0.0574578158557415,
0.08980297297239304,
0.0025794561952352524,
0.002750125015154481,
0.01528474036604166,
0.024677937850356102,
-0.0048272996209561825,
0.0076934583485126495,
-0.0023810267448425293,
-0.05304739251732826,
0.012088216841220856,
0.040670908987522125,
0.017813364043831825,
-0.07963665574789047,
0.01725596748292446,
0.054840948432683945,
0.00830100942403078,
0.03291553258895874,
0.044724464416503906,
-0.03196648135781288,
-0.010091551579535007,
0.007311144378036261,
-0.0011148357298225164,
-0.00281823449768126,
0.003523588180541992,
-0.004241089802235365,
0.05943369120359421,
0.02246377430856228,
-0.01720476523041725,
-0.03595007583498955,
0.04089739918708801,
-0.013115433044731617,
0.05961490049958229,
0.06617169827222824,
-0.04844034090638161,
0.018197400495409966,
-0.03682735189795494,
0.020198918879032135,
-0.008109193295240402,
0.007924550212919712,
0.0014486957807093859,
0.026743512600660324,
0.010117262601852417,
0.010655682533979416,
0.0018446582835167646,
-0.06361237168312073,
-0.03317028284072876,
0.0297886673361063,
-0.062395066022872925,
0.03010520525276661,
-0.020227862522006035,
-0.024105872958898544,
-0.014242752455174923,
-0.012088126502931118,
0.028745455667376518,
0.019346389919519424,
0.08773434907197952,
-0.034620676189661026,
-0.03231438249349594,
-0.0403384231030941,
-0.03886053338646889,
0.047501951456069946,
-0.05313548073172569,
-0.03676090016961098,
0.019657164812088013,
-0.03372255340218544,
-0.024927303194999695,
0.05063493177294731,
-0.015086907893419266,
-0.010743390768766403,
0.017179574817419052,
-0.020734190940856934,
-0.0539717823266983,
-0.023708274587988853,
0.008039084263145924,
0.04326307401061058,
-0.020060203969478607,
-0.013844164088368416,
0.06337660551071167,
-0.022017214447259903,
-0.04979722574353218,
-0.016582420095801353,
-0.022775528952479362,
-0.020540326833724976,
0.0008480619289912283,
0.0008798926137387753,
0.02237674966454506,
-0.031575944274663925,
-0.015776092186570168,
-0.010719644837081432,
-0.0467715710401535,
-0.024384545162320137,
0.0039109583012759686,
-0.05761551111936569,
0.009200493805110455,
-0.009995763190090656,
0.048081330955028534,
0.020707126706838608,
-0.05162534862756729,
0.05010426416993141,
-0.01225539855659008,
-0.0002290306583745405,
0.005706604104489088,
-0.012990745715796947,
-0.033705852925777435,
-0.0208901297301054,
0.013441544026136398,
0.051540691405534744,
-0.005023687146604061,
0.005801824387162924,
0.04886023700237274,
0.024033797904849052,
0.09257721155881882,
0.0005953750223852694,
0.009017624892294407,
-0.025146424770355225,
0.010645393282175064,
-0.039131153374910355,
0.05852881446480751,
0.008328806608915329,
-0.04235456511378288,
0.010055925697088242,
0.001778814010322094,
0.011504556983709335,
0.04020939767360687,
0.012452752329409122,
0.009593862108886242,
-0.03983120620250702,
-0.014750346541404724,
-0.03470996394753456,
0.026059411466121674,
0.012297927401959896,
0.03581255301833153,
-0.005661012139171362,
0.03220806270837784,
0.03770909830927849,
-0.060564037412405014,
0.008729415945708752,
0.038641221821308136,
0.027766861021518707,
-0.03185638040304184,
-0.03637876734137535,
0.0318438820540905,
-0.03634965047240257,
0.048464011400938034,
-0.04203846678137779,
-0.02787068486213684,
0.049423422664403915,
-0.008721643127501011,
0.005422688089311123,
0.02430228516459465,
-0.05732777714729309,
0.005831985734403133,
-0.07284120470285416,
0.005611033644527197,
-0.010771715082228184,
0.027944691479206085,
-0.01438151765614748,
0.052827466279268265,
0.029970455914735794,
-0.024905536323785782,
0.021797096356749535,
-0.010245499201118946,
-0.07378414273262024,
0.017564035952091217,
0.012231804430484772,
0.020196583122015,
-0.02895703911781311,
0.011414186097681522,
0.008196829818189144,
-0.02587895281612873,
-0.007785633206367493,
-0.028341950848698616,
-0.0045371768064796925,
-0.041378993541002274,
0.053387001156806946,
-0.0018284033285453916,
-0.0047258236445486546,
-0.032722122967243195,
-0.029316507279872894,
0.013107824139297009,
-0.025189433246850967,
0.03407178074121475,
0.03555977717041969,
-0.01943732425570488,
0.019623372703790665,
0.00409289263188839,
0.009149639867246151,
0.025750039145350456,
-0.011275607161223888,
0.01935376040637493,
0.023006798699498177,
0.011045586317777634,
-0.016501110047101974,
0.01418792363256216,
0.06645525246858597,
0.02000759355723858,
-0.06140877678990364,
-0.015137280337512493,
-0.06463111937046051,
-0.012249071151018143,
-0.029956616461277008,
0.04598008468747139,
0.00621072668582201,
-0.0002006679424084723,
0.0513295903801918,
0.01542661339044571,
-0.02229173295199871,
0.06209380924701691,
0.039531316608190536,
0.024137942120432854,
-0.052197717130184174,
-0.0642201378941536,
-0.018386831507086754,
-0.029037918895483017,
0.019823577255010605,
0.025377264246344566,
0.021705614402890205,
-0.04096345230937004,
-0.006795775145292282,
0.033727094531059265,
0.021771453320980072,
0.006117339711636305,
0.02795911394059658,
0.00012651781435124576,
0.010026926174759865,
0.008741949684917927,
-0.023539861664175987,
0.01120015699416399,
0.011699107475578785,
0.019967181608080864,
0.01884230598807335,
-0.039255764335393906,
-0.07224403321743011,
-0.013424204662442207,
0.05032438784837723,
0.01848554238677025,
-0.03823760896921158,
0.018848713487386703,
-0.025146881118416786,
-0.009099913761019707,
0.07078944146633148,
-0.045057643204927444,
0.03407434746623039,
-0.02803850919008255,
0.02256743051111698,
-0.04079553484916687,
-0.0067892721854150295,
-0.0076511618681252,
0.04788831248879433,
-0.00964431930333376,
0.034109313040971756,
-0.02786293998360634,
0.014271538704633713,
-0.05179461091756821,
-0.017713945358991623,
0.0480622835457325,
0.07551977783441544,
0.001544744591228664,
-0.014070380479097366,
0.017407407984137535,
0.02572270669043064,
-0.016434360295534134,
-0.0478382371366024,
0.016897061839699745,
-0.022168708965182304,
0.00015115676796995103,
0.04459214583039284,
-0.02470526471734047,
-0.02773267775774002,
-0.004938803613185883,
-0.016315491870045662,
0.01421965379267931,
-0.0026156813837587833,
-0.0013861489715054631,
0.04864306375384331,
0.031014392152428627,
-0.015077250078320503,
0.0781034603714943,
-0.023139474913477898,
-0.030835416167974472,
-0.0012675914913415909,
-0.005655442364513874,
-0.009064069017767906,
-0.022395750507712364,
-0.017230624333024025,
0.004920023027807474,
0.020996179431676865,
-0.06230327486991882,
0.031915269792079926,
-0.027476243674755096,
0.050167422741651535,
-0.02452235110104084,
-0.012999252416193485,
0.007886430248618126,
0.023053253069519997,
0.000907539448235184,
-0.0065458910539746284,
-0.01891903579235077,
0.013807886280119419,
0.00624494906514883,
-0.021274326369166374,
0.00030897962278686464,
-0.009908327832818031,
0.02159283310174942,
-0.008702090010046959,
0.016383029520511627,
-0.006526270415633917,
-0.05841139331459999,
-0.01312193088233471,
-0.0004072940500918776,
-0.043220799416303635,
0.03809376060962677,
0.024738138541579247,
-0.0017268649535253644,
0.017200902104377747,
-0.03909830003976822,
-0.0714753046631813,
0.01635863073170185,
0.001955997897312045,
0.0015295477351173759,
-0.08657917380332947,
0.03695026412606239,
0.0015405475860461593,
0.010671893134713173,
-0.05805749446153641,
-0.0816853940486908,
0.02138620987534523,
0.05012275651097298,
0.015670841559767723,
-0.000006605165253859013,
0.030627747997641563,
0.027566438540816307,
-0.033323273062705994,
-0.002740604104474187,
0.059685152024030685,
-0.032032229006290436,
-0.02729751169681549,
-0.025592586025595665,
0.013987431302666664,
0.08207817375659943,
0.022315453737974167,
-0.009020294062793255,
-0.012677241116762161,
-0.05437776818871498,
-0.009032043628394604,
-0.02897333726286888,
0.007171222008764744,
-0.03016692027449608,
-0.029074925929307938,
-0.017910024151206017,
-0.005525621585547924,
0.05735202133655548,
-0.04312850907444954,
-0.00663449801504612,
0.021359441801905632,
0.0026545131113380194,
-0.028150685131549835,
-0.008013278245925903,
0.0074370685033500195,
-0.02506266161799431,
0.012858475558459759,
0.03244270756840706,
-0.04678478464484215,
-0.02645387500524521,
-0.027979694306850433,
-0.015355769544839859,
0.03415951877832413,
-0.00438929907977581,
-0.0037407323252409697,
0.02056955359876156,
-0.0028556683100759983,
-0.003291043918579817,
0.036249302327632904,
0.010469608008861542,
0.009619018994271755,
-0.014785626903176308,
-0.008900652639567852,
-0.005138826090842485,
0.0027178374584764242,
-0.006416409742087126,
0.0000761775445425883,
-0.041744548827409744,
0.0021303389221429825,
0.03369950130581856,
0.00448951218277216,
0.06656146049499512,
0.051341671496629715,
0.002764593344181776,
-0.002800824586302042,
-0.007922994904220104,
0.00318365846760571,
-0.011804468929767609,
0.021365299820899963,
0.03224026411771774,
-0.0603833943605423,
0.004870663397014141,
0.013401367701590061,
0.03779223561286926,
-0.019549569115042686,
-0.010281495749950409,
0.01863177865743637,
0.00428857421502471,
0.010492512956261635,
0.007379106245934963,
-0.02050677500665188,
0.02876865118741989,
-0.02955004572868347,
-0.021401915699243546,
0.0029854762833565474,
-0.030289992690086365,
0.035427287220954895,
0.034449588507413864,
-0.020195916295051575,
-0.04702823609113693,
-0.012046688236296177,
-0.03836455196142197,
0.023195601999759674,
0.01421645749360323,
0.015980269759893417,
0.013217227533459663,
-0.008169547654688358,
0.04069283604621887,
0.020960312336683273,
0.05245043337345123,
-0.04967610538005829,
-0.04529877007007599,
-0.027046697214245796,
-0.008530231192708015,
-0.017329029738903046,
0.022951796650886536,
0.008504757657647133,
-0.03729991987347603,
-0.030861536040902138,
-0.003739043604582548,
0.051358722150325775,
0.031547706574201584,
0.026177605614066124,
-0.0010338284773752093,
0.05576790124177933,
-0.03449569642543793,
0.0018374465871602297,
0.006043435540050268,
-0.012701286934316158,
0.11677835136651993,
0.02864491380751133,
0.008027223870158195,
-0.07205202430486679,
0.014241746626794338,
0.008298108354210854,
0.024585537612438202,
-0.040422599762678146,
0.01577453874051571,
0.0070194764994084835,
0.029746824875473976,
0.01563984900712967,
0.02610376477241516,
0.021480098366737366,
0.024188626557588577,
0.05682562291622162,
-0.0424504391849041,
-0.021570198237895966,
-0.00982617773115635,
0.056114424020051956,
-0.02145070768892765,
0.04448739439249039,
-0.032427504658699036,
0.029167883098125458,
-0.028155766427516937,
-0.013292260468006134,
-0.03239232674241066,
-0.00429192092269659,
0.07686322927474976,
0.017424367368221283,
-0.008061490021646023,
0.029976405203342438,
0.05193690210580826,
-0.011790105141699314,
-0.04481621831655502,
0.007567329332232475,
0.013607648201286793,
-0.02910446748137474,
0.006699919700622559,
-0.018169619143009186,
0.017859075218439102,
-0.008539416827261448,
0.02914019115269184,
0.0012823996366932988,
-0.032315339893102646,
0.00148233852814883,
-0.023351022973656654,
0.022733042016625404,
0.02670147269964218,
-0.004855522885918617,
0.013705103658139706,
0.029454467818140984,
0.01469410490244627,
-0.0804920643568039,
-0.03290964290499687,
-0.00591933773830533,
0.004069498740136623,
-0.05054217576980591,
-0.03599683195352554,
-0.06823176890611649,
0.029330434277653694,
-0.011766494251787663,
0.019379541277885437,
-0.018071677535772324,
-0.016280198469758034,
0.0030117861460894346,
-0.014245271682739258,
0.010292970575392246,
-0.01882391981780529,
0.01620895229279995,
-0.03143885359168053,
0.037122637033462524,
-0.027133526280522346,
-0.0403493195772171,
0.01896250620484352,
0.01201839279383421,
0.005581121426075697,
-0.013799772597849369,
-0.01187951397150755,
0.02274162508547306,
-0.0453011654317379,
0.03403383493423462,
-0.013614244759082794,
0.010300838388502598,
0.010167760774493217,
0.014590281993150711,
0.04931838810443878,
0.03973917290568352,
-0.00719441706314683,
0.029459519311785698,
0.005985910538583994,
0.017121676355600357,
0.032972611486911774,
-0.03741910308599472,
-0.009690440259873867,
-0.011960193514823914,
-0.06746387481689453,
0.013803696259856224,
-0.023997001349925995,
0.031096410006284714,
0.023679135367274284,
0.009225107729434967,
-0.017425183206796646,
0.017041059210896492,
-0.03487037867307663,
-0.018356207758188248,
-0.027354666963219643,
-0.0289735347032547,
-0.0005949619808234274,
-0.00032109706080518663,
0.031431954354047775,
-0.008030381053686142,
-0.01150928158313036,
-0.020346278324723244,
0.00851691234856844,
0.006227415520697832,
0.024915801361203194,
-0.02321942150592804,
0.03628907725214958,
-0.021574730053544044,
0.042687512934207916,
-0.00913901999592781,
-0.029335835948586464,
-0.015643088147044182,
-0.004833865910768509,
0.02790808491408825,
-0.012725225649774075,
-0.0162831861525774,
0.009090105071663857,
-0.0025915964506566525,
0.011509943753480911,
0.024691995233297348,
0.017785845324397087,
0.0033500809222459793,
-0.013089043088257313,
-0.005349851679056883,
-0.032833877950906754,
0.025530386716127396,
-0.024570604786276817,
-0.029440348967909813,
0.040792472660541534,
0.0066139111295342445,
-0.02871512621641159,
-0.02962062880396843,
0.012532779946923256,
0.04521042853593826,
0.030577227473258972,
-0.00001600556970515754,
-0.009607839398086071,
0.024043694138526917,
-0.014193736016750336,
0.008185898885130882,
-0.015497748740017414,
0.009988565929234028,
-0.015960613265633583,
0.01325513981282711,
0.01069435104727745,
-0.040818825364112854,
0.023816918954253197,
-0.012572637759149075,
0.04267849400639534,
0.028623050078749657,
-0.05007927492260933,
0.017001265659928322,
0.010126407258212566,
0.012461292557418346,
0.023384900763630867,
0.016149798408150673,
0.03432827442884445,
0.024486692622303963,
-0.014926182106137276,
0.01397121325135231,
-0.02087581157684326,
0.01816064864397049,
-0.046849749982357025,
-0.013547194190323353,
-0.005128968041390181,
-0.013300499878823757,
0.03285796195268631,
-0.0010923579102382064,
-0.032590486109256744,
0.04603187367320061,
-0.01876564510166645,
-0.010858516208827496,
-0.04697820916771889,
-0.04599097743630409,
-0.00239205127581954,
-0.008401383645832539,
0.015340235084295273,
0.03138427063822746,
0.0031057270243763924,
0.04184625297784805,
0.013913349248468876,
0.00504072941839695,
0.00825688149780035,
-0.030889645218849182,
-0.01648435927927494,
0.012325060553848743,
0.0025534501764923334,
-0.050225626677274704,
0.06428056210279465,
-0.0037335455417633057,
-0.018250104039907455,
0.03480590507388115,
-0.007026366423815489,
-0.031219972297549248,
0.01435481570661068,
0.038482874631881714,
0.0021555661223828793,
0.06646817177534103,
-0.01084286067634821,
-0.05594179034233093,
-0.05782987177371979,
-0.019185906276106834,
0.04250066727399826,
0.015570433810353279,
0.0000809181437944062,
0.026064379140734673,
0.031117191538214684,
-0.015872905030846596,
-0.04471468925476074,
-0.011210332624614239,
-0.027882974594831467,
-0.06443934887647629,
-0.006950514391064644,
-0.01838056370615959,
0.043838609009981155,
-0.02654496394097805,
0.0409846231341362,
-0.03400323539972305,
-0.018125036731362343,
0.01610250398516655,
-0.0012118652230128646,
0.04630477353930473,
-0.013522704131901264,
-0.00208046636544168,
-0.05615655332803726,
0.02046598121523857,
0.01270477008074522,
-0.009408353827893734,
-0.061697375029325485,
-0.0034945313818752766,
0.020800160244107246,
-0.03172917291522026,
-0.021253718063235283,
-0.07678455859422684,
-0.014633631333708763,
0.042009614408016205,
0.023441361263394356,
-0.013503190129995346,
0.000459813978523016,
-0.05682464689016342,
-0.013910995796322823,
-0.04019836336374283,
0.037736449390649796,
0.00827811285853386,
-0.03626823425292969,
-0.05282164737582207,
-0.037412986159324646,
-0.03383171930909157,
0.031144380569458008,
0.07316877692937851,
-0.013098153285682201,
-0.028005637228488922,
-0.022583546116948128,
0.0013222285779193044,
0.038997333496809006,
-0.06567465513944626,
-0.010324541479349136,
0.05955035611987114,
-0.01599756069481373,
-0.015150432474911213,
-0.041008688509464264,
0.012869940139353275,
0.016747601330280304,
0.03293880075216293,
0.02690405584871769,
0.014445661567151546,
0.0032164680305868387,
-0.000903888198081404,
0.024119606241583824,
0.034019581973552704,
-0.02065613865852356,
0.05531395226716995,
-0.009290763176977634,
-0.0018895555986091495,
0.04658691957592964,
-0.03375985845923424,
-0.05300001800060272,
-0.013683554716408253,
-0.022912753745913506,
-0.005221627652645111,
-0.012623174116015434,
0.005558487959206104,
0.036468375474214554,
-0.06936988234519958,
-0.0451081283390522,
0.030603766441345215,
-0.05192025005817413,
-0.009151585400104523,
0.08694224059581757,
-0.023405684158205986,
0.009347151964902878,
-0.019302017986774445,
0.01676248013973236,
0.0007013056892901659,
0.006533902138471603,
-0.0009735322091728449,
0.018080001696944237,
0.044026926159858704,
-0.00820304173976183,
0.01943228580057621,
0.027038471773266792,
-0.012265021912753582,
0.014827409759163857,
-0.023332297801971436,
0.01827066019177437,
-0.010102599859237671,
-0.008954823017120361,
-0.01726866140961647,
-0.025260359048843384,
-0.016931375488638878,
0.034376516938209534,
-0.034934502094984055,
0.0820656269788742,
-0.06252855062484741,
0.003080796217545867,
-0.0014699690509587526,
0.00355359329842031,
-0.01947774551808834,
-0.03450203314423561,
0.014110598713159561,
-0.001547257648780942,
-0.024686425924301147,
-0.012938443571329117,
-0.01904217340052128,
-0.030786478891968727,
0.05846182629466057,
-0.021433694288134575,
0.028865870088338852,
-0.01488892175257206,
0.013833843171596527,
0.01284762006253004,
0.014435560442507267,
-0.07593441009521484,
-0.04226124659180641,
0.03245938941836357,
0.014243213459849358,
0.026769202202558517,
-0.020523129031062126,
-0.010679994709789753,
-0.029017208144068718,
0.041089847683906555,
-0.06311003118753433,
-0.013938290067017078,
-0.0005486856680363417,
0.006794463377445936,
0.016582639887928963,
-0.008303296752274036
] |
<p>I have been asked this question by a student, but I was able and in the same time incapable to give a good answer for this without equations, so do you have ideas how one can explain this in a simple way? </p>
<p>(Answers like we can take time as an imaginary, or our space is actually pseudo-Euclidean will be hard to grasp for new students.)</p>
<p>Note that the problem is <em>not</em> in visualizing the 4th dimension, that an easy thing to explain. The problem is more related to why we are in 3D that moving along 1D time dimension? In Differential geometry this interpreted by fiber bundles, but how to explain it to usual student.</p> | 1,512 | [
-0.00025961181381717324,
-0.009424994699656963,
-0.0060018510557711124,
-0.03573773056268692,
0.040961284190416336,
0.017117897048592567,
-0.0340784452855587,
0.014137055724859238,
-0.004747156519442797,
-0.019475057721138,
0.01664615236222744,
0.04015696793794632,
0.050884928554296494,
0.0005809979629702866,
0.010780790820717812,
-0.005316717550158501,
-0.018322033807635307,
-0.027804940938949585,
-0.03437071293592453,
-0.03869836404919624,
0.036017753183841705,
0.013173357583582401,
0.013342715799808502,
0.004821056965738535,
-0.003804060397669673,
0.015229669399559498,
0.05256161466240883,
0.02572859823703766,
0.010643964633345604,
0.052021902054548264,
-0.015311336144804955,
-0.002572069177404046,
0.0175283495336771,
0.0498274564743042,
0.004656728822737932,
-0.022385844960808754,
-0.027795253321528435,
-0.006044682580977678,
0.022275423631072044,
0.023103591054677963,
-0.018322521820664406,
-0.0022496264427900314,
-0.019136054441332817,
0.06091466546058655,
-0.0062005347572267056,
0.04858952388167381,
0.009564087726175785,
0.019456636160612106,
0.07144974172115326,
-0.05763942003250122,
0.06996689736843109,
-0.011702046729624271,
0.02022498846054077,
-0.0028385003097355366,
0.01570761576294899,
0.009872708469629288,
0.060289524495601654,
0.05572407692670822,
-0.027667414397001266,
-0.023700015619397163,
-0.03513561934232712,
-0.012209399603307247,
0.00196168664842844,
-0.04213897883892059,
-0.0028648548759520054,
0.003897392889484763,
-0.0021641638595610857,
0.0023115838412195444,
0.012918957509100437,
-0.03306090086698532,
-0.02883189544081688,
0.020281165838241577,
0.05439291149377823,
-0.0019311639480292797,
0.02301051653921604,
-0.002942402381449938,
0.028953569009900093,
0.018262488767504692,
0.06585441529750824,
0.013426697812974453,
-0.05343208834528923,
-0.022182220593094826,
0.011147290468215942,
0.018314216285943985,
0.003953318111598492,
-0.00407427828758955,
0.05075959116220474,
0.0015663988888263702,
0.023569010198116302,
0.06528950482606888,
-0.024719692766666412,
-0.012774117290973663,
0.038153063505887985,
0.00962097942829132,
0.014244761317968369,
0.027857862412929535,
0.004346542526036501,
0.040161117911338806,
0.036318328231573105,
-0.025286728516221046,
0.012287658639252186,
-0.024679914116859436,
0.019680950790643692,
0.056746941059827805,
0.006141562946140766,
0.036558911204338074,
-0.04161784425377846,
0.02278084307909012,
-0.0023181915748864412,
-0.025662988424301147,
-0.04415687546133995,
0.014969484880566597,
0.03372975066304207,
0.024754788726568222,
0.008254388347268105,
-0.04078086465597153,
0.031221255660057068,
-0.024518832564353943,
0.03201858326792717,
0.06559836119413376,
0.023429812863469124,
-0.054308369755744934,
0.03729751706123352,
-0.009396977722644806,
-0.07417862117290497,
0.0049280463717877865,
0.029390841722488403,
-0.02134973742067814,
-0.004129517357796431,
0.010601328685879707,
0.011190169490873814,
0.005729303695261478,
0.017777275294065475,
0.00602458231151104,
0.0851781889796257,
-0.010363531298935413,
-0.1096603199839592,
-0.07353833317756653,
0.054193004965782166,
0.02260529436171055,
-0.02387530542910099,
-0.09136847406625748,
0.025246454402804375,
0.00048628466902300715,
0.059612952172756195,
-0.027104102075099945,
0.010085109621286392,
0.0433402918279171,
0.0025655445642769337,
0.014786319807171822,
-0.011180868372321129,
0.013094963505864143,
-0.022181561216711998,
-0.03917461261153221,
0.011736252345144749,
-0.021316152065992355,
0.030427247285842896,
0.05019330605864525,
0.017536498606204987,
-0.03898836672306061,
0.048147257417440414,
-0.01096414029598236,
-0.007737212814390659,
0.038844771683216095,
-0.023972224444150925,
-0.011213533580303192,
0.09008519351482391,
0.008232377469539642,
0.010142628103494644,
0.014224681071937084,
0.022662829607725143,
0.03904829919338226,
0.0021143651101738214,
0.046638403087854385,
0.010998180136084557,
-0.010278530418872833,
-0.018565502017736435,
0.03755643218755722,
-0.03383542224764824,
0.010714229196310043,
-0.010726380161941051,
-0.05701170489192009,
-0.011334049515426159,
0.0017544205766171217,
-0.014021633192896843,
0.024638570845127106,
-0.005624941550195217,
-0.00036035143421031535,
-0.003658769652247429,
-0.039366547018289566,
-0.014830025844275951,
-0.06588850915431976,
0.021757004782557487,
0.052443407475948334,
-0.007530733477324247,
-0.007049232721328735,
0.004362159874290228,
0.027559565380215645,
-0.055755432695150375,
-0.02913346327841282,
-0.03917573392391205,
0.03267376124858856,
0.02255815640091896,
-0.031119199469685555,
0.012080296874046326,
0.03218567371368408,
0.046003084629774094,
-0.024429775774478912,
0.007883059792220592,
0.011365226469933987,
0.021786971017718315,
0.0027004519943147898,
-0.014857269823551178,
0.02395622618496418,
0.01166046317666769,
-0.006228474900126457,
-0.025602763518691063,
0.011324118822813034,
-0.027368560433387756,
0.0503622405230999,
-0.009315182454884052,
0.07998059689998627,
0.03761683776974678,
-0.015717238187789917,
-0.013494886457920074,
0.041434042155742645,
-0.00032310845563188195,
-0.005519624333828688,
0.02133733220398426,
-0.037950240075588226,
-0.010588032193481922,
-0.02898634783923626,
0.028302941471338272,
0.06402743607759476,
-0.02480153739452362,
0.01892479881644249,
0.012718132697045803,
0.05807216465473175,
0.028444550931453705,
0.015120251104235649,
-0.007939509116113186,
-0.026331385597586632,
-0.0038571651093661785,
-0.010275120846927166,
0.012403307482600212,
0.0015485731419175863,
0.022031612694263458,
-0.002855288563296199,
0.0011055141221731901,
-0.00811426155269146,
-0.016201676800847054,
0.031920433044433594,
-0.036253612488508224,
0.021544968709349632,
0.009904587641358376,
0.0034472676925361156,
0.03918970376253128,
-0.023974813520908356,
0.015516018494963646,
0.037789952009916306,
-0.012522172182798386,
-0.00916413962841034,
-0.00926364865154028,
-0.027665993198752403,
0.028109580278396606,
0.025970153510570526,
-0.0192231647670269,
-0.02062062919139862,
0.03524959459900856,
-0.02422497235238552,
0.04150385409593582,
-0.014738012105226517,
-0.0486866794526577,
-0.03035181574523449,
-0.0041007474064826965,
0.017715448513627052,
0.001995231956243515,
0.03405546024441719,
-0.014185837469995022,
-0.04976049065589905,
0.03784406557679176,
-0.0019320856081321836,
0.007275085896253586,
0.010180003009736538,
-0.029615918174386024,
0.03978690877556801,
-0.01868344284594059,
-0.023303689435124397,
0.047386668622493744,
0.00705969100818038,
0.01951008103787899,
0.030346253886818886,
-0.03491619974374771,
-0.03814171254634857,
-0.03793160989880562,
-0.04767580330371857,
0.021655719727277756,
-0.02753358706831932,
0.0032467360142618418,
0.06371870636940002,
-0.04643947631120682,
-0.04021328315138817,
-0.0063415332697331905,
-0.03499347344040871,
-0.06850987672805786,
-0.009770503267645836,
-0.0039412472397089005,
0.014674962498247623,
-0.030160214751958847,
-0.003646610304713249,
-0.010475372895598412,
-0.01888587698340416,
-0.014880012720823288,
-0.03175244480371475,
-0.05384095385670662,
0.03310395032167435,
0.0043174587190151215,
0.028592118993401527,
-0.013995555229485035,
-0.06380800157785416,
0.04485734552145004,
0.012653921730816364,
-0.022887252271175385,
-0.023042213171720505,
-0.026507360860705376,
-0.006253126543015242,
-0.030797073617577553,
0.026698999106884003,
0.019785717129707336,
-0.02445005066692829,
0.013700242154300213,
0.035734303295612335,
0.018751684576272964,
0.053270142525434494,
0.01544367428869009,
-0.024221984669566154,
-0.019067103043198586,
-0.0010029986733570695,
0.014261129312217236,
0.015174861997365952,
0.017106685787439346,
-0.023790350183844566,
0.0074971201829612255,
-0.02157893031835556,
0.036208730190992355,
0.008957416750490665,
-0.03623895347118378,
0.03972723335027695,
0.005914543755352497,
0.031867049634456635,
-0.028213586658239365,
0.006556312087923288,
-0.02143758349120617,
-0.013090796768665314,
-0.002865532413125038,
0.020543010905385017,
0.019732464104890823,
-0.021836133673787117,
0.01958988606929779,
0.020990008488297462,
0.012047626078128815,
-0.04809955880045891,
0.007346253376454115,
0.007504723966121674,
-0.0030928333289921284,
0.03979121521115303,
-0.027873052284121513,
-0.018456870689988136,
0.04156456142663956,
0.02467266283929348,
-0.007759717758744955,
-0.007759332191199064,
-0.042026132345199585,
-0.01549890823662281,
-0.0705004632472992,
0.010125897824764252,
0.013261066749691963,
0.04987931251525879,
0.012106472626328468,
0.015420285984873772,
0.006219503935426474,
0.003013740526512265,
0.012901566922664642,
-0.01496809534728527,
-0.08280865848064423,
0.00860841479152441,
-0.028500834479928017,
0.012185890227556229,
-0.03394773602485657,
-0.011440454982221127,
0.01783127896487713,
-0.03197066858410835,
-0.03305773437023163,
0.009313302114605904,
-0.049083005636930466,
-0.06876048445701599,
0.004684648010879755,
-0.003985052928328514,
-0.00959565956145525,
-0.041240621358156204,
0.03176354244351387,
0.06622124463319778,
0.019747434183955193,
0.013532224111258984,
0.061089374125003815,
-0.024844517931342125,
0.01639384962618351,
-0.026621101424098015,
-0.009548378176987171,
0.029543742537498474,
0.005125108174979687,
0.0017896539065986872,
-0.002366237109526992,
-0.022832442075014114,
0.029023459181189537,
0.008690517395734787,
0.04114073887467384,
-0.04116184636950493,
-0.007467410992830992,
-0.0022228704765439034,
-0.053405020385980606,
-0.0013782784808427095,
-0.010506749153137207,
0.05431656166911125,
0.00573362922295928,
0.019973402842879295,
0.022837335243821144,
0.02715720422565937,
-0.01610403321683407,
0.02086208574473858,
0.041938889771699905,
-0.01500772312283516,
-0.059762995690107346,
-0.04335818812251091,
-0.021365534514188766,
-0.01883966103196144,
-0.010754690505564213,
0.033420007675886154,
0.0008662560139782727,
-0.014387576840817928,
0.023697923868894577,
-0.0034807149786502123,
-0.014227584935724735,
0.02849806658923626,
-0.003858388401567936,
-0.010730266571044922,
-0.000368017063010484,
0.028707055374979973,
-0.0028305368032306433,
0.0023492362815886736,
0.05396931245923042,
0.06154714152216911,
-0.00605282187461853,
-0.023009145632386208,
-0.10284960269927979,
-0.04481371492147446,
0.018060388043522835,
0.022444603964686394,
0.004993833135813475,
-0.010171069763600826,
-0.04821188375353813,
-0.02425541542470455,
0.05638185515999794,
-0.019382866099476814,
0.03459722176194191,
-0.0038650648202747107,
-0.019261160865426064,
-0.03218729794025421,
-0.0008564524468965828,
-0.01925884746015072,
0.02352982573211193,
-0.014229471795260906,
0.027376053854823112,
0.023411935195326805,
0.030089085921645164,
-0.008906785398721695,
0.02618464082479477,
0.0077367001213133335,
0.027992092072963715,
0.0194177757948637,
-0.005926497746258974,
0.0003426005714572966,
0.0319906584918499,
-0.049890726804733276,
-0.055249568074941635,
0.04172291234135628,
0.014175387099385262,
-0.02585538476705551,
0.008657137863337994,
-0.035187989473342896,
-0.04309213161468506,
0.012918124906718731,
-0.00411188043653965,
0.01341236475855112,
0.003469295334070921,
-0.03336078301072121,
0.011867797933518887,
0.026974689215421677,
-0.013885858468711376,
0.016019823029637337,
0.02478043921291828,
0.020199615508317947,
-0.016874151304364204,
-0.017778733745217323,
0.05268492177128792,
-0.013413364998996258,
-0.011548584327101707,
0.0033730517607182264,
-0.01057938951998949,
-0.03974362835288048,
0.05110958218574524,
0.0038093305192887783,
-0.0013218747917562723,
-0.030214285477995872,
-0.02104061283171177,
-0.008971520699560642,
0.008756779134273529,
0.029352832585573196,
-0.013107857666909695,
-0.037916433066129684,
-0.02601291611790657,
-0.003299380885437131,
-0.026646586135029793,
-0.0073471274226903915,
-0.014626936987042427,
-0.029217470437288284,
0.0487825833261013,
0.029470380395650864,
0.03498179465532303,
-0.014095906168222427,
-0.02410782128572464,
0.008206347934901714,
-0.06071745976805687,
0.0074776350520551205,
-0.030322862789034843,
0.003183219116181135,
0.016408557072281837,
-0.04765668883919716,
-0.021882979199290276,
-0.01391566265374422,
0.004489998798817396,
0.00445995107293129,
-0.04539676383137703,
-0.004596424754709005,
0.0017471506725996733,
-0.008357768878340721,
-0.10546213388442993,
-0.09614092111587524,
0.03269896283745766,
0.02249506488442421,
-0.04783099517226219,
-0.0670166164636612,
0.01370355486869812,
-0.03332260996103287,
-0.03228752315044403,
0.006361977197229862,
0.06158500164747238,
-0.017129143700003624,
-0.013370007276535034,
0.008938726969063282,
0.015401838347315788,
0.04328272491693497,
-0.04091186076402664,
-0.007757802493870258,
-0.00895183626562357,
-0.014674627222120762,
-0.017916779965162277,
-0.011071428656578064,
0.05344688892364502,
-0.024847598746418953,
-0.02215232141315937,
-0.015630321577191353,
-0.0022596768103539944,
0.022172171622514725,
-0.04678834602236748,
0.027862416580319405,
0.03426003083586693,
0.026170484721660614,
0.009367691352963448,
-0.06750507652759552,
0.006376955192536116,
0.01806986704468727,
0.024626677855849266,
-0.012659627944231033,
0.023757006973028183,
-0.0060788714326918125,
-0.04447232186794281,
0.044000983238220215,
-0.010546543635427952,
-0.0015212430153042078,
-0.020785553380846977,
0.03389492258429527,
-0.003999488893896341,
-0.018680371344089508,
0.012482895515859127,
0.005836385767906904,
0.020630592480301857,
0.035344067960977554,
-0.042051732540130615,
0.027193520218133926,
0.032944370061159134,
-0.038127075880765915,
-0.0282027255743742,
-0.016616540029644966,
0.02371041104197502,
0.06521248072385788,
-0.037350788712501526,
0.08511234819889069,
0.03302362561225891,
-0.0005474379286170006,
0.016784142702817917,
0.02218388207256794,
0.00008009579323697835,
0.02833828143775463,
-0.007985376752912998,
0.02405630424618721,
-0.035148344933986664,
-0.002245355164632201,
0.0206153467297554,
0.04741765186190605,
-0.06461124867200851,
0.04600626975297928,
0.04550934210419655,
-0.0320206843316555,
0.0516132190823555,
0.0026639620773494244,
-0.04090934991836548,
0.057885900139808655,
-0.001714757177978754,
0.03825598582625389,
0.0030973688699305058,
-0.012842279858887196,
0.05213980749249458,
0.010321985930204391,
0.012322187423706055,
-0.019081003963947296,
-0.002048433991149068,
-0.026970217004418373,
-0.047406360507011414,
0.02177801914513111,
0.045310456305742264,
-0.006329033058136702,
0.015709901228547096,
0.0447133406996727,
-0.021467681974172592,
0.03554240241646767,
0.009734999388456345,
-0.036951836198568344,
-0.05120784416794777,
-0.033172037452459335,
-0.009058094583451748,
0.07062249630689621,
0.025258518755435944,
-0.02610727958381176,
-0.014580047689378262,
-0.03338472172617912,
-0.018294690176844597,
-0.01911747269332409,
0.06567618250846863,
-0.034500155597925186,
0.0520336851477623,
0.02693791873753071,
0.007114453706890345,
-0.03724392130970955,
0.03374766558408737,
0.08869163691997528,
0.07642979174852371,
-0.005593625828623772,
-0.06478224694728851,
0.024774711579084396,
-0.014086801558732986,
-0.013439523056149483,
-0.06122038513422012,
0.06105106696486473,
0.008936933241784573,
0.030967935919761658,
0.018507476896047592,
0.05919031798839569,
-0.00481486925855279,
-0.016729839146137238,
0.044771984219551086,
-0.04607197642326355,
-0.021849218755960464,
-0.02489045076072216,
0.0030959234572947025,
0.006907613482326269,
0.010906304232776165,
-0.05601739138364792,
0.05936155095696449,
-0.041728340089321136,
-0.0049656773917376995,
-0.016071263700723648,
-0.055316075682640076,
0.019819708541035652,
-0.013614987023174763,
-0.051565129309892654,
0.01924622617661953,
0.026891173794865608,
-0.03341011703014374,
-0.054930802434682846,
0.0027910901699215174,
-0.009041858837008476,
-0.008632991462945938,
0.042289551347494125,
0.04185006394982338,
0.008819827809929848,
0.004438899923115969,
0.004330595955252647,
0.04003063589334488,
-0.03722274675965309,
-0.05358443409204483,
-0.02097180113196373,
0.056275416165590286,
-0.0016586995916441083,
-0.00009722053073346615,
-0.010099739767611027,
-0.004145554732531309,
0.00013623065024148673,
-0.08166979998350143,
-0.03571305051445961,
-0.009824099019169807,
0.060229141265153885,
0.022461233660578728,
0.007449041120707989,
0.004787313286215067,
-0.019275059923529625,
-0.025640735402703285,
0.02409990318119526,
-0.025050248950719833,
-0.00043908614316023886,
0.02628570981323719,
-0.023723335936665535,
0.0021425425074994564,
-0.012578682042658329,
0.006798349786549807,
-0.04127965122461319,
-0.0061197769828140736,
-0.0020043470431119204,
0.02575547993183136,
0.03256342187523842,
0.02954716980457306,
0.01801675744354725,
-0.013359231874346733,
-0.035732582211494446,
0.03139498829841614,
-0.013391855172812939,
-0.0032285875640809536,
0.013781516812741756,
-0.02048242837190628,
-0.01922711543738842,
-0.012319847010076046,
0.0394899956882,
0.038164786994457245,
-0.004559516906738281,
-0.01022117119282484,
-0.028163926675915718,
0.00213534920476377,
0.027237188071012497,
-0.020727459341287613,
-0.003104091389104724,
0.005437049083411694,
-0.010127102956175804,
-0.027188368141651154,
-0.0062982770614326,
0.02129426971077919,
0.02071993798017502,
-0.016295187175273895,
0.00781773217022419,
0.057225652039051056,
0.00478332070633769,
0.021518055349588394,
0.03422887995839119,
-0.048268936574459076,
0.00447129039093852,
0.004659602884203196,
0.014502418227493763,
-0.069870725274086,
-0.016070080921053886,
-0.02219441719353199,
0.009001444093883038,
-0.011460613459348679,
0.03731365501880646,
-0.004379624966531992,
0.0038687048945575953,
-0.02683766931295395,
0.0016411918913945556,
-0.032670892775058746,
-0.011884801089763641,
-0.08264529705047607,
0.02181188017129898,
0.006333213299512863,
0.0014035715721547604,
-0.004662260878831148,
0.02033168263733387,
-0.029244638979434967,
-0.016098372638225555,
0.03463670238852501,
0.0011637575225904584,
-0.03327314555644989,
0.01047704927623272,
0.016904359683394432,
0.025588376447558403,
0.01648765802383423,
0.004542939364910126,
-0.03320205211639404,
0.0052129775285720825,
-0.0376393161714077,
-0.0542999729514122,
0.0016152479220181704,
-0.023129237815737724,
0.03425413370132446,
0.022719288244843483,
-0.02543257363140583,
-0.030373917892575264,
0.02361551858484745,
-0.040323588997125626,
0.006008201278746128,
0.013336366042494774,
-0.018918657675385475,
-0.03508906066417694,
-0.032480638474226,
-0.009389637969434261,
-0.007759569212794304,
-0.010127011686563492,
-0.018159661442041397,
-0.0024499287828803062,
0.013856744393706322,
-0.020722437649965286,
-0.004577929154038429,
-0.016092242673039436,
-0.00041184708243235946,
0.030292339622974396,
-0.003933753352612257,
0.0348401740193367,
0.056159377098083496,
-0.030149677768349648,
0.014211601577699184,
0.02109644189476967,
0.011302405036985874,
-0.08245716243982315,
-0.002971596783027053,
0.02311277575790882,
-0.0015493078390136361,
0.05616367608308792,
-0.05787646397948265,
0.01064610667526722,
0.033024806529283524,
-0.10286694765090942,
0.040582481771707535,
-0.04487958922982216,
-0.013459019362926483,
-0.016035636886954308,
-0.0383845716714859,
0.004892123397439718,
0.08615627884864807,
0.050616100430488586,
0.0460384264588356,
-0.02443847805261612,
-0.01408088207244873,
-0.01993500627577305,
-0.03477885574102402,
0.024275941774249077,
0.030724743381142616,
-0.0012471808586269617,
-0.006624749395996332,
0.03351464867591858,
0.01679992862045765,
-0.019718816503882408,
0.0342521145939827,
-0.025257553905248642,
0.012922460213303566,
0.030599066987633705,
-0.01407056674361229,
0.011532729491591454,
-0.003829212160781026,
0.02848953753709793,
-0.028180141001939774,
-0.023867910727858543,
0.013759295456111431,
0.03037458285689354,
0.012102584354579449,
0.023472189903259277,
-0.0016752463998273015,
0.01599794067442417,
-0.04467818886041641,
-0.006717239040881395,
0.03370891883969307,
0.014396813698112965,
-0.027618587017059326,
-0.013388387858867645,
-0.012725023552775383,
0.017680658027529716,
-0.03254437819123268,
-0.006855928339064121,
-0.04447964206337929,
-0.01962355338037014,
0.02616746537387371,
0.005858221556991339,
-0.009505731984972954,
0.013769274577498436,
-0.023250415921211243,
-0.011094898916780949,
0.007962405681610107,
0.007615178823471069,
0.0117169925943017,
-0.03331179916858673,
-0.009795978665351868,
-0.0031537546310573816,
-0.010402427054941654,
0.005770265124738216,
-0.03523441031575203,
-0.007362418342381716,
0.058857452124357224,
0.04382481053471565,
0.028056785464286804,
-0.017151908949017525,
-0.05777769163250923,
-0.03107539750635624,
-0.06612914800643921,
0.036233872175216675,
0.02691972441971302,
-0.015255591832101345,
-0.039951544255018234,
0.025120941922068596,
-0.030628932639956474,
0.057211849838495255,
0.07394663244485855,
-0.03220425918698311,
-0.005630869884043932,
0.026138968765735626,
0.02979503758251667,
0.0357997864484787,
-0.0342341810464859,
-0.02775299921631813,
0.019134122878313065,
-0.0208926759660244,
-0.008445055224001408,
-0.0010486047249287367,
-0.04022493213415146,
-0.005793420132249594,
-0.01084380503743887,
0.006498825270682573,
0.045936278998851776,
0.01726965233683586,
-0.029060272499918938,
0.018951134756207466,
0.01253873948007822,
-0.023196831345558167,
0.039122965186834335,
0.02242426760494709,
-0.018356526270508766,
0.029508056119084358,
-0.01711573824286461,
0.002920136321336031,
-0.000047893321607261896,
-0.05438010022044182,
0.005820860154926777,
-0.005631298758089542,
-0.0076365708373487,
0.05866415798664093,
-0.06923677772283554,
-0.019854657351970673,
0.027354853227734566,
-0.0413188561797142,
-0.003536149626597762,
0.025995660573244095,
0.012919188477098942,
0.030611321330070496,
-0.03726119548082352,
0.008839093148708344,
0.005043852608650923,
0.030239207670092583,
0.03890879824757576,
0.04395361989736557,
0.0006252479506656528,
-0.029612571001052856,
0.006393440533429384,
0.028088340535759926,
-0.008789424784481525,
0.000973092915955931,
0.007857674732804298,
0.07520481199026108,
-0.015287129208445549,
0.024649538099765778,
-0.015362159349024296,
-0.032355811446905136,
0.012326404452323914,
0.03968512639403343,
-0.006007038988173008,
0.08239508420228958,
-0.01852637529373169,
0.033295173197984695,
-0.007914763875305653,
-0.0030563659965991974,
-0.06676022708415985,
0.033113475888967514,
0.040583282709121704,
0.0614732950925827,
-0.02144668810069561,
-0.014503814280033112,
-0.0022106135729700327,
-0.012493729591369629,
0.0096049839630723,
0.004730948247015476,
-0.0013307718327268958,
0.006193256936967373,
-0.03566452115774155,
0.026326389983296394,
-0.008496132679283619,
-0.04574136808514595,
-0.02984646148979664,
0.04980122670531273,
0.024899117648601532,
0.05881815031170845,
-0.008592844009399414,
-0.01068201195448637,
-0.04744130000472069,
0.06743324548006058,
-0.09537987411022186,
-0.02959951013326645,
0.006699305959045887,
0.03290414437651634,
-0.021721098572015762,
-0.034322015941143036
] |
<p>I'm thinking about trying to do a numerical simulation of some very simple QM problems.</p>
<p>How much space do I need? To simulate the Hilbert space?</p>
<p>I'd like to eventually simulate the absorption or emission of a photon by a hydrogen atom. So at least three particles (two fermions, one boson). Let's generalize that to three particles with arbitrary spin, so I can look at three photons or three electrons if I want to.</p>
<p>In order to do a numerical simulation I need to replace the continuous spacetime with a rectangular grid or lattice. I'd like to eventually get more precision, but let's start with just ten cells per dimension to begin with. So including time, I need ten thousand cells in a four dimensional lattice. `</p>
<p>How many cells do I need to simulate the Hilbert space? and what goes in each cell? </p>
<p>If I put restrictions on the shape of the wavefunction, does that help?</p> | 1,513 | [
-0.000037905629142187536,
-0.02239803597331047,
0.0009403142612427473,
-0.0488741435110569,
0.05643659830093384,
0.014417093247175217,
-0.040829550474882126,
-0.04750773683190346,
0.029028471559286118,
-0.017895642668008804,
0.06735379993915558,
0.026736997067928314,
0.056782156229019165,
0.01429987046867609,
0.01121645700186491,
0.009315624833106995,
0.005398853216320276,
-0.019468635320663452,
-0.035122159868478775,
-0.028754621744155884,
0.05157316476106644,
0.03452425077557564,
0.0023726753424853086,
-0.046994779258966446,
-0.015093553811311722,
0.03652532398700714,
0.0080811632797122,
0.008014672435820103,
0.02156257815659046,
0.040951669216156006,
-0.027022017166018486,
-0.03953774273395538,
0.02902163937687874,
0.04381518065929413,
0.023063024505972862,
-0.022243816405534744,
-0.059777144342660904,
-0.04285236820578575,
0.023225441575050354,
-0.0363263264298439,
-0.04056698456406593,
-0.007078377064317465,
-0.031030653044581413,
0.032261017709970474,
0.010340207256376743,
0.02746826782822609,
-0.005378373898565769,
-0.04251633584499359,
0.034483831375837326,
-0.0412234328687191,
0.045026201754808426,
0.02276471070945263,
0.04618736729025841,
0.01267792284488678,
0.0075166355818510056,
-0.03079490177333355,
0.039111603051424026,
0.05687950924038887,
0.020997190847992897,
-0.032155126333236694,
0.006993420422077179,
-0.0003557850723154843,
0.01648079603910446,
-0.03693837672472,
-0.009117635898292065,
0.01090332679450512,
0.01051164511591196,
-0.029894093051552773,
0.004503919743001461,
-0.03799358382821083,
0.0007437265594489872,
0.0038820989429950714,
0.052077021449804306,
-0.009006515145301819,
0.031105760484933853,
0.014638202264904976,
0.021549154072999954,
0.01379917562007904,
0.04266941174864769,
0.02192998118698597,
-0.031115463003516197,
0.026653802022337914,
-0.006173088680952787,
0.016698194667696953,
-0.0013036089949309826,
0.016725314781069756,
0.03975863382220268,
-0.028262926265597343,
-0.02062670886516571,
0.03522607311606407,
-0.016632352024316788,
0.037908732891082764,
0.07616718113422394,
0.016056593507528305,
-0.02685570903122425,
0.011400436982512474,
0.0003331181069370359,
0.06761731952428818,
0.0032069527078419924,
-0.03446468338370323,
-0.022776806727051735,
-0.040244437754154205,
-0.0015564128989353776,
0.09098609536886215,
-0.007787581533193588,
0.020000386983156204,
0.0031261276453733444,
0.02172008343040943,
-0.02236681990325451,
-0.014779826626181602,
-0.03895247355103493,
0.019909124821424484,
-0.025670768693089485,
-0.011646440252661705,
0.01838964968919754,
-0.047613006085157394,
-0.0021912669762969017,
-0.03036213293671608,
0.02083977684378624,
0.07467808574438095,
0.04479702562093735,
-0.032100334763526917,
0.038150954991579056,
-0.03456363081932068,
-0.08811672776937485,
0.021052246913313866,
0.013000547885894775,
0.008705951273441315,
-0.05790800601243973,
0.005962864495813847,
0.01424475573003292,
-0.011881492100656033,
0.03818125277757645,
-0.004531302023679018,
0.02813783846795559,
-0.039775099605321884,
-0.10467535257339478,
-0.07184769213199615,
0.019802341237664223,
-0.0017204484902322292,
-0.02364390902221203,
-0.07241048663854599,
0.013755141757428646,
0.025545842945575714,
0.07391554117202759,
0.01047177892178297,
0.004545955453068018,
-0.007201072759926319,
0.051966093480587006,
0.01677931472659111,
-0.04041150212287903,
0.04228968918323517,
-0.03535372391343117,
0.01379618514329195,
0.00022306964092422277,
-0.03401640057563782,
0.03915766626596451,
0.05227673426270485,
0.009934131056070328,
-0.015564311295747757,
0.06199927628040314,
0.004901496227830648,
-0.015473922714591026,
0.011482658796012402,
-0.037398289889097214,
-0.013326568529009819,
0.04769419506192207,
-0.008224517107009888,
0.01981196738779545,
0.009371334686875343,
-0.03486809879541397,
-0.016080720350146294,
-0.0009909026557579637,
-0.0023283520713448524,
0.031544290482997894,
0.0004975643823854625,
0.011638916097581387,
-0.025871314108371735,
0.015336721204221249,
0.006601465400308371,
-0.03900938481092453,
-0.021556010469794273,
0.010507345199584961,
-0.0030242411885410547,
-0.00422782963141799,
0.019587835296988487,
0.006839583162218332,
-0.015611639246344566,
-0.016409188508987427,
-0.005046586040407419,
-0.027490811422467232,
-0.050164248794317245,
0.03349650278687477,
0.022860988974571228,
0.00746310967952013,
0.015477260574698448,
0.01617906615138054,
-0.014759611338376999,
-0.021342739462852478,
-0.05632472410798073,
-0.0420607328414917,
0.034373074769973755,
0.0007445149240083992,
-0.011041548103094101,
0.038449905812740326,
0.0874413400888443,
0.039839617908000946,
-0.020487064495682716,
0.03358643129467964,
0.0030534297693520784,
-0.024304496124386787,
-0.040967028588056564,
-0.033220961689949036,
0.025754623115062714,
0.02427879348397255,
-0.0059959921054542065,
-0.01523593533784151,
-0.03406624495983124,
-0.02135247178375721,
0.026651663705706596,
-0.02392195165157318,
0.07911313325166702,
0.028434554114937782,
-0.014936923049390316,
0.02695286087691784,
0.007599254604429007,
-0.021811677142977715,
0.01715719886124134,
0.04717668518424034,
-0.014424673281610012,
-0.04120897501707077,
0.0164877250790596,
0.05689206346869469,
-0.005143042653799057,
-0.03643755987286568,
0.013545962981879711,
0.024075059220194817,
0.03222351521253586,
0.05640385299921036,
0.009504127316176891,
-0.0671866238117218,
-0.0051689427345991135,
0.024122433736920357,
0.008256746456027031,
0.03609475865960121,
0.01881195232272148,
-0.002107448410242796,
0.02010674960911274,
-0.016670996323227882,
-0.030597129836678505,
-0.019249550998210907,
0.029755793511867523,
-0.03658214956521988,
0.0010204189456999302,
-0.03331529349088669,
-0.03892524167895317,
0.00275217043235898,
-0.024480778723955154,
-0.012751433067023754,
0.0002225983189418912,
-0.02140151895582676,
0.0035715580452233553,
-0.031855061650276184,
-0.054109811782836914,
-0.012252936139702797,
0.0278193186968565,
-0.02420511469244957,
0.017749562859535217,
0.02660025656223297,
-0.01703919842839241,
0.014822620898485184,
-0.03099105693399906,
0.01836540549993515,
-0.02089265175163746,
-0.013577984645962715,
0.0379302091896534,
0.03217505291104317,
0.032536253333091736,
-0.03449304774403572,
-0.029658513143658638,
0.011307716369628906,
-0.006735010538250208,
0.01944773830473423,
-0.0007803717162460089,
-0.029129499569535255,
0.02453237771987915,
-0.028988981619477272,
-0.05046667531132698,
0.027707010507583618,
-0.020506056025624275,
-0.004500710405409336,
0.023413188755512238,
-0.007116983179003,
-0.03369592875242233,
-0.0033801861573010683,
0.008318234235048294,
0.005573897622525692,
-0.019633911550045013,
0.010411560535430908,
0.02895853854715824,
0.013797290623188019,
-0.0555870421230793,
0.018637478351593018,
-0.004988382570445538,
-0.027500690892338753,
-0.05107733607292175,
-0.0021826555021107197,
0.010703057050704956,
-0.03838420286774635,
0.010811497457325459,
0.0581529475748539,
-0.025872552767395973,
0.03159918636083603,
-0.06198549270629883,
-0.053366709500551224,
0.002058741170912981,
-0.010520191863179207,
0.04149800166487694,
-0.010289613157510757,
-0.015199108049273491,
0.10064762085676193,
0.03349107876420021,
-0.055973201990127563,
-0.014271050691604614,
0.017928024753928185,
-0.006589986849576235,
-0.030580736696720123,
0.04748813062906265,
0.014380271546542645,
0.0017643780447542667,
-0.006247116252779961,
0.0018778078956529498,
0.025493165478110313,
0.03674255311489105,
0.015179211273789406,
0.02230663225054741,
0.014417331665754318,
0.008343544788658619,
0.008699110709130764,
0.0692528784275055,
-0.006197105161845684,
-0.025081567466259003,
0.022222885861992836,
-0.0238400399684906,
-0.029052264988422394,
0.012988210655748844,
-0.038211531937122345,
0.05152612924575806,
0.00937124714255333,
0.026434002444148064,
-0.00010268496407661587,
0.03909092769026756,
-0.03515096753835678,
-0.04852128028869629,
0.02736847847700119,
0.02437392808496952,
0.023337971419095993,
-0.005286074243485928,
-0.044216133654117584,
-0.001027373713441193,
0.05428086221218109,
-0.037606388330459595,
0.010833106935024261,
-0.0032137916423380375,
0.014861910603940487,
0.03354385495185852,
-0.04836014658212662,
-0.05041442811489105,
0.04495159164071083,
0.07325492054224014,
0.04565642774105072,
0.003982716705650091,
-0.026131359860301018,
-0.029873356223106384,
-0.055876560509204865,
-0.02634534426033497,
-0.0063321846537292,
0.08251114189624786,
-0.00373465777374804,
0.04456321522593498,
0.0024854489602148533,
-0.015430955216288567,
0.010685152374207973,
-0.03971654176712036,
-0.0812346562743187,
-0.006132282316684723,
-0.010319815948605537,
-0.011329371482133865,
0.01576269418001175,
-0.01669583097100258,
0.005878007970750332,
0.005234239622950554,
-0.03582373633980751,
0.001070259721018374,
-0.01205010898411274,
-0.04852256551384926,
-0.003023216500878334,
-0.02200140990316868,
-0.015506446361541748,
-0.028708942234516144,
0.04697081446647644,
0.03999748453497887,
0.016698354855179787,
-0.001982804387807846,
0.028538115322589874,
-0.038864102214574814,
-0.025696266442537308,
0.03622059524059296,
0.01349246222525835,
0.0042823078110814095,
0.0388203002512455,
0.03865579143166542,
0.04364125803112984,
-0.021921779960393906,
-0.019823338836431503,
0.00557996379211545,
0.06322219967842102,
0.010031178593635559,
0.0009031096124090254,
0.008338969200849533,
-0.03224645182490349,
0.01786157302558422,
0.009195475839078426,
0.04515821486711502,
-0.013861491344869137,
0.0023555841762572527,
0.03789782151579857,
0.012269892729818821,
-0.02443990856409073,
-0.019137194380164146,
0.07783712446689606,
-0.010817669332027435,
-0.019577357918024063,
-0.03923932835459709,
0.0017345371888950467,
-0.007389165461063385,
-0.008868889883160591,
-0.0071271685883402824,
0.010407078079879284,
-0.010404793545603752,
0.036436766386032104,
0.02231852523982525,
-0.04049011319875717,
-0.024625491350889206,
0.028704723343253136,
0.026247043162584305,
0.022944847121834755,
-0.0013265518937259912,
0.03793349862098694,
0.0235292911529541,
0.0151490718126297,
0.051805853843688965,
0.011155810207128525,
-0.015670815482735634,
-0.0792350247502327,
-0.0021844885777682066,
0.04897383227944374,
0.03420872613787651,
0.04143885150551796,
-0.005883848760277033,
-0.06079563871026039,
-0.022027624770998955,
0.04836726188659668,
-0.03848792612552643,
0.013977362774312496,
-0.00878151785582304,
-0.035552676767110825,
-0.029995722696185112,
-0.019863322377204895,
0.002016582293435931,
-0.00009954249981092289,
-0.02446943148970604,
0.06386911123991013,
-0.053317438811063766,
0.005675968248397112,
-0.010821578092873096,
0.05952214449644089,
0.016399512067437172,
0.04456394910812378,
-0.005032094195485115,
0.007466025184839964,
0.008440308272838593,
0.01467992179095745,
-0.03303682804107666,
-0.09341886639595032,
0.02470887452363968,
0.030955694615840912,
0.014238010160624981,
0.041917577385902405,
-0.01743321307003498,
-0.04696831852197647,
0.012896038591861725,
-0.017471659928560257,
0.008894575759768486,
0.016475483775138855,
-0.036295995116233826,
0.05616765096783638,
0.0027929916977882385,
0.023157736286520958,
0.031993284821510315,
-0.000043978729081572965,
-0.0001905162789626047,
0.026385890319943428,
-0.04229239374399185,
0.020026572048664093,
0.0068243201822042465,
0.052373964339494705,
-0.05060200393199921,
-0.025692183524370193,
-0.016014540567994118,
0.017512384802103043,
-0.026365214958786964,
0.004734600428491831,
0.010270620696246624,
-0.02922821417450905,
-0.011840326711535454,
0.036218054592609406,
0.005493805278092623,
-0.005236727185547352,
-0.03503207117319107,
-0.002766889752820134,
-0.015168857760727406,
-0.02214815467596054,
0.013083121739327908,
-0.0031395109836012125,
0.021467551589012146,
0.04305092617869377,
-0.008241883479058743,
0.0068704974837601185,
-0.03840753436088562,
0.013733661733567715,
0.002443933393806219,
-0.04439590126276016,
0.06303252279758453,
-0.010021881200373173,
0.039053551852703094,
0.030939780175685883,
-0.0653843879699707,
-0.016597531735897064,
0.011820889078080654,
-0.021442949771881104,
0.02537861466407776,
-0.02862459048628807,
-0.001984005095437169,
-0.018795249983668327,
0.026683660224080086,
-0.07450105249881744,
-0.050716202706098557,
0.005219672340899706,
0.002836359664797783,
-0.008682647719979286,
-0.07753434032201767,
-0.012926040217280388,
-0.01536349393427372,
-0.02500711753964424,
-0.006027559284120798,
0.029859010130167007,
-0.02996159717440605,
-0.004945164080709219,
0.014497488737106323,
0.010137992911040783,
0.05510733276605606,
0.025708865374326706,
-0.00048205436905846,
0.013636631891131401,
-0.020973486825823784,
-0.014205238781869411,
-0.0078088343143463135,
0.014813708141446114,
-0.04505947604775429,
-0.009262697771191597,
-0.0307048037648201,
0.01613488793373108,
0.028504079207777977,
-0.047621604055166245,
-0.036902062594890594,
0.03165028616786003,
-0.012473287992179394,
-0.005337809212505817,
-0.029493091627955437,
-0.008546769618988037,
-0.02918902598321438,
0.03754274547100067,
-0.020653599873185158,
-0.015174520201981068,
0.0024228598922491074,
-0.00921568088233471,
0.011102680116891861,
0.0051056090742349625,
-0.005263237282633781,
0.010659578256309032,
0.039645880460739136,
-0.023041561245918274,
-0.0182367991656065,
0.02960903011262417,
-0.030898865312337875,
0.018072310835123062,
-0.03221052139997482,
-0.017100870609283447,
0.016724921762943268,
0.023377494886517525,
-0.014765892177820206,
-0.06908892840147018,
-0.07555811107158661,
0.01656429097056389,
0.03426112234592438,
0.005161532666534185,
0.04032810404896736,
0.058744534850120544,
0.018956629559397697,
-0.020362969487905502,
-0.00814624410122633,
-0.012601515278220177,
0.04642859846353531,
0.016081420704722404,
0.03210805729031563,
-0.0070390538312494755,
-0.007530545350164175,
0.02108147367835045,
0.04745562747120857,
-0.02123231813311577,
0.015406115911900997,
0.01201812457293272,
0.018721790984272957,
0.006354170385748148,
-0.03246113657951355,
-0.02633933536708355,
0.011781550012528896,
-0.04965629801154137,
0.03586088865995407,
-0.03032415732741356,
-0.02063574455678463,
0.04687439277768135,
0.027771083638072014,
0.02267329767346382,
0.007104860618710518,
0.001245145802386105,
-0.03260207176208496,
-0.0041746217757463455,
0.0025271663907915354,
0.010773385874927044,
-0.009529824368655682,
0.02227620594203472,
0.045104846358299255,
0.010437129996716976,
-0.0058036078698933125,
-0.004002124071121216,
-0.042341914027929306,
-0.05039126053452492,
-0.04763006418943405,
-0.06238703429698944,
0.03177764639258385,
0.07114559412002563,
-0.04635604843497276,
0.004237364046275616,
-0.03040659800171852,
0.049496982246637344,
-0.016712255775928497,
0.04864443466067314,
-0.044551536440849304,
0.027330216020345688,
0.0018589157843962312,
0.00012000613787677139,
-0.006630843970924616,
0.021925797685980797,
0.11776071041822433,
0.04910872504115105,
0.023287586867809296,
-0.04950759932398796,
-0.01481770258396864,
-0.03885158896446228,
0.030387641862034798,
-0.01859857514500618,
0.008789917454123497,
0.0004137686628382653,
0.0045821997337043285,
-0.02957889996469021,
0.03939114883542061,
-0.008626634255051613,
-0.007676247972995043,
0.022432908415794373,
-0.0476507842540741,
-0.05020203813910484,
0.01932194083929062,
0.011833217926323414,
0.019677624106407166,
0.023514794185757637,
-0.05156217887997627,
0.01749046891927719,
-0.025785142555832863,
0.0024525062181055546,
-0.05412689968943596,
-0.0029092575423419476,
0.03280141204595566,
0.02110826037824154,
-0.05334943160414696,
-0.004977438598871231,
-0.03298692777752876,
-0.01652361825108528,
-0.034668371081352234,
0.04679913446307182,
0.019716117531061172,
-0.015943210572004318,
0.009545695967972279,
0.03627137839794159,
-0.027966808527708054,
0.008528828620910645,
-0.027692001312971115,
-0.012106800451874733,
-0.003964620176702738,
-0.017084985971450806,
-0.009123384021222591,
0.0673164576292038,
-0.010100090876221657,
-0.031965222209692,
0.036716219037771225,
0.0030882994178682566,
0.010295608080923557,
-0.0747818872332573,
0.0034708541352301836,
0.015159863978624344,
0.040909599512815475,
-0.005103453528136015,
0.00015117402654141188,
-0.002419613068923354,
0.030538570135831833,
-0.023218471556901932,
-0.006625047884881496,
-0.01253103744238615,
-0.03225986286997795,
0.013526452705264091,
-0.013567676767706871,
0.022450480610132217,
-0.033537209033966064,
-0.014673000201582909,
-0.03670395538210869,
-0.026270482689142227,
-0.030440909788012505,
-0.045072559267282486,
0.04013945162296295,
0.035721782594919205,
0.049011483788490295,
-0.0030419458635151386,
-0.014608724974095821,
0.032568201422691345,
-0.03419053554534912,
-0.01813357137143612,
-0.01745475083589554,
-0.03169587254524231,
-0.01078916247934103,
0.0037521894555538893,
-0.005461000371724367,
0.04412652179598808,
-0.029064511880278587,
-0.02692599594593048,
-0.0031949770636856556,
-0.02343032695353031,
0.05309450253844261,
-0.0032065708655864,
0.004891583230346441,
0.018288321793079376,
-0.020205868408083916,
0.02799479477107525,
-0.01755075715482235,
0.03480413556098938,
-0.004916838835924864,
-0.022080913186073303,
0.033267926424741745,
0.047694288194179535,
-0.004300503991544247,
0.002918657846748829,
-0.003705705516040325,
-0.04612775892019272,
0.007914853282272816,
0.01866288110613823,
0.02302623726427555,
-0.06723687797784805,
-0.0280081145465374,
-0.038350384682416916,
-0.016350463032722473,
0.002613048767670989,
0.021704252809286118,
-0.04038376361131668,
0.03284657001495361,
-0.0027386294677853584,
0.016215739771723747,
-0.025749383494257927,
0.02620929293334484,
-0.0205534677952528,
0.02203177660703659,
-0.0037649504374712706,
-0.01285666972398758,
0.009124875999987125,
-0.014715349301695824,
-0.0004305725742597133,
-0.0198830533772707,
0.022828930988907814,
0.03252476453781128,
-0.011855516582727432,
0.018013793975114822,
-0.0006084712222218513,
0.028048550710082054,
0.039793577045202255,
-0.03449356183409691,
-0.015421679243445396,
0.023154616355895996,
-0.0695553570985794,
-0.013087624683976173,
0.010846241377294064,
-0.045743491500616074,
0.042495548725128174,
0.06708725541830063,
-0.0049886093474924564,
-0.012677204795181751,
0.03979214280843735,
-0.014491253532469273,
-0.015687985345721245,
0.024481553584337234,
-0.0006727289874106646,
0.005054950714111328,
-0.03175785019993782,
0.024980541318655014,
0.001380456960760057,
0.009157025255262852,
0.022261641919612885,
-0.0053283944725990295,
-0.026500830426812172,
0.018618838861584663,
-0.01342710480093956,
-0.00944601185619831,
0.0160736832767725,
0.000676635536365211,
-0.024521643295884132,
-0.021345127373933792,
0.03999647870659828,
-0.048664044588804245,
0.051167942583560944,
0.028036020696163177,
0.035208966583013535,
-0.10597182810306549,
-0.008380597457289696,
0.004856429994106293,
-0.009197443723678589,
0.012072552926838398,
-0.03328676521778107,
0.015186607837677002,
0.028480010107159615,
-0.08095468580722809,
0.07547087967395782,
-0.0035660644061863422,
-0.001669716089963913,
-0.046651482582092285,
-0.019865430891513824,
-0.032918039709329605,
0.03528119996190071,
0.02075672522187233,
0.030174460262060165,
0.011714097112417221,
0.0000029633811209350824,
-0.0020528140012174845,
-0.05897880345582962,
0.007274993695318699,
0.029826460406184196,
-0.04508189111948013,
0.02337857149541378,
-0.0007285825558938086,
-0.014316868968307972,
-0.036085743457078934,
-0.016688654199242592,
0.0002886242000386119,
0.0007003284990787506,
-0.009905382059514523,
-0.006214857567101717,
-0.008233502507209778,
0.0736161395907402,
0.03433459624648094,
-0.028312942013144493,
0.01928531564772129,
0.004200130235403776,
0.019699562340974808,
-0.016389504075050354,
-0.010226062498986721,
0.03978605195879936,
0.04057895764708519,
-0.028169400990009308,
-0.024207916110754013,
0.03159789368510246,
0.05572080984711647,
0.014035815373063087,
-0.002522530732676387,
-0.00402385788038373,
0.013297799974679947,
-0.009553078562021255,
-0.00938123557716608,
-0.02701018750667572,
-0.0011072080815210938,
0.04474520683288574,
0.023570405319333076,
0.00045571388909593225,
0.012291898019611835,
-0.03145812451839447,
-0.03316169232130051,
-0.0028996162582188845,
-0.01118473056703806,
-0.054011642932891846,
-0.05974484607577324,
-0.0025688617024570704,
0.04012361168861389,
0.02738383412361145,
0.008590469136834145,
-0.014735632576048374,
-0.04634442180395126,
0.004723879974335432,
-0.013909689150750637,
-0.007288767956197262,
-0.005576503928750753,
0.0022216252982616425,
-0.03310856223106384,
-0.08438178151845932,
0.04654749110341072,
-0.0018735616467893124,
0.015123323537409306,
-0.014865728095173836,
0.003997902851551771,
-0.016634469851851463,
0.04116755723953247,
0.0654941201210022,
0.030001014471054077,
-0.019901053979992867,
-0.041794467717409134,
-0.019545791670680046,
0.007278024684637785,
-0.03241848200559616,
-0.007830288261175156,
-0.029219357296824455,
-0.018165025860071182,
-0.012196322903037071,
0.0010969016002491117,
0.004286686424165964,
-0.020318813621997833,
0.011763567104935646,
-0.003994953352957964,
-0.022721782326698303,
-0.014941457659006119,
-0.03996758162975311,
0.06743230670690536,
0.0009259716607630253,
0.028545495122671127,
0.04489152505993843,
0.03578730672597885,
0.011423485353589058,
0.02444939874112606,
0.008332679979503155,
-0.00995962880551815,
0.0009668165585026145,
-0.027440881356596947,
-0.017932385206222534,
0.014757257886230946,
-0.0060035125352442265,
0.029274245724081993,
-0.03715960308909416,
-0.010996940545737743,
0.05713436380028725,
-0.03208663687109947,
-0.000563786132261157,
0.04532063379883766,
0.008063027635216713,
0.047804512083530426,
0.023101767525076866,
0.029293851926922798,
0.019869480282068253,
0.008676503784954548,
0.008396088145673275,
0.03203153982758522,
0.01885196380317211,
-0.006746778730303049,
0.06146019697189331,
0.044188883155584335,
-0.04895078018307686,
-0.008235707879066467,
0.05288493260741234,
0.03548869490623474,
-0.011495853774249554,
0.001485925749875605,
0.042971596121788025,
-0.007691339123994112,
-0.013013330288231373,
0.004401898942887783,
-0.035704564303159714,
0.10449434816837311,
-0.005032951012253761,
0.010500527918338776,
-0.041196513921022415,
0.038635630160570145,
-0.03263881802558899,
0.02758008986711502,
-0.0014610548969358206,
0.06567419320344925,
-0.027586348354816437,
-0.009118553251028061,
-0.05386305972933769,
0.017086803913116455,
0.036009859293699265,
-0.0829034224152565,
0.011656860820949078,
0.017986858263611794,
-0.0135060278698802,
0.009634344838559628,
0.0005294069997034967,
-0.01112675666809082,
-0.01838473603129387,
0.039272792637348175,
0.04714416712522507,
0.030246777459979057,
0.005614390596747398,
-0.019780408591032028,
0.02135371044278145,
0.013601012527942657,
-0.0254450011998415,
-0.020309478044509888,
-0.016737056896090508,
0.018182044848799706,
-0.014770496636629105,
0.030252350494265556
] |
<p>I wanted to know why there is a hole in the ball (basketball, volleyball, handball) to fill the ball with air. Why can't the ball come with filled in air and fully sealed so that there is no loss of air?</p> | 1,514 | [
-0.06248096749186516,
0.011175489984452724,
-0.009957512840628624,
-0.004680895246565342,
0.011797180399298668,
0.004797065630555153,
0.017360564321279526,
-0.02127871662378311,
-0.013889600522816181,
0.030366308987140656,
0.013332843780517578,
0.0321231447160244,
-0.0016241823323071003,
0.023231910541653633,
-0.0019456603331491351,
-0.029708074405789375,
0.01402197778224945,
-0.033703628927469254,
-0.018002141267061234,
-0.01697385311126709,
-0.014403728768229485,
-0.020813902840018272,
-0.03962164372205734,
0.020823374390602112,
-0.01905241422355175,
0.0078135896474123,
0.020820820704102516,
-0.029775578528642654,
0.06949350982904434,
0.03803185746073723,
-0.006350355222821236,
0.004799569491297007,
0.011951341293752193,
0.020531531423330307,
0.008344542235136032,
-0.04550157114863396,
-0.016604671254754066,
0.00927768275141716,
-0.023252109065651894,
-0.005118582397699356,
-0.04164084419608116,
-0.03405703604221344,
0.00622566370293498,
0.047862738370895386,
0.015477475710213184,
0.0588068887591362,
0.014237641356885433,
-0.02149871177971363,
0.040406521409749985,
-0.08561065047979355,
0.01984478533267975,
0.009674991481006145,
0.044290948659181595,
0.011808057315647602,
0.0007220113184303045,
0.03863910213112831,
0.07926805317401886,
0.07824920862913132,
-0.022490672767162323,
-0.051118046045303345,
0.03104088082909584,
-0.004583233967423439,
-0.022043529897928238,
-0.013132407329976559,
0.00792374461889267,
0.03801615908741951,
-0.033434417098760605,
-0.027388373389840126,
0.05062779784202576,
-0.0017735728761181235,
0.02591927908360958,
0.010666045360267162,
0.03419015184044838,
-0.04083024337887764,
0.0512421689927578,
-0.007272660732269287,
0.029047371819615364,
-0.02137899585068226,
0.039361532777547836,
0.04947564750909805,
-0.025619085878133774,
0.00768692372366786,
0.054461147636175156,
-0.006171152926981449,
-0.007987339980900288,
-0.006824943237006664,
0.057089630514383316,
-0.021456388756632805,
0.01352300401777029,
0.009386254474520683,
-0.010082653723657131,
-0.03687489405274391,
0.04422290623188019,
0.009275144897401333,
-0.014722287654876709,
0.011486438103020191,
-0.006727194879204035,
0.04774456098675728,
0.004515296779572964,
-0.031177742406725883,
0.0326811708509922,
0.024779221042990685,
0.03546910732984543,
0.046249326318502426,
0.02104206569492817,
-0.02577977068722248,
-0.06019020453095436,
0.018187586218118668,
0.00017333809228148311,
0.04775753244757652,
-0.042438436299562454,
-0.004661228973418474,
-0.04122051224112511,
0.014031743630766869,
0.03144374117255211,
-0.027841582894325256,
0.0011922805570065975,
-0.0006913287215866148,
0.028358090668916702,
0.05551820620894432,
0.03968806937336922,
-0.02572433091700077,
0.028671877458691597,
-0.014886836521327496,
-0.07816183567047119,
0.040863361209630966,
-0.005382118746638298,
0.011808515526354313,
-0.009517543017864227,
0.013818860054016113,
-0.01922919601202011,
-0.01861928589642048,
0.035723648965358734,
0.05385807529091835,
0.06829933077096939,
-0.04327726364135742,
-0.10826533287763596,
-0.05699428543448448,
0.05110754817724228,
0.004894641228020191,
-0.06702428311109543,
-0.08492600917816162,
0.032718706876039505,
0.0009926238562911749,
0.09237530827522278,
0.02315104566514492,
0.0050797732546925545,
0.002378239296376705,
0.0397493876516819,
0.016482263803482056,
-0.007181511726230383,
-0.04709916189312935,
-0.000953394512180239,
-0.03992702066898346,
0.03284711763262749,
-0.04787145182490349,
0.022846287116408348,
0.021986663341522217,
0.02064361609518528,
-0.06188058853149414,
-0.000867632043082267,
-0.03317185491323471,
-0.037960320711135864,
-0.03464093431830406,
-0.025896698236465454,
-0.030765658244490623,
0.015472933650016785,
-0.027003459632396698,
0.019869502633810043,
0.048270195722579956,
-0.0028455143328756094,
0.04325632005929947,
-0.002041471190750599,
0.02449873648583889,
-0.0015852979850023985,
-0.019668713212013245,
-0.005773372482508421,
-0.005591187626123428,
0.03934649005532265,
-0.008814467117190361,
-0.041528407484292984,
0.01875379867851734,
0.030381156131625175,
0.03486345708370209,
-0.0014044070849195123,
0.03812127187848091,
0.03265783190727234,
-0.015382456593215466,
0.01138363778591156,
-0.0670223981142044,
-0.034184083342552185,
-0.08565206080675125,
0.04098905622959137,
-0.014493683353066444,
0.0015863582957535982,
-0.007300238125026226,
0.01663028635084629,
0.01769617758691311,
-0.026595761999487877,
0.011358794756233692,
-0.019879499450325966,
0.031533509492874146,
-0.00439556036144495,
-0.032738037407398224,
0.00822608545422554,
0.055758893489837646,
0.06477697193622589,
0.01465554442256689,
0.04820867255330086,
-0.0034799876157194376,
-0.014036495238542557,
0.0053792367689311504,
-0.03512142226099968,
0.008866424672305584,
-0.034780919551849365,
-0.007962099276483059,
0.04788836091756821,
0.005464958492666483,
0.02467755414545536,
0.017649272456765175,
-0.017065344378352165,
0.05949369817972183,
0.04619787260890007,
-0.008108371868729591,
-0.015508938580751419,
0.02541804499924183,
-0.020706670358777046,
0.0020997896790504456,
0.03393775224685669,
-0.0461171455681324,
-0.03581932932138443,
0.011332022957503796,
0.007200476713478565,
0.0247004684060812,
-0.030723240226507187,
0.0011654563713818789,
0.005759772378951311,
0.006514525506645441,
-0.012881744652986526,
0.01813761331140995,
-0.02593286894261837,
-0.0527300089597702,
0.000523288850672543,
0.039238668978214264,
0.012251337990164757,
0.04332413896918297,
0.02077975682914257,
0.02235342562198639,
0.015530996024608612,
-0.022421864792704582,
-0.0035767671652138233,
0.02704811468720436,
-0.0002514322695787996,
0.03965034708380699,
0.022025832906365395,
0.013616476207971573,
-0.003399675013497472,
-0.020280785858631134,
0.007677776739001274,
-0.009612197056412697,
0.015941254794597626,
0.00936575885862112,
-0.03836541622877121,
-0.013563728891313076,
0.009657840244472027,
0.06959614157676697,
0.015161104500293732,
-0.013061132282018661,
0.015874097123742104,
-0.0570337288081646,
-0.0021518925204873085,
-0.01796460524201393,
0.03261541947722435,
-0.021935543045401573,
0.00823740754276514,
0.03767610341310501,
0.00220774975605309,
0.0014252306427806616,
-0.006830540020018816,
-0.027122706174850464,
-0.026273740455508232,
0.00252727628685534,
-0.019273631274700165,
-0.016472918912768364,
-0.016468429937958717,
0.04243667796254158,
-0.0054416959173977375,
-0.013264229521155357,
0.016245638951659203,
-0.027744092047214508,
0.013917268253862858,
0.01836530491709709,
-0.004245103802531958,
-0.005686919670552015,
0.003379646921530366,
-0.031218498945236206,
0.021062452346086502,
0.03237815201282501,
0.02325309067964554,
0.04439840838313103,
-0.018924571573734283,
-0.028836892917752266,
0.0025147495325654745,
-0.05569673329591751,
-0.0394148975610733,
-0.069984570145607,
-0.04870285838842392,
0.0496266633272171,
-0.0483078733086586,
0.0008784146048128605,
0.0045235916040837765,
-0.015787387266755104,
0.0025262637063860893,
-0.009236582554876804,
-0.04154417663812637,
0.007018503732979298,
-0.006954621989279985,
0.027852319180965424,
-0.003449051408097148,
-0.03382960334420204,
0.05464821681380272,
0.003259338904172182,
-0.022452279925346375,
-0.006208816543221474,
-0.015727045014500618,
-0.01224525272846222,
-0.04521160200238228,
0.018569134175777435,
0.032418716698884964,
-0.01734006218612194,
0.0562148354947567,
0.01953830011188984,
0.011436717584729195,
0.03754185512661934,
0.03711923211812973,
-0.025231139734387398,
-0.047046009451150894,
0.01346209179610014,
-0.00882891844958067,
0.023952415212988853,
-0.0150737464427948,
-0.01550067588686943,
-0.02552267350256443,
-0.00246351957321167,
0.02694328874349594,
0.03298337385058403,
-0.03184236213564873,
0.01783772185444832,
-0.04573274031281471,
-0.0015178575413301587,
-0.027229685336351395,
0.028170404955744743,
-0.0259014293551445,
-0.011053774505853653,
0.027090635150671005,
0.025173453614115715,
0.02062961645424366,
-0.01678134687244892,
-0.011820297688245773,
0.03516102209687233,
0.035131245851516724,
-0.08260126411914825,
-0.004002086352556944,
0.007502041757106781,
0.053807709366083145,
0.06826840341091156,
0.00021311607270035893,
-0.015451508574187756,
0.030222328379750252,
0.03715474158525467,
0.02918420545756817,
0.0029382098000496626,
-0.012024074792861938,
0.00982813909649849,
-0.03813047707080841,
0.0009867949411273003,
-0.004887960385531187,
0.026070022955536842,
-0.007537444122135639,
0.05066843703389168,
0.020622707903385162,
0.020588183775544167,
0.030865667387843132,
-0.00933142565190792,
-0.06935044378042221,
0.0061889709904789925,
-0.02248530462384224,
0.015138075686991215,
-0.030705321580171585,
-0.0026993239298462868,
0.0016364898765459657,
-0.03541986644268036,
-0.05721840262413025,
-0.009361226111650467,
-0.03268829733133316,
-0.074592225253582,
0.021366242319345474,
-0.005140392575412989,
-0.039746467024087906,
0.003524151863530278,
0.043452031910419464,
0.018951961770653725,
0.034369032829999924,
0.04563169553875923,
0.03920473903417587,
-0.011907239444553852,
0.0036541884765028954,
0.007958192378282547,
0.017622029408812523,
0.02421831712126732,
0.022948555648326874,
0.04326530173420906,
0.0313795767724514,
-0.006610014010220766,
-0.044980064034461975,
0.0037533456925302744,
0.03580329939723015,
-0.026013027876615524,
0.028213167563080788,
-0.03504811227321625,
-0.04948936775326729,
-0.013051425106823444,
-0.01420800480991602,
0.0453757680952549,
-0.014013574458658695,
0.03546396642923355,
0.004590160679072142,
-0.0297782514244318,
-0.012302989140152931,
-0.006581538822501898,
0.02442801184952259,
0.034735798835754395,
-0.03913090378046036,
-0.03280384838581085,
-0.013023287989199162,
-0.046163637191057205,
-0.010842334479093552,
-0.006991901900619268,
0.02343890815973282,
-0.034465059638023376,
-0.016446096822619438,
0.019466720521450043,
-0.013360987417399883,
0.013876955956220627,
0.0327366404235363,
-0.0013876419980078936,
0.0004280023567844182,
-0.018278438597917557,
0.0030277122277766466,
0.016036884859204292,
0.04661627486348152,
0.026178820058703423,
0.024794768542051315,
-0.02989836037158966,
-0.0278445016592741,
-0.033017341047525406,
0.027009526267647743,
0.03521795943379402,
-0.010749182663857937,
0.005554518196731806,
-0.04758202284574509,
-0.04984765872359276,
0.06433846801519394,
-0.03641465678811073,
0.016529474407434464,
-0.07124079763889313,
-0.003997576888650656,
-0.028245126828551292,
0.013220677152276039,
-0.018283944576978683,
0.003107828088104725,
-0.006572505924850702,
0.006658471655100584,
0.015590254217386246,
-0.013496505096554756,
0.0011076002847403288,
0.017695054411888123,
0.03672269731760025,
0.04256289079785347,
0.015891263261437416,
0.012073399499058723,
-0.018903296440839767,
0.0012607781682163477,
-0.030501674860715866,
-0.06463497132062912,
-0.010276343673467636,
0.009324000217020512,
-0.01012285053730011,
-0.019098257645964622,
-0.027512328699231148,
-0.0471651554107666,
-0.008233552798628807,
0.0008567433105781674,
0.01875896379351616,
0.02649628557264805,
-0.06906973570585251,
0.017201650887727737,
0.009104792028665543,
-0.007960483431816101,
0.022793903946876526,
0.016070667654275894,
-0.02731928788125515,
-0.04058481380343437,
-0.04019923135638237,
0.010606848634779453,
-0.038766779005527496,
-0.0012059399159625173,
-0.04390078783035278,
0.005429863464087248,
-0.004778363276273012,
0.07027822732925415,
0.005119015462696552,
0.01665012165904045,
0.00622124969959259,
-0.07058416306972504,
-0.026416853070259094,
0.04667428880929947,
0.004480879288166761,
0.0013962704688310623,
-0.016654254868626595,
0.010458813048899174,
0.023099385201931,
0.001235293922945857,
-0.0017221842426806688,
0.004651174880564213,
-0.011080301366746426,
0.03666048124432564,
0.014633224345743656,
0.039981208741664886,
-0.04171879589557648,
-0.018427344039082527,
-0.013570618815720081,
-0.07947210222482681,
0.055438436567783356,
-0.027598602697253227,
-0.031015686690807343,
0.055186353623867035,
-0.07211984694004059,
-0.01794479228556156,
-0.02696031518280506,
0.010162891820073128,
0.049962885677814484,
-0.048636142164468765,
0.040159210562705994,
-0.0013509212294593453,
-0.011629877611994743,
-0.06545168161392212,
-0.038066763430833817,
0.025148997083306313,
-0.0011348327388986945,
-0.017361802980303764,
-0.03353429213166237,
-0.00024051651416812092,
-0.006323880050331354,
-0.04491544887423515,
0.010036526247859001,
0.00655266223475337,
-0.03006143309175968,
0.00731544429436326,
0.04332173615694046,
0.006825048942118883,
0.005195955280214548,
0.038997456431388855,
-0.0032151425257325172,
0.01939471997320652,
0.003625919111073017,
-0.03782590106129646,
-0.00745032262057066,
0.020208705216646194,
-0.028454352170228958,
-0.032944876700639725,
0.026411069557070732,
-0.008860628120601177,
0.03922174125909805,
-0.00787690281867981,
-0.0007986419950611889,
-0.0004915679455734789,
0.01911371946334839,
0.01093410886824131,
0.0030432844068855047,
0.026377614587545395,
0.0059267617762088776,
0.040682364255189896,
0.007243443746119738,
-0.0005043924320489168,
-0.02503911219537258,
-0.022976228967308998,
0.02605830505490303,
0.002395401708781719,
0.04560086503624916,
-0.016670675948262215,
0.038076307624578476,
-0.050466690212488174,
-0.06514127552509308,
-0.008394604548811913,
-0.0005164314061403275,
0.06037596985697746,
0.018147803843021393,
-0.040076844394207,
0.01675407774746418,
0.0434504859149456,
-0.013691072352230549,
-0.04882413521409035,
0.01530015841126442,
0.023530099540948868,
0.020186301320791245,
-0.04212497919797897,
0.03788268193602562,
0.013057920150458813,
-0.011711024679243565,
-0.01681574061512947,
-0.029148278757929802,
0.002815311774611473,
0.04582434892654419,
-0.008462774567306042,
0.02095932327210903,
-0.0022485379595309496,
0.005475600715726614,
0.04454652965068817,
0.019336484372615814,
-0.0054704281501472,
0.046673744916915894,
0.04970751330256462,
0.03226320818066597,
-0.011708052828907967,
0.0028165546245872974,
-0.021921854466199875,
0.022341635078191757,
-0.019448159262537956,
0.0631544291973114,
0.01333996094763279,
-0.0037051828112453222,
0.04127953201532364,
-0.02245369181036949,
0.0024109811056405306,
-0.035152189433574677,
-0.011586726643145084,
-0.06662482768297195,
0.02619282715022564,
0.012461544945836067,
0.004213524051010609,
0.016588380560278893,
0.01183641143143177,
0.00954253226518631,
-0.0038453962188214064,
-0.008700396865606308,
-0.021157704293727875,
-0.04035639762878418,
-0.007184469606727362,
-0.04395386576652527,
-0.01754176989197731,
0.031491655856370926,
0.006970842368900776,
-0.007426355965435505,
-0.00149475724902004,
-0.009423724375665188,
-0.007779494859278202,
-0.0238322913646698,
0.017499292269349098,
-0.040994953364133835,
0.05787203460931778,
0.04010400176048279,
0.022019462659955025,
-0.013725824654102325,
0.03597991168498993,
0.13948513567447662,
0.001804777537472546,
0.003822839120402932,
-0.047284919768571854,
0.0029300216119736433,
-0.01370102446526289,
-0.019537614658474922,
-0.025318268686532974,
0.0443214513361454,
-0.014214113354682922,
0.026728836819529533,
0.05230768024921417,
0.0501050166785717,
-0.020553767681121826,
0.033635638654232025,
0.02454652637243271,
-0.04604480415582657,
-0.015703950077295303,
-0.03436635062098503,
0.023051142692565918,
-0.025573190301656723,
0.047523584216833115,
0.007967710494995117,
0.03386446461081505,
-0.005544798448681831,
-0.015319657512009144,
-0.01972116157412529,
-0.057121362537145615,
0.03390048071742058,
-0.00819416344165802,
-0.06796201318502426,
0.005028722807765007,
0.03137998655438423,
-0.019108090549707413,
-0.0718231052160263,
0.017800506204366684,
0.029297102242708206,
-0.023557594045996666,
-0.013768065720796585,
-0.004597702529281378,
0.04538394510746002,
0.015918899327516556,
0.012035376392304897,
0.043455008417367935,
-0.05324435234069824,
-0.018057484179735184,
-0.024795707315206528,
0.01722012646496296,
-0.015747450292110443,
0.023389482870697975,
-0.012591914273798466,
-0.01604052446782589,
-0.0010456073796376586,
-0.04754739627242088,
-0.0513712614774704,
-0.008663966320455074,
0.019451115280389786,
-0.012277520261704922,
-0.04858004301786423,
0.002395858522504568,
-0.005187124013900757,
0.011695136316120625,
0.01869746297597885,
-0.056857820600271225,
0.01400304026901722,
0.01704532839357853,
-0.020476726815104485,
0.04346514493227005,
-0.04506673291325569,
-0.0037640074733644724,
-0.027134008705615997,
0.02830035239458084,
-0.038730185478925705,
0.008139414712786674,
0.007490856572985649,
0.02953544445335865,
0.04017338529229164,
0.022013047710061073,
0.006776284426450729,
0.028280653059482574,
-0.01822224259376526,
0.006221457850188017,
-0.013387514278292656,
-0.016694650053977966,
-0.045607343316078186,
-0.0106100644916296,
-0.029425382614135742,
0.043213486671447754,
-0.046086546033620834,
-0.006544196046888828,
-0.020565209910273552,
0.025839637964963913,
-0.02311108075082302,
-0.02255643531680107,
-0.07007183879613876,
0.004438167903572321,
-0.054813917726278305,
0.02378188446164131,
-0.0014145737513899803,
0.026940466836094856,
0.03572196140885353,
0.06070086359977722,
0.032915133982896805,
-0.01035718247294426,
-0.02487923577427864,
0.005764378234744072,
-0.007375752087682486,
-0.021425297483801842,
-0.011541750282049179,
0.01241978257894516,
0.022164206951856613,
-0.03203941881656647,
-0.035245753824710846,
-0.042295198887586594,
-0.0030396687798202038,
-0.01776796020567417,
0.025329669937491417,
-0.008607047609984875,
0.038984302431344986,
-0.02992824837565422,
0.0021255675237625837,
-0.024675045162439346,
0.006805524230003357,
-0.0878138467669487,
-0.016452765092253685,
0.054417967796325684,
-0.010397597216069698,
-0.005412489641457796,
0.006972785573452711,
-0.05981538072228432,
0.016513757407665253,
0.004849760327488184,
0.0029743039049208164,
-0.009822284802794456,
-0.020722877234220505,
0.012062016874551773,
0.014569726772606373,
0.05133478716015816,
-0.036406729370355606,
-0.026190591976046562,
0.014819944277405739,
-0.04560646787285805,
-0.06048506870865822,
0.012620266526937485,
0.017870072275400162,
0.025514742359519005,
0.0028096006717532873,
0.007828783243894577,
-0.004620225168764591,
0.05310586467385292,
-0.01878940500319004,
0.014945684000849724,
-0.0031921614427119493,
-0.021988630294799805,
0.013798949308693409,
0.0027126730419695377,
0.01790982484817505,
-0.04618100821971893,
-0.0016500153578817844,
0.05598773434758186,
-0.006767424289137125,
0.02031887136399746,
0.005250213202089071,
0.015268301591277122,
-0.0020531376358121634,
0.033662453293800354,
0.026190700009465218,
0.028603659942746162,
0.010967027395963669,
0.03814804181456566,
0.0352775938808918,
0.048255447298288345,
0.052615538239479065,
-0.019764695316553116,
-0.11039596050977707,
-0.001184834516607225,
-0.0036098246928304434,
0.0014178116107359529,
0.020552389323711395,
-0.020626211538910866,
0.03192947804927826,
0.017126578837633133,
-0.059380706399679184,
0.00012074765254510567,
-0.033493414521217346,
0.00030578370206058025,
-0.057017870247364044,
-0.02479974925518036,
-0.023443877696990967,
0.019851483404636383,
0.05766597390174866,
0.011122013442218304,
0.0030008822213858366,
0.003331358777359128,
-0.010971439070999622,
0.013492235913872719,
-0.044196560978889465,
0.039348479360342026,
-0.018621141090989113,
-0.0005539938574656844,
0.06508175283670425,
0.00032121289405040443,
0.0029977746307849884,
-0.011633801274001598,
-0.02969471551477909,
0.009635730646550655,
0.024898748844861984,
-0.009311480447649956,
-0.04295135289430618,
-0.00032073335023596883,
0.045255061239004135,
0.02064969390630722,
0.02098628506064415,
0.0204838328063488,
0.01700347661972046,
-0.02349388226866722,
-0.016663003712892532,
0.032005056738853455,
0.0030247096437960863,
-0.03204231336712837,
-0.0260868389159441,
0.007627055048942566,
-0.02652193047106266,
-0.016949545592069626,
-0.002474938752129674,
0.009609241969883442,
0.03310718387365341,
-0.019586168229579926,
-0.04685031622648239,
-0.004609739873558283,
-0.003815677482634783,
0.030081672593951225,
0.025919556617736816,
-0.022853944450616837,
0.04413335770368576,
-0.031441815197467804,
-0.010909276083111763,
-0.02291456051170826,
0.06303984671831131,
0.0023010168224573135,
0.005172573495656252,
-0.000771770253777504,
0.03052506223320961,
-0.030486784875392914,
-0.012645178474485874,
-0.039735183119773865,
-0.02866085059940815,
0.006696878466755152,
0.06146027147769928,
0.031448449939489365,
0.03401025012135506,
-0.03416529670357704,
-0.01636364683508873,
-0.07892011106014252,
0.03127731382846832,
-0.02884400635957718,
-0.022250475361943245,
-0.012475033290684223,
-0.03912800922989845,
0.005262795835733414,
0.025027520954608917,
0.0610334575176239,
-0.006517239846289158,
-0.034703221172094345,
0.013224069960415363,
0.03968869894742966,
0.028257014229893684,
-0.008436637930572033,
0.01959286630153656,
0.001048241974785924,
-0.005620281212031841,
0.03596165403723717,
-0.004233240615576506,
0.023687517270445824,
0.004852015990763903,
0.04228372871875763,
-0.03558484837412834,
0.03642818331718445,
-0.0414542555809021,
-0.017760857939720154,
0.021367667242884636,
0.05620960146188736,
-0.03584546595811844,
0.08276545256376266,
-0.024991776794195175,
-0.00885079801082611,
-0.009217980317771435,
-0.019842568784952164,
-0.02969745360314846,
0.03811529278755188,
-0.020459894090890884,
-0.002441358519718051,
-0.02015698328614235,
-0.03248579055070877,
0.016664519906044006,
-0.06330128014087677,
0.023245248943567276,
0.07292168587446213,
-0.01011610683053732,
-0.01786394603550434,
0.04140544682741165,
0.04384447634220123,
0.01734885573387146,
-0.028477510437369347,
-0.00866077933460474,
-0.005447457078844309,
-0.012783471494913101,
-0.04028305783867836,
0.058393217623233795,
0.02537338063120842,
0.0128322783857584,
-0.0390140637755394,
0.014221206307411194,
0.020303187891840935,
0.008296758867800236,
0.029107077047228813,
0.08874794840812683,
-0.019366886466741562,
-0.04038037732243538,
-0.026688212528824806,
-0.020030589774250984,
0.015716856345534325,
-0.002379766898229718,
-0.01957518979907036,
0.05998891219496727,
-0.005002171732485294,
0.015260561369359493,
-0.02316903881728649,
0.0542280487716198,
-0.02128928154706955,
-0.013443248346447945,
0.06564796715974808,
0.013492556288838387,
0.028421442955732346,
-0.010076481848955154,
-0.006732023321092129,
-0.0032799181062728167,
0.013285391964018345,
0.010763761587440968,
0.008558765053749084,
-0.0046636564657092094,
-0.009117725305259228,
-0.037776656448841095,
-0.011686873622238636,
0.020879853516817093,
-0.025747675448656082,
0.05430588871240616,
0.02287900447845459,
0.027567023411393166,
0.014720761217176914,
-0.014487373642623425,
-0.034629225730895996,
0.07817006856203079,
-0.06997110694646835,
-0.006292643956840038,
-0.03816364333033562,
0.030656268820166588,
-0.029610635712742805,
0.03612186387181282
] |
<p>I'm wondering if there is a textbook that describes the handiwork of a particle physics analysis. There are a bunch of books about theory, about the experimental aspects like detectors, and about statistical methods, but I haven't seen one that focused on the actual work of an analyzer.</p>
<p>I mean stuff like:</p>
<ul>
<li>How to conduct a search vs. a measurement</li>
<li>What backgrounds to consider for a final state, and how to model them</li>
<li>What distributions to look at -- pT of various objects or MET are obvious, but there are things like transverse masses, $\cos \theta^*$, aplanarity, the Florida variable (seriously), or ptBalance, that you first have to know about</li>
<li>How to choose signal regions, sidebands</li>
<li>How to determine systematic errors concretely</li>
<li>How to perform a cutflow</li>
<li>How to do tag-and-probe</li>
<li>How to perform a multivariate analysis, and how to choose btw. techniques</li>
<li>How to set limits, and how to perform combinations</li>
</ul>
<p>Most of this stuff is covered in various books, but mostly from a different perspective. For example, its nice to know how to solve an integral with Monte Carlo methods, and what the factorization theorem does. But for someone working on an analysis its more useful to know what the main differences between MC generators are, and how to deal with negative event weights in various situations. Similarly, there are a couple of textbooks about statistics for high energy physics, but those I've found tend to focus on derivations, instead of practical issues of the analysis.</p>
<p>Does anyone know of a book that fits my description?</p>
<p><em>(Note I don't believe this fits very well under the current <a href="http://meta.physics.stackexchange.com/questions/4697/are-resource-recommendations-allowed">book policy</a>. Resource recommendation questions tend to be fairly broad, and thus the answers have to be very descriptive. In this case, the question is already descriptive, so a brief answer would also be OK, even a negative answer (a la "I've been a expert for 20 years and can say for certain that such a book doesn't exist").)</em></p> | 1,515 | [
-0.007162848021835089,
-0.038047775626182556,
0.009146018885076046,
-0.0228717178106308,
0.06943017989397049,
0.06656751036643982,
-0.0002738925686571747,
-0.05436720699071884,
0.012040846981108189,
-0.02032456174492836,
0.06033358350396156,
0.01520104706287384,
0.04385757818818092,
0.026567501947283745,
-0.006558937951922417,
0.003120020730420947,
-0.009826404973864555,
-0.049572959542274475,
-0.03329414501786232,
0.0012146978406235576,
0.03913654386997223,
0.0310797318816185,
-0.01723109371960163,
0.0114747891202569,
-0.039021749049425125,
0.009634377434849739,
0.01132089551538229,
-0.007371850777417421,
-0.007901758886873722,
0.05158955231308937,
-0.06214696168899536,
-0.013772784732282162,
0.013973415829241276,
-0.0007158767548389733,
0.009548789821565151,
0.030326468870043755,
0.015159150585532188,
-0.035796500742435455,
0.0008633582037873566,
0.013072379864752293,
-0.06606590002775192,
-0.017593445256352425,
-0.010083076544106007,
0.023430539295077324,
0.0026333723217248917,
0.031590498983860016,
-0.03365303948521614,
-0.009663754142820835,
0.05113312229514122,
-0.07693886756896973,
0.03815143182873726,
0.010350195690989494,
0.016399085521697998,
0.028826093301177025,
0.027071472257375717,
-0.0129757234826684,
0.04265904426574707,
0.08259856700897217,
0.0021366975270211697,
-0.07746904343366623,
-0.033486444503068924,
-0.03507324680685997,
0.0006198432529345155,
-0.02075158804655075,
-0.008831499144434929,
0.010467683896422386,
0.024005357176065445,
-0.008287475444376469,
0.010050342418253422,
-0.014847670681774616,
0.019724104553461075,
0.013997476547956467,
0.015458127483725548,
-0.004003362264484167,
-0.007970776408910751,
-0.0030238935723900795,
0.02072305791079998,
-0.0009009561617858708,
0.03255079686641693,
0.0312936045229435,
-0.0024238508194684982,
0.007709479425102472,
-0.010122902691364288,
0.03437818959355354,
-0.0035840775817632675,
-0.02133609913289547,
0.08320058137178421,
-0.026741713285446167,
-0.06798947602510452,
-0.009909065440297127,
-0.01869353838264942,
-0.00005663833144353703,
0.00011134306259918958,
-0.027781333774328232,
-0.03696073219180107,
0.02815733104944229,
0.0126648535951972,
0.018857711926102638,
-0.015323406085371971,
0.011305246502161026,
-0.015124992467463017,
-0.030313260853290558,
-0.011007865890860558,
0.06775569170713425,
0.007079406175762415,
-0.018045347183942795,
-0.01972327195107937,
0.023204021155834198,
-0.034185200929641724,
-0.015899505466222763,
0.004042393062263727,
0.012356490828096867,
0.02005729451775551,
0.009373242035508156,
-0.013158508576452732,
-0.01885310374200344,
0.0186702199280262,
-0.01660078577697277,
0.07744990289211273,
0.058816928416490555,
0.0527658686041832,
-0.025121521204710007,
-0.009796405211091042,
-0.035954177379608154,
-0.07463414967060089,
-0.027093959972262383,
0.05191633850336075,
-0.0178130641579628,
-0.07286093384027481,
0.046484094113111496,
0.023028066381812096,
-0.00017287384252995253,
0.01883362978696823,
0.03329534828662872,
-0.010448850691318512,
0.014501848258078098,
-0.09629697352647781,
-0.07918830960988998,
0.04491721838712692,
-0.03385360166430473,
-0.07696506381034851,
-0.03224610537290573,
-0.031201958656311035,
0.035040538758039474,
0.042007189244031906,
-0.008460860699415207,
0.01337884645909071,
-0.011219903826713562,
0.03096373938024044,
-0.005784136708825827,
-0.022604772821068764,
0.0044838846661150455,
-0.015723885968327522,
0.013510837219655514,
-0.012946699745953083,
-0.05223144590854645,
0.04850723594427109,
0.020733794197440147,
0.001877878326922655,
0.004129135515540838,
0.05930006504058838,
0.014520341530442238,
-0.011954166926443577,
0.00226612389087677,
-0.035113345831632614,
-0.009870932437479496,
0.053964756429195404,
0.024696141481399536,
0.02588110789656639,
-0.008200140669941902,
-0.015363325364887714,
0.012503018602728844,
-0.04477182775735855,
-0.00973319448530674,
0.06047610938549042,
-0.030123112723231316,
-0.05894352123141289,
-0.006132217589765787,
-0.01989920809864998,
-0.02519066073000431,
-0.002565906383097172,
-0.04106493294239044,
-0.028478870168328285,
0.009905891492962837,
0.008056577295064926,
0.00623993668705225,
0.04181444272398949,
0.009036955423653126,
0.017491210252046585,
-0.04165159538388252,
-0.012731942348182201,
-0.025535112246870995,
-0.04869840294122696,
-0.024424875155091286,
-0.027861902490258217,
0.06612357497215271,
-0.02808661200106144,
-0.012961168773472309,
-0.00812132004648447,
-0.05590072646737099,
0.0026139705441892147,
0.03823976591229439,
0.02517549879848957,
0.012754674069583416,
0.006597887724637985,
0.02221464365720749,
0.005019771866500378,
-0.03661763668060303,
0.022524774074554443,
-0.040310245007276535,
-0.04841925948858261,
-0.036912597715854645,
-0.03416477143764496,
0.024446051567792892,
0.023301366716623306,
-0.003191526047885418,
0.016351889818906784,
0.00014614142128266394,
-0.010113630443811417,
0.0013658227398991585,
-0.029086271300911903,
0.04611339420080185,
0.06726396083831787,
0.012041688896715641,
-0.0007128345314413309,
0.04389522969722748,
0.014730507507920265,
0.02740427665412426,
-0.0041007972322404385,
0.009876938536763191,
-0.03470980376005173,
-0.020701589062809944,
0.042957719415426254,
0.006771461572498083,
-0.03300987184047699,
0.044090528041124344,
0.03779888153076172,
0.025029463693499565,
0.03339018300175667,
0.025337766855955124,
-0.02966657094657421,
-0.051414672285318375,
0.029380759224295616,
0.02390798181295395,
-0.018977701663970947,
0.02674476057291031,
-0.005961109884083271,
-0.01457185111939907,
-0.007440246641635895,
0.015027136541903019,
-0.003640027018263936,
0.01126132532954216,
0.027247020974755287,
-0.007129200734198093,
0.0032599864061921835,
-0.029221005737781525,
0.029551483690738678,
0.015600484795868397,
0.057631973177194595,
0.0018642159411683679,
-0.016955271363258362,
0.021330799907445908,
-0.0283758956938982,
-0.02785525843501091,
-0.0011197748826816678,
-0.0020540172699838877,
0.013467364013195038,
0.02112348936498165,
0.03955778852105141,
-0.050103407353162766,
0.03561721742153168,
0.010313568636775017,
-0.026235094293951988,
-0.02527625672519207,
-0.01878373883664608,
0.0030092629604041576,
-0.0036853018682450056,
0.02874107100069523,
-0.021209144964814186,
-0.007913993671536446,
-0.0016882069176062942,
-0.013266167603433132,
0.026276765391230583,
0.014410730451345444,
-0.06091389060020447,
-0.01300720777362585,
-0.08966869115829468,
-0.026144590228796005,
0.024276956915855408,
-0.02159009501338005,
0.013004201464354992,
0.04441843554377556,
0.0432409830391407,
-0.049024298787117004,
-0.03624696657061577,
0.010739163495600224,
-0.02814853936433792,
-0.04682942479848862,
-0.015207193791866302,
0.040663592517375946,
0.019879719242453575,
-0.056155234575271606,
-0.004367591347545385,
-0.01588035747408867,
-0.026186184957623482,
-0.03587457910180092,
-0.00978894717991352,
0.02956622838973999,
-0.03131120651960373,
-0.010088497772812843,
0.03125739470124245,
-0.006263773888349533,
-0.0005922875134274364,
-0.04639227315783501,
-0.005320425145328045,
-0.03065776638686657,
0.007620656862854958,
0.026147039607167244,
0.00817323848605156,
0.02079145237803459,
0.07214436680078506,
0.04286924749612808,
-0.030620181933045387,
0.006151274312287569,
0.007673553191125393,
-0.015242334455251694,
-0.04713090509176254,
0.027654066681861877,
0.01731589436531067,
-0.012529834173619747,
0.009778352454304695,
0.007734041195362806,
0.01736191101372242,
0.033735036849975586,
0.03668311610817909,
0.013262314721941948,
0.04404784366488457,
-0.0035650443751364946,
-0.002611874369904399,
0.04082382842898369,
-0.003042731899768114,
-0.027848826721310616,
-0.007372566964477301,
0.027224846184253693,
0.019966568797826767,
0.05012771487236023,
-0.03613917529582977,
0.03423395752906799,
0.00553143722936511,
-0.02954484149813652,
-0.06753619760274887,
0.03740581497550011,
0.00860158447176218,
-0.03627029061317444,
0.020130157470703125,
0.009966358542442322,
0.011757483705878258,
0.00509823951870203,
0.015097826719284058,
0.0396956130862236,
0.05435831472277641,
-0.025391289964318275,
-0.009417333640158176,
-0.03402162715792656,
-0.0039043521974235773,
0.0019442758057266474,
-0.028614411130547523,
-0.0009664660901762545,
0.0628170594573021,
0.05977795645594597,
0.008580969646573067,
-0.01864807866513729,
-0.026002081111073494,
-0.008504876866936684,
-0.06958834081888199,
-0.016354165971279144,
-0.055965106934309006,
0.06729146093130112,
-0.008596369996666908,
0.029401341453194618,
0.010683978907763958,
-0.015345708467066288,
-0.0022050212137401104,
-0.003785553853958845,
-0.09036634862422943,
0.01653819903731346,
-0.022130349650979042,
-0.03602904826402664,
-0.0076228538528084755,
0.0018000004347413778,
0.030651530250906944,
0.0004792000399902463,
-0.009969047270715237,
-0.02267533168196678,
0.03292177617549896,
-0.008247585967183113,
0.028905121609568596,
-0.03245920315384865,
-0.05240604281425476,
-0.01700231432914734,
0.04353024810552597,
0.040544405579566956,
-0.017289023846387863,
0.01282335352152586,
-0.016935160383582115,
-0.02323140576481819,
-0.019391760230064392,
-0.00327941682189703,
0.037274956703186035,
-0.0059640733525156975,
0.04482168331742287,
-0.004843582399189472,
0.024428855627775192,
-0.03040539287030697,
0.0044313897378742695,
0.062206558883190155,
0.061744533479213715,
-0.006057228893041611,
-0.05600489675998688,
0.01248821709305048,
-0.04309103637933731,
-0.010386592708528042,
0.007237627170979977,
0.043194886296987534,
0.0077297138050198555,
-0.04619250446557999,
0.04827313497662544,
-0.0002875056234188378,
-0.05609593167901039,
0.03927301988005638,
0.03833349049091339,
-0.031555745750665665,
-0.017152752727270126,
-0.005009741988033056,
-0.0017429203726351261,
-0.013916334137320518,
0.016911499202251434,
-0.0019842854235321283,
0.016269518062472343,
0.009787723422050476,
-0.002839435590431094,
-0.00023895959020592272,
0.04698316752910614,
-0.04825684428215027,
0.010104229673743248,
0.015751447528600693,
0.0056161293759942055,
-0.0213336031883955,
-0.029020633548498154,
0.034866154193878174,
0.020723706111311913,
0.060904793441295624,
0.019438205286860466,
0.04233239218592644,
-0.05215590447187424,
-0.022387711331248283,
0.04974361136555672,
0.06890631467103958,
-0.03232121095061302,
0.009437762200832367,
-0.0606374628841877,
-0.019747601822018623,
0.05437738075852394,
-0.02260582707822323,
0.02613246440887451,
-0.048671480268239975,
0.02568514086306095,
-0.04837876558303833,
-0.02995959483087063,
-0.059434209018945694,
0.00017870373267214745,
0.021083088591694832,
0.03194516524672508,
-0.04639188200235367,
-0.011017882265150547,
-0.04548005759716034,
0.013991745188832283,
0.055400341749191284,
0.04441244527697563,
-0.011095501482486725,
0.02428787760436535,
-0.0072814407758414745,
0.01703696697950363,
-0.016616452485322952,
-0.07709614187479019,
-0.01111636869609356,
0.0033298106864094734,
-0.021723322570323944,
0.036001525819301605,
0.02357259951531887,
-0.0395241342484951,
0.017855670303106308,
0.01776394620537758,
-0.028689885511994362,
-0.029513653367757797,
-0.06193852424621582,
0.05008121579885483,
0.011578058823943138,
0.008756948634982109,
0.07198012620210648,
0.020408375188708305,
-0.037037093192338943,
0.0015756952343508601,
-0.028124434873461723,
0.030202098190784454,
-0.0253729447722435,
0.00931752659380436,
-0.042959291487932205,
-0.050824929028749466,
-0.03953753784298897,
0.014126960188150406,
-0.02472349815070629,
0.020876748487353325,
-0.009616575203835964,
-0.017895083874464035,
-0.00790166761726141,
0.01333682332187891,
-0.011459901928901672,
-0.004068364389240742,
0.030779577791690826,
-0.0035085014533251524,
0.006736683193594217,
-0.0021126565989106894,
0.030065029859542847,
0.00553755322471261,
0.016824694350361824,
-0.004019677173346281,
0.009760146029293537,
0.0024139864835888147,
-0.05830898508429527,
-0.0013880733167752624,
0.00501430407166481,
-0.006407293491065502,
0.08811221271753311,
0.037864819169044495,
0.029127100482583046,
0.023424023762345314,
0.006945433560758829,
-0.0572940893471241,
0.03502294048666954,
0.0055263894610106945,
0.0029139292892068624,
-0.03573019057512283,
0.012408081442117691,
-0.04124368354678154,
0.022288432344794273,
-0.031077368184924126,
0.005501206964254379,
0.009072799235582352,
-0.01714642345905304,
-0.036215897649526596,
-0.02812989242374897,
0.02882576920092106,
-0.006766485515981913,
-0.026351284235715866,
-0.033278170973062515,
0.021641938015818596,
-0.06862453371286392,
-0.004156008362770081,
-0.018626468256115913,
0.038590457290410995,
0.06157683581113815,
0.01119662169367075,
-0.000865460722707212,
0.03997209668159485,
0.03811885789036751,
-0.011544470675289631,
-0.002983140992000699,
0.003631182014942169,
-0.002958443248644471,
-0.01608303189277649,
-0.004458428360521793,
0.028679102659225464,
0.02695777453482151,
-0.028196945786476135,
0.004929428920149803,
0.03483765199780464,
0.015085360035300255,
-0.0231302659958601,
0.009980021975934505,
-0.013846450485289097,
0.027521304786205292,
0.02803305722773075,
-0.02504812180995941,
-0.020663190633058548,
0.0014617525739595294,
-0.02216971665620804,
0.005645334720611572,
-0.029246613383293152,
0.0022731213830411434,
0.005890270229429007,
-0.001450966577976942,
0.005723071284592152,
0.015134579502046108,
0.034713421016931534,
-0.0016906147357076406,
0.013754491694271564,
-0.0270804725587368,
0.03667066618800163,
0.04076874628663063,
-0.028867412358522415,
-0.014204802922904491,
-0.062458835542201996,
-0.06999645382165909,
-0.020672181621193886,
0.037431228905916214,
0.04650915041565895,
0.02001921460032463,
0.06285911053419113,
-0.026107173413038254,
-0.027038510888814926,
-0.036826878786087036,
-0.02043141797184944,
-0.03773248568177223,
0.03010844998061657,
0.04380341246724129,
-0.040701400488615036,
-0.0042402721010148525,
0.0018420356791466475,
0.01904970034956932,
-0.031954292207956314,
-0.001378953573293984,
-0.012518168427050114,
0.039479609578847885,
0.04097257927060127,
-0.05122185871005058,
-0.029290543869137764,
0.04798565432429314,
-0.05144721642136574,
-0.008697091601788998,
-0.0025396100245416164,
-0.008340922184288502,
0.031618185341358185,
0.04929042235016823,
0.011575852520763874,
-0.04211539775133133,
-0.001987491035833955,
-0.07556553184986115,
0.002107687760144472,
0.024617349728941917,
-0.00604541040956974,
-0.0002787487755995244,
0.01826336979866028,
0.03173805773258209,
-0.04814271628856659,
0.015563346445560455,
0.012918181717395782,
-0.051248081028461456,
-0.04217527061700821,
-0.027627278119325638,
-0.06946667283773422,
0.027779964730143547,
-0.03414508327841759,
-0.006588336080312729,
-0.010635003447532654,
-0.05720548704266548,
0.08048940449953079,
0.03309011831879616,
0.027374999597668648,
-0.02156643196940422,
0.03270455822348595,
-0.06337929517030716,
-0.005672408267855644,
-0.012482263147830963,
-0.010959235951304436,
0.1549070179462433,
0.03506644815206528,
0.007017678581178188,
-0.04812420532107353,
0.009452165104448795,
-0.024688558652997017,
0.049516014754772186,
-0.03410790115594864,
0.009936226531863213,
0.020188307389616966,
-0.0016294787637889385,
0.020681435242295265,
0.052603185176849365,
0.005941655021160841,
-0.02785373665392399,
0.053457580506801605,
-0.0336121991276741,
-0.05506458133459091,
0.002910142531618476,
0.04654669389128685,
-0.03165952488780022,
0.011187834665179253,
-0.030821504071354866,
0.00781880784779787,
-0.001261207857169211,
0.033682532608509064,
-0.03524819761514664,
-0.041001442819833755,
-0.000952568429056555,
-0.014155080541968346,
-0.03218895196914673,
-0.010230045765638351,
0.001084847841411829,
0.01026388444006443,
0.009377500973641872,
0.02194994129240513,
0.04957779496908188,
-0.019236650317907333,
0.007107378914952278,
0.030206987634301186,
0.0364530049264431,
0.00610178941860795,
0.019169140607118607,
0.015417556278407574,
-0.036298349499702454,
-0.046696219593286514,
0.003897308139130473,
0.07908826321363449,
-0.01113886572420597,
-0.02357618883252144,
-0.02570459060370922,
0.0061791278421878815,
0.036854375153779984,
0.005131961777806282,
0.00729692867025733,
0.010368039831519127,
0.036465834826231,
-0.050173070281744,
0.02230260521173477,
-0.0025203723926097155,
0.03809890151023865,
-0.014371413737535477,
-0.0009571185219101608,
0.01015369314700365,
-0.011550391092896461,
-0.033458031713962555,
-0.0194261334836483,
0.02313629910349846,
0.008711738511919975,
-0.022183028981089592,
-0.03446115925908089,
0.02688387595117092,
-0.013472192920744419,
-0.007383736781775951,
0.022731158882379532,
0.016877474263310432,
0.03095361217856407,
0.019639406353235245,
0.0031189308501780033,
-0.0021074062678962946,
-0.031056782230734825,
0.06062328815460205,
-0.04910304397344589,
-0.01863706111907959,
0.003279851982370019,
-0.0043046735227108,
-0.026092302054166794,
0.04651063680648804,
0.040021784603595734,
-0.006848688703030348,
0.015276055783033371,
0.043845221400260925,
0.05004206672310829,
-0.0023539867252111435,
-0.016527561470866203,
0.00531318224966526,
-0.012942013330757618,
0.015655284747481346,
0.02262083627283573,
0.041093770414590836,
0.018014373257756233,
0.0037927438970655203,
0.012889982201159,
0.010232439264655113,
0.009722250513732433,
-0.011125332675874233,
0.02614479325711727,
-0.03992150351405144,
-0.008682710118591785,
0.017637373879551888,
0.05008251219987869,
-0.024479325860738754,
-0.02375977858901024,
0.004594134632498026,
0.01014875341206789,
0.014658172614872456,
0.021501924842596054,
-0.00921698845922947,
0.034553416073322296,
-0.02239922247827053,
0.01621798239648342,
-0.0034057681914418936,
0.033284079283475876,
-0.04174727573990822,
0.004373214207589626,
-0.03759654611349106,
-0.010073285549879074,
0.002796070883050561,
0.022394493222236633,
-0.004077867139130831,
-0.025019440799951553,
0.0020492307376116514,
0.020143108442425728,
-0.00486784428358078,
-0.006554877385497093,
0.00571350147947669,
-0.015966327860951424,
0.027341801673173904,
0.019085993990302086,
0.035404935479164124,
0.04746197909116745,
-0.01976817660033703,
-0.04004626348614693,
0.006722863297909498,
0.009374993853271008,
0.024406015872955322,
0.014061713591217995,
-0.014449023641645908,
-0.038728635758161545,
0.05591645836830139,
0.0038758155424147844,
-0.027379747480154037,
-0.004970733076334,
-0.010784493759274483,
0.01216290332376957,
-0.009112329222261906,
0.047806497663259506,
0.006058357190340757,
-0.009626374579966068,
0.02821865864098072,
-0.010196524672210217,
0.0029731309041380882,
0.011037257499992847,
-0.005811683833599091,
-0.017585881054401398,
0.03717288747429848,
-0.013060336001217365,
-0.0037379679270088673,
0.02580377645790577,
0.043274786323308945,
-0.012208545580506325,
0.04267696663737297,
0.0006065343623049557,
0.005784040782600641,
-0.09253687411546707,
-0.025325072929263115,
-0.021087342873215675,
0.03671378642320633,
0.02567904442548752,
-0.03719855472445488,
-0.009918440133333206,
0.030759528279304504,
-0.0695144310593605,
0.03851071000099182,
-0.0015825991285964847,
-0.017709648236632347,
-0.021844666451215744,
0.02003103867173195,
-0.010950173251330853,
0.024432336911559105,
0.0039083403535187244,
0.039842456579208374,
0.020661981776356697,
-0.002596450038254261,
0.015255587175488472,
-0.014916907995939255,
-0.021322403103113174,
0.011996069923043251,
0.006796153262257576,
-0.038710251450538635,
0.034819308668375015,
-0.0261075459420681,
-0.01803804375231266,
-0.0054590459913015366,
0.01305085327476263,
0.008924750611186028,
-0.039785973727703094,
0.012716997414827347,
0.004162924364209175,
0.05820965766906738,
0.04485413804650307,
-0.01641067862510681,
0.01610167883336544,
-0.006697461009025574,
0.016276611015200615,
0.0459710918366909,
0.00345086632296443,
0.03446925804018974,
-0.002328092698007822,
-0.0390968844294548,
-0.037218231707811356,
0.059400513768196106,
0.0010914361337199807,
-0.05647268146276474,
0.02935459464788437,
-0.01225532591342926,
0.035735055804252625,
0.008603408001363277,
0.024958666414022446,
-0.035154078155756,
0.009915837086737156,
0.007178322412073612,
0.012303398922085762,
0.053793299943208694,
0.010178795084357262,
-0.03236991539597511,
-0.02754548005759716,
0.036607809364795685,
0.03572927787899971,
-0.030315492302179337,
-0.04114958271384239,
-0.0344172939658165,
0.01235760934650898,
0.021835308521986008,
-0.0026586069725453854,
-0.029742615297436714,
-0.08017559349536896,
0.00811788346618414,
0.0017387494444847107,
0.020539607852697372,
0.012865596450865269,
-0.018520690500736237,
0.0030123230535537004,
-0.05390012636780739,
0.037728339433670044,
0.01724156178534031,
0.038499992340803146,
-0.028699180111289024,
-0.015961414203047752,
0.015440558083355427,
0.003920489922165871,
0.020900141447782516,
0.0041341534815728664,
-0.018561910837888718,
-0.012817403301596642,
-0.049532610923051834,
0.016291631385684013,
-0.030820826068520546,
0.03721272945404053,
-0.012768293730914593,
0.004793223924934864,
-0.0012415016535669565,
-0.0019018579041585326,
0.008977485820651054,
0.026954200118780136,
0.007918874733150005,
0.05560719221830368,
0.014196938835084438,
-0.026617381721735,
-0.013226844370365143,
0.08087261021137238,
0.03005337528884411,
0.005650928243994713,
0.03426097705960274,
-0.002070364309474826,
0.025735123082995415,
0.028466053307056427,
-0.056543152779340744,
-0.006096677854657173,
0.03917212411761284,
-0.0325029231607914,
-0.06846021860837936,
-0.0035878790076822042,
-0.012054799124598503,
0.011821555905044079,
-0.03388853371143341,
0.01742083579301834,
0.05426495522260666,
0.00025639895466156304,
-0.025944603607058525,
0.048495013266801834,
0.03350509703159332,
0.016525372862815857,
0.021630585193634033,
0.02062396891415119,
0.03494887426495552,
-0.04425480589270592,
-0.022229192778468132,
-0.005746321752667427,
0.033580657094717026,
0.021689850836992264,
0.003002587705850601,
0.02860090136528015,
0.031183434650301933,
-0.013653282076120377,
0.010333310812711716,
0.0243078526109457,
-0.0073566860519349575,
0.006114940159022808,
0.016809888184070587,
-0.008501024916768074,
0.010866490192711353,
0.019534310325980186,
-0.022406060248613358,
0.06107624992728233,
-0.044815633445978165,
-0.010917691513895988,
-0.03321601450443268,
0.0048325639218091965,
-0.010510767810046673,
-0.0016005962388589978,
-0.0365469790995121,
0.06973611563444138,
-0.006625571753829718,
-0.015152670443058014,
-0.0548875592648983,
0.016122153028845787,
0.03509978950023651,
-0.07310882210731506,
0.004916283767670393,
0.019823554903268814,
0.001986141549423337,
-0.008805369958281517,
-0.03170616179704666,
-0.04410015791654587,
-0.05590931326150894,
0.021028846502304077,
0.046252746134996414,
0.008555020205676556,
-0.012135319411754608,
-0.047299329191446304,
-0.04269496724009514,
0.04861091822385788,
-0.02433832176029682,
0.00799204595386982,
-0.034244608134031296,
-0.0041643469594419,
-0.03958699479699135,
0.028879940509796143
] |
<p>I was studying a <a href="http://en.wikipedia.org/wiki/GRE_Physics_Test" rel="nofollow">GRE Physics Test</a> problem where optical light with a wavelength of 500 nm travels through a gas with refractive index $n$.</p>
<p>If we look at the equations for wave motion and index of refraction</p>
<p>$$c=\lambda_0\nu\quad\text{(in vacuum)}$$</p>
<p>$$v = \lambda\nu\quad\text{(in medium)}$$</p>
<p>$$n = c/v$$</p>
<p>we see that, if the frequency is constant, the <strong><em>wavelength decreases in the medium compared to vacuum</em></strong>. Is this a consistent property at all frequencies and for all mediums with refractive index real and greater than 1?</p>
<p>Are there dielectrics which change the frequency (still for <code>n</code> > 1), and is there an example of that?</p> | 1,516 | [
-0.03080851025879383,
-0.018054747954010963,
-0.0010748989880084991,
-0.016204051673412323,
0.040074340999126434,
0.021517109125852585,
-0.0011584610911086202,
-0.04970058053731918,
0.0018719169311225414,
-0.04801914468407631,
0.048163801431655884,
0.057889048010110855,
0.06724710762500763,
0.009667817503213882,
0.0213838592171669,
0.014743734151124954,
0.009097402915358543,
0.0005053518689237535,
-0.04557185620069504,
-0.013153856620192528,
-0.021170513704419136,
0.028638675808906555,
-0.019801974296569824,
-0.0003776459489017725,
-0.045655958354473114,
0.05197133868932724,
-0.009878699667751789,
-0.007335159461945295,
0.037830885499715805,
0.010569984093308449,
-0.01017746701836586,
0.011856109835207462,
0.0002732356369961053,
0.02132115699350834,
0.004417753778398037,
0.016554204747080803,
-0.03985759615898132,
-0.023492582142353058,
-0.02206224948167801,
0.007244783453643322,
-0.009178866632282734,
-0.0031186677515506744,
-0.007112292572855949,
0.049933791160583496,
-0.003642891999334097,
0.021266117691993713,
0.05091862380504608,
-0.004707694053649902,
0.06675311177968979,
-0.05891799554228783,
0.05134500935673714,
-0.01867355965077877,
0.05809136852622032,
0.021577661857008934,
-0.04228758066892624,
-0.029500562697649002,
0.07627324759960175,
0.06720200926065445,
-0.03149746358394623,
-0.04641951248049736,
0.000047399691538885236,
-0.027654103934764862,
-0.01679583266377449,
0.013895675539970398,
-0.04638853296637535,
0.009309757500886917,
-0.02161300741136074,
-0.025913342833518982,
0.025728151202201843,
0.03143881633877754,
-0.02517707645893097,
-0.010503588244318962,
0.011027643457055092,
0.00430311867967248,
0.004881192930042744,
-0.03448033705353737,
0.005350850056856871,
0.044978734105825424,
0.01767176389694214,
0.07871665060520172,
-0.04276357591152191,
-0.0047342791222035885,
0.02065872959792614,
0.010204847902059555,
-0.02307501621544361,
-0.040430858731269836,
0.06918543577194214,
0.003825998865067959,
0.03386828303337097,
0.045179203152656555,
-0.012691364623606205,
-0.012416284531354904,
0.019698627293109894,
-0.0029214750975370407,
-0.005551816429942846,
0.012698043137788773,
-0.005674299318343401,
0.02512325532734394,
0.01173466444015503,
-0.04411398246884346,
0.00023388642875943333,
-0.010532439686357975,
0.06694036722183228,
0.07044137269258499,
-0.010914219543337822,
-0.061009299010038376,
-0.03777822479605675,
-0.006044017616659403,
-0.009770133532583714,
0.0022790112998336554,
-0.03313698619604111,
-0.012713782489299774,
0.007335277274250984,
-0.003943605814129114,
0.0031464085914194584,
-0.02216283231973648,
0.024465788155794144,
-0.04394260793924332,
0.06153975427150726,
0.08430782705545425,
0.0538056418299675,
-0.027217166498303413,
0.02692355029284954,
-0.0480605848133564,
-0.047271888703107834,
0.0063583203591406345,
0.012613351456820965,
0.02468039281666279,
-0.0277301874011755,
0.015728263184428215,
-0.015377205796539783,
0.01077837310731411,
0.012339213863015175,
-0.008875526487827301,
0.04022132232785225,
-0.02104286290705204,
-0.07855017483234406,
-0.07406926900148392,
0.03551925718784332,
-0.006341866217553616,
-0.014565841294825077,
-0.06754688918590546,
0.021038684993982315,
0.014640704728662968,
0.06378133594989777,
0.011071102693676949,
0.031196510419249535,
-0.0396975614130497,
0.030715232715010643,
0.022455314174294472,
-0.0012279311195015907,
-0.023712219670414925,
0.016354434192180634,
-0.04910384491086006,
-0.00511289993301034,
-0.06588427722454071,
0.0024363878183066845,
0.014522542245686054,
0.015023397281765938,
-0.010153369978070259,
0.05692882090806961,
-0.04450897127389908,
0.004086948931217194,
0.010474623180925846,
0.00236084358766675,
-0.04949382320046425,
0.0625641793012619,
0.032416000962257385,
0.04774231091141701,
0.025111904367804527,
-0.00028263332205824554,
0.04441943019628525,
-0.00011852099123643711,
0.006879024673253298,
0.03859098628163338,
-0.02262488566339016,
-0.002635840093716979,
-0.03256145119667053,
0.009060202166438103,
0.006924847140908241,
-0.010267931967973709,
-0.04265719652175903,
0.012573685497045517,
0.0262798722833395,
-0.04107853025197983,
0.04919897019863129,
-0.013717363588511944,
0.023740507662296295,
0.03533318266272545,
-0.04873766377568245,
0.01042572595179081,
0.01728173904120922,
0.050579413771629333,
0.027483921498060226,
-0.009937204420566559,
0.005542829632759094,
-0.00701804319396615,
-0.004820342641323805,
-0.009392959997057915,
-0.04315997287631035,
-0.0154719278216362,
0.02802351303398609,
-0.004193740431219339,
-0.011775869876146317,
0.005664421711117029,
0.018629813566803932,
-0.019146814942359924,
-0.014227446168661118,
0.007060801610350609,
-0.04033684730529785,
-0.01107611134648323,
0.015428577549755573,
-0.0041863988153636456,
0.03948875889182091,
-0.025057174265384674,
0.0009141606860794127,
0.027498887851834297,
-0.014431431889533997,
0.00896158255636692,
0.022281227633357048,
-0.06170623004436493,
0.03709227591753006,
0.03858400136232376,
0.008809348568320274,
0.0265005175024271,
0.05045182630419731,
-0.027836132794618607,
0.005299735348671675,
0.0001101908492273651,
-0.03518805652856827,
-0.05760621279478073,
-0.008861039765179157,
0.0342138446867466,
0.02357732132077217,
-0.043517518788576126,
-0.001380442758090794,
0.021110594272613525,
0.05506867915391922,
0.05680679902434349,
0.029537327587604523,
0.005283846519887447,
-0.07337871193885803,
0.028934387490153313,
0.01566053181886673,
0.01318748202174902,
0.04189039021730423,
0.03682168573141098,
0.014844593591988087,
0.0283227376639843,
-0.02778872475028038,
0.02939707227051258,
0.016249220818281174,
0.029505889862775803,
0.038252267986536026,
0.020433083176612854,
-0.008332695811986923,
0.024595832452178,
-0.032234400510787964,
0.019413555040955544,
0.0695880576968193,
-0.006536077242344618,
0.003611232154071331,
-0.020536011084914207,
0.011160518042743206,
0.01745663583278656,
0.01586139388382435,
-0.037415992468595505,
0.003819103119894862,
0.019257428124547005,
-0.056101564317941666,
0.0027703542727977037,
-0.013314593583345413,
0.017758456990122795,
-0.03554203733801842,
0.008205716498196125,
0.018036872148513794,
0.03430916368961334,
0.0361056923866272,
-0.049741730093955994,
-0.031558118760585785,
0.027138525620102882,
-0.07984437048435211,
-0.03507021442055702,
-0.0041252244263887405,
0.004216433968394995,
0.028179792687296867,
-0.015557399019598961,
-0.04748484864830971,
0.03333244100213051,
-0.02220635861158371,
-0.048689018934965134,
0.0446852445602417,
-0.038367703557014465,
-0.07799939066171646,
-0.002962567377835512,
-0.01866578496992588,
0.010117379017174244,
-0.04507119208574295,
0.0183726754039526,
0.0467645488679409,
-0.016443172469735146,
-0.016111327335238457,
0.024409465491771698,
-0.02014441415667534,
-0.02665298618376255,
-0.020712513476610184,
-0.009976744651794434,
0.029285263270139694,
-0.03842608630657196,
-0.005737216677516699,
0.03875143826007843,
0.01520401332527399,
0.0117031903937459,
-0.046806756407022476,
-0.04622705280780792,
0.05911844223737717,
0.0006739582750014961,
0.06870626658201218,
-0.013053862378001213,
0.0036508648190647364,
0.04580651968717575,
0.0701868012547493,
-0.03405633568763733,
-0.016570555046200752,
-0.020625032484531403,
-0.011803245171904564,
-0.05365948751568794,
0.016248418018221855,
0.019462620839476585,
-0.011946775950491428,
0.02210322767496109,
0.03863227739930153,
0.022644374519586563,
0.02467237412929535,
0.03953433409333229,
-0.010027538985013962,
0.01103000994771719,
0.012293829582631588,
-0.010642269626259804,
0.07370644807815552,
0.031825169920921326,
-0.023705845698714256,
0.011847817339003086,
-0.011301510967314243,
0.036587875336408615,
0.03939085453748703,
-0.05107714980840683,
0.05431581661105156,
0.026011120527982712,
-0.002028608927503228,
0.012650083750486374,
0.025655118748545647,
0.013288202695548534,
0.020315518602728844,
-0.007478171028196812,
0.03141651302576065,
0.01393170841038227,
0.011840017512440681,
0.00808947253972292,
0.013894501142203808,
0.05906425788998604,
-0.017350010573863983,
0.012245417572557926,
-0.0030976065900176764,
-0.0023544265422970057,
0.029000533744692802,
-0.057441700249910355,
-0.0008796762558631599,
0.046398211270570755,
0.028371402993798256,
0.05142427980899811,
-0.03235436603426933,
-0.050799768418073654,
-0.004732897505164146,
-0.004432775545865297,
-0.03972523286938667,
0.003683963790535927,
0.0622190460562706,
0.0005326332757249475,
0.06146829575300217,
0.05084216594696045,
0.053714264184236526,
0.038278911262750626,
0.002572254743427038,
-0.08731818199157715,
0.014619806781411171,
-0.009942700155079365,
-0.041960928589105606,
0.002878005150705576,
-0.001382392249070108,
-0.032642241567373276,
-0.012021555565297604,
-0.002202447270974517,
0.006870485842227936,
-0.029692262411117554,
-0.0593152716755867,
0.008739039301872253,
-0.008272514678537846,
-0.03698812797665596,
-0.0035976150538772345,
0.04800493270158768,
-0.005315328948199749,
-0.026907961815595627,
-0.024382159113883972,
0.02179723046720028,
-0.04242085665464401,
0.03831659257411957,
-0.012537052854895592,
-0.0209965817630291,
0.022370513528585434,
0.06437569111585617,
0.03935201093554497,
0.016980335116386414,
-0.0011597169796004891,
0.04290401563048363,
0.037117552012205124,
0.011091889813542366,
0.016469847410917282,
-0.010134032927453518,
-0.033955685794353485,
-0.040163248777389526,
-0.015491004101932049,
-0.021226808428764343,
0.06103980168700218,
0.010765149258077145,
-0.014226313680410385,
0.027179619297385216,
-0.016188915818929672,
-0.03751624748110771,
0.04214126244187355,
0.004495757631957531,
0.004391768015921116,
0.010744561441242695,
-0.0029599815607070923,
0.0022628747392445803,
-0.01386081613600254,
0.011628114618360996,
0.029831072315573692,
0.01907344162464142,
-0.02023054100573063,
-0.0061794170178473,
0.03148440271615982,
0.036454688757658005,
-0.035400789231061935,
-0.013715522363781929,
-0.020019162446260452,
-0.022948388010263443,
-0.02690473571419716,
-0.02444034069776535,
-0.01783938892185688,
0.0497005432844162,
0.008554305881261826,
-0.025028171017766,
-0.023220567032694817,
-0.12107373774051666,
-0.021828269585967064,
0.009869859553873539,
0.026374362409114838,
-0.02285606414079666,
-0.0030683723744004965,
-0.042390111833810806,
-0.01888154074549675,
-0.0017329193651676178,
-0.02578555792570114,
0.025935498997569084,
-0.011841826140880585,
0.00959743745625019,
-0.008228771388530731,
-0.041140396147966385,
0.01189647801220417,
0.01764681003987789,
0.012666763737797737,
0.012685458175837994,
-0.03457042947411537,
0.001951455371454358,
0.007776128593832254,
0.015856243669986725,
0.031237896531820297,
0.039211805909872055,
-0.04559862241148949,
-0.009233182296156883,
0.019542254507541656,
-0.014645243994891644,
-0.03052980825304985,
-0.0656183585524559,
-0.00008458756929030642,
0.0421144925057888,
0.04912655055522919,
0.030794989317655563,
-0.03199360892176628,
-0.04645484685897827,
0.011926262639462948,
0.0572219043970108,
0.01025816798210144,
-0.004585249349474907,
0.015863608568906784,
0.05176239088177681,
-0.008177141658961773,
-0.01587742567062378,
0.022068189457058907,
0.04366206377744675,
0.033429745584726334,
0.03133758530020714,
-0.040821705013513565,
0.04682944715023041,
-0.02413702942430973,
0.005759916268289089,
0.02239682339131832,
-0.014618637971580029,
-0.013374573551118374,
0.08256065845489502,
0.016667934134602547,
0.00360804027877748,
0.014588006772100925,
-0.0049726334400475025,
-0.012077598832547665,
0.01422208547592163,
0.0010870439000427723,
0.01828494481742382,
0.0027304012328386307,
-0.00601027300581336,
-0.00931283924728632,
-0.009170004166662693,
0.018326014280319214,
0.011209889315068722,
-0.015908239409327507,
0.03291473165154457,
0.008442191407084465,
-0.001602016156539321,
-0.04000389203429222,
-0.0211989413946867,
-0.023941123858094215,
-0.050909362733364105,
0.05695637688040733,
0.01615549810230732,
0.014132061041891575,
0.0431508906185627,
-0.02316923812031746,
-0.047293417155742645,
0.01840236783027649,
-0.017057891935110092,
0.006565557327121496,
-0.03777887672185898,
-0.0008765512029640377,
0.04671264812350273,
0.028240852057933807,
-0.04155496507883072,
-0.05275304988026619,
0.018022222444415092,
0.043942030519247055,
-0.014848791994154453,
-0.009033345617353916,
-0.0013627439038828015,
-0.044479645788669586,
-0.013568678870797157,
-0.001884871511720121,
0.02773170918226242,
-0.01133942510932684,
-0.048545513302087784,
0.028790008276700974,
0.016409099102020264,
0.05906936526298523,
-0.02639814466238022,
-0.015411349944770336,
-0.015036216005682945,
0.014653235673904419,
0.009993406012654305,
0.0128097552806139,
0.04572458937764168,
-0.018215037882328033,
-0.0555419959127903,
-0.015208877623081207,
0.00043689823360182345,
0.018752260133624077,
0.0052714222110807896,
0.010879379697144032,
0.057869166135787964,
-0.03513452783226967,
0.0063059828244149685,
0.0009399268892593682,
0.010094189085066319,
0.004006256349384785,
0.032173968851566315,
-0.011068726889789104,
0.005707822740077972,
-0.029515311121940613,
-0.0388202890753746,
0.031728096306324005,
-0.00692690908908844,
0.049051836133003235,
0.03365058824419975,
0.0823511853814125,
-0.017697567120194435,
-0.001875688903965056,
0.005656996741890907,
-0.02645287476480007,
0.007204062771052122,
0.0010042960057035089,
-0.023902375251054764,
0.016200276091694832,
0.010905923321843147,
-0.00847945362329483,
-0.06169790402054787,
-0.03550456464290619,
0.013234268873929977,
0.04583824425935745,
-0.013083724305033684,
0.01596243493258953,
-0.0027221767231822014,
-0.03675736486911774,
-0.004168806131929159,
-0.020573129877448082,
-0.011793996207416058,
0.017054034397006035,
-0.03380708768963814,
0.015462084673345089,
0.00018937619461212307,
0.00467152614146471,
0.011313244700431824,
0.04623212665319443,
0.007432379759848118,
-0.010109838098287582,
0.020126216113567352,
0.028898391872644424,
0.030688859522342682,
-0.036539237946271896,
-0.035978976637125015,
0.07001059502363205,
-0.05181466042995453,
0.06144595146179199,
0.021707644686102867,
-0.013321367092430592,
0.030917303636670113,
-0.0068493010476231575,
0.004052201751619577,
-0.040488965809345245,
-0.015839703381061554,
-0.04450030252337456,
0.010734371840953827,
0.010078953579068184,
-0.0007402910268865526,
0.036035504192113876,
-0.038588471710681915,
0.03418780490756035,
0.007105191238224506,
0.006304728798568249,
-0.010511129163205624,
-0.04284137859940529,
-0.005793693941086531,
-0.007402293849736452,
-0.014784383587539196,
0.053059808909893036,
-0.00494673615321517,
-0.03216837719082832,
0.03788519650697708,
-0.060732271522283554,
0.03418432176113129,
0.04861124977469444,
0.002427194267511368,
0.011919002048671246,
0.07059639692306519,
-0.024625170975923538,
0.04702436551451683,
-0.01609867438673973,
-0.00024114595726132393,
0.11129657179117203,
0.053101614117622375,
-0.013171929866075516,
-0.013263980858027935,
-0.024230357259511948,
-0.023914191871881485,
0.03655949607491493,
-0.038931623101234436,
-0.011561854742467403,
-0.014159890823066235,
0.004611573647707701,
0.02620198391377926,
0.079707570374012,
0.012529709376394749,
-0.0003684755356516689,
0.01375280786305666,
-0.016708677634596825,
-0.008828726597130299,
-0.013241002336144447,
-0.011231870390474796,
0.019052401185035706,
0.029554778710007668,
-0.0005960837006568909,
0.02840912714600563,
-0.010942564345896244,
-0.05782824754714966,
-0.03668045625090599,
-0.008036662824451923,
0.05087247118353844,
-0.008453012444078922,
-0.025556029751896858,
-0.004140846896916628,
-0.006667765323072672,
-0.03117140755057335,
-0.03644656017422676,
0.011295984499156475,
0.05022577568888664,
0.01624850556254387,
0.0003564652579370886,
0.01893582195043564,
-0.03704174980521202,
0.01074204407632351,
0.014221634715795517,
0.015596156008541584,
-0.019268909469246864,
-0.020048409700393677,
-0.035351868718862534,
0.018893077969551086,
0.006331496872007847,
-0.006651758216321468,
0.0041839443147182465,
-0.00614591920748353,
-0.011781790293753147,
-0.05501860752701759,
-0.013724317774176598,
0.024105343967676163,
0.01891118474304676,
-0.02734789252281189,
-0.004228368867188692,
-0.022977307438850403,
0.02162753790616989,
0.033282678574323654,
0.007359067443758249,
0.011948063969612122,
-0.0045939343981444836,
-0.020176008343696594,
-0.008907470852136612,
0.03180486708879471,
-0.0352187417447567,
-0.04359356313943863,
-0.017637761309742928,
0.002644772408530116,
-0.017941536381840706,
-0.01472694892436266,
-0.012372520752251148,
0.04824087396264076,
0.03531192988157272,
-0.042141448706388474,
-0.00657364958897233,
0.0015371507033705711,
-0.10635951906442642,
0.015460862778127193,
-0.001687942654825747,
-0.03469010442495346,
-0.04096928611397743,
-0.05560554563999176,
-0.0016929855337366462,
0.011134015396237373,
-0.0017687635263428092,
-0.016964728012681007,
0.0030737589113414288,
0.005370683968067169,
0.06462263315916061,
-0.045744024217128754,
-0.060477159917354584,
-0.011950199492275715,
-0.03456650674343109,
0.0030995334964245558,
-0.009992295876145363,
0.05652270466089249,
0.008615016005933285,
0.0004093133029527962,
0.02338266931474209,
0.013745637610554695,
-0.038262344896793365,
0.012385868467390537,
-0.011991157196462154,
-0.012952834367752075,
0.01293891854584217,
0.02621043287217617,
0.009453663602471352,
-0.031202252954244614,
-0.03681616857647896,
-0.039703864604234695,
-0.012061478570103645,
-0.01740829087793827,
0.014875081367790699,
0.021756106987595558,
0.03508733585476875,
-0.01736374944448471,
-0.007377933710813522,
-0.08636977523565292,
-0.028013499453663826,
-0.01807304471731186,
0.012133613228797913,
0.01169223990291357,
-0.015298333019018173,
-0.00991049874573946,
0.016827166080474854,
-0.026155972853302956,
-0.029770176857709885,
0.010145368985831738,
0.008868220262229443,
0.008045715279877186,
-0.028508085757493973,
-0.004680771846324205,
-0.009323661215603352,
0.01747717149555683,
-0.025390299037098885,
-0.05663730949163437,
0.04676045849919319,
-0.035257186740636826,
-0.03874966502189636,
0.029500925913453102,
-0.01754828728735447,
0.002446158556267619,
0.03698774427175522,
-0.003853341331705451,
0.03971744701266289,
0.07059021294116974,
0.005779427010565996,
0.010588699951767921,
-0.013312333263456821,
-0.0467648021876812,
0.03938519209623337,
-0.036292366683483124,
-0.008036348968744278,
-0.01189715601503849,
-0.00032435142202302814,
0.05705014243721962,
0.03292177617549896,
0.005736995488405228,
0.012057113461196423,
0.014643278904259205,
-0.03143903240561485,
-0.020690247416496277,
0.042701974511146545,
0.05424022674560547,
0.016680290922522545,
0.05984455347061157,
-0.014937547035515308,
0.05839743837714195,
0.045639753341674805,
-0.00370968459174037,
-0.09740640968084335,
-0.03118673898279667,
0.03407696262001991,
0.023422973230481148,
0.0495116151869297,
-0.04505540430545807,
0.02124812826514244,
-0.02171902172267437,
-0.08270500600337982,
0.012019691057503223,
-0.0410090871155262,
0.0013382050674408674,
-0.08771073073148727,
-0.001739088213071227,
-0.029943222180008888,
-0.03166527301073074,
0.03270704299211502,
0.011923287063837051,
0.011848253197968006,
0.028592199087142944,
-0.01258666068315506,
-0.028381552547216415,
0.012744483537971973,
0.021475037559866905,
-0.01673141121864319,
-0.030336707830429077,
0.03073425032198429,
-0.007275007199496031,
-0.015182328410446644,
0.016301460564136505,
-0.02923726662993431,
0.0024090486112982035,
0.006236122455447912,
-0.013212720863521099,
-0.0040354421362280846,
0.031163014471530914,
0.03434987738728523,
-0.005457019433379173,
-0.011117887683212757,
0.015670521184802055,
0.0036727075930684805,
-0.0035763727501034737,
0.007259957492351532,
0.006564486771821976,
0.04104145988821983,
-0.08297803997993469,
0.010027705691754818,
-0.019288409501314163,
-0.003533680457621813,
0.009909514337778091,
0.027823887765407562,
0.002480536699295044,
-0.018251469358801842,
0.010329916141927242,
-0.011790081858634949,
-0.08897539973258972,
-0.011164193041622639,
0.032878655940294266,
0.02501157484948635,
-0.010081012733280659,
-0.03488711640238762,
0.0038619842380285263,
-0.028292763978242874,
0.009259400889277458,
0.003365214914083481,
-0.006071486510336399,
-0.02406351827085018,
-0.0004898429033346474,
-0.00649273069575429,
0.014794111251831055,
0.010921070352196693,
-0.0037608796264976263,
-0.017859583720564842,
0.03854500129818916,
-0.021420223638415337,
-0.010218394920229912,
-0.05483098328113556,
-0.018928252160549164,
-0.004394925199449062,
-0.052984051406383514,
-0.0027465939056128263,
0.03229762241244316,
0.0053812675178050995,
-0.06403510272502899,
-0.03970026969909668,
-0.04933631792664528,
0.047005221247673035,
0.049873046576976776,
-0.00871600117534399,
-0.02928725816309452,
-0.004678575787693262,
-0.034610848873853683,
0.001163313165307045,
-0.021762710064649582,
0.008159689605236053,
-0.01095623429864645,
-0.028082024306058884,
-0.025942916050553322,
0.047554634511470795,
-0.02354840748012066,
0.008148390799760818,
0.020600995048880577,
-0.006062555592507124,
0.021812086924910545,
-0.01364098023623228,
-0.032050102949142456,
0.01180355530232191,
0.01720406487584114,
-0.012033351697027683,
0.07281216979026794,
-0.005318853072822094,
0.02268902026116848,
0.01203311700373888,
-0.008812708780169487,
-0.044157933443784714,
0.010138633660972118,
-0.038778990507125854,
-0.034415166825056076,
0.007153902668505907,
0.015867633745074272,
0.02885650098323822,
-0.04512202367186546,
0.015698671340942383,
0.02438848838210106,
-0.059178583323955536,
-0.03306504711508751,
0.033755961805582047,
-0.008239435032010078,
-0.0034970715641975403,
0.014256875962018967,
0.009737557731568813,
0.007166268303990364,
-0.008479033596813679,
-0.04664156213402748,
0.04552198573946953,
-0.014758124016225338,
-0.016209641471505165,
0.055593572556972504,
0.044643815606832504,
-0.02087089605629444,
-0.025851953774690628,
0.018232043832540512,
0.029376953840255737,
-0.022196587175130844,
-0.03201023489236832,
0.042165376245975494,
-0.004877466708421707,
-0.05691738426685333,
0.062117334455251694,
-0.014252837747335434,
0.04997267574071884,
-0.045176148414611816,
0.03423777595162392,
-0.019592996686697006,
0.017818188294768333,
0.0035293891560286283,
0.041028331965208054,
-0.007822115905582905,
-0.004445222206413746,
-0.00712704798206687,
0.02226141095161438,
0.005399768240749836,
-0.026286879554390907,
0.010021951049566269,
-0.05041574686765671,
-0.0031651072204113007,
0.0050309584476053715,
-0.033187385648489,
0.0020002704113721848,
-0.008133183233439922,
-0.01202862337231636,
-0.00047068047570064664,
0.008223941549658775,
-0.0000747997110011056,
-0.00804379303008318,
-0.00800690334290266,
-0.001576715148985386,
0.0031809238716959953,
0.05963544175028801,
-0.031254012137651443,
0.0261909831315279,
-0.002807008568197489,
0.011570123955607414,
-0.015160948969423771,
-0.021497676149010658
] |
<p>One can expand any periodic function in sines and cosines. When calculating the coefficients $a_0$, $a_n$, and $b_n$ one find that $a_1>a_2>...>a_n>...$, similarly for $b_n$. </p>
<p>Is there an intuitive reason to understand this, I mean why would one expect this to happen? It looks miraculous and mysterious to me that the coefficients came out "ordered" in a way that made the convergence manifest.</p> | 1,517 | [
-0.01701086200773716,
0.005017266143113375,
-0.04524713382124901,
0.0021469800267368555,
0.0489753857254982,
0.03344954922795296,
0.0026018861681222916,
-0.01868727058172226,
-0.008561951108276844,
-0.04036179184913635,
0.02100268006324768,
0.0011601701844483614,
0.04164977744221687,
-0.004173777066171169,
0.0418444462120533,
0.0031034082639962435,
-0.03573872148990631,
0.004300386644899845,
0.0017662320751696825,
-0.011782793328166008,
-0.020932216197252274,
0.06118188425898552,
0.010625285096466541,
0.006791150197386742,
-0.02925773523747921,
-0.013933336362242699,
0.033662017434835434,
0.0016184949781745672,
0.025117823854088783,
0.05465713143348694,
-0.015683496370911598,
-0.011676866561174393,
-0.0024563998449593782,
0.031482845544815063,
0.033906787633895874,
-0.0022557189222425222,
-0.0364166684448719,
-0.019554372876882553,
0.013106358237564564,
0.03466935083270073,
-0.04788042977452278,
-0.053148746490478516,
-0.039692606776952744,
0.027518706396222115,
0.005202554166316986,
0.02327406220138073,
-0.022127419710159302,
-0.0009080219315364957,
0.037839945405721664,
-0.038637761026620865,
0.08666078746318817,
0.00260862335562706,
0.026881588622927666,
0.030684947967529297,
-0.010456555522978306,
0.004700616002082825,
0.06192073971033096,
0.04519858956336975,
-0.0371590219438076,
-0.03110838681459427,
0.017445435747504234,
-0.019041502848267555,
-0.013018066994845867,
0.005443697329610586,
-0.02093985676765442,
0.021165212616324425,
0.014501477591693401,
-0.025770440697669983,
0.005137214902788401,
-0.013832714408636093,
-0.013620831072330475,
0.02175293304026127,
0.048854514956474304,
-0.04662526026368141,
0.0014786202227696776,
-0.014336193911731243,
0.013921650126576424,
-0.01466351468116045,
0.029582789167761803,
0.038710396736860275,
-0.019230687990784645,
0.020496802404522896,
0.004892662167549133,
0.035073161125183105,
0.032108332961797714,
0.0006142331985756755,
0.05401990935206413,
-0.01967400312423706,
0.03391442075371742,
0.015791617333889008,
0.01039322093129158,
0.004599368665367365,
0.046352315694093704,
-0.020453883334994316,
-0.02404615841805935,
0.011764340102672577,
0.007169879507273436,
-0.0039694420993328094,
0.05924327298998833,
-0.00030378048541024327,
0.007313721813261509,
-0.02444600500166416,
0.012383735738694668,
0.04908125475049019,
-0.012149990536272526,
0.00752040883526206,
-0.05569262057542801,
0.04460325464606285,
-0.009808037430047989,
-0.012528259307146072,
-0.00111964566167444,
0.03136683255434036,
0.0006089172675274312,
0.048114288598299026,
0.0034183310344815254,
0.017339492216706276,
0.005098591558635235,
0.005731641780585051,
0.033896554261446,
0.1073521226644516,
0.050407782196998596,
0.004613915923982859,
0.04912764951586723,
-0.017082300037145615,
-0.027409261092543602,
-0.0031829262152314186,
-0.005741643253713846,
-0.04413481056690216,
-0.01998467557132244,
0.054690416902303696,
0.007590031251311302,
-0.024074608460068703,
0.014473768882453442,
0.00533745251595974,
0.0013731304788962007,
0.013927573338150978,
-0.10252773016691208,
-0.050973646342754364,
0.0419483557343483,
-0.022109948098659515,
-0.009663315489888191,
-0.06237471476197243,
0.07753026485443115,
0.029807493090629578,
0.0766930803656578,
-0.00612297561019659,
0.026560533791780472,
0.007076018024235964,
0.04782596230506897,
0.00230347434990108,
-0.01776047609746456,
-0.0050534759648144245,
-0.003348127007484436,
-0.03441239520907402,
0.00757555803284049,
-0.05785307288169861,
0.015691887587308884,
0.022419171407818794,
0.010539080947637558,
-0.04223451390862465,
0.06465955823659897,
-0.010759652592241764,
-0.006254817824810743,
-0.038314905017614365,
0.02061319909989834,
0.0011957213282585144,
0.07711473107337952,
0.020516758784651756,
-0.01081935502588749,
0.04038314148783684,
0.014449039474129677,
0.02039499208331108,
0.029200492426753044,
0.07161234319210052,
0.03264662250876427,
-0.03797140344977379,
-0.0012150356778874993,
-0.03689024969935417,
0.031790073961019516,
0.006788785103708506,
-0.020823922008275986,
-0.04040367528796196,
0.01700870878994465,
-0.004411900881677866,
0.004674120340496302,
0.038384683430194855,
0.008488744497299194,
-0.03366013988852501,
0.008119327947497368,
-0.06469123810529709,
0.013512473553419113,
-0.0651567205786705,
0.0056598796509206295,
0.01213895808905363,
-0.02661064825952053,
0.04365232214331627,
0.009890217334032059,
0.03341975063085556,
0.022579163312911987,
0.0170880276709795,
-0.047928113490343094,
0.007934119552373886,
-0.0014420287916436791,
-0.014474263414740562,
0.04213542118668556,
0.04686594754457474,
0.017107460647821426,
0.031977176666259766,
0.047852542251348495,
-0.023385247215628624,
0.00585867278277874,
0.05011308193206787,
-0.046570319682359695,
0.006489154417067766,
-0.02642998658120632,
-0.004504619166254997,
0.03739752247929573,
-0.007349266204982996,
-0.02042730152606964,
0.06810970604419708,
-0.05112883076071739,
0.06906690448522568,
0.046086665242910385,
0.026680786162614822,
-0.007326123770326376,
0.05136968567967415,
0.04187103733420372,
-0.006661107763648033,
-0.01534163299947977,
-0.038327932357788086,
-0.027407139539718628,
-0.019806722179055214,
0.03847397863864899,
0.07659735530614853,
-0.02928510680794716,
-0.017821360379457474,
0.027459096163511276,
0.019057340919971466,
-0.006994977127760649,
0.03138136863708496,
-0.0011926365550607443,
0.013463085517287254,
-0.008160872384905815,
0.004341670777648687,
0.018045704811811447,
-0.0039387536235153675,
-0.0012939202133566141,
0.004467076156288385,
0.018335243687033653,
0.0222548246383667,
-0.023975089192390442,
0.000055914711992954835,
0.002316039986908436,
0.033916883170604706,
-0.017382865771651268,
0.029633551836013794,
-0.009887532331049442,
-0.07579057663679123,
-0.003051241859793663,
-0.003066303441300988,
0.015997502952814102,
-0.003463164670392871,
-0.019057340919971466,
-0.001160159008577466,
0.06321077793836594,
-0.016424817964434624,
-0.03765510395169258,
-0.021715495735406876,
0.05295810475945473,
-0.04281715676188469,
0.013120632618665695,
-0.05296491086483002,
-0.04199089854955673,
-0.022960280999541283,
-0.01612788811326027,
0.03144701197743416,
0.012277052737772465,
0.023060444742441177,
-0.046106986701488495,
-0.018506953492760658,
-0.00830061174929142,
0.024660790339112282,
0.03736675903201103,
0.017514405772089958,
-0.011014759540557861,
0.011667286045849323,
0.02361907809972763,
-0.05198994278907776,
0.03429115191102028,
0.00746557442471385,
-0.02844012901186943,
0.016817882657051086,
-0.03859599679708481,
-0.050325412303209305,
-0.009342662058770657,
0.0011395468609407544,
0.003592129098251462,
-0.04635755717754364,
-0.021467948332428932,
0.06670431792736053,
-0.016144048422574997,
-0.03687790036201477,
0.007472500670701265,
-0.04589616879820824,
-0.010953173041343689,
-0.007145973853766918,
-0.007221441250294447,
-0.00827252771705389,
-0.03204929828643799,
0.017436346039175987,
-0.010121346451342106,
-0.02880958467721939,
-0.022867267951369286,
-0.01997014507651329,
-0.031749092042446136,
-0.028640422970056534,
-0.029481995850801468,
0.043068718165159225,
-0.009579531848430634,
-0.019106054678559303,
0.08887651562690735,
0.0341569259762764,
-0.006798175163567066,
0.021157577633857727,
-0.009294834919273853,
-0.0023811168503016233,
-0.007715168409049511,
0.041318345814943314,
0.08392791450023651,
-0.027736786752939224,
0.034110330045223236,
0.017493024468421936,
0.05844688415527344,
0.07689440995454788,
-0.011989844962954521,
0.008841151371598244,
0.029509354382753372,
0.008335127495229244,
0.012173805385828018,
0.0038944436237215996,
0.021062633022665977,
-0.013888015411794186,
0.022803587839007378,
0.02679288573563099,
0.02934333123266697,
0.05403514578938484,
-0.042503803968429565,
0.021314416080713272,
0.0073686023242771626,
0.0021468400955200195,
-0.04672646149992943,
0.06813084334135056,
0.05066442862153053,
-0.015906626358628273,
-0.060361530631780624,
0.03345179185271263,
0.02645295485854149,
-0.02959878370165825,
-0.0031186388805508614,
-0.0002946046006400138,
0.02151750586926937,
-0.06323713064193726,
0.004753728397190571,
-0.02430655062198639,
0.004982029087841511,
0.03394168242812157,
-0.012107099406421185,
-0.0020191550720483065,
0.03589029982686043,
0.013359732925891876,
-0.01650417596101761,
-0.05069463700056076,
-0.05544997379183769,
0.019803902134299278,
-0.053807225078344345,
-0.0562727153301239,
-0.019062137231230736,
0.05245577171444893,
-0.02928406558930874,
0.059998951852321625,
-0.000044656102545559406,
0.02747935988008976,
0.022344108670949936,
0.020396355539560318,
-0.07848285138607025,
0.004583421163260937,
-0.005835843272507191,
-0.016137348487973213,
-0.04357663542032242,
-0.022167447954416275,
0.02739189751446247,
-0.003911262843757868,
-0.0280726570636034,
-0.05287281051278114,
-0.03257257491350174,
-0.04970911517739296,
0.00937068834900856,
-0.02320474199950695,
-0.0061168372631073,
0.0010931144934147596,
0.023257078602910042,
0.017431428655982018,
-0.019555559381842613,
0.037397462874650955,
0.014659622684121132,
-0.03195963054895401,
0.009124730713665485,
-0.03802241384983063,
0.027416720986366272,
-0.005737097468227148,
-0.02120872214436531,
0.01964544877409935,
0.050795622169971466,
-0.011365462094545364,
-0.040394820272922516,
-0.0299257580190897,
0.05611103028059006,
0.026524271816015244,
0.014231790788471699,
0.012271412648260593,
-0.021983804181218147,
-0.0057128798216581345,
0.03021286241710186,
0.05016680061817169,
0.02200923301279545,
0.000645209162030369,
0.055607911199331284,
0.029845910146832466,
-0.022294919937849045,
0.05831633508205414,
0.006578077096492052,
0.02331896312534809,
-0.01353830099105835,
-0.03809809684753418,
-0.014192472212016582,
0.009590617381036282,
-0.0004953392199240625,
0.005848976783454418,
-0.031373847275972366,
-0.022872528061270714,
-0.006245496682822704,
0.013922419399023056,
-0.0023312761913985014,
-0.0026649446226656437,
0.0070724282413721085,
0.0005925703444518149,
0.05225362628698349,
0.008140824735164642,
0.0029441590886563063,
-0.01406373642385006,
0.00042527465848252177,
0.05458318442106247,
0.009593154303729534,
-0.01210273988544941,
-0.059063397347927094,
0.009607953019440174,
0.026347827166318893,
-0.016372090205550194,
-0.026913752779364586,
0.008533408865332603,
-0.07448096573352814,
-0.03022690676152706,
0.054378025233745575,
-0.0019956170581281185,
0.03391040861606598,
-0.005777335725724697,
-0.028830260038375854,
-0.0369563065469265,
-0.02350216917693615,
-0.021005455404520035,
0.008765660226345062,
-0.00437546381726861,
0.04233879968523979,
-0.03181913495063782,
0.006036071106791496,
-0.048884645104408264,
0.013897132128477097,
0.021683117374777794,
0.06484441459178925,
-0.04272672161459923,
-0.013755597174167633,
-0.020486555993556976,
0.00579201290383935,
0.024962740018963814,
-0.048175666481256485,
0.05733112990856171,
0.010415242053568363,
0.019598960876464844,
0.004962997976690531,
-0.047007929533720016,
-0.049514494836330414,
-0.02121736668050289,
-0.02129760943353176,
0.0007760582957416773,
0.017084071412682533,
-0.02161247283220291,
0.041342832148075104,
0.03597398102283478,
0.007102963514626026,
0.03921503201127052,
0.024726061150431633,
0.022864414379000664,
0.023080606013536453,
-0.002399098128080368,
0.0360318124294281,
-0.04084678366780281,
-0.004071252420544624,
-0.0162242092192173,
-0.008642042987048626,
-0.03526787832379341,
0.06314460188150406,
0.01938234642148018,
0.024597372859716415,
-0.017121052369475365,
-0.007115975022315979,
0.01409108191728592,
0.02334754355251789,
-0.01966560259461403,
-0.001428805524483323,
0.0006293750484474003,
0.05222344771027565,
0.007729359436780214,
0.008207470178604126,
0.05850446596741676,
-0.02326352149248123,
0.04475514963269234,
0.05269036442041397,
0.012672430835664272,
-0.006538831163197756,
-0.048995647579431534,
0.00007392447878373787,
0.01994282566010952,
-0.037821732461452484,
0.030116023495793343,
-0.02950815111398697,
-0.005545875523239374,
-0.004075825214385986,
-0.09036344289779663,
-0.05554705113172531,
-0.019556771963834763,
-0.024428656324744225,
0.049708012491464615,
-0.04117079824209213,
-0.004798733629286289,
0.03574546054005623,
-0.0338665135204792,
-0.06646910309791565,
-0.06948317587375641,
0.025185974314808846,
0.01014980673789978,
-0.011319245211780071,
-0.023021642118692398,
0.00011096958041889593,
-0.025727104395627975,
-0.02011273428797722,
0.018390320241451263,
0.005770426709204912,
-0.013538356870412827,
-0.008738315664231777,
0.026461074128746986,
-0.0017410014988854527,
0.04542486369609833,
0.007917579263448715,
-0.013133285567164421,
0.04074356332421303,
-0.014340100809931755,
-0.011512532830238342,
-0.013446141965687275,
0.03967534378170967,
-0.011564373038709164,
-0.018283206969499588,
0.0022397139109671116,
-0.009100720286369324,
0.03929956629872322,
-0.03803034871816635,
-0.04087299108505249,
0.010671762749552727,
0.00013655790826305747,
0.03278728574514389,
-0.029371662065386772,
-0.029133526608347893,
-0.011263418011367321,
0.017925450578331947,
-0.03614845126867294,
-0.015716958791017532,
-0.011359130032360554,
-0.07180262356996536,
-0.014257194474339485,
0.006976691540330648,
0.004735592752695084,
0.01709871180355549,
0.03633323684334755,
-0.027289919555187225,
-0.03152288869023323,
0.020858915522694588,
0.016046704724431038,
0.03619401156902313,
0.05221517011523247,
0.025102438405156136,
0.01860651560127735,
0.016576768830418587,
-0.036767154932022095,
-0.018743427470326424,
-0.03526608273386955,
0.02193388156592846,
0.060883816331624985,
-0.04952366277575493,
0.05131775885820389,
0.01283450610935688,
-0.025360582396388054,
0.020716441795229912,
0.0030351593159139156,
-0.012060318142175674,
-0.016991930082440376,
-0.009437286294996738,
0.013893949799239635,
-0.043140020221471786,
-0.021046383306384087,
0.022050317376852036,
0.035839278250932693,
0.002044420223683119,
0.00764815928414464,
0.010649709962308407,
-0.0005148501950316131,
0.0017940521938726306,
0.030010217800736427,
-0.06801944971084595,
0.03194468468427658,
-0.008354769088327885,
0.0004422590136528015,
-0.025480695068836212,
0.005297948140650988,
0.04856874793767929,
0.00372177897952497,
0.027950532734394073,
-0.04880090057849884,
-0.024847090244293213,
-0.03966834396123886,
0.005226034205406904,
0.009520993568003178,
0.019712621346116066,
0.038277171552181244,
-0.030096551403403282,
0.030039958655834198,
0.02813884988427162,
0.027183514088392258,
0.011044277809560299,
-0.05066443234682083,
-0.03412163630127907,
-0.014507514424622059,
-0.045100897550582886,
0.037635110318660736,
-0.026165686547756195,
-0.002654040465131402,
-0.000679347722325474,
-0.013313882984220982,
0.0036289936397224665,
0.03992515802383423,
0.008496377617120743,
-0.03910449519753456,
0.1148679256439209,
0.021257421001791954,
0.0067843045108020306,
-0.001176059595309198,
-0.005941695999354124,
0.08989980071783066,
0.024023067206144333,
0.025220004841685295,
-0.07634755969047546,
0.009239262901246548,
0.0007230475312098861,
-0.010190315544605255,
-0.04857486113905907,
0.06929908692836761,
0.03639758378267288,
0.0018620860064402223,
-0.013783582486212254,
0.038486383855342865,
0.0025739448610693216,
0.029690923169255257,
0.02316744066774845,
-0.040500421077013016,
-0.02043088711798191,
0.02914709411561489,
0.014284190721809864,
0.008748937398195267,
0.01660674437880516,
-0.05209339037537575,
-0.017979828640818596,
-0.04582095146179199,
-0.022502176463603973,
-0.0323910117149353,
-0.029029538854956627,
-0.007945938035845757,
-0.0005478542298078537,
-0.04625530540943146,
0.0387401208281517,
0.054949186742305756,
-0.01915062591433525,
-0.004933514632284641,
0.021347813308238983,
0.02551003359258175,
0.01618208922445774,
0.031687770038843155,
0.024345573037862778,
0.018510039895772934,
0.006561751943081617,
0.01583324931561947,
0.006517835892736912,
-0.017906950786709785,
-0.026247918605804443,
-0.05002836138010025,
0.019047988578677177,
-0.02754557691514492,
-0.0037581378128379583,
-0.014774831011891365,
0.004915517754852772,
-0.003884713165462017,
-0.07334692776203156,
-0.003469695569947362,
0.005616320762783289,
-0.015212254598736763,
-0.04149377718567848,
-0.03639531880617142,
-0.00032651456422172487,
-0.022748837247490883,
-0.013392037712037563,
0.02051646262407303,
-0.03940185531973839,
-0.05880143120884895,
0.0025304255541414022,
0.028905102983117104,
0.02947624959051609,
-0.020119154825806618,
-0.0069927335716784,
0.013238772749900818,
-0.007609913125634193,
-0.03924344852566719,
-0.008543206378817558,
-0.004737372510135174,
-0.00971226766705513,
0.018705634400248528,
0.02686227858066559,
-0.012652146629989147,
-0.028852859511971474,
-0.02600914239883423,
-0.014000136405229568,
0.003956501837819815,
-0.01043145265430212,
-0.028337351977825165,
-0.05360836535692215,
0.011077712289988995,
0.04990898817777634,
-0.023615477606654167,
0.022306617349386215,
-0.0008149826899170876,
0.04108317196369171,
0.01929749920964241,
-0.04535876587033272,
-0.014774007722735405,
0.008905618451535702,
-0.017877796664834023,
-0.02244984731078148,
0.010303493589162827,
0.02701832540333271,
0.029824305325746536,
0.010548803955316544,
0.004932521376758814,
0.041202109307050705,
-0.02841336280107498,
0.01587263122200966,
-0.009499112144112587,
-0.04884229227900505,
0.02908422239124775,
0.03193727880716324,
-0.02953254245221615,
-0.039915531873703,
-0.044034022837877274,
-0.014142761938273907,
0.03295373171567917,
0.007932008244097233,
-0.005502593703567982,
-0.018504668027162552,
-0.012527537532150745,
-0.0277638491243124,
0.029393300414085388,
-0.037551358342170715,
-0.0360480360686779,
-0.03717491775751114,
0.010960433632135391,
-0.017214449122548103,
-0.01934441551566124,
-0.029456347227096558,
0.0033728312700986862,
-0.03968364745378494,
-0.03945596143603325,
0.0655219554901123,
0.01505259983241558,
-0.001537543605081737,
-0.06331130862236023,
-0.010706269182264805,
-0.07182369381189346,
0.009621827863156796,
-0.02147524431347847,
-0.07344582676887512,
0.00954462867230177,
-0.01313099730759859,
-0.052266694605350494,
-0.0000617217447143048,
-0.026427632197737694,
0.018960624933242798,
0.015286752954125404,
-0.00419570179656148,
-0.0258035846054554,
0.05445701628923416,
-0.028542136773467064,
-0.007058447692543268,
-0.004849767312407494,
0.02727760747075081,
0.0022685332223773003,
-0.013910737819969654,
-0.00012435494863893837,
-0.03108900412917137,
0.0052669234573841095,
-0.008820295333862305,
0.03284445405006409,
0.005432634148746729,
-0.017578260973095894,
0.02464212290942669,
-0.019990501925349236,
0.016388749703764915,
-0.008470574393868446,
0.006860601715743542,
0.02225266955792904,
0.03781929239630699,
-0.005096225067973137,
0.049192190170288086,
0.012874295935034752,
0.02933323197066784,
-0.0528738871216774,
-0.0060595981776714325,
0.008379371836781502,
-0.02839050255715847,
0.021158412098884583,
-0.030613448470830917,
0.0025257915258407593,
0.020455429330468178,
-0.0653333067893982,
0.02456645481288433,
-0.027349701151251793,
-0.02045854739844799,
-0.036576561629772186,
-0.048245374113321304,
-0.018202388659119606,
0.028407137840986252,
0.06505296379327774,
0.012222318910062313,
0.023852476850152016,
-0.0011767090763896704,
-0.03681715950369835,
-0.007538928650319576,
-0.0007583471015095711,
0.007240606937557459,
-0.02238691784441471,
-0.027337107807397842,
0.0478530190885067,
-0.01666833646595478,
-0.06615185737609863,
0.015812626108527184,
-0.0049723731353878975,
-0.054258882999420166,
0.018841957673430443,
0.024407008662819862,
0.015143074095249176,
0.03381330519914627,
-0.002307570306584239,
-0.019569771364331245,
-0.013086170889437199,
0.03694259375333786,
0.02577943354845047,
-0.013817941769957542,
-0.013471211306750774,
0.0010303169256076217,
0.05584896355867386,
-0.0011218773433938622,
-0.0400523878633976,
-0.028612656518816948,
0.004361375235021114,
0.026283062994480133,
0.01514370832592249,
0.011597862467169762,
0.035907160490751266,
-0.0015588921960443258,
0.02774125710129738,
-0.016839822754263878,
-0.044267699122428894,
-0.0071858675219118595,
0.04995143786072731,
-0.04896892234683037,
0.020340824499726295,
0.002954980591312051,
-0.016825690865516663,
0.013528578914701939,
0.027585821226239204,
-0.010313792154192924,
-0.02610735408961773,
0.027353009209036827,
0.025036556646227837,
0.016501741483807564,
-0.01104465126991272,
-0.040068887174129486,
-0.005424900446087122,
0.020721929147839546,
0.040005411952733994,
0.008962064050137997,
0.0034964391961693764,
-0.042824845761060715,
-0.03712492808699608,
-0.06326589733362198,
0.05428339168429375,
-0.0042910147458314896,
-0.011860329657793045,
-0.02066616527736187,
-0.008655122481286526,
-0.01980215683579445,
0.026209110394120216,
0.06412720680236816,
-0.008354177698493004,
0.009399807080626488,
-0.003198497463017702,
0.04818767309188843,
0.04184367507696152,
-0.01709241047501564,
0.038060203194618225,
0.015048719942569733,
-0.014368672855198383,
0.018890831619501114,
-0.0017482709372416139,
-0.02691495046019554,
0.027588864788413048,
-0.019679158926010132,
-0.02539415843784809,
0.02979898639023304,
-0.03930116444826126,
-0.0004746289923787117,
0.041375286877155304,
0.017099445685744286,
-0.017719222232699394,
0.06601616740226746,
-0.00455758161842823,
-0.010101479478180408,
0.0016695816302672029,
-0.005068956408649683,
-0.09545331448316574,
0.02609369345009327,
-0.01582331769168377,
-0.012683440931141376,
-0.03966507315635681,
0.025666937232017517,
0.01263369806110859,
-0.030571628361940384,
0.008640614338219166,
0.007467174436897039,
-0.016069890931248665,
-0.015887215733528137,
0.046642761677503586,
0.002059099730104208,
0.05439036339521408,
-0.009747259318828583,
0.01702447049319744,
0.019821925088763237,
-0.008037110790610313,
0.02743195742368698,
0.07552052289247513,
0.04286203905940056,
-0.003489658934995532,
0.01695994660258293,
-0.0007620573742315173,
0.0008143365266732872,
0.0258674044162035,
-0.02614467218518257,
0.05334612727165222,
-0.0653010830283165,
-0.02399655058979988,
0.00028558456688188016,
-0.07119051367044449,
0.016366641968488693,
0.0200410857796669,
-0.015378651209175587,
0.07231307774782181,
-0.01711915247142315,
0.03913232684135437,
-0.013972891494631767,
0.021761031821370125,
-0.014900957234203815,
-0.03105502761900425,
-0.009155088104307652,
-0.01460319198668003,
-0.03410885110497475,
-0.02082057297229767,
-0.008250216953456402,
-0.023511657491326332,
0.04198121279478073,
-0.024496955797076225,
-0.01573679782450199,
0.0246769767254591,
0.004048061557114124,
0.0031087128445506096,
0.01548254769295454,
-0.04297293350100517,
-0.022796522825956345,
0.04144025593996048,
0.06145583838224411,
0.0009780611144378781,
0.003226520726457238,
-0.01900061033666134,
-0.04099084064364433,
0.03861314430832863,
-0.061112500727176666,
0.001104744616895914,
-0.03936378285288811,
0.03603959456086159,
-0.010221609845757484,
-0.0376681312918663
] |
<p>Here is the problem:</p>
<p><img src="http://i.stack.imgur.com/iojG5.jpg" alt="Here is the problem"></p>
<p>In the above figure I want help on finding the potential difference between X and Y.
It is getting quite confusing due to the battery in the middle. I found the current in both the loops using Kirchhoff's Voltage law but then I'm confused on the proper method to find the potential drop between the two loops.</p> | 1,518 | [
-0.02350350096821785,
0.014099850319325924,
-0.010000736452639103,
0.024831153452396393,
0.016484934836626053,
-0.01639503985643387,
-0.010595518164336681,
-0.031029757112264633,
0.02031172439455986,
0.03460780531167984,
0.037945982068777084,
0.04683198407292366,
0.051332730799913406,
0.07097485661506653,
0.06658077985048294,
0.004017390310764313,
0.0006282839458435774,
-0.039194051176309586,
0.02942437306046486,
-0.012396646663546562,
-0.03944849967956543,
0.009887081570923328,
0.018859563395380974,
0.029435191303491592,
-0.012416431680321693,
0.05038774386048317,
0.06619558483362198,
-0.011125507764518261,
-0.003798901103436947,
0.044538434594869614,
-0.01797867938876152,
-0.06863737106323242,
-0.00792718306183815,
0.01463854406028986,
0.024218210950493813,
0.012681749649345875,
-0.03271344304084778,
-0.026163989678025246,
-0.04758882522583008,
0.013080639764666557,
0.006454210262745619,
0.02426915243268013,
-0.01784290000796318,
0.04974757134914398,
-0.01514816377311945,
0.00846676155924797,
-0.029745860025286674,
-0.00027513853274285793,
0.01866694912314415,
-0.059163909405469894,
0.09996503591537476,
-0.026875387877225876,
0.06880148500204086,
0.046759482473134995,
-0.011359892785549164,
0.03036029264330864,
0.05800509825348854,
0.06580628454685211,
-0.006598044186830521,
-0.039713118225336075,
-0.03755605220794678,
-0.023943211883306503,
-0.04218839854001999,
-0.03464372083544731,
-0.017759643495082855,
0.03364109620451927,
-0.01620221883058548,
-0.0412798635661602,
-0.007207891903817654,
-0.006687258370220661,
-0.005701584275811911,
0.03631790354847908,
0.03463141620159149,
-0.05987958610057831,
0.021404489874839783,
-0.01987769640982151,
0.007488108240067959,
0.02988780476152897,
0.032103944569826126,
0.03325531259179115,
-0.04880736023187637,
0.03634081780910492,
0.0334029383957386,
0.05949848145246506,
-0.0022675811778753996,
-0.069388248026371,
0.05276249721646309,
-0.017915720120072365,
-0.013549530878663063,
0.021670781075954437,
0.02756255492568016,
0.020939869806170464,
0.036220479756593704,
0.023684067651629448,
-0.006300810258835554,
0.04620300605893135,
-0.004046683199703693,
0.08110146969556808,
0.0057225301861763,
-0.02919739857316017,
0.010764352045953274,
-0.015966374427080154,
0.04607177898287773,
0.07214768975973129,
0.014649934135377407,
-0.0008816043264232576,
-0.01595129445195198,
0.0511297807097435,
0.03228836879134178,
-0.022898858413100243,
-0.04958036541938782,
0.02836119756102562,
-0.013749702833592892,
0.006747500970959663,
0.002398331183940172,
-0.03348277136683464,
-0.034653376787900925,
-0.009076503105461597,
-0.0033936272375285625,
0.012964889407157898,
0.02979637309908867,
-0.026170063763856888,
0.04451887309551239,
-0.020635690540075302,
-0.08332909643650055,
-0.0028578375931829214,
-0.01690644770860672,
-0.022310130298137665,
-0.011125046759843826,
0.027010800316929817,
-0.03366444259881973,
0.017849555239081383,
-0.033707521855831146,
-0.0004492375592235476,
0.03251956030726433,
-0.017524341121315956,
-0.0764428973197937,
-0.06723709404468536,
-0.0021283291280269623,
-0.009561860002577305,
0.0094899982213974,
-0.03607102483510971,
-0.007109669968485832,
0.030520258471369743,
0.051041651517152786,
-0.0009504298795945942,
-0.014032449573278427,
0.01658448576927185,
-0.0028174645267426968,
-0.005506423767656088,
0.010015347972512245,
-0.029869701713323593,
-0.020758284255862236,
-0.011011350899934769,
0.030307749286293983,
-0.0360507108271122,
0.009949659928679466,
0.05367084965109825,
0.01074210461229086,
0.0024119759909808636,
0.012721979059278965,
0.016679512336850166,
-0.022383935749530792,
0.0091342618688941,
-0.007043437100946903,
-0.036679212003946304,
0.08173909038305283,
-0.007590383756905794,
-0.017644090577960014,
0.0506359338760376,
-0.024171600118279457,
0.039052221924066544,
-0.01118581835180521,
0.03370159864425659,
0.06445417553186417,
-0.011204340495169163,
-0.02535827085375786,
-0.04198279231786728,
0.007010906934738159,
0.013634460978209972,
-0.03003327175974846,
-0.07026379555463791,
0.0002564266324043274,
0.015190967358648777,
0.018622638657689095,
0.06309335678815842,
-0.014332908205688,
-0.0034194032195955515,
0.019291207194328308,
-0.01603963039815426,
-0.03658325597643852,
-0.055112574249506,
0.023666759952902794,
0.002099831821396947,
-0.026775376871228218,
-0.0026478020008653402,
0.0017175788525491953,
0.05721879377961159,
-0.03743564337491989,
-0.0024265332613140345,
-0.0009744777344167233,
0.027068575844168663,
-0.023047981783747673,
0.0029671730007976294,
0.004451915621757507,
0.06756807863712311,
0.041077058762311935,
0.025287486612796783,
0.05485849827528,
-0.04453232139348984,
0.015064223669469357,
-0.02012314647436142,
-0.03694206848740578,
-0.0026544644497334957,
0.011764648370444775,
-0.025194954127073288,
-0.004924455191940069,
0.023553378880023956,
0.00939207524061203,
0.020411167293787003,
-0.023325560614466667,
0.0818849727511406,
0.05283374339342117,
0.0037328607868403196,
-0.013544425368309021,
-0.014311892911791801,
0.011638234369456768,
0.03391564264893532,
0.01922190934419632,
-0.006568289827555418,
-0.043273698538541794,
-0.004077563062310219,
0.03590691462159157,
0.04208308085799217,
-0.02657875418663025,
-0.0013791549718007445,
0.03496656194329262,
-0.0023081519175320864,
-0.0008083798456937075,
0.03909065201878548,
0.002854848513379693,
0.01924717053771019,
0.012273972854018211,
0.03685528784990311,
-0.019481074064970016,
0.009327922947704792,
0.03523719310760498,
0.030784184113144875,
0.033391185104846954,
-0.02969376929104328,
-0.046582743525505066,
0.035687435418367386,
-0.0050401100888848305,
0.05327353626489639,
0.025511423125863075,
-0.03560261428356171,
0.059570975601673126,
-0.0030487722251564264,
0.018007813021540642,
0.02349214255809784,
-0.026059487834572792,
0.017731906846165657,
-0.002112806774675846,
0.0012962872860953212,
0.0002740045019891113,
0.022298913449048996,
-0.013828149065375328,
0.015065730549395084,
0.01626942865550518,
0.00707419216632843,
0.016484340652823448,
0.0029750687535852194,
-0.015247121453285217,
-0.041155941784381866,
0.001466318848542869,
-0.0022273845970630646,
-0.004650648683309555,
0.008364971727132797,
-0.03423605114221573,
-0.015488740988075733,
-0.02910422720015049,
-0.015365878120064735,
0.017672287300229073,
-0.026463955640792847,
-0.00736931012943387,
0.020448952913284302,
-0.028787171468138695,
-0.013103109784424305,
0.061894387006759644,
0.03592967614531517,
0.026781678199768066,
0.007923168130218983,
-0.020647000521421432,
-0.04649068042635918,
-0.00767176691442728,
-0.007052218075841665,
0.05138063430786133,
0.013482902199029922,
-0.022894233465194702,
0.0540609285235405,
0.007834174670279026,
-0.0325784757733345,
0.05121001973748207,
-0.04000357165932655,
-0.02356543578207493,
-0.01359412632882595,
0.007151391822844744,
0.01172205526381731,
0.010793361812829971,
0.017296457663178444,
0.015223275870084763,
-0.027851726859807968,
-0.0058221882209181786,
-0.060161661356687546,
-0.04469382017850876,
-0.0016237229574471712,
0.014451049268245697,
0.011258954182267189,
-0.0238169115036726,
-0.0313289575278759,
0.10001068562269211,
0.027290869504213333,
0.0013640540419146419,
-0.0033869820181280375,
-0.06220037862658501,
-0.022219695150852203,
0.016264667734503746,
0.02125491574406624,
0.03176162391901016,
-0.03369302302598953,
-0.008615932427346706,
0.015858640894293785,
0.0657939463853836,
0.07019757479429245,
-0.003398394677788019,
0.02340693585574627,
-0.003135101404041052,
0.03556978330016136,
-0.02191912569105625,
0.0799676775932312,
0.0017298944294452667,
-0.019138120114803314,
-0.019614342600107193,
0.009861436672508717,
0.041483256965875626,
0.012695065699517727,
-0.03217050060629845,
0.007350640371441841,
-0.027342647314071655,
-0.002757209585979581,
-0.03490213304758072,
0.019851751625537872,
-0.008305457420647144,
-0.04050566256046295,
0.004174547735601664,
0.019716056063771248,
0.06409455090761185,
-0.018228592351078987,
-0.026694513857364655,
0.029454877600073814,
0.008297819644212723,
-0.05104267597198486,
-0.055418066680431366,
0.023475367575883865,
-0.028712313622236252,
0.03367958217859268,
-0.013427979312837124,
-0.05345534160733223,
0.020979510620236397,
0.028294537216424942,
0.026830000802874565,
-0.000694900460075587,
-0.018969153985381126,
0.030834892764687538,
-0.10192378610372543,
-0.006994530092924833,
0.00750002171844244,
0.07460856437683105,
0.00903474073857069,
0.05802908167243004,
0.008568672463297844,
0.004598662722855806,
0.021402601152658463,
-0.019200626760721207,
-0.06533633172512054,
0.055837471038103104,
-0.005491171032190323,
-0.025163082405924797,
-0.0006767932209186256,
0.008969936519861221,
0.03810542821884155,
-0.01818976365029812,
0.026386015117168427,
-0.013877836056053638,
-0.012899010442197323,
-0.060007620602846146,
0.02474755235016346,
-0.005578023847192526,
0.00525845168158412,
-0.026416892185807228,
0.009922933764755726,
0.041111186146736145,
-0.03808112069964409,
0.050610240548849106,
0.011712195351719856,
-0.031187240034341812,
-0.008385112509131432,
-0.030806170776486397,
-0.009827949106693268,
0.019686002284288406,
0.0033690710552036762,
-0.010878772474825382,
0.04858679324388504,
0.023060940206050873,
-0.02075599506497383,
-0.01723923161625862,
0.05865318328142166,
0.012345322407782078,
-0.04141809418797493,
-0.007770642172545195,
-0.050965167582035065,
-0.012572642415761948,
-0.03565458208322525,
0.05748990178108215,
-0.025114716961979866,
0.08379978686571121,
0.0011664332123473287,
0.014655322767794132,
-0.021525928750634193,
0.045956265181303024,
0.08532081544399261,
0.0033534022513777018,
-0.03403971344232559,
-0.037038762122392654,
-0.004298822954297066,
-0.0768934041261673,
0.0067926691845059395,
0.045493993908166885,
0.009613544680178165,
-0.0034837103448808193,
-0.02967827022075653,
0.07182030379772186,
-0.0029806424863636494,
0.004540508612990379,
0.025295553728938103,
0.015748485922813416,
0.02092757262289524,
-0.021094588562846184,
-0.006450551096349955,
0.06522268801927567,
0.00753365084528923,
0.043540652841329575,
-0.01143687404692173,
-0.012368962168693542,
-0.060566894710063934,
-0.038494691252708435,
0.06104541942477226,
0.037198662757873535,
-0.033771954476833344,
-0.024809159338474274,
-0.05303097516298294,
0.018304940313100815,
0.07269865274429321,
-0.05160351097583771,
0.0631086602807045,
-0.015357484109699726,
0.009326836094260216,
-0.011018016375601292,
-0.020033886656165123,
-0.04541144520044327,
0.012488109990954399,
0.005502503830939531,
0.03622983768582344,
0.002476572059094906,
-0.01109405793249607,
0.01696818321943283,
0.024839973077178,
0.0228855200111866,
0.06564943492412567,
0.010552073828876019,
-0.0012257358757779002,
0.013133097440004349,
0.01106970477849245,
-0.02868242748081684,
-0.04393920674920082,
0.061709679663181305,
-0.03470003232359886,
-0.005602922756224871,
0.03399946168065071,
-0.024347594007849693,
-0.05809434503316879,
0.03608253225684166,
0.00362784112803638,
0.016252724453806877,
-0.025506604462862015,
-0.028661983087658882,
0.004259392619132996,
0.06948886811733246,
-0.011907355859875679,
0.02046371065080166,
0.0257245022803545,
-0.02172909677028656,
-0.01837312988936901,
-0.0003528684610500932,
-0.005043980665504932,
-0.02908257395029068,
0.002769125858321786,
-0.004646196961402893,
0.03184822201728821,
-0.01890452206134796,
0.035404834896326065,
-0.013730405829846859,
0.050503529608249664,
-0.03348725661635399,
-0.02986675687134266,
0.0014377485495060682,
0.014354241080582142,
-0.022187523543834686,
-0.010826277546584606,
0.012146081775426865,
-0.006015281192958355,
-0.012513577938079834,
-0.01944269798696041,
-0.005842962302267551,
-0.03202405944466591,
0.0072081200778484344,
-0.00355342635884881,
-0.02488625794649124,
-0.020462999120354652,
-0.025171590968966484,
-0.007910216227173805,
0.00018220586935058236,
-0.014743774197995663,
0.02127169258892536,
-0.033824872225522995,
0.0147326048463583,
0.014859195798635483,
-0.020377013832330704,
-0.03493470326066017,
-0.001248482265509665,
0.019982395693659782,
0.01845416985452175,
-0.08126664906740189,
0.05126208811998367,
0.01575368642807007,
0.021250799298286438,
-0.06035497784614563,
-0.0699247196316719,
0.03244714438915253,
-0.008741422556340694,
-0.015759963542222977,
-0.05846470221877098,
-0.005175474099814892,
0.013393213972449303,
-0.005610006395727396,
0.017628496512770653,
-0.000213766485103406,
-0.03334953263401985,
-0.023886172100901604,
-0.0022697816602885723,
-0.010803647339344025,
0.06600069999694824,
0.01976858638226986,
0.014347074553370476,
-0.003828981425613165,
-0.05679285526275635,
-0.01852344162762165,
-0.008275468833744526,
0.06154729425907135,
-0.023292554542422295,
-0.03241341561079025,
-0.005453999154269695,
-0.019651440903544426,
0.07638679444789886,
-0.07118909060955048,
-0.0031269793398678303,
0.006040379870682955,
0.04399910196661949,
-0.016130557283759117,
-0.030441664159297943,
0.02442212775349617,
-0.006730002351105213,
0.0008105714223347604,
-0.0030302240047603846,
-0.002728954190388322,
-0.013210993260145187,
-0.021036308258771896,
0.016449492424726486,
0.02229853719472885,
-0.014788929373025894,
-0.0034293041098862886,
0.07938244193792343,
-0.02453966997563839,
-0.00853756070137024,
0.028435012325644493,
-0.006864003837108612,
0.0006088816444389522,
-0.031525272876024246,
0.004665100947022438,
0.02373565547168255,
0.019385045394301414,
-0.03856387361884117,
-0.021338999271392822,
-0.04360577464103699,
0.02357911691069603,
0.069196417927742,
-0.0005520408740267158,
0.012999226339161396,
0.054225362837314606,
-0.00994731206446886,
0.01712670736014843,
0.002729272237047553,
-0.030655885115265846,
0.0033671366982162,
0.014085094444453716,
0.0282942745834589,
-0.0035534279886633158,
0.022724878042936325,
0.033299319446086884,
0.013298765756189823,
-0.010197396390140057,
-0.02263862080872059,
0.0406915545463562,
-0.0168196689337492,
0.0016587561694905162,
-0.004608288872987032,
-0.05815637484192848,
0.00457549374550581,
-0.000535635044798255,
0.04605857655405998,
-0.02896309085190296,
-0.03434158116579056,
0.0630648210644722,
0.014410492964088917,
-0.01255976501852274,
-0.02400357834994793,
-0.01733236201107502,
-0.03462297469377518,
-0.024819709360599518,
0.03799695149064064,
0.023078475147485733,
-0.007096296641975641,
0.06820248812437057,
0.036133673042058945,
0.02518697828054428,
0.021790970116853714,
-0.030995458364486694,
-0.056541040539741516,
0.008577375672757626,
-0.028322873637080193,
-0.040216196328401566,
0.05058282986283302,
0.015053697861731052,
-0.030740071088075638,
0.034241192042827606,
0.011802686378359795,
0.02095114253461361,
0.03545704483985901,
0.021264072507619858,
-0.03194178268313408,
0.07092098146677017,
0.0038255578838288784,
0.011819320730865002,
-0.0007503647939302027,
0.00362483155913651,
0.09552650153636932,
0.023209737613797188,
-0.00037434292607940733,
-0.06310201436281204,
0.027087602764368057,
-0.03202960640192032,
-0.020829131826758385,
-0.025258691981434822,
0.013619384728372097,
-0.010219096206128597,
0.005546975415199995,
0.02226397581398487,
-0.024251924827694893,
-0.009876308962702751,
0.006479697301983833,
0.04345441237092018,
-0.02617035247385502,
-0.017880870029330254,
0.02758152410387993,
0.02346666343510151,
-0.019221823662519455,
0.017588164657354355,
-0.06649193167686462,
0.04695434123277664,
-0.04804401099681854,
-0.020798198878765106,
-0.0411924310028553,
-0.03341149538755417,
0.033273737877607346,
0.0005184270557947457,
-0.02422269992530346,
0.032234203070402145,
-0.0017095371149480343,
-0.016006028279662132,
-0.01534181833267212,
0.03595766797661781,
0.041019000113010406,
-0.017302727326750755,
0.014790309593081474,
0.017692575231194496,
-0.011857659555971622,
-0.011888781562447548,
0.002429848536849022,
0.013780605979263783,
-0.04235532507300377,
0.0022115157917141914,
-0.02287553809583187,
0.029590312391519547,
0.0020818894263356924,
-0.00030998620786704123,
-0.005132916383445263,
0.031672392040491104,
-0.005738021340221167,
-0.026661917567253113,
-0.04257383570075035,
0.018168970942497253,
0.030800918117165565,
-0.038922399282455444,
-0.00603299867361784,
-0.01976403035223484,
0.014985806308686733,
-0.01978394016623497,
-0.016324371099472046,
0.01009748037904501,
0.012891852296888828,
-0.0009841152932494879,
0.012069670483469963,
0.03711742162704468,
-0.031478624790906906,
-0.005066074896603823,
0.01194361224770546,
-0.013654611073434353,
0.010352607816457748,
-0.030511416494846344,
0.003907747101038694,
0.013257190585136414,
-0.0044919224455952644,
0.001330179045908153,
-0.0497518852353096,
0.0029132687486708164,
-0.07598686218261719,
0.01564610004425049,
0.02269962802529335,
0.016739629209041595,
-0.05845077708363533,
0.01655818149447441,
0.02535909228026867,
0.015899326652288437,
0.02196595072746277,
0.027809016406536102,
0.029151417315006256,
-0.008996553719043732,
0.005192609038203955,
-0.02237396501004696,
-0.010564888827502728,
0.014487775973975658,
-0.03785442188382149,
-0.005964077077805996,
-0.0038458697963505983,
0.04486582428216934,
-0.004920944571495056,
0.011388438753783703,
-0.0169540848582983,
0.03341472148895264,
-0.033384885638952255,
0.014331734739243984,
-0.022783992812037468,
-0.009814742021262646,
-0.038838230073451996,
-0.00734718656167388,
0.02629815973341465,
-0.04226105287671089,
0.015246085822582245,
-0.02008538320660591,
-0.015601422637701035,
0.062062110751867294,
0.024266459047794342,
0.0007667319150641561,
-0.006217996124178171,
-0.05102066323161125,
-0.005754029378294945,
-0.05789920687675476,
-0.004916931502521038,
-0.04544827342033386,
-0.031501054763793945,
0.004431311506778002,
0.008993168361485004,
-0.035028550773859024,
0.0027646853122860193,
-0.011364612728357315,
0.027967417612671852,
0.013123473152518272,
0.0026926982682198286,
0.0035254592075943947,
-0.023398395627737045,
0.03270188346505165,
-0.002692384412512183,
0.01672770269215107,
-0.047599099576473236,
-0.05280948430299759,
0.052471987903118134,
-0.014274002984166145,
0.004075017757713795,
-0.01531953550875187,
0.011688982136547565,
0.044612955302000046,
0.010684589855372906,
-0.022382378578186035,
-0.007759826257824898,
0.012233827263116837,
-0.00962554756551981,
-0.019919317215681076,
0.02167321741580963,
-0.0420401357114315,
0.01667976751923561,
0.017447074875235558,
-0.02071347087621689,
-0.03490257263183594,
0.0017810501158237457,
0.0030984748154878616,
0.008305924944579601,
-0.006481675896793604,
0.004938372876495123,
0.03337860107421875,
0.043904948979616165,
0.021114645525813103,
0.02316117100417614,
-0.011679824441671371,
0.026680996641516685,
0.0010648175375536084,
-0.012916064821183681,
-0.01238687802106142,
-0.0043544527143239975,
-0.0003724627022165805,
-0.040322672575712204,
0.019977247342467308,
-0.0036787285935133696,
-0.01973453164100647,
0.021999366581439972,
-0.062241073697805405,
0.0016284665325656533,
0.02399607188999653,
-0.05218394845724106,
-0.02522786520421505,
0.01959793083369732,
0.009502670727670193,
-0.026232730597257614,
-0.0015709048602730036,
-0.006846138276159763,
0.034232597798109055,
0.016150152310729027,
0.06957077980041504,
0.03353983908891678,
-0.00117143162060529,
0.00902041606605053,
-0.03736633062362671,
-0.008584512397646904,
0.007968505844473839,
-0.006404058542102575,
-0.022624794393777847,
-0.0045587243512272835,
-0.039201606065034866,
0.0017001803498715162,
0.024311477318406105,
-0.019725827500224113,
0.00715220021083951,
-0.020909270271658897,
0.023396305739879608,
0.02007274702191353,
0.04597792401909828,
-0.03832002729177475,
-0.0003314486821182072,
-0.03961511328816414,
-0.011388407088816166,
0.029555410146713257,
0.03897600248456001,
0.014885729178786278,
0.011756804771721363,
0.030884969979524612,
-0.057863201946020126,
-0.05100686848163605,
0.042566679418087006,
-0.011509988456964493,
-0.0008566469186916947,
-0.02410215325653553,
0.0027829203754663467,
0.023582477122545242,
-0.05955272167921066,
-0.052799876779317856,
-0.011341446079313755,
-0.03815512731671333,
0.04093271493911743,
-0.043285347521305084,
-0.010271159000694752,
0.0029758771415799856,
-0.022295717149972916,
-0.03510332852602005,
-0.002362300641834736,
0.005493592005223036,
-0.008106805384159088,
-0.06807965785264969,
0.006000638473778963,
-0.00011481608089525253,
-0.023042907938361168,
0.021263321861624718,
-0.03889709711074829,
-0.0357515811920166,
0.042689453810453415,
-0.005686462391167879,
-0.014431554824113846,
0.010503893718123436,
-0.02303617261350155,
-0.011825409717857838,
-0.04925566166639328,
0.03206050768494606,
-0.00700248870998621,
-0.08211540430784225,
-0.017481964081525803,
-0.021836230531334877,
-0.0329023040831089,
0.017564624547958374,
0.07218128442764282,
-0.003085969714447856,
-0.03778393939137459,
-0.008810718543827534,
-0.029434919357299805,
0.016134746372699738,
-0.055808454751968384,
0.013481906615197659,
0.0057353731244802475,
-0.012806876562535763,
0.02577504701912403,
-0.030542325228452682,
-0.022140461951494217,
0.02586052194237709,
0.03114328347146511,
0.005291413515806198,
-0.0000746876685298048,
-0.02914987877011299,
0.003903282806277275,
-0.007053897716104984,
-0.01831776462495327,
-0.027200182899832726,
0.06844743341207504,
-0.033561233431100845,
0.007936151698231697,
0.004287064075469971,
0.026973674073815346,
-0.0523497611284256,
0.030343955382704735,
-0.07523049414157867,
0.012100103311240673,
-0.014887804165482521,
-0.0648210197687149,
0.05068069323897362,
-0.045018307864665985,
-0.033882055431604385,
0.029904792085289955,
-0.04431772977113724,
-0.00048049731412902474,
0.06679321080446243,
-0.0032689834479242563,
0.034550610929727554,
0.0003212041046936065,
0.0381915457546711,
0.0026124552823603153,
-0.009234165772795677,
0.0061549236997962,
-0.00625968910753727,
0.03700092434883118,
0.005533484276384115,
-0.04931188374757767,
0.03497300297021866,
0.024601781740784645,
0.033079780638217926,
0.015927713364362717,
0.012286344543099403,
0.005977089051157236,
-0.01283264346420765,
0.0033715665340423584,
-0.02789001725614071,
-0.009513827040791512,
0.0018802621634677052,
-0.02842070534825325,
0.06669967621564865,
-0.03265579044818878,
0.0189678855240345,
-0.015082540921866894,
-0.016144121065735817,
-0.019850991666316986,
0.02234683744609356,
-0.011330028995871544,
0.008210165426135063,
-0.01185504999011755,
-0.034918952733278275,
-0.01600993238389492,
0.00408964091911912,
0.024828322231769562,
-0.022698011249303818,
0.05090007558465004,
-0.015337497927248478,
-0.006556638050824404,
0.008833859115839005,
0.005413375794887543,
-0.04054491966962814,
-0.008466051891446114,
0.048390891402959824,
0.06078190356492996,
0.006580809131264687,
-0.029366319999098778,
0.010174275375902653,
-0.01974281668663025,
0.031037217006087303,
-0.034751176834106445,
-0.019187236204743385,
-0.01391949038952589,
-0.013200512155890465,
0.03502672165632248,
-0.008856799453496933
] |
<p>I have often seen diagrams, like <a href="http://en.wikipedia.org/wiki/Lens_%28optics%29#Imaging_properties">this one</a> on Wikipedia for a thin convex lens that show three lines from a point on the object converging at the image. Do all the other lines from that point on the object that pass through the lens converge at the same point on the image?</p>
<p>*<em>Updated question: *</em> to say, "from that point on the object"</p> | 1,519 | [
-0.04672183841466904,
-0.01382449734956026,
0.017067592591047287,
-0.034822069108486176,
0.02402488701045513,
0.027946336194872856,
-0.019315587356686592,
0.008879796601831913,
-0.0060135070234537125,
-0.030506715178489685,
0.04714541882276535,
0.0268744807690382,
0.04996031895279884,
0.007824541069567204,
0.03452729433774948,
0.0012242839438840747,
-0.03020593151450157,
-0.006288495380431414,
-0.004589742515236139,
-0.017801053822040558,
0.003098938846960664,
0.016260430216789246,
-0.0006247353740036488,
0.015267099253833294,
-0.028335073962807655,
0.005117660388350487,
0.017418205738067627,
-0.01883057691156864,
0.07106103748083115,
0.03555836156010628,
-0.011896338313817978,
-0.006837037857621908,
0.009194069541990757,
0.05576692149043083,
0.03482063487172127,
0.0014041868271306157,
0.007524043321609497,
-0.021702764555811882,
0.014134538359940052,
0.01880156435072422,
-0.003111824858933687,
0.006461712997406721,
0.017880335450172424,
0.06216807663440704,
-0.040253859013319016,
-0.013550051487982273,
-0.013600063510239124,
-0.03710123524069786,
0.008380434475839138,
-0.03537515178322792,
0.09018279612064362,
-0.013151569291949272,
0.04592957720160484,
0.07552855461835861,
0.013164013624191284,
0.03305212780833244,
0.05321924388408661,
0.04620163515210152,
-0.01981961913406849,
-0.02636333741247654,
-0.022403130307793617,
-0.02514146827161312,
0.006668143440037966,
-0.008953877724707127,
-0.007546721957623959,
0.029838206246495247,
-0.006131583359092474,
-0.041017357259988785,
0.042830564081668854,
-0.0006544291973114014,
-0.012775332666933537,
0.04763709753751755,
0.0689796507358551,
0.00023984898871276528,
-0.018613766878843307,
-0.015123746357858181,
0.009427043609321117,
-0.00472653191536665,
0.05760917440056801,
0.0005392964230850339,
-0.01997336931526661,
-0.0008851466118358076,
0.018198993057012558,
0.03880072012543678,
0.040907956659793854,
0.0036242722999304533,
0.07449039071798325,
-0.013733644969761372,
0.021933797746896744,
-0.0028404714539647102,
0.005344802513718605,
0.0057413713075220585,
-0.002915301825851202,
-0.030743515118956566,
-0.021533790975809097,
0.036401793360710144,
-0.02323293499648571,
0.03409607708454132,
0.02950839139521122,
-0.003978927154093981,
0.012634801678359509,
-0.024209659546613693,
0.000394825532566756,
0.03685018792748451,
0.007655849680304527,
-0.010407472960650921,
-0.04900370165705681,
0.03508424758911133,
-0.033719252794981,
0.02842964231967926,
-0.030736159533262253,
0.02417072281241417,
0.027034252882003784,
0.07283239811658859,
-0.001205485314130783,
-0.00378003460355103,
0.018044423311948776,
-0.006973802577704191,
0.06715690344572067,
0.05493665859103203,
0.03858352452516556,
-0.027165239676833153,
0.03099249303340912,
-0.04262994974851608,
-0.06682877242565155,
0.039967238903045654,
0.005490413401275873,
-0.015599846839904785,
-0.015921149402856827,
0.02145327441394329,
0.035681694746017456,
0.0007788747316226363,
0.007903829216957092,
0.013446403667330742,
0.006729367189109325,
-0.010395905002951622,
-0.08895757049322128,
-0.07268829643726349,
0.008692271076142788,
0.008652448654174805,
0.006458309944719076,
-0.0585976168513298,
0.026439951732754707,
0.04007729887962341,
0.0782131478190422,
-0.021384617313742638,
-0.007199673447757959,
-0.009418515488505363,
0.02164621464908123,
-0.05833486095070839,
-0.010867270641028881,
0.004622713662683964,
0.01527862623333931,
-0.019266098737716675,
0.001628561643883586,
-0.0855446308851242,
0.00586610147729516,
0.060514338314533234,
0.02916664630174637,
-0.07292383164167404,
0.0691443681716919,
-0.02927253395318985,
0.03245844691991806,
-0.003780967788770795,
-0.016869056969881058,
-0.035409800708293915,
0.0642937645316124,
0.028272638097405434,
-0.0023081754334270954,
0.030649177730083466,
0.02479025535285473,
0.05752222612500191,
-0.03267444670200348,
0.014688431285321712,
0.06359446793794632,
-0.0326278880238533,
0.019836517050862312,
-0.021919097751379013,
0.007480829954147339,
0.03650174289941788,
-0.010743861086666584,
-0.04705262929201126,
0.02087121643126011,
0.020159263163805008,
0.006199660710990429,
0.04806594178080559,
-0.04473625123500824,
-0.029869765043258667,
-0.013364829123020172,
-0.030115650966763496,
0.01696118339896202,
-0.04080460965633392,
0.033786170184612274,
-0.05398138612508774,
-0.0011557888938114047,
0.014566458761692047,
0.024671100080013275,
0.019151104614138603,
-0.010273809544742107,
-0.01854414865374565,
-0.0349755696952343,
0.020748013630509377,
0.006741628050804138,
-0.005613808054476976,
0.028513474389910698,
0.04257320240139961,
0.039070021361112595,
0.008994846604764462,
0.012832608073949814,
-0.05645131319761276,
0.018773918971419334,
0.0161700751632452,
0.007230766117572784,
0.01712426356971264,
0.011360100470483303,
0.050814758986234665,
-0.026060203090310097,
0.04993351548910141,
-0.014088842086493969,
0.03070647083222866,
-0.0372166708111763,
0.0511503666639328,
0.04134363681077957,
0.026446769014000893,
-0.026188453659415245,
0.0017186494078487158,
0.028238272294402122,
0.029917174950242043,
0.013830902986228466,
-0.05856824293732643,
-0.03897665813565254,
-0.009609404951334,
0.013199911452829838,
0.04506666585803032,
-0.04343250021338463,
-0.002247608033940196,
0.053150784224271774,
0.06325652450323105,
0.007442337926477194,
0.01454043760895729,
-0.04111748933792114,
-0.01532965898513794,
-0.046051908284425735,
0.009205461479723454,
0.00961921364068985,
0.022406980395317078,
-0.0020655631087720394,
0.0030998806469142437,
0.031249381601810455,
0.01104541402310133,
0.022536765784025192,
0.015133872628211975,
-0.00907482672482729,
-0.0019823326729238033,
0.001953692641109228,
0.03241564705967903,
0.019075186923146248,
-0.006185347680002451,
0.015788154676556587,
-0.0026799137704074383,
0.0064710406586527824,
-0.02138126641511917,
-0.051321856677532196,
-0.003953820560127497,
0.009164511226117611,
0.051043253391981125,
-0.05136888846755028,
-0.0074524106457829475,
0.030014842748641968,
-0.03290009871125221,
-0.0002010034950217232,
-0.07007553428411484,
-0.0219939686357975,
-0.014519871212542057,
0.030835727229714394,
0.044056668877601624,
-0.004566228482872248,
0.04413774609565735,
-0.07217662036418915,
-0.0629066452383995,
-0.01617705449461937,
-0.015225175768136978,
0.0184803307056427,
0.003058158792555332,
-0.03928540274500847,
0.004413104150444269,
-0.012250972911715508,
-0.03709199279546738,
0.039004623889923096,
0.015717703849077225,
0.00811944343149662,
0.01632286049425602,
-0.00534936273470521,
-0.06100733205676079,
-0.017246514558792114,
-0.01974348910152912,
0.02193383499979973,
-0.0050253490917384624,
0.015814270824193954,
0.02828497253358364,
0.00718133756890893,
-0.02165663056075573,
0.019563613459467888,
-0.0573272779583931,
-0.042924076318740845,
-0.009588051587343216,
0.0014572413638234138,
0.03636375442147255,
-0.023812953382730484,
0.022094786167144775,
0.03762257099151611,
-0.034474991261959076,
0.02360384911298752,
-0.046531859785318375,
-0.07151039689779282,
0.05433445796370506,
-0.01338163297623396,
0.04017072170972824,
-0.015310494229197502,
-0.02119937725365162,
0.08969046175479889,
0.027326837182044983,
-0.06762976944446564,
-0.026705965399742126,
0.02028735727071762,
-0.00016716949176043272,
-0.04999784752726555,
-0.0066984184086322784,
0.000838357605971396,
-0.03064577654004097,
0.043947286903858185,
0.014363558031618595,
0.020865943282842636,
0.04435517266392708,
0.020431919023394585,
0.02468775026500225,
-0.008111709728837013,
0.01970098726451397,
-0.018451539799571037,
0.010141846723854542,
0.06853600591421127,
-0.060436051338911057,
0.024095730856060982,
0.0027990369126200676,
0.06880712509155273,
-0.0014321103226393461,
-0.031302958726882935,
0.033464670181274414,
-0.008157428354024887,
-0.003147437237203121,
-0.00484180124476552,
0.03067035973072052,
0.033635515719652176,
0.03312727436423302,
-0.015353379771113396,
0.015590486116707325,
0.07844431698322296,
-0.02011863701045513,
-0.009648425504565239,
0.01958877220749855,
0.020194178447127342,
-0.0510319322347641,
-0.021207494661211967,
-0.0007879963959567249,
-0.001424437970854342,
-0.010143212974071503,
-0.022550854831933975,
-0.019595758989453316,
0.005543207749724388,
0.025696981698274612,
-0.01969868130981922,
0.008209927938878536,
-0.02117077261209488,
0.03474004566669464,
-0.054771922528743744,
-0.01380945648998022,
0.02336377650499344,
0.0008555752574466169,
-0.0034422329626977444,
0.0669056698679924,
0.01866416074335575,
0.01723531447350979,
0.029132409021258354,
0.016500335186719894,
-0.05958107113838196,
-0.02227204665541649,
-0.006170999258756638,
-0.040484413504600525,
-0.04140355810523033,
-0.0342169888317585,
0.012215375900268555,
-0.05525268614292145,
-0.023138660937547684,
-0.038962170481681824,
-0.015140056610107422,
-0.03322191908955574,
0.009893102571368217,
-0.02769359201192856,
-0.04704179987311363,
0.00929567962884903,
0.04886932298541069,
0.007815578952431679,
-0.03925934433937073,
0.023613182827830315,
0.021110787987709045,
-0.009532257914543152,
-0.006525685545057058,
0.0059503414668142796,
0.03587116301059723,
-0.012935124337673187,
0.05389009416103363,
-0.006739234086126089,
0.04521019011735916,
-0.04362354800105095,
0.03613746538758278,
-0.007380142342299223,
0.051343414932489395,
-0.0027982695028185844,
-0.06674542278051376,
-0.02267751842737198,
-0.05145232379436493,
-0.040126048028469086,
-0.01750553771853447,
0.05214321240782738,
0.0022594095207750797,
-0.011260533705353737,
0.042451851069927216,
0.011949746869504452,
-0.02179829031229019,
0.005747659597545862,
0.024892568588256836,
0.00767976650968194,
-0.04420523717999458,
-0.09389534592628479,
-0.025812609121203423,
-0.003793431678786874,
0.017392266541719437,
0.03936444967985153,
0.02059035748243332,
-0.029909281060099602,
0.0043287319131195545,
-0.0003247692948207259,
-0.014391671866178513,
-0.02230541780591011,
0.02182607911527157,
-0.015729842707514763,
-0.015027307905256748,
0.013362569734454155,
-0.01190197467803955,
0.0407024510204792,
0.0414763018488884,
0.05634939298033714,
0.03713065758347511,
-0.00968919787555933,
-0.06265705078840256,
-0.0015636528842151165,
0.027607470750808716,
0.012309793382883072,
-0.01088603213429451,
-0.010985610075294971,
-0.027861973270773888,
-0.00739391939714551,
0.059737496078014374,
0.004972629249095917,
0.025745708495378494,
-0.019089780747890472,
0.016111837700009346,
-0.011614710092544556,
-0.01568431779742241,
-0.046252042055130005,
0.007513299584388733,
0.002142509911209345,
0.019663218408823013,
-0.01651562936604023,
0.0019782797899097204,
-0.0028019859455525875,
0.01583137921988964,
0.029168464243412018,
0.050983890891075134,
-0.0010916711762547493,
0.00028774215024895966,
0.0021651724819093943,
0.008786329999566078,
-0.01936539076268673,
-0.03946368768811226,
0.028472039848566055,
0.018817342817783356,
-0.04741889238357544,
0.015847845003008842,
-0.029958654195070267,
0.010065261274576187,
0.03622880205512047,
0.00010091775766341016,
0.004181346856057644,
0.042862702161073685,
-0.018504194915294647,
0.019407812505960464,
0.0513029471039772,
0.02071560174226761,
0.04316641017794609,
0.011549563147127628,
0.0041423579677939415,
0.011178881861269474,
-0.0536501407623291,
0.04354332759976387,
-0.015959179028868675,
-0.022239074110984802,
-0.03066353127360344,
0.0009201340144500136,
-0.01721133105456829,
0.048525720834732056,
-0.005216040648519993,
0.01491208653897047,
0.006419271696358919,
-0.021637694910168648,
-0.0012830209452658892,
0.008017713204026222,
0.006957858335226774,
0.03308796137571335,
0.016171885654330254,
0.03293038159608841,
0.034877367317676544,
-0.024355480447411537,
0.010607529431581497,
-0.014818716794252396,
0.02109483815729618,
0.018487518653273582,
0.006497962865978479,
-0.00606250436976552,
-0.0356682613492012,
0.013979139737784863,
0.0038428904954344034,
-0.058045513927936554,
0.0451275035738945,
-0.02351333387196064,
-0.009386307559907436,
0.04353335127234459,
-0.055462248623371124,
-0.032567549496889114,
0.01862853206694126,
-0.03453218936920166,
0.015018078498542309,
-0.05040581524372101,
0.010452673770487309,
0.03751225769519806,
0.04642977938055992,
-0.0457327663898468,
-0.04284592717885971,
0.01927318051457405,
0.015460541471838951,
-0.003835706738755107,
0.0006226949626579881,
0.0132485032081604,
0.01742647960782051,
-0.052689023315906525,
-0.03033304214477539,
0.05133619159460068,
-0.02708909660577774,
-0.057805124670267105,
-0.010026556439697742,
0.0024196242447942495,
0.047588054090738297,
0.012798462063074112,
-0.02392294816672802,
0.0386616550385952,
-0.014656620100140572,
-0.013772489503026009,
0.0026886563282459974,
0.054787084460258484,
-0.03973691165447235,
-0.01855497807264328,
-0.0493457205593586,
-0.002934196265414357,
0.03656553849577904,
-0.03356000408530235,
0.00592348538339138,
0.005993851460516453,
0.009012950584292412,
-0.0070551373064517975,
-0.024971051141619682,
0.0223147701472044,
-0.0007824429194442928,
-0.00422605499625206,
-0.003075661603361368,
0.014793110080063343,
-0.003906643949449062,
-0.06866700202226639,
0.047030866146087646,
0.02777770347893238,
0.015791822224855423,
-0.0012360851978883147,
0.06393498927354813,
-0.011043020524084568,
0.00562992412596941,
-0.006511000916361809,
-0.010581720620393753,
0.03891073912382126,
0.012808423489332199,
0.01773286610841751,
0.014703439548611641,
0.03388219699263573,
-0.015592166222631931,
0.01699267327785492,
-0.028034726157784462,
0.014313435181975365,
0.10151804983615875,
-0.01520038116723299,
0.05830316245555878,
0.05400587618350983,
0.0009401211864314973,
0.01807985082268715,
-0.025962181389331818,
-0.013798154890537262,
-0.027374867349863052,
-0.00806617084890604,
0.062398698180913925,
-0.0553436316549778,
0.0024151415564119816,
-0.003523873630911112,
0.050551462918519974,
-0.021433521062135696,
0.004667783156037331,
-0.02132677286863327,
0.014681669883430004,
0.03199589252471924,
0.010059131309390068,
-0.055581096559762955,
0.014905944466590881,
-0.05153730884194374,
0.02427513897418976,
-0.0057681286707520485,
-0.028108075261116028,
0.022066155448555946,
-0.024352403357625008,
0.003988762851804495,
-0.056563105434179306,
-0.051565010100603104,
-0.027754830196499825,
0.0323568657040596,
-0.012494922615587711,
0.018443770706653595,
-0.04300989210605621,
-0.027143772691488266,
0.02233283594250679,
0.0007095776381902397,
0.014179201796650887,
-0.03085583634674549,
-0.08425333350896835,
-0.03917083144187927,
-0.01786538027226925,
-0.02592681348323822,
0.011617264710366726,
-0.0006092211697250605,
-0.01909731701016426,
-0.028712285682559013,
-0.04444229602813721,
0.013948843814432621,
0.048548534512519836,
0.03911178186535835,
0.006103258579969406,
0.04146408662199974,
0.0024282659869641066,
0.06218620017170906,
-0.022618886083364487,
-0.009379814378917217,
0.08697488158941269,
0.05223402380943298,
-0.018113896250724792,
-0.03817703574895859,
0.020964838564395905,
-0.029263712465763092,
-0.02579137682914734,
-0.021029377356171608,
0.03789311274886131,
-0.022814916446805,
0.002121182857081294,
0.026900876313447952,
0.04082649573683739,
0.0022128925193101168,
0.008286030031740665,
0.04635854810476303,
-0.04753388464450836,
-0.027646904811263084,
0.02401936613023281,
0.035708483308553696,
0.0015216736355796456,
0.023512860760092735,
-0.02116948552429676,
-0.0039995755068957806,
-0.005792859476059675,
-0.021235238760709763,
-0.002735304646193981,
-0.04098105430603027,
0.03731381148099899,
0.010240858420729637,
-0.008044871501624584,
-0.0037412745878100395,
0.025362808257341385,
-0.062446415424346924,
-0.059197790920734406,
0.011186475865542889,
0.05023195967078209,
-0.019498540088534355,
0.010987309738993645,
0.008975687436759472,
0.02333235554397106,
0.014812404289841652,
-0.0030744841787964106,
-0.007398942485451698,
-0.020293550565838814,
-0.011929984204471111,
-0.017693370580673218,
-0.002038799226284027,
-0.017847366631031036,
0.026990413665771484,
-0.04305698722600937,
0.030143404379487038,
0.05104879289865494,
-0.0868145078420639,
-0.02290952019393444,
0.004631287883967161,
-0.012977952137589455,
0.014577767811715603,
-0.036396246403455734,
0.006404918152838945,
0.007991470396518707,
-0.0007674561929889023,
-0.005882478319108486,
0.010905320756137371,
0.002006248105317354,
0.001473778858780861,
-0.021652331575751305,
0.017399316653609276,
-0.027247177436947823,
-0.04200439900159836,
-0.027194196358323097,
0.007292093709111214,
-0.017206266522407532,
0.00473686121404171,
0.0038911195006221533,
0.006385951302945614,
0.03020551986992359,
0.015565594658255577,
0.009831374511122704,
0.028259119018912315,
-0.06459487974643707,
0.011515084654092789,
-0.022120552137494087,
-0.022803431376814842,
-0.042324140667915344,
-0.0020303549244999886,
0.054458439350128174,
0.052119284868240356,
0.011521294713020325,
0.018414035439491272,
-0.015183408744633198,
0.04548293352127075,
0.02322513982653618,
0.0016946634277701378,
-0.05241817235946655,
0.03227953240275383,
-0.023701729252934456,
-0.006754751782864332,
-0.03130103647708893,
0.028437897562980652,
0.03326744586229324,
0.02360433153808117,
0.018799763172864914,
0.027407772839069366,
-0.007165031973272562,
0.03405177220702171,
-0.01859336532652378,
-0.02677994593977928,
0.026425661519169807,
0.014326981268823147,
-0.011603455059230328,
-0.011003018356859684,
-0.02228463441133499,
-0.026881247758865356,
0.0007425585645250976,
-0.00652413722127676,
-0.005323390476405621,
0.01234127301722765,
0.0017235379200428724,
-0.030562903732061386,
0.024492010474205017,
-0.022463420405983925,
-0.02895648404955864,
-0.04514560475945473,
-0.015156925655901432,
0.0354512594640255,
0.0037078072782605886,
0.010160135105252266,
0.025623207911849022,
-0.0060113039799034595,
-0.04737598076462746,
0.012472014874219894,
0.012167925015091896,
-0.018858470022678375,
0.0015456158434972167,
0.013761280104517937,
-0.014669768512248993,
0.03537769988179207,
-0.010048599913716316,
-0.027181698009371758,
0.018090033903717995,
-0.02845243737101555,
-0.0090406509116292,
0.01952158287167549,
0.02940201945602894,
-0.0033752864692360163,
0.009835425764322281,
0.005418425425887108,
-0.010397621430456638,
0.028608622029423714,
0.005771317519247532,
-0.017505310475826263,
0.03481182083487511,
-0.03340031951665878,
0.025388874113559723,
0.0015550620155408978,
0.03840303421020508,
-0.035911403596401215,
-0.0026659586001187563,
0.005408284720033407,
0.0034192672464996576,
0.011505043134093285,
-0.03148730844259262,
0.008969534188508987,
-0.040654491633176804,
-0.03440327197313309,
-0.0037079358007758856,
0.005783322267234325,
0.03093315288424492,
0.019610675051808357,
-0.040063463151454926,
0.06613493710756302,
0.07655142992734909,
-0.009354501031339169,
-0.07622262835502625,
-0.0037500071339309216,
-0.0036743904929608107,
0.024651478976011276,
0.00012012806837446988,
-0.07249688357114792,
0.02776789665222168,
0.009754396043717861,
-0.08363666385412216,
0.01847594417631626,
-0.011965167708694935,
-0.042970407754182816,
-0.06736239790916443,
0.017881685867905617,
0.0302230566740036,
0.04960153251886368,
-0.009466730989515781,
0.05219724029302597,
0.0027135645505040884,
0.004837095737457275,
-0.021259430795907974,
-0.014402260072529316,
-0.015133315697312355,
0.03981110081076622,
-0.00297866971231997,
-0.03732738643884659,
0.07155701518058777,
-0.004927787464112043,
-0.036401499062776566,
-0.009041275829076767,
-0.012689333409070969,
0.03230893984436989,
0.028343504294753075,
0.00854738149791956,
-0.00153365230653435,
-0.024440603330731392,
0.0028572154697030783,
-0.00579432537779212,
-0.022982148453593254,
0.00899867620319128,
0.01029552798718214,
0.01885257288813591,
-0.04043564945459366,
-0.0037092012353241444,
0.030868738889694214,
-0.06572601199150085,
-0.05912184342741966,
0.012010719627141953,
-0.004835193976759911,
-0.02450108714401722,
-0.012078529223799706,
0.002742748474702239,
0.02824612520635128,
-0.01725921966135502,
0.017698420211672783,
-0.0781596302986145,
0.008439412340521812,
0.019580280408263206,
-0.0003404683666303754,
-0.023758303374052048,
0.0056993733160197735,
-0.005719668697565794,
-0.04135005921125412,
0.01745450310409069,
-0.022594863548874855,
-0.0005406339769251645,
-0.06032777950167656,
-0.006758730858564377,
0.029290903359651566,
-0.0036833779886364937,
0.00832326989620924,
-0.04990687221288681,
-0.01707986183464527,
0.03085884265601635,
0.017567966133356094,
-0.0034565692767500877,
0.04944130405783653,
-0.06386223435401917,
-0.05532028526067734,
-0.058984678238630295,
0.03740609437227249,
0.0057783303782343864,
-0.01497836783528328,
-0.034515999257564545,
-0.01844361238181591,
-0.034412432461977005,
0.03160340338945389,
0.04543287307024002,
-0.019388407468795776,
0.034700099378824234,
-0.00927514024078846,
0.018027370795607567,
0.040573038160800934,
-0.06020160764455795,
-0.021224290132522583,
0.011941557750105858,
0.0028788179624825716,
-0.03772129863500595,
-0.0016223290003836155,
-0.03193702548742294,
-0.0003392024082131684,
0.02290366217494011,
0.02312878705561161,
0.06088365614414215,
-0.008128122426569462,
-0.02407119609415531,
0.024922234937548637,
0.0412183478474617,
-0.018609503284096718,
0.07375804334878922,
-0.029289457947015762,
-0.03405766934156418,
0.016046104952692986,
-0.0577656552195549,
-0.04636000469326973,
-0.021798577159643173,
-0.04826243594288826,
0.006532459054142237,
-0.010167539119720459,
0.004250949248671532,
0.045452143996953964,
-0.04881337285041809,
0.005620102398097515,
-0.011149081401526928,
-0.019676508381962776,
-0.0318453311920166,
0.0454852357506752,
0.00851802434772253,
0.011868431232869625,
-0.029243020340800285,
-0.015055184252560139,
0.001085326774045825,
-0.04650401696562767,
-0.030501307919621468,
0.04170982167124748,
0.04415011405944824,
0.01095587108284235,
0.013248525559902191,
0.01650640368461609,
0.011756525374948978,
0.004283536691218615,
-0.041834842413663864,
0.025136038661003113,
-0.012749838642776012,
-0.024327976629137993,
0.010966135188937187,
-0.0016633148770779371,
-0.012246251106262207,
-0.004207463935017586,
-0.016805946826934814,
0.052058443427085876,
-0.04341210797429085,
-0.007564496248960495,
-0.011100503616034985,
0.02362861856818199,
-0.03692631796002388,
0.03164823353290558,
0.02604125626385212,
0.02139359340071678,
0.005079897120594978,
-0.02929927594959736,
-0.009162296541035175,
-0.0027965388726443052,
0.015868810936808586,
-0.034164972603321075,
0.03523724153637886,
-0.007735536899417639,
-0.009662787429988384,
-0.010152309201657772,
-0.0033827400766313076,
-0.028513921424746513,
0.017998043447732925,
0.024209417402744293,
0.03628223016858101,
0.011360601522028446,
0.011512302793562412,
0.009086830541491508,
-0.03168349713087082,
0.03543412685394287,
-0.09627413004636765,
-0.024987535551190376,
-0.0017482746625319123,
0.05239301919937134,
0.02447095513343811,
-0.008403223007917404
] |
<p>I was at a lecture yesterday and there was a demo of a van de graff generator. He held the smaller metal globe which is attached by a wire, about 4cm from the main globe. This created a spark between the two globes.
At the same time the spark happened the speakers in the hall would click loudly, the projector (on the other side of the room) would turn yellow and the text moved down, then flashed black and back to normal. And the plasma globe that was next to the van de graff generator which was switched off (but on at the wall) would briefly turn on. </p>
<p>Is it possible for a spark to do that? Or is there something else happening at the same time? </p> | 1,520 | [
-0.061740513890981674,
-0.04427193105220795,
-0.00525003531947732,
-0.04595950245857239,
0.06246878579258919,
-0.015475842170417309,
-0.025079766288399696,
0.01192742120474577,
0.040682628750801086,
-0.0089030796661973,
0.049208227545022964,
0.05013880133628845,
0.09264498203992844,
-0.015065820887684822,
0.027031254023313522,
-0.025405453518033028,
0.021777231246232986,
0.0039960159920156,
0.007372979074716568,
-0.03012935072183609,
-0.026539109647274017,
0.03252113610506058,
0.01248127594590187,
-0.0014426143607124686,
-0.02740473486483097,
0.0030183952767401934,
0.014808647334575653,
0.031427592039108276,
-0.0019665260333567858,
0.024005815386772156,
-0.051312465220689774,
-0.010248241946101189,
0.007212825119495392,
-0.019465340301394463,
0.023380160331726074,
0.0032694025430828333,
-0.04205635190010071,
-0.06873322278261185,
0.005846634041517973,
-0.004717602860182524,
-0.02376370318233967,
0.012901819311082363,
-0.018459519371390343,
0.08581303805112839,
-0.03836144134402275,
0.005606769118458033,
-0.0399135947227478,
-0.013889767229557037,
0.05401676520705223,
-0.05698051303625107,
0.06211191043257713,
-0.02971545048058033,
0.05764194577932358,
0.03584267571568489,
-0.005900783464312553,
0.05563107877969742,
0.06794016063213348,
0.08165809512138367,
-0.013253038749098778,
-0.026775645092129707,
0.0106952590867877,
0.0005943349096924067,
-0.02626044489443302,
-0.03440285846590996,
-0.043374788016080856,
0.02522297017276287,
-0.008695635944604874,
-0.013026813045144081,
0.03820468485355377,
0.033295027911663055,
0.013369498774409294,
-0.01248646154999733,
0.052630506455898285,
-0.0005913731292821467,
0.013745924457907677,
0.0007406563381664455,
0.022981414571404457,
0.00014214114344213158,
0.03219171240925789,
0.0263529010117054,
-0.0005848405417054892,
-0.010776993818581104,
0.00722856679931283,
0.02116171270608902,
0.027991650626063347,
-0.017551029101014137,
0.035062022507190704,
-0.05725947767496109,
0.050398435443639755,
0.01576228067278862,
-0.05449911952018738,
0.0013523532543331385,
0.01246041338890791,
0.02234281599521637,
-0.03554832190275192,
0.013097977265715599,
-0.026494113728404045,
0.0666293054819107,
0.010129713453352451,
-0.020048081874847412,
0.028215603902935982,
0.021557308733463287,
0.014244239777326584,
0.047680482268333435,
-0.01834838278591633,
-0.042863860726356506,
-0.025685880333185196,
-0.012693609111011028,
-0.005816544406116009,
0.01460022758692503,
-0.09132707118988037,
0.03581520542502403,
0.014594493433833122,
-0.0189207810908556,
-0.009669334627687931,
0.012251134030520916,
0.0011575705138966441,
-0.003651675069704652,
0.02334827370941639,
0.050527967512607574,
-0.020991696044802666,
-0.017245156690478325,
0.03726348280906677,
-0.04716920480132103,
-0.059094324707984924,
-0.015815667808055878,
0.010789415799081326,
-0.018237385898828506,
-0.0035583204589784145,
0.04319973662495613,
-0.019197581335902214,
-0.013044112361967564,
-0.0019055117154493928,
0.006051192060112953,
0.05239444598555565,
-0.02392427623271942,
-0.09848223626613617,
-0.061449356377124786,
0.02198229730129242,
-0.038547128438949585,
0.010294180363416672,
-0.06705492734909058,
-0.009556915611028671,
0.012262260541319847,
0.04693726822733879,
-0.011359177529811859,
-0.060200825333595276,
-0.053738512098789215,
0.042933687567710876,
0.046467240899801254,
-0.015366267412900925,
0.004103752784430981,
0.007995778694748878,
-0.03500598296523094,
0.008017098531126976,
-0.04256223142147064,
0.040440890938043594,
0.04217926785349846,
-0.007172175217419863,
-0.01139692310243845,
0.02004755474627018,
0.02935875952243805,
0.011110791936516762,
-0.0018918877467513084,
0.014102471992373466,
-0.003985969815403223,
0.08374171704053879,
0.023834185674786568,
-0.010045909322798252,
0.031209580600261688,
0.03833439201116562,
0.03854987025260925,
-0.011604555882513523,
0.030849900096654892,
0.021662652492523193,
-0.0377754345536232,
-0.008666099980473518,
0.01275175716727972,
0.03978901728987694,
-0.02915310673415661,
-0.01733618788421154,
-0.014857187867164612,
0.006419345736503601,
0.020946219563484192,
-0.015417549759149551,
0.07318849861621857,
-0.0052539026364684105,
-0.004740586504340172,
-0.017207080498337746,
-0.027984358370304108,
-0.04043257609009743,
-0.05550609156489372,
0.040809519588947296,
-0.017617706209421158,
-0.007666007615625858,
0.007499151397496462,
0.010338447988033295,
0.03973155841231346,
-0.021559271961450577,
0.00038405280793085694,
-0.025783443823456764,
0.06070677936077118,
-0.006149790715426207,
-0.010046404786407948,
-0.028035692870616913,
0.05842769145965576,
-0.0012950367527082562,
0.01768842339515686,
0.020530983805656433,
-0.035097636282444,
-0.027989208698272705,
-0.0102850291877985,
-0.035207223147153854,
0.0205996036529541,
0.016926893964409828,
0.0026930002495646477,
0.0400095172226429,
0.062586709856987,
-0.012962320819497108,
0.02695566602051258,
-0.012894430197775364,
0.04890736937522888,
0.06949189305305481,
0.017817899584770203,
-0.008582575246691704,
0.03304297849535942,
0.04871893674135208,
-0.01963270641863346,
0.036437034606933594,
-0.02414090558886528,
-0.04313873127102852,
0.036667026579380035,
0.042036157101392746,
0.014396856538951397,
-0.017183903604745865,
0.04411005228757858,
0.04396955668926239,
0.007458128035068512,
-0.0007728995988145471,
0.02584892138838768,
-0.019010532647371292,
0.011607658118009567,
0.0064884573221206665,
0.01521699782460928,
0.023051690310239792,
-0.0028407955542206764,
0.0647471472620964,
0.005181293003261089,
0.022688893601298332,
-0.056165874004364014,
-0.0035258696880191565,
0.03875168412923813,
-0.048152122646570206,
-0.005374380853027105,
-0.00586447399109602,
-0.02657165750861168,
0.025410789996385574,
-0.03170277178287506,
0.0361931174993515,
-0.008369033224880695,
0.02242225594818592,
0.02337186224758625,
-0.028281424194574356,
-0.026200981810688972,
0.020549660548567772,
-0.02762022241950035,
-0.02691844291985035,
0.011190243996679783,
0.04111462086439133,
-0.05585978925228119,
0.016837920993566513,
0.007126344833523035,
0.019118765369057655,
-0.02234034426510334,
0.011227073147892952,
-0.024126900359988213,
-0.004084452986717224,
0.042386457324028015,
-0.02074544131755829,
-0.04486113041639328,
-0.022143593057990074,
-0.030308514833450317,
0.01999390311539173,
0.02576378360390663,
-0.014275908470153809,
0.01609938219189644,
0.01625569351017475,
-0.03753858804702759,
0.012606053613126278,
-0.008003640919923782,
-0.002623203909024596,
0.03331604599952698,
-0.011740632355213165,
-0.05299929156899452,
0.020957333967089653,
-0.016378158703446388,
0.009754428640007973,
-0.03465178981423378,
-0.003639630740508437,
0.03431978076696396,
-0.003577302908524871,
-0.05473001301288605,
0.016341788694262505,
-0.037356842309236526,
-0.008236213587224483,
-0.01718142069876194,
-0.014661265537142754,
0.022074956446886063,
-0.05054684728384018,
0.003266001120209694,
0.014045770280063152,
-0.02255817875266075,
-0.029958859086036682,
-0.014857746660709381,
-0.031415101140737534,
-0.019587308168411255,
-0.008037801831960678,
0.050702884793281555,
-0.04228723421692848,
-0.052632711827754974,
0.045390114188194275,
0.016133872792124748,
-0.01497772615402937,
-0.05404996499419212,
-0.03506658598780632,
-0.04178733751177788,
-0.07297708094120026,
0.029102107509970665,
0.05363643541932106,
-0.0231737419962883,
0.003999166190624237,
0.037551335990428925,
0.0018876726971939206,
0.01887214370071888,
0.031393468379974365,
-0.02335651032626629,
0.01621347665786743,
-0.01954767107963562,
-0.007043065503239632,
0.05944325402379036,
0.003291542176157236,
-0.029850753024220467,
-0.013491201214492321,
-0.03326171636581421,
0.012123564258217812,
0.015460940077900887,
-0.032795220613479614,
0.03767288476228714,
0.0007617487572133541,
0.004923088941723108,
-0.04363997280597687,
0.014826448634266853,
0.024175358936190605,
-0.0064896163530647755,
-0.006920492276549339,
0.02505548484623432,
0.08086981624364853,
-0.003514687530696392,
-0.01331011950969696,
0.03521598130464554,
0.01876761205494404,
-0.010923189111053944,
-0.030261803418397903,
0.002076951786875725,
0.0390843041241169,
0.03526913747191429,
-0.025565404444932938,
-0.011944165453314781,
0.057210810482501984,
0.008849394507706165,
0.0049347588792443275,
0.017380354925990105,
-0.0012868354097008705,
0.014324093237519264,
-0.061161428689956665,
0.03418060764670372,
-0.00961293000727892,
0.03344350680708885,
0.018997451290488243,
0.060882940888404846,
-0.0036797714419662952,
0.021226059645414352,
-0.0010418635793030262,
-0.021236728876829147,
-0.1117744967341423,
0.01500016637146473,
-0.0259084552526474,
-0.013336393982172012,
-0.02379831299185753,
0.023293636739253998,
-0.06038348004221916,
0.011875719763338566,
-0.03011201322078705,
-0.027338633313775063,
-0.03155078738927841,
-0.09041597694158554,
0.007729831617325544,
-0.004260159097611904,
-0.027602020651102066,
-0.009786508046090603,
0.0014610406942665577,
0.049386411905288696,
-0.019775863736867905,
0.041061881929636,
0.0035459750797599554,
-0.01069688145071268,
0.051223352551460266,
-0.007262778002768755,
-0.027294594794511795,
0.018538402393460274,
0.06025025621056557,
0.0049762362614274025,
0.043344415724277496,
-0.04837898537516594,
0.02966013178229332,
0.0191026721149683,
0.037080712616443634,
0.009301725775003433,
-0.03866836801171303,
-0.03182874992489815,
-0.02239009365439415,
-0.035697367042303085,
0.018229402601718903,
0.06069798767566681,
-0.03656340017914772,
-0.00575780775398016,
0.0010312848025932908,
0.01808065176010132,
0.0005045110592618585,
-0.005038764793425798,
0.033727530390024185,
-0.015709564089775085,
-0.029496965929865837,
-0.020529022440314293,
0.008056431077420712,
-0.0028586597181856632,
-0.0064580682665109634,
-0.006213923450559378,
-0.003125343471765518,
-0.0002197072171838954,
0.0003321344265714288,
-0.003047052538022399,
0.01856370083987713,
-0.0003501808678265661,
-0.009601886384189129,
0.0076187988743186,
-0.020575933158397675,
0.0073408447206020355,
0.0067984964698553085,
0.034261323511600494,
-0.007614513393491507,
0.030455315485596657,
-0.0045805578120052814,
-0.03836915269494057,
-0.080764040350914,
-0.033673010766506195,
0.04627574235200882,
0.03228465095162392,
-0.0042918589897453785,
0.0007924453821033239,
-0.05528751388192177,
0.002908590715378523,
0.016605686396360397,
-0.05272834748029709,
0.021964769810438156,
-0.026797832921147346,
-0.004326810594648123,
-0.015504810959100723,
-0.044007278978824615,
0.010680248960852623,
0.029873676598072052,
0.008667994290590286,
0.03147624433040619,
-0.04071087762713432,
-0.04860818758606911,
0.03568517044186592,
0.037583447992801666,
0.04371318966150284,
0.03638940677046776,
0.015182451345026493,
0.0015731493476778269,
-0.01843070052564144,
0.041518017649650574,
0.004643579944968224,
-0.06464552134275436,
0.013243540190160275,
0.005044696852564812,
-0.02916662208735943,
0.052767254412174225,
-0.027403999119997025,
-0.05695446580648422,
0.0027636841405183077,
-0.007918398827314377,
-0.005650472827255726,
-0.021432258188724518,
-0.008150594308972359,
0.02396257035434246,
0.039110876619815826,
-0.012601948343217373,
0.04730392247438431,
0.03470797464251518,
-0.044174954295158386,
0.010655543766915798,
-0.029202233999967575,
0.03356063365936279,
-0.01534332800656557,
0.014320568181574345,
0.0125411506742239,
0.01245329063385725,
-0.023480327799916267,
0.07367385178804398,
-0.01646875962615013,
0.009708786383271217,
-0.007161433808505535,
-0.013653227128088474,
-0.0013908277032896876,
0.03402724117040634,
0.0253544170409441,
-0.018698111176490784,
-0.04876873642206192,
0.025660153478384018,
0.0260157510638237,
0.017488619312644005,
0.039141688495874405,
-0.04010096192359924,
0.03545217216014862,
0.03046269156038761,
-0.0054825120605528355,
-0.002080691745504737,
-0.042506393045186996,
0.0012623704969882965,
0.0032441955991089344,
-0.06140913441777229,
0.038586732000112534,
-0.0251335259526968,
0.007248608395457268,
0.0516328401863575,
-0.05568099766969681,
-0.03054383583366871,
-0.006176449358463287,
0.03131766617298126,
0.020728157833218575,
-0.04163312911987305,
0.022628359496593475,
-0.02915201149880886,
-0.00758353853598237,
-0.051555830985307693,
-0.06002398952841759,
0.0648472011089325,
0.027557944878935814,
-0.017141778022050858,
-0.03753923624753952,
-0.03541259467601776,
-0.01007931400090456,
-0.04991473630070686,
0.012878088280558586,
0.020796697586774826,
-0.031683262437582016,
0.005715381819754839,
0.009304095059633255,
-0.027985647320747375,
0.004662576597183943,
0.01163020171225071,
-0.0006776712252758443,
-0.013625312596559525,
-0.012473647482693195,
-0.020835233852267265,
-0.012115027755498886,
0.0405387207865715,
-0.03068898618221283,
-0.042075611650943756,
0.020790988579392433,
0.002799087669700384,
0.02167033776640892,
-0.06092749536037445,
-0.014076092280447483,
0.07375499606132507,
0.0061455112881958485,
0.024089505895972252,
-0.02420470304787159,
0.03245161846280098,
0.0030649437103420496,
0.023341167718172073,
0.02517867647111416,
0.018848134204745293,
-0.011494699865579605,
-0.02145470306277275,
-0.007441658992320299,
0.019961321726441383,
0.01151615846902132,
0.002688047708943486,
0.03858654573559761,
-0.021441880613565445,
-0.0001442936045350507,
0.042593929916620255,
-0.03033701702952385,
0.024648161605000496,
-0.0355667918920517,
-0.0005327176186256111,
0.006750588770955801,
0.012096543796360493,
-0.05051511526107788,
0.017686448991298676,
-0.012969541363418102,
-0.05040783807635307,
0.05467400699853897,
-0.011010914109647274,
0.04922787472605705,
0.009727003052830696,
-0.0017488963203504682,
-0.025315482169389725,
-0.02714425139129162,
0.023626795038580894,
-0.0309776421636343,
-0.001958319451659918,
0.014005464501678944,
-0.023573093116283417,
0.04811501502990723,
0.04650620371103287,
0.045172255486249924,
0.005126034840941429,
0.030435940250754356,
0.048396822065114975,
0.007170015014708042,
0.0398075245320797,
0.019635790959000587,
-0.03124382719397545,
0.022198820486664772,
-0.07180804014205933,
0.04976561293005943,
-0.027095550671219826,
0.03613080829381943,
0.019736211746931076,
-0.004256985150277615,
-0.002750784158706665,
-0.039155058562755585,
0.014542634598910809,
-0.04970989748835564,
-0.017140761017799377,
0.007061731535941362,
0.007944023236632347,
0.005501516629010439,
-0.0058729383163154125,
0.018205001950263977,
0.023265810683369637,
0.004513142630457878,
-0.044594988226890564,
-0.0704052597284317,
-0.03130239248275757,
0.0034926971420645714,
-0.038659024983644485,
0.06203377619385719,
-0.03519222512841225,
-0.026644185185432434,
0.02216399647295475,
-0.021872462704777718,
0.04798106104135513,
0.006521024275571108,
0.10295825451612473,
-0.0009583074715919793,
0.04927639663219452,
-0.01737253926694393,
0.03462650254368782,
-0.006346476264297962,
0.032662272453308105,
0.10880380123853683,
0.010234015993773937,
0.001886210055090487,
-0.026268403977155685,
0.029735121876001358,
-0.022753870114684105,
0.04169118404388428,
-0.017273617908358574,
0.0013056265888735652,
-0.02973293326795101,
0.019171617925167084,
0.06273926049470901,
0.045475639402866364,
0.051653940230607986,
0.028897607699036598,
0.028355393558740616,
-0.009263609535992146,
-0.010778273455798626,
-0.054965682327747345,
0.028242211788892746,
-0.0034055113792419434,
0.034313179552555084,
-0.033215831965208054,
0.03318231552839279,
-0.03680313378572464,
-0.006011680234223604,
-0.03721309080719948,
-0.026912547647953033,
0.05662493407726288,
-0.014096410013735294,
-0.04071204736828804,
0.004680808167904615,
-0.002004992449656129,
-0.027209052816033363,
-0.014105577021837234,
0.01449765358120203,
0.025427810847759247,
0.029472388327121735,
0.003823245642706752,
0.014728115871548653,
0.010485533624887466,
0.028598327189683914,
0.018601255491375923,
0.006998594384640455,
-0.03813592344522476,
-0.027685334905982018,
0.002987443935126066,
0.0184292234480381,
0.04582047089934349,
0.0340467169880867,
-0.0253862664103508,
0.02806789241731167,
0.05496111884713173,
-0.027791135013103485,
-0.07297127693891525,
-0.007801476866006851,
-0.032263100147247314,
-0.004277511034160852,
0.016641689464449883,
-0.055951859802007675,
0.045998796820640564,
-0.02456609159708023,
-0.001689493888989091,
-0.022223979234695435,
0.012364448048174381,
0.01563747227191925,
0.0033747979905456305,
0.028541866689920425,
-0.010413877665996552,
-0.018063807860016823,
-0.007572920992970467,
-0.008370199240744114,
-0.007680058479309082,
-0.0046519017778337,
0.012723353691399097,
0.055497907102108,
0.024124223738908768,
-0.009761345572769642,
-0.04364500194787979,
-0.018347565084695816,
-0.05323829501867294,
0.04624992236495018,
0.004152295645326376,
-0.027790868654847145,
-0.0007871404523029923,
-0.0071549443528056145,
0.03673391789197922,
-0.01608922705054283,
-0.012748700566589832,
-0.004814144689589739,
0.014550616964697838,
0.03269364312291145,
0.021792065352201462,
-0.016399091109633446,
-0.02601706050336361,
0.00665476405993104,
-0.010509015060961246,
-0.03452598303556442,
-0.009844277054071426,
0.035311661660671234,
0.0017983033321797848,
-0.003793605836108327,
0.030330553650856018,
0.026705248281359673,
-0.03615451231598854,
-0.0007983825053088367,
0.0274698156863451,
-0.016024896875023842,
-0.02355545572936535,
0.0017440366791561246,
-0.008782259188592434,
0.011302156373858452,
-0.01340479962527752,
0.021335164085030556,
-0.008038928732275963,
-0.002807456301525235,
0.024005811661481857,
-0.017878662794828415,
-0.028136612847447395,
0.0015258966013789177,
0.03831631690263748,
-0.005778185557574034,
-0.009107504971325397,
-0.04188130795955658,
-0.01437925361096859,
0.013279283419251442,
-0.018947329372167587,
0.0204401183873415,
0.010458525270223618,
-0.032707784324884415,
0.013986428268253803,
0.007924756035208702,
-0.0047689806669950485,
-0.028360629454255104,
-0.02723695896565914,
0.01655597984790802,
-0.01004132442176342,
0.03835725784301758,
0.003662858856841922,
-0.06066364794969559,
0.0674138143658638,
-0.029482465237379074,
-0.06609931588172913,
0.04180734232068062,
0.011035148054361343,
0.02249458059668541,
0.05897414684295654,
-0.028510943055152893,
0.006573128513991833,
0.09666932374238968,
0.0018786456203088164,
0.0013871039263904095,
0.030795950442552567,
-0.009297018870711327,
-0.004905479494482279,
0.04070308059453964,
-0.0011273538693785667,
-0.03397049382328987,
-0.004910624586045742,
0.04413635656237602,
0.00024591581313870847,
-0.014401240274310112,
0.01808273419737816,
-0.010160380974411964,
-0.05198084935545921,
0.038757745176553726,
0.003665470751002431,
0.030811771750450134,
0.032367732375860214,
0.04186840355396271,
-0.019736651331186295,
0.022382501512765884,
0.00734236603602767,
-0.025507867336273193,
-0.08835094422101974,
-0.03264804929494858,
0.00812843069434166,
-0.02090642601251602,
0.003322241362184286,
-0.04119649529457092,
-0.00006175168527988717,
0.023115171119570732,
-0.06970643997192383,
-0.027366982772946358,
0.02924591861665249,
-0.05861537158489227,
-0.051034536212682724,
0.0037041595205664635,
-0.008132229559123516,
-0.007302182726562023,
0.030279984697699547,
0.07321550697088242,
0.0167740099132061,
0.01316837128251791,
-0.03386951610445976,
-0.018546108156442642,
-0.0215290617197752,
0.008770664222538471,
-0.007672681473195553,
0.028118422254920006,
0.06258431822061539,
-0.06113513186573982,
-0.012152701616287231,
0.022478695958852768,
0.002239147201180458,
0.0071322559379041195,
-0.004378566984087229,
0.03553719446063042,
0.03968452289700508,
0.018180958926677704,
0.006075530778616667,
-0.03386733680963516,
-0.017779428511857986,
0.06180238351225853,
0.012976182624697685,
0.00005837259959662333,
-0.042996037751436234,
-0.03164416551589966,
0.017726829275488853,
-0.010927882976830006,
0.030790986493229866,
0.0066037834621965885,
-0.028237786144018173,
-0.03491758927702904,
0.02493966557085514,
0.03951035439968109,
-0.0008053333731368184,
-0.00637016911059618,
-0.018904080614447594,
-0.07416348159313202,
-0.037664830684661865,
0.004394888412207365,
0.01537581067532301,
0.013971266336739063,
0.006782212760299444,
-0.06966834515333176,
-0.010818961076438427,
0.03079257532954216,
-0.0035914890468120575,
-0.036608580499887466,
-0.030018974095582962,
-0.039866141974925995,
0.000297256134217605,
0.01133735105395317,
0.03407316282391548,
0.004671027883887291,
0.00423474470153451,
0.02459264174103737,
-0.005536414682865143,
0.05232661962509155,
0.03207141160964966,
-0.05661888048052788,
-0.03309839963912964,
-0.0324065200984478,
0.03226517140865326,
-0.0011742794886231422,
0.012152012437582016,
-0.03982757031917572,
-0.033969081938266754,
0.008360566571354866,
0.03085201419889927,
0.021709607914090157,
-0.02267441339790821,
-0.019770408049225807,
0.0234612338244915,
-0.018453670665621758,
0.04038041830062866,
-0.044279735535383224,
0.00885695219039917,
0.007667504251003265,
0.027333855628967285,
-0.0008247157093137503,
-0.03789136931300163,
-0.011246240697801113,
0.0008006053976714611,
0.0042700013145804405,
-0.01132885366678238,
0.0034481901675462723,
-0.01469503529369831,
-0.03374633938074112,
0.02528512291610241,
0.033709023147821426,
-0.036356065422296524,
0.04730572924017906,
-0.022334706038236618,
-0.006968561094254255,
-0.01301517989486456,
-0.011377465911209583,
-0.016642114147543907,
0.018046479672193527,
-0.015582233667373657,
0.03392934799194336,
-0.020924106240272522,
-0.0440814346075058,
0.017720133066177368,
-0.03760579228401184,
0.004686843138188124,
-0.02674061991274357,
-0.013044648803770542,
0.009269720874726772,
0.07561956346035004,
0.004077933728694916,
-0.018880506977438927,
-0.016037166118621826,
-0.022350100800395012,
-0.004559593740850687,
0.014043805189430714,
-0.051425445824861526,
0.05656292289495468,
-0.02595163881778717,
0.0029633445665240288,
0.0234740749001503,
0.02257448248565197,
0.002843237714841962,
0.012331266887485981,
0.020863741636276245,
0.010315137915313244,
-0.02074374444782734,
-0.04346642270684242,
-0.00470779137685895,
0.024588029831647873,
0.005212137009948492,
0.010596911422908306,
-0.006045081652700901,
0.07543210685253143,
0.006322134751826525,
-0.006847806740552187,
-0.010557546280324459,
0.02407672628760338,
-0.026075029745697975,
0.021896082907915115,
-0.0012627231189981103,
0.011922548525035381,
-0.03921814262866974,
-0.016633138060569763,
-0.03384796157479286,
-0.014446321874856949,
0.04062265157699585,
-0.043369587510824203,
0.011307117529213428,
-0.01118185929954052,
0.03006592206656933,
0.037871796637773514,
0.02056434564292431,
-0.02145327627658844,
-0.012924041599035263,
0.01553650014102459,
-0.00018535017443355173,
0.010009017772972584,
-0.023146411404013634,
-0.007071313913911581,
-0.0032230743672698736,
0.039292916655540466,
-0.04351743310689926,
-0.012437212280929089,
-0.01373961754143238,
0.018640439957380295,
0.004232481122016907,
0.020088262856006622
] |
<p>As far as I've read online, there isn't a good explanation for the <a href="http://en.wikipedia.org/wiki/Born_rule" rel="nofollow">Born Rule</a>. Is this the case? Why does taking the square of the wave function give you the Probability? Naturally it removes negatives and imaginary numbers, but why is it the square, not the fourth or some higher power?</p> | 23 | [
-0.003099398221820593,
-0.056938536465168,
0.03263892978429794,
-0.05523419752717018,
0.04290304705500603,
0.004051914904266596,
-0.024042291566729546,
-0.009969349019229412,
0.01899684965610504,
-0.03035137429833412,
0.037009261548519135,
0.03738388791680336,
0.055724967271089554,
-0.008138068951666355,
-0.003401370020583272,
0.023416610434651375,
0.003332568099722266,
-0.0034866798669099808,
-0.030641358345746994,
-0.02609609253704548,
0.005842046346515417,
0.04368066415190697,
0.010633008554577827,
0.003889618208631873,
-0.05134093761444092,
0.01747974567115307,
0.011977221816778183,
0.03337043151259422,
0.026607738807797432,
0.09676825255155563,
0.00323000131174922,
0.008105129934847355,
0.014517921023070812,
0.0465974360704422,
0.02923385053873062,
-0.03342244029045105,
0.007696664426475763,
-0.008097866550087929,
-0.013611079193651676,
0.009291944094002247,
-0.009392816573381424,
-0.009228646755218506,
-0.03368252143263817,
0.040379151701927185,
-0.034231092780828476,
0.007401981856673956,
-0.011769399046897888,
-0.027886731550097466,
0.031530413776636124,
-0.06161830574274063,
0.04666243493556976,
-0.005192831624299288,
0.05299505963921547,
0.014078629203140736,
0.014387168921530247,
0.0002621217572595924,
0.07145822048187256,
0.06561606377363205,
-0.02849799394607544,
-0.046383317559957504,
-0.022375566884875298,
-0.029904110357165337,
-0.01583731919527054,
-0.0013152695028111339,
-0.01598411612212658,
0.025996878743171692,
0.01626432128250599,
-0.044894129037857056,
0.021102510392665863,
-0.02573275938630104,
0.02494877763092518,
0.029582755640149117,
0.024103734642267227,
-0.038194481283426285,
0.01561885979026556,
-0.011279327794909477,
0.03639722242951393,
0.001049711718223989,
0.01941107213497162,
-0.006029248703271151,
-0.004701799247413874,
0.03340163826942444,
0.01887582428753376,
-0.000642511120531708,
0.00597153976559639,
-0.0018961034948006272,
0.05777154117822647,
-0.003457097103819251,
0.002760385861620307,
0.013899963349103928,
-0.02095213532447815,
0.006296639796346426,
0.054168395698070526,
-0.024315711110830307,
-0.03593289107084274,
0.0326295867562294,
0.014394012279808521,
0.05155661702156067,
0.025844376534223557,
-0.004351743962615728,
0.007545439526438713,
-0.021474862471222878,
0.04505627974867821,
0.06590664386749268,
-0.042972318828105927,
-0.03854982927441597,
-0.041233304888010025,
0.03733561933040619,
0.01777062378823757,
-0.03276687487959862,
-0.02957773767411709,
0.023419924080371857,
-0.007076623849570751,
0.002741337986662984,
-0.01131393201649189,
-0.0403367355465889,
-0.0020475885830819607,
-0.01608390174806118,
0.04847178980708122,
0.06275100260972977,
0.00928417406976223,
-0.04239291697740555,
0.027165476232767105,
-0.02050103433430195,
-0.015139625407755375,
0.015937969088554382,
0.010861404240131378,
0.003186426591128111,
-0.015238205902278423,
0.03960196301341057,
0.02085035853087902,
-0.01031254418194294,
0.027947895228862762,
0.014185822568833828,
0.03543592244386673,
0.008554831147193909,
-0.1139119490981102,
-0.05848896503448486,
0.029299156740307808,
-0.030910268425941467,
-0.045015815645456314,
-0.07724104821681976,
0.023023422807455063,
0.043974198400974274,
0.1074613556265831,
-0.007810331415385008,
0.02066968008875847,
-0.010561189614236355,
0.02417329140007496,
0.0422024242579937,
-0.012349060736596584,
-0.0021819809917360544,
-0.01728680543601513,
-0.037494443356990814,
0.014212206937372684,
-0.0656188577413559,
0.03698553517460823,
-0.007049368694424629,
-0.024021267890930176,
-0.05780063942074776,
0.04594136029481888,
-0.02514277957379818,
-0.012234565801918507,
-0.0030048792250454426,
-0.008637137711048126,
-0.012791131623089314,
0.11631305515766144,
0.02865927666425705,
-0.028658704832196236,
0.04961322247982025,
-0.0009096937719732523,
0.06634555757045746,
0.0023469196166843176,
0.04940245673060417,
0.006290830206125975,
-0.012413074262440205,
-0.031869616359472275,
-0.053434818983078,
0.05619893968105316,
-0.012788310647010803,
-0.02507704310119152,
0.02070271410048008,
-0.011792276054620743,
0.025676129385828972,
-0.009048286825418472,
0.020337846130132675,
0.0005344456876628101,
-0.009003735147416592,
0.010997303761541843,
-0.04818437248468399,
-0.00949106551706791,
-0.08120416104793549,
0.03145211562514305,
0.019744612276554108,
-0.03946642205119133,
0.012953447178006172,
0.04128730669617653,
0.04478947073221207,
-0.04382794350385666,
-0.020983362570405006,
-0.003331804182380438,
0.04008325934410095,
0.007963866926729679,
-0.02518250048160553,
0.03643777221441269,
0.07217178493738174,
0.02015787921845913,
0.011124088428914547,
0.03333664685487747,
-0.01121511310338974,
-0.021889453753829002,
0.006088606547564268,
-0.030220389366149902,
0.014190101996064186,
-0.005074304062873125,
-0.02730213664472103,
-0.01631340943276882,
0.001269359141588211,
-0.0018570281099528074,
0.04132959246635437,
-0.04215957224369049,
0.05334228277206421,
0.0021697382908314466,
0.0061944629997015,
-0.0072335051372647285,
0.056616563349962234,
0.009016015566885471,
-0.008173923008143902,
0.013190497644245625,
-0.02063829079270363,
-0.03155491128563881,
0.030531125143170357,
0.019313296303153038,
0.014242065139114857,
-0.025581171736121178,
0.005381610710173845,
0.014575610868632793,
0.016237851232290268,
0.022595049813389778,
0.03610669821500778,
-0.029537446796894073,
-0.0390734001994133,
-0.01663355901837349,
0.00490169320255518,
0.0006647653644904494,
0.023013241589069366,
0.017848841845989227,
0.02297068014740944,
0.004984600003808737,
-0.016599638387560844,
-0.06356382369995117,
0.011794626712799072,
-0.060336943715810776,
0.039397209882736206,
-0.00671401247382164,
-0.03929731994867325,
0.00787961483001709,
-0.04257917404174805,
-0.012205356732010841,
0.006638781633228064,
-0.019487956538796425,
-0.01459403708577156,
-0.05390605330467224,
-0.036365944892168045,
0.025032324716448784,
0.010824202559888363,
-0.07974085956811905,
0.018804550170898438,
0.020340071991086006,
-0.03569549694657326,
-0.018586205318570137,
0.012364417314529419,
0.009531776420772076,
-0.009564351290464401,
-0.007777042221277952,
-0.0010092840529978275,
0.01408783346414566,
0.04329119622707367,
-0.014178275130689144,
-0.06756216287612915,
-0.011142082512378693,
-0.04314557462930679,
0.005099896807223558,
0.017142843455076218,
-0.04347217082977295,
-0.00464380718767643,
-0.06480467319488525,
-0.030445650219917297,
0.033581607043743134,
-0.030884889885783195,
0.010653038509190083,
0.0018867608159780502,
0.0038244305178523064,
-0.022922491654753685,
-0.007155787665396929,
-0.03551964461803436,
0.0048286328092217445,
-0.019796881824731827,
-0.0037970722187310457,
0.019453132525086403,
-0.025421645492315292,
-0.0188430305570364,
0.032845523208379745,
-0.031177157536149025,
-0.07443263381719589,
-0.0005665881908498704,
0.014488856308162212,
0.013576204888522625,
-0.045722272247076035,
0.02825433574616909,
0.041333019733428955,
-0.05667795613408089,
0.004977191798388958,
-0.012777998112142086,
-0.0658651813864708,
0.010997972451150417,
0.0029551805928349495,
0.028720753267407417,
-0.004300052300095558,
-0.01679852418601513,
0.08175258338451385,
0.02409631758928299,
-0.021646417677402496,
-0.0031121373176574707,
-0.02231944538652897,
-0.00871834997087717,
-0.020872285589575768,
0.017346464097499847,
0.06521882116794586,
-0.009492160752415657,
0.05689391866326332,
0.012148875743150711,
0.04739748686552048,
0.02318350225687027,
0.006299066822975874,
-0.026317497715353966,
0.012171920388936996,
-0.005097472108900547,
-0.030034227296710014,
0.05113125219941139,
-0.010280461050570011,
-0.019234348088502884,
0.040070466697216034,
-0.0020013710018247366,
0.011052882298827171,
0.0008985911845229566,
-0.01948225125670433,
0.06935225427150726,
0.0020747771486639977,
0.041985347867012024,
-0.03610275313258171,
0.04713902994990349,
-0.022826222702860832,
0.019285131245851517,
0.020861322060227394,
0.003515601856634021,
0.0377141609787941,
-0.024734415113925934,
0.011694162152707577,
0.023548411205410957,
0.008796070702373981,
-0.024933479726314545,
-0.01447963435202837,
-0.021124957129359245,
-0.020389527082443237,
0.0405452623963356,
0.016884591430425644,
-0.029874520376324654,
0.04418650269508362,
0.04759499430656433,
0.012652709148824215,
-0.013231005519628525,
-0.03677832707762718,
-0.016661206260323524,
-0.02522212825715542,
0.004722164943814278,
0.002543551614508033,
0.021182015538215637,
-0.010866166092455387,
0.04896245151758194,
0.019893651828169823,
0.010860010981559753,
0.008917929604649544,
-0.002972113434225321,
-0.07586859166622162,
0.019018299877643585,
-0.03959380462765694,
-0.009651127271354198,
-0.028997618705034256,
-0.016659995540976524,
-0.0001634952932363376,
-0.02065458707511425,
-0.043885208666324615,
-0.031014837324619293,
-0.022533675655722618,
-0.05337320268154144,
0.019863788038492203,
-0.009457862004637718,
-0.008394666947424412,
-0.060552891343832016,
0.01365439873188734,
0.02253103256225586,
-0.010381100699305534,
-0.017841441556811333,
0.036233048886060715,
-0.04261096939444542,
0.03186674416065216,
-0.004383570048958063,
-0.015662183985114098,
0.030537638813257217,
0.008611589670181274,
0.05683375149965286,
0.010763495229184628,
-0.016475051641464233,
-0.011759771965444088,
-0.007214145734906197,
0.06308262795209885,
0.04370450600981712,
-0.026585759595036507,
0.008794736117124557,
-0.028027068823575974,
-0.0023167887702584267,
-0.021198542788624763,
0.006303123198449612,
0.008321982808411121,
0.05077081546187401,
0.03015553578734398,
-0.02257586643099785,
-0.012804384343326092,
-0.014266029000282288,
0.07726301997900009,
0.002092514419928193,
-0.002542495261877775,
-0.042624056339263916,
0.003676666645333171,
-0.02596336044371128,
-0.01804351806640625,
0.008010584861040115,
-0.007872027345001698,
-0.01494249701499939,
-0.007655770052224398,
0.029420696198940277,
0.0024099922738969326,
-0.008293014951050282,
0.000541972927749157,
-0.041180189698934555,
0.02242320030927658,
-0.022086087614297867,
-0.0041837734170258045,
0.019688062369823456,
0.01864713244140148,
0.028881356120109558,
0.04132150858640671,
-0.0184169989079237,
-0.029648277908563614,
-0.006151407025754452,
0.029186714440584183,
0.05964960157871246,
0.004174825735390186,
-0.002202035626396537,
-0.04897814244031906,
-0.06799835711717606,
0.06397853791713715,
-0.014271050691604614,
0.031642504036426544,
-0.025695759803056717,
-0.012249005027115345,
-0.023306356742978096,
-0.02227502129971981,
0.0011191762750968337,
-0.00037126531242392957,
0.006979212164878845,
0.0153134660795331,
-0.013106552883982658,
0.01664567179977894,
-0.02563648298382759,
0.0011118447873741388,
0.008798819966614246,
0.08290316164493561,
-0.0252496600151062,
-0.0010542289819568396,
-0.044595569372177124,
0.04604383558034897,
-0.030437221750617027,
-0.07134781032800674,
-0.010617106221616268,
0.006413710303604603,
-0.0024603179190307856,
0.03689953312277794,
-0.04055871069431305,
-0.06001872569322586,
-0.00010345902410335839,
-0.01913665607571602,
-0.03359197452664375,
0.028729476034641266,
-0.0012411113129928708,
0.02917441725730896,
0.020920101553201675,
-0.021859750151634216,
0.04944697394967079,
0.029823416844010353,
-0.018370861187577248,
-0.01867159642279148,
-0.03029611147940159,
0.04364869371056557,
-0.034747280180454254,
-0.022084122523665428,
-0.049890995025634766,
-0.01633288711309433,
-0.02591998502612114,
0.023852447047829628,
-0.02978874184191227,
0.023242752999067307,
-0.01737792231142521,
-0.019046470522880554,
-0.018767574802041054,
0.01933332346379757,
-0.008117097429931164,
-0.006200812291353941,
-0.02529778704047203,
0.03263118118047714,
0.00691462866961956,
-0.031386032700538635,
0.010911368764936924,
0.01139403972774744,
0.016835326328873634,
0.012741298414766788,
-0.006876256782561541,
0.02367592416703701,
0.002469651633873582,
-0.024615179747343063,
0.028916673734784126,
-0.05005747079849243,
0.0217973031103611,
-0.010879366658627987,
-0.026297714561223984,
-0.00318835093639791,
-0.0692443698644638,
-0.02737838216125965,
-0.008900619111955166,
-0.021168604493141174,
0.04247873276472092,
-0.04658585786819458,
0.033262789249420166,
-0.009894737042486668,
0.015595660544931889,
-0.0856361985206604,
-0.04251337796449661,
-0.016424357891082764,
0.01964731141924858,
-0.029417695477604866,
-0.009946567937731743,
-0.0071764541789889336,
-0.010592004284262657,
-0.019518977031111717,
-0.016924282535910606,
0.04186772555112839,
-0.007069835439324379,
-0.008070487529039383,
0.039358630776405334,
-0.010341965593397617,
0.05502881482243538,
-0.021611155942082405,
-0.049551088362932205,
0.034502509981393814,
-0.025615351274609566,
0.0016295177629217505,
0.026499655097723007,
0.04545846953988075,
-0.036309078335762024,
-0.02729218266904354,
0.013160929083824158,
0.012601329013705254,
0.020283706486225128,
-0.022550545632839203,
-0.04367000609636307,
-0.004475099965929985,
0.042361773550510406,
-0.0029215447138994932,
-0.043623678386211395,
0.004746297374367714,
-0.005050248466432095,
0.014687541872262955,
0.03986740484833717,
-0.005673903040587902,
-0.034601785242557526,
-0.03182540088891983,
-0.005032059736549854,
-0.004897965118288994,
0.03628147393465042,
0.0034781619906425476,
0.027652790769934654,
0.02855490706861019,
-0.025969045236706734,
0.003168592695146799,
-0.027680175378918648,
-0.0024974681437015533,
-0.004219386260956526,
0.018042581155896187,
0.011510924436151981,
0.04343733936548233,
-0.030758993700146675,
-0.01272901613265276,
-0.04600273072719574,
0.0238997433334589,
0.06905762851238251,
-0.026956595480442047,
0.062058597803115845,
0.013269742019474506,
-0.00450493348762393,
-0.011831558309495449,
-0.005309026222676039,
-0.003565027844160795,
-0.00824395939707756,
0.002838582033291459,
0.01830926537513733,
-0.021251579746603966,
0.037606533616781235,
0.039786215871572495,
0.026866627857089043,
-0.018314260989427567,
0.03361762687563896,
0.04253215342760086,
0.02903192862868309,
0.039320677518844604,
0.0230785571038723,
-0.02579861506819725,
0.021433483809232712,
-0.030535152181982994,
0.03567110002040863,
0.005920432507991791,
-0.020652398467063904,
0.05135618522763252,
-0.02782135270535946,
-0.005256312899291515,
-0.03449006751179695,
-0.02816743403673172,
-0.012561253271996975,
-0.011418224312365055,
0.02684582769870758,
0.0034985847305506468,
0.021545693278312683,
0.00025217325310222805,
-0.006033916492015123,
0.04231170192360878,
0.014233974739909172,
-0.00007294947135960683,
-0.07747255265712738,
-0.026859017089009285,
-0.03949941694736481,
-0.06776141375303268,
0.033328209072351456,
-0.008690930902957916,
-0.04146851971745491,
0.009675064124166965,
-0.03316418081521988,
0.014473727904260159,
-0.004681519698351622,
0.036848586052656174,
-0.012207219377160072,
0.07453978061676025,
0.0276858601719141,
0.009724073112010956,
0.001663366099819541,
0.027786100283265114,
0.09058193862438202,
0.07030919194221497,
0.010121576488018036,
-0.0836992934346199,
0.024900522083044052,
-0.03412935137748718,
0.017621831968426704,
-0.0051149167120456696,
0.021426772698760033,
-0.007171192672103643,
0.026768838986754417,
0.017758656293153763,
0.05675335228443146,
0.03632264956831932,
0.0024741904344409704,
0.0321788489818573,
-0.03277239948511124,
-0.06848879158496857,
0.009878079406917095,
0.0355694442987442,
-0.000535879866220057,
0.016614196822047234,
-0.032631270587444305,
-0.02376902662217617,
-0.01734529621899128,
-0.012495760805904865,
-0.008560607209801674,
-0.009798402898013592,
0.015157375484704971,
-0.013195141218602657,
-0.027347896248102188,
-0.012868611142039299,
0.039316993206739426,
-0.00505165196955204,
-0.04147517308592796,
0.027598906308412552,
0.012468982487916946,
-0.02960433065891266,
0.010015713050961494,
0.014206025749444962,
0.023130014538764954,
-0.01891571842133999,
0.013186480849981308,
0.00794252660125494,
-0.04031560197472572,
0.007680495735257864,
-0.013650062493979931,
0.027692219242453575,
-0.016155272722244263,
0.002763341646641493,
0.003802207065746188,
-0.020875994116067886,
0.040541160851716995,
-0.0735408216714859,
-0.003873443230986595,
0.007759750820696354,
0.056188542395830154,
-0.013381506316363811,
-0.04661973565816879,
0.01565387286245823,
0.01140165887773037,
-0.009925837628543377,
0.012111734598875046,
-0.0038237583357840776,
-0.019700434058904648,
-0.013094636611640453,
-0.008553888648748398,
-0.02406284399330616,
-0.021725300699472427,
-0.014001820236444473,
-0.027931801974773407,
-0.0034949863329529762,
-0.08020845055580139,
-0.03427664563059807,
0.04395381361246109,
0.019492117688059807,
0.06583271920681,
-0.014083532616496086,
-0.0020619272254407406,
0.008616185747087002,
-0.06523321568965912,
0.0050916774198412895,
-0.053845372051000595,
0.0016723908483982086,
-0.00009139198664342985,
0.04812542721629143,
0.026968546211719513,
0.05650646984577179,
-0.017936021089553833,
0.024367282167077065,
0.008047325536608696,
-0.01208806224167347,
0.008684784173965454,
-0.05950559675693512,
0.014314363710582256,
0.06091226264834404,
-0.01363519299775362,
-0.0034313455689698458,
-0.007213965058326721,
0.0073478491976857185,
0.011227588169276714,
0.02905970811843872,
-0.010778089985251427,
0.035163115710020065,
-0.025192204862833023,
0.009300537407398224,
-0.019227653741836548,
-0.043418921530246735,
-0.019088780507445335,
0.013001893647015095,
0.008445894345641136,
-0.043493352830410004,
-0.056994665414094925,
-0.02673070691525936,
-0.009965385310351849,
0.014278782531619072,
0.04330228269100189,
-0.0381702221930027,
-0.009573616087436676,
0.002242686925455928,
0.022074081003665924,
0.011410664767026901,
-0.020069308578968048,
-0.03673684224486351,
0.03150113299489021,
-0.0029314979910850525,
-0.009743417613208294,
-0.014717547222971916,
0.01992875710129738,
0.046048033982515335,
-0.022455845028162003,
0.020671067759394646,
0.03876104578375816,
-0.0007399129681289196,
0.0014912736369296908,
0.01206132397055626,
-0.029894359409809113,
0.02628360502421856,
-0.009902548044919968,
0.013292764313519001,
0.025728728622198105,
-0.06590569019317627,
-0.049859486520290375,
0.04559164494276047,
-0.0006128287641331553,
0.012649266049265862,
0.02518804930150509,
0.005640705116093159,
0.007239467930048704,
0.041302312165498734,
-0.033819589763879776,
0.011353525333106518,
-0.018231142312288284,
0.00037246235297061503,
0.005682034883648157,
0.0014683217741549015,
-0.0005274936556816101,
0.008975598961114883,
0.007111630868166685,
0.04100862517952919,
0.013105775229632854,
-0.019942494109272957,
0.007621739059686661,
0.008874707855284214,
-0.012356799095869064,
0.042577046900987625,
0.03421960771083832,
0.006409205961972475,
0.034811750054359436,
0.03548164665699005,
-0.0003781821287702769,
0.08697845041751862,
0.0025244764983654022,
0.013748480007052422,
-0.0885235145688057,
-0.021679701283574104,
0.015008593909442425,
-0.0007835060823708773,
0.058198582381010056,
-0.036464277654886246,
0.02701651304960251,
0.020169606432318687,
-0.06828746944665909,
-0.0028119811322540045,
-0.02377566695213318,
-0.004141755402088165,
-0.011192195117473602,
0.0016946860123425722,
-0.02544955536723137,
0.05558489263057709,
0.01671418361365795,
0.021097028627991676,
0.037901174277067184,
-0.009147503413259983,
-0.011371773667633533,
-0.020640714094042778,
-0.011682886630296707,
0.045198339968919754,
-0.021728554740548134,
-0.030316874384880066,
0.03514686971902847,
-0.034455377608537674,
-0.02546645700931549,
0.0559452548623085,
-0.03220148757100105,
0.01321117952466011,
0.009666255675256252,
0.027013419196009636,
0.016817059367895126,
0.0008966771420091391,
0.013294199481606483,
-0.026615843176841736,
-0.0007247336325235665,
0.004763307981193066,
0.04790196940302849,
0.032098330557346344,
0.008522703312337399,
-0.016633393242955208,
0.007471887394785881,
-0.029597416520118713,
-0.04356682300567627,
0.03278722986578941,
0.02288614958524704,
0.01871410571038723,
-0.011713300831615925,
0.008313016965985298,
0.02404475025832653,
-0.03632393479347229,
0.05425673723220825,
-0.0432664155960083,
0.0018274768954142928,
0.017179209738969803,
0.009223653934895992,
0.0003405824245419353,
-0.01703774556517601,
-0.019131910055875778,
-0.05109812691807747,
0.01861686259508133,
0.016178961843252182,
-0.019915593788027763,
-0.05337705835700035,
0.0041506970301270485,
0.0018732617609202862,
0.009544724598526955,
0.04190966859459877,
-0.06232846528291702,
-0.04237814620137215,
0.006555064115673304,
0.017384815961122513,
0.012390202842652798,
-0.03136341646313667,
-0.04383121058344841,
-0.021891774609684944,
-0.0968635305762291,
0.07230811566114426,
-0.011581999249756336,
0.006215277593582869,
-0.04806309565901756,
0.0037595247849822044,
0.014505579136312008,
-0.004146485589444637,
0.03677445650100708,
-0.006575515028089285,
-0.005234534852206707,
-0.014539950527250767,
0.024020230397582054,
0.004135174676775932,
-0.02623370848596096,
-0.0050752898678183556,
-0.020403379574418068,
-0.003077765693888068,
-0.047204114496707916,
-0.00774815957993269,
0.0035534135531634092,
0.0276471097022295,
-0.003738390514627099,
-0.026840558275580406,
0.02307792380452156,
-0.008967546746134758,
-0.0019525891402736306,
0.08033294975757599,
0.0278624314814806,
-0.017007233574986458,
0.05518646910786629,
-0.027900729328393936,
0.011375866830348969,
0.04159851744771004,
-0.030132915824651718,
-0.03181726485490799,
0.03754417970776558,
-0.012081646360456944,
-0.0257862601429224,
-0.006759714800864458,
0.015552563592791557,
0.03567857667803764,
-0.026791442185640335,
-0.012797903269529343,
0.03683042153716087,
-0.05560590326786041,
0.0009071335662156343,
0.04503666236996651,
0.02760804072022438,
0.05252866819500923,
0.020332539454102516,
-0.019001759588718414,
-0.03265776485204697,
0.006801894400268793,
-0.00006028196003171615,
0.032697927206754684,
0.03992997854948044,
-0.01246798224747181,
0.04133045673370361,
0.056878462433815,
-0.005550502799451351,
0.020757192745804787,
0.025978872552514076,
0.06475183367729187,
-0.04526614397764206,
0.005026726517826319,
-0.0008484118152409792,
-0.01798188127577305,
0.04651011526584625,
0.002380620688199997,
-0.03448556363582611,
0.09927806258201599,
-0.004634013865143061,
0.023988209664821625,
-0.007239864207804203,
0.003988876007497311,
-0.013111458159983158,
-0.02608015388250351,
0.054192520678043365,
0.05455877631902695,
-0.01878662034869194,
-0.027129366993904114,
-0.033267851918935776,
-0.0079336604103446,
0.049870289862155914,
-0.047505684196949005,
0.03858938813209534,
-0.0036938220728188753,
-0.008853502571582794,
-0.02230406366288662,
-0.006600924301892519,
-0.014694605022668839,
-0.014565915800631046,
-0.0020856079645454884,
0.04542280361056328,
0.04484277591109276,
0.022874845191836357,
-0.010714602656662464,
-0.004090331960469484,
0.03723069280385971,
-0.04443416744470596,
0.0015508949290961027,
-0.038735829293727875,
0.05548275634646416,
-0.011060940101742744,
-0.007444826420396566
] |
<p>While reading a paper I ran into this particular way of writing a $\cal{N}=3$ fields (in a theory with $N_f$ hypermultiplets) that I couldn't relate to anything I had seen before in the text-books (typically Weinberg's) The claim is that $q^{Aa}$ and $\psi_{\alpha}^{Aa}$ are scalar and fermions such that $a,b$ are $SU(R)_R$ indices, $A,B$ are denoting them to transform in the fundamental representation of $USp(2N_f)$ (why?) and $\alpha, \beta$ are $SO(2,1)$ spinor indices (theory is in $2+1$) </p>
<p>Apparently these fields satisfy some reality conditions given by, the following equations,</p>
<p>$(q^\dagger)_{Aa} = \omega_{AB}\epsilon_{ab}q^{Bb}$</p>
<p>and</p>
<p>$\bar{\psi} ^\alpha _{Aa} = \omega_{AB} \epsilon_{ab} \epsilon ^{\alpha \beta} \psi _{\beta} ^{Bb}$</p>
<p>(where $\omega$ is some symplectic form, which I have no clue about) </p>
<p>I find the above equations very unfamiliar. For one thing why do the scalar and the fermion have $R$ charge indices? (I am only familiar with the supercharges having a R-symmetry when the central charges are absent) Also I don't understand the $USp(2N_f)$ index. </p>
<p>Apparently this can be related to usual $\cal{N}=2$ fields $(Q,\tilde{Q})$ as,</p>
<p>$q^{A1} = (Q,\tilde{Q})$</p>
<p>and</p>
<p>$q^{A2} = (-\bar{\tilde{Q}}, \bar{Q})$</p>
<p>I am completely unfamiliar with such a relationship or this thinking of $\cal{N}=2$ fields as being thought of as a pair of $Qs$. </p>
<p>Once I understand the meaning of the above I will post another about its curious way of writing the supersymmetry transformation and the lagrangian with this field content. </p> | 1,521 | [
0.015343251638114452,
0.0035308224614709616,
0.025846397504210472,
-0.015601230785250664,
0.035518255084753036,
-0.004911303054541349,
-0.045255400240421295,
-0.042779047042131424,
0.006585285533219576,
-0.05522320792078972,
0.013805518858134747,
-0.023469315841794014,
0.03623908758163452,
-0.020692678168416023,
0.0010980528313666582,
0.0012279972434043884,
-0.011743898503482342,
0.00045782217057421803,
-0.026064211502671242,
-0.03349517658352852,
0.04390190541744232,
0.0506802499294281,
-0.025262203067541122,
-0.0071054426953196526,
-0.008674963377416134,
0.021558642387390137,
0.01262618787586689,
0.001683772075921297,
0.005623857025057077,
0.009394668973982334,
0.0317487008869648,
-0.025886835530400276,
0.030862510204315186,
-0.042403388768434525,
-0.010228817351162434,
-0.002384533639997244,
-0.02105080708861351,
-0.037817008793354034,
-0.01922719180583954,
0.017550436779856682,
-0.02715826965868473,
-0.022904768586158752,
-0.04254508763551712,
-0.0051276967860758305,
-0.009840071201324463,
0.020379582419991493,
-0.02061307616531849,
0.0018072067759931087,
0.05099736899137497,
-0.06945820897817612,
0.05420496687293053,
0.054815344512462616,
0.014825821854174137,
-0.0004070688155479729,
-0.0041665141470730305,
-0.013269004411995411,
0.05806659907102585,
0.05312204360961914,
0.0037299678660929203,
-0.0626080185174942,
-0.04217900335788727,
-0.02563086524605751,
-0.0008351648575626314,
-0.018187114968895912,
-0.03756915032863617,
0.0064488910138607025,
0.03295515477657318,
0.004379751160740852,
0.007510341703891754,
-0.0121593177318573,
0.036868929862976074,
-0.03602012246847153,
0.011924223974347115,
-0.03731858357787132,
0.007265926338732243,
-0.002699356060475111,
-0.007088859099894762,
-0.018597083166241646,
0.029341205954551697,
0.010565625503659248,
-0.010679547674953938,
0.023731132969260216,
-0.022092638537287712,
-0.038050636649131775,
-0.0021016928367316723,
0.016004865989089012,
0.030149172991514206,
0.0016267208848148584,
0.0006074546836316586,
0.006780798081308603,
-0.06005658954381943,
-0.00005439211963675916,
0.04204007610678673,
-0.04805900529026985,
-0.01807945966720581,
0.020627671852707863,
0.04437769576907158,
0.04787818714976311,
-0.005236229859292507,
0.003663902170956135,
-0.04630744084715843,
-0.054031241685152054,
-0.02521786279976368,
0.09657265990972519,
0.0012710250448435545,
-0.016612473875284195,
-0.02983407862484455,
0.005875374656170607,
-0.04127666726708412,
0.004358980804681778,
-0.04367475211620331,
0.0034699025563895702,
-0.036949411034584045,
-0.02539554238319397,
0.020481359213590622,
-0.008332698605954647,
0.011543984524905682,
0.017916478216648102,
0.04172086343169212,
0.07520340383052826,
0.02270657755434513,
0.0109732486307621,
-0.015249930322170258,
0.00022595422342419624,
-0.0619635283946991,
0.006517608650028706,
0.02625625766813755,
0.016086725518107414,
-0.037852607667446136,
-0.025824010372161865,
0.01731698401272297,
-0.027026362717151642,
0.01563517190515995,
0.02801566570997238,
0.00426596961915493,
0.004754676949232817,
-0.1141706258058548,
-0.03701184689998627,
0.004457856062799692,
-0.0077850595116615295,
-0.01933034136891365,
-0.07439836114645004,
0.006014205515384674,
0.02799323759973049,
0.1099073514342308,
-0.013786316849291325,
-0.0014782377984374762,
0.036859072744846344,
0.020512137562036514,
0.05663013458251953,
0.020316103473305702,
-0.019840659573674202,
-0.020987357944250107,
-0.02606177143752575,
-0.043311383575201035,
-0.042635831981897354,
0.04034966230392456,
0.0038701719604432583,
-0.011437424458563328,
-0.0025071098934859037,
0.08339065313339233,
-0.003418730106204748,
0.025549927726387978,
0.03608743101358414,
-0.02330959215760231,
-0.015484376810491085,
0.07677645981311798,
-0.030810296535491943,
0.0037267145235091448,
0.060176413506269455,
-0.028348570689558983,
0.025194980204105377,
0.0031093950383365154,
0.0727202519774437,
0.030774705111980438,
-0.03459016978740692,
-0.047630418092012405,
-0.0497593954205513,
0.010412038303911686,
-0.010623998008668423,
-0.03413712605834007,
-0.04271715506911278,
-0.009402765892446041,
0.016713108867406845,
-0.002953421324491501,
0.03052874654531479,
-0.00484821991994977,
-0.019224686548113823,
0.011935138143599033,
-0.04792910814285278,
-0.0018005056772381067,
-0.01965653896331787,
-0.032488688826560974,
-0.013293304480612278,
-0.021045630797743797,
0.05857747420668602,
0.015701625496149063,
-0.037887997925281525,
0.016263635829091072,
-0.04485303908586502,
0.005424888338893652,
0.06383673846721649,
0.01419172715395689,
-0.015748359262943268,
0.06779312342405319,
0.016592031344771385,
0.005687506403774023,
0.005734562873840332,
0.05100755766034126,
-0.03648289665579796,
-0.020018331706523895,
0.025111455470323563,
-0.003776807803660631,
0.05069243535399437,
0.0118629802018404,
0.0035444723907858133,
0.02257702872157097,
0.01360404398292303,
-0.030417272821068764,
0.011345356702804565,
-0.03818802908062935,
0.07907110452651978,
0.03692762926220894,
-0.004592897370457649,
-0.004779791459441185,
0.04649757966399193,
-0.006724132690578699,
0.057996246963739395,
-0.026968423277139664,
-0.0184854157269001,
-0.03559068217873573,
-0.04540538042783737,
0.023773174732923508,
0.020675353705883026,
-0.025663573294878006,
0.023676574230194092,
0.032077569514513016,
0.03994788974523544,
0.03058893233537674,
0.0168857891112566,
0.022512132301926613,
-0.04852474480867386,
0.014560102485120296,
-0.02435680851340294,
-0.011953303590416908,
-0.005292525049299002,
0.017169300466775894,
-0.007267128676176071,
0.03161366656422615,
-0.03065635822713375,
-0.06221983581781387,
0.05022842437028885,
0.0036398153752088547,
-0.035629402846097946,
0.013498171232640743,
-0.034456200897693634,
0.042072784155607224,
-0.02097131498157978,
0.09250293672084808,
0.06680578738451004,
-0.008892255835235119,
0.02609005570411682,
0.00942836981266737,
0.006983541417866945,
0.04124700650572777,
0.031455859541893005,
-0.028564564883708954,
-0.034645479172468185,
0.007591182366013527,
-0.05027864873409271,
0.00029898821958340704,
-0.015454864129424095,
-0.02423281967639923,
-0.0001667895121499896,
-0.03948225826025009,
0.011737867258489132,
0.008116966113448143,
0.03709796443581581,
-0.04205785691738129,
0.019858697429299355,
0.0662928894162178,
0.022158529609441757,
0.038550082594156265,
0.027527594938874245,
-0.04856378212571144,
0.025514710694551468,
-0.08190196752548218,
-0.008504742756485939,
0.03429344296455383,
0.008283422328531742,
-0.011835196055471897,
-0.0033615673892199993,
-0.040793199092149734,
-0.021695710718631744,
-0.05983555689454079,
-0.016665654256939888,
0.02259591408073902,
-0.06224604323506355,
-0.001698764506727457,
0.0799655169248581,
0.0008468391606584191,
-0.011122740805149078,
-0.03442944958806038,
-0.005083948373794556,
-0.029350511729717255,
0.003908205311745405,
0.00027983979089185596,
-0.017355481162667274,
-0.01503262110054493,
0.0304940827190876,
-0.004458581563085318,
-0.025505665689706802,
-0.020055655390024185,
-0.04806635528802872,
-0.04883753880858421,
0.0020946816075593233,
0.00820145197212696,
0.007625546772032976,
0.014029194600880146,
-0.07961131632328033,
0.08614929020404816,
0.027470700442790985,
-0.030713645741343498,
-0.006856896914541721,
0.02925853058695793,
-0.014249072410166264,
-0.03483743220567703,
0.01871425472199917,
0.03621433302760124,
0.014284996315836906,
0.05288679897785187,
-0.020453594624996185,
0.06563812494277954,
0.01726028509438038,
-0.0038817604072391987,
-0.06742382049560547,
0.036330025643110275,
-0.0008716403390280902,
0.005504433996975422,
0.048308052122592926,
-0.03156347572803497,
0.010282052680850029,
0.0040337033569812775,
0.013241525739431381,
0.005095282103866339,
0.0197893213480711,
-0.04944475367665291,
0.056018371134996414,
0.035611819475889206,
0.011675948277115822,
0.017829135060310364,
0.026019679382443428,
-0.030550699681043625,
-0.03328341245651245,
-0.009414026513695717,
0.05178450793027878,
0.05250029265880585,
-0.04505671188235283,
0.02013695053756237,
0.021692246198654175,
0.04768810421228409,
-0.054292064160108566,
-0.0036965336184948683,
0.007769098039716482,
-0.029879631474614143,
0.019235650077462196,
-0.014996484853327274,
-0.012556095607578754,
0.0094231516122818,
0.04348296299576759,
0.01596689224243164,
0.02359863370656967,
-0.024695366621017456,
-0.008846045471727848,
-0.036804381757974625,
0.007394773419946432,
-0.0163781326264143,
0.038219522684812546,
0.018425995483994484,
0.07001751661300659,
0.014243743382394314,
0.01743089035153389,
-0.02630113810300827,
0.009583095088601112,
-0.06622439622879028,
-0.005784515291452408,
-0.005433053243905306,
0.016722634434700012,
-0.03335149213671684,
-0.028817474842071533,
0.02536688558757305,
0.03882570192217827,
-0.057588037103414536,
-0.03458544611930847,
-0.02833211049437523,
-0.04318275302648544,
0.031942009925842285,
-0.035627059638500214,
-0.028821907937526703,
-0.013246763497591019,
0.055227141827344894,
0.03702359274029732,
-0.06555391103029251,
-0.03420460969209671,
0.03191852197051048,
-0.035586822777986526,
-0.009958296082913876,
-0.01187411043792963,
0.01947992853820324,
0.018832730129361153,
0.030423736199736595,
0.006815019994974136,
-0.013299466110765934,
-0.0230159442871809,
0.00026092995540238917,
0.0335652194917202,
0.05475487932562828,
-0.007721249014139175,
-0.019925348460674286,
0.017028342932462692,
-0.03359821438789368,
0.00551075441762805,
0.0034667067229747772,
0.0654059499502182,
0.009007296524941921,
0.009197523817420006,
0.04321881756186485,
-0.005246455781161785,
-0.030141739174723625,
0.011696901172399521,
0.04962646961212158,
0.007492133881896734,
-0.00931498222053051,
-0.06529704481363297,
0.01045082788914442,
0.005107801873236895,
-0.008816749788820744,
-0.022566920146346092,
0.012803983874619007,
-0.02582406997680664,
-0.001641762093640864,
0.033621203154325485,
-0.027921073138713837,
-0.03347960487008095,
-0.006631231866776943,
-0.003715025493875146,
-0.029721155762672424,
0.002453082473948598,
-0.03380290046334267,
0.007332539185881615,
0.031885478645563126,
0.04501859471201897,
0.018320877104997635,
0.0132970679551363,
-0.024936003610491753,
0.009962332434952259,
0.022178877145051956,
-0.00019671162590384483,
0.025880401954054832,
-0.00972979050129652,
-0.07093565911054611,
-0.013806289993226528,
0.01611504890024662,
-0.021409524604678154,
0.051812998950481415,
0.025003379210829735,
-0.00803015660494566,
-0.0018953351536765695,
-0.04818512871861458,
-0.008294628001749516,
0.048273228108882904,
0.00003413932063267566,
0.002599417231976986,
-0.01828770898282528,
-0.007058693096041679,
0.03135528042912483,
-0.0020090288016945124,
-0.003351645777001977,
0.03611067682504654,
0.023259593173861504,
-0.001872614724561572,
0.014647835865616798,
0.00854974053800106,
-0.02104353718459606,
-0.0653318539261818,
-0.017200743779540062,
0.015162596479058266,
0.03253377228975296,
0.03859167546033859,
-0.053704939782619476,
-0.05569009855389595,
-0.004495764616876841,
-0.009251154959201813,
0.02513229474425316,
0.02335112728178501,
-0.04215623810887337,
0.04800654575228691,
0.04620771482586861,
-0.028858158737421036,
0.03165016695857048,
0.03060881793498993,
-0.022056499496102333,
-0.016775622963905334,
-0.034200381487607956,
-0.023998335003852844,
0.005757608450949192,
0.009698601439595222,
-0.029970452189445496,
0.0341988168656826,
-0.03281892091035843,
0.07011650502681732,
-0.04382660612463951,
-0.002810499630868435,
0.005255842115730047,
-0.03570869565010071,
-0.022733015939593315,
0.009545891545712948,
0.025392567738890648,
0.001871368265710771,
-0.017550582066178322,
-0.015395620837807655,
0.05491628497838974,
-0.014251804910600185,
0.048789169639348984,
-0.017768925055861473,
-0.00378257199190557,
0.03999634087085724,
0.004134306684136391,
0.008086546324193478,
0.0071373796090483665,
-0.010034257546067238,
0.010457072407007217,
-0.07913472503423691,
0.04197518527507782,
-0.003360417205840349,
-0.03006790019571781,
0.006499726325273514,
-0.011296197772026062,
-0.02567365951836109,
0.01596679538488388,
-0.03772406652569771,
-0.005951880943030119,
-0.011255016550421715,
-0.026548784226179123,
0.04465533792972565,
0.0040338546968996525,
-0.04120505228638649,
-0.040766190737485886,
0.018954871222376823,
-0.018902620300650597,
-0.03871070593595505,
-0.008858832530677319,
0.0008621500455774367,
0.015277447178959846,
-0.04648229852318764,
0.051032889634370804,
0.05927480384707451,
-0.07591849565505981,
-0.02795226313173771,
0.020437270402908325,
0.08582378178834915,
0.02575286105275154,
-0.00568310497328639,
-0.0006707365391775966,
0.029264608398079872,
0.0030252879951149225,
0.03953409567475319,
0.02070961520075798,
0.009498859755694866,
-0.018181078135967255,
0.004778479691594839,
-0.04292285069823265,
-0.04759238287806511,
0.03978179395198822,
-0.0008831878658384085,
-0.01206986140459776,
0.024509765207767487,
0.027838382869958878,
-0.0007323048776015639,
-0.012406262569129467,
-0.005676572676748037,
0.0038066026754677296,
-0.00436134310439229,
-0.03458195552229881,
-0.008470562286674976,
-0.02920105867087841,
-0.017047565430402756,
0.04405948519706726,
-0.041035670787096024,
-0.004010232165455818,
0.0018813610076904297,
0.04869120568037033,
-0.029784686863422394,
0.0036053797230124474,
0.004787012003362179,
-0.032157186418771744,
0.0028519402258098125,
0.00822441466152668,
0.014243090525269508,
0.008363223634660244,
0.006764042191207409,
0.041624750941991806,
-0.027431970462203026,
-0.03977546840906143,
0.032526738941669464,
0.04350974038243294,
0.02133667655289173,
0.005283343140035868,
0.03905463591217995,
-0.033009305596351624,
-0.012055185623466969,
-0.020090429112315178,
-0.0102467592805624,
0.020029574632644653,
-0.014630760066211224,
0.019200779497623444,
-0.07724276930093765,
-0.005134168080985546,
0.014045060612261295,
0.05619580298662186,
-0.046141330152750015,
0.0356995165348053,
0.007118247915059328,
0.027556875720620155,
0.007409999612718821,
-0.021625183522701263,
-0.058036863803863525,
0.0867052674293518,
-0.041407693177461624,
0.04140585660934448,
0.03650753200054169,
-0.025237372145056725,
0.007330409251153469,
0.06486749649047852,
-0.00022428081138059497,
-0.009350615553557873,
-0.019022632390260696,
-0.025236506015062332,
0.026853419840335846,
0.031166821718215942,
-0.01864798553287983,
-0.006369143258780241,
-0.00795022863894701,
0.08374807238578796,
-0.012953406199812889,
0.011765602976083755,
0.010540053248405457,
-0.02241654135286808,
-0.01995755173265934,
-0.036882638931274414,
-0.029865840449929237,
0.020287983119487762,
-0.03616559877991676,
0.010138403624296188,
-0.01210071425884962,
-0.016176626086235046,
0.026489553973078728,
0.016044164076447487,
0.04739847034215927,
-0.02389136143028736,
0.046263232827186584,
-0.0055729979649186134,
0.00411536218598485,
0.0027627660892903805,
-0.017286166548728943,
0.13312168419361115,
0.0733853280544281,
0.005027866456657648,
-0.07439465075731277,
0.019021302461624146,
0.005563388112932444,
0.0219411663711071,
0.011612611822783947,
0.001486469293013215,
-0.029257407411932945,
-0.007012579124420881,
-0.00016053470608312637,
0.06948524713516235,
-0.025633348152041435,
-0.005708047188818455,
0.013495259918272495,
-0.012970560230314732,
-0.021154632791876793,
-0.020442748442292213,
0.03214039281010628,
-0.023582113906741142,
0.004994472488760948,
-0.0610952153801918,
-0.012717355042696,
0.003332500346004963,
0.016575371846556664,
-0.030660483986139297,
-0.006221211049705744,
0.03437389060854912,
0.01151201967149973,
-0.036054305732250214,
-0.02445848658680916,
0.012898045592010021,
0.012623573653399944,
0.00872829370200634,
0.023974725976586342,
0.029984531924128532,
-0.031526029109954834,
0.026675431057810783,
0.043992698192596436,
0.00954010896384716,
-0.009268813766539097,
0.028678085654973984,
0.035162508487701416,
-0.03559943288564682,
-0.036554500460624695,
-0.015823248773813248,
0.009300059638917446,
-0.038845308125019073,
-0.024351907894015312,
-0.01286591961979866,
0.003916725981980562,
0.027610741555690765,
-0.010455267503857613,
0.022441141307353973,
-0.0171868484467268,
-0.01870117150247097,
-0.03966289758682251,
0.022380255162715912,
-0.0001424619258614257,
0.02878454141318798,
0.01683652587234974,
-0.0007820178871043026,
-0.022643398493528366,
-0.007964596152305603,
0.0292960237711668,
-0.006077037658542395,
0.01588001847267151,
0.03911151736974716,
-0.012112521566450596,
-0.00830709096044302,
-0.008347880095243454,
-0.04719505459070206,
-0.005994970910251141,
-0.010866410098969936,
0.05142759531736374,
0.039095163345336914,
0.04618288576602936,
-0.009862362407147884,
-0.026009662076830864,
-0.032000549137592316,
0.023351678624749184,
-0.030778730288147926,
-0.036172978579998016,
-0.005366883706301451,
-0.031097518280148506,
0.005680867470800877,
0.05249914899468422,
-0.04068893939256668,
0.016066616401076317,
0.011343357153236866,
0.010497534647583961,
0.039015837013721466,
-0.02496177703142166,
-0.03267199173569679,
-0.0014543983852490783,
-0.053299903869628906,
0.016890913248062134,
-0.012960430234670639,
-0.026025142520666122,
0.03008761815726757,
-0.03674239292740822,
0.013207963667809963,
0.05245320498943329,
-0.0021520256996154785,
-0.0315471775829792,
0.034509625285863876,
-0.010732781141996384,
0.03338634595274925,
0.023015394806861877,
0.042632944881916046,
-0.03236620873212814,
-0.012047996744513512,
0.03044353798031807,
0.009951216168701649,
-0.011402418836951256,
0.032947342842817307,
-0.04669409617781639,
-0.0472724474966526,
-0.008489346131682396,
0.00343596120364964,
-0.06739203631877899,
0.015355268493294716,
-0.0093222726136446,
0.08093734830617905,
-0.029054513201117516,
0.03595888987183571,
-0.053381673991680145,
0.04776919633150101,
-0.011536527425050735,
-0.004490147810429335,
0.007748675066977739,
0.012468122877180576,
-0.05131782591342926,
-0.0015323845436796546,
0.013758455403149128,
0.03031197562813759,
-0.001950370380654931,
0.023676590994000435,
-0.037209402769804,
0.002152452478185296,
-0.01745523326098919,
-0.04444978013634682,
0.0327802374958992,
0.009802893735468388,
-0.004142113961279392,
0.040998559445142746,
0.020742889493703842,
-0.016061751171946526,
0.034399811178445816,
-0.02669900842010975,
-0.02701772190630436,
-0.008641396649181843,
-0.0558660589158535,
-0.017519643530249596,
-0.05975077673792839,
-0.011147995479404926,
0.015204060822725296,
-0.0006308577721938491,
0.008220706135034561,
0.012567426078021526,
-0.059180792421102524,
0.011414519511163235,
-0.0023777128662914038,
0.002338400576263666,
0.00398616585880518,
0.009481942281126976,
0.01702972687780857,
-0.011053416877985,
-0.0036908197216689587,
-0.025435440242290497,
0.031326405704021454,
0.002631274051964283,
0.0056009190157055855,
-0.05140283703804016,
-0.03212586045265198,
0.02316352166235447,
0.022818634286522865,
0.038403384387493134,
-0.02730666659772396,
0.009342951700091362,
0.019945675507187843,
-0.04329508915543556,
0.04446810856461525,
-0.017296157777309418,
-0.01514922920614481,
0.0011540123960003257,
0.027892328798770905,
-0.027530372142791748,
0.04292542487382889,
0.0024232189171016216,
0.004695013631135225,
-0.003340942319482565,
-0.033932000398635864,
-0.017766445875167847,
-0.005687806289643049,
-0.03582612797617912,
-0.007030635606497526,
0.0057625556364655495,
-0.01678726263344288,
0.04153232276439667,
-0.010653216391801834,
-0.010176039300858974,
0.035635776817798615,
0.014587542042136192,
-0.01251312717795372,
0.02044944278895855,
0.025054803118109703,
-0.022668827325105667,
0.02796371653676033,
0.019375048577785492,
0.005575437564402819,
-0.0005461765686050057,
-0.04625870659947395,
0.02778021991252899,
0.032175034284591675,
-0.005950437393039465,
0.004498268011957407,
-0.012570126913487911,
-0.027565287426114082,
-0.03795851022005081,
0.026880253106355667,
-0.031300678849220276,
0.0018611267441883683,
-0.0052043478935956955,
-0.02870938554406166,
0.011082306504249573,
-0.008884184993803501,
0.03989765793085098,
-0.02787809818983078,
0.033184297382831573,
0.010430021211504936,
0.009405612014234066,
0.03620002791285515,
0.0683373361825943,
-0.014505889266729355,
-0.00743837421759963,
0.04136349633336067,
0.05899549275636673,
0.006211616098880768,
-0.03677346929907799,
-0.025578368455171585,
-0.01823112927377224,
0.043199323117733,
-0.0229584239423275,
-0.014986519701778889,
-0.025839557871222496,
0.022165218368172646,
0.0190782118588686,
0.012626566924154758,
-0.034866854548454285,
-0.025446215644478798,
0.020731084048748016,
-0.046577852219343185,
0.02663281559944153,
0.0019984401296824217,
0.004168909974396229,
0.012265754863619804,
-0.01168025005608797,
-0.005845226347446442,
0.01700013130903244,
0.05252876877784729,
0.003898660186678171,
-0.024056704714894295,
0.015417234972119331,
-0.0274921003729105,
0.021874921396374702,
-0.014535043388605118,
-0.008417234756052494,
0.013738199137151241,
0.005284564103931189,
-0.0007781226304359734,
-0.0032782177440822124,
-0.024554848670959473,
0.035873811691999435,
0.008369240909814835,
-0.003543055383488536,
-0.0029200646094977856,
0.026021413505077362,
-0.030686309561133385,
0.006079020444303751,
-0.04256729036569595,
-0.011226781643927097,
0.06475238502025604,
0.020161258056759834,
0.022181464359164238,
0.05225038155913353,
-0.02392987720668316,
-0.010386119596660137,
0.0021166757214814425,
0.01109545398503542,
-0.014478974975645542,
-0.025753123685717583,
-0.03942238539457321,
0.04489072412252426,
-0.06898853927850723,
0.018747780472040176,
0.04051334410905838,
-0.008883286267518997,
-0.03452025726437569,
0.055186256766319275,
-0.013454240746796131,
0.0328301377594471,
0.033854804933071136,
0.021265577524900436,
0.00914173386991024,
-0.010168449953198433,
0.021244626492261887,
0.053817324340343475,
0.009061839431524277,
0.019558927044272423,
0.015910368412733078,
0.07720281183719635,
-0.00892486423254013,
0.028842011466622353,
-0.015014435164630413,
0.0005817947676405311,
-0.0302230603992939,
0.019436482340097427,
0.06148664280772209,
-0.03491746634244919,
0.05841777101159096,
0.04701019078493118,
-0.03539973869919777,
0.06015970930457115,
-0.030949315056204796,
0.007178290747106075,
-0.035796988755464554,
0.01292972732335329,
-0.03768899664282799,
0.006106589455157518,
-0.026117192581295967,
0.03411233797669411,
-0.02083437144756317,
-0.008640068583190441,
-0.04495992138981819,
-0.013357357122004032,
0.010544192977249622,
-0.036349162459373474,
-0.010043756105005741,
0.030499419197440147,
0.011437099426984787,
0.0034015835262835026,
-0.040571022778749466,
-0.00044313445687294006,
-0.006160032469779253,
0.011394680477678776,
-0.000784506497438997,
0.004005551803857088,
0.011453432030975819,
0.01348266564309597,
-0.01970631442964077,
0.02508639544248581,
-0.005025018006563187,
-0.03573846444487572,
-0.02609301172196865,
0.028668714687228203,
0.0024019526317715645,
0.0014752238057553768
] |
<p>A thin spherical shell made of plastic carries a uniformly distributed negative charge of -Q coulombs. Two large thin disks made of glass carry uniformly distributed positive and negative charges S coulombs and -S coulombs. The radius of the plastic spherical shell is R1, and the radius of the glass disks is R2. The distance from the center of the spherical shell to the positive disk is d.</p>
<p>I want to know how to find two things:</p>
<ul>
<li><p>The potential difference V1-V2. Point 1 is at the center of the plastic sphere, and point 2 is just outside the sphere.</p></li>
<li><p>The potential difference V2-V3. Point 2 is just below the sphere, and point 3 is right beside the positive glass disk.</p></li>
</ul> | 1,522 | [
-0.032919831573963165,
-0.018423626199364662,
0.009592979215085506,
0.011550173163414001,
-0.025052780285477638,
-0.030617104843258858,
0.007922709919512272,
0.012095318175852299,
0.01223641075193882,
-0.00023240411246661097,
0.03833474591374397,
0.052208784967660904,
0.0704696848988533,
0.008502623066306114,
0.03037901036441326,
-0.01881767064332962,
0.01218461338430643,
-0.052004605531692505,
0.006428103893995285,
-0.0310418289154768,
-0.007273131515830755,
0.00787570420652628,
0.01276807114481926,
-0.0037447381764650345,
-0.0044892048463225365,
0.04289919510483742,
0.05333862826228142,
-0.0250430628657341,
-0.00682512391358614,
0.058455243706703186,
-0.02830285020172596,
-0.011863651685416698,
0.021643703803420067,
0.007442285306751728,
0.038573093712329865,
0.02253183349967003,
-0.05000631511211395,
-0.0054084258154034615,
-0.031186936423182487,
0.013866299763321877,
-0.028183814138174057,
0.021065393462777138,
0.007192331366240978,
0.06468567997217178,
-0.013289653696119785,
-0.016333647072315216,
0.014480520971119404,
-0.005941686686128378,
0.019402412697672844,
-0.06112859398126602,
0.06369789689779282,
0.01504810992628336,
0.03955511748790741,
0.03471466153860092,
-0.02655506134033203,
0.011294161900877953,
0.04164518788456917,
0.08135523647069931,
0.018085939809679985,
-0.03965125232934952,
-0.036302510648965836,
-0.004315134137868881,
-0.02908294089138508,
-0.0422532856464386,
0.007773329969495535,
0.0188066978007555,
-0.01284153200685978,
-0.007230424787849188,
0.01942911557853222,
-0.030871601775288582,
0.025939026847481728,
0.05469600856304169,
0.0247472133487463,
-0.03303054720163345,
0.03034682385623455,
-0.031114941462874413,
0.00020536151714622974,
0.016375860199332237,
0.004027784336358309,
-0.013272338546812534,
-0.016988152638077736,
0.02967049926519394,
0.027367256581783295,
0.06765547394752502,
0.010131613351404667,
-0.038584183901548386,
0.047628264874219894,
-0.012055444531142712,
-0.03132925182580948,
0.05099327862262726,
0.007573397364467382,
0.00516451895236969,
0.03773239254951477,
0.016502056270837784,
-0.00933354813605547,
0.022557049989700317,
-0.008546904660761356,
0.06770752370357513,
-0.0174435805529356,
-0.007969692349433899,
-0.042519692331552505,
-0.018645942211151123,
0.07070349156856537,
0.0825469121336937,
-0.015398346818983555,
-0.011860757134854794,
-0.010806122794747353,
-0.0047218832187354565,
0.03061857633292675,
-0.0018762308172881603,
-0.048833202570676804,
0.03433247655630112,
0.011208764277398586,
0.0014952268684282899,
0.011588942259550095,
-0.0240190327167511,
-0.026036370545625687,
-0.014074079692363739,
0.021294862031936646,
0.010867981240153313,
0.05106630176305771,
-0.017767759039998055,
-0.009068278595805168,
-0.06069310009479523,
-0.06820694357156754,
0.015560762025415897,
0.05294409766793251,
-0.006688261870294809,
-0.005361589603126049,
0.02856479212641716,
0.015295141376554966,
0.019827518612146378,
-0.01170448400080204,
0.0034109470434486866,
0.009135661646723747,
-0.02448008581995964,
-0.09380325675010681,
-0.04702261462807655,
0.0007861555204726756,
0.02043621614575386,
0.00017057299555744976,
-0.02291264757514,
-0.0007167960866354406,
0.010969194583594799,
0.04849035292863846,
0.00865948386490345,
-0.022042114287614822,
-0.017937801778316498,
0.048755042254924774,
0.0021000660490244627,
-0.006006534676998854,
0.010897236876189709,
-0.033072277903556824,
0.0289748664945364,
-0.00964084267616272,
-0.051946986466646194,
0.013054916635155678,
0.030561132356524467,
-0.014912424609065056,
0.001207381603308022,
0.06738565862178802,
-0.035143252462148666,
0.012788768857717514,
-0.018600694835186005,
-0.02772792987525463,
-0.00870983675122261,
0.05414127930998802,
0.0041886973194777966,
-0.04443571716547012,
0.0480227917432785,
-0.010866929776966572,
0.039442986249923706,
-0.015370255336165428,
-0.010824131779372692,
0.08915384113788605,
-0.026444338262081146,
0.0028352695517241955,
-0.03303306922316551,
0.0293552465736866,
-0.007231251336634159,
-0.010370652191340923,
-0.01932728849351406,
0.006952155381441116,
0.006005185190588236,
-0.012971485033631325,
0.0742207020521164,
0.0020478912629187107,
-0.004466403741389513,
-0.024487022310495377,
-0.013816342689096928,
-0.020116792991757393,
-0.04113256558775902,
0.0473218634724617,
0.011724990792572498,
-0.04809555783867836,
0.03313317894935608,
0.0002670371322892606,
0.01436356920748949,
0.008609519340097904,
-0.01812349259853363,
-0.000590206531342119,
0.06248309835791588,
-0.000702967750839889,
0.001787537825293839,
0.03594231605529785,
0.053754594177007675,
0.04272041097283363,
-0.024941423907876015,
0.026675255969166756,
-0.062383104115724564,
0.033024564385414124,
0.019883861765265465,
-0.027089526876807213,
0.0170774944126606,
0.05221889913082123,
-0.01954573579132557,
-0.001825425773859024,
0.052530016750097275,
0.009948641061782837,
0.000419083284214139,
-0.026447223499417305,
0.07229297608137131,
0.0606650672852993,
0.014941437169909477,
-0.002981396159157157,
0.027404028922319412,
0.002267423551529646,
0.03760427236557007,
0.011742249131202698,
-0.02354508824646473,
-0.016566235572099686,
-0.01695922203361988,
0.037604402750730515,
0.015523886308073997,
-0.012742062099277973,
0.008490587584674358,
0.005790913011878729,
0.012922975234687328,
0.011645161546766758,
0.001378016546368599,
-0.012417176738381386,
-0.0008534998632967472,
0.003395355073735118,
-0.0022015422582626343,
-0.03969734162092209,
0.01305755041539669,
0.015568080358207226,
0.0091006550937891,
0.021887602284550667,
-0.010193598456680775,
-0.008350105956196785,
0.025471020489931107,
0.001990777673199773,
-0.007984355092048645,
0.016779327765107155,
-0.023374726995825768,
0.03197164461016655,
0.0007219085237011313,
0.007293860428035259,
0.013951468281447887,
-0.016230542212724686,
0.015695126727223396,
-0.012349177151918411,
-0.009645190089941025,
0.016257543116807938,
0.02219817042350769,
0.004929797258228064,
0.04756402224302292,
0.024192914366722107,
-0.08869423717260361,
0.009150258265435696,
0.005997869651764631,
0.0015125853242352605,
-0.02566741593182087,
0.004475796595215797,
-0.00892514269798994,
0.026175498962402344,
0.004286321811378002,
-0.012674761936068535,
0.0012604922521859407,
-0.023226503282785416,
-0.03332304209470749,
0.011125560849905014,
0.018959753215312958,
-0.041308946907520294,
0.01912614516913891,
-0.017866428941488266,
-0.013642934150993824,
0.02301323413848877,
0.007928923703730106,
-0.006357504520565271,
0.02286078780889511,
0.002142785582691431,
-0.029711058363318443,
0.017322145402431488,
-0.0006702540558762848,
0.0400879792869091,
-0.03183851018548012,
0.013777508400380611,
0.03311990574002266,
0.06666287034749985,
-0.04464653134346008,
0.012479995377361774,
-0.03000686690211296,
-0.06313807517290115,
-0.04114838317036629,
-0.008189241401851177,
0.02006140910089016,
-0.0011692793341353536,
-0.001800555270165205,
0.0000836086182971485,
0.015445982106029987,
-0.016995152458548546,
-0.05051117017865181,
-0.02643047645688057,
0.012220069766044617,
0.024999963119626045,
0.05592602491378784,
-0.054168764501810074,
-0.022664140909910202,
0.09853048622608185,
-0.011125766672194004,
-0.0014621842419728637,
-0.013928869739174843,
-0.014630800113081932,
-0.04492602497339249,
0.01262683141976595,
-0.005812793038785458,
0.029166607186198235,
-0.016997961327433586,
0.026040473952889442,
0.01762545108795166,
0.030243895947933197,
0.023819996044039726,
-0.0036282555665820837,
-0.002590683987364173,
0.00008920628897612914,
0.017429880797863007,
-0.02521340921521187,
0.07525860518217087,
0.007533632684499025,
-0.027296768501400948,
0.019368795678019524,
-0.025285495445132256,
0.01985243707895279,
0.011111794970929623,
-0.010047315619885921,
-0.007098623085767031,
0.00013975003093946725,
0.01603446528315544,
-0.009439495392143726,
0.04267624393105507,
0.03860419616103172,
-0.039876312017440796,
-0.011819743551313877,
0.014857446774840355,
0.047460734844207764,
-0.031205208972096443,
-0.03946557641029358,
0.037729520350694656,
0.04866204410791397,
-0.036840055137872696,
-0.04149271547794342,
-0.016198214143514633,
-0.018223879858851433,
0.017902184277772903,
-0.02236419916152954,
-0.03575553372502327,
0.028745466843247414,
0.03998490795493126,
0.012533899396657944,
-0.008103160187602043,
-0.02806040458381176,
-0.019605379551649094,
-0.08362851291894913,
0.0020555523224174976,
0.01717541366815567,
0.07025540620088577,
-0.016172589734196663,
0.05670637637376785,
0.044669728726148605,
0.0010287791956216097,
0.015275033190846443,
0.017707904800772667,
-0.07561300694942474,
0.04783548787236214,
-0.012908665463328362,
-0.01583361066877842,
-0.022771785035729408,
-0.009082519449293613,
-0.01526038721203804,
-0.0156994815915823,
-0.028498154133558273,
-0.008415304124355316,
0.008121860213577747,
-0.03227822110056877,
-0.001119460677728057,
-0.05153072625398636,
-0.014563056640326977,
-0.013216427527368069,
0.024751676246523857,
0.02835005894303322,
-0.051112499088048935,
0.03129538521170616,
0.04284399002790451,
-0.0558917373418808,
0.020769184455275536,
-0.02759949117898941,
-0.0020159913692623377,
0.012363404035568237,
0.04772735387086868,
0.001856980612501502,
0.0381486751139164,
0.004471688997000456,
-0.015237972140312195,
-0.03635641932487488,
0.038820311427116394,
0.03185255825519562,
-0.027072478085756302,
-0.010584210976958275,
-0.03896132856607437,
0.019472507759928703,
-0.032445456832647324,
0.09370145201683044,
-0.04982401430606842,
0.022700147703289986,
0.03685570880770683,
-0.014281935058534145,
-0.000574802397750318,
0.02086574211716652,
0.08125247061252594,
-0.004662478342652321,
-0.039302121847867966,
-0.0491725392639637,
-0.028682218864560127,
-0.022389007732272148,
-0.009139136411249638,
0.01224364060908556,
0.01632915437221527,
0.0016327605117112398,
-0.006355971097946167,
0.03558594360947609,
-0.01934826746582985,
-0.0008637505816295743,
0.011225956492125988,
-0.0035531623288989067,
0.008307596668601036,
-0.03118814155459404,
-0.011559797450900078,
0.04299163445830345,
0.0106889009475708,
0.05729061737656593,
-0.01783911883831024,
0.018803250044584274,
-0.060709305107593536,
-0.025789406150579453,
0.056258562952280045,
0.05596114695072174,
0.013067447580397129,
-0.013841395266354084,
-0.0378338024020195,
-0.011406402103602886,
0.08495985716581345,
-0.061222612857818604,
0.042743973433971405,
-0.01151953637599945,
-0.008020534180104733,
-0.017120884731411934,
-0.039024632424116135,
-0.06394131481647491,
0.0004683682054746896,
-0.02300715632736683,
0.03727762773633003,
0.005399282556027174,
0.012432376854121685,
-0.023458510637283325,
0.02599509246647358,
0.03353025019168854,
0.07475704699754715,
-0.0014084441354498267,
0.000016599244190729223,
0.00802950095385313,
0.0003236275224480778,
0.00532096391543746,
-0.05221634730696678,
0.0049093933776021,
-0.032238464802503586,
-0.03150366246700287,
0.05822271853685379,
-0.0435703881084919,
-0.010539798066020012,
0.036856260150671005,
-0.01355862244963646,
0.004469707142561674,
-0.004356770310550928,
-0.004531801678240299,
0.021065669134259224,
0.05120869725942612,
0.02099897712469101,
0.028267936781048775,
0.005434163846075535,
-0.02093813568353653,
-0.019736481830477715,
-0.037513814866542816,
-0.01782737858593464,
0.012062552385032177,
-0.022879354655742645,
-0.013312849216163158,
0.004411275032907724,
-0.03185861557722092,
0.022340428084135056,
0.009904314763844013,
0.03560125082731247,
-0.04308682680130005,
-0.012706413865089417,
0.0016536350594833493,
0.014807746745646,
-0.03427897021174431,
0.02564108371734619,
0.004264308605343103,
0.01108256820589304,
0.036035582423210144,
-0.04706401377916336,
-0.005575421266257763,
-0.017863014712929726,
0.015194764360785484,
0.006254458334296942,
-0.009192590601742268,
0.004556278698146343,
-0.04126667603850365,
-0.041725147515535355,
0.002413775073364377,
-0.08734515309333801,
0.05874573811888695,
-0.025307416915893555,
-0.006925884634256363,
0.05093783140182495,
-0.055317532271146774,
-0.038568127900362015,
0.021708110347390175,
-0.017285289242863655,
0.03228096663951874,
-0.06763126701116562,
0.06115478649735451,
0.04373116046190262,
0.0017180999275296926,
-0.04951506480574608,
-0.027292924001812935,
0.03516306355595589,
0.021005231887102127,
-0.014344108290970325,
-0.0389380156993866,
-0.023907268419861794,
0.022108959034085274,
-0.008174208924174309,
0.007722245994955301,
0.021717607975006104,
-0.043192535638809204,
-0.03624413162469864,
0.024707341566681862,
0.009649323299527168,
0.04939856007695198,
-0.022321082651615143,
0.025084445253014565,
-0.014906488358974457,
0.0060400571674108505,
-0.03964388370513916,
-0.011423013173043728,
0.04207465052604675,
-0.02467954158782959,
-0.060732509940862656,
-0.01154902670532465,
0.01929481327533722,
0.011649060994386673,
-0.046860430389642715,
-0.030013786628842354,
0.005515282042324543,
0.007736390922218561,
-0.03266084939241409,
-0.013842804357409477,
0.020065853372216225,
0.004560899920761585,
-0.01550118625164032,
-0.033994805067777634,
0.02434694394469261,
-0.032626792788505554,
-0.03283582627773285,
0.025202136486768723,
0.03981943055987358,
-0.02386491186916828,
-0.01813199184834957,
0.04781261458992958,
-0.026832129806280136,
0.01901221089065075,
0.05439667031168938,
0.01830103248357773,
0.011315296404063702,
-0.03251997381448746,
-0.02729196846485138,
-0.013340430334210396,
0.028302175924181938,
-0.027394860982894897,
-0.016765069216489792,
-0.025131015107035637,
0.02109738625586033,
0.08209393173456192,
0.008072057738900185,
0.05518258735537529,
0.019482461735606194,
0.0060187941417098045,
-0.01378836203366518,
-0.00713935075327754,
-0.032255519181489944,
-0.006714692804962397,
-0.014533288776874542,
0.05236377194523811,
-0.07139347493648529,
0.04735235869884491,
0.007159793749451637,
0.059251539409160614,
-0.06154433265328407,
0.005757688544690609,
-0.01024754997342825,
0.001973711885511875,
0.019418610259890556,
-0.032943326979875565,
-0.03761908784508705,
0.02915150113403797,
-0.04659976065158844,
0.01151853147894144,
0.01180124282836914,
-0.03681738302111626,
0.05127790570259094,
-0.0032950432505458593,
-0.0016074426239356399,
-0.039182212203741074,
-0.02678726613521576,
-0.055330559611320496,
0.045557741075754166,
0.01807318441569805,
-0.0012079692678526044,
-0.04287825897336006,
0.025624411180615425,
0.027323082089424133,
0.02034510299563408,
-0.010472540743649006,
-0.06223069876432419,
-0.05058206617832184,
-0.017792554572224617,
-0.057419754564762115,
-0.05836407467722893,
-0.013211237266659737,
-0.019524255767464638,
-0.06968915462493896,
0.06656313687562943,
0.005046415608376265,
0.05794354900717735,
0.06690682470798492,
0.009137424640357494,
-0.019234122708439827,
0.08115096390247345,
-0.004821266978979111,
0.011904565617442131,
-0.007991299033164978,
0.004083834122866392,
0.13180296123027802,
0.0433773510158062,
-0.016474977135658264,
-0.05763399228453636,
-0.0027559888549149036,
-0.007506826892495155,
-0.009149188175797462,
0.004384324420243502,
0.01720748282968998,
-0.047668613493442535,
0.013733993284404278,
-0.005766401533037424,
0.027793867513537407,
0.008093126118183136,
0.02738921344280243,
0.023323414847254753,
-0.01981494203209877,
-0.021346507593989372,
0.01603228598833084,
0.030921204015612602,
-0.006834688596427441,
0.027284467592835426,
-0.03176472708582878,
0.06336428970098495,
-0.0625891163945198,
-0.016558464616537094,
-0.059817325323820114,
-0.03231869637966156,
0.04551404342055321,
0.04097125679254532,
-0.036142174154520035,
0.035521309822797775,
-0.003402749774977565,
0.004858082626014948,
-0.0169101320207119,
0.04818816855549812,
0.01946221850812435,
-0.02758169360458851,
0.0018552904948592186,
0.012304073199629784,
0.026983557268977165,
0.004138641525059938,
-0.018893521279096603,
0.005337727256119251,
-0.060058705508708954,
0.01960902288556099,
-0.015484410338103771,
0.02667839080095291,
-0.019735213369131088,
-0.014162324368953705,
0.0016753749223425984,
-0.01447299961000681,
0.034532032907009125,
-0.0233080442994833,
-0.03745529055595398,
0.013570546172559261,
0.008534510619938374,
0.006301082205027342,
0.011013868264853954,
-0.004941136110574007,
0.030817212536931038,
-0.009322980418801308,
-0.004296946804970503,
-0.06045375391840935,
0.028978848829865456,
0.025298304855823517,
0.022824984043836594,
0.037326693534851074,
-0.05928723141551018,
-0.019902514293789864,
-0.025163015350699425,
0.008847596123814583,
-0.016047067940235138,
-0.0036350649315863848,
-0.009778380393981934,
0.03289478272199631,
0.023287178948521614,
-0.012393193319439888,
0.01027173176407814,
0.0039494838565588,
-0.039790213108062744,
0.00023302367480937392,
-0.03517221286892891,
-0.014665897935628891,
-0.023023711517453194,
-0.0026344447396695614,
0.021843530237674713,
0.0237943883985281,
0.005251509603112936,
-0.017755920067429543,
0.028748588636517525,
0.061787575483322144,
0.005747851449996233,
-0.010303057730197906,
-0.036835093051195145,
-0.0023673460818827152,
-0.057589977979660034,
0.03495945781469345,
-0.03412348031997681,
0.028976278379559517,
0.023552892729640007,
0.023916834965348244,
0.018273120746016502,
0.0195033960044384,
-0.02658051624894142,
0.007244845852255821,
0.036919184029102325,
-0.008485340513288975,
-0.03417385369539261,
0.02005852945148945,
-0.0006088746595196426,
-0.00595209002494812,
-0.005495811812579632,
-0.01039236318320036,
-0.011085876263678074,
-0.00986532773822546,
0.00334674259647727,
-0.007696537300944328,
-0.03807852417230606,
-0.016965685412287712,
-0.019381094723939896,
-0.0374981090426445,
0.026730792596936226,
-0.03468513488769531,
-0.0031989270355552435,
-0.000005217030320636695,
0.01914885826408863,
-0.012543664313852787,
0.034896932542324066,
-0.045724835246801376,
0.001495832926593721,
-0.0001625572331249714,
-0.009073924273252487,
0.015078362077474594,
0.0016719154082238674,
0.029396673664450645,
0.006436752155423164,
0.020822476595640182,
-0.016212869435548782,
-0.0032456479966640472,
-0.0006429911009036005,
-0.05751456320285797,
-0.05497269704937935,
-0.0035723289474844933,
0.0021580469328910112,
0.033904194831848145,
0.012356577441096306,
-0.018454112112522125,
-0.02213461510837078,
0.0668749138712883,
0.0018775667995214462,
-0.031975261867046356,
-0.004958119709044695,
-0.04318932071328163,
0.00990742351859808,
-0.0071747153997421265,
0.0221755038946867,
-0.039352402091026306,
-0.02722342684864998,
0.012483938597142696,
0.0028771485667675734,
-0.05028638243675232,
0.019804904237389565,
0.00810349453240633,
-0.009860764257609844,
-0.01882411539554596,
-0.0026840113569051027,
0.009332229383289814,
0.049661844968795776,
0.04953986033797264,
-0.022045079618692398,
0.020294640213251114,
0.02729855477809906,
-0.025367433205246925,
-0.08951430767774582,
-0.014360976405441761,
-0.003805111860856414,
0.004636560101062059,
0.017929773777723312,
-0.0794466882944107,
0.006833813618868589,
0.010463660582900047,
-0.07439395040273666,
0.013343337923288345,
-0.03637323155999184,
-0.026705872267484665,
-0.03039330057799816,
0.014926980249583721,
-0.003513306612148881,
0.015140934847295284,
-0.00510003138333559,
0.03556085750460625,
0.01763385534286499,
0.03446361422538757,
-0.03265506401658058,
-0.019066933542490005,
-0.036129746586084366,
0.017828285694122314,
0.018876096233725548,
-0.013219623826444149,
0.02031499706208706,
-0.03748207166790962,
0.03004446253180504,
0.0034030445385724306,
-0.059892553836107254,
-0.001743724336847663,
-0.009042507968842983,
0.010906746610999107,
0.006211066618561745,
0.06486773490905762,
-0.007432491052895784,
0.042552702128887177,
-0.014154934324324131,
-0.04795367270708084,
0.04300606623291969,
-0.009094898588955402,
-0.030008627101778984,
0.00064476253464818,
0.02972860261797905,
-0.01848386786878109,
-0.004042649641633034,
0.03768935427069664,
0.004417559131979942,
0.010109472088515759,
-0.018575549125671387,
0.04040773957967758,
0.025335030630230904,
-0.03759580850601196,
-0.009278425015509129,
-0.044800613075494766,
-0.0014917857479304075,
0.02380336821079254,
0.012736532837152481,
-0.03810971975326538,
0.030628696084022522,
-0.017083963379263878,
-0.031952157616615295,
0.00589865492656827,
0.012285924516618252,
-0.0022613515611737967,
-0.05000506341457367,
-0.04818962141871452,
-0.005252707749605179,
0.022513756528496742,
-0.0015932981623336673,
-0.011418054811656475,
-0.07844160497188568,
0.031944964081048965,
0.005419764202088118,
0.012875750660896301,
0.04474039748311043,
0.005317007191479206,
-0.0028588285204023123,
-0.07885057479143143,
0.012069405056536198,
0.0048873545601964,
-0.04748699441552162,
-0.01767798140645027,
-0.043681029230356216,
-0.020382385700941086,
0.03245829418301582,
0.06223824992775917,
-0.0035982688423246145,
-0.007793312426656485,
0.01071142591536045,
-0.044845931231975555,
0.05600482225418091,
-0.04145609587430954,
-0.014885290525853634,
0.04057959094643593,
0.008684545755386353,
0.049086928367614746,
0.008267061784863472,
-0.005485686473548412,
0.03662813827395439,
0.02863467112183571,
0.0052739656530320644,
0.0038791359402239323,
0.010393984615802765,
-0.027814241126179695,
0.007286371663212776,
-0.028675969690084457,
0.024217011407017708,
0.0796763077378273,
-0.0035365899093449116,
0.022148728370666504,
-0.00685531459748745,
-0.007020966149866581,
0.002965101506561041,
0.03649917617440224,
-0.07175447046756744,
-0.011653760448098183,
-0.020174363628029823,
-0.04633993282914162,
0.03847579285502434,
-0.04935380816459656,
-0.035306137055158615,
0.04593104124069214,
-0.028350772336125374,
-0.01801280863583088,
0.03919905424118042,
-0.004566825460642576,
0.053544219583272934,
-0.03913913294672966,
0.004053030163049698,
0.028345264494419098,
-0.01498571876436472,
0.008074852637946606,
0.03760354220867157,
0.03155240789055824,
0.010948363691568375,
0.004649532493203878,
0.06531424075365067,
0.002283718204125762,
0.020462187007069588,
-0.039192065596580505,
-0.0010630596661940217,
0.023522302508354187,
-0.004445611033588648,
0.010450358502566814,
0.0023644010070711374,
0.01516587845981121,
-0.0020277881994843483,
-0.01838689297437668,
0.06260978430509567,
-0.028406711295247078,
-0.03032604418694973,
-0.011814315803349018,
0.0012780382530763745,
0.003082594135776162,
0.021514367312192917,
0.008340148255228996,
-0.004284457303583622,
-0.0051306248642504215,
-0.02537880651652813,
-0.027440199628472328,
0.01203066948801279,
0.00028133130399510264,
-0.015063032507896423,
0.04868292808532715,
-0.008315171115100384,
0.03461034223437309,
-0.03376246988773346,
-0.013793318532407284,
0.011569907888770103,
0.037180203944444656,
0.03092186711728573,
0.03757157176733017,
0.01820734702050686,
0.0009797755628824234,
0.022533591836690903,
-0.013487609103322029,
0.053003743290901184,
-0.03176518529653549,
-0.022363808006048203,
-0.008914104662835598,
-0.02266857586801052,
0.004567209631204605,
-0.012450491078197956
] |
<p>Can one measure the Higgs field? Or is the higgs field not measurable?</p>
<p>I know that the higgs boson is a indication for the presence of the higgs field. But it is the only way of the presence of the higgs field?</p>
<p>When the higgs field is not measurable, what is the reason?</p> | 1,523 | [
0.0017536529339849949,
0.009343777783215046,
0.01725989393889904,
-0.06087810546159744,
0.05329836532473564,
0.026840755715966225,
-0.03936406597495079,
-0.050749171525239944,
-0.00502527691423893,
0.012266232632100582,
0.047171708196401596,
-0.008861023932695389,
0.027013622224330902,
0.008171304129064083,
0.007462975103408098,
0.01750187948346138,
-0.005848467815667391,
0.023243553936481476,
-0.018519502133131027,
-0.014877649955451488,
-0.015667129307985306,
0.03980035334825516,
0.026671472936868668,
0.003462034510448575,
-0.01611582562327385,
0.017642149701714516,
0.020493626594543457,
0.05589417368173599,
-0.004396162927150726,
0.06335549056529999,
-0.022237082943320274,
-0.03409535065293312,
0.025363555178046227,
0.042535923421382904,
0.012620060704648495,
-0.017950257286429405,
0.007209597621113062,
-0.017998434603214264,
0.005571932066231966,
0.0019028711831197143,
-0.04605216532945633,
-0.030762264505028725,
0.013426179066300392,
0.054786570370197296,
-0.036938924342393875,
-0.006081667263060808,
-0.03683023527264595,
0.020452063530683517,
0.07976498454809189,
-0.056653689593076706,
0.050164200365543365,
0.021783342584967613,
0.031071238219738007,
0.018562598153948784,
-0.001882676500827074,
-0.016266414895653725,
0.048376213759183884,
0.06431148201227188,
-0.006491043139249086,
-0.04676558077335358,
-0.0563746877014637,
-0.031182335689663887,
0.007077409420162439,
-0.04512329772114754,
0.00043602680671028793,
0.08365381509065628,
-0.026912540197372437,
-0.0256609246134758,
0.028688203543424606,
0.007286702282726765,
0.0024597300216555595,
-0.013635780662298203,
0.0058630118146538734,
0.021693149581551552,
0.03926602751016617,
-0.035908136516809464,
0.018297193571925163,
0.03986189886927605,
0.04081292822957039,
0.03391781076788902,
0.002371929818764329,
-0.008983747102320194,
0.033846545964479446,
0.0044382489286363125,
0.03233013302087784,
-0.008048123680055141,
0.05331133306026459,
-0.025540372356772423,
0.007331571076065302,
0.047816596925258636,
-0.005997753702104092,
0.011626760475337505,
0.0279744453728199,
-0.006347088608890772,
-0.039636749774217606,
0.02453906461596489,
0.004304554779082537,
0.05128670856356621,
-0.013328948058187962,
0.026384610682725906,
0.016730602830648422,
-0.004263009876012802,
0.007021710276603699,
0.0655333548784256,
-0.017176952213048935,
0.002482655690982938,
-0.003346238750964403,
-0.007194384466856718,
-0.019088009372353554,
-0.015447991900146008,
-0.05335955321788788,
-0.00799130741506815,
0.009649040177464485,
-0.005791381932795048,
0.026089569553732872,
-0.022777128964662552,
0.0004352800315245986,
-0.028036516159772873,
0.07999499887228012,
0.060614462941884995,
0.03351251035928726,
-0.03743041679263115,
-0.004174587782472372,
-0.028478501364588737,
-0.06271260231733322,
0.013942045159637928,
0.023716654628515244,
0.005970347207039595,
-0.05364267900586128,
0.028742216527462006,
-0.003229373600333929,
-0.0006226912373676896,
-0.0008818475180305541,
0.020902248099446297,
0.04543931782245636,
-0.035518623888492584,
-0.1167367622256279,
-0.047921549528837204,
0.06755383312702179,
-0.01620032638311386,
-0.02161131426692009,
-0.0418350026011467,
0.0013800386805087328,
0.04240439087152481,
0.06832502037286758,
-0.012714345008134842,
0.012267328798770905,
0.013572539202868938,
0.035505786538124084,
-0.009758437052369118,
-0.017206046730279922,
-0.026085808873176575,
0.01036732830107212,
-0.026818525046110153,
-0.023505864664912224,
-0.04683408513665199,
-0.0024878152180463076,
0.04264945909380913,
-0.019587622955441475,
-0.026901617646217346,
0.029870033264160156,
0.018234407529234886,
0.007285830564796925,
0.03040439262986183,
-0.012113208882510662,
-0.03728621453046799,
0.053310148417949677,
-0.006281924434006214,
0.028429286554455757,
0.041938651353120804,
-0.002219596179202199,
0.01579541526734829,
0.019253112375736237,
0.015873389318585396,
0.0315079428255558,
-0.010873871855437756,
-0.047938425093889236,
0.00820503942668438,
0.01971857249736786,
-0.0014919961104169488,
-0.05307983234524727,
0.008236990310251713,
-0.03712933138012886,
0.018698927015066147,
0.027965867891907692,
0.033609677106142044,
-0.0014087676536291838,
-0.01249011605978012,
0.04454735293984413,
-0.0673060417175293,
-0.057997021824121475,
-0.07503912597894669,
-0.012639912776648998,
0.014808925800025463,
0.0064973533153533936,
0.014253838919103146,
0.01811257377266884,
0.0022203526459634304,
-0.06870099902153015,
-0.05283920466899872,
0.011523565277457237,
0.03158474713563919,
0.014366439543664455,
0.004826091229915619,
0.002440006472170353,
0.050262391567230225,
0.03790483996272087,
0.0038441671058535576,
0.03306785598397255,
0.006085834465920925,
-0.04298527538776398,
-0.001680846093222499,
-0.04597502946853638,
-0.007389608304947615,
-0.006208375561982393,
0.003461226122453809,
-0.006393979769200087,
-0.006902007851749659,
-0.02501034177839756,
0.06430143117904663,
-0.014940622262656689,
0.08029945194721222,
0.0012091262033209205,
0.0078003923408687115,
0.011784978210926056,
0.024158047512173653,
-0.017018580809235573,
-0.0013582855463027954,
-0.02463819645345211,
-0.007360231596976519,
-0.07116562128067017,
-0.004617529921233654,
0.026379933580756187,
0.048542171716690063,
-0.017712974920868874,
0.01874074712395668,
0.04350155591964722,
0.020321479067206383,
-0.005205326713621616,
0.015991130843758583,
-0.03845607861876488,
-0.07003413140773773,
0.007234786171466112,
0.008907612413167953,
0.01361384242773056,
0.025108560919761658,
0.02288711629807949,
0.0006739023956470191,
0.016441265121102333,
-0.016881577670574188,
-0.0077142780646681786,
0.039835695177316666,
-0.03180312365293503,
0.0035009447019547224,
-0.015590635128319263,
-0.02532598190009594,
0.031131187453866005,
-0.0021705839317291975,
0.05792127549648285,
0.0003974688006564975,
-0.004944626707583666,
-0.004775790497660637,
-0.005183640401810408,
-0.020402710884809494,
0.01849721185863018,
0.00885538849979639,
-0.031952641904354095,
-0.03657941147685051,
0.03424105793237686,
-0.037361908704042435,
0.030348191037774086,
-0.022359615191817284,
0.016271084547042847,
-0.05299338698387146,
-0.003533067414537072,
0.05207803472876549,
-0.03704231232404709,
0.03484075516462326,
-0.03888185694813728,
-0.032738491892814636,
0.030025728046894073,
-0.055770762264728546,
0.017510583624243736,
0.02154732309281826,
-0.038312871009111404,
0.006031215190887451,
-0.06240202113986015,
-0.028854675590991974,
-0.002797425491735339,
-0.023545442149043083,
-0.003310217522084713,
0.0010837811278179288,
0.005247520748525858,
-0.03283430263400078,
-0.017456866800785065,
-0.02610887587070465,
-0.004665991757065058,
-0.010797049850225449,
-0.001580887706950307,
0.015472663566470146,
0.00022919998446013778,
-0.04221637547016144,
0.014429646544158459,
-0.02062862366437912,
-0.07385560870170593,
-0.033455703407526016,
0.01919201761484146,
0.0016593269538134336,
-0.03216433525085449,
0.054251037538051605,
0.05771568790078163,
-0.07231348007917404,
-0.018921010196208954,
-0.029782896861433983,
-0.04095345735549927,
0.02546304650604725,
-0.027877822518348694,
0.024822961539030075,
-0.012084437534213066,
-0.05836386978626251,
0.07429155707359314,
0.0757046565413475,
-0.021874533966183662,
-0.009510093368589878,
-0.0048335641622543335,
-0.03169235587120056,
-0.0456048846244812,
-0.023729313164949417,
-0.007224738132208586,
0.0071996403858065605,
0.011108893901109695,
0.010798368602991104,
0.030398240312933922,
0.0014123170403763652,
0.03597179055213928,
-0.011121743358671665,
-0.015580806881189346,
0.006102806888520718,
0.0012762508122250438,
0.05440652370452881,
0.009502842091023922,
-0.022982003167271614,
-0.043911874294281006,
-0.0051412684842944145,
0.03119032457470894,
-0.007419473025947809,
-0.037338901311159134,
0.08271825313568115,
0.0034624170511960983,
0.012313085608184338,
-0.04111212119460106,
0.0064150067046284676,
0.03968135640025139,
0.018429819494485855,
0.03752417862415314,
-0.01207229495048523,
0.0015928951324895024,
0.01690744236111641,
0.0029248457867652178,
0.04573329538106918,
0.022619204595685005,
-0.04416487365961075,
-0.047708865255117416,
-0.020746324211359024,
0.022767173126339912,
0.034993384033441544,
-0.00299588730558753,
-0.04097313806414604,
0.016284620389342308,
0.07704638689756393,
0.004888115916401148,
-0.01609490066766739,
-0.019972702488303185,
-0.043850820511579514,
-0.04202914610505104,
0.002237723907455802,
0.0030996319837868214,
0.024438150227069855,
0.032097093760967255,
0.019015571102499962,
0.009362584911286831,
-0.006268010940402746,
0.006243474781513214,
-0.03764713555574417,
-0.07998654991388321,
0.005589811597019434,
-0.06712592393159866,
-0.006706627085804939,
-0.040001578629016876,
-0.05285966768860817,
-0.0011781854555010796,
-0.010022052563726902,
-0.000784603354986757,
-0.048142313957214355,
0.009134853258728981,
-0.08800343424081802,
0.003965124022215605,
-0.01615004800260067,
-0.012067727744579315,
-0.024729909375309944,
0.016466062515974045,
0.04625345394015312,
-0.019358579069375992,
-0.0030251157004386187,
0.026929842308163643,
-0.03954388201236725,
-0.006832445971667767,
0.0023459417279809713,
0.014052451588213444,
-0.015402340330183506,
0.03416598588228226,
0.03682845085859299,
0.035381678491830826,
-0.05119618400931358,
0.01826881244778633,
0.020675398409366608,
0.05086975917220116,
0.005156611558049917,
-0.0025659087114036083,
-0.00866793841123581,
-0.047094449400901794,
-0.021853815764188766,
0.009520678780972958,
0.05632549151778221,
-0.010127708315849304,
0.009022669866681099,
0.05423920601606369,
0.016931291669607162,
-0.03558516874909401,
0.039679087698459625,
0.037028759717941284,
0.006009188946336508,
-0.007638381794095039,
-0.04390553757548332,
-0.008867211639881134,
-0.028765728697180748,
-0.0060781813226640224,
-0.009322091937065125,
-0.0008321936475113034,
-0.0323658362030983,
-0.008577296510338783,
0.01928584650158882,
0.039422206580638885,
-0.004525220487266779,
0.009283103048801422,
0.007073844783008099,
0.022159159183502197,
0.020356183871626854,
-0.003563174046576023,
0.008469928056001663,
0.0883345901966095,
0.02347015216946602,
0.035603031516075134,
-0.02038024552166462,
-0.07478070259094238,
-0.021373186260461807,
0.035169895738363266,
0.008730332367122173,
-0.03335913270711899,
-0.016541248187422752,
-0.030182689428329468,
-0.026963215321302414,
0.0682513639330864,
-0.02413872815668583,
0.034895025193691254,
-0.03864716365933418,
0.006993917748332024,
-0.03898536041378975,
-0.01099234540015459,
-0.02087542414665222,
0.03238850459456444,
-0.004621297121047974,
-0.023513732478022575,
-0.029842140153050423,
0.010769362561404705,
0.0007914385641925037,
0.009285436943173409,
-0.003502732375636697,
0.05530473217368126,
0.02180572785437107,
0.03883879631757736,
-0.0001666239113546908,
0.013316333293914795,
-0.01410727296024561,
-0.08849892020225525,
-0.0003775418153963983,
0.03642026335000992,
-0.03212061896920204,
0.03761213272809982,
-0.01200115866959095,
-0.08400671184062958,
0.021437283605337143,
-0.01583380438387394,
0.0011747278040274978,
0.03008957952260971,
-0.06956706196069717,
0.02039964497089386,
0.0350712426006794,
0.016424965113401413,
0.07222135365009308,
0.024625003337860107,
-0.003288322128355503,
0.014911025762557983,
0.015387763269245625,
0.018810758367180824,
-0.05856362730264664,
0.010812549851834774,
-0.00004576771243591793,
-0.020720666274428368,
-0.040301717817783356,
0.06767574697732925,
0.014749668538570404,
0.025173978880047798,
0.008887571282684803,
-0.026221878826618195,
-0.01976417936384678,
0.008114038035273552,
0.020325936377048492,
-0.02108377031981945,
-0.058222923427820206,
0.002513743005692959,
0.02665206976234913,
-0.03670545294880867,
0.012967308983206749,
0.017590610310435295,
0.016074229031801224,
0.00153670075815171,
-0.03152750805020332,
0.024083999916911125,
0.005659886170178652,
-0.01773020066320896,
0.0413530059158802,
-0.03412980958819389,
0.020391179248690605,
-0.028164926916360855,
-0.007833871990442276,
-0.020074576139450073,
-0.04590807855129242,
-0.03134584799408913,
-0.0021645131055265665,
0.029070930555462837,
0.018450865522027016,
-0.014760302379727364,
0.05055885389447212,
0.006289753597229719,
0.003961303271353245,
-0.07178618758916855,
-0.023822132498025894,
-0.027170982211828232,
0.02268395572900772,
0.010907399468123913,
-0.010665162466466427,
0.00396875711157918,
-0.03233400732278824,
-0.03960401192307472,
-0.017698420211672783,
0.022588245570659637,
-0.020396562293171883,
-0.006333876866847277,
-0.0026268414221704006,
0.014964408241212368,
0.052419792860746384,
-0.011577286757528782,
-0.03618846833705902,
0.03495552018284798,
0.014758690260350704,
-0.0013114579487591982,
0.02535439282655716,
0.04404868185520172,
-0.009428530000150204,
-0.04394589364528656,
-0.010202126577496529,
0.01017029769718647,
0.01896965317428112,
0.002553574973717332,
-0.0044153002090752125,
0.03468960151076317,
-0.017572274431586266,
-0.027943577617406845,
-0.03483819589018822,
0.029782593250274658,
0.008673977106809616,
0.03716408833861351,
-0.013452915474772453,
0.0010291849030181766,
0.0005147244082763791,
-0.022579334676265717,
0.04933585971593857,
-0.006323348265141249,
0.00846849475055933,
-0.01479392684996128,
-0.004196634981781244,
0.01059374213218689,
-0.029643826186656952,
0.0027240258641541004,
-0.0077272686176002026,
0.006952497176826,
-0.035971201956272125,
0.06003771349787712,
0.007093325722962618,
0.015711601823568344,
-0.053305305540561676,
-0.012516381219029427,
-0.03788723051548004,
-0.025435609742999077,
0.05738621577620506,
-0.00442679226398468,
0.05765974894165993,
0.0226888544857502,
-0.04871997982263565,
0.00948795210570097,
-0.028710737824440002,
0.018759170547127724,
0.017001673579216003,
0.025938918814063072,
0.02538320980966091,
0.0005158121348358691,
0.004768764600157738,
0.05585069954395294,
0.004562587011605501,
-0.01418718695640564,
0.0034042259212583303,
0.01541297510266304,
0.05382923781871796,
0.04062808305025101,
-0.0024932639207690954,
-0.02946862392127514,
0.03508558124303818,
-0.022136090323328972,
0.014974107034504414,
-0.02166440524160862,
-0.009248832240700722,
0.03325758874416351,
-0.0016356540145352483,
0.011358272284269333,
0.0011934594949707389,
-0.01585184969007969,
-0.03835500404238701,
0.002843444235622883,
0.004456778522580862,
0.03005935251712799,
0.0018204831285402179,
0.017621425911784172,
0.012108426541090012,
-0.0034800369758158922,
0.0003703493857756257,
0.016242066398262978,
-0.07403118163347244,
-0.048404913395643234,
-0.029916463419795036,
-0.041462257504463196,
0.061917077749967575,
0.0099648367613554,
-0.03074338100850582,
-0.01490457821637392,
-0.02536630816757679,
0.02215740829706192,
-0.0058571770787239075,
0.030248448252677917,
-0.03456971049308777,
0.03040080890059471,
-0.01274116337299347,
0.04564378410577774,
-0.020442446693778038,
0.03728114068508148,
0.09853488206863403,
0.08549901098012924,
0.001478605787269771,
-0.06825302541255951,
0.05073188990354538,
-0.04241298884153366,
0.007454024627804756,
-0.057389140129089355,
0.02641570009291172,
-0.03130369260907173,
-0.009234526194632053,
0.0010328644420951605,
0.06915903091430664,
0.012382280081510544,
-0.029913416132330894,
0.042462609708309174,
-0.034575700759887695,
-0.032098039984703064,
-0.008071278221905231,
0.028839262202382088,
0.0005384248215705156,
0.01237515639513731,
-0.030097974464297295,
0.04019436612725258,
-0.003946569282561541,
0.0046097650192677975,
0.014734776690602303,
-0.01747756078839302,
-0.028409475460648537,
0.006169721018522978,
-0.03462519496679306,
-0.014004047960042953,
0.013072528876364231,
-0.01570948027074337,
-0.055809903889894485,
-0.016701923683285713,
-0.0009721212554723024,
-0.014259309507906437,
0.020366674289107323,
0.04737388342618942,
0.008679956197738647,
-0.03242010250687599,
-0.011894107796251774,
0.030374109745025635,
-0.04471952095627785,
-0.023357711732387543,
0.016695544123649597,
0.09134773910045624,
-0.0034447929356247187,
-0.016157936304807663,
0.010060447268188,
0.018839742988348007,
-0.0015637417091056705,
-0.03756953030824661,
-0.02204802632331848,
-0.015356328338384628,
0.026852112263441086,
-0.03404024988412857,
-0.048856381326913834,
-0.005510659422725439,
0.027623308822512627,
-0.0350019596517086,
0.01746032014489174,
-0.0012431571958586574,
0.008785399608314037,
-0.02742196060717106,
-0.008535457774996758,
0.036935336887836456,
0.007557442411780357,
0.006744594778865576,
-0.020779870450496674,
0.001121282926760614,
-0.04952482506632805,
0.011987554840743542,
0.01178860105574131,
0.0035557164810597897,
-0.00053049111738801,
0.046476658433675766,
-0.02795523591339588,
0.0015647626714780927,
-0.027178894728422165,
0.04621515050530434,
-0.03204462677240372,
-0.007787770126014948,
-0.03841010108590126,
-0.007457691710442305,
0.018841013312339783,
0.051998596638441086,
0.00818817038089037,
0.00522146001458168,
-0.009269078262150288,
0.009122970513999462,
0.014089393429458141,
-0.015347898006439209,
-0.000612688425462693,
0.027234582230448723,
-0.02853812277317047,
-0.004074084106832743,
-0.004507438745349646,
0.013484707102179527,
0.046553805470466614,
0.0004166769504081458,
0.018130382522940636,
0.02547672763466835,
-0.009153690189123154,
-0.0047232708893716335,
0.021972576156258583,
-0.03802960366010666,
-0.013185081072151661,
-0.007524256128817797,
0.016484439373016357,
-0.0356440506875515,
-0.031101450324058533,
-0.04054129123687744,
0.035415999591350555,
0.027805451303720474,
0.022414930164813995,
-0.04677632078528404,
-0.0066522820852696896,
0.017122602090239525,
0.05949172005057335,
-0.05909183621406555,
0.0027687684632837772,
-0.04869009554386139,
0.01250238437205553,
-0.013994303531944752,
-0.004781999625265598,
-0.009677142836153507,
0.02234497480094433,
0.011050345376133919,
-0.011561988852918148,
0.019948845729231834,
0.02414451166987419,
-0.00991522241383791,
0.007318698335438967,
0.01709628663957119,
-0.005735345650464296,
0.03553628921508789,
-0.010267521254718304,
-0.010469110682606697,
0.04984476789832115,
-0.04329097643494606,
-0.030068106949329376,
0.060516998171806335,
-0.0042531355284154415,
0.033916786313056946,
0.05110346898436546,
-0.00033439419348724186,
-0.028398333117365837,
0.018233032897114754,
-0.021335162222385406,
-0.003680154914036393,
0.0034685085993260145,
-0.0065437559969723225,
-0.056628115475177765,
-0.007436100393533707,
0.03171834722161293,
0.015637574717402458,
-0.016412625089287758,
0.030619679018855095,
-0.0007013445720076561,
0.007063153199851513,
-0.01658298820257187,
-0.013247247785329819,
-0.022584950551390648,
0.052606575191020966,
0.038935452699661255,
0.0037807035259902477,
-0.001034475164487958,
0.05625515431165695,
-0.036843206733465195,
0.03291932865977287,
0.02010783739387989,
0.024086343124508858,
-0.09586122632026672,
-0.03597009554505348,
-0.011368824169039726,
0.002877043094485998,
0.056712616235017776,
-0.04294518753886223,
0.023359479382634163,
0.05949975922703743,
-0.06286968290805817,
0.023331936448812485,
-0.01924254558980465,
-0.019987162202596664,
-0.018007934093475342,
-0.02187296748161316,
0.0070417835377156734,
0.060257378965616226,
0.04280143976211548,
0.04822826385498047,
-0.00245298002846539,
0.03661716729402542,
0.01788610778748989,
-0.02027900330722332,
-0.033002302050590515,
0.020435117185115814,
0.005064493976533413,
-0.03770163655281067,
0.07152584195137024,
-0.005442865192890167,
0.007920980453491211,
0.039193615317344666,
0.018186751753091812,
0.0245220810174942,
0.0032033901661634445,
0.012749914079904556,
0.013912327587604523,
0.05466591194272041,
0.015847837552428246,
-0.01887539029121399,
-0.00865053292363882,
0.026456141844391823,
-0.018253246322274208,
0.014739643782377243,
0.008624694310128689,
-0.0067908791825175285,
0.025315899401903152,
-0.01811128668487072,
0.008323042653501034,
0.02467426098883152,
-0.011802922934293747,
-0.0310065820813179,
-0.008970309980213642,
0.005768170580267906,
0.009004747495055199,
-0.013771121390163898,
-0.0013957832707092166,
-0.040787115693092346,
0.023058339953422546,
0.03422536700963974,
0.0018894416280090809,
-0.047402385622262955,
-0.009250866249203682,
-0.024252934381365776,
-0.005683532450348139,
0.04284362494945526,
0.017772866412997246,
-0.011586307547986507,
-0.06130910664796829,
-0.015553063713014126,
-0.016337556764483452,
0.00012021172005916014,
0.0495833195745945,
-0.005570004228502512,
-0.06324102729558945,
0.03104170598089695,
0.003128640353679657,
0.034284502267837524,
-0.04155857861042023,
-0.023538941517472267,
-0.024906661361455917,
-0.0435582660138607,
0.04124372452497482,
0.016482412815093994,
0.00030318170320242643,
-0.025408875197172165,
-0.0017992971697822213,
-0.00853008683770895,
-0.015362548641860485,
0.04325880855321884,
0.002152414992451668,
-0.025921333581209183,
0.028431501239538193,
0.029863236472010612,
0.0252275038510561,
-0.043533846735954285,
-0.007518272381275892,
-0.029669277369976044,
-0.01647801138460636,
-0.019697006791830063,
-0.04272874444723129,
-0.0030035660602152348,
0.04023013263940811,
0.044243961572647095,
-0.010207361541688442,
0.04584807530045509,
-0.011579271405935287,
-0.02665959857404232,
0.05960879847407341,
-0.008301904425024986,
-0.03031649813055992,
0.03783748298883438,
-0.014708387665450573,
0.026920925825834274,
0.047170981764793396,
-0.01959316059947014,
-0.03340760990977287,
-0.02234732359647751,
-0.03256341442465782,
-0.022333942353725433,
0.004159084055572748,
0.004661530256271362,
-0.006782920099794865,
-0.011873232200741768,
-0.015651313588023186,
0.04722728207707405,
-0.041406918317079544,
-0.0264667309820652,
0.05697024613618851,
0.010174070484936237,
0.03623329475522041,
0.018281536176800728,
-0.00021666982502210885,
0.02295059897005558,
0.020700136199593544,
0.018332606181502342,
0.05064169690012932,
0.030999189242720604,
-0.0077172815799713135,
0.007347820792347193,
0.021409502252936363,
-0.012768036685883999,
0.013630547560751438,
0.037231430411338806,
0.060150597244501114,
-0.03342640399932861,
-0.029408657923340797,
-0.020550232380628586,
-0.005428015254437923,
0.031710632145404816,
0.016325386241078377,
-0.01677628606557846,
0.08387472480535507,
-0.0346832200884819,
-0.018704893067479134,
-0.023641901090741158,
-0.00263506593182683,
-0.01485973410308361,
0.020279154181480408,
0.030513884499669075,
0.0559900626540184,
-0.006937982514500618,
0.009353929199278355,
-0.005642465315759182,
0.037579137831926346,
0.0036242445930838585,
-0.07797205448150635,
-0.007205585949122906,
0.012166693806648254,
-0.027282439172267914,
0.00010517051123315468,
-0.001439044950529933,
-0.028666313737630844,
0.0003001352306455374,
0.010421720333397388,
0.02313874289393425,
0.061987437307834625,
0.0012512808898463845,
-0.020542925223708153,
-0.03568334877490997,
0.025997981429100037,
-0.04402253031730652,
0.019408073276281357,
-0.06737057119607925,
0.013020819053053856,
-0.05076513811945915,
-0.02916231006383896
] |
<p>Really short question, but I cannot find anything on the internet.</p>
<p>What is meant <em>proton polarisation</em>?</p>
<p>Is it to do with the spin of the proton?
I guess the spin of the proton is obtained from the vector addition of the 3 quarks' individual spins, so it can't be 0...
Can we have <em>unpolarised</em> protons then?</p>
<p>Thanks!</p> | 1,524 | [
-0.005980849731713533,
0.009068586863577366,
-0.011124890297651291,
-0.019334768876433372,
0.05831955745816231,
0.04407493770122528,
-0.04778793454170227,
0.009404991753399372,
0.005125631578266621,
-0.06414298713207245,
0.033536121249198914,
0.03977406024932861,
0.043904151767492294,
0.028880491852760315,
0.010585924610495567,
0.004409541841596365,
0.012709032744169235,
-0.02725030481815338,
0.02824888937175274,
-0.03208361566066742,
0.010536718182265759,
0.034240011125802994,
0.01835535652935505,
0.058217450976371765,
-0.027958979830145836,
0.02516012452542782,
0.038170553743839264,
0.030726520344614983,
0.037412166595458984,
0.03248340263962746,
0.0058227707631886005,
-0.041131019592285156,
0.02708916738629341,
-0.0013859161408618093,
0.03783562034368515,
-0.009296311996877193,
-0.014661271125078201,
-0.015896784141659737,
-0.032775793224573135,
0.008502745069563389,
-0.02774657867848873,
-0.022820651531219482,
-0.009255883283913136,
0.05228347331285477,
-0.010792006738483906,
0.028180593624711037,
0.012591599486768246,
-0.025731703266501427,
0.07255016267299652,
-0.0647529736161232,
0.03803341090679169,
0.029548417776823044,
0.030848100781440735,
0.0122313117608428,
-0.017212020233273506,
0.004044717643409967,
0.08597211539745331,
0.04516591131687164,
-0.015262464061379433,
-0.0363062359392643,
-0.033082183450460434,
-0.01584787480533123,
0.025690875947475433,
-0.004862947389483452,
-0.040183790028095245,
0.028478600084781647,
0.003838685806840658,
-0.028845472261309624,
0.02880719304084778,
0.015314866788685322,
0.026945075020194054,
0.007423269096761942,
0.029678532853722572,
-0.05000699684023857,
-0.004406067077070475,
-0.03397347778081894,
0.013069301843643188,
0.02747735008597374,
0.01552311796694994,
-0.017053714022040367,
-0.010631583631038666,
0.025650445371866226,
0.010933875106275082,
0.019266411662101746,
-0.012130252085626125,
-0.02881355956196785,
0.06280460208654404,
-0.022312045097351074,
0.013047546148300171,
0.05911711975932121,
-0.018634073436260223,
0.01986258290708065,
0.054430823773145676,
0.026472393423318863,
-0.0168332289904356,
0.03554879501461983,
0.01717350073158741,
0.048651471734046936,
-0.01676623336970806,
-0.02011936902999878,
0.029213596135377884,
-0.00012483005411922932,
0.0010561103699728847,
0.069107785820961,
-0.006179221905767918,
0.012260773219168186,
-0.036078084260225296,
0.022711103782057762,
-0.0021627829410135746,
-0.030325502157211304,
-0.03522045910358429,
0.008213906548917294,
-0.008894815109670162,
-0.04993096739053726,
-0.003572457004338503,
-0.04995949566364288,
0.00537535035982728,
-0.005991261452436447,
0.05339185521006584,
0.08856968581676483,
0.010307913646101952,
-0.017430879175662994,
0.007147021126002073,
-0.02474362589418888,
-0.11330601572990417,
-0.014727357774972916,
0.028028203174471855,
0.028001757338643074,
-0.01032325066626072,
0.045821432024240494,
-0.010295380838215351,
-0.002376860473304987,
-0.0006073393160477281,
-0.004078555852174759,
0.010595754720270634,
-0.0486501045525074,
-0.13517238199710846,
-0.05342485010623932,
0.013614172115921974,
-0.028493337333202362,
-0.023462651297450066,
-0.05516219511628151,
0.0017335155280306935,
0.019467659294605255,
0.061072368174791336,
-0.029551342129707336,
-0.016208205372095108,
-0.016540443524718285,
0.012831619940698147,
0.012072023935616016,
-0.01034867949783802,
0.01695636659860611,
-0.01564709097146988,
-0.03295024484395981,
-0.009100494906306267,
-0.06022361293435097,
0.029403185471892357,
0.04720339551568031,
-0.01711815968155861,
0.00694944616407156,
0.026725076138973236,
-0.024608375504612923,
0.01599705219268799,
0.03478338196873665,
-0.036871857941150665,
-0.022782614454627037,
0.06747186183929443,
0.024613002315163612,
0.014412453398108482,
0.01626887358725071,
-0.013025492429733276,
0.030930623412132263,
0.0029957015067338943,
0.048919469118118286,
0.04193396866321564,
-0.048157889395952225,
-0.06620987504720688,
-0.01949162408709526,
0.03968245908617973,
-0.02687199041247368,
-0.03966623172163963,
-0.015536206774413586,
0.026272714138031006,
0.03335816413164139,
-0.034094180911779404,
0.042383451014757156,
-0.024867700412869453,
0.002842283109202981,
-0.0018532243557274342,
-0.03992226719856262,
-0.010390523821115494,
-0.08347051590681076,
0.03302409127354622,
0.0036075483076274395,
-0.022314216941595078,
0.027956990525126457,
0.01718968152999878,
-0.0029373313300311565,
-0.020828956738114357,
-0.06616539508104324,
0.0007082956144586205,
0.033006370067596436,
0.011531855911016464,
-0.016242723912000656,
0.029190892353653908,
0.046977341175079346,
-0.033027853816747665,
-0.02059875801205635,
0.05823080986738205,
0.0011742000933736563,
-0.013851993717253208,
-0.00043408130295574665,
-0.018425332382321358,
0.03040458634495735,
-0.021456299349665642,
-0.012086746282875538,
-0.0025092223659157753,
-0.0004456124152056873,
0.001200882368721068,
0.034795913845300674,
-0.036091554909944534,
0.09450891613960266,
0.007830704562366009,
0.018532779067754745,
-0.016242459416389465,
0.013771898113191128,
0.004167853854596615,
0.02543051913380623,
-0.007143627852201462,
-0.031131040304899216,
-0.010491900146007538,
0.0014357261825352907,
0.04175138846039772,
0.016954921185970306,
-0.03991732746362686,
0.009876901283860207,
0.0035120348911732435,
0.03461483120918274,
-0.0038025302346795797,
0.0059875682927668095,
-0.029020758345723152,
-0.018442267552018166,
0.010170579887926579,
0.01138745341449976,
-0.022460471838712692,
0.02739342860877514,
0.023939907550811768,
-0.01487355399876833,
0.0038532796315848827,
0.0022159891668707132,
-0.03998422622680664,
0.07964449375867844,
-0.01712883450090885,
-0.008911012671887875,
0.008058907464146614,
-0.07840640842914581,
0.03253483027219772,
0.002125886967405677,
0.08241068571805954,
0.0042669931426644325,
-0.02005169726908207,
0.002132205758243799,
-0.006350304465740919,
-0.0030432010535150766,
-0.014841808937489986,
0.00014729806571267545,
-0.04234396666288376,
0.02405705489218235,
0.02979060262441635,
-0.02502063661813736,
0.013401634991168976,
-0.013633093796670437,
-0.00036072562215849757,
-0.003982592839747667,
-0.01774301938712597,
0.07646166533231735,
0.02408832125365734,
0.01798299141228199,
-0.014410843141376972,
-0.013447105884552002,
0.039077501744031906,
-0.03200419992208481,
0.023609377443790436,
0.017023252323269844,
-0.04282429814338684,
-0.0026022528763860464,
-0.03969138488173485,
-0.04330679774284363,
-0.008353037759661674,
-0.005198377184569836,
0.01417576428502798,
0.009622781537473202,
-0.04449162259697914,
-0.026985835283994675,
-0.015532109886407852,
-0.029872016981244087,
0.03315124660730362,
-0.0034523357171565294,
0.02417764998972416,
0.01740174926817417,
0.028837360441684723,
-0.012312418781220913,
0.0014309766702353954,
-0.048034634441137314,
-0.03319801762700081,
-0.014263625256717205,
0.002245076699182391,
0.01630866527557373,
-0.029851412400603294,
0.03250807523727417,
0.08178588002920151,
-0.04511963948607445,
-0.013178633525967598,
-0.04781638830900192,
-0.01565604843199253,
0.027742262929677963,
0.01706458255648613,
0.009497196413576603,
-0.004273067694157362,
-0.03952557593584061,
0.0872749388217926,
0.02678828500211239,
-0.04501068592071533,
0.008411809802055359,
-0.013615083880722523,
0.01176281925290823,
-0.06387906521558762,
-0.010731203481554985,
0.0027675721794366837,
0.025055376812815666,
0.0070627001114189625,
0.018550600856542587,
0.06642364710569382,
-0.013181952759623528,
-0.0040515512228012085,
-0.028988201171159744,
-0.009897514246404171,
-0.014447066001594067,
-0.005880321376025677,
0.016246845945715904,
0.04595727100968361,
-0.03381730616092682,
-0.0050246333703398705,
0.03587440401315689,
0.028699273243546486,
-0.01403232291340828,
-0.02132825180888176,
0.05805990844964981,
0.04423321411013603,
0.033179230988025665,
-0.025133784860372543,
0.04207151010632515,
-0.02196800522506237,
-0.003890950232744217,
0.054885607212781906,
0.004069836810231209,
0.020426146686077118,
-0.03529021516442299,
-0.01721455343067646,
0.0413723886013031,
0.03535177931189537,
-0.023310713469982147,
-0.017811384052038193,
-0.022212011739611626,
-0.03104594722390175,
0.025902295485138893,
0.00014938043022993952,
-0.02462957426905632,
0.03596946597099304,
0.045109499245882034,
0.04491202533245087,
-0.019984345883131027,
-0.045251138508319855,
0.017565347254276276,
-0.06934668123722076,
0.013166810385882854,
0.022490274161100388,
0.012301088310778141,
0.0351792573928833,
0.05307932198047638,
0.005806713830679655,
0.0029769728425890207,
0.008080909959971905,
0.005087520927190781,
-0.0665128156542778,
0.003977211657911539,
-0.037882693111896515,
-0.019452793523669243,
-0.0167252104729414,
-0.009497624821960926,
-0.023898424580693245,
-0.027014536783099174,
-0.057026661932468414,
-0.0261886864900589,
-0.002781471237540245,
-0.025053558871150017,
0.014019581489264965,
-0.020957786589860916,
0.0010899591725319624,
-0.028375251218676567,
0.027632061392068863,
0.027862854301929474,
-0.02673957124352455,
0.008857879787683487,
0.009424129500985146,
-0.030239976942539215,
-0.03365868702530861,
-0.0030930417124181986,
0.039617232978343964,
0.0099509721621871,
0.039128467440605164,
0.037951309233903885,
0.045150671154260635,
-0.03289739787578583,
-0.01779281534254551,
0.017262842506170273,
0.055617984384298325,
0.023341583088040352,
-0.04125667363405228,
0.0056051230058074,
-0.04978834092617035,
0.007732501719146967,
-0.013538450933992863,
0.042255204170942307,
0.009325011633336544,
0.012569897808134556,
0.0015840459382161498,
-0.004046901594847441,
-0.03331206738948822,
0.03128894791007042,
0.07276877015829086,
0.039395738393068314,
-0.025430772453546524,
-0.04676396772265434,
0.0031543304212391376,
0.00443499768152833,
0.00943254865705967,
-0.0015116260619834065,
-0.013964738696813583,
-0.0005522636347450316,
-0.002969086403027177,
0.0028977752663195133,
0.017929060384631157,
-0.017877917736768723,
0.032455481588840485,
0.003237531054764986,
0.0013809144729748368,
-0.01902286894619465,
0.01580468937754631,
0.024101534858345985,
0.0348794162273407,
0.015284035354852676,
0.03702094033360481,
-0.028635414317250252,
-0.07760555297136307,
0.01794714666903019,
0.025493770837783813,
0.061389222741127014,
0.004465767648071051,
-0.02870132587850094,
-0.0308018010109663,
0.0125102698802948,
0.0441785603761673,
-0.038087934255599976,
0.009810347110033035,
-0.021539269015192986,
-0.02450942061841488,
0.002290218835696578,
0.026271725073456764,
-0.022769203409552574,
0.033428821712732315,
-0.015899168327450752,
0.0213595163077116,
-0.01985371671617031,
-0.025554930791258812,
-0.004616092890501022,
0.007055757567286491,
-0.01496016327291727,
0.014826048165559769,
0.011587973684072495,
0.04348411783576012,
-0.006796639878302813,
0.05864548683166504,
0.009028700180351734,
-0.11012919247150421,
-0.0015706679550930858,
-0.0020369288977235556,
-0.003556086216121912,
0.07735789567232132,
-0.05769490450620651,
-0.05383634939789772,
0.008171526715159416,
0.021851446479558945,
-0.015383529476821423,
-0.02315400168299675,
-0.06738726794719696,
0.019256411120295525,
0.005197574384510517,
-0.006103298161178827,
0.02898738719522953,
0.03387635201215744,
-0.026006251573562622,
-0.0465877540409565,
-0.03928002342581749,
0.03624534606933594,
-0.04500638693571091,
0.025773989036679268,
-0.032874833792448044,
-0.004963757004588842,
-0.009759804233908653,
0.02591855265200138,
-0.019395263865590096,
0.04509920999407768,
0.0008255501743406057,
-0.037874385714530945,
-0.05224250257015228,
-0.029995737597346306,
-0.009212383069097996,
-0.017285097390413284,
-0.016415245831012726,
-0.005461558233946562,
-0.0014889240264892578,
-0.0059183682315051556,
-0.008130216971039772,
-0.02201070636510849,
0.01699015125632286,
0.01489329431205988,
-0.0032332618720829487,
0.0041734748519957066,
0.0035394609440118074,
-0.010369375348091125,
0.010431801900267601,
-0.011437374167144299,
0.04106195271015167,
-0.017515338957309723,
0.0016331328079104424,
0.014374061487615108,
-0.07568395882844925,
-0.028377220034599304,
0.031422290951013565,
-0.032794054597616196,
0.03157016634941101,
-0.04110824316740036,
0.03602764382958412,
0.00042410785681568086,
0.025452563539147377,
-0.039997369050979614,
-0.03787640482187271,
0.04691895470023155,
0.019194221124053,
-0.029081931337714195,
0.005559764336794615,
-0.022349903360009193,
0.012008762918412685,
-0.049116022884845734,
0.0010644779540598392,
0.07594779133796692,
-0.04777787998318672,
-0.03049096092581749,
0.026464637368917465,
0.03705771267414093,
0.03392422944307327,
-0.007169458549469709,
-0.04218646511435509,
0.006137087941169739,
0.0001917901827255264,
-0.0034244845155626535,
-0.01975042000412941,
0.04516623541712761,
-0.015326756983995438,
-0.020979801192879677,
-0.0044655040837824345,
0.013726172037422657,
0.016025768592953682,
-0.039283979684114456,
-0.008908712305128574,
0.004481308162212372,
-0.0038915888871997595,
-0.0036536813713610172,
-0.009142223745584488,
0.004941157530993223,
0.010969151742756367,
0.018375836312770844,
0.005306164268404245,
-0.005760360974818468,
-0.026913266628980637,
-0.03327690064907074,
0.039445869624614716,
-0.007898179814219475,
-0.02515828050673008,
-0.006972512695938349,
0.04165671393275261,
0.005160969216376543,
-0.024945607408881187,
0.016344305127859116,
-0.045400477945804596,
-0.0033175807911902666,
0.0328981876373291,
0.022629501298069954,
-0.0007480655331164598,
0.0034478413872420788,
-0.0044974954798817635,
-0.001132256118580699,
-0.01696101389825344,
0.03492559865117073,
0.08017630875110626,
-0.007436739280819893,
0.04064809903502464,
0.02333184704184532,
0.023258203640580177,
-0.05506051331758499,
-0.0031906794756650925,
-0.05561327561736107,
0.008611196652054787,
0.01723933033645153,
0.04237987473607063,
-0.022991884499788284,
0.021033192053437233,
0.00855813454836607,
0.0628814697265625,
-0.015287871472537518,
0.004145256243646145,
0.038253650069236755,
0.015391053631901741,
0.009609847329556942,
0.004115286283195019,
-0.0647202581167221,
0.04729451984167099,
-0.013938399963080883,
0.01052404660731554,
0.025945540517568588,
-0.04290875419974327,
0.03634306788444519,
-0.02028793841600418,
0.051782503724098206,
-0.023112228140234947,
-0.013312873430550098,
-0.059934865683317184,
0.029385404661297798,
0.025496594607830048,
-0.007064401637762785,
-0.02853393740952015,
0.007364643272012472,
0.02774401567876339,
0.02602805197238922,
0.023186739534139633,
0.019754908978939056,
-0.08478516340255737,
-0.04622756689786911,
-0.03331509977579117,
-0.010953248478472233,
0.02794799767434597,
-0.010195782408118248,
-0.027346458286046982,
0.012453419156372547,
0.006996824871748686,
0.05292082577943802,
0.0024180724285542965,
0.053728483617305756,
-0.04579777270555496,
0.05749668553471565,
0.01012472901493311,
0.01935340091586113,
0.0024093068204820156,
-0.002818870125338435,
0.10003601014614105,
0.04788162186741829,
0.03845842182636261,
-0.05556369200348854,
0.0037392459344118834,
-0.02346612885594368,
0.020343195647001266,
-0.004052978474646807,
0.06415706127882004,
0.007012134417891502,
0.028845151886343956,
-0.0005819996003992856,
0.02979949489235878,
0.028157049790024757,
-0.009956727735698223,
0.07370635122060776,
-0.02830681763589382,
-0.056872960180044174,
-0.0153098925948143,
0.05524371564388275,
0.003943067509680986,
-0.0087191853672266,
-0.07326272130012512,
0.014204281382262707,
0.02896704711019993,
0.01763555407524109,
-0.028941504657268524,
-0.015668118372559547,
0.02331276424229145,
0.012261718511581421,
-0.027850933372974396,
-0.02562761679291725,
-0.023879924789071083,
-0.010685715824365616,
-0.07661839574575424,
0.022832883521914482,
0.03296075761318207,
-0.014113922603428364,
-0.00010146191925741732,
0.00675191218033433,
0.02585032396018505,
-0.012432483956217766,
0.012270724400877953,
0.03143824264407158,
-0.0361778661608696,
0.009320714510977268,
0.011661170981824398,
0.053774140775203705,
-0.02087431773543358,
-0.04059400036931038,
-0.028110893443226814,
0.025303207337856293,
0.005402801558375359,
-0.06443753093481064,
-0.019449807703495026,
-0.012785721570253372,
-0.011035395786166191,
-0.037695396691560745,
-0.007343077566474676,
-0.005924894940108061,
0.012204108759760857,
-0.0468989759683609,
0.020629622042179108,
-0.015510587953031063,
0.017307467758655548,
0.0046151732094585896,
0.0031473045237362385,
0.019013958051800728,
0.008351409807801247,
-0.01742856577038765,
-0.014673789963126183,
-0.0031103044748306274,
-0.057384055107831955,
-0.01601356454193592,
0.04416197910904884,
0.04103744402527809,
0.05358466878533363,
0.0026447789277881384,
-0.03276173397898674,
0.006316237151622772,
-0.028370562940835953,
0.08066198974847794,
-0.011249572038650513,
-0.011077145114541054,
0.005649504717439413,
0.03434421122074127,
0.031169917434453964,
0.043131474405527115,
-0.007407469674944878,
-0.01112760603427887,
0.006305486895143986,
0.004416090901941061,
0.008362175896763802,
-0.015628578141331673,
-0.02950555458664894,
0.037485938519239426,
-0.03805394843220711,
-0.020058443769812584,
-0.002576642669737339,
-0.0024792018812149763,
0.037745047360658646,
0.0074958037585020065,
-0.005797634832561016,
0.017560604959726334,
-0.005124125629663467,
0.00006524129275931045,
0.035838935524225235,
-0.036858074367046356,
0.012076745741069317,
-0.005144089460372925,
-0.013395821675658226,
-0.05712267383933067,
-0.018740244209766388,
0.0008196940761990845,
-0.0040757604874670506,
0.03025512583553791,
0.004199536517262459,
-0.00870431773364544,
-0.0320780910551548,
-0.04375504329800606,
0.022573435679078102,
0.005740025546401739,
-0.013143263757228851,
-0.04853073135018349,
0.017715254798531532,
-0.03153803199529648,
0.023171326145529747,
-0.005263817496597767,
0.013619688339531422,
-0.0008042420377023518,
-0.018317870795726776,
0.027591831982135773,
0.018900344148278236,
-0.03366164490580559,
0.012823470868170261,
0.054957907646894455,
-0.014012891799211502,
0.01688164658844471,
-0.0010439769830554724,
-0.03651290386915207,
0.020914219319820404,
-0.06278631836175919,
-0.07407611608505249,
-0.012593949213624,
-0.01664702035486698,
0.018667137250304222,
0.03868069127202034,
-0.01983937993645668,
-0.04120226204395294,
0.0663481280207634,
-0.018793612718582153,
-0.013142929412424564,
0.02592727355659008,
-0.0035521520767360926,
-0.010871774516999722,
-0.013564903289079666,
-0.06254493445158005,
-0.004068007227033377,
-0.02092830464243889,
0.057568542659282684,
0.0009830872295424342,
-0.0319778136909008,
0.011872400529682636,
-0.0400884747505188,
0.036987774074077606,
-0.003448782255873084,
0.027635300531983376,
0.01727805845439434,
-0.03543910011649132,
0.02860882133245468,
-0.021925335749983788,
0.04042012244462967,
0.0060275462456047535,
0.019672097638249397,
-0.1005815789103508,
-0.012702717445790768,
0.003781053703278303,
-0.014685718342661858,
0.04169444739818573,
-0.024470968171954155,
0.03344915434718132,
0.0446593351662159,
-0.07380112260580063,
0.04267342388629913,
-0.015616494230926037,
-0.03393501415848732,
-0.004882597830146551,
-0.009246626868844032,
-0.028964897617697716,
0.07485692948102951,
0.01945509947836399,
0.018706131726503372,
0.03518562763929367,
0.01681648939847946,
-0.023815056309103966,
0.0010830078972503543,
-0.03328440710902214,
0.017033075913786888,
-0.011458303779363632,
-0.03759116679430008,
0.03751460090279579,
-0.024198826402425766,
-0.02063382975757122,
0.04934662953019142,
-0.02497944049537182,
-0.01700400374829769,
-0.010901122353971004,
0.04424118623137474,
0.019903430715203285,
0.02542215585708618,
-0.00920911505818367,
-0.01690131053328514,
-0.026880014687776566,
-0.003070451784878969,
0.022348521277308464,
0.032802555710077286,
-0.004697734024375677,
0.018500709906220436,
0.0007760346052236855,
-0.021707620471715927,
-0.023198982700705528,
0.016721416264772415,
-0.039586443454027176,
0.008372688665986061,
-0.016584213823080063,
-0.009520229883491993,
0.010045995935797691,
-0.03802896663546562,
0.01471282821148634,
-0.05219006538391113,
0.016816038638353348,
0.004157810937613249,
-0.013520734384655952,
0.014861849136650562,
0.02204439789056778,
-0.02373356558382511,
-0.00518064945936203,
0.03483182191848755,
-0.017883608117699623,
-0.013450326398015022,
-0.03884879872202873,
0.014403842389583588,
0.028730234131217003,
0.013326154090464115,
0.030644839629530907,
-0.05837506055831909,
-0.042777664959430695,
0.007562761660665274,
-0.015222609043121338,
0.00486754858866334,
-0.009278494864702225,
-0.02996170148253441,
-0.01753273233771324,
-0.0557551346719265,
0.0349486768245697,
0.021759778261184692,
0.020198041573166847,
-0.05106273293495178,
-0.03063705936074257,
-0.038505785167217255,
0.0454893596470356,
0.0342220775783062,
-0.002054276643320918,
0.012416869401931763,
-0.009035333059728146,
0.026697855442762375,
0.020664038136601448,
-0.00376267172396183,
-0.008740928024053574,
0.009397308342158794,
-0.01342142652720213,
-0.007561052683740854,
-0.026498442515730858,
-0.035776566714048386,
-0.0010019387118518353,
0.03179745003581047,
0.020455019548535347,
-0.0060136509127914906,
0.003693080274388194,
-0.05693165212869644,
0.05038972944021225,
-0.0039036443922668695,
0.00833197496831417,
0.07841765135526657,
0.016421925276517868,
-0.0010801602620631456,
0.014201630838215351,
-0.029087534174323082,
-0.03835611790418625,
0.001073020393960178,
-0.025917258113622665,
-0.002319218125194311,
-0.03201659396290779,
-0.016036171466112137,
0.05031723529100418,
-0.013617470860481262,
0.03966279327869415,
0.030369864776730537,
-0.04633422568440437,
0.003444237168878317,
0.03404219448566437,
0.011540759354829788,
0.01943538524210453,
0.0016918295295909047,
-0.0049660843797028065,
0.009448413737118244,
-0.0116023113951087,
0.03237668797373772,
0.08485514670610428,
0.006937201600521803,
0.039746351540088654,
0.010726172477006912,
0.0209355428814888,
-0.0005808484856970608,
0.007531958166509867,
0.04169338196516037,
0.022379279136657715,
-0.029075028374791145,
-0.01652541197836399,
0.01883830688893795,
-0.009157293476164341,
0.033956002444028854,
0.0335773304104805,
-0.021693598479032516,
0.05702688917517662,
-0.05218878015875816,
0.010417364537715912,
-0.03214627876877785,
0.006556354463100433,
-0.010494847781956196,
0.0057390471920371056,
0.011611782014369965,
0.061961203813552856,
-0.021330412477254868,
-0.04128333926200867,
0.008290520869195461,
-0.01475002896040678,
0.06405041366815567,
-0.04374406859278679,
0.019939027726650238,
0.019890107214450836,
0.0035084192641079426,
-0.023399215191602707,
-0.015562278218567371,
-0.0020014839246869087,
0.007573132403194904,
0.018705110996961594,
0.022897204384207726,
0.025607118383049965,
-0.018427202478051186,
-0.01523813046514988,
-0.0362866148352623,
0.044966571033000946,
-0.03704550117254257,
-0.013371146284043789,
-0.022822748869657516,
0.01057745236903429,
-0.02680855430662632,
-0.01283948589116335
] |
<p>Approaching the speed of sound in an aircraft is relatively difficult, because the closer you get to Mach 1, the denser the pressure is around you (sound accumulates causing vibrations).</p>
<p>Is there a similar effect as you approach the speed of light? Does the Doppler Effect apply for light as it does with sound? Will light accumulate around your aircraft causing heat? </p>
<p>Speaking strictly hypothetical.</p> | 1,525 | [
-0.005947290454059839,
-0.07561782002449036,
0.00012335568317212164,
-0.003376383101567626,
0.049685508012771606,
0.045575689524412155,
-0.037410713732242584,
-0.04845375567674637,
-0.015712879598140717,
-0.028775732964277267,
0.021471207961440086,
0.05182015150785446,
0.03488459438085556,
-0.010101117193698883,
0.009331770241260529,
0.002254678402096033,
0.005495406221598387,
-0.013903672806918621,
-0.0013525956310331821,
-0.0152962701395154,
-0.007356974296271801,
0.012442356906831264,
0.026824425905942917,
0.005983432289212942,
-0.025465581566095352,
0.03887973725795746,
-0.014877078123390675,
-0.012370292097330093,
0.010998711921274662,
-0.000851333315949887,
0.024310672655701637,
0.015884798020124435,
0.01953291706740856,
0.053724318742752075,
0.02582201361656189,
0.013494284823536873,
-0.043028369545936584,
0.004152136854827404,
-0.0030586784705519676,
-0.02321874164044857,
-0.01927841268479824,
-0.031561605632305145,
0.008045830763876438,
0.0013881721533834934,
-0.013159486465156078,
-0.013163737952709198,
-0.0005024744896218181,
-0.031325481832027435,
0.04493321478366852,
-0.0665128082036972,
0.04980991408228874,
-0.0003959528112318367,
0.005563503131270409,
0.028486579656600952,
0.012821920216083527,
0.010766253806650639,
0.08443473279476166,
0.07530146837234497,
0.0033226043451577425,
-0.028556985780596733,
0.014291973784565926,
0.0339868888258934,
-0.01266554370522499,
-0.019607895985245705,
-0.0025126244872808456,
0.035485900938510895,
-0.048772163689136505,
-0.02163749188184738,
0.009759118780493736,
0.0030561587773263454,
-0.011210940778255463,
0.017363570630550385,
0.02962592989206314,
-0.004795092158019543,
0.015510673634707928,
-0.03819398209452629,
-0.009567108005285263,
0.008434525690972805,
0.05717669427394867,
0.05534674972295761,
-0.015630384907126427,
0.012506410479545593,
0.022456755861639977,
0.00894245132803917,
0.016980452463030815,
0.0028225588612258434,
0.06773253530263901,
-0.0051327478140592575,
-0.0034532989375293255,
0.047126635909080505,
0.014792008325457573,
0.031807512044906616,
-0.005209683906286955,
0.02192041277885437,
0.001886154292151332,
0.00481728371232748,
-0.04221868887543678,
0.05772892013192177,
0.021070973947644234,
-0.03937783092260361,
-0.003969437442719936,
0.03753404691815376,
0.05647413060069084,
0.0439278818666935,
0.006581326015293598,
-0.036915067583322525,
-0.04287151247262955,
0.014568652026355267,
-0.0013174437917768955,
-0.04475292190909386,
-0.059804290533065796,
0.01785239763557911,
0.011402232572436333,
-0.019594714045524597,
-0.00228317198343575,
-0.030098682269454002,
0.022662926465272903,
-0.021415269002318382,
0.06126390025019646,
0.062020838260650635,
0.03683043643832207,
-0.01238276157528162,
0.026488913223147392,
0.0001917821355164051,
-0.010756080970168114,
0.009654129855334759,
0.035536251962184906,
-0.05742202699184418,
-0.02130560204386711,
0.032977405935525894,
-0.05246859788894653,
-0.0327153354883194,
-0.004071479197591543,
-0.019242912530899048,
0.002065153094008565,
-0.019490255042910576,
-0.08525475859642029,
-0.06074848026037216,
0.04106930270791054,
-0.009656778536736965,
-0.053910769522190094,
-0.057199545204639435,
-0.0010018005268648267,
0.02342441864311695,
0.09625166654586792,
-0.011558959260582924,
0.004998408257961273,
-0.01361755933612585,
0.04768639802932739,
0.010166631080210209,
-0.032999422401189804,
-0.030413933098316193,
-0.0004754515830427408,
-0.03476483374834061,
0.0024282929953187704,
-0.06923139095306396,
-0.012485358864068985,
0.040032852441072464,
-0.014429617673158646,
-0.03881632164120674,
0.02858915366232395,
-0.0332815945148468,
0.004249164368957281,
-0.00015586926019750535,
-0.002729223109781742,
-0.02962261252105236,
0.09787943214178085,
0.04219628870487213,
-0.014355388469994068,
0.024635687470436096,
0.05092548951506615,
0.01723458617925644,
-0.027774084359407425,
-0.007661436218768358,
0.05215299129486084,
-0.04544716328382492,
0.023967687040567398,
-0.0028869006782770157,
0.015227708965539932,
0.008536807261407375,
-0.018405096605420113,
-0.033767614513635635,
-0.009636095724999905,
-0.018269268795847893,
0.015567757189273834,
0.06222290173172951,
0.008417206816375256,
0.012243164703249931,
0.007479244377464056,
-0.03134874999523163,
-0.008263272233307362,
-0.059039998799562454,
0.028156599029898643,
0.01322334073483944,
-0.005159339401870966,
-0.0047024632804095745,
0.016574561595916748,
0.05494073033332825,
-0.03065378963947296,
-0.020565753802657127,
0.009555554017424583,
0.02717677876353264,
0.03437002748250961,
-0.006953587289899588,
0.0067195771262049675,
0.06222400441765785,
0.020164530724287033,
-0.004146905615925789,
-0.025250839069485664,
-0.020884500816464424,
-0.04381987079977989,
0.01485402137041092,
-0.02579536847770214,
0.04123971238732338,
-0.003070623381063342,
0.03145741671323776,
0.027147531509399414,
-0.01496176514774561,
-0.00986393541097641,
0.006110047921538353,
0.0017489501042291522,
0.04225680232048035,
0.025040486827492714,
-0.0100620212033391,
0.00912774819880724,
0.04158589616417885,
0.01606982760131359,
-0.01696961373090744,
0.010255664587020874,
-0.012549013830721378,
-0.03328613564372063,
-0.007943292148411274,
0.04596587270498276,
0.005368223413825035,
-0.06900884956121445,
0.02111433446407318,
0.02812621183693409,
0.021181097254157066,
0.038346074521541595,
0.03847096115350723,
-0.015333929099142551,
-0.037070464342832565,
0.01744990609586239,
0.017025742679834366,
0.017925018444657326,
0.006614949554204941,
0.018913840875029564,
-0.0023542894050478935,
-0.007336749229580164,
-0.01775289513170719,
-0.04207676276564598,
0.027460144832730293,
0.007655021268874407,
0.0004429898108355701,
-0.014921686612069607,
-0.025063056498765945,
0.02875003218650818,
-0.014873692765831947,
-0.007713363505899906,
0.006133509334176779,
-0.00538975652307272,
-0.026251625269651413,
0.00410029711201787,
0.005543616134673357,
-0.03745372220873833,
0.01193156186491251,
-0.0014138881815597415,
0.004543549381196499,
0.04041413962841034,
-0.09023705869913101,
0.04022156447172165,
-0.04119515046477318,
0.027685292065143585,
-0.0395219624042511,
-0.02062584087252617,
0.010498263873159885,
-0.019279399886727333,
0.029964542016386986,
-0.029964808374643326,
-0.03726355731487274,
0.014966833405196667,
-0.03872629627585411,
-0.03053990751504898,
0.005165215115994215,
-0.022631578147411346,
0.030683116987347603,
-0.03012331947684288,
-0.04366142302751541,
0.028875812888145447,
-0.0249840896576643,
0.004494066350162029,
0.04415800794959068,
-0.041589874774217606,
-0.09262867271900177,
-0.011233249679207802,
-0.03572128340601921,
-0.03771945461630821,
-0.025113729760050774,
0.01119455136358738,
0.041986074298620224,
0.004671262111514807,
-0.02632305398583412,
0.006905591115355492,
-0.04314560443162918,
-0.01710440032184124,
-0.038228217512369156,
-0.0029172867070883512,
0.00023327064991462976,
-0.036570485681295395,
0.0294579416513443,
0.002036278834566474,
-0.06637529283761978,
0.03390625864267349,
-0.02387971431016922,
-0.014268746599555016,
0.08453019708395004,
0.03680843859910965,
0.04613169655203819,
0.004145332146435976,
-0.022183554247021675,
0.024074437096714973,
0.03683833032846451,
-0.020254801958799362,
-0.03550640121102333,
-0.0023396972101181746,
-0.00018913713574875146,
0.00363339576870203,
-0.008581077679991722,
0.05003926157951355,
-0.029257439076900482,
-0.03216155990958214,
0.013977992348372936,
0.009843461215496063,
0.029167043045163155,
0.019094467163085938,
-0.0031124078668653965,
-0.014639370143413544,
-0.02950829640030861,
0.04505692422389984,
0.03470305725932121,
0.049348343163728714,
-0.005593719892203808,
0.021964315325021744,
-0.022114628925919533,
0.032651882618665695,
0.04324094578623772,
-0.02132069319486618,
0.03648577630519867,
0.028930023312568665,
0.0006737348157912493,
-0.055000923573970795,
0.054808109998703,
0.021411502733826637,
0.025134535506367683,
-0.02508390136063099,
0.029653027653694153,
0.01711719110608101,
0.02994021773338318,
-0.02436058782041073,
0.02730220928788185,
0.06918550282716751,
-0.0004520445945672691,
-0.029471833258867264,
0.0004404306528158486,
-0.004515815060585737,
0.03020494058728218,
-0.003663242794573307,
0.007335526868700981,
0.04833110794425011,
0.017549535259604454,
0.008540879003703594,
0.033514682203531265,
-0.02073741890490055,
0.017713181674480438,
-0.0735883042216301,
-0.02955012209713459,
-0.02620752528309822,
0.06089194491505623,
0.013010920025408268,
0.06363315880298615,
-0.016809022054076195,
0.012613550759851933,
0.05159524083137512,
-0.007648283615708351,
-0.1180911436676979,
0.01500678714364767,
-0.034112073481082916,
-0.0411246195435524,
-0.025010447949171066,
-0.003791593946516514,
-0.04440702870488167,
-0.04577093943953514,
-0.0032095799688249826,
-0.011356021277606487,
-0.015203002840280533,
-0.04422728344798088,
0.049817416816949844,
-0.020235037431120872,
-0.05113331973552704,
-0.006663566455245018,
0.025471264496445656,
0.0496346578001976,
-0.016124160960316658,
0.04670075699687004,
0.05395422875881195,
-0.033122044056653976,
-0.029190918430685997,
-0.007314408663660288,
-0.0014312600251287222,
-0.014216338284313679,
0.05476980656385422,
0.031719062477350235,
0.014521623030304909,
-0.02142234705388546,
0.02419024333357811,
-0.006669817958027124,
0.0077629052102565765,
-0.006867615506052971,
0.009766273200511932,
-0.04451169818639755,
-0.004017317667603493,
-0.00443178741261363,
0.018872426822781563,
0.020585980266332626,
-0.052314434200525284,
0.01932704448699951,
-0.012874387204647064,
-0.006199497263878584,
0.0035584871657192707,
0.04558279737830162,
0.01662488281726837,
0.015166847966611385,
0.0005035722861066461,
-0.043603699654340744,
0.019210560247302055,
-0.023433532565832138,
-0.02050289884209633,
0.004714404232800007,
0.009009924717247486,
0.00009957346628652886,
0.025989048182964325,
0.00736682815477252,
0.012526403181254864,
-0.017706256359815598,
-0.008328819647431374,
0.028763044625520706,
-0.007336344104260206,
0.03020617924630642,
0.0053493366576731205,
-0.026278307661414146,
0.02952299825847149,
0.02308468148112297,
-0.024045413359999657,
0.00950529146939516,
-0.1153416857123375,
-0.01085490919649601,
0.012872954830527306,
0.054521504789590836,
-0.010845989920198917,
0.043635036796331406,
-0.02352982759475708,
-0.032415807247161865,
0.03441690281033516,
0.012407438829541206,
0.010635622777044773,
-0.02603909745812416,
-0.025044014677405357,
-0.042218808084726334,
-0.03630346432328224,
-0.020809989422559738,
0.0453576035797596,
-0.005940360017120838,
-0.022761434316635132,
-0.006801701616495848,
0.006306405644863844,
0.004620017949491739,
0.019172484055161476,
0.05586240440607071,
0.03163796290755272,
-0.014129264280200005,
0.005336268804967403,
-0.0038842118810862303,
-0.0037311420310288668,
-0.007196496240794659,
-0.04206700995564461,
0.008564257062971592,
0.02771594375371933,
-0.04623031988739967,
0.04508214443922043,
-0.02582477778196335,
-0.0062612551264464855,
0.053599972277879715,
0.02094119042158127,
-0.02683948539197445,
-0.03847396373748779,
-0.04207945242524147,
0.02998928539454937,
-0.012026024051010609,
-0.022229155525565147,
-0.00039904945879243314,
0.042088933289051056,
-0.006278405897319317,
-0.0031030892860144377,
0.03665105998516083,
0.053568318486213684,
-0.03201139345765114,
-0.004752136766910553,
0.020991915836930275,
-0.04086805507540703,
-0.0329761803150177,
0.053072355687618256,
-0.0250715259462595,
-0.00015743427502457052,
0.012944340705871582,
-0.023892834782600403,
0.0013982041273266077,
0.01868518441915512,
0.0025176643393933773,
0.02150869555771351,
-0.05442015081644058,
0.017250636592507362,
0.0053289299830794334,
-0.03235394507646561,
0.017566664144396782,
0.027218397706747055,
0.011485306546092033,
0.036825813353061676,
-0.016221117228269577,
0.019976602867245674,
-0.02821730077266693,
0.0068127308040857315,
0.016280289739370346,
-0.04866158589720726,
0.061310894787311554,
0.00009322288678959012,
0.009252073243260384,
0.044227153062820435,
-0.03080768696963787,
0.011685322038829327,
0.04226053133606911,
-0.0253687035292387,
0.022157592698931694,
-0.04030008614063263,
0.023205535486340523,
0.0018124956404790282,
-0.010488529689610004,
-0.031666941940784454,
-0.02873414382338524,
0.02750646322965622,
0.04595574364066124,
0.0028554422315210104,
-0.048373155295848846,
-0.0012733485782518983,
-0.0764622613787651,
-0.034615546464920044,
-0.01187411230057478,
-0.006860506720840931,
-0.012761496938765049,
-0.008066901937127113,
0.0003945367643609643,
-0.03137054294347763,
0.05183911696076393,
-0.0194392129778862,
-0.06855352967977524,
0.0260575283318758,
-0.005368450190871954,
-0.005800063256174326,
-0.04230840876698494,
0.045813433825969696,
-0.03162934631109238,
-0.0462099127471447,
-0.009441615082323551,
-0.013612322509288788,
0.02734277956187725,
-0.001661828369833529,
0.02036975510418415,
0.03286105766892433,
0.01019417867064476,
-0.0002708899264689535,
-0.032981134951114655,
0.0342235192656517,
0.009959415532648563,
0.01949252374470234,
0.008613926358520985,
0.0018347603036090732,
-0.0048572225496172905,
-0.029078692197799683,
0.04113737866282463,
0.04099288582801819,
0.023170527070760727,
-0.02062613144516945,
0.05697281286120415,
-0.009158325381577015,
-0.006164353806525469,
-0.0007004014914855361,
-0.015944842249155045,
0.007019876968115568,
-0.006790148559957743,
-0.0030574891716241837,
0.014047197066247463,
0.008245659060776234,
-0.014993210323154926,
-0.012374332174658775,
-0.016271818429231644,
-0.04985921084880829,
0.06628678739070892,
-0.0517435222864151,
0.04218525439500809,
-0.014423842541873455,
-0.019111433997750282,
0.007191619370132685,
-0.003195766592398286,
-0.012245488353073597,
-0.0075426907278597355,
-0.025578022003173828,
0.01803838461637497,
-0.004996766336262226,
-0.02442704327404499,
0.004418703727424145,
0.032179396599531174,
0.0338282585144043,
-0.010817290283739567,
0.02538452297449112,
0.022781329229474068,
0.02729787304997444,
-0.016041623428463936,
-0.008529530838131905,
0.0180612001568079,
-0.055280279368162155,
0.028848951682448387,
-0.0010371592361479998,
0.026171982288360596,
0.03988775983452797,
0.010319135151803493,
0.022267790511250496,
-0.04323834925889969,
-0.020062020048499107,
-0.02599245123565197,
0.02695525996387005,
-0.014517194591462612,
0.03676953539252281,
0.024313874542713165,
-0.008586643263697624,
0.03465210646390915,
0.012023880146443844,
0.008919735439121723,
0.03404098004102707,
-0.04119699448347092,
-0.07829472422599792,
-0.010218690149486065,
-0.02589961513876915,
0.06195610389113426,
0.01095255184918642,
-0.013792428188025951,
0.007925322279334068,
-0.03815896436572075,
0.02007880061864853,
0.0037823221646249294,
0.033405836671590805,
-0.006408587098121643,
0.041811488568782806,
0.015092155896127224,
0.029192857444286346,
-0.014932215213775635,
0.04651312530040741,
0.11170537024736404,
0.03843400627374649,
0.01935685984790325,
-0.04979029297828674,
0.021619386970996857,
-0.031680479645729065,
0.016672460362315178,
-0.06544094532728195,
-0.020012397319078445,
-0.019434629008173943,
0.012639107182621956,
0.038138967007398605,
0.052908770740032196,
-0.005485701374709606,
-0.010678744874894619,
0.026765326038002968,
-0.05712023749947548,
-0.005632030311971903,
0.0324443094432354,
0.0011613034876063466,
-0.021487891674041748,
0.0748734325170517,
-0.024116044864058495,
0.001740122213959694,
-0.05165667459368706,
-0.007213434670120478,
-0.019174600020051003,
-0.07662811875343323,
0.04042686149477959,
0.01778828352689743,
-0.057708073407411575,
-0.010927563533186913,
0.0487133152782917,
-0.03816978633403778,
-0.04469980299472809,
0.013857968151569366,
0.002188551239669323,
-0.007200915366411209,
0.014321529306471348,
0.013902035541832447,
0.014129417948424816,
0.02578284777700901,
-0.01740730181336403,
0.002646762179210782,
-0.03161071613430977,
0.0073792156763374805,
0.017008233815431595,
0.004805267788469791,
0.013032529503107071,
0.009480953216552734,
-0.005525419022887945,
0.024888549000024796,
-0.007589107844978571,
-0.07801774889230728,
-0.011801186017692089,
0.023920409381389618,
-0.002115878276526928,
0.00846567191183567,
-0.03982200101017952,
-0.02105049230158329,
0.021279973909258842,
0.04816059768199921,
0.011916449293494225,
-0.018656732514500618,
0.02310457080602646,
0.015616316348314285,
-0.02254178188741207,
0.034023892134428024,
-0.03962375223636627,
-0.018834678456187248,
-0.023084815591573715,
0.02092115581035614,
-0.08370757102966309,
-0.007004807237535715,
0.013942983001470566,
0.029807351529598236,
-0.00890020839869976,
0.046770572662353516,
-0.0063482727855443954,
-0.05209546536207199,
-0.09430168569087982,
0.032364342361688614,
0.005858407821506262,
-0.026570430025458336,
-0.019629202783107758,
-0.031970903277397156,
0.02398592047393322,
0.024445373564958572,
-0.016162848100066185,
-0.006320130079984665,
0.0009547296212986112,
0.09373901039361954,
0.014540405943989754,
0.012800033204257488,
-0.006447488907724619,
0.031017549335956573,
-0.00503499573096633,
0.026116210967302322,
-0.003198744263499975,
0.06550977379083633,
0.00877206027507782,
-0.01961859129369259,
-0.00801017601042986,
0.02300090342760086,
-0.013224462978541851,
-0.005844008177518845,
-0.008090426214039326,
-0.022893095389008522,
-0.008131110109388828,
-0.008583533577620983,
0.038084160536527634,
-0.01241388451308012,
-0.04770324006676674,
-0.02717616967856884,
-0.008970403112471104,
-0.04493091255426407,
-0.0035042203962802887,
0.01842525042593479,
0.05938875302672386,
-0.006434422917664051,
0.006270873825997114,
-0.024634450674057007,
0.002456407295539975,
-0.03031896986067295,
0.060084205120801926,
-0.02469191700220108,
-0.008709286339581013,
-0.0009573823190294206,
0.03843255341053009,
-0.06868133693933487,
-0.0027781662065535784,
0.019118204712867737,
0.01950487494468689,
0.03078889474272728,
0.011411619372665882,
0.002356630051508546,
-0.023022284731268883,
0.04891331493854523,
-0.033812470734119415,
-0.038939740508794785,
0.030875524505972862,
-0.030809268355369568,
-0.057938046753406525,
0.05752952769398689,
-0.008465196006000042,
0.03468872606754303,
0.03497964143753052,
0.02678496576845646,
-0.03592606261372566,
0.05990900471806526,
0.012814710848033428,
-0.007692068349570036,
0.01548987627029419,
-0.01569981873035431,
0.006535043474286795,
0.009710272774100304,
0.025635195896029472,
-0.020614447072148323,
-0.03183139115571976,
0.019167035818099976,
0.029985837638378143,
-0.03421449288725853,
0.033952757716178894,
-0.013654032722115517,
-0.053339362144470215,
-0.00022694111976306885,
-0.005836781580001116,
-0.00035202610888518393,
0.04256194084882736,
0.039318185299634933,
-0.021981962025165558,
0.03700258210301399,
0.021529441699385643,
-0.041108690202236176,
-0.15561968088150024,
0.00971792358905077,
0.015835806727409363,
0.0284550990909338,
0.012648947536945343,
-0.04149096831679344,
0.050186678767204285,
0.017645295709371567,
-0.07521975785493851,
0.024102162569761276,
-0.01652902364730835,
-0.016483379527926445,
-0.0650010034441948,
0.027052199468016624,
0.006272267550230026,
0.024756206199526787,
0.06223473697900772,
0.011893964372575283,
0.018210165202617645,
0.03854675963521004,
0.017013028264045715,
-0.0203530415892601,
0.03465588390827179,
0.015190036036074162,
-0.001958973705768585,
-0.003873570589348674,
0.02464771270751953,
-0.009116748347878456,
-0.017391882836818695,
0.0119539275765419,
0.02123047597706318,
0.03552747517824173,
-0.022247055545449257,
0.008746371604502201,
0.005010307300835848,
0.005311840679496527,
0.023578617721796036,
-0.0032821721397340298,
-0.015554552897810936,
0.06064924970269203,
0.00979742780327797,
-0.02043997123837471,
-0.049360573291778564,
-0.026224197819828987,
0.030435390770435333,
-0.030111163854599,
-0.021818313747644424,
0.07501652836799622,
0.0022651467006653547,
-0.01880909875035286,
0.0014839809155091643,
0.039753109216690063,
-0.010620526038110256,
-0.017578188329935074,
-0.01912289299070835,
-0.06450723111629486,
0.00951294880360365,
0.006269895471632481,
0.035014133900403976,
-0.03133302927017212,
0.019605254754424095,
-0.0028170784935355186,
-0.009256528690457344,
-0.014268267899751663,
-0.027759790420532227,
-0.01489186566323042,
-0.031011901795864105,
-0.012591563165187836,
-0.007252249866724014,
-0.005389704834669828,
-0.008587805554270744,
-0.01780056580901146,
-0.011075018905103207,
0.05432160198688507,
0.005811450071632862,
0.018624691292643547,
-0.0013455874286592007,
-0.006689069326967001,
-0.04062766209244728,
-0.0653023049235344,
-0.0033988638315349817,
-0.014514852315187454,
0.0003651882288977504,
-0.04611381143331528,
-0.000576185411773622,
-0.015133360400795937,
0.015385792590677738,
0.0647098571062088,
0.008708159439265728,
-0.03596037998795509,
0.04120759665966034,
-0.014354148879647255,
-0.0006560886977240443,
-0.027175558730959892,
-0.029084263369441032,
-0.011651953682303429,
-0.037375446408987045,
-0.06614245474338531,
-0.007766251917928457,
-0.03523285314440727,
0.018300827592611313,
0.027401553466916084,
-0.006057775113731623,
0.036987949162721634,
-0.001913433545269072,
-0.02291075885295868,
0.05100945383310318,
0.029533356428146362,
0.025862643495202065,
0.06052250787615776,
-0.01784680411219597,
0.006432254798710346,
0.034063976258039474,
-0.03538001701235771,
-0.04943845793604851,
0.04360528290271759,
-0.022826600819826126,
-0.04003159701824188,
0.001991481985896826,
0.008349617943167686,
0.015588019043207169,
-0.03234383836388588,
0.06283950060606003,
0.0331600047647953,
-0.03459744155406952,
-0.009621317498385906,
0.0380350761115551,
-0.0031147110275924206,
0.024186598137021065,
-0.02056928537786007,
0.0035326657816767693,
0.013141831383109093,
-0.006318733096122742,
-0.014269310049712658,
0.04034816846251488,
0.005623697768896818,
-0.01724839396774769,
0.024769211187958717,
0.016665611416101456,
0.021618356928229332,
-0.014554272405803204,
0.039806999266147614,
0.016799699515104294,
-0.028509652242064476,
-0.0057255784049630165,
-0.005527170840650797,
-0.027175597846508026,
-0.00635935552418232,
-0.0000416243783547543,
0.00686114514246583,
0.062907375395298,
-0.026557382196187973,
0.027696656063199043,
-0.027250899001955986,
-0.03241453692317009,
-0.012646544724702835,
0.004549909383058548,
-0.008201847784221172,
0.029732298105955124,
0.012907476164400578,
-0.014917324297130108,
-0.0019169154111295938,
-0.016276134178042412,
-0.0018197500612586737,
-0.042305510491132736,
0.01812177151441574,
-0.032064344733953476,
-0.014567743055522442,
-0.006095700431615114,
-0.007406630553305149,
-0.0152057446539402,
0.01656963862478733,
-0.007777328137308359,
0.03361426666378975,
0.005194563418626785,
0.02538936585187912,
0.014894063584506512,
0.0002736789465416223,
0.015521827153861523,
-0.0314771831035614,
0.015616794116795063,
-0.013015017844736576,
0.05330122262239456,
-0.01900654472410679,
-0.010743323713541031
] |
<p>(I apologize if this question is too theoretical for this site.)</p>
<p>This is related to the answer <a href="http://physics.stackexchange.com/a/11124">here</a>, although I came up with it independently of that. $\:$ Suppose we
<br>
have a unit mass planet at each integer point in 1-d space. $\:$ As described in that answer, the sum
<br>of the forces acting on any particular planet is absolutely convergent. $\;\;$ Suppose we move planet_0
<br>
to point $\epsilon$, where $\: 0< \epsilon< \frac12 \:$. $\;\;$ For similar reasons, those sums will still be absolutely convergent.
<br>
Now we let Newtonian gravity apply. $\:$ What will happen?</p>
<p><br><br></p>
<p>If it's unclear what an answer might look like, you could consider the following more specific questions:
<br><br><br>
planet_0 will start out moving right, and all of the other planets will start out moving to the left.
<br>
Will there be a positive amount of time before any of them turn around?
<br>
(As opposed to, for example, each planet_n for $\: n\neq 0 \:$ turning around at time 1/|n|.)</p>
<p>Will there be a positive amount of time before any collisions occur?</p>
<p>"Obviously" (at least, I hope I'm right), planet_0 will collide with planet_1. $\:$ Will that be the first collision?</p>
<p>How long will it be before there are any collisions? $\:\:$ (perhaps just an approximation for small $\:\epsilon\:$)
<br><br></p> | 1,526 | [
-0.023373620584607124,
-0.03986337408423424,
-0.040132734924554825,
-0.0076960171572864056,
0.03846096619963646,
0.012529078871011734,
-0.01885959878563881,
-0.01614522933959961,
0.013238845393061638,
-0.017393719404935837,
0.03589934855699539,
0.053172219544649124,
0.015731343999505043,
0.03457149118185043,
0.042346030473709106,
0.011563544161617756,
-0.02602492645382881,
-0.03296215087175369,
0.010713767260313034,
-0.009793607518076897,
0.03192371502518654,
-0.020357957109808922,
0.07007777690887451,
0.021148234605789185,
-0.02906133607029915,
0.016296474263072014,
-0.002780848415568471,
-0.03534571826457977,
0.016370689496397972,
0.06949377059936523,
0.003116949927061796,
-0.008716128766536713,
0.023955609649419785,
0.04840194806456566,
0.01737934537231922,
0.03182801231741905,
-0.0008875814964994788,
-0.002855373779311776,
-0.01039317436516285,
-0.013468830846250057,
-0.04741674289107323,
-0.01130484975874424,
0.004011509474366903,
0.016780827194452286,
-0.013738973066210747,
0.007471146062016487,
0.011862758547067642,
-0.004795493092387915,
0.06919808685779572,
-0.04359923675656319,
0.06431034952402115,
0.010717329569160938,
0.03618254512548447,
-0.0042382581159472466,
0.0041150725446641445,
-0.026597924530506134,
0.06219667196273804,
0.06905853748321533,
0.000016854739442351274,
-0.047021906822919846,
-0.025024864822626114,
-0.04545332491397858,
0.004524543881416321,
-0.009093249216675758,
-0.022885946556925774,
0.09057462960481644,
-0.053850483149290085,
-0.011935918591916561,
0.004084753803908825,
0.00497085228562355,
0.00036032372736372054,
0.019855331629514694,
0.018157746642827988,
-0.004681757185608149,
-0.005319315008819103,
-0.004974469542503357,
0.0006789486506022513,
-0.006082924082875252,
0.056569114327430725,
0.06518556922674179,
-0.050137486308813095,
-0.0010374389821663499,
0.021791212260723114,
0.034814223647117615,
0.030491523444652557,
0.021290672942996025,
0.0455578975379467,
-0.000768616737332195,
-0.022273363545536995,
0.024734796956181526,
0.028134576976299286,
-0.014448911882936954,
0.02015930600464344,
-0.03609360754489899,
-0.0038288601208478212,
0.05736406147480011,
0.022936388850212097,
0.017318084836006165,
-0.015616142190992832,
-0.02834339439868927,
-0.005072079133242369,
-0.021220512688159943,
-0.04122554510831833,
0.03642604500055313,
0.03248463571071625,
0.0014156375546008348,
-0.07386578619480133,
0.0024975365959107876,
-0.014964209869503975,
-0.04000387340784073,
-0.028532909229397774,
0.01745622232556343,
-0.0004396234289743006,
0.025675449520349503,
-0.007959430105984211,
-0.03898627683520317,
-0.0007312950911000371,
-0.024438638240098953,
0.023775795474648476,
0.06999924778938293,
0.07823770493268967,
-0.018092408776283264,
0.023092757910490036,
-0.05338768661022186,
-0.052190545946359634,
0.02359042502939701,
0.0427003875374794,
-0.013452011160552502,
-0.03195302188396454,
0.005050816107541323,
0.0020830754656344652,
-0.016985338181257248,
-0.03995780274271965,
-0.0257209874689579,
0.05603119730949402,
0.008581309579312801,
-0.054916076362133026,
-0.04088649898767471,
0.003280986798927188,
-0.040206585079431534,
-0.05119359865784645,
-0.03706886246800423,
0.007237041834741831,
0.007195314392447472,
0.0670439600944519,
0.002006125869229436,
-0.0029452629387378693,
0.016057362779974937,
0.041935283690690994,
0.02337423898279667,
-0.040619317442178726,
0.010649144649505615,
-0.0031881695613265038,
-0.04608400538563728,
-0.0036944763269275427,
-0.06478376686573029,
0.02777220867574215,
0.013157172128558159,
0.03960151970386505,
-0.03244779631495476,
0.04579871892929077,
-0.03420773893594742,
0.021653980016708374,
-0.010980354622006416,
-0.001149512710981071,
0.01903836615383625,
0.0846472755074501,
0.053630996495485306,
-0.006035408936440945,
0.03323780745267868,
0.020184015855193138,
0.032324597239494324,
0.012479370459914207,
0.022879434749484062,
0.06741893291473389,
-0.03738639876246452,
-0.005867644678801298,
-0.019003279507160187,
-0.007847527042031288,
0.009647657163441181,
-0.007626251317560673,
-0.014217089861631393,
-0.008612618781626225,
0.004316018894314766,
0.012336698360741138,
0.04675120860338211,
-0.009478757157921791,
0.012282285839319229,
-0.007143848109990358,
-0.02007710374891758,
-0.004162970930337906,
-0.06303774565458298,
0.015422742813825607,
-0.00020427248091436923,
0.01371772214770317,
0.03838512301445007,
0.012166816741228104,
0.011840556748211384,
-0.03461472690105438,
-0.0035361896734684706,
-0.03074076399207115,
0.0481455959379673,
0.009074273519217968,
-0.004607883747667074,
-0.012959357351064682,
0.07458263635635376,
0.03194088488817215,
-0.006368756759911776,
-0.011901458725333214,
-0.01779167354106903,
0.002782918978482485,
0.005521201994270086,
-0.030690997838974,
0.024079717695713043,
0.008778332732617855,
0.03368065878748894,
0.015356075949966908,
0.005471907090395689,
0.032465845346450806,
-0.003518505487591028,
-0.06010708212852478,
0.07016178965568542,
0.06282011419534683,
0.007461979053914547,
0.0072675361298024654,
0.016115954145789146,
0.0018845105078071356,
0.010254383087158203,
0.006240711081773043,
-0.022442881017923355,
-0.061639994382858276,
-0.013096231035888195,
0.0002834117622114718,
0.06493078917264938,
-0.015287652611732483,
0.02480304427444935,
0.0686316192150116,
0.03207932412624359,
-0.008072725497186184,
-0.017644956707954407,
-0.029977040365338326,
0.0013072909787297249,
0.015394069254398346,
-0.024542463943362236,
0.021486278623342514,
-0.004690608941018581,
-0.0035918033681809902,
0.01704908162355423,
-0.008707002736628056,
0.024850765243172646,
-0.04429630562663078,
-0.010718139819800854,
0.032643117010593414,
0.032823801040649414,
-0.022898681461811066,
-0.0265628844499588,
0.028984399512410164,
0.006370012182742357,
-0.015080482698976994,
0.04772152751684189,
0.013863425701856613,
-0.020491918548941612,
-0.06975074112415314,
-0.019120151177048683,
-0.004620011430233717,
0.006327860523015261,
-0.01321446429938078,
-0.02764611318707466,
0.033360984176397324,
-0.050472721457481384,
0.022477170452475548,
-0.00008416229684371501,
-0.04351523146033287,
-0.014954308047890663,
-0.003766536246985197,
0.02570638619363308,
0.02287413738667965,
-0.00389702501706779,
-0.04563214257359505,
0.028923703357577324,
-0.00010142708924831823,
-0.01756557635962963,
-0.011421951465308666,
-0.0002936940873041749,
-0.06584420055150986,
0.02240515500307083,
-0.02748933620750904,
-0.027857016772031784,
0.05407555401325226,
0.02793058753013611,
-0.007322780322283506,
0.03624672070145607,
0.001296179136261344,
-0.047414422035217285,
-0.02570485509932041,
-0.06600897759199142,
-0.00821682345122099,
-0.06711207330226898,
0.03089442104101181,
0.058442387729883194,
-0.00722940219566226,
-0.047270163893699646,
0.01803155243396759,
-0.07956714183092117,
-0.035821303725242615,
-0.03769537806510925,
-0.00646582618355751,
-0.005839652847498655,
-0.021336382254958153,
0.006512923166155815,
0.00844922848045826,
-0.0041590845212340355,
0.03031538613140583,
-0.06481067836284637,
-0.0669689029455185,
-0.012193461880087852,
-0.029049010947346687,
0.06715229153633118,
-0.007215292192995548,
-0.04443231225013733,
0.059851694852113724,
0.02914486639201641,
0.00038321284228004515,
-0.01622472144663334,
0.021865585818886757,
-0.00045459443936124444,
-0.015144596807658672,
0.029356714338064194,
0.009625638835132122,
0.007993664592504501,
-0.0032759252935647964,
0.0334957018494606,
0.05521732196211815,
0.0029379085171967745,
-0.020437393337488174,
0.02680387906730175,
0.01041731983423233,
0.00024279739591293037,
-0.012278620153665543,
0.0054949866607785225,
0.04494633898139,
0.0055119628086686134,
0.017267756164073944,
-0.021854111924767494,
0.022748449817299843,
0.008144556544721127,
-0.06105989217758179,
0.03311266005039215,
-0.0030019660480320454,
-0.0018815520452335477,
0.008441383019089699,
0.05149242654442787,
0.003241494530811906,
-0.010850281454622746,
0.01623483933508396,
0.03624928370118141,
0.05936191603541374,
-0.012820165604352951,
0.013983296230435371,
0.015572060830891132,
0.06338916718959808,
-0.02230784296989441,
-0.04729871451854706,
0.018677549436688423,
0.007496105507016182,
0.04753294959664345,
-0.02282308042049408,
0.023114213719964027,
-0.007607805542647839,
0.014483352191746235,
0.002822943963110447,
0.025345562025904655,
-0.0004467527905944735,
0.002924136584624648,
-0.06105119362473488,
-0.05847562849521637,
-0.01779876835644245,
0.05248767137527466,
0.005351039115339518,
0.02863207273185253,
-0.006833688355982304,
-0.003046129597350955,
-0.0029159127734601498,
0.013503918424248695,
-0.08558854460716248,
0.021955927833914757,
-0.02004796452820301,
-0.04417809471487999,
-0.00792678166180849,
0.021202677860856056,
-0.0024180542677640915,
-0.03366933763027191,
0.040117181837558746,
-0.017800001427531242,
-0.01521683856844902,
-0.06183682382106781,
-0.0019902531057596207,
-0.033014919608831406,
-0.06737567484378815,
0.01898176409304142,
0.024911409243941307,
0.043336935341358185,
-0.009507495909929276,
0.04376395419239998,
0.0453789085149765,
-0.006849054712802172,
-0.03227166086435318,
-0.013977386057376862,
-0.012226706370711327,
-0.03748856484889984,
0.03166546672582626,
0.03201984614133835,
0.032096125185489655,
-0.019159361720085144,
0.008841617032885551,
0.005770817399024963,
0.02915792725980282,
-0.004997478798031807,
-0.004451012704521418,
0.011916606687009335,
-0.06051494926214218,
-0.010905437171459198,
0.00836960133165121,
0.016729138791561127,
-0.00889368075877428,
0.024217922240495682,
0.05344240739941597,
0.01401809323579073,
0.004979822784662247,
0.06344775855541229,
0.05800068750977516,
-0.0016707924660295248,
-0.023097725585103035,
-0.030458737164735794,
0.003623748430982232,
-0.03437180817127228,
0.020395278930664062,
0.035146795213222504,
-0.012023210525512695,
0.0037435670383274555,
0.0059719267301261425,
0.0017724838107824326,
0.029086394235491753,
-0.01715780422091484,
0.006352420896291733,
-0.015255868434906006,
0.03244640305638313,
-0.01955103874206543,
0.010035732761025429,
-0.009390749037265778,
0.013515097089111805,
0.03428542613983154,
-0.03745757043361664,
-0.007979868911206722,
-0.06026343256235123,
-0.020555969327688217,
0.01710563898086548,
0.03865129128098488,
-0.023165231570601463,
-0.012716395780444145,
-0.02960450015962124,
-0.03208900988101959,
0.044083498418331146,
-0.042604319751262665,
0.03115798532962799,
0.008513839915394783,
0.005817078985273838,
-0.0062906756065785885,
-0.01902235671877861,
-0.04917343333363533,
0.015525782480835915,
0.0075367894023656845,
0.019871175289154053,
-0.0015682465163990855,
0.02511742152273655,
-0.04545534402132034,
0.018789468333125114,
0.04789760708808899,
0.07130005210638046,
-0.012115220539271832,
0.0028317521791905165,
-0.026842037215828896,
-0.03273323178291321,
-0.019945241510868073,
-0.06694690138101578,
0.0366973876953125,
-0.006669937167316675,
-0.06542928516864777,
0.029331903904676437,
-0.050788454711437225,
-0.05169980973005295,
0.0547708123922348,
-0.010748594999313354,
-0.01719077117741108,
0.012450824491679668,
-0.01682423986494541,
0.046812254935503006,
0.03495115041732788,
-0.0038623404689133167,
-0.006988645065575838,
0.024235375225543976,
-0.038135211914777756,
0.028360744938254356,
-0.018290799111127853,
0.0010614567436277866,
-0.018052618950605392,
0.0033413178753107786,
-0.019001273438334465,
-0.011274920776486397,
-0.0386628732085228,
0.01341626700013876,
0.0009027458727359772,
-0.01908368617296219,
-0.011963929980993271,
0.00022766504844184965,
-0.0073568508960306644,
0.029669316485524178,
0.02864515222609043,
0.03548792749643326,
0.017502710223197937,
0.006304443348199129,
0.025480002164840698,
-0.01728866994380951,
0.043537821620702744,
-0.017594672739505768,
0.04483354091644287,
0.023127490654587746,
-0.015136395581066608,
0.007256858982145786,
-0.017718622460961342,
0.03423043712973595,
-0.014362987130880356,
-0.07234297692775726,
0.059384431689977646,
0.02567904442548752,
-0.008053849451243877,
0.047152064740657806,
-0.051322322338819504,
-0.020597973838448524,
-0.005457258317619562,
-0.0012985666980966926,
-0.01540817879140377,
-0.021348396316170692,
-0.0033891722559928894,
0.02395867183804512,
0.015415046364068985,
-0.06296256929636002,
-0.017081044614315033,
0.027909450232982635,
0.02243337593972683,
-0.014596247114241123,
-0.03591497242450714,
-0.013475440442562103,
-0.037573885172605515,
-0.00176903884857893,
-0.013479572720825672,
0.060982804745435715,
-0.0373777411878109,
-0.021460283547639847,
0.00532634649425745,
0.015193966217339039,
0.04911331087350845,
0.011349561624228954,
-0.0037119269836694,
0.026188137009739876,
-0.016101650893688202,
0.011819501407444477,
-0.02474359981715679,
0.07503008842468262,
-0.056665897369384766,
-0.037344545125961304,
-0.022980261594057083,
-0.057919856160879135,
0.003697925014421344,
-0.029409518465399742,
0.006508293561637402,
0.014235436916351318,
-0.0053264605812728405,
-0.018556945025920868,
-0.014572346583008766,
0.013738994486629963,
-0.03025536611676216,
0.015202315524220467,
0.022097669541835785,
-0.00781888235360384,
-0.0056980992667376995,
-0.06862638890743256,
0.006961830426007509,
-0.0075060101225972176,
-0.00728173553943634,
-0.00488033564761281,
0.04503596946597099,
0.017759347334504128,
-0.02009350061416626,
0.02568231150507927,
0.019127456471323967,
0.06500845402479172,
-0.0071868677623569965,
-0.04076310992240906,
0.0084086824208498,
0.0015445852186530828,
-0.035520605742931366,
-0.02455291710793972,
-0.048613570630550385,
0.01663598045706749,
0.06646090745925903,
-0.036601338535547256,
0.057702042162418365,
-0.018191058188676834,
0.03886609897017479,
0.00834061112254858,
-0.007158799096941948,
0.01721585914492607,
-0.05234469473361969,
0.03233964741230011,
0.021594002842903137,
-0.023657703772187233,
0.0032032285816967487,
0.028868449851870537,
0.04648476094007492,
-0.005766215268522501,
-0.006503384094685316,
-0.009002016857266426,
-0.003345212433487177,
0.047296326607465744,
-0.022431571036577225,
0.0030798171646893024,
0.002844924805685878,
-0.06881602108478546,
0.027529047802090645,
0.01622641459107399,
-0.04032595455646515,
0.036849264055490494,
0.014126552268862724,
0.009494900703430176,
-0.04271130636334419,
-0.046632926911115646,
-0.011330492794513702,
0.019026173278689384,
0.014161309227347374,
0.03316188231110573,
0.0013421267503872514,
0.017728861421346664,
0.02187739498913288,
0.007423783652484417,
0.011368107050657272,
-0.01947338692843914,
-0.07416221499443054,
-0.04382701963186264,
-0.00951459538191557,
-0.05633988231420517,
0.02401677519083023,
0.0366879366338253,
-0.007804803550243378,
0.011184144765138626,
-0.01927836611866951,
0.025686955079436302,
0.019747870042920113,
0.0004365302447695285,
-0.02491740696132183,
0.06209087744355202,
-0.0074623324908316135,
0.026589741930365562,
-0.061333704739809036,
0.018079690635204315,
0.11734641343355179,
0.045645397156476974,
0.012063228525221348,
-0.02512384206056595,
0.014719330705702305,
0.029218481853604317,
-0.028132401406764984,
-0.04852414131164551,
0.01711377687752247,
0.018952783197164536,
0.008808878250420094,
0.034097909927368164,
0.04053786024451256,
-0.011554805561900139,
-0.03715573623776436,
0.04488317668437958,
-0.03601360321044922,
-0.039996299892663956,
-0.02384752407670021,
0.003098623361438513,
-0.006901685614138842,
0.04180741682648659,
-0.03305415064096451,
0.02024531364440918,
-0.032611146569252014,
0.019942058250308037,
-0.052020542323589325,
-0.01112593524158001,
0.01633443310856819,
0.011809303425252438,
-0.022550754249095917,
0.04180695489048958,
0.009751114062964916,
-0.034973226487636566,
-0.031401265412569046,
0.03820722550153732,
0.026662860065698624,
-0.011005024425685406,
0.02135603316128254,
0.06019285321235657,
-0.02986045926809311,
0.043072499334812164,
0.009292921982705593,
-0.004163195379078388,
-0.04224745184183121,
-0.012868362478911877,
-0.07370726019144058,
0.06914839148521423,
-0.004396584816277027,
0.02892613224685192,
0.007680975366383791,
0.030583007261157036,
0.009904234670102596,
-0.04719844087958336,
0.012259336188435555,
0.0030449596233665943,
0.02859540656208992,
-0.00430366862565279,
-0.030130447819828987,
0.006245623808354139,
0.016268650069832802,
-0.009060285054147243,
0.011047402396798134,
-0.012136848643422127,
-0.035354189574718475,
-0.010624002665281296,
-0.019453367218375206,
0.060547273606061935,
-0.0019881560001522303,
0.006744443438947201,
-0.02725464105606079,
-0.013856040313839912,
-0.050918806344270706,
0.02131054922938347,
0.0020899309311062098,
0.03446836397051811,
-0.0033261864446103573,
0.015484463423490524,
-0.0011670800158753991,
-0.03956977277994156,
-0.05341373383998871,
0.026584038510918617,
-0.027473868802189827,
-0.021446309983730316,
-0.02946332097053528,
-0.04063486307859421,
0.0049006701447069645,
0.04300050064921379,
-0.019832851365208626,
-0.014073248021304607,
0.0018482081359252334,
0.09609638154506683,
0.012690785340964794,
0.0323367714881897,
-0.0075755855068564415,
-0.015580352395772934,
-0.04487331956624985,
0.033517155796289444,
-0.02516024187207222,
0.05365427955985069,
0.01251100841909647,
-0.025964589789509773,
0.048829756677150726,
0.007337613962590694,
-0.025652656331658363,
0.026554398238658905,
0.024090826511383057,
-0.023143814876675606,
-0.012020375579595566,
0.036740999668836594,
-0.012794299982488155,
-0.01929505541920662,
-0.02719302847981453,
-0.009135573171079159,
0.0048355418257415295,
-0.00791823212057352,
0.02530183084309101,
-0.05053763464093208,
0.06136041879653931,
-0.025968462228775024,
0.015350227244198322,
-0.04344922676682472,
-0.02893476001918316,
-0.04281799867749214,
0.006475276313722134,
-0.0017898738151416183,
-0.00034116540336981416,
0.018400542438030243,
0.0016454642172902822,
0.012695899233222008,
-0.01859411783516407,
0.029040837660431862,
-0.0041566696017980576,
0.021894697099924088,
-0.00119304982945323,
0.014882768504321575,
-0.038695428520441055,
0.024746406823396683,
-0.029001275077462196,
-0.03155037388205528,
0.0680680051445961,
-0.047184135764837265,
-0.08466152101755142,
0.03158358484506607,
-0.010687915608286858,
0.051770396530628204,
-0.00021076320263091475,
-0.015408874489367008,
-0.01883689872920513,
0.07592538744211197,
-0.006875925697386265,
0.010404521599411964,
0.00034142975346185267,
-0.026795972138643265,
-0.027614785358309746,
0.00878195557743311,
0.018659135326743126,
-0.028026942163705826,
0.010029105469584465,
-0.000032042582461144775,
0.059120237827301025,
-0.03408345207571983,
-0.004943482577800751,
-0.023471476510167122,
-0.015122323296964169,
0.000952733273152262,
0.0005591448280028999,
-0.008972938172519207,
0.0075246961787343025,
0.028475522994995117,
-0.0508727952837944,
0.03294562175869942,
0.0003332291671540588,
-0.027355384081602097,
-0.051227279007434845,
-0.014395071193575859,
0.015716437250375748,
0.007338290568441153,
0.01424296386539936,
-0.07600584626197815,
0.012500589713454247,
0.04095546528697014,
-0.08959569036960602,
0.019169937819242477,
-0.041192471981048584,
0.014816446229815483,
-0.003885238664224744,
0.025333454832434654,
-0.0014369930140674114,
0.020895110443234444,
0.014591610990464687,
0.04097556322813034,
0.016436895355582237,
0.0009836811805143952,
-0.01792861521244049,
-0.02939358726143837,
0.02538224868476391,
0.0253080315887928,
-0.026596101000905037,
0.005409031640738249,
0.044551968574523926,
0.009935345500707626,
-0.03993021324276924,
0.03455100953578949,
-0.005836715921759605,
0.019058547914028168,
-0.020308436825871468,
0.00894215889275074,
-0.0015004946617409587,
-0.002653311938047409,
-0.006914622616022825,
-0.007395925000309944,
-0.004135163500905037,
0.02949763834476471,
0.003751505631953478,
0.013333046808838844,
-0.01519566960632801,
0.004151581320911646,
0.06242813169956207,
0.0013219094835221767,
-0.042165081948041916,
0.013745471835136414,
0.026817278936505318,
-0.0012751189060509205,
-0.007716498337686062,
0.01349701825529337,
-0.009403487667441368,
-0.022644685581326485,
-0.004152882378548384,
-0.03274620696902275,
-0.00037101059569977224,
0.02153155393898487,
0.021876757964491844,
-0.0027503059245646,
0.04242348298430443,
-0.009847475215792656,
-0.019130438566207886,
-0.010133006609976292,
-0.02356693707406521,
-0.0008320948109030724,
-0.02848159521818161,
-0.007415867876261473,
-0.004333773162215948,
0.023095520213246346,
-0.023377621546387672,
-0.05843691527843475,
-0.03727112337946892,
0.019722847267985344,
0.014305000193417072,
-0.004327358212321997,
-0.005739954765886068,
-0.058580007404088974,
-0.010478775016963482,
-0.08622122555971146,
0.026246972382068634,
0.02270853891968727,
0.01803784817457199,
-0.029208993539214134,
-0.017042599618434906,
-0.02793051488697529,
-0.023137474432587624,
0.029346251860260963,
-0.005012148525565863,
-0.009869832545518875,
0.017381347715854645,
-0.0119578056037426,
0.027972372248768806,
-0.06210185959935188,
-0.036077409982681274,
-0.02145017683506012,
0.015947779640555382,
-0.003253784729167819,
-0.029569342732429504,
0.030290512368083,
-0.009459148161113262,
-0.003924453631043434,
-0.0031943076755851507,
0.03537844121456146,
0.011457346379756927,
-0.04670434817671776,
0.05173446983098984,
0.0027143906336277723,
0.03510841727256775,
0.07186032086610794,
0.006915976759046316,
0.009468126110732555,
0.0019081877544522285,
-0.051283642649650574,
-0.039362575858831406,
-0.006146707106381655,
-0.06804278492927551,
-0.04884500429034233,
-0.044214218854904175,
0.011534000746905804,
0.025109587237238884,
-0.07708597183227539,
0.019929220899939537,
0.043138109147548676,
0.014203825034201145,
-0.010820313356816769,
0.00020459255028981715,
-0.012454848736524582,
0.03972030431032181,
0.01778353564441204,
0.008889097720384598,
0.004635270219296217,
0.0026329646352678537,
-0.02854340523481369,
0.025716479867696762,
0.04068807139992714,
-0.010387669317424297,
0.02865995466709137,
0.008052447810769081,
0.018075693398714066,
0.05253710597753525,
0.01571875438094139,
0.05444057285785675,
0.01125617977231741,
-0.008563589304685593,
0.04238276928663254,
0.02318473905324936,
0.00478394003584981,
0.02723056636750698,
0.017386838793754578,
0.0636327788233757,
0.0012294435873627663,
0.023629985749721527,
0.0011074021458625793,
-0.011424595490098,
-0.061863869428634644,
-0.017549872398376465,
0.008724726736545563,
0.03179357945919037,
-0.029634378850460052,
-0.022431930527091026,
-0.03129640221595764,
0.0022803645115345716,
0.025391511619091034,
-0.042256224900484085,
0.027699947357177734,
0.04394444078207016,
0.04611188545823097,
0.00015438652189914137,
-0.005423211958259344,
-0.03776298090815544,
-0.006971618626266718,
0.03283897414803505,
0.03439838066697121,
0.02870107814669609,
-0.02948826551437378,
0.022459352388978004,
-0.033847060054540634,
0.046071361750364304,
-0.05051633343100548,
-0.030381811782717705,
-0.015279530547559261,
0.024015087634325027,
0.02279536984860897,
0.010465792380273342
] |
<p>We know that the light gets refracted when it enter a medium low/high refractive index. </p>
<p>But why light is not refracted when it comes out from the vertex of a prism.</p> | 1,527 | [
-0.03983796387910843,
0.015859972685575485,
0.009338688105344772,
-0.04452507942914963,
0.02407585084438324,
0.06124250590801239,
-0.038874849677085876,
-0.012442950159311295,
-0.01319766603410244,
-0.02808857150375843,
0.043218404054641724,
0.05431807413697243,
0.05387398973107338,
0.058872904628515244,
0.02531745657324791,
0.018879365175962448,
-0.008485629223287106,
0.0038201995193958282,
-0.0018024331657215953,
-0.021117473021149635,
-0.030576961115002632,
0.019476214423775673,
-0.02690245769917965,
0.012414079159498215,
-0.05899317190051079,
-0.004575799684971571,
0.02312937192618847,
-0.009951138868927956,
0.042878154665231705,
0.05304365232586861,
0.004866904113441706,
-0.002806946402415633,
0.011511859484016895,
0.007205349858850241,
0.027026984840631485,
-0.015090194530785084,
-0.016283540055155754,
-0.012984915636479855,
0.0025712428614497185,
0.003095230320468545,
0.002419812371954322,
0.0035596247762441635,
-0.02587224915623665,
0.07650772482156754,
-0.009707983583211899,
0.011018278077244759,
0.03705354034900665,
-0.017550552263855934,
0.05671180784702301,
-0.08098189532756805,
0.030016692355275154,
-0.016150275245308876,
0.03729601204395294,
0.046300433576107025,
-0.010997067205607891,
-0.0076820701360702515,
0.08667270839214325,
0.06816861033439636,
-0.03125709667801857,
-0.02109835296869278,
0.017017746344208717,
-0.011049994267523289,
0.010115222074091434,
-0.006171814631670713,
-0.005830742418766022,
-0.018656393513083458,
-0.013238883577287197,
-0.05067102983593941,
0.006733414717018604,
-0.003448039060458541,
-0.027932588011026382,
-0.014459830708801746,
0.00493375351652503,
-0.010829972103238106,
0.037696655839681625,
-0.01695103384554386,
0.019476110115647316,
0.005578927230089903,
0.03888079896569252,
0.03128596395254135,
0.01103909220546484,
0.018767254427075386,
0.038267869502305984,
0.016072938218712807,
-0.021997258067131042,
-0.03360700607299805,
0.05401970073580742,
-0.01154236774891615,
-0.007545080967247486,
0.030589884147047997,
-0.020957015454769135,
0.013519042171537876,
0.032668109983205795,
0.006622299086302519,
-0.014156699180603027,
0.011651289649307728,
-0.02296954020857811,
0.051157522946596146,
0.01621064357459545,
-0.04012732207775116,
0.029009373858571053,
0.0076434495858848095,
0.011756989173591137,
0.07569124549627304,
0.006131294649094343,
-0.030777182430028915,
-0.045069873332977295,
0.018680540844798088,
-0.021165402606129646,
0.005236985627561808,
0.005366336554288864,
0.019490137696266174,
-0.01504402607679367,
-0.006508359685540199,
0.000930017966311425,
-0.05499666929244995,
0.0256892628967762,
-0.04587579518556595,
0.05189719423651695,
0.08005107194185257,
-0.002361447550356388,
-0.020298613235354424,
-0.01331657636910677,
-0.01602676697075367,
-0.06878466159105301,
0.026929790154099464,
0.015400870703160763,
-0.008176634088158607,
-0.017562462016940117,
-0.024771999567747116,
0.032404348254203796,
-0.01181027665734291,
0.022238697856664658,
-0.02290436252951622,
-0.005174773745238781,
0.021777717396616936,
-0.11476854234933853,
-0.08514406532049179,
0.061350610107183456,
0.027097389101982117,
-0.06208660826086998,
-0.06812561303377151,
0.028148600831627846,
0.03218584507703781,
0.09153413772583008,
-0.011277633719146252,
0.0370376855134964,
-0.017433058470487595,
0.025809133425354958,
-0.01758587546646595,
-0.021226966753602028,
0.000007656961315660737,
0.025826791301369667,
-0.009462389163672924,
0.010995462536811829,
-0.0778995156288147,
0.014920399524271488,
0.027419978752732277,
-0.0243145152926445,
-0.01971711777150631,
0.03622816130518913,
-0.052828941494226456,
-0.003225823398679495,
0.026952257379889488,
-0.0019255341030657291,
-0.03210369870066643,
0.09769850224256516,
0.06156086176633835,
0.04577088728547096,
0.030584288761019707,
0.001197159057483077,
0.051294080913066864,
-0.012288019061088562,
0.00841678399592638,
0.029712768271565437,
-0.012774702161550522,
-0.019428789615631104,
0.025348026305437088,
0.018458552658557892,
0.009882090613245964,
-0.04465296491980553,
-0.025204824283719063,
0.0278598852455616,
0.040571507066488266,
-0.019650602713227272,
0.03697903826832771,
-0.018782969564199448,
-0.007640884257853031,
0.023291220888495445,
-0.054322294890880585,
-0.01402935478836298,
-0.03912165388464928,
0.001612168620340526,
0.010386201553046703,
-0.0027719822246581316,
0.006624713074415922,
0.02408692240715027,
-0.01637398637831211,
-0.01759469322860241,
0.01046170387417078,
-0.03246380388736725,
0.01562128122895956,
0.009783852845430374,
-0.027108972892165184,
0.04248593747615814,
0.03933248668909073,
0.07193566113710403,
0.026586810126900673,
0.004305490292608738,
-0.016704991459846497,
-0.02017880231142044,
0.019839318469166756,
-0.0007641602423973382,
0.0014357914915308356,
-0.01391793042421341,
-0.01184972282499075,
-0.004739119205623865,
0.04800952970981598,
0.0025644435081630945,
0.030319511890411377,
-0.025896942242980003,
0.09198220074176788,
0.05063220113515854,
0.013372591696679592,
-0.015183954499661922,
0.02909848652780056,
-0.0057405089028179646,
0.006186719052493572,
0.012829293496906757,
-0.015424317680299282,
-0.021245097741484642,
-0.025670334696769714,
-0.005073320120573044,
0.003285316051915288,
-0.05042378604412079,
0.04203636571764946,
-0.002649386879056692,
0.031183410435914993,
0.006383914966136217,
0.047720227390527725,
0.002026415430009365,
-0.04333142936229706,
0.03350365534424782,
0.018808498978614807,
0.02478807605803013,
0.0425117053091526,
0.019071293994784355,
0.0053054168820381165,
-0.01458661537617445,
-0.039209529757499695,
-0.009690201841294765,
0.018098806962370872,
0.008039353415369987,
0.00968693196773529,
0.023778660222887993,
-0.025273751467466354,
0.008019985631108284,
-0.027891753241419792,
-0.015381226316094398,
0.00817275419831276,
0.018466129899024963,
-0.003901934949681163,
-0.06751430779695511,
0.0025545547250658274,
0.024577882140874863,
0.009174687787890434,
-0.04605685919523239,
-0.02534285932779312,
0.0360066220164299,
-0.04300035163760185,
0.02961231954395771,
-0.05425810068845749,
-0.0003376636595930904,
-0.03635483607649803,
-0.008935853838920593,
0.02629837766289711,
0.0191597081720829,
0.026679372414946556,
-0.04618219658732414,
-0.05290737748146057,
0.0034530246630311012,
-0.03986906632781029,
-0.009982864372432232,
-0.007937517017126083,
-0.011813993565738201,
0.044388093054294586,
-0.020565932616591454,
-0.034320637583732605,
0.030390888452529907,
-0.0031400183215737343,
-0.007499001454561949,
-0.009256439283490181,
-0.015073275193572044,
-0.05058083310723305,
-0.027081681415438652,
-0.008170496672391891,
-0.022132426500320435,
-0.011221985332667828,
-0.004969874396920204,
0.042351678013801575,
-0.02349630557000637,
-0.013665050268173218,
-0.01097603514790535,
-0.039262913167476654,
-0.028659218922257423,
-0.008941092528402805,
-0.031347863376140594,
0.004373547621071339,
-0.021516969427466393,
0.027026068419218063,
0.010524011217057705,
-0.04929234832525253,
0.04238500818610191,
-0.05648205429315567,
-0.041081685572862625,
0.02686823531985283,
-0.010223853401839733,
0.030750667676329613,
-0.026915404945611954,
-0.006923467852175236,
0.050669413059949875,
-0.0005769502022303641,
-0.0231329258531332,
-0.01343352347612381,
-0.01995101571083069,
-0.014007842168211937,
-0.025434158742427826,
0.026117397472262383,
0.03794604167342186,
0.007346007507294416,
0.015066870488226414,
-0.0011620237492024899,
0.02721749059855938,
0.0350351445376873,
0.024389754980802536,
0.005964348558336496,
-0.018014337867498398,
0.011084078811109066,
-0.004424231126904488,
0.02842758409678936,
0.03616743162274361,
-0.055693138390779495,
0.019636381417512894,
0.003356676548719406,
0.058638978749513626,
0.02542252652347088,
-0.05852751061320305,
0.029582975432276726,
-0.027687110006809235,
0.05648057162761688,
0.004382685758173466,
0.04353588819503784,
0.005180050618946552,
0.026431670412421227,
0.0012442745501175523,
0.024921299889683723,
0.04703148826956749,
-0.016367711126804352,
-0.01931355521082878,
0.017001593485474586,
0.017182674258947372,
-0.010128943249583244,
-0.021578596904873848,
0.003940280061215162,
-0.022133493795990944,
0.032425738871097565,
-0.0015699934447184205,
0.012161835096776485,
0.05524731054902077,
0.025918662548065186,
0.002823148388415575,
0.0016221447149291635,
-0.027775494381785393,
-0.007207430433481932,
0.011625558137893677,
0.011408313177525997,
-0.025181381031870842,
0.027583889663219452,
-0.007818302139639854,
0.044556815177202225,
0.04388288035988808,
0.05842979624867439,
0.010751721449196339,
0.0028777315746992826,
-0.09404238313436508,
-0.02568565309047699,
-0.02792993187904358,
-0.004769430961459875,
-0.05105636641383171,
-0.011502115055918694,
-0.021182741969823837,
-0.011832881718873978,
-0.020007222890853882,
-0.01702628657221794,
0.004946928471326828,
-0.02035670354962349,
0.030823513865470886,
0.001439527841284871,
-0.026516156271100044,
-0.0288649033755064,
-0.007535072974860668,
0.01998933032155037,
-0.00440631341189146,
0.024387437850236893,
0.03307926282286644,
-0.009245394729077816,
0.011359408497810364,
0.011826131492853165,
0.006162693724036217,
0.024950310587882996,
0.04114573821425438,
0.017695214599370956,
0.017502756789326668,
-0.009908545762300491,
-0.010668830946087837,
0.028574878349900246,
0.05065266042947769,
-0.0036308905109763145,
0.007930446416139603,
0.001711705350317061,
-0.0159586351364851,
-0.03265635296702385,
-0.0581291988492012,
0.04404332861304283,
-0.04168085753917694,
-0.02556079998612404,
0.009897123090922832,
-0.01266537606716156,
-0.022336401045322418,
0.03717675805091858,
-0.012850590981543064,
0.05046498402953148,
-0.0061470759101212025,
-0.026069292798638344,
0.004417498596012592,
-0.031054718419909477,
-0.03271498158574104,
0.034640852361917496,
-0.01110883429646492,
-0.02759554237127304,
-0.021520966663956642,
0.02393089048564434,
-0.0013568499125540257,
0.004048444796353579,
0.015424509532749653,
-0.030977953225374222,
-0.0060005998238921165,
-0.004385547246783972,
0.019419468939304352,
0.023309556767344475,
0.039251089096069336,
0.01810104213654995,
-0.011734540574252605,
-0.01112112496048212,
-0.06557338684797287,
-0.034789688885211945,
0.046271517872810364,
0.03483056277036667,
-0.02428600750863552,
0.01637832261621952,
-0.09441984444856644,
-0.048441726714372635,
0.028638437390327454,
-0.01885364018380642,
-0.005029915366321802,
-0.03740941360592842,
0.005069416482001543,
-0.02943241596221924,
-0.005469419062137604,
-0.02652539499104023,
-0.01793668605387211,
-0.008778421208262444,
0.026284975931048393,
-0.024458065629005432,
0.0025590010918676853,
-0.03025919944047928,
-0.01059122383594513,
0.01876956783235073,
0.04048347473144531,
0.026097483932971954,
0.02538110315799713,
0.01114578079432249,
0.00437770364806056,
-0.04909563809633255,
-0.08402325958013535,
0.0006665687542408705,
0.03106440044939518,
0.019037296995520592,
0.06048854440450668,
-0.046091992408037186,
-0.04697409272193909,
0.012921273708343506,
-0.001090208999812603,
0.006517739035189152,
0.004798328038305044,
-0.02744794636964798,
-0.004644217900931835,
-0.005329109262675047,
-0.03778857737779617,
0.040220506489276886,
0.03877322003245354,
-0.008965043351054192,
-0.032014742493629456,
-0.050314806401729584,
0.05292389914393425,
-0.03426387533545494,
-0.015544293448328972,
0.007566486950963736,
-0.014718133956193924,
0.004483103286474943,
0.06542704254388809,
-0.0030789736192673445,
0.012446558102965355,
-0.0012226857943460345,
-0.03582209721207619,
-0.013324065133929253,
0.03633547201752663,
0.007322501391172409,
0.0216069258749485,
-0.02043135277926922,
0.01267621573060751,
0.030766502022743225,
-0.016983939334750175,
0.04012380912899971,
-0.020471559837460518,
0.008182520046830177,
0.047441449016332626,
0.017059894278645515,
0.01243894174695015,
-0.047329407185316086,
-0.008793030865490437,
-0.0279757771641016,
-0.03344662860035896,
0.07313603907823563,
-0.005413990467786789,
0.02246434986591339,
0.051596980541944504,
-0.0367332324385643,
-0.053309205919504166,
0.007941918447613716,
-0.026125438511371613,
0.05851825326681137,
-0.046258434653282166,
0.04772862046957016,
-0.004573817830532789,
0.011245038360357285,
-0.07981888204813004,
-0.024780627340078354,
-0.023063281551003456,
0.028360869735479355,
-0.010955655947327614,
0.0046808128245174885,
0.003970671445131302,
-0.001531663234345615,
-0.04539391025900841,
0.024266498163342476,
0.007982144132256508,
-0.0441899374127388,
-0.023216255009174347,
-0.004475038032978773,
-0.0011214434634894133,
0.05284588411450386,
-0.019700169563293457,
-0.03583121299743652,
-0.0078091491013765335,
-0.03188443183898926,
0.0050293318927288055,
-0.001962024252861738,
0.04952237010002136,
0.00002714030233619269,
-0.05583745613694191,
-0.00469170743599534,
-0.0034704157151281834,
0.014028167352080345,
0.013493038713932037,
0.04571976512670517,
0.019031411036849022,
-0.0032417122274637222,
-0.044923096895217896,
-0.007556338328868151,
0.004024883732199669,
0.01477124635130167,
0.03296560421586037,
0.005024292040616274,
0.01703072153031826,
-0.04753704369068146,
-0.008154531009495258,
0.03885333240032196,
-0.03451528400182724,
0.028564145788550377,
-0.005549649707973003,
0.09114227443933487,
-0.047140464186668396,
0.03961540013551712,
0.005274901632219553,
-0.0050182463601231575,
-0.019336191937327385,
0.002797418739646673,
-0.008618108928203583,
0.012346690520644188,
0.028240157291293144,
-0.009458152577280998,
-0.05214148759841919,
-0.016432635486125946,
0.0252651646733284,
0.0602908581495285,
-0.031501539051532745,
0.046178024262189865,
-0.02565387636423111,
-0.01795104332268238,
0.003407035255804658,
-0.002441847464069724,
-0.00563492625951767,
-0.01636967621743679,
-0.0077392845414578915,
0.02557467296719551,
-0.015087911859154701,
0.00422047870233655,
0.059245865792036057,
0.06540461629629135,
-0.031805478036403656,
-0.0069918264634907246,
0.03941738232970238,
0.020899739116430283,
0.012160386890172958,
-0.004969139117747545,
-0.04275043308734894,
0.0396387055516243,
-0.029169579967856407,
0.03874114155769348,
-0.01000738050788641,
-0.023379001766443253,
0.0472165122628212,
-0.021465204656124115,
0.024516407400369644,
-0.046092692762613297,
0.008165224455296993,
-0.032945357263088226,
0.00990938302129507,
0.005850873421877623,
0.02014009654521942,
-0.011796725913882256,
-0.008285967633128166,
0.021698812022805214,
0.008764775469899178,
0.0041688778437674046,
-0.0015774982748553157,
-0.06138848140835762,
-0.03254971280694008,
-0.050813328474760056,
-0.017216917127370834,
0.04735841229557991,
-0.007843229919672012,
-0.0013640545075759292,
-0.005328913684934378,
-0.019513430073857307,
0.00021270425349939615,
0.020243003964424133,
0.061389464884996414,
-0.02743583358824253,
0.015600268729031086,
0.008886829949915409,
0.03970276191830635,
0.0043711899779737,
-0.0042069703340530396,
0.12579308450222015,
0.027291106060147285,
-0.0114648612216115,
-0.055707868188619614,
0.01005669217556715,
-0.02125592716038227,
0.013847689144313335,
-0.03685000166296959,
0.03185628727078438,
-0.028283430263400078,
0.046751804649829865,
0.04705251753330231,
0.00922151654958725,
-0.025447698310017586,
0.013046126812696457,
0.028593270108103752,
-0.05441417545080185,
-0.04208178445696831,
-0.008519506081938744,
0.008057468570768833,
-0.03379341587424278,
0.038507699966430664,
-0.010896559804677963,
0.022716982290148735,
-0.052920203655958176,
-0.03270426765084267,
-0.022890761494636536,
-0.04082323610782623,
0.03369772434234619,
0.016541240736842155,
-0.04337228834629059,
0.008536011911928654,
0.04023043438792229,
-0.03540588915348053,
-0.04735962301492691,
0.036468807607889175,
0.04068633168935776,
0.005580780562013388,
0.018661245703697205,
0.020240701735019684,
-0.0035174426157027483,
-0.00666055316105485,
0.021528802812099457,
0.02717054821550846,
-0.059761058539152145,
-0.022946227341890335,
0.023466255515813828,
0.04032120108604431,
-0.002207823796197772,
0.002278018044307828,
0.005908408667892218,
-0.0016584631521254778,
-0.027282847091555595,
-0.07367885112762451,
0.0026842067018151283,
-0.012663359753787518,
-0.0057741859927773476,
-0.015803223475813866,
-0.04655631631612778,
0.022140664979815483,
0.0030543070752173662,
-0.028910579159855843,
0.011864389292895794,
-0.015237811021506786,
0.03514424338936806,
-0.019188493490219116,
-0.004740544129163027,
-0.009872949682176113,
-0.01286228559911251,
-0.041172340512275696,
-0.05675524100661278,
-0.011363085359334946,
-0.019262904301285744,
-0.04650403559207916,
-0.0010164640843868256,
0.02356814406812191,
0.017102397978305817,
0.01689743436872959,
-0.015644429251551628,
-0.023392118513584137,
-0.05623411759734154,
0.03120916336774826,
-0.0034718129318207502,
-0.026670390740036964,
-0.03669244423508644,
0.0020743939094245434,
0.036028243601322174,
0.06869925558567047,
-0.014781052246689796,
-0.03116036020219326,
-0.014509432017803192,
0.02078281156718731,
0.030808795243501663,
0.005654656328260899,
-0.03961063548922539,
0.022794002667069435,
0.0014747817767784,
0.013719649985432625,
0.03508146479725838,
0.0340108647942543,
0.04305216670036316,
0.05057505518198013,
0.022970516234636307,
0.03393729031085968,
-0.01957598328590393,
-0.004998530726879835,
-0.01769357919692993,
-0.01691901683807373,
0.042072683572769165,
0.018108883872628212,
0.018770812079310417,
-0.0343807190656662,
-0.02967592142522335,
0.004432239569723606,
-0.0050069051794707775,
0.04354947805404663,
0.03361622616648674,
0.01194072887301445,
-0.014593708328902721,
0.0134535888209939,
0.019764015451073647,
-0.034641120582818985,
-0.03774836286902428,
-0.03788035362958908,
-0.00029179101693443954,
0.0019799047149717808,
-0.006694301497191191,
-0.02454756386578083,
0.051897186785936356,
0.020907077938318253,
-0.04313603788614273,
0.040269508957862854,
0.03667788207530975,
0.002755336929112673,
0.010578622110188007,
0.021431514993309975,
-0.005435445345938206,
0.03941452503204346,
0.01280894223600626,
-0.05992298573255539,
0.037351854145526886,
-0.01919344812631607,
-0.04020264372229576,
-0.010653918609023094,
-0.012149554677307606,
0.022304758429527283,
-0.00528719462454319,
-0.011546009220182896,
0.03618685528635979,
0.0367053858935833,
0.0012627725955098867,
-0.02944902703166008,
-0.009879139252007008,
-0.027957146987318993,
0.027407197281718254,
-0.028384525328874588,
-0.011018306948244572,
-0.039396874606609344,
-0.014101739041507244,
0.08047696948051453,
-0.004106185864657164,
0.010577344335615635,
-0.004077142104506493,
0.009052437730133533,
-0.014116666279733181,
-0.03566461056470871,
0.01100742444396019,
-0.004589367192238569,
-0.0028251754119992256,
0.018494034186005592,
-0.032982151955366135,
0.07417965680360794,
0.03071124665439129,
-0.014607461169362068,
-0.11304765939712524,
-0.014682968147099018,
-0.013543561100959778,
0.012948350049555302,
0.05210017040371895,
-0.04160835221409798,
0.026302967220544815,
0.058786388486623764,
-0.08898498862981796,
0.012079442851245403,
0.00955833587795496,
-0.027985062450170517,
-0.03505037724971771,
-0.0018219612538814545,
-0.008105502463877201,
0.05882403999567032,
0.03214431554079056,
0.041031092405319214,
0.03699127584695816,
-0.0003491135430522263,
-0.01877421885728836,
0.012862339615821838,
-0.020902307704091072,
0.02532929927110672,
-0.04010850936174393,
0.01911296136677265,
0.054902080446481705,
0.01878420077264309,
0.004537968896329403,
0.005704050417989492,
-0.001833767513744533,
0.006625672802329063,
0.027888614684343338,
-0.007467977236956358,
-0.018887797370553017,
0.030943488702178,
0.017937103286385536,
-0.030580956488847733,
-0.020579025149345398,
0.01122236903756857,
-0.00279565853998065,
0.017802806571125984,
-0.0029123243875801563,
0.009792708791792393,
0.007903492078185081,
-0.07452722638845444,
-0.022105270996689796,
0.005096930544823408,
-0.0006544776842929423,
-0.0015026527689769864,
-0.0011109892511740327,
0.014574232511222363,
0.028169553726911545,
-0.020908454433083534,
0.0022989290300756693,
-0.040683314204216,
-0.024105601012706757,
0.06230601668357849,
0.00834288727492094,
-0.03479835391044617,
0.01881759613752365,
-0.034263867884874344,
-0.057190973311662674,
0.0030024342704564333,
-0.004608100280165672,
-0.031627386808395386,
-0.022996416315436363,
-0.018847716972231865,
-0.0014822910306975245,
-0.0242796428501606,
0.012143469415605068,
-0.020224472507834435,
-0.026143912225961685,
0.05124571546912193,
0.016407042741775513,
-0.002980724908411503,
0.006422616075724363,
-0.021676385775208473,
-0.06769248098134995,
-0.05088360235095024,
0.03984525427222252,
-0.0005754127632826567,
-0.014368344098329544,
-0.034846168011426926,
-0.0035241413861513138,
-0.028643155470490456,
0.02795315720140934,
0.06369780749082565,
0.05855540186166763,
-0.00849525909870863,
0.0026509114541113377,
0.004260746296495199,
0.025975901633501053,
-0.0557023249566555,
-0.016391152516007423,
0.007476654835045338,
0.005701161455363035,
-0.030055010691285133,
-0.03030291199684143,
-0.02580074965953827,
0.015939000993967056,
-0.01624632254242897,
-0.005578077398240566,
0.032427020370960236,
0.03513268008828163,
-0.010862165130674839,
0.029546819627285004,
0.02206818200647831,
-0.031670648604631424,
0.08075454086065292,
-0.01058876607567072,
0.015566694550216198,
0.04540098458528519,
-0.03981790691614151,
-0.0817531868815422,
-0.01797936111688614,
-0.026372717693448067,
-0.01148891355842352,
-0.0006071517709642649,
0.011060691438615322,
0.025713730603456497,
-0.019181743264198303,
0.02394912764430046,
0.007213550619781017,
-0.07742343842983246,
0.02212430164217949,
0.05020745098590851,
0.00029315127176232636,
0.040930554270744324,
-0.00459996797144413,
0.011666650883853436,
0.02788824774324894,
-0.009260392747819424,
0.013822045177221298,
0.07408737391233444,
0.0051489626057446,
-0.006051252130419016,
-0.0016863062046468258,
0.05235788971185684,
0.0198152307420969,
-0.020602300763130188,
0.006867746822535992,
0.05440842732787132,
-0.04175984114408493,
-0.028142469003796577,
0.008819916285574436,
-0.03681735321879387,
0.00026134640211239457,
0.05141545087099075,
0.0012429720954969525,
0.07259050756692886,
-0.023607075214385986,
0.03098553605377674,
-0.01493067853152752,
-0.002158482326194644,
-0.034081701189279556,
0.020702900364995003,
0.04594197869300842,
0.029870200902223587,
-0.0005030148313380778,
-0.04636549577116966,
0.005244463682174683,
-0.010440928861498833,
0.013212068937718868,
0.008248875848948956,
0.016389833763241768,
0.0016112293815240264,
-0.03397282958030701,
-0.025366032496094704,
-0.01170207466930151,
-0.00876046996563673,
-0.020347388461232185,
0.012037137523293495,
0.027719350531697273,
0.007887778803706169,
0.05217527225613594,
0.002653875621035695,
-0.02125065214931965,
0.013855754397809505,
-0.06152363121509552,
0.015573999844491482,
-0.01234840415418148,
0.01320980116724968,
-0.03784007951617241,
-0.009556774981319904
] |
<p>Consider the quantum system $\mathcal{B}(\mathbb{C}^d\otimes\mathbb{C}^d)$ and $|\psi\rangle=\frac{1}{\sqrt{d}}\sum_{i=0}^{d-1}|i,i\rangle$ be the (standard) maximally entangled state. Consider the state </p>
<p>$\rho_\lambda=\lambda \frac{\mathbb{I}_{d^2}}{d^2}+(1-\lambda)|\psi\rangle\langle\psi|.$</p>
<p>Now for some values of $\lambda$ this state is entangled (example $\lambda=0$ it is $|\psi\rangle\langle\psi|$) and hence its entanglement can be detected by partial transpose operation. </p>
<p>Can $\rho(\lambda)$ be an entangled state which is positive under partial transpose (known in literature as PPT entangled state) for some values $\lambda$? My intuition tells me that this is the case. However, I was told (without reference) that this is not the case and for the values of $\lambda$ we get only separable states or not PPT entangled states. I could not find the corresponding paper. May be I am not giving the proper string for searching. Advanced thanks for any suggestion, reference or comment.</p> | 1,528 | [
-0.0024673191364854574,
0.011833085678517818,
-0.00026573549257591367,
-0.0339408814907074,
0.03785087540745735,
0.009823298081755638,
-0.018966970965266228,
-0.0328354649245739,
0.054561179131269455,
-0.05000627785921097,
0.0436173714697361,
0.02522220090031624,
0.05192628130316734,
0.0404936820268631,
-0.0026275841519236565,
-0.002963618841022253,
-0.037196941673755646,
-0.011557717807590961,
-0.015231885015964508,
-0.008396852761507034,
0.01399930752813816,
0.05781354010105133,
0.014264632016420364,
0.006765276193618774,
0.007972508668899536,
0.033749792724847794,
0.003901646239683032,
0.017289845272898674,
0.007278457749634981,
0.08099600672721863,
-0.015630031004548073,
-0.010138081386685371,
-0.023096537217497826,
0.04663419350981712,
0.0010906144743785262,
-0.03227829188108444,
-0.039856601506471634,
-0.03568695858120918,
0.002410998335108161,
-0.0029735644347965717,
-0.03520537167787552,
-0.05035765469074249,
0.0016152941389009356,
0.047001320868730545,
-0.017095087096095085,
0.008557146415114403,
0.02026096172630787,
-0.038987405598163605,
0.04595573619008064,
-0.09055685997009277,
0.03301050513982773,
0.035028599202632904,
0.020317578688263893,
-0.012005885131657124,
0.005818110425025225,
0.0016963662346825004,
0.052336614578962326,
0.07822441309690475,
-0.0026859077624976635,
-0.05295560881495476,
-0.014491098932921886,
0.001510057714767754,
0.02960984967648983,
-0.006700845435261726,
-0.052888017147779465,
-0.009581586346030235,
0.004346157889813185,
-0.024942288175225258,
0.01997133158147335,
-0.02262394316494465,
0.005050939042121172,
0.008040477521717548,
0.04661921411752701,
-0.0485769622027874,
0.019041262567043304,
-0.021692926064133644,
0.014662746340036392,
0.05170915648341179,
0.039207540452480316,
0.017039623111486435,
0.019711889326572418,
0.005312041379511356,
0.0171070396900177,
0.032571371644735336,
-0.0016900954069569707,
-0.01797863095998764,
0.04270393028855324,
0.005727364681661129,
0.007819128222763538,
0.026627440005540848,
0.003965300507843494,
-0.023415951058268547,
0.03749808296561241,
-0.014542324468493462,
-0.03378523886203766,
-0.0005177417187951505,
-0.01114573609083891,
0.025207506492733955,
0.010808192193508148,
-0.04384700581431389,
-0.02852701209485531,
-0.04061097279191017,
0.0033107977360486984,
0.07563082873821259,
0.006333560682833195,
0.024386899545788765,
-0.008787344209849834,
0.023616163060069084,
-0.006724535021930933,
-0.00008946172602009028,
-0.026449056342244148,
0.009902950376272202,
0.032348837703466415,
-0.03426691144704819,
-0.02561524324119091,
-0.03795896843075752,
-0.00855565257370472,
-0.02381996065378189,
0.06740570813417435,
0.07016555964946747,
-0.006930888630449772,
-0.014384206384420395,
0.013683260418474674,
-0.05523962900042534,
-0.06559092551469803,
0.03291865065693855,
0.03925832733511925,
0.00668462086468935,
-0.0831802561879158,
0.043756820261478424,
0.045107681304216385,
-0.0032802450004965067,
0.01411243062466383,
0.017041746526956558,
0.02291855774819851,
-0.03405786678195,
-0.11966298520565033,
-0.0463254414498806,
0.0245344415307045,
-0.021647289395332336,
0.007939819246530533,
-0.049873556941747665,
0.031236425042152405,
0.03021237999200821,
0.08812739700078964,
-0.012608746066689491,
0.019826965406537056,
0.011743251234292984,
0.007496518082916737,
0.05443858727812767,
0.0003348661120980978,
-0.021653499454259872,
0.02199762500822544,
-0.051238253712654114,
-0.012530257925391197,
-0.0456048883497715,
-0.009208089672029018,
0.04999286308884621,
-0.014854053035378456,
0.032768696546554565,
0.062339115887880325,
-0.008094856515526772,
-0.013211997225880623,
0.04514170438051224,
-0.012544809840619564,
-0.03027106635272503,
0.08098554611206055,
0.024993181228637695,
0.030777698382735252,
0.05220852047204971,
0.0006368722533807158,
0.01842254027724266,
0.009690651670098305,
0.032813116908073425,
0.008986953645944595,
-0.03751799836754799,
-0.053616005927324295,
-0.029870888218283653,
0.02662569284439087,
-0.02504657953977585,
-0.02912876009941101,
-0.013255804777145386,
-0.07047868520021439,
0.030317068099975586,
0.008900600485503674,
0.025538435205817223,
0.0010149237932637334,
-0.021839603781700134,
0.007034361828118563,
-0.04830622300505638,
0.016032114624977112,
-0.02205010876059532,
0.057275429368019104,
0.03165040165185928,
-0.05379214510321617,
0.035118069499731064,
0.013607519678771496,
0.02878437004983425,
-0.013806934468448162,
-0.007374226115643978,
-0.031901389360427856,
0.009968707337975502,
0.0370878241956234,
-0.025635458528995514,
0.014153512194752693,
0.027645496651530266,
0.0348210372030735,
0.02967717871069908,
-0.009611154906451702,
-0.012402712367475033,
-0.02792477421462536,
-0.0029249603394418955,
0.0023731968831270933,
0.014446926303207874,
-0.014020492322742939,
-0.008146865293383598,
0.011578742414712906,
0.0039945258758962154,
-0.0038343798369169235,
0.03844728320837021,
-0.06367502361536026,
0.023280173540115356,
0.02451714314520359,
0.019905023276805878,
-0.00640409579500556,
0.022295216098427773,
0.028750106692314148,
-0.0015185810625553131,
-0.04072435572743416,
-0.02976325713098049,
-0.061265215277671814,
0.022046905010938644,
-0.0005100022535771132,
0.05585455894470215,
-0.05970754474401474,
0.01619708724319935,
0.03642818331718445,
0.02858305349946022,
0.027783015742897987,
0.026050960645079613,
-0.02658693678677082,
-0.030327077955007553,
0.0007187771843746305,
0.014696063473820686,
0.01896239072084427,
0.010825677774846554,
-0.0040395925752818584,
-0.01691751927137375,
0.07838983088731766,
-0.007144258823245764,
-0.028733449056744576,
0.02261454425752163,
-0.032465431839227676,
0.046081528067588806,
-0.016640812158584595,
-0.025033297017216682,
0.02842184156179428,
-0.026760995388031006,
0.021502234041690826,
0.026226691901683807,
-0.023187151178717613,
-0.004171000327914953,
-0.021946122869849205,
-0.04692719876766205,
-0.00018096908752340823,
-0.0017457975773140788,
-0.046898290514945984,
-0.06039147824048996,
0.014775174669921398,
-0.03671273589134216,
0.03692297264933586,
-0.029366739094257355,
-0.004683204926550388,
-0.014788895845413208,
0.01947811059653759,
0.05703241378068924,
-0.016842802986502647,
0.02930358611047268,
-0.044131383299827576,
-0.03457878530025482,
-0.01308044046163559,
-0.02635849080979824,
0.033942561596632004,
0.005779595114290714,
-0.06959164887666702,
-0.012962530367076397,
-0.07562880218029022,
-0.01721983589231968,
0.023516101762652397,
-0.016909431666135788,
0.03529253229498863,
0.013048212975263596,
-0.016113581135869026,
-0.024720456451177597,
-0.044826045632362366,
-0.03237846493721008,
0.01934673823416233,
-0.055119361728429794,
0.004253465682268143,
0.0012651775032281876,
-0.009084919467568398,
-0.03301957622170448,
-0.013328677974641323,
-0.043958764523267746,
-0.02463032305240631,
-0.02030772715806961,
-0.05066234618425369,
0.025898979976773262,
-0.027775229886174202,
0.035886019468307495,
0.02090127021074295,
-0.03163579851388931,
0.020995330065488815,
-0.061040401458740234,
-0.07475198060274124,
0.05449781194329262,
0.012629890814423561,
0.027855336666107178,
-0.006553239189088345,
-0.029574329033493996,
0.05713580921292305,
0.0033262704964727163,
-0.03766718879342079,
0.006527321878820658,
0.0278717540204525,
-0.006736638955771923,
-0.0018314715707674623,
-0.02881707064807415,
0.009830694645643234,
0.007478342391550541,
0.05970443785190582,
0.00033871299820020795,
0.022578805685043335,
0.05062836408615112,
0.0014200957957655191,
-0.06210072711110115,
0.026627445593476295,
0.009380302391946316,
0.0057698930613696575,
0.060902711004018784,
-0.004832166247069836,
-0.004562433809041977,
-0.0041968668811023235,
0.017152829095721245,
0.008485740050673485,
-0.02521505206823349,
-0.03962484747171402,
0.052898287773132324,
-0.0017752418061718345,
0.013243330642580986,
-0.015886561945080757,
0.01808316446840763,
-0.009097129106521606,
-0.0008968387264758348,
-0.01546061597764492,
0.0471932478249073,
-0.0026358889881521463,
-0.018228895962238312,
-0.006769559346139431,
0.05965053290128708,
-0.0306025892496109,
-0.013239985331892967,
0.0016453138086944818,
0.01763536036014557,
0.007827277295291424,
0.0487624816596508,
-0.03195168450474739,
-0.026333024725317955,
0.03612632304430008,
0.013456368818879128,
0.012394835241138935,
-0.005563016515225172,
-0.011304888874292374,
0.02291078120470047,
-0.054856788367033005,
-0.004298800136893988,
-0.01272732112556696,
0.0366939976811409,
-0.014509184285998344,
0.03902319073677063,
0.03637618571519852,
0.012364120222628117,
0.0023070245515555143,
-0.027573198080062866,
-0.07882317155599594,
-0.011542821303009987,
-0.005506360437721014,
0.0063307518139481544,
-0.0009722562972456217,
-0.03250332921743393,
-0.031391553580760956,
-0.05721685662865639,
-0.03293812647461891,
0.00288450182415545,
-0.001845584250986576,
-0.07644972950220108,
0.02020985446870327,
0.006391467526555061,
-0.02771054022014141,
-0.024083301424980164,
0.04282497242093086,
0.004635400604456663,
-0.02072182670235634,
0.020723573863506317,
0.0529174841940403,
-0.0427568145096302,
0.018235944211483,
0.005308192223310471,
0.0011143303709104657,
0.012385208159685135,
0.04301416873931885,
0.03174061328172684,
0.05236625671386719,
-0.02390218712389469,
0.030251864343881607,
-0.02486519142985344,
0.04578085616230965,
-0.01159463357180357,
-0.03823235630989075,
0.0054275100119411945,
-0.02776876837015152,
-0.024811958894133568,
-0.013210318051278591,
0.05336013808846474,
0.03323592245578766,
-0.012158953584730625,
0.037189651280641556,
0.00842542015016079,
-0.02922467142343521,
0.016463078558444977,
0.06293492019176483,
-0.02259952761232853,
-0.031157050281763077,
-0.03223885968327522,
-0.021951330825686455,
-0.03766847401857376,
0.014318283647298813,
0.024792110547423363,
-0.013823924586176872,
-0.018023967742919922,
0.012296933680772781,
0.044270940124988556,
0.04179041087627411,
-0.011483176611363888,
-0.0025682218838483095,
-0.005973010323941708,
0.006424420513212681,
-0.005530893336981535,
0.020514346659183502,
0.028349043801426888,
0.0060200137086212635,
0.030846714973449707,
0.013059534132480621,
0.017200008034706116,
-0.05562416464090347,
-0.0413685217499733,
0.013622703030705452,
0.03183160349726677,
0.008039934560656548,
0.023952819406986237,
-0.021605582907795906,
-0.050187088549137115,
0.020937465131282806,
-0.003204032313078642,
0.08511664718389511,
-0.02604524791240692,
-0.03320125490427017,
-0.020946914330124855,
-0.01773718371987343,
-0.01787373796105385,
0.018581734970211983,
0.02071050927042961,
-0.0012284322874620557,
-0.021265653893351555,
-0.006001886911690235,
-0.002136882161721587,
-0.022909564897418022,
0.005630890838801861,
0.04437337815761566,
0.0005557200638577342,
-0.0025783476885408163,
-0.0071755568496882915,
0.016557617112994194,
-0.03687728941440582,
-0.08142094314098358,
0.029183726757764816,
-0.013480090536177158,
0.0009461180306971073,
0.039005350321531296,
-0.026389529928565025,
-0.033632632344961166,
-0.004882228095084429,
0.024170653894543648,
-0.02249736711382866,
0.04763444513082504,
-0.0029805507510900497,
0.04682277515530586,
0.002062019892036915,
-0.062153641134500504,
0.03924999013543129,
0.029191534966230392,
-0.0033643224742263556,
-0.011368398554623127,
0.0014573519583791494,
0.07154179364442825,
-0.03927440568804741,
0.03755584731698036,
-0.026305442675948143,
0.031111380085349083,
-0.012416461482644081,
0.037639643996953964,
-0.006120673380792141,
0.026760965585708618,
0.0023323153145611286,
-0.026731444522738457,
0.00791159551590681,
0.03148934245109558,
-0.0030092375818639994,
0.0007302048034034669,
0.012486622668802738,
0.04847867414355278,
0.010501885786652565,
-0.02152964100241661,
0.008315272629261017,
-0.004178815521299839,
0.02006903849542141,
0.024399112910032272,
-0.012921598739922047,
0.03041781298816204,
-0.013222737237811089,
-0.005698542110621929,
0.014237591996788979,
-0.032275114208459854,
0.02872963808476925,
-0.010240008123219013,
0.008014516904950142,
-0.006734991911798716,
-0.057992830872535706,
-0.03720596060156822,
0.026463519781827927,
0.0024856608361005783,
-0.0025108095724135637,
-0.06027941778302193,
0.014489040710031986,
-0.008433863520622253,
-0.013272181153297424,
-0.05629757046699524,
-0.019811563193798065,
0.022376051172614098,
0.0014877979410812259,
-0.02880213037133217,
-0.021759800612926483,
0.01265294011682272,
-0.010700251907110214,
-0.010602721944451332,
-0.07758339494466782,
0.06272987276315689,
-0.013312571682035923,
-0.01799750328063965,
0.021472137421369553,
0.03220149129629135,
-0.0034222432877868414,
-0.03970736265182495,
0.012871758081018925,
-0.012704667635262012,
0.03703547641634941,
0.00039018390816636384,
0.010550417006015778,
0.04319985955953598,
-0.01809718646109104,
-0.02793114446103573,
-0.00834834948182106,
0.024165060371160507,
0.017180750146508217,
-0.033075883984565735,
-0.012583455070853233,
-0.027892544865608215,
-0.002755239140242338,
0.02591584250330925,
0.011379823088645935,
-0.01272087637335062,
-0.00846866425126791,
0.009149914607405663,
0.017709266394376755,
-0.0015016603283584118,
-0.035137079656124115,
-0.04918061941862106,
0.015733947977423668,
-0.01695309393107891,
-0.002473395550623536,
-0.017895996570587158,
0.05530907213687897,
0.0526745580136776,
-0.0008915052167139947,
0.007674173917621374,
-0.014878944493830204,
0.01053987629711628,
0.006770431529730558,
-0.0009210050338879228,
0.017247524112462997,
-0.00013567283167503774,
-0.028289929032325745,
-0.041238512843847275,
-0.04079671576619148,
0.019022522494196892,
0.06018323078751564,
0.03336038812994957,
0.045253098011016846,
0.023683900013566017,
-0.034833576530218124,
-0.025594662874937057,
-0.04723304137587547,
-0.025618715211749077,
0.025216329842805862,
-0.00349705689586699,
0.04978684335947037,
-0.03429234027862549,
0.01084503997117281,
0.02561117149889469,
0.04104045778512955,
-0.012781484052538872,
0.04297364503145218,
0.04669948294758797,
0.02016075886785984,
0.04701463505625725,
-0.02210681140422821,
-0.017870498821139336,
0.04934779182076454,
-0.060308072715997696,
-0.000188073783647269,
0.009397913701832294,
-0.018433215096592903,
0.004777493420988321,
0.01592184230685234,
0.04413947835564613,
-0.0313773974776268,
-0.006011886056512594,
-0.046532951295375824,
0.02062673680484295,
0.01519406121224165,
-0.014163347892463207,
0.007472944911569357,
0.0014602246228605509,
0.018277481198310852,
-0.008191602304577827,
0.0313558429479599,
0.0008609904907643795,
-0.029270045459270477,
-0.026804206892848015,
-0.01950768008828163,
-0.009889548644423485,
0.03717043623328209,
-0.030570456758141518,
0.010107512585818768,
0.01814648136496544,
-0.038805924355983734,
0.027574637904763222,
0.013089626096189022,
0.044302139431238174,
0.009759210050106049,
0.04784519225358963,
-0.013416817411780357,
-0.00853449571877718,
-0.001733478158712387,
0.003968234173953533,
0.12306585162878036,
0.076315738260746,
-0.0017264016205444932,
-0.06908715516328812,
0.017707163468003273,
0.02513022907078266,
0.035836078226566315,
-0.0481131374835968,
0.036373503506183624,
-0.005660424008965492,
0.0032827730756253004,
0.017565429210662842,
0.06190590560436249,
0.03546242043375969,
-0.021714992821216583,
0.016234856098890305,
-0.04266565665602684,
-0.058461472392082214,
0.03161932900547981,
0.01684265211224556,
-0.013982060365378857,
-0.02948758378624916,
0.0021511262748390436,
-0.01614755392074585,
0.0049748909659683704,
0.008275402709841728,
-0.03185413032770157,
0.02790726348757744,
-0.009529086761176586,
0.0006465105107054114,
-0.03439314290881157,
-0.0036596949212253094,
0.005281217861920595,
-0.006532387342303991,
-0.04012807458639145,
0.0041244723834097385,
0.023448023945093155,
0.011354063637554646,
-0.005070706829428673,
0.023058012127876282,
-0.0018703722162172198,
-0.007495260331779718,
0.03703698143362999,
0.01478348858654499,
-0.05681733042001724,
0.01150038093328476,
0.014493766240775585,
0.0579255074262619,
-0.037658266723155975,
0.01638491451740265,
0.011774271726608276,
-0.043889738619327545,
-0.012932232581079006,
-0.03636348992586136,
-0.026164453476667404,
-0.001633228617720306,
0.01962210051715374,
-0.01352051179856062,
-0.016843082383275032,
-0.010114846751093864,
-0.02403535135090351,
-0.017016613855957985,
0.031878773123025894,
-0.059451255947351456,
-0.022575803101062775,
0.0029075765050947666,
-0.007289961911737919,
0.040578294545412064,
0.01054751593619585,
0.03086620382964611,
-0.010130858980119228,
-0.002008527284488082,
-0.02109272964298725,
-0.02437405288219452,
0.021855562925338745,
-0.011201988905668259,
0.05243833363056183,
0.010359215550124645,
-0.03224410116672516,
-0.0007757979328744113,
-0.06058603525161743,
0.012256803922355175,
-0.0394335500895977,
-0.014901846647262573,
-0.010164028964936733,
-0.009856367483735085,
0.06411205232143402,
0.04735729098320007,
-0.0034682208206504583,
-0.044318534433841705,
0.011964729055762291,
0.029998142272233963,
0.03149295225739479,
-0.0019511368591338396,
-0.016339635476469994,
-0.021472783759236336,
-0.014726406894624233,
0.02032364532351494,
-0.05529326573014259,
-0.0002898687671404332,
0.02535792998969555,
0.03504358232021332,
-0.02294914610683918,
0.01516517624258995,
-0.02001764625310898,
-0.004394298419356346,
0.02296588569879532,
-0.03860270231962204,
0.000007396033197437646,
-0.007751558441668749,
0.03300756588578224,
-0.015438314527273178,
-0.006500924937427044,
-0.033543478697538376,
-0.010191383771598339,
0.023206809535622597,
0.003927004057914019,
-0.047340452671051025,
-0.023369036614894867,
0.012502865865826607,
-0.013822266831994057,
-0.01258090790361166,
-0.06667003035545349,
-0.03942651301622391,
0.007001686841249466,
0.01836877129971981,
0.022184161469340324,
-0.00043387283221818507,
-0.001851869048550725,
-0.0002213928528362885,
-0.01967461407184601,
0.0378318652510643,
0.023463591933250427,
-0.04441399872303009,
-0.018223382532596588,
0.011313789524137974,
0.012897072359919548,
0.050001658499240875,
0.0029296965803951025,
-0.04708479344844818,
0.055474165827035904,
-0.04251199960708618,
0.004819483961910009,
0.04571134224534035,
0.025835465639829636,
0.008272433653473854,
0.028857344761490822,
0.020269054919481277,
-0.04509361833333969,
0.02705230377614498,
0.00857471115887165,
0.007591606117784977,
0.03146049380302429,
-0.03106209821999073,
-0.003248515771701932,
0.006642072461545467,
0.01187058910727501,
-0.01860741712152958,
-0.01535730343312025,
0.017630698159337044,
0.009763282723724842,
0.03551783412694931,
0.027891026809811592,
0.020448807626962662,
0.002024179557338357,
0.0687796100974083,
0.05744354426860809,
-0.01135233137756586,
0.016780920326709747,
0.04833822697401047,
-0.03955632075667381,
0.03574444726109505,
0.03170115873217583,
-0.00771174905821681,
-0.08410566300153732,
-0.012919597327709198,
-0.00259739370085299,
0.00620298134163022,
0.009962517768144608,
-0.05712547525763512,
0.007220002356916666,
0.024435581639409065,
-0.07677294313907623,
0.02443472109735012,
-0.012117622420191765,
0.021377138793468475,
-0.03102058544754982,
0.022713951766490936,
-0.06341774016618729,
0.051448602229356766,
0.02856646478176117,
0.027132710441946983,
0.03148414194583893,
0.0061597623862326145,
-0.023489290848374367,
-0.035388704389333725,
-0.03565162047743797,
0.021423717960715294,
0.022653738036751747,
-0.06292427331209183,
0.08187662810087204,
-0.010807444341480732,
-0.03853108733892441,
-0.0007433094433508813,
-0.036606255918741226,
-0.04044146463274956,
-0.03953556343913078,
0.024694498628377914,
0.02237163856625557,
0.04599890485405922,
0.03671629726886749,
-0.026038987562060356,
0.0042631542310118675,
0.010426456108689308,
0.005909224972128868,
0.024124369025230408,
-0.006178080569952726,
-0.016704512760043144,
0.037400469183921814,
-0.012044224888086319,
-0.04285414144396782,
0.03925507143139839,
-0.0032562841661274433,
-0.027849247679114342,
0.002175798872485757,
-0.009532813914120197,
0.021604539826512337,
-0.03286401554942131,
0.051167093217372894,
-0.052956365048885345,
-0.015745259821414948,
0.008461127988994122,
0.03451919928193092,
-0.002487011719495058,
0.013972374610602856,
-0.01976136490702629,
-0.054776716977357864,
0.04196518287062645,
0.014426063746213913,
0.03521689772605896,
-0.05435867980122566,
-0.05312815308570862,
0.01930004358291626,
-0.002730485750362277,
0.014379091560840607,
-0.05402802303433418,
-0.02446010708808899,
0.030124995857477188,
-0.01910017617046833,
0.038176774978637695,
-0.022357380017638206,
-0.045814137905836105,
-0.011730704456567764,
-0.057349953800439835,
0.038346078246831894,
0.03952840715646744,
0.03108162432909012,
-0.027232717722654343,
-0.026000306010246277,
-0.02121911384165287,
-0.01778203248977661,
0.026101812720298767,
0.02253960631787777,
-0.04645802825689316,
-0.0015456007095053792,
-0.00003169125920976512,
0.041712354868650436,
-0.0023986794985830784,
0.007603904698044062,
-0.020919255912303925,
0.006271105259656906,
-0.02258763276040554,
-0.0033775160554796457,
0.02026318572461605,
0.003440852975472808,
0.014475032687187195,
-0.0087661724537611,
0.0001560209784656763,
0.00652974471449852,
-0.015032220631837845,
0.09751911461353302,
0.005601059179753065,
0.02627665176987648,
0.08976355940103531,
0.013067363761365414,
0.03851540386676788,
0.009842379949986935,
-0.042767614126205444,
-0.0641929879784584,
-0.015184720046818256,
-0.007185859140008688,
-0.029335089027881622,
0.01917494833469391,
0.03781965374946594,
-0.0034876910503953695,
-0.010192656889557838,
-0.008356349542737007,
0.05339837446808815,
-0.04277971386909485,
-0.014944801107048988,
0.07664068043231964,
0.0071261064149439335,
0.03380851075053215,
0.021545154973864555,
0.04706598445773125,
0.04937802627682686,
0.0031263818964362144,
-0.0017037040088325739,
0.05241662263870239,
0.009889286942780018,
0.018480457365512848,
-0.003417345229536295,
0.00806820672005415,
-0.04089847952127457,
0.05555151030421257,
-0.0002917922683991492,
0.009631924331188202,
-0.02125120908021927,
-0.007635707035660744,
0.006840856745839119,
-0.026284845545887947,
-0.002387603046372533,
-0.008447240106761456,
-0.018377838656306267,
0.06000649183988571,
-0.035611070692539215,
0.027118979021906853,
-0.017180727794766426,
-0.012363110668957233,
-0.02372673526406288,
0.005805572494864464,
0.01970558986067772,
0.06521391868591309,
-0.028526658192276955,
-0.016702156513929367,
-0.02442263998091221,
-0.02212820202112198,
-0.016777001321315765,
-0.044637713581323624,
0.029728712514042854,
0.024463331326842308,
-0.026603369042277336,
0.007121049799025059,
-0.03349518030881882,
-0.005489992443472147,
-0.03916136175394058,
0.016525816172361374,
0.009586535394191742,
0.010798720642924309,
-0.02169439196586609,
-0.0011599858989939094,
-0.00936271995306015,
0.021971696987748146,
-0.03985840082168579,
-0.008518602699041367,
-0.012308544479310513,
0.02526981197297573,
-0.008827237412333488,
-0.019039351493120193
] |
<p>I'm currently learning about symmetry between particles. For a simple case of two non-interacting particles at $x_1$ and $x_2$, we know that the wavefunction can be written as $\psi_{n_1, n_2} = \phi_{n_1}(x_1) \phi_{n_2}(x_2)$</p>
<p>Let's consider two cases in ground state and first excited state.</p>
<p>(a) Two particles are not identical, and have spin zero</p>
<p>(b) Two identical particles, each with spin zero</p>
<p>We know that the energy is given by $E_n = (n_1 + n_2 + 1)\hbar \omega$.</p>
<p><strong>For case (a)</strong></p>
<p>Since they are not identical, the wavefunction at ground state would be $\phi_1(x_1) \phi_1 (x_2)$ right? Then the degeneracy would be 0 right? Since $n_1 = n_2 = 1$.</p>
<p>For the first excited state, the wavefunction would be $\phi_2(x_1)\phi_1(x_2)$, assuming $E_2(x_1) < E_2(x_2)$, meaning we just take whatever is lower. The degeneracy would be 0, since they are distinguishable?</p>
<p><strong>For case (b)</strong></p>
<p>Now they are identical, ground state wavefunction would still be $\phi_1(x_1)\phi_1(x_2)$ right? Degeneracy of ground state would be 0, since $n_1=n_2=1$?</p>
<p>But for the first excited state, the degeneracy would be 2, since either $n_1=2$ and $n_2=1$ or $n_1=1$ and $n_2=2$? Spin 0 particles are bosons, so the wavefunction must be symmetric right? So I'm thinking $\psi = \frac{1}{2} \left[ \phi_2(x_1)\phi_1(x_2) + \phi_1(x_1)\phi_2(x_2)\right]$</p>
<p>The concept of symmetry and exchange symmetry is still new to me, I'd appreciate any response!</p> | 1,529 | [
-0.02755257859826088,
-0.01314962562173605,
-0.005324549973011017,
-0.012644140049815178,
0.05031177029013634,
-0.02352636493742466,
-0.014238540083169937,
-0.05154230445623398,
0.03811664879322052,
-0.04557153955101967,
0.02425692044198513,
0.010384401306509972,
0.014352723024785519,
-0.020502112805843353,
0.02272351272404194,
0.020704494789242744,
0.019757341593503952,
-0.01734294928610325,
-0.009358431212604046,
0.0058174338191747665,
-0.002297621686011553,
0.039444342255592346,
0.0294219721108675,
-0.0009180746856145561,
-0.03966594487428665,
0.043957289308309555,
0.007271519396454096,
-0.00899523589760065,
-0.018733996897935867,
0.06216499209403992,
-0.005049118306487799,
-0.032453861087560654,
0.007303688675165176,
0.04130913317203522,
-0.00024519310682080686,
-0.002209244528785348,
-0.046092838048934937,
-0.04207615554332733,
0.016866100952029228,
0.0007633088389411569,
-0.02494059130549431,
-0.02681811712682247,
0.009815484285354614,
0.030942950397729874,
-0.01798572950065136,
0.003566192463040352,
0.028143566101789474,
-0.01486713532358408,
0.024220602586865425,
-0.0416567288339138,
0.06715472042560577,
-0.02199329435825348,
0.04296933487057686,
-0.0032363522332161665,
-0.005457714200019836,
-0.03576241433620453,
0.046564776450395584,
0.06372819095849991,
0.014228790067136288,
-0.06768687069416046,
-0.041240282356739044,
-0.025130581110715866,
-0.011385363526642323,
0.008550485596060753,
-0.05690177530050278,
-0.022772500291466713,
0.04481149837374687,
0.0054412055760622025,
0.026651300489902496,
0.01327027752995491,
0.007934898138046265,
0.004981218371540308,
0.04458833858370781,
-0.047555554658174515,
0.02473587356507778,
-0.004178284667432308,
0.019122984260320663,
0.020086776465177536,
-0.0027856635861098766,
0.023660678416490555,
-0.01118412334471941,
0.008846643380820751,
0.004813280887901783,
0.025047466158866882,
-0.0006390517228282988,
-0.013301895931363106,
0.04286680370569229,
-0.00803112331777811,
-0.018366485834121704,
0.028798624873161316,
0.0134441452100873,
0.01516100112348795,
0.056222934275865555,
-0.025546103715896606,
-0.012884923256933689,
0.03395269438624382,
0.007063120137900114,
-0.001354467705823481,
-0.01498013362288475,
-0.014330580830574036,
-0.022898323833942413,
-0.05643274635076523,
0.051383256912231445,
0.08098388463258743,
-0.00022149797587189823,
-0.008076079189777374,
-0.05495774373412132,
0.026771286502480507,
0.022204890847206116,
-0.021788807585835457,
-0.03609415143728256,
0.02595759741961956,
-0.024257322773337364,
0.005835418589413166,
-0.018273072317242622,
-0.02409587986767292,
0.014012455940246582,
-0.022944092750549316,
0.054810091853141785,
0.06724615395069122,
0.043363939970731735,
0.007226753514260054,
0.027200307697057724,
-0.013988836668431759,
-0.06754136830568314,
-0.016035398468375206,
0.04503834247589111,
0.004710239823907614,
-0.04880305752158165,
0.02862665243446827,
0.00556314829736948,
0.008573661558330059,
-0.005572920199483633,
0.019254418089985847,
0.015150644816458225,
-0.020494207739830017,
-0.11412271857261658,
-0.03136441484093666,
0.014003803953528404,
-0.04798521474003792,
-0.004668545909225941,
-0.06360090523958206,
0.010800165124237537,
0.06494218856096268,
0.09588664025068283,
-0.03487798571586609,
0.009053765796124935,
0.017177434638142586,
0.0473812110722065,
0.041816309094429016,
0.0423118881881237,
-0.03979736194014549,
-0.006679849699139595,
-0.03202090784907341,
-0.0343593992292881,
-0.04259491711854935,
0.035165201872587204,
0.026466963812708855,
-0.02389276959002018,
0.0073389397002756596,
0.07132359594106674,
-0.02085951901972294,
0.04200277850031853,
-0.012926245108246803,
0.01747824065387249,
0.002673935843631625,
0.0825289785861969,
-0.0024458568077534437,
-0.006701908074319363,
0.06383364647626877,
-0.036746811121702194,
0.016977475956082344,
-0.033235855400562286,
0.023009726777672768,
0.026077991351485252,
-0.03388237953186035,
-0.027403488755226135,
-0.03901302069425583,
-0.004704874940216541,
-0.0038023670203983784,
-0.058390162885189056,
0.011334202252328396,
-0.028862273320555687,
0.028924811631441116,
0.014255266636610031,
0.020455529913306236,
0.021520836278796196,
-0.01812722347676754,
-0.028422705829143524,
-0.03361112251877785,
-0.04642119258642197,
-0.06413304805755615,
-0.00008059954416239634,
-0.0003963291528634727,
-0.03561141714453697,
0.055350348353385925,
0.011568207293748856,
-0.023875314742326736,
-0.020113324746489525,
-0.029560329392552376,
-0.004131409339606762,
0.058493077754974365,
0.008771945722401142,
-0.05482012405991554,
0.03894056752324104,
0.06639940291643143,
0.02842799760401249,
0.005144669208675623,
0.05339941754937172,
-0.016231846064329147,
-0.01560696866363287,
0.023657627403736115,
-0.012598142959177494,
-0.010170932859182358,
0.013212712481617928,
0.036468829959630966,
0.0023836339823901653,
0.01983635313808918,
-0.015607261098921299,
0.02499351277947426,
-0.07820267230272293,
0.043337251991033554,
0.02430705353617668,
-0.004311142954975367,
0.0002805605181492865,
0.007239853031933308,
0.00813849363476038,
0.02532058209180832,
0.01379766408354044,
-0.023352917283773422,
-0.05545511096715927,
-0.016677740961313248,
-0.00032757603912614286,
0.03455745801329613,
-0.03635523468255997,
0.00041372724808752537,
0.008281051181256771,
0.021907253190875053,
0.009546535089612007,
-0.016885824501514435,
-0.010374937206506729,
-0.025796355679631233,
0.041791174560785294,
0.021989673376083374,
0.008121659979224205,
0.03988281264901161,
0.012342276982963085,
0.005293593741953373,
0.049136966466903687,
-0.009217384271323681,
-0.007396973669528961,
0.06252014636993408,
-0.0049656652845442295,
-0.020520629361271858,
-0.0245426744222641,
-0.04079493507742882,
0.012237431481480598,
0.014766041189432144,
0.04283317178487778,
0.03140243515372276,
-0.015591581352055073,
-0.011798698455095291,
-0.020485496148467064,
-0.03749822825193405,
-0.0033702831715345383,
-0.016864869743585587,
-0.02276848815381527,
-0.01476533617824316,
0.009733906015753746,
-0.033813148736953735,
-0.01207669172435999,
-0.018107784911990166,
-0.012492875568568707,
-0.004907373338937759,
-0.02014699950814247,
0.04658234864473343,
0.00662276241928339,
0.00049401173600927,
-0.046561166644096375,
-0.0023473487235605717,
-0.01246315985918045,
0.0023693700786679983,
0.03694695234298706,
0.04434887692332268,
-0.07380280643701553,
0.02649783529341221,
-0.06495640426874161,
-0.01297767274081707,
0.017825331538915634,
0.009376787580549717,
-0.001435600221157074,
0.039068177342414856,
0.007310895714908838,
-0.08911401033401489,
-0.023142604157328606,
-0.02648589201271534,
0.013620588928461075,
-0.08226552605628967,
-0.030525485053658485,
0.03515787422657013,
0.006230841390788555,
-0.02427423745393753,
0.010573301464319229,
0.00010045620001619682,
-0.03938726708292961,
0.0007365746423602104,
0.00794797670096159,
0.003733697347342968,
-0.033144161105155945,
0.03208616003394127,
0.0248490609228611,
0.021781601011753082,
-0.026504701003432274,
-0.06203468516469002,
-0.046374253928661346,
-0.005700479727238417,
0.0038858321495354176,
0.032610032707452774,
-0.010480337776243687,
-0.014560033567249775,
0.07927176356315613,
0.009362841956317425,
-0.0009710413287393749,
-0.016078172251582146,
0.018235228955745697,
-0.016204187646508217,
-0.01804165355861187,
0.012346133589744568,
0.05154809728264809,
0.03248623013496399,
0.046083759516477585,
0.009454496204853058,
0.041415050625801086,
0.008078081533312798,
-0.007355258800089359,
0.018753215670585632,
0.03651319816708565,
0.02341538853943348,
-0.0004330072260927409,
0.07800735533237457,
-0.02552037686109543,
0.004359982907772064,
0.04675401374697685,
0.019015897065401077,
-0.0035551711916923523,
0.007020294666290283,
-0.02768060937523842,
0.07097968459129333,
0.016013406217098236,
0.019605036824941635,
-0.027731290087103844,
0.04343743249773979,
0.020593304187059402,
-0.0022284453734755516,
-0.01343535352498293,
-0.011185617186129093,
0.043916184455156326,
-0.03290160745382309,
0.005416364874690771,
0.05542563647031784,
0.029941126704216003,
-0.04890242964029312,
-0.034821972250938416,
-0.02298486791551113,
0.020977940410375595,
0.03919386491179466,
-0.044023703783750534,
-0.03010181151330471,
0.0031794060487300158,
0.042263876646757126,
0.01930844970047474,
-0.0137966712936759,
-0.015492429956793785,
-0.009027107618749142,
-0.058395806699991226,
0.011854023672640324,
-0.01784519851207733,
0.05462241172790527,
-0.010081002488732338,
0.07807163894176483,
0.02560601942241192,
0.012859117239713669,
-0.009504467248916626,
0.008206038735806942,
-0.08281947672367096,
-0.003748882794752717,
-0.017026731744408607,
0.01644539274275303,
0.011975420638918877,
-0.04094858840107918,
-0.008844555355608463,
-0.016349151730537415,
-0.023300236091017723,
-0.015651701018214226,
-0.0016913118306547403,
-0.04619092494249344,
-0.009433972649276257,
-0.07002385705709457,
-0.024814970791339874,
-0.016050079837441444,
0.08294404298067093,
-0.0049401805736124516,
-0.00164266605861485,
-0.007817806676030159,
0.053094156086444855,
-0.05111946538090706,
0.039021190255880356,
-0.023381926119327545,
-0.02247825264930725,
0.027206839993596077,
0.051972322165966034,
0.023419447243213654,
0.0387888103723526,
-0.00452549709007144,
-0.05696701630949974,
0.014092635363340378,
0.08323627710342407,
0.029878709465265274,
-0.005069045815616846,
0.02801942452788353,
-0.00145907502155751,
-0.02748706191778183,
-0.022729843854904175,
0.08164412528276443,
-0.010015173815190792,
0.021636882796883583,
-0.00019080030324403197,
0.014014158397912979,
-0.030430927872657776,
0.016917303204536438,
0.038126710802316666,
0.016670336946845055,
0.017804943025112152,
-0.0005674342392012477,
-0.013840412721037865,
-0.07409262657165527,
-0.009998798370361328,
-0.01686255633831024,
-0.010083927772939205,
-0.025680162012577057,
0.024407153949141502,
0.025958770886063576,
0.037959493696689606,
-0.03257317468523979,
-0.01783657819032669,
-0.04212040826678276,
-0.017287248745560646,
0.011874843388795853,
-0.033409181982278824,
-0.014830777421593666,
0.02688085287809372,
0.02271455153822899,
-0.006879047024995089,
0.024436388164758682,
-0.034086376428604126,
-0.04426444321870804,
0.03286036103963852,
0.02985207363963127,
0.023521265015006065,
-0.032242514193058014,
-0.03926605358719826,
-0.02436864748597145,
0.014247950166463852,
-0.05265532061457634,
0.05001555755734444,
0.00805674772709608,
-0.023390555754303932,
-0.03031487576663494,
-0.055419329553842545,
-0.01576162874698639,
0.030059676617383957,
0.0028132498264312744,
0.03568258509039879,
-0.02700052596628666,
-0.012835022062063217,
-0.012865698896348476,
-0.0017467356519773602,
0.017700964584946632,
0.040626056492328644,
-0.02449573390185833,
-0.012309121899306774,
0.0011644625337794423,
0.03397119417786598,
-0.013287806883454323,
-0.08367318660020828,
0.012786757200956345,
0.007895899936556816,
-0.001599969225935638,
0.05935032293200493,
-0.036877866834402084,
-0.06399372965097427,
0.010138053447008133,
0.002222226932644844,
0.021621380001306534,
0.03760425001382828,
-0.04816511645913124,
0.07782702147960663,
0.0412108451128006,
-0.019487906247377396,
0.042570505291223526,
0.023314202204346657,
-0.022196544334292412,
0.02460566535592079,
-0.030293947085738182,
0.00048383648390881717,
-0.05420251935720444,
0.021222438663244247,
-0.06747491657733917,
0.0004025111556984484,
-0.05567179620265961,
0.044355519115924835,
-0.0501345656812191,
0.03342597559094429,
0.010748903267085552,
-0.04573375731706619,
0.006534332409501076,
0.019264843314886093,
-0.00863901898264885,
0.01160180289298296,
-0.014179674908518791,
-0.0029141365084797144,
0.026116393506526947,
-0.010118676349520683,
0.008669188246130943,
-0.03646446764469147,
-0.008586352691054344,
0.03088272176682949,
-0.007969321683049202,
0.0460871085524559,
-0.062040429562330246,
-0.02933090180158615,
0.0019138501957058907,
-0.052272405475378036,
0.03409041464328766,
0.003959381487220526,
0.017635803669691086,
0.005854295566678047,
-0.01265665516257286,
-0.05193347483873367,
0.062025174498558044,
0.0015381540870293975,
-0.02199423685669899,
-0.019342057406902313,
-0.0027444977313280106,
0.03507514297962189,
-0.017524030059576035,
-0.07047669589519501,
-0.035911351442337036,
0.010091454721987247,
-0.007464648690074682,
0.016606856137514114,
-0.0203221645206213,
0.010660870000720024,
-0.00018274461035616696,
-0.03265410289168358,
0.0032999201212078333,
0.030952733010053635,
-0.020094258710741997,
0.008148282766342163,
0.02314741723239422,
0.012560619972646236,
0.029712563380599022,
-0.0036432777997106314,
-0.04089690372347832,
-0.026522310450673103,
-0.031072795391082764,
0.004441580269485712,
0.01605209894478321,
0.01555243507027626,
-0.017975863069295883,
-0.03615392744541168,
-0.03264893218874931,
0.01202053390443325,
0.032187268137931824,
-0.012928083539009094,
-0.043211933225393295,
0.009014817886054516,
0.001693681813776493,
-0.019975153729319572,
-0.00005645998680847697,
-0.0213306937366724,
-0.021137304604053497,
0.02621867135167122,
0.0023914978373795748,
-0.011005262844264507,
-0.007567028980702162,
-0.053984906524419785,
0.013925094157457352,
-0.011058969423174858,
-0.010859169997274876,
0.046878620982170105,
0.0814882218837738,
0.0001321628806181252,
0.00649647181853652,
0.01058481726795435,
-0.028783759102225304,
-0.0005541446153074503,
-0.013901619240641594,
0.013291542418301105,
-0.009226972237229347,
0.0465799905359745,
-0.011429516598582268,
-0.026309426873922348,
-0.03554898872971535,
-0.0044869412668049335,
0.033466123044490814,
0.03574533388018608,
0.008351605385541916,
0.017383703961968422,
0.02780313976109028,
-0.041653525084257126,
-0.014190379530191422,
-0.0037923071067780256,
0.0035343675408512354,
-0.002472911961376667,
0.040979623794555664,
-0.02214791439473629,
-0.012616230174899101,
0.06622933596372604,
0.05020662769675255,
-0.00683399336412549,
0.019528690725564957,
0.037962622940540314,
-0.019167916849255562,
0.016660181805491447,
-0.012165580876171589,
-0.0385158397257328,
0.06392185389995575,
-0.030905719846487045,
0.04907360300421715,
-0.01308407261967659,
-0.020943647250533104,
0.009323827922344208,
0.02373841404914856,
0.03185850754380226,
-0.042757317423820496,
-0.02838394232094288,
-0.0439835749566555,
0.022340526804327965,
0.00003409323107916862,
-0.018025491386651993,
0.0041779689490795135,
0.027337655425071716,
0.03560909256339073,
-0.025607464835047722,
0.010952671058475971,
-0.011953385546803474,
-0.049796320497989655,
0.01584332436323166,
-0.0313696563243866,
-0.05054047703742981,
0.025231819599866867,
-0.04903801903128624,
-0.03326040878891945,
0.05147698521614075,
-0.017937086522579193,
0.025839315727353096,
-0.01647307351231575,
0.00999267864972353,
-0.02458643913269043,
0.024384964257478714,
0.0020016839262098074,
0.05613509938120842,
0.04408534616231918,
0.012249295599758625,
0.11763352900743484,
0.06673594564199448,
0.025898821651935577,
-0.0464031882584095,
0.019228491932153702,
0.011483476497232914,
0.020179880782961845,
-0.00514991907402873,
-0.013712047599256039,
0.01780943013727665,
0.0290911253541708,
-0.02477138675749302,
0.03145945072174072,
0.009802675805985928,
-0.0050649745389819145,
0.026959320530295372,
-0.02678924985229969,
-0.04379967600107193,
-0.02322413958609104,
0.032822754234075546,
0.03263728693127632,
0.00025499227922409773,
0.014468335546553135,
-0.003950121346861124,
-0.02446330152451992,
0.014931640587747097,
-0.04696867614984512,
-0.028453795239329338,
0.05771053954958916,
-0.0023662305902689695,
-0.015514928847551346,
0.01613835245370865,
-0.011139584705233574,
-0.02290337160229683,
-0.005662354175001383,
0.02987849712371826,
0.0005328577244654298,
-0.05064254254102707,
0.05256623402237892,
0.05139037221670151,
0.009932193905115128,
0.003710073884576559,
0.041209183633327484,
0.013693023473024368,
-0.028187086805701256,
-0.002992891473695636,
-0.023989826440811157,
0.07026678323745728,
-0.02880079671740532,
-0.040991559624671936,
0.008514219895005226,
0.0014630069490522146,
0.0027831769548356533,
-0.052300166338682175,
-0.02086643874645233,
0.020426757633686066,
0.020602479577064514,
-0.02749437652528286,
0.012710921466350555,
-0.029521604999899864,
0.03425068035721779,
0.02389618009328842,
0.009319941513240337,
-0.02558121643960476,
-0.02646464668214321,
0.012415958568453789,
-0.016962626948952675,
0.035935625433921814,
0.0007119798683561385,
0.014258887618780136,
0.004826187156140804,
-0.025313813239336014,
-0.046590689569711685,
-0.038173891603946686,
0.023891931399703026,
0.03270076587796211,
0.0483202300965786,
0.008582997135818005,
-0.014701050706207752,
-0.02792993374168873,
-0.05850102752447128,
0.022984569892287254,
-0.011936220340430737,
-0.023371657356619835,
0.02693290449678898,
0.005762371700257063,
-0.011587399989366531,
0.05759838968515396,
-0.0033337834756821394,
0.02073577232658863,
0.04074490815401077,
0.020261887460947037,
0.04231683909893036,
-0.049393583089113235,
-0.03553163260221481,
-0.013854056596755981,
-0.03266744315624237,
0.006318988744169474,
0.006957711651921272,
-0.00873894989490509,
0.004985342733561993,
0.006376749370247126,
0.0033123879693448544,
0.016625884920358658,
-0.022470176219940186,
-0.03873061388731003,
0.0061980951577425,
-0.038545962423086166,
0.021679619327187538,
0.048893533647060394,
0.03677377477288246,
-0.026360653340816498,
-0.02451450191438198,
-0.012074826285243034,
0.018521422520279884,
-0.0010144932894036174,
-0.039364639669656754,
-0.033659595996141434,
-0.047960348427295685,
-0.0218220092356205,
0.018296172842383385,
-0.00819817278534174,
-0.04453205317258835,
-0.00812272634357214,
0.01973726972937584,
0.010881849564611912,
-0.022470222786068916,
-0.0012324444251134992,
0.0407898873090744,
0.0364600233733654,
-0.016431378200650215,
0.03904328867793083,
0.06298115849494934,
0.004892679862678051,
-0.028935063630342484,
0.043276842683553696,
-0.020529529079794884,
0.009336431510746479,
0.018200619146227837,
-0.0021890876814723015,
-0.0031141801737248898,
-0.02454662322998047,
-0.0159060787409544,
0.02324889786541462,
0.03274596109986305,
0.00004192190681351349,
0.018123794347047806,
-0.04881151765584946,
-0.03716924414038658,
0.030596299096941948,
-0.031407855451107025,
-0.034408845007419586,
-0.02080574445426464,
-0.01968933269381523,
0.012199711054563522,
-0.033652570098638535,
0.02042406052350998,
0.006979088764637709,
-0.027847716584801674,
0.05240821838378906,
0.02566266432404518,
-0.02580965682864189,
-0.01413706410676241,
-0.0065666688606143,
0.037981268018484116,
0.06916350871324539,
0.038897547870874405,
0.021389666944742203,
-0.012044140137732029,
0.04095977172255516,
-0.007599253207445145,
0.031143873929977417,
-0.0013609258458018303,
-0.004704933613538742,
-0.04720473662018776,
-0.012656050734221935,
0.021242650225758553,
-0.020690234377980232,
0.04976184666156769,
-0.0038700527511537075,
0.06065400689840317,
0.03698871657252312,
-0.05379262939095497,
0.03400687500834465,
-0.004500985145568848,
0.026518531143665314,
-0.020440589636564255,
0.015395044349133968,
-0.07946282625198364,
0.03182634338736534,
0.02655746415257454,
0.0404595285654068,
0.02144717425107956,
0.012639084830880165,
-0.020620528608560562,
-0.032819412648677826,
-0.0019513812148943543,
0.028538715094327927,
-0.003550927620381117,
-0.040055565536022186,
0.024057235568761826,
-0.030363965779542923,
-0.026433754712343216,
0.02144392766058445,
-0.03705117106437683,
-0.04221638664603233,
-0.023243067786097527,
0.031423863023519516,
0.01596851833164692,
0.008695680648088455,
-0.026432035490870476,
0.031977396458387375,
0.004074468277394772,
0.021189559251070023,
0.036536846309900284,
0.012453161180019379,
-0.006832349579781294,
-0.022380519658327103,
0.026280729100108147,
-0.028633685782551765,
-0.039294686168432236,
0.05994256213307381,
0.01291778776794672,
-0.02218610793352127,
-0.0004166676080785692,
-0.01780518889427185,
-0.010989625938236713,
-0.019118009135127068,
0.014443711377680302,
-0.04547249898314476,
-0.0021379273384809494,
-0.003066305536776781,
0.01296654250472784,
-0.015632623806595802,
0.014258571900427341,
-0.00814870186150074,
-0.024516746401786804,
0.05694018304347992,
0.02971627190709114,
-0.003579661948606372,
-0.022248361259698868,
-0.0339478999376297,
-0.00020891500753350556,
0.07078542560338974,
-0.011099658906459808,
-0.04892836883664131,
-0.0352039635181427,
0.00082629598909989,
-0.013521669432520866,
0.017829198390245438,
-0.04030700400471687,
-0.016766706481575966,
-0.028049565851688385,
-0.06994049996137619,
0.0257872287184,
0.022712966427206993,
0.002391454065218568,
-0.05145752429962158,
0.012814093381166458,
-0.010043487884104252,
0.01728241890668869,
0.025583507493138313,
0.036404144018888474,
-0.01764458604156971,
0.015609602443873882,
0.023121988400816917,
-0.006121213547885418,
-0.003847650485113263,
0.018808582797646523,
-0.0028890299145132303,
-0.03477314114570618,
0.013026748783886433,
0.03186224400997162,
-0.04412828013300896,
0.053115688264369965,
0.02223355695605278,
-0.013175327330827713,
0.003661690279841423,
-0.002425394020974636,
-0.019308507442474365,
0.052811190485954285,
-0.058770257979631424,
0.00379636837169528,
0.06709080934524536,
-0.0023686683271080256,
-0.0026971972547471523,
0.02716134674847126,
-0.010609295219182968,
-0.043101321905851364,
0.008301536552608013,
-0.04516823589801788,
-0.044176362454891205,
0.012223253026604652,
-0.015779688954353333,
0.014281213283538818,
-0.03748910874128342,
0.018638139590620995,
0.025738311931490898,
-0.0289852786809206,
-0.028890641406178474,
0.03424806520342827,
0.033752165734767914,
0.03876477852463722,
0.014417785219848156,
0.01559005118906498,
-0.0012839306145906448,
-0.011926776729524136,
0.04670938104391098,
0.03749164193868637,
0.03098994493484497,
0.022965766489505768,
0.02392970770597458,
0.004348219837993383,
-0.010322128422558308,
0.020612962543964386,
-0.01219398807734251,
0.01570119336247444,
-0.017746813595294952,
-0.0028560301288962364,
0.05902082473039627,
-0.006764800287783146,
0.019530192017555237,
0.03145476430654526,
-0.0223502479493618,
0.07451517134904861,
-0.02824869565665722,
-0.0038956599310040474,
-0.017431287094950676,
0.05143190547823906,
0.0031652397010475397,
-0.004187260288745165,
0.009004423394799232,
0.029933160170912743,
-0.012199764139950275,
-0.0006218905909918249,
-0.04211784154176712,
0.0030067721381783485,
-0.00506112864241004,
-0.0743095874786377,
-0.012871730141341686,
0.029794124886393547,
-0.006121999584138393,
-0.012010940350592136,
-0.024974577128887177,
0.0012228136183694005,
-0.021450389176607132,
0.03329716995358467,
0.03115222416818142,
0.0020293965935707092,
-0.0006534481653943658,
-0.007243975065648556,
0.000944173545576632,
0.02850947342813015,
-0.02256367728114128,
-0.024689361453056335,
-0.008367537520825863,
-0.02029850333929062,
-0.02637072652578354,
-0.01028447039425373
] |
<p>The force for revolution of earth is provided by the gravitational force of attraction between earth and the sun. What provides the force(torque) for the rotation of earth? </p> | 1,530 | [
-0.030017944052815437,
0.02209225296974182,
-0.0388372465968132,
0.01324489712715149,
0.04433313384652138,
0.008570404723286629,
-0.04264024272561073,
-0.009619447402656078,
0.0022183244582265615,
-0.03285136818885803,
0.01768573932349682,
0.049472641199827194,
0.04520184174180031,
0.012784101068973541,
0.005533766001462936,
0.004087763372808695,
-0.004010828677564859,
0.013598483055830002,
-0.002927110530436039,
-0.013819320127367973,
-0.01526585128158331,
-0.004013170022517443,
-0.009217675775289536,
0.012264339253306389,
-0.031582485884428024,
0.016212111338973045,
0.07861851900815964,
0.0007070079445838928,
0.03086705505847931,
0.0850260779261589,
0.02528461441397667,
-0.02218235284090042,
0.024505499750375748,
0.04031473770737648,
0.01442023552954197,
0.020713070407509804,
-0.015523131005465984,
-0.009325860999524593,
-0.009904767386615276,
0.03075573407113552,
-0.04794875904917717,
-0.004228874109685421,
-0.009898395277559757,
0.02651689015328884,
-0.015948479995131493,
0.05268586054444313,
-0.009697340428829193,
0.004222522489726543,
0.060036551207304,
-0.05922891944646835,
0.06426586955785751,
-0.02466869167983532,
0.04117036238312721,
0.002267156494781375,
-0.0037212383467704058,
-0.021908195689320564,
0.060808539390563965,
0.040292900055646896,
-0.009354563429951668,
-0.04564100503921509,
-0.019143765792250633,
-0.033134859055280685,
-0.014295880682766438,
-0.06186961382627487,
-0.008089186623692513,
0.03262421116232872,
-0.01725659891963005,
-0.003146591130644083,
0.03955477103590965,
0.03685027360916138,
0.028643861413002014,
0.011037245392799377,
-0.012883114628493786,
-0.019971758127212524,
-0.02689833752810955,
-0.057019174098968506,
0.02105291187763214,
0.008005031384527683,
0.009006376378238201,
0.026973623782396317,
-0.013800770975649357,
0.025123875588178635,
0.044385816901922226,
0.039362527430057526,
0.02337457984685898,
0.012223334982991219,
0.049509819597005844,
0.020015783607959747,
-0.0018744181143119931,
0.027588704600930214,
0.005769447423517704,
0.0059523130767047405,
-0.007148643024265766,
-0.03452892228960991,
-0.0032492701429873705,
0.011978664435446262,
-0.013236050494015217,
0.03487056493759155,
0.022806944325566292,
0.024764366447925568,
0.0306625347584486,
-0.024104155600070953,
0.01960916444659233,
0.06120024621486664,
0.01703227125108242,
-0.0023987856693565845,
0.0028301000129431486,
0.0031049016397446394,
-0.011166451498866081,
-0.046552326530218124,
-0.02434556372463703,
0.0100594162940979,
-0.03991454094648361,
-0.017367925494909286,
0.021446585655212402,
-0.01137926522642374,
0.009812233038246632,
-0.017344869673252106,
0.05480646342039108,
0.03748041391372681,
0.031573034822940826,
-0.02538047917187214,
0.0015718924114480615,
-0.04274669662117958,
-0.04209157079458237,
0.009767614305019379,
0.02672339789569378,
-0.03249364346265793,
-0.0003616714966483414,
0.024566886946558952,
0.004241094924509525,
-0.07565624266862869,
-0.04882071912288666,
0.013570957817137241,
0.03408270701766014,
-0.01227980013936758,
-0.112128846347332,
-0.06465905159711838,
0.0471278615295887,
-0.00294094136916101,
-0.0312071293592453,
-0.06587378680706024,
0.05299961566925049,
0.008336828090250492,
0.054574623703956604,
0.0045605916529893875,
0.008861943148076534,
0.0201981533318758,
0.03556978330016136,
-0.023472053930163383,
-0.0028086963575333357,
-0.015133080072700977,
0.00901952013373375,
-0.045904740691185,
-0.020495576784014702,
-0.08581667393445969,
0.027198096737265587,
0.029278023168444633,
0.013029061257839203,
-0.02636239305138588,
0.03191833570599556,
-0.023363720625638962,
0.016172880306839943,
0.035838328301906586,
0.020521733909845352,
-0.0502035990357399,
0.05103737860918045,
0.004667309112846851,
-0.002482210285961628,
0.05324295908212662,
0.008638274855911732,
0.02919643186032772,
0.03139202296733856,
0.012203037738800049,
0.010413958691060543,
-0.04016357660293579,
-0.0010042547946795821,
-0.03111676126718521,
0.010729747824370861,
0.0044967737048864365,
-0.0298793762922287,
-0.02846013568341732,
0.011678989976644516,
-0.015231302008032799,
0.004642971325665712,
0.07628636807203293,
-0.013237535953521729,
-0.00559035362675786,
-0.031005345284938812,
-0.04382902383804321,
0.004154955968260765,
-0.0361844003200531,
0.017193248495459557,
-0.021037178114056587,
-0.020961781963706017,
-0.03033406101167202,
0.03819671645760536,
0.04138536378741264,
-0.009171663783490658,
0.001507798209786415,
-0.0086214579641819,
0.03977951407432556,
-0.00694455299526453,
0.013590119779109955,
0.01870051585137844,
0.06235334649682045,
0.06019056960940361,
0.01077127456665039,
0.020634833723306656,
0.004380777943879366,
-0.026265034452080727,
-0.011096206493675709,
-0.00261153862811625,
0.02375021018087864,
-0.015551522374153137,
-0.005973151884973049,
-0.021548153832554817,
0.028988465666770935,
-0.012298095971345901,
0.049315012991428375,
-0.014848555438220501,
0.07945087552070618,
0.05421653389930725,
0.023376204073429108,
0.04272986575961113,
0.05724456533789635,
0.007724951021373272,
-0.01609446480870247,
-0.02896398864686489,
0.0053253816440701485,
-0.03401201590895653,
0.01333941612392664,
0.03194521740078926,
0.009572758339345455,
-0.030454270541667938,
0.03333384916186333,
0.057242438197135925,
0.05371556431055069,
0.007014960050582886,
0.03267522528767586,
-0.03896446153521538,
-0.03654760867357254,
0.01636277511715889,
-0.003344038501381874,
0.013326042331755161,
0.03810245916247368,
0.007871348410844803,
0.026850638911128044,
-0.022999363020062447,
0.03808913752436638,
-0.048979636281728745,
0.0587921068072319,
-0.0041585699655115604,
0.004659418482333422,
0.025263017043471336,
-0.018907811492681503,
0.052916307002305984,
-0.013366753235459328,
-0.017514944076538086,
-0.006954711861908436,
-0.00411183713003993,
0.005996085237711668,
-0.002985313767567277,
0.0028829844668507576,
0.017048301175236702,
-0.022053055465221405,
-0.001046098186634481,
-0.013128683902323246,
0.04435842111706734,
-0.03809703513979912,
0.003301715012639761,
-0.009530028328299522,
0.004917568992823362,
-0.0025873156264424324,
-0.018441325053572655,
0.0017540997359901667,
0.002720592776313424,
0.04232914745807648,
0.024746958166360855,
0.005959687754511833,
-0.023749997839331627,
-0.04538893699645996,
-0.04161751642823219,
0.006026460789144039,
-0.046850599348545074,
0.03624333441257477,
0.0012523563345894217,
-0.016410280019044876,
0.07551980763673782,
0.02751881442964077,
0.00537078594788909,
0.01604708656668663,
-0.001846407656557858,
-0.04946005716919899,
-0.0254935622215271,
-0.05496995151042938,
0.010344116017222404,
-0.03585298731923103,
0.007708558347076178,
0.03392216935753822,
-0.0088357450440526,
-0.012915859930217266,
0.016534537076950073,
-0.08124116063117981,
-0.06364943832159042,
0.006835779640823603,
0.014914330095052719,
0.021398350596427917,
-0.04295269772410393,
0.0017379345372319221,
-0.0008838483481667936,
-0.03019046224653721,
0.013036203570663929,
-0.03147206827998161,
-0.021389387547969818,
0.005663061048835516,
-0.018120475113391876,
0.05747976154088974,
0.008421216160058975,
-0.05942171812057495,
0.06320372223854065,
0.023462099954485893,
-0.030439389869570732,
-0.0438600517809391,
-0.031789910048246384,
-0.006482397671788931,
-0.02844039350748062,
0.018516670912504196,
0.035893764346838,
0.012658635154366493,
0.0014224607730284333,
0.02133861742913723,
-0.0247135479003191,
0.0025828462094068527,
0.0237015001475811,
0.005390407517552376,
0.012618809007108212,
0.001083484385162592,
-0.008227048441767693,
0.054971009492874146,
0.018281418830156326,
-0.001735039404593408,
-0.0007539168000221252,
0.0016181452665477991,
0.039684396237134933,
-0.010659356601536274,
-0.04670101776719093,
0.024897204712033272,
-0.019452620297670364,
0.005472828168421984,
-0.004430567845702171,
0.0665234699845314,
-0.003494182601571083,
0.010607847012579441,
0.03562987223267555,
-0.0006289779557846487,
0.02288149483501911,
-0.010966907255351543,
-0.05197656527161598,
0.036504123359918594,
0.029681909829378128,
-0.03548264130949974,
-0.027493329718708992,
-0.009669192135334015,
0.003290826454758644,
0.035643238574266434,
-0.017990101128816605,
-0.006719921249896288,
0.02712971158325672,
0.017541030421853065,
0.02736825868487358,
0.016991257667541504,
-0.051812056452035904,
-0.00034415433765389025,
-0.06323414295911789,
0.017813095822930336,
-0.011258576065301895,
0.0502295047044754,
-0.013122271746397018,
0.043346431106328964,
0.008318275213241577,
0.013343975879251957,
0.015959223732352257,
0.012649095617234707,
-0.07313290983438492,
0.05516859143972397,
-0.05440915375947952,
-0.025411076843738556,
-0.0007412944687530398,
0.009703422896564007,
0.009519458748400211,
-0.03072667308151722,
-0.016244741156697273,
-0.044681549072265625,
-0.03947210684418678,
-0.03783067315816879,
0.006664443761110306,
-0.004449078347533941,
-0.019733678549528122,
-0.005214716773480177,
0.017133774235844612,
0.02932989038527012,
-0.02141634374856949,
0.03306346386671066,
0.059448644518852234,
-0.017431657761335373,
0.011309832334518433,
-0.017878007143735886,
-0.020591510459780693,
-0.016971124336123466,
-0.005142501089721918,
0.027888277545571327,
0.00029811885906383395,
-0.0007556681521236897,
-0.02254457026720047,
-0.026954181492328644,
0.015599626116454601,
0.04686015471816063,
0.010909788310527802,
-0.02522537112236023,
-0.0451989471912384,
0.0048414734192192554,
-0.01797659508883953,
0.04908743128180504,
-0.04022437706589699,
0.002563826274126768,
0.03317780792713165,
-0.009037419222295284,
0.006359477061778307,
0.05950593203306198,
0.04739445447921753,
0.03661232441663742,
-0.00902421586215496,
-0.03455207124352455,
0.017932690680027008,
-0.03933024778962135,
0.011651365086436272,
0.019607072696089745,
-0.006047355476766825,
-0.048734087496995926,
-0.03198651224374771,
0.00729327043518424,
0.004849993623793125,
0.0038665186148136854,
0.040083080530166626,
0.03554157167673111,
0.07955505698919296,
0.0012367378221824765,
0.009128863923251629,
0.0005816417396999896,
0.022701259702444077,
0.0570034421980381,
0.0016623035771772265,
-0.030724909156560898,
-0.06589159369468689,
-0.017802413552999496,
0.027772240340709686,
0.02334570698440075,
-0.052295081317424774,
-0.031312741339206696,
-0.05535108968615532,
-0.026809360831975937,
0.027058351784944534,
-0.033715199679136276,
0.026226164773106575,
-0.01714913919568062,
0.01577492244541645,
0.006950623355805874,
-0.03649095445871353,
-0.011629787273705006,
0.005123663693666458,
-0.017327168956398964,
0.02869775891304016,
-0.02256561815738678,
0.006380261853337288,
-0.0039678593166172504,
0.042251985520124435,
0.057728130370378494,
0.007096973713487387,
0.05017179623246193,
-0.007238270249217749,
-0.013965464197099209,
0.028114421293139458,
-0.03983622044324875,
-0.07396291196346283,
-0.018996231257915497,
0.017711583524942398,
-0.03701678663492203,
-0.0072502451948821545,
-0.04627841338515282,
-0.07054027915000916,
-0.013313256204128265,
-0.003720153821632266,
-0.00515780271962285,
-0.0017537472303956747,
-0.0722481831908226,
-0.018653668463230133,
0.007033888716250658,
-0.006564425304532051,
0.05470798909664154,
0.01350170187652111,
-0.04716183990240097,
-0.020253507420420647,
-0.017035827040672302,
0.0022384377662092447,
-0.01930103451013565,
-0.04134174808859825,
0.019124403595924377,
0.004392250906676054,
-0.04792887717485428,
0.015689898282289505,
0.012026322074234486,
0.01358745340257883,
-0.01901271753013134,
-0.034451983869075775,
-0.03971230983734131,
0.03376147523522377,
0.036230333149433136,
-0.010613278485834599,
-0.014138451777398586,
0.014588593505322933,
-0.006793072912842035,
-0.016448944807052612,
0.02459910698235035,
0.019092507660388947,
0.0006763960118405521,
0.004448274150490761,
0.0008256774162873626,
0.007877379655838013,
-0.014303101226687431,
-0.02867061085999012,
-0.014388634823262691,
-0.046637941151857376,
0.09084083139896393,
-0.017731202766299248,
-0.003956347703933716,
0.030386438593268394,
-0.05702618882060051,
-0.0426822304725647,
0.011898811906576157,
0.02806985192000866,
0.053036950528621674,
-0.025562701746821404,
0.01546454057097435,
0.021362723782658577,
-0.016002023592591286,
-0.041046593338251114,
-0.054871927946805954,
0.015608297660946846,
0.010303751565515995,
0.0025942232459783554,
0.006442836951464415,
-0.003597996197640896,
-0.034043893218040466,
-0.04650888592004776,
-0.011546783149242401,
0.07957714796066284,
-0.03261252120137215,
0.026536261662840843,
0.00926973670721054,
-0.0006234458996914327,
0.04755778983235359,
-0.0250952560454607,
-0.00955771841108799,
0.012860936112701893,
-0.03663836047053337,
0.023598896339535713,
-0.01062628161162138,
0.08172459900379181,
-0.01626542955636978,
-0.03895566985011101,
-0.008590635843575,
0.0009742658003233373,
0.008642025291919708,
0.014993253163993359,
0.011587555520236492,
0.057947155088186264,
0.021147245541214943,
-0.03472289815545082,
-0.038051001727581024,
0.05202861875295639,
0.017315497621893883,
0.04495186731219292,
-0.01371777430176735,
0.013621811755001545,
-0.03230351209640503,
-0.03688092157244682,
0.007456697057932615,
-0.02795892395079136,
0.013299467973411083,
0.004870712291449308,
0.06674239039421082,
-0.0047020502388477325,
-0.012031147256493568,
0.023737825453281403,
0.007571667432785034,
0.04085909202694893,
0.018354568630456924,
0.011733687482774258,
0.015614609234035015,
-0.0287383571267128,
-0.03591058775782585,
-0.02482222206890583,
0.01641147956252098,
-0.012337583117187023,
0.10562601685523987,
-0.05432354286313057,
0.08572917431592941,
0.03277229517698288,
0.02457251213490963,
0.000027494446840137243,
-0.0023325090296566486,
0.017736470326781273,
0.0005575965042226017,
0.016407916322350502,
0.013816539198160172,
-0.01943603716790676,
0.012923323549330235,
0.04453223571181297,
0.03539462760090828,
-0.023266078904271126,
0.018747294321656227,
0.019113849848508835,
0.009312487207353115,
-0.0052825710736215115,
-0.0004335904086474329,
-0.04126262292265892,
-0.020164433866739273,
-0.0005974379600957036,
0.07480988651514053,
0.008660567924380302,
-0.00006546015356434509,
0.04289538413286209,
-0.008691263385117054,
0.03733168542385101,
-0.007966226898133755,
-0.023748718202114105,
-0.02633141539990902,
-0.016290582716464996,
-0.0037715169601142406,
0.0017096784431487322,
-0.020489702001214027,
0.04003589600324631,
0.02073558233678341,
-0.0034718436654657125,
0.004595622885972261,
-0.02939579077064991,
-0.07305792719125748,
-0.01858738251030445,
-0.010714108124375343,
-0.0658288449048996,
0.03485286235809326,
0.01308342907577753,
-0.041055746376514435,
0.001195835298858583,
-0.02331526391208172,
-0.010213424451649189,
0.042188648134469986,
0.02138437144458294,
-0.03655749186873436,
0.09324994683265686,
-0.022338783368468285,
-0.000023685321139055304,
-0.03197477385401726,
0.006142957601696253,
0.09661684185266495,
0.016803355887532234,
0.012624401599168777,
-0.07823117077350616,
0.02191491425037384,
-0.023275017738342285,
-0.029079390689730644,
-0.04906805232167244,
0.017029790207743645,
0.011765336617827415,
0.01767374947667122,
0.03383418545126915,
0.032948799431324005,
-0.017171869054436684,
-0.03515678271651268,
0.03333744406700134,
-0.013607465662062168,
-0.05173850432038307,
-0.013989986851811409,
0.011318270117044449,
-0.0067999656312167645,
0.021414058282971382,
-0.023160407319664955,
-0.0018726259004324675,
-0.06672461330890656,
-0.022855333983898163,
-0.033417195081710815,
-0.04670290648937225,
0.004853966645896435,
-0.005289388820528984,
-0.07735462486743927,
0.022313324734568596,
-0.005690173711627722,
-0.03440839424729347,
-0.06821834295988083,
0.03855714574456215,
-0.009159254841506481,
-0.013080710545182228,
0.01767668128013611,
0.0070145102217793465,
-0.015699733048677444,
0.02679871954023838,
0.01575469598174095,
0.003959179390221834,
-0.04305322468280792,
0.027155056595802307,
-0.022638332098722458,
0.02532150410115719,
-0.007522400468587875,
0.043702516704797745,
0.030366607010364532,
0.005745125934481621,
-0.05340065434575081,
-0.03911551833152771,
-0.007093856111168861,
-0.0013298247940838337,
0.04661029577255249,
-0.018329069018363953,
-0.0548829510807991,
-0.01385688129812479,
0.03654789179563522,
-0.026429433375597,
0.03537273779511452,
-0.010881511494517326,
0.008632085286080837,
0.03201253339648247,
0.020217737182974815,
0.03487566486001015,
-0.05645567178726196,
-0.02041156403720379,
-0.03541996330022812,
-0.039633359760046005,
-0.02282562293112278,
0.012226114049553871,
0.03777675703167915,
0.02905558981001377,
0.017250074073672295,
-0.006547329016029835,
0.001577069633640349,
-0.026037704199552536,
-0.04334605112671852,
0.0350923016667366,
-0.03607663884758949,
-0.045995235443115234,
-0.02045360952615738,
0.010267888195812702,
0.03079984150826931,
0.013436811976134777,
-0.005137327127158642,
0.027006970718503,
0.009868885390460491,
-0.011948700994253159,
0.030949609354138374,
-0.04734516888856888,
-0.002311215503141284,
0.03672558814287186,
-0.011350471526384354,
-0.04150441661477089,
-0.021098263561725616,
0.025231193751096725,
0.06024133414030075,
0.012026838958263397,
-0.014763507060706615,
0.03293576091527939,
0.00041852283175103366,
0.024672314524650574,
0.021157341077923775,
-0.0026979148387908936,
-0.013818178325891495,
0.04668915644288063,
-0.048135481774806976,
-0.04313243180513382,
0.00022215646458789706,
-0.01950988918542862,
-0.037756022065877914,
0.02034772001206875,
0.02786012925207615,
-0.062986820936203,
0.017818113788962364,
-0.02872191183269024,
0.033998921513557434,
-0.0461067333817482,
0.023165306076407433,
-0.056651800870895386,
-0.010474427603185177,
0.024874959141016006,
-0.03283686563372612,
-0.02449292689561844,
0.029886437579989433,
-0.0013375238049775362,
0.015739573165774345,
0.020181208848953247,
-0.0021822433918714523,
0.029011625796556473,
0.023827215656638145,
-0.005472222808748484,
-0.04873665049672127,
0.06179200857877731,
-0.025111690163612366,
-0.013749883510172367,
0.05195058137178421,
-0.03797861933708191,
-0.029845714569091797,
0.04495399445295334,
-0.04046068713068962,
0.05562276765704155,
0.017272265627980232,
-0.029169633984565735,
0.009513587690889835,
0.04669205844402313,
-0.023496387526392937,
0.004300229251384735,
-0.016039561480283737,
0.015061557292938232,
0.011671122163534164,
-0.005045736208558083,
-0.0021080293226987123,
-0.032806992530822754,
-0.00491219200193882,
0.04138563200831413,
0.05294887721538544,
-0.03998147323727608,
0.010570449754595757,
0.024686506018042564,
0.016887422651052475,
0.008343086577951908,
0.03387082740664482,
0.019539926201105118,
0.010522592812776566,
0.021457508206367493,
-0.02914896048605442,
0.04113936051726341,
0.001839111209847033,
0.018393071368336678,
-0.0682908296585083,
-0.023670293390750885,
-0.01133996807038784,
-0.008838585577905178,
0.04116145893931389,
-0.03198397532105446,
-0.017441730946302414,
0.049136802554130554,
-0.06953484565019608,
-0.0023459296207875013,
-0.01967066153883934,
-0.005327997729182243,
0.018996505066752434,
-0.03198418766260147,
0.054935794323682785,
0.03921344131231308,
0.013046782463788986,
0.027438649907708168,
0.008456449024379253,
-0.0014556272653862834,
-0.023837709799408913,
-0.035457536578178406,
0.001144771813414991,
0.03710251301527023,
-0.015498260967433453,
0.018673526123166084,
0.03828514739871025,
-0.003454857971519232,
-0.025568850338459015,
0.036029521375894547,
0.0012287634890526533,
0.05114271864295006,
-0.010683367028832436,
-0.005335147492587566,
0.006624685134738684,
0.022137803956866264,
-0.00822308287024498,
-0.04950746148824692,
-0.038944780826568604,
0.026134397834539413,
-0.016345078125596046,
0.05340573564171791,
-0.025030244141817093,
-0.015340710058808327,
0.00032743028714321554,
-0.013538405299186707,
-0.0011379215866327286,
0.033391498029232025,
-0.028622133657336235,
0.014941203407943249,
0.005074501037597656,
0.023125817999243736,
-0.020956767722964287,
-0.03562421351671219,
-0.033907368779182434,
-0.04480651766061783,
-0.00036085720057599247,
0.021958844736218452,
-0.03472113609313965,
-0.009115106426179409,
0.014148649759590626,
0.024239161983132362,
0.013147417455911636,
-0.005577418487519026,
-0.012877297587692738,
-0.012433604337275028,
-0.05657108873128891,
0.020879382267594337,
0.03059696964919567,
-0.02820076420903206,
-0.005002806428819895,
-0.04989592730998993,
-0.01875351369380951,
0.042647164314985275,
0.023077260702848434,
0.01622258499264717,
0.0013161466922610998,
-0.05171295627951622,
-0.008464905433356762,
-0.027474047616124153,
0.022668274119496346,
0.024890385568141937,
-0.022785348817706108,
-0.019214322790503502,
-0.050786007195711136,
-0.01615460030734539,
-0.008559820242226124,
0.02592102438211441,
0.032688483595848083,
-0.015477937646210194,
0.021937908604741096,
-0.022099461406469345,
0.012894612736999989,
-0.04354926198720932,
0.03411383926868439,
-0.014764072373509407,
-0.021487316116690636,
0.004956978373229504,
-0.018663913011550903,
-0.009210384450852871,
-0.003921170253306627,
-0.0054549481719732285,
0.0067662824876606464,
0.07814927399158478,
0.0006443256861530244,
-0.016546932980418205,
0.04346782714128494,
0.022077128291130066,
0.016706282272934914,
0.06354407966136932,
-0.006020445842295885,
0.02099565789103508,
0.026914449408650398,
-0.017051538452506065,
-0.03688003495335579,
0.0328865721821785,
-0.05458857864141464,
-0.0070487745106220245,
-0.015174943953752518,
-0.011546236462891102,
0.045373354107141495,
-0.03577016294002533,
-0.002564546884968877,
0.06053498759865761,
-0.026611600071191788,
0.010264082811772823,
0.008837244473397732,
0.019082527607679367,
0.03995678946375847,
-0.04569358006119728,
0.039703331887722015,
0.005229419097304344,
-0.021259354427456856,
0.021066296845674515,
-0.0031355354003608227,
0.0328565314412117,
0.004843940492719412,
-0.021232489496469498,
0.06799965351819992,
0.009348283521831036,
0.043288394808769226,
0.012083476409316063,
0.0231490395963192,
-0.04702547937631607,
-0.05681341141462326,
-0.0009491060627624393,
-0.022303182631731033,
0.015012035146355629,
0.019590552896261215,
-0.012229210697114468,
0.07169743627309799,
-0.03597166761755943,
0.0050573088228702545,
0.0046317605301737785,
0.015076326206326485,
-0.02446616068482399,
-0.005712228827178478,
-0.007179178763180971,
0.02382395602762699,
-0.011109474115073681,
-0.022966690361499786,
0.01020659226924181,
-0.000673130911309272,
0.030716972425580025,
-0.008999607525765896,
0.012904098257422447,
0.00898009818047285,
0.010058378800749779,
-0.04425754025578499,
-0.022581160068511963,
-0.026943456381559372,
-0.024666618555784225,
0.0454329177737236,
0.03978826105594635,
0.021196912974119186,
-0.031861964613199234,
0.007008953019976616,
-0.02847862057387829,
0.03647444397211075,
-0.08200860023498535,
-0.05412590876221657,
-0.022324591875076294,
0.0423152856528759,
-0.016051344573497772,
-0.008677448146045208
] |
<p>What kind of significant impacts have originated from $E=mc^2$.</p>
<p>Generally, it is regarded as the most famous equation of all time. Except for nuclear energy (fission and fusion) I do not know any other way in which this equation has made an impact on the world. </p>
<p>Can somebody list some developments and impacts based on this equation?</p> | 1,531 | [
-0.02286999300122261,
-0.041956670582294464,
-0.011439534835517406,
-0.020486656576395035,
0.059589870274066925,
0.012583709321916103,
-0.05114355683326721,
-0.03990839421749115,
-0.02370787225663662,
-0.051027096807956696,
-0.001273766509257257,
0.031136376783251762,
0.04467775672674179,
0.00022072315914556384,
-0.00029678124701604247,
0.0018791486509144306,
0.02544938400387764,
0.0025089511182159185,
-0.003019060008227825,
-0.017034482210874557,
0.004424614366143942,
-0.017941106110811234,
0.01698242500424385,
0.012351115234196186,
-0.046201709657907486,
0.05186953768134117,
0.03637804836034775,
0.008702905848622322,
0.021672261878848076,
0.0489063560962677,
-0.02011185884475708,
-0.024942779913544655,
0.01800769381225109,
0.04091103747487068,
-0.027184706181287766,
-0.00958393793553114,
-0.005748656112700701,
-0.0371248684823513,
0.025655172765254974,
0.03676154464483261,
-0.04399044066667557,
-0.03267267718911171,
0.002575742546468973,
0.025223029777407646,
-0.036734726279973984,
0.035309262573719025,
-0.009342234581708908,
-0.04160688444972038,
0.057741641998291016,
-0.04419110342860222,
0.08072347193956375,
0.009248453192412853,
0.02963082306087017,
-0.009676630608737469,
0.002641309518367052,
0.006256415508687496,
0.0645371526479721,
0.0301810372620821,
0.026147959753870964,
-0.05455344170331955,
-0.007201674859970808,
0.024205783382058144,
0.01548850443214178,
0.0006063773180358112,
0.011829519644379616,
0.0631248950958252,
-0.002194135682657361,
-0.0033396361395716667,
0.043970219790935516,
0.009723820723593235,
0.01284955907613039,
0.02891436405479908,
0.054951202124357224,
0.012090297415852547,
0.030910661444067955,
-0.046239420771598816,
0.015855856239795685,
-0.012050110846757889,
0.023456482216715813,
0.04013550654053688,
-0.032428279519081116,
-0.0004925996763631701,
0.03241987153887749,
0.03206561133265495,
-0.0004250294005032629,
0.01785140484571457,
0.0645616352558136,
0.007648847531527281,
0.0162506140768528,
0.007404947187751532,
-0.008022679947316647,
-0.011020158417522907,
0.046873487532138824,
-0.013980596326291561,
0.0065445383079349995,
0.04521196708083153,
0.0050014713779091835,
0.059689491987228394,
0.04280488193035126,
-0.012233946472406387,
0.03019551746547222,
0.021751809865236282,
0.010034453123807907,
0.0727529302239418,
0.018407395109534264,
-0.022398514673113823,
-0.050025682896375656,
-0.004254824481904507,
-0.02244994044303894,
0.0028049179818481207,
-0.02917327731847763,
-0.03496827557682991,
0.014049353078007698,
0.008177166804671288,
0.018566256389021873,
-0.017626618966460228,
0.00948671530932188,
-0.005242982413619757,
0.06894099712371826,
0.0919545516371727,
0.018117694184184074,
-0.025741519406437874,
0.020892981439828873,
-0.009400845505297184,
-0.08361949771642685,
0.028516938909888268,
0.020746465772390366,
-0.016684936359524727,
-0.00494030537083745,
0.01770635135471821,
-0.0367395244538784,
-0.008141639642417431,
-0.009527293033897877,
-0.018592549487948418,
0.037819355726242065,
-0.017314281314611435,
-0.12427648901939392,
-0.07170355319976807,
0.03651479259133339,
0.006619318854063749,
-0.03504059463739395,
-0.04172768071293831,
0.014782785438001156,
0.022804053500294685,
0.08162381500005722,
0.012330804951488972,
-0.02049371972680092,
-0.007755351718515158,
0.06765346974134445,
-0.015016398392617702,
-0.03876978158950806,
-0.03562401980161667,
0.03427812084555626,
-0.017861677333712578,
0.027362067252397537,
-0.07188847661018372,
-0.003983138129115105,
0.03975308686494827,
-0.004961152095347643,
-0.006995229981839657,
0.08572545647621155,
-0.039955221116542816,
-0.040216460824012756,
0.015405317768454552,
0.004421178717166185,
-0.016473393887281418,
0.0661071240901947,
0.021235575899481773,
0.03018537536263466,
0.027284348383545876,
0.03279854729771614,
0.06664558500051498,
0.04093426465988159,
0.021048953756690025,
0.004830715246498585,
-0.043801624327898026,
-0.02196737565100193,
0.005204352550208569,
-0.024385318160057068,
-0.012479732744395733,
-0.037309903651475906,
-0.045012664049863815,
-0.0022792869713157415,
-0.012598571367561817,
0.03146142140030861,
0.06403657793998718,
-0.04660293459892273,
-0.004311228170990944,
0.027797147631645203,
-0.044187769293785095,
-0.0535648837685585,
-0.06659616529941559,
0.039856940507888794,
-0.012528757564723492,
0.0028382218442857265,
0.01558886282145977,
0.00007597154763061553,
0.02556391805410385,
-0.022058730944991112,
-0.0356915183365345,
0.0024709070567041636,
0.04915842041373253,
0.016207803040742874,
0.001070600119419396,
0.013650735840201378,
0.03770008310675621,
0.02598612941801548,
0.00026762785273604095,
-0.015281789004802704,
-0.007938908413052559,
-0.029197756201028824,
0.005346210207790136,
-0.008705024607479572,
0.015604246407747269,
-0.006093546282500029,
0.0052687921561300755,
0.00014868396101519465,
-0.02144056372344494,
-0.01341299805790186,
0.040278464555740356,
-0.021952923387289047,
0.09072377532720566,
0.02793312259018421,
0.03218385949730873,
-0.0009772386401891708,
0.05117984116077423,
0.040969327092170715,
0.00888007041066885,
-0.012273871339857578,
-0.00956304557621479,
-0.05849669128656387,
-0.011849264614284039,
-0.011764765717089176,
0.026792272925376892,
-0.05737897381186485,
0.006886458955705166,
0.014268637634813786,
0.040966909378767014,
0.01422699261456728,
-0.0006475444533862174,
-0.012442653998732567,
-0.03210337087512016,
0.006650265771895647,
-0.003036632901057601,
0.019114557653665543,
0.005241152364760637,
0.01951230689883232,
0.01271880604326725,
-0.0022976379841566086,
-0.016380636021494865,
0.0020587497856467962,
0.03533114120364189,
-0.01884038932621479,
-0.0026877406053245068,
-0.009382853284478188,
-0.029918842017650604,
0.02373467944562435,
-0.07012941688299179,
0.004436836577951908,
0.03016195446252823,
-0.006144016515463591,
-0.007799460086971521,
-0.018176555633544922,
-0.03776409476995468,
0.005592425353825092,
-0.0008674627169966698,
-0.004064035601913929,
0.007244918495416641,
0.028302639722824097,
-0.030928729102015495,
0.02254006266593933,
0.022326191887259483,
-0.03067334182560444,
-0.05374516174197197,
0.018691858276724815,
0.019435662776231766,
-0.02021239511668682,
0.00031865175697021186,
0.01369483396410942,
-0.05204765126109123,
-0.015392567962408066,
-0.026663092896342278,
-0.042296867817640305,
0.012877250090241432,
-0.031889867037534714,
0.03428145498037338,
-0.022677147760987282,
-0.021845655515789986,
0.05256811901926994,
-0.032986439764499664,
0.009759523905813694,
0.065926194190979,
0.021446648985147476,
-0.049744606018066406,
-0.0029084011912345886,
-0.01282100286334753,
-0.0030858018435537815,
-0.010739203542470932,
-0.030040325596928596,
0.056429173797369,
-0.025956442579627037,
-0.03627035394310951,
0.008783440105617046,
-0.033414896577596664,
-0.05367209017276764,
-0.05275573581457138,
-0.03121604397892952,
0.025023341178894043,
-0.04619342461228371,
0.02905902825295925,
0.007250298745930195,
-0.04108114540576935,
0.003440026892349124,
-0.060881391167640686,
-0.04754897579550743,
0.035730358213186264,
-0.034249234944581985,
0.06025543808937073,
-0.03988874703645706,
-0.02934079058468342,
0.017798401415348053,
0.04948558658361435,
-0.04592626914381981,
-0.020962487906217575,
-0.010267851874232292,
0.037628501653671265,
-0.030994290485978127,
0.00351217039860785,
0.022601710632443428,
0.010279498994350433,
0.014235394075512886,
0.002413650741800666,
0.044089313596487045,
-0.0189884714782238,
0.01680176518857479,
-0.03647231683135033,
-0.00603480963036418,
-0.02079288475215435,
0.0012078451691195369,
0.025722481310367584,
0.02734239771962166,
-0.034653645008802414,
0.033364757895469666,
0.0034111742861568928,
0.023749995976686478,
0.021418750286102295,
-0.04612522944808006,
0.0308814849704504,
0.017647739499807358,
-0.011947679333388805,
-0.045622099190950394,
0.012792348861694336,
-0.0031204121187329292,
0.01600577123463154,
-0.003571273060515523,
-0.01406596414744854,
0.007572075352072716,
-0.012423763051629066,
0.005540279671549797,
0.021568836644291878,
0.022056519985198975,
-0.011583198793232441,
-0.03491600602865219,
-0.024291537702083588,
0.013744775205850601,
0.008996699936687946,
0.002598018851131201,
-0.00652717612683773,
0.05507096275687218,
0.03768381476402283,
0.02047806978225708,
-0.016283834353089333,
-0.007609391584992409,
-0.02708776481449604,
-0.05272670090198517,
-0.02502593770623207,
-0.026226019486784935,
0.04400775954127312,
-0.0019040380138903856,
0.08828052878379822,
-0.011986494064331055,
-0.011542683467268944,
0.045298125594854355,
-0.021760201081633568,
-0.05534107983112335,
-0.0006179686752147973,
-0.07973817735910416,
-0.008379999548196793,
0.013239849358797073,
0.010820498690009117,
0.0019184243865311146,
-0.011770381592214108,
-0.03026628866791725,
-0.045166417956352234,
0.015833264216780663,
-0.04311392456293106,
-0.01611119695007801,
-0.028244690969586372,
-0.05498785153031349,
-0.010652884840965271,
0.02146381512284279,
0.030030710622668266,
0.024601953104138374,
-0.002704502549022436,
0.05567063391208649,
-0.0567663349211216,
-0.023433208465576172,
0.004087899345904589,
-0.018117498606443405,
0.013442105613648891,
0.02121203951537609,
0.022307278588414192,
-0.00015359255485236645,
-0.0394446924328804,
0.031824011355638504,
0.029630741104483604,
0.024351703003048897,
-0.016302676871418953,
0.00678638182580471,
-0.023201169446110725,
-0.023191552609205246,
-0.030152468010783195,
-0.025681020691990852,
0.007706171367317438,
0.014949546195566654,
0.04061476141214371,
0.026515306904911995,
0.0008879961678758264,
-0.017724376171827316,
0.06509876996278763,
0.052205756306648254,
-0.002015519654378295,
-0.031962424516677856,
-0.028445815667510033,
-0.0068058292381465435,
0.00003160782580380328,
-0.02529103308916092,
-0.0078072273172438145,
0.014760478399693966,
-0.014069544151425362,
0.00992128811776638,
0.021204082295298576,
0.02557077631354332,
-0.03457503393292427,
-0.02578720822930336,
0.01146776881068945,
0.021604441106319427,
0.008414320647716522,
-0.011437471956014633,
-0.02561960369348526,
0.013151003047823906,
0.036678247153759,
-0.01628914475440979,
-0.0012758789816871285,
-0.05729487165808678,
0.02230442501604557,
0.025958126410841942,
0.043179187923669815,
-0.04503236338496208,
0.004542171489447355,
-0.06471919268369675,
-0.004320986568927765,
0.04540812596678734,
-0.05852225050330162,
-0.0065469760447740555,
-0.0028983985539525747,
0.003291067900136113,
-0.0010059549240395427,
-0.00893771555274725,
-0.014289646409451962,
0.04396793618798256,
0.016537688672542572,
0.02250540256500244,
-0.013689421117305756,
-0.02218875288963318,
0.002819031709805131,
0.02689366787672043,
0.033360645174980164,
0.0523005947470665,
0.034591928124427795,
-0.011986921541392803,
-0.015976060181856155,
0.05066114291548729,
-0.031378552317619324,
-0.07141236215829849,
-0.019040264189243317,
-0.007523176725953817,
-0.01774848811328411,
0.006389552261680365,
-0.026953350752592087,
-0.05660225823521614,
-0.006864557508379221,
0.012071284465491772,
-0.03687224164605141,
-0.04047999903559685,
-0.04264525696635246,
0.00902053527534008,
0.04568369686603546,
-0.01920267567038536,
0.03929057717323303,
0.05003033205866814,
-0.04736028611660004,
0.00858247745782137,
-0.0044012232683598995,
0.015707891434431076,
-0.015244681388139725,
-0.008300420828163624,
0.0028585540130734444,
0.03524681180715561,
-0.05748002603650093,
0.021396232768893242,
-0.008106601424515247,
0.03389115631580353,
-0.018512025475502014,
-0.025326954200863838,
-0.015380308963358402,
0.042595844715833664,
-0.012584779411554337,
-0.005624635145068169,
-0.028193557634949684,
0.0000774170330259949,
0.016452232375741005,
-0.0354861319065094,
0.04849470034241676,
0.06040911376476288,
-0.016286715865135193,
-0.012197073549032211,
-0.004745272919535637,
0.015864305198192596,
-0.006203710567206144,
-0.006356101483106613,
0.04210734739899635,
-0.030733957886695862,
0.0281055960804224,
-0.018133040517568588,
-0.0127263767644763,
0.03917327895760536,
-0.077451691031456,
-0.054919131100177765,
0.05173412710428238,
-0.00652060704305768,
0.05306049436330795,
-0.013719658367335796,
-0.0013540014624595642,
-0.02361242100596428,
0.030062327161431313,
-0.06368710845708847,
-0.06905948370695114,
0.014966650865972042,
-0.033578161150217056,
0.036782700568437576,
0.0076329512521624565,
-0.029195331037044525,
-0.03580682724714279,
-0.0077594127506017685,
0.009649096988141537,
0.058085549622774124,
0.0030576330609619617,
-0.016748834401369095,
-0.009838051162660122,
0.0025668542366474867,
0.040847450494766235,
-0.009680609218776226,
-0.017008056864142418,
0.01628068834543228,
0.009107627905905247,
0.02012205682694912,
0.02298448421061039,
0.06960941106081009,
-0.028489837422966957,
-0.01853227987885475,
0.01805376447737217,
-0.028887083753943443,
-0.010106867179274559,
-0.035009995102882385,
0.005161283537745476,
0.043462589383125305,
0.0037180399522185326,
-0.004863604437559843,
-0.005977833177894354,
0.03436997905373573,
-0.023150168359279633,
0.02642778307199478,
0.030242498964071274,
-0.016665775328874588,
-0.004336665850132704,
-0.04053855314850807,
0.04043420031666756,
-0.0023542738053947687,
-0.029505154117941856,
-0.011549641378223896,
0.034785158932209015,
0.0059408457018435,
-0.02349652536213398,
0.0203890111297369,
-0.026239063590765,
0.03428781032562256,
-0.027292529121041298,
0.0034393302630633116,
-0.018046531826257706,
0.035353586077690125,
-0.03245523199439049,
-0.03677403926849365,
-0.017607659101486206,
-0.013775697909295559,
0.06351564824581146,
-0.019540823996067047,
0.0440216064453125,
0.005303503945469856,
-0.02315579541027546,
-0.003800405189394951,
-0.02968229539692402,
-0.003823717823252082,
0.01208330225199461,
0.017744168639183044,
0.0040006437338888645,
0.014641405083239079,
0.021235434338450432,
0.03791327401995659,
0.017237205058336258,
-0.00893696304410696,
0.021042820066213608,
0.013534527271986008,
0.013202344998717308,
0.026332832872867584,
-0.040392033755779266,
-0.04923814535140991,
0.0684335008263588,
-0.03515896946191788,
-0.011137501336634159,
-0.0036630372051149607,
-0.02160070091485977,
0.030042579397559166,
-0.004102014005184174,
-0.02487187646329403,
-0.015001873485744,
0.011680342257022858,
-0.04174339398741722,
0.011006576009094715,
0.020312882959842682,
-0.02456803061068058,
0.0172836035490036,
0.016448717564344406,
0.010159633122384548,
0.010583113878965378,
-0.01086251437664032,
-0.02870173007249832,
-0.08886100351810455,
-0.015814485028386116,
-0.044839803129434586,
-0.03682288900017738,
0.03321106731891632,
0.008733591064810753,
-0.016483312472701073,
-0.028804387897253036,
-0.013098469004034996,
-0.015139183960855007,
0.009396424517035484,
-0.0026736275758594275,
-0.030767643824219704,
0.05865174159407616,
-0.025875577703118324,
0.000006809871592849959,
-0.0074437400326132774,
0.0049659921787679195,
0.09560221433639526,
0.03824463486671448,
0.025728246197104454,
-0.0641026422381401,
0.03510664403438568,
-0.01727975718677044,
0.005817021708935499,
-0.032408248633146286,
0.01868556998670101,
-0.030553938820958138,
0.02869325689971447,
0.03803442046046257,
0.04025217890739441,
0.045712895691394806,
0.013313970528542995,
0.051668282598257065,
-0.03614090383052826,
-0.05655024200677872,
-0.005390569102019072,
-0.0069925799034535885,
-0.03863387182354927,
0.034201450645923615,
-0.0353933684527874,
-0.007202683947980404,
-0.06039944291114807,
-0.02024431712925434,
-0.015625517815351486,
-0.02910628542304039,
0.03330548480153084,
0.03541501238942146,
-0.0454278402030468,
-0.017967192456126213,
0.01604202389717102,
-0.012408682145178318,
-0.04555613547563553,
-0.02432980202138424,
0.04048456996679306,
0.0003702617541421205,
0.024295076727867126,
0.03016025945544243,
0.023721279576420784,
-0.02667795494198799,
-0.023743970319628716,
0.015505660325288773,
-0.04819158464670181,
-0.018838992342352867,
-0.027179313823580742,
0.03966532275080681,
-0.00695926696062088,
0.003960990346968174,
-0.006177629344165325,
0.006919912528246641,
-0.01444310788065195,
0.013780846260488033,
-0.044813089072704315,
-0.011703341268002987,
0.02682597003877163,
-0.03654024004936218,
-0.011653056368231773,
-0.020525550469756126,
0.008881684392690659,
-0.02947084978222847,
0.03600061312317848,
-0.002543108072131872,
-0.019657064229249954,
-0.03222082182765007,
-0.022898320108652115,
0.020565126091241837,
-0.0256909541785717,
-0.03283657506108284,
-0.021954311057925224,
-0.026201166212558746,
-0.043326348066329956,
-0.024049175903201103,
0.021790090948343277,
0.06548264622688293,
0.012697425670921803,
0.0028607575222849846,
0.013621898368000984,
-0.04877857863903046,
-0.024266958236694336,
0.06368228048086166,
0.0015588535461574793,
0.010476126335561275,
-0.046629857271909714,
-0.0019511664286255836,
0.031137552112340927,
0.001615235349163413,
-0.03257868438959122,
0.01451354194432497,
-0.03660989925265312,
0.011922386474907398,
0.01911056414246559,
-0.027905495837330818,
-0.010919138789176941,
0.0025533814914524555,
-0.02503356896340847,
0.0015202976064756513,
-0.04234446585178375,
0.03454221412539482,
0.012964139692485332,
-0.03309141471982002,
0.03448396548628807,
0.026994850486516953,
-0.017651373520493507,
0.018581600859761238,
0.03543626889586449,
-0.014827275648713112,
-0.014806516468524933,
-0.029458507895469666,
0.04593568667769432,
0.015025685541331768,
0.016796942800283432,
-0.02762182056903839,
0.0004599338280968368,
-0.021602943539619446,
0.016993826255202293,
-0.027625160291790962,
0.06053373962640762,
-0.040462419390678406,
0.05383583530783653,
-0.0490080825984478,
-0.006597897037863731,
-0.06718309968709946,
0.012816271744668484,
0.011177907697856426,
-0.016891740262508392,
0.040455352514982224,
0.01773747242987156,
-0.01320905052125454,
0.016444409266114235,
0.010382204316556454,
0.04296181723475456,
-0.018776867538690567,
0.0031119093764573336,
0.004952262621372938,
0.00599011080339551,
0.04256661981344223,
-0.005226093344390392,
-0.022238103672862053,
0.03174472972750664,
-0.03528355062007904,
-0.059154972434043884,
0.039604369550943375,
-0.010175715200603008,
0.021648377180099487,
0.02099216729402542,
-0.008769569918513298,
-0.05346233770251274,
0.06911186873912811,
-0.016419172286987305,
-0.0004358957230579108,
0.014631195925176144,
-0.025354957208037376,
-0.02834409475326538,
0.03484797105193138,
-0.006876535248011351,
-0.000044384694774635136,
-0.03075072169303894,
0.026937806978821754,
0.06303983181715012,
-0.007259620353579521,
0.023429473862051964,
0.003598265815526247,
-0.011525826528668404,
0.0001608766324352473,
0.03528871014714241,
0.02235640585422516,
0.04418417811393738,
0.05194642394781113,
-0.03566437587141991,
0.020703155547380447,
0.044946830719709396,
0.008504434488713741,
-0.08253670483827591,
0.017603900283575058,
-0.0013695287052541971,
-0.0063971360214054585,
0.05204857140779495,
-0.01134516391903162,
0.03533780202269554,
0.03957971930503845,
-0.04676869139075279,
-0.0013238039100542665,
-0.050974003970623016,
-0.0026000936049968004,
0.01357093546539545,
-0.0020102132111787796,
0.019408075138926506,
0.07858291268348694,
0.053073763847351074,
0.023607999086380005,
0.053045257925987244,
0.013909070752561092,
0.015013977885246277,
-0.024691572412848473,
0.0029522052500396967,
0.00676961662247777,
-0.021347396075725555,
0.0050794100388884544,
0.03615860268473625,
-0.01746685989201069,
-0.014269396662712097,
0.029768018051981926,
0.006350286770612001,
0.05795322358608246,
-0.030728090554475784,
0.01688997820019722,
0.0052912430837750435,
0.05956234410405159,
0.02364426665008068,
-0.01136771123856306,
-0.02484227903187275,
0.03303716704249382,
-0.00804013293236494,
0.003895042696967721,
0.021488182246685028,
-0.01035687793046236,
-0.010112378746271133,
-0.02862565964460373,
-0.0015973341651260853,
0.04680192843079567,
0.015397290699183941,
-0.039228249341249466,
-0.01556771993637085,
0.007866863161325455,
0.02057928964495659,
-0.020310360938310623,
0.025956442579627037,
-0.03852584958076477,
-0.027602510526776314,
0.03327462822198868,
-0.008134323172271252,
0.010941941291093826,
0.025470301508903503,
0.014880354516208172,
-0.01507597230374813,
0.011667691171169281,
-0.004462118726223707,
-0.018264858052134514,
-0.09229873865842819,
-0.002312486059963703,
0.025011537596583366,
0.007530503440648317,
0.005043855868279934,
-0.03229984641075134,
-0.058022789657115936,
0.03520410135388374,
0.01026790402829647,
0.024012966081500053,
0.009123856201767921,
-0.05419788882136345,
0.015863925218582153,
-0.02740383893251419,
0.039256736636161804,
-0.02420472726225853,
0.026150202378630638,
-0.0318293422460556,
-0.017406126484274864,
0.01754463091492653,
0.013557858765125275,
0.07599041610956192,
-0.03023580089211464,
-0.03624538332223892,
0.017686987295746803,
0.02203468792140484,
-0.004024361725896597,
-0.0493011437356472,
0.014278411865234375,
0.005659856367856264,
-0.0016127385897561908,
-0.03686004877090454,
-0.004428787622600794,
-0.0035824745427817106,
-0.008841787464916706,
0.02366684004664421,
0.007471960503607988,
0.033903419971466064,
0.003719866508617997,
-0.010578703135251999,
0.05092374235391617,
0.02839399129152298,
-0.052119653671979904,
0.0781463012099266,
-0.025307487696409225,
0.03682103753089905,
-0.0022259592078626156,
-0.03042084164917469,
-0.02590552344918251,
0.04566154628992081,
-0.013229497708380222,
-0.029434317722916603,
0.015763064846396446,
0.008528079837560654,
0.026525139808654785,
-0.05037785694003105,
0.016748351976275444,
0.008808009326457977,
-0.03257807344198227,
-0.015043586492538452,
0.060495778918266296,
0.022276941686868668,
0.03391851484775543,
0.01646784506738186,
0.000046215816837502643,
-0.008799957111477852,
0.019539153203368187,
-0.009601062163710594,
0.05156408250331879,
0.05370223522186279,
0.0038224421441555023,
0.009960533119738102,
0.017150769010186195,
0.0015518422005698085,
0.005384520627558231,
0.04297808185219765,
-0.00928803626447916,
-0.06193945184350014,
-0.03642924502491951,
0.004940446466207504,
-0.0020971314515918493,
0.046262308955192566,
0.022090502083301544,
-0.01386174000799656,
0.08218824863433838,
-0.029137451201677322,
0.023625532165169716,
0.0050179921090602875,
0.00017107004532590508,
-0.034434836357831955,
-0.02423449233174324,
-0.031930211931467056,
0.05848013982176781,
0.01575399748980999,
0.017506293952465057,
0.0051694647409021854,
0.03585286810994148,
0.0082587581127882,
-0.019574346020817757,
0.020039794966578484,
0.012018406763672829,
-0.02425926737487316,
-0.018298227339982986,
0.016195999458432198,
-0.012969797477126122,
-0.03208262473344803,
0.03677941858768463,
0.0450640507042408,
0.03551995009183884,
-0.0031281509436666965,
-0.034888844937086105,
-0.00238003209233284,
0.07013798505067825,
-0.0354699082672596,
-0.01688910461962223,
-0.025015007704496384,
0.025898821651935577,
-0.04973879083991051,
-0.020100953057408333
] |
<p>The process of exchange of energy between a photon and an electron only occur after a specific energy called work-function of the material. Thus, the energy transferred is quantised due to the fact that the electron can reside only in quantised orbits. </p>
<p>But, why doesn't the process happen in steps? I mean the electron getting excited to a higher orbit and before the electron gets de-excited another photon gives it energy to escape from the metal. Is it theoretically possible?</p> | 1,532 | [
-0.019631097093224525,
-0.04074208438396454,
0.03892456367611885,
-0.049347881227731705,
-0.011873519979417324,
0.007790584582835436,
-0.04323667287826538,
-0.022922798991203308,
0.013679972849786282,
-0.010613405145704746,
0.04460401087999344,
-0.009620090015232563,
0.03268532082438469,
0.010636040940880775,
-0.016592975705862045,
0.030030980706214905,
0.0012352903140708804,
-0.030670206993818283,
-0.01631229929625988,
-0.037977345287799835,
0.001133567187935114,
0.026752742007374763,
-0.014114719815552235,
0.0037384629249572754,
-0.03850068524479866,
-0.0329643152654171,
0.0168219693005085,
0.02864629402756691,
0.017895791679620743,
0.06625979393720627,
-0.018014155328273773,
-0.03845036029815674,
0.008359091356396675,
0.02587122656404972,
0.01011792290955782,
-0.0004124742408748716,
-0.05520675331354141,
-0.08454953134059906,
0.008576258085668087,
-0.0232198778539896,
-0.014537297189235687,
0.013561321422457695,
-0.01301531121134758,
0.046547725796699524,
-0.002757952082902193,
0.0028498093597590923,
0.0032885181717574596,
-0.00304169999435544,
0.035523343831300735,
-0.04579031467437744,
0.020797327160835266,
-0.03504087030887604,
0.03205161169171333,
0.0027595744468271732,
0.00219165300950408,
0.0049827927723526955,
0.05652431771159172,
0.09064381569623947,
-0.016737913712859154,
0.027750950306653976,
-0.021479802206158638,
-0.008940349332988262,
-0.005945319309830666,
-0.023634804412722588,
-0.011542202904820442,
0.03305104374885559,
-0.0003002485609613359,
-0.01673867739737034,
0.030962927266955376,
0.0235530324280262,
0.015029942616820335,
0.0038966448046267033,
0.040687717497348785,
-0.02129955030977726,
-0.0005342139629647136,
-0.0182346124202013,
0.026223571971058846,
-0.005734758917242289,
0.04627930372953415,
0.04698000103235245,
-0.0060087572783231735,
0.002873361576348543,
0.014770827256143093,
0.03733598068356514,
0.012550010345876217,
-0.015582789666950703,
0.05769499018788338,
-0.015052772127091885,
0.015355254523456097,
0.032935190945863724,
-0.008066937327384949,
0.04102339223027229,
0.06479261070489883,
0.015449034981429577,
-0.008039640262722969,
0.010170120745897293,
0.01291678473353386,
0.04756311699748039,
0.01227942481637001,
-0.01602395996451378,
0.049803778529167175,
-0.009416651912033558,
0.028919044882059097,
0.04290122538805008,
0.018435407429933548,
-0.00677521713078022,
-0.016279982402920723,
0.027068711817264557,
0.022229144349694252,
-0.019357040524482727,
-0.030750714242458344,
0.017487352713942528,
0.01068336982280016,
0.010448355227708817,
-0.013199800625443459,
-0.024978065863251686,
-0.00931798666715622,
-0.016736499965190887,
0.05674385279417038,
0.0765126422047615,
-0.013303788378834724,
-0.03862394765019417,
0.028639934957027435,
-0.01478542760014534,
-0.044101014733314514,
0.01224671769887209,
0.019531186670064926,
-0.039523206651210785,
-0.025110656395554543,
0.005829681642353535,
-0.007000312674790621,
-0.05045456066727638,
0.02731204777956009,
-0.02807736024260521,
0.0064104595221579075,
-0.0017399986973032355,
-0.11888609826564789,
-0.05013241618871689,
0.018154358491301537,
-0.042811378836631775,
-0.015648128464818,
-0.03271012753248215,
0.05387803539633751,
0.026299139484763145,
0.0946180447936058,
0.0019093136070296168,
-0.024171316996216774,
-0.03942832723259926,
0.021247101947665215,
-0.008738333359360695,
0.002581835025921464,
-0.005586355924606323,
0.030530575662851334,
-0.010469081811606884,
0.028491346165537834,
-0.04646668955683708,
0.06514065712690353,
0.048695437610149384,
0.014686523005366325,
-0.015302436426281929,
0.031595997512340546,
-0.009721703827381134,
0.006254168227314949,
-0.0016886827070266008,
0.0036582204047590494,
-0.025156475603580475,
0.11339414119720459,
0.017416615039110184,
0.030538339167833328,
0.02037058025598526,
0.022199714556336403,
0.004517940804362297,
-0.026023870334029198,
0.03653330355882645,
-0.018621375784277916,
-0.06132502481341362,
-0.0488031841814518,
-0.0317518413066864,
0.016902804374694824,
-0.010348431766033173,
-0.027582922950387,
-0.04790321737527847,
0.01734444871544838,
0.01831180974841118,
-0.015578515827655792,
0.016736401244997978,
-0.0011229424271732569,
-0.016671951860189438,
-0.05723712593317032,
-0.040845129638910294,
0.005913769826292992,
-0.05954127758741379,
0.03594289347529411,
0.01816706173121929,
-0.008985963650047779,
-0.021088354289531708,
-0.013169084675610065,
0.025727370753884315,
-0.004389822483062744,
-0.03131546452641487,
-0.0018326628487557173,
0.020844245329499245,
-0.03317883610725403,
-0.005695453379303217,
0.04736514389514923,
0.08575105667114258,
0.054204244166612625,
0.04747028276324272,
0.03151148557662964,
-0.008895928040146828,
-0.002638069912791252,
0.017965197563171387,
-0.0037132150027900934,
0.003974307328462601,
0.03012162819504738,
-0.018450627103447914,
0.0053726676851511,
-0.019496453925967216,
-0.011435695923864841,
0.05667675659060478,
-0.005228764843195677,
0.07410942018032074,
0.06573766469955444,
-0.0039826263673603535,
-0.01046461146324873,
0.03959348425269127,
-0.008807511068880558,
0.04618548974394798,
0.012265377677977085,
-0.07030797004699707,
-0.03475762531161308,
-0.012737326323986053,
0.04071715474128723,
0.004210543818771839,
-0.03924521431326866,
0.015118383802473545,
0.03083615005016327,
0.0336189866065979,
0.04300248622894287,
0.05037648603320122,
-0.03591849282383919,
0.010412049479782581,
0.046256136149168015,
-0.0019300705753266811,
-0.0017614056123420596,
0.0012862490257248282,
0.03903323411941528,
-0.00779951736330986,
-0.01113871205598116,
-0.020603101700544357,
-0.01624101772904396,
0.031623899936676025,
0.017185015603899956,
-0.00537966238334775,
-0.02871776558458805,
-0.04559437185525894,
0.043613091111183167,
-0.05223280191421509,
0.03601505979895592,
0.00028410047525539994,
0.002683284692466259,
0.0422491617500782,
-0.014283998869359493,
-0.04460815712809563,
0.019247356802225113,
0.0008694728021509945,
-0.006326673086732626,
-0.006333858706057072,
0.024933384731411934,
-0.04587554186582565,
0.0015439788112416863,
-0.049879468977451324,
-0.014051448553800583,
-0.026170386001467705,
-0.010893681086599827,
0.03072001226246357,
0.0035597672685980797,
0.03607665002346039,
-0.04804655537009239,
-0.05187321454286575,
-0.030408425256609917,
-0.02695997804403305,
0.030238118022680283,
0.014566758647561073,
-0.01424541138112545,
0.007320891600102186,
-0.010469998233020306,
-0.047877222299575806,
0.06133511662483215,
-0.005151249468326569,
0.04424307867884636,
0.021520890295505524,
-0.017917703837156296,
-0.04863813892006874,
0.0020682290196418762,
0.009287819266319275,
-0.036183543503284454,
-0.011100701056420803,
0.00017212919192388654,
0.06034010648727417,
-0.031187573447823524,
-0.045706313103437424,
-0.0008751005516387522,
-0.0057720886543393135,
-0.05587053671479225,
-0.015755122527480125,
0.023130519315600395,
0.015787700191140175,
-0.015771618112921715,
0.05247775465250015,
0.016897493973374367,
-0.051538851112127304,
0.020243313163518906,
-0.061168815940618515,
-0.005931118968874216,
0.006716140545904636,
-0.01613476686179638,
-0.01793760247528553,
-0.03783474490046501,
-0.022728249430656433,
0.07097429782152176,
0.00870856549590826,
-0.020589618012309074,
0.014061945490539074,
-0.035015277564525604,
-0.024141184985637665,
-0.01955769769847393,
0.03603062033653259,
0.025065159425139427,
0.004380938597023487,
0.04687489569187164,
-0.0046665258705616,
0.043395739048719406,
0.016663486137986183,
-0.007969350554049015,
-0.007977258414030075,
0.008381426334381104,
0.010253780521452427,
0.01588699035346508,
0.013678712770342827,
0.003760553663596511,
-0.05268286168575287,
0.05213100463151932,
-0.010914183221757412,
-0.0020616513211280107,
0.054302215576171875,
-0.07675968110561371,
0.0645078644156456,
0.0017645234474912286,
0.003845291445031762,
-0.056329838931560516,
0.031690701842308044,
0.01733979769051075,
-0.028358733281493187,
-0.010248531587421894,
0.0325758270919323,
0.06895174086093903,
-0.0019456751178950071,
0.0038140660617500544,
0.009572834707796574,
0.033256545662879944,
-0.02249535173177719,
-0.01204938255250454,
-0.017682330682873726,
-0.01263224333524704,
0.018125617876648903,
-0.017181120812892914,
-0.014703495427966118,
0.013959383592009544,
0.044978052377700806,
0.052318066358566284,
0.003744433168321848,
-0.008261142298579216,
-0.047267649322748184,
-0.03965717554092407,
-0.027767859399318695,
0.016525905579328537,
0.04505753889679909,
0.023924484848976135,
0.05273963883519173,
0.05806471034884453,
0.04263138025999069,
-0.004689167253673077,
-0.004546535201370716,
-0.09555043280124664,
0.016382016241550446,
-0.002253025770187378,
-0.0087104057893157,
0.004602524451911449,
-0.00045177421998232603,
-0.05006777122616768,
-0.04063371568918228,
-0.09110501408576965,
-0.02493341639637947,
-0.00071762251900509,
-0.04144152253866196,
0.027584420517086983,
-0.03098118305206299,
-0.07892952859401703,
-0.021795520558953285,
0.01577359437942505,
0.06638633459806442,
-0.02394741401076317,
0.01895996555685997,
0.02641073614358902,
-0.037316497415304184,
0.025941025465726852,
-0.003090194659307599,
-0.012208550237119198,
0.006541057955473661,
0.03453108295798302,
0.021739184856414795,
-0.01479792594909668,
-0.02810634672641754,
0.004488721024245024,
0.03427615761756897,
0.050218041986227036,
0.03569077327847481,
-0.040775783360004425,
-0.03483317419886589,
-0.0019490784034132957,
-0.012343432754278183,
0.010913523845374584,
0.046275150030851364,
-0.013175038620829582,
0.02846132405102253,
-0.0016883701318874955,
-0.018391966819763184,
-0.034446828067302704,
-0.0036693355068564415,
0.04793621227145195,
0.02624552696943283,
-0.02979392744600773,
-0.033234260976314545,
-0.04800470918416977,
-0.021896664053201675,
-0.019645031541585922,
0.0014601396396756172,
-0.004960041493177414,
-0.016287384554743767,
0.016060644760727882,
0.0225643590092659,
0.055267658084630966,
-0.0036503500305116177,
-0.02660929039120674,
0.0019644955173134804,
0.006358163896948099,
0.0016449273098260164,
0.002400633180513978,
0.03354235365986824,
0.013983611948788166,
0.02857285737991333,
0.006829812657088041,
0.027714064344763756,
-0.06549755483865738,
-0.0031955898739397526,
0.017717931419610977,
0.029030058532953262,
-0.010698282159864902,
0.008371486328542233,
-0.02744116447865963,
-0.015544134192168713,
0.033343397080898285,
-0.028930755332112312,
0.03629426285624504,
-0.04509406536817551,
-0.0011340429773554206,
-0.0169833991676569,
-0.02497117593884468,
-0.015178177505731583,
0.043124258518218994,
0.014158190228044987,
-0.00013115309411659837,
-0.0348699688911438,
-0.011179402470588684,
0.029774531722068787,
-0.0004977496573701501,
0.024624787271022797,
0.05262090265750885,
-0.032002419233322144,
0.02414078451693058,
-0.01707182452082634,
0.015144502744078636,
-0.006949334405362606,
-0.07142264395952225,
-0.0003903015749529004,
0.012269866652786732,
-0.001999364700168371,
0.035957325249910355,
-0.047449830919504166,
-0.06146315485239029,
0.007872023619711399,
0.010521731339395046,
0.04290087893605232,
-0.02207840047776699,
-0.0342833511531353,
0.04368115961551666,
0.03461568430066109,
-0.03691383823752403,
0.07464053481817245,
0.04893844574689865,
-0.03728550672531128,
0.021563682705163956,
-0.010723377577960491,
0.04361503943800926,
-0.019260631874203682,
0.026007860898971558,
-0.018433695659041405,
0.021267490461468697,
-0.023055529221892357,
0.06060405448079109,
-0.03134097531437874,
-0.008889825083315372,
-0.027397407218813896,
-0.03434057906270027,
0.021254057064652443,
-0.005720709450542927,
-0.0036923130974173546,
-0.036862097680568695,
-0.0277570653706789,
0.03188661113381386,
-0.012186274863779545,
-0.009156567044556141,
-0.01456169318407774,
-0.0161795262247324,
0.004242346156388521,
0.04192879796028137,
0.04130256548523903,
-0.014888649806380272,
-0.05447310209274292,
0.019149458035826683,
0.040516436100006104,
-0.01602058671414852,
0.03515632823109627,
-0.013898608274757862,
0.0023355798330157995,
0.02861703373491764,
-0.035729147493839264,
0.0022473903372883797,
-0.010601281188428402,
-0.008674373850226402,
0.005906140431761742,
-0.02702862210571766,
0.03492092341184616,
0.03820393234491348,
-0.0035957375075668097,
-0.08247479796409607,
-0.05015235394239426,
0.009668641723692417,
0.02703414298593998,
-0.017025424167513847,
-0.015136169269680977,
0.01793077401816845,
-0.03976656496524811,
-0.013871222734451294,
0.006731085479259491,
-0.029791831970214844,
-0.05057195946574211,
0.06270141899585724,
-0.01639377512037754,
-0.01669297181069851,
0.020267469808459282,
0.005309336818754673,
-0.012948798947036266,
-0.007065377198159695,
0.007124337367713451,
-0.025024808943271637,
0.004537672270089388,
0.02112322859466076,
-0.007226947229355574,
-0.051391854882240295,
0.008235415443778038,
-0.014614158309996128,
0.021339893341064453,
-0.005010455381125212,
-0.023673148825764656,
0.051823075860738754,
0.024282533675432205,
0.041678279638290405,
0.003279918571934104,
0.05471497029066086,
0.022124463692307472,
0.053001295775175095,
0.024040650576353073,
0.009921826422214508,
-0.03330153971910477,
-0.04941911622881889,
0.02020242251455784,
-0.01785704493522644,
-0.0022358205169439316,
0.015373500995337963,
0.0672857016324997,
-0.04291190952062607,
0.016244174912571907,
0.05752326175570488,
-0.02084961347281933,
-0.01738973893225193,
-0.04418926686048508,
0.030864030122756958,
-0.014472725801169872,
-0.01705322228372097,
-0.009067577309906483,
-0.03721814230084419,
-0.0004643661668524146,
0.0011630577500909567,
0.03244202956557274,
-0.015486259944736958,
0.04243772476911545,
-0.0211937353014946,
-0.010221951641142368,
-0.01599404774606228,
-0.02840735763311386,
-0.020402083173394203,
-0.018663670867681503,
0.001889806124381721,
0.02721329778432846,
0.020123101770877838,
0.04623354971408844,
0.015021183528006077,
0.07906929403543472,
-0.014926320873200893,
0.06629280745983124,
0.038377873599529266,
-0.00925461295992136,
0.010991067625582218,
0.007843347266316414,
-0.021959394216537476,
0.0033721188083291054,
-0.04144846275448799,
0.03486787527799606,
-0.010060330852866173,
-0.010568929836153984,
0.042610056698322296,
-0.025574054569005966,
0.01002774853259325,
-0.028107233345508575,
-0.0074948943220078945,
-0.0735517144203186,
0.03882843628525734,
-0.0040703266859054565,
0.026129813864827156,
0.014438568614423275,
0.029823709279298782,
0.007309688255190849,
0.007898722775280476,
0.000426597980549559,
-0.015445088967680931,
-0.03569260239601135,
-0.03587060794234276,
-0.0869160071015358,
-0.04710628464818001,
0.04344991594552994,
-0.04676289111375809,
-0.022316234186291695,
-0.011655634269118309,
-0.028659638017416,
0.014675759710371494,
0.0017066996078938246,
0.02849637158215046,
-0.0007763542234897614,
0.04557034373283386,
0.004856734070926905,
0.03922241926193237,
0.00661539426073432,
0.04832260310649872,
0.14766192436218262,
0.013693617656826973,
-0.002956101205199957,
-0.048687320202589035,
-0.047303538769483566,
-0.04274141043424606,
0.034209031611680984,
0.008046544156968594,
0.0027519604191184044,
-0.01989276520907879,
-0.0005192210082896054,
-0.006781633943319321,
0.03679381683468819,
-0.008630454540252686,
0.007325087673962116,
0.002709524007514119,
-0.03713436424732208,
-0.019328730180859566,
0.02578502520918846,
0.008497080765664577,
-0.0003241002559661865,
0.013545669615268707,
-0.03933468088507652,
-0.01840890385210514,
-0.033394042402505875,
0.002220262074843049,
-0.001919295871630311,
-0.030206752941012383,
0.04559900984168053,
0.01360307913273573,
-0.0489066019654274,
0.0019290848867967725,
0.03312433138489723,
-0.03287800773978233,
0.02677125856280327,
0.02635769359767437,
0.06102251261472702,
0.0009853870142251253,
0.02175803855061531,
0.022307999432086945,
0.028439411893486977,
0.007062997203320265,
-0.00983648095279932,
-0.0074134026654064655,
-0.04861218482255936,
0.006623783148825169,
-0.02527437172830105,
0.04207152873277664,
-0.025266174226999283,
-0.013526026159524918,
0.01643325574696064,
-0.05842934921383858,
0.013734442181885242,
-0.030741654336452484,
-0.02541237697005272,
-0.00442572683095932,
-0.015968991443514824,
0.010402983985841274,
-0.03312506526708603,
-0.027509566396474838,
-0.015257681719958782,
0.008404982276260853,
-0.021302396431565285,
0.016001546755433083,
-0.02440706454217434,
0.013264354318380356,
0.010133776813745499,
0.014490336179733276,
-0.022784419357776642,
-0.021549738943576813,
0.00681676808744669,
-0.010585293173789978,
-0.03762432560324669,
0.0008248198428191245,
-0.006065306253731251,
0.011834587901830673,
0.038134172558784485,
-0.006843962240964174,
-0.004948259796947241,
-0.025718549266457558,
-0.05757707357406616,
0.02535143308341503,
0.017718758434057236,
-0.039317693561315536,
-0.020910117775201797,
0.006840516813099384,
0.021957986056804657,
0.04487333074212074,
-0.027674295008182526,
0.022254817187786102,
0.02837943844497204,
-0.00275483843870461,
0.03783378377556801,
-0.049779824912548065,
0.008497236296534538,
0.019527703523635864,
0.024073760956525803,
-0.027046063914895058,
-0.054684143513441086,
0.021480347961187363,
0.0104490015655756,
0.0011236598948016763,
-0.015964586287736893,
0.015001373365521431,
-0.02897227741777897,
-0.004085416905581951,
0.02452322095632553,
0.018120886757969856,
0.001869537285529077,
-0.014243723824620247,
-0.022945808246731758,
-0.018114281818270683,
-0.014193755574524403,
-0.040631718933582306,
-0.0002880302199628204,
-0.03812091052532196,
0.01884186826646328,
-0.060143180191516876,
0.046105679124593735,
-0.009753411635756493,
0.04284757748246193,
-0.046081628650426865,
-0.01705043762922287,
-0.005541293416172266,
0.03391934931278229,
-0.004833667539060116,
0.015835924074053764,
-0.01477337721735239,
0.01871962659060955,
0.001506348024122417,
-0.040688421577215195,
0.015447111800312996,
0.038740403950214386,
-0.008430726826190948,
0.004868514835834503,
0.04278978705406189,
-0.01787601411342621,
0.034104734659194946,
-0.01389485877007246,
0.0070105986669659615,
0.01395739521831274,
-0.053179726004600525,
-0.04244241118431091,
0.02751891128718853,
-0.00767104746773839,
0.03211278095841408,
0.04091379791498184,
-0.006969559472054243,
-0.009394827298820019,
0.025287238880991936,
-0.014110696502029896,
0.015861650928854942,
0.014800919219851494,
-0.022496484220027924,
-0.025091297924518585,
-0.02621268853545189,
0.011851289309561253,
-0.04065538942813873,
-0.008306501433253288,
0.04701739177107811,
-0.01355865877121687,
0.022881748154759407,
-0.008834676817059517,
-0.03223998099565506,
-0.021066879853606224,
0.01823858730494976,
0.04610126465559006,
-0.015282167121767998,
-0.004324915818870068,
0.05215729773044586,
-0.008010637015104294,
0.058090075850486755,
0.007825071923434734,
-0.027376852929592133,
-0.07437242567539215,
-0.00750688137486577,
-0.024584244936704636,
0.0001983935944736004,
-0.0024392122868448496,
-0.018171673640608788,
0.042955514043569565,
0.020651912316679955,
-0.0967407077550888,
0.06431752443313599,
-0.030931074172258377,
-0.021272247657179832,
-0.022841738536953926,
0.0304313562810421,
-0.053176794201135635,
0.03872694820165634,
0.021760815754532814,
0.04799266904592514,
0.015430927276611328,
0.031886082142591476,
-0.008150349371135235,
-0.024059632793068886,
-0.029461024329066277,
0.019318660721182823,
-0.04710496962070465,
0.017069252207875252,
0.08612451702356339,
-0.019300157204270363,
-0.00042180749005638063,
0.008452366106212139,
-0.04778645932674408,
0.006726281251758337,
0.013756128028035164,
0.04062367230653763,
0.004618357867002487,
-0.0007930501597002149,
-0.006029713898897171,
-0.008659849874675274,
-0.012840521521866322,
0.015843965113162994,
0.036773040890693665,
0.0015541922766715288,
-0.021696629002690315,
-0.011212700046598911,
0.04502591863274574,
0.009134208783507347,
-0.054844535887241364,
0.05350186303257942,
0.002917578909546137,
0.010580999776721,
0.015103897079825401,
0.032678745687007904,
0.022396830841898918,
-0.0036480557173490524,
-0.018470365554094315,
-0.04928288981318474,
-0.007953888736665249,
-0.03860663250088692,
0.005542797036468983,
-0.006329548545181751,
-0.012363474816083908,
-0.0351690798997879,
-0.04108314961194992,
0.006383735686540604,
0.011677046306431293,
0.014788823202252388,
-0.025255829095840454,
0.012742881663143635,
0.013271334581077099,
0.008824544958770275,
0.01707221195101738,
-0.039344124495983124,
-0.009969182312488556,
0.008195018395781517,
-0.0043835872784256935,
0.02928507700562477,
0.02368140034377575,
-0.01671515591442585,
-0.04572058841586113,
-0.0941401943564415,
0.028703322634100914,
-0.03280438482761383,
-0.041691433638334274,
-0.009742309339344501,
-0.048582322895526886,
-0.014770583249628544,
0.003987822216004133,
0.06563564389944077,
-0.004325009882450104,
-0.021316738799214363,
0.014412857592105865,
-0.031023545190691948,
0.02073787711560726,
-0.01972476951777935,
-0.006880306638777256,
-0.03757944703102112,
0.010203256271779537,
-0.007656883914023638,
0.018179871141910553,
-0.036266788840293884,
0.056323640048503876,
0.015282905660569668,
-0.04158779978752136,
0.008519167080521584,
-0.016928985714912415,
-0.0054474021308124065,
0.051743555814027786,
0.003208901034668088,
0.009759461507201195,
0.04670573025941849,
-0.011313365772366524,
0.05177873373031616,
0.00039570609806105494,
-0.004959945101290941,
-0.04719274118542671,
0.0037623450625687838,
-0.018022898584604263,
0.017868008464574814,
-0.02015332505106926,
-0.02102809026837349,
0.05018298327922821,
-0.05539467930793762,
0.017886752262711525,
0.02637895941734314,
-0.01674872264266014,
0.021854164078831673,
0.01799018867313862,
0.019846253097057343,
0.010300986468791962,
0.005610145628452301,
0.019556501880288124,
-0.017509568482637405,
0.008276280015707016,
0.016100717708468437,
0.05697391554713249,
0.005125881172716618,
-0.011000885628163815,
0.05198382958769798,
0.02205757237970829,
-0.030010433867573738,
-0.015510214492678642,
0.020073790103197098,
0.016381433233618736,
0.002482253359630704,
0.024174094200134277,
0.027769742533564568,
-0.0040245396085083485,
-0.02810065634548664,
0.02356412261724472,
-0.0688663199543953,
0.08618631213903427,
-0.011222847737371922,
0.008256271481513977,
-0.01205457653850317,
0.036733582615852356,
-0.007385036442428827,
0.009042969904839993,
0.017642397433519363,
0.02882303111255169,
-0.021504035219550133,
-0.005400314927101135,
-0.034827787429094315,
0.022328374907374382,
0.052520520985126495,
-0.015294896438717842,
0.024914145469665527,
-0.007486723363399506,
-0.03343364968895912,
0.02453288808465004,
0.008575370535254478,
-0.028898395597934723,
-0.037206780165433884,
0.016369899734854698,
0.019648022949695587,
0.006441656034439802,
-0.0026297939475625753,
0.004901152104139328,
0.00855429656803608,
0.029622383415699005,
-0.04137561842799187,
-0.007170484866946936,
-0.008496607653796673,
0.029835490509867668,
-0.038829781115055084,
0.0032113580964505672
] |
<p>Why is electron presented in books, pictures as a sphere, when in fact it's not?</p> | 1,533 | [
-0.06135287135839462,
-0.0034453251864761114,
0.04603162407875061,
-0.044699348509311676,
-0.011119251139461994,
-0.006578413303941488,
-0.016225585713982582,
0.002747065620496869,
-0.004253618884831667,
-0.014239250682294369,
0.04585825279355049,
0.03425890952348709,
0.07272787392139435,
-0.0008011599420569837,
-0.005133428610861301,
0.014071257784962654,
0.000628942740149796,
0.0008617369458079338,
-0.03035777620971203,
-0.008389558643102646,
0.000563219131436199,
0.008216973394155502,
0.004556907340884209,
0.008198180235922337,
0.019749624654650688,
0.0326743945479393,
0.04821619391441345,
-0.003927759826183319,
0.057485584169626236,
0.06233825534582138,
-0.021446865051984787,
-0.008274728432297707,
0.05937079340219498,
-0.02935783565044403,
0.025743519887328148,
-0.03962493687868118,
0.01905744895339012,
-0.0444183424115181,
-0.006679526064544916,
0.004425765946507454,
-0.008944124914705753,
-0.013468172401189804,
-0.005570793058723211,
0.07945826649665833,
-0.02922169864177704,
0.049702033400535583,
-0.0319080613553524,
-0.01718147285282612,
0.04398062080144882,
-0.044269122183322906,
0.026717534288764,
0.008773180656135082,
0.03236928582191467,
0.024484336376190186,
0.02866416983306408,
0.012316778302192688,
0.07617872953414917,
0.045154448598623276,
-0.015656989067792892,
-0.05700809881091118,
-0.02048858255147934,
-0.04737577587366104,
0.004146465566009283,
-0.015569428913295269,
-0.0050398060120642185,
0.028853533789515495,
0.00006249379657674581,
-0.05244044214487076,
0.027513740584254265,
-0.0017562001012265682,
0.0007986401906237006,
0.019042622298002243,
0.012143989093601704,
-0.018508808687329292,
0.001400383422151208,
-0.0177232064306736,
0.0404229462146759,
0.005763905588537455,
0.0316399522125721,
0.012074328027665615,
-0.016370797529816628,
-0.011157950386404991,
0.05077926814556122,
-0.018897397443652153,
0.000010257691428705584,
0.004476899281144142,
0.06115502864122391,
-0.00793350487947464,
-0.02896696887910366,
0.04510689154267311,
-0.013305782340466976,
0.016583463177084923,
0.06448931992053986,
-0.03714311495423317,
-0.01244442630559206,
0.02983192168176174,
-0.005871178116649389,
0.039175160229206085,
-0.0012966676149517298,
-0.01838032342493534,
0.01766872964799404,
0.0009352429187856615,
0.026037249714136124,
0.07468698173761368,
0.01274462416768074,
-0.022602153941988945,
-0.0448637455701828,
0.009094832465052605,
0.0074917022138834,
-0.009212763980031013,
-0.020156018435955048,
0.016269132494926453,
-0.006366441026329994,
0.040341559797525406,
0.016215026378631592,
-0.0037662929389625788,
0.020159678533673286,
-0.003852927591651678,
0.034857481718063354,
0.04490477591753006,
-0.013750850223004818,
-0.0420837476849556,
0.003313328605145216,
-0.03152134269475937,
-0.07085230201482773,
0.03491397947072983,
0.05510878190398216,
-0.000011851186172862072,
-0.006476324982941151,
0.009552348405122757,
0.008928140625357628,
0.007482101209461689,
0.019203869625926018,
0.019322523847222328,
0.04445745050907135,
0.004391512367874384,
-0.08937130123376846,
-0.06341119855642319,
0.025193318724632263,
-0.001423663692548871,
-0.03878661245107651,
-0.06859219819307327,
0.022638967260718346,
0.027052830904722214,
0.0603862889111042,
0.0008029097807593644,
-0.01240200363099575,
0.004009651020169258,
0.04562360420823097,
0.015369819477200508,
0.0008422518731094897,
0.0161299929022789,
0.010808517225086689,
-0.0251869335770607,
0.035893261432647705,
-0.028924360871315002,
0.020311350002884865,
0.006007201038300991,
0.022945642471313477,
-0.061265215277671814,
0.03870728611946106,
-0.01703646220266819,
-0.019577180966734886,
-0.012611601501703262,
-0.01652642898261547,
-0.06520064920186996,
0.07124878466129303,
0.011838573031127453,
0.025609727948904037,
0.06290070712566376,
-0.01399440411478281,
0.05644896999001503,
0.007616221904754639,
0.004374871961772442,
0.028340639546513557,
-0.014291766099631786,
-0.027674030512571335,
-0.01328117586672306,
0.02164980210363865,
0.008524569682776928,
-0.05803067609667778,
-0.012940838001668453,
0.0028460193425416946,
0.024421358481049538,
-0.002189073245972395,
0.05394135043025017,
-0.018359022215008736,
-0.008319179527461529,
-0.012409198097884655,
-0.04780707135796547,
-0.02484818547964096,
-0.06413524597883224,
0.04509793967008591,
0.009573563933372498,
-0.013044057413935661,
0.052198369055986404,
-0.01101014856249094,
0.0019579953514039516,
-0.0017903069965541363,
-0.016030626371502876,
-0.03837540000677109,
0.05247991159558296,
0.0014947975287213922,
-0.026485750451683998,
0.01894637942314148,
0.06774278730154037,
0.042182568460702896,
0.001014706795103848,
-0.0029739399906247854,
-0.01930108107626438,
-0.03128858655691147,
-0.018579130992293358,
0.0027857099194079638,
0.009316888637840748,
0.023768583312630653,
-0.026598123833537102,
-0.0045807273127138615,
0.013892164453864098,
-0.044796790927648544,
0.04778580740094185,
-0.022340215742588043,
0.06188502162694931,
0.010072712786495686,
-0.024733753874897957,
0.003024347359314561,
0.033475570380687714,
0.021104075014591217,
0.015895942226052284,
0.03536028414964676,
-0.00953024160116911,
-0.03725428879261017,
0.004154117312282324,
0.035780057311058044,
0.011590373702347279,
-0.022980406880378723,
0.005589612293988466,
-0.018730174750089645,
0.05546686425805092,
-0.00028773958911187947,
0.017648164182901382,
-0.039528727531433105,
-0.06977931410074234,
0.031544554978609085,
-0.037815190851688385,
0.015287919901311398,
-0.0005070072948001325,
0.02435341104865074,
0.026477424427866936,
0.026547972112894058,
-0.029668381437659264,
-0.021602964028716087,
0.019141308963298798,
-0.036655884236097336,
-0.006633971352130175,
0.023491840809583664,
-0.00922910962253809,
0.025165816769003868,
-0.04272376000881195,
0.0016228011809289455,
-0.010656904429197311,
-0.03548535332083702,
0.013610254973173141,
-0.06631416827440262,
-0.028857508674263954,
0.026745187118649483,
0.022951537743210793,
-0.024719884619116783,
-0.00803444068878889,
0.025105435401201248,
-0.07268209010362625,
0.001352509018033743,
-0.034337129443883896,
-0.0031519532203674316,
0.015042073093354702,
0.022866269573569298,
0.03276033699512482,
0.013015846721827984,
0.010380744002759457,
-0.016596855595707893,
-0.0323994979262352,
-0.01741134375333786,
-0.038528937846422195,
0.020004136487841606,
0.032633356750011444,
-0.027628449723124504,
0.034981619566679,
-0.040505118668079376,
-0.04232306405901909,
0.030266134068369865,
-0.004177842289209366,
0.022674791514873505,
-0.006743995938450098,
0.02470392920076847,
-0.005350243300199509,
0.0007398052839562297,
-0.026605049148201942,
-0.003459521569311619,
-0.013780249282717705,
-0.008044141344726086,
0.029284514486789703,
-0.055636823177337646,
-0.002160552190616727,
-0.004860869608819485,
-0.027251677587628365,
-0.07114318013191223,
0.00926229264587164,
-0.031062554568052292,
0.038332246243953705,
-0.030528957024216652,
-0.008481469936668873,
0.036713603883981705,
-0.04421791434288025,
-0.024450257420539856,
-0.036624860018491745,
-0.02127056010067463,
-0.0069015477783977985,
-0.0026387253310531378,
0.04701109230518341,
-0.0195616427809,
-0.027532044798135757,
0.0851994976401329,
-0.007728673983365297,
-0.03866998851299286,
-0.018891023471951485,
0.0039903889410197735,
-0.03979218006134033,
-0.06463402509689331,
0.017285648733377457,
0.05101414769887924,
-0.0017819561762735248,
0.012521986849606037,
0.005818086210638285,
0.0354427807033062,
0.0039029077161103487,
0.013067726045846939,
-0.011021548882126808,
0.002011750591918826,
-0.029508084058761597,
-0.016716333106160164,
0.027670826762914658,
-0.010454903356730938,
-0.04071589559316635,
0.016003400087356567,
0.0055686612613499165,
0.04180819168686867,
0.012936202809214592,
-0.03801244869828224,
0.05174150690436363,
-0.026065774261951447,
0.0212273970246315,
-0.01770990714430809,
0.019792065024375916,
0.010117834433913231,
-0.03185313194990158,
0.016739921644330025,
0.021362653002142906,
0.052072227001190186,
0.0050265248864889145,
-0.031799547374248505,
0.028226155787706375,
0.0351853147149086,
-0.03662111982703209,
-0.012793954461812973,
0.0005624037585221231,
0.04896668717265129,
0.00894636195152998,
-0.022857749834656715,
-0.02142282761633396,
0.06417162716388702,
0.023819223046302795,
0.039592843502759933,
0.009372948668897152,
-0.036945946514606476,
-0.010907953605055809,
-0.03242873027920723,
0.01590883918106556,
-0.0092074079439044,
0.03675053268671036,
0.002531084232032299,
0.06347183138132095,
0.010379347018897533,
0.04493533819913864,
-0.026555070653557777,
0.020651865750551224,
-0.05898188054561615,
-0.02677752450108528,
-0.046765025705099106,
0.030550271272659302,
-0.05758175626397133,
0.00956086628139019,
-0.04095764085650444,
-0.01782410778105259,
-0.017476730048656464,
-0.026726437732577324,
-0.018751857802271843,
-0.02838709205389023,
0.012683121487498283,
-0.003274685936048627,
0.002402112353593111,
-0.05056324973702431,
0.04035870358347893,
-0.0057009742595255375,
-0.025940051302313805,
0.04953392595052719,
0.05257970839738846,
-0.0002834811748471111,
0.0140971839427948,
-0.014249419793486595,
0.02992725558578968,
0.010697602294385433,
0.007384968921542168,
0.023173075169324875,
0.003896350273862481,
-0.02605985663831234,
-0.00893609318882227,
0.024001529440283775,
0.06805619597434998,
-0.009254012256860733,
-0.0014262540498748422,
-0.044601839035749435,
-0.06042558699846268,
-0.0076939440332353115,
-0.04241873323917389,
0.030309082940220833,
-0.02937532775104046,
0.027220388874411583,
0.024664534255862236,
-0.01951509341597557,
0.03697015345096588,
0.028132572770118713,
0.010912581346929073,
-0.0020293970592319965,
-0.05376246199011803,
-0.025475889444351196,
-0.0038913339376449585,
-0.051711246371269226,
-0.007562648039311171,
0.03959772735834122,
0.010883551090955734,
-0.013264444656670094,
-0.020412378013134003,
0.03370029851794243,
-0.008848519995808601,
-0.04084211215376854,
-0.02032167837023735,
-0.030614417046308517,
-0.025192711502313614,
-0.013056331314146519,
0.00480412133038044,
0.00878908857703209,
0.01669563725590706,
0.03417225182056427,
0.009116662666201591,
-0.04266061633825302,
-0.04739530384540558,
-0.02073567546904087,
0.041921526193618774,
0.037401046603918076,
0.017296485602855682,
-0.010122119449079037,
-0.08214280754327774,
-0.010002377443015575,
0.040059108287096024,
-0.01722523756325245,
-0.01191667839884758,
-0.07838818430900574,
0.02533026598393917,
-0.036599431186914444,
-0.030005859211087227,
-0.001661471207626164,
0.0009754008497111499,
0.0005892901099286973,
0.005927440710365772,
-0.04693203046917915,
0.024987563490867615,
-0.013430371880531311,
0.025211891159415245,
0.001885236706584692,
0.054496582597494125,
0.05165249854326248,
-0.0027391724288463593,
0.015084397979080677,
0.02215915359556675,
-0.03882379084825516,
-0.07528680562973022,
-0.02902849018573761,
0.006532343570142984,
0.002115095965564251,
0.001596845337189734,
-0.04410311579704285,
-0.06115097180008888,
0.01977316476404667,
-0.011061140336096287,
0.00021673155424650759,
-0.023770788684487343,
-0.0588025264441967,
0.036691002547740936,
0.003083472605794668,
-0.01304649468511343,
0.025372983887791634,
0.01793069578707218,
-0.009005178697407246,
-0.02023947611451149,
-0.06819058954715729,
0.040803637355566025,
-0.03354877233505249,
-0.007135642226785421,
-0.019315151497721672,
0.013232557103037834,
-0.031352922320365906,
0.028349174186587334,
-0.003211001632735133,
0.03570481762290001,
0.0055707041174173355,
-0.06825628876686096,
-0.007217498496174812,
0.0023139137774705887,
-0.00707285525277257,
-0.0025477076414972544,
-0.0003663439129013568,
-0.020992817357182503,
-0.010297372005879879,
-0.03326280787587166,
-0.0019799075089395046,
-0.008479149080812931,
0.0008367080590687692,
0.024049224331974983,
-0.0017411961453035474,
0.018826337531208992,
-0.027560880407691002,
-0.018857985734939575,
0.007649634033441544,
-0.06532207131385803,
0.047378428280353546,
-0.03601149097084999,
-0.019369246438145638,
0.03792277351021767,
-0.08235884457826614,
-0.045628342777490616,
0.02151268534362316,
-0.01973315328359604,
0.039309028536081314,
-0.03368927165865898,
0.005834484007209539,
0.00852881744503975,
0.036905426532030106,
-0.05721312388777733,
-0.04710521921515465,
0.006948140915483236,
0.00960456021130085,
-0.026115426793694496,
0.005133509170264006,
0.030477341264486313,
-0.015981515869498253,
-0.027675572782754898,
0.017732148990035057,
0.01725519448518753,
-0.05021218955516815,
-0.015324684791266918,
0.006487945094704628,
0.01040063425898552,
0.05616241320967674,
-0.020274298265576363,
-0.03193181753158569,
-0.005136746913194656,
-0.018827738240361214,
0.005388983525335789,
0.0034228453878313303,
0.06932688504457474,
-0.003054254222661257,
-0.04436009004712105,
-0.0014122268185019493,
-0.014988337643444538,
0.02724670246243477,
-0.016009043902158737,
0.001462595071643591,
0.051534052938222885,
0.00698495889082551,
-0.02799488604068756,
0.007691887207329273,
0.019303182139992714,
-0.020337272435426712,
0.06833218038082123,
-0.0033995250705629587,
-0.0008474989444948733,
-0.0424112007021904,
-0.033529121428728104,
0.048031046986579895,
0.013226652517914772,
0.024343300610780716,
0.0026154518127441406,
0.03696850314736366,
-0.011607731692492962,
0.008468213491141796,
0.031951915472745895,
-0.02004309557378292,
0.01813296414911747,
-0.01678900048136711,
0.0024704940151423216,
0.022994721308350563,
0.0435902439057827,
-0.017692184075713158,
-0.024986952543258667,
-0.011845963075757027,
0.03231186792254448,
0.03854067996144295,
-0.023192714899778366,
0.04508116468787193,
0.0019473792053759098,
-0.013232683762907982,
-0.007236018311232328,
-0.03008456900715828,
-0.008977333083748817,
0.0005169400246813893,
-0.01840922422707081,
0.045084673911333084,
-0.03531594201922417,
0.01974465325474739,
0.017948532477021217,
0.053227733820676804,
-0.037463974207639694,
0.015065103769302368,
0.014674603007733822,
0.004260685294866562,
0.004764697048813105,
0.016330551356077194,
-0.02622433938086033,
0.03855011612176895,
-0.030836446210741997,
0.05005967244505882,
-0.00909669790416956,
-0.01843712292611599,
0.057189904153347015,
-0.05498369410634041,
-0.009071806445717812,
-0.005807145033031702,
-0.005353613756597042,
-0.03213047608733177,
0.02147601544857025,
0.025488441810011864,
-0.019982000812888145,
-0.04729881510138512,
0.015960263088345528,
0.023472176864743233,
-0.031768932938575745,
-0.002601971384137869,
-0.0011539546540006995,
-0.08005567640066147,
0.010155284777283669,
-0.04492124915122986,
-0.034377701580524445,
0.03458210080862045,
-0.009977450594305992,
0.0009765212307684124,
-0.01308019831776619,
-0.016608478501439095,
0.03383214399218559,
0.01837758906185627,
0.031179219484329224,
-0.046986173838377,
0.03983555734157562,
-0.02810332365334034,
0.01612599939107895,
-0.01288465317338705,
0.004506528843194246,
0.1384229212999344,
0.012569062411785126,
-0.0035994357895106077,
-0.06055477634072304,
0.02968333661556244,
-0.0346674770116806,
0.04454202577471733,
-0.00683157192543149,
0.005270048975944519,
-0.03250186890363693,
0.036904726177453995,
-0.014641102403402328,
0.053398970514535904,
0.03932966664433479,
0.03244815394282341,
0.03469443321228027,
-0.05131140723824501,
-0.051125418394804,
-0.00005279117249301635,
0.03539305552840233,
-0.008068108931183815,
0.05921672284603119,
-0.07610370218753815,
0.01526305079460144,
-0.04270008206367493,
0.0130686080083251,
-0.03560800477862358,
-0.016093576326966286,
0.06662489473819733,
0.016585243865847588,
-0.0700230523943901,
-0.0015172106213867664,
0.01575385220348835,
-0.02279197983443737,
-0.04248858988285065,
0.011623273603618145,
0.047045521438121796,
-0.005171333905309439,
0.027075154706835747,
0.01633678749203682,
0.020794274285435677,
0.03442085161805153,
-0.005641465075314045,
0.026647400110960007,
-0.04110274091362953,
0.0009987510275095701,
-0.016255708411335945,
0.04374002665281296,
-0.03752788528800011,
0.027834666892886162,
0.0015145153738558292,
0.006447565741837025,
-0.03431279957294464,
-0.0692381039261818,
-0.008026142604649067,
-0.04039512947201729,
0.012265153229236603,
0.04725641384720802,
-0.042282190173864365,
-0.0070500681176781654,
0.025972971692681313,
-0.013311287388205528,
0.06042790040373802,
0.00861325953155756,
0.015613486990332603,
0.03510047122836113,
-0.0005420930683612823,
0.010971643030643463,
-0.0038816581945866346,
-0.007292079273611307,
-0.003735242411494255,
-0.0013619705568999052,
-0.03443264588713646,
-0.04330137372016907,
0.01708320714533329,
0.04325364902615547,
0.05473722890019417,
0.00010511279106140137,
0.013842196203768253,
0.004954374860972166,
-0.025390127673745155,
0.032131072133779526,
-0.0013506620889529586,
-0.009969357401132584,
-0.03707968071103096,
0.015847966074943542,
0.03812208026647568,
0.027879200875759125,
-0.03561555594205856,
-0.0020243406761437654,
-0.02595791220664978,
-0.022534538060426712,
-0.0004116850614082068,
-0.028861962258815765,
-0.029150836169719696,
0.040464553982019424,
-0.014249054715037346,
-0.01115527655929327,
-0.027682270854711533,
0.0033035720698535442,
0.043199650943279266,
-0.0063034724444150925,
0.013151480816304684,
0.04021047055721283,
-0.005023248493671417,
-0.01804165728390217,
0.022713959217071533,
-0.015718158334493637,
0.007583402097225189,
0.034886833280324936,
-0.024217426776885986,
-0.03262538090348244,
0.01405760645866394,
-0.045854367315769196,
0.0072773173451423645,
-0.012965110130608082,
0.0521683432161808,
0.006860900204628706,
0.018398037180304527,
-0.025303419679403305,
0.04254130646586418,
-0.003078215755522251,
0.006330274511128664,
-0.06595124304294586,
0.011363530531525612,
0.004653140902519226,
-0.013564292341470718,
-0.02634371817111969,
0.05772576853632927,
-0.006166062317788601,
0.005991702899336815,
0.012256603688001633,
0.016892587766051292,
0.004456103313714266,
0.005335178226232529,
-0.0133897103369236,
-0.011461039073765278,
0.03766504302620888,
-0.015761733055114746,
-0.01930711604654789,
0.03873492404818535,
-0.014484426937997341,
-0.06559716165065765,
0.010450311005115509,
-0.012373632751405239,
0.026082998141646385,
0.018111104145646095,
-0.007331920322030783,
-0.007116484921425581,
0.04877058044075966,
-0.05875878408551216,
0.009917641058564186,
0.021504223346710205,
-0.03289743512868881,
-0.013066045008599758,
-0.02169639803469181,
0.015481800772249699,
-0.029069630429148674,
0.011420900002121925,
0.0699671134352684,
-0.007661914452910423,
-0.004069804679602385,
-0.014071227051317692,
-0.012338538654148579,
-0.013763315975666046,
0.04744047671556473,
0.05446035414934158,
0.03536323457956314,
0.014233528636395931,
0.014548254199326038,
-0.054865896701812744,
0.05713896453380585,
0.04814765229821205,
-0.018217146396636963,
-0.07043206691741943,
-0.023828621953725815,
-0.01862945221364498,
0.015508443117141724,
0.030566664412617683,
-0.022680239751935005,
-0.009245089255273342,
0.031866636127233505,
-0.11419999599456787,
0.02271130122244358,
-0.021966643631458282,
-0.04669306427240372,
-0.01714584417641163,
-0.03531244769692421,
-0.02535119093954563,
0.048440974205732346,
0.02892902120947838,
0.03506046161055565,
0.03515125438570976,
0.018602458760142326,
-0.011336182244122028,
-0.02229769341647625,
-0.053254175931215286,
0.04569760337471962,
-0.029476964846253395,
-0.006454680114984512,
0.01859758049249649,
-0.0010970423463732004,
-0.013933860696852207,
0.02630629390478134,
0.026449115946888924,
0.009706096723675728,
-0.021866029128432274,
-0.00020011316519230604,
0.0266409944742918,
0.02348567731678486,
0.05391073599457741,
-0.024685127660632133,
-0.0342424139380455,
-0.0002677098964340985,
0.058212365955114365,
0.010023251175880432,
-0.005390483886003494,
-0.0010172799229621887,
-0.0007267390610650182,
-0.02442161738872528,
-0.039457645267248154,
0.029369503259658813,
0.003510527079924941,
-0.021141476929187775,
-0.03424740955233574,
0.03632683306932449,
0.03131317347288132,
-0.03370025008916855,
0.004875411279499531,
-0.046346891671419144,
-0.0012310162419453263,
-0.005240674130618572,
-0.003496680175885558,
0.017892230302095413,
0.05376410111784935,
-0.0031491375993937254,
-0.0448651984333992,
0.007132429629564285,
0.03163875266909599,
0.01010248064994812,
-0.047989849001169205,
0.02362121269106865,
0.04269127920269966,
0.008687886409461498,
0.03661305457353592,
-0.044721417129039764,
-0.039542920887470245,
-0.000563794921617955,
0.04124542698264122,
0.011716675944626331,
-0.005508119706064463,
-0.023574555292725563,
-0.020738385617733,
-0.037873972207307816,
0.029051650315523148,
-0.01614699512720108,
-0.024333899840712547,
0.00408101174980402,
-0.025497106835246086,
0.013883393257856369,
0.0564265139400959,
0.04946145787835121,
0.030702749267220497,
-0.005376714747399092,
0.008993028663098812,
0.013528048992156982,
0.024830279871821404,
-0.04224596545100212,
-0.006413443945348263,
0.007771849632263184,
-0.030974937602877617,
0.05721084028482437,
-0.00367665383964777,
-0.02775040827691555,
0.03317457064986229,
0.026333266869187355,
0.016756627708673477,
0.025223860517144203,
-0.03366691246628761,
-0.04102646932005882,
0.048932693898677826,
0.06559722125530243,
-0.04387850686907768,
0.07482918351888657,
-0.004442539997398853,
-0.0026350365951657295,
0.003737781662493944,
-0.003765799105167389,
-0.001884495373815298,
0.008841114118695259,
-0.006332281976938248,
-0.019279643893241882,
-0.023101400583982468,
-0.013285811059176922,
0.021322038024663925,
-0.045936468988657,
-0.01467912271618843,
0.05418388172984123,
-0.02289489097893238,
0.013976022601127625,
0.0724395141005516,
0.019416311755776405,
0.02768831141293049,
0.011847740970551968,
-0.019829142838716507,
0.03371601924300194,
-0.0184404868632555,
0.0035254762042313814,
0.022338146343827248,
0.045149896293878555,
0.006193212699145079,
0.013456120155751705,
0.057298239320516586,
0.0027514323592185974,
0.017559275031089783,
0.003487318754196167,
0.06971399486064911,
-0.03031078167259693,
-0.004233896266669035,
0.01813618279993534,
-0.032036907970905304,
0.009315096773207188,
0.01697988621890545,
-0.0102694658562541,
0.08104492723941803,
-0.024014810100197792,
0.005276300944387913,
-0.0025796133559197187,
0.002198723377659917,
-0.012346730567514896,
0.027065401896834373,
0.03349209576845169,
0.04751497134566307,
-0.02290440909564495,
-0.03875354304909706,
-0.03719690442085266,
-0.01758546382188797,
0.03431076556444168,
-0.01948489621281624,
0.005641311407089233,
-0.0008622428285889328,
-0.025281276553869247,
-0.009176655672490597,
0.03739942982792854,
0.009401104412972927,
0.004306213464587927,
0.020575696602463722,
0.005881974473595619,
0.026154352352023125,
-0.0023809715639799833,
-0.026114871725440025,
-0.018741916865110397,
0.030736615881323814,
-0.06483308970928192,
-0.023393822833895683,
0.0036530671641230583,
0.036387693136930466,
-0.03237754851579666,
0.008656222373247147
] |
<p>Is it possible to know whether a lightning bolt travel from the ground to the sky or from the sky to the ground? </p>
<p>Alternatively, it could be both sides approaching</p> | 1,534 | [
-0.056434258818626404,
-0.03041236475110054,
-0.01628396287560463,
0.028012502938508987,
0.010802493430674076,
0.00545980641618371,
-0.010438336990773678,
-0.006771598011255264,
0.041063111275434494,
0.019303325563669205,
0.03488944098353386,
0.042415421456098557,
0.013207999058067799,
0.027700260281562805,
0.015907300636172295,
0.033915262669324875,
-0.017722237855196,
-0.011436600238084793,
0.007231454830616713,
-0.03751979023218155,
-0.028889870271086693,
0.007154017221182585,
0.01682756096124649,
0.011739636771380901,
-0.016550742089748383,
0.025363529101014137,
0.04110574349761009,
0.0024212391581386328,
0.0330769419670105,
0.03505556285381317,
-0.024493511766195297,
-0.01760648749768734,
0.029072748497128487,
0.03834282606840134,
0.04467766359448433,
-0.02068859338760376,
-0.010775051079690456,
-0.025974389165639877,
-0.029317330569028854,
-0.008961010724306107,
-0.0015398621326312423,
-0.04886932671070099,
0.000930977170355618,
0.05519799515604973,
-0.047205839306116104,
0.036657966673374176,
-0.019431013613939285,
-0.02857436239719391,
0.03258509933948517,
-0.09051849693059921,
0.047773104161024094,
-0.029999691992998123,
0.007994740270078182,
0.046058617532253265,
0.011390246450901031,
0.0060386997647583485,
0.06270910054445267,
0.06834109127521515,
-0.0028872431721538305,
-0.04439608380198479,
0.008119321428239346,
-0.021805375814437866,
-0.006321540102362633,
-0.032224178314208984,
-0.0318901389837265,
0.011759178712964058,
0.007044595200568438,
-0.015162027440965176,
0.007399203721433878,
0.006281635724008083,
-0.025656508281826973,
-0.00725898053497076,
0.01981572061777115,
0.0497160330414772,
0.031196197494864464,
-0.00948544591665268,
0.012830125167965889,
0.027310242876410484,
0.0803922563791275,
0.038163624703884125,
-0.008245699107646942,
-0.021745773032307625,
0.008123399689793587,
-0.018288016319274902,
0.042924102395772934,
-0.02970464713871479,
0.07647547125816345,
0.014646773226559162,
-0.005695597734302282,
0.0004703731101471931,
-0.001570295076817274,
-0.0008228993392549455,
-0.013350834138691425,
0.0010737022385001183,
-0.008304278366267681,
0.05538834258913994,
0.00696925213560462,
0.0008535573142580688,
0.0072223832830786705,
-0.030325066298246384,
0.008955514058470726,
0.030815251171588898,
0.031215956434607506,
0.04990726709365845,
0.009766844101250172,
-0.012357426807284355,
-0.012816434726119041,
-0.005532683338969946,
-0.02534535713493824,
0.0007413558196276426,
-0.04693550989031792,
0.0271332785487175,
0.0032416197936981916,
0.01513492688536644,
-0.018898876383900642,
-0.011379408650100231,
0.031149862334132195,
-0.028178615495562553,
0.02000652253627777,
0.045013491064310074,
0.040879521518945694,
0.007362088654190302,
0.030553780496120453,
0.008604902774095535,
-0.0381757915019989,
-0.009435068815946579,
0.05195125192403793,
0.007992097176611423,
-0.020330024883151054,
0.03815188258886337,
0.005108084063977003,
0.00009412134386366233,
-0.004450161475688219,
-0.008927293121814728,
0.039071161299943924,
0.014228743501007557,
-0.12755659222602844,
-0.04009732976555824,
0.014632892794907093,
0.03449581190943718,
-0.0003439142310526222,
-0.08346541225910187,
0.02947336807847023,
0.02859942801296711,
0.04824697598814964,
-0.006125965621322393,
0.03425370901823044,
0.01054229773581028,
0.01177432481199503,
0.0123440558090806,
-0.002057884121313691,
-0.0011067385785281658,
0.0076927123591303825,
-0.03180902078747749,
0.012034418992698193,
-0.03491957113146782,
0.0034708536695688963,
0.03222740441560745,
0.0074478392489254475,
-0.003863793332129717,
0.052759796380996704,
0.006869650911539793,
0.030241645872592926,
0.017607176676392555,
0.01136395987123251,
-0.0044811442494392395,
0.08549218624830246,
0.0261362474411726,
-0.009764946065843105,
0.04056224226951599,
0.03074277937412262,
0.036516401916742325,
0.02111109159886837,
-0.009636030532419682,
0.08024374395608902,
-0.05766832083463669,
-0.025114135816693306,
-0.013533242046833038,
0.007728960830718279,
-0.057525139302015305,
-0.040526844561100006,
-0.011297640390694141,
-0.014999018050730228,
0.0076791332103312016,
0.01517396792769432,
0.05270674452185631,
-0.016702819615602493,
-0.005200853105634451,
0.011227088049054146,
-0.009995661675930023,
-0.018185770139098167,
-0.023050609976053238,
0.022621259093284607,
-0.0036175318527966738,
0.010680217295885086,
0.009810303337872028,
-0.008421903476119041,
0.015179203823208809,
-0.03225309029221535,
-0.00030122752650640905,
-0.007383502554148436,
0.0582808181643486,
0.028237977996468544,
-0.04712336137890816,
-0.0007149481680244207,
0.05925996974110603,
0.02363577112555504,
0.01530663762241602,
0.00786456186324358,
-0.03360525518655777,
-0.038599587976932526,
-0.02855893410742283,
-0.012544697150588036,
0.00006634341843891889,
0.045031242072582245,
-0.00045830264571122825,
0.035120561718940735,
0.04094170406460762,
-0.012346581555902958,
0.010204707272350788,
-0.02820553630590439,
0.04422307014465332,
0.042098019272089005,
-0.009411192499101162,
0.01452725101262331,
0.014701100066304207,
0.013070676475763321,
-0.021956438198685646,
0.01455321442335844,
-0.02559075504541397,
-0.09179865568876266,
-0.011784547008574009,
0.04267308861017227,
-0.020888881757855415,
-0.021352732554078102,
0.01233003381639719,
0.02275099791586399,
0.051655109971761703,
-0.017440930008888245,
0.05076678469777107,
-0.006809593643993139,
-0.035904694348573685,
0.018913857638835907,
0.016091417521238327,
0.0029221405275166035,
0.002840410452336073,
0.0709143653512001,
0.0014300320763140917,
0.011230132542550564,
-0.04184594750404358,
-0.016702711582183838,
0.019716989248991013,
-0.02629810757935047,
0.0296491589397192,
0.023227350786328316,
-0.04528434947133064,
0.02726500667631626,
-0.007955913431942463,
0.027257857844233513,
0.0029984621796756983,
0.012139958329498768,
-0.008904353715479374,
0.0018599126487970352,
0.0061701396480202675,
0.027404002845287323,
-0.000834078062325716,
-0.02857770211994648,
-0.0052574737928807735,
0.05802310258150101,
-0.07562431693077087,
0.04424997791647911,
-0.002072183880954981,
0.0021398337557911873,
-0.000014460077181865927,
-0.010471933521330357,
0.059162650257349014,
0.023551030084490776,
0.03459727019071579,
-0.026140088215470314,
-0.082378089427948,
0.0013789009535685182,
-0.025923311710357666,
0.0013436650624498725,
0.030727237462997437,
-0.03713862597942352,
0.02071209065616131,
-0.045156218111515045,
-0.02910919114947319,
0.03486122936010361,
-0.016139650717377663,
0.0015849871560931206,
0.029294945299625397,
0.015089642256498337,
-0.04289954528212547,
-0.0018370193429291248,
-0.019893202930688858,
-0.009251529350876808,
-0.025271248072385788,
-0.02758111245930195,
0.04013485088944435,
-0.04234727472066879,
-0.04050895944237709,
-0.004384058993309736,
-0.02023138850927353,
-0.044842030853033066,
0.006917313206940889,
-0.016093678772449493,
0.009069849736988544,
-0.0009489257354289293,
0.003931890241801739,
0.008254477754235268,
-0.025360366329550743,
-0.010117979720234871,
-0.06125862896442413,
-0.05241118744015694,
0.02371019311249256,
0.01617484539747238,
0.020462898537516594,
-0.018176889047026634,
-0.03153417631983757,
0.03113800846040249,
0.029994163662195206,
-0.008772280998528004,
0.012110818177461624,
0.003801691345870495,
-0.052164092659950256,
0.015721792355179787,
-0.04192867875099182,
0.03363770246505737,
-0.01212136261165142,
0.015505580231547356,
0.026925349608063698,
0.025920186191797256,
0.014601263217628002,
0.021807769313454628,
-0.01189050916582346,
-0.025387568399310112,
-0.0008299550972878933,
0.01059169415384531,
0.02697969228029251,
0.010354832746088505,
-0.023944737389683723,
0.005271767731755972,
-0.026974214240908623,
0.016361791640520096,
0.01797829568386078,
-0.0030484346207231283,
0.047507189214229584,
-0.00801925454288721,
-0.010619769804179668,
-0.020481545478105545,
0.011967189610004425,
0.023157794028520584,
0.0022152417805045843,
-0.02749970555305481,
0.037182506173849106,
0.08066007494926453,
-0.003900084877386689,
-0.013105434365570545,
0.022689083591103554,
0.061690639704465866,
-0.04647776857018471,
-0.06835342943668365,
0.023597272112965584,
0.009424393065273762,
0.01400087121874094,
-0.004308510571718216,
-0.0001926674449350685,
0.01662449911236763,
0.009750776924192905,
0.0038841678760945797,
0.03357392176985741,
-0.02366235852241516,
-0.027129098773002625,
-0.03618882596492767,
0.011594414710998535,
-0.009586600586771965,
0.003297251183539629,
-0.0006735650240443647,
0.04696476086974144,
0.014147411100566387,
0.04343976825475693,
0.010258297435939312,
0.0331374853849411,
-0.0849551409482956,
0.02000601403415203,
-0.05243422091007233,
-0.006473834626376629,
-0.04349086433649063,
-0.008476792834699154,
-0.0641786977648735,
-0.03343956917524338,
-0.0028719601687043905,
-0.03369316831231117,
-0.021240022033452988,
-0.035069771111011505,
0.0037166785914450884,
-0.03506992384791374,
-0.06330863386392593,
-0.01790499873459339,
0.026208551600575447,
0.026258785277605057,
-0.011072314344346523,
0.02253970317542553,
0.06181730329990387,
-0.003107164055109024,
-0.01861090399324894,
-0.02199138142168522,
0.00825956929475069,
-0.007029230240732431,
0.030527302995324135,
-0.022466452792286873,
-0.001375484513118863,
-0.025662017986178398,
0.007341551594436169,
-0.001684740767814219,
-0.00181053567212075,
0.009715821593999863,
-0.026600992307066917,
-0.03545970469713211,
-0.034498728811740875,
-0.004973406903445721,
-0.0007222886779345572,
0.038498226553201675,
-0.024209361523389816,
0.02414952777326107,
0.03374144434928894,
0.0032656737603247166,
-0.0036190159153193235,
-0.001288590719923377,
0.03796882927417755,
-0.0036956772673875093,
-0.013783152215182781,
-0.054407019168138504,
-0.015161320567131042,
-0.025622431188821793,
-0.011478112079203129,
0.022733444347977638,
0.0010571213206276298,
-0.01885370910167694,
0.011921755038201809,
0.051319096237421036,
0.021522903814911842,
0.009442695416510105,
0.032427046447992325,
-0.024149220436811447,
0.002074482152238488,
0.004917802754789591,
0.015221884474158287,
0.022961879149079323,
0.012456731870770454,
0.035310402512550354,
0.02231355756521225,
-0.039724092930555344,
-0.10178309679031372,
-0.03520842641592026,
0.06010513752698898,
0.03979692980647087,
-0.023336751386523247,
-0.040039047598838806,
-0.06179262325167656,
-0.02112451381981373,
0.027851015329360962,
0.010301999747753143,
0.032015882432460785,
-0.0022614537738263607,
0.00940481573343277,
-0.01809651404619217,
-0.032750241458415985,
-0.026277028024196625,
0.03136260807514191,
0.009290464222431183,
-0.028546685352921486,
0.0006791372434236109,
0.0000495061649417039,
0.0029479253571480513,
0.026540976017713547,
0.021059399470686913,
0.061116717755794525,
0.011166846379637718,
0.012294837273657322,
-0.04736765846610069,
-0.04226062074303627,
-0.022166330367326736,
-0.06424859166145325,
-0.008096431382000446,
0.018935229629278183,
-0.022260233759880066,
0.054607540369033813,
-0.0009274984477087855,
-0.0836150124669075,
0.02938106097280979,
-0.02342159114778042,
-0.014875264838337898,
-0.016160495579242706,
-0.03376225009560585,
0.016775446012616158,
0.03812546283006668,
0.023030616343021393,
0.0660245269536972,
0.006475456524640322,
-0.011900224722921848,
-0.00613954896107316,
0.02498789317905903,
0.041621699929237366,
0.010964431799948215,
-0.006004238501191139,
0.016886010766029358,
0.0029249482322484255,
-0.033055379986763,
0.06536848098039627,
-0.0288724172860384,
0.021971140056848526,
0.0019358292920514941,
-0.050224099308252335,
-0.05690000206232071,
0.0359187126159668,
0.015760254114866257,
-0.009909267537295818,
-0.05059957876801491,
0.02373509481549263,
-0.003361872863024473,
-0.019141875207424164,
-0.005503222346305847,
-0.014291784726083279,
0.0518006794154644,
0.0194955226033926,
-0.01288057491183281,
-0.006204609293490648,
-0.07138427346944809,
-0.01447242684662342,
-0.002864380367100239,
-0.07806757837533951,
0.10165560990571976,
0.0201795045286417,
-0.04296961799263954,
0.05744478106498718,
-0.026658950373530388,
-0.026374733075499535,
0.04118609428405762,
-0.00025637802900746465,
0.01392572745680809,
-0.04912867024540901,
0.010221941396594048,
-0.0045844134874641895,
0.011838356964290142,
-0.048732977360486984,
-0.02875310182571411,
0.009255710057914257,
0.05643052980303764,
-0.023405546322464943,
-0.047866906970739365,
-0.008565733209252357,
-0.02747397869825363,
-0.034737713634967804,
-0.026987886056303978,
0.02844596654176712,
-0.022287432104349136,
-0.005768428556621075,
0.011333510279655457,
-0.022607875987887383,
0.04882246255874634,
-0.007920850068330765,
0.004358098842203617,
0.011267561465501785,
-0.03971278667449951,
-0.005953330080956221,
-0.024006575345993042,
0.041872937232255936,
-0.00920791644603014,
-0.04698240011930466,
-0.04197646677494049,
0.004948884714394808,
0.045721445232629776,
0.003167773364111781,
-0.0007517164922319353,
0.02957102283835411,
-0.01655329391360283,
-0.02808106318116188,
-0.00745315570384264,
0.02955632284283638,
0.04738209769129753,
0.03209425508975983,
-0.014161703176796436,
-0.006803442724049091,
-0.00977757666260004,
-0.008202465251088142,
0.016218939796090126,
0.04632703959941864,
-0.010846387594938278,
-0.012854678556323051,
0.03660737723112106,
-0.033764082938432693,
-0.02160993032157421,
0.037378739565610886,
-0.006039679981768131,
0.035598933696746826,
-0.03756493702530861,
-0.020353348925709724,
0.03449294716119766,
0.02116634137928486,
-0.01814625784754753,
-0.025009414181113243,
0.0053502279333770275,
-0.04641465097665787,
0.05194442719221115,
-0.04220259562134743,
0.05292155221104622,
0.009826155379414558,
0.028745334595441818,
0.013727495446801186,
-0.0028820738662034273,
0.005069251637905836,
-0.00534653477370739,
-0.010902582667768002,
0.019575858488678932,
-0.03277336433529854,
0.06052716076374054,
0.022893808782100677,
0.05421833321452141,
-0.015435140579938889,
0.022511769086122513,
0.022844983264803886,
-0.0021998067386448383,
0.06053870543837547,
0.000554156955331564,
-0.023449508473277092,
0.03258891776204109,
-0.07816775888204575,
0.00031815932015888393,
0.02487625740468502,
-0.002479385817423463,
0.07395422458648682,
0.00472874054685235,
-0.048883844166994095,
-0.003639461938291788,
0.021874578669667244,
-0.03704148158431053,
0.025200115516781807,
0.003356901928782463,
0.05084598436951637,
-0.013863944448530674,
0.0062725902535021305,
0.0074824742041528225,
-0.019228234887123108,
-0.010582162998616695,
0.013765225186944008,
-0.04470934346318245,
-0.03649849444627762,
-0.017687665298581123,
-0.026430780068039894,
0.0699106976389885,
0.018933070823550224,
-0.02062142826616764,
0.0364973321557045,
-0.016816282644867897,
0.052500225603580475,
-0.01292006578296423,
0.06491974741220474,
-0.0246929619461298,
0.04469233751296997,
-0.023423640057444572,
-0.0023520714603364468,
0.0010567408753558993,
0.042749498039484024,
0.11791790276765823,
0.026183797046542168,
0.013839432038366795,
-0.052851542830467224,
0.0002118146076099947,
-0.01251702755689621,
0.012575298547744751,
-0.03563227504491806,
-0.0037474201526492834,
-0.03227640688419342,
0.060537006705999374,
0.03465526923537254,
0.01632372848689556,
0.004449912812560797,
-0.042566895484924316,
0.049162860959768295,
-0.026558252051472664,
-0.007465951610356569,
0.010575351305305958,
0.02113042213022709,
-0.012026593089103699,
0.029318369925022125,
-0.024493440985679626,
0.03631892427802086,
-0.03288688138127327,
0.004968874156475067,
-0.045320164412260056,
-0.042198460549116135,
0.035989850759506226,
-0.012124967761337757,
-0.0586843304336071,
-0.008942896500229836,
0.08221439272165298,
-0.007543598301708698,
-0.03986770659685135,
0.005124118644744158,
0.03562534227967262,
0.0028521984349936247,
0.0051858266815543175,
0.022024499252438545,
0.03578715771436691,
-0.008430912159383297,
0.014308902435004711,
0.02490970492362976,
-0.07576429843902588,
-0.018451090902090073,
-0.014295142143964767,
-0.015305125154554844,
0.012613555416464806,
0.024229487404227257,
-0.02962813340127468,
0.007918396033346653,
0.012966010719537735,
-0.060209762305021286,
-0.02411925047636032,
0.003908457234501839,
0.025726089254021645,
-0.007552371360361576,
-0.018351731821894646,
-0.05046189948916435,
0.0053391591645777225,
0.024476518854498863,
0.002050649607554078,
0.00030673950095660985,
0.018822956830263138,
0.0039384313859045506,
0.007435251027345657,
0.04599931463599205,
-0.024527134373784065,
-0.02279926836490631,
-0.03843382000923157,
0.001568510546348989,
-0.03809409961104393,
-0.02659820392727852,
0.0263872891664505,
0.01786215789616108,
0.015371321700513363,
0.042185209691524506,
-0.01528120692819357,
-0.02801945060491562,
-0.026386313140392303,
0.027404658496379852,
-0.0010987275745719671,
0.011251899413764477,
-0.024034982547163963,
-0.00802598986774683,
0.04068798944354057,
-0.001452589756809175,
-0.007290002889931202,
0.03261547535657883,
-0.0008284087525680661,
0.05033205449581146,
0.014332268387079239,
-0.02594144642353058,
-0.029036222025752068,
0.015590829774737358,
-0.043090417981147766,
0.042137496173381805,
-0.01849403604865074,
0.017732208594679832,
0.0032508631702512503,
0.022909678518772125,
0.009700153954327106,
0.006024375092238188,
-0.042987074702978134,
0.028892401605844498,
0.028852637857198715,
-0.03265881910920143,
-0.03559830039739609,
-0.011552678421139717,
-0.011966216377913952,
0.006675782613456249,
-0.0051837218925356865,
-0.011968601495027542,
0.01017746515572071,
0.004981806967407465,
0.0141982426866889,
-0.033230096101760864,
0.022135162726044655,
0.009113757871091366,
0.028339305892586708,
-0.032746244221925735,
-0.023729955777525902,
-0.037925321608781815,
-0.03772361949086189,
-0.007021996192634106,
-0.049728501588106155,
-0.006455648224800825,
0.04490003362298012,
-0.06982113420963287,
0.020796814933419228,
0.050202369689941406,
0.012496969662606716,
0.018158433958888054,
0.007367740385234356,
0.020238488912582397,
-0.027465518563985825,
0.057672902941703796,
-0.01662158966064453,
-0.035764921456575394,
0.04849637299776077,
0.0023765796795487404,
-0.05681673437356949,
0.04894359037280083,
0.015100319869816303,
0.06926330924034119,
0.007708065677434206,
-0.033817511051893234,
0.01438798476010561,
0.0585046261548996,
-0.01515874732285738,
-0.020780052989721298,
-0.009044676087796688,
-0.0010039570042863488,
0.01428304985165596,
-0.002498429734259844,
0.014416773803532124,
-0.0376998670399189,
-0.02460612915456295,
0.049406006932258606,
-0.010436012409627438,
0.0006982680642977357,
-0.004764060024172068,
-0.000546057301107794,
-0.04584196209907532,
0.01398236770182848,
0.02513943985104561,
0.013330911286175251,
0.028518669307231903,
0.044754792004823685,
0.0258647333830595,
0.04738067463040352,
-0.008276127278804779,
0.0008823440875858068,
-0.0864240899682045,
-0.014158029109239578,
0.018454289063811302,
0.023210782557725906,
0.030958741903305054,
-0.04813436046242714,
0.01281819585710764,
0.03684735298156738,
-0.04534447193145752,
0.020234569907188416,
0.008211759850382805,
-0.04318669065833092,
-0.029213961213827133,
0.014863263815641403,
-0.008805046789348125,
-0.0009993026033043861,
0.0359276607632637,
0.03737684339284897,
0.0004316620761528611,
0.05940732732415199,
-0.01723206788301468,
-0.020195605233311653,
-0.0419493168592453,
0.017441844567656517,
0.01874728500843048,
-0.028473708778619766,
0.06524370610713959,
-0.03339691087603569,
-0.010259103961288929,
0.02381540648639202,
-0.004566797520965338,
0.029856430366635323,
0.004457527305930853,
0.01280318945646286,
0.05332008749246597,
0.0173873919993639,
-0.00006096379001974128,
-0.019706284627318382,
-0.03173982724547386,
0.031662844121456146,
-0.003953243605792522,
0.021215643733739853,
-0.038049668073654175,
-0.055481020361185074,
-0.020306376740336418,
-0.02919754758477211,
-0.056984566152095795,
0.025196919217705727,
-0.045464370399713516,
-0.02726304531097412,
-0.030095241963863373,
0.01753738336265087,
0.013281812891364098,
-0.013268805108964443,
-0.028541022911667824,
-0.05043957754969597,
0.02315433882176876,
0.023780886083841324,
-0.012831805273890495,
-0.019767742604017258,
0.01499131228774786,
-0.0380740761756897,
-0.059799522161483765,
0.01906992495059967,
-0.010040529072284698,
-0.008700253441929817,
-0.0363013930618763,
-0.002310978714376688,
0.015320227481424809,
0.013885578140616417,
0.005105958320200443,
-0.023262256756424904,
-0.00737678213045001,
0.011575726792216301,
0.012043382972478867,
0.05442648380994797,
0.05562610551714897,
-0.05332067236304283,
-0.040231719613075256,
-0.058024533092975616,
0.03067866526544094,
-0.029874304309487343,
-0.023636288940906525,
-0.06566181033849716,
-0.05810144171118736,
-0.02197258546948433,
-0.01150279026478529,
0.05662498623132706,
-0.038180798292160034,
-0.013202198781073093,
0.022954119369387627,
0.0013155705528333783,
0.032400619238615036,
-0.04678025096654892,
-0.04830262064933777,
-0.021010255441069603,
-0.030943479388952255,
-0.006451752502471209,
-0.02386905439198017,
-0.01711665280163288,
0.025098763406276703,
-0.004806128330528736,
0.009926650673151016,
0.037983424961566925,
-0.02560940943658352,
-0.029344864189624786,
0.011780607514083385,
0.02240731194615364,
-0.02130976691842079,
0.034010663628578186,
0.003927521873265505,
-0.01165164727717638,
0.002860223175957799,
-0.05536412447690964,
-0.01193124521523714,
0.06337855011224747,
-0.025539347901940346,
-0.04582787677645683,
0.011570259928703308,
0.006760094780474901,
0.03505414351820946,
-0.05193034186959267,
-0.016731172800064087,
0.028175367042422295,
-0.03882076218724251,
0.002207117388024926,
0.07055576145648956,
-0.0233414638787508,
0.03434451296925545,
-0.02984401024878025,
0.03342650458216667,
0.04993639141321182,
-0.026078399270772934,
-0.018540993332862854,
0.003525771666318178,
0.0435054674744606,
-0.014826701954007149,
0.015045073814690113,
0.03593090921640396,
0.02907177433371544,
0.010280445218086243,
-0.009060962125658989,
0.029338296502828598,
-0.0174065250903368,
-0.0074950940907001495,
0.05048874765634537,
0.015583508647978306,
-0.0041246842592954636,
0.029726849868893623,
0.008362374268472195,
0.036360062658786774,
-0.014625835232436657,
0.012923144735395908,
-0.03392546623945236,
0.013972547836601734,
0.014183268882334232,
0.04291191324591637,
0.015346216037869453,
-0.021251190453767776,
0.03752967715263367,
-0.006491592153906822,
-0.009289593435823917,
0.0018553424160927534,
0.03440134599804878,
-0.04171550273895264,
0.022397713735699654,
-0.035239409655332565,
0.004194796551018953,
-0.017730476334691048,
0.0162772499024868,
-0.05173790827393532,
-0.014165624044835567,
0.03594370558857918,
0.0015809877077117562,
0.0334952250123024,
0.009358318522572517,
0.002665142994374037,
-0.015808336436748505,
0.017190927639603615,
-0.07708437740802765,
-0.015348412096500397,
-0.0711904913187027,
0.035260483622550964,
0.005009754095226526,
-0.027806514874100685
] |
<p>I'm having trouble understanding what a problem I have is seeking.</p>
<p>To simplify the problem:</p>
<blockquote>
<p>A particle reaches a speed of 1.6 m/s in a 5.0 micrometer launch. The speed is reduced to zero in 1.0 mm by the air. Assume constant acceleration and find the acceleration in terms of g during a) the launch and b) the speed reduction. </p>
</blockquote>
<p>The basic strategy to find acceleration I am using is to calculate two velocity equations: one between (0 m/s, 0 m) and (1.6 m/s, 5.0 micrometers); the second between (1.6 m/s, 5.0 micrometers) and (0 m/s, 1.0 mm). Then I will derive the acceleration value for each. Because acceleration is constant I can expect a linear velocity equation. </p>
<p>What is confusing me is that we are to assume constant acceleration. Thus the acceleration equation will merely be some real number. So, what exactly is expected if it is to be in terms of g? Is my strategy to find acceleration incorrect?</p> | 1,535 | [
0.002846222836524248,
0.009281902574002743,
-0.040113914757966995,
0.003950853832066059,
0.01626102440059185,
0.002208201913163066,
-0.02626342885196209,
-0.013607589527964592,
-0.009558034129440784,
0.004240294452756643,
0.03149097040295601,
0.03289768099784851,
0.04803363233804703,
0.006012410391122103,
0.038209494203329086,
0.011290372349321842,
-0.019069617614150047,
-0.013920735567808151,
-0.004017346538603306,
-0.009934106841683388,
0.0030399723909795284,
0.012464448809623718,
-0.022070614621043205,
-0.0306173637509346,
-0.005069286562502384,
0.03668922930955887,
0.01675286889076233,
0.0004910117131657898,
0.014183685183525085,
0.01476873829960823,
-0.03476879745721817,
0.007624342106282711,
0.000934203271754086,
0.012741689570248127,
0.00886821560561657,
0.03427586704492569,
-0.051116593182086945,
-0.022327162325382233,
0.0005237993318587542,
0.006579207256436348,
-0.015206526964902878,
-0.001957450993359089,
0.0011328839464113116,
0.03453043848276138,
-0.02070583403110504,
0.011201513931155205,
0.019611794501543045,
0.006105844862759113,
0.0516691729426384,
-0.05368967726826668,
0.0921286791563034,
-0.008370116353034973,
0.03788512200117111,
0.0007499924395233393,
-0.016925787553191185,
0.002006426453590393,
0.07397603988647461,
0.06691992282867432,
-0.011279175989329815,
-0.0015322909457609057,
0.008903621695935726,
-0.03724689036607742,
-0.018999958410859108,
-0.0028944446239620447,
0.028045177459716797,
0.028078334406018257,
-0.03630819544196129,
-0.010198622941970825,
0.005152605473995209,
0.016058223322033882,
0.04836016520857811,
-0.015853991732001305,
0.02018727920949459,
-0.03600082919001579,
0.025692669674754143,
-0.028741076588630676,
0.00020643491006921977,
0.017031770199537277,
0.029488809406757355,
0.06749741733074188,
-0.022560641169548035,
0.03378283977508545,
0.04958849027752876,
0.023497004061937332,
0.00920478068292141,
-0.04102226719260216,
0.05751398578286171,
0.009947716258466244,
0.01560440193861723,
0.03577908128499985,
-0.010842499323189259,
0.025271564722061157,
0.023258786648511887,
0.005748230963945389,
-0.01387111283838749,
0.03825218603014946,
0.011476274579763412,
0.04214328154921532,
0.00772768585011363,
-0.019666288048028946,
-0.01761956699192524,
-0.0479658879339695,
0.018548347055912018,
0.05797646939754486,
-0.02759510464966297,
0.009866682812571526,
-0.030237706378102303,
0.006736967246979475,
-0.020835578441619873,
-0.030210375785827637,
-0.023737704381346703,
-0.005004565697163343,
0.01139772217720747,
0.02206985093653202,
-0.011549079790711403,
0.017376070842146873,
-0.005963858217000961,
-0.008110983297228813,
0.07007843255996704,
0.01586170494556427,
0.04953382909297943,
-0.04177624359726906,
0.018209699541330338,
0.007612727582454681,
-0.06740401685237885,
-0.010803109034895897,
-0.007596171461045742,
-0.00813999306410551,
-0.037061046808958054,
0.005590151995420456,
0.0008538247784599662,
-0.032127730548381805,
-0.012129231356084347,
-0.02699567750096321,
0.026707205921411514,
-0.010205266997218132,
-0.08137113600969315,
-0.09036079794168472,
0.0010151226306334138,
0.022059135138988495,
-0.022795764729380608,
-0.08486077189445496,
-0.019183631986379623,
0.01636851206421852,
0.06863653659820557,
-0.009272540919482708,
0.018683096393942833,
-0.008790035732090473,
0.012911204248666763,
0.0030761866364628077,
-0.01141679473221302,
-0.006395602598786354,
0.002627704758197069,
-0.026907358318567276,
-0.012611637823283672,
-0.05473943054676056,
0.029667116701602936,
0.007389332167804241,
0.04153411462903023,
-0.010744612663984299,
0.01735219545662403,
-0.01302968617528677,
-0.01605340465903282,
-0.01640246994793415,
0.018813481554389,
-0.0019708131439983845,
0.036385729908943176,
0.012890379875898361,
0.02001648209989071,
0.05491618067026138,
0.03507827967405319,
0.002611049683764577,
-0.017745980992913246,
-0.026407165452837944,
0.08175897598266602,
-0.037429362535476685,
-0.014955827966332436,
-0.023521728813648224,
-0.000308819639030844,
0.024104537442326546,
-0.02031681500375271,
-0.05398039519786835,
0.0056961579248309135,
-0.007195985410362482,
0.005281622987240553,
0.014302833937108517,
0.028874287381768227,
0.039206426590681076,
-0.02865660935640335,
-0.008012508973479271,
-0.07380522042512894,
-0.09693245589733124,
0.02436945214867592,
0.010441752150654793,
0.012325212359428406,
0.026472773402929306,
0.001363691408187151,
0.0016048914985731244,
-0.01980563811957836,
-0.010154316201806068,
0.011543731205165386,
0.02097955346107483,
0.009475154802203178,
-0.0324278362095356,
-0.0031596096232533455,
0.059025172144174576,
0.009974610060453415,
0.03146849200129509,
0.017871243879199028,
0.015094241127371788,
0.034713756293058395,
-0.009531681425869465,
-0.01174926944077015,
0.009349469095468521,
0.04643992334604263,
0.006215736269950867,
0.030605118721723557,
-0.060635246336460114,
0.00003163390647387132,
0.026600193232297897,
-0.07510385662317276,
0.09079056233167648,
0.07375141233205795,
0.01668800413608551,
0.020682141184806824,
0.018890244886279106,
-0.020465614274144173,
-0.007683988194912672,
0.020042793825268745,
-0.016094790771603584,
-0.012670624069869518,
-0.02041517198085785,
0.007851668633520603,
0.04407450184226036,
-0.022750765085220337,
0.00024844336439855397,
0.05293283239006996,
0.026620909571647644,
0.01458403468132019,
0.056970395147800446,
0.007063419092446566,
-0.059142082929611206,
0.047955140471458435,
0.03920518234372139,
-0.015672095119953156,
0.0330517441034317,
0.01752733252942562,
-0.0016595064662396908,
0.0035463902167975903,
-0.030099978670477867,
0.03111906349658966,
0.04430041089653969,
0.02447214163839817,
0.007049875799566507,
-0.001977854408323765,
0.007381848990917206,
0.041689611971378326,
-0.00930303055793047,
0.024685081094503403,
0.058289382606744766,
-0.019273674115538597,
-0.015395035035908222,
-0.03186487406492233,
0.005339081399142742,
-0.014133349992334843,
-0.01892811991274357,
-0.005082473624497652,
-0.04537026211619377,
0.0266913790255785,
-0.052586447447538376,
-0.007210169453173876,
-0.040562957525253296,
-0.02042514830827713,
-0.024148674681782722,
-0.029427433386445045,
0.004336625337600708,
0.04293845221400261,
0.049117591232061386,
-0.0497821681201458,
-0.04310688003897667,
-0.007906735874712467,
-0.03604536131024361,
0.003664933377876878,
0.03118755668401718,
-0.03155441954731941,
0.03599347919225693,
-0.02795134112238884,
-0.03735216334462166,
0.0378790982067585,
0.0024913260713219643,
-0.002823831979185343,
0.03505481407046318,
0.0034951830748468637,
-0.05591495707631111,
-0.024399176239967346,
-0.02287534810602665,
0.005639237351715565,
-0.014904022216796875,
0.026290636509656906,
0.05237170681357384,
-0.0017473495099693537,
-0.03545263037085533,
0.012716079130768776,
-0.04534917697310448,
-0.015259369276463985,
-0.04581186920404434,
0.003913280088454485,
0.006314650643616915,
-0.03220245987176895,
0.020882220938801765,
0.007073522545397282,
0.030803589150309563,
-0.006135527044534683,
-0.06929720938205719,
-0.04813934862613678,
0.01972358301281929,
-0.014703338034451008,
0.04194440320134163,
0.008146713487803936,
-0.039928216487169266,
0.12305325269699097,
0.02806997485458851,
-0.010099564678966999,
-0.04880739375948906,
-0.016998672857880592,
0.0018193478463217616,
-0.02968171052634716,
-0.017903445288538933,
0.029300203546881676,
-0.021372757852077484,
0.0034428287763148546,
0.02205188199877739,
0.017754055559635162,
0.05297039821743965,
-0.010577094741165638,
0.04400680586695671,
-0.05538511276245117,
0.01770349033176899,
0.016182122752070427,
0.03716270253062248,
0.025121135637164116,
-0.023338424041867256,
0.053676310926675797,
-0.007618706673383713,
0.03503628075122833,
0.016815265640616417,
-0.06492189317941666,
0.0264844112098217,
-0.013634301722049713,
-0.012426906265318394,
-0.02304220385849476,
0.017969416454434395,
0.018597304821014404,
-0.016512615606188774,
0.020579256117343903,
-0.00577694782987237,
0.01736939512193203,
-0.01732378453016281,
-0.011161522939801216,
0.017354194074869156,
0.030002286657691002,
-0.024116937071084976,
-0.035214100033044815,
0.022529413923621178,
0.00008366016118088737,
0.008829863741993904,
-0.013035192154347897,
-0.0010863508796319366,
0.04092744365334511,
0.017783448100090027,
0.038083259016275406,
-0.007999752648174763,
-0.05479045212268829,
0.004891190677881241,
-0.04933669790625572,
0.012957742437720299,
-0.009877578355371952,
0.057695113122463226,
-0.03030693158507347,
0.07413597404956818,
0.027197569608688354,
0.039928875863552094,
0.05532635375857353,
-0.00958353653550148,
-0.08109527826309204,
0.061940744519233704,
-0.04884034022688866,
-0.047895126044750214,
-0.005484875291585922,
0.005156788509339094,
0.002855634782463312,
-0.01764841191470623,
-0.007947441190481186,
0.0210091732442379,
0.0133816571906209,
-0.022839510813355446,
0.029739325866103172,
-0.0385705791413784,
-0.022519340738654137,
-0.015146982856094837,
0.0012212886940687895,
0.01606048457324505,
0.0012449664063751698,
0.017405370250344276,
0.025318892672657967,
0.011968307197093964,
0.010342982597649097,
-0.007425498683005571,
-0.013644549995660782,
0.024730296805500984,
0.04461659491062164,
0.020214593037962914,
0.06030126288533211,
0.006959131918847561,
0.038520511239767075,
0.0012335946084931493,
0.042793817818164825,
0.004871403332799673,
0.0031817143317312002,
-0.06181350350379944,
-0.06003975495696068,
-0.03269214555621147,
0.019622212275862694,
0.006088369991630316,
0.00047722263843752444,
-0.011018834076821804,
0.00971749797463417,
0.02534998394548893,
0.038709912449121475,
0.0072043598629534245,
0.07264199107885361,
-0.025423020124435425,
0.006600405555218458,
-0.022092090919613838,
-0.005325176753103733,
-0.03296763077378273,
-0.012045242823660374,
0.05658099800348282,
0.02432803437113762,
0.000021611031115753576,
-0.007904963567852974,
0.0664987862110138,
0.010504716075956821,
-0.013162617571651936,
0.012071610428392887,
-0.020281879231333733,
0.014479578472673893,
0.01961752586066723,
-0.0364077053964138,
0.014086655341088772,
0.06873347610235214,
0.02699526771903038,
0.0019408721709623933,
-0.0012873996747657657,
-0.08362288773059845,
-0.026932666078209877,
0.025198692455887794,
0.05294692888855934,
-0.03787456452846527,
0.0031724160071462393,
-0.06366325914859772,
-0.003937805537134409,
0.014054822735488415,
-0.03698573634028435,
0.048284467309713364,
-0.021453531458973885,
0.047500088810920715,
0.01252591423690319,
-0.004163846839219332,
-0.04393159970641136,
-0.000932868744712323,
-0.026319429278373718,
-0.02581707201898098,
-0.03487575799226761,
-0.00046046971692703664,
-0.027263768017292023,
-0.00007982581882970408,
0.01183593925088644,
0.05044276639819145,
-0.0037371572107076645,
-0.003538665361702442,
0.004833736456930637,
-0.009044351987540722,
-0.03325561806559563,
-0.06198561564087868,
0.011066462844610214,
-0.016510434448719025,
0.004968839231878519,
0.045800816267728806,
-0.047336965799331665,
-0.04104923829436302,
0.05339379608631134,
0.024909429252147675,
-0.002518606837838888,
-0.052722036838531494,
-0.046320971101522446,
0.032066866755485535,
0.06312070041894913,
0.006868830882012844,
0.013114767149090767,
0.0007889370899647474,
-0.02311689220368862,
-0.0065514869056642056,
-0.029317865148186684,
0.0069342562928795815,
-0.03467712178826332,
0.0035329570528119802,
-0.023546764627099037,
0.03310433402657509,
0.00801648199558258,
0.033688418567180634,
0.02532544545829296,
0.04320172965526581,
0.010276876389980316,
-0.06367237120866776,
0.009112030267715454,
-0.0013618995435535908,
-0.022845963016152382,
0.005337683483958244,
-0.006244463846087456,
0.03292493522167206,
0.0034886838402599096,
-0.046082522720098495,
-0.0012827753089368343,
0.02162949927151203,
0.0023711794055998325,
0.05103474110364914,
-0.013907239772379398,
0.0011825785040855408,
-0.004583073314279318,
-0.026907987892627716,
0.009883386082947254,
-0.07586224377155304,
0.05525563284754753,
-0.007972849532961845,
-0.0003483615873847157,
0.0524417906999588,
-0.06795169413089752,
-0.04490959644317627,
-0.016221972182393074,
0.03267458826303482,
0.035408686846494675,
-0.06388887763023376,
0.018728166818618774,
0.0023421989753842354,
0.04446864873170853,
-0.06587338447570801,
-0.03847517445683479,
0.023475298658013344,
0.011914905160665512,
-0.0154127087444067,
-0.037784505635499954,
-0.0167658980935812,
-0.03672783821821213,
-0.019762197509407997,
0.027498455718159676,
0.005558264907449484,
-0.0030981609597802162,
-0.023536352440714836,
0.035371094942092896,
0.04720369726419449,
0.04487547278404236,
-0.015352416783571243,
0.017140889540314674,
0.014672618359327316,
-0.00900433212518692,
0.018000641837716103,
0.005359923932701349,
0.08263931423425674,
-0.02329769916832447,
-0.028743326663970947,
-0.005678081884980202,
-0.01767386496067047,
0.03766539320349693,
-0.02176656760275364,
-0.00018499759607948363,
0.05616537481546402,
0.0029156978707760572,
-0.015051216818392277,
-0.021306907758116722,
0.016984973102808,
-0.012891541235148907,
0.022194191813468933,
0.006129113957285881,
-0.009942393749952316,
-0.022542845457792282,
-0.006068417336791754,
0.07443608343601227,
-0.009010285139083862,
-0.0026332158595323563,
0.0411989800632,
0.07135562598705292,
-0.05972323566675186,
-0.011574497446417809,
0.038995400071144104,
-0.016079124063253403,
0.0016838511219248176,
-0.031875528395175934,
-0.024535583332180977,
0.012223773635923862,
-0.01281667873263359,
-0.05279070883989334,
-0.010863324627280235,
-0.033389411866664886,
0.011899897828698158,
0.061168599873781204,
-0.01840704120695591,
0.05705010145902634,
0.007553103845566511,
0.0031796973198652267,
-0.005353094078600407,
-0.008706287480890751,
0.010658521205186844,
-0.01286145206540823,
0.005100658163428307,
0.027870390564203262,
-0.03739931806921959,
-0.0280534066259861,
0.03955380618572235,
0.023363618180155754,
-0.004651847295463085,
-0.018564242869615555,
0.006288851145654917,
-0.013435274362564087,
0.0035921065136790276,
-0.011419869028031826,
-0.024496231228113174,
0.04537980630993843,
-0.008382681757211685,
0.08095881342887878,
-0.009462161920964718,
-0.006329557858407497,
0.05874770134687424,
0.02307985909283161,
-0.03377154469490051,
-0.07627548277378082,
-0.0053923726081848145,
-0.03492526710033417,
0.014057992957532406,
0.03686242178082466,
-0.02375795505940914,
0.0251302607357502,
0.018815889954566956,
0.030293792486190796,
0.038343384861946106,
0.02901778370141983,
-0.02435930073261261,
-0.04093027487397194,
0.020717794075608253,
-0.05366142466664314,
-0.05607464909553528,
0.008703697472810745,
0.006416505202651024,
-0.010645668022334576,
0.03037329576909542,
-0.01684989407658577,
0.013881843537092209,
0.025129497051239014,
0.03606914356350899,
0.012404722161591053,
0.09132244437932968,
-0.023204728960990906,
-0.01660352386534214,
-0.0028942308854311705,
0.019959043711423874,
0.09727519005537033,
0.04076967015862465,
-0.020226649940013885,
-0.037104178220033646,
0.002574447775259614,
-0.026918508112430573,
0.009470967575907707,
0.017945358529686928,
0.04741399735212326,
-0.03953220322728157,
-0.022008433938026428,
0.02483804151415825,
0.023866930976510048,
-0.011992691084742546,
0.0019410611130297184,
0.027307191863656044,
-0.023848967626690865,
-0.039675597101449966,
-0.029037220403552055,
0.007926039397716522,
0.02016565017402172,
0.010271063074469566,
0.024862319231033325,
0.026545938104391098,
-0.028820211067795753,
-0.02552310936152935,
-0.010855982080101967,
-0.031026367098093033,
0.034490425139665604,
-0.02230219729244709,
-0.08084364980459213,
0.025838492438197136,
0.02222483418881893,
-0.017017098143696785,
-0.0677061378955841,
-0.017098013311624527,
0.01311023160815239,
-0.013531768694519997,
0.00862667802721262,
0.02985001727938652,
0.007654094602912664,
0.020082443952560425,
0.015988390892744064,
-0.014847226440906525,
-0.03675096854567528,
-0.012984322383999825,
-0.04164919629693031,
0.08158902078866959,
0.00038522406248375773,
0.003509639296680689,
-0.0017319460166618228,
0.0016719542909413576,
-0.01638299785554409,
-0.07737238705158234,
0.004981489852070808,
0.006981567479670048,
0.028498712927103043,
-0.02057339809834957,
-0.0038627234753221273,
-0.023476678878068924,
0.024324851110577583,
0.0034497114829719067,
0.003350426908582449,
0.020153317600488663,
0.011837311089038849,
0.018419545143842697,
-0.01510898768901825,
0.0531025230884552,
-0.06260040402412415,
-0.033459778875112534,
-0.01028471440076828,
-0.007199730724096298,
-0.035916417837142944,
-0.012370995245873928,
0.0035020969808101654,
0.010701197199523449,
0.04393696039915085,
-0.005523945204913616,
-0.010450275614857674,
-0.03536760434508324,
-0.05864287540316582,
0.035641398280858994,
0.012626162730157375,
-0.010722539387643337,
-0.02299412712454796,
-0.03552551940083504,
0.012065562419593334,
0.028475314378738403,
-0.05084360018372536,
-0.013410095125436783,
-0.011972599662840366,
0.013197524473071098,
0.004215407185256481,
-0.01232994720339775,
-0.01560535654425621,
0.0053998688235878944,
-0.006110607646405697,
0.022258466109633446,
0.017326198518276215,
0.03856183961033821,
0.0044580926187336445,
0.035531189292669296,
0.002159187803044915,
0.03693031147122383,
-0.033946435898542404,
0.014228287152945995,
0.009957998991012573,
-0.004780641756951809,
-0.001473688636906445,
0.03557819128036499,
0.023444252088665962,
-0.02935878559947014,
0.005108717828989029,
-0.03084428980946541,
-0.011558794416487217,
-0.002104388317093253,
0.03888486698269844,
0.01749230921268463,
0.05143806338310242,
-0.015254816971719265,
0.011873669922351837,
-0.041020557284355164,
0.014308528043329716,
-0.016433686017990112,
0.032509926706552505,
0.005859211087226868,
-0.01599184423685074,
-0.011352142319083214,
0.028105642646551132,
-0.024942509829998016,
0.004801149480044842,
0.03495139628648758,
0.03431767597794533,
0.0015944282058626413,
-0.0364522822201252,
0.049432191997766495,
-0.04223746433854103,
0.029088051989674568,
-0.041797034442424774,
0.0008176096598617733,
-0.0044979071244597435,
-0.023279400542378426,
-0.026455966755747795,
0.020292866975069046,
-0.000036787911085411906,
0.05475722253322601,
0.0033733139280229807,
-0.05871221795678139,
-0.021744409576058388,
0.08155573159456253,
-0.01092678401619196,
0.025687018409371376,
-0.02558610402047634,
-0.023873047903180122,
-0.0113449078053236,
-0.05305739864706993,
-0.009122747927904129,
0.017346419394016266,
0.02195621468126774,
0.01995057985186577,
-0.013352077454328537,
-0.03259226679801941,
0.012666928581893444,
-0.0000807922042440623,
0.0014079082757234573,
-0.023469820618629456,
0.039650846272706985,
0.010079947300255299,
0.016743525862693787,
0.05466197058558464,
-0.0247760321944952,
0.01837722584605217,
0.04160105064511299,
0.016491319984197617,
-0.08717461675405502,
0.016977481544017792,
0.015034124255180359,
0.008360042236745358,
0.03627965226769447,
-0.07442857325077057,
0.020456453785300255,
0.023634769022464752,
-0.052347902208566666,
-0.058285851031541824,
-0.05649460479617119,
-0.01879742182791233,
-0.04725134000182152,
-0.04145032539963722,
0.024318356066942215,
-0.0014912370825186372,
0.03371346741914749,
0.012183924205601215,
0.030357377603650093,
-0.003361394861713052,
-0.035803552716970444,
-0.04295766353607178,
0.0007336261915042996,
0.02303171716630459,
-0.0033447432797402143,
-0.029301268979907036,
0.060714609920978546,
-0.025835905224084854,
0.008608066476881504,
0.018497752025723457,
-0.012160095386207104,
0.04766981303691864,
0.01047262828797102,
0.07089777290821075,
0.02167980931699276,
0.023201433941721916,
0.03557812049984932,
0.018099093809723854,
-0.038012195378541946,
0.015466107055544853,
0.01706591807305813,
0.014837536960840225,
-0.006654815748333931,
0.0253932885825634,
-0.0065862033516168594,
-0.01884320005774498,
-0.04258198291063309,
-0.0011654108529910445,
-0.000042414114432176575,
-0.02897161804139614,
-0.00965637806802988,
-0.005555674899369478,
-0.002336776116862893,
-0.058342345058918,
0.009801028296351433,
-0.039100244641304016,
0.004598659463226795,
0.029242414981126785,
0.012985420413315296,
-0.06797735393047333,
-0.007216145284473896,
-0.021185532212257385,
-0.00819583423435688,
-0.01035427674651146,
-0.002365955850109458,
-0.008513207547366619,
-0.02873554266989231,
-0.014294823631644249,
0.016033658757805824,
-0.024163320660591125,
0.004927965346723795,
-0.04937636852264404,
-0.018844280391931534,
0.04402896389365196,
0.021145468577742577,
-0.0012916059931740165,
0.0033851973712444305,
0.010131143033504486,
-0.016115330159664154,
-0.10020896047353745,
0.03835521638393402,
-0.0007194525096565485,
-0.034807078540325165,
-0.02050585299730301,
-0.0591912716627121,
-0.01466576661914587,
0.01927756704390049,
0.06747724860906601,
-0.00814863946288824,
-0.01822870597243309,
0.03992416709661484,
0.019603202119469643,
-0.019816681742668152,
-0.04479512572288513,
-0.014106109738349915,
-0.015473753213882446,
-0.014568084850907326,
-0.016064152121543884,
0.004107709974050522,
-0.03634634241461754,
0.02300613559782505,
0.013561480678617954,
0.006842005532234907,
0.025988878682255745,
-0.01315861102193594,
-0.01716543734073639,
0.004558209795504808,
0.050250325351953506,
-0.010715523734688759,
0.05592615529894829,
0.00583281135186553,
0.001245618797838688,
0.03266317769885063,
0.005047802813351154,
-0.06735657900571823,
0.058118052780628204,
-0.03521673008799553,
-0.009161814115941525,
-0.030579185113310814,
-0.003807252738624811,
0.02089982107281685,
-0.07711505889892578,
0.002789938123896718,
-0.017728736624121666,
-0.03061331808567047,
-0.028439044952392578,
0.02140442468225956,
0.008863493800163269,
0.020216431468725204,
-0.01721709780395031,
0.04025162383913994,
0.04257526993751526,
-0.028910348191857338,
-0.021604739129543304,
0.034950222820043564,
0.009919783100485802,
-0.007200841326266527,
0.030662765726447105,
0.04653812199831009,
-0.008447743952274323,
0.009192919358611107,
-0.0069521768018603325,
0.022072648629546165,
0.006211348343640566,
-0.005242646671831608,
-0.02392016351222992,
-0.013517089188098907,
-0.02114911936223507,
0.04140067100524902,
0.0007901288336142898,
0.06941734254360199,
-0.033513735979795456,
0.0005008997395634651,
0.019390299916267395,
0.0186765119433403,
-0.02274634689092636,
0.014993255026638508,
-0.00926232524216175,
-0.0033796075731515884,
0.04677341505885124,
0.002766086719930172,
-0.015058348886668682,
-0.022734083235263824,
0.005940572824329138,
-0.02237774059176445,
-0.0033992715179920197,
0.010109920985996723,
-0.03211313486099243,
-0.010232752189040184,
-0.044318005442619324,
-0.032823704183101654,
-0.01477535255253315,
0.026688644662499428,
0.027251847088336945,
-0.010120920836925507,
-0.028304193168878555,
-0.0038064634427428246,
-0.010860069654881954,
0.04160357266664505,
-0.0448550209403038,
-0.003548871725797653,
-0.02911318838596344,
-0.021080555394291878,
0.0029607026372104883,
-0.0164792537689209
] |
<p>How does the nonlinear absorption coefficient depend on the band gap?
How can that coefficient be calculated theoretically? (Preferably with an example)</p> | 1,536 | [
-0.03248007968068123,
-0.0270678773522377,
0.025735195726156235,
-0.008695734664797783,
0.02210783213376999,
0.034486230462789536,
-0.027820097282528877,
-0.03457992523908615,
0.0061017246916890144,
-0.036695271730422974,
0.04506745934486389,
0.0004246907774358988,
0.032354965806007385,
-0.0042898706160485744,
-0.01098551880568266,
0.019036859273910522,
-0.024705328047275543,
-0.01515961904078722,
-0.029306193813681602,
-0.009901224635541439,
-0.02273518405854702,
0.039583753794431686,
-0.02234761416912079,
0.0031871977262198925,
-0.027500011026859283,
0.03661350533366203,
0.038245998322963715,
0.05653238669037819,
0.043871164321899414,
0.02857746183872223,
-0.01015000231564045,
-0.031499233096838,
0.0170458797365427,
0.037735048681497574,
0.04448649659752846,
0.02084241434931755,
-0.035001516342163086,
-0.07460900396108627,
-0.04552643001079559,
0.03759489580988884,
-0.008761853910982609,
-0.015499074012041092,
-0.01304108090698719,
0.014008622616529465,
0.0012481032172217965,
-0.008495697751641273,
-0.0035221693105995655,
-0.024201905354857445,
0.01029672846198082,
-0.09386952966451645,
0.04583856090903282,
-0.0044680628925561905,
0.06773591786623001,
0.029109099879860878,
-0.00981495063751936,
0.012184231542050838,
0.05955333262681961,
0.08818087726831436,
-0.042038898915052414,
-0.04860011115670204,
0.02684820629656315,
-0.008105313405394554,
-0.029976075515151024,
-0.017080411314964294,
-0.02922036685049534,
0.023029012605547905,
0.011638800613582134,
-0.03761838749051094,
0.046196285635232925,
0.00513854343444109,
-0.01955476589500904,
-0.0297990869730711,
0.027559353038668633,
-0.042575009167194366,
-0.009762262925505638,
-0.018385255709290504,
0.021845262497663498,
0.02784402295947075,
0.034234482795000076,
0.02550150454044342,
-0.025627240538597107,
-0.0005073699867352843,
0.0020163983572274446,
0.017074864357709885,
-0.017348378896713257,
-0.020851830020546913,
0.055687908083200455,
-0.007940512150526047,
0.0269427839666605,
-0.008564083836972713,
-0.009454340673983097,
0.017037060111761093,
0.03055838868021965,
0.010583939962089062,
-0.026526233181357384,
0.034933995455503464,
-0.01732615940272808,
0.0747302994132042,
0.033212240785360336,
-0.0069317929446697235,
0.027374502271413803,
0.01905263587832451,
0.057012367993593216,
0.05919727310538292,
-0.0017988914623856544,
-0.044976428151130676,
-0.020199058577418327,
0.04795512557029724,
0.02006196603178978,
-0.010868247598409653,
-0.030573008581995964,
0.009018028154969215,
-0.02159043215215206,
-0.020448682829737663,
0.046952418982982635,
-0.00442047044634819,
0.03325461223721504,
-0.044496189802885056,
0.031745124608278275,
0.06404948234558105,
-0.009027396328747272,
-0.023420127108693123,
0.0369565524160862,
-0.0054248846136033535,
-0.058087896555662155,
0.02217908203601837,
0.018326133489608765,
-0.017907146364450455,
-0.04321752116084099,
0.0034349015913903713,
-0.01706192083656788,
-0.03205174580216408,
0.004944758955389261,
-0.019469603896141052,
0.037549447268247604,
-0.014781279489398003,
-0.07771515101194382,
-0.05514899268746376,
0.007134550251066685,
-0.025254547595977783,
-0.02895890362560749,
-0.06935811787843704,
0.008854786865413189,
0.0393337644636631,
0.09511213004589081,
0.0007113188621588051,
0.004906977526843548,
-0.01613631285727024,
0.04419642686843872,
0.049665361642837524,
-0.017240259796380997,
-0.038556020706892014,
0.039109066128730774,
-0.03581930696964264,
0.0054265595972537994,
-0.07997845113277435,
0.02478376217186451,
0.02358185313642025,
0.002493279054760933,
-0.03436390683054924,
0.06727005541324615,
-0.01354126539081335,
-0.02042732760310173,
0.028872020542621613,
-0.007744322065263987,
-0.020995184779167175,
0.08455698937177658,
-0.013432704843580723,
0.01956409029662609,
0.03340352326631546,
-0.011999734677374363,
0.023240340873599052,
-0.0017038363730534911,
0.035299669951200485,
0.039354193955659866,
-0.025823429226875305,
-0.01776144653558731,
-0.05318612977862358,
0.013080661185085773,
0.0007503575179725885,
-0.03754127025604248,
-0.03745465353131294,
-0.007361996453255415,
0.04281581938266754,
0.005391034763306379,
0.008218379691243172,
0.014121864922344685,
0.00030830074683763087,
-0.012009001336991787,
-0.060500916093587875,
0.012226944789290428,
-0.036425866186618805,
0.0466899648308754,
0.023307671770453453,
-0.016233783215284348,
0.005175628233700991,
0.004647743888199329,
-0.009583625942468643,
-0.008230306208133698,
-0.027700113132596016,
-0.0013162076938897371,
0.005505931098014116,
0.001773068099282682,
-0.027219804003834724,
0.030958371236920357,
0.05249395966529846,
0.036379437893629074,
0.023495128378272057,
0.06482817977666855,
-0.02603958174586296,
-0.033198438584804535,
0.011521527543663979,
-0.04651328921318054,
0.043357912451028824,
-0.02588708885014057,
-0.004456300288438797,
-0.004896086174994707,
-0.022048894315958023,
-0.0046938518062233925,
0.035281337797641754,
-0.030231067910790443,
0.09781481325626373,
0.06033403426408768,
0.01666088216006756,
-0.010833601467311382,
0.02840811386704445,
-0.018945375457406044,
-0.0016431740950793028,
-0.012428493238985538,
-0.016414133831858635,
-0.04307698830962181,
0.006533458828926086,
0.02564411051571369,
0.014131749980151653,
-0.030410945415496826,
0.02289886772632599,
0.012421545572578907,
0.025481227785348892,
0.05926383659243584,
0.013066221959888935,
-0.023376695811748505,
-0.0064182765781879425,
0.03251362964510918,
-0.005894653964787722,
-0.014398148283362389,
-0.009547541849315166,
0.008512967266142368,
0.028294110670685768,
0.02902238257229328,
-0.01835007034242153,
0.011267581023275852,
0.043949782848358154,
0.018781913444399834,
-0.008971350267529488,
-0.022138098254799843,
-0.042478132992982864,
0.016393130645155907,
-0.0395146869122982,
0.018163936212658882,
0.048427555710077286,
-0.017397485673427582,
0.02436530962586403,
-0.003753385739400983,
-0.03593941405415535,
0.007789773866534233,
-0.013223337940871716,
-0.04228213429450989,
0.02183573693037033,
0.016443628817796707,
-0.028709663078188896,
0.022212013602256775,
-0.021731361746788025,
0.05544651672244072,
-0.04251006990671158,
-0.05393163114786148,
0.00920620933175087,
0.0024478179402649403,
0.05584699288010597,
-0.041301995515823364,
-0.020367221906781197,
0.010077186860144138,
-0.0011342237703502178,
0.020436320453882217,
-0.005212141200900078,
-0.014774689450860023,
-0.0017461652169004083,
-0.006072706077247858,
-0.035618528723716736,
0.028696618974208832,
-0.019697459414601326,
-0.02358229272067547,
0.00014687838847748935,
-0.03434130921959877,
-0.04763976112008095,
-0.002908515278249979,
0.005357319954782724,
-0.007994698360562325,
-0.017162038013339043,
-0.002423051279038191,
0.025370679795742035,
0.000008934885045164265,
-0.05118155851960182,
0.028386233374476433,
0.004210787359625101,
-0.028381912037730217,
-0.023055093362927437,
-0.002606152556836605,
-0.015866445377469063,
-0.049233876168727875,
0.029575223103165627,
0.01908220537006855,
-0.0246107317507267,
0.01925342157483101,
-0.04168679565191269,
-0.018293101340532303,
0.03253917396068573,
0.03141704946756363,
0.035834699869155884,
-0.0069660828448832035,
-0.02698032185435295,
0.0874260812997818,
0.02446366474032402,
-0.008867861703038216,
-0.02034793049097061,
0.00024288475106004626,
-0.012063669972121716,
0.015997203066945076,
0.03186136111617088,
0.05051914229989052,
0.039720434695482254,
0.014372137375175953,
0.004398058168590069,
0.01933114230632782,
0.08229773491621017,
0.011071230284869671,
-0.005059658549726009,
0.0010408613597974181,
-0.010900458320975304,
-0.012125203385949135,
0.04933997988700867,
0.009638828225433826,
-0.03552805632352829,
0.030173853039741516,
-0.005803267005831003,
0.001249123364686966,
0.013637338764965534,
-0.06312867999076843,
0.024032047018408775,
-0.0206968504935503,
-0.00648450804874301,
-0.04703109711408615,
0.03904874622821808,
0.003197778481990099,
0.014967581257224083,
0.028619511052966118,
0.03091372735798359,
0.029124699532985687,
-0.006357708480209112,
-0.0005703124334104359,
0.021182266995310783,
0.06278210878372192,
-0.018364451825618744,
-0.025451675057411194,
0.041093967854976654,
0.0022531382273882627,
0.027118079364299774,
-0.025684485211968422,
-0.02012391947209835,
0.053274787962436676,
0.017893493175506592,
0.011058337055146694,
-0.018143435940146446,
-0.0013158697402104735,
-0.008007940836250782,
-0.05325648933649063,
-0.023667743429541588,
0.0024980802554637194,
0.07193666696548462,
-0.01045719999819994,
0.04773513600230217,
0.008612321689724922,
0.03478896990418434,
0.03588695824146271,
0.014455078169703484,
-0.09168977290391922,
0.009757469408214092,
-0.02349920943379402,
-0.02746625803411007,
-0.017004530876874924,
0.023932408541440964,
-0.012257636524736881,
0.00014213260146789253,
-0.014617673121392727,
-0.034677207469940186,
-0.009214084595441818,
-0.038125235587358475,
0.00781144667416811,
-0.015966126695275307,
0.0006894106045365334,
-0.01904403232038021,
0.01631169766187668,
-0.00015579332830384374,
-0.017979729920625687,
-0.0067986357025802135,
0.02512487769126892,
-0.016596227884292603,
0.019473036751151085,
-0.015907779335975647,
0.02183736488223076,
0.022290173918008804,
0.03419174626469612,
0.03765592351555824,
0.035531289875507355,
-0.016846684738993645,
-0.029847171157598495,
-0.002837054431438446,
0.05091173201799393,
0.03760790452361107,
0.01564505323767662,
0.009083506651222706,
-0.007781681139022112,
-0.0076085287146270275,
-0.028833694756031036,
0.0453469417989254,
-0.025141574442386627,
0.008573096245527267,
0.036287300288677216,
-0.005325478035956621,
-0.04693422466516495,
0.02220340445637703,
-0.025896677747368813,
0.03373485803604126,
-0.01802225410938263,
-0.038864076137542725,
-0.014401047490537167,
-0.036522481590509415,
0.014521142467856407,
0.01159575954079628,
0.009994667023420334,
-0.02143579162657261,
0.027651743963360786,
0.0329582542181015,
0.022594567388296127,
0.003081772243604064,
-0.026673855260014534,
0.030358653515577316,
0.02424207143485546,
0.006439925171434879,
-0.010872156359255314,
-0.011279948055744171,
0.03144108131527901,
0.07196179777383804,
-0.004246110562235117,
0.01645831950008869,
-0.0847727432847023,
-0.017907116562128067,
0.0277886800467968,
-0.014494480565190315,
-0.006555135827511549,
-0.026851948350667953,
-0.028469394892454147,
-0.01301344484090805,
0.024853629991412163,
0.005146052222698927,
0.04528120905160904,
0.0069790855050086975,
-0.008866231888532639,
-0.03290242329239845,
-0.009623885154724121,
-0.015680726617574692,
0.03152143582701683,
0.017968513071537018,
0.008668297901749611,
-0.038181837648153305,
-0.023577352985739708,
-0.010190468281507492,
0.03244313225150108,
0.0372183620929718,
0.09058450907468796,
-0.028552565723657608,
-0.0003667777928058058,
0.045797206461429596,
0.013089125975966454,
-0.007069680839776993,
-0.043440625071525574,
-0.0031411144882440567,
0.01968526281416416,
0.001914161373861134,
0.04402116686105728,
-0.02702728658914566,
-0.045228611677885056,
0.03144332766532898,
0.04465198144316673,
-0.001625280943699181,
-0.01923949643969536,
-0.005264981184154749,
0.04636990651488304,
0.014796284027397633,
-0.020221740007400513,
0.066785529255867,
0.016587689518928528,
-0.017176611348986626,
0.014555106870830059,
-0.043121784925460815,
0.026205960661172867,
-0.035309042781591415,
-0.009281170554459095,
0.015539733693003654,
0.013993947766721249,
-0.018983762711286545,
0.06396277993917465,
-0.018580850213766098,
0.010798875242471695,
-0.0031907239463180304,
-0.059592198580503464,
0.009031188674271107,
-0.0016150468727573752,
-0.01939535327255726,
0.016433073207736015,
0.005050809122622013,
0.03698808699846268,
0.04371390491724014,
-0.02517186664044857,
0.03284463286399841,
0.013861734420061111,
0.04575603827834129,
0.03187723085284233,
-0.015544180758297443,
0.01610240712761879,
-0.05432051792740822,
-0.006721044424921274,
0.0028745599556714296,
-0.015058986842632294,
0.08278711885213852,
-0.039437636733055115,
0.008442957885563374,
0.008421841077506542,
-0.045238934457302094,
-0.016168000176548958,
0.015412645414471626,
-0.03773372247815132,
0.03632630780339241,
-0.054784394800662994,
0.03262351453304291,
0.01690232753753662,
-0.02630970999598503,
-0.10159099102020264,
-0.06535284966230392,
0.012509486638009548,
0.020573947578668594,
-0.028086429461836815,
-0.032316625118255615,
0.012667045928537846,
-0.015181674621999264,
-0.03852242976427078,
0.054381243884563446,
0.017657730728387833,
-0.0265823882073164,
-0.02164960280060768,
-0.03301351144909859,
-0.021756723523139954,
0.04849645122885704,
-0.009402425959706306,
-0.038126587867736816,
0.0002863294503185898,
-0.05530636012554169,
0.0009249311406165361,
0.002706910250708461,
0.0247857216745615,
-0.020635738968849182,
-0.0054077934473752975,
-0.028156017884612083,
0.011861884966492653,
0.05918208509683609,
-0.0013367139035835862,
-0.030990850180387497,
0.030105063691735268,
0.005503387190401554,
0.009411185048520565,
-0.03543800115585327,
0.02323934994637966,
-0.015083326026797295,
0.02941184490919113,
0.018924584612250328,
-0.032401666045188904,
-0.02531559206545353,
-0.03986931964755058,
0.042066361755132675,
0.02282550558447838,
-0.0023707267828285694,
-0.013228396885097027,
0.09081219881772995,
-0.01269532274454832,
-0.002824107650667429,
0.010686677880585194,
-0.04535834863781929,
0.040147144347429276,
-0.0053450437262654305,
0.00933744478970766,
0.00825619138777256,
0.028724702075123787,
-0.04322132468223572,
-0.06559089571237564,
-0.045447781682014465,
-0.006922940257936716,
0.0400308221578598,
-0.056902214884757996,
0.02831258438527584,
0.010709893889725208,
0.003188119735568762,
-0.001002524746581912,
-0.02063589170575142,
0.0042806509882211685,
0.01597732864320278,
-0.026285631582140923,
0.05977454409003258,
-0.011502525769174099,
0.004274298902601004,
0.03454237058758736,
0.05752032250165939,
0.002662013052031398,
0.04436551779508591,
0.049130287021398544,
0.04840969666838646,
0.03840288147330284,
-0.016622763127088547,
-0.03289586678147316,
0.029581965878605843,
-0.045450277626514435,
0.042627256363630295,
0.02311689220368862,
-0.021439863368868828,
0.0505455918610096,
0.0013294327072799206,
0.005451556295156479,
-0.01622394472360611,
-0.018342049792408943,
-0.011729215271770954,
0.005360882729291916,
0.01851448230445385,
0.012331707403063774,
0.0339856781065464,
0.020527433604002,
-0.008660685271024704,
0.0032888513524085283,
0.029934801161289215,
-0.011882944032549858,
-0.038001492619514465,
-0.02003004588186741,
-0.016402415931224823,
-0.04651084542274475,
-0.00921479519456625,
0.015132619999349117,
-0.05068235471844673,
0.024685749784111977,
-0.04588335379958153,
0.015485379844903946,
-0.003921578172594309,
0.03644195944070816,
0.01913434825837612,
0.04946619272232056,
-0.01927916333079338,
0.04223224148154259,
0.0110098198056221,
0.010559632442891598,
0.10490235686302185,
0.04145153611898422,
0.02121887542307377,
-0.0699087530374527,
0.005577179603278637,
-0.0038603765424340963,
0.0030769030563533306,
-0.028191640973091125,
0.014838777482509613,
-0.0003683221584651619,
0.022098785266280174,
-0.00405973382294178,
0.06271502375602722,
-0.02956310473382473,
-0.008157637901604176,
-0.0009256461053155363,
-0.03685138002038002,
0.004958306904882193,
0.06236924231052399,
0.006253107450902462,
0.008586361072957516,
0.0018536662682890892,
-0.022874638438224792,
0.01496731024235487,
-0.020566139370203018,
-0.0019032768905162811,
-0.04169105365872383,
-0.04811461642384529,
0.05504783242940903,
-0.029012447223067284,
-0.03954249247908592,
0.0018204618245363235,
0.0026232271920889616,
-0.02034730277955532,
-0.018748559057712555,
0.01792197674512863,
0.03189980238676071,
0.0034049649257212877,
-0.009360775351524353,
0.0007130301091820002,
-0.0036050300113856792,
0.003576176008209586,
0.01041766069829464,
-0.004961451981216669,
-0.030001536011695862,
-0.015627199783921242,
0.0068464684300124645,
0.007408388890326023,
0.001974482089281082,
-0.017619658261537552,
0.029672686010599136,
0.007308242842555046,
-0.023994266986846924,
-0.02698584459722042,
-0.032110556960105896,
0.01676233857870102,
0.03763693943619728,
-0.022482989355921745,
-0.024957485496997833,
0.018917955458164215,
0.01240621879696846,
0.01809166744351387,
0.0071300966665148735,
-0.03720833733677864,
-0.033361710608005524,
0.013832329772412777,
-0.006092395633459091,
-0.0007310693035833538,
-0.025017499923706055,
-0.0516316294670105,
-0.01270173117518425,
-0.027166759595274925,
-0.02413864992558956,
-0.0707659125328064,
0.017525937408208847,
0.014985243789851665,
0.03695410117506981,
-0.006805173587054014,
-0.005009589716792107,
0.007656127214431763,
-0.09594838321208954,
0.02444119192659855,
-0.007981260307133198,
0.01141518633812666,
-0.05678892880678177,
-0.015104854479432106,
0.046294502913951874,
0.03684982657432556,
-0.03339536115527153,
0.02709086239337921,
-0.030881762504577637,
0.01492380816489458,
0.013693994842469692,
-0.045018699020147324,
-0.0380941741168499,
0.005792755633592606,
-0.01924758590757847,
0.020339665934443474,
0.012788237072527409,
0.04137894883751869,
0.019415104761719704,
0.017008116468787193,
-0.0069208270870149136,
0.02689169906079769,
-0.029336879029870033,
-0.011755667626857758,
-0.0265215914696455,
-0.02931097149848938,
-0.01877647452056408,
0.031840384006500244,
0.03775487095117569,
-0.019990406930446625,
-0.016519825905561447,
-0.029244929552078247,
-0.025993945077061653,
0.036450281739234924,
0.020583203062415123,
0.01354751642793417,
0.018566874787211418,
0.0007577459909953177,
0.0009896273259073496,
-0.04521530121564865,
-0.01990918070077896,
-0.025892818346619606,
0.0034009041264653206,
0.01929936558008194,
-0.0006006856565363705,
-0.016646627336740494,
-0.001188952475786209,
-0.03279534727334976,
0.0065060765482485294,
0.05169127136468887,
0.05083932355046272,
0.02045527659356594,
0.05205902084708214,
0.01246300246566534,
-0.0274543184787035,
0.039538752287626266,
-0.02307409979403019,
-0.03323107212781906,
0.027335505932569504,
-0.06791480630636215,
-0.04664815962314606,
0.013141029514372349,
0.02460753545165062,
0.028668077662587166,
-0.01462012529373169,
0.016387417912483215,
-0.040179792791604996,
0.046033088117837906,
-0.043215736746788025,
-0.02121157944202423,
-0.003351325634866953,
-0.02057604305446148,
-0.015666048973798752,
-0.025533465668559074,
-0.024532373994588852,
-0.023994341492652893,
-0.009294486604630947,
0.02881072834134102,
0.0025168773718178272,
-0.015510271303355694,
0.00037647737190127373,
0.011347324587404728,
-0.024281123653054237,
0.023533692583441734,
0.030495818704366684,
0.017040938138961792,
0.02827802672982216,
0.05351997911930084,
0.014371026307344437,
0.06829098612070084,
0.01910982094705105,
0.009513380005955696,
-0.08578129857778549,
-0.012579298578202724,
0.00917608942836523,
-0.020488910377025604,
0.023448802530765533,
-0.03591508790850639,
0.026347976177930832,
0.0273278821259737,
-0.07710044085979462,
-0.015000434592366219,
-0.0186526570469141,
-0.025699950754642487,
-0.046663567423820496,
0.00402179965749383,
-0.019804641604423523,
0.01060496550053358,
0.03458072245121002,
0.029213514178991318,
-0.00961694959551096,
-0.004635993856936693,
-0.00506907794624567,
0.016428224742412567,
0.01496149692684412,
0.007556659169495106,
-0.017529720440506935,
-0.022728331387043,
0.03187452629208565,
0.004523135721683502,
-0.011726608499884605,
-0.02097020484507084,
-0.027574369683861732,
-0.011072836816310883,
0.01894298754632473,
0.016634618863463402,
-0.01751578599214554,
0.060690898448228836,
-0.002457288559526205,
-0.009132616221904755,
0.010460603050887585,
0.0038364564534276724,
0.017939405515789986,
0.022740215063095093,
-0.005384148098528385,
-0.007038123905658722,
0.032298024743795395,
-0.04773258417844772,
-0.002173888962715864,
0.004188796505331993,
0.0011857450008392334,
-0.01826067827641964,
0.01950087398290634,
0.009499204345047474,
0.012420352548360825,
-0.03497686609625816,
-0.019827429205179214,
-0.0635317862033844,
-0.03276090696454048,
0.01013851910829544,
0.041054535657167435,
0.003590076696127653,
0.03098151460289955,
-0.023692606016993523,
-0.052576325833797455,
0.008685000240802765,
0.009543142281472683,
-0.001067152596078813,
-0.04404521733522415,
-0.010857905261218548,
0.03136302903294563,
-0.045411549508571625,
0.014995194971561432,
-0.04103086516261101,
-0.046100739389657974,
0.03695167228579521,
-0.007926682941615582,
-0.008735665120184422,
-0.00540778087452054,
-0.08319602906703949,
-0.0025783744640648365,
-0.07992537319660187,
0.03549824655056,
-0.017205171287059784,
-0.03775415197014809,
0.0013361138990148902,
0.007012464571744204,
-0.036582160741090775,
0.04256901890039444,
0.07041923701763153,
-0.03648429736495018,
-0.043512072414159775,
0.0100032864138484,
-0.01941028982400894,
0.02430514432489872,
-0.0350257083773613,
0.01903676427900791,
0.019475283101201057,
-0.017297130078077316,
-0.03672998026013374,
0.01086683664470911,
-0.05463036522269249,
0.00971724558621645,
0.01177611481398344,
-0.012228715233504772,
0.024866128340363503,
0.01319171953946352,
0.011667595244944096,
0.06759409606456757,
0.025920992717146873,
-0.009589404799044132,
0.06346412003040314,
-0.004564535804092884,
0.004092643968760967,
0.03943604975938797,
0.02224949188530445,
-0.11325326561927795,
0.004741416312754154,
-0.0054899780079722404,
-0.013020052574574947,
0.011415528133511543,
-0.04015795886516571,
0.033111829310655594,
-0.057395052164793015,
0.01457840483635664,
0.05214579030871391,
-0.03208751603960991,
-0.010366448201239109,
0.04725511744618416,
-0.00851988885551691,
0.023852821439504623,
-0.01957915537059307,
0.009437724947929382,
0.01103710662573576,
0.029998779296875,
-0.023908428847789764,
0.018695665523409843,
0.01475191954523325,
0.028518619015812874,
0.02512642741203308,
0.012632456608116627,
-0.000034868353395722806,
0.015762973576784134,
0.015350802801549435,
-0.008737572468817234,
-0.046485643833875656,
-0.022274350747466087,
0.024572180584073067,
-0.013801327906548977,
0.011828962713479996,
0.027726851403713226,
-0.0007909807027317584,
0.08400247991085052,
-0.047798868268728256,
0.020980719476938248,
-0.026271015405654907,
0.023461736738681793,
-0.016597872599959373,
-0.016358036547899246,
0.0341622456908226,
0.025196971371769905,
-0.012261802330613136,
-0.0018450565403327346,
-0.011457721702754498,
0.006251548882573843,
0.03933965414762497,
-0.08657852560281754,
0.029310718178749084,
0.01590554043650627,
-0.022545207291841507,
-0.019162049517035484,
0.0039662569761276245,
-0.004091261420398951,
0.0017551843775436282,
0.02585664391517639,
0.030046526342630386,
-0.018864573910832405,
0.04621676728129387,
-0.0024613607674837112,
-0.011334680020809174,
0.06172142177820206,
-0.07971528172492981,
-0.019139191135764122,
-0.015028519555926323,
-0.01934797316789627,
-0.05032387003302574,
-0.039179928600788116
] |
<p>The latent heat of vaporization of water is what we normally use to calculate the heat transfer that occurs at 373 K when liquid water transits to vapor phase. But there are curves for latent heat of vaporization at different temperatures. What is meant by latent heat of vaporization at a temperature different from its boiling point?</p> | 1,537 | [
-0.014947040006518364,
-0.02689901553094387,
-0.011322420090436935,
0.004475289490073919,
0.026536935940384865,
0.015384537167847157,
-0.05432813614606857,
-0.0265224389731884,
0.0051673538982868195,
-0.02137593738734722,
0.06549254059791565,
0.03181540593504906,
0.05711512267589569,
-0.024300402030348778,
0.030213911086320877,
0.03172774612903595,
0.020314404740929604,
-0.03295845910906792,
-0.02401958778500557,
-0.0025193998590111732,
0.003705698996782303,
0.018062466755509377,
-0.0016393415862694383,
-0.016848020255565643,
0.013183665461838245,
0.023386750370264053,
-0.006805371027439833,
-0.007206793874502182,
0.03463052958250046,
0.02148176170885563,
-0.01018124632537365,
-0.05841268226504326,
0.005174126010388136,
0.006128164939582348,
-0.0036437083035707474,
0.00658804178237915,
-0.027684831991791725,
-0.04061264917254448,
-0.031213976442813873,
0.009699204005300999,
-0.060170430690050125,
-0.027806110680103302,
0.007667957339435816,
0.04996493458747864,
-0.015748847275972366,
0.00999386701732874,
-0.0037087302189320326,
-0.027885643765330315,
0.04136832058429718,
-0.03349677473306656,
0.011571305803954601,
0.03817327693104744,
0.04842648282647133,
0.02066454477608204,
-0.0014092266792431474,
0.04267304763197899,
0.08642497658729553,
0.05244530364871025,
-0.034129831939935684,
-0.07426148653030396,
-0.047725364565849304,
-0.03694142773747444,
0.009853735566139221,
-0.009615723043680191,
-0.017088793218135834,
0.02130749076604843,
0.011347534134984016,
-0.019084226340055466,
-0.03020511381328106,
0.005554720759391785,
0.009239944629371166,
-0.01946255937218666,
0.03905126079916954,
-0.021391725167632103,
0.03137393668293953,
-0.009912477806210518,
-0.00644680904224515,
0.060997579246759415,
0.009549204260110855,
0.06049545481801033,
-0.009870392270386219,
0.05696433037519455,
0.021571144461631775,
-0.008302152156829834,
-0.047034844756126404,
-0.031762462109327316,
0.0670483261346817,
-0.00653115613386035,
0.030299508944153786,
0.04746376350522041,
0.002236350905150175,
0.04239070415496826,
0.01594497635960579,
0.029703576117753983,
0.017235159873962402,
-0.018711023032665253,
-0.0004118326469324529,
0.03622187674045563,
-0.002529481193050742,
-0.035957980901002884,
0.0435493104159832,
0.011134061962366104,
0.042595889419317245,
0.08479734510183334,
0.026473186910152435,
-0.05170160531997681,
-0.018133461475372314,
0.0011839320650324225,
0.022082876414060593,
-0.007413330487906933,
-0.01858254335820675,
0.004651866387575865,
0.006076241843402386,
-0.036518506705760956,
-0.012794909067451954,
-0.013566053472459316,
-0.020134517922997475,
-0.04493013396859169,
0.0204674880951643,
-0.006016552913933992,
0.008175007998943329,
-0.00289250654168427,
0.04246944189071655,
-0.02160067670047283,
-0.05257958546280861,
0.029525525867938995,
0.024957068264484406,
-0.020746449008584023,
-0.04259607568383217,
0.011602119542658329,
-0.01586916856467724,
-0.01236000843346119,
-0.0017173930536955595,
-0.023540468886494637,
-0.004115677438676357,
0.00512532377615571,
-0.09972206503152847,
-0.04367576539516449,
0.04127856343984604,
-0.006851508282124996,
-0.015234997496008873,
-0.06894754618406296,
0.05309199169278145,
0.027104629203677177,
0.043968863785266876,
-0.03108690120279789,
-0.004766877740621567,
-0.035155732184648514,
0.008198623545467854,
0.005803043022751808,
-0.019310055300593376,
-0.025046786293387413,
0.007519167382270098,
-0.06160997599363327,
0.008097146637737751,
-0.04238438233733177,
0.024203741922974586,
0.09051268547773361,
-0.021576087921857834,
-0.014701600186526775,
0.03167043626308441,
-0.01545004267245531,
-0.011093846522271633,
0.0066208927892148495,
0.03771652281284332,
-0.05774753913283348,
0.0679694265127182,
-0.022846534848213196,
0.03959944099187851,
0.02125391736626625,
0.002472509630024433,
0.020059756934642792,
0.002641162136569619,
0.03809816390275955,
0.02798358164727688,
0.0023373491130769253,
0.030242187902331352,
-0.027253257110714912,
0.03728894144296646,
0.041046205908060074,
-0.07174911350011826,
0.04924020916223526,
0.006480786949396133,
-0.008512710221111774,
-0.016618166118860245,
0.036035265773534775,
0.005839048884809017,
-0.008781538344919682,
-0.008409889414906502,
-0.04833879694342613,
-0.031857386231422424,
-0.06437774747610092,
0.03627865016460419,
0.0050012641586363316,
0.0290665403008461,
-0.005125509575009346,
0.05288669466972351,
0.043299298733472824,
-0.012828158214688301,
-0.0266003105789423,
0.013721713796257973,
0.010527987964451313,
-0.006157680880278349,
-0.0184734258800745,
0.009872356429696083,
0.0439777746796608,
0.047957420349121094,
0.00038571449113078415,
0.015955165028572083,
-0.04074375703930855,
-0.0406152606010437,
-0.028642278164625168,
-0.014853201806545258,
0.02122686803340912,
0.0000810146375442855,
-0.05508891120553017,
-0.02223776839673519,
0.009331364184617996,
-0.02001439407467842,
0.030331255868077278,
-0.009354465641081333,
0.0479407012462616,
0.06746312230825424,
0.033313047140836716,
-0.01866135373711586,
-0.0035924359690397978,
0.005362880881875753,
-0.014304712414741516,
-0.025385266169905663,
-0.04602034017443657,
-0.02428010106086731,
-0.036392033100128174,
0.02861872687935829,
0.039979007095098495,
-0.027282508090138435,
-0.0060183885507285595,
0.02885214425623417,
0.04931020364165306,
0.034954607486724854,
0.0038429670967161655,
-0.025187991559505463,
-0.026590542867779732,
0.051519978791475296,
-0.0009573689312674105,
0.019811008125543594,
0.013097692281007767,
0.03360731899738312,
0.035048000514507294,
0.028743324801325798,
-0.035652559250593185,
-0.04164039343595505,
0.06019650399684906,
0.0005243141204118729,
-0.014189468696713448,
-0.03899958357214928,
-0.016209399327635765,
0.018938226625323296,
-0.040589507669210434,
0.011023437604308128,
-0.010392842814326286,
0.007550826761871576,
0.026035970076918602,
-0.028102753683924675,
-0.03061937913298607,
0.02991384267807007,
0.03586132451891899,
0.0019205862190574408,
-0.007435666862875223,
0.024555614218115807,
-0.061337314546108246,
0.05403776094317436,
-0.049108922481536865,
0.012914787046611309,
-0.013154909946024418,
0.022022873163223267,
0.0429011732339859,
-0.020044779404997826,
0.04626569151878357,
-0.05000818520784378,
-0.07217416167259216,
-0.014732296578586102,
-0.016995230689644814,
-0.034417279064655304,
-0.004099308978766203,
-0.04325510933995247,
-0.010481744073331356,
-0.000989226857200265,
-0.017853304743766785,
0.041227616369724274,
-0.022865554317831993,
-0.006323548033833504,
0.01938221976161003,
-0.01676127128303051,
-0.0593847781419754,
-0.026230156421661377,
-0.010505747981369495,
-0.001519074896350503,
-0.0033923364244401455,
-0.0029391671996563673,
0.04218095541000366,
-0.04470182582736015,
-0.01569167897105217,
0.035273998975753784,
-0.009907967410981655,
-0.04537934064865112,
-0.013572318479418755,
-0.0248351339250803,
0.01136111468076706,
-0.04559598118066788,
0.026815176010131836,
0.04990960285067558,
-0.06537259370088577,
0.005633431486785412,
-0.023355746641755104,
-0.07802602648735046,
0.04380842298269272,
-0.012809100560843945,
0.029962830245494843,
-0.0005373271997086704,
-0.024482065811753273,
0.04653262719511986,
0.006244461052119732,
-0.04758593812584877,
-0.0007163460250012577,
-0.020640723407268524,
-0.04327506944537163,
0.01946977525949478,
-0.003183043794706464,
0.028510764241218567,
-0.00023042749671731144,
-0.00225820136256516,
0.008655907586216927,
0.014215607196092606,
0.04997541755437851,
0.009335963986814022,
0.02615167759358883,
-0.00445404089987278,
0.03803401440382004,
0.01583177223801613,
0.017911238595843315,
-0.0413384847342968,
-0.017663005739450455,
0.01813262701034546,
-0.0006899608415551484,
0.0507967509329319,
0.0376289077103138,
-0.03631886467337608,
0.07126009464263916,
-0.0008459588862024248,
-0.004036884754896164,
-0.04741313308477402,
0.06481494754552841,
-0.029334433376789093,
-0.00520498538389802,
0.0004357082361821085,
0.04736023023724556,
0.02925610914826393,
-0.0086705032736063,
0.00546258594840765,
0.016392631456255913,
0.06791402399539948,
-0.0339781828224659,
-0.012762503698468208,
-0.014951198361814022,
-0.027149228379130363,
0.018782498314976692,
0.02053154446184635,
-0.013914774172008038,
0.046307265758514404,
-0.010341069661080837,
-0.019233813509345055,
0.0009130343096330762,
-0.01579475961625576,
-0.0038960555102676153,
-0.01148006971925497,
-0.012790479697287083,
0.028376970440149307,
0.04273717850446701,
-0.02567869797348976,
0.06266748160123825,
0.030627654865384102,
0.016918212175369263,
0.008391816169023514,
0.0009960333118215203,
-0.07091963291168213,
0.04305513948202133,
-0.04538288339972496,
-0.023432914167642593,
-0.011608254164457321,
0.020105410367250443,
0.009900694712996483,
-0.012442787177860737,
-0.04126180335879326,
0.019333040341734886,
0.011050150729715824,
-0.041990406811237335,
0.017735712230205536,
-0.0022853328846395016,
-0.011294263415038586,
-0.025475669652223587,
0.02568783424794674,
0.02502335235476494,
-0.020139623433351517,
0.037099990993738174,
0.06262671202421188,
-0.014615911059081554,
-0.02094261161983013,
-0.0004789284721482545,
0.04602811112999916,
0.025778470560908318,
0.0258574690669775,
0.0024459471460431814,
0.00497417850419879,
-0.01919405162334442,
0.012335491366684437,
0.02422558329999447,
0.020176710560917854,
0.046740688383579254,
-0.0275430791079998,
-0.03375859186053276,
-0.04484114795923233,
-0.009558544494211674,
0.029933825135231018,
0.01710733398795128,
-0.009804083965718746,
0.028933465480804443,
-0.017548952251672745,
-0.016559552401304245,
-0.036921944469213486,
0.044737447053194046,
0.07090705633163452,
0.027703318744897842,
-0.01754527911543846,
-0.04888575151562691,
-0.021121198311448097,
-0.03946554660797119,
-0.004669966176152229,
0.024716898798942566,
0.03471023216843605,
-0.025430703535676003,
-0.017438363283872604,
0.020177504047751427,
-0.047286055982112885,
-0.0351114384829998,
-0.024291766807436943,
0.018093291670084,
0.002227935940027237,
-0.015069323591887951,
-0.03532460704445839,
0.014826148748397827,
0.03797464445233345,
0.010172405280172825,
-0.019205020740628242,
0.015362024307250977,
-0.06688717007637024,
-0.03280970826745033,
-0.0013124578399583697,
0.017310721799731255,
-0.006998373195528984,
-0.0017551180208101869,
-0.060100357979536057,
-0.016134491190314293,
0.05326273664832115,
0.019822126254439354,
0.012033727951347828,
0.004621854983270168,
0.007546834647655487,
-0.022771885618567467,
-0.0059651262126863,
0.015153472311794758,
0.0104226591065526,
-0.005354402121156454,
0.015525849536061287,
-0.026297811418771744,
-0.015440195798873901,
-0.005092978943139315,
-0.00003811356145888567,
-0.010479073971509933,
0.05063245818018913,
0.01145775057375431,
0.016585269942879677,
-0.0007396703003905714,
0.04108905792236328,
0.00047995027853176,
-0.04086804389953613,
0.004405145533382893,
-0.002488938393071294,
-0.009436890482902527,
0.028676947578787804,
-0.05544624850153923,
-0.052003178745508194,
0.02908450923860073,
0.016479728743433952,
-0.013809852302074432,
-0.024235622957348824,
-0.03912264481186867,
0.0237838514149189,
0.01964537240564823,
-0.01568317785859108,
0.0645056739449501,
0.03937821835279465,
-0.027834678068757057,
-0.024406714364886284,
-0.05100413039326668,
0.06072048470377922,
-0.032807424664497375,
-0.010667945258319378,
-0.014760126359760761,
-0.009223411791026592,
-0.019825439900159836,
0.0511397086083889,
-0.039372436702251434,
0.007211853750050068,
-0.02673625387251377,
-0.04148011654615402,
-0.012080143205821514,
-0.005246685352176428,
0.055638182908296585,
-0.031147558242082596,
0.019106799736618996,
0.0228701401501894,
0.009706477634608746,
-0.0047325994819402695,
0.031099148094654083,
-0.004626957233995199,
0.02451334521174431,
0.00941883958876133,
0.0033090354409068823,
0.01493031159043312,
0.004314641933888197,
0.0062624686397612095,
0.02491970732808113,
-0.060829129070043564,
0.02153739519417286,
0.023608503863215446,
-0.010731970891356468,
0.022792913019657135,
-0.05138678103685379,
0.021842991933226585,
0.012052945792675018,
0.02755957469344139,
0.028850071132183075,
-0.08504801243543625,
0.02137497067451477,
0.012032676488161087,
0.018322233110666275,
-0.06749708950519562,
-0.045862119644880295,
0.023189328610897064,
-0.001816618605516851,
-0.019416263327002525,
-0.03989119082689285,
-0.018304074183106422,
-0.04857740178704262,
-0.02192256785929203,
0.02343713492155075,
0.030346442013978958,
0.021710596978664398,
-0.01451130025088787,
-0.006818610709160566,
-0.0028286180458962917,
0.05070571228861809,
0.011429373174905777,
-0.018297698348760605,
0.030957788228988647,
-0.01421995460987091,
-0.0006060866289772093,
0.009248671121895313,
0.04967804625630379,
-0.030815966427326202,
0.000021445646780193783,
0.004831934347748756,
-0.028515778481960297,
0.04365648329257965,
-0.02234208583831787,
-0.019687876105308533,
-0.003527754684910178,
0.02207767590880394,
-0.028061015531420708,
-0.007684081792831421,
0.029710587114095688,
0.04887585714459419,
0.05933498963713646,
0.021040964871644974,
-0.011323045939207077,
0.00753049599006772,
0.000431221880717203,
-0.018885577097535133,
0.0028905600775033236,
-0.0239716749638319,
0.03435368090867996,
0.06644653528928757,
0.00025626897695474327,
0.02521047182381153,
-0.012103724293410778,
-0.0349416546523571,
0.031770505011081696,
0.043454818427562714,
-0.019589349627494812,
-0.03400534391403198,
0.01666058786213398,
-0.0312814824283123,
-0.0306636281311512,
-0.06058301776647568,
-0.04120694473385811,
0.029782505705952644,
-0.024829847738146782,
0.05456201359629631,
0.02544589713215828,
-0.02728784643113613,
0.01773318648338318,
-0.03796224668622017,
-0.016290314495563507,
0.03615862503647804,
-0.04265565797686577,
0.011309988796710968,
-0.0028794826939702034,
-0.03049221634864807,
0.03560904785990715,
0.03917995095252991,
-0.023143699392676353,
0.05866137519478798,
0.008547910489141941,
0.0054475003853440285,
-0.012141140177845955,
-0.009246686473488808,
-0.03636075556278229,
0.00671992776915431,
-0.043191421777009964,
0.02672325074672699,
-0.033046904951334,
0.01484614796936512,
0.02603999897837639,
-0.05471528321504593,
0.028749831020832062,
-0.05943399295210838,
-0.0033801489043980837,
-0.039935190230607986,
0.028947360813617706,
0.03094497136771679,
0.02579999901354313,
0.006301044020801783,
0.02556183561682701,
-0.002574978629127145,
-0.004716853145509958,
0.02463080734014511,
0.0219777449965477,
-0.027415607124567032,
-0.02228541485965252,
-0.00042929479968734086,
-0.014585340395569801,
0.0037882591132074594,
-0.017388612031936646,
-0.01870611123740673,
-0.015784235671162605,
-0.03212759271264076,
-0.02076902985572815,
-0.04410888999700546,
0.02560853213071823,
0.0006184678641147912,
0.06805311888456345,
0.006391559727489948,
0.028910547494888306,
-0.0009312196052633226,
0.028393253684043884,
0.13180407881736755,
0.03664034232497215,
0.0038325421046465635,
-0.06095854192972183,
0.01864847168326378,
-0.010003823786973953,
-0.026209641247987747,
-0.027338704094290733,
-0.010732774622738361,
-0.014139188453555107,
0.052772652357816696,
0.026482416316866875,
0.023502828553318977,
-0.03375381603837013,
0.027468612417578697,
0.011485664173960686,
-0.06723912805318832,
-0.025616278871893883,
0.011746538802981377,
-0.0019763270393013954,
-0.011582178995013237,
0.025127481669187546,
0.0006402070284821093,
-0.024862445890903473,
-0.026103222742676735,
-0.016400283202528954,
-0.0017547340830788016,
-0.022121762856841087,
0.04622330889105797,
-0.0252080038189888,
-0.036568839102983475,
0.008879676461219788,
0.005615228321403265,
-0.002544670132920146,
-0.011487155221402645,
0.017202645540237427,
0.033323705196380615,
0.0005355880130082369,
-0.007222119718790054,
0.03143487498164177,
-0.0320109948515892,
-0.03382761776447296,
0.025485975667834282,
0.04261508584022522,
-0.043402206152677536,
-0.0014025077689439058,
-0.0023629385977983475,
-0.011783343739807606,
0.022169094532728195,
-0.004988434258848429,
-0.01659476011991501,
-0.013735166750848293,
0.016425160691142082,
-0.008504585362970829,
-0.04371898993849754,
0.01681162603199482,
0.05134540796279907,
-0.00025833770632743835,
-0.04667874053120613,
-0.05855955183506012,
-0.02323341742157936,
-0.014183458872139454,
0.03959396854043007,
-0.0011380850337445736,
0.025701230391860008,
-0.0027324671391397715,
0.016870807856321335,
0.012009254656732082,
-0.044720910489559174,
-0.007580761332064867,
-0.014848214574158192,
0.008843946270644665,
-0.007738955784589052,
-0.005632667802274227,
0.007245062850415707,
-0.03329552337527275,
0.037461478263139725,
0.014201879501342773,
0.013929199427366257,
-0.030953573063015938,
-0.09076055139303207,
0.041504085063934326,
-0.00314758880995214,
0.0017437986098229885,
-0.03543813154101372,
0.00782119669020176,
0.04284092038869858,
0.04186530038714409,
-0.022045960649847984,
0.003312525572255254,
0.0007757444982416928,
0.025333346799016,
0.07724170386791229,
-0.01837230660021305,
0.007274731528013945,
0.02776268497109413,
-0.03898994252085686,
-0.02466089278459549,
-0.015907354652881622,
0.042100246995687485,
0.04606243222951889,
-0.020092008635401726,
-0.008487265557050705,
0.013168834149837494,
0.010773010551929474,
-0.008624234236776829,
0.015478410758078098,
0.013357319869101048,
-0.05122716724872589,
0.024291880428791046,
-0.013432317413389683,
0.005842017941176891,
-0.04106953740119934,
-0.03617032617330551,
-0.008515281602740288,
0.002982301404699683,
0.017046641558408737,
-0.0061772605404257774,
0.009398408234119415,
0.018763359636068344,
0.010048209689557552,
-0.03976030647754669,
0.0055959573946893215,
-0.04393910989165306,
0.01807727850973606,
0.012405521236360073,
0.009561615996062756,
0.006885250099003315,
0.023717500269412994,
-0.0434018075466156,
-0.0026022959500551224,
0.040298186242580414,
0.03542247787117958,
0.013571136631071568,
-0.03013111650943756,
0.017344698309898376,
-0.01287909783422947,
0.08691766858100891,
-0.04560938477516174,
-0.05078313127160072,
0.034972358494997025,
-0.04263751953840256,
-0.07491420209407806,
0.049796245992183685,
0.025521889328956604,
0.03889109939336777,
0.04819256439805031,
0.011879714205861092,
0.014048541896045208,
0.05106780678033829,
-0.04961958900094032,
-0.009689375758171082,
-0.011402927339076996,
0.00034699789830483496,
0.006956855766475201,
0.0017307826783508062,
-0.01387057639658451,
-0.0058587538078427315,
0.016902096569538116,
0.047876548022031784,
0.030330907553434372,
-0.02628306671977043,
0.0005209717783145607,
0.005690536927431822,
-0.002617296064272523,
0.02365877665579319,
0.04502436891198158,
0.02033153548836708,
0.05677897483110428,
0.05128367990255356,
-0.011310182511806488,
0.03367336839437485,
0.010383001528680325,
0.02055744081735611,
-0.08263450860977173,
0.024191953241825104,
-0.027487244457006454,
-0.008641316555440426,
0.01338291633874178,
-0.013639136217534542,
0.015743263065814972,
0.033714987337589264,
-0.053486477583646774,
0.013784697279334068,
-0.034272123128175735,
-0.005842708516865969,
-0.04552637040615082,
-0.00033216355950571597,
-0.01060195080935955,
0.07932340353727341,
0.04501716420054436,
0.03615971654653549,
0.026148203760385513,
0.011484986171126366,
0.0032643915619701147,
-0.034626275300979614,
0.000717672985047102,
0.040392227470874786,
-0.008606752380728722,
-0.03853493928909302,
0.03987547382712364,
-0.022674860432744026,
-0.03534455597400665,
0.021421238780021667,
-0.05210443586111069,
-0.018069373443722725,
0.01726819947361946,
0.00226396881043911,
0.01199419517070055,
0.029498500749468803,
0.01849409192800522,
-0.003898323979228735,
-0.03801196068525314,
0.056603606790304184,
0.04716876521706581,
0.040739476680755615,
-0.004648539703339338,
-0.010013850405812263,
-0.01365623902529478,
-0.010743481107056141,
-0.02109331078827381,
0.06829666346311569,
-0.0340702161192894,
-0.03238460421562195,
0.0275310967117548,
-0.03940076753497124,
0.03745211288332939,
-0.04086306318640709,
-0.016414379701018333,
-0.03322124108672142,
-0.01455361396074295,
0.05139052867889404,
-0.008262001909315586,
0.01860189251601696,
-0.012094113975763321,
-0.011855242773890495,
-0.03959912061691284,
0.018542401492595673,
-0.0030136408749967813,
-0.017736107110977173,
-0.03181887045502663,
-0.01704508252441883,
0.008002367801964283,
-0.04027745500206947,
-0.040766309946775436,
-0.01861768215894699,
-0.020639805123209953,
0.05204019322991371,
0.006709561683237553,
0.037026163190603256,
0.006657795049250126,
-0.011561312712728977,
-0.03521208465099335,
-0.041416216641664505,
0.026570869609713554,
-0.029858315363526344,
-0.016732722520828247,
-0.04323269799351692,
0.011010506190359592,
-0.015815479680895805,
0.01726483181118965,
0.05333438515663147,
0.0230115856975317,
-0.025898491963744164,
-0.009433873929083347,
-0.005178791005164385,
0.01623564399778843,
-0.03375326469540596,
-0.003203991102054715,
0.008843343704938889,
-0.02218659780919552,
-0.01167082879692316,
0.0037293077912181616,
-0.01682605966925621,
0.02549644559621811,
0.029833486303687096,
-0.017500320449471474,
0.008993451483547688,
-0.005675795488059521,
0.006655596662312746,
0.04820190370082855,
0.04036882519721985,
-0.061659764498472214,
0.06550940871238708,
-0.04356234893202782,
0.03722183778882027,
0.0185555312782526,
0.02130736969411373,
-0.08400408923625946,
0.0001381606125505641,
-0.010587155818939209,
-0.013113129884004593,
0.03112182766199112,
-0.016803395003080368,
-0.0051728724502027035,
-0.05586887151002884,
0.0031399945728480816,
0.0359935536980629,
-0.02917466312646866,
0.018030298873782158,
0.06259499490261078,
0.025197723880410194,
0.027425091713666916,
-0.004365250002592802,
-0.009950503706932068,
-0.010314136743545532,
0.007994825951755047,
-0.003083133837208152,
0.04353121668100357,
0.0633440688252449,
-0.0018793510971590877,
0.05179144814610481,
0.002881305990740657,
-0.032228659838438034,
0.00502752186730504,
0.0474819540977478,
0.03779173269867897,
-0.02934056706726551,
-0.008307606913149357,
0.028845861554145813,
-0.000007995166015462019,
0.012020299211144447,
0.01133942324668169,
0.005600217264145613,
0.07373840361833572,
-0.01884196698665619,
-0.029764030128717422,
-0.0442882739007473,
0.005412467289716005,
-0.011033544316887856,
0.01390279084444046,
0.024703992530703545,
0.038453057408332825,
0.015928342938423157,
-0.01958220638334751,
0.0053862957283854485,
-0.013490053825080395,
0.002055176766589284,
-0.024388005957007408,
-0.0009154458530247211,
-0.016502713784575462,
0.015578728169202805,
-0.06357865035533905,
-0.0522715225815773,
-0.04457506164908409,
-0.02109072357416153,
0.006872247438877821,
0.0255263838917017,
0.022939220070838928,
0.051772892475128174,
-0.022315289825201035,
-0.02461700141429901,
0.04840818792581558,
-0.04960506409406662,
-0.01778278313577175,
-0.012762995436787605,
0.042990390211343765,
-0.0012607126263901591,
-0.027143657207489014
] |
<p>If we consider a classical field theory for a massless particle of integer spin $s$, in a curved space-time, one finds that it is "naturally" conformal in a space-time of dimension $2+2s$</p>
<p>For instance, the free massless scalar field theory is conformal in $2$ dimensions, the electromagnetic field theory is conformal in $4$ dimensions, etc...</p>
<p>But does it work for half-integer spin, for instance is a spin $\frac{1}{2}$ field theory conformal in a $3$ dimensional space-time , and is a spin $\frac{3}{2}$ field theory conformal in a $5$ dimensional space-time ?</p> | 1,538 | [
0.01682397723197937,
-0.006513842381536961,
-0.009905272163450718,
-0.0369635708630085,
0.03633909299969673,
0.00976597797125578,
-0.0461474172770977,
-0.03883882984519005,
0.02405904233455658,
-0.04876678064465523,
0.025677194818854332,
0.005079477094113827,
0.037206221371889114,
0.0537036657333374,
0.011871535331010818,
-0.00015787698794156313,
-0.019638335332274437,
-0.012874670326709747,
-0.01123955100774765,
-0.03929862752556801,
0.03269553929567337,
0.04321618378162384,
-0.025828072801232338,
0.021792607381939888,
-0.005901085678488016,
-0.005256380420178175,
0.004877016413956881,
0.010637784376740456,
0.02321622334420681,
0.05013018101453781,
-0.010132595896720886,
-0.0019716399256139994,
0.02034366875886917,
0.036890413612127304,
0.02216249331831932,
-0.011452163569629192,
-0.013616510666906834,
-0.02660433202981949,
0.012178556993603706,
0.005625634919852018,
-0.048775315284729004,
-0.05690053477883339,
-0.03688851743936539,
0.012208131141960621,
0.005243214312940836,
0.03862224891781807,
-0.01062049251049757,
-0.03655943274497986,
0.049292705953121185,
-0.06709106266498566,
0.06720413267612457,
0.008864251896739006,
0.004426832310855389,
-0.039016518741846085,
-0.0010093599557876587,
-0.016916722059249878,
0.07069028168916702,
0.05655844509601593,
0.014020144008100033,
-0.03347612917423248,
-0.055010151118040085,
-0.05979594588279724,
0.012175381183624268,
-0.03694799914956093,
-0.037659645080566406,
0.03831373155117035,
0.012101849541068077,
-0.011082393117249012,
0.025277094915509224,
-0.011859187856316566,
-0.019510110840201378,
0.00903779361397028,
0.05576243996620178,
-0.02646121382713318,
0.006956122349947691,
0.01957045868039131,
0.022739384323358536,
-0.008844003081321716,
0.028251679614186287,
0.005418490618467331,
-0.03000502847135067,
0.04168110340833664,
0.011240546591579914,
0.01896095834672451,
0.011458911001682281,
-0.007208768278360367,
0.063947893679142,
0.018081827089190483,
-0.012591148726642132,
0.05036047473549843,
-0.015361476689577103,
-0.020892903208732605,
0.06738124042749405,
-0.04349825158715248,
-0.041679464280605316,
0.05733620002865791,
0.013678528368473053,
0.03374450281262398,
-0.00610295869410038,
-0.010340215638279915,
-0.027058904990553856,
-0.01821749471127987,
0.0003726602590177208,
0.06436120718717575,
0.012570398859679699,
0.030873987823724747,
-0.06189534440636635,
0.0033947050105780363,
-0.04653727263212204,
-0.018642781302332878,
-0.021822813898324966,
0.022622205317020416,
-0.031665753573179245,
-0.007464312948286533,
0.014592899940907955,
0.00024245916574727744,
-0.01489400677382946,
-0.039097096771001816,
0.0402245856821537,
0.058125704526901245,
0.05202404037117958,
-0.011043835431337357,
0.0035756085999310017,
-0.028048820793628693,
-0.06306532770395279,
0.017345936968922615,
0.028621535748243332,
0.00574067048728466,
-0.029808657243847847,
0.017121504992246628,
0.04136244207620621,
-0.03700073063373566,
0.006884464528411627,
0.029959119856357574,
0.04243621230125427,
-0.02939126454293728,
-0.042049992829561234,
-0.06023868918418884,
0.0033500159624964,
-0.014035697095096111,
-0.02503167651593685,
-0.07984291762113571,
0.002842341549694538,
0.028597896918654442,
0.1249561756849289,
0.00244321976788342,
0.04335548356175423,
0.02608633227646351,
0.044799551367759705,
0.04485362768173218,
-0.042037125676870346,
-0.019236620515584946,
0.00015354181232396513,
-0.025930313393473625,
-0.0067937555722892284,
-0.06154248118400574,
0.020280279219150543,
0.019623201340436935,
0.00010608676529955119,
-0.025593223050236702,
0.0649096891283989,
-0.026356402784585953,
0.023137105628848076,
0.020798567682504654,
-0.010953828692436218,
0.007325071841478348,
0.02861468866467476,
-0.004066495690494776,
-0.006221396382898092,
0.014335928484797478,
0.010023390874266624,
0.011266968213021755,
-0.010743934661149979,
0.062419261783361435,
0.027257101610302925,
-0.0476093627512455,
-0.027966277673840523,
0.009603818878531456,
0.01798766851425171,
0.008595401421189308,
0.0009943494806066155,
-0.005291087552905083,
-0.004595809616148472,
0.04498055949807167,
-0.03302513808012009,
0.03006904013454914,
0.005210304167121649,
-0.03446735441684723,
0.018424969166517258,
-0.04764704406261444,
0.025017723441123962,
-0.06134727597236633,
0.017423005774617195,
0.0219684187322855,
-0.01885036937892437,
0.06703275442123413,
0.037094637751579285,
0.02994445338845253,
-0.03676852956414223,
-0.04565589502453804,
0.008892670273780823,
0.05356733500957489,
0.014803181402385235,
-0.01737022027373314,
0.017868224531412125,
0.020267145708203316,
0.01756753958761692,
-0.008458663709461689,
0.015393516048789024,
0.01669994555413723,
-0.04846338927745819,
0.018608754500746727,
0.012111873365938663,
0.026846271008253098,
0.010356259532272816,
0.017612868919968605,
-0.0017814849270507693,
-0.01792897656559944,
-0.024361034855246544,
0.07492396980524063,
-0.025514481589198112,
0.04858621209859848,
0.022109733894467354,
-0.03283669799566269,
0.026542572304606438,
0.04590019956231117,
-0.001981387846171856,
0.01289430819451809,
0.022852227091789246,
-0.025747474282979965,
-0.04678502306342125,
-0.038874778896570206,
0.05260179936885834,
0.05065545812249184,
-0.03262166678905487,
0.018596552312374115,
0.049697451293468475,
0.025810481980443,
-0.0018087029457092285,
0.036742549389600754,
-0.011758467182517052,
-0.05100665241479874,
0.0313093475997448,
-0.020349299535155296,
-0.001972620375454426,
0.02218734100461006,
0.02670747973024845,
0.004207738675177097,
0.00758221885189414,
-0.00007099385402398184,
-0.06212481111288071,
0.04684288054704666,
-0.05714854970574379,
-0.01231466419994831,
0.017794515937566757,
-0.02824704349040985,
0.027690107002854347,
-0.036136444658041,
0.0012281336821615696,
0.03365655615925789,
-0.01828775741159916,
-0.0038810884580016136,
-0.020634103566408157,
0.010726342909038067,
0.019120359793305397,
0.0302831269800663,
-0.01027999073266983,
-0.042494382709264755,
0.00741308368742466,
-0.038674693554639816,
-0.029877256602048874,
-0.019177544862031937,
-0.0014163750456646085,
0.01065831258893013,
0.02372712641954422,
0.042590249329805374,
-0.017312636598944664,
0.03116142377257347,
-0.03701498359441757,
-0.043107181787490845,
0.046689607203006744,
-0.02562575228512287,
0.032510511577129364,
0.0073267617262899876,
-0.040778350085020065,
0.023273274302482605,
-0.075718954205513,
-0.011715639382600784,
0.009755118750035763,
-0.02333759143948555,
0.0433838926255703,
-0.02311793528497219,
-0.05517930909991264,
0.01348122674971819,
-0.01420881412923336,
-0.006783861201256514,
0.03655806928873062,
-0.0250861756503582,
0.000798828958068043,
0.06824809312820435,
0.038037434220314026,
-0.010451244190335274,
-0.024327395483851433,
-0.008174935355782509,
-0.036373186856508255,
-0.019700899720191956,
-0.008435165509581566,
0.04732486978173256,
-0.05907105281949043,
0.05391567945480347,
0.012811184860765934,
-0.06467865407466888,
0.018400689586997032,
-0.08255396038293839,
-0.039179373532533646,
0.017133327201008797,
-0.01800272800028324,
0.005095070693641901,
0.006832438055425882,
-0.024121228605508804,
0.04777985438704491,
0.006592880934476852,
-0.022746620699763298,
-0.00657194759696722,
-0.01802855171263218,
-0.01606018655002117,
-0.019188737496733665,
-0.009417092427611351,
0.011710550636053085,
-0.025508664548397064,
0.021246975287795067,
0.016069624572992325,
0.045036934316158295,
-0.003022676333785057,
-0.006762145087122917,
-0.03675408288836479,
0.02939429320394993,
0.02207140251994133,
-0.0011206429917365313,
0.03820722550153732,
0.009611446410417557,
-0.010795926675200462,
0.03365403786301613,
-0.018801599740982056,
-0.023642314597964287,
-0.008931133896112442,
-0.03964164853096008,
0.05492277815937996,
-0.0031500430777668953,
0.057043418288230896,
0.019539179280400276,
0.03803228214383125,
-0.011995936743915081,
-0.013862334191799164,
-0.017244838178157806,
0.028068777173757553,
0.008743057027459145,
-0.0190751813352108,
0.01636524312198162,
0.016250107437372208,
0.042725905776023865,
-0.027735186740756035,
-0.02157723903656006,
-0.007751964032649994,
-0.008968817070126534,
0.02497226931154728,
-0.016010962426662445,
-0.008753699250519276,
0.026571670547127724,
0.03880695998668671,
0.03454094007611275,
-0.034020714461803436,
-0.02093418687582016,
0.009865948930382729,
-0.05560501292347908,
-0.022678358480334282,
-0.008156955242156982,
0.013586857356131077,
-0.0006600927445106208,
0.02393369749188423,
0.03533312305808067,
-0.007418318651616573,
0.000018695860489970073,
0.006822366267442703,
-0.07328573614358902,
-0.04435700550675392,
-0.025386199355125427,
0.04284953325986862,
0.01854848675429821,
-0.005372819025069475,
0.0016355940606445074,
-0.047732435166835785,
-0.0286568570882082,
0.009469697251915932,
-0.008632579818367958,
-0.029016684740781784,
0.03940074145793915,
-0.03238658607006073,
-0.03485424071550369,
-0.010904163122177124,
0.041119445115327835,
0.044222477823495865,
-0.01139806304126978,
0.009015966206789017,
0.03367724269628525,
-0.0332147479057312,
0.0012735078344121575,
0.02399362623691559,
0.03834609314799309,
0.00377775845117867,
0.03462883085012436,
0.048001911491155624,
0.002299980027601123,
-0.040549084544181824,
0.003456190461292863,
-0.0021022495348006487,
0.06857012212276459,
-0.0011681471951305866,
-0.020486952736973763,
-0.005666906945407391,
-0.09016019105911255,
-0.001776413293555379,
-0.030852867290377617,
0.08372773975133896,
0.009609788656234741,
0.007982528768479824,
0.04805462807416916,
-0.00989202968776226,
-0.021620668470859528,
-0.007706375326961279,
0.06636414676904678,
-0.011077218689024448,
-0.056551020592451096,
-0.015667730942368507,
-0.018115032464265823,
-0.0017228408250957727,
-0.012511521577835083,
0.004642809741199017,
-0.027645617723464966,
-0.03911085054278374,
0.02538357861340046,
0.028705177828669548,
-0.02119300700724125,
-0.0535430945456028,
0.020584430545568466,
0.0319828987121582,
0.021073047071695328,
-0.013779107481241226,
-0.0038072748575359583,
-0.015357869677245617,
0.04406849667429924,
0.025807751342654228,
0.00871795043349266,
-0.02356807328760624,
-0.05092422664165497,
0.01508702989667654,
0.03879661485552788,
0.07138673216104507,
0.0031194142065942287,
-0.013695293106138706,
-0.04905850440263748,
0.002648394787684083,
0.04950157552957535,
-0.011812451295554638,
0.0007493162993341684,
0.002683429978787899,
-0.022219892591238022,
-0.00429916474968195,
0.004352444317191839,
-0.03812110424041748,
0.021707676351070404,
-0.005985995288938284,
-0.01661340706050396,
-0.042776141315698624,
0.028428183868527412,
-0.010354178957641125,
0.01846678927540779,
0.02165272645652294,
0.010515940375626087,
0.018463360145688057,
0.05936644971370697,
0.005218475125730038,
0.020292356610298157,
-0.03259995952248573,
-0.045904625207185745,
0.0005193331162445247,
0.020181776955723763,
-0.012244189158082008,
0.008210444822907448,
-0.055695731192827225,
-0.04370208829641342,
-0.02574501931667328,
-0.026059910655021667,
0.024244258180260658,
0.022566622123122215,
-0.029501665383577347,
0.0462057888507843,
0.00829562172293663,
-0.022464843466877937,
0.013283238746225834,
0.053603291511535645,
0.012388227507472038,
-0.037719063460826874,
-0.019304664805531502,
0.030855000019073486,
-0.02796720713376999,
0.004769334103912115,
-0.0341181606054306,
-0.020886557176709175,
-0.010840276256203651,
0.023074455559253693,
-0.030829062685370445,
-0.007060658652335405,
-0.012310870923101902,
-0.015839654952287674,
-0.05154435709118843,
0.007748465985059738,
-0.011961891315877438,
-0.006018501240760088,
0.0035522955004125834,
0.006724460516124964,
0.02300967089831829,
-0.020256610587239265,
0.014106223359704018,
0.009092598222196102,
-0.005687846802175045,
0.014495640061795712,
0.009847600944340229,
0.0008737370953895152,
-0.05222175270318985,
0.017291462048888206,
-0.0010531798470765352,
-0.04174967110157013,
0.059634145349264145,
-0.015238205902278423,
-0.02644357830286026,
-0.02962593547999859,
-0.039232827723026276,
0.020910996943712234,
-0.0065808105282485485,
-0.012445777654647827,
-0.0020741531625390053,
-0.021331893280148506,
0.0010844380594789982,
0.041367463767528534,
0.0011842931853607297,
-0.08255179971456528,
-0.01668798178434372,
0.017869969829916954,
0.024878017604351044,
-0.00545190554112196,
0.00015587490634061396,
-0.022372709587216377,
-0.05576883628964424,
-0.018647929653525352,
-0.012109261937439442,
0.09601131081581116,
-0.048621516674757004,
-0.009795662015676498,
0.043423477560281754,
0.04651834815740585,
0.033290017396211624,
-0.01094450056552887,
-0.029323145747184753,
0.022949352860450745,
-0.00609962735325098,
-0.000921360042411834,
-0.006016985047608614,
0.048919156193733215,
-0.022104231640696526,
-0.017504125833511353,
0.01387654896825552,
0.00020554028742481023,
0.018998319283127785,
-0.03616534173488617,
-0.020637577399611473,
0.0038118548691272736,
-0.016945751383900642,
0.020641982555389404,
-0.00903000682592392,
0.00966951809823513,
0.0028809416107833385,
0.009913250803947449,
-0.0418117381632328,
0.008664548397064209,
-0.031349293887615204,
-0.014269826002418995,
0.033314064145088196,
-0.009933212772011757,
0.014777256175875664,
-0.026449106633663177,
0.014483554288744926,
0.01633301004767418,
-0.03074418194591999,
-0.0038977395743131638,
-0.03265300765633583,
-0.020479800179600716,
-0.00450490228831768,
0.04125747084617615,
0.03662995249032974,
0.009019396267831326,
-0.01723426766693592,
-0.02202432230114937,
-0.005138944834470749,
0.019208839163184166,
0.060113370418548584,
-0.009110180661082268,
0.03566284105181694,
0.040121711790561676,
-0.016168463975191116,
0.016510451212525368,
-0.01972995139658451,
-0.01641027070581913,
0.0153040811419487,
0.019728608429431915,
0.041440200060606,
-0.05170232430100441,
0.025426089763641357,
0.04191422089934349,
0.055278170853853226,
-0.000936690135858953,
0.026792196556925774,
0.034702934324741364,
0.009425589814782143,
0.014814700931310654,
-0.008322566747665405,
-0.032802388072013855,
0.08776501566171646,
-0.009149636141955853,
0.04515625536441803,
0.013541928492486477,
-0.02729801833629608,
0.030242176726460457,
0.02424928918480873,
0.03094085305929184,
-0.016918940469622612,
-0.05098418518900871,
-0.04075139760971069,
-0.017344677820801735,
0.026342224329710007,
0.0012547766091302037,
-0.012830249965190887,
0.00686434144154191,
0.031071046367287636,
-0.001327846897765994,
0.006225532852113247,
0.02614353410899639,
-0.06208239123225212,
-0.002597356680780649,
-0.05461777001619339,
-0.028215818107128143,
0.05348203331232071,
0.04271979257464409,
-0.011584412306547165,
0.026225309818983078,
-0.016195865347981453,
0.011241971515119076,
0.014770688489079475,
0.007989780977368355,
-0.04341097176074982,
0.04076308384537697,
-0.012175355106592178,
0.0496765561401844,
-0.024747218936681747,
0.012639024294912815,
0.11088158190250397,
0.05356421694159508,
0.0035167131572961807,
-0.08815230429172516,
0.015058447606861591,
-0.06813737004995346,
0.026024647057056427,
-0.016001664102077484,
0.000007460630513378419,
-0.021020978689193726,
-0.02075343020260334,
-0.006657163146883249,
0.08336932957172394,
-0.017985237762331963,
-0.02094545215368271,
0.03595748171210289,
-0.03545285761356354,
-0.038825035095214844,
-0.01874724216759205,
0.02931690774857998,
0.015763528645038605,
0.026696866378188133,
-0.03457753732800484,
0.004540018737316132,
0.0020287774968892336,
0.036782171577215195,
-0.015162906609475613,
-0.035162243992090225,
0.020474279299378395,
0.0042211515828967094,
-0.052088357508182526,
-0.01409494411200285,
0.0244724303483963,
-0.03785233572125435,
-0.034919846802949905,
-0.0011169019853696227,
0.021722009405493736,
-0.01809089258313179,
0.0013755372492596507,
0.03851752355694771,
0.010460459627211094,
0.03448391333222389,
0.015847142785787582,
0.056392818689346313,
-0.049373187124729156,
-0.010591194964945316,
-0.022103479132056236,
0.021873710677027702,
-0.03802096098661423,
0.0016404628986492753,
-0.01103905402123928,
-0.027517182752490044,
0.021416371688246727,
-0.043463364243507385,
-0.009107380174100399,
-0.011030842550098896,
0.008372313342988491,
-0.029642146080732346,
0.02817516401410103,
-0.011964667588472366,
0.05732576549053192,
-0.007724654395133257,
0.012636163271963596,
-0.01457839086651802,
-0.04327041283249855,
0.029420925304293633,
0.002630380215123296,
0.024973899126052856,
0.007581583224236965,
-0.022419340908527374,
-0.008676075376570225,
0.019826659932732582,
-0.04749763384461403,
0.011143459938466549,
0.012718708254396915,
-0.0028550554998219013,
0.06514447182416916,
0.01736719161272049,
-0.03231263905763626,
-0.026012184098362923,
-0.043579597026109695,
0.010140127502381802,
-0.050463274121284485,
0.011778498999774456,
-0.044901203364133835,
0.015701860189437866,
0.038401905447244644,
0.029338618740439415,
-0.020283088088035583,
-0.01307632215321064,
-0.0353056862950325,
-0.02022191509604454,
0.03610590845346451,
-0.01848600059747696,
0.0038727910723537207,
-0.013223430141806602,
-0.04632778838276863,
0.0046862163580954075,
-0.05037917196750641,
0.0005032720509916544,
0.0235295332968235,
0.006266472395509481,
-0.03300458937883377,
0.045963775366544724,
0.006855095736682415,
0.006461381446570158,
0.018378719687461853,
-0.011412139981985092,
0.004673732910305262,
0.022836577147245407,
0.026913560926914215,
-0.05514071136713028,
-0.05502212420105934,
-0.01769290864467621,
0.0014904196141287684,
0.014734170399606228,
0.013807038776576519,
-0.041108228266239166,
0.007841484621167183,
-0.0010518397903069854,
-0.004913976415991783,
-0.020997686311602592,
-0.021479977294802666,
-0.04440396651625633,
0.01713654212653637,
-0.004324454814195633,
-0.0015873104566708207,
-0.0018218611367046833,
0.018905017524957657,
-0.013355101458728313,
-0.035586655139923096,
0.0037076971493661404,
0.040947627276182175,
-0.03626323863863945,
0.005421089474111795,
0.036338817328214645,
0.02415621466934681,
0.038184940814971924,
-0.04133987054228783,
-0.05405573919415474,
0.03860382363200188,
-0.012393261305987835,
-0.058305129408836365,
0.02572592720389366,
-0.05774863436818123,
0.022588269785046577,
-0.00014531833585351706,
-0.020118355751037598,
-0.037535157054662704,
0.022909296676516533,
-0.03439825400710106,
-0.010566545650362968,
0.02600269392132759,
-0.04399333521723747,
0.04070740193128586,
-0.02557281032204628,
0.020284879952669144,
0.04420909658074379,
-0.048476796597242355,
0.04302890971302986,
0.02124590426683426,
0.001216783537529409,
0.006038979161530733,
-0.0006560351466760039,
0.008342527784407139,
0.013774950988590717,
0.04206668585538864,
-0.029905451461672783,
0.000010777508578030393,
0.04388592764735222,
-0.02794085070490837,
0.03709908947348595,
0.010663866996765137,
-0.011406730860471725,
-0.09742777794599533,
-0.0064629302360117435,
0.035926055163145065,
0.03837701305747032,
0.034600913524627686,
-0.054193027317523956,
-0.016699301078915596,
-0.015949193388223648,
-0.05800351873040199,
0.051810186356306076,
-0.030821064487099648,
-0.052122149616479874,
-0.03570112586021423,
-0.03640689328312874,
-0.02492041140794754,
0.03453603759407997,
0.03913301229476929,
0.04088159278035164,
-0.014146536588668823,
-0.007823794148862362,
-0.006003134418278933,
-0.033688463270664215,
-0.010384648106992245,
0.0032950148452073336,
-0.005650477949529886,
-0.036031484603881836,
0.07335826754570007,
-0.012407309375703335,
-0.015996035188436508,
0.04797503724694252,
0.004426233004778624,
0.000636219629086554,
-0.015037620440125465,
-0.011000880040228367,
0.008718867786228657,
0.042073655873537064,
0.007165899034589529,
-0.0032682479359209538,
-0.001374683459289372,
-0.0224592387676239,
0.02353951521217823,
0.019021855667233467,
-0.010910685174167156,
0.012500033713877201,
-0.020258726552128792,
-0.025915104895830154,
0.000045778186176903546,
0.03479790315032005,
-0.005435117520391941,
-0.030982933938503265,
-0.03744667023420334,
-0.011552575044333935,
0.027346311137080193,
-0.00712072616443038,
0.05483786016702652,
-0.04813571646809578,
0.014336149208247662,
0.004013432655483484,
0.02169167809188366,
-0.004275597166270018,
0.0685330480337143,
0.008539986796677113,
0.003971623722463846,
0.021541506052017212,
0.023774825036525726,
0.003940599039196968,
-0.02991568297147751,
-0.018435699865221977,
0.027532249689102173,
0.010281389579176903,
-0.01382901705801487,
-0.0453893318772316,
-0.0002323722728760913,
0.03475751355290413,
0.006087339948862791,
0.05723942443728447,
-0.0011525152949616313,
-0.019752275198698044,
-0.018826628103852272,
-0.06353653222322464,
0.03464895859360695,
-0.008240018971264362,
0.015536748804152012,
-0.03628277778625488,
0.005433282349258661,
-0.023664042353630066,
-0.00290890084579587,
0.07097667455673218,
0.012608946301043034,
0.005196273792535067,
0.008735237643122673,
-0.0013992510503157973,
0.012133010663092136,
-0.05355686694383621,
-0.038079213351011276,
-0.012992807663977146,
-0.047004587948322296,
-0.013271327130496502,
-0.0005814200267195702,
-0.011431031860411167,
0.010535219684243202,
0.004071861505508423,
-0.021969502791762352,
0.006906130351126194,
0.042499251663684845,
-0.026689665392041206,
0.030981572344899178,
-0.01384357362985611,
-0.015516058541834354,
0.05783291906118393,
0.02193826623260975,
0.009085862897336483,
0.056243304163217545,
-0.00631601270288229,
0.009247896261513233,
0.005790780298411846,
-0.0013801908353343606,
-0.05363249406218529,
-0.026121636852622032,
-0.0000358177421730943,
0.02093304879963398,
-0.014480781741440296,
0.012190684676170349,
0.07156283408403397,
-0.01800931617617607,
0.032963287085294724,
0.04947351664304733,
0.005209086928516626,
0.011567194014787674,
0.013263140805065632,
-0.0014917533844709396,
0.07777263969182968,
0.017371581867337227,
0.017482925206422806,
0.014985532499849796,
0.019899392500519753,
-0.03391050919890404,
-0.02637653984129429,
0.038555391132831573,
-0.025312155485153198,
-0.0002478057867847383,
0.016114309430122375,
0.05194558948278427,
0.011166811920702457,
0.001227579079568386,
0.05086726322770119,
-0.03299447521567345,
0.05477999895811081,
-0.01936342380940914,
-0.058193158358335495,
0.09453366696834564,
-0.013494184240698814,
0.03208395838737488,
-0.028211994096636772,
-0.011007596738636494,
0.01224158238619566,
-0.027771499007940292,
0.0035189997870475054,
0.03445706143975258,
0.0016098986379802227,
-0.03382572531700134,
-0.006457601208239794,
-0.017965620383620262,
0.032503578811883926,
-0.017767323181033134,
0.014780616387724876,
-0.0066177514381706715,
0.001901897368952632,
0.00920721422880888,
-0.030001776292920113,
-0.00337973702698946,
-0.011038081720471382,
0.028583360835909843,
0.03281203657388687,
0.05347210913896561,
-0.0421474352478981,
0.01630483940243721,
-0.012314117513597012,
0.041630301624536514,
-0.0822417140007019,
-0.010145453736186028,
-0.013224218040704727,
0.026360249146819115,
0.03071597032248974,
-0.01727628894150257
] |
<p>I have the cross-sections as a function of $\sqrt{s}$ for a process with a $u$-quark and $u$-antiquark in the initial state (eg.: $u \bar{u} \to e^- e^+$). I have a standard parton distribution function table (say, CTEQ). With these, how do I find the corresponding cross-sections for a process with protons in the initial state (e.g. $p p \to e^- e^+$ as at the LHC)?</p>
<p>Specifically, should I use some sort of convolution? How?</p> | 1,539 | [
0.0482863113284111,
-0.03448285534977913,
-0.008362690918147564,
-0.017222879454493523,
0.024722879752516747,
0.04374965652823448,
-0.002970353700220585,
-0.01696464791893959,
0.02809308096766472,
-0.04125933721661568,
0.05580093711614609,
-0.008228468708693981,
0.050672922283411026,
-0.027409860864281654,
0.007319493684917688,
0.013206833973526955,
0.0022578199859708548,
-0.003760237479582429,
-0.004782544448971748,
-0.03037079982459545,
0.018567591905593872,
0.035829097032547,
-0.019867775961756706,
0.003659175243228674,
-0.01396169513463974,
0.06447967141866684,
-0.0013211481273174286,
0.037303946912288666,
0.011475097388029099,
0.05321371182799339,
-0.009198872372508049,
-0.01930953375995159,
0.01365188043564558,
0.036893606185913086,
0.010198422707617283,
0.04273056238889694,
-0.025450918823480606,
-0.03190632909536362,
-0.05416843667626381,
-0.0034212979953736067,
-0.04912974685430527,
-0.03196728229522705,
-0.009540299884974957,
0.045998163521289825,
0.030250318348407745,
0.016834989190101624,
-0.03565054014325142,
-0.02413533441722393,
0.055823273956775665,
-0.08563240617513657,
0.03593960404396057,
0.050422996282577515,
0.042103979736566544,
0.018615342676639557,
-0.019272735342383385,
-0.012208499014377594,
0.06183461844921112,
0.06061761453747749,
0.0023991907946765423,
-0.01679304987192154,
-0.010601121000945568,
-0.04367484524846077,
0.008536581881344318,
-0.042939815670251846,
-0.018248483538627625,
0.012525551952421665,
-0.021089725196361542,
0.005468952003866434,
0.012160316109657288,
-0.03648240491747856,
0.04243422672152519,
0.011593140661716461,
0.03484216704964638,
-0.017293738201260567,
0.013705636374652386,
-0.004496393259614706,
0.03759611025452614,
0.013419167138636112,
0.04136550426483154,
0.028872398659586906,
-0.035895489156246185,
-0.006963879335671663,
0.020501861348748207,
0.01618930697441101,
-0.007151503581553698,
0.014356797561049461,
0.020593320950865746,
-0.011229806579649448,
-0.009083525277674198,
0.018125468865036964,
-0.014914005063474178,
-0.01442612987011671,
0.05288373678922653,
-0.009903774596750736,
0.0072089494206011295,
0.010137815028429031,
-0.00609190296381712,
0.04516366496682167,
0.013998017646372318,
-0.0493805967271328,
0.0045606656931340694,
-0.024799227714538574,
0.008925394155085087,
0.09129016101360321,
-0.03158702701330185,
0.019495084881782532,
-0.026728367432951927,
-0.006877615116536617,
-0.02985484153032303,
-0.025798650458455086,
-0.028485078364610672,
0.012704811990261078,
0.005480627529323101,
0.001414154190570116,
-0.0044957720674574375,
-0.05225458741188049,
-0.02167692594230175,
-0.019995233044028282,
0.07903183251619339,
0.06481388211250305,
0.07806096225976944,
0.0035793057177215815,
0.020491285249590874,
-0.023489627987146378,
-0.05685478821396828,
0.00517331762239337,
0.04101286083459854,
0.006239942740648985,
-0.03441547229886055,
0.0435992106795311,
-0.03053981438279152,
-0.012135127559304237,
0.015157997608184814,
-0.02636929415166378,
0.0473562590777874,
-0.002894093282520771,
-0.0953919067978859,
-0.050363823771476746,
0.009067886509001255,
-0.0253025870770216,
-0.038360629230737686,
-0.04991188645362854,
-0.023884516209363937,
0.03953937813639641,
0.04392337054014206,
-0.030061397701501846,
0.004611629527062178,
-0.005182269029319286,
0.04782673716545105,
0.026882143691182137,
-0.0038057402707636356,
-0.01791033148765564,
-0.05244804173707962,
0.01877537928521633,
0.03551514074206352,
-0.05187883973121643,
0.047783900052309036,
0.010696984827518463,
0.008321594446897507,
-0.008525446988642216,
0.07922396808862686,
-0.0031283958815038204,
0.02624092437326908,
0.004927541129291058,
0.007758723571896553,
-0.020590612664818764,
0.05321216955780983,
0.03197966143488884,
-0.022922148928046227,
0.025657285004854202,
-0.004699816461652517,
-0.015008838847279549,
0.026916828006505966,
-0.005566001404076815,
0.04518824443221092,
-0.02421443909406662,
-0.026209652423858643,
-0.017529629170894623,
-0.0025231018662452698,
-0.015498340129852295,
0.0012004028540104628,
-0.04380841925740242,
-0.03332631289958954,
-0.003431959543377161,
-0.004568730480968952,
0.025003671646118164,
0.009393175132572651,
-0.007952549494802952,
0.02804606221616268,
-0.04609294235706329,
-0.06687465310096741,
-0.05999521166086197,
0.012727857567369938,
-0.012734896503388882,
-0.0056086089462041855,
0.045098286122083664,
0.011294910684227943,
0.009207874536514282,
0.0017943356651812792,
-0.06728692352771759,
0.022346874698996544,
0.036428291350603104,
0.008093679323792458,
-0.024524232372641563,
0.007833804003894329,
0.023426953703165054,
0.01813512295484543,
-0.012350447475910187,
0.04213571548461914,
-0.01585043966770172,
-0.03465970605611801,
-0.009941665455698967,
-0.03467801213264465,
0.005177641287446022,
-0.002236034255474806,
-0.027059242129325867,
-0.03565286099910736,
-0.002606538124382496,
0.009883061051368713,
0.003391618374735117,
-0.04451990872621536,
0.06425786018371582,
0.05986904352903366,
0.006567556876689196,
0.014321623370051384,
0.007919598370790482,
0.04390798881649971,
0.05616988241672516,
0.01070580817759037,
-0.020004188641905785,
-0.04725690558552742,
-0.029392410069704056,
0.04480433836579323,
0.008412213996052742,
-0.04769110307097435,
-0.009951859712600708,
0.03738043084740639,
-0.02240576781332493,
0.021699365228414536,
0.02230246737599373,
-0.047665074467659,
-0.03828362748026848,
0.012056590989232063,
0.03831014037132263,
-0.030988838523626328,
0.0029665834736078978,
0.0013004641514271498,
0.005802537780255079,
-0.006096821278333664,
-0.016917014494538307,
-0.029941633343696594,
0.028754359111189842,
-0.02956262044608593,
-0.01627536118030548,
-0.021849388256669044,
-0.0558781772851944,
0.027946459129452705,
0.004354551434516907,
0.030181098729372025,
-0.010460668243467808,
-0.017352338880300522,
-0.0015072213718667626,
0.008589928038418293,
-0.0248788520693779,
0.0021351242903620005,
0.0029650521464645863,
-0.014415333047509193,
0.009528045542538166,
0.0301694143563509,
-0.08716527372598648,
0.03528018295764923,
-0.0073890360072255135,
-0.02053982950747013,
-0.026613295078277588,
-0.001003527780994773,
0.044541750103235245,
0.02905850112438202,
0.00009701472299639136,
-0.04263804107904434,
-0.04857631027698517,
0.04172336310148239,
-0.0000638087367406115,
0.040304310619831085,
0.042940132319927216,
-0.04313458129763603,
0.02947212941944599,
-0.06950469315052032,
-0.01174776442348957,
0.0227583646774292,
-0.01595206744968891,
-0.008656986057758331,
0.005879840347915888,
-0.016496378928422928,
0.003738113446161151,
-0.01582956314086914,
-0.024283945560455322,
0.0005928358878009021,
-0.006918493192642927,
0.022171560674905777,
0.04105575010180473,
0.03148485720157623,
-0.02800939977169037,
0.02577030099928379,
-0.039239302277565,
-0.0016922930954024196,
-0.014044971205294132,
0.027267776429653168,
0.0010578142246231437,
-0.024296186864376068,
0.06100509315729141,
0.0389355793595314,
-0.036719489842653275,
0.027613181620836258,
-0.04171481728553772,
-0.01876804232597351,
-0.01451054122298956,
0.04119843989610672,
0.02918744459748268,
0.019503053277730942,
-0.05250491946935654,
0.06164132058620453,
0.0028587121050804853,
-0.05260835215449333,
-0.00014754774747416377,
0.013766882009804249,
-0.017318833619356155,
-0.03302930295467377,
0.009632663801312447,
-0.012651253491640091,
-0.03056679293513298,
0.007799462880939245,
-0.010871623642742634,
0.04267998784780502,
0.060697074979543686,
0.037865862250328064,
0.002302467357367277,
-0.003886240068823099,
-0.019325915724039078,
0.001067245495505631,
0.005899719428271055,
-0.00210259179584682,
-0.01654563657939434,
0.039665430784225464,
0.010992887429893017,
0.0011530850315466523,
0.0183323472738266,
-0.020078172907233238,
0.04925653710961342,
-0.0015716779744252563,
-0.03298860043287277,
-0.025204654783010483,
0.0344863124191761,
-0.007947642356157303,
-0.01779598742723465,
0.006634605582803488,
0.012941474094986916,
-0.0069820089265704155,
0.005124709568917751,
0.010841084644198418,
0.017009589821100235,
0.05658832564949989,
-0.027119791135191917,
-0.0603359155356884,
-0.0550757460296154,
-0.020259471610188484,
0.03552044928073883,
0.01985534280538559,
-0.004190271720290184,
0.0068647293373942375,
0.05577389895915985,
0.016851171851158142,
-0.024287445470690727,
-0.012534969486296177,
-0.030407289043068886,
-0.07593294233083725,
-0.010160393081605434,
-0.021878546103835106,
0.030822837725281715,
0.0392947681248188,
0.06046410650014877,
0.001038100104779005,
-0.0053968108259141445,
-0.00831090658903122,
0.01687042787671089,
-0.07600758224725723,
0.02995709702372551,
-0.017663436010479927,
-0.019657479599118233,
-0.034263838082551956,
-0.002608179347589612,
-0.027567649260163307,
0.00798843614757061,
-0.04952734336256981,
0.0015033358940854669,
0.004255375359207392,
0.006514083594083786,
0.013587296940386295,
-0.03299180790781975,
-0.011495474725961685,
-0.026648351922631264,
0.017636790871620178,
0.013398521579802036,
-0.04283798485994339,
0.011827001348137856,
0.03444607928395271,
-0.0578426755964756,
-0.014087900519371033,
-0.012969009578227997,
0.07472540438175201,
-0.008998359553515911,
0.03641624376177788,
0.03923924267292023,
0.01853693462908268,
-0.0611756257712841,
0.034645501524209976,
0.02040717378258705,
0.07957036048173904,
0.027744049206376076,
-0.027483969926834106,
-0.0021532620303332806,
-0.061252888292074203,
-0.022648055106401443,
0.025268839672207832,
0.04379498213529587,
0.00997865665704012,
-0.0011885624844580889,
0.05920274183154106,
0.01685202121734619,
-0.04144822433590889,
0.015294223092496395,
0.09369823336601257,
-0.006782571319490671,
-0.04578985273838043,
-0.08038945496082306,
0.024283168837428093,
0.028797784820199013,
-0.0042090993374586105,
0.016539625823497772,
0.0514163076877594,
0.00569121865555644,
0.018532339483499527,
0.017754852771759033,
0.025566088035702705,
-0.05586574226617813,
-0.0024507082998752594,
0.020861487835645676,
0.01726214773952961,
-0.02151583507657051,
-0.020775487646460533,
0.037900544703006744,
0.056524381041526794,
0.04516599327325821,
-0.011585893109440804,
0.02207936905324459,
-0.057481952011585236,
0.019530288875102997,
0.05201120302081108,
0.08274666965007782,
-0.001620468683540821,
-0.04060627892613411,
-0.0571589395403862,
-0.020614536479115486,
0.059819892048835754,
0.00018302137323189527,
-0.0019203403498977423,
0.007379465736448765,
-0.00034090911503881216,
0.01373464148491621,
-0.008212721906602383,
-0.045138388872146606,
0.03562581166625023,
-0.03916860371828079,
-0.006272933445870876,
-0.033858414739370346,
-0.006421541329473257,
-0.033762019127607346,
0.01732778549194336,
0.03016945905983448,
0.03342071920633316,
-0.026722585782408714,
0.004979996010661125,
-0.012305143289268017,
0.03134936839342117,
-0.0034924200735986233,
-0.06723222136497498,
0.012585951946675777,
-0.04770214855670929,
-0.0037968335673213005,
0.04028534144163132,
0.004343351814895868,
-0.011481005698442459,
0.027148721739649773,
0.01656392216682434,
0.0038366466760635376,
-0.02845437452197075,
-0.03458575904369354,
0.04137430712580681,
0.05428610369563103,
0.014647508971393108,
0.07023710757493973,
0.02010117657482624,
-0.0029863137751817703,
0.0018366239964962006,
-0.007331640459597111,
0.027002952992916107,
-0.013458295725286007,
-0.0011129004415124655,
-0.02570538967847824,
-0.0073656984604895115,
-0.027403714135289192,
0.002495376393198967,
-0.05898856744170189,
0.044209517538547516,
-0.022279568016529083,
-0.0401931032538414,
-0.015678102150559425,
0.017014119774103165,
-0.018100716173648834,
-0.005751762539148331,
0.018205493688583374,
0.03229370713233948,
0.007341389078646898,
-0.030147969722747803,
-0.0007840427570044994,
-0.01347971148788929,
0.031268905848264694,
-0.05700761824846268,
-0.00395266804844141,
0.0059412880800664425,
-0.017209375277161598,
-0.02704884298145771,
0.020452897995710373,
-0.01641172170639038,
0.025885729119181633,
-0.027743155136704445,
0.012904687784612179,
0.020382802933454514,
-0.06107232719659805,
-0.006154655944555998,
0.043409563601017,
0.012393919751048088,
0.02417713776230812,
-0.08067779242992401,
0.02590763010084629,
0.0012593423016369343,
0.006104330066591501,
-0.10145033150911331,
-0.02460618130862713,
0.045620840042829514,
-0.016457336023449898,
-0.008446947671473026,
-0.03884604573249817,
-0.03241131827235222,
-0.013947498053312302,
-0.017141520977020264,
-0.035691455006599426,
0.06336276233196259,
-0.029356997460126877,
0.002842712216079235,
0.0010589155135676265,
0.041661232709884644,
0.05236179381608963,
-0.005156917497515678,
0.02642796002328396,
0.003453801851719618,
-0.011785455048084259,
-0.00973725039511919,
0.021145768463611603,
0.034336354583501816,
-0.020783308893442154,
-0.01854781247675419,
-0.0028892806731164455,
0.0021956181153655052,
0.014498709701001644,
-0.06930553913116455,
0.01069373544305563,
0.018285296857357025,
0.017362413927912712,
0.02826770953834057,
0.03168157860636711,
0.01772242598235607,
-0.02466682344675064,
-0.013865618966519833,
-0.02123647928237915,
-0.03093506023287773,
0.0023981390986591578,
-0.009688985534012318,
0.046200837939977646,
-0.03169981390237808,
0.010514767840504646,
0.011915726587176323,
0.0062848664820194244,
0.0026790404226630926,
-0.026623718440532684,
0.03176150470972061,
-0.014162949286401272,
0.01825687102973461,
0.013613584451377392,
0.004414406139403582,
0.029872871935367584,
-0.005857141222804785,
-0.01063208281993866,
-0.026859503239393234,
-0.02767276018857956,
-0.041134312748909,
0.052762940526008606,
-0.014886262826621532,
0.044087257236242294,
0.021831940859556198,
0.030991358682513237,
-0.01239553838968277,
-0.021857010200619698,
-0.021301867440342903,
0.007019626442342997,
0.017229875549674034,
0.04463236406445503,
0.008000005036592484,
0.014299883507192135,
-0.03167075663805008,
0.01206725463271141,
-0.0016125368420034647,
0.025811491534113884,
0.009748478420078754,
0.030789315700531006,
0.03478195518255234,
-0.025049244984984398,
-0.02457389235496521,
0.016682451590895653,
-0.030171135440468788,
0.015466206707060337,
-0.025565288960933685,
-0.018874241039156914,
0.050332821905612946,
-0.0019930407870560884,
0.01809839718043804,
0.010065052658319473,
-0.021919356659054756,
-0.059973862022161484,
0.04192870482802391,
0.047663018107414246,
-0.01121059712022543,
0.00868559442460537,
0.06870950013399124,
0.04685758054256439,
-0.01372165884822607,
0.04961317032575607,
0.013787592761218548,
-0.06969932466745377,
-0.06276237964630127,
-0.03952287510037422,
-0.050093721598386765,
0.03264846280217171,
-0.02799733355641365,
0.0015103366458788514,
-0.004989829380065203,
0.011364458128809929,
0.0056609357707202435,
-0.025970885530114174,
0.0433436781167984,
-0.032963111996650696,
0.03933582454919815,
-0.003355457214638591,
-0.01538451761007309,
-0.003929178696125746,
-0.005408168770372868,
0.10757018625736237,
0.0541483499109745,
0.03681432083249092,
-0.05730679631233215,
-0.01653253845870495,
0.0026951890904456377,
0.01384276058524847,
0.008720168843865395,
0.0361802764236927,
0.025843648239970207,
0.007492621894925833,
0.02861473150551319,
0.06902814656496048,
0.02973860688507557,
0.0031871572136878967,
0.06653399020433426,
-0.045012108981609344,
-0.024782691150903702,
0.017076732590794563,
0.04628482460975647,
-0.02671338990330696,
-0.001659568166360259,
-0.029848260805010796,
0.009102126583456993,
0.00798891857266426,
0.01868932694196701,
-0.05533479154109955,
-0.0554099977016449,
-0.005791109520941973,
-0.03090423159301281,
-0.027172723785042763,
0.009174956940114498,
-0.008050404489040375,
0.034948404878377914,
-0.017651015892624855,
-0.003198679070919752,
0.0017260897438973188,
-0.05107487738132477,
0.030294174328446388,
0.04497342184185982,
0.022733861580491066,
-0.02121095545589924,
0.0028761448338627815,
0.030780786648392677,
-0.012754798866808414,
-0.014076043851673603,
-0.026298293843865395,
0.05002845451235771,
-0.013008583337068558,
-0.007882188074290752,
-0.012044847011566162,
0.04350437968969345,
0.044548410922288895,
-0.028602538630366325,
-0.006175441201776266,
0.02035742625594139,
0.006308062467724085,
-0.03662190958857536,
0.009067297913134098,
0.009450425393879414,
0.02959061786532402,
0.004357820376753807,
0.006095339544117451,
0.02379307895898819,
0.00841599889099598,
-0.013398096896708012,
-0.02638426050543785,
0.008943791501224041,
0.0068641104735434055,
-0.005105510354042053,
-0.010836989618837833,
0.023588836193084717,
-0.04428008943796158,
0.0034472232218831778,
0.03384995833039284,
0.011463998816907406,
0.05703004449605942,
0.0026371346320956945,
-0.024128926917910576,
-0.02715432643890381,
-0.055798448622226715,
0.05934598296880722,
-0.03579872474074364,
-0.013487109914422035,
-0.029142392799258232,
0.017499377951025963,
0.026731764897704124,
0.05051059648394585,
0.0005323318764567375,
0.00007019934128038585,
-0.00032300507882609963,
0.06251165270805359,
0.022047245875000954,
-0.04172336682677269,
-0.016149206086993217,
0.019661996513605118,
-0.0001401258778059855,
-0.030787581577897072,
-0.02435431443154812,
0.04590345546603203,
0.011819815263152122,
0.010074798949062824,
-0.03973214700818062,
0.0012139759492129087,
-0.02390233241021633,
0.023647136986255646,
-0.001759799662977457,
-0.04464271292090416,
-0.005687805358320475,
-0.028967875987291336,
0.019358232617378235,
-0.01226746290922165,
-0.005740789696574211,
-0.009594650939106941,
-0.00419136555865407,
0.017874745652079582,
-0.0004284004680812359,
0.002751029096543789,
0.03696957603096962,
-0.04567521810531616,
0.01559956930577755,
0.028519591316580772,
-0.004484907258301973,
-0.03184571489691734,
0.010005559772253036,
-0.01509805116802454,
-0.02648766152560711,
-0.0029689406510442495,
0.023129092529416084,
0.006012034136801958,
-0.026831097900867462,
-0.035210981965065,
0.007764464244246483,
-0.041597649455070496,
-0.031395141035318375,
0.028952285647392273,
-0.018210971727967262,
0.03129567205905914,
0.023240268230438232,
0.012661685235798359,
0.030124394223093987,
-0.06204871088266373,
-0.05152564123272896,
0.026878846809267998,
0.020517338067293167,
0.033405303955078125,
0.03914192318916321,
-0.0038177238311618567,
-0.0018998461309820414,
0.00895758718252182,
-0.034661103039979935,
-0.051616620272397995,
0.008459382690489292,
-0.00034571660216897726,
0.003648758167400956,
-0.009002898819744587,
0.03689252957701683,
0.009723355062305927,
0.009718197397887707,
0.01339025143533945,
0.00857943668961525,
-0.028800686821341515,
0.03961313143372536,
-0.022807175293564796,
-0.02763497084379196,
0.06025415286421776,
0.021275483071804047,
0.017548810690641403,
-0.008136055432260036,
0.04677959904074669,
-0.011617394164204597,
0.012449468486011028,
0.01588974893093109,
-0.002257030690088868,
-0.09766826033592224,
-0.03022160567343235,
0.017011716961860657,
-0.005338422022759914,
0.07066871225833893,
-0.09438818693161011,
0.024583257734775543,
0.04491887241601944,
-0.0468846932053566,
0.0439053550362587,
-0.030292220413684845,
-0.016255615279078484,
-0.037283554673194885,
-0.010605551302433014,
-0.002040023682639003,
0.054094038903713226,
0.02933867648243904,
0.01120232604444027,
0.004950899630784988,
-0.024144161492586136,
0.008267304860055447,
0.011639181524515152,
-0.025788137689232826,
-0.006813342217355967,
0.013811160810291767,
-0.040450748056173325,
0.0674283355474472,
-0.041521091014146805,
-0.019328024238348007,
0.011336298659443855,
0.00580214150249958,
0.022861989215016365,
-0.03802134469151497,
0.0021828480530530214,
0.026813112199306488,
0.034196894615888596,
0.009243660606443882,
-0.017939968034625053,
0.029806623235344887,
0.007597425486892462,
0.002037027385085821,
0.016804322600364685,
-0.009900318458676338,
0.034788187593221664,
0.0053526489064097404,
-0.013347604312002659,
-0.04555903747677803,
0.04936320334672928,
0.006355649325996637,
-0.03029607981443405,
0.017911171540617943,
-0.02306455187499523,
0.040538154542446136,
0.002207019366323948,
0.03477681428194046,
-0.0463491827249527,
0.048383284360170364,
0.00944271869957447,
-0.005335808731615543,
-0.0025637485086917877,
0.011475489474833012,
-0.02636236511170864,
-0.023035328835248947,
0.03298066928982735,
0.007681932300329208,
-0.02339109219610691,
-0.049640849232673645,
-0.007566631305962801,
0.008672087453305721,
-0.006978810764849186,
-0.005979935172945261,
-0.053378455340862274,
-0.03066612407565117,
0.027100959792733192,
-0.03313498944044113,
0.028443221002817154,
0.01860952563583851,
0.009700414724647999,
-0.02398809790611267,
-0.05359681695699692,
0.008701802231371403,
0.02067922055721283,
-0.018076801672577858,
0.007899309508502483,
-0.010494093410670757,
-0.0009686612174846232,
0.030837727710604668,
0.02870926260948181,
0.001970093697309494,
-0.023429451510310173,
0.003821695689111948,
0.015467929653823376,
0.013635387644171715,
-0.04932182654738426,
-0.010859368368983269,
-0.014196114614605904,
-0.02225346677005291,
-0.04347723722457886,
0.00736395176500082,
0.008046351373195648,
0.059461794793605804,
0.007929876446723938,
0.005303984507918358,
-0.023639844730496407,
-0.02300487831234932,
-0.050439249724149704,
0.06295426189899445,
0.01581575907766819,
0.00029137113597244024,
0.03411552309989929,
0.014007573015987873,
-0.0015913756797090173,
0.0413837730884552,
-0.014854740351438522,
-0.04927690327167511,
0.0203170794993639,
-0.0332036055624485,
-0.04514607787132263,
-0.007896249182522297,
-0.009270170703530312,
0.0037049194797873497,
-0.05824756994843483,
-0.016817275434732437,
0.04167810454964638,
-0.06544829905033112,
-0.0056380415335297585,
0.027591101825237274,
0.020287837833166122,
0.02475052699446678,
0.0011383241508156061,
-0.005143446382135153,
0.02389482595026493,
-0.005047625862061977,
0.020860562101006508,
0.022115634754300117,
0.019183339551091194,
0.004408479668200016,
0.022855164483189583,
0.0034669097512960434,
-0.047215718775987625,
0.004200933501124382,
-0.013399035669863224,
0.03885948657989502,
-0.003805978922173381,
-0.0052926912903785706,
0.02153959311544895,
-0.017074432224035263,
0.005651095882058144,
0.008980512619018555,
-0.05939628183841705,
0.08090038597583771,
-0.049448948353528976,
0.030853120610117912,
-0.055120330303907394,
-0.030715234577655792,
0.0029261456802487373,
-0.012677512131631374,
0.006634457036852837,
0.047520771622657776,
-0.011421752162277699,
-0.029094334691762924,
-0.012850343249738216,
-0.009063303470611572,
0.03846438229084015,
-0.04984995350241661,
0.013058598153293133,
0.013773344457149506,
-0.00480083841830492,
-0.024891529232263565,
-0.05480673909187317,
-0.025514399632811546,
-0.019304625689983368,
0.04241360351443291,
0.04914518818259239,
-0.006122252903878689,
0.01975400559604168,
-0.032283954322338104,
-0.03129849210381508,
0.057253554463386536,
-0.03072749637067318,
0.00598716689273715,
-0.0034292812924832106,
0.005517023149877787,
-0.011473912745714188,
0.02286357246339321
] |
<p>It is said that the universe is expanding and the galaxies are moving apart. I understand that the space between every two galaxies is increasing. Doesn't this seem to imply that the galaxies will have relative motion and so have a moving velocity. According to relativity and the modern belief in physics, it is said that everything depends on relative motion and nothing else (I am talking about the concepts such as Time Dilation etc.). So in brief I would like to ask that why is it said that galaxies do not move even though the distance between them is increasing.</p> | 1,540 | [
-0.0037994051817804575,
-0.02841455675661564,
0.0088959326967597,
-0.02762637473642826,
0.04717939719557762,
0.02231886237859726,
-0.03713572025299072,
-0.01365570817142725,
-0.01675889827311039,
-0.048074185848236084,
0.011368151754140854,
0.03549644351005554,
0.043303344398736954,
-0.007102905306965113,
0.011192021891474724,
0.003081022761762142,
-0.023092344403266907,
-0.0038085654377937317,
-0.001023682882077992,
-0.019211381673812866,
0.0001692409423412755,
0.020612793043255806,
0.05136258155107498,
0.003328613704070449,
-0.01768263801932335,
0.022628704085946083,
0.021260671317577362,
0.02297922782599926,
0.030188623815774918,
0.05495428293943405,
0.01655605062842369,
-0.020052317529916763,
-0.0021535444539040327,
0.04727107658982277,
0.018325792625546455,
-0.008276505395770073,
-0.027206825092434883,
-0.009412725456058979,
-0.01420439500361681,
0.0014847780112177134,
-0.06419090181589127,
-0.04221450909972191,
-0.01027564238756895,
0.07335502654314041,
-0.05125940218567848,
0.001176872057840228,
0.006334049627184868,
0.0069048479199409485,
0.04935014620423317,
-0.03292137384414673,
0.06474623084068298,
-0.017029691487550735,
0.049193236976861954,
0.026233403012156487,
0.012205448001623154,
0.02948247641324997,
0.09491907805204391,
0.07219979166984558,
-0.06339681148529053,
-0.01607028767466545,
-0.02699415385723114,
-0.013758346438407898,
0.01791202649474144,
-0.007426136638969183,
-0.010502107441425323,
0.05266086384654045,
-0.037410397082567215,
0.00850808434188366,
0.020197667181491852,
0.023020654916763306,
0.028822263702750206,
0.014728013426065445,
0.03927893191576004,
-0.03579533100128174,
0.00009861352009465918,
-0.018556298688054085,
0.03273583576083183,
0.010260846465826035,
0.021741244941949844,
0.0565374530851841,
-0.016039006412029266,
-0.018443375825881958,
0.047467973083257675,
0.009028599597513676,
0.01412740908563137,
-0.0006829332560300827,
0.05569605156779289,
-0.020994175225496292,
0.018802015110850334,
0.017375396564602852,
-0.008588182739913464,
-0.004431420471519232,
0.025003373622894287,
0.0044445861130952835,
-0.0023715109564363956,
0.03713991492986679,
0.007259031757712364,
0.04262668639421463,
0.01964682713150978,
-0.031618520617485046,
0.0024706979747861624,
-0.0068832156248390675,
0.021473785862326622,
0.049410175532102585,
-0.0028121948707848787,
-0.028669757768511772,
-0.08142309635877609,
0.026523733511567116,
-0.05396478250622749,
-0.015100192278623581,
0.007123093586415052,
0.003434065030887723,
0.016738707199692726,
0.01557968556880951,
0.0344993956387043,
-0.03155606612563133,
0.009205258451402187,
-0.004579308442771435,
0.05466721951961517,
0.06793510168790817,
0.0364355705678463,
-0.046017635613679886,
0.009630529209971428,
0.005004213657230139,
-0.03167478367686272,
0.02279595471918583,
0.03327418491244316,
-0.012961429543793201,
-0.03558418154716492,
0.03520691394805908,
0.023080924525856972,
-0.00496191531419754,
-0.006381004583090544,
0.005864109843969345,
0.06131698563694954,
0.008151254616677761,
-0.11010973900556564,
-0.06217841058969498,
0.06568850576877594,
-0.02414502203464508,
0.00006096293145674281,
-0.06249716505408287,
0.017896194010972977,
0.01236724853515625,
0.0946103036403656,
0.0014153752708807588,
-0.01118404883891344,
-0.01785864494740963,
0.03962593898177147,
-0.01241016574203968,
-0.029753489419817924,
-0.05166994035243988,
-0.011257441714406013,
-0.05075349658727646,
0.0035637496039271355,
-0.10179267823696136,
-0.007337500341236591,
0.039196502417325974,
-0.003599322633817792,
-0.059625085443258286,
0.045896731317043304,
-0.01729716546833515,
0.001377407694235444,
-0.0073551274836063385,
0.014032851904630661,
-0.006360233761370182,
0.08886055648326874,
0.006742846220731735,
-0.01387628074735403,
0.06839779019355774,
0.019115176051855087,
0.022287998348474503,
0.005734829697757959,
0.029702045023441315,
0.03151267394423485,
-0.012471762485802174,
-0.038799628615379333,
0.0005054674111306667,
-0.006998986005783081,
0.029963942244648933,
-0.04128754511475563,
-0.015928175300359726,
-0.02342751808464527,
-0.0071543133817613125,
0.007568338420242071,
0.020533084869384766,
0.01683291792869568,
-0.0023220095317810774,
0.007646113634109497,
-0.031573861837387085,
-0.007292774505913258,
-0.08722516149282455,
0.0015312363393604755,
-0.0030492148362100124,
0.01035309862345457,
-0.0231634471565485,
0.03795989975333214,
0.018469765782356262,
-0.007100502960383892,
-0.017172545194625854,
-0.01865122653543949,
0.03773798793554306,
-0.01758134365081787,
-0.019984081387519836,
0.034445010125637054,
0.05088376626372337,
0.04765716940164566,
0.016866860911250114,
-0.00485152006149292,
-0.005947525147348642,
-0.017093736678361893,
0.0430041179060936,
-0.003780145663768053,
-0.018574057146906853,
-0.004187177401036024,
0.009908772073686123,
-0.0062583195976912975,
0.02001035027205944,
0.013278637081384659,
0.02799190953373909,
-0.03352373465895653,
0.1063731238245964,
0.012384140864014626,
-0.0037252726033329964,
-0.0006410055793821812,
0.051381856203079224,
-0.008013271726667881,
-0.006671307608485222,
-0.0005753519362770021,
-0.03896781802177429,
-0.05952238664031029,
-0.02008088305592537,
0.046057578176259995,
0.019628483802080154,
-0.03035430610179901,
0.011996441520750523,
0.03701958805322647,
0.04010563716292381,
0.007050008978694677,
0.015110577456653118,
-0.0306983795017004,
-0.053566135466098785,
-0.019475949928164482,
0.0010948326671496034,
0.017062868922948837,
-0.0007340763113461435,
0.04510967433452606,
0.025110358372330666,
-0.0009520514868199825,
-0.012695680372416973,
-0.00867962185293436,
0.04563811421394348,
0.0360138937830925,
-0.00781074445694685,
0.014711533673107624,
-0.05100856348872185,
0.022986367344856262,
-0.02655790187418461,
0.01729716546833515,
0.02613505721092224,
-0.007323191035538912,
0.015183106996119022,
-0.036025598645210266,
-0.027030441910028458,
0.001061332761310041,
0.00864353682845831,
-0.06400852650403976,
-0.006274632643908262,
0.0036207514349371195,
-0.05390764772891998,
0.012708461843430996,
-0.03952322527766228,
-0.006737925577908754,
-0.00921911932528019,
-0.028949519619345665,
0.04008718207478523,
0.0331684872508049,
0.05340078845620155,
-0.01452565100044012,
-0.020097991451621056,
0.002534695668146014,
-0.02152995765209198,
-0.0030055863317102194,
0.010468533262610435,
-0.03168484568595886,
0.04864470660686493,
0.01477972511202097,
-0.05146859213709831,
0.02315714955329895,
-0.013176391832530499,
0.030583538115024567,
0.028421850875020027,
0.007736770901829004,
-0.0618562214076519,
0.0018378801178187132,
-0.03354768082499504,
-0.01110871136188507,
-0.01029497291892767,
0.01342566218227148,
0.06590195000171661,
-0.038313329219818115,
-0.022757066413760185,
0.010294370353221893,
-0.06829241663217545,
-0.032276373356580734,
-0.012920836918056011,
0.020445479080080986,
0.01889633573591709,
-0.03428439423441887,
0.009271535091102123,
0.013432107865810394,
-0.04787900298833847,
-0.018522780388593674,
-0.01995254121720791,
-0.049080949276685715,
0.03778615966439247,
-0.00027113110991194844,
0.05231655389070511,
-0.031148452311754227,
-0.020949168130755424,
0.06373031437397003,
0.010179837234318256,
-0.015745321288704872,
-0.01391355600208044,
0.0057324510999023914,
-0.02422771230340004,
-0.011058145202696323,
0.0330045148730278,
0.00738961948081851,
0.011940025724470615,
0.028823642060160637,
0.06632773578166962,
0.03782375901937485,
0.027031609788537025,
-0.01590610295534134,
-0.014791343361139297,
-0.003964642994105816,
0.025778446346521378,
0.0067849732004106045,
0.035377878695726395,
0.03435325622558594,
-0.056344274431467056,
-0.003804730251431465,
0.021126097068190575,
0.0626252219080925,
0.007977588102221489,
-0.04138454422354698,
0.055882278829813004,
-0.007266131229698658,
0.009876640513539314,
-0.009954661130905151,
0.022043291479349136,
-0.007159154862165451,
0.015547468326985836,
0.007937668822705746,
-0.003363900352269411,
0.02158321440219879,
0.0013468937249854207,
0.0030867878813296556,
0.002275318605825305,
-0.006411383859813213,
-0.03668355941772461,
0.0176850538700819,
-0.009968524798750877,
-0.03509494289755821,
0.03269553929567337,
-0.01730821281671524,
-0.02698398567736149,
0.026164133101701736,
0.018179187551140785,
-0.006306589115411043,
-0.0158300269395113,
-0.039998576045036316,
0.010229814797639847,
-0.061012960970401764,
0.011025692336261272,
0.0255531445145607,
0.020314838737249374,
0.004917844198644161,
0.052031952887773514,
0.01845576800405979,
0.009935234673321247,
0.02854493074119091,
-0.03301245719194412,
-0.06938305497169495,
-0.007600748911499977,
-0.04644668102264404,
-0.036617424339056015,
-0.024549465626478195,
-0.023821888491511345,
-0.03705037757754326,
-0.010077476501464844,
-0.024253342300653458,
-0.05611313134431839,
-0.024203453212976456,
-0.03722693771123886,
-0.015012779273092747,
-0.033754654228687286,
-0.034125011414289474,
-0.004027079790830612,
0.027422646060585976,
0.021747391670942307,
-0.029904529452323914,
0.05708989128470421,
0.03376917913556099,
0.014323815703392029,
-0.045481953769922256,
-0.024156084284186363,
-0.010747571475803852,
0.023550424724817276,
0.00483057601377368,
0.02826686203479767,
0.003708647796884179,
-0.031777363270521164,
0.01402032095938921,
0.03749218210577965,
0.00013636655057780445,
-0.004687110893428326,
0.0012726070126518607,
-0.013753295876085758,
-0.005804575979709625,
-0.01174783706665039,
-0.016548320651054382,
0.055325500667095184,
0.025562254711985588,
0.007719540968537331,
0.05770910903811455,
0.007783978711813688,
-0.017694206908345222,
0.022586185485124588,
0.04771173745393753,
-0.008075617253780365,
-0.013548321090638638,
-0.03625490143895149,
-0.021567804738879204,
-0.03509127348661423,
-0.03862401470541954,
0.04272550716996193,
-0.019165875390172005,
-0.02694774605333805,
0.006510707549750805,
-0.012710786424577236,
0.013566353358328342,
-0.011736628599464893,
-0.01861516945064068,
-0.021157903596758842,
-0.0036357755307108164,
-0.012745298445224762,
0.00356065621599555,
-0.008914321660995483,
0.03862818330526352,
0.043223362416028976,
-0.013027273118495941,
-0.017381060868501663,
-0.07153189182281494,
0.02537652477622032,
0.020740531384944916,
0.033142391592264175,
-0.047107744961977005,
0.004650581628084183,
-0.0480380617082119,
-0.023302817717194557,
0.046661488711833954,
-0.03789765387773514,
0.0047116465866565704,
-0.02269977331161499,
-0.02199864573776722,
0.004765604622662067,
-0.0019248491153120995,
-0.003385275835171342,
0.0017307514790445566,
0.0024415398947894573,
-0.017441874369978905,
-0.016827762126922607,
0.04262172430753708,
-0.025818534195423126,
-0.02469552494585514,
0.022350706160068512,
0.053290944546461105,
0.009090576320886612,
0.012859986163675785,
-0.013620118610560894,
0.021818706765770912,
-0.005452379584312439,
-0.03023465722799301,
0.05490614473819733,
0.0016055041924118996,
-0.01042470708489418,
0.024347521364688873,
-0.03136385232210159,
-0.01091325655579567,
0.019794125109910965,
-0.0042193070985376835,
-0.027152948081493378,
0.006790061481297016,
-0.014676164835691452,
0.01655578427016735,
0.013089091517031193,
-0.003620339557528496,
0.0607789121568203,
0.04590277001261711,
-0.00420405063778162,
-0.0007901507196947932,
-0.022602519020438194,
0.03578692302107811,
-0.05062055215239525,
-0.00697616022080183,
-0.006586151197552681,
0.005930536426603794,
-0.029688630253076553,
0.06565763801336288,
-0.035653792321681976,
-0.003403240581974387,
-0.005230761133134365,
-0.010124105960130692,
-0.005600159987807274,
0.052918441593647,
0.018652690574526787,
0.028883159160614014,
-0.016915662214159966,
0.018966851755976677,
-0.038527242839336395,
-0.03956853598356247,
0.015537180937826633,
0.001397930784150958,
-0.06010930612683296,
0.03689536824822426,
-0.0044631981290876865,
-0.001458158832974732,
0.008043691515922546,
-0.005984192714095116,
0.033051278442144394,
-0.02998177520930767,
-0.0023436699993908405,
-0.016900964081287384,
0.006361273117363453,
0.03882690146565437,
-0.07094063609838486,
-0.034435246139764786,
-0.015300048515200615,
-0.03522265702486038,
0.025225790217518806,
-0.05559631064534187,
0.03852527216076851,
-0.009935220703482628,
0.027948232367634773,
-0.10580162703990936,
-0.041389912366867065,
0.037885889410972595,
0.0001812322880141437,
-0.0019223983399569988,
-0.05171499028801918,
0.02410392090678215,
-0.03920963779091835,
-0.000876365986187011,
-0.02843441627919674,
0.061911728233098984,
0.016391437500715256,
-0.038323648273944855,
-0.006005497183650732,
-0.02423916570842266,
0.04045325890183449,
-0.012059079483151436,
0.011322781443595886,
-0.0070825363509356976,
-0.00229501910507679,
-0.011162102222442627,
-0.01604733057320118,
0.06967388093471527,
-0.032085977494716644,
-0.028723813593387604,
-0.022579137235879898,
-0.03449426591396332,
0.027355767786502838,
-0.05957997962832451,
-0.01507169846445322,
0.033764783293008804,
0.016242947429418564,
0.02401936799287796,
-0.003852197201922536,
0.03220214322209358,
-0.031802717596292496,
0.005972415208816528,
-0.02997085079550743,
0.007973389700055122,
0.0009506608475930989,
-0.055449750274419785,
0.04456956684589386,
0.002095925621688366,
0.02247978374361992,
0.008557875640690327,
0.06698191910982132,
0.017006173729896545,
-0.010044536553323269,
0.007777805905789137,
-0.00162682740483433,
0.019181028008461,
-0.011869235895574093,
-0.003461222629994154,
-0.024967443197965622,
0.006090905983000994,
-0.030519966036081314,
0.00602699862793088,
0.0094305370002985,
0.014466891065239906,
0.06647083163261414,
-0.03248433768749237,
0.06726715713739395,
-0.022889431565999985,
-0.019522711634635925,
-0.0006713808979839087,
-0.03236778825521469,
-0.0024177818559110165,
0.00029902136884629726,
0.0002139421267202124,
0.013215611688792706,
-0.06556840240955353,
0.014920327812433243,
0.02384183555841446,
0.06374113261699677,
0.0006418436532840133,
0.0066231535747647285,
0.02535398304462433,
0.018831836059689522,
0.01833716779947281,
0.009203452616930008,
-0.04737914726138115,
0.01961977779865265,
-0.007936212234199047,
0.03509850427508354,
0.014730837196111679,
-0.016742048785090446,
0.05387984588742256,
-0.007353594526648521,
0.007620253600180149,
-0.011239389888942242,
-0.007851985283195972,
-0.03952139988541603,
-0.009386688470840454,
-0.020137887448072433,
0.05001116916537285,
0.0017987024039030075,
0.0010196915827691555,
-0.018194392323493958,
0.026325730606913567,
0.02573203481733799,
-0.012471010908484459,
-0.08304861187934875,
-0.050397761166095734,
-0.03413042426109314,
-0.030458524823188782,
0.059813614934682846,
0.0227629654109478,
-0.03763347119092941,
-0.04132378473877907,
0.005063578020781279,
-0.019944023340940475,
0.012365888804197311,
0.022365408018231392,
-0.008003730326890945,
0.09065623581409454,
0.025188932195305824,
0.010509194806218147,
-0.034815605729818344,
0.018181022256612778,
0.08269384503364563,
0.0197832640260458,
0.004183485638350248,
-0.037545185536146164,
0.025579089298844337,
-0.02553885616362095,
-0.025882024317979813,
-0.04018028452992439,
0.05219028517603874,
0.01762275956571102,
0.04871378466486931,
0.008815942332148552,
0.08254820108413696,
0.0029897871427237988,
-0.02730044536292553,
0.06844080239534378,
-0.02131262794137001,
-0.03745463490486145,
0.008893580175936222,
0.026635244488716125,
-0.009284560568630695,
0.01981898956000805,
-0.032390255481004715,
0.007638612762093544,
-0.019840890541672707,
0.00636143796145916,
-0.011859691701829433,
-0.043698132038116455,
-0.013886078260838985,
0.019648581743240356,
-0.09351366758346558,
0.010045187547802925,
0.03764032945036888,
-0.019131110981106758,
-0.07055698335170746,
0.006599430926144123,
0.017977887764573097,
-0.033349357545375824,
0.022515183314681053,
-0.007926943711936474,
0.005644598975777626,
0.038719553500413895,
0.001840911339968443,
0.005372312851250172,
-0.03160600736737251,
0.006930068135261536,
-0.016312945634126663,
0.033539868891239166,
-0.0007776904967613518,
0.012426679022610188,
0.02509719878435135,
0.016395095735788345,
-0.009546872228384018,
-0.05155365169048309,
-0.00273770815692842,
0.0156598798930645,
0.00784026738256216,
0.009062943048775196,
-0.016148170456290245,
-0.028762131929397583,
-0.004131628666073084,
-0.009543163701891899,
0.036903150379657745,
0.007336229085922241,
0.025329288095235825,
0.0042409938760101795,
-0.029432406648993492,
0.04341008886694908,
-0.06495102494955063,
0.013766278512775898,
-0.014159014448523521,
0.021545637398958206,
-0.05076882615685463,
0.028354737907648087,
0.0049511827528476715,
0.04087305814027786,
0.008920179679989815,
-0.02318156510591507,
-0.003616926958784461,
-0.0008220789022743702,
-0.050002571195364,
0.025944259017705917,
-0.010519073344767094,
-0.02614501491189003,
-0.019381286576390266,
0.01658604107797146,
0.07975895702838898,
0.023511111736297607,
-0.02972828596830368,
-0.01911286823451519,
-0.05092308670282364,
0.020917054265737534,
0.02848396822810173,
-0.01530885137617588,
-0.003644797718152404,
0.008904065005481243,
-0.018834399059414864,
-0.019649814814329147,
-0.023822326213121414,
0.00818141084164381,
0.04801696166396141,
-0.007987638004124165,
-0.008340244181454182,
0.006234550382941961,
-0.03691234439611435,
0.037531111389398575,
0.0256485678255558,
-0.033071015030145645,
-0.000558480795007199,
-0.000730290194042027,
0.010770691558718681,
-0.01777094416320324,
-0.02933044172823429,
-0.025169992819428444,
0.014549105428159237,
-0.002635821932926774,
0.01839364506304264,
-0.034128833562135696,
0.009971849620342255,
0.004989935085177422,
0.03083634003996849,
-0.06245935708284378,
-0.010400159284472466,
-0.07315618544816971,
0.02040824666619301,
-0.003281025215983391,
-0.0017461811657994986,
-0.033039484173059464,
0.01051214151084423,
-0.026357684284448624,
-0.03886180743575096,
0.029981888830661774,
-0.01317539345473051,
-0.026826266199350357,
0.001962214708328247,
0.020938178524374962,
-0.021494949236512184,
0.04687652364373207,
-0.022499166429042816,
-0.0200435109436512,
0.01976063847541809,
-0.035197217017412186,
-0.0629417896270752,
0.0030143389012664557,
-0.019482651725411415,
0.048838697373867035,
0.022324496880173683,
-0.0004157104413025081,
-0.02086767926812172,
0.061897069215774536,
-0.01947292499244213,
0.01019141636788845,
0.008379556238651276,
-0.011342436075210571,
0.0012282233219593763,
-0.030539559200406075,
0.0025662966072559357,
-0.012990990653634071,
-0.016378413885831833,
0.030806096270680428,
0.0380571112036705,
-0.007317554671317339,
0.00028949425905011594,
-0.009129040874540806,
-0.025567902252078056,
-0.011593888513743877,
0.01783984899520874,
0.021785898134112358,
0.043409496545791626,
0.05920042842626572,
-0.0433441624045372,
0.06083618849515915,
0.020541952922940254,
0.005031074397265911,
-0.10894432663917542,
0.02882828563451767,
-0.01751144975423813,
0.010281406342983246,
0.016690174117684364,
-0.04846152663230896,
0.022688331082463264,
0.016077760607004166,
-0.06323723495006561,
0.024129047989845276,
-0.06294242292642593,
-0.02958403155207634,
-0.009676016867160797,
-0.008767550811171532,
0.02691560797393322,
0.06554234027862549,
0.05537060648202896,
0.040172915905714035,
0.011471468023955822,
-0.011886678636074066,
-0.011263127438724041,
-0.012697955593466759,
-0.007804814726114273,
0.012220993638038635,
-0.017519213259220123,
0.024843543767929077,
0.05148325487971306,
-0.0019695772789418697,
-0.023818988353013992,
0.03809644654393196,
-0.000635791860986501,
0.016406109556555748,
0.02281113900244236,
-0.020074833184480667,
-0.0026138601824641228,
-0.006488791201263666,
0.0059180050157010555,
-0.015477300621569157,
-0.020951908081769943,
0.027120959013700485,
0.00515174213796854,
0.02011788636445999,
-0.017728373408317566,
-0.028051668778061867,
0.025040235370397568,
-0.07569561898708344,
-0.02639055997133255,
-0.0031806635670363903,
0.00789047870784998,
0.012169023044407368,
-0.007127388380467892,
0.018760820850729942,
0.045956578105688095,
-0.009928176179528236,
-0.0012920154258608818,
-0.0067467098124325275,
-0.013199220411479473,
0.013617370277643204,
0.017253953963518143,
-0.023817000910639763,
0.005702928639948368,
0.010045698843896389,
0.004730981308966875,
-0.02091234177350998,
-0.0032484238035976887,
0.038030534982681274,
-0.05845576152205467,
-0.019928133115172386,
0.013810273259878159,
-0.025770632550120354,
0.013770608231425285,
-0.031502414494752884,
-0.034902241080999374,
0.04727755859494209,
0.030021535232663155,
0.013270864263176918,
-0.010422577150166035,
-0.028828207403421402,
-0.029494041576981544,
-0.06053829938173294,
0.0231977179646492,
-0.0017037020297721028,
-0.01094524934887886,
-0.04683321341872215,
-0.05082029104232788,
-0.023911239579319954,
-0.010030722245573997,
0.07271141558885574,
-0.015579729340970516,
-0.009971431456506252,
-0.0013709975173696876,
0.003208413952961564,
0.030638664960861206,
-0.03786884993314743,
-0.016526315361261368,
-0.002127182437106967,
-0.04136863350868225,
0.001150453113950789,
-0.039461180567741394,
-0.032434072345495224,
0.01922127790749073,
0.01344237569719553,
-0.00691926758736372,
0.07086130976676941,
0.0312371626496315,
-0.0232734102755785,
0.056418873369693756,
0.02745259553194046,
-0.004992689471691847,
0.05393209308385849,
-0.0076250797137618065,
0.010479392483830452,
0.053106553852558136,
0.026250245049595833,
-0.031125735491514206,
0.04297403246164322,
-0.0316590890288353,
0.001177846104837954,
-0.0014651380479335785,
0.02087223343551159,
0.016222266480326653,
-0.03632501885294914,
-0.028475744649767876,
0.05984830483794212,
-0.01871318928897381,
-0.0003900342562701553,
0.035862036049366,
0.007405337877571583,
0.010791311040520668,
-0.019581105560064316,
0.01578955352306366,
0.009858277626335621,
0.03439764678478241,
0.02097931131720543,
0.052214015275239944,
0.015867535024881363,
0.007985591888427734,
0.04821251705288887,
0.02056152932345867,
0.02091287635266781,
0.011792800389230251,
-0.022769110277295113,
0.05099142715334892,
-0.04615258425474167,
-0.0036166838835924864,
-0.036153826862573624,
-0.038397837430238724,
0.036593805998563766,
0.05190448835492134,
-0.01626838743686676,
0.08974375575780869,
-0.04280400276184082,
0.041142385452985764,
0.01939791813492775,
-0.007407771423459053,
-0.035046979784965515,
0.010596536099910736,
0.009150868281722069,
0.011505167931318283,
0.0018250372959300876,
0.0018564710626378655,
0.013524802401661873,
0.01928667165338993,
0.017284300178289413,
-0.009476497769355774,
-0.0027283737435936928,
-0.007667364086955786,
-0.015945816412568092,
-0.020999709144234657,
0.029249999672174454,
-0.011427619494497776,
0.007629760541021824,
0.06253247708082199,
0.05887765437364578,
0.02618415094912052,
-0.0036133481189608574,
0.016416111961007118,
-0.05709445849061012,
0.05676809698343277,
-0.04730799421668053,
-0.01765204593539238,
-0.02526193857192993,
-0.0041271536611020565,
-0.026029469445347786,
-0.02738322876393795
] |
<p>To derive Bose-Einstein and Fermi-Dirac distribution, we need to apply grand canonical ensemble:$Z(z,V,T)=\displaystyle\sum_{N=0}^{\infty}[z^N\sideset{}{'}\sum\limits_{\{n_j\}}e^{-\beta\sum\limits_{j}n_j\epsilon_j}]$. There is a constraint $\sideset{}{'}\sum\limits_{\{n_j\}}$ for quantum particles(bosons and fermions) in grand canonical ensemble:$\sum\limits_{j}n_j=N$, but why is there no such a constraint for classical particels?</p> | 1,541 | [
-0.019576845690608025,
-0.022435536608099937,
0.015688974410295486,
-0.01268844585865736,
0.053540538996458054,
-0.01729128509759903,
-0.02456643246114254,
-0.01040311437100172,
0.009827735833823681,
-0.04125211015343666,
0.055850207805633545,
0.008192882873117924,
0.06752152740955353,
0.0074103944934904575,
0.008454067632555962,
0.004905863665044308,
-0.014951648190617561,
0.004537571687251329,
-0.04888353496789932,
-0.0014117765240371227,
-0.025694850832223892,
0.08407173305749893,
0.024835089221596718,
-0.0009149257093667984,
-0.013258496299386024,
0.023167220875620842,
-0.021230287849903107,
0.009614499285817146,
0.022110484540462494,
0.05210883915424347,
-0.018877340480685234,
-0.024459684267640114,
0.06311168521642685,
0.028402205556631088,
0.012932570651173592,
-0.004071689676493406,
-0.0695594921708107,
-0.0671132355928421,
-0.04771760478615761,
-0.017007173970341682,
-0.06212828680872917,
-0.017198096960783005,
-0.047646090388298035,
0.01390810962766409,
-0.0362156443297863,
0.042903583496809006,
0.018068455159664154,
-0.031458064913749695,
0.07231089472770691,
-0.05912861227989197,
0.025113891810178757,
0.03825150802731514,
0.028275636956095695,
0.004001657944172621,
-0.006543611641973257,
-0.03119034320116043,
0.037034302949905396,
0.09089044481515884,
0.01748180016875267,
-0.024197973310947418,
-0.01446736790239811,
-0.02999887615442276,
0.029311224818229675,
-0.016953811049461365,
0.013311024755239487,
0.03968692943453789,
0.029872899875044823,
-0.0355134941637516,
0.0011139620328322053,
-0.012688406743109226,
0.031135138124227524,
0.02363426797091961,
0.029054882004857063,
-0.012500549666583538,
0.007259084843099117,
0.00756935216486454,
-0.007978667505085468,
0.014509566128253937,
0.040190163999795914,
-0.005965786520391703,
0.004380405880510807,
0.029294051229953766,
0.03310893476009369,
-0.006367258261889219,
0.01686619594693184,
-0.03552279621362686,
0.0621035173535347,
-0.049065377563238144,
-0.011110786348581314,
0.033781759440898895,
-0.013149458914995193,
0.009611054323613644,
0.07538139075040817,
-0.0009631620487198234,
-0.0620683878660202,
0.01786608248949051,
0.0018399894470348954,
0.020536821335554123,
-0.007954251952469349,
-0.04105397313833237,
0.02069832943379879,
-0.01615891046822071,
0.0190237145870924,
0.06814450025558472,
-0.007155373692512512,
0.004210451617836952,
-0.05073738843202591,
-0.014818072319030762,
-0.02821243181824684,
-0.00715505750849843,
-0.03489486500620842,
-0.0029215009417384863,
-0.023012738674879074,
0.029896914958953857,
0.0056414916180074215,
0.0018408067990094423,
0.004473160486668348,
-0.020551281049847603,
0.05831585451960564,
0.060340166091918945,
-0.007924499921500683,
0.01974761113524437,
-0.009427979588508606,
-0.019201720133423805,
-0.0580945760011673,
0.0029930362943559885,
0.05831991508603096,
0.0064820582047104836,
-0.044612277299165726,
0.02542249858379364,
0.005362398456782103,
-0.009466405026614666,
0.021611126139760017,
0.03557547554373741,
-0.010208403691649437,
-0.024991150945425034,
-0.09867575019598007,
-0.02899983339011669,
0.040526002645492554,
-0.038749657571315765,
-0.03372783213853836,
-0.06824937462806702,
0.012285564094781876,
0.02510729804635048,
0.09133125841617584,
-0.021107245236635208,
0.06848848611116409,
-0.02025710418820381,
0.029877126216888428,
0.02328258939087391,
-0.021810388192534447,
-0.030164504423737526,
-0.010675573721528053,
-0.01983056589961052,
-0.02308354526758194,
-0.06518121063709259,
0.06294763833284378,
0.02139335870742798,
0.02242649532854557,
0.018208999186754227,
0.014279089868068695,
-0.017995258793234825,
-0.0025376894045621157,
0.009378723800182343,
0.006340693682432175,
-0.07557573914527893,
0.04431694373488426,
0.02761843055486679,
0.03767535835504532,
0.02902272529900074,
-0.022189658135175705,
0.02146296016871929,
-0.003235144540667534,
0.05219054967164993,
-0.001612500287592411,
-0.05270581692457199,
-0.035342346876859665,
0.016231801360845566,
0.013888354413211346,
0.000821826746687293,
-0.021630359813570976,
-0.042672500014305115,
-0.010594073683023453,
0.026028629392385483,
-0.002262817695736885,
0.04662466421723366,
0.026217766106128693,
-0.02075919881463051,
-0.0051598683930933475,
-0.05751408636569977,
-0.008650568313896656,
-0.075422003865242,
0.00739154452458024,
0.026305411010980606,
-0.045735422521829605,
0.04680635780096054,
0.028620198369026184,
0.021454518660902977,
0.009025131352245808,
-0.03364123776555061,
0.008198992349207401,
0.03853577747941017,
0.00485561927780509,
-0.0199261624366045,
0.029618488624691963,
0.02674405835568905,
0.054889608174562454,
0.0002546455943956971,
0.03388429433107376,
-0.007152849342674017,
-0.0947674959897995,
0.012574666179716587,
-0.027447184547781944,
0.04623212665319443,
0.044084519147872925,
-0.014068758115172386,
0.018531078472733498,
-0.011286563239991665,
-0.04870167002081871,
0.046685654670000076,
-0.0061506833881139755,
0.033678751438856125,
0.045164939016103745,
-0.010272474028170109,
-0.019447514787316322,
0.05247821286320686,
0.0031017607543617487,
0.028797555714845657,
-0.022049346938729286,
-0.002019354375079274,
-0.04213642328977585,
-0.006870265118777752,
0.05408705770969391,
0.06701365858316422,
-0.03382466360926628,
0.017431480810046196,
0.026631372049450874,
0.020601483061909676,
0.0036225812509655952,
-0.008614829741418362,
-0.023047400638461113,
-0.05114546790719032,
0.034839026629924774,
-0.006294877268373966,
0.020701130852103233,
-0.034127525985240936,
-0.00007827157969586551,
0.008588881231844425,
0.004148424137383699,
-0.05067973956465721,
-0.04420848563313484,
0.014015245251357555,
0.01664610207080841,
-0.023015785962343216,
-0.020804760977625847,
-0.03247964009642601,
0.01832941733300686,
-0.0307218749076128,
0.04477819800376892,
0.019924534484744072,
0.008335514925420284,
-0.0030790120363235474,
-0.016194337978959084,
-0.03906198963522911,
0.004365214612334967,
0.027176909148693085,
-0.030417969450354576,
-0.02545543760061264,
0.01837870106101036,
-0.014389296993613243,
-0.01228672917932272,
0.007275054696947336,
-0.012903578579425812,
0.00343734840862453,
0.03286784514784813,
0.025618605315685272,
0.01968487724661827,
0.02966793067753315,
0.01025860570371151,
-0.040687162429094315,
0.01228550635278225,
0.005420910660177469,
0.024447256699204445,
0.0732300728559494,
-0.03333432599902153,
-0.0051550306379795074,
-0.049853239208459854,
-0.021910354495048523,
0.043735142797231674,
-0.010239756666123867,
0.047690097242593765,
0.0015245710965245962,
-0.027882341295480728,
-0.04256562516093254,
-0.03987938538193703,
0.00010770198423415422,
-0.034353107213974,
-0.046893518418073654,
-0.008157833479344845,
0.0670693963766098,
-0.0061390334740281105,
-0.028736086562275887,
-0.010379964485764503,
-0.016973940655589104,
-0.08628422021865845,
-0.008649919182062149,
-0.0020106264855712652,
0.019969245418906212,
-0.05584144964814186,
0.04129527509212494,
0.025569895282387733,
-0.029688760638237,
-0.003938458859920502,
-0.062411483377218246,
-0.040946293622255325,
0.006375259719789028,
-0.007908444851636887,
0.042269017547369,
0.02433210425078869,
-0.017226869240403175,
0.06161603704094887,
0.010329009033739567,
-0.024016743525862694,
0.01002646703273058,
-0.016705989837646484,
-0.007740589324384928,
-0.06014864146709442,
0.009417939931154251,
0.03266807645559311,
0.0023668219801038504,
0.05385691300034523,
0.037247464060783386,
0.005526599939912558,
0.010527733713388443,
0.006951244082301855,
-0.004995076917111874,
0.01963544450700283,
-0.018617751076817513,
0.010694155469536781,
0.03850223869085312,
0.003053523600101471,
-0.014682872220873833,
-0.012194889597594738,
0.009025371633470058,
0.024786384776234627,
0.010336953215301037,
-0.09558412432670593,
0.03136235103011131,
0.013855192810297012,
0.02695067971944809,
-0.03392639011144638,
0.0454024001955986,
-0.007377519737929106,
-0.033736035227775574,
0.031944390386343,
0.025844311341643333,
0.015069839544594288,
-0.016274256631731987,
-0.009040063247084618,
0.040482308715581894,
0.021204451099038124,
-0.023526476696133614,
-0.030501337721943855,
-0.01997997984290123,
-0.029124349355697632,
0.014684750698506832,
-0.04036325961351395,
0.014753284864127636,
0.028530988842248917,
0.04097035154700279,
0.023781858384609222,
-0.04305524006485939,
-0.037654150277376175,
-0.018681013956665993,
-0.03384498506784439,
0.003356875851750374,
-0.0518653467297554,
0.04960063099861145,
0.017909273505210876,
0.04811617732048035,
-0.00041667072218842804,
0.0099040437489748,
0.011972744017839432,
-0.02714093029499054,
-0.08003245294094086,
-0.005038522183895111,
0.004620988853275776,
-0.019070828333497047,
-0.000029276894565555267,
-0.011636392213404179,
0.019197456538677216,
-0.02920980378985405,
-0.002793298801407218,
-0.029524654150009155,
0.022376378998160362,
-0.010866613127291203,
0.012347124516963959,
-0.028906038030982018,
-0.0448882095515728,
-0.0016046372475102544,
0.028084663674235344,
-0.015654297545552254,
-0.01488183531910181,
0.016745373606681824,
0.057460762560367584,
-0.008885957300662994,
-0.006129696499556303,
-0.015523171052336693,
0.06368754059076309,
0.001786255743354559,
0.04506774991750717,
0.03735417500138283,
0.01759478636085987,
-0.020131023600697517,
-0.02672835998237133,
0.016696972772479057,
0.06928905099630356,
0.022617554292082787,
0.01970459148287773,
0.013526367023587227,
-0.04843980446457863,
-0.004417198710143566,
0.015010139904916286,
0.04147941991686821,
0.03168216347694397,
-0.00840804260224104,
0.03275901824235916,
0.011033889837563038,
0.01131497323513031,
0.011639991775155067,
0.07163963466882706,
-0.008946234360337257,
-0.0509168803691864,
-0.02966180257499218,
0.030996449291706085,
-0.03782860189676285,
0.004392804577946663,
-0.007319767493754625,
-0.009436012245714664,
-0.04448305070400238,
0.002216694410890341,
0.024952173233032227,
0.028350742533802986,
-0.01375198271125555,
-0.005002801772207022,
0.01817307434976101,
0.04303331300616264,
0.009284719824790955,
-0.03213631361722946,
0.022122491151094437,
0.027020050212740898,
0.04826195165514946,
-0.021464090794324875,
-0.03562454506754875,
-0.030871955677866936,
0.0007857502205297351,
0.01730504259467125,
0.02639463171362877,
-0.00638857576996088,
-0.02020318992435932,
-0.07896404713392258,
0.008945295587182045,
0.05069154500961304,
-0.032516494393348694,
-0.002591146854683757,
-0.04160783812403679,
-0.007275518495589495,
-0.0038119833916425705,
-0.047091878950595856,
0.006657748948782682,
0.052744582295417786,
0.003764327382668853,
0.009365333244204521,
-0.060290805995464325,
-0.0002811424492392689,
0.005396427121013403,
0.0139161990955472,
0.02442009001970291,
0.0420449860394001,
0.008634913712739944,
0.017339635640382767,
0.0086279371753335,
0.025596119463443756,
-0.01614188961684704,
-0.09516999125480652,
-0.015535207465291023,
-0.018128734081983566,
0.0220757108181715,
0.03828192874789238,
-0.039191875606775284,
-0.0474364347755909,
-0.009461848996579647,
0.013112567365169525,
0.013537180610001087,
0.01922144554555416,
0.01109483651816845,
0.06432358175516129,
0.0049373432993888855,
-0.0023312775883823633,
0.06820184737443924,
0.017376650124788284,
-0.0015545381465926766,
0.011214662343263626,
-0.021622654050588608,
0.011787875555455685,
-0.00210387771949172,
0.007785452529788017,
-0.027978137135505676,
0.02348741702735424,
0.0033563394099473953,
0.007105415686964989,
-0.042451027780771255,
-0.0017264648340642452,
0.02902991883456707,
-0.06321411579847336,
-0.003905216231942177,
-0.012418434023857117,
0.01578984409570694,
-0.010690413415431976,
-0.008980782702565193,
0.02416279725730419,
0.01909618265926838,
-0.007629496976733208,
0.05537639930844307,
0.025150233879685402,
-0.0001647054887143895,
0.033834487199783325,
-0.00036516107502393425,
0.02791220135986805,
-0.01142516452819109,
-0.005133914295583963,
0.0600360631942749,
-0.02758129872381687,
0.014015351422131062,
0.0028042453341186047,
0.031209170818328857,
0.026716157793998718,
-0.00853678211569786,
-0.024008994922041893,
-0.023786332458257675,
-0.04359304532408714,
0.018159106373786926,
-0.041427917778491974,
-0.005287789739668369,
0.027791554108262062,
-0.0023887099232524633,
-0.06725069880485535,
-0.010167505592107773,
0.01666523516178131,
0.006322946399450302,
-0.024589398875832558,
-0.011085501872003078,
-0.020589139312505722,
-0.0064406064338982105,
-0.03835093975067139,
0.0018359238747507334,
0.03753529489040375,
0.0155791612342,
-0.04814211279153824,
-0.0032180945854634047,
0.08436901867389679,
0.045953068882226944,
-0.019969897344708443,
0.009889069013297558,
-0.006277557462453842,
-0.0279270950704813,
0.025084253400564194,
0.01194681040942669,
0.05448490008711815,
-0.02057698555290699,
-0.03393718972802162,
0.023026160895824432,
-0.0027945542242377996,
0.011471630074083805,
-0.003118843073025346,
-0.019632890820503235,
0.019188687205314636,
-0.024967359378933907,
-0.018153872340917587,
-0.0025299880653619766,
-0.0069930944591760635,
0.001961079193279147,
0.02494613267481327,
-0.017561938613653183,
-0.012926342897117138,
-0.03612355515360832,
-0.03669947385787964,
0.05924369767308235,
-0.02625521831214428,
-0.016874823719263077,
-0.004904084838926792,
0.043514177203178406,
0.02407381497323513,
-0.02638782560825348,
0.022984487935900688,
-0.029122833162546158,
0.025441749021410942,
0.021670958027243614,
-0.008851888589560986,
0.056388452649116516,
0.013765202835202217,
-0.00811067409813404,
-0.027164699509739876,
-0.04493565484881401,
0.05556771531701088,
0.024143846705555916,
-0.012080172076821327,
0.054845064878463745,
0.02451571635901928,
-0.00846308283507824,
-0.02062082476913929,
-0.038500938564538956,
0.006058285478502512,
0.05523620545864105,
-0.006983334198594093,
0.014097812585532665,
-0.008054153062403202,
-0.019787458702921867,
0.013142390176653862,
0.024256262928247452,
-0.0230436809360981,
0.026285704225301743,
0.018705569207668304,
0.006959443911910057,
-0.009630255401134491,
-0.02696123905479908,
-0.024575382471084595,
0.04922863095998764,
-0.04377919062972069,
0.03222370147705078,
0.017184237018227577,
-0.018001507967710495,
0.009389029815793037,
0.015264770947396755,
0.001071603735908866,
-0.05939900875091553,
-0.008454566821455956,
0.0020385116804391146,
0.02987555041909218,
0.03576524183154106,
0.019190127030014992,
0.030257759615778923,
-0.014036446809768677,
0.021955212578177452,
0.004830827936530113,
0.004251881968230009,
0.0013391377869993448,
-0.05111202597618103,
-0.02637072652578354,
-0.05521564930677414,
-0.050477586686611176,
0.03465111926198006,
0.012364426627755165,
-0.02575463429093361,
-0.003337416797876358,
-0.013264007866382599,
0.02936188317835331,
0.023828769102692604,
-0.00006856740219518542,
0.008683403953909874,
0.0451425164937973,
0.0031951412092894316,
-0.014768312685191631,
-0.011092286556959152,
0.032247692346572876,
0.16508032381534576,
0.03622748702764511,
0.03720951825380325,
-0.05396031588315964,
-0.021252796053886414,
0.005632149986922741,
0.006964176893234253,
-0.01923353038728237,
0.008553288877010345,
-0.018268030136823654,
0.0058294013142585754,
-0.013709885068237782,
0.05433850362896919,
0.02188398875296116,
-0.029518090188503265,
0.02885155938565731,
-0.06433263421058655,
-0.02523079700767994,
0.021944090723991394,
0.02951016277074814,
-0.022109027951955795,
0.011254845187067986,
-0.05281264707446098,
-0.015117920935153961,
-0.006676673889160156,
0.033398643136024475,
-0.030527254566550255,
-0.04937208443880081,
-0.004492131061851978,
-0.01592685654759407,
-0.02404697798192501,
0.0018336833454668522,
0.046265918761491776,
0.00003944693526136689,
0.003999482840299606,
-0.0491684190928936,
0.002765738172456622,
-0.027667975053191185,
0.025858676061034203,
0.0071080825291574,
0.008581443689763546,
0.0242262352257967,
-0.002946424065157771,
0.03211456909775734,
-0.008693545125424862,
-0.017474928870797157,
-0.020916448906064034,
0.07116135954856873,
-0.058633897453546524,
-0.03417905792593956,
0.006637346465140581,
-0.04726329445838928,
0.001920000766403973,
-0.03081335499882698,
0.021522747352719307,
-0.03396341949701309,
0.015873845666646957,
-0.003872812259942293,
-0.016787810251116753,
-0.029544003307819366,
0.02487456612288952,
-0.0038878710474818945,
0.04306187853217125,
-0.03640500828623772,
-0.03049813210964203,
0.02906825952231884,
0.014557518064975739,
0.01885439269244671,
-0.01799638755619526,
0.014497700147330761,
-0.01875518262386322,
-0.011320723220705986,
-0.07465751469135284,
-0.05246090516448021,
0.008719438686966896,
-0.02360118366777897,
0.05223647132515907,
-0.0037613846361637115,
0.00294556119479239,
-0.01230106595903635,
-0.034713711589574814,
0.02323385514318943,
-0.0335378460586071,
-0.035088375210762024,
-0.04634978249669075,
0.007777190301567316,
-0.016936030238866806,
0.06377563625574112,
-0.0629144087433815,
0.01338931079953909,
-0.0008833764586597681,
0.02569969929754734,
0.014693007804453373,
-0.02329612337052822,
0.002274101134389639,
-0.008842806331813335,
-0.00876412633806467,
0.021255139261484146,
-0.01570718362927437,
0.01792495884001255,
0.010629905387759209,
0.03524006903171539,
-0.025228137150406837,
0.0347452238202095,
0.004852058831602335,
-0.0011829647701233625,
0.029162762686610222,
-0.030730584636330605,
-0.0005176921258680522,
0.045717913657426834,
0.026544664055109024,
-0.06033309921622276,
-0.004552565049380064,
-0.05056668072938919,
0.004127344582229853,
0.027773158624768257,
0.020371394231915474,
-0.043422214686870575,
-0.0251168143004179,
-0.020830197259783745,
0.014775238931179047,
-0.021427297964692116,
0.01695011369884014,
-0.01774769462645054,
0.07286591827869415,
-0.015235872007906437,
-0.00022830956731922925,
-0.04088514670729637,
0.013090693391859531,
-0.012732937932014465,
-0.03150641918182373,
0.0017704644706100225,
0.050143808126449585,
-0.004142356105148792,
0.013244712725281715,
0.00406396621838212,
-0.0018172042910009623,
-0.00017597097030375153,
-0.011838359758257866,
-0.022743133828043938,
0.013230491429567337,
-0.022593768313527107,
-0.06659369170665741,
0.03029847890138626,
-0.009313694201409817,
0.04006194323301315,
0.03566918522119522,
-0.001963510410860181,
-0.020597022026777267,
0.024701368063688278,
-0.051084451377391815,
0.01661410741508007,
-0.011737546883523464,
-0.011451158672571182,
-0.011466351337730885,
-0.032301146537065506,
0.03973178192973137,
0.030742879956960678,
-0.008758574724197388,
0.02308378368616104,
0.050450973212718964,
-0.013621474616229534,
-0.014174218289554119,
0.010407533496618271,
-0.009383455850183964,
0.03959956392645836,
0.04201621562242508,
0.042017657309770584,
0.011971418745815754,
0.07633626461029053,
-0.04477842152118683,
0.03625822439789772,
0.0021214832086116076,
0.01905245892703533,
-0.07014922797679901,
-0.013636494986712933,
0.012709605507552624,
-0.0038328554946929216,
0.015181970782577991,
-0.03591453656554222,
0.015665676444768906,
0.005768525414168835,
-0.05323012173175812,
0.02217414788901806,
-0.01039133034646511,
-0.05199197307229042,
-0.025844136252999306,
-0.017340008169412613,
-0.00759460125118494,
0.06479433178901672,
0.03481820970773697,
0.008850201033055782,
0.039902083575725555,
0.017879866063594818,
0.002056979341432452,
-0.04300231859087944,
-0.029282277449965477,
-0.009426882490515709,
0.004346089903265238,
-0.017483975738286972,
0.06156768649816513,
-0.01605686917901039,
-0.028772253543138504,
0.01782313920557499,
0.02857472561299801,
-0.019765201956033707,
-0.0037995106540620327,
0.02418185956776142,
0.013454759493470192,
0.06616365909576416,
0.048808857798576355,
-0.005559700541198254,
-0.0031789911445230246,
0.001007239567115903,
0.019826246425509453,
0.017029093578457832,
0.00858588982373476,
0.03443513438105583,
-0.0026719735469669104,
-0.02163785696029663,
-0.05282645300030708,
0.011055252514779568,
0.007262383587658405,
-0.0353630967438221,
-0.009859178215265274,
0.005724233575165272,
0.010684097185730934,
-0.024816030636429787,
0.02031208574771881,
-0.03292533755302429,
0.007885649800300598,
0.027542736381292343,
0.029471321031451225,
0.01684066466987133,
-0.015149198472499847,
-0.008812974207103252,
-0.03907207027077675,
0.03407461941242218,
0.03938070312142372,
-0.004089543130248785,
-0.0204433836042881,
0.0001391425175825134,
-0.007508932612836361,
-0.014425452798604965,
-0.0011276939185336232,
-0.0807763859629631,
-0.047820623964071274,
0.032508257776498795,
0.009498517960309982,
0.019194692373275757,
-0.05337568372488022,
-0.021463947370648384,
0.00975014641880989,
-0.04293321445584297,
0.027515340596437454,
-0.028726331889629364,
0.013458339497447014,
0.01328414399176836,
-0.020184257999062538,
-0.020222241058945656,
-0.02467043697834015,
0.03276871517300606,
0.031995274126529694,
-0.011594168841838837,
0.01066907960921526,
0.0006674387259408832,
0.023230912163853645,
-0.0071740103885531425,
0.016348151490092278,
-0.02225610986351967,
-0.0318947359919548,
-0.01678568311035633,
0.002885071560740471,
-0.016342904418706894,
0.02832457236945629,
0.03063701093196869,
-0.016876384615898132,
0.023675596341490746,
0.030231615528464317,
-0.011197169311344624,
0.03705563768744469,
0.01276983693242073,
-0.004506704863160849,
0.043561678379774094,
-0.02997543103992939,
0.03755282983183861,
0.004128643311560154,
-0.02332833781838417,
-0.019668839871883392,
-0.029427407309412956,
-0.0164137315005064,
-0.049358807504177094,
-0.026407014578580856,
0.020434081554412842,
-0.009297356940805912,
-0.012076477520167828,
0.024289825931191444,
0.06196887418627739,
-0.01285592745989561,
-0.03023356758058071,
0.03476351872086525,
0.016421904787421227,
0.04739769175648689,
-0.028543617576360703,
-0.0066179255954921246,
0.015761053189635277,
-0.01529094111174345,
0.0061424714513123035,
0.06483825296163559,
0.03097439929842949,
0.0023916619829833508,
0.003598300041630864,
0.015690555796027184,
0.00011637285206234083,
0.002733691595494747,
0.034917689859867096,
0.016669005155563354,
-0.015182029455900192,
-0.02026720717549324,
0.01948365941643715,
-0.021925365552306175,
0.042642053216695786,
-0.008416208438575268,
-0.006562710274010897,
0.08803930878639221,
-0.03448951616883278,
0.042140863835811615,
0.004928387701511383,
-0.013623017817735672,
-0.028134295716881752,
-0.013489878736436367,
-0.040288057178258896,
0.03135989233851433,
-0.01898771896958351,
-0.02748027816414833,
-0.021886926144361496,
-0.001537761534564197,
0.012496857903897762,
-0.06612524390220642,
-0.027781706303358078,
0.0077596548944711685,
0.007615060079842806,
0.0544152706861496,
-0.021371759474277496,
-0.042483992874622345,
-0.021876314654946327,
0.03679371625185013,
0.03955560177564621,
0.006741134449839592,
-0.02110297977924347,
-0.03532521799206734,
-0.01805523969233036,
0.050148360431194305,
-0.046717241406440735,
-0.014239787124097347,
-0.020989561453461647,
0.021214280277490616,
-0.02431386709213257,
-0.0166028942912817
] |
<p>The figure shows an LR circuit with a switch and a 240-volt battery. At the instant the switch is closed the current in the circuit and the potential difference between points a and b, Vab, are</p>
<p><img src="http://i.stack.imgur.com/Xs9ak.png" alt="enter image description here"></p>
<p>Choices : </p>
<pre><code>a. 0 A, 0 V
b. 0 A, -240 V
c. 0 A, +240 V
d. 0.024 A, 0 V
e. 0.024 A, +240 V
</code></pre>
<p>Answer : c. 0 A, +240 V</p>
<hr>
<p><strong>My Questions</strong></p>
<ul>
<li><p>When the battery discharging, the voltage will drop continuously, the voltage across a and b at the start instant should be equal to the original voltage of the battery 240V. However, how can we determine whether Vab is +240V or -240V?</p></li>
<li><p>Moreover, if the potential different at the start instant is 240V, why should the current equals 0A?</p></li>
</ul>
<hr>
<p>Thank you for your help.</p> | 1,542 | [
-0.034530483186244965,
-0.02197306603193283,
-0.015351610258221626,
0.0312324371188879,
0.012999449856579304,
-0.0385800302028656,
-0.017056278884410858,
-0.004704643506556749,
0.009007320739328861,
0.021253466606140137,
0.027359941974282265,
0.02845781482756138,
0.0013588310685008764,
0.023649025708436966,
0.020081887021660805,
-0.010145120322704315,
0.018428729847073555,
-0.049008119851350784,
-0.020527228713035583,
0.03465328365564346,
-0.03332503139972687,
-0.017756493762135506,
0.048019297420978546,
0.03174878656864166,
-0.03179791197180748,
0.014309760183095932,
0.03673919290304184,
-0.024095600470900536,
-0.0158066563308239,
0.09613440185785294,
-0.011471106670796871,
-0.018639953806996346,
-0.004895508289337158,
-0.006999984383583069,
-0.008938916958868504,
0.029333023354411125,
-0.010435215197503567,
-0.035067178308963776,
-0.026459837332367897,
0.04702167585492134,
0.022809408605098724,
0.018011348322033882,
-0.016150956973433495,
0.06849925965070724,
0.01488683745265007,
0.004631104413419962,
-0.038079652935266495,
0.0036640982143580914,
0.03134812414646149,
-0.04154359921813011,
0.054998405277729034,
-0.03932064399123192,
0.059429898858070374,
0.039657171815633774,
0.011523768305778503,
-0.02225041575729847,
0.043100569397211075,
0.07676280289888382,
-0.005833067465573549,
-0.007857026532292366,
-0.016549276188015938,
-0.018070684745907784,
-0.027404051274061203,
-0.032372429966926575,
-0.019650660455226898,
0.030341248959302902,
0.0028913591522723436,
-0.0013711528154090047,
0.015064292587339878,
-0.017034931108355522,
0.007967361249029636,
0.01170797273516655,
-0.009369570761919022,
-0.058737266808748245,
0.04132666438817978,
-0.03396819159388542,
0.0020728602539747953,
0.04178055748343468,
0.04982099309563637,
0.05763685703277588,
-0.04662094637751579,
0.007002220023423433,
0.02655814029276371,
0.05048183724284172,
0.03134592995047569,
-0.049618907272815704,
0.036369312554597855,
0.01180907990783453,
0.01143991481512785,
0.01006119605153799,
0.026167722418904305,
0.014064472168684006,
0.008094564080238342,
-0.04994230344891548,
-0.02483447641134262,
0.07171326875686646,
0.008804881013929844,
0.045376766473054886,
0.03653011843562126,
-0.06283724308013916,
0.03969373553991318,
-0.022693386301398277,
0.04559166729450226,
0.05884818732738495,
-0.018515584990382195,
-0.00356745021417737,
0.002459586365148425,
0.04130394756793976,
0.023065654560923576,
-0.005148322321474552,
-0.0600929856300354,
0.03416210040450096,
0.043479807674884796,
0.02162497490644455,
-0.007114235777407885,
-0.02025866135954857,
0.004938839003443718,
-0.017202304676175117,
0.024640770629048347,
0.003934503998607397,
0.03220880776643753,
-0.03877626731991768,
0.011864621192216873,
-0.026428861543536186,
-0.04210956022143364,
-0.0431322380900383,
-0.018422704190015793,
0.030890561640262604,
0.00757646095007658,
0.028486356139183044,
-0.008072512224316597,
-0.023277198895812035,
-0.010439945384860039,
-0.011017744429409504,
0.04680844768881798,
0.006122590973973274,
-0.06296074390411377,
-0.06551457941532135,
-0.004287331365048885,
-0.008137946017086506,
-0.014812982641160488,
-0.05253986641764641,
-0.014114885590970516,
0.04251863434910774,
0.02456245943903923,
-0.0010938150808215141,
0.00592806888744235,
0.02372061274945736,
-0.005141657777130604,
-0.02111051045358181,
-0.0254999827593565,
-0.015267189592123032,
-0.011057460680603981,
-0.011995452456176281,
0.021067429333925247,
-0.028196880593895912,
0.02789323590695858,
0.04948824271559715,
0.00791201926767826,
0.000304644025163725,
0.014242374338209629,
-0.03042793460190296,
0.005269865971058607,
0.0013681667624041438,
-0.0473092682659626,
-0.01807299815118313,
0.10863905400037766,
0.0451355017721653,
-0.025800542905926704,
0.04369540885090828,
0.022766100242733955,
0.049082159996032715,
0.006061534397304058,
0.026934703812003136,
0.060216449201107025,
-0.029292315244674683,
-0.05305185914039612,
-0.02120952494442463,
0.05121412128210068,
-0.0003446723858360201,
-0.04346666857600212,
-0.023823382332921028,
-0.0039884732104837894,
0.007111941929906607,
0.025757143273949623,
0.060622334480285645,
-0.007903413847088814,
0.015462901443243027,
-0.010555477812886238,
-0.03225165605545044,
-0.023064812645316124,
-0.04496454820036888,
0.033231690526008606,
0.005735513288527727,
-0.033935949206352234,
-0.00968792662024498,
-0.028613612055778503,
0.027474451810121536,
-0.033870138227939606,
0.0005385516560636461,
0.007375878281891346,
0.036548808217048645,
-0.019717784598469734,
-0.018267905339598656,
-0.00022820143203716725,
0.040200017392635345,
0.0418127067387104,
-0.02263553999364376,
0.060857124626636505,
-0.013681061565876007,
-0.0070893727242946625,
0.016525736078619957,
-0.030584178864955902,
0.02638491615653038,
0.03466581925749779,
0.010976236313581467,
-0.016371101140975952,
0.0454329177737236,
-0.009021494537591934,
0.039711471647024155,
-0.03363584354519844,
0.06683677434921265,
0.06326958537101746,
-0.012931004166603088,
0.009079323150217533,
0.038877397775650024,
0.01486988179385662,
0.03699659928679466,
0.03341590240597725,
-0.007124402094632387,
-0.021764976903796196,
-0.007404578849673271,
0.021036114543676376,
-0.010091162286698818,
-0.021853849291801453,
0.03572825342416763,
0.03389468789100647,
-0.010381159372627735,
-0.012585650198161602,
-0.003145782742649317,
-0.045364681631326675,
-0.016502808779478073,
0.030132528394460678,
0.03544255346059799,
-0.010031948797404766,
0.014657273888587952,
0.03616804629564285,
0.03598229959607124,
0.005448735784739256,
-0.018283022567629814,
-0.01193329133093357,
0.050421301275491714,
-0.027154821902513504,
0.013765079900622368,
0.0009815399535000324,
-0.04151873663067818,
0.047138508409261703,
-0.014383278787136078,
0.036864396184682846,
-0.026831861585378647,
-0.006887634284794331,
-0.003649759339168668,
-0.010870547965168953,
-0.004065417218953371,
0.015718819573521614,
-0.011274254880845547,
-0.006184654776006937,
0.004614923615008593,
0.016856105998158455,
-0.06567942351102829,
0.04544150456786156,
-0.019066352397203445,
-0.012632445432245731,
-0.03400837630033493,
-0.024784639477729797,
0.02996605634689331,
-0.00633292505517602,
0.0026567475870251656,
-0.042794182896614075,
-0.01518136914819479,
-0.05079793930053711,
-0.030914725735783577,
0.04200443997979164,
-0.00010336293780710548,
-0.015313233248889446,
0.03540045768022537,
0.007748090662062168,
-0.02485167793929577,
0.07799703627824783,
0.06388992071151733,
0.0026833799201995134,
0.020361294969916344,
-0.01980922929942608,
-0.07619311660528183,
0.011655447073280811,
-0.038012221455574036,
0.032298922538757324,
-0.009253897704184055,
-0.007443332578986883,
0.05622982978820801,
0.011818064376711845,
-0.04635099694132805,
0.04257761314511299,
-0.05173201486468315,
0.0007615888607688248,
0.023772306740283966,
-0.0075593614019453526,
0.03130648657679558,
-0.025420963764190674,
0.009546670131385326,
0.0021252024453133345,
-0.03176391124725342,
0.011698799207806587,
-0.07816066592931747,
-0.025700613856315613,
-0.03626387193799019,
-0.02856755629181862,
0.047264501452445984,
0.008721337653696537,
-0.022215161472558975,
0.06871654093265533,
0.04101524129509926,
0.001385729992762208,
-0.007657868321985006,
-0.019916139543056488,
-0.032557252794504166,
0.0008723643841221929,
-0.0033639981411397457,
0.05831223353743553,
0.007489848416298628,
0.029365604743361473,
-0.01128254272043705,
0.07114514708518982,
0.045785609632730484,
-0.0006666264380328357,
0.010355004109442234,
-0.020287346094846725,
0.015039049088954926,
-0.008153227157890797,
0.054913412779569626,
-0.006230780854821205,
0.01958640292286873,
0.0025352530647069216,
-0.025731036439538002,
0.014632508158683777,
0.01670040562748909,
-0.0049124835059046745,
0.028968118131160736,
-0.01748184859752655,
0.004180301446467638,
-0.01809106580913067,
0.059277284890413284,
-0.020326269790530205,
0.014862319454550743,
-0.022164486348628998,
-0.01336503867059946,
0.06287643313407898,
-0.028720127418637276,
-0.01958189532160759,
0.03083512932062149,
0.022722823545336723,
-0.04893316701054573,
-0.08115784823894501,
0.024097900837659836,
-0.014079860411584377,
0.02951119840145111,
-0.009698120877146721,
-0.019744032993912697,
0.02831902913749218,
0.039681147783994675,
0.023780284449458122,
0.0018978818552568555,
-0.04399916157126427,
-0.015204014256596565,
-0.042925264686346054,
-0.023721039295196533,
0.03345039486885071,
0.05525877699255943,
0.014536913484334946,
0.04254578426480293,
0.01336739957332611,
0.019350595772266388,
-0.01169514562934637,
0.025344369933009148,
-0.08772090077400208,
0.04652044177055359,
-0.018077218905091286,
-0.01996886171400547,
-0.004329664632678032,
0.005828547291457653,
0.018846554681658745,
-0.014237361028790474,
-0.04462294280529022,
-0.012561321258544922,
0.005526545457541943,
-0.05487029254436493,
0.008467803709208965,
-0.0025702554266899824,
-0.0007619202369824052,
-0.08098424971103668,
0.011144176125526428,
0.0023535308428108692,
-0.005568085238337517,
0.04104521870613098,
0.033001214265823364,
-0.027258679270744324,
0.0010714103700593114,
-0.010770561173558235,
-0.0004006897215731442,
0.004652290139347315,
0.03188003972172737,
0.020418304949998856,
0.03337398171424866,
0.009334278292953968,
-0.027410931885242462,
0.01136994268745184,
0.035529978573322296,
-0.012526541948318481,
-0.0485042966902256,
-0.02269280143082142,
-0.07166118174791336,
-0.03137342259287834,
-0.026797465980052948,
0.028942426666617393,
-0.011019926518201828,
0.026898004114627838,
0.015190967358648777,
0.03162366524338722,
-0.007647512946277857,
0.05325928330421448,
0.07433385401964188,
0.023666473105549812,
-0.012009850703179836,
-0.03843842074275017,
0.019717438146471977,
-0.04391634091734886,
-0.020056236535310745,
0.03221100568771362,
-0.02823023684322834,
-0.01477216649800539,
-0.004881787579506636,
0.03364822268486023,
0.022393278777599335,
-0.02214234136044979,
0.013862399384379387,
-0.0033164070919156075,
0.008338172920048237,
0.018277499824762344,
-0.0037032037507742643,
0.03101130574941635,
-0.010134341195225716,
0.031780846416950226,
-0.010326126590371132,
-0.02270151488482952,
-0.08850905299186707,
-0.023464592173695564,
0.036071695387363434,
0.04215193912386894,
-0.018378902226686478,
-0.03483831137418747,
-0.0710788294672966,
-0.020668135955929756,
0.06017448753118515,
-0.05058308690786362,
0.03715810179710388,
-0.003962315618991852,
0.053319595754146576,
-0.024517502635717392,
-0.045207854360342026,
-0.052290234714746475,
0.021140681579709053,
0.012750532478094101,
0.055286869406700134,
-0.003335652407258749,
-0.009520366787910461,
0.028734223917126656,
0.01582082360982895,
0.0063615404069423676,
0.08590157330036163,
-0.03896978497505188,
-0.0016991718439385295,
0.005162352230399847,
-0.0005540180718526244,
-0.040498681366443634,
-0.07955373078584671,
0.02385064959526062,
-0.03614993393421173,
0.026475626975297928,
0.04339149594306946,
-0.011528315022587776,
-0.04195038229227066,
0.011703313328325748,
-0.00046604304225184023,
0.005431865341961384,
-0.021224653348326683,
-0.012150540947914124,
0.049991827458143234,
0.026469174772500992,
-0.0019730308558791876,
0.017987336963415146,
0.00226430781185627,
-0.012074793688952923,
-0.025241874158382416,
-0.01932206191122532,
-0.005752196069806814,
-0.026394402608275414,
0.016973556950688362,
-0.03238174691796303,
0.033602651208639145,
-0.03623393177986145,
0.04168779030442238,
-0.01124545931816101,
0.0001159197636297904,
-0.03365210071206093,
-0.030489826574921608,
0.0003267974534537643,
-0.021679967641830444,
-0.01443085353821516,
-0.03171082213521004,
0.012538126669824123,
-0.016980508342385292,
0.015490678139030933,
0.011272978037595749,
0.03506800904870033,
-0.04755881056189537,
0.03205890581011772,
0.008225335739552975,
-0.0037038312293589115,
0.01241401769220829,
0.0017276430735364556,
0.0033382857218384743,
-0.008554313331842422,
-0.04694533720612526,
0.02762724831700325,
0.019783252850174904,
0.018590006977319717,
0.04119352623820305,
-0.02967185527086258,
-0.036492764949798584,
0.02998652122914791,
0.011553104966878891,
0.0022339122369885445,
-0.09804573655128479,
0.061733659356832504,
0.02469572238624096,
0.0022759633138775826,
-0.060144104063510895,
-0.08367162942886353,
0.026223832741379738,
0.02073517069220543,
-0.008315534330904484,
-0.038619983941316605,
-0.0030865545850247145,
0.03421873599290848,
-0.006270997226238251,
0.011291583068668842,
0.019007697701454163,
-0.022418636828660965,
0.002573867794126272,
0.05083032697439194,
0.007676942273974419,
0.07161419838666916,
0.025066567584872246,
0.029785798862576485,
-0.0030435086227953434,
-0.039472099393606186,
-0.024494880810379982,
0.011752727441489697,
0.06453624367713928,
-0.030877521261572838,
-0.06024283543229103,
0.01001945324242115,
-0.004309117328375578,
0.06736672669649124,
-0.013825394213199615,
-0.009305870160460472,
-0.021989643573760986,
-0.00418747728690505,
-0.012394680641591549,
-0.01889541931450367,
0.035594820976257324,
-0.0013351619709283113,
-0.009655624628067017,
0.026349781081080437,
0.004129831679165363,
-0.04507767781615257,
-0.007186726201325655,
-0.02747391350567341,
0.01037667877972126,
0.003076764987781644,
0.007783814799040556,
0.051157593727111816,
-0.0381266288459301,
-0.004227873403578997,
0.05456382781267166,
0.017328066751360893,
0.038431331515312195,
-0.0189344584941864,
-0.01862059161067009,
0.006487750913947821,
-0.040258895605802536,
-0.03848843649029732,
-0.010538829490542412,
-0.03280363604426384,
-0.006491506937891245,
0.022268125787377357,
0.028158731758594513,
0.05972885340452194,
0.005577159579843283,
0.007282532285898924,
-0.004496945533901453,
-0.02858501859009266,
-0.016737595200538635,
-0.015711940824985504,
0.005531707778573036,
0.005886811297386885,
-0.021948236972093582,
0.02924329973757267,
-0.0004525571421254426,
0.006099628284573555,
-0.0014601723523810506,
-0.007441216614097357,
0.04945947229862213,
0.0034172788728028536,
0.04723586514592171,
-0.012251713313162327,
-0.026551268994808197,
0.025034915655851364,
-0.006113303359597921,
0.052942823618650436,
0.0074495128355920315,
-0.03262614831328392,
0.059442564845085144,
-0.024676937609910965,
-0.012931141071021557,
-0.05027712136507034,
-0.030382642522454262,
-0.05221598967909813,
-0.00789754930883646,
0.04020584002137184,
0.01261797733604908,
0.0033475833479315042,
0.041729073971509933,
0.018916120752692223,
-0.0037471456453204155,
0.04091690853238106,
-0.01952691562473774,
-0.04161861166357994,
0.0028131315484642982,
-0.014490888454020023,
-0.03414732217788696,
0.06338369101285934,
-0.021371185779571533,
-0.03671840578317642,
0.010457033291459084,
-0.03357759490609169,
0.02583906427025795,
0.049892693758010864,
0.049148574471473694,
0.014455183409154415,
0.08291614055633545,
-0.007158658467233181,
0.03309829160571098,
-0.043583061546087265,
0.019380560144782066,
0.13666725158691406,
0.049664516001939774,
-0.006646940018981695,
-0.06759177148342133,
0.023983800783753395,
0.02132066898047924,
-0.009495317004621029,
-0.03044484183192253,
0.030265897512435913,
-0.018679797649383545,
0.036996543407440186,
0.03504740074276924,
-0.0074432166293263435,
-0.009402906522154808,
0.007187271025031805,
0.014004076831042767,
-0.026621682569384575,
-0.061621662229299545,
-0.009619437158107758,
0.03893672674894333,
-0.009009616449475288,
0.018180817365646362,
-0.06380937993526459,
0.008166249841451645,
-0.020751750096678734,
-0.01585657335817814,
-0.0414172038435936,
-0.035121459513902664,
0.01997852697968483,
-0.0013934050220996141,
0.0033476720564067364,
0.036055948585271835,
0.04726579785346985,
-0.001179344835691154,
-0.022442469373345375,
0.008769377134740353,
0.03771734610199928,
0.030146760866045952,
0.02817651815712452,
0.036913901567459106,
0.009170777164399624,
-0.0264031570404768,
-0.006961188744753599,
0.03165179491043091,
-0.06746836006641388,
-0.006078698672354221,
-0.057277612388134,
0.023461170494556427,
0.013396834954619408,
-0.015447048470377922,
0.00809117779135704,
-0.007002185098826885,
0.013392017222940922,
-0.01892719976603985,
-0.046200498938560486,
0.019382094964385033,
-0.0013544145040214062,
-0.02845729887485504,
-0.06203391030430794,
-0.03635914623737335,
0.03288650140166283,
-0.002865653485059738,
-0.02446022629737854,
-0.0044156331568956375,
-0.01525485422462225,
0.009358220733702183,
-0.012180418707430363,
0.023135961964726448,
-0.03017723187804222,
0.007089747115969658,
0.013134823180735111,
0.0023480127565562725,
-0.013465051539242268,
-0.0223690252751112,
0.01746443845331669,
0.01941327378153801,
0.035920150578022,
-0.01967252790927887,
-0.007979147136211395,
0.02540924958884716,
-0.08638742566108704,
0.02539782226085663,
0.001519777812063694,
0.0001968378492165357,
-0.028325434774160385,
0.04037763923406601,
0.0008331489516422153,
0.025378944352269173,
-0.015317579731345177,
0.020026735961437225,
0.04665044695138931,
0.05736372992396355,
-0.033265676349401474,
-0.015497456304728985,
-0.007487352937459946,
0.021643726155161858,
-0.03155367076396942,
0.03065742552280426,
0.00602548336610198,
0.04883266240358353,
0.0063980938866734505,
0.009111504070460796,
-0.025966627523303032,
0.006051173433661461,
-0.02343609742820263,
0.002150110201910138,
0.01646062731742859,
0.003926775883883238,
-0.024406686425209045,
0.009860372170805931,
0.013558203354477882,
0.005841963924467564,
0.016135023906826973,
-0.011768476106226444,
0.008494270965456963,
0.01965843327343464,
0.009366928599774837,
0.006947519723325968,
0.0007872479036450386,
-0.045287493616342545,
0.003869145642966032,
-0.06133321672677994,
-0.0025762119330465794,
-0.028293846175074577,
-0.03206261247396469,
0.012259402312338352,
0.003505377797409892,
-0.009154933504760265,
0.06079498305916786,
0.006521177478134632,
-0.002198759699240327,
-0.002367945620790124,
0.023515449836850166,
-0.021056991070508957,
-0.010039106011390686,
-0.0027282785158604383,
-0.000969071639701724,
0.026551412418484688,
-0.02813985012471676,
-0.06179897114634514,
0.037674542516469955,
-0.02869824878871441,
0.0009688672726042569,
-0.013677963986992836,
0.0035564019344747066,
0.02043232135474682,
0.009435374289751053,
-0.0314071923494339,
0.04860808327794075,
0.03300746530294418,
0.013338025659322739,
0.0135186230763793,
-0.028304869309067726,
-0.039511144161224365,
-0.017709072679281235,
0.04505071043968201,
-0.029256219044327736,
-0.00006238210335141048,
-0.007099239155650139,
-0.001740713487379253,
-0.005816947668790817,
-0.011496590450406075,
-0.01538547221571207,
0.02925403229892254,
0.02458350546658039,
-0.0013367368374019861,
0.05685136467218399,
0.010404183529317379,
-0.01727967895567417,
0.018328186124563217,
0.011237524449825287,
0.009540343657135963,
-0.022860903292894363,
-0.006544335279613733,
-0.07466760277748108,
-0.017034543678164482,
0.019785309210419655,
-0.022384950891137123,
0.003067207522690296,
-0.0345224067568779,
-0.02068427763879299,
0.035432394593954086,
-0.059933438897132874,
-0.04464396834373474,
-0.007341847755014896,
0.003635569242760539,
-0.016265295445919037,
0.0023220661096274853,
-0.016127869486808777,
0.04328560829162598,
0.01149884331971407,
0.059630271047353745,
0.037040144205093384,
-0.010563015937805176,
-0.004632492084056139,
-0.03781474009156227,
-0.014690971933305264,
0.021194567903876305,
0.007012567948549986,
-0.009492874145507812,
0.057542502880096436,
-0.04412534087896347,
-0.006972996052354574,
-0.0009741749381646514,
-0.040537796914577484,
0.010358608327805996,
0.0045831892639398575,
0.018939198926091194,
0.01950744353234768,
0.059938929975032806,
-0.0003524584462866187,
0.010145870968699455,
-0.0425962395966053,
-0.007740366738289595,
0.018743105232715607,
0.03659053519368172,
-0.029766788706183434,
0.01678168773651123,
0.0051887426525354385,
-0.014440766535699368,
-0.04391570761799812,
0.017585542052984238,
-0.03468845412135124,
-0.004515625070780516,
-0.0065853470005095005,
0.02565813437104225,
-0.003234143601730466,
-0.05155425891280174,
-0.03605750575661659,
-0.02092634327709675,
-0.03545146808028221,
0.031929198652505875,
-0.004300021566450596,
0.014257560484111309,
0.0021250969730317593,
-0.020981233566999435,
-0.018128100782632828,
0.06030851602554321,
-0.0009013819508254528,
-0.03197193518280983,
-0.059012092649936676,
-0.018719859421253204,
-0.0041777826845645905,
-0.013285068795084953,
-0.024678349494934082,
-0.05264763534069061,
-0.028822002932429314,
0.027697227895259857,
-0.0052655101753771305,
-0.003914146684110165,
-0.023389743641018867,
-0.03818953037261963,
-0.03620578348636627,
-0.088651143014431,
0.021619288250803947,
0.019485417753458023,
-0.054989006370306015,
-0.048657726496458054,
-0.04493333399295807,
-0.057048335671424866,
0.04900052025914192,
0.024824421852827072,
0.006398751866072416,
-0.050049081444740295,
0.008363337256014347,
-0.024303870275616646,
0.013226806186139584,
-0.053554803133010864,
0.004437841475009918,
0.009756622835993767,
-0.009591893292963505,
0.031405769288539886,
-0.0017513252096250653,
-0.02477973885834217,
0.018868999555706978,
0.011569350026547909,
0.0028208885341882706,
-0.040431153029203415,
-0.05569567531347275,
-0.011163568124175072,
0.04864652827382088,
0.018911274150013924,
-0.0010221500415354967,
0.1111333817243576,
0.015821760520339012,
0.03393692523241043,
-0.00004316114791436121,
0.029345260933041573,
-0.024993620812892914,
0.04352683573961258,
-0.029760317876935005,
0.00788173172622919,
-0.0001079914000001736,
-0.022060543298721313,
0.052402906119823456,
-0.04185935854911804,
0.01456158421933651,
0.013240167871117592,
-0.013483887538313866,
-0.007198850624263287,
0.012570608407258987,
0.0007770486990921199,
0.031376149505376816,
-0.01573001779615879,
-0.005684236995875835,
-0.026524990797042847,
-0.0015768358716741204,
0.007407811935991049,
-0.016638822853565216,
0.02790810354053974,
-0.02800285629928112,
0.021271416917443275,
0.06330987066030502,
-0.01399451494216919,
0.02039104327559471,
0.0006942477775737643,
-0.005976622924208641,
-0.006609128322452307,
-0.008350465446710587,
0.03108084760606289,
-0.00805999618023634,
-0.03900071606040001,
0.012703504413366318,
-0.009038073010742664,
0.05873654782772064,
-0.014260150492191315,
0.014037420973181725,
0.026443157345056534,
0.031169893220067024,
-0.015915604308247566,
-0.004435635171830654,
0.009616436436772346,
0.0032607540488243103,
-0.015054271556437016,
-0.005761923734098673,
-0.02709132246673107,
-0.005939566995948553,
0.004451694432646036,
-0.024615751579403877,
0.025166912004351616,
-0.003090043319389224,
-0.013537629507482052,
-0.023122234269976616,
0.01430595200508833,
-0.006572419311851263,
-0.0411994643509388,
0.03788197040557861,
0.02993013709783554,
-0.0038112211041152477,
-0.04471970349550247,
-0.010744379833340645,
-0.013659675605595112,
0.05431218445301056,
-0.02192704938352108,
-0.029807250946760178,
-0.0038692927919328213,
-0.018036721274256706,
-0.016467489302158356,
-0.021810203790664673
] |
<p>The spatially flat FRW metric in cartesian co-ordinates is given by:
$$ds^2 = -dt^2 + a^2(t)(dx^2 + dy^2 + dz^2)$$
As I understand it there are Killing vectors in the $x$, $y$, $z$ directions implying that momentum is conserved but there is no Killing vector in the $t$-direction which implies that energy is not conserved. I don't know much about Killing vectors. Is this correct?</p>
<p>If I transform the time co-ordinate $t$ to conformal time $\tau$ using the relationship:
$$d\tau = \frac{dt}{a(t)}$$
the metric now becomes:
$$ds^2 = a^2(\tau)(-d\tau^2 + dx^2 + dy^2 + dz^2)$$
Does this metric now have a Killing vector in the $\tau$-direction as well as in the $x$, $y$ and $z$ directions?</p> | 1,543 | [
-0.01254916749894619,
-0.04386850446462631,
-0.01595451682806015,
-0.05382620543241501,
0.0719878077507019,
0.008280590176582336,
-0.049017492681741714,
-0.03733152523636818,
-0.02082539163529873,
-0.05550660192966461,
-0.00783073902130127,
0.01902100071310997,
0.0461379773914814,
0.022989017888903618,
0.022734327241778374,
-0.015059010125696659,
-0.017549358308315277,
0.013490335084497929,
-0.013065743260085583,
-0.046761538833379745,
0.016865577548742294,
-0.01987561210989952,
0.006790409795939922,
-0.025945231318473816,
-0.000821134599391371,
0.012223655357956886,
0.021880177780985832,
-0.030798330903053284,
-0.013146188110113144,
0.04584028199315071,
-0.020942265167832375,
-0.013345996849238873,
-0.01317692268639803,
0.03832500800490379,
-0.0029347711242735386,
-0.017820989713072777,
-0.04921403527259827,
-0.05035972222685814,
-0.019462401047348976,
0.03338964283466339,
-0.01735568791627884,
-0.02394966408610344,
-0.02251846343278885,
0.06900167465209961,
-0.01872226782143116,
0.0204872265458107,
-0.006524285767227411,
0.01737123914062977,
0.055293165147304535,
-0.037868089973926544,
0.08219970017671585,
0.00986037589609623,
0.03991064801812172,
-0.010391008108854294,
-0.004936206620186567,
-0.006800595670938492,
0.0615549199283123,
0.059397563338279724,
-0.007813614793121815,
-0.018022846430540085,
-0.008404871448874474,
0.0007226102170534432,
0.007175031583756208,
-0.020969783887267113,
0.004404438193887472,
0.03192725405097008,
0.012213516980409622,
-0.00160388951189816,
0.04308142885565758,
-0.004692643880844116,
-0.010839900933206081,
0.0019439890747889876,
-0.019484980031847954,
-0.004179937765002251,
0.0013664456782862544,
-0.022186465561389923,
0.03636019676923752,
0.017979081720113754,
0.04276987165212631,
0.034015025943517685,
-0.0028980057686567307,
-0.0265810489654541,
0.03603537753224373,
0.06299670040607452,
0.012513292022049427,
0.0186808742582798,
0.05169384926557541,
0.01717747002840042,
-0.03053261525928974,
0.03839154541492462,
0.025468995794653893,
0.000035423694498604164,
0.026049232110381126,
-0.03028561919927597,
-0.00613170163705945,
0.055928368121385574,
-0.0005912451888434589,
0.07252854853868484,
-0.010672405362129211,
-0.02896367572247982,
-0.011400576680898666,
-0.004977827426046133,
0.00432733166962862,
0.06850487738847733,
0.046037618070840836,
-0.0340721420943737,
-0.05695318058133125,
-0.0009407332399860024,
-0.0682467445731163,
-0.01555028185248375,
-0.07435411959886551,
-0.017086775973439217,
-0.04512016475200653,
-0.003165941219776869,
0.015993757173419,
-0.02101951837539673,
0.018235204741358757,
0.004874919541180134,
0.03624553978443146,
0.06526869535446167,
0.055840980261564255,
0.006450317334383726,
0.03892330080270767,
-0.021390177309513092,
-0.05994352698326111,
0.006634776946157217,
0.01834329590201378,
0.01752222143113613,
-0.019755078479647636,
-0.017621345818042755,
0.025787916034460068,
-0.02422128990292549,
0.010557605884969234,
-0.007070968393236399,
0.04462271183729172,
-0.007834075018763542,
-0.05619179829955101,
-0.03833771497011185,
0.026036569848656654,
-0.013852386735379696,
0.0011149822967126966,
-0.10663940012454987,
-0.05204808712005615,
-0.004189490806311369,
0.0684572383761406,
-0.029333319514989853,
0.008870088495314121,
0.02620779722929001,
0.04190368205308914,
-0.019584013149142265,
-0.019000766798853874,
0.013797235675156116,
-0.01775236800312996,
-0.05453411117196083,
-0.02167060412466526,
-0.05468966066837311,
0.004816725384443998,
0.02451344206929207,
0.05657625570893288,
-0.008277902379631996,
0.08657628297805786,
-0.010355832055211067,
-0.001153903198428452,
0.00937681831419468,
-0.037467945367097855,
-0.0034466381184756756,
0.062440212815999985,
0.02127850241959095,
-0.03168189153075218,
0.004968563560396433,
0.007788957096636295,
0.018883811309933662,
-0.020838288590312004,
0.004648124799132347,
0.059797290712594986,
-0.03684874251484871,
-0.02593836933374405,
-0.004683227743953466,
-0.009801644831895828,
-0.024790721014142036,
-0.020412391051650047,
-0.05564561486244202,
-0.022993717342615128,
0.009960387833416462,
-0.003113184357061982,
0.054905716329813004,
0.00762736052274704,
0.008145746774971485,
-0.01009686291217804,
-0.04272275045514107,
0.011921786703169346,
-0.04457821696996689,
0.023592324927449226,
-0.027793843299150467,
0.010890663601458073,
0.04658692330121994,
0.014803212136030197,
0.037875715643167496,
-0.02747807838022709,
-0.031569741666316986,
-0.01023552194237709,
0.05904209241271019,
0.012674682773649693,
-0.00592008838430047,
0.00055087631335482,
0.03593651205301285,
0.040836967527866364,
0.002041942672803998,
0.011865457519888878,
0.0002142684970749542,
0.007154534570872784,
-0.019895385950803757,
-0.011463037692010403,
0.023807261139154434,
-0.016257021576166153,
-0.009250294417142868,
0.0026708622463047504,
0.026987839490175247,
-0.02131655625998974,
0.0543028824031353,
-0.0357048474252224,
0.051848433911800385,
0.06683967262506485,
-0.025882871821522713,
0.0238958727568388,
0.06374330073595047,
-0.007059231400489807,
0.04388880357146263,
0.01792178489267826,
-0.00525942025706172,
-0.030720990151166916,
0.020914701744914055,
0.04473590850830078,
-0.00624970905482769,
-0.05138589069247246,
0.008218086324632168,
0.03656749054789543,
0.03063884936273098,
0.04635394737124443,
0.034400928765535355,
0.025119256228208542,
-0.07829244434833527,
0.045258715748786926,
-0.00303885736502707,
0.019395194947719574,
-0.00445702625438571,
0.006331314332783222,
-0.0034322389401495457,
0.014733189716935158,
0.004092338029295206,
-0.008300824090838432,
0.032298021018505096,
-0.04133377596735954,
-0.0021031545475125313,
0.03446247801184654,
0.004120380152016878,
0.016286831349134445,
0.006851968355476856,
0.018621128052473068,
0.06122539937496185,
0.0330069437623024,
-0.0236569344997406,
-0.02840164117515087,
-0.008375760167837143,
0.008944259956479073,
0.04619557783007622,
0.046637412160634995,
-0.011617106385529041,
0.0050031645223498344,
-0.015995055437088013,
-0.01007109135389328,
0.039679087698459625,
-0.010717160999774933,
0.028407223522663116,
0.014094332233071327,
0.02888195961713791,
0.030855722725391388,
0.022435937076807022,
-0.0341152660548687,
-0.05725206062197685,
0.013336786068975925,
0.006267429795116186,
-0.006720193661749363,
0.03688385710120201,
-0.03876323997974396,
0.024579033255577087,
-0.09505853801965714,
-0.003896055044606328,
0.047407664358615875,
-0.002697152551263571,
0.029837200418114662,
0.01916895993053913,
-0.01938854157924652,
-0.05480838194489479,
-0.024781348183751106,
-0.02801632694900036,
0.044651344418525696,
-0.041118521243333817,
0.01842784695327282,
0.04969248175621033,
0.004344233777374029,
-0.03618507832288742,
0.008837969042360783,
-0.03410941734910011,
-0.04046038165688515,
0.007525211200118065,
-0.0010385856730863452,
0.029169544577598572,
-0.023881109431385994,
0.04431193321943283,
0.02857879176735878,
-0.04790734499692917,
0.02899191901087761,
-0.05144188925623894,
-0.017471980303525925,
0.03324954956769943,
-0.0007075179019011557,
0.012658895924687386,
-0.037631891667842865,
-0.04377550259232521,
0.05208178609609604,
0.008875489234924316,
-0.0060172853991389275,
0.010170560330152512,
0.019969258457422256,
0.01148515846580267,
-0.057578083127737045,
-0.023469218984246254,
-0.000546917668543756,
-0.036925915628671646,
0.015309625305235386,
-0.00034542547655291855,
0.05412929132580757,
0.03407493978738785,
-0.007399654947221279,
-0.04740146920084953,
0.01695038191974163,
0.03271179273724556,
0.02139979414641857,
0.05299163982272148,
0.027195369824767113,
0.011682474985718727,
0.0012842852156609297,
0.020430224016308784,
0.016375137493014336,
0.014722944237291813,
-0.050794292241334915,
0.05057009309530258,
0.008640933781862259,
0.009392736479640007,
0.02798880636692047,
0.04356490820646286,
-0.008139591664075851,
-0.04451115429401398,
-0.01850559189915657,
0.008454209193587303,
0.05867217481136322,
-0.011519328691065311,
0.03869539499282837,
0.034025754779577255,
0.023907840251922607,
-0.0028975950554013252,
-0.02442055568099022,
-0.004817391745746136,
-0.0018335373606532812,
0.005201727617532015,
-0.003301611403003335,
-0.003194657154381275,
0.022601695731282234,
0.05298660695552826,
0.02763557992875576,
0.03674831986427307,
-0.0500980019569397,
0.02143029309809208,
-0.06086514890193939,
0.010878145694732666,
-0.032923683524131775,
0.01697545126080513,
0.011138848029077053,
0.027686364948749542,
0.04231035336852074,
0.028182554990053177,
0.046070393174886703,
0.00030924950260668993,
-0.04366796836256981,
-0.0006344428984448314,
-0.0418451651930809,
0.005106136668473482,
-0.0175077673047781,
-0.02969086915254593,
-0.031312692910432816,
-0.016160769388079643,
-0.0022006970830261707,
-0.005002269055694342,
-0.009829617105424404,
-0.04210013523697853,
0.015910876914858818,
-0.060972265899181366,
-0.046645160764455795,
-0.019250543788075447,
0.06668213754892349,
0.06492346525192261,
-0.04065186530351639,
-0.0080709932371974,
0.04769311472773552,
-0.042374949902296066,
0.01415740605443716,
-0.03003387711942196,
0.011069335974752903,
0.0036268660333007574,
0.013314710929989815,
0.0007123134564608335,
0.015634741634130478,
0.0463993102312088,
0.00407788110896945,
0.04940560832619667,
0.04194982349872589,
-0.0183993149548769,
-0.02098633348941803,
-0.03435351699590683,
-0.0558617003262043,
-0.010775469243526459,
-0.0012988928938284516,
0.0537656731903553,
0.0075131687335669994,
0.006386565510183573,
0.0323483943939209,
0.05196589604020119,
0.019564254209399223,
0.001381246722303331,
0.04405074194073677,
-0.02861364558339119,
-0.041274115443229675,
-0.037704795598983765,
-0.01572851464152336,
-0.022727373987436295,
-0.02810290828347206,
-0.005300750955939293,
-0.02672634832561016,
-0.050486136227846146,
0.023725971579551697,
-0.018261751160025597,
0.01839449070394039,
-0.013359005562961102,
-0.022468769922852516,
-0.016908811405301094,
-0.011008347384631634,
0.019255196675658226,
-0.011450918391346931,
0.013173350133001804,
0.03319054841995239,
0.01041093934327364,
0.02251155488193035,
-0.006330049596726894,
-0.02765083499252796,
0.019447149708867073,
0.015069129876792431,
0.034972064197063446,
0.017064377665519714,
-0.023117857053875923,
-0.06484051048755646,
-0.024216432124376297,
0.028433602303266525,
-0.0011529017938300967,
0.040780216455459595,
0.01095273345708847,
0.0015197383472695947,
-0.01872069574892521,
-0.02254517562687397,
-0.03468127176165581,
-0.0012713312171399593,
-0.012414168566465378,
0.0140951257199049,
-0.027778122574090958,
0.01813393086194992,
-0.0009535704739391804,
0.03558443859219551,
0.007638484239578247,
0.0200527124106884,
0.029509559273719788,
0.002140222117304802,
0.020304003730416298,
0.046731047332286835,
-0.04619881138205528,
-0.059783972799777985,
-0.02046077884733677,
0.04733758419752121,
-0.004684280604124069,
0.05042659863829613,
0.0004048619302920997,
-0.01840110868215561,
0.05881720408797264,
-0.0104482127353549,
0.006556082982569933,
0.07482805103063583,
-0.030802231281995773,
0.05022282525897026,
0.021050605922937393,
-0.0036557395942509174,
0.020436236634850502,
0.016280652955174446,
-0.015199231915175915,
-0.009839311242103577,
-0.0027115135453641415,
0.05491142347455025,
-0.019799822941422462,
0.00991189107298851,
-0.04891069233417511,
0.0016639241948723793,
-0.04630753770470619,
0.019072500988841057,
-0.02943706512451172,
-0.019670289009809494,
-0.005562653765082359,
-0.002049161121249199,
0.0309904795140028,
0.028815021738409996,
0.006675449665635824,
-0.022633090615272522,
-0.006349814590066671,
0.014135899022221565,
-0.04218726232647896,
-0.0009002970764413476,
-0.015661092475056648,
-0.02689833752810955,
-0.015035701915621758,
0.03567972779273987,
0.014719122089445591,
0.019895896315574646,
-0.03312069550156593,
-0.0029817738104611635,
0.035532113164663315,
-0.006142058875411749,
0.02502855472266674,
0.02046024426817894,
-0.028801048174500465,
0.012944410555064678,
-0.02969360537827015,
-0.03359144926071167,
0.002751959254965186,
-0.022045033052563667,
0.0061386036686599255,
-0.02593752183020115,
0.058452095836400986,
0.036905571818351746,
0.022895053029060364,
-0.09859253466129303,
-0.011229044757783413,
-0.009774034842848778,
0.005920044146478176,
-0.03164497762918472,
0.006744939833879471,
0.000711029046215117,
-0.04680848866701126,
-0.005370131693780422,
-0.03329963609576225,
0.061338260769844055,
-0.02696123719215393,
-0.01024050172418356,
-0.0024669133126735687,
0.03528276085853577,
0.009212296456098557,
-0.012133783660829067,
-0.01960119605064392,
0.031181445345282555,
0.004876217804849148,
-0.022821538150310516,
0.02143986150622368,
0.06360656768083572,
-0.012211817316710949,
-0.012503686361014843,
0.012305162847042084,
-0.0066133481450378895,
0.020054906606674194,
0.004668061155825853,
0.019265668466687202,
0.017262134701013565,
-0.014677158556878567,
-0.014696151949465275,
-0.027461247518658638,
0.0007926647085696459,
-0.02399667724967003,
0.012549834325909615,
-0.024664917960762978,
0.0022272246424108744,
-0.030245469883084297,
-0.014983157627284527,
0.03540664538741112,
-0.026253055781126022,
0.023784754797816277,
-0.03011307492852211,
0.04642513021826744,
0.027416175231337547,
-0.008644712157547474,
-0.039992671459913254,
-0.01870790868997574,
0.013898827135562897,
-0.007473986130207777,
0.00850307010114193,
-0.00024478425621055067,
-0.027623476460576057,
-0.02000022865831852,
-0.03236132487654686,
-0.010151986964046955,
0.0424310527741909,
0.09692727774381638,
-0.017131498083472252,
0.009912887588143349,
-0.006521904841065407,
0.01040436327457428,
0.019777260720729828,
-0.02546464093029499,
-0.007031189743429422,
-0.0033829661551862955,
0.032863449305295944,
0.016860850155353546,
-0.024207942187786102,
-0.031435396522283554,
0.011716335080564022,
0.006620929576456547,
-0.025893062353134155,
0.029692726209759712,
0.01662811078131199,
0.0059607382863759995,
0.015765031799674034,
-0.0007191086770035326,
-0.06402771174907684,
0.03794577717781067,
-0.018966617062687874,
0.0336640439927578,
-0.01572180911898613,
-0.020275499671697617,
0.024586115032434464,
0.04504553601145744,
0.004324368201196194,
-0.033059000968933105,
-0.02561739645898342,
-0.057726599276065826,
-0.0032356414012610912,
-0.007959673181176186,
-0.00635287631303072,
0.0010176660725846887,
0.008916380815207958,
0.06901469826698303,
-0.006440806668251753,
0.004603920038789511,
0.0006691325106658041,
-0.05327170342206955,
-0.004829900339245796,
-0.04208079352974892,
-0.027112476527690887,
0.05021011084318161,
-0.012796436436474323,
-0.01541144773364067,
-0.028645312413573265,
-0.0351492315530777,
-0.008241578936576843,
0.005834232550114393,
0.017951566725969315,
-0.02120906673371792,
0.06391621381044388,
-0.03372357785701752,
0.04031871631741524,
-0.01808873750269413,
0.014279518276453018,
0.11087902635335922,
0.07316979765892029,
0.015259995125234127,
-0.0321393683552742,
0.009346159175038338,
-0.016885612159967422,
0.015095837414264679,
-0.05235859751701355,
0.044564735144376755,
0.0024870531633496284,
-0.02311747893691063,
0.027857081964612007,
0.056790418922901154,
-0.01582704670727253,
-0.05225309729576111,
0.03179091960191727,
-0.052461978048086166,
-0.03886879235506058,
0.027017494663596153,
0.00010121437662746757,
-0.043396174907684326,
-0.015819115564227104,
-0.017707619816064835,
0.01921480894088745,
-0.027330374345183372,
0.01866423897445202,
-0.03665684908628464,
-0.05176468566060066,
-0.02470334991812706,
-0.017516419291496277,
-0.0599391832947731,
0.03804739937186241,
-0.024571575224399567,
0.0005667783552780747,
-0.03357388451695442,
0.01906820386648178,
0.012154181487858295,
-0.01260189525783062,
0.0332905538380146,
0.02925056591629982,
0.027858663350343704,
0.037847571074962616,
-0.009930121712386608,
0.02171933650970459,
-0.04196809232234955,
-0.014100393280386925,
0.009498493745923042,
0.07068894058465958,
-0.03944624960422516,
-0.006683378014713526,
-0.014350234530866146,
-0.011528096161782742,
0.031515248119831085,
-0.04752606153488159,
0.023241320624947548,
-0.01902635581791401,
0.02290947176516056,
0.01197093352675438,
0.024134928360581398,
-0.05042729154229164,
0.010376431047916412,
0.014072682708501816,
0.008145971223711967,
-0.018354132771492004,
0.0006548246601596475,
0.002942384220659733,
-0.010205968283116817,
0.07385488599538803,
0.005983318202197552,
-0.00817074254155159,
-0.03362041339278221,
-0.01524091325700283,
-0.03408696502447128,
-0.0288153775036335,
0.019117288291454315,
-0.029834069311618805,
0.02409069612622261,
0.00611839210614562,
-0.0038763321936130524,
-0.021374786272644997,
-0.06940383464097977,
0.0445530079305172,
-0.018793173134326935,
-0.008954090997576714,
-0.010915464721620083,
0.01649448648095131,
0.02319410629570484,
0.04234324395656586,
-0.04874096065759659,
0.015555541031062603,
-0.059340715408325195,
0.03932993859052658,
0.0037031141109764576,
0.014942260459065437,
-0.03458891063928604,
0.01604362390935421,
-0.013810432516038418,
-0.015836596488952637,
-0.038468457758426666,
-0.004188257269561291,
0.029592519626021385,
0.04414485767483711,
-0.01939203403890133,
0.030989831313490868,
-0.034064698964357376,
-0.005802819970995188,
0.01616836152970791,
-0.04754894599318504,
0.010071356780827045,
0.03497041389346123,
0.014279407449066639,
-0.04134175926446915,
-0.012632103636860847,
-0.011376037262380123,
0.016011139377951622,
0.012850657105445862,
0.013233164325356483,
-0.039355967193841934,
0.01146824099123478,
-0.04944984242320061,
-0.006807721219956875,
-0.08035731315612793,
0.0013368710642680526,
-0.037438083440065384,
0.07402155548334122,
-0.010722346603870392,
0.0006527180084958673,
-0.005687433294951916,
0.05955908074975014,
-0.01969418115913868,
-0.014096359722316265,
-0.005085759796202183,
0.00981762446463108,
-0.034010209143161774,
0.010519769974052906,
0.045101359486579895,
0.027303621172904968,
0.06532759964466095,
0.010118497535586357,
-0.018625637516379356,
0.021269896999001503,
-0.022764988243579865,
-0.057125598192214966,
0.0529206283390522,
0.0065017323940992355,
-0.002434290712699294,
0.0003594153095036745,
-0.03126109018921852,
-0.00930329691618681,
0.04994378238916397,
0.007605215534567833,
0.008932266384363174,
-0.005302329547703266,
-0.0879613533616066,
-0.004920170176774263,
-0.02830895408987999,
0.030181631445884705,
0.009215387515723705,
0.006744652986526489,
0.02512110397219658,
-0.005496138706803322,
-0.015835382044315338,
0.02465517446398735,
-0.002546696225181222,
-0.02768157236278057,
0.02997552789747715,
0.009666026569902897,
-0.0034404986072331667,
0.025869525969028473,
0.06030379608273506,
-0.006194598972797394,
-0.009057375602424145,
0.00984759908169508,
-0.005286799743771553,
-0.08465079963207245,
0.024019857868552208,
0.026432905346155167,
0.018629085272550583,
0.05975675955414772,
-0.06779084354639053,
0.001218851888552308,
0.012134034186601639,
-0.0817083790898323,
0.02002686634659767,
-0.02328619733452797,
0.020494632422924042,
-0.03068256378173828,
-0.01808461733162403,
-0.045791562646627426,
0.06369374692440033,
0.039706237614154816,
0.04852546378970146,
-0.01320443395525217,
0.009274409152567387,
0.0009238849161192775,
-0.02690993808209896,
-0.005512915551662445,
0.0317743755877018,
-0.0033900251146405935,
0.0020283437334001064,
0.09654362499713898,
0.009088363498449326,
-0.013403848744928837,
0.009561445564031601,
-0.005142370238900185,
-0.006853225640952587,
-0.014968357048928738,
0.011945129372179508,
0.028727445751428604,
-0.019400162622332573,
0.03353963419795036,
0.01416527945548296,
-0.0026501603424549103,
-0.0014023700496181846,
-0.006747010163962841,
-0.015332415699958801,
0.0055242921225726604,
0.014136136509478092,
-0.01781623251736164,
-0.05109422281384468,
0.0039710174314677715,
0.010852307081222534,
-0.04620729759335518,
-0.025943530723452568,
0.005386590491980314,
-0.05924958735704422,
0.050131481140851974,
-0.023469125851988792,
0.0005680660251528025,
-0.03547094017267227,
-0.009499012492597103,
0.03315988555550575,
0.008610647171735764,
0.004890209063887596,
0.027865566313266754,
-0.01865275576710701,
-0.032373107969760895,
0.01972714066505432,
-0.0009280149242840707,
-0.0005177785642445087,
-0.0317230187356472,
-0.020610347390174866,
-0.01678781770169735,
0.0014917243970558047,
0.015984725207090378,
-0.037878818809986115,
0.006174396723508835,
0.04297666996717453,
0.027308499440550804,
0.004556586965918541,
-0.02809249982237816,
-0.014053164049983025,
-0.006704356055706739,
-0.0567065104842186,
0.003512241877615452,
-0.03484483063220978,
-0.019928425550460815,
-0.015138993039727211,
-0.0023154611699283123,
-0.00236662570387125,
0.03941608592867851,
0.014258144423365593,
-0.014544013887643814,
0.02681826613843441,
0.04737580567598343,
-0.03344537317752838,
0.01506172027438879,
-0.08112697303295135,
-0.0028631098102778196,
0.0011465162970125675,
-0.011441430076956749,
-0.003769219620153308,
0.01126653328537941,
-0.029651256278157234,
0.02460995502769947,
0.02806176245212555,
-0.055925216525793076,
0.009685098193585873,
0.0027819438837468624,
-0.04295571520924568,
0.005566639360040426,
-0.01756894402205944,
-0.017500100657343864,
0.0482931062579155,
0.036530204117298126,
-0.0037764166481792927,
0.046624887734651566,
-0.017040906473994255,
-0.017950106412172318,
0.0052573420107364655,
-0.02708694525063038,
-0.010690261609852314,
-0.0026706347707659006,
-0.03906647488474846,
0.03493442013859749,
-0.04006502777338028,
-0.03139536455273628,
0.06818051636219025,
-0.06241447106003761,
0.017385704442858696,
0.048371750861406326,
0.0114493602886796,
-0.000989732681773603,
0.04075049236416817,
0.00666261650621891,
0.01325131207704544,
0.028106369078159332,
0.016013583168387413,
0.02615031786262989,
0.013820587657392025,
-0.0010377699509263039,
-0.029811225831508636,
0.0013980927178636193,
-0.040862806141376495,
0.015436392277479172,
-0.0277072973549366,
0.06669513881206512,
-0.012367229908704758,
-0.027202092111110687,
0.004926295019686222,
0.01050745602697134,
0.026464330032467842,
0.007300595752894878,
-0.025711549445986748,
0.037583716213703156,
-0.023000264540314674,
0.02521030604839325,
-0.0370129719376564,
-0.005674102809280157,
-0.054186321794986725,
0.06561078131198883,
0.029808714985847473,
0.04574764892458916,
-0.007832590490579605,
-0.0002639588783495128,
-0.03582780808210373,
-0.01654632017016411,
0.012164483778178692,
-0.04654553532600403,
-0.01343509741127491,
-0.009313265793025494,
-0.026979291811585426,
0.027984535321593285,
-0.036681342869997025,
-0.02252081409096718,
0.00192611466627568,
-0.002150510670617223,
0.03442491590976715,
0.03135504201054573,
-0.024094127118587494,
0.012675757519900799,
-0.02409675158560276,
0.0652574747800827,
-0.06259758025407791,
-0.023077234625816345,
0.01581508480012417,
0.002324105706065893,
0.02439085766673088,
0.01675404980778694
] |
<p>The Lagrangian of the Yang-Mills fields is given by
$$
\mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu}
D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+
\bar{c}^a(\partial\cdot D^{ab})c^b
$$
where the metric is $(-,+,+,+)$, and the conventions are the following:
$$
[D_{\mu},D_{\nu}]=-igF_{\mu\nu},\quad
D_{\mu}=\partial_{\mu}-igA^a_{\mu}t^a, \quad
D^{ab}_{\mu}=\delta^{ab}\partial_{\mu}-gf^{abc}A^c_{\mu}
$$</p>
<p>Let $\epsilon$ be an infinitesimal anticummuting parameter, and consider the BRST transformation:
$$
\delta\psi=ig\epsilon c^at^a\psi,\quad
\delta A^a_{\mu}=\epsilon D^{ab}_{\mu}c^b,\quad
\delta c^a=-\frac{1}{2}g\epsilon f^{abc}c^bc^c,\quad
\delta\bar{c}^a=\frac{1}{\xi}\epsilon\partial^{\mu}A^a_{\mu}
$$</p>
<p>I have calculated the corresponding Noether current as
$$
j_{BRST}^{\mu}=-g\bar{\psi}\gamma^{\mu}c^at^a\psi-F^{a\mu\nu}D^{ab}_{\nu}c^b-
\frac{1}{\xi}(\partial\cdot A^a)D^{ab\mu}c^b+
\frac{1}{2}gf^{abc}(\partial^{\mu}\bar{c}^a)c^bc^c
$$</p>
<p>I am not sure whether the result is correct or not, so I would like to check that $\partial_{\mu}j^{\mu}_{BRST}=0$. Even though I have used the equation of motion
$$
\partial_{\mu}F^{a\mu\nu}=-g\bar{\psi}\gamma^{\nu}t^a\psi-
gf^{abc}A^b_{\mu}F^{c\mu\nu}-\frac{1}{\xi}\partial^{\nu}
(\partial\cdot A^a)-gf^{abc}(\partial^{\nu}\bar{c}^b)c^c
$$
$$
(i\gamma^{\mu}D_{\mu}-m)\psi=0,\quad \partial^{\mu}D^{ab}_{\mu}c^b=0
$$
and spent about four hours, I still cannot get it right. Could someone help me check this? Thanks a lot.</p> | 1,544 | [
-0.01896403357386589,
-0.007164782378822565,
0.04243004322052002,
-0.0333874449133873,
0.04767689108848572,
0.026265565305948257,
-0.047183286398649216,
-0.02377784065902233,
-0.0016141749219968915,
-0.02475571632385254,
0.04514138400554657,
-0.00141996203456074,
0.09270808100700378,
0.0371943861246109,
0.020410677418112755,
0.001652442035265267,
-0.00782991386950016,
0.014998234808444977,
0.0019517644541338086,
-0.03546819090843201,
0.03614061698317528,
0.056312065571546555,
-0.014266589656472206,
0.005484438501298428,
-0.028305940330028534,
-0.0008405680418945849,
-0.02501089870929718,
-0.000248525757342577,
-0.0637604296207428,
0.08078277856111526,
-0.007164229638874531,
-0.003843392711132765,
0.04248668625950813,
0.009374613873660564,
-0.007950271479785442,
0.023859268054366112,
-0.0007583196857012808,
-0.05700283497571945,
-0.016779201105237007,
0.0187011007219553,
-0.05990566685795784,
-0.017086513340473175,
-0.06310681998729706,
0.033702999353408813,
-0.011813550256192684,
-0.007075528614223003,
-0.02594398707151413,
-0.008922932669520378,
0.04934597387909889,
-0.055086567997932434,
0.06778772175312042,
0.01032881997525692,
0.015348726883530617,
0.014044683426618576,
-0.046841707080602646,
-0.047555968165397644,
0.03531840443611145,
0.042266011238098145,
0.02434006705880165,
-0.07024682313203812,
-0.03199978172779083,
-0.005600533913820982,
0.019596897065639496,
-0.025316787883639336,
-0.022053048014640808,
0.03507871553301811,
0.029296239838004112,
0.01893334835767746,
0.022436214610934258,
-0.03187205269932747,
0.032980479300022125,
-0.03372896835207939,
0.05078436806797981,
-0.02820158191025257,
0.06440296769142151,
0.0008602127199992537,
-0.022478803992271423,
0.0037781873252242804,
0.0016010710969567299,
0.04309319332242012,
0.009092452004551888,
0.035265129059553146,
0.0048283906653523445,
-0.00457693450152874,
-0.003062912030145526,
-0.008975254371762276,
0.05109095945954323,
-0.014463808387517929,
-0.013120369054377079,
0.02843761257827282,
0.015082013793289661,
-0.016031045466661453,
0.03866381570696831,
-0.04468794912099838,
0.0008053472847677767,
0.041706301271915436,
0.014803031459450722,
0.028837351128458977,
-0.045743707567453384,
-0.004928239155560732,
-0.04547993093729019,
0.012750357389450073,
-0.0010061911307275295,
0.09041600674390793,
0.018280338495969772,
0.02779357135295868,
-0.016629958525300026,
-0.023243192583322525,
-0.027774907648563385,
-0.030165277421474457,
-0.05757635086774826,
0.006404577754437923,
-0.029915742576122284,
-0.031915757805109024,
-0.0008850496960803866,
-0.015440101735293865,
0.0020196749828755856,
-0.03703155741095543,
0.04902089759707451,
0.04066358134150505,
0.0653056874871254,
0.006967206951230764,
0.0010269841877743602,
0.01577833481132984,
-0.012330804951488972,
-0.005811584182083607,
0.06908299028873444,
0.003228953341022134,
-0.04478791356086731,
-0.02590288780629635,
0.02354384958744049,
-0.016106581315398216,
0.017214961349964142,
-0.008184653706848621,
0.016355156898498535,
-0.030473269522190094,
-0.08350472897291183,
-0.08460976928472519,
0.013720577582716942,
-0.008588824421167374,
-0.028955422341823578,
-0.04404208064079285,
-0.04528481885790825,
0.025130106136202812,
0.09051494300365448,
0.012331911362707615,
0.0030111351516097784,
0.004832798149436712,
0.026617297902703285,
0.02581542544066906,
0.005861798767000437,
0.0012804364087060094,
0.014427115209400654,
-0.041383203119039536,
-0.05456205829977989,
-0.049641452729701996,
-0.0028774584643542767,
0.03069055639207363,
0.004630193114280701,
0.008613724261522293,
0.06685436517000198,
0.012881185859441757,
0.009070250205695629,
0.012547214515507221,
-0.009948701597750187,
-0.041280828416347504,
0.027630509808659554,
0.008061172440648079,
0.029195785522460938,
0.01658753678202629,
-0.014617258682847023,
0.023128805682063103,
0.007261157967150211,
0.041146840900182724,
0.07158683240413666,
-0.048566754907369614,
-0.002763633616268635,
-0.03318936750292778,
-0.010891339741647243,
0.024336770176887512,
-0.020083162933588028,
-0.055180326104164124,
-0.04632450267672539,
0.024545572698116302,
0.020133502781391144,
0.015965193510055542,
-0.00901691522449255,
0.0036123127210885286,
0.033166710287332535,
-0.08064430207014084,
-0.017526347190141678,
-0.04167073965072632,
0.007598533295094967,
0.018390916287899017,
-0.027519352734088898,
0.04874889552593231,
-0.0009164001676253974,
-0.006796005181968212,
-0.011721224524080753,
-0.050576455891132355,
0.007881169207394123,
0.043044429272413254,
-0.0021760459057986736,
0.03250743821263313,
0.025672733783721924,
0.016933126375079155,
0.011056000366806984,
-0.0015669395215809345,
0.039698533713817596,
-0.01328253373503685,
-0.015092520974576473,
-0.01160380057990551,
-0.012364571914076805,
0.03966710343956947,
-0.018229225650429726,
0.02661864086985588,
0.005464652087539434,
0.016576603055000305,
-0.02947152592241764,
0.04171299561858177,
-0.039987269788980484,
0.059288471937179565,
0.04622747749090195,
-0.023319195955991745,
-0.0018451004289090633,
0.05143754929304123,
-0.022095972672104836,
0.07845529168844223,
-0.03578775003552437,
-0.022336289286613464,
-0.02578788436949253,
-0.010440045036375523,
0.03462062403559685,
0.023719534277915955,
-0.03677893802523613,
-0.008106074295938015,
0.024357033893465996,
0.011217385530471802,
0.05178023874759674,
0.03335973620414734,
-0.01641041785478592,
-0.054011810570955276,
0.009020243771374226,
0.025597374886274338,
-0.016659364104270935,
-0.036580540239810944,
0.01303703524172306,
-0.05007890984416008,
0.00792594812810421,
-0.028215376660227776,
-0.016335856169462204,
0.009216847829520702,
0.005900944583117962,
-0.028949813917279243,
-0.021906493231654167,
-0.006560223642736673,
0.07242898643016815,
-0.008607365190982819,
0.06478245556354523,
0.056643664836883545,
-0.01940029300749302,
-0.021692495793104172,
-0.0016748483758419752,
-0.01816205307841301,
0.021151816472411156,
-0.0065886350348591805,
0.012112816795706749,
0.00019891878764610738,
-0.00922632496803999,
-0.021460624411702156,
0.006005899980664253,
0.007067058701068163,
-0.009403465315699577,
-0.021554341539740562,
-0.025529244914650917,
-0.007972309365868568,
0.04864883795380592,
0.04942718893289566,
-0.018307730555534363,
-0.00871348101645708,
0.05960727855563164,
0.029401270672678947,
0.03340454027056694,
0.036788392812013626,
0.0075888303108513355,
-0.03044051118195057,
-0.04858485609292984,
-0.02042066864669323,
0.036563728004693985,
-0.027811340987682343,
-0.00787855964154005,
-0.004357373341917992,
-0.0007661403506062925,
-0.040835995227098465,
-0.029513172805309296,
0.012014871463179588,
0.018636852502822876,
-0.03151482716202736,
0.007118783425539732,
0.0531887523829937,
0.05578102916479111,
-0.05656703561544418,
-0.0061259157955646515,
-0.003158444771543145,
-0.035293661057949066,
-0.001946158823557198,
0.024781404063105583,
-0.03926555812358856,
-0.05289015918970108,
0.04627591371536255,
0.026999149471521378,
-0.00872046034783125,
0.04198894649744034,
-0.04869068041443825,
-0.02031264267861843,
0.02794768661260605,
0.009483079425990582,
0.008102167397737503,
0.021864376962184906,
-0.07158879190683365,
0.10476424545049667,
0.06510011106729507,
-0.038107238709926605,
-0.002199232578277588,
-0.006515884306281805,
0.004339173436164856,
-0.029268236830830574,
0.02156912535429001,
0.03706425428390503,
-0.01870073564350605,
0.023227591067552567,
0.03639605641365051,
0.056368421763181686,
0.024624960497021675,
0.017143087461590767,
-0.011319516226649284,
0.03862226381897926,
0.008731112815439701,
-0.00714381318539381,
0.0816415399312973,
-0.02218613401055336,
0.02287735976278782,
-0.013536792248487473,
0.01388919074088335,
-0.013302993960678577,
-0.009119907394051552,
-0.029581816866993904,
0.05678334832191467,
0.0023031816817820072,
0.0008181983139365911,
-0.02628670260310173,
0.020265528932213783,
0.0006891234079375863,
-0.06206170842051506,
-0.015813494101166725,
0.016702942550182343,
-0.010371400974690914,
-0.011154946871101856,
-0.01260245032608509,
0.00593084329739213,
0.03668241575360298,
-0.031714845448732376,
-0.03403778374195099,
-0.01563134603202343,
-0.020425288006663322,
0.0322461761534214,
-0.03299533948302269,
-0.005490583833307028,
-0.019313503056764603,
0.04000212252140045,
-0.027741245925426483,
-0.0010536200134083629,
-0.012043178081512451,
0.006792737636715174,
-0.08195733278989792,
-0.01833507977426052,
-0.0022832988761365414,
0.06716399639844894,
0.039604853838682175,
0.013767997734248638,
0.03116457350552082,
0.018984712660312653,
-0.01895567961037159,
0.0045700776390731335,
-0.06424466520547867,
0.029263900592923164,
-0.026656629517674446,
-0.00977223552763462,
-0.004410637076944113,
-0.04631546884775162,
0.011201768182218075,
-0.02312787063419819,
-0.023986293002963066,
-0.018944064155220985,
0.02085568569600582,
-0.027933375909924507,
0.05249718949198723,
-0.05157608166337013,
-0.020286008715629578,
-0.022676188498735428,
0.05530001223087311,
0.025012148544192314,
-0.003890598425641656,
-0.006413815077394247,
0.01668635942041874,
-0.04384719207882881,
-0.0445898212492466,
0.0007222624262794852,
0.02770412527024746,
0.028319265693426132,
0.028358522802591324,
0.029617473483085632,
0.028070911765098572,
-0.028322365134954453,
-0.009797095321118832,
0.06307381391525269,
0.019259018823504448,
-0.011412759311497211,
-0.026148933917284012,
-0.013060614466667175,
-0.05932305008172989,
-0.03244321793317795,
0.017629249021410942,
0.05952753126621246,
0.02006993629038334,
0.003364702919498086,
0.02463037148118019,
0.00813683308660984,
0.00999159924685955,
0.01928642764687538,
0.05310552939772606,
0.014172259718179703,
-0.024183524772524834,
-0.0555945485830307,
0.01983758620917797,
0.022138085216283798,
-0.0022025550715625286,
-0.0038207448087632656,
-0.00404867809265852,
-0.017871664837002754,
-0.003334938082844019,
0.03767037019133568,
0.033293966203927994,
-0.04073500260710716,
0.008034083992242813,
0.0025041913613677025,
0.017809046432375908,
0.023484282195568085,
0.009966556914150715,
0.02998049557209015,
0.05148734524846077,
0.024710392579436302,
0.000644360261503607,
0.010361201129853725,
-0.04688580334186554,
-0.01575908623635769,
0.046041492372751236,
0.03028782084584236,
0.010038686916232109,
0.009119907394051552,
-0.053796056658029556,
0.014477452263236046,
0.01123100146651268,
-0.0038139030802994967,
0.03746521845459938,
0.06096388399600983,
-0.0007633715867996216,
-0.007606261409819126,
-0.024624260142445564,
-0.03635432571172714,
0.06441732496023178,
-0.03106813319027424,
-0.02584763988852501,
-0.07796237617731094,
0.0034910247195512056,
0.00633463729172945,
0.050148043781518936,
-0.0320127010345459,
0.03246260806918144,
0.003628042060881853,
0.013418485410511494,
-0.011656996794044971,
0.02817413955926895,
-0.0008805902907624841,
-0.08037857711315155,
-0.001812754082493484,
0.016445640474557877,
-0.016020672395825386,
0.04127729684114456,
0.01138376910239458,
-0.020563995465636253,
0.041790835559368134,
0.03242621570825577,
0.05437065660953522,
0.022523218765854836,
-0.07110816240310669,
0.04378616064786911,
0.0046762628480792046,
-0.02717536874115467,
0.03947528079152107,
0.001755274715833366,
-0.009523505344986916,
0.0004431371053215116,
-0.032714053988456726,
0.02039763331413269,
-0.012892497703433037,
0.022899458184838295,
-0.0172563623636961,
-0.0013068336993455887,
-0.027630778029561043,
0.03218919783830643,
-0.05664239451289177,
0.02434365265071392,
0.00035955742350779474,
-0.026255043223500252,
-0.012050548568367958,
0.007789713330566883,
-0.00376888201572001,
-0.012665187940001488,
0.01853983663022518,
0.027059316635131836,
0.015411755070090294,
0.007258773781359196,
0.018696319311857224,
-0.034853700548410416,
0.008215988986194134,
0.021739942952990532,
-0.04767459258437157,
-0.013946539722383022,
-0.003162731882184744,
-0.0026677283458411694,
-0.016239289194345474,
-0.014842858538031578,
0.025702308863401413,
0.033123139292001724,
0.004614046774804592,
0.03419012576341629,
-0.003484063781797886,
-0.05208900570869446,
0.012090528383851051,
-0.009016776457428932,
0.0017211056547239423,
-0.047420065850019455,
-0.019886009395122528,
0.014647476375102997,
0.024052632972598076,
-0.08387866616249084,
-0.017608288675546646,
-0.012200843542814255,
-0.02437850646674633,
-0.026269854977726936,
-0.0024157934822142124,
-0.00016395557031501085,
0.013825230300426483,
-0.037030935287475586,
-0.00008876510401023552,
0.048554763197898865,
-0.044339485466480255,
0.008087929338216782,
0.00209675426594913,
0.056421518325805664,
0.02361444942653179,
-0.020436037331819534,
-0.016712263226509094,
-0.000339305232046172,
-0.001286383718252182,
0.012293846346437931,
0.031995370984077454,
0.04004594683647156,
-0.009814775548875332,
-0.032527703791856766,
-0.025742068886756897,
-0.0027734392788261175,
0.039135176688432693,
-0.0012987947557121515,
-0.00046164909144863486,
0.020704567432403564,
0.01975187472999096,
0.006099947262555361,
-0.0009110049577429891,
-0.026234596967697144,
-0.033360034227371216,
0.026660531759262085,
-0.012836241163313389,
-0.019551536068320274,
-0.004255656152963638,
-0.019261682406067848,
0.039933010935783386,
-0.008206904865801334,
-0.004114049021154642,
-0.02658907324075699,
0.045238252729177475,
-0.022103482857346535,
-0.04496174678206444,
-0.0009501004824414849,
-0.004015537444502115,
-0.024484384804964066,
-0.04333183169364929,
0.03221892565488815,
0.005093275103718042,
-0.013174799270927906,
-0.029087506234645844,
-0.010547238402068615,
-0.03040781244635582,
0.02761324867606163,
0.04195678234100342,
0.04037945345044136,
0.046747010201215744,
0.02823021076619625,
-0.008313266560435295,
0.010038030333817005,
-0.014010554179549217,
-0.0035159767139703035,
0.02139631099998951,
0.017360297963023186,
0.005367306061089039,
-0.029429299756884575,
-0.016700750216841698,
0.019481657072901726,
0.04199567437171936,
-0.050607144832611084,
-0.00332705513574183,
0.007281893398612738,
0.004470540210604668,
-0.005764500703662634,
0.012280918657779694,
-0.02986992709338665,
0.05707909166812897,
-0.05831850320100784,
0.07779231667518616,
-0.0020275830756872892,
-0.016616687178611755,
0.034388575702905655,
0.041065603494644165,
0.0048723830841481686,
0.007977365516126156,
-0.028684310615062714,
-0.04225343093276024,
0.0034104555379599333,
0.04595131427049637,
0.012638945132493973,
0.029823394492268562,
0.01360973808914423,
0.06079092621803284,
-0.012871423736214638,
0.014487058855593204,
-0.005248488392680883,
-0.02022118680179119,
-0.006697721779346466,
-0.02229967713356018,
-0.07202675938606262,
0.08233145624399185,
-0.05089033395051956,
-0.006437311414629221,
-0.0007129148580133915,
-0.010769804008305073,
0.041500575840473175,
0.017748359590768814,
0.025619423016905785,
-0.03634774684906006,
0.078675776720047,
-0.02669108845293522,
0.028935911133885384,
-0.006650459486991167,
-0.0005449625314213336,
0.12681689858436584,
0.04877936840057373,
0.0024860305711627007,
-0.08318492025136948,
0.020381804555654526,
0.0041832816787064075,
0.025780193507671356,
-0.06467483192682266,
0.03936897590756416,
-0.04455059394240379,
-0.021485457196831703,
-0.03181029111146927,
0.05037011206150055,
-0.020289232954382896,
-0.028854036703705788,
0.03788699582219124,
-0.014813221991062164,
-0.03628856688737869,
0.023759331554174423,
-0.006506697274744511,
-0.03506774455308914,
-0.002692955080419779,
-0.004702042322605848,
0.031720440834760666,
-0.0148615762591362,
0.03032052516937256,
-0.00687382509931922,
-0.04085773974657059,
0.002338477410376072,
-0.014611034654080868,
-0.03641501069068909,
-0.008956225588917732,
-0.0012324658455327153,
0.018551064655184746,
-0.017973221838474274,
-0.014151575043797493,
0.016162261366844177,
0.0024395158980041742,
0.061024874448776245,
0.038196999579668045,
-0.027234256267547607,
0.04195123538374901,
0.01534517016261816,
0.00729396240785718,
-0.023095358163118362,
-0.009964406490325928,
-0.02208792045712471,
0.04819038137793541,
-0.01267889142036438,
0.011627218686044216,
0.027310863137245178,
-0.01987173594534397,
0.02989104762673378,
-0.019093776121735573,
0.007787234149873257,
0.0024088064674288034,
-0.009851240552961826,
-0.047016389667987823,
0.003758606966584921,
-0.0036519840359687805,
0.038901131600141525,
0.015901939943432808,
0.03080172836780548,
-0.05178339034318924,
-0.03086942434310913,
0.012700400315225124,
-0.0032394896261394024,
0.02912716381251812,
0.03522275760769844,
-0.011273376643657684,
-0.04107466712594032,
0.016096627339720726,
-0.023601064458489418,
-0.02351215109229088,
-0.0025826748460531235,
0.02855650894343853,
0.0774475634098053,
-0.013416546396911144,
0.0034458979498595,
-0.045521996915340424,
-0.06808432191610336,
-0.012433729134500027,
-0.008033201098442078,
0.006819691509008408,
-0.028280384838581085,
-0.000863405701238662,
0.012586218304932117,
0.061962876468896866,
0.005005471408367157,
-0.017225317656993866,
0.0007780870073474944,
0.05334629863500595,
0.03519822284579277,
0.008238829672336578,
-0.014296183362603188,
0.014736366458237171,
-0.02841275744140148,
-0.00008248243830166757,
-0.00730805704370141,
0.018555764108896255,
0.019399384036660194,
0.015153774991631508,
-0.011113886721432209,
0.04521442949771881,
0.0017919500824064016,
-0.054263073951005936,
0.015585862100124359,
0.004136398434638977,
0.021610038354992867,
0.043908726423978806,
-0.030686618760228157,
-0.02489873394370079,
-0.017674753442406654,
0.020245205610990524,
0.01080950628966093,
0.005652701947838068,
0.0029500978998839855,
-0.02324380911886692,
-0.01759275421500206,
-0.006753858178853989,
-0.004108356311917305,
-0.042932748794555664,
0.0002151736553059891,
-0.016714856028556824,
0.02619146555662155,
-0.05429074540734291,
0.01614636369049549,
-0.015620749443769455,
0.05279166251420975,
-0.02619367279112339,
0.0029537302907556295,
0.013610614463686943,
0.018151994794607162,
-0.018085097894072533,
-0.012664220295846462,
-0.02019071765244007,
0.022955888882279396,
0.01559151615947485,
0.028555965051054955,
-0.03826333209872246,
0.023016588762402534,
-0.02094876766204834,
-0.02958039566874504,
0.05223066732287407,
0.019786501303315163,
0.025191038846969604,
0.012808547355234623,
-0.0025648593436926603,
-0.021392596885561943,
0.017152106389403343,
-0.014682859182357788,
-0.006011561024934053,
-0.039967238903045654,
-0.03573845699429512,
0.024321360513567924,
-0.04311808943748474,
0.016079131513834,
0.010944751091301441,
0.019263766705989838,
-0.014257583767175674,
-0.010835415683686733,
-0.057677268981933594,
0.001069515012204647,
-0.014235656708478928,
-0.025488408282399178,
-0.004807399120181799,
-0.02594984509050846,
0.02268725447356701,
-0.023510659113526344,
0.03038552589714527,
-0.030691366642713547,
0.007085723336786032,
-0.007300828583538532,
-0.00654942449182272,
-0.06496928632259369,
-0.03704666718840599,
0.018495265394449234,
0.02863403782248497,
0.07804565876722336,
-0.059930574148893356,
0.024406645447015762,
0.04614916071295738,
-0.06619876623153687,
0.030209047719836235,
-0.046586401760578156,
-0.008635323494672775,
-0.03386217728257179,
-0.03890194743871689,
-0.022190917283296585,
0.057675816118717194,
0.030948389321565628,
0.00956539437174797,
0.010665967129170895,
-0.022651871666312218,
0.0016162908868864179,
-0.026866119354963303,
-0.021290110424160957,
0.013894269242882729,
0.039555564522743225,
-0.044124674052000046,
0.04950397461652756,
0.001352291670627892,
-0.0404004231095314,
0.0003496271383482963,
0.002887297421693802,
-0.01522352546453476,
0.0005178477149456739,
0.038937389850616455,
0.05089303106069565,
0.018522268161177635,
0.022272123023867607,
-0.0007869541877880692,
-0.014042596332728863,
-0.02135062962770462,
0.039259668439626694,
0.05224505811929703,
-0.04729028791189194,
0.028821587562561035,
-0.006635830271989107,
-0.03476455807685852,
-0.052619751542806625,
0.013209264725446701,
-0.06385292857885361,
-0.025397304445505142,
-0.007108277175575495,
-0.002309574047103524,
-0.022192686796188354,
-0.007076120935380459,
-0.008484462276101112,
-0.015032008290290833,
0.014408021233975887,
0.046208251267671585,
0.0037328540347516537,
-0.0027246989775449038,
0.01610303483903408,
-0.005689576268196106,
-0.014764632098376751,
0.008755724877119064,
0.013765792362391949,
-0.012962930835783482,
-0.01862667314708233,
-0.0312676839530468,
-0.026254409924149513,
0.006426336709409952,
-0.014896445907652378,
-0.02779172547161579,
-0.04032214730978012,
0.026055311784148216,
-0.015277481637895107,
-0.01619419828057289,
-0.08275867253541946,
-0.020938964560627937,
0.010550573468208313,
-0.049034323543310165,
0.035775814205408096,
0.001565861632116139,
-0.02133181504905224,
-0.007289198227226734,
-0.018401721492409706,
-0.006902746856212616,
0.013465302996337414,
0.02938620187342167,
-0.030198276042938232,
-0.03724644333124161,
0.012784074060618877,
-0.01018604263663292,
0.008057487197220325,
-0.019368290901184082,
-0.007573991548269987,
0.023474857211112976,
0.01364157348871231,
0.007659572176635265,
0.026805564761161804,
-0.004731304477900267,
0.039436373859643936,
0.0039571006782352924,
-0.02305806614458561,
0.028836393728852272,
0.04834572598338127,
-0.05059459060430527,
0.028491683304309845,
-0.029807820916175842,
-0.0024633740540593863,
0.05018102377653122,
0.04711523652076721,
0.036313313990831375,
0.033063020557165146,
-0.03327831253409386,
-0.03679194673895836,
0.00047206858289428055,
-0.0115292277187109,
0.0021905298344790936,
-0.0192047581076622,
-0.002553145168349147,
0.010760821402072906,
-0.03189205750823021,
0.016757596284151077,
0.052285317331552505,
-0.029489316046237946,
-0.028854986652731895,
0.05417082458734512,
-0.012872930616140366,
0.006186394486576319,
0.02195337601006031,
0.0018382861744612455,
-0.001985500566661358,
0.02596951462328434,
-0.0006357126403599977,
0.024694601073861122,
0.0076391627080738544,
-0.006745262537151575,
0.016412150114774704,
0.003096513682976365,
-0.02161024510860443,
-0.004696812480688095,
-0.013165771961212158,
0.007391577120870352,
-0.029237471520900726,
-0.022380154579877853,
0.055584367364645004,
-0.0016853627748787403,
0.05646273493766785,
0.041764967143535614,
-0.05199924483895302,
0.070126473903656,
-0.0357380285859108,
0.027063263580203056,
-0.022216850891709328,
0.010554998181760311,
-0.021492162719368935,
0.0583813451230526,
0.005949877668172121,
0.04230443015694618,
-0.002646101638674736,
-0.01449573878198862,
-0.02214782126247883,
-0.008195631206035614,
-0.011296084150671959,
-0.0688215047121048,
-0.029727524146437645,
0.03394145146012306,
-0.008135372772812843,
0.021027391776442528,
-0.046276118606328964,
-0.028099296614527702,
-0.045032255351543427,
0.01259130984544754,
-0.0027769585140049458,
0.005831133108586073,
0.02160314843058586,
-0.016944540664553642,
0.02637377940118313,
0.041642528027296066,
0.005915755406022072,
-0.02239760011434555,
0.01691829040646553,
0.0019946538377553225,
-0.03685200586915016,
-0.016602395102381706
] |
<p>Any finite & non empty set of masses has a computable center of gravity:
$\vec{OG} = \frac{\sum_i m_i \vec{OM}_i}{\sum_i m_i}$ .</p>
<p>Does the contrapositive permits to conclude that a mass system with
physical evidence that it doesn't have a gravity center is an infinite
set of mass (i.e. of cardinal larger than $\aleph_0$) ?</p>
<p>On the other hand,
an infinite set of masses may have a computable center of gravity.
Ex. : within a 2D infinite plan, an infinite set of equal masses linearly distributed along the x and y axis will have a gravity center at its origin O.
Unfortunately, this example doesn't have a center of gravity since the integral of masses in this particular topology doesn't converge. </p> | 1,545 | [
-0.02863365411758423,
0.009791371412575245,
0.01338167954236269,
-0.011477896943688393,
0.03976060450077057,
0.0010572080500423908,
-0.009578350931406021,
-0.04159877076745033,
0.019371822476387024,
-0.011294920928776264,
0.009040587581694126,
0.010567866265773773,
0.06092222034931183,
0.04626725986599922,
-0.005891344044357538,
0.016910215839743614,
-0.0416610948741436,
0.012982177548110485,
-0.005040488671511412,
-0.06641902029514313,
0.00696470495313406,
0.06140545383095741,
0.04018053412437439,
-0.01013620663434267,
-0.024239860475063324,
0.018913153558969498,
-0.03133898600935936,
-0.007960307411849499,
-0.005125933792442083,
0.08017690479755402,
-0.040320731699466705,
-0.027190672233700752,
-0.019897863268852234,
0.059514645487070084,
0.045161694288253784,
0.022606076672673225,
-0.00558372912928462,
-0.013265890069305897,
0.017500055953860283,
0.0002774499007500708,
0.0013276495737954974,
-0.041529327630996704,
-0.016587289050221443,
0.04524199292063713,
0.020078497007489204,
-0.007335941772907972,
0.00041462128865532577,
-0.011283752508461475,
0.04251515492796898,
-0.0491579994559288,
0.05617433413863182,
-0.009457219392061234,
0.014893637038767338,
0.032328832894563675,
0.009206603281199932,
-0.01387020107358694,
0.021070538088679314,
0.05311300978064537,
-0.0019808209035545588,
-0.041165947914123535,
-0.04208327457308769,
0.015097818337380886,
0.01803526282310486,
-0.05491148307919502,
-0.037321340292692184,
0.03786325454711914,
0.018439162522554398,
-0.0036505151074379683,
0.009546559303998947,
-0.0130592817440629,
0.004157025367021561,
0.05886411294341087,
-0.009510746225714684,
-0.004529725760221481,
0.015211375430226326,
0.002567413728684187,
0.011768992990255356,
-0.02138756588101387,
0.022179260849952698,
0.016805164515972137,
0.019652212038636208,
-0.015347585082054138,
0.06232848018407822,
0.05780939385294914,
0.029445171356201172,
-0.012047901749610901,
0.020623141899704933,
-0.03536628559231758,
0.02670532837510109,
0.04880226403474808,
-0.019524596631526947,
-0.03251924738287926,
0.03778361156582832,
-0.02367527410387993,
-0.025057706981897354,
0.029732191935181618,
-0.016978127881884575,
0.0345180407166481,
0.008046111091971397,
-0.013399090617895126,
-0.008014830760657787,
-0.02029615081846714,
-0.003036386100575328,
0.06482958048582077,
0.024143116548657417,
-0.02204085700213909,
-0.052530039101839066,
0.027473866939544678,
-0.033351603895425797,
-0.018141407519578934,
-0.0579356923699379,
0.05697779729962349,
0.019940560683608055,
0.043556228280067444,
0.05738777294754982,
0.0031578673515468836,
-0.0029790576081722975,
-0.0159002672880888,
-0.000592240015976131,
0.02217921055853367,
0.04233632981777191,
0.0056124222464859486,
-0.011714814230799675,
-0.04967384785413742,
-0.04281463474035263,
0.0003823656006716192,
0.043390076607465744,
-0.004485912621021271,
-0.014322157949209213,
0.03098660334944725,
0.032128166407346725,
0.02307143434882164,
-0.00816285703331232,
0.030938057228922844,
0.04818717762827873,
0.0015794377541169524,
-0.07076191157102585,
-0.04076646268367767,
0.03709305077791214,
0.010539088398218155,
-0.03049149177968502,
-0.03286944329738617,
-0.02552897296845913,
0.06789965182542801,
0.029388288035988808,
-0.004523108247667551,
-0.010159231722354889,
0.002312898403033614,
0.039743490517139435,
0.03316151723265648,
-0.02860001102089882,
-0.05130255967378616,
-0.030678875744342804,
-0.05678574740886688,
-0.014444733038544655,
-0.07230673730373383,
0.05909270420670509,
0.02706490084528923,
-0.002209853380918503,
-0.03447418659925461,
0.03657044842839241,
0.00006756420043529943,
0.019734490662813187,
-0.002897249534726143,
-0.0035747040528804064,
-0.024369539692997932,
0.06530415266752243,
0.05621795356273651,
-0.01503333356231451,
0.032486170530319214,
0.018980156630277634,
0.022102592512965202,
0.024924209341406822,
0.01710262894630432,
0.04973173514008522,
-0.03770582005381584,
-0.029185669496655464,
-0.03340098261833191,
0.04100885987281799,
0.024872424080967903,
-0.03315422683954239,
-0.03425487130880356,
-0.024241911247372627,
-0.009673820808529854,
-0.009857166558504105,
0.05279518663883209,
-0.02709980495274067,
-0.020627539604902267,
0.03379768878221512,
-0.02443072199821472,
0.010715563781559467,
-0.07600320130586624,
-0.0052402690052986145,
0.02416171319782734,
-0.00832856260240078,
0.014914900064468384,
0.016012806445360184,
-0.001441001775674522,
-0.05485448241233826,
-0.0079873101785779,
0.01313887070864439,
0.029077783226966858,
0.03366483375430107,
-0.03194291144609451,
0.017845317721366882,
0.022605562582612038,
-0.0004634785873349756,
0.011000514030456543,
0.022655021399259567,
-0.025798479095101357,
-0.07036436349153519,
0.008509702049195766,
-0.013658303767442703,
0.0231167059391737,
0.029050378128886223,
0.014913813211023808,
-0.010870239697396755,
0.03744983300566673,
-0.009042584337294102,
0.07485738396644592,
-0.03800484165549278,
0.0737735852599144,
0.053679049015045166,
0.014728495851159096,
-0.004475932102650404,
0.027348536998033524,
0.011433851905167103,
0.020366737619042397,
-0.007124640047550201,
-0.04213254526257515,
-0.03615659102797508,
-0.05597870051860809,
-0.008496100082993507,
0.04951540753245354,
-0.03949962928891182,
0.0350678414106369,
0.049979694187641144,
0.06725657731294632,
-0.013361083343625069,
-0.01257771160453558,
-0.02096240036189556,
-0.01970241218805313,
0.004188996739685535,
0.010877215303480625,
0.03480519726872444,
0.008558250032365322,
-0.00023235476692207158,
0.027623364701867104,
-0.024721110239624977,
0.00849459320306778,
0.01327672228217125,
-0.01462476421147585,
-0.0005447090952657163,
-0.01581537164747715,
-0.018860120326280594,
-0.024998145177960396,
0.017152834683656693,
0.03668074309825897,
0.032169047743082047,
0.05564112216234207,
-0.01170913316309452,
-0.02953306958079338,
-0.08571059256792068,
-0.02521272376179695,
0.02255408465862274,
0.015593423508107662,
-0.04076821357011795,
-0.01905186101794243,
0.03799347206950188,
-0.0077848671935498714,
0.0194091759622097,
-0.04037315025925636,
-0.010445164516568184,
-0.004707162268459797,
0.017289360985159874,
0.006586682517081499,
-0.007453931961208582,
0.004467886872589588,
-0.023481473326683044,
0.01656523533165455,
0.0027362441178411245,
-0.00214584544301033,
-0.014866657555103302,
0.019195403903722763,
-0.07203880697488785,
-0.01777896285057068,
-0.03454609960317612,
-0.02857392467558384,
0.05230186879634857,
0.010426226072013378,
0.008851089514791965,
-0.004216526169329882,
0.005116589367389679,
-0.024765677750110626,
-0.02607942931354046,
-0.02900184504687786,
0.0032472277525812387,
0.00019468460232019424,
-0.008623859845101833,
0.02442568726837635,
0.012777440249919891,
-0.07508464902639389,
0.03252848610281944,
-0.028230704367160797,
-0.05695207789540291,
-0.0014419519575312734,
-0.016656609252095222,
0.007877379655838013,
-0.03350077569484711,
0.026537172496318817,
0.002872324548661709,
-0.04163460060954094,
-0.015244117937982082,
-0.08077903091907501,
-0.0684456080198288,
0.02321682870388031,
-0.03465573117136955,
0.04502151161432266,
0.02131902240216732,
-0.07095080614089966,
0.07666566222906113,
0.04868946224451065,
-0.05144709348678589,
-0.0022074314765632153,
-0.001245011924766004,
0.03689366206526756,
0.008494286797940731,
0.0013437679735943675,
-0.0179587472230196,
0.014387188479304314,
0.011727354489266872,
0.06356184929609299,
0.010301300324499607,
0.005472299177199602,
-0.032194990664720535,
0.03050319477915764,
0.013560614548623562,
0.014981385320425034,
0.012600606307387352,
0.03390498831868172,
0.005804778542369604,
0.01704695075750351,
0.01322233211249113,
-0.0006980729522183537,
0.018533950671553612,
-0.01616303063929081,
-0.07387959212064743,
0.02382085844874382,
-0.003798984456807375,
0.030117148533463478,
-0.010345453396439552,
0.058138251304626465,
0.0267527736723423,
-0.01409448403865099,
-0.010004428215324879,
0.04761306568980217,
0.0466017909348011,
-0.019115490838885307,
0.010971599258482456,
0.042685747146606445,
0.02291395328938961,
-0.02896786481142044,
-0.01508202776312828,
0.02094489336013794,
-0.016599280759692192,
0.01260928064584732,
-0.02331695705652237,
-0.02280401811003685,
0.041193149983882904,
0.04727506637573242,
0.005913506727665663,
0.012363712303340435,
-0.004252930637449026,
-0.009495830163359642,
-0.08108542114496231,
-0.0038400066550821066,
0.00283335754647851,
0.029110543429851532,
-0.009515422396361828,
0.0025284599978476763,
0.01510047260671854,
0.02075188048183918,
-0.0608002208173275,
0.011982031166553497,
-0.11378248780965805,
-0.022981325164437294,
-0.05351772904396057,
0.022524714469909668,
-0.016677625477313995,
-0.03526751697063446,
-0.01625884138047695,
-0.008995885960757732,
-0.008985637687146664,
0.0006661754450760782,
-0.01478536520153284,
-0.07816766202449799,
-0.005853545386344194,
-0.05749192833900452,
-0.03194339573383331,
0.020321864634752274,
-0.012213795445859432,
0.024698762223124504,
-0.04471125826239586,
0.024049948900938034,
0.007354123517870903,
-0.029353078454732895,
-0.017523368820548058,
-0.015892811119556427,
0.04824646934866905,
-0.025436516851186752,
0.01350138708949089,
0.04784980043768883,
0.03479141741991043,
-0.020987283438444138,
0.023580966517329216,
0.0051550171338021755,
0.057828690856695175,
-0.019954120740294456,
-0.03694929555058479,
-0.007064344827085733,
-0.06019096449017525,
-0.02554543875157833,
0.031174790114164352,
0.01983839087188244,
-0.0077973781153559685,
-0.03186565265059471,
0.0700274407863617,
0.00778772821649909,
-0.004710094071924686,
0.05749909207224846,
0.07892941683530807,
0.044390831142663956,
-0.002429516986012459,
-0.0263407900929451,
-0.02240603044629097,
-0.004665530286729336,
-0.019372420385479927,
0.053639840334653854,
-0.002242320915684104,
-0.0033649257384240627,
0.02568882144987583,
-0.005647422280162573,
0.02533447928726673,
0.010522129014134407,
0.01182583812624216,
-0.0032560487743467093,
0.022342799231410027,
-0.002573043340817094,
0.007749170530587435,
0.019779998809099197,
0.004501613322645426,
0.033877722918987274,
0.016422297805547714,
-0.007995018735527992,
-0.06102115660905838,
-0.02261376939713955,
0.05760763958096504,
0.004284176975488663,
0.0020253839902579784,
-0.004667340312153101,
-0.032948561012744904,
-0.05758976936340332,
0.05940437689423561,
-0.010580012574791908,
0.03316221758723259,
-0.027906781062483788,
-0.01635834202170372,
0.0007835592841729522,
-0.006958070211112499,
-0.019681956619024277,
-0.02690987102687359,
0.0027889602351933718,
0.04051204398274422,
0.0028671319596469402,
0.011407454498112202,
-0.04894603043794632,
-0.015111290849745274,
0.002308356110006571,
0.024379927664995193,
0.0374041311442852,
-0.0226752869784832,
0.0022692459169775248,
0.022976992651820183,
0.002638245699927211,
-0.07252603769302368,
-0.003138925414532423,
0.014900010079145432,
-0.04847487434744835,
0.03442613035440445,
-0.0007920550997368991,
-0.024595243856310844,
0.044925790280103683,
0.006004287861287594,
-0.0041349222883582115,
0.04283301532268524,
0.0013622762635350227,
0.04225904867053032,
0.052981723099946976,
0.035661689937114716,
0.03519003465771675,
0.031128153204917908,
-0.005460070911794901,
-0.027716465294361115,
-0.03425535187125206,
0.03208636865019798,
0.0020645353943109512,
0.023430678993463516,
-0.021902304142713547,
0.004566350020468235,
-0.04180821403861046,
0.015872105956077576,
0.036965519189834595,
0.0005908168386667967,
0.006129387766122818,
-0.006000599358230829,
-0.007312266156077385,
0.03584374114871025,
0.015186786651611328,
0.011994629167020321,
-0.0037971073761582375,
0.05055003613233566,
-0.00270972796715796,
0.00011302441998850554,
0.024318184703588486,
-0.024358518421649933,
0.05227397382259369,
-0.003580911783501506,
-0.011859450489282608,
0.013922667130827904,
-0.04040545970201492,
0.013830805197358131,
0.011525317095220089,
0.0017722324701026082,
0.046552691608667374,
0.010792804881930351,
0.0054893349297344685,
0.008265231736004353,
-0.057387400418519974,
-0.053485553711652756,
-0.01039289403706789,
0.02339714951813221,
-0.013837812468409538,
-0.029716329649090767,
0.005839670076966286,
0.03661492094397545,
0.03219880908727646,
-0.05706009641289711,
-0.026735689491033554,
-0.012807680293917656,
0.056555747985839844,
-0.008776853792369366,
-0.06395328789949417,
0.016730502247810364,
-0.008392861112952232,
-0.004569227807223797,
-0.02518436126410961,
0.03982583433389664,
-0.03357907757163048,
0.00256974040530622,
0.008686067536473274,
0.020151324570178986,
0.037541311234235764,
-0.018469084054231644,
-0.02276116982102394,
0.04551516845822334,
0.001588158425875008,
0.004095991607755423,
-0.0020798356272280216,
0.05520109832286835,
-0.020938938483595848,
-0.02140207588672638,
0.0012482155580073595,
-0.03373678773641586,
0.04240670055150986,
-0.004528694320470095,
-0.061189357191324234,
-0.0012106928043067455,
-0.021398592740297318,
-0.005970998201519251,
0.009010589681565762,
-0.025067854672670364,
-0.008253497071564198,
-0.0009611470741219819,
0.013379682786762714,
-0.02995680458843708,
0.041995201259851456,
-0.04370710253715515,
0.03508048877120018,
0.01337724644690752,
-0.0232356209307909,
0.060395706444978714,
0.046615779399871826,
0.024852199479937553,
0.00935478787869215,
0.000626712164375931,
-0.011823390610516071,
0.012699649669229984,
-0.0020626909099519253,
-0.002979737240821123,
0.023950006812810898,
0.020463895052671432,
-0.02265316992998123,
-0.01671721041202545,
-0.03226528316736221,
0.031988151371479034,
0.042699702084064484,
0.007459911517798901,
0.040257249027490616,
-0.009604569524526596,
0.013738048262894154,
0.00389789673499763,
-0.005233310163021088,
0.006368084345012903,
-0.016461333259940147,
0.01013706624507904,
0.004992789123207331,
-0.054294999688863754,
-0.01714130863547325,
0.04721164330840111,
0.03146922215819359,
-0.022916138172149658,
-0.00735885975882411,
0.03494739904999733,
0.0012349257012829185,
0.02330363355576992,
-0.018886836245656013,
-0.0284512210637331,
0.03374466300010681,
-0.04579271376132965,
0.007443978451192379,
-0.027539148926734924,
-0.032813623547554016,
-0.008166313171386719,
0.038772474974393845,
0.006639569532126188,
-0.024066505953669548,
-0.03710028529167175,
-0.023302121087908745,
0.005761654116213322,
0.020802684128284454,
0.035690490156412125,
-0.04191257804632187,
-0.046086736023426056,
0.019742494449019432,
-0.02344740740954876,
-0.029235340654850006,
-0.004706116393208504,
-0.06024302542209625,
-0.03235885500907898,
-0.0273003950715065,
-0.048529427498579025,
0.03822832554578781,
0.022748302668333054,
-0.01883452758193016,
0.03979478403925896,
-0.02021368034183979,
0.023566123098134995,
0.016669709235429764,
0.044825129210948944,
-0.03886294364929199,
0.07301780581474304,
-0.023648016154766083,
0.014623430557549,
-0.024902820587158203,
-0.02574276365339756,
0.12466022372245789,
0.045885778963565826,
0.011983281001448631,
-0.05935540050268173,
0.0011070453329011798,
-0.000022623064069193788,
-0.0093064084649086,
-0.060280848294496536,
0.020958635956048965,
0.01584208942949772,
0.010388350114226341,
0.005298932082951069,
0.05421849340200424,
-0.027250561863183975,
-0.03255946561694145,
0.05786372721195221,
-0.059427738189697266,
-0.024960896000266075,
0.026670923456549644,
0.0050423932261765,
-0.020142914727330208,
0.0024708982091397047,
-0.043129052966833115,
0.033372726291418076,
0.007351809646934271,
0.018765488639473915,
-0.030529050156474113,
0.020684199407696724,
0.0239519365131855,
0.031674809753894806,
-0.029987314715981483,
-0.013118528760969639,
0.021015681326389313,
-0.04628700762987137,
-0.04443895444273949,
0.003449519630521536,
-0.010207746177911758,
-0.009940117597579956,
0.036760397255420685,
0.044196080416440964,
-0.01234414428472519,
0.055490877479314804,
0.010065478272736073,
0.010689949616789818,
-0.04999447613954544,
0.0014903736300766468,
-0.0481005422770977,
0.021020859479904175,
-0.02271769568324089,
0.028998462483286858,
0.006164903752505779,
-0.032901082187891006,
-0.019517920911312103,
-0.03195551782846451,
-0.018799299374222755,
-0.025469349697232246,
0.014560097828507423,
0.01063772477209568,
-0.021745143458247185,
-0.0011149070924147964,
0.03970440849661827,
-0.00825082790106535,
-0.00010427513916511089,
-0.028899872675538063,
-0.0275499876588583,
0.006338393781334162,
0.011999087408185005,
0.03935354948043823,
0.05190470069646835,
-0.00948289968073368,
-0.006498092319816351,
-0.04188362881541252,
-0.03402112051844597,
0.0015543317422270775,
-0.009352984838187695,
0.012213376350700855,
0.020160816609859467,
0.03617190569639206,
0.013418070040643215,
0.0055443113669753075,
-0.020513972267508507,
-0.0034862742759287357,
-0.032027468085289,
-0.030099716037511826,
-0.04541117325425148,
-0.002828926080837846,
-0.01933744177222252,
0.029325027018785477,
0.016401341184973717,
-0.032427333295345306,
0.025570418685674667,
0.01677473820745945,
-0.011191299185156822,
-0.025170080363750458,
-0.04335557296872139,
-0.024567481130361557,
-0.043381549417972565,
0.0249492097645998,
-0.029752248898148537,
-0.0119932247325778,
0.01873650960624218,
0.021359190344810486,
0.009311613626778126,
0.03968922048807144,
0.02631683275103569,
0.02940811589360237,
0.017912529408931732,
-0.012121448293328285,
-0.0035666555631905794,
0.04660530760884285,
0.04151766002178192,
-0.07969231903553009,
-0.043402861803770065,
-0.024146201089024544,
-0.029882559552788734,
0.004232738632708788,
0.013167252764105797,
-0.06650108098983765,
0.003211848670616746,
-0.0037393132224678993,
0.02397691085934639,
-0.0024575754068791866,
-0.01741005852818489,
-0.03770492970943451,
-0.025081006810069084,
-0.008468334563076496,
-0.013928198255598545,
-0.004039092920720577,
0.003066838951781392,
-0.052001580595970154,
-0.01968931220471859,
0.02899766154587269,
0.0038819466717541218,
-0.021416977047920227,
0.008932024240493774,
0.03616392984986305,
-0.0022995290346443653,
0.04652119800448418,
-0.028212787583470345,
-0.005611189641058445,
0.05301508679986,
-0.002930674934759736,
-0.04371877387166023,
0.04579377546906471,
-0.017990222200751305,
0.014446408487856388,
0.016406025737524033,
-0.002289147349074483,
-0.0017112706555053592,
0.02202489785850048,
-0.005383600480854511,
0.009142417460680008,
-0.011631712317466736,
-0.022456398233771324,
-0.04338579624891281,
0.02865285612642765,
0.015647877007722855,
-0.016926396638154984,
0.0010283389128744602,
-0.014242074452340603,
0.04858998954296112,
-0.021890051662921906,
-0.011496066115796566,
0.006405187770724297,
-0.025545800104737282,
-0.03528972715139389,
0.033399324864149094,
0.02560444176197052,
-0.01500841323286295,
0.02456575445830822,
-0.03657681867480278,
0.019081413745880127,
0.04267626255750656,
-0.013492335565388203,
-0.1037774607539177,
-0.05094076693058014,
0.01083203312009573,
0.028964487835764885,
0.02493389882147312,
-0.0048027196899056435,
-0.013494156301021576,
0.030874911695718765,
-0.09134386479854584,
0.04927769675850868,
-0.04039252549409866,
-0.039955753833055496,
-0.04727940633893013,
-0.03710082918405533,
-0.01508739311248064,
0.03521828353404999,
0.019815126433968544,
0.06652163714170456,
-0.006883830763399601,
0.009437518194317818,
-0.03705347329378128,
-0.015332510694861412,
-0.009593046270310879,
0.000999561045318842,
-0.017849473282694817,
-0.050475917756557465,
0.06934530287981033,
-0.012554407119750977,
-0.039337899535894394,
0.039361800998449326,
0.006996468175202608,
-0.02396005019545555,
0.0022937189787626266,
-0.009052740409970284,
0.0023694660048931837,
0.0465182289481163,
0.006487203296273947,
-0.0008066483424045146,
-0.04292786121368408,
0.03209768980741501,
0.015086287632584572,
-0.001008907100185752,
-0.05013309791684151,
-0.01570233143866062,
0.02931256964802742,
-0.0063129146583378315,
-0.00463790213689208,
0.0014048072043806314,
-0.01344352401793003,
-0.009834273718297482,
-0.002158160088583827,
0.03839927539229393,
-0.018130941316485405,
-0.01810547523200512,
0.02088860608637333,
-0.05244739353656769,
0.0003164573572576046,
0.05753383785486221,
0.01815755106508732,
0.010649689473211765,
-0.004825611598789692,
0.03152977675199509,
0.0013928967528045177,
0.017658019438385963,
0.019959550350904465,
-0.006537918001413345,
-0.05586233362555504,
-0.00019774217798840255,
-0.02015112154185772,
0.007928763516247272,
0.02936198003590107,
-0.037522658705711365,
-0.017563244327902794,
0.02640407346189022,
-0.015433024615049362,
0.029648495838046074,
-0.021481914445757866,
-0.006020747125148773,
-0.02212902344763279,
-0.07514921575784683,
0.019886557012796402,
0.017024235799908638,
0.02393188700079918,
-0.008486250415444374,
0.03032062016427517,
-0.01825704798102379,
-0.035051826387643814,
0.04540631175041199,
-0.0057227215729653835,
-0.010809244588017464,
0.04419558495283127,
-0.002283048117533326,
0.008902328088879585,
-0.023027556017041206,
0.02077818289399147,
-0.0000014010938684805296,
-0.029788153246045113,
0.034005675464868546,
-0.016148407012224197,
-0.023998867720365524,
-0.008816192857921124,
0.03967205435037613,
0.013754338026046753,
0.007431728765368462,
-0.008586498908698559,
-0.019933922216296196,
0.02802918292582035,
0.017025472596287727,
0.02488936483860016,
0.06974271684885025,
-0.003599076298996806,
0.017965689301490784,
0.006179598160088062,
-0.02711164765059948,
-0.03490404039621353,
0.04925063997507095,
-0.010205120779573917,
-0.018876753747463226,
-0.045279696583747864,
0.010371820069849491,
0.00681054312735796,
-0.05273998901247978,
-0.013819394633173943,
0.06119266152381897,
-0.010953105054795742,
-0.05043565109372139,
0.029888495802879333,
0.0015633261064067483,
0.059360913932323456,
0.008553083054721355,
0.01992504484951496,
0.01934157870709896,
-0.035340551286935806,
0.04932349547743797,
0.027790267020463943,
0.019369453191757202,
-0.0036319263745099306,
-0.011076928116381168,
0.05982409045100212,
-0.019630396738648415,
0.06702318787574768,
0.03308964520692825,
0.05858336389064789,
-0.03691691905260086,
-0.04271022975444794,
0.014049195684492588,
-0.008310110308229923,
0.01941695809364319,
0.013440806418657303,
-0.00006483371544163674,
0.06936370581388474,
-0.005147199146449566,
-0.010750670917332172,
-0.0309415515512228,
-0.02417466603219509,
-0.0128229521214962,
-0.026196273043751717,
-0.008756485767662525,
0.016496025025844574,
-0.010397901758551598,
0.00871590618044138,
-0.017990386113524437,
-0.011048773303627968,
0.03044232353568077,
-0.016512608155608177,
0.020228354260325432,
0.04243144765496254,
0.026150062680244446,
0.03960564360022545,
-0.004469802137464285,
-0.04631921648979187,
0.0007923564407974482,
0.007985511794686317,
0.071979820728302,
0.06019395962357521,
-0.025728322565555573,
-0.009306542575359344,
-0.03706737235188484,
0.018960829824209213,
-0.04371987655758858,
0.001964275725185871,
-0.05984324961900711,
0.012003612704575062,
0.014719675295054913,
-0.019757233560085297
] |
<p>Why do the propellers on helicopter appear to be so slow when the propellers is going at full speed? Can you please explain this particular optical illusion to me? </p> | 1,546 | [
-0.041680265218019485,
-0.04741411656141281,
-0.004435987677425146,
-0.0013105954276397824,
0.04397246241569519,
-0.01784132421016693,
-0.023509573191404343,
-0.009588843211531639,
-0.009150460362434387,
-0.027527060359716415,
0.0035848314873874187,
0.07618051022291183,
0.04733719676733017,
0.03396539390087128,
0.02024034969508648,
-0.028317008167505264,
-0.03565022721886635,
-0.018255267292261124,
-0.005051012150943279,
0.005632226355373859,
-0.03687434643507004,
0.012002868577837944,
0.03706606850028038,
-0.007254426367580891,
-0.0012020455906167626,
0.035726744681596756,
0.03832075744867325,
-0.00917742121964693,
0.02726566605269909,
0.03519608825445175,
-0.002373279072344303,
0.034287676215171814,
-0.011467862874269485,
0.055305253714323044,
0.0007093726308085024,
0.0038518377114087343,
-0.018689854070544243,
-0.003241203725337982,
-0.014249453321099281,
0.04700204357504845,
-0.029411569237709045,
0.01132912002503872,
-0.007004975341260433,
0.041411254554986954,
-0.0022521265782415867,
0.03453605994582176,
-0.028969138860702515,
0.0013679073890671134,
0.04868051037192345,
-0.05570969358086586,
0.05594365671277046,
-0.01429105643182993,
0.0008875909261405468,
0.031139368191361427,
0.060519926249980927,
0.033657513558864594,
0.08747261762619019,
0.08907955884933472,
-0.06577786803245544,
-0.04369548335671425,
0.021179696545004845,
-0.012792855501174927,
-0.01737908273935318,
-0.03652945160865784,
-0.008869974873960018,
0.045404694974422455,
-0.0069997310638427734,
-0.05095835030078888,
0.02852817438542843,
0.029690561816096306,
-0.02114325761795044,
-0.010966229252517223,
0.04483833909034729,
-0.0022369532380253077,
0.00617087772116065,
-0.058725159615278244,
0.02243232913315296,
0.018337981775403023,
0.028146468102931976,
0.04159972444176674,
-0.025285186246037483,
0.012052595615386963,
0.025239359587430954,
0.011220658197999,
0.007633665110915899,
0.005593849346041679,
0.08313539624214172,
0.005526222288608551,
0.025992440059781075,
0.020408211275935173,
-0.03649836406111717,
0.016206031665205956,
0.0053502949886024,
-0.0105319544672966,
-0.005711457692086697,
0.026133766397833824,
-0.008281437680125237,
0.051843032240867615,
0.02057257480919361,
-0.06019817292690277,
-0.00977796409279108,
-0.009371082298457623,
0.016313035041093826,
0.0420805886387825,
-0.01696157455444336,
0.025165069848299026,
-0.04999765753746033,
0.033906321972608566,
-0.02736283279955387,
-0.009693797677755356,
-0.04276200011372566,
0.03265272453427315,
0.021842967718839645,
0.0021069939248263836,
-0.01122018601745367,
-0.026729298755526543,
0.03573588654398918,
0.007066022604703903,
0.04475141316652298,
0.0702490508556366,
0.04405656084418297,
-0.033416323363780975,
0.01236328948289156,
0.012686672620475292,
-0.0497758723795414,
0.04499193653464317,
0.014815502800047398,
-0.038955189287662506,
-0.039295874536037445,
0.024795088917016983,
0.020594116300344467,
-0.042915571480989456,
0.029739337041974068,
0.014119102619588375,
0.05915116146206856,
0.004502260126173496,
-0.09591124951839447,
-0.038549914956092834,
0.04988158494234085,
-0.020450109615921974,
0.030863912776112556,
-0.10338480025529861,
0.010926484130322933,
0.03613225743174553,
0.08745715022087097,
-0.007649049162864685,
-0.0211909469217062,
-0.015320491045713425,
0.0032207907643169165,
0.01516290009021759,
-0.0043724398128688335,
-0.02886720560491085,
0.023798495531082153,
-0.041841059923172,
0.02403503842651844,
-0.05048549175262451,
-0.028473112732172012,
0.025297926738858223,
-0.018339918926358223,
-0.04041152074933052,
-0.017269758507609367,
0.003892892971634865,
-0.021937262266874313,
-0.004825751297175884,
-0.005353120155632496,
-0.04085163399577141,
0.0665278434753418,
-0.007722022477537394,
0.007773746270686388,
0.029828213155269623,
0.005938871763646603,
0.04664736986160278,
-0.013867431320250034,
0.04074062034487724,
0.03439807891845703,
-0.00439478550106287,
0.019210807979106903,
0.001262212754227221,
0.009414410218596458,
-0.014733104035258293,
-0.019212719053030014,
-0.027813667431473732,
-0.0037438152357935905,
0.02534247376024723,
0.017272984609007835,
0.05266449600458145,
0.012058925814926624,
-0.0178569033741951,
0.006401308812201023,
-0.04779684171080589,
-0.03274141624569893,
-0.06438877433538437,
0.013914243318140507,
0.007457940839231014,
-0.02072761207818985,
0.05166799947619438,
0.02722794935107231,
0.02261059172451496,
-0.045901939272880554,
0.01687799021601677,
-0.022629113867878914,
0.011210279539227486,
0.01420477032661438,
-0.023067904636263847,
0.022046592086553574,
0.043626174330711365,
0.019472915679216385,
0.02097346819937229,
0.019297510385513306,
0.009000667370855808,
-0.0026783549692481756,
0.00918096024543047,
-0.00291824690066278,
-0.013788082636892796,
-0.0022714543156325817,
0.02156982384622097,
0.01987566240131855,
0.025092290714383125,
0.011135997250676155,
-0.002397980075329542,
-0.036452505737543106,
0.0295207891613245,
0.04964946210384369,
-0.007164834067225456,
0.00032868378912098706,
0.02488918974995613,
-0.003339212853461504,
-0.02007673867046833,
0.012315715663135052,
-0.01893153414130211,
-0.030879247933626175,
0.007816007360816002,
0.05087935924530029,
0.02071305923163891,
-0.054089952260255814,
0.019308151677250862,
0.004452074412256479,
0.06076087802648544,
0.036372505128383636,
0.009410515427589417,
-0.031885214149951935,
-0.024068571627140045,
-0.004096498247236013,
0.003948760684579611,
-0.016605179756879807,
0.01766178384423256,
0.00845272932201624,
0.020402949303388596,
0.02893213741481304,
0.007844560779631138,
-0.039806440472602844,
0.057615555822849274,
-0.018700335174798965,
0.032177720218896866,
0.005620175506919622,
-0.035804495215415955,
0.00829489715397358,
0.002945856424048543,
0.015196907334029675,
-0.0009621177450753748,
0.00813171174377203,
0.022539297118782997,
-0.020022043958306313,
0.004891056567430496,
0.04957536980509758,
0.01807432435452938,
0.0009301561512984335,
-0.0130669130012393,
0.04030167683959007,
-0.034839607775211334,
0.018123256042599678,
-0.04658577963709831,
0.0076216780580580235,
-0.04163094237446785,
0.0009417706751264632,
0.03373781219124794,
0.00972787756472826,
0.05416088551282883,
-0.016256773844361305,
-0.04128354415297508,
0.01999203860759735,
-0.03855450451374054,
0.06034153327345848,
-0.01477181538939476,
-0.019115189090371132,
0.027208220213651657,
0.005199389532208443,
-0.023578187450766563,
0.044483840465545654,
-0.01823611743748188,
0.014316120184957981,
0.01962294615805149,
-0.031630825251340866,
-0.0628647431731224,
0.013753091916441917,
-0.026730913668870926,
0.017779285088181496,
-0.009934528730809689,
0.003283626167103648,
0.005665435455739498,
-0.02414708025753498,
-0.005590457934886217,
0.01917046308517456,
-0.057586975395679474,
-0.032105378806591034,
-0.0008698618621565402,
-0.01322277169674635,
0.0014944035792723298,
-0.03658602759242058,
0.006187603808939457,
-0.022229604423046112,
-0.04585703834891319,
0.0015050849178805947,
-0.0006422652513720095,
-0.027620824053883553,
0.01762349158525467,
0.011938260868191719,
0.045690037310123444,
-0.021028004586696625,
-0.03946111723780632,
0.044246699661016464,
0.01692976802587509,
-0.025341268628835678,
-0.0476730652153492,
-0.021399537101387978,
-0.022260380908846855,
-0.027862707152962685,
0.039633721113204956,
0.06560049951076508,
-0.016865041106939316,
0.05986528843641281,
0.028627479448914528,
0.00589862372726202,
0.0589466318488121,
0.0015642278594896197,
-0.0213495921343565,
-0.009289972484111786,
-0.02738233283162117,
-0.00013509616837836802,
0.008957145735621452,
0.024500146508216858,
-0.06691626459360123,
0.0107786376029253,
-0.009307817555963993,
0.0363854244351387,
0.01708574779331684,
-0.014522067271173,
0.05315735191106796,
-0.03292430192232132,
0.010119864717125893,
0.005219366401433945,
0.047737445682287216,
0.0024833576753735542,
0.010930685326457024,
-0.03626437485218048,
0.028696265071630478,
0.042336609214544296,
-0.014031300321221352,
-0.02460096962749958,
0.04828261956572533,
-0.013601422309875488,
-0.025958731770515442,
-0.0062112160958349705,
-0.012305576354265213,
-0.03238222375512123,
0.00854924414306879,
-0.030468029901385307,
-0.057627879083156586,
0.06761766225099564,
0.03138570114970207,
-0.0003335495130158961,
0.043361932039260864,
0.003347760532051325,
0.04246611148118973,
-0.07561254501342773,
0.005563261918723583,
0.0058869789354503155,
0.03809241205453873,
0.007519292179495096,
0.07796122133731842,
0.012740873731672764,
0.055728934705257416,
-0.014783950522542,
-0.013860992155969143,
-0.08697694540023804,
0.035668399184942245,
-0.017356939613819122,
-0.024807870388031006,
-0.03261499106884003,
-0.027201933786273003,
-0.035783059895038605,
-0.07579002529382706,
-0.021439995616674423,
0.0006660348153673112,
-0.0038408576510846615,
-0.046855103224515915,
0.00936700589954853,
0.01148018054664135,
0.009752665646374226,
-0.033193010836839676,
0.009868579916656017,
0.007702327799052,
-0.0072090825997292995,
0.06420066207647324,
0.05753416568040848,
-0.0447419136762619,
0.0034551513381302357,
-0.030044499784708023,
0.022031433880329132,
-0.013854787684977055,
0.010252567939460278,
0.01072162576019764,
-0.005442924331873655,
-0.022350290790200233,
0.011725001968443394,
-0.001831809408031404,
0.03668699786067009,
-0.02982163615524769,
-0.000040059854654828086,
-0.05697857588529587,
-0.031212519854307175,
-0.013233933597803116,
0.004412889946252108,
0.044854115694761276,
-0.01215965673327446,
0.01703048311173916,
-0.006191258784383535,
0.005776799749583006,
0.004404737614095211,
0.014707324095070362,
-0.0032671645749360323,
0.015782669186592102,
-0.01732979528605938,
-0.07412752509117126,
-0.0267436895519495,
-0.04865821450948715,
0.004734726622700691,
0.03555956110358238,
-0.0041916160844266415,
0.011889415793120861,
-0.0008182732271961868,
0.04878094792366028,
-0.03888273239135742,
0.007193577941507101,
0.014504141174256802,
-0.019736934453248978,
-0.025144919753074646,
0.0019165538251399994,
0.04129965603351593,
0.02176341786980629,
0.053100086748600006,
0.030980460345745087,
0.021128486841917038,
-0.008752338588237762,
-0.08802775293588638,
-0.04485836252570152,
0.041421402245759964,
-0.009889698587357998,
-0.03812654688954353,
0.0057733976282179356,
-0.037506408989429474,
-0.030848443508148193,
0.032740358263254166,
-0.027033407241106033,
0.033214911818504333,
-0.0667852908372879,
-0.01898650825023651,
-0.02881447598338127,
0.009479118511080742,
-0.008397532626986504,
0.03137485310435295,
-0.01245278213173151,
-0.0006109031965024769,
0.007177919615060091,
0.01226022094488144,
0.016381388530135155,
-0.00841362401843071,
0.0417676605284214,
0.04253862053155899,
0.0379786491394043,
-0.007802428212016821,
-0.017844734713435173,
0.030452856793999672,
-0.04370908439159393,
-0.04058729112148285,
0.015905844047665596,
-0.020262807607650757,
-0.004103980492800474,
0.026078931987285614,
-0.050606973469257355,
-0.027301864698529243,
0.0009305226849392056,
0.004791053477674723,
0.011610662564635277,
-0.021091094240546227,
-0.03667333722114563,
-0.019509565085172653,
0.013811963610351086,
-0.004354262258857489,
0.008822874166071415,
0.051080554723739624,
-0.0362706296145916,
-0.019983291625976562,
0.021734746173024178,
0.07519441097974777,
-0.02956034615635872,
-0.028356680646538734,
-0.0004092338203918189,
0.003773697651922703,
-0.03321654349565506,
0.07508227974176407,
-0.040840547531843185,
0.05434364825487137,
-0.027332326397299767,
0.002611888572573662,
-0.01598348096013069,
0.03840687498450279,
0.020479507744312286,
-0.018875109031796455,
-0.014732510782778263,
0.005993906408548355,
0.03638768941164017,
-0.009710471145808697,
-0.022788072004914284,
0.009840966202318668,
-0.010135512799024582,
0.029581166803836823,
-0.008051391690969467,
0.021715417504310608,
-0.05451389402151108,
-0.02636704221367836,
0.009852892719209194,
-0.05966589227318764,
0.0280239786952734,
-0.034730371087789536,
-0.025397974997758865,
0.017759205773472786,
-0.08297880738973618,
-0.02883058227598667,
0.0035887020640075207,
-0.0039016210939735174,
0.037560198456048965,
-0.062247198075056076,
0.015051988884806633,
0.016755422577261925,
0.017914045602083206,
-0.030672598630189896,
-0.08840372413396835,
0.04253985360264778,
0.039373986423015594,
0.015734585002064705,
-0.04785631597042084,
0.0035949000157415867,
-0.0104341059923172,
-0.06616214662790298,
-0.009837716817855835,
0.028570277616381645,
0.028688564896583557,
0.0013479577610269189,
0.013955597765743732,
-0.026662638410925865,
0.056944381445646286,
0.0008280149777419865,
-0.02018251270055771,
0.004159534350037575,
-0.051256030797958374,
-0.03759029880166054,
-0.013269368559122086,
0.05320527032017708,
-0.027861589565873146,
-0.017174072563648224,
-0.005778725724667311,
-0.02517661824822426,
0.015110027976334095,
-0.012169087305665016,
0.07475762069225311,
0.002725642640143633,
0.011365966871380806,
0.03884320706129074,
-0.017601698637008667,
-0.006124058272689581,
-0.000011973742402915377,
0.042032551020383835,
0.013928726315498352,
-0.03972329944372177,
-0.009612487629055977,
-0.0555129274725914,
0.058266885578632355,
0.057825967669487,
-0.005817633122205734,
-0.040889013558626175,
0.031706567853689194,
-0.03576536476612091,
-0.02686501480638981,
-0.0022756897378712893,
-0.010338454507291317,
-0.013844848610460758,
0.014881917275488377,
-0.009194792248308659,
0.03203532099723816,
0.02125445194542408,
0.011716006323695183,
0.011286824941635132,
0.008294283412396908,
0.005348109174519777,
0.06674496829509735,
-0.038824427872896194,
0.0548325777053833,
0.003532578470185399,
-0.01352531649172306,
-0.037773046642541885,
-0.010348653420805931,
-0.03374183177947998,
0.0030221387278288603,
-0.009735843166708946,
0.021899938583374023,
-0.00040179319330491126,
0.019014272838830948,
0.011537536047399044,
0.043271563947200775,
0.012860683724284172,
0.001005099038593471,
0.026890767738223076,
0.03231576085090637,
0.004351578652858734,
0.003818787168711424,
-0.015903839841485023,
0.027822211384773254,
-0.016032585874199867,
0.04981183633208275,
-0.0006988110835663974,
0.01789550483226776,
0.024245090782642365,
0.0038917791098356247,
-0.003714553080499172,
-0.06381355226039886,
0.009934431873261929,
-0.020116927102208138,
-0.029971392825245857,
-0.005918179173022509,
-0.026333406567573547,
0.01002156175673008,
-0.0006467831553891301,
0.02384665422141552,
-0.0015993926208466291,
0.04042636975646019,
-0.032815344631671906,
-0.037249211221933365,
-0.041050251573324203,
0.006696030963212252,
-0.009578004479408264,
0.016438940539956093,
0.0003590573905967176,
-0.010552062653005123,
0.008036275394260883,
0.000052955292630940676,
0.015209497883915901,
0.010690656490623951,
0.010961239226162434,
-0.01796289160847664,
0.07290695607662201,
0.030081432312726974,
0.03740524500608444,
0.02440284751355648,
0.0029014786705374718,
0.10176192224025726,
-0.012911394238471985,
-0.006916841957718134,
-0.06471909582614899,
0.0038082345854490995,
-0.027706479653716087,
0.02590937912464142,
-0.039924271404743195,
0.029917700216174126,
0.014509693719446659,
0.006937677972018719,
0.021748481318354607,
0.04508689045906067,
0.0585821270942688,
0.01123103778809309,
0.023422500118613243,
-0.024513831362128258,
-0.00725769717246294,
-0.018211541697382927,
0.03241895139217377,
-0.028317438438534737,
0.03389865532517433,
-0.04611755535006523,
0.01807446964085102,
-0.026027338579297066,
-0.010426895692944527,
0.024169839918613434,
-0.04079330712556839,
0.018362605944275856,
0.014852955006062984,
-0.06142140552401543,
0.018221622332930565,
0.009514722041785717,
-0.031830478459596634,
-0.033305905759334564,
0.027221933007240295,
0.0034742560237646103,
-0.011063202284276485,
-0.0048628030344843864,
-0.017838260158896446,
0.016997717320919037,
0.02857593074440956,
0.011825195513665676,
-0.004881138447672129,
-0.02838173508644104,
-0.006302184425294399,
-0.03443792834877968,
0.028247138485312462,
-0.01296895183622837,
0.024739261716604233,
-0.025683412328362465,
0.00679937144741416,
-0.01032876968383789,
-0.09501491487026215,
-0.014282047748565674,
-0.03177827224135399,
-0.013637554831802845,
-0.011926650069653988,
-0.07410851866006851,
0.001765661290846765,
0.0009174190927296877,
0.01651841402053833,
0.02983851172029972,
-0.03043089620769024,
0.022206081077456474,
0.0526433102786541,
-0.00852300226688385,
0.056433454155921936,
-0.013604083098471165,
-0.002517515793442726,
0.029328161850571632,
0.05065872147679329,
-0.035522278398275375,
0.01676114834845066,
0.02680513821542263,
0.004680161364376545,
-0.004311551805585623,
-0.01543575618416071,
-0.049190230667591095,
0.013005843386054039,
-0.09583695232868195,
0.01985991932451725,
0.012646140530705452,
-0.02959011122584343,
-0.038216255605220795,
-0.027764100581407547,
0.04725980386137962,
0.013476667925715446,
-0.01980230025947094,
0.03787902742624283,
-0.0422196239233017,
0.059690725058317184,
-0.0025212555192410946,
-0.0323602557182312,
-0.05612519383430481,
0.03433547168970108,
-0.03875178471207619,
-0.02269078977406025,
-0.0018961435416713357,
0.04834900051355362,
0.06031357869505882,
-0.0011637769639492035,
0.009767049923539162,
0.029681384563446045,
-0.0051965899765491486,
-0.0016321211587637663,
0.025572404265403748,
-0.019962193444371223,
-0.002087979344651103,
0.0037863943725824356,
0.02794891968369484,
-0.06671847403049469,
-0.03418022394180298,
-0.03254145756363869,
-0.006044468376785517,
-0.018464842811226845,
0.01646469160914421,
0.05061487853527069,
-0.006038074381649494,
-0.02436390146613121,
0.009792080149054527,
-0.015119221061468124,
0.0017244549235329032,
-0.06318195164203644,
0.05614303797483444,
-0.01895596832036972,
0.013459880836308002,
-0.023639468476176262,
0.019369594752788544,
-0.028667645528912544,
0.017045944929122925,
0.020019132643938065,
-0.02649482525885105,
0.021166138350963593,
0.020310839638113976,
0.026405280455946922,
-0.0007243302534334362,
0.03764614462852478,
-0.009960638359189034,
-0.020811935886740685,
0.03443183749914169,
-0.029407069087028503,
-0.03793346509337425,
0.004376133903861046,
0.0016814745031297207,
0.03540537506341934,
0.012772428803145885,
-0.008842319250106812,
-0.015819387510418892,
0.028413614258170128,
-0.02148452028632164,
-0.005652651656419039,
-0.0015129316598176956,
0.03718617931008339,
0.020161351189017296,
-0.018824152648448944,
0.005776677746325731,
-0.0562068410217762,
-0.028806274756789207,
0.01630047895014286,
0.016464345157146454,
-0.0008159864228218794,
-0.006913377903401852,
0.0004942313535138965,
0.01166202500462532,
0.0287826769053936,
0.02892022579908371,
0.015468932688236237,
0.02661612071096897,
0.015947559848427773,
-0.030112624168395996,
0.03119605965912342,
-0.000266192335402593,
-0.005378172732889652,
-0.09633788466453552,
0.01565702073276043,
-0.029744137078523636,
0.03586990386247635,
0.037407226860523224,
-0.0409298799932003,
0.005513459909707308,
0.04933707416057587,
-0.0849393904209137,
-0.0058739278465509415,
-0.02486274763941765,
-0.022248856723308563,
-0.08178447932004929,
0.006490744650363922,
0.028638500720262527,
0.042948879301548004,
0.018279675394296646,
0.02387184277176857,
0.04053930938243866,
-0.022165410220623016,
-0.04418359324336052,
-0.005219792481511831,
0.011006051674485207,
0.03917313739657402,
0.007522773463279009,
-0.005478753708302975,
0.0250644963234663,
-0.023373186588287354,
-0.027409294620156288,
0.03504685312509537,
-0.00008027385774767026,
0.061807505786418915,
-0.03463070094585419,
0.019019439816474915,
0.000809282239060849,
0.013747584074735641,
0.033446088433265686,
-0.01872793585062027,
-0.028344595804810524,
0.03738202154636383,
0.02328692562878132,
0.031683195382356644,
-0.014984558336436749,
0.02178632654249668,
0.015974650159478188,
-0.042802922427654266,
-0.03431440889835358,
0.0025287875905632973,
-0.026117876172065735,
-0.03913339972496033,
0.00580725958570838,
-0.0026607075706124306,
0.015187096782028675,
-0.03423021361231804,
0.03800671920180321,
-0.03991738334298134,
-0.034095291048288345,
0.005203657317906618,
-0.011805950663983822,
0.004593471996486187,
0.05374540016055107,
-0.014409571886062622,
-0.020344361662864685,
-0.015360690653324127,
0.008102894760668278,
0.014377221465110779,
-0.010284455493092537,
0.0006710452726110816,
0.021700453013181686,
-0.04254869371652603,
-0.004816307686269283,
0.007163932081311941,
-0.035678304731845856,
0.05626777559518814,
0.0273452028632164,
0.0075925784185528755,
0.017991216853260994,
-0.011458705179393291,
-0.04415469244122505,
-0.043221764266490936,
0.0227779783308506,
-0.002197560155764222,
-0.009896214120090008,
-0.040037427097558975,
-0.034890931099653244,
-0.011174354702234268,
0.03571082279086113,
0.030892666429281235,
-0.0027260472998023033,
-0.006599194370210171,
-0.006973313167691231,
0.007036150433123112,
0.020613661035895348,
-0.015410271473228931,
0.0024944618344306946,
0.00612817145884037,
-0.05811816081404686,
0.007393381558358669,
-0.031467005610466,
-0.018741950392723083,
-0.004202680196613073,
0.016932807862758636,
0.007592129986733198,
0.06733695417642593,
0.006247868295758963,
-0.03114190138876438,
0.034909747540950775,
0.03448551520705223,
0.010523945093154907,
0.04253523796796799,
-0.03874531760811806,
0.006715644150972366,
0.012877047061920166,
-0.00596756674349308,
-0.0557236410677433,
0.024753808975219727,
-0.015198210254311562,
0.0047151087783277035,
-0.008541416376829147,
-0.023474475368857384,
0.015491373836994171,
-0.0633116140961647,
0.02468271367251873,
0.011452662758529186,
-0.001707296702079475,
0.006370577495545149,
0.07088838517665863,
0.004388193599879742,
0.012266842648386955,
-0.033659063279628754,
0.011261158622801304,
-0.03222692385315895,
0.008584102615714073,
0.018427131697535515,
0.03300125151872635,
-0.01399844791740179,
0.007955560460686684,
0.03484068438410759,
0.01986013911664486,
-0.03877464309334755,
0.03262164816260338,
-0.01351931318640709,
0.03524578735232353,
-0.017260612919926643,
-0.0243554525077343,
-0.028709260746836662,
-0.06593627482652664,
-0.00559533666819334,
0.01998547464609146,
-0.014193663373589516,
0.08206278830766678,
-0.03283340856432915,
0.03734917938709259,
0.031047550961375237,
-0.003013334237039089,
-0.011422688141465187,
-0.03641825541853905,
0.015210818499326706,
0.022811906412243843,
0.01497011911123991,
-0.021349769085645676,
0.006617793347686529,
0.0003346068842802197,
0.018869932740926743,
0.0015845800517126918,
0.01301051490008831,
-0.014457891695201397,
-0.032662320882081985,
0.010274607688188553,
-0.023068265989422798,
-0.0213359072804451,
-0.009411190636456013,
0.04105515778064728,
0.023480696603655815,
0.0006686990964226425,
0.0048048608005046844,
-0.058856718242168427,
-0.0317099504172802,
0.042061660438776016,
-0.09592343121767044,
0.01165796723216772,
0.0024680125061422586,
0.024055127054452896,
0.01123697217553854,
0.007022796664386988
] |
<p>$u^{\mu}$ - 4-velocity</p>
<p>$b^{\mu}$ - 4-vector of magnetic field</p>
<p>$
u_{\mu}u^{\mu}=-1, \qquad u_{\mu}b^{\mu}=0
$</p>
<p>$$
u_{\beta}u^{\alpha}\nabla_{\alpha}b^{\beta}-u_{\beta}b^{\alpha}\nabla_{\alpha}u^{\beta}+\nabla_{\alpha}b^{\alpha}=0
$$
I don't understand why this equation gives this
$$
u^{\alpha}u^{\beta}\nabla_{\alpha}b^{\beta}+\nabla_{\alpha}b^{\alpha}=0
$$</p>
<p>Help me please!</p> | 1,547 | [
-0.009307718835771084,
0.0203151386231184,
-0.031616538763046265,
-0.008649175055325031,
0.05714914947748184,
0.031276509165763855,
-0.03577643260359764,
0.022400837391614914,
-0.00775871379300952,
-0.03690363094210625,
0.04228900745511055,
0.040923651307821274,
0.05242210626602173,
0.007305840961635113,
0.03602704405784607,
0.005409053061157465,
-0.0199116338044405,
0.017762616276741028,
-0.0027060622815042734,
-0.0018788226880133152,
0.00026595217059366405,
0.002262433525174856,
0.03192514181137085,
0.017316721379756927,
-0.014649368822574615,
0.024413518607616425,
0.025789860635995865,
0.015225491486489773,
0.002782776253297925,
0.022277630865573883,
0.012765561230480671,
-0.01994982734322548,
0.014402694068849087,
-0.004604873713105917,
-0.004230457823723555,
0.027420442551374435,
-0.015504804439842701,
-0.003841229248791933,
-0.02324724569916725,
0.04359757900238037,
-0.01884145848453045,
-0.02759474888443947,
-0.023635320365428925,
0.056364402174949646,
-0.027519049122929573,
-0.04772749915719032,
0.04974335432052612,
0.054601166397333145,
0.03003493882715702,
-0.054479219019412994,
0.08154652267694473,
0.01218783762305975,
0.05091787502169609,
-0.009622272104024887,
-0.018650753423571587,
-0.042653605341911316,
0.06316816806793213,
0.08621155470609665,
0.028849277645349503,
-0.07164349406957626,
0.011838012374937534,
0.005494336131960154,
-0.007665024604648352,
-0.0018198022153228521,
-0.01654338464140892,
0.06451736390590668,
0.005951076280325651,
0.01376782264560461,
0.05066434293985367,
-0.0030819473322480917,
0.019280100241303444,
-0.014168022200465202,
0.01174599677324295,
-0.026362089440226555,
0.019630830734968185,
-0.05417858809232712,
-0.009386284276843071,
0.01464164350181818,
0.007407941855490208,
0.02794620580971241,
-0.03618577867746353,
0.034587688744068146,
0.01084201317280531,
0.008009782992303371,
-0.014151197858154774,
-0.003843676531687379,
0.055131491273641586,
0.022684969007968903,
0.0506100058555603,
0.021135419607162476,
0.019320013001561165,
0.027262696996331215,
0.003598647890612483,
0.0005934764631092548,
0.009329117834568024,
0.03573094308376312,
0.01161030400544405,
0.02587747760117054,
0.050087787210941315,
-0.06687648594379425,
0.0022209915332496166,
-0.014479309320449829,
0.007846662774682045,
0.05993986502289772,
0.003192542353644967,
-0.021602027118206024,
-0.045877695083618164,
0.02266915701329708,
-0.0475718230009079,
-0.019748058170080185,
-0.012481608428061008,
0.013470234349370003,
0.00011072817142121494,
-0.020538832992315292,
0.003572485176846385,
-0.0651557520031929,
0.0280920322984457,
-0.020294586196541786,
0.03042701631784439,
0.04395098611712456,
0.021697670221328735,
-0.03466334939002991,
0.02831982634961605,
0.010270657017827034,
-0.07356084883213043,
-0.00782390683889389,
0.014543034136295319,
0.002561175962910056,
-0.011838877573609352,
0.020589295774698257,
-0.03230426087975502,
-0.014575517736375332,
-0.014790421351790428,
0.013738205656409264,
0.02361338771879673,
0.00997020211070776,
-0.11574389040470123,
-0.07186967879533768,
0.02091805823147297,
-0.03661131486296654,
0.007026448845863342,
-0.07386653870344162,
-0.004801681265234947,
0.023194769397377968,
0.08409681916236877,
-0.03854329138994217,
-0.016157152131199837,
0.021200960502028465,
0.02954806387424469,
-0.005791542120277882,
0.02544029988348484,
0.020167730748653412,
-0.07258466631174088,
-0.03773069754242897,
-0.0077095627784729,
-0.0736662819981575,
-0.003703402355313301,
-0.018441181629896164,
-0.004160924814641476,
-0.01857408881187439,
0.07240592688322067,
-0.00623813783749938,
0.025087706744670868,
0.007679511792957783,
-0.022489063441753387,
-0.004768917802721262,
0.06274048238992691,
0.021747637540102005,
0.009258316829800606,
0.04310346022248268,
0.016687149181962013,
0.022087184712290764,
-0.03025861456990242,
0.05375239625573158,
0.06575680524110794,
-0.028224147856235504,
-0.01691887155175209,
-0.0198405459523201,
0.011909489519894123,
-0.0011082288110628724,
-0.037100061774253845,
-0.04581233859062195,
0.00418121088296175,
0.014499928802251816,
-0.006509948987513781,
0.041433654725551605,
-0.0047315387055277824,
-0.0027769131120294333,
0.016740329563617706,
-0.00686864135786891,
-0.005934978369623423,
-0.06364515423774719,
0.024391498416662216,
0.023168480023741722,
-0.013513692654669285,
0.02026551403105259,
0.007530673872679472,
0.0031449105590581894,
-0.03365357965230942,
-0.0017154267989099026,
0.00748743349686265,
0.034393299371004105,
0.022477801889181137,
-0.00814442615956068,
-0.01435260009020567,
0.04104810580611229,
0.038465458899736404,
0.01179140992462635,
0.054325129836797714,
-0.005435606464743614,
0.010012307204306126,
-0.0015736966161057353,
0.006924672517925501,
0.013380329124629498,
-0.005287065636366606,
-0.023005468770861626,
0.008373732678592205,
-0.02044818364083767,
-0.029809679836034775,
0.0028062148485332727,
-0.05904287099838257,
0.06298140436410904,
0.026244105771183968,
0.007213305216282606,
0.03650793805718422,
0.04219629243016243,
0.028093606233596802,
0.04025404527783394,
-0.01924731209874153,
-0.0016270402120426297,
-0.01968824490904808,
0.03706929087638855,
0.02208886854350567,
-0.017508534714579582,
-0.020750652998685837,
0.012418258003890514,
0.006305499002337456,
0.041560228914022446,
0.0393548384308815,
0.0037311092019081116,
0.008707660250365734,
-0.033832333981990814,
0.0015665681567043066,
0.011340095661580563,
-0.02234870195388794,
0.03811714053153992,
0.02902848646044731,
0.003538865363225341,
0.049732375890016556,
-0.023217419162392616,
-0.033023759722709656,
0.042289018630981445,
-0.011729985475540161,
-0.027811212465167046,
0.02531963586807251,
-0.026430897414684296,
0.07113266736268997,
-0.0012874543899670243,
0.05362400785088539,
0.03759162127971649,
0.015362873673439026,
0.029128188267350197,
0.010404258966445923,
0.01652125082910061,
0.005574100650846958,
-0.003518580226227641,
0.010678686201572418,
-0.05185755714774132,
0.012427113018929958,
-0.023083239793777466,
0.005529175046831369,
-0.01090211234986782,
-0.024212302640080452,
-0.03747674822807312,
-0.009472743608057499,
0.015088419429957867,
0.03975846245884895,
0.013471183367073536,
-0.022298775613307953,
-0.011413934640586376,
0.024167271330952644,
-0.024927359074354172,
0.011865103617310524,
0.02927023358643055,
-0.04259299114346504,
0.029782487079501152,
-0.05774805322289467,
-0.013372517190873623,
0.06071954220533371,
0.033697742968797684,
-0.012730157002806664,
0.03855890408158302,
-0.03499952703714371,
-0.05214860662817955,
-0.04916932061314583,
-0.03277720883488655,
0.008996172808110714,
-0.033107589930295944,
0.017816219478845596,
0.08916737884283066,
-0.028371546417474747,
0.01288805715739727,
-0.011641041375696659,
-0.07698043435811996,
-0.04614971950650215,
0.002407212508842349,
-0.012226448394358158,
0.02974686212837696,
-0.002729443134739995,
0.061403319239616394,
0.018032707273960114,
-0.047151118516922,
-0.01783781498670578,
-0.043367840349674225,
-0.030482109636068344,
-0.004492529202252626,
-0.012719250284135342,
0.03250157833099365,
-0.0108153335750103,
-0.033634018152952194,
0.07844266295433044,
0.054927751421928406,
-0.011469261720776558,
-0.024502649903297424,
0.004354090895503759,
-0.04284924641251564,
-0.06073930859565735,
-0.01154644787311554,
0.043932754546403885,
0.013193311169743538,
-0.022907918319106102,
-0.018343765288591385,
0.04969301074743271,
0.008498496375977993,
0.03525446355342865,
-0.008709307760000229,
0.015279819257557392,
-0.02913728728890419,
0.009000157006084919,
0.046677909791469574,
0.006841395050287247,
0.014297785237431526,
0.04875209927558899,
0.036501139402389526,
0.04068821296095848,
0.025994770228862762,
-0.0319034568965435,
0.02634057216346264,
0.00042054150253534317,
0.030896391719579697,
-0.053822875022888184,
0.03906816244125366,
-0.01929890736937523,
0.01011018268764019,
-0.03444566950201988,
-0.031887538731098175,
0.05707997828722,
-0.013823337852954865,
-0.004191748797893524,
0.033523209393024445,
-0.019050680100917816,
-0.05456947162747383,
-0.013723302632570267,
-0.02410092204809189,
-0.018765587359666824,
0.04051942750811577,
-0.03544013947248459,
0.008129935711622238,
0.038653042167425156,
0.05487528070807457,
-0.023792732506990433,
0.009155284613370895,
-0.04655154421925545,
-0.03659629076719284,
-0.07320252060890198,
0.012011062353849411,
-0.03814542293548584,
0.030002212151885033,
0.015547462739050388,
0.019155947491526604,
0.014118919149041176,
0.02471606619656086,
0.016285059973597527,
0.013989514671266079,
-0.0872214213013649,
0.034519631415605545,
-0.007200669497251511,
-0.026890119537711143,
-0.02723335660994053,
-0.014429774135351181,
-0.024566547945141792,
-0.03414411470293999,
-0.027944404631853104,
-0.016066594049334526,
-0.028162527829408646,
-0.038204796612262726,
0.02946813404560089,
-0.00214593717828393,
-0.022147508338093758,
-0.03594497963786125,
0.023320728912949562,
0.03104579634964466,
-0.0082698380574584,
0.011123782955110073,
0.031396400183439255,
-0.0002729032130446285,
0.015387819148600101,
-0.0562649704515934,
-0.029634101316332817,
0.03465602174401283,
0.019309336319565773,
-0.01901974342763424,
-0.006596296560019255,
-0.01912461780011654,
0.001683462760411203,
0.016150400042533875,
0.042439378798007965,
-0.001473314710892737,
-0.005723089445382357,
-0.04152728617191315,
-0.048014312982559204,
0.01796121336519718,
-0.0006622230284847319,
0.042205486446619034,
0.010370729491114616,
0.02855105884373188,
0.03668242320418358,
0.00866050086915493,
0.010223261080682278,
0.033544398844242096,
0.057785764336586,
0.010425709187984467,
0.0048425341956317425,
-0.04191949963569641,
0.003419213928282261,
-0.028697650879621506,
0.00014857426867820323,
0.00131087691988796,
-0.01664642244577408,
-0.05768831819295883,
-0.05782118812203407,
-0.00396490003913641,
-0.009597097523510456,
0.006018010433763266,
0.003586821723729372,
0.004270691890269518,
-0.009167554788291454,
0.01257102657109499,
-0.008416339755058289,
0.0641566663980484,
0.06658610701560974,
0.054906997829675674,
-0.017521444708108902,
-0.0004241008427925408,
-0.06183193251490593,
0.0030156809370964766,
-0.004609131719917059,
0.026170749217271805,
0.018100881949067116,
-0.02201005630195141,
-0.06375104188919067,
-0.0073120188899338245,
0.0026436212938278913,
-0.0407828614115715,
0.07128545641899109,
0.026769913733005524,
0.02309465780854225,
-0.0010119969956576824,
-0.03114997409284115,
-0.044964972883462906,
0.008144327439367771,
-0.020903317257761955,
0.017673252150416374,
-0.02409672550857067,
0.02050081454217434,
-0.016728198155760765,
0.0193317998200655,
0.017834492027759552,
0.04716646671295166,
-0.006627777591347694,
-0.0053282747976481915,
0.01254838053137064,
0.018610814586281776,
-0.04134558141231537,
-0.06862316280603409,
0.018336346372961998,
0.017643846571445465,
-0.020553454756736755,
0.027804676443338394,
-0.015163036063313484,
-0.06143590062856674,
0.035389065742492676,
0.0038130958564579487,
0.01319634448736906,
-0.021688589826226234,
-0.0601033978164196,
0.021284906193614006,
0.015797412022948265,
-0.0012706081615760922,
0.04501928389072418,
-0.009202713146805763,
-0.028951337561011314,
-0.034074816852808,
-0.07453975826501846,
0.006620693486183882,
-0.010635064914822578,
-0.011016628704965115,
-0.011684653349220753,
0.018386129289865494,
-0.0065101212821900845,
0.057966794818639755,
-0.0332910530269146,
-0.014549355022609234,
-0.036276835948228836,
-0.018712949007749557,
-0.022038854658603668,
0.010422779247164726,
0.03386852145195007,
-0.041462745517492294,
0.02519899047911167,
-0.013705511577427387,
0.0047098686918616295,
-0.05063607543706894,
0.055015530437231064,
-0.014360599219799042,
-0.016308201476931572,
0.040879204869270325,
-0.03663099557161331,
-0.003135010600090027,
0.008764824829995632,
-0.0179086085408926,
-0.02928120456635952,
-0.06364515423774719,
0.011463082395493984,
-0.0030285525135695934,
-0.003991817124187946,
0.00041338789742439985,
-0.01697048544883728,
-0.04961350932717323,
-0.01110508106648922,
-0.020615961402654648,
0.014839261770248413,
-0.03740143030881882,
0.044247325509786606,
0.044655945152044296,
0.018264956772327423,
-0.04782220721244812,
-0.06143692880868912,
0.030433598905801773,
-0.012688962742686272,
-0.01841961406171322,
-0.0029497467912733555,
-0.028236357495188713,
-0.02047673612833023,
-0.05556177720427513,
0.021199127659201622,
0.03349974751472473,
-0.021014072000980377,
-0.015198306180536747,
0.031664855778217316,
0.0434248186647892,
0.05306418612599373,
0.00596284307539463,
-0.04173297435045242,
0.026598071679472923,
-0.033434249460697174,
-0.04577600583434105,
0.0019085366511717439,
0.05606212094426155,
-0.017674364149570465,
-0.04174349829554558,
0.00900273397564888,
-0.01229556929320097,
0.036226604133844376,
0.003271213499829173,
0.0060071093030273914,
0.020271550863981247,
0.028756635263562202,
-0.014099590480327606,
-0.03165242448449135,
0.013752046041190624,
0.01598254032433033,
0.01000056229531765,
0.0016162972897291183,
-0.010915947146713734,
-0.0358351394534111,
-0.05403764173388481,
0.02659844607114792,
-0.020372316241264343,
0.017532890662550926,
-0.006868727970868349,
0.06153857335448265,
-0.02133975923061371,
-0.015267821028828621,
-0.00431941170245409,
0.012123939581215382,
0.02213083580136299,
0.032940544188022614,
0.01037169061601162,
0.009414179250597954,
0.025671256706118584,
-0.05368123948574066,
-0.001188600086607039,
-0.010477358475327492,
0.026887863874435425,
0.08145873993635178,
-0.010070654563605785,
0.05938515439629555,
0.040372706949710846,
0.01088311430066824,
0.000722212775144726,
-0.02193836309015751,
-0.016457807272672653,
0.020322591066360474,
0.012705154716968536,
0.04453340917825699,
-0.010666243731975555,
0.00021649124391842633,
-0.009990544989705086,
0.032519154250621796,
-0.01332904864102602,
-0.01869341731071472,
0.016460996121168137,
0.0335700623691082,
0.005493578501045704,
0.025550512596964836,
-0.06892557442188263,
0.04154711589217186,
-0.005227752961218357,
0.013604480773210526,
0.027856040745973587,
-0.013866450637578964,
0.05392387509346008,
-0.002882894594222307,
0.008156898431479931,
-0.05371561646461487,
0.010820488445460796,
-0.008745674975216389,
0.0031822079326957464,
0.050463348627090454,
-0.013055943883955479,
-0.008962810039520264,
0.002629899885505438,
0.040574297308921814,
-0.005876528099179268,
0.04077822342514992,
0.0012520847376435995,
-0.029621470719575882,
-0.006817730609327555,
-0.04140247404575348,
-0.042983561754226685,
0.061548057943582535,
-0.004406931344419718,
0.008933193981647491,
-0.017478827387094498,
-0.029035158455371857,
0.007529350463300943,
0.0387553907930851,
0.008937671780586243,
-0.014833911322057247,
0.0450674444437027,
0.023619573563337326,
-0.0017300089821219444,
-0.005617357790470123,
0.017793286591768265,
0.11367359012365341,
0.05675503611564636,
0.03824453800916672,
-0.04902523383498192,
0.007663443684577942,
-0.03923199325799942,
0.007222397718578577,
-0.043039415031671524,
0.05603207275271416,
-0.03939146548509598,
0.0046609677374362946,
0.02836132049560547,
0.03212331235408783,
-0.0014455197378993034,
0.006949781905859709,
0.030431536957621574,
-0.017467083409428596,
-0.03911372646689415,
-0.03118869662284851,
0.011179623194038868,
-0.04726928845047951,
0.025056300684809685,
-0.03483372554183006,
0.026276372373104095,
-0.02862812578678131,
-0.02737317606806755,
-0.04216087982058525,
-0.03671841323375702,
0.03264954313635826,
-0.0140449870377779,
-0.03838759660720825,
0.02946043387055397,
-0.0038456462789326906,
-0.01985279470682144,
-0.020225046202540398,
-0.010765927843749523,
0.03136315941810608,
-0.03773060813546181,
0.017956256866455078,
0.03914019092917442,
0.004666415508836508,
0.017827583476901054,
0.005915795918554068,
0.04673169180750847,
-0.019467990845441818,
0.03414503484964371,
-0.05057769641280174,
0.0742856115102768,
-0.014399792067706585,
0.027850186452269554,
-0.021484501659870148,
0.04909612610936165,
-0.025882447138428688,
-0.06393668055534363,
-0.053109776228666306,
-0.005068019963800907,
0.024407563731074333,
-0.011248241178691387,
0.010201468132436275,
-0.020800163969397545,
0.00785443838685751,
0.03990419954061508,
0.0010648543247953057,
0.020479371771216393,
0.01815282180905342,
0.020276296883821487,
-0.014931629411876202,
0.03457298129796982,
-0.031109660863876343,
0.011494304984807968,
-0.008823330514132977,
-0.028688544407486916,
-0.05727760121226311,
0.015536187216639519,
0.014767216518521309,
0.006984379608184099,
0.011449746787548065,
-0.012351052835583687,
-0.03660581260919571,
-0.011085962876677513,
-0.07610399276018143,
0.0013010691618546844,
-0.0044867368414998055,
-0.002861832734197378,
-0.025237705558538437,
0.002591582713648677,
-0.008748299442231655,
0.03990945592522621,
-0.03879377618432045,
-0.028708577156066895,
0.0368206724524498,
0.029563097283244133,
0.012679544277489185,
0.0003675753250718117,
-0.07834664732217789,
0.027199432253837585,
-0.023788785561919212,
0.0194991584867239,
0.02013678103685379,
0.026996362954378128,
0.04099424555897713,
0.001020504510961473,
0.006497913971543312,
0.055637966841459274,
-0.03461047261953354,
-0.021375611424446106,
0.008903702720999718,
-0.038965776562690735,
0.024682166054844856,
0.010846861638128757,
-0.0024191364645957947,
0.013206463307142258,
0.006507145240902901,
-0.015111551620066166,
0.03423460200428963,
0.02000795118510723,
0.020084111019968987,
-0.038795534521341324,
-0.01428705733269453,
0.008245264180004597,
0.02854672260582447,
-0.029649008065462112,
-0.0031859970185905695,
-0.05288092792034149,
0.02614336647093296,
0.006380421109497547,
-0.017148489132523537,
-0.020625196397304535,
0.013473336584866047,
-0.035926926881074905,
0.017457298934459686,
0.01537795178592205,
-0.010232662782073021,
0.0011597839184105396,
-0.002072390867397189,
0.050100360065698624,
0.011272311210632324,
0.032766398042440414,
0.034432876855134964,
-0.009707734920084476,
0.024123860523104668,
-0.01976991631090641,
-0.04319760575890541,
0.04537169635295868,
0.03812943398952484,
0.022644463926553726,
0.03884502500295639,
-0.01612735167145729,
-0.020473456010222435,
0.08520857989788055,
-0.03637844696640968,
0.02681563049554825,
-0.006853314582258463,
-0.04239654168486595,
-0.012255517765879631,
-0.003528621746227145,
0.004136218223720789,
0.014774361625313759,
-0.018514059484004974,
-0.028810007497668266,
0.003911534324288368,
-0.03379375860095024,
-0.019289318472146988,
-0.010565988719463348,
0.02999243140220642,
-0.006454607006162405,
0.06323722004890442,
-0.011329537257552147,
-0.0018189947586506605,
0.042378589510917664,
0.002940402366220951,
0.04756491631269455,
0.006531132385134697,
0.008000590838491917,
-0.08895237743854523,
-0.04023711383342743,
0.007127154618501663,
0.018145734444260597,
0.0481862910091877,
-0.0775018036365509,
0.05080385133624077,
0.041319482028484344,
-0.009267482906579971,
-0.03607247769832611,
-0.048679932951927185,
0.008831184357404709,
-0.03820784389972687,
-0.04835105314850807,
0.010600603185594082,
0.06511335074901581,
0.03197759389877319,
0.018034055829048157,
-0.0007718029082752764,
-0.0070414068177342415,
-0.030488913878798485,
-0.011099033057689667,
0.005598956253379583,
0.02856082282960415,
-0.00045750016579404473,
0.00210326979868114,
0.00947523396462202,
-0.008362919092178345,
-0.015626855194568634,
0.03314208984375,
-0.019386686384677887,
-0.01404554396867752,
0.031028877943754196,
0.05465063452720642,
0.03614669665694237,
0.028937574476003647,
0.031486060470342636,
-0.003002359764650464,
-0.011155722662806511,
0.006988734472543001,
0.01206694170832634,
0.05213873088359833,
-0.03817889839410782,
-0.01694200374186039,
0.0007653303910046816,
-0.03408226743340492,
-0.008653809316456318,
0.007150867022573948,
-0.06469576805830002,
-0.005241199862211943,
-0.028324173763394356,
-0.034174464643001556,
-0.0065297288820147514,
-0.0673944503068924,
0.021700061857700348,
0.000529359735082835,
-0.02057024836540222,
0.005679722409695387,
-0.011314379051327705,
-0.021446317434310913,
0.00861870776861906,
0.012570299208164215,
-0.01803380250930786,
-0.0033294677268713713,
0.015019827522337437,
0.013564209453761578,
-0.04577329754829407,
0.021182658150792122,
-0.000999540206976235,
-0.026807356625795364,
-0.004295824561268091,
-0.04738335683941841,
-0.028447695076465607,
0.018610898405313492,
0.03883982077240944,
-0.005094508640468121,
-0.049804650247097015,
-0.04735065624117851,
-0.02070322073996067,
-0.059988606721162796,
0.02606908604502678,
-0.01868881843984127,
-0.04152675345540047,
-0.016360998153686523,
-0.03231054171919823,
-0.01492003258317709,
0.03617524728178978,
0.042457934468984604,
-0.012598984874784946,
-0.0018378195818513632,
0.04311990365386009,
0.014436611905694008,
0.025985179468989372,
-0.034114085137844086,
0.005669465288519859,
0.048108525574207306,
-0.019611194729804993,
0.0385221466422081,
0.016474684700369835,
-0.01954762451350689,
0.018921831622719765,
-0.029318561777472496,
-0.004769727122038603,
-0.007668079808354378,
-0.006937810685485601,
-0.04235175997018814,
0.004720123019069433,
-0.002558697247877717,
-0.04105053097009659,
0.032923705875873566,
-0.016896739602088928,
0.0316825807094574,
0.015711193904280663,
-0.027907034382224083,
-0.021418189629912376,
0.006274186074733734,
-0.03042742609977722,
0.014589617028832436,
-0.0014247538056224585,
-0.00518673425540328,
0.05488373339176178,
-0.0399763248860836,
-0.00543768098577857,
0.016017043963074684,
-0.02856915071606636,
-0.0012674153549596667,
0.03726595640182495,
-0.017452389001846313,
0.034361787140369415,
-0.023436004295945168,
0.0014659410808235407,
-0.030131246894598007,
-0.008649167604744434,
0.02763449214398861,
0.06829848885536194,
0.0004348158836364746,
0.004303449764847755,
0.0015000937273725867,
0.0498017892241478,
-0.014892838895320892,
-0.018328187987208366,
0.008630168624222279,
0.010818122886121273,
-0.0276026614010334,
-0.01086043193936348,
0.0130413006991148,
-0.03102569282054901,
0.020127635449171066,
0.025771720334887505,
-0.00670249480754137,
0.08592402935028076,
-0.052074283361434937,
0.010053847916424274,
-0.011906884610652924,
0.023248933255672455,
-0.010063882917165756,
0.03845064342021942,
-0.02277953363955021,
0.03403015062212944,
-0.004906204994767904,
-0.04822877421975136,
-0.008369947783648968,
-0.013810043223202229,
0.045631494373083115,
-0.025278160348534584,
-0.024571074172854424,
0.016273608431220055,
0.004801125731319189,
-0.014634756371378899,
-0.015211167745292187,
0.006114214658737183,
-0.02117517963051796,
-0.010187409818172455,
0.025276081636548042,
-0.0023871413432061672,
-0.024230487644672394,
-0.01039509940892458,
-0.040701914578676224,
0.04001402482390404,
-0.034662652760744095,
-0.03331872820854187,
-0.020624306052923203,
0.01355236116796732,
-0.013117353431880474,
0.029337620362639427
] |
<p>OK, so my textbook says that in time dilation and length contraction, the proper time and the proper length is "That which is in the frame of reference of the observer at rest relative to the event". </p>
<p>This means that the proper time/length is that which is observed by the observer moving close to the speed of light, and the dilated time and contracted length is that which is observed by an observer moving relative to the event, i.e. is watching something move close to the speed of light. Am I correct so far?</p>
<p>So, for example, if we have a beam of protons moving with a velocity of 0.99c and a stationary electron watching them, the proper time/length is that which the protons observe whereas the dilated time/contracted length is that which the electrons would see. </p>
<p>Assuming I am correct so far (which I very well may not be, please tell me if I'm wrong), I have just been confused by an exam question. Here it is:</p>
<blockquote>
<p>In an experiment, a beam of protons moving along a straight line at a
constant speed of $1.8$x$10^8$$ms^{-1}$ took 95ns to travel between
two detectors at a fixed distance $d_0$ apart. Calculate the distance
$d_0$ between the two detectors in the frame of reference of the
detectors.</p>
</blockquote>
<p>Well, according to my understanding above, this would be the contracted distance, since the observer (detectors) are in motion relative to the event. However, they calculate the distance using $d=vt$, which would mean it's the proper distance.</p>
<p>Someone please explain. </p> | 1,548 | [
0.0394863560795784,
-0.028633609414100647,
-0.018794866278767586,
-0.02990845777094364,
0.042720433324575424,
0.02006448060274124,
-0.014294547960162163,
-0.01199636235833168,
-0.0034159913193434477,
0.0018492852104827762,
0.045323844999074936,
0.02622426487505436,
0.03464658930897713,
-0.01564331352710724,
0.02225940302014351,
0.011167524382472038,
-0.019606776535511017,
-0.007132671773433685,
0.006236137356609106,
-0.04939810186624527,
0.042745042592287064,
0.010598169639706612,
0.05698610469698906,
0.008927113376557827,
-0.021728817373514175,
0.027204152196645737,
-0.025246543809771538,
0.030811265110969543,
-0.004459818359464407,
0.041958779096603394,
-0.02070651948451996,
-0.04388764500617981,
0.005529225803911686,
0.006808832287788391,
-0.0019722324796020985,
-0.011295969597995281,
-0.023933274671435356,
-0.036017775535583496,
0.008010094985365868,
0.02914641797542572,
-0.04073464125394821,
-0.037014029920101166,
0.005352841690182686,
0.06051734462380409,
-0.0027870694175362587,
-0.015483709052205086,
0.02914905734360218,
-0.030502261593937874,
0.05723949894309044,
-0.026776351034641266,
0.05467868596315384,
-0.007957490161061287,
0.03878325596451759,
-0.00964267272502184,
0.002016612095758319,
-0.003053480526432395,
0.058107759803533554,
0.06730084866285324,
-0.035822395235300064,
-0.022006312385201454,
-0.0038421452045440674,
-0.034249212592840195,
-0.012462439946830273,
0.010714367032051086,
0.004958942532539368,
-0.014176121912896633,
-0.05061067268252373,
-0.01573811285197735,
0.02471013180911541,
-0.025398030877113342,
0.02764737606048584,
0.004810804966837168,
0.04384728893637657,
-0.010828506201505661,
0.0438074916601181,
-0.04493783041834831,
0.023456472903490067,
0.04531343653798103,
0.04140929877758026,
0.04949226975440979,
-0.018806632608175278,
0.006931308191269636,
0.026065075770020485,
0.044770918786525726,
0.006909217685461044,
-0.051323674619197845,
0.051184333860874176,
-0.0030463021248579025,
-0.013599681667983532,
0.05193503201007843,
-0.039995480328798294,
0.0210137777030468,
0.0004957000492140651,
0.025665972381830215,
0.0002903110289480537,
0.032559026032686234,
0.005303883459419012,
0.06126914173364639,
0.024625714868307114,
-0.045002516359090805,
0.0076157706789672375,
-0.026069121435284615,
0.04870724305510521,
0.08698686212301254,
0.006516213994473219,
-0.006793664302676916,
-0.05219707638025284,
0.037619829177856445,
-0.03872072324156761,
0.004110438283532858,
-0.04230553284287453,
0.00862780213356018,
0.011545917019248009,
0.03991682827472687,
-0.006307756528258324,
-0.01322821993380785,
0.024091485887765884,
-0.006073453929275274,
0.08174155652523041,
0.04497712478041649,
0.028771014884114265,
-0.015645120292901993,
0.014021281152963638,
-0.011494521982967854,
-0.0673363208770752,
0.021021470427513123,
0.029782770201563835,
-0.0021116810385137796,
0.02033228799700737,
0.03793833404779434,
-0.0012324118288233876,
-0.02384219318628311,
0.016002194955945015,
0.028871875256299973,
0.019587909802794456,
0.004473553039133549,
-0.10375364869832993,
-0.09273936599493027,
0.054429128766059875,
0.030305979773402214,
-0.022222846746444702,
-0.11822077631950378,
0.0013954032910987735,
-0.0013812060933560133,
0.08755490928888321,
0.006712376140058041,
-0.004029944539070129,
-0.03036605939269066,
0.0250792745500803,
-0.0005631365347653627,
-0.020539971068501472,
0.00691221933811903,
-0.015954963862895966,
-0.022134900093078613,
0.0021566031500697136,
-0.03022974729537964,
-0.0017104829894378781,
0.023730266839265823,
-0.022837137803435326,
-0.023684605956077576,
0.07692281156778336,
0.02649257704615593,
0.018280591815710068,
0.019022980704903603,
-0.017711900174617767,
-0.023260176181793213,
0.07478711754083633,
0.01424124464392662,
-0.027750441804528236,
0.042114339768886566,
0.023678218945860863,
0.004774882923811674,
-0.01625727489590645,
0.020539797842502594,
0.015180489048361778,
-0.025387374684214592,
-0.02400965429842472,
0.024368762969970703,
-0.011885319836437702,
0.038519278168678284,
0.008267645724117756,
-0.03361782804131508,
-0.012317988090217113,
-0.002636189106851816,
0.007762714754790068,
0.057099420577287674,
0.00010271585051668808,
0.02901901677250862,
-0.02181968465447426,
-0.031804680824279785,
-0.01626676879823208,
-0.06867261976003647,
-0.012610821053385735,
0.01747928373515606,
0.004324123729020357,
0.05053228139877319,
-0.019543934613466263,
0.0004847752279601991,
-0.015190382488071918,
-0.02537843957543373,
-0.030074579641222954,
0.03662649914622307,
0.007662036456167698,
-0.023348407819867134,
0.03355386480689049,
0.06395712494850159,
0.03612782433629036,
0.02042667381465435,
-0.004302849527448416,
-0.012986241839826107,
-0.00779985124245286,
0.011599150486290455,
-0.024112936109304428,
0.029616929590702057,
0.038619037717580795,
-0.00021914845274295658,
-0.03926195949316025,
-0.02285664901137352,
0.02028672955930233,
0.043594714254140854,
-0.005702535156160593,
0.07418522238731384,
0.02057434432208538,
-0.009040869772434235,
-0.022096501663327217,
0.023223429918289185,
0.01731168106198311,
0.017890464514493942,
-0.004917987156659365,
-0.04210592433810234,
-0.026705244556069374,
-0.015999600291252136,
0.047808937728405,
0.003365197451785207,
-0.019934924319386482,
-0.0022262809798121452,
0.019734539091587067,
0.035382963716983795,
0.02340957522392273,
0.010515243746340275,
-0.03390637785196304,
-0.07175637036561966,
-0.007200808264315128,
0.024364763870835304,
-0.04488912597298622,
-0.0018617600435391068,
0.012278134003281593,
0.01630774885416031,
0.04670783877372742,
0.009448819793760777,
0.029258448630571365,
0.013841350562870502,
-0.003420945955440402,
0.015454830601811409,
0.002792455954477191,
-0.025347264483571053,
0.005862375255674124,
0.015552717261016369,
0.03371946141123772,
0.02720745839178562,
-0.028565268963575363,
0.023325061425566673,
-0.03421023488044739,
-0.009550003334879875,
0.023852253332734108,
-0.010842551477253437,
-0.017965996637940407,
-0.022651173174381256,
0.02166260965168476,
-0.07152526080608368,
-0.000949743262026459,
-0.0340503491461277,
0.0023148914333432913,
-0.009964503347873688,
-0.0035681554581969976,
0.05477839708328247,
0.039358630776405334,
0.018593523651361465,
-0.06138002127408981,
-0.03355094790458679,
-0.006187206134200096,
-0.03565605729818344,
0.03913944587111473,
0.02987123467028141,
-0.035065747797489166,
0.030365008860826492,
-0.056630998849868774,
-0.03326050937175751,
0.016738897189497948,
-0.009486418217420578,
0.022121256217360497,
0.012504864484071732,
-0.027551744133234024,
-0.05136429890990257,
-0.03091726079583168,
0.0004254002415109426,
-0.013620467856526375,
-0.026888323947787285,
0.0028507125098258257,
0.05270954221487045,
0.0023598296102136374,
-0.026069551706314087,
0.03933678939938545,
-0.030677052214741707,
-0.023042360320687294,
-0.01260443776845932,
0.0019309234339743853,
0.00346776214428246,
-0.025896083563566208,
0.03677044063806534,
0.002116152783855796,
-0.021396778523921967,
-0.013827990740537643,
-0.047550830990076065,
-0.08365793526172638,
0.031170807778835297,
0.037763673812150955,
0.031214993447065353,
0.017309624701738358,
-0.021979723125696182,
0.09721383452415466,
0.020378652960062027,
0.0018176850862801075,
-0.04566650465130806,
0.03923920914530754,
-0.012769532389938831,
-0.027630919590592384,
-0.02787483111023903,
0.045902714133262634,
-0.02793281525373459,
-0.0026701255701482296,
0.00565969105809927,
0.07775223255157471,
0.05415209382772446,
0.022788960486650467,
0.024778002873063087,
-0.008540975861251354,
0.006896979175508022,
-0.009628835134208202,
0.05376396328210831,
0.01081093493849039,
-0.019202187657356262,
0.00024068867787718773,
-0.01605985313653946,
0.04841294884681702,
0.021028202027082443,
-0.06265759468078613,
0.03877510130405426,
0.018125900998711586,
-0.013052497059106827,
-0.009396448731422424,
-0.005808811169117689,
0.00409214710816741,
0.014503560028970242,
-0.01050327718257904,
0.01813906617462635,
0.0164734348654747,
-0.024164561182260513,
-0.01343875378370285,
0.015122363343834877,
0.010813687928020954,
0.003810669295489788,
-0.04272053763270378,
-0.028680533170700073,
-0.03882792592048645,
0.06320388615131378,
-0.04773794859647751,
-0.027417412027716637,
0.032189399003982544,
0.015550731681287289,
0.029129283502697945,
-0.005875135771930218,
-0.048594504594802856,
-0.0016812109388411045,
-0.03960660099983215,
0.01198637392371893,
0.030472101643681526,
0.010839243419468403,
0.009682021103799343,
0.03094632551074028,
0.055244121700525284,
0.022148193791508675,
0.03748070448637009,
-0.005806413944810629,
-0.05430655926465988,
0.030928486958146095,
-0.03901167958974838,
-0.04928324744105339,
-0.032934535294771194,
0.012865097261965275,
-0.01147728506475687,
-0.030276518315076828,
0.032072070986032486,
-0.024291059002280235,
-0.008896651677787304,
-0.05250193551182747,
0.011397307738661766,
-0.01618911698460579,
-0.02582715079188347,
-0.033741544932127,
0.02426093816757202,
0.01054517924785614,
-0.028668642044067383,
0.009889401495456696,
0.03406476601958275,
-0.037420835345983505,
0.01887175627052784,
0.0069398158229887486,
-0.00004404103310662322,
0.04471726343035698,
0.02005595713853836,
0.08137987554073334,
0.04150092229247093,
-0.07528389245271683,
0.020852770656347275,
0.026373103260993958,
0.05323881283402443,
-0.010286054573953152,
-0.029032645747065544,
-0.0653964951634407,
-0.013288515619933605,
-0.023262230679392815,
-0.012732830829918385,
0.0774495080113411,
0.03410671278834343,
0.01965547725558281,
0.03618883714079857,
0.016198769211769104,
0.010832428932189941,
0.03556324541568756,
0.040017176419496536,
-0.009182699024677277,
-0.02511560171842575,
-0.04542455077171326,
0.004807890392839909,
-0.014967246912419796,
0.0007498133345507085,
0.006466763559728861,
-0.002258829539641738,
-0.006700257770717144,
-0.00973642896860838,
0.016896894201636314,
0.030010191723704338,
-0.013806511647999287,
0.019833022728562355,
-0.015460493974387646,
0.005119799170643091,
0.03929109498858452,
-0.000649165827780962,
-0.0038566302973777056,
0.0074087753891944885,
0.020728467032313347,
0.0032696814741939306,
-0.0034884214401245117,
-0.08617694675922394,
0.004029369447380304,
0.015452532097697258,
0.03962668403983116,
-0.0061667137779295444,
-0.015891041606664658,
-0.03700151666998863,
-0.008490298874676228,
0.03506908565759659,
-0.03268688917160034,
0.038414593786001205,
0.0042371610179543495,
-0.016988443210721016,
-0.01590273156762123,
-0.003004153724759817,
-0.05193255841732025,
0.009336975403130054,
-0.012314445339143276,
0.01239217072725296,
-0.019573509693145752,
-0.010171566158533096,
-0.0049316552467644215,
-0.014354006387293339,
0.035423729568719864,
0.056614603847265244,
0.01044886652380228,
-0.013505371287465096,
0.013052577152848244,
0.02063988707959652,
-0.03451269492506981,
-0.05364709720015526,
-0.017103571444749832,
0.018433449789881706,
-0.00689627043902874,
0.053320154547691345,
-0.023892531171441078,
-0.018552841618657112,
0.04065924510359764,
0.014769750647246838,
0.010014265775680542,
-0.013018212281167507,
-0.04447692632675171,
0.03938930481672287,
0.0344291590154171,
0.0072024730034172535,
0.03705105930566788,
-0.006173043977469206,
0.007979068905115128,
0.013302850537002087,
-0.008430925197899342,
0.05918896943330765,
-0.0487135574221611,
0.009711142629384995,
0.0006355211953632534,
0.008957618847489357,
-0.03213923051953316,
0.07419879734516144,
-0.04384525120258331,
0.010738816112279892,
-0.012517930008471012,
-0.05909886583685875,
-0.0006537146982736886,
0.04133577644824982,
-0.000727152859326452,
0.01627468690276146,
-0.02350900135934353,
-0.0067736185155808926,
0.0012949529336765409,
-0.031028909608721733,
-0.009702243842184544,
-0.007504528388381004,
0.006834528408944607,
0.005604213569313288,
-0.022105678915977478,
-0.0011247735237702727,
-0.0041816504672169685,
-0.009081508032977581,
0.06386953592300415,
-0.041547566652297974,
0.0282453503459692,
-0.013274326920509338,
-0.0166368018835783,
-0.005502780899405479,
-0.036711495369672775,
-0.05787332355976105,
0.024665633216500282,
-0.03156614303588867,
0.05016327649354935,
-0.07390111684799194,
0.0032767876982688904,
-0.004225701559334993,
0.030690543353557587,
-0.0763673186302185,
-0.03326038643717766,
-0.0037324274890124798,
0.02336292900145054,
-0.035828884690999985,
-0.0021051550284028053,
-0.010086103342473507,
-0.004805439151823521,
-0.031054630875587463,
-0.0363171361386776,
0.03144391253590584,
-0.022249652072787285,
-0.05303133279085159,
-1.5693434818331298e-7,
0.010321241803467274,
0.04076942801475525,
-0.0035809469409286976,
0.022478919476270676,
-0.07044004648923874,
0.020091727375984192,
-0.038995832204818726,
-0.003254119772464037,
0.0324927382171154,
-0.030450789257884026,
-0.03434723615646362,
-0.031168533489108086,
0.004244900308549404,
0.021941162645816803,
-0.025029122829437256,
-0.0025854462292045355,
0.04622472822666168,
0.03297274932265282,
-0.006576330401003361,
-0.013065080158412457,
0.005944099277257919,
-0.005632299929857254,
0.018479442223906517,
0.006695689633488655,
0.015297525562345982,
-0.014196628704667091,
-0.035565756261348724,
0.008431949652731419,
0.00894252210855484,
0.016328949481248856,
-0.005031437147408724,
0.0065803444012999535,
-0.020007042214274406,
0.03642437234520912,
0.025388656184077263,
0.020015928894281387,
0.04866206645965576,
-0.02156936191022396,
-0.004336601123213768,
0.00894633587449789,
0.014314725063741207,
-0.031185487285256386,
0.004508709069341421,
-0.043588683009147644,
0.009139175526797771,
0.07850285619497299,
-0.0024231134448200464,
0.041813924908638,
-0.0035449990537017584,
-0.00048748470726422966,
0.02614111453294754,
-0.01445795688778162,
-0.030460041016340256,
0.0012882451992481947,
0.03856031969189644,
0.006192915607243776,
-0.04301130771636963,
-0.03780446946620941,
0.021885033696889877,
0.03809426724910736,
-0.01325664110481739,
-0.011531558819115162,
0.012165709398686886,
0.022036917507648468,
0.004845856223255396,
-0.00012520943710114807,
-0.045286890119314194,
0.009276133961975574,
-0.0012607030803337693,
0.020858658477663994,
-0.008337360806763172,
-0.03423761576414108,
0.04423241317272186,
-0.007784697227180004,
0.029543861746788025,
-0.010141436941921711,
-0.035169199109077454,
-0.06163383275270462,
0.009284282103180885,
0.025983739644289017,
0.0020494675263762474,
-0.02796095795929432,
-0.0008494181092828512,
0.030989699065685272,
0.0052407109178602695,
0.049865756183862686,
0.009586925618350506,
-0.06414641439914703,
-0.047398295253515244,
-0.024848230183124542,
-0.009395691566169262,
0.04916367679834366,
-0.04048950970172882,
-0.027506668120622635,
0.005519878584891558,
-0.032555148005485535,
0.007482621353119612,
0.019689468666911125,
0.028670985251665115,
-0.01789630949497223,
0.07177802920341492,
-0.0020502666011452675,
0.017325997352600098,
-0.005498476792126894,
0.004334506578743458,
0.07658611238002777,
0.023265128955245018,
-0.00425114668905735,
-0.0467807836830616,
0.00947045162320137,
-0.01415451429784298,
0.03137210011482239,
-0.003472820157185197,
0.043748412281274796,
-0.0017729243263602257,
0.0030035388190299273,
0.013008254580199718,
0.022994069382548332,
0.004647132474929094,
0.009411931037902832,
0.0617382675409317,
-0.003523793537169695,
-0.04606352373957634,
0.021962307393550873,
0.028709547594189644,
0.005180448293685913,
-0.014864016324281693,
0.026224154978990555,
0.033921003341674805,
-0.03891719877719879,
-0.002573017729446292,
-0.050503797829151154,
-0.04164859279990196,
0.004514985252171755,
-0.017724139615893364,
-0.042259566485881805,
-0.00860403198748827,
0.005818385165184736,
-0.039047181606292725,
-0.05338035151362419,
0.009805908426642418,
0.031017472967505455,
-0.020571334287524223,
0.03620978444814682,
0.03091530315577984,
0.004574965685606003,
0.00890521239489317,
0.019963372498750687,
0.010387381538748741,
-0.0577097162604332,
-0.007803738582879305,
-0.012796485796570778,
0.04141528904438019,
-0.010443814098834991,
-0.01679867133498192,
0.03563229367136955,
0.03035947121679783,
0.006071294657886028,
-0.07315999269485474,
-0.0036055962555110455,
0.017445096746087074,
-0.031940728425979614,
0.009573684073984623,
0.01221221499145031,
-0.05639016628265381,
0.029224999248981476,
-0.011071219108998775,
-0.001730936812236905,
0.004324503242969513,
0.046369295567274094,
0.0380098819732666,
0.004595786798745394,
0.048332881182432175,
-0.030414626002311707,
-0.01222158782184124,
-0.032431863248348236,
0.02178056724369526,
-0.026632007211446762,
-0.009090741164982319,
0.029304370284080505,
0.020793799310922623,
0.026923861354589462,
-0.0021164221689105034,
-0.01181485690176487,
-0.010391462594270706,
-0.07666019350290298,
0.031049683690071106,
-0.02464347891509533,
-0.02621050924062729,
-0.03527561202645302,
0.02707584574818611,
0.03500547632575035,
0.036249686032533646,
-0.05380794778466225,
0.00037509005051106215,
-0.016596518456935883,
0.0188203826546669,
0.006485507357865572,
-0.030890781432390213,
0.007562723010778427,
0.005595069378614426,
-0.010346239432692528,
0.004340660758316517,
-0.025762539356946945,
0.04122161865234375,
0.042076073586940765,
0.025031499564647675,
0.01581556163728237,
0.002434842986986041,
-0.024550095200538635,
0.023621395230293274,
-0.00518127903342247,
-0.024107899516820908,
0.017295535653829575,
0.0030251438729465008,
0.011949918232858181,
-0.04889421910047531,
-0.01785869151353836,
-0.026516180485486984,
-0.0147696016356349,
0.020396307110786438,
0.011042600497603416,
-0.007278257980942726,
0.030961988493800163,
0.000930804293602705,
-0.016717994585633278,
-0.03955792635679245,
-0.0016021642368286848,
-0.057749368250370026,
0.04389750957489014,
-0.009296318516135216,
-0.010367544367909431,
-0.017542440444231033,
0.03200094774365425,
-0.02636157162487507,
-0.041886162012815475,
0.013500789180397987,
0.027808042243123055,
0.006858217529952526,
-0.024306708946824074,
0.028573298826813698,
0.004137817770242691,
0.019206443801522255,
-0.058014772832393646,
-0.01418716087937355,
-0.0028634662739932537,
-0.03271475061774254,
-0.028530091047286987,
0.0739915668964386,
0.01593715324997902,
0.013439381495118141,
-0.007612322922796011,
0.03070145472884178,
0.015536542981863022,
0.06088264659047127,
-0.01184608694165945,
-0.03360205888748169,
0.007634964305907488,
-0.07118986546993256,
-0.0027966436464339495,
-0.007413341198116541,
0.023044301196932793,
0.008371174335479736,
0.000492708757519722,
0.040813807398080826,
0.0023495035711675882,
-0.018191296607255936,
0.05745573341846466,
-0.06309422850608826,
0.008563203737139702,
-0.010247101075947285,
0.028425591066479683,
-0.012990996241569519,
-0.007466040551662445,
0.059574004262685776,
-0.003832706715911627,
0.036369163542985916,
0.005596852861344814,
-0.007347998674958944,
-0.09203606843948364,
-0.011319835670292377,
-0.02420136146247387,
0.04115188494324684,
0.014092429541051388,
-0.025148676708340645,
0.022159148007631302,
0.054677076637744904,
-0.05599852278828621,
0.009552208706736565,
-0.048012860119342804,
-0.014695767313241959,
-0.023531025275588036,
0.022146105766296387,
0.019950633868575096,
0.061379652470350266,
0.03091469220817089,
0.03767076134681702,
0.034598059952259064,
0.00716598704457283,
-0.014139612205326557,
-0.054920781403779984,
-0.036738768219947815,
0.02018505148589611,
0.03470025956630707,
-0.028966255486011505,
0.055820632725954056,
-0.029388120397925377,
0.00847314577549696,
0.04228469729423523,
0.015090820379555225,
0.02163124270737171,
-0.008402951061725616,
0.004663174040615559,
0.030354546383023262,
0.01505772303789854,
0.0262588020414114,
-0.005701612215489149,
-0.006631458643823862,
0.004850751254707575,
0.02543031983077526,
0.01380646601319313,
0.0044268649071455,
-0.032631952315568924,
0.006027329713106155,
-0.08011560142040253,
-0.047340475022792816,
0.014531861990690231,
0.003952445462346077,
-0.016965316608548164,
0.03797303885221481,
-0.0083981454372406,
0.015048372559249401,
-0.05435918644070625,
-0.010452103801071644,
-0.04498892277479172,
-0.0013529600109905005,
0.03876257315278053,
0.006286667659878731,
-0.034644484519958496,
0.02303645946085453,
-0.02764212340116501,
-0.030253181234002113,
-0.0021206182427704334,
-0.00006223548552952707,
-0.0036608302034437656,
-0.042438432574272156,
-0.021359790116548538,
0.004067570436745882,
0.005227194167673588,
0.016619354486465454,
-0.03656257688999176,
-0.052941419184207916,
0.021330060437321663,
-0.007432022597640753,
-0.0002488609170541167,
0.023111512884497643,
-0.033321771770715714,
-0.044536739587783813,
-0.045514337718486786,
0.003581730416044593,
0.04269517585635185,
-0.023997219279408455,
-0.035455476492643356,
-0.007421189919114113,
-0.051418203860521317,
0.016815105453133583,
0.058431126177310944,
0.040244393050670624,
-0.011870894581079483,
0.026661699637770653,
-0.03442084416747093,
-0.0031760232523083687,
-0.044621676206588745,
-0.02463320456445217,
-0.001090200268663466,
-0.014764802530407906,
0.027362413704395294,
-0.012180237099528313,
-0.056592218577861786,
-0.0040723178535699844,
0.006852251011878252,
0.019214564934372902,
0.03965916484594345,
0.015154188498854637,
-0.030714446678757668,
0.057609282433986664,
0.01341085322201252,
0.0297806728631258,
0.08545578271150589,
0.02362208068370819,
0.012362785637378693,
0.05035330727696419,
-0.042956773191690445,
-0.045549746602773666,
0.00194277404807508,
-0.04326605424284935,
-0.026017535477876663,
-0.01713961735367775,
-0.013171210885047913,
0.013427617959678173,
-0.08451168239116669,
-0.012738749384880066,
0.03472273796796799,
-0.053957536816596985,
-0.0009158960892818868,
0.0317726694047451,
0.040209054946899414,
0.008214635774493217,
-0.026627739891409874,
0.014556024223566055,
0.00032187471515499055,
-0.009111433289945126,
0.010026090778410435,
0.04319259896874428,
0.05334215238690376,
-0.024268636479973793,
0.029223425313830376,
0.046089932322502136,
0.011981861665844917,
-0.0016763724852353334,
-0.020711619406938553,
0.06753384321928024,
0.009827100671827793,
-0.012105269357562065,
0.007703825365751982,
-0.04544004052877426,
-0.008431605063378811,
0.04478534683585167,
-0.0044693611562252045,
0.06537346541881561,
-0.05720052868127823,
0.038056183606386185,
0.011612984351813793,
-0.031417664140462875,
-0.04070084169507027,
0.038506608456373215,
0.0030652503482997417,
0.015079420059919357,
-0.020413262769579887,
-0.007718542590737343,
0.0033139092847704887,
-0.02019830234348774,
0.023285742849111557,
-0.05876335874199867,
-0.011811817064881325,
-0.01910834014415741,
-0.03448896110057831,
0.009359842166304588,
-0.004850217141211033,
-0.004125540144741535,
0.02171378582715988,
0.033924028277397156,
0.018443532288074493,
0.0024171387776732445,
-0.009451629593968391,
0.00221252697519958,
0.017017316073179245,
0.012931992299854755,
-0.08278179913759232,
-0.004319459665566683,
-0.033740442246198654,
0.009146529249846935,
-0.0362069234251976,
-0.012078603729605675
] |
<p>I would like to know how one could show and prove that a given motion is simple harmonic motion.</p>
<p>Once given an answer, I'll apply that technique to an example I am trying to figure out. </p>
<p>Thank you in advance!</p>
<p>I believe a motion can be proved simple harmonic, if the relation between its is as such:
$$
a_x = - \omega^2\cdot x
$$</p>
<p>And as such the period time is:
$$
T =\frac{2\pi}{\omega}
$$</p>
<p>Question-so-far: How do you prove such for a given force $F = \frac{G\cdot m_e \cdot M}{R_E} \cdot r$ ? Or any force that has non-trivial constants?</p> | 1,549 | [
0.0021323387045413256,
0.00017357732576783746,
-0.006486295256763697,
0.013923059217631817,
0.0372934490442276,
-0.0006639874773100019,
-0.003854360431432724,
-0.019914651289582253,
0.011194352060556412,
-0.03187245875597,
0.009739294648170471,
0.00965382531285286,
0.04732011631131172,
0.0009911529486998916,
0.03187369182705879,
-0.029205981642007828,
-0.06054957956075668,
-0.029232850298285484,
-0.008018904365599155,
-0.05341703072190285,
0.012171788141131401,
-0.006107789929956198,
0.016219325363636017,
-0.00006970934191485867,
-0.018734248355031013,
0.00004921425716020167,
0.04357954487204552,
0.008883845061063766,
0.006747003179043531,
0.048976168036460876,
-0.04047410935163498,
-0.0023478271905332804,
0.0019408023217692971,
0.05936940386891365,
0.034983690828084946,
0.030430808663368225,
-0.053092047572135925,
0.010762021876871586,
0.024420354515314102,
0.022278854623436928,
-0.03884408622980118,
-0.006896700244396925,
0.007503595668822527,
0.027769699692726135,
-0.01693256013095379,
0.024227200075984,
0.03144344314932823,
0.007952572777867317,
0.07581896334886551,
-0.03588861599564552,
0.08590158075094223,
0.014670014381408691,
0.0566214844584465,
-0.0024250911083072424,
-0.014467745088040829,
-0.021945012733340263,
0.02653333730995655,
0.05075975880026817,
-0.04127463698387146,
-0.014988372102379799,
-0.027030184864997864,
-0.02909933216869831,
-0.005673854611814022,
-0.0606696680188179,
-0.03439132869243622,
0.016331791877746582,
-0.007208638358861208,
0.01836378499865532,
0.025730669498443604,
-0.007014357019215822,
-0.0024722320958971977,
0.01577906124293804,
0.03181467205286026,
-0.008118546567857265,
-0.027277186512947083,
-0.03789262846112251,
0.03377886489033699,
0.03139285370707512,
-0.000843539834022522,
0.04015981778502464,
-0.017960693687200546,
-0.010633868165314198,
0.034921031445264816,
0.06068291887640953,
-0.00890270248055458,
-0.014934050850570202,
0.045166272670030594,
0.03647870197892189,
0.009953860193490982,
0.013568645343184471,
0.023129727691411972,
-0.01725807785987854,
0.021150995045900345,
-0.009619778022170067,
-0.026394274085760117,
0.021719099953770638,
0.005670307669788599,
0.023663807660341263,
0.02755029685795307,
-0.031716618686914444,
0.02056269906461239,
-0.05991269275546074,
0.03869873657822609,
0.06879115104675293,
-0.003607930149883032,
-0.012745599262416363,
-0.03250199183821678,
0.012031298130750656,
0.009899022057652473,
-0.001574845751747489,
-0.020636415109038353,
-0.00980804581195116,
0.014802669174969196,
-0.0219491608440876,
-0.024387018755078316,
0.016939256340265274,
-0.01675206981599331,
-0.020970027893781662,
0.06098387390375137,
0.06855235993862152,
0.04634227603673935,
-0.02367604710161686,
0.027397308498620987,
-0.04595658555626869,
-0.04069606587290764,
-0.010840094648301601,
0.027653126046061516,
-0.02854323759675026,
0.0015390999615192413,
0.056545622646808624,
0.03910834714770317,
-0.042826537042856216,
-0.026904316619038582,
0.016976039856672287,
0.04925873130559921,
-0.03122507408261299,
-0.10583803057670593,
-0.06937818229198456,
0.02953001670539379,
0.0010940023930743337,
-0.012800841592252254,
-0.07874524593353271,
0.026654593646526337,
0.05194076895713806,
0.07471001893281937,
0.003197259968146682,
-0.015184478834271431,
0.011709463782608509,
0.03279563784599304,
0.003980086650699377,
-0.010433056391775608,
-0.04795600473880768,
0.01411167811602354,
-0.04280081391334534,
0.010712871327996254,
-0.03593716025352478,
0.006893896032124758,
0.0014161012368276715,
0.009491347707808018,
-0.001674768514931202,
0.0826663225889206,
0.003674324369058013,
-0.012459074147045612,
0.03104822151362896,
0.002556153805926442,
-0.047410283237695694,
0.08601118624210358,
0.01658208854496479,
-0.04896273836493492,
0.02580869011580944,
0.0036701643839478493,
0.051678042858839035,
-0.006752849090844393,
0.012906208634376526,
0.02669587731361389,
-0.0539836585521698,
-0.04379510506987572,
0.021360348910093307,
-0.010525968857109547,
0.01755233108997345,
-0.04136551916599274,
-0.03636470437049866,
-0.0023542018607258797,
0.005954654887318611,
0.010859297588467598,
0.04476394131779671,
-0.004378697834908962,
0.03637499362230301,
0.03058587573468685,
-0.053610652685165405,
-0.014166698791086674,
-0.06705331802368164,
0.057434625923633575,
-0.01377764530479908,
-0.057498566806316376,
0.01733614131808281,
-0.011622725985944271,
0.010500594973564148,
-0.035743098706007004,
-0.03617803379893303,
-0.0016089777927845716,
0.0330558642745018,
-0.01889975741505623,
-0.06276271492242813,
0.05408324673771858,
0.0244616586714983,
0.041661959141492844,
0.022088628262281418,
0.012795014306902885,
-0.013434311375021935,
0.013501367531716824,
-0.008545985445380211,
-0.027242818847298622,
0.02655171975493431,
0.005611530505120754,
-0.011690480634570122,
-0.0027977535501122475,
-0.062191542237997055,
-0.011661042459309101,
0.06289691478013992,
-0.04556262120604515,
0.08995306491851807,
0.05681147426366806,
-0.00930875912308693,
0.008251810446381569,
0.03729230538010597,
0.03298702836036682,
0.008973564952611923,
-0.012342079542577267,
-0.020894793793559074,
-0.053487107157707214,
-0.027354281395673752,
0.05810333788394928,
0.04221042990684509,
-0.03060542233288288,
0.010781544260680676,
0.06241907179355621,
0.018567614257335663,
0.023971406742930412,
0.041962478309869766,
0.021654196083545685,
-0.04132413491606712,
0.046746060252189636,
0.041531652212142944,
-0.007479657884687185,
0.017210625112056732,
0.03778049349784851,
0.037076763808727264,
0.02630988322198391,
0.026902765035629272,
-0.0011145587777718902,
0.047273702919483185,
-0.005722817499190569,
0.007178638130426407,
0.04503978416323662,
0.0016571045853197575,
0.04926285892724991,
-0.009974909014999866,
0.05089377984404564,
0.03054274246096611,
-0.021940888836979866,
0.02414241060614586,
-0.004941493272781372,
0.021214816719293594,
0.016517601907253265,
-0.05013316497206688,
-0.028912296518683434,
-0.032933857291936874,
0.02716175466775894,
-0.0449654646217823,
-0.03150742128491402,
-0.020360685884952545,
-0.01992938481271267,
-0.01868775673210621,
-0.007249344140291214,
0.03922029957175255,
0.019125722348690033,
0.020935000851750374,
-0.012930835597217083,
-0.027160707861185074,
0.00987167377024889,
-0.029619857668876648,
0.010613763704895973,
0.01222121063619852,
-0.024479428306221962,
0.012058932334184647,
-0.03427962213754654,
-0.027163872495293617,
0.07465774565935135,
-0.015506934374570847,
0.023053737357258797,
-0.0075910803861916065,
0.02262437716126442,
-0.06599698215723038,
-0.008408144116401672,
-0.05370857194066048,
0.00967954657971859,
-0.06977742165327072,
0.010359462350606918,
0.06112082675099373,
-0.022347467020154,
-0.046166177839040756,
0.00885317474603653,
-0.004560790024697781,
-0.01735556684434414,
-0.010542192496359348,
-0.022420769557356834,
0.027425577864050865,
-0.05978657677769661,
0.0467023029923439,
-0.02477428689599037,
-0.05656743422150612,
-0.02105707861483097,
-0.029386943206191063,
-0.006731133442372084,
-0.004752890672534704,
0.025198351591825485,
0.060837652534246445,
0.02844890207052231,
-0.06766285747289658,
0.06505849212408066,
0.046040959656238556,
-0.04859213903546333,
-0.01205635629594326,
-0.007698611356317997,
0.0013559976359829307,
-0.03988063707947731,
-0.014310227707028389,
0.045280106365680695,
-0.028494473546743393,
0.02495737187564373,
0.013722870498895645,
-0.012313419952988625,
0.02571149729192257,
0.0033030249178409576,
0.015162546187639236,
-0.008878246881067753,
-0.007268855348229408,
0.03379082307219505,
0.0474882535636425,
0.01670965366065502,
-0.013951512984931469,
0.007858199998736382,
0.02186012826859951,
0.01603875309228897,
-0.017855456098914146,
-0.08020902425050735,
0.0259096696972847,
-0.0050269244238734245,
-0.022151796147227287,
-0.02131642773747444,
0.03149427846074104,
0.00746097881346941,
0.012489652261137962,
0.008491961285471916,
0.045663975179195404,
0.021059243008494377,
0.001365349511615932,
0.023195825517177582,
0.022274097427725792,
0.02461027167737484,
-0.0035359924659132957,
-0.012264142744243145,
-0.03330346569418907,
-0.00726786395534873,
0.036083199083805084,
-0.018555838614702225,
-0.022713789716362953,
0.03981078416109085,
0.002065059030428529,
0.05269966274499893,
-0.0023184071760624647,
-0.02984403632581234,
0.0007523344247601926,
-0.05010400712490082,
-0.029881717637181282,
-0.010687967762351036,
0.035620108246803284,
0.002165826503187418,
0.06105668470263481,
0.01748797856271267,
0.009979154914617538,
0.02161688543856144,
-0.008069864474236965,
-0.0770018920302391,
0.05999206006526947,
-0.023994171991944313,
-0.008634715341031551,
0.010829462669789791,
0.018605221062898636,
-0.026989111676812172,
-0.02427714318037033,
-0.021691570058465004,
-0.02038760297000408,
-0.020421616733074188,
-0.04287027195096016,
-0.013034764677286148,
-0.0028752870857715607,
-0.04805094376206398,
-0.0002204038028139621,
0.0118873855099082,
0.02068566530942917,
-0.005241166800260544,
-0.008036642335355282,
0.04805811122059822,
-0.019556205719709396,
-0.0017175294924527407,
-0.01576910726726055,
-0.02439037337899208,
-0.00407188106328249,
-0.008258379064500332,
-0.0050908238627016544,
0.035741329193115234,
0.0399138480424881,
0.009811332449316978,
-0.008570319972932339,
0.05589619651436806,
0.011644548736512661,
0.02685447596013546,
-0.007642962504178286,
-0.027717124670743942,
0.004030916374176741,
0.03659459203481674,
0.04389813542366028,
0.013229858130216599,
-0.02605142816901207,
0.021353747695684433,
0.010351908393204212,
-0.0032875847537070513,
0.07489317655563354,
0.03326623514294624,
0.02191220596432686,
-0.0021126149222254753,
-0.07062903791666031,
-0.012046178802847862,
0.0014043997507542372,
-0.003564022947102785,
0.01026060152798891,
-0.03293377533555031,
0.015532397665083408,
-0.00033059011911973357,
0.004810896702110767,
0.03263089805841446,
0.02697605825960636,
-0.0026039527729153633,
-0.02520453743636608,
0.028668398037552834,
-0.004828996025025845,
-0.009338147938251495,
0.02307210862636566,
0.023206213489174843,
0.049488406628370285,
-0.004114005248993635,
-0.005021356977522373,
-0.08221419155597687,
0.01715819537639618,
0.031794026494026184,
0.007397075649350882,
0.02613823674619198,
0.029302915558218956,
-0.02768864668905735,
-0.06145405396819115,
0.0298922136425972,
0.011911489069461823,
0.043942272663116455,
-0.024011485278606415,
0.01087132003158331,
-0.018474100157618523,
-0.038218799978494644,
-0.05224338546395302,
0.0011368246050551534,
0.007794147357344627,
-0.0034723554272204638,
-0.02201566845178604,
-0.013988389633595943,
-0.02518000267446041,
-0.04368313029408455,
0.04505256190896034,
0.0595296286046505,
0.03338363394141197,
-0.03690023720264435,
-0.006525891367346048,
0.021145997568964958,
-0.028459077700972557,
-0.07364330440759659,
-0.000997505965642631,
-0.00719248503446579,
-0.010225783102214336,
0.0047033135779201984,
-0.037126682698726654,
-0.053901784121990204,
0.021068187430500984,
0.00960210245102644,
0.0036272797733545303,
0.01653929241001606,
-0.01800766959786415,
0.007489745505154133,
0.03061251901090145,
0.017242465168237686,
0.052118655294179916,
0.06797792762517929,
-0.014309263788163662,
-0.023436009883880615,
0.02061588689684868,
0.031321775168180466,
-0.03720785677433014,
-0.019851714372634888,
-0.031011922284960747,
0.003196336794644594,
-0.025898650288581848,
0.047380480915308,
-0.0004924655077047646,
0.010448424145579338,
-0.001188053865917027,
-0.02977408841252327,
0.007043684832751751,
0.023903850466012955,
-0.003917198162525892,
0.000786664430052042,
-0.003950762562453747,
0.0058137886226177216,
-0.004494176246225834,
-0.022236382588744164,
-0.005068715661764145,
0.012751413509249687,
0.0181058831512928,
0.03416960686445236,
0.000023211123334476724,
0.018503878265619278,
-0.03527156263589859,
-0.00970730371773243,
-0.027175143361091614,
-0.04855707660317421,
0.04787968471646309,
-0.016742374747991562,
-0.012798458337783813,
0.009832726791501045,
-0.052103783935308456,
-0.04026215523481369,
0.03126528486609459,
0.019173510372638702,
0.011516068130731583,
-0.012427805922925472,
-0.03305719047784805,
0.04229309409856796,
-0.000916160352062434,
-0.0748521089553833,
-0.07475186139345169,
0.016309482976794243,
0.025088274851441383,
-0.013509968295693398,
-0.009866874665021896,
-0.0022602519020438194,
-0.03296970948576927,
-0.024052878841757774,
0.03478222340345383,
0.04291028156876564,
-0.0035753767006099224,
0.018900597468018532,
0.016144705936312675,
0.009901388548314571,
0.0533280111849308,
0.00038879274507053196,
-0.0381767638027668,
0.0015917698619887233,
-0.022114906460046768,
-0.030377300456166267,
0.00020939360547345132,
0.05909572169184685,
-0.03323837369680405,
-0.007936572656035423,
0.0014062513364478946,
-0.02205848880112171,
0.00461209611967206,
-0.034899670630693436,
-0.033309902995824814,
0.05340989679098129,
0.013668441213667393,
-0.0066772024147212505,
-0.03845036029815674,
0.01017937995493412,
-0.01660086214542389,
0.05543001368641853,
-0.007144594099372625,
-0.011763683520257473,
-0.029248256236314774,
-0.05715816840529442,
0.013034502975642681,
0.0004131186578888446,
-0.0003277639043517411,
0.004456609487533569,
0.07068652659654617,
-0.023036345839500427,
-0.004944645334035158,
0.04260637238621712,
0.012429730035364628,
0.0034981672652065754,
-0.016936643049120903,
0.0026877811178565025,
-0.0008868630393408239,
0.004561277572065592,
-0.03395529091358185,
-0.0298854261636734,
-0.019386759027838707,
0.033954475075006485,
0.06844791769981384,
-0.01235993579030037,
0.055056001991033554,
0.033380378037691116,
0.013954700902104378,
-0.035507120192050934,
0.021898604929447174,
-0.01172082219272852,
-0.05731384828686714,
0.031056588515639305,
0.01359444297850132,
-0.03577901050448418,
0.015659969300031662,
0.016690077260136604,
0.023122038692235947,
-0.03968857228755951,
-0.012932891957461834,
0.01479541789740324,
0.030035221949219704,
0.013993613421916962,
0.007898887619376183,
-0.025541435927152634,
0.03661292791366577,
-0.0027767294086515903,
0.0720655769109726,
-0.02311819978058338,
-0.020421087741851807,
0.002579913940280676,
0.03137386590242386,
0.01087391097098589,
-0.03253282606601715,
-0.011850330047309399,
-0.025244375690817833,
0.04323205351829529,
0.015030520036816597,
-0.004265224561095238,
0.032395992428064346,
0.02200200781226158,
0.04146786406636238,
-0.024637531489133835,
0.021000441163778305,
0.016358934342861176,
-0.029761888086795807,
-0.00468716723844409,
-0.017882123589515686,
-0.03431637957692146,
0.03669591620564461,
-0.0022899818141013384,
-0.04292547330260277,
0.002486731857061386,
-0.017834564670920372,
0.0031409296207129955,
0.04367136210203171,
-0.003157869214192033,
-0.04759347066283226,
0.08694806694984436,
-0.0017847373383119702,
-0.0016638846136629581,
0.0115375816822052,
0.021037599071860313,
0.10863976925611496,
0.03891661390662193,
0.004998259712010622,
-0.048018161207437515,
0.012847534380853176,
-0.03481298312544823,
-0.008266997523605824,
-0.035252735018730164,
0.015549658797681332,
-0.008519228547811508,
-0.03987599164247513,
0.004439521115273237,
0.0561988390982151,
-0.0181622002273798,
-0.02445010468363762,
0.06162640079855919,
-0.003452130127698183,
-0.028811436146497726,
-0.029780596494674683,
0.0029777358286082745,
-0.0173089150339365,
-0.0024100691080093384,
0.005842430982738733,
0.031643666326999664,
-0.06163172051310539,
-0.028680862858891487,
-0.0240104291588068,
-0.06301664561033249,
0.02565341629087925,
0.023465583100914955,
-0.03774547204375267,
0.008695856668055058,
0.03967621549963951,
-0.04350478574633598,
-0.031674399971961975,
0.040480535477399826,
-0.0032128586899489164,
-0.0224472526460886,
0.028647739440202713,
0.027487825602293015,
0.01304949726909399,
-0.004704308230429888,
0.015370219945907593,
-0.0010560184018686414,
-0.042186737060546875,
-0.007477988954633474,
-0.06424248963594437,
0.04013650864362717,
0.006907584611326456,
0.005311660468578339,
0.017055785283446312,
-0.010751234367489815,
-0.03912951052188873,
-0.07863455265760422,
0.012101820670068264,
-0.011464554816484451,
0.03782540187239647,
-0.05274953693151474,
-0.021355753764510155,
-0.015147190541028976,
0.0030372105538845062,
0.0039797076024115086,
0.019121333956718445,
-0.0031031935941427946,
-0.01742136850953102,
-0.018352000042796135,
0.019205421209335327,
0.019075732678174973,
-0.016964958980679512,
-0.05148150026798248,
-0.0015153398271650076,
-0.008095012977719307,
-0.027436506003141403,
-0.016174418851733208,
0.024426976218819618,
0.03163941204547882,
0.03218498453497887,
0.025869684293866158,
-0.04982610419392586,
-0.004652990493923426,
-0.060731157660484314,
0.019664892926812172,
0.017404241487383842,
-0.058539122343063354,
-0.020113134756684303,
-0.02718259021639824,
0.03206740319728851,
0.04840518906712532,
-0.02975725568830967,
0.02490275725722313,
-0.02039536088705063,
0.01702786050736904,
0.05153002217411995,
-0.036088451743125916,
-0.025230737403035164,
0.0448564812541008,
-0.00463860621675849,
0.009327019564807415,
-0.002531088422983885,
0.018295207992196083,
0.04611458256840706,
0.018887583166360855,
-0.023086244240403175,
0.005336640402674675,
-0.033636629581451416,
0.008476481772959232,
0.01273515447974205,
-0.011178935877978802,
0.012596257030963898,
0.0015396743547171354,
0.0089035639539361,
-0.07905984669923782,
-0.05739752948284149,
-0.04830016568303108,
0.01716010831296444,
0.007236487232148647,
-0.010347572155296803,
-0.02933451347053051,
0.05525074526667595,
-0.009632918983697891,
0.015341744758188725,
-0.06396068632602692,
-0.009282564744353294,
-0.019075626507401466,
-0.01259788777679205,
0.02247965894639492,
0.014724650420248508,
-0.019215716049075127,
0.004565950017422438,
-0.02188006602227688,
-0.031749606132507324,
0.04752574488520622,
0.06467742472887039,
-0.004920050967484713,
-0.0002003340923693031,
0.050094302743673325,
-0.031663522124290466,
0.03767984360456467,
-0.012445207685232162,
-0.0023217194247990847,
0.026908239349722862,
-0.06015029549598694,
-0.02242063172161579,
0.03206058591604233,
-0.013679012656211853,
0.011253478936851025,
-0.008431893773376942,
-0.020264143124222755,
0.03210597485303879,
0.02354022115468979,
0.0020929884631186724,
0.004149181768298149,
-0.00626005232334137,
-0.01752411760389805,
-0.03583052009344101,
-0.02771737240254879,
0.025877978652715683,
-0.050147101283073425,
0.029047146439552307,
0.000754387176129967,
0.029499884694814682,
0.0004875812737736851,
-0.0407174751162529,
0.016798967495560646,
-0.006465994752943516,
-0.011513476260006428,
0.04074057936668396,
0.03836418315768242,
0.03624385595321655,
0.017332138493657112,
-0.009808920323848724,
0.02066877670586109,
-0.027950763702392578,
-0.003589739790186286,
-0.10550078749656677,
-0.014530817046761513,
-0.0015056130941957235,
0.011456920765340328,
0.06694191694259644,
-0.04510566219687462,
-0.011351843364536762,
0.03029407560825348,
-0.051553141325712204,
0.004716205410659313,
-0.02386307530105114,
0.010025473311543465,
0.0034798854030668736,
-0.03895483911037445,
-0.004874842241406441,
0.02481788396835327,
-0.008261646144092083,
0.048721786588430405,
0.04493669047951698,
0.04150960221886635,
-0.011903395876288414,
0.002321497304365039,
0.021697964519262314,
0.022012140601873398,
-0.002769523998722434,
-0.021227430552244186,
0.0438072495162487,
0.003706186544150114,
-0.023366622626781464,
0.04863924905657768,
-0.005029481835663319,
0.0008936072117649019,
-0.009190356358885765,
0.03319088742136955,
-0.016261961311101913,
0.046263936907052994,
0.02703138068318367,
-0.022401772439479828,
-0.025273682549595833,
0.023452911525964737,
0.022714274004101753,
0.024974048137664795,
-0.04025739058852196,
-0.0256165973842144,
0.015054791234433651,
-0.036271095275878906,
-0.037076495587825775,
0.014505311846733093,
0.0023024289403110743,
-0.022916538640856743,
0.006247817073017359,
-0.03857682645320892,
0.006683409214019775,
-0.008951456286013126,
0.03743461146950722,
-0.011711309663951397,
-0.008312172256410122,
0.020783133804798126,
-0.0132394814863801,
-0.024152470752596855,
0.021852076053619385,
0.007473542355000973,
-0.05317830294370651,
0.052931562066078186,
-0.0011882851831614971,
-0.03349379450082779,
-0.053949132561683655,
0.012251047417521477,
0.01223780307918787,
0.0014724783832207322,
-0.0030111961532384157,
-0.02815454639494419,
-0.026087796315550804,
0.04454200714826584,
0.021154489368200302,
0.005616292357444763,
-0.027562452480196953,
0.008368228562176228,
-0.018787702545523643,
-0.05312558263540268,
0.019793104380369186,
0.033422257751226425,
-0.03079809993505478,
-0.042784687131643295,
-0.02172696962952614,
-0.015328668989241123,
-0.02550833486020565,
0.06019658222794533,
-0.05556635931134224,
0.01477784477174282,
0.0019830025266855955,
-0.010030074045062065,
0.008237396366894245,
-0.05030585825443268,
0.021461794152855873,
-0.019143782556056976,
-0.019957372918725014,
0.01772911474108696,
-0.007018355652689934,
-0.02445225603878498,
-0.004740090575069189,
-0.004007851239293814,
-0.024434084072709084,
0.02730047143995762,
0.0023759708274155855,
-0.03585313633084297,
0.0321088582277298,
0.009602940641343594,
0.0031042983755469322,
0.0495838038623333,
-0.01601846143603325,
-0.008705664426088333,
0.028913218528032303,
-0.04811197891831398,
-0.05535103380680084,
0.021613799035549164,
-0.06573646515607834,
-0.016404008492827415,
-0.03036470152437687,
-0.008398905396461487,
0.014009658247232437,
-0.05792145058512688,
-0.01867845095694065,
0.025155991315841675,
-0.01752464845776558,
-0.004230791702866554,
0.001827981323003769,
-0.00401889905333519,
0.039106111973524094,
0.007100502960383892,
0.028123797848820686,
0.022870196029543877,
-0.0011579249985516071,
0.021692851558327675,
0.0040710316970944405,
0.03367143124341965,
0.0023357144091278315,
-0.006179461255669594,
0.03618183359503746,
0.00009971863619284704,
0.04783019423484802,
0.00554824760183692,
0.03993034362792969,
-0.016460414975881577,
-0.007934758439660072,
0.011876816861331463,
-0.05299251154065132,
0.000032459131034556776,
0.03210664540529251,
-0.008873135782778263,
0.05907212570309639,
-0.045963890850543976,
0.01464007142931223,
-0.026592591777443886,
0.007883120328187943,
-0.025083715096116066,
0.0026806676760315895,
0.020820477977395058,
0.02552519552409649,
-0.01571962796151638,
0.03135475888848305,
-0.009371334686875343,
-0.020909197628498077,
0.016730859875679016,
-0.00404855003580451,
0.01329495944082737,
0.027558617293834686,
-0.013680560514330864,
0.0036032707430422306,
0.0001868379331426695,
-0.005673374980688095,
-0.036644358187913895,
0.03707380220293999,
0.053491465747356415,
0.0215280894190073,
-0.009159324690699577,
0.023057494312524796,
-0.027836991474032402,
0.049991048872470856,
-0.09169551730155945,
-0.0014970190823078156,
-0.015305074863135815,
0.014605415984988213,
0.009346243925392628,
0.01946805790066719
] |
<p>David Albert is a philosopher of Science at Columbia. His book "Time and Chance" includes this example (p 36). </p>
<p>A gas is confined on one side of a box with a removable wall. "Draw the wall out, <em>slowly</em>, and <em>perpendicular</em> to its surface, like a piston. Now it happens to be the case, it happens to be a consequence of the Newtonian laws of motion, that a billiard ball which bounces off a receding wall will move more slowly <em>after</em> the collision than <em>before</em> it. (Footnote. Proof: consider the fame of reference in which the wall is at rest.) And so gas particles that bounce off the wall as it it's being drawn out will have their kinetic energy somewhat <em>depleted</em>."</p>
<p>Why is that? We are assuming that an externally applied force is pulling the wall out. It's not the gas that is pushing the wall out. So why is energy lost. Why doesn't that violate conservation of energy.</p>
<p>Another way to look at it is to assume a series of walls very close to each other. Remove them one by one parallel to the surface. There will be no change in the total kinetic energy of the gas. Why is this different?</p> | 1,550 | [
-0.08135213702917099,
-0.0237762201577425,
0.008082345128059387,
-0.03494460880756378,
0.02636573277413845,
0.007644152734428644,
-0.022302718833088875,
0.02666337601840496,
-0.03257979452610016,
0.028025873005390167,
0.00538937421515584,
0.04429710656404495,
0.03231390193104744,
0.033123988658189774,
0.011571662500500679,
0.010222174227237701,
-0.0053407130762934685,
-0.024830535054206848,
0.007876344956457615,
-0.05244598910212517,
-0.029997900128364563,
-0.0007818858721293509,
0.020876212045550346,
0.005646048113703728,
-0.034603774547576904,
0.026957472786307335,
0.009350208565592766,
-0.0397619754076004,
0.016147233545780182,
0.042383868247270584,
-0.029556196182966232,
0.02464723400771618,
-0.028401119634509087,
-0.03228321298956871,
-0.00911129079759121,
0.008485019207000732,
0.001666608965024352,
0.004654730204492807,
0.001307863974943757,
0.014668368734419346,
-0.049991969019174576,
-0.0024480102583765984,
0.014058554545044899,
0.050647083669900894,
-0.043747011572122574,
0.028804754838347435,
0.03043447434902191,
-0.0021201730705797672,
0.0682099312543869,
-0.06608164310455322,
0.05166354775428772,
-0.013037475757300854,
0.05879265442490578,
0.04661252349615097,
-0.04412298649549484,
0.017991837114095688,
0.051558613777160645,
0.10163867473602295,
-0.028713658452033997,
-0.03520976006984711,
-0.014371627941727638,
-0.019053887575864792,
-0.031250882893800735,
0.027423817664384842,
0.01190862711519003,
0.021086951717734337,
-0.0036739639472216368,
-0.04541541263461113,
0.015838177874684334,
-0.0017108269967138767,
0.0007529173162765801,
0.023105015978217125,
0.031604330986738205,
-0.008399461396038532,
0.0451761856675148,
0.01084545161575079,
0.03413551673293114,
0.00593543378636241,
0.04724719375371933,
0.04558956250548363,
-0.016788210719823837,
-0.010863560251891613,
0.09729855507612228,
0.0778234675526619,
0.03173626959323883,
-0.010109947063028812,
0.06135059520602226,
-0.029891112819314003,
0.03269678354263306,
0.05149783194065094,
0.012793095782399178,
0.00011697613808792084,
0.022491613402962685,
0.021426284685730934,
-0.0300504881888628,
0.03823164105415344,
0.015207568183541298,
0.06066150590777397,
0.0039061966817826033,
-0.0016218832461163402,
-0.04392221197485924,
0.000781875743996352,
0.04341435432434082,
0.023548295721411705,
-0.005690569989383221,
-0.024335743859410286,
-0.061511021107435226,
0.04911116883158684,
0.00973821897059679,
0.014971954748034477,
-0.03794384375214577,
-0.006373483221977949,
-0.007398487534373999,
0.008797870948910713,
0.017106199637055397,
-0.00864210445433855,
-0.022969333454966545,
0.003791054943576455,
0.04258763790130615,
0.02978498302400112,
0.03135256469249725,
-0.008396829478442669,
-0.01833428256213665,
-0.02848576195538044,
-0.04426571726799011,
0.013948979787528515,
0.041211873292922974,
-0.05483900383114815,
-0.0356597863137722,
0.004373085685074329,
0.001208694651722908,
-0.005107419565320015,
-0.030952002853155136,
0.013553164899349213,
0.04989698529243469,
-0.026188280433416367,
-0.09198353439569473,
-0.04669603332877159,
0.06786075234413147,
0.004674552008509636,
-0.032994192093610764,
-0.06481750309467316,
-0.02641058713197708,
0.008944847621023655,
0.09217603504657745,
0.0041162362322211266,
-0.01904381811618805,
-0.033118486404418945,
0.04442187026143074,
-0.022907929494976997,
-0.019665079191327095,
0.0005647731013596058,
0.009833692573010921,
-0.0376371294260025,
0.01723846048116684,
-0.059601202607154846,
0.02521122619509697,
0.03341560810804367,
-0.010377375409007072,
-0.010166604071855545,
0.05520946532487869,
-0.0363767184317112,
-0.030866442248225212,
-0.01738862134516239,
-0.022487327456474304,
-0.037144020199775696,
0.08724339306354523,
0.03533640503883362,
0.003543384838849306,
-0.0009080218733288348,
0.07086366415023804,
0.04186386987566948,
-0.003913721535354853,
-0.014561385847628117,
0.025422126054763794,
-0.024095116183161736,
-0.010697311721742153,
-0.001128688221797347,
0.009199295192956924,
0.0029292493127286434,
-0.020763736218214035,
-0.0063530863262712955,
0.00989842601120472,
-0.03121456876397133,
-0.007637040689587593,
-0.001740506268106401,
0.005260423291474581,
0.023478509858250618,
-0.008830709382891655,
-0.013047548942267895,
-0.030849935486912727,
-0.09303505718708038,
0.04891788214445114,
-0.005263615865260363,
-0.00031464299536310136,
-0.01826748065650463,
0.036860059946775436,
0.027838902547955513,
-0.03263760730624199,
-0.03800741210579872,
-0.002969219349324703,
0.021310608834028244,
-0.01976010389626026,
-0.014474012888967991,
-0.009680338203907013,
0.03304348140954971,
0.03272145614027977,
0.020267048850655556,
0.01945946179330349,
0.004591186530888081,
-0.03361644223332405,
-0.006243790965527296,
-0.019403181970119476,
-0.0021729744039475918,
0.0033153374679386616,
0.005462859757244587,
0.05076073482632637,
-0.01576554775238037,
0.02657202072441578,
0.000756893481593579,
-0.008664383552968502,
0.05347403138875961,
0.030234629288315773,
0.035246822983026505,
-0.011714726686477661,
0.08097381144762039,
-0.024810785427689552,
-0.0015365671133622527,
0.012230603955686092,
-0.05343848839402199,
-0.02317260205745697,
-0.03823818638920784,
0.008934129029512405,
0.0328877829015255,
-0.01708352565765381,
0.019277598708868027,
0.015165667980909348,
-0.0033371190074831247,
-0.015532147139310837,
0.02139717899262905,
0.03142501041293144,
-0.02551935613155365,
0.024666935205459595,
-0.0021827963646501303,
0.02368835173547268,
0.0021349629387259483,
0.05525714159011841,
0.0014129847986623645,
-0.01764548569917679,
-0.010465621948242188,
-0.0005812443559989333,
-0.014472228474915028,
0.009311972185969353,
0.02862938493490219,
0.003371181897819042,
-0.0362987294793129,
0.011663168668746948,
-0.02946527674794197,
0.014697622507810593,
0.020084314048290253,
-0.004845150280743837,
0.011081254109740257,
-0.05386066436767578,
-0.009873790666460991,
-0.001957426778972149,
0.01439435314387083,
0.01534249447286129,
0.010619363747537136,
0.02787308767437935,
-0.03115788847208023,
0.020139919593930244,
0.0019222836708649993,
-0.0158378928899765,
-0.007298307027667761,
0.011956512928009033,
-0.016008730977773666,
0.008196981623768806,
0.019123658537864685,
-0.025619754567742348,
-0.02822776883840561,
-0.006052296608686447,
-0.04274392127990723,
-0.024650583043694496,
0.014222580939531326,
-0.01677648164331913,
0.046358298510313034,
-0.02750689536333084,
-0.028699200600385666,
0.017920950427651405,
-0.0057425349950790405,
-0.0009637753246352077,
0.06403102725744247,
0.010256524197757244,
-0.04601544141769409,
-0.009087546728551388,
-0.006738882977515459,
-0.02186133898794651,
-0.0025231281761080027,
0.02749946154654026,
0.06981651484966278,
-0.013790980912744999,
-0.04685221612453461,
0.030615996569395065,
-0.03929051384329796,
-0.051717471331357956,
-0.04594334959983826,
0.0055449786596000195,
0.04819943383336067,
0.005514482967555523,
-0.02103797346353531,
0.028828592970967293,
-0.06319586932659149,
-0.04391435533761978,
-0.01115245558321476,
-0.07112067192792892,
-0.012718250043690205,
-0.020319348201155663,
0.058628667145967484,
-0.03836677223443985,
-0.009285337291657925,
0.05217668041586876,
0.03563679754734039,
-0.009036018513143063,
0.023546524345874786,
-0.02807804010808468,
0.0038914962206035852,
-0.017024362459778786,
0.0006578995962627232,
0.014111433178186417,
-0.028366001322865486,
0.02529405988752842,
-0.02350727654993534,
0.06413210183382034,
-0.008215724490582943,
-0.02499239332973957,
-0.018424931913614273,
-0.007659677416086197,
0.004134500864893198,
0.0003469749935902655,
0.024685313925147057,
-0.005967877805233002,
-0.03359616920351982,
0.006194459740072489,
-0.011716091074049473,
0.05977823585271835,
0.03378955274820328,
-0.08461473137140274,
0.06736689805984497,
-0.005956681910902262,
0.03412476181983948,
-0.020633485168218613,
0.015570362098515034,
-0.02605487033724785,
-0.01608993485569954,
0.03426988422870636,
-0.004692429676651955,
0.029937997460365295,
0.006660252343863249,
0.03697523474693298,
0.035149771720170975,
0.07553867995738983,
-0.007572037633508444,
-0.02284921146929264,
-0.0013365072663873434,
0.0002868525043595582,
0.05324702337384224,
-0.015276181511580944,
-0.004217869136482477,
0.032597776502370834,
0.020467596128582954,
0.03546695038676262,
-0.005391316954046488,
-0.03695014864206314,
-0.010195408947765827,
-0.04946683347225189,
0.01011359691619873,
0.00941637996584177,
0.057425521314144135,
-0.007298869546502829,
0.04507198929786682,
0.005852653179317713,
0.032683804631233215,
0.018440844491124153,
-0.028925295919179916,
-0.09315028786659241,
0.009910223074257374,
-0.0018476183759048581,
-0.023439697921276093,
-0.0173729807138443,
0.01916109025478363,
0.022902430966496468,
-0.025726180523633957,
-0.018126338720321655,
0.011125436052680016,
-0.009657000191509724,
-0.08458761870861053,
0.007628147955983877,
-0.0657598003745079,
-0.07237004488706589,
-0.01085808128118515,
0.027247067540884018,
0.046458423137664795,
-0.02945716679096222,
0.03572702035307884,
0.056873466819524765,
-0.01748715713620186,
0.003466799156740308,
-0.005001611541956663,
-0.0059312814846634865,
0.0461956262588501,
0.031587325036525726,
0.02177754044532776,
0.009969166480004787,
0.014887767843902111,
0.010348791256546974,
0.0299285389482975,
0.007525234017521143,
-0.023385126143693924,
0.02148962952196598,
-0.0336860790848732,
-0.041414182633161545,
-0.018017800524830818,
-0.014412361197173595,
0.045004330575466156,
-0.006035120692104101,
0.0238842461258173,
-0.013740415684878826,
0.03388369083404541,
0.005813641473650932,
0.03388509899377823,
0.0016705928137525916,
0.030780738219618797,
-0.004556981381028891,
-0.04011072590947151,
-0.007852483540773392,
-0.03295549377799034,
-0.006733128800988197,
0.020517000928521156,
0.010090742260217667,
-0.01666119322180748,
0.004928600508719683,
-0.008073659613728523,
0.019521230831742287,
-0.010577860288321972,
0.0006940153543837368,
-0.044489189982414246,
-0.017743755131959915,
-0.04341032728552818,
0.03523056209087372,
0.0108865424990654,
-0.014434046112000942,
0.009402231313288212,
0.0028464666102081537,
-0.005587027873843908,
-0.04605381563305855,
-0.010237539187073708,
0.037576984614133835,
0.04231840744614601,
0.005198323633521795,
0.0023920380044728518,
-0.020465748384594917,
-0.0071287997998297215,
0.04064019024372101,
-0.039437465369701385,
-0.007203792687505484,
-0.009485980495810509,
0.033000677824020386,
-0.0012694846373051405,
-0.0631491020321846,
-0.002337879966944456,
0.0033608446829020977,
0.0006848456105217338,
0.023138409480452538,
0.007976416498422623,
-0.01637931354343891,
-0.03295357897877693,
-0.007809139788150787,
0.011257640086114407,
0.028304211795330048,
-0.018914569169282913,
-0.0041225505992770195,
-0.020578918978571892,
-0.017273539677262306,
-0.03269558399915695,
-0.06626927852630615,
-0.01955300010740757,
-0.03759142383933067,
-0.0011244735214859247,
-0.006028219126164913,
-0.04541764408349991,
-0.04033546522259712,
0.0024703070521354675,
-0.022054027765989304,
-0.024067969992756844,
-0.003775644348934293,
-0.028159786015748978,
0.05353773012757301,
0.013357892632484436,
0.012890308164060116,
0.033050183206796646,
0.04839726537466049,
-0.03326530382037163,
0.0045807817950844765,
-0.02084873430430889,
0.0462665818631649,
-0.01752910017967224,
0.01769631914794445,
-0.07198674231767654,
-0.026921741664409637,
0.0070399572141468525,
0.008377745747566223,
0.020287880674004555,
0.01747019588947296,
-0.017443059012293816,
-0.05757323279976845,
-0.0182198453694582,
-0.0073416708037257195,
0.007497766986489296,
0.016010494902729988,
-0.010160290636122227,
-0.009707157500088215,
-0.014358903281390667,
-0.025906551629304886,
0.01514876913279295,
0.022282566875219345,
-0.004077982623130083,
0.050230834633111954,
-0.01627192460000515,
0.01550264935940504,
-0.025646857917308807,
-0.00432637007907033,
0.006232450716197491,
-0.03428516536951065,
0.015414571389555931,
-0.04338705912232399,
0.011106809601187706,
0.034823499619960785,
-0.007450886070728302,
-0.009282378479838371,
-0.027933694422245026,
-0.028205791488289833,
-0.016473451629281044,
-0.06544382125139236,
0.03734876587986946,
0.007143308408558369,
0.03554084524512291,
-0.07944365590810776,
-0.015002995729446411,
-0.014811253175139427,
0.023368366062641144,
-0.025844378396868706,
-0.044263992458581924,
-0.027213409543037415,
-0.05535260587930679,
-0.013792094774544239,
-0.00845127459615469,
0.029728256165981293,
0.00019121309742331505,
0.005074829328805208,
0.04009075090289116,
0.010195866227149963,
0.04772091656923294,
-0.008958017453551292,
-0.010307584889233112,
0.0033115819096565247,
-0.023885579779744148,
-0.018314054235816002,
-0.024351058527827263,
0.04318922385573387,
-0.01369987428188324,
-0.018903536722064018,
0.03680643439292908,
-0.005792212672531605,
0.02493877150118351,
-0.031648773699998856,
0.03022395260632038,
0.05822915583848953,
-0.0124875633046031,
-0.006309615448117256,
0.024403149262070656,
0.03589370846748352,
-0.005414050538092852,
0.07252366095781326,
0.00870679970830679,
0.013396810740232468,
0.011132215149700642,
-0.03934893757104874,
-0.015699028968811035,
0.004568358417600393,
0.02886287495493889,
0.00592382438480854,
0.0865563228726387,
-0.01832137070596218,
0.0017544555012136698,
-0.000322618056088686,
-0.029083523899316788,
0.04217829555273056,
-0.010186021216213703,
-0.0005729823024012148,
-0.028382711112499237,
-0.005225521977990866,
-0.023645780980587006,
-0.03941383212804794,
-0.03318151459097862,
0.02562512271106243,
0.011928449384868145,
-0.023824214935302734,
0.05921853333711624,
-0.00353268813341856,
-0.025178074836730957,
0.026043714955449104,
-0.028719084337353706,
0.002438618801534176,
-0.018037207424640656,
-0.02109496109187603,
0.02268301509320736,
-0.000054900283430470154,
-0.012418999336659908,
0.04629592224955559,
0.029650915414094925,
-0.024686874821782112,
0.005480085499584675,
0.009486005641520023,
0.035653553903102875,
0.02292422018945217,
-0.0007787778740748763,
-0.021372592076659203,
0.05000336468219757,
-0.01381587889045477,
0.06130576878786087,
-0.00025151544832624495,
-0.0044658007100224495,
0.05087823048233986,
0.017236102372407913,
-0.028152121230959892,
-0.04806247353553772,
0.007793935015797615,
-0.034991852939128876,
0.031839530915021896,
-0.013051711954176426,
0.016530226916074753,
0.0027524749748408794,
-0.003984863869845867,
0.02804647386074066,
0.01635228842496872,
-0.002333307173103094,
-0.011791152879595757,
-0.0421597920358181,
-0.0012716769706457853,
-0.04113027825951576,
-0.02149828150868416,
0.0366227813065052,
-0.018665453419089317,
-0.02259756252169609,
0.021779417991638184,
-0.022613976150751114,
0.0041693528182804585,
-0.018855880945920944,
0.001586006605066359,
-0.006529355887323618,
0.06216328963637352,
0.011645869351923466,
0.03738247975707054,
-0.06268016993999481,
0.04872281476855278,
0.14777617156505585,
0.0227325689047575,
-0.006372133269906044,
-0.013626346364617348,
0.0025797055568546057,
-0.021760324016213417,
-0.008281858637928963,
-0.01591765508055687,
-0.009288392961025238,
-0.010813038796186447,
-0.006861382629722357,
0.015445491299033165,
0.06909919530153275,
-0.008042042143642902,
-0.01508045569062233,
0.013383114710450172,
-0.06476801633834839,
-0.027577880769968033,
0.002134497044607997,
0.015461906790733337,
-0.005788042210042477,
0.027460230514407158,
-0.03044734336435795,
0.007346297614276409,
-0.003170655807480216,
-0.012500185519456863,
-0.012777306139469147,
-0.05335146561264992,
0.005949986632913351,
-0.003164430381730199,
-0.04300354793667793,
0.043752167373895645,
0.02302144095301628,
-0.025214577093720436,
-0.04557029530405998,
0.0053045256063342094,
0.0735357478260994,
0.025582104921340942,
0.014391434378921986,
0.04419757425785065,
0.01933332346379757,
0.01041702926158905,
-0.007595967501401901,
0.04469776898622513,
-0.013134593144059181,
-0.006058458238840103,
-0.03754546120762825,
0.05972234532237053,
-0.011350571177899837,
0.020670505240559578,
0.0036422989796847105,
-0.04301967844367027,
0.0029227356426417828,
-0.051881466060876846,
-0.01929575391113758,
-0.006402270402759314,
0.03905406966805458,
0.023202404379844666,
-0.010958947241306305,
-0.014152766205370426,
0.029237888753414154,
0.011360141448676586,
-0.009835347533226013,
-0.00027213417342863977,
0.011745791882276535,
0.012767554260790348,
0.02742219716310501,
0.016352860257029533,
-0.03929983451962471,
-0.029161827638745308,
-0.04511413350701332,
0.003103532362729311,
-0.04721946269273758,
-0.006149190943688154,
0.00025351892691105604,
0.030930550768971443,
0.02689487114548683,
-0.014255714602768421,
0.019076943397521973,
-0.0062720756977796555,
-0.06530707329511642,
0.05357654392719269,
-0.017118429765105247,
-0.033612143248319626,
-0.019371282309293747,
0.0037046438083052635,
0.01606174372136593,
0.04553258791565895,
-0.04497643932700157,
-0.03972230479121208,
0.02016616240143776,
0.024031704291701317,
0.003377806395292282,
0.0034051574766635895,
-0.03895648196339607,
0.003780137514695525,
-0.02445998042821884,
-0.007285464089363813,
-0.020052799955010414,
-0.004450935870409012,
-0.007073673419654369,
-0.0036519262939691544,
-0.012051929719746113,
0.029569655656814575,
-0.02274923399090767,
0.025493403896689415,
0.040245700627565384,
-0.01933259144425392,
-0.04140869528055191,
0.04051005840301514,
0.016521034762263298,
-0.03937969356775284,
-0.03438257426023483,
-0.03900689259171486,
0.017823757603764534,
-0.04105911776423454,
0.03575257211923599,
-0.027074335142970085,
0.017467014491558075,
-0.021271392703056335,
0.05016307532787323,
-0.043951366096735,
-0.000010224787729384843,
-0.08877701312303543,
-0.02139897830784321,
0.014980677515268326,
0.00592272263020277,
-0.00805923156440258,
0.026694227010011673,
-0.030346205458045006,
-0.017703508958220482,
-0.005247675348073244,
0.026800746098160744,
-0.01834707520902157,
-0.006182019133120775,
0.01755833439528942,
-0.019394416362047195,
0.031969331204891205,
-0.02629098854959011,
-0.015132500790059566,
0.038927603513002396,
-0.03637769818305969,
-0.06840310990810394,
-0.014396058395504951,
-0.04072544351220131,
-0.008746434934437275,
0.01957833394408226,
-0.031600140035152435,
-0.030155761167407036,
0.05692737177014351,
-0.07113893330097198,
0.0027354841586202383,
-0.016905277967453003,
-0.04326149448752403,
-0.01765141636133194,
-0.01945224218070507,
0.01856318674981594,
-0.0008650979725643992,
0.01202868390828371,
0.048125043511390686,
0.01670416072010994,
-0.01623806729912758,
0.014959275722503662,
0.009415238164365292,
-0.032323334366083145,
-0.02578231319785118,
0.012644129805266857,
0.004554427228868008,
0.02973458357155323,
0.07736678421497345,
-0.042709603905677795,
0.0072684274055063725,
0.03249732404947281,
-0.0013668588362634182,
-0.09456727653741837,
0.006051345728337765,
-0.03134201467037201,
-0.015154019929468632,
0.030397603288292885,
-0.0490429550409317,
0.03005727380514145,
0.02489776350557804,
-0.09502474218606949,
0.0009682110976427794,
-0.044258370995521545,
0.009437168948352337,
-0.010166329331696033,
0.002979907440021634,
-0.00573029275983572,
0.016725771129131317,
0.03276889771223068,
0.014180206693708897,
-0.011918425559997559,
0.020292911678552628,
0.016577575355768204,
0.0009333149646408856,
-0.0018090406665578485,
0.05167725309729576,
-0.06526844948530197,
0.04566420614719391,
0.06532717496156693,
0.002357131103053689,
-0.003886780235916376,
0.04039015993475914,
-0.012381957843899727,
-0.0029403436928987503,
-0.026887444779276848,
-0.0046652136370539665,
-0.0010519960196688771,
0.02584509551525116,
0.034873317927122116,
0.016115454956889153,
0.04364510253071785,
0.03786309435963631,
0.038146961480379105,
-0.022537238895893097,
0.001521214609965682,
-0.028884708881378174,
0.048858240246772766,
-0.02960069105029106,
0.005700233392417431,
-0.011751104146242142,
0.015069947578012943,
0.014951569028198719,
0.00046074195415712893,
0.04023408144712448,
0.03695644810795784,
0.038022201508283615,
-0.022959208115935326,
-0.010891865938901901,
-0.023180482909083366,
0.05002816766500473,
-0.01049705222249031,
-0.023338789120316505,
0.009107189252972603,
-0.011977064423263073,
0.0003176214813720435,
0.009651054628193378,
0.0034877019934356213,
-0.0168408565223217,
-0.01588720828294754,
-0.030102578923106194,
0.00012500936281867325,
0.011959602124989033,
-0.02365194447338581,
-0.03029361180961132,
-0.02434522472321987,
0.00046571018174290657,
0.034562449902296066,
0.03218752518296242,
-0.031171007081866264,
-0.053062040358781815,
-0.021481864154338837,
-0.09120756387710571,
0.037182435393333435,
-0.014108874835073948,
-0.015277723781764507,
-0.06337496638298035,
-0.021755976602435112,
0.05747942253947258,
0.008773693814873695,
0.09107840061187744,
-0.009498563595116138,
-0.008016168139874935,
0.024689611047506332,
-0.02552388608455658,
0.036744505167007446,
-0.04024963080883026,
0.011408197693526745,
-0.019912509247660637,
0.02647905983030796,
0.018845129758119583,
0.009084631688892841,
-0.013016436249017715,
0.025929400697350502,
0.041807979345321655,
-0.03948898985981941,
-0.0034116082824766636,
0.00401275372132659,
-0.013497422449290752,
0.0520751029253006,
0.012816066853702068,
-0.011030231602489948,
0.07582484930753708,
-0.009623950347304344,
0.04978341981768608,
0.015470478683710098,
0.00433418108150363,
-0.02565092407166958,
0.02108772099018097,
-0.038095977157354355,
-0.03480609878897667,
-0.03692607581615448,
-0.009063065983355045,
0.040135253220796585,
-0.01442097220569849,
0.02298891544342041,
0.03646069020032883,
-0.05052106827497482,
-0.013502252288162708,
0.03390338644385338,
0.001969287870451808,
0.04074686020612717,
-0.01757621578872204,
0.004317461512982845,
-0.00458344304934144,
0.037651918828487396,
-0.032980356365442276,
0.07374734431505203,
0.04744059965014458,
0.006610906682908535,
-0.007827190682291985,
0.040691960602998734,
-0.031803835183382034,
0.02262277901172638,
0.02014501951634884,
0.03227182477712631,
0.003127864096313715,
-0.049964647740125656,
-0.005112230312079191,
0.0017955972580239177,
-0.014920931309461594,
0.010938744992017746,
0.011775646358728409,
0.060207489877939224,
0.018684500828385353,
0.009104029275476933,
-0.017868157476186752,
-0.013818325474858284,
0.017371956259012222,
0.012901962734758854,
0.02952844277024269,
0.018567737191915512,
0.01160400453954935,
-0.020610477775335312,
-0.04631980136036873,
0.02020404487848282,
0.00948654767125845,
-0.009626238606870174,
0.0005540749989449978,
0.026396041736006737,
0.005590906832367182,
-0.02960703894495964,
0.009875963442027569,
0.002826291834935546,
-0.011195346713066101,
0.024885941296815872,
0.03968137502670288,
0.023782450705766678,
0.003230341011658311,
0.022121520712971687,
-0.04311639815568924,
0.07096874713897705,
-0.05247305706143379,
-0.0033980142325162888,
0.004800511058419943,
0.05124621093273163,
-0.0037569876294583082,
0.0364995151758194
] |
<p>I've been told to revise the derivation that proves $\frac{\mathrm{d}P}{\mathrm{d}r} =\frac{GM(r)p(r)}{r^2}$ where brackets indicate a function of, P is pressure and p is density. Rather helpfully he hasn't given us it to revise, so if anyone knows it I'd be really grateful. Thanks. </p> | 1,551 | [
-0.004027663264423609,
0.014597500674426556,
0.009812566451728344,
0.000684151949826628,
0.04394877701997757,
0.009756547398865223,
-0.019126294180750847,
0.012885740958154202,
0.02450570836663246,
-0.031283654272556305,
0.005618060473352671,
0.050073232501745224,
0.08595773577690125,
0.017454562708735466,
0.025049906224012375,
-0.002355667296797037,
-0.016787810251116753,
0.025499217212200165,
0.03528105095028877,
-0.07054292410612106,
0.01026593241840601,
0.019327500835061073,
0.015880562365055084,
-0.01108250580728054,
-0.012769474647939205,
0.05767638236284256,
0.015574165619909763,
0.008156313560903072,
0.006873635109513998,
0.04849394038319588,
-0.04484075307846069,
-0.001965705305337906,
0.01291488204151392,
0.04380641132593155,
0.019879626110196114,
0.02231159433722496,
-0.03587372973561287,
-0.029378294944763184,
-0.03902502730488777,
0.03527742251753807,
-0.046524129807949066,
-0.01856400817632675,
0.04890579730272293,
0.01769702136516571,
-0.018441911786794662,
0.020860200747847557,
0.040628161281347275,
-0.03224163502454758,
0.06522557884454727,
-0.07233815640211105,
0.07536987215280533,
0.0086830984801054,
0.048547692596912384,
0.06158822774887085,
-0.02442220412194729,
0.01541534997522831,
0.07015120983123779,
0.09913671016693115,
-0.015319358557462692,
-0.05431158095598221,
0.004012107849121094,
-0.03282446786761284,
-0.013108129613101482,
-0.03325048089027405,
-0.007092509884387255,
-0.004154537338763475,
0.0006135352305136621,
-0.02869759500026703,
0.009665856137871742,
-0.00380321335978806,
0.015680067241191864,
0.015670595690608025,
0.01826418749988079,
0.003980875480920076,
0.02052563801407814,
-0.006441395729780197,
0.022168541327118874,
0.006059046369045973,
0.01880689337849617,
0.012184078805148602,
-0.0024218198377639055,
0.02010716311633587,
0.04735013470053673,
0.06528918445110321,
-0.024746667593717575,
-0.004220097325742245,
0.06381092220544815,
0.010188397020101547,
0.009932562708854675,
0.024880148470401764,
0.0101776709780097,
-0.014845827594399452,
0.014530601911246777,
-0.025677593424916267,
-0.012981172651052475,
0.0055609336122870445,
-0.03251420706510544,
0.07206124812364578,
-0.03201381117105484,
-0.015867115929722786,
-0.019897911697626114,
-0.04266976937651634,
0.011899910867214203,
0.058767981827259064,
0.018406322225928307,
-0.03367478772997856,
-0.05250635743141174,
0.014485934749245644,
-0.01635824330151081,
-0.014641018584370613,
-0.05145305022597313,
0.030175909399986267,
0.017557315528392792,
-0.03985121101140976,
-0.03880523517727852,
-0.02100842073559761,
0.0006703748367726803,
-0.0002319338673260063,
0.04806796461343765,
0.03436660394072533,
0.04710444062948227,
0.00048527438775636256,
0.013146958313882351,
-0.028601352125406265,
-0.060655124485492706,
0.028690500184893608,
0.02131408266723156,
-0.013460989110171795,
-0.00034375747782178223,
0.01764203980565071,
-0.012546757236123085,
0.0032630269415676594,
-0.021080514416098595,
0.034374039620161057,
0.017918769270181656,
-0.014207908883690834,
-0.09057726711034775,
-0.028418583795428276,
0.03187093883752823,
0.02257494069635868,
0.010770849883556366,
-0.06770417839288712,
0.00965240877121687,
0.028599711135029793,
0.046701718121767044,
-0.01738542504608631,
-0.014738012105226517,
-0.0282280333340168,
0.03430488705635071,
-0.012684938497841358,
-0.04094831272959709,
-0.07192081212997437,
0.006197382230311632,
-0.04587901383638382,
-0.004908136557787657,
-0.10296691954135895,
0.01131297368556261,
0.017214279621839523,
-0.0003551984846126288,
-0.005264220293611288,
0.09126263856887817,
-0.04692356660962105,
-0.02189924195408821,
-0.008983280509710312,
0.0044317059218883514,
-0.02117648348212242,
0.06978380680084229,
0.023375868797302246,
-0.003464257577434182,
0.01372726634144783,
0.04644346237182617,
0.05141730234026909,
0.002739276736974716,
0.024952903389930725,
0.0594111792743206,
-0.04448637366294861,
-0.006451144814491272,
-0.022472232580184937,
0.011608653701841831,
0.014099550433456898,
-0.0020356117747724056,
-0.016500892117619514,
0.008811316452920437,
-0.028286585584282875,
-0.0035499196965247393,
-0.0085286321118474,
0.02272285334765911,
0.002469439059495926,
-0.02004910074174404,
-0.028836021199822426,
-0.013521510176360607,
-0.06319586932659149,
0.023349404335021973,
-0.030899295583367348,
-0.007988577708601952,
0.002687407424673438,
0.017189472913742065,
0.026295172050595284,
-0.01107159536331892,
-0.04132290557026863,
0.03956184908747673,
-0.005049942526966333,
0.01757255755364895,
-0.030345510691404343,
-0.011136824265122414,
0.024599317461252213,
0.037316273897886276,
0.03385460376739502,
0.006939758080989122,
-0.04296397045254707,
-0.018173500895500183,
0.01997070200741291,
0.0008655582787469029,
0.03544607385993004,
-0.050100382417440414,
-0.03304252773523331,
0.026325177401304245,
0.017189567908644676,
0.022291705012321472,
0.031530123203992844,
-0.06332773715257645,
0.038424935191869736,
0.06717328727245331,
0.04298118129372597,
-0.003130744444206357,
0.02982148714363575,
0.00859784334897995,
-0.002012491226196289,
-0.02032216265797615,
-0.04013518989086151,
-0.04922015592455864,
0.006558732595294714,
0.0505220852792263,
0.008092079311609268,
-0.023645488545298576,
0.021570967510342598,
0.04126063361763954,
0.018922731280326843,
0.03914158046245575,
0.03195677325129509,
-0.022014569491147995,
-0.03682897239923477,
0.016681086272001266,
0.0276739951223135,
0.009976565837860107,
-0.0005454166093841195,
0.01461919117718935,
0.010501854121685028,
0.042153675109148026,
-0.031994786113500595,
-0.048628248274326324,
0.02351227030158043,
-0.02838708646595478,
0.024088291451334953,
0.019349878653883934,
-0.00809104461222887,
0.041749730706214905,
-0.035783302038908005,
0.008829890750348568,
0.05283963680267334,
0.001759610720910132,
0.00424567935988307,
-0.062450360506772995,
-0.005933620501309633,
0.013950343243777752,
0.013902254402637482,
-0.04344237968325615,
-0.010052823461592197,
0.028660666197538376,
-0.04637428745627403,
0.008349490351974964,
-0.025608165189623833,
-0.008088032715022564,
-0.010788620449602604,
-0.01583736389875412,
-0.009211807511746883,
0.01776222325861454,
0.008439137600362301,
0.00006840812420705333,
-0.026530005037784576,
-0.0033900898415595293,
-0.013908810913562775,
-0.011540654115378857,
0.0027646622620522976,
-0.04080047085881233,
0.008028698153793812,
-0.006224653217941523,
-0.017606036737561226,
0.02805010974407196,
0.0018386627780273557,
-0.01910007745027542,
-0.013439272530376911,
-0.018992122262716293,
-0.04161379486322403,
-0.014352455735206604,
-0.010500817559659481,
0.019789058715105057,
-0.05539693310856819,
-0.0006049626390449703,
0.029599176719784737,
-0.0012485285988077521,
-0.013007299974560738,
0.015109444037079811,
-0.03500248119235039,
-0.019271893426775932,
-0.03526410087943077,
-0.012181595899164677,
0.020916571840643883,
-0.007597149349749088,
0.0470685176551342,
0.03311512619256973,
-0.02304777316749096,
-0.028499877080321312,
-0.04056287184357643,
-0.05185170844197273,
0.041003767400979996,
0.005790822673588991,
0.04501622915267944,
-0.012052556499838829,
-0.06246780976653099,
0.03923847898840904,
0.021530145779252052,
-0.010704084299504757,
0.010067736729979515,
0.027598951011896133,
0.0010690090712159872,
-0.041363101452589035,
0.002715268637984991,
0.01341962069272995,
-0.01989203877747059,
0.01893918588757515,
0.011774348095059395,
0.028377261012792587,
0.05266030877828598,
-0.017806321382522583,
-0.021701110526919365,
0.037496499717235565,
-0.00761076994240284,
0.028448184952139854,
0.062064845114946365,
0.015567084774374962,
-0.010014825500547886,
0.005429166369140148,
-0.011237935163080692,
0.04861491546034813,
0.014605093747377396,
-0.07067620009183884,
0.039070937782526016,
0.017107704654335976,
-0.006640131119638681,
-0.029297083616256714,
0.013451910577714443,
-0.0043252864852547646,
-0.037787482142448425,
0.028787679970264435,
0.009285416454076767,
0.03486132621765137,
-0.04585300385951996,
-0.00804749596863985,
0.035730376839637756,
0.03019452467560768,
-0.014591663144528866,
-0.05878492444753647,
0.003653988242149353,
-0.029416590929031372,
0.038691215217113495,
0.021732822060585022,
-0.014743420295417309,
0.04705251753330231,
-0.012808053754270077,
0.00667849974706769,
-0.014080114662647247,
-0.0365569107234478,
0.020034167915582657,
-0.07962293177843094,
0.022963492199778557,
0.0037542395293712616,
0.037580784410238266,
-0.006608008407056332,
0.08394742757081985,
-0.00452095502987504,
0.004959564656019211,
0.04700139909982681,
0.02342924475669861,
-0.0796617940068245,
0.008950567804276943,
-0.020869333297014236,
-0.02438310533761978,
0.0002731547865550965,
-0.029065590351819992,
0.0017834778409451246,
-0.052754875272512436,
-0.03450390696525574,
-0.02163853496313095,
-0.03570472076535225,
-0.09321951121091843,
-0.001272672670893371,
-0.036816488951444626,
-0.07466979324817657,
-0.030338507145643234,
0.006974076386541128,
0.0310477614402771,
0.014795418828725815,
0.030437851324677467,
0.06589585542678833,
-0.016702905297279358,
-0.0034125039819628,
-0.03560697287321091,
0.012307900935411453,
0.04134455695748329,
0.0103196632117033,
0.01426662690937519,
-0.0027795482892543077,
0.01717284880578518,
0.02168004959821701,
0.010698460042476654,
0.046742718666791916,
0.010646713897585869,
-0.033683065325021744,
-0.027056055143475533,
-0.05263557285070419,
-0.006317827384918928,
0.00101090082898736,
0.0022261617705225945,
-0.00942338164895773,
0.010787411592900753,
0.01729712076485157,
0.005170902702957392,
0.005863011348992586,
0.040365949273109436,
0.05616018548607826,
0.0019482950447127223,
-0.027420394122600555,
-0.06090262532234192,
0.0035073398612439632,
-0.02392871305346489,
0.005523358006030321,
0.005535645876079798,
0.01973184011876583,
-0.024844730272889137,
-0.008849645033478737,
-0.00008490809705108404,
0.019569095224142075,
0.010753714479506016,
-0.0322771780192852,
0.012972152791917324,
0.02448493055999279,
-0.019252264872193336,
-0.0018060726579278708,
0.031511832028627396,
0.042641475796699524,
0.01928880624473095,
0.010276674292981625,
-0.0067292810417711735,
-0.0636884868144989,
-0.006313734222203493,
0.009545132517814636,
0.0281137116253376,
0.00739588076248765,
0.016912341117858887,
-0.04725927859544754,
-0.01341983675956726,
0.04201820492744446,
-0.0017605548491701484,
0.014413164928555489,
0.018899038434028625,
0.002141617937013507,
0.0370483435690403,
-0.04118305817246437,
-0.0425100140273571,
0.014278417453169823,
-0.024617880582809448,
0.014779111370444298,
-0.010371497832238674,
-0.011769191361963749,
-0.05115784704685211,
0.0029396775644272566,
0.03388458117842674,
0.08347725123167038,
0.009351964108645916,
-0.025229651480913162,
-0.02227284573018551,
0.005106156226247549,
-0.034144263714551926,
-0.06527971476316452,
-0.018482252955436707,
-0.03513571247458458,
-0.0012512427056208253,
0.03313283622264862,
-0.024541422724723816,
-0.05534391105175018,
0.04104374349117279,
-0.000024648059479659423,
-0.029571207240223885,
0.03660642355680466,
-0.010063773952424526,
0.04523240774869919,
0.02727787010371685,
-0.021540462970733643,
0.05385209992527962,
0.013056671246886253,
-0.010113751515746117,
-0.00711830984801054,
-0.053097791969776154,
0.03505909815430641,
-0.01229760143905878,
-0.029760010540485382,
-0.021254509687423706,
0.00245398236438632,
-0.04633773863315582,
-0.012132042087614536,
-0.003133900696411729,
0.029575182124972343,
-0.02539536915719509,
-0.05326953902840614,
0.04293309152126312,
0.010709655471146107,
-0.004043507855385542,
0.03979438170790672,
-0.002859266474843025,
0.007724616210907698,
0.07068194448947906,
-0.006300888489931822,
0.01163993589580059,
0.025898974388837814,
-0.0035365079529583454,
0.015442724339663982,
-0.02869064174592495,
0.030467936769127846,
-0.01787491701543331,
-0.03138679638504982,
0.03532061353325844,
-0.00893746130168438,
0.07636787742376328,
-0.0006956201395951211,
-0.010483277030289173,
0.02302606590092182,
-0.018104389309883118,
-0.03687174990773201,
0.005038629285991192,
-0.009054180234670639,
0.00417003408074379,
-0.07668963074684143,
0.015598220750689507,
-0.027212224900722504,
0.0030148110818117857,
-0.10129832476377487,
-0.026911815628409386,
0.05249210074543953,
0.00256501417607069,
-0.04955105483531952,
-0.02404708042740822,
0.0009808186441659927,
-0.017647679895162582,
-0.0444154366850853,
0.01378579344600439,
0.049235448241233826,
-0.005324972793459892,
-0.012040073052048683,
-0.007990214042365551,
0.01134931854903698,
0.04829857125878334,
-0.036246851086616516,
-0.017405064776539803,
-0.007030395325273275,
-0.0024547583889216185,
0.00866802129894495,
-0.004486708901822567,
0.06539248675107956,
-0.02715936489403248,
-0.0035836435854434967,
-0.028765618801116943,
-0.032705534249544144,
0.0185855720192194,
-0.04662767052650452,
0.014534594491124153,
0.007333104033023119,
0.007816561497747898,
0.009296177886426449,
-0.00785804819315672,
-0.006165288854390383,
-0.027767391875386238,
-0.0013022928033024073,
-0.009301169775426388,
0.01339675672352314,
0.014371790923178196,
-0.016501203179359436,
0.010935267433524132,
-0.00934470072388649,
0.03508444130420685,
-0.018226874992251396,
0.10420241206884384,
-0.0037537417374551296,
-0.0007337529677897692,
0.02003755047917366,
-0.037100449204444885,
0.0026217796839773655,
0.03334157541394234,
-0.010889183729887009,
0.04234819486737251,
-0.02722446620464325,
-0.03013819456100464,
-0.030830034986138344,
-0.0518549382686615,
0.0334308035671711,
0.09853453189134598,
-0.015723612159490585,
0.033208250999450684,
-0.013823877088725567,
0.02112395688891411,
0.015128131955862045,
0.005456944927573204,
-0.04530799016356468,
0.012418678030371666,
-0.020344536751508713,
0.04796157777309418,
-0.015222286805510521,
0.014015134423971176,
0.035483621060848236,
0.032810844480991364,
-0.02986455149948597,
0.0058990041725337505,
0.002786186058074236,
0.02917099930346012,
0.0054496778175234795,
-0.006326434668153524,
-0.026829928159713745,
0.05872875079512596,
-0.017719518393278122,
0.04236125946044922,
-0.015736259520053864,
0.012211172841489315,
0.044896721839904785,
-0.0025896599981933832,
-0.005051257088780403,
-0.019717320799827576,
-0.018363939598202705,
-0.013907590880990028,
-0.006827462464570999,
0.049903616309165955,
-0.007475983817130327,
0.02844841778278351,
0.02192791737616062,
0.030147209763526917,
0.0189039409160614,
0.013379685580730438,
0.00466841459274292,
-0.0018428791081532836,
0.011878990568220615,
-0.011205684393644333,
-0.05093538388609886,
0.005569336470216513,
-0.008862560614943504,
-0.03226622939109802,
-0.007493429351598024,
0.020379967987537384,
-0.01381475105881691,
0.06036226078867912,
0.0012486904161050916,
0.02838204614818096,
0.09906172007322311,
-0.001006501610390842,
0.030241817235946655,
-0.000952771573793143,
-0.016059301793575287,
0.0819280743598938,
0.054157763719558716,
0.042102690786123276,
-0.028147229924798012,
0.027460217475891113,
-0.030937960371375084,
0.004802261013537645,
-0.030437985435128212,
0.0508786141872406,
-0.008324439637362957,
-0.0010441566118970513,
0.03488801047205925,
0.060822296887636185,
-0.030450301244854927,
-0.0005212455871514976,
0.042328473180532455,
-0.005720196757465601,
-0.021995659917593002,
-0.0024537828285247087,
0.025252552703022957,
-0.034922897815704346,
0.015824317932128906,
-0.030071480199694633,
0.019263507798314095,
-0.05268076807260513,
0.004693233873695135,
-0.06244653835892677,
-0.04380396008491516,
0.0077665154822170734,
0.0024162940680980682,
-0.03209158033132553,
0.01923810876905918,
-0.02013232558965683,
-0.0038070385344326496,
-0.014013090170919895,
0.007633883971720934,
0.025780698284506798,
-0.006505419034510851,
0.0020205224864184856,
0.04181955009698868,
-0.009779882617294788,
0.02983706071972847,
-0.009591679088771343,
0.020271627232432365,
-0.02794375643134117,
0.00868342537432909,
-0.014283458702266216,
0.06935148686170578,
-0.050564948469400406,
0.0007042884244583547,
0.02983766421675682,
-0.024179240688681602,
-0.03227445110678673,
-0.07239380478858948,
-0.011626430787146091,
0.006520526949316263,
0.026469964534044266,
-0.018847091123461723,
-0.029646841809153557,
-0.031038321554660797,
0.02696128748357296,
0.0196901373565197,
0.025618361309170723,
-0.028822004795074463,
0.004453510511666536,
-0.005036742892116308,
0.009019026532769203,
0.05942542850971222,
-0.057240694761276245,
-0.009924544021487236,
-0.03612206503748894,
0.030539369210600853,
-0.050898440182209015,
-0.03468707576394081,
-0.0004169416497461498,
-0.0012870894279330969,
0.028054483234882355,
-0.005031203851103783,
0.017641643062233925,
0.01662159524857998,
-0.06725463271141052,
0.04603082314133644,
-0.030149491503834724,
-0.009865117259323597,
-0.02482309751212597,
-0.0061998264864087105,
-0.009966428391635418,
0.04657353088259697,
-0.03305382654070854,
0.014092263765633106,
-0.021360250189900398,
0.02450399659574032,
0.02639934979379177,
-0.04935301095247269,
-0.022730480879545212,
0.014951812103390694,
-0.03291790187358856,
-0.0016829483211040497,
0.004968036897480488,
0.026983041316270828,
0.04188942536711693,
0.022757593542337418,
-0.018831145018339157,
0.011440514586865902,
-0.02021365612745285,
0.034535251557826996,
-0.035602714866399765,
-0.03586825728416443,
0.006959295831620693,
-0.010436533950269222,
-0.0061919474974274635,
-0.015362863428890705,
0.0006543092313222587,
-0.009091106243431568,
-0.015663539990782738,
-0.01405118778347969,
-0.03786727786064148,
-0.013957735151052475,
-0.008420148864388466,
-0.02185361087322235,
0.0038058930076658726,
-0.030441008508205414,
0.01083009596914053,
-0.03202110528945923,
0.011654178611934185,
0.015790019184350967,
0.03220343962311745,
-0.03267828747630119,
0.052964068949222565,
-0.03375408053398132,
-0.005964955780655146,
0.04763289913535118,
0.009745750576257706,
-0.018979260697960854,
-0.020527752116322517,
0.04754302650690079,
0.01656557247042656,
0.0594974160194397,
-0.024177126586437225,
-0.04335986450314522,
0.01968933828175068,
-0.008679752238094807,
-0.053774524480104446,
0.010215585120022297,
0.036241479218006134,
0.034011226147413254,
-0.02030344307422638,
-0.004366445355117321,
-0.01574789360165596,
0.058949366211891174,
-0.000769559177570045,
-0.0032895945478230715,
-0.006279496010392904,
-0.0281418114900589,
0.029876677319407463,
-0.026634065434336662,
0.019927918910980225,
-0.012808997184038162,
0.0249363761395216,
0.014917006716132164,
0.0031335894018411636,
-0.03575234115123749,
0.04655371606349945,
0.018641386181116104,
-0.030043261125683784,
0.011259198188781738,
-0.003349364036694169,
0.010864154435694218,
0.03936557471752167,
0.03692125156521797,
-0.01161918044090271,
0.017227452248334885,
-0.0029947611037641764,
0.0014787003165110946,
-0.06997267156839371,
0.001922363881021738,
-0.009028091095387936,
-0.013693738728761673,
0.06779675930738449,
-0.06602409482002258,
0.017780017107725143,
0.017782481387257576,
-0.05739150196313858,
-0.01378124300390482,
-0.021796977147459984,
-0.021893780678510666,
-0.006906846072524786,
-0.029920613393187523,
0.01656532660126686,
0.07024279981851578,
0.019231054931879044,
0.03951968252658844,
0.004461074713617563,
0.011653733439743519,
-0.009500512853264809,
0.005725306924432516,
-0.0192732997238636,
0.0315302275121212,
0.009601456113159657,
-0.014770181849598885,
0.0640227422118187,
-0.007283694576472044,
0.015333587303757668,
0.03348740562796593,
-0.015134228393435478,
0.01690765470266342,
-0.028760848566889763,
0.011876864358782768,
0.00038958914228715,
0.019817715510725975,
0.01212481502443552,
0.013468779623508453,
-0.019918715581297874,
-0.008034099824726582,
-0.0045507545582950115,
0.006512236315757036,
-0.03141392394900322,
-0.030452387407422066,
0.003228846937417984,
-0.015447811223566532,
-0.028704117983579636,
0.061615414917469025,
-0.01922372169792652,
0.015232985839247704,
0.028271669521927834,
-0.01464366540312767,
-0.02223513089120388,
-0.0031284757424145937,
0.052016858011484146,
-0.04447466507554054,
-0.017462659627199173,
0.033446405082941055,
-0.013106058351695538,
-0.02942289412021637,
0.044010210782289505,
0.018782561644911766,
-0.04345151409506798,
0.012156697921454906,
-0.022578224539756775,
-0.02931329235434532,
-0.0704551711678505,
0.008913452737033367,
-0.013812534511089325,
-0.025490498170256615,
0.013360685668885708,
-0.04673434793949127,
-0.03068244457244873,
0.018248600885272026,
0.0514041967689991,
0.011087882332503796,
0.0027558994479477406,
-0.044065531343221664,
0.0005367083940654993,
-0.06374252587556839,
0.050623819231987,
-0.0015769896563142538,
-0.03005647286772728,
-0.04642254486680031,
-0.009236017242074013,
-0.019319584593176842,
-0.011301320046186447,
0.05104077234864235,
0.01326708309352398,
-0.023974789306521416,
0.01849198155105114,
0.012291827239096165,
0.01817615143954754,
-0.08263817429542542,
0.017555871978402138,
0.01104668714106083,
-0.0020282049663364887,
-0.00848300103098154,
0.003538089105859399,
0.0027840635739266872,
0.014943978749215603,
-0.021083923056721687,
0.011806362308561802,
0.03305596485733986,
0.029363242909312248,
-0.020465055480599403,
0.04134455695748329,
-0.011612649075686932,
-0.01145173516124487,
0.07119177281856537,
-0.03717537596821785,
0.030356628820300102,
0.02230042964220047,
-0.020853159949183464,
-0.05298770219087601,
0.017417607828974724,
-0.025958489626646042,
-0.03130071237683296,
-0.007570901419967413,
-0.027372343465685844,
-0.0016068039694800973,
-0.03147329390048981,
0.0048545245081186295,
0.00982868205755949,
-0.05517562851309776,
-0.00571507029235363,
0.06163914501667023,
0.01653413474559784,
0.07264648377895355,
-0.03124193660914898,
0.0022294167429208755,
0.02839513309299946,
-0.0006575763109140098,
-0.017207400873303413,
0.026061350479722023,
0.04428861290216446,
0.013622735626995564,
0.0003800738195423037,
0.07252311706542969,
-0.018463853746652603,
0.024319829419255257,
0.030248502269387245,
0.009859018959105015,
-0.03159446269273758,
-0.019702361896634102,
0.010931117460131645,
-0.038490958511829376,
0.011974946595728397,
0.008182498626410961,
-0.01136793103069067,
0.06560544669628143,
-0.0013969105202704668,
0.00507505564019084,
-0.024067247286438942,
-0.008355755358934402,
-0.041146524250507355,
0.010859204456210136,
0.02458522468805313,
0.023590629920363426,
-0.0044134934432804585,
0.008600910194218159,
-0.007605656050145626,
0.0008509324979968369,
0.008858478628098965,
0.007208628114312887,
0.008601258508861065,
0.0331837423145771,
-0.026116758584976196,
-0.037781354039907455,
-0.010311753489077091,
0.012796544469892979,
0.004579700063914061,
0.03974324092268944,
0.02422257699072361,
0.021837325766682625,
0.024783112108707428,
0.010789254680275917,
-0.02826697565615177,
0.08137720823287964,
-0.07588549703359604,
-0.028439629822969437,
-0.025438182055950165,
0.029167335480451584,
0.010124446824193,
-0.057253651320934296
] |
<p>With all the recent discoveries of supermassive black holes being at the center of nearly every galaxy, and the proposed "at least one planet" around (probably) every star.</p>
<p>Does this affect the estimated total mass of our universe?</p>
<p>Is Dark Matter necessary when planets and black holes are included in the calculation?</p> | 1,552 | [
-0.013219122774899006,
-0.026689328253269196,
0.010022797621786594,
-0.05663395673036575,
0.07200063019990921,
0.006425413303077221,
-0.05546595901250839,
-0.06211785599589348,
-0.0324130654335022,
-0.07362224906682968,
0.010218795388936996,
0.059280894696712494,
0.05066164210438728,
0.009754572995007038,
0.0032065031118690968,
0.010049508884549141,
0.00886126235127449,
-0.019495775923132896,
-0.010891699232161045,
-0.03295357525348663,
-0.0023991591297090054,
0.039083246141672134,
0.028671754524111748,
0.006208032835274935,
-0.02685745619237423,
0.06515403836965561,
0.010860173031687737,
-0.0007513151504099369,
0.030575744807720184,
0.046645376831293106,
0.006772531196475029,
-0.026520557701587677,
0.03559572622179985,
0.0625409334897995,
0.021982671692967415,
-0.008422302082180977,
-0.016056323423981667,
-0.01946396753191948,
-0.005029684863984585,
0.03884339705109596,
-0.04371305927634239,
-0.03203526884317398,
-0.017406867817044258,
0.020201565697789192,
-0.04680796340107918,
0.014626276679337025,
0.000047493173042312264,
0.028554566204547882,
0.06482797116041183,
-0.042005278170108795,
0.07104633748531342,
0.026655254885554314,
0.04248090460896492,
0.020561743527650833,
-0.013626954518258572,
0.0035470996517688036,
0.07946712523698807,
0.05738675221800804,
0.008014712482690811,
-0.04288480803370476,
-0.029809895902872086,
0.01570909656584263,
0.018889639526605606,
-0.02642851322889328,
0.0065006110817193985,
0.06436775624752045,
-0.039817821234464645,
0.004017275758087635,
0.011691408231854439,
0.016823014244437218,
0.024926690384745598,
-0.0022744592279195786,
-0.006510126404464245,
0.0007222909480333328,
0.0037754953373223543,
-0.05425163358449936,
0.018909811973571777,
-0.00826346967369318,
0.025317369028925896,
0.03714302182197571,
-0.015211844816803932,
0.0066368491388857365,
0.06020471826195717,
0.01980457827448845,
0.027883337810635567,
0.02875487692654133,
0.06705313920974731,
0.01821926236152649,
-0.008990653790533543,
0.027618005871772766,
-0.009935208596289158,
0.016439002007246017,
0.056139566004276276,
-0.024454962462186813,
-0.013644679449498653,
0.03477040305733681,
-0.016274917870759964,
0.0528155192732811,
0.0022937930189073086,
0.000020664358089561574,
-0.007576263044029474,
0.012317798100411892,
0.02485695295035839,
0.06909476965665817,
0.019752515479922295,
-0.005116448737680912,
-0.09080500900745392,
0.011194036342203617,
-0.030808325856924057,
-0.015898192301392555,
-0.03819837048649788,
0.011147239245474339,
-0.00939442403614521,
-0.033237747848033905,
0.013234254904091358,
-0.0005535795935429633,
0.016238342970609665,
-0.023219581693410873,
0.046140942722558975,
0.04287666082382202,
0.01543478388339281,
-0.0017281861510127783,
-0.0011102791177108884,
-0.04690154269337654,
-0.04311273247003555,
0.010729854926466942,
0.034956321120262146,
-0.019880877807736397,
-0.04391845688223839,
0.03005969151854515,
0.013772840611636639,
0.004608362913131714,
-0.008923298679292202,
-0.004530663136392832,
0.04042753949761391,
-0.0263412743806839,
-0.07945812493562698,
-0.07492818683385849,
0.03009432554244995,
-0.0251588374376297,
0.006329623516649008,
0.01925635151565075,
0.002323732478544116,
0.017410479485988617,
0.08904958516359329,
-0.008778275921940804,
-0.004212924279272556,
0.016252633184194565,
0.0554848238825798,
-0.013832425698637962,
-0.016190174967050552,
-0.0206136591732502,
-0.011195032857358456,
-0.03780175745487213,
-0.017771320417523384,
-0.11450710892677307,
0.023643992841243744,
0.04882984980940819,
0.025310777127742767,
-0.014394250698387623,
0.030885644257068634,
-0.025223303586244583,
0.014227223582565784,
-0.006430971436202526,
0.008152940310537815,
-0.033683884888887405,
0.026656286790966988,
0.01383154932409525,
0.022054020315408707,
0.05080484226346016,
0.008447496220469475,
0.029869671911001205,
0.0290143471211195,
0.029584385454654694,
0.05722474679350853,
-0.032356083393096924,
-0.010172088630497456,
-0.04608047381043434,
0.025083616375923157,
0.007564362604171038,
-0.019860895350575447,
-0.0161980502307415,
-0.002019127830862999,
-0.010696075856685638,
0.03625515103340149,
0.04392235726118088,
-0.004611663054674864,
0.0015982968034222722,
0.026763426139950752,
-0.018313076347112656,
-0.020381566137075424,
-0.06957891583442688,
-0.006740632001310587,
-0.004442994017153978,
-0.0022529102861881256,
-0.008906863629817963,
0.06670906394720078,
0.031386468559503555,
-0.013876279816031456,
-0.01685035414993763,
0.007743505761027336,
0.054603297263383865,
0.0004783625772688538,
0.011890553869307041,
0.02218475192785263,
0.04520488902926445,
0.058931756764650345,
-0.024853097274899483,
-0.017500076442956924,
-0.01263655535876751,
-0.07278868556022644,
-0.0005007924628444016,
-0.005685084033757448,
0.014627914875745773,
-0.009476706385612488,
-0.008862690068781376,
0.03446819633245468,
0.038690391927957535,
0.014740195125341415,
0.02775932289659977,
-0.04439905285835266,
0.09018191695213318,
0.0030186695512384176,
-0.002587468596175313,
0.02392217144370079,
0.0382794514298439,
0.025165734812617302,
-0.0025177868083119392,
0.003756776452064514,
-0.00442615756765008,
-0.08270886540412903,
-0.012081876397132874,
0.03318103775382042,
0.018526941537857056,
-0.015039882622659206,
0.014179512858390808,
0.04184766858816147,
0.021158931776881218,
-0.005749990697950125,
-0.024036254733800888,
-0.01986563391983509,
-0.05781669169664383,
-0.004060405772179365,
0.012150252237915993,
0.021781565621495247,
0.02276192419230938,
0.05192618817090988,
0.025977708399295807,
-0.0020669084042310715,
0.009723144583404064,
-0.009237278252840042,
0.03870106115937233,
0.02421293407678604,
0.002221545437350869,
0.005061390809714794,
-0.04875435307621956,
0.030869845300912857,
-0.03377144783735275,
0.023178787901997566,
0.020161468535661697,
-0.010035320185124874,
-0.022403860464692116,
-0.03722715005278587,
-0.013573787175118923,
-0.022873234003782272,
0.026935504749417305,
-0.03960977494716644,
-0.005595396272838116,
0.037387244403362274,
-0.07584891468286514,
0.02356899343430996,
-0.035485126078128815,
-0.020169977098703384,
-0.043256524950265884,
0.014771363697946072,
0.015974462032318115,
-0.013089112006127834,
0.0445864163339138,
-0.03111066296696663,
-0.00927608460187912,
-0.0007206731825135648,
-0.0007430443074554205,
-0.05274886637926102,
0.03784472495317459,
-0.07638177275657654,
0.020439589396119118,
-0.031834911555051804,
-0.05873109772801399,
0.03605308756232262,
-0.00176177266985178,
0.021382203325629234,
0.027473129332065582,
0.006836027838289738,
-0.03637085109949112,
-0.004225760232657194,
-0.002540233777835965,
-0.011584647931158543,
-0.06764476746320724,
0.023509472608566284,
0.011396887712180614,
0.013963931240141392,
-0.03652450814843178,
-0.00968529935926199,
-0.023647261783480644,
-0.03412223234772682,
-0.03341236338019371,
-0.019932152703404427,
0.02104070782661438,
-0.03897635266184807,
-0.006350693758577108,
0.021815134212374687,
-0.044416189193725586,
0.015603219158947468,
-0.04866410791873932,
-0.05638156086206436,
0.05571210756897926,
-0.04146288335323334,
0.0373711958527565,
-0.011811405420303345,
-0.02119912952184677,
0.08853238075971603,
0.04909646138548851,
0.0007333128014579415,
-0.028786160051822662,
-0.008315294049680233,
0.01049640029668808,
0.014965062960982323,
0.010216069407761097,
0.024364272132515907,
0.009457907639443874,
0.003563094651326537,
0.04008765146136284,
0.003483252599835396,
0.005193526856601238,
0.015278981998562813,
-0.013021253049373627,
0.006141259800642729,
-0.025887975469231606,
-0.019497167319059372,
0.05591246113181114,
-0.012905038893222809,
-0.0009770008036866784,
0.003778223879635334,
-0.020101722329854965,
0.05776112899184227,
0.0028960593044757843,
-0.023487908765673637,
0.04214974492788315,
-0.013497618027031422,
0.014828861691057682,
-0.01002153567969799,
0.02049030177295208,
0.03691748529672623,
-0.01020090002566576,
0.017516572028398514,
-0.014136379584670067,
0.06262779235839844,
0.02473878487944603,
-0.02409619837999344,
0.02672918140888214,
0.043351076543331146,
-0.02785463258624077,
-0.03563341870903969,
0.009575098752975464,
0.002624527318403125,
0.0008331275312229991,
-0.03822474554181099,
-0.02568872831761837,
0.018259702250361443,
0.04492570832371712,
-0.002285266062244773,
-0.007738982792943716,
-0.02295396476984024,
-0.010532191023230553,
-0.08694103360176086,
-0.0066739642061293125,
-0.00815278198570013,
0.04130873829126358,
0.007823069579899311,
0.03538990020751953,
0.011379489675164223,
-0.007946284487843513,
-0.007671542465686798,
-0.010663098655641079,
-0.06622642278671265,
0.0033416019286960363,
-0.06545312702655792,
-0.010877232998609543,
0.0023014498874545097,
-0.015535162761807442,
-0.018388355150818825,
-0.006552132777869701,
0.008554338477551937,
-0.07944177091121674,
-0.01915309950709343,
-0.056176476180553436,
0.0009490944794379175,
-0.02366413176059723,
-0.043967537581920624,
0.032854992896318436,
0.027441587299108505,
0.03467681631445885,
-0.012839346192777157,
0.00576308649033308,
0.01801762916147709,
-0.012067483738064766,
-0.044519636780023575,
-0.01233732420951128,
0.023913083598017693,
-0.017958085983991623,
0.06736171245574951,
0.03656047210097313,
0.022932836785912514,
-0.05550818145275116,
-0.002048204420134425,
0.05090823769569397,
0.03217994049191475,
-0.028652416542172432,
-0.04081706702709198,
-0.019789354875683784,
-0.038600675761699677,
-0.04117719456553459,
0.004332114011049271,
0.03451467677950859,
-0.029868977144360542,
0.0356278121471405,
0.05280671268701553,
0.0009198313928209245,
-0.01573546975851059,
0.01716817170381546,
0.04431822896003723,
-0.008035235106945038,
-0.011047478765249252,
-0.052540507167577744,
-0.009424361400306225,
-0.02932223305106163,
0.005268217530101538,
0.028541967272758484,
0.026017844676971436,
-0.024158848449587822,
0.009123642928898335,
-0.014106796123087406,
-0.021720504388213158,
-0.030356749892234802,
-0.02123640850186348,
0.003060215851292014,
0.02960067242383957,
-0.03873632475733757,
0.02694712206721306,
0.038934916257858276,
0.04729997739195824,
0.0425405278801918,
-0.006360966246575117,
-0.01926521584391594,
-0.0683579221367836,
0.0058875433169305325,
0.05907822027802467,
0.05813760682940483,
-0.014166494831442833,
-0.016309704631567,
-0.055829547345638275,
0.008673582226037979,
0.043647121638059616,
-0.01319266390055418,
0.02418375574052334,
-0.01984783262014389,
0.010281589813530445,
0.007137875072658062,
-0.02991521544754505,
0.007045249920338392,
0.04342932254076004,
-0.02799134887754917,
0.01877683959901333,
-0.0076026152819395065,
0.023399673402309418,
-0.028114916756749153,
0.02679263986647129,
0.043264929205179214,
0.07069205492734909,
0.0373523086309433,
-0.016610966995358467,
0.01398777961730957,
-0.008670139126479626,
-0.023973999544978142,
-0.07639247924089432,
-0.009962952695786953,
-0.030132966116070747,
-0.06011034548282623,
0.02668038010597229,
-0.024979684501886368,
-0.04879644885659218,
0.029047243297100067,
-0.003443770343437791,
-0.02861892618238926,
-0.011610756628215313,
-0.03685074299573898,
0.018295349553227425,
0.05517441779375076,
-0.015928322449326515,
0.040148597210645676,
0.016171937808394432,
-0.04103192314505577,
0.03060159832239151,
-0.04883596673607826,
0.0262545645236969,
-0.03064245916903019,
-0.0001345674245385453,
0.000880642794072628,
-0.04798403009772301,
-0.048362553119659424,
0.006593111902475357,
-0.004583105444908142,
0.007223471533507109,
0.012502223253250122,
-0.013084500096738338,
-0.00008930311014410108,
0.013546645641326904,
0.02793150395154953,
0.03395235911011696,
-0.008452752605080605,
0.031548645347356796,
0.005533655174076557,
-0.032910313457250595,
0.056776221841573715,
0.03798651322722435,
0.0032917025964707136,
-0.002673826878890395,
-0.006376693956553936,
0.026153186336159706,
-0.0059855165891349316,
-0.027162672951817513,
0.028214190155267715,
-0.045171089470386505,
0.034959010779857635,
-0.006190554704517126,
0.013711386360228062,
0.007182908710092306,
-0.07483863085508347,
-0.04922184720635414,
-0.009676151908934116,
-0.0462292917072773,
-0.0016995674232020974,
-0.0349767729640007,
0.033872611820697784,
-0.0056540872901678085,
0.03305932134389877,
-0.05194675177335739,
-0.015214531682431698,
-0.0004524340038187802,
0.010589485056698322,
0.026154998689889908,
-0.011717796325683594,
0.04284077137708664,
-0.07297924906015396,
-0.001299893599934876,
-0.02718505822122097,
0.040019843727350235,
-0.012666541151702404,
-0.037183135747909546,
0.0024468691553920507,
-0.017203383147716522,
0.04782886803150177,
-0.013516056351363659,
-0.022324420511722565,
0.019792474806308746,
0.010763728059828281,
0.01899457909166813,
-0.00888894870877266,
0.02739815041422844,
-0.035130977630615234,
-0.04574492201209068,
-0.025644101202487946,
-0.015376465395092964,
0.014280115254223347,
-0.03847045823931694,
0.011865689419209957,
0.05688128620386124,
0.015191726386547089,
-0.014407035894691944,
0.0018294698093086481,
0.04389374703168869,
-0.045457735657691956,
0.0270445067435503,
0.006850020028650761,
0.024310072883963585,
0.002743212739005685,
-0.03535506874322891,
0.04704003408551216,
-0.004662307910621166,
-0.012381591834127903,
0.004822957329452038,
0.04596202075481415,
0.04831366613507271,
-0.01718083955347538,
-0.018160399049520493,
-0.03879111260175705,
0.025191040709614754,
0.011746758595108986,
0.03407036140561104,
0.011160009540617466,
0.002327421447262168,
-0.012847639620304108,
-0.004962349776178598,
-0.01936711184680462,
-0.006571075413376093,
0.03728203475475311,
0.00810601469129324,
0.025128213688731194,
-0.01739741489291191,
0.003137851133942604,
0.013675319962203503,
-0.05749686062335968,
0.0009823652217164636,
0.02324748784303665,
0.005811519455164671,
0.016420701518654823,
-0.0263014305382967,
-0.008661461062729359,
0.03782348707318306,
0.013116253539919853,
-0.006162469740957022,
0.02145160734653473,
0.029154960066080093,
-0.013866840861737728,
0.019437560811638832,
-0.005470021162182093,
-0.027585631236433983,
0.00949026271700859,
-0.03516948223114014,
0.018927274271845818,
-0.010415085591375828,
-0.017838409170508385,
0.036336567252874374,
0.0016152539756149054,
0.02338634617626667,
-0.012626899406313896,
-0.03193093463778496,
-0.005117038730531931,
0.00919062364846468,
-0.004091102629899979,
0.025114407762885094,
-0.0013340495061129332,
0.003198455786332488,
0.008452371694147587,
0.014315459877252579,
0.002330123446881771,
-0.0006104980129748583,
-0.0867399200797081,
-0.05715247988700867,
-0.025895897299051285,
-0.06817305833101273,
0.02059386484324932,
0.009250420145690441,
-0.026787301525473595,
0.014669795520603657,
0.014911702834069729,
0.02165314555168152,
0.008719133213162422,
0.017764082178473473,
-0.02020593360066414,
0.05759887397289276,
0.0014278641901910305,
0.012520852498710155,
-0.045089542865753174,
0.024366674944758415,
0.09590640664100647,
0.0367404967546463,
0.024543913081288338,
-0.061460744589567184,
0.018726162612438202,
-0.005938992369920015,
0.014243897050619125,
-0.003077564062550664,
0.019452080130577087,
-0.033421434462070465,
0.010137275792658329,
0.01394813321530819,
0.002358817495405674,
-0.0007917143520899117,
-0.05401858687400818,
0.023061899468302727,
-0.04782847315073013,
-0.012234112247824669,
0.0038617390673607588,
0.028260359540581703,
0.011798505671322346,
0.005460329353809357,
-0.04366733133792877,
0.024136444553732872,
-0.02803095616400242,
0.0005515743978321552,
-0.0053344895131886005,
-0.0074583194218575954,
-0.023866824805736542,
-0.006736561190336943,
-0.05966216325759888,
-0.0067976308055222034,
0.013203263282775879,
-0.04820529371500015,
-0.0402112752199173,
0.009338145144283772,
0.030500296503305435,
-0.02845025435090065,
-0.00223285099491477,
0.03182242065668106,
-0.017875302582979202,
0.022744087502360344,
-0.020823251456022263,
-0.008846389129757881,
-0.05999021232128143,
0.001014486188068986,
-0.006333466153591871,
0.04941926151514053,
-0.010341895744204521,
0.006232535466551781,
0.008816855028271675,
0.013518642634153366,
0.007231468800455332,
-0.049557432532310486,
0.015182158909738064,
0.012512370944023132,
0.0020073815248906612,
0.013315510004758835,
-0.05792778357863426,
-0.0009611219284124672,
0.025047073140740395,
0.011913941241800785,
0.05430617928504944,
-0.0014705306384712458,
0.029357988387346268,
0.0019865550566464663,
-0.010074065066874027,
0.05102960020303726,
-0.053440432995557785,
0.003937460482120514,
-0.029977090656757355,
0.015939930453896523,
-0.06715823709964752,
0.003558219876140356,
-0.0026389462873339653,
0.028484364971518517,
0.01134815625846386,
-0.005960109643638134,
0.05047059804201126,
-0.03169983997941017,
-0.039268895983695984,
0.005410167388617992,
-0.037143051624298096,
-0.0330108143389225,
-0.024537624791264534,
0.00645978469401598,
0.02794836089015007,
0.028918787837028503,
-0.020469265058636665,
-0.013269491493701935,
-0.0015395149821415544,
0.03949243947863579,
0.007102094125002623,
-0.02248862385749817,
0.004976463038474321,
-0.014830343425273895,
-0.02378217875957489,
0.025199836120009422,
-0.03112446703016758,
-0.004596416838467121,
0.02730662189424038,
-0.010025208815932274,
0.011518899351358414,
0.043159570544958115,
-0.005384248681366444,
0.02744312398135662,
-0.003674232168123126,
-0.025316141545772552,
-0.02469487488269806,
0.016264120116829872,
0.033109452575445175,
-0.042940013110637665,
-0.009156815707683563,
-0.06368445605039597,
-0.02713317610323429,
0.00817545410245657,
0.01331197191029787,
-0.055369339883327484,
0.04456474632024765,
0.0033469742629677057,
0.00780795281752944,
-0.045412708073854446,
0.02114228345453739,
-0.05221974849700928,
-0.008988767862319946,
0.00095254962798208,
-0.03334864601492882,
0.027459178119897842,
0.013583057560026646,
-0.019822822883725166,
-0.001490990398451686,
0.016181766986846924,
-0.01567257195711136,
-0.009804420173168182,
0.008891048841178417,
0.03068237192928791,
-0.034453168511390686,
0.047631047666072845,
0.004152756650000811,
-0.0014491776237264276,
0.024602439254522324,
-0.037730488926172256,
-0.045681845396757126,
0.034805282950401306,
-0.03207909315824509,
0.018438562750816345,
0.020315391942858696,
-0.016680985689163208,
-0.007803268730640411,
0.020900782197713852,
-0.04405362904071808,
-0.02422003075480461,
0.020556310191750526,
0.007489731535315514,
0.0066852569580078125,
0.04146907478570938,
0.011787328869104385,
-0.015333191491663456,
-0.024449890479445457,
0.0322171188890934,
0.03764326125383377,
-0.002894218545407057,
0.003166511422023177,
0.021204737946391106,
-0.05643094331026077,
0.028516119346022606,
0.012673971243202686,
0.016934841871261597,
0.02526877261698246,
0.01943403109908104,
-0.043963901698589325,
0.08684325218200684,
0.05234552174806595,
-0.025761203840374947,
-0.09182379394769669,
-0.01908937841653824,
-0.008215196430683136,
-0.009472844190895557,
0.04155564308166504,
-0.015661533921957016,
0.03728221729397774,
-0.02762550115585327,
-0.06702567636966705,
0.03587387129664421,
-0.024757731705904007,
-0.013653877191245556,
-0.0012081816093996167,
-0.010844429023563862,
-0.002074240241199732,
0.04242604598402977,
0.030449751764535904,
0.014982468448579311,
-0.0063050007447600365,
-0.003960995003581047,
-0.0057495227083563805,
-0.03558243438601494,
0.003118011634796858,
0.009878143668174744,
-0.006560992915183306,
-0.013436554931104183,
0.052528396248817444,
-0.012163188308477402,
-0.026777023449540138,
0.03646136075258255,
0.02866259030997753,
0.028069384396076202,
-0.015491653233766556,
0.001471112365834415,
0.005818352103233337,
0.023520182818174362,
0.032374538481235504,
-0.0028817225247621536,
-0.01718904823064804,
0.015686366707086563,
-0.0018824910512194037,
0.02325679361820221,
-0.005725163035094738,
0.004533533006906509,
-0.004962916485965252,
-0.04799497872591019,
0.02002730593085289,
-0.016424955800175667,
0.016398247331380844,
0.011727972887456417,
-0.03181655332446098,
0.038329001516103745,
-0.03245224058628082,
-0.03927307203412056,
0.024948643520474434,
-0.04278004169464111,
-0.013347354717552662,
0.06219830736517906,
0.021478423848748207,
-0.013352874666452408,
0.01411737035959959,
0.047517720609903336,
-0.017098305746912956,
0.011313291266560555,
0.0008938948158174753,
-0.0227254256606102,
-0.046764690428972244,
0.026840370148420334,
0.01123660709708929,
0.018177270889282227,
0.019789498299360275,
-0.03044017031788826,
-0.042429786175489426,
0.06402688473463058,
-0.013255548663437366,
0.011690677143633366,
-0.011906158179044724,
-0.06212359294295311,
-0.005729429889470339,
-0.05510174110531807,
0.030153555795550346,
0.01552980300039053,
0.035614121705293655,
-0.02486393228173256,
-0.028195053339004517,
0.011651519685983658,
-0.05429903045296669,
0.052064165472984314,
0.009112264961004257,
-0.006159537937492132,
0.005448613781481981,
0.011581753380596638,
0.007711560465395451,
-0.06968861073255539,
-0.0043562473729252815,
0.0074079157784581184,
-0.03650760278105736,
0.0004288484051357955,
-0.03296513855457306,
0.00867769867181778,
0.0005144895985722542,
0.0325438417494297,
-0.017428230494260788,
0.06773193925619125,
0.03149931877851486,
0.012224376201629639,
0.0652870237827301,
0.02467477135360241,
-0.001287816558033228,
0.05212133005261421,
-0.01712629199028015,
0.024713968858122826,
0.049731429666280746,
-0.00008027930743992329,
-0.03736524283885956,
-0.02108319289982319,
-0.03573716804385185,
-0.016941044479608536,
0.0006331996410153806,
0.02273227833211422,
0.019407127052545547,
-0.04385855793952942,
-0.003928213845938444,
0.0518028661608696,
0.014512710273265839,
-0.02816564030945301,
0.03167084977030754,
-0.018594078719615936,
0.059648480266332626,
-0.004525337368249893,
0.015337426215410233,
0.011615829542279243,
-0.017005514353513718,
-0.02792087197303772,
0.04541487991809845,
0.020849622786045074,
0.022385384887456894,
0.015232887119054794,
0.03176981955766678,
0.024086488410830498,
0.016704080626368523,
0.003465555375441909,
0.04142937436699867,
-0.04624204337596893,
-0.027083655819296837,
-0.00708669051527977,
0.010590631514787674,
0.05390097200870514,
-0.0031371633522212505,
0.002322429558262229,
0.08895771205425262,
-0.009600890800356865,
-0.002943862695246935,
-0.019113365560770035,
-0.06410783529281616,
-0.013554885983467102,
0.02312433533370495,
-0.03026054985821247,
0.04829903692007065,
0.017844662070274353,
-0.017777329310774803,
-0.00024217138707172126,
0.022968366742134094,
0.022401047870516777,
-0.059432316571474075,
0.0149235213175416,
-0.011742894537746906,
0.012130480259656906,
-0.013065868988633156,
0.015653833746910095,
-0.005024383310228586,
-0.019231479614973068,
0.06708730012178421,
0.07576025277376175,
0.009514073841273785,
0.0020239842124283314,
0.011220129206776619,
-0.012926984578371048,
0.01292355451732874,
-0.034939512610435486,
-0.029452567920088768,
-0.04263658449053764,
0.0321059376001358,
-0.021916618570685387,
-0.044990308582782745
] |
<p>An object of mass m is slowly lowered into a black hole of mass 1000 m. Is the amount of braking energy larger than $0.6 mc^2$? </p>
<p>Now what if, after lowering the mass close to the event horizon, we wait the black hole to shrink to mass 100 m, by emitting Hawking radiation, and then we lower the mass some more? Is the braking energy of the second lowering process larger than $0.5 mc^2$? </p>
<p>I wonder can we extract more than $E=mc^2$ energy from mass m?</p>
<p>(In this thought experiment we use a wire and a winch, or anything that works)</p> | 1,553 | [
-0.03178592398762703,
-0.041438791900873184,
0.010693500749766827,
-0.018429027870297432,
-0.00847384799271822,
-0.006789383944123983,
-0.0783892348408699,
-0.054252784699201584,
-0.01767723076045513,
-0.02644958905875683,
0.008252842351794243,
0.018666934221982956,
0.0330149382352829,
0.020696498453617096,
0.0051273442804813385,
0.031220167875289917,
-0.033081043511629105,
-0.03312815725803375,
0.00003810954149230383,
-0.0444595068693161,
0.02012530155479908,
0.0034031220711767673,
-0.0016843525227159262,
0.0016078455373644829,
-0.028076909482479095,
0.008072749711573124,
0.02670844830572605,
-0.0209942739456892,
-0.016550224274396896,
0.0467732809484005,
-0.013460012152791023,
-0.02440176159143448,
0.0012669835705310106,
0.04141995310783386,
-0.002270159311592579,
-0.024748235940933228,
-0.025099938735365868,
-0.04126686230301857,
0.008888864889740944,
0.017314596101641655,
-0.01320885680615902,
-0.036801256239414215,
-0.026464857161045074,
0.048685092478990555,
-0.03525317460298538,
-0.02913268841803074,
0.024280855432152748,
-0.05822623521089554,
0.020861303433775902,
-0.04047796502709389,
0.052371587604284286,
0.016270559281110764,
0.014239701442420483,
0.009155109524726868,
-0.006564592942595482,
-0.0023090457543730736,
0.0613173171877861,
0.06663940846920013,
-0.02417009323835373,
-0.016647150740027428,
-0.02144855633378029,
-0.024154329672455788,
-0.016116173937916756,
0.01862776093184948,
-0.0029953850898891687,
0.03125442564487457,
-0.0359170027077198,
0.013409464620053768,
0.02542959526181221,
-0.017990779131650925,
0.03808712586760521,
0.003494356060400605,
0.01679021492600441,
-0.009902107529342175,
0.015725232660770416,
-0.01947736367583275,
-0.0029625094030052423,
0.01229309756308794,
0.04125003144145012,
0.06583955138921738,
-0.016290901228785515,
0.0020705738570541143,
0.09384717792272568,
0.0797649398446083,
0.012702698819339275,
0.005345503333956003,
0.07572680711746216,
-0.014484480023384094,
0.04613759368658066,
0.022012948989868164,
-0.006396460812538862,
-0.020154768601059914,
0.005655205342918634,
-0.03518693149089813,
-0.004223640076816082,
0.05095856264233589,
0.0007958502392284572,
0.060490142554044724,
-0.0027121128514409065,
-0.01002733688801527,
-0.02207697555422783,
0.016961226239800453,
0.017846576869487762,
0.040474310517311096,
0.03335363045334816,
-0.009752633050084114,
-0.059059787541627884,
0.052050698548555374,
-0.04499604552984238,
-0.022465603426098824,
-0.032517436891794205,
0.007463838439434767,
-0.0050398437306284904,
-0.027546413242816925,
-0.0008510539191775024,
-0.027827320620417595,
-0.007750038057565689,
-0.045904453843832016,
0.052012816071510315,
0.04228980466723442,
0.03026147186756134,
-0.014465127140283585,
0.029516752809286118,
-0.036108024418354034,
-0.034386374056339264,
0.031992435455322266,
0.06335071474313736,
-0.02402055263519287,
-0.047176338732242584,
-0.016445692628622055,
-0.014926053583621979,
0.003913012333214283,
-0.001968550495803356,
0.018221423029899597,
0.024570537731051445,
0.015947526320815086,
-0.07350245863199234,
-0.06738661974668503,
0.03412383794784546,
-0.010348365642130375,
0.0070128976367414,
-0.050676651298999786,
-0.009377188049256802,
0.034929562360048294,
0.1097683310508728,
0.01370577048510313,
0.021715130656957626,
-0.017435800284147263,
0.025917816907167435,
-0.005172160919755697,
0.0036809893790632486,
-0.019201328977942467,
0.007084315177053213,
-0.011699827387928963,
-0.003113793907687068,
-0.07837115973234177,
-0.012767231091856956,
0.028980212286114693,
0.027162905782461166,
0.008256977424025536,
0.0456620417535305,
-0.005577521864324808,
-0.005377388559281826,
-0.01031462848186493,
-0.01384411659091711,
-0.0015621716156601906,
0.09817858040332794,
0.020716777071356773,
-0.004864370916038752,
0.03363128751516342,
0.04113677144050598,
0.029421858489513397,
-0.004906937479972839,
-0.00044831554987467825,
0.03679780662059784,
-0.06988740712404251,
0.01136653684079647,
-0.03617478162050247,
0.032499320805072784,
-0.0002728246327023953,
-0.037061408162117004,
-0.03349733352661133,
-0.014882409013807774,
-0.024143168702721596,
0.03980615362524986,
0.024777544662356377,
-0.016346752643585205,
-0.02714931033551693,
0.0076125203631818295,
-0.0454961396753788,
-0.016382990404963493,
-0.051322195678949356,
0.02105662226676941,
0.03307062387466431,
0.011622338555753231,
0.02229410596191883,
-0.01262541115283966,
0.023093068972229958,
-0.030712826177477837,
-0.025016477331519127,
0.031125083565711975,
0.05646219849586487,
-0.012582412920892239,
-0.01126544363796711,
-0.01007789932191372,
0.043237607926130295,
0.04877655580639839,
0.01458579022437334,
-0.006080434191972017,
0.0035026189871132374,
-0.06477715075016022,
0.0020724362693727016,
-0.015035334974527359,
0.0024070250801742077,
0.017034703865647316,
0.028676491230726242,
0.04992368817329407,
-0.026514455676078796,
0.006077449768781662,
0.0286964513361454,
-0.0032101022079586983,
0.08742944151163101,
0.019285203889012337,
0.03457570821046829,
-0.005880317185074091,
0.025323722511529922,
0.017947368323802948,
0.01755329966545105,
-0.0072086467407643795,
-0.01897425390779972,
-0.027635550126433372,
0.0028625293634831905,
-0.010617970488965511,
0.03742111101746559,
-0.07665039598941803,
0.02735104039311409,
0.03266405686736107,
0.0064858500845730305,
0.04327535629272461,
0.007909239269793034,
0.007517567835748196,
-0.02457304298877716,
0.00020577690156642348,
0.027771426364779472,
-0.007059940602630377,
0.013361467979848385,
0.05873444676399231,
0.023739447817206383,
-0.007349671330302954,
-0.01767140068113804,
0.03198704123497009,
0.035289205610752106,
-0.019404146820306778,
0.0087357796728611,
-0.011424429714679718,
-0.021087709814310074,
0.01570325903594494,
-0.05470519885420799,
0.01377078890800476,
0.02725997194647789,
0.003227273700758815,
-0.004472087137401104,
-0.04308369383215904,
-0.005626081954687834,
0.014793331734836102,
0.001964524621143937,
0.009057460352778435,
-0.013387835584580898,
0.026603151112794876,
-0.03844541311264038,
0.016581980511546135,
-0.025024738162755966,
-0.008415372110903263,
-0.05962584912776947,
0.021497033536434174,
0.021245406940579414,
-0.01191019732505083,
0.05718154460191727,
-0.05114108696579933,
-0.05071265995502472,
0.0025682649575173855,
-0.03993726149201393,
-0.004836203996092081,
0.024014079943299294,
-0.05309034883975983,
0.02074243687093258,
-0.03585604950785637,
-0.035467036068439484,
0.0575728565454483,
0.0037275569047778845,
0.010026983916759491,
0.049594756215810776,
-0.0072413343004882336,
-0.03135467320680618,
0.01884298399090767,
-0.0009482431341893971,
-0.0258433036506176,
-0.028358634561300278,
-0.02027308940887451,
0.08180919289588928,
-0.011059178039431572,
-0.02226303517818451,
0.023118063807487488,
-0.032599397003650665,
-0.031170332804322243,
-0.025457484647631645,
0.02026723511517048,
0.006859141867607832,
-0.010858348570764065,
0.05231212079524994,
-0.006617262959480286,
-0.024040844291448593,
0.008463614620268345,
-0.06461191177368164,
-0.04516143724322319,
0.011021992191672325,
-0.012944814749062061,
0.016425780951976776,
0.00007368601654889062,
-0.03177415952086449,
0.08397071808576584,
-0.0009924828773364425,
-0.01830879971385002,
-0.015639929100871086,
-0.016680976375937462,
0.016916409134864807,
0.007491498254239559,
-0.029325542971491814,
0.03247125446796417,
-0.03219166398048401,
-0.018347768113017082,
0.031926900148391724,
0.025727106258273125,
0.022412583231925964,
0.024887923151254654,
-0.03987044095993042,
-0.031058628112077713,
-0.003699762746691704,
0.03376029059290886,
0.031019842252135277,
-0.026283372193574905,
-0.023952152580022812,
0.010597644373774529,
-0.009069315157830715,
0.06451673060655594,
-0.005569258239120245,
-0.04323591664433479,
0.03243125602602959,
0.023629626259207726,
0.001759168691933155,
-0.004904875997453928,
0.026213236153125763,
0.016606241464614868,
-0.0468817763030529,
0.01692977547645569,
-0.02461538463830948,
0.04272971674799919,
-0.003396975342184305,
0.026763655245304108,
0.015062193386256695,
0.05327706038951874,
-0.04592224210500717,
-0.04133382439613342,
-0.012823939323425293,
-0.02454839088022709,
0.026694508269429207,
-0.01839565671980381,
-0.012685637921094894,
0.03753973916172981,
0.015623945742845535,
0.06489141285419464,
0.00212116283364594,
-0.015384521335363388,
0.030566781759262085,
-0.07524840533733368,
-0.05312551558017731,
-0.008536265231668949,
0.03893158212304115,
0.0018204913940280676,
0.02687118574976921,
0.04377450793981552,
0.013139715418219566,
0.022731106728315353,
-0.023627713322639465,
-0.10157619416713715,
0.008120112121105194,
-0.05721210688352585,
-0.041246142238378525,
0.030143646523356438,
-0.011637089774012566,
0.005612663459032774,
-0.028554879128932953,
0.024936048313975334,
-0.007075169123709202,
0.011745487339794636,
-0.04838446527719498,
0.01332950871437788,
-0.05169418081641197,
-0.04936446622014046,
0.007746578194200993,
0.030130552127957344,
0.07483913749456406,
0.006777461618185043,
-0.012133221141994,
0.0010069726267829537,
-0.01365920901298523,
0.027360649779438972,
0.026538554579019547,
0.005761425010859966,
-0.01834866590797901,
0.024622052907943726,
0.030628100037574768,
0.03618526831269264,
-0.029761437326669693,
0.022692207247018814,
0.048773393034935,
0.012249837629497051,
0.0006082206964492798,
-0.001966550014913082,
-0.03749760240316391,
-0.027502838522195816,
-0.05104462802410126,
0.0003704410919453949,
0.07251770049333572,
-0.02368488721549511,
-0.033653624355793,
0.011485369876027107,
-0.004781623836606741,
-0.004513524938374758,
0.030171193182468414,
0.06369415670633316,
-0.01310467254370451,
-0.03973991051316261,
-0.0617348849773407,
-0.04406387358903885,
-0.015168869867920876,
-0.0031935987062752247,
-0.0006485155317932367,
-0.020571447908878326,
-0.03953000530600548,
0.014455132186412811,
0.03148670867085457,
0.024536680430173874,
-0.0070051588118076324,
-0.0029881265945732594,
0.008476320654153824,
0.03745528683066368,
-0.00047871077549643815,
0.022662177681922913,
0.008451561443507671,
0.011185428127646446,
0.03592865914106369,
-0.017276057973504066,
0.040286269038915634,
-0.08688995242118835,
-0.04259507730603218,
0.009720300324261189,
0.06715451180934906,
-0.012770682573318481,
-0.016643481329083443,
-0.06135668605566025,
0.010299904271960258,
0.03761029243469238,
-0.021988067775964737,
0.0334012396633625,
0.0003976288135163486,
0.02931988053023815,
-0.018716495484113693,
-0.007575977127999067,
-0.010520449839532375,
0.04805894196033478,
-0.0012005454627797008,
-0.02705959603190422,
-0.02439894527196884,
0.019851146265864372,
0.017157677561044693,
0.02249872125685215,
0.024890564382076263,
0.056102536618709564,
0.04221245273947716,
0.0016025900840759277,
-0.00952007807791233,
-0.01355458702892065,
-0.016916701570153236,
-0.07713824510574341,
0.0005595238180831075,
-0.0048333085142076015,
-0.08247912675142288,
0.01998964138329029,
-0.053568653762340546,
-0.015328650362789631,
0.03526235744357109,
0.01654496230185032,
-0.017998890951275826,
0.0052638272754848,
-0.07147887349128723,
0.02420181594789028,
0.042345080524683,
0.019573664292693138,
0.044699735939502716,
0.023195771500468254,
0.0014881787355989218,
0.0218978151679039,
0.0033990966621786356,
0.02210385352373123,
-0.0636657327413559,
-0.0010900684865191579,
-0.025517262518405914,
-0.007002091035246849,
-0.036745063960552216,
0.057783227413892746,
0.010454725474119186,
0.026956407353281975,
0.004917146638035774,
-0.03648608550429344,
-0.021769369021058083,
0.026172645390033722,
0.009025591425597668,
0.0002882478875108063,
0.01403916347771883,
0.0146320266649127,
-0.01367596723139286,
-0.03248399868607521,
-0.0009784189751371741,
0.021823866292834282,
0.007387873250991106,
0.029533065855503082,
-0.015660494565963745,
0.038984838873147964,
-0.025539346039295197,
0.00016684124420862645,
0.037217531353235245,
-0.018568936735391617,
0.0460289791226387,
-0.030867114663124084,
-0.0003860174911096692,
0.007017721422016621,
-0.03605087101459503,
-0.010328431613743305,
-0.0019455183064565063,
0.01441610511392355,
-0.01575782708823681,
-0.027067411690950394,
0.03597145155072212,
0.050442397594451904,
0.032497603446245193,
-0.04850988835096359,
-0.02189553715288639,
0.023493479937314987,
-0.0016731099458411336,
0.014647123403847218,
-0.031696729362010956,
0.016762394458055496,
-0.096503846347332,
-0.0056151170283555984,
-0.026993878185749054,
0.02859838306903839,
-0.03629430755972862,
0.03997182473540306,
0.004628563765436411,
-0.009883448481559753,
0.009691556915640831,
-0.028810391202569008,
-0.02960635907948017,
0.0010789277730509639,
0.010475303046405315,
0.0029702147003263235,
0.003853537840768695,
0.05253657326102257,
-0.026539281010627747,
-0.008157593198120594,
0.005266936030238867,
-0.045724205672740936,
0.04484681785106659,
-0.008007105439901352,
0.013964229263365269,
0.08309050649404526,
0.04337204992771149,
0.028388015925884247,
0.013127795420587063,
0.028732459992170334,
-0.021733857691287994,
0.024241354316473007,
0.011608370579779148,
-0.020630953833460808,
0.006070740986615419,
-0.04299894720315933,
0.03000667504966259,
0.040722012519836426,
-0.02417362853884697,
-0.028552308678627014,
0.0486840158700943,
-0.013925466686487198,
-0.03569547086954117,
-0.012777719646692276,
-0.018587246537208557,
0.010910451412200928,
0.008621088229119778,
0.007611686363816261,
0.05076437443494797,
-0.015690311789512634,
-0.00853098277002573,
-0.032067954540252686,
-0.017292479053139687,
-0.02956395596265793,
0.05608024448156357,
0.01141333393752575,
0.03184588998556137,
0.012701461091637611,
-0.03432583436369896,
0.01803434267640114,
-0.04177604988217354,
0.018439000472426414,
0.021660897880792618,
0.022855790331959724,
0.005537028424441814,
-0.019587842747569084,
0.014230559580028057,
0.051256582140922546,
0.03577542304992676,
-0.017651334404945374,
0.04177350550889969,
0.020067449659109116,
0.033133819699287415,
0.01816619746387005,
-0.02974015660583973,
-0.034345708787441254,
0.036086101084947586,
-0.0073384069837629795,
0.022558903321623802,
-0.02414962276816368,
0.0015736673958599567,
0.029782196506857872,
0.04143530875444412,
0.0371311753988266,
-0.03790207952260971,
-0.013186218217015266,
-0.06733451783657074,
-0.007606700528413057,
0.0016791429370641708,
-0.007569760084152222,
0.02329052984714508,
0.00025464248028583825,
-0.017514953389763832,
0.029408862814307213,
0.0471777617931366,
0.012541194446384907,
-0.040288250893354416,
-0.025813283398747444,
-0.04736576974391937,
-0.05970050022006035,
0.04279817268252373,
0.016860356554389,
-0.002055118791759014,
0.040154509246349335,
-0.04623701050877571,
-0.008498327806591988,
0.01272258535027504,
0.03208810091018677,
0.014118369668722153,
0.05890658497810364,
-0.00794691126793623,
0.030115552246570587,
-0.002913141157478094,
-0.001331362989731133,
0.11520610749721527,
0.06436356157064438,
-0.004260405898094177,
-0.040496617555618286,
0.024094298481941223,
-0.02310384064912796,
-0.015158914029598236,
-0.041699960827827454,
0.02188640646636486,
-0.04638006165623665,
-0.0014688430819660425,
0.016676029190421104,
0.05750012770295143,
-0.031144650653004646,
-0.0029121222905814648,
0.0662572830915451,
-0.027946114540100098,
0.015427659265697002,
0.026414010673761368,
0.00853979866951704,
-0.004944084212183952,
0.01014077477157116,
0.006306267809122801,
0.029431909322738647,
-0.006555154919624329,
-0.015641747042536736,
-0.020455097779631615,
-0.013161147013306618,
0.022520439699292183,
-0.04057956859469414,
-0.06890920549631119,
-0.009902028366923332,
-0.0011411840096116066,
-0.029459945857524872,
-0.02470405027270317,
0.02744302526116371,
0.02911888249218464,
0.0015989632811397314,
0.008230415172874928,
0.030377140268683434,
0.011411608196794987,
0.04067259654402733,
0.0038022028747946024,
0.021489664912223816,
-0.048839762806892395,
0.00747350649908185,
-0.011539306491613388,
0.051515597850084305,
-0.004857721738517284,
-0.011381471529603004,
0.024991827085614204,
-0.0060910070315003395,
0.039657581597566605,
0.0017531058983877301,
-0.006315506994724274,
-0.0339936800301075,
-0.024433650076389313,
0.0027408504392951727,
-0.025085769593715668,
-0.039638370275497437,
0.029707910493016243,
0.03492731600999832,
0.016878752037882805,
-0.03234778717160225,
-0.0013885486405342817,
-0.011577936820685863,
0.009297221899032593,
0.050333984196186066,
-0.007426246535032988,
-0.005509606096893549,
-0.015950188040733337,
-0.003482609521597624,
-0.018445348367094994,
-0.003219011938199401,
0.00013930651766713709,
0.018847890198230743,
-0.011264779604971409,
0.017162470147013664,
-0.006786802317947149,
-0.04027596861124039,
-0.04244866967201233,
0.03160868212580681,
-0.004872993566095829,
0.0021055047400295734,
-0.033347032964229584,
-0.005187629256397486,
-0.00458117388188839,
0.04225870594382286,
-0.0154111934825778,
-0.01931292563676834,
0.0030808160081505775,
0.035098847001791,
-0.002669628243893385,
-0.015991335734725,
-0.013592305593192577,
-0.004640862345695496,
-0.05511532351374626,
0.005020590033382177,
-0.012895660474896431,
0.057040441781282425,
-0.01817973330616951,
-0.01328963041305542,
-0.004084580112248659,
0.001094865147024393,
-0.032933253794908524,
-0.002522131195291877,
0.020771795883774757,
-0.02113272249698639,
-0.013521146029233932,
0.016423603519797325,
0.012797177769243717,
-0.02155516855418682,
-0.02234533429145813,
-0.01793699897825718,
-0.006289003882557154,
-0.034599557518959045,
0.05697191134095192,
-0.0008803848759271204,
0.050041887909173965,
-0.020491627976298332,
0.005329254548996687,
-0.04428422078490257,
0.014764565974473953,
-0.0579911470413208,
0.01871335133910179,
0.015466627664864063,
-0.03650743141770363,
-0.006224725861102343,
0.01729736104607582,
-0.04453050345182419,
-0.0007377931615337729,
0.02005484513938427,
0.040123846381902695,
-0.0486113578081131,
-0.025923335924744606,
0.05057375133037567,
-0.011485065333545208,
0.037610314786434174,
0.008042463101446629,
-0.03704799339175224,
0.031967855989933014,
-0.06446313112974167,
-0.019296450540423393,
0.04925275593996048,
0.0233513992279768,
0.048797186464071274,
0.01463383063673973,
-0.048133302479982376,
-0.027587883174419403,
0.05872861668467522,
-0.03515055403113365,
-0.03572508320212364,
0.02068435214459896,
-0.05884280428290367,
-0.037947509437799454,
0.004296686965972185,
0.023664459586143494,
-0.042596641927957535,
0.004784323740750551,
0.035657383501529694,
0.004897290840744972,
-0.0032583591528236866,
-0.014647978357970715,
-0.017768222838640213,
0.017252963036298752,
0.016426129266619682,
0.00372317130677402,
-0.016387272626161575,
0.02604156732559204,
0.09287891536951065,
-0.030044162645936012,
0.04192682355642319,
0.019414111971855164,
0.021871624514460564,
-0.12207434326410294,
0.0052550239488482475,
-0.004775424487888813,
0.010210270993411541,
0.05639849975705147,
-0.04324304312467575,
0.032990097999572754,
-0.009061571210622787,
-0.0645795613527298,
0.03817278519272804,
-0.03429752215743065,
0.0009235222823917866,
-0.04133981466293335,
-0.012498468160629272,
0.005398373119533062,
0.01210133358836174,
0.0410383976995945,
0.05973894149065018,
-0.0004996543866582215,
-0.004963253624737263,
0.010681708343327045,
-0.03733871132135391,
-0.010126789100468159,
0.01879051700234413,
-0.02146328240633011,
-0.0026343129575252533,
0.09753213077783585,
-0.022471262142062187,
-0.030534224584698677,
-0.013132190331816673,
0.014086454175412655,
-0.005786334630101919,
-0.007336286827921867,
0.021258724853396416,
0.0036886034067720175,
0.008620607666671276,
-0.00005752826473326422,
-0.010532607324421406,
0.002181048970669508,
0.014137987047433853,
-0.0022575289476662874,
-0.00034640266676433384,
-0.020359696820378304,
-0.007832824252545834,
0.018752476200461388,
-0.03724389895796776,
-0.009989459998905659,
0.056070439517498016,
-0.02696535550057888,
-0.035874344408512115,
0.02283623069524765,
0.021633541211485863,
0.020716845989227295,
-0.010228701867163181,
-0.028136851266026497,
-0.04954591020941734,
-0.025281334295868874,
0.017317645251750946,
-0.0314357653260231,
-0.006806488614529371,
0.029330261051654816,
-0.010254545137286186,
-0.008292589336633682,
0.015144952572882175,
-0.006970284506678581,
0.007873877882957458,
-0.04540776088833809,
-0.00711516197770834,
0.0024770284071564674,
0.01930815353989601,
-0.0042655495926737785,
-0.07899833470582962,
-0.0021359107922762632,
0.008087009191513062,
-0.012989602982997894,
0.014422258362174034,
0.002559507731348276,
-0.03348436951637268,
-0.013621272519230843,
-0.08625450730323792,
-0.017573881894350052,
-0.0333750881254673,
0.024086959660053253,
-0.026598546653985977,
-0.04319804534316063,
-0.0007627562736161053,
-0.030837010592222214,
0.05843924358487129,
-0.001666878699325025,
-0.03337133303284645,
0.030979594215750694,
-0.019278135150671005,
0.004174267407506704,
-0.017720894888043404,
0.005378096364438534,
0.00577404024079442,
-0.016065310686826706,
-0.0237461868673563,
0.009909073822200298,
0.011287754401564598,
-0.0009054134716279805,
0.020564105361700058,
0.018538275733590126,
0.028489843010902405,
-0.02054702676832676,
0.0022283392027020454,
0.04892660677433014,
-0.0070923203602433205,
-0.0009970186511054635,
0.05425488203763962,
0.003437767503783107,
0.04455314949154854,
0.01153626199811697,
-0.023437928408384323,
-0.03350002318620682,
0.053883228451013565,
-0.024828409776091576,
0.005863466765731573,
-0.018603166565299034,
-0.02416270226240158,
0.045312341302633286,
-0.03247147798538208,
0.010469017550349236,
0.012325072661042213,
-0.057371221482753754,
-0.013996662572026253,
0.04465669021010399,
0.02311979979276657,
0.02544913813471794,
-0.014680435881018639,
0.03985786437988281,
0.00769853126257658,
0.008866531774401665,
0.002869091695174575,
0.05094411224126816,
0.02561025694012642,
-0.017034530639648438,
0.002257749205455184,
0.024679651483893394,
0.00747068552300334,
-0.01960957795381546,
0.016305705532431602,
0.026558678597211838,
-0.0015935716219246387,
-0.0605178102850914,
-0.03719046339392662,
0.007795289624482393,
-0.010888482443988323,
-0.01064505148679018,
-0.01760600134730339,
0.04525553807616234,
0.02739674784243107,
0.0037064109928905964,
-0.018262960016727448,
0.012161299586296082,
-0.03337854519486427,
0.04044066369533539,
-0.0066705369390547276,
0.05423272028565407,
0.03241633251309395,
-0.007981885224580765,
-0.010143804363906384,
0.023197142407298088,
0.007463718298822641,
-0.005846852902323008,
0.021904578432440758,
-0.014551552943885326,
-0.009199759922921658,
-0.01746623031795025,
-0.03093406930565834,
0.007255596108734608,
-0.05096239596605301,
0.03816308081150055,
0.025616822764277458,
0.050893139094114304,
0.00898737646639347,
-0.016008753329515457,
-0.02343618869781494,
0.04900442063808441,
-0.025455232709646225,
-0.00984575878828764,
-0.007361091207712889,
0.02114327810704708,
-0.009154080413281918,
-0.04175380617380142
] |
<p>Well, that's easy: the sand is wet, and my shoes are wet, and hydrogen bonding adheres the wet sand to my wet feet and to my shoes.</p>
<p>But then I walk home, and my shoes dry, and the sand on them dries, and some of the sand falls off. But some does not. It's really stuck: even several days later I can turn the shoe upside-down and it won't fall off. What holds it on?</p>
<p>Sand sticks to my feet after my feed dry and the sand dries. Is this the same?</p> | 1,554 | [
-0.06520071625709534,
-0.022766320034861565,
0.029368335381150246,
0.009372247382998466,
0.005456463433802128,
0.0018420630367472768,
-0.008187418803572655,
0.04636978730559349,
-0.005549770779907703,
-0.02370690554380417,
0.04196798801422119,
0.030713392421603203,
0.0014102415880188346,
0.047732073813676834,
0.003965765703469515,
-0.030370691791176796,
0.025931190699338913,
-0.07161845266819,
-0.010895522311329842,
0.009939946234226227,
-0.008540546521544456,
0.006605866365134716,
0.002491800347343087,
0.009502739645540714,
-0.01751832105219364,
-0.0015408344333991408,
0.021718844771385193,
-0.03357860445976257,
0.02918718196451664,
0.01745258830487728,
-0.011351622641086578,
-0.0016833432018756866,
0.016789378598332405,
-0.011100714094936848,
0.012380488216876984,
-0.01401273999363184,
-0.0253999512642622,
-0.013091610744595528,
-0.06323746591806412,
0.018335189670324326,
-0.008889973163604736,
-0.01287329476326704,
-0.02539617009460926,
0.060716792941093445,
-0.06038786470890045,
0.028532560914754868,
0.008808656595647335,
0.01729031652212143,
0.060746654868125916,
-0.04637156054377556,
0.026186281815171242,
0.014434099197387695,
0.0541280098259449,
0.04013315588235855,
0.0032299666199833155,
-0.003077430883422494,
0.045285798609256744,
0.039439234882593155,
-0.011467589065432549,
-0.05381917953491211,
-0.04165155068039894,
-0.032523758709430695,
-0.008110246621072292,
-0.0227817390114069,
-0.008185070008039474,
0.001301183132454753,
0.023054437711834908,
-0.052519749850034714,
0.04690832272171974,
-0.0021827081218361855,
0.0032876001205295324,
0.009507900103926659,
0.051777731627225876,
0.012831748463213444,
-0.00045199962914921343,
-0.039152730256319046,
-0.0020102804992347956,
0.02401912398636341,
0.05393155291676521,
0.05071186274290085,
-0.013417963869869709,
-0.0050721620209515095,
0.010444187559187412,
0.029345126822590828,
0.00666110310703516,
-0.07801958918571472,
0.08061058074235916,
0.005385467316955328,
-0.0006207053666003048,
0.05423886328935623,
0.013252229429781437,
0.007171585690230131,
-0.00019824797345791012,
0.03793291002511978,
-0.023468313738703728,
-0.005956979468464851,
0.02384622022509575,
0.02939695306122303,
-0.008538139052689075,
0.01463707722723484,
-0.038176342844963074,
0.008979704231023788,
0.06319998949766159,
0.042751263827085495,
-0.012520693242549896,
-0.07338409870862961,
-0.04710410162806511,
0.016823766753077507,
-0.004558647517114878,
-0.009781434200704098,
-0.01462286151945591,
-0.002173640765249729,
-0.029837576672434807,
-0.006112285889685154,
0.006042130291461945,
-0.036826424300670624,
-0.016734477132558823,
-0.02746044471859932,
0.027137724682688713,
0.07436099648475647,
0.0571797639131546,
-0.009985076263546944,
0.008181876502931118,
-0.018865982070565224,
-0.07392603158950806,
0.02703370340168476,
0.04201970621943474,
-0.04887858033180237,
-0.015896916389465332,
0.013057563453912735,
0.00823139026761055,
0.02856079675257206,
-0.006657033693045378,
-0.025075050070881844,
-0.002054754877462983,
-0.006297254469245672,
-0.07616268843412399,
-0.025136465206742287,
0.040871743112802505,
-0.007201875559985638,
-0.012984142638742924,
-0.06953778862953186,
0.010101399384438992,
-0.01812133379280567,
0.05428184196352959,
-0.014627407304942608,
0.03776836395263672,
0.004141238518059254,
0.00883218552917242,
0.007548473309725523,
-0.008785158395767212,
-0.02629452757537365,
-0.003552852664142847,
-0.053373824805021286,
-0.02072402834892273,
-0.08155404031276703,
0.0210618544369936,
0.010621809400618076,
0.0247010737657547,
-0.044238731265068054,
0.04954606294631958,
0.0023362552747130394,
0.00920106004923582,
-0.006501850206404924,
-0.018418630585074425,
-0.04413490742444992,
0.0483136847615242,
-0.0084983566775918,
-0.009778153151273727,
0.024832850322127342,
0.006744224112480879,
0.011302869766950607,
-0.0245787613093853,
0.0443585179746151,
0.005557193420827389,
0.0193159356713295,
0.021845504641532898,
-0.015936264768242836,
-0.009051911532878876,
0.008263763040304184,
-0.05583973973989487,
-0.005613982677459717,
-0.01854916661977768,
0.032866206020116806,
-0.014836588874459267,
-0.009113818407058716,
0.007159871514886618,
-0.01639692671597004,
-0.007659148424863815,
-0.04729786887764931,
0.00414939783513546,
-0.08052404224872589,
0.011614036746323109,
-0.03545313701033592,
0.025466442108154297,
0.007018580101430416,
-0.028545575216412544,
0.0031500335317105055,
-0.062287837266922,
-0.028962882235646248,
-0.0013728522462770343,
0.016467414796352386,
0.020659418776631355,
-0.019054988399147987,
-0.0070699667558074,
0.02472270093858242,
0.02440546080470085,
-0.01602664217352867,
-0.005707846488803625,
-0.03799592703580856,
-0.00022053852444514632,
0.03229283168911934,
-0.015112086199223995,
0.020401742309331894,
0.008332791738212109,
-0.0011080293916165829,
-0.024392202496528625,
-0.0067346044816076756,
-0.004392703995108604,
0.02468249946832657,
0.002722966019064188,
0.030789252370595932,
0.028338991105556488,
-0.05291634425520897,
0.03850368410348892,
0.03564852103590965,
-0.02532223053276539,
0.0052716899663209915,
0.000598276499658823,
0.0018479455029591918,
-0.022394729778170586,
-0.0223439559340477,
0.05302681401371956,
0.040646106004714966,
0.035065658390522,
0.02351834625005722,
-0.01520248781889677,
0.04404393956065178,
0.004060239996761084,
0.023169413208961487,
0.0025859836023300886,
0.013955979607999325,
0.025168508291244507,
0.02119039185345173,
0.015477302484214306,
0.010722649283707142,
0.015064225532114506,
0.008950400166213512,
0.012620066292583942,
-0.06251014024019241,
-0.020748432725667953,
0.03725544363260269,
0.037802696228027344,
0.03850127384066582,
0.011526643298566341,
-0.03228466585278511,
0.03778759762644768,
-0.025405926629900932,
-0.0014961434062570333,
0.000838636769913137,
0.03979077562689781,
-0.02981235459446907,
-0.05148504674434662,
-0.021394208073616028,
0.017985887825489044,
0.01877628266811371,
0.011348997242748737,
-0.0034267199225723743,
0.04514216631650925,
-0.027665553614497185,
0.008065793663263321,
-0.007994795218110085,
-0.0017633133102208376,
0.018628519028425217,
0.008263541385531425,
0.025319306179881096,
0.0011682845652103424,
0.06057754158973694,
-0.018476024270057678,
-0.05174827203154564,
0.026143111288547516,
-0.028282152488827705,
0.007203924003988504,
-0.00507477717474103,
-0.005642996169626713,
0.020818954333662987,
0.0074909757822752,
0.01248305942863226,
0.04050256311893463,
-0.02177293784916401,
-0.022059477865695953,
0.02045239508152008,
0.009981296956539154,
-0.029762085527181625,
-0.026313677430152893,
-0.0410182923078537,
-0.0064468695782125,
-0.02098950929939747,
0.0007881386554799974,
0.050488825887441635,
-0.03790276497602463,
-0.013324879109859467,
0.04509396851062775,
-0.021646762266755104,
-0.030110426247119904,
-0.0017229007789865136,
-0.014410031959414482,
-0.029680263251066208,
-0.014879358001053333,
0.006020869594067335,
0.020859409123659134,
-0.04498959705233574,
0.0035885318648070097,
-0.0723077729344368,
-0.06706137955188751,
0.001584175624884665,
0.0043474044650793076,
0.00748094916343689,
-0.030001360923051834,
0.02843346633017063,
0.07566092908382416,
0.018582623451948166,
-0.026420198380947113,
0.0051601049490273,
-0.05350615829229355,
-0.021593360230326653,
-0.040606144815683365,
0.007039735093712807,
0.08043728768825531,
0.007663394790142775,
0.04761653020977974,
0.01939643919467926,
0.022787662222981453,
0.023093676194548607,
0.04484368860721588,
-0.024390822276473045,
-0.0012393493670970201,
0.021973399445414543,
0.007353098597377539,
0.0413130521774292,
0.06075455620884895,
-0.04699193686246872,
0.0008219082374125719,
-0.0032610015477985144,
0.016731709241867065,
0.01562945730984211,
-0.04758410528302193,
0.056787360459566116,
-0.004443963058292866,
0.0021013265941292048,
-0.04921802505850792,
-0.003166543785482645,
-0.020076923072338104,
-0.03216615319252014,
0.009038751013576984,
-0.02936507575213909,
0.05267277732491493,
0.0024580571334809065,
-0.020491190254688263,
0.015525110065937042,
0.07838687300682068,
-0.03295363113284111,
-0.015295885503292084,
-0.005270543973892927,
0.022506969049572945,
-0.0014326905366033316,
-0.01715451292693615,
-0.0084025664255023,
0.010503399185836315,
-0.010727823711931705,
0.02193015068769455,
-0.0012420086422935128,
-0.08383630961179733,
-0.0452253594994545,
-0.06931274384260178,
-0.013504477217793465,
0.011529892683029175,
0.042272113263607025,
0.01942952163517475,
0.02080048806965351,
-0.022878585383296013,
0.017821548506617546,
-0.014508225955069065,
-0.002840624889358878,
-0.0628826767206192,
-0.019621502608060837,
0.01628132537007332,
-0.02624419704079628,
0.011702812276780605,
0.0018973127007484436,
-0.00010126442793989554,
-0.03820347785949707,
0.011407937854528427,
0.01552989799529314,
0.004068599548190832,
-0.007462604437023401,
0.024661056697368622,
-0.026153890416026115,
-0.04092887043952942,
-0.032423071563243866,
-0.0007015664014033973,
0.028697200119495392,
-0.009126069024205208,
0.017505019903182983,
0.010296855121850967,
-0.03565189614892006,
0.029907310381531715,
-0.026865648105740547,
-0.0301181860268116,
0.030812988057732582,
-0.026026809588074684,
0.018606876954436302,
0.013153760693967342,
0.035561684519052505,
-0.015021886676549911,
0.00656265951693058,
-0.013226641342043877,
0.005770115647464991,
0.01881820149719715,
-0.04120325669646263,
-0.03544076532125473,
-0.030802380293607712,
0.0007656182860955596,
0.05884428322315216,
-0.020016973838210106,
0.036000411957502365,
0.021033650264143944,
-0.005874789785593748,
-0.010672328993678093,
0.04533463716506958,
0.03878861665725708,
0.007468455005437136,
-0.03432255983352661,
-0.02011958323419094,
-0.009544968605041504,
-0.03470887988805771,
0.015303168445825577,
0.009595484472811222,
0.01775478385388851,
-0.02215583249926567,
-0.00942915678024292,
0.00099355133716017,
0.02016851305961609,
0.015629269182682037,
0.026643231511116028,
-0.01603325828909874,
0.05552668124437332,
-0.020580759271979332,
0.04734675586223602,
0.002906318986788392,
0.031628016382455826,
0.06005224213004112,
0.04571561887860298,
0.0018749687587842345,
-0.05213236063718796,
0.02816963568329811,
0.017457686364650726,
0.02396494895219803,
0.004322482272982597,
0.0021068451460450888,
-0.04674782231450081,
-0.016113033518195152,
0.022489609196782112,
-0.061977434903383255,
-0.0009576242882758379,
-0.017742134630680084,
-0.0095625976100564,
-0.03376566991209984,
-0.04364617168903351,
-0.04024331271648407,
-0.0454886257648468,
0.010250570252537727,
0.023042596876621246,
0.008667630143463612,
0.002395980292931199,
-0.01659933105111122,
0.06317844241857529,
0.006871731951832771,
0.06231318414211273,
-0.003917079418897629,
0.03112860582768917,
0.004443094599992037,
-0.01491055078804493,
-0.06364014744758606,
-0.08390552550554276,
0.006340836640447378,
0.022156769409775734,
0.016589835286140442,
0.04134068638086319,
-0.05539407581090927,
-0.05819254741072655,
0.009481314569711685,
-0.03333960473537445,
-0.0393201969563961,
0.0005502869025804102,
-0.04996331408619881,
-0.018877988681197166,
0.044494446367025375,
0.028706029057502747,
0.049961723387241364,
-0.005870900582522154,
-0.010549536906182766,
0.004558401647955179,
-0.014137310907244682,
0.01857180707156658,
-0.01784714125096798,
0.0010864257346838713,
-0.009751088917255402,
0.025904810056090355,
-0.04082237556576729,
0.03193669393658638,
0.015198550187051296,
0.012061337009072304,
0.014474206604063511,
-0.03585013002157211,
-0.027892017737030983,
0.0062875403091311455,
-0.007934432476758957,
-0.041350483894348145,
0.015994155779480934,
0.011070890352129936,
-0.019418882206082344,
-0.003179362276569009,
0.020553139969706535,
0.012725253589451313,
-0.03801708295941353,
0.032702453434467316,
0.0072762747295200825,
0.03734324499964714,
-0.0146303940564394,
0.00456926180049777,
-0.012109101749956608,
-0.05189314857125282,
0.006287354044616222,
-0.023485904559493065,
0.014783686026930809,
0.01173586305230856,
-0.003863272722810507,
0.0054619223810732365,
0.020909791812300682,
-0.003500723745673895,
0.01995059847831726,
-0.0065641640685498714,
0.03761995583772659,
0.036803968250751495,
-0.007019032724201679,
-0.026040153577923775,
-0.05094079673290253,
0.0381263829767704,
0.03158237412571907,
-0.05822206661105156,
-0.039299171417951584,
0.02300795167684555,
-0.0013546304544433951,
-0.060955505818128586,
0.015976950526237488,
0.07255731523036957,
-0.08550406247377396,
0.011187000200152397,
0.028011925518512726,
0.06261193752288818,
0.07154721766710281,
-0.012236608192324638,
0.04164851829409599,
-0.013553003780543804,
-0.026596523821353912,
-0.028993412852287292,
0.004892756696790457,
0.01858975738286972,
-0.033576782792806625,
-0.013326000422239304,
0.019070694223046303,
0.0218022670596838,
0.04655048996210098,
-0.04274089261889458,
-0.011926602572202682,
0.012768116779625416,
0.045779936015605927,
-0.038248077034950256,
-0.023124568164348602,
0.03574717044830322,
0.007474743761122227,
0.026709966361522675,
-0.020349936559796333,
0.042911700904369354,
0.0049950429238379,
-0.036488115787506104,
0.022524122148752213,
0.027791719883680344,
0.03769126161932945,
-0.0045661162585020065,
0.06136264279484749,
-0.004633278585970402,
-0.0046149748377501965,
0.0833527222275734,
-0.02007341757416725,
0.06237771362066269,
0.00887377467006445,
0.006952988915145397,
-0.004469761624932289,
-0.0038679547142237425,
-0.010365727357566357,
-0.03403579071164131,
-0.0004884466179646552,
-0.012641197070479393,
0.033752016723155975,
0.010392941534519196,
0.03270537406206131,
0.02406015619635582,
-0.02086099609732628,
0.004856922198086977,
0.00013910597772337496,
-0.009616254828870296,
0.026590092107653618,
0.01239765714854002,
0.046343594789505005,
-0.022480009123682976,
0.03241405263543129,
0.0040198080241680145,
0.04431114345788956,
0.022926127538084984,
-0.013170634396374226,
0.04708971083164215,
0.013655344024300575,
0.03107191063463688,
-0.046838074922561646,
-0.07275225967168808,
0.023853648453950882,
-0.03679877892136574,
0.033366117626428604,
-0.009865333326160908,
-0.040326010435819626,
0.0747108906507492,
0.018254676833748817,
0.03643673658370972,
-0.024033846333622932,
-0.06085965037345886,
-0.03440285846590996,
-0.018255973234772682,
0.00011150915815960616,
0.02821091003715992,
-0.010027310810983181,
-0.007083028554916382,
0.034188248217105865,
-0.006027864292263985,
0.0059266905300319195,
-0.02818501926958561,
-0.05351504310965538,
0.0013789897784590721,
0.009845166467130184,
-0.0019946331158280373,
0.060513686388731,
-0.007872394286096096,
-0.062257587909698486,
-0.0006550753023475409,
-0.04714559391140938,
0.019261054694652557,
-0.003301838180050254,
-0.015682058408856392,
-0.023475510999560356,
0.01659657247364521,
0.0005627884529531002,
0.020599937066435814,
-0.002816242864355445,
-0.0169240552932024,
0.12102611362934113,
0.036207277327775955,
0.038152024149894714,
-0.013959527015686035,
-0.021602598950266838,
-0.029972001910209656,
0.023990532383322716,
-0.03534146398305893,
-0.016330569982528687,
-0.010599365457892418,
0.07172540575265884,
0.012915287166833878,
0.04586459696292877,
0.0011506832670420408,
0.009236018173396587,
0.040200792253017426,
-0.059876229614019394,
-0.009179739281535149,
0.011429461650550365,
-0.032591093331575394,
-0.03148123249411583,
0.03334277868270874,
-0.010755080729722977,
0.023800410330295563,
0.01147815864533186,
0.022088533267378807,
-0.04568084329366684,
-0.043874986469745636,
0.018200065940618515,
0.018721304833889008,
-0.0447210930287838,
0.009121192619204521,
0.005695499014109373,
-0.0029059576336294413,
-0.005781360436230898,
0.0385105237364769,
0.02484751306474209,
-0.038961514830589294,
0.02464730478823185,
-0.018025152385234833,
0.03781251609325409,
-0.0033729574643075466,
0.017887722700834274,
0.008902759291231632,
-0.026127276942133904,
-0.03916154429316521,
-0.026615208014845848,
0.05035317689180374,
-0.043695807456970215,
-0.003282952355220914,
-0.001599745242856443,
-0.009215223602950573,
0.02652769722044468,
-0.04928051680326462,
-0.015356085263192654,
0.008381719700992107,
0.05655517429113388,
0.003727959468960762,
-0.029008682817220688,
-0.051503706723451614,
0.023571349680423737,
0.019721899181604385,
-0.014424147084355354,
0.03963332623243332,
0.005219561513513327,
0.008342322893440723,
0.000018953827748191543,
0.041332196444272995,
-0.055111806839704514,
0.009516244754195213,
-0.04871005564928055,
0.0002630497619975358,
-0.024545943364501,
0.009978660382330418,
-0.03667651489377022,
0.024539053440093994,
0.04469186067581177,
-0.027842480689287186,
-0.0177779458463192,
-0.036125604063272476,
-0.04406611993908882,
0.02679676190018654,
-0.06088881567120552,
-0.024633893743157387,
-0.04172928258776665,
-0.033169012516736984,
0.020966986194252968,
0.03679203242063522,
-0.009795261546969414,
0.026820391416549683,
-0.00793019961565733,
0.005968555808067322,
0.010763943195343018,
0.0061623589135706425,
-0.0017033357871696353,
0.048007067292928696,
-0.023790014907717705,
0.020612703636288643,
-0.000589606468565762,
0.006106590386480093,
-0.0075650811195373535,
0.009191317483782768,
0.004539829678833485,
0.009811230935156345,
-0.016306672245264053,
0.04234381020069122,
0.033215317875146866,
0.02503781020641327,
-0.027413396164774895,
0.04030470922589302,
-0.00464893551543355,
-0.026097839698195457,
-0.03197223320603371,
-0.03796621784567833,
0.0006278477376326919,
-0.0028246198780834675,
0.019542356953024864,
-0.023673638701438904,
0.0081776212900877,
-0.03735456243157387,
0.07767394930124283,
-0.02034703642129898,
0.017320139333605766,
-0.11698242276906967,
-0.025095509365200996,
-0.016155065968632698,
0.02326091006398201,
-0.013722897507250309,
0.017687156796455383,
-0.06199921667575836,
0.004243406932801008,
0.0072294496931135654,
-0.026814091950654984,
-0.011909116990864277,
-0.014926164411008358,
-0.02399064414203167,
0.0047625149600207806,
0.060070447623729706,
-0.028107894584536552,
-0.05100226402282715,
0.040251225233078,
-0.04534692317247391,
-0.008507546968758106,
-0.0026774853467941284,
0.007777748629450798,
0.024004491046071053,
0.027838150039315224,
0.004645229317247868,
0.010774655267596245,
0.034925345331430435,
-0.016332097351551056,
-0.02786659449338913,
-0.008694170974195004,
-0.05178374424576759,
0.018509171903133392,
0.005748532712459564,
-0.017267504706978798,
0.009784434922039509,
-0.05173910781741142,
0.05167516693472862,
-0.006143325474113226,
0.017905978485941887,
0.008730151690542698,
-0.0026781228370964527,
0.010732543654739857,
0.0005206648493185639,
-0.020681729540228844,
0.03556835651397705,
-0.0121182044968009,
0.03958800435066223,
-0.021721981465816498,
0.017629234120249748,
0.00799635425209999,
-0.013364934362471104,
-0.03170660510659218,
0.017820853739976883,
-0.03708972781896591,
0.010918237268924713,
0.030156686902046204,
-0.047162510454654694,
-0.012352783232927322,
0.03190286457538605,
-0.06299642473459244,
0.03617478534579277,
-0.032821252942085266,
-0.0006775590591132641,
-0.047058768570423126,
0.02798409014940262,
-0.003874307032674551,
0.022269802168011665,
-0.007833790965378284,
0.0391080416738987,
-0.00825249869376421,
0.018879905343055725,
0.01022215373814106,
0.0008664865745231509,
0.0285109281539917,
0.02099372074007988,
-0.019802860915660858,
0.021321160718798637,
0.10109550505876541,
0.013308098539710045,
-0.01883956789970398,
0.01302324328571558,
-0.02229326404631138,
-0.014270395040512085,
0.031155750155448914,
-0.006616704165935516,
-0.0073934318497776985,
0.015214298851788044,
-0.013157680630683899,
-0.007760731503367424,
-0.03248200565576553,
0.04741581529378891,
0.017498016357421875,
0.030306903645396233,
0.04423414170742035,
0.008746693842113018,
-0.004711373709142208,
-0.02111939713358879,
-0.020848410204052925,
0.03124704770743847,
-0.01623191125690937,
0.036816615611314774,
0.021347304806113243,
0.007220038678497076,
0.036008406430482864,
-0.0019599921070039272,
-0.07140495628118515,
-0.03595030680298805,
0.0575747974216938,
0.04656900092959404,
0.0023714140988886356,
0.009480653330683708,
0.03733162581920624,
-0.02623380906879902,
0.008462531492114067,
-0.011299170553684235,
0.0056868684478104115,
-0.017759470269083977,
-0.05169442296028137,
-0.029016200453042984,
0.007706893142312765,
-0.02279014326632023,
-0.008865752257406712,
0.022060036659240723,
-0.030654212459921837,
0.06944675743579865,
0.039639510214328766,
0.0511576347053051,
0.015869658440351486,
-0.05796525999903679,
0.015561194159090519,
-0.04603267088532448,
0.024848053231835365,
0.002452797954902053,
-0.015884295105934143,
-0.03330074995756149,
-0.07137734442949295,
0.02162381447851658,
0.02166595309972763,
0.07790936529636383,
-0.041691649705171585,
-0.009333156049251556,
-0.037034548819065094,
-0.03914228826761246,
0.0067998385056853294,
0.008438357152044773,
0.03033697046339512,
0.011886393651366234,
0.02501296065747738,
-0.015559674240648746,
0.01229865849018097,
-0.012185418047010899,
-0.0323210284113884,
0.0492607019841671,
-0.02119809202849865,
0.014600446447730064,
-0.018210692331194878,
0.008899616077542305,
0.02098945714533329,
0.0014031747123226523,
0.0005652700201608241,
0.06473460793495178,
0.006469022482633591,
-0.005914479494094849,
0.027720114216208458,
-0.06340570002794266,
-0.028022360056638718,
0.09232471883296967,
-0.02810957282781601,
-0.010654204525053501,
0.03802214935421944,
-0.01759491302073002,
0.06625398993492126,
-0.008213736116886139,
0.006573905702680349,
0.01038280501961708,
0.02353684976696968,
-0.013403435237705708,
0.046941474080085754,
0.0442185178399086,
0.017369167879223824,
-0.0313166119158268,
-0.024508235976099968,
-0.008135206997394562,
0.0026639949064701796,
0.016600005328655243,
0.07845333963632584,
0.03207661584019661,
-0.025517454370856285,
0.0017516204388812184,
0.007098356727510691,
0.009871239773929119,
0.002570495242252946,
-0.0032627263572067022,
0.0276961587369442,
0.005161036737263203,
-0.0222778283059597,
0.01406570803374052,
-0.03772007301449776,
-0.00787411443889141,
-0.01615564152598381,
-0.025912992656230927,
0.07295385748147964,
-0.035910941660404205,
0.006105337291955948,
0.003772107185795903,
0.04789886251091957,
-0.006226998288184404,
0.022943515330553055,
-0.003050214610993862,
0.03310608118772507,
0.0303892083466053,
-0.05943096801638603,
-0.05792192369699478,
0.024421272799372673,
-0.006552868522703648,
0.005405031144618988,
0.0036441488191485405,
0.010304593481123447,
0.019512612372636795,
0.020108606666326523,
0.012847252190113068,
-0.03420839086174965,
-0.02455429919064045,
0.06272668391466141,
0.014537372626364231,
0.0003941176983062178,
0.005457352381199598,
0.000007631716471223626,
-0.01747107319533825,
0.07316805422306061,
-0.06206105276942253,
-0.05298751965165138,
-0.01918068900704384,
0.004822628106921911,
-0.050845082849264145,
-0.02069653570652008
] |
<p>Can anyone give an example of when infinite-dimensional <a href="http://en.wikipedia.org/wiki/Hilbert_space" rel="nofollow">Hilbert spaces</a> are required to describe a physical system? The standard answer to this question is yes, and I'm sure some of you will be quick to point out several clear examples:</p>
<p>Ex. 1: Photon number states $\left\{ |0\rangle,|1\rangle,...,|n\rangle \right\}$</p>
<p>Ex. 2: Harmonic oscillator number states (same as above).</p>
<p>Ex. 3: Continuous-variable basis of a single free particle $\left\{ |x\rangle \right\} \forall x \in \mathbb{R}$</p>
<p>From the infinite number of basis vectors in these examples, it is generally concluded that the dimension of the Hilbert space is also infinite.</p>
<p>However, it is clear that a photon number state such as $|\psi\rangle=|100\rangle$ is unphysical (to be clear, this is the <a href="http://en.wikipedia.org/wiki/Fock_state" rel="nofollow">Fock number state</a> with $n=100$, not a tripartite state with one photon in one channel). If you dispute this, I would suggest you try preparing such a state in a single-mode fiber in an optics lab. For this reason, we can apply a (somewhat arbitrary) cutoff value of $n$ and recover a finite-dimensional Hilbert space.</p>
<p>Similarly, the <a href="http://en.wikipedia.org/wiki/Cardinality" rel="nofollow">cardinality</a> of the basis set for a free particle is actually $\mathbb{N}$, not $\mathbb{R}$ (due to the properties of the function space), and although this set of orthogonal functions is infinite, we can also apply a similar cutoff for any reasonably behaved wavefunction.</p>
<p>Can anyone give an example of a system described by an infinite-dimensional vector space for which such a cutoff cannot be applied?</p> | 1,555 | [
-0.01123835425823927,
-0.006892499979585409,
0.02867237664759159,
-0.05199025571346283,
0.04132567718625069,
-0.022322015836834908,
-0.02735578641295433,
-0.05202535167336464,
0.04001715034246445,
-0.03798690065741539,
0.07986518740653992,
0.02068469673395157,
-0.003506541019305587,
0.021043531596660614,
-0.02659102901816368,
0.03387531265616417,
-0.03682360798120499,
0.0023924303241074085,
-0.02379414066672325,
-0.014361233450472355,
0.01183965615928173,
0.058914195746183395,
-0.021566936746239662,
-0.0015067121712490916,
-0.02107688970863819,
0.02606596052646637,
-0.015086093917489052,
0.0007195054786279798,
0.03918073698878288,
0.06006801873445511,
0.005875791423022747,
-0.020917916670441628,
0.031145285815000534,
0.05919209495186806,
0.025035979226231575,
-0.009714333340525627,
-0.009367000311613083,
0.0004282641166355461,
0.021418269723653793,
-0.013238235376775265,
-0.031577467918395996,
-0.011828328482806683,
0.0009217333281412721,
0.047041673213243484,
-0.0014371771831065416,
0.015309227630496025,
0.03557783365249634,
-0.05437663942575455,
0.035671982914209366,
-0.03358468413352966,
0.048344504088163376,
-0.027530474588274956,
0.03894233703613281,
-0.012524455785751343,
0.019026443362236023,
-0.0290137380361557,
0.06538165360689163,
0.06493104994297028,
0.01927168108522892,
-0.05764371529221535,
-0.045668136328458786,
0.0005704694776795805,
-0.008522288873791695,
-0.013414640910923481,
-0.020058952271938324,
-0.003844655118882656,
0.006390407215803862,
-0.005881959572434425,
0.01112830825150013,
-0.035198550671339035,
0.01526422705501318,
-0.004287953022867441,
0.04007865861058235,
-0.03251681104302406,
-0.0026443989481776953,
0.024152621626853943,
0.018639860674738884,
-0.029561974108219147,
0.027399232611060143,
0.010957954451441765,
-0.03404458612203598,
-0.004993289243429899,
0.027273761108517647,
-0.001402064342983067,
0.046148356050252914,
-0.023448333144187927,
0.06621040403842926,
-0.02523121051490307,
0.0069536129012703896,
0.04910609498620033,
-0.01183791272342205,
-0.005901888478547335,
0.03529389202594757,
0.004454188048839569,
-0.03791999816894531,
0.04144642874598503,
0.0024007833562791348,
0.012191272340714931,
-0.023734821006655693,
-0.044403620064258575,
0.02695353515446186,
-0.0440104715526104,
0.017141731455922127,
0.10207945108413696,
-0.028697773814201355,
0.01453508622944355,
-0.013082421384751797,
0.04346783831715584,
-0.017473774030804634,
0.006434780545532703,
-0.02385331317782402,
0.04800096154212952,
-0.008843568153679371,
0.044855497777462006,
0.0004602480330504477,
-0.024841053411364555,
-0.0010796126443892717,
-0.02148192562162876,
0.08379418402910233,
0.08988819271326065,
0.04354967549443245,
-0.03808876872062683,
-0.005242745857685804,
-0.029277535155415535,
-0.057296328246593475,
-0.0005957984831184149,
0.04910983890295029,
0.03587561845779419,
-0.05556776374578476,
0.030949484556913376,
0.03217332065105438,
0.01874535344541073,
0.004825489595532417,
0.00150199793279171,
0.025604238733649254,
-0.0371130034327507,
-0.11976919323205948,
-0.05071977898478508,
0.046383172273635864,
-0.019612789154052734,
-0.02602778561413288,
-0.05922321230173111,
0.024255702272057533,
0.05528031662106514,
0.06016094237565994,
-0.028100498020648956,
0.022806167602539062,
-0.005072473082691431,
0.02148478664457798,
-0.00508639682084322,
-0.015100181102752686,
0.0231890007853508,
-0.0000626002365606837,
-0.02528548426926136,
-0.007986484095454216,
-0.0318625271320343,
0.041993673890829086,
0.04918528348207474,
0.029459260404109955,
0.0063033089973032475,
0.029156731441617012,
0.00776732387021184,
-0.0007633052300661802,
0.03049537166953087,
-0.013906492851674557,
-0.03252048417925835,
0.0760185718536377,
0.01760358363389969,
0.03508453816175461,
0.05482211336493492,
-0.05624471977353096,
0.003092319006100297,
-0.009616872295737267,
0.016077307984232903,
-0.007461547385901213,
-0.0030922750011086464,
-0.024380670860409737,
-0.035617779940366745,
0.04152985289692879,
-0.0006728305015712976,
-0.028494246304035187,
0.00500223133713007,
-0.0025307938922196627,
0.03568947687745094,
0.012726358138024807,
0.0059864455834031105,
0.013736332766711712,
-0.0065680695697665215,
-0.0023761498741805553,
-0.0660487487912178,
0.02766226977109909,
-0.015503999777138233,
0.02977677248418331,
0.03834841027855873,
-0.01170109212398529,
0.06040874868631363,
-0.03064611181616783,
0.0032425103709101677,
-0.03046566992998123,
-0.041351400315761566,
-0.04204581305384636,
0.017667997628450394,
0.017450083047151566,
-0.03310937061905861,
0.047297004610300064,
0.04055970162153244,
0.03922857344150543,
0.00923600047826767,
0.01207219623029232,
-0.012057080864906311,
-0.026745818555355072,
-0.009817265905439854,
-0.016280977055430412,
0.07176295667886734,
-0.01513507030904293,
-0.004165142308920622,
-0.0038244707975536585,
-0.02033218741416931,
-0.04465536028146744,
0.02121884562075138,
-0.06425130367279053,
0.025993958115577698,
0.02851000986993313,
0.0026671295054256916,
-0.013497672975063324,
0.03269600495696068,
0.011514442041516304,
-0.0316847488284111,
0.02395474538207054,
-0.028828511014580727,
-0.06507720798254013,
-0.001413669902831316,
0.02022639475762844,
0.038297343999147415,
-0.030911646783351898,
0.018702547997236252,
0.02488000877201557,
0.0460657924413681,
0.024321872740983963,
0.005957481451332569,
-0.045737460255622864,
-0.02598189003765583,
0.0187066737562418,
0.00432346947491169,
0.0027511201333254576,
0.04886283725500107,
0.030707674100995064,
-0.026499059051275253,
0.01390531100332737,
0.013341516256332397,
-0.005093153566122055,
0.007336686365306377,
-0.04908229410648346,
-0.028520124033093452,
-0.019206061959266663,
-0.017518801614642143,
0.01851566694676876,
-0.0379343144595623,
0.020469728857278824,
0.023918157443404198,
-0.02823181450366974,
-0.03503334894776344,
-0.05297548323869705,
-0.01337895542383194,
-0.004940317943692207,
-0.0008193342946469784,
-0.04760916903614998,
-0.0013582477113232017,
0.01853748969733715,
-0.050068095326423645,
-0.031380657106637955,
-0.03041694313287735,
0.014605939388275146,
-0.02272213064134121,
-0.01088656485080719,
0.037751827389001846,
0.005431875120848417,
-0.007204386871308088,
-0.037503186613321304,
0.011605575680732727,
0.040574945509433746,
-0.03676716610789299,
0.01865190826356411,
-0.010360718704760075,
-0.0365629680454731,
0.016751796007156372,
-0.01883268915116787,
-0.012528005987405777,
0.0005990018835291266,
-0.061305515468120575,
0.02351616881787777,
0.00955361407250166,
-0.011961116455495358,
-0.06399347633123398,
-0.016561711207032204,
-0.024400124326348305,
0.02373315766453743,
-0.03057972341775894,
0.016000892966985703,
0.02273043990135193,
-0.009351939894258976,
-0.05741707980632782,
-0.028864968568086624,
-0.0010366265196353197,
-0.04136909171938896,
-0.034279726445674896,
0.0017596023390069604,
0.008928932249546051,
-0.032581787556409836,
0.010261014103889465,
0.011283989064395428,
-0.016410447657108307,
0.004452458117157221,
-0.07910007238388062,
-0.07007668912410736,
-0.016311300918459892,
0.010268837213516235,
0.02915159985423088,
-0.0076822517439723015,
-0.0029885759577155113,
0.06031433492898941,
0.02102109044790268,
-0.06166964769363403,
-0.03288976475596428,
0.03248890861868858,
0.017321409657597542,
-0.03325904533267021,
0.011408621445298195,
-0.005030571948736906,
-0.011352593079209328,
0.04291313514113426,
0.01445767655968666,
0.010943591594696045,
0.024656979367136955,
0.011780197732150555,
-0.0152988750487566,
0.02246619202196598,
-0.01146332360804081,
-0.02123287320137024,
0.04351761192083359,
0.012744218111038208,
-0.0190690066665411,
-0.003219541162252426,
-0.018312497064471245,
0.022946961224079132,
-0.023104045540094376,
-0.029343847185373306,
0.06347472220659256,
0.02709653601050377,
0.0334203839302063,
-0.01779731921851635,
0.009231113828718662,
-0.02667798101902008,
-0.004971082787960768,
-0.023096932098269463,
0.028638355433940887,
0.018067672848701477,
-0.06265686452388763,
0.01691238023340702,
0.04498659074306488,
0.026330068707466125,
-0.024093035608530045,
-0.0068103233352303505,
0.01207105815410614,
-0.006757525727152824,
0.025054840371012688,
-0.05062495917081833,
-0.036979611963033676,
0.0057929884642362595,
0.032656632363796234,
0.04681449383497238,
-0.030439257621765137,
0.01189277321100235,
-0.009726145304739475,
-0.038039933890104294,
-0.016429059207439423,
-0.03007803112268448,
0.039255790412425995,
0.00954445730894804,
0.015077258460223675,
0.006677335128188133,
0.011288123205304146,
-0.039476290345191956,
-0.022613197565078735,
-0.08877017349004745,
-0.01814265549182892,
-0.012043079361319542,
0.011190877296030521,
-0.0029787556268274784,
-0.022689348086714745,
0.009087972342967987,
-0.0007064813398756087,
-0.03411587327718735,
-0.0035312799736857414,
0.016156194731593132,
-0.05551180988550186,
0.0026174644008278847,
-0.024494562298059464,
-0.04003995284438133,
-0.03125521168112755,
0.033631499856710434,
0.03450735658407211,
-0.008083024993538857,
-0.011716274544596672,
0.0015285232802852988,
-0.02351320907473564,
-0.0033037408720701933,
0.0021859442349523306,
0.024505047127604485,
0.018725669011473656,
0.05063094571232796,
0.02727728709578514,
0.06517684459686279,
-0.015260232612490654,
-0.011223461478948593,
0.008359375409781933,
0.0466451570391655,
0.01050109975039959,
0.009701195172965527,
0.01680535450577736,
-0.030508793890476227,
0.0081017492339015,
-0.01605813391506672,
0.05677324905991554,
0.010017858818173409,
-0.039723679423332214,
0.032630275934934616,
0.006801299750804901,
0.010471445508301258,
0.02401610091328621,
0.006907950155436993,
-0.013298762030899525,
-0.010309704579412937,
0.001141703105531633,
0.019818948581814766,
-0.045005206018686295,
0.01629745028913021,
-0.012961016036570072,
0.029810842126607895,
-0.0018143467605113983,
0.02716783806681633,
0.02785126306116581,
0.02479037642478943,
-0.005279906094074249,
-0.00944552756845951,
0.012921077199280262,
-0.0037636554334312677,
-0.03318646177649498,
0.013780327513813972,
-0.013884050771594048,
0.023047808557748795,
0.026411348953843117,
0.03781120851635933,
0.01795545592904091,
-0.06100333482027054,
-0.012589234858751297,
0.04722678288817406,
0.025451824069023132,
0.03401739522814751,
0.013798329047858715,
-0.01530847791582346,
-0.017618292942643166,
0.02393154986202717,
-0.014505963772535324,
0.039371076971292496,
-0.033055879175662994,
0.013905387371778488,
-0.005525873973965645,
-0.03935693949460983,
-0.0027489897329360247,
0.01115150935947895,
0.02448083646595478,
0.019237631931900978,
-0.0359346903860569,
0.023599795997142792,
0.0021178319584578276,
0.054152246564626694,
0.013973250053822994,
0.05407125875353813,
0.015414317138493061,
-0.018664708361029625,
0.025040939450263977,
0.006811793427914381,
-0.023676399141550064,
-0.06532344222068787,
0.04637189209461212,
0.019317686557769775,
-0.0073137166909873486,
0.025677962228655815,
-0.024753911420702934,
-0.043905336409807205,
0.02395847626030445,
0.023577528074383736,
-0.008432220667600632,
0.04183163121342659,
-0.02673647552728653,
0.0898788571357727,
0.009851246140897274,
0.014194183982908726,
0.05327440798282623,
0.03279129043221474,
0.015565406531095505,
-0.01340594980865717,
-0.052844952791929245,
0.05236583948135376,
-0.06277072429656982,
-0.02361263334751129,
-0.04208460450172424,
-0.0129731809720397,
-0.0033691159915179014,
0.05063335970044136,
-0.0010995102347806096,
-0.0018165841465815902,
0.00426529673859477,
-0.0024236394092440605,
-0.0033001506235450506,
0.012293512001633644,
-0.01864817924797535,
0.008332730270922184,
-0.04382433369755745,
0.010504237376153469,
-0.01572677120566368,
-0.021483711898326874,
-0.017823023721575737,
-0.004163577686995268,
0.01999060995876789,
0.05021115392446518,
-0.005290931090712547,
0.014706277288496494,
-0.03511173650622368,
0.006864081136882305,
0.003451413242146373,
-0.05092231184244156,
0.04296416416764259,
-0.010659716092050076,
0.02393033541738987,
0.023150254040956497,
-0.0569830946624279,
-0.03812900558114052,
0.011200915090739727,
0.0038497522473335266,
-0.02211882919073105,
-0.04025702178478241,
-0.028230682015419006,
0.006950758397579193,
0.013925350271165371,
-0.05271900072693825,
-0.023279743269085884,
0.011522985994815826,
0.0051778340712189674,
-0.004926249384880066,
-0.0207943357527256,
0.027599038556218147,
-0.032633163034915924,
0.016743697226047516,
-0.044452931731939316,
0.04935269057750702,
-0.05118664354085922,
-0.020734338089823723,
0.005842562764883041,
0.021835917606949806,
0.031209560111165047,
-0.00020417269843164831,
-0.03461446985602379,
0.0167088583111763,
0.02965247631072998,
0.0019392546964809299,
-0.020673777908086777,
0.03525041416287422,
-0.016462186351418495,
-0.02446863055229187,
-0.018957240507006645,
-0.043892811983823776,
-0.030544068664312363,
-0.01238424051553011,
-0.04689176008105278,
0.021318692713975906,
-0.01126242708414793,
0.02360236458480358,
0.010589751414954662,
-0.024009155109524727,
0.003293795743957162,
0.015279424376785755,
0.022424103692173958,
-0.029826093465089798,
-0.024389006197452545,
-0.050913721323013306,
0.008718096651136875,
-0.008113197050988674,
-0.010464945808053017,
0.013947470113635063,
0.030747748911380768,
0.01719670742750168,
-0.0076528796926140785,
-0.005929660517722368,
-0.0025187102146446705,
-0.025069475173950195,
-0.03312542289495468,
0.01984294317662716,
-0.008471144363284111,
-0.0009762434056028724,
-0.03306039795279503,
-0.06399542838335037,
-0.04414237290620804,
0.0184869896620512,
0.031478025019168854,
0.019039569422602654,
0.003397981869056821,
0.029360678046941757,
-0.011508086696267128,
-0.00037321209674701095,
-0.01863001100718975,
-0.02654227241873741,
0.02109977975487709,
0.01827586069703102,
0.01973690651357174,
-0.02451498620212078,
-0.020961113274097443,
0.009557129815220833,
0.024883491918444633,
-0.017633957788348198,
0.021542174741625786,
0.02692355588078499,
0.006225897930562496,
0.026546623557806015,
-0.05564669147133827,
-0.051821477711200714,
0.04872554540634155,
-0.03755691647529602,
0.016191108152270317,
0.035040438175201416,
-0.020793551579117775,
0.006997554562985897,
0.018708456307649612,
0.036339689046144485,
-0.05797884985804558,
-0.007145104464143515,
-0.04703811556100845,
0.0003774841607082635,
0.02007639966905117,
0.013452772051095963,
0.011733196675777435,
-0.03303072601556778,
0.013856794685125351,
0.024468014016747475,
0.007687219884246588,
0.007479432504624128,
-0.024822784587740898,
-0.06375705450773239,
-0.03512202575802803,
-0.05196294188499451,
0.051178980618715286,
-0.03157583996653557,
-0.014293448999524117,
0.014498849399387836,
-0.028599638491868973,
0.0653623566031456,
0.006808069068938494,
0.0495828352868557,
-0.007954947650432587,
0.0038474216125905514,
0.0017373933224007487,
0.03855091333389282,
-0.02051137574017048,
0.014533286914229393,
0.1343943476676941,
0.0699608251452446,
0.008999022655189037,
-0.025561558082699776,
-0.02545929327607155,
-0.002713962225243449,
0.03012409619987011,
-0.05117274820804596,
-0.012284956872463226,
-0.016423024237155914,
0.010503750294446945,
0.0036098682321608067,
0.03591371327638626,
-0.011406710371375084,
0.0017637943383306265,
0.04570474848151207,
-0.043547701090574265,
-0.035525254905223846,
0.02682286873459816,
0.03729303181171417,
0.00045666415826417506,
0.010772058740258217,
-0.03680143132805824,
0.018161790445446968,
-0.007441334426403046,
0.015153168700635433,
-0.009507318027317524,
0.015844663605093956,
0.036985691636800766,
0.018478013575077057,
-0.013868031091988087,
-0.026734158396720886,
-0.004975485149770975,
0.013912619091570377,
-0.014578544534742832,
0.0022057278547436,
0.0271623395383358,
-0.01946498453617096,
-0.023752130568027496,
0.030621008947491646,
0.0011791532160714269,
-0.0052343690767884254,
0.019752444699406624,
-0.0020134549122303724,
-0.03358028084039688,
-0.018692269921302795,
-0.0017442131647840142,
0.0720282644033432,
-0.043595507740974426,
-0.009367858991026878,
-0.010544768534600735,
-0.03190566226840019,
0.01955428719520569,
-0.04047606885433197,
-0.006113938055932522,
0.005213200114667416,
0.049627628177404404,
-0.0005933307111263275,
0.003769873408600688,
0.004896737169474363,
-0.0027806363068521023,
0.004812275525182486,
0.018280794844031334,
-0.03692324459552765,
-0.004386262036859989,
0.021654339507222176,
0.026958566159009933,
0.04312412068247795,
0.019431302323937416,
-0.01922043412923813,
-0.013252953067421913,
-0.01500970870256424,
-0.015382658690214157,
-0.048969533294439316,
0.05546504631638527,
0.0167529433965683,
0.070738784968853,
0.019390078261494637,
-0.02348168194293976,
0.03104085475206375,
-0.06497740745544434,
0.0033755439799278975,
0.00016964522365015,
-0.06804610788822174,
0.00915256142616272,
-0.003984081093221903,
-0.03464679792523384,
0.03836444765329361,
-0.006919490173459053,
-0.023728851228952408,
0.02334490604698658,
0.035669274628162384,
0.06971427798271179,
-0.03549540042877197,
-0.01052878238260746,
0.013066913932561874,
-0.012330312281847,
0.0031005109194666147,
-0.049511320888996124,
0.013699151575565338,
0.01293555460870266,
0.018489638343453407,
0.00863772351294756,
0.06724799424409866,
-0.035203639417886734,
-0.0234074704349041,
0.038052938878536224,
-0.012277146801352501,
0.016364887356758118,
0.03356359526515007,
0.04952877014875412,
-0.06382825970649719,
-0.08154575526714325,
-0.01787881925702095,
0.000708926294464618,
0.010842042043805122,
-0.008000005036592484,
-0.029104139655828476,
-0.019972659647464752,
0.01654115691781044,
0.0034596524201333523,
0.022891173139214516,
-0.02444450743496418,
-0.003932880703359842,
0.028388289734721184,
-0.012736780568957329,
-0.01731295883655548,
-0.017931373789906502,
0.009310955181717873,
-0.01200563833117485,
-0.03401924669742584,
0.04799864441156387,
0.045426592230796814,
-0.002062134677544236,
-0.02440095879137516,
-0.013296843506395817,
0.03418147563934326,
0.014057786203920841,
0.011179866269230843,
0.006830765400081873,
0.033368680626153946,
-0.05072621628642082,
-0.01292219664901495,
0.016109004616737366,
-0.025044173002243042,
0.04126027226448059,
0.053751878440380096,
-0.0266526248306036,
-0.022058449685573578,
0.04068993031978607,
-0.016665220260620117,
0.015362335368990898,
0.008450955152511597,
-0.01648663729429245,
0.016009939834475517,
0.0037316130474209785,
0.0034136769827455282,
0.003403093433007598,
-0.01170468982309103,
0.013136952184140682,
0.029691185802221298,
0.035144951194524765,
0.002218261593952775,
0.02319352701306343,
-0.017797643318772316,
0.006703189108520746,
0.016966605558991432,
-0.005307196639478207,
-0.012222543358802795,
0.03452753648161888,
-0.04786890000104904,
0.031373415142297745,
0.056514911353588104,
0.01865617372095585,
-0.13791179656982422,
-0.026018617674708366,
0.005234412383288145,
0.042095817625522614,
0.024973953142762184,
-0.03886054456233978,
0.003155000973492861,
0.018390106037259102,
-0.11450345814228058,
0.05922281742095947,
-0.004645519889891148,
-0.02958916872739792,
-0.026266273111104965,
0.009122384712100029,
-0.055244773626327515,
0.022623151540756226,
0.014674563892185688,
0.06153567135334015,
-0.004967986606061459,
0.005982877686619759,
-0.026130858808755875,
-0.026218153536319733,
-0.027558820322155952,
0.04622415453195572,
-0.030331114307045937,
-0.021972108632326126,
0.060765497386455536,
-0.01489229779690504,
-0.01774044707417488,
-0.0018800714751705527,
-0.01784363016486168,
0.01273707952350378,
-0.025747569277882576,
0.030322903767228127,
0.02625809796154499,
0.045576050877571106,
0.0045955851674079895,
-0.02678176388144493,
-0.021221373230218887,
-0.002899607876315713,
0.04485728591680527,
0.011862442828714848,
-0.0014512897469103336,
-0.018768394365906715,
0.04265616089105606,
-0.044473081827163696,
-0.05074329674243927,
0.02246057614684105,
0.03006901405751705,
0.01479695551097393,
0.02385997213423252,
-0.011888805776834488,
-0.02332671545445919,
-0.01167728565633297,
0.0006909765070304275,
-0.059049006551504135,
-0.044450271874666214,
-0.029440000653266907,
0.020607272163033485,
-0.01705504208803177,
0.008659986779093742,
-0.027183236554265022,
-0.053765762597322464,
0.07317449897527695,
-0.01650683581829071,
-0.004109509754925966,
-0.06984512507915497,
-0.026225650683045387,
0.020984485745429993,
0.0038575141225010157,
0.02061956748366356,
-0.029896557331085205,
-0.05563213303685188,
0.00010031517740571871,
-0.033650875091552734,
0.05267694219946861,
-0.011796454899013042,
-0.019955949857831,
-0.03483303263783455,
-0.07887230813503265,
0.02669123373925686,
0.039192549884319305,
0.027188275009393692,
-0.03367743641138077,
-0.0029010027647018433,
-0.00004319081926951185,
0.015644077211618423,
0.0628957599401474,
-0.007418990600854158,
-0.014505571685731411,
-0.016101041808724403,
-0.007974454201757908,
0.017650747671723366,
-0.01592155359685421,
0.017767325043678284,
-0.020684683695435524,
-0.021375257521867752,
-0.020744429901242256,
-0.017541727051138878,
0.004530006088316441,
-0.011809433810412884,
0.0442391075193882,
0.006418800447136164,
-0.0074899871833622456,
0.008890758268535137,
-0.03871528059244156,
0.07915017008781433,
0.02282623015344143,
0.006024407688528299,
0.036922603845596313,
0.00006264526018640026,
0.00765268737450242,
0.01207403838634491,
-0.023131638765335083,
-0.018934890627861023,
-0.030008522793650627,
-0.006361434701830149,
0.0017181533621624112,
-0.003653021529316902,
0.024729331955313683,
0.03513874486088753,
-0.018574321642518044,
-0.004273609723895788,
0.08408170193433762,
0.008906135335564613,
-0.00846642255783081,
0.06742171943187714,
0.009798766113817692,
0.024084310978651047,
-0.012397495098412037,
0.04528892785310745,
0.029140939936041832,
-0.007159552536904812,
0.024913176894187927,
0.02133893594145775,
0.007544502150267363,
-0.0035041929222643375,
0.04410604387521744,
0.05902489647269249,
-0.02550435997545719,
-0.025042813271284103,
0.027309104800224304,
0.05264037474989891,
-0.039978161454200745,
-0.016667937859892845,
0.027661003172397614,
0.01572314091026783,
-0.036282360553741455,
0.0036173765547573566,
-0.014814434573054314,
0.08408733457326889,
0.005053728818893433,
-0.002762114629149437,
-0.016527079045772552,
0.03082592412829399,
0.001625837292522192,
0.01561372447758913,
0.02559187449514866,
0.06557990610599518,
-0.019645798951387405,
0.006501970812678337,
-0.0346674807369709,
0.0029267005156725645,
0.016707750037312508,
-0.08117107301950455,
-0.003414618782699108,
-0.010142800398170948,
0.020950723439455032,
0.008769369684159756,
0.004944921471178532,
0.006131536792963743,
-0.029223497956991196,
0.03400096669793129,
0.014832626096904278,
0.019310805946588516,
-0.010415902361273766,
0.014904983341693878,
-0.020230574533343315,
0.07893354445695877,
-0.01517878845334053,
0.0014569564955309033,
-0.025145050138235092,
0.0006740093231201172,
0.0018433267250657082,
0.017863942310214043
] |
<p>Let's consider an electron-positron pair with total spin equal to zero. When it annihilates it can not emit only one photon because it would have zero momentum and nonzero energy. The pair emits two photons with opposite momenta but on the momentum-energy plain it looks like the particle goes through a forbidden state (red path on the picture below).</p>
<p>The first question is: How is it possible? I suppose this is because of the energy-time uncertainty. The annihilation process is instant (at least looks like on Feynman diagram) and the energy of the intermediate state is not determined. Is it correct?</p>
<p>If we can go through any forbidden state, why doesn't the annihilation go the blue path? This is the second question.</p>
<p>And the third question: Why do electron-hole pairs in semiconductors always emit photons with energy equal to the band gap? Is it just because the interaction with one photon has higher probability or there is a fundamental difference?</p>
<p><img src="http://i.stack.imgur.com/XtNu2.png" alt="enter image description here"></p> | 1,556 | [
-0.02106305956840515,
-0.03410661593079567,
0.015388733707368374,
-0.03877951577305794,
0.002795102773234248,
-0.006059554405510426,
-0.035592541098594666,
-0.008144034072756767,
-0.007946515455842018,
-0.004543180111795664,
0.015671860426664352,
0.02693040855228901,
0.02245323359966278,
0.011411299929022789,
-0.013520815409719944,
0.013665292412042618,
-0.007762230932712555,
-0.019199252128601074,
-0.046218063682317734,
-0.02246089093387127,
-0.008227200247347355,
0.01072501577436924,
-0.02080344781279564,
-0.00864467304199934,
-0.03411896526813507,
0.014915641397237778,
0.03288782387971878,
0.04959597811102867,
0.012503175996243954,
0.05520264431834221,
-0.020830990746617317,
-0.03363894671201706,
0.005811236798763275,
-0.01830415241420269,
0.027437325567007065,
0.000028204896807437763,
-0.02695106528699398,
-0.05734401196241379,
-0.006215832196176052,
0.022771380841732025,
-0.03052395209670067,
-0.00011947246093768626,
-0.02513956092298031,
0.015388663858175278,
-0.027446022257208824,
0.0023294761776924133,
0.014901424758136272,
0.02247106097638607,
0.06307029724121094,
-0.06509320437908173,
0.038926366716623306,
-0.005120051559060812,
0.0542459562420845,
-0.02689913474023342,
0.02943107672035694,
-0.012065351009368896,
0.06929387152194977,
0.09473917633295059,
-0.011680619791150093,
-0.03441528230905533,
-0.012677617371082306,
-0.022019507363438606,
-0.019530659541487694,
-0.02323232777416706,
-0.035878777503967285,
0.0011833604658022523,
0.043680768460035324,
-0.016367437317967415,
0.011180299334228039,
-0.016802800819277763,
0.013798669911921024,
-0.01620681770145893,
0.026346823200583458,
-0.0021878827828913927,
-0.012752167880535126,
-0.04205113276839256,
0.06820819526910782,
0.030508922412991524,
0.028109339997172356,
0.06005120649933815,
-0.009523320011794567,
0.0264911986887455,
-0.013453361578285694,
0.016597112640738487,
0.0373125895857811,
0.006095274351537228,
0.0760493129491806,
0.016405880451202393,
-0.007463250309228897,
0.0346430167555809,
-0.0056157708168029785,
0.04435739293694496,
0.025547422468662262,
-0.0017433894099667668,
-0.04094218090176582,
0.035907816141843796,
0.0045395223423838615,
0.06697787344455719,
-0.0007970916922204196,
-0.025488991290330887,
0.016923466697335243,
-0.017674429342150688,
0.03394988179206848,
0.0444822683930397,
-0.013157173059880733,
-0.028276842087507248,
-0.023456741124391556,
0.04128958657383919,
-0.016846565529704094,
0.004384618252515793,
-0.0007311466033570468,
0.025753818452358246,
-0.013000836595892906,
-0.02856377512216568,
0.014512874186038971,
-0.011011235415935516,
0.0028212182223796844,
-0.02725931815803051,
0.060697928071022034,
0.05792717635631561,
0.004370808135718107,
-0.013283261097967625,
0.02393690124154091,
-0.0391065888106823,
-0.08448327332735062,
0.0028408083599060774,
0.06155315414071083,
-0.000619000697042793,
-0.04443728178739548,
-0.003987540025264025,
-0.010535646229982376,
-0.005664716009050608,
0.011181565001606941,
-0.01956828124821186,
0.017440546303987503,
-0.02772192656993866,
-0.11167420446872711,
-0.06189759075641632,
0.03852980211377144,
-0.0327182412147522,
-0.023450549691915512,
-0.06226449832320213,
-0.007943063974380493,
0.03641800582408905,
0.080072782933712,
-0.05000954121351242,
-0.0020392935257405043,
-0.02649134024977684,
0.01657613180577755,
0.013859652914106846,
0.012454384006559849,
-0.00226596649736166,
0.017640279605984688,
-0.022918522357940674,
0.01111510582268238,
-0.07064394652843475,
0.06733063608407974,
0.02655944973230362,
0.029402052983641624,
-0.011217432096600533,
0.057068344205617905,
-0.016296695917844772,
-0.0005656838184222579,
0.01005020271986723,
-0.01450604759156704,
-0.02513783983886242,
0.10693249851465225,
0.04109208658337593,
0.005369665566831827,
0.030665431171655655,
-0.0034948873799294233,
0.009426956064999104,
0.01346173882484436,
0.017158154398202896,
0.027870843186974525,
-0.013930218294262886,
-0.031244918704032898,
-0.04740755259990692,
0.018961889669299126,
-0.03105970285832882,
-0.04040209576487541,
-0.036649834364652634,
-0.03443087264895439,
0.02628261037170887,
0.01670626923441887,
0.03211064636707306,
-0.01559336669743061,
-0.007643398363143206,
-0.012304904870688915,
-0.040651820600032806,
-0.028988340869545937,
-0.07424390316009521,
-0.0032156952656805515,
0.05214960128068924,
-0.01945100724697113,
0.00403157714754343,
-0.002128387801349163,
0.013455604203045368,
-0.02381318435072899,
-0.016996946185827255,
-0.027036691084504128,
0.0032832520082592964,
-0.0034801270812749863,
0.0020291635300964117,
0.02117397077381611,
0.054278261959552765,
0.052461832761764526,
0.005399939604103565,
0.0262068472802639,
-0.014606655575335026,
-0.06176212430000305,
0.025083068758249283,
-0.012243766337633133,
0.032726410776376724,
0.03427967056632042,
0.04523150995373726,
0.014276166446506977,
0.008112582378089428,
-0.01751651242375374,
-0.0019347351044416428,
0.008986979722976685,
0.055721841752529144,
0.03173314034938812,
-0.02202145755290985,
-0.012459587305784225,
0.020142974331974983,
0.017482083290815353,
0.011944274418056011,
-0.03384101018309593,
-0.04831201583147049,
-0.019722390919923782,
-0.002530864207074046,
-0.013415874913334846,
0.024356720969080925,
0.003556320443749428,
0.03325977176427841,
-0.015377037227153778,
0.01893235743045807,
0.009404684416949749,
0.05453461408615112,
-0.03475575894117355,
-0.012878907844424248,
0.009777978993952274,
0.003564688377082348,
-0.02133738435804844,
0.0452222116291523,
0.0444742776453495,
-0.013870521448552608,
-0.007699275854974985,
-0.0005718724569305778,
-0.007481948938220739,
0.031704843044281006,
-0.0013954245951026678,
-0.009241150692105293,
-0.0015673870220780373,
-0.051538098603487015,
0.016330255195498466,
-0.006117657758295536,
0.0014468467561528087,
0.0011818690691143274,
-0.02787742204964161,
-0.0018385756993666291,
-0.029020370915532112,
-0.0324145145714283,
-0.02011529542505741,
-0.02591872401535511,
0.004267578478902578,
-0.012544160708785057,
0.0136209512129426,
-0.0355062410235405,
0.036367010325193405,
-0.027175432071089745,
-0.02225865237414837,
-0.011166874319314957,
-0.005102543625980616,
0.06874106079339981,
-0.0009123571217060089,
0.05349927395582199,
-0.04528726637363434,
-0.040662627667188644,
-0.0006635823519900441,
-0.02673349715769291,
0.039649877697229385,
0.04563421756029129,
-0.03871139511466026,
0.048599787056446075,
-0.05106278136372566,
-0.024402350187301636,
0.03109589032828808,
-0.006273893639445305,
0.022215424105525017,
0.024843614548444748,
-0.03082401119172573,
-0.04334578663110733,
-0.01495403703302145,
-0.027130933478474617,
-0.025373157113790512,
-0.0188069436699152,
-0.009423838928341866,
0.0432676300406456,
-0.01950802654027939,
-0.061653975397348404,
0.009509703144431114,
-0.0337291844189167,
-0.03368518501520157,
0.0030506604816764593,
0.015628574416041374,
0.04718044027686119,
-0.01989082619547844,
0.01353287510573864,
0.03924255445599556,
-0.034074921160936356,
-0.005456497427076101,
-0.0658358559012413,
-0.03468824177980423,
0.015891551971435547,
0.00971746165305376,
-0.0056181554682552814,
-0.04531298950314522,
-0.037326645106077194,
0.07492358982563019,
0.026902560144662857,
0.006149706430733204,
-0.010671860538423061,
-0.01704774796962738,
-0.04735865071415901,
-0.03696228563785553,
0.017864735797047615,
0.04585590958595276,
0.0022290623746812344,
0.02996792085468769,
-0.004206882324069738,
0.051259174942970276,
0.00423803273588419,
0.017310932278633118,
0.008677316829562187,
0.004072524141520262,
0.026277828961610794,
-0.01350532379001379,
0.02773924358189106,
0.0286304522305727,
-0.034629303961992264,
0.009312114678323269,
-0.0023475470952689648,
0.02352663315832615,
-0.01682830974459648,
-0.05241433531045914,
0.05763913691043854,
-0.003102491609752178,
0.013059805147349834,
-0.04427795112133026,
0.044783033430576324,
0.028597647324204445,
-0.015435305424034595,
0.021597588434815407,
0.006349699571728706,
0.03327278792858124,
-0.028346918523311615,
0.016556695103645325,
0.053909897804260254,
0.011383934877812862,
-0.009876820258796215,
-0.04219796881079674,
0.02976355329155922,
0.00039650333928875625,
0.016601944342255592,
-0.029081523418426514,
-0.018630439415574074,
0.050848640501499176,
0.026010720059275627,
0.05414779856801033,
-0.008352530188858509,
-0.01278014574199915,
-0.0591447576880455,
-0.04196334630250931,
0.007593903690576553,
0.011395365931093693,
0.06221790984272957,
0.021966194733977318,
0.06795546412467957,
0.02179916761815548,
0.01677042432129383,
-0.023036658763885498,
-0.014000927098095417,
-0.11737297475337982,
0.012259108014404774,
0.009980890899896622,
-0.017501087859272957,
-0.01685958355665207,
-0.0033774320036172867,
-0.0008347939583472908,
-0.03740619122982025,
-0.037056975066661835,
-0.02226412110030651,
0.006987977772951126,
-0.056152742356061935,
0.024046801030635834,
-0.07083544135093689,
-0.04967888072133064,
-0.03320299834012985,
0.02788451500236988,
0.03386031836271286,
-0.020397650077939034,
-0.018897248432040215,
0.010061395354568958,
-0.04615132510662079,
0.04824957251548767,
-0.024590520188212395,
-0.0022831582464277744,
0.008349817246198654,
0.048150982707738876,
0.0651366263628006,
0.010735408402979374,
-0.0018073910614475608,
-0.02074705995619297,
0.019377348944544792,
0.04854155704379082,
0.023230837658047676,
0.03173026069998741,
-0.010012885555624962,
0.0024386150762438774,
-0.01666368916630745,
-0.0021000218112021685,
0.05368253216147423,
-0.04716198518872261,
0.037135858088731766,
0.005977094639092684,
0.028917519375681877,
-0.004887595772743225,
0.032414089888334274,
0.03811430558562279,
-0.0035498731303960085,
0.006880974862724543,
-0.029317399486899376,
-0.009158169850707054,
-0.02239249087870121,
-0.01302497461438179,
0.003927647136151791,
0.018394356593489647,
-0.02964295633137226,
-0.00021182309137657285,
0.04626046493649483,
0.024649489670991898,
-0.013736335560679436,
-0.016764936968684196,
-0.00641795014962554,
0.004573557525873184,
0.022762686014175415,
0.015862835571169853,
-0.023284833878278732,
0.003627968253567815,
0.05147182196378708,
-0.002028909046202898,
0.01553447637706995,
-0.027080945670604706,
-0.024224819615483284,
0.03682569041848183,
0.05583488568663597,
0.015065656043589115,
-0.04544133320450783,
-0.04483910650014877,
0.013885811902582645,
0.0138266421854496,
-0.02704768441617489,
0.023586561903357506,
-0.001808274770155549,
-0.0223636943846941,
-0.04114162549376488,
-0.03347976878285408,
-0.0023563983850181103,
0.029651395976543427,
-0.004629725124686956,
-0.00573170930147171,
-0.021900467574596405,
-0.03326889127492905,
-0.009593198075890541,
0.020872140303254128,
0.031915146857500076,
0.06111650913953781,
-0.03731962665915489,
0.013080610893666744,
0.04626038670539856,
0.010331735946238041,
0.0051316022872924805,
-0.14409612119197845,
-0.010648814029991627,
0.016895800828933716,
-0.007369452156126499,
0.08384610712528229,
-0.052075762301683426,
-0.08307390660047531,
-0.005037268623709679,
-0.0036040355917066336,
-0.023007720708847046,
0.002084603998810053,
-0.04915519431233406,
0.024509279057383537,
0.017248043790459633,
-0.03065231256186962,
0.03986959904432297,
0.03119596280157566,
-0.012078084982931614,
0.008188729174435139,
-0.030331522226333618,
0.04615463316440582,
-0.018240604549646378,
0.023090271279215813,
-0.05621246621012688,
0.038711775094270706,
-0.0014048264129087329,
0.04659273475408554,
-0.014247906394302845,
0.0034012175165116787,
0.014816347509622574,
-0.03603328391909599,
-0.006889491807669401,
0.01740114577114582,
-0.01346075814217329,
0.010751310735940933,
-0.048263926059007645,
-0.0017123876605182886,
-0.04461553692817688,
-0.03816266730427742,
0.008755241520702839,
-0.004660434555262327,
0.008965258486568928,
0.02876668982207775,
0.022425547242164612,
0.060031358152627945,
-0.04078938439488411,
0.007486328948289156,
0.0022669262252748013,
-0.04087018221616745,
0.026921547949314117,
0.005624666810035706,
0.014962929300963879,
0.005703290458768606,
-0.003081205300986767,
-0.046229057013988495,
0.007850048132240772,
-0.005707448348402977,
0.03502057492733002,
-0.03477764129638672,
0.037327345460653305,
0.03400387987494469,
-0.02216155268251896,
-0.08395776152610779,
-0.03577357530593872,
0.023375971242785454,
0.016652865335345268,
-0.047025080770254135,
-0.006023097783327103,
-0.004704995080828667,
-0.004911996889859438,
-0.02079625613987446,
0.038147054612636566,
0.004900653380900621,
-0.03222087025642395,
-0.025173651054501534,
-0.003807628760114312,
0.005101802293211222,
0.028138374909758568,
-0.0008228596416302025,
-0.01279438566416502,
-0.016501368954777718,
-0.0008422136888839304,
-0.008065406233072281,
0.029544712975621223,
0.020014688372612,
0.016727501526474953,
-0.0772276446223259,
-0.012756714597344398,
0.024586234241724014,
0.03780042752623558,
-0.013310219161212444,
0.00986019242554903,
0.040179092437028885,
0.05201869457960129,
0.0013398261507973075,
0.015389732085168362,
0.021220754832029343,
-0.00144572660792619,
0.041455499827861786,
0.02690795250236988,
-0.004123750142753124,
-0.007266208995133638,
-0.05380292981863022,
-0.002787315519526601,
0.0026749884709715843,
0.028893450275063515,
-0.003883939003571868,
0.03962920978665352,
-0.019266581162810326,
-0.02031964436173439,
0.011488375253975391,
-0.018785705789923668,
0.021601498126983643,
-0.031158175319433212,
-0.000032465999538544565,
-0.007205507718026638,
0.025279086083173752,
-0.01657702587544918,
-0.04007263481616974,
-0.05951917916536331,
-0.00509461248293519,
0.043398305773735046,
-0.034165505319833755,
0.04789673537015915,
0.011022865772247314,
-0.0024209211114794016,
-0.011300127021968365,
-0.030344737693667412,
-0.025726132094860077,
-0.028462661430239677,
-0.005472738761454821,
0.01828717067837715,
-0.0032828522380441427,
-0.006119279190897942,
0.0438263975083828,
0.06249760463833809,
0.004660819657146931,
0.047286491841077805,
0.045666929334402084,
0.0024402248673141003,
0.03878404200077057,
0.005419683177024126,
-0.056137699633836746,
0.02462298981845379,
-0.04632066190242767,
0.030712857842445374,
0.03565992787480354,
-0.04565472528338432,
0.038471147418022156,
-0.002408666303381324,
0.00391171220690012,
-0.022662412375211716,
-0.025943433865904808,
-0.05136846750974655,
0.041554372757673264,
-0.03816962242126465,
0.02138550393283367,
-0.009697450324892998,
0.011165454052388668,
0.005384769756346941,
0.015088570304214954,
0.022613847628235817,
-0.012647422030568123,
-0.046083543449640274,
-0.061745546758174896,
-0.03571849688887596,
-0.0043421839363873005,
0.039942558854818344,
-0.024240216240286827,
-0.028614399954676628,
0.025659335777163506,
-0.04511738196015358,
0.006608862429857254,
-0.006577583029866219,
0.03757906332612038,
-0.011164210736751556,
0.005336325149983168,
0.009070180356502533,
0.0074531035497784615,
-0.009180638939142227,
0.03997676447033882,
0.1355743408203125,
0.031501688063144684,
0.01256921049207449,
-0.07422789186239243,
-0.025582406669855118,
-0.016042426228523254,
0.02668008767068386,
-0.007736906874924898,
0.05132430046796799,
0.0031153832096606493,
0.006067089736461639,
-0.007529484573751688,
0.021367758512496948,
0.028383871540427208,
-0.01668311469256878,
0.026324501261115074,
-0.04184824600815773,
-0.026617810130119324,
0.0034891413524746895,
0.02891596034169197,
0.017250459641218185,
0.012555962428450584,
-0.01640700362622738,
0.0014804246602579951,
-0.029192576184868813,
0.03817368671298027,
0.00661488575860858,
-0.03663145378232002,
0.024355169385671616,
0.009944038465619087,
-0.022251131013035774,
-0.008047385141253471,
0.03661532700061798,
0.0005571713554672897,
-0.023908846080303192,
0.012271741405129433,
0.012804645113646984,
-0.01891455054283142,
0.013899268582463264,
0.02359902113676071,
0.031906578689813614,
-0.032842524349689484,
0.03788180276751518,
0.0011560486163944006,
-0.05101753771305084,
-0.028311440721154213,
0.008395170792937279,
0.0674537718296051,
-0.01569691114127636,
-0.009663752280175686,
0.005854048766195774,
-0.023365527391433716,
0.022758789360523224,
-0.012515046633780003,
-0.019880298525094986,
-0.02884257398545742,
0.014347170479595661,
0.005097521003335714,
0.004148924257606268,
0.015911489725112915,
-0.02589089423418045,
0.011890276335179806,
0.016895009204745293,
-0.010821943171322346,
0.005702609661966562,
-0.014035736210644245,
-0.005471636075526476,
0.05504642799496651,
-0.026533259078860283,
-0.010803998447954655,
0.00945048127323389,
-0.04626878350973129,
-0.01967543177306652,
-0.023623503744602203,
0.06287861615419388,
0.0019320077262818813,
0.02195321023464203,
0.034526750445365906,
-0.007154886145144701,
0.005851874127984047,
-0.05835815519094467,
-0.007728294935077429,
-0.013234229758381844,
-0.02762758359313011,
-0.007832871749997139,
0.011005637235939503,
0.017516300082206726,
0.018345970660448074,
-0.023154282942414284,
0.0012266740668565035,
0.02407805249094963,
0.01752539537847042,
-0.0015637825708836317,
-0.05604158714413643,
-0.023552322760224342,
-0.0004979444784112275,
-0.006254540756344795,
0.011061549186706543,
-0.014804043807089329,
0.02265351638197899,
0.011228019371628761,
0.03201265260577202,
0.003788719419389963,
0.018561922013759613,
-0.004092209506779909,
-0.009640109725296497,
0.0282916110008955,
-0.01547246053814888,
-0.010212737135589123,
0.013527756556868553,
0.03570689633488655,
-0.00820922665297985,
-0.0033540786243975163,
-0.012628771364688873,
-0.012761108577251434,
-0.007227691356092691,
0.020161055028438568,
-0.026000360026955605,
-0.008439951576292515,
-0.0036931470967829227,
0.027975643053650856,
-0.012658351100981236,
0.0020959004759788513,
-0.02783580869436264,
0.029763909056782722,
0.013485708273947239,
-0.012186200357973576,
-0.017768332734704018,
0.04881653934717178,
-0.0019361841259524226,
-0.047360461205244064,
0.0028960525523871183,
0.062261246144771576,
0.012904706411063671,
0.007062098942697048,
0.03250680863857269,
-0.010019966401159763,
0.06510782241821289,
0.012727923691272736,
0.005276234354823828,
0.051225725561380386,
-0.028240405023097992,
-0.059722259640693665,
0.013532162643969059,
0.033404551446437836,
0.042779676616191864,
0.01723305508494377,
-0.05916961655020714,
-0.019667070358991623,
0.07220429927110672,
-0.015387451276183128,
-0.028093907982110977,
-0.00956941582262516,
-0.035593852400779724,
-0.02917107194662094,
-0.009019266813993454,
-0.016267064958810806,
0.016892608255147934,
-0.011994498781859875,
0.013816112652420998,
-0.008727646432816982,
0.005203383043408394,
0.0038207892794162035,
-0.05132526904344559,
0.0013338291319087148,
0.049932293593883514,
0.02105681598186493,
-0.00044656245154328644,
0.009129559621214867,
0.042406123131513596,
0.023748885840177536,
0.05846225842833519,
0.017664628103375435,
0.016044456511735916,
-0.08846145868301392,
-0.019151069223880768,
-0.020602528005838394,
-0.0032566282898187637,
-0.012003963813185692,
-0.017405549064278603,
0.026310032233595848,
0.02850380912423134,
-0.08216062933206558,
0.03613749518990517,
-0.01836893893778324,
-0.036103036254644394,
-0.04535790905356407,
0.016318228095769882,
-0.04789964109659195,
0.029166556894779205,
0.013567427173256874,
0.035002708435058594,
0.010192596353590488,
0.010320917703211308,
-0.021350916475057602,
-0.01584959588944912,
-0.06478701531887054,
0.022718027234077454,
-0.014978757128119469,
0.003926166798919439,
0.055531878024339676,
-0.03659844025969505,
0.028648944571614265,
0.009851327165961266,
-0.04453285411000252,
-0.042094625532627106,
-0.018828967586159706,
0.006406750995665789,
-0.007479094434529543,
0.022960495203733444,
0.028938133269548416,
0.015703560784459114,
0.0009526658104732633,
-0.017089074477553368,
0.0047555966302752495,
0.02360493317246437,
0.027503764256834984,
0.017177674919366837,
0.022076070308685303,
-0.00032829525298438966,
-0.024372339248657227,
0.04507285729050636,
0.01638059876859188,
-0.03793775662779808,
0.02510211616754532,
0.054226044565439224,
-0.005852827336639166,
-0.03880001977086067,
0.021271657198667526,
-0.07753662765026093,
-0.01998600922524929,
-0.00578733067959547,
0.035920631140470505,
0.04997457191348076,
0.022899750620126724,
-0.030918041244149208,
-0.028293561190366745,
0.03314032033085823,
-0.0013263782020658255,
0.011561771854758263,
-0.015945181250572205,
-0.007099789101630449,
0.028133440762758255,
0.01252054888755083,
0.010151504538953304,
-0.04208385944366455,
-0.037369970232248306,
0.02614508382976055,
-0.010935191996395588,
0.02791690081357956,
-0.015202033333480358,
-0.06307726353406906,
-0.035866983234882355,
-0.05734844505786896,
0.044183142483234406,
-0.00894230417907238,
0.033903833478689194,
-0.05194639414548874,
-0.019540198147296906,
0.01957240328192711,
0.03976238891482353,
0.05868949741125107,
0.006263307761400938,
-0.0335380882024765,
0.022806715220212936,
-0.00801787432283163,
0.030672775581479073,
0.0010820823954418302,
-0.00007087834092089906,
-0.024542566388845444,
-0.023288544267416,
0.002558525186032057,
0.03938639536499977,
-0.04131198674440384,
0.04817298427224159,
0.011041692458093166,
-0.009542078711092472,
0.016363020986318588,
0.022728320211172104,
-0.038207609206438065,
0.075118787586689,
-0.011108851060271263,
0.002499030437320471,
0.043016090989112854,
0.0008125733002088964,
0.02379232831299305,
0.023137254640460014,
-0.006514186505228281,
-0.05257401987910271,
0.018685679882764816,
-0.012242121621966362,
-0.023358900099992752,
-0.009403734467923641,
-0.01862548477947712,
0.054754260927438736,
-0.06257409602403641,
0.004969651345163584,
0.032971885055303574,
-0.02385755255818367,
0.01778983883559704,
0.060361552983522415,
0.014720735140144825,
0.04608197137713432,
-0.005900549236685038,
0.021739380434155464,
-0.002711394801735878,
0.009699494577944279,
-0.016131658107042313,
0.00683556916192174,
0.009239898063242435,
0.017103884369134903,
0.015285610221326351,
0.010890781879425049,
-0.01598394475877285,
-0.009893468581140041,
-0.0060033309273421764,
0.03491677716374397,
-0.006148467306047678,
-0.005596168804913759,
0.046888869255781174,
0.008000651374459267,
-0.014205191284418106,
-0.02000504359602928,
-0.00893024168908596,
0.09817677736282349,
-0.029118595644831657,
0.0297527015209198,
-0.002733299508690834,
0.029919316992163658,
-0.006118496414273977,
0.0014140373095870018,
0.008870191872119904,
0.05405430123209953,
0.01451831590384245,
-0.0340738520026207,
-0.029567962512373924,
0.028241079300642014,
0.029988760128617287,
-0.06599259376525879,
0.012040551751852036,
0.018603963777422905,
-0.031025275588035583,
-0.01984759420156479,
-0.02488945983350277,
-0.012652892619371414,
-0.014730611816048622,
0.02922418713569641,
0.02543323114514351,
0.011586593464016914,
-0.012714668177068233,
-0.011239086277782917,
-0.024886608123779297,
0.035501934587955475,
-0.058617863804101944,
-0.0022649518214166164,
-0.02046012133359909,
0.017673712223768234,
-0.06018158048391342,
-0.02092602849006653
] |
<p><img src="http://i.stack.imgur.com/v7mfP.png" alt="enter image description here"></p>
<p>The question asked was "what should be the acceleration such that the pressure at both the points marked by thick dots be equal? the vessel is <strong>open</strong> and cubic with side 5m?" </p>
<p>Initially i considered the diagram to be resembling the figure B where $$\tan(\theta)=a/g$$
but then i realized since the both points are the midpoints of the respective sides, the height of the liquid above the lower point must be half of the height above the point on the side. I took the diagram then to resemble D. Then i got the answer as $a=2g$. Is this CORRECT?<br>
<strong>If this had been a closed vessel what would the answer have been?</strong> Figure C That is my question.</p> | 1,557 | [
-0.015311473049223423,
0.007771844044327736,
-0.036328352987766266,
0.007976900786161423,
0.04893580079078674,
0.00023842918744776398,
-0.036156006157398224,
-0.01877211406826973,
0.01266633253544569,
0.01723862998187542,
0.06206917762756348,
0.019029513001441956,
0.06371396034955978,
0.011769725941121578,
0.026737021282315254,
0.027454117313027382,
0.00921823363751173,
-0.02111174166202545,
0.025660337880253792,
-0.0072266412898898125,
-0.008015359751880169,
0.007971353828907013,
-0.03630930930376053,
-0.036714766174554825,
-0.011442751623690128,
0.035418760031461716,
0.034756191074848175,
-0.00530911423265934,
-0.018227621912956238,
0.05379520356655121,
-0.013896435499191284,
-0.03932543843984604,
0.0011644851183518767,
0.016256380826234818,
0.01916114054620266,
0.014518831856548786,
-0.026981892064213753,
-0.012202819809317589,
-0.01212127972394228,
0.046281713992357254,
-0.0021250031422823668,
-0.03130059689283371,
0.003644327400252223,
0.029330294579267502,
-0.022894686087965965,
-0.009192068129777908,
0.007411228027194738,
-0.018185459077358246,
0.04319814592599869,
-0.0524459183216095,
0.02614251710474491,
-0.021778017282485962,
0.024654649198055267,
0.06173713877797127,
-0.02745676040649414,
-0.0032314658164978027,
0.04320589825510979,
0.05001732334494591,
-0.014358490705490112,
-0.04321851581335068,
0.031932730227708817,
0.013911556452512741,
-0.019834863021969795,
-0.002616815036162734,
-0.03563217446208,
-0.00848042219877243,
-0.029410408809781075,
-0.012826529331505299,
-0.007098851725459099,
0.011661511845886707,
-0.0173486340790987,
0.020785614848136902,
0.03929673135280609,
-0.018983973190188408,
0.0131594343110919,
-0.02754494547843933,
0.024633917957544327,
0.024266844615340233,
0.029118679463863373,
0.030451610684394836,
-0.012199431657791138,
0.020418934524059296,
0.06299765408039093,
0.0429796427488327,
-0.0014432132011279464,
0.030470628291368484,
0.04891284927725792,
0.029238231480121613,
-0.0064700511284172535,
0.03301228582859039,
-0.009287736378610134,
0.03887110948562622,
-0.015612906776368618,
-0.022857973352074623,
-0.003097412409260869,
-0.023738685995340347,
-0.019938286393880844,
0.03301570937037468,
0.02799484133720398,
-0.009098189882934093,
0.00775110675022006,
-0.03747006878256798,
0.00827760063111782,
0.09389415383338928,
0.02943449653685093,
-0.005669467616826296,
-0.03355029597878456,
-0.022762887179851532,
-0.001417094492353499,
-0.027007753029465675,
-0.021200604736804962,
0.016080761328339577,
0.0013461256166920066,
-0.03492475301027298,
-0.06136079877614975,
-0.00006645309622399509,
-0.00006380100967362523,
-0.001970265293493867,
0.0438377745449543,
-0.026345660910010338,
0.03866703063249588,
-0.00904031004756689,
0.04107358679175377,
-0.007159342058002949,
-0.06590789556503296,
-0.006099464371800423,
-0.000017416090486221947,
-0.04615397751331329,
-0.042132049798965454,
0.03629300743341446,
0.010262912139296532,
0.009898298420011997,
0.0009321712423115969,
0.038903284817934036,
0.034244757145643234,
-0.020598847419023514,
-0.07944202423095703,
-0.10050966590642929,
0.05069304257631302,
0.020752541720867157,
0.001324067241512239,
-0.09581036120653152,
0.01016580406576395,
0.07096892595291138,
0.0509575791656971,
-0.01919919066131115,
-0.01695093885064125,
-0.026778927072882652,
0.035333577543497086,
0.017280656844377518,
0.016505714505910873,
0.015643300488591194,
-0.017432693392038345,
-0.05183035880327225,
0.006156344432383776,
-0.058870211243629456,
0.006701870821416378,
0.010205144993960857,
0.0010417172452434897,
-0.026331216096878052,
0.07498568296432495,
-0.036024924367666245,
0.013150406070053577,
-0.007199983578175306,
-0.0083113182336092,
-0.010603399947285652,
0.0809977650642395,
-0.004474036395549774,
0.00838353019207716,
0.02964862994849682,
-0.013426213525235653,
0.028652625158429146,
-0.005708449985831976,
-0.009649924002587795,
0.05220027640461922,
-0.011402897536754608,
0.0047742645256221294,
-0.019216623157262802,
0.035776473581790924,
0.019877854734659195,
0.007650330197066069,
-0.045612286776304245,
-0.04586382955312729,
-0.010434776544570923,
-0.00024587404914200306,
0.03619348257780075,
-0.013098119758069515,
0.00038181411218829453,
-0.050908226519823074,
0.0029770375695079565,
-0.030672309920191765,
-0.03747520223259926,
0.02629629708826542,
-0.03181130439043045,
0.017256341874599457,
0.008681990206241608,
-0.012793068774044514,
0.015566129237413406,
-0.0177350752055645,
0.0002950840280391276,
0.028932299464941025,
0.028110288083553314,
0.03345703333616257,
-0.013826653361320496,
0.03484978526830673,
0.04391118884086609,
0.038204312324523926,
0.00114295759703964,
-0.02262306399643421,
-0.02870955690741539,
0.02783232182264328,
-0.0026503275148570538,
-0.013290983624756336,
0.002390332752838731,
-0.012855476699769497,
0.001494150492362678,
0.0005277834716252983,
0.03410942107439041,
0.018782848492264748,
0.03689540922641754,
-0.05447259917855263,
0.07607955485582352,
0.0663975402712822,
-0.02252676710486412,
0.02230849117040634,
-0.019915828481316566,
-0.00595901207998395,
0.03952046483755112,
0.022765040397644043,
-0.002649100264534354,
-0.03575387969613075,
0.00920204445719719,
-0.016162388026714325,
0.005913184490054846,
-0.011559243313968182,
-0.0076429699547588825,
0.03987107425928116,
0.01314613875001669,
0.012588392943143845,
0.006923404056578875,
-0.03258009999990463,
-0.036065369844436646,
0.012173713184893131,
0.06983334571123123,
-0.024228567257523537,
0.008980842307209969,
0.006534750107675791,
0.004810155835002661,
0.006443294696509838,
-0.01809217967092991,
0.0338410809636116,
0.004875893238931894,
0.008535204455256462,
0.01790894940495491,
-0.02941458486020565,
0.033851154148578644,
0.05130540207028389,
-0.04055741801857948,
-0.011067982763051987,
0.06000851094722748,
0.002434043912217021,
0.0018447223119437695,
-0.04969615116715431,
0.037678830325603485,
-0.006821268238127232,
0.009101392701268196,
-0.0014785975217819214,
-0.03299809247255325,
0.027318505570292473,
-0.007194985635578632,
0.012041669338941574,
-0.059208620339632034,
-0.014718270860612392,
0.0029412212315946817,
-0.019457612186670303,
0.004203053656965494,
0.010733721777796745,
0.006753083784133196,
-0.030896343290805817,
-0.015156109817326069,
-0.022061266005039215,
-0.009617372415959835,
0.0010767205385491252,
0.0262261014431715,
-0.04939885437488556,
0.001627773279324174,
-0.04495416581630707,
-0.01660263165831566,
0.016775349155068398,
0.025873376056551933,
-0.0013155987253412604,
0.03937198594212532,
0.018029360100626945,
-0.019434191286563873,
-0.022852681577205658,
-0.007294540759176016,
0.023139160126447678,
-0.0598318986594677,
-0.02076888270676136,
0.02431139349937439,
0.04624113813042641,
-0.011456838808953762,
0.002325008623301983,
-0.04690667241811752,
-0.03227396309375763,
-0.024563664570450783,
0.030271118506789207,
0.01700904779136181,
-0.018163004890084267,
0.007188898045569658,
0.03613388538360596,
0.016214633360505104,
-0.01564732752740383,
-0.07016574591398239,
-0.03735924884676933,
-0.00294619076885283,
-0.006411710754036903,
0.03447989001870155,
0.0034200060181319714,
-0.046969830989837646,
0.055362239480018616,
0.014848501421511173,
-0.07024441659450531,
-0.04463755711913109,
-0.00807807594537735,
-0.0037372035440057516,
-0.027369901537895203,
-0.012741451151669025,
0.0763779729604721,
-0.03386365994811058,
0.009143974632024765,
0.017961228266358376,
0.02361413463950157,
0.031093623489141464,
0.03274483233690262,
0.026803098618984222,
0.0289168544113636,
0.06665144115686417,
0.01660257764160633,
0.03755227103829384,
0.03678443282842636,
0.0056815375573933125,
0.027389563620090485,
-0.005669350735843182,
0.036937545984983444,
0.03436897322535515,
-0.035910464823246,
0.044479914009571075,
0.012690221890807152,
-0.005815121810883284,
-0.02883000858128071,
0.02659137174487114,
0.029038574546575546,
-0.016920242458581924,
0.009409951977431774,
0.020091744139790535,
0.03705841302871704,
-0.027499642223119736,
-0.02962997555732727,
0.041696298867464066,
0.013651212677359581,
-0.030362997204065323,
-0.06005970761179924,
0.014714779332280159,
0.0074300882406532764,
0.026781758293509483,
-0.016564156860113144,
-0.009377581998705864,
0.04871588200330734,
0.021827371791005135,
0.014736903831362724,
0.017936106771230698,
-0.040124714374542236,
0.019877059385180473,
-0.06963515281677246,
-0.00625541340559721,
0.021353768184781075,
0.039097707718610764,
-0.008279540576040745,
0.06116022169589996,
0.03020501881837845,
0.015156376175582409,
0.05144279822707176,
0.04537254944443703,
-0.09159420430660248,
0.01045942772179842,
0.0011119956616312265,
-0.006081707309931517,
0.031668923795223236,
-0.04611612856388092,
0.005989894736558199,
-0.018912995234131813,
-0.006960620172321796,
-0.00019813547260127962,
0.004370774142444134,
-0.04506094381213188,
0.03413302078843117,
-0.02183404378592968,
0.015433995053172112,
0.004742729943245649,
0.048190902918577194,
0.0012515236157923937,
-0.03550027683377266,
0.027693036943674088,
0.03277139365673065,
0.011644329875707626,
0.005263507831841707,
0.0037180487997829914,
-0.004967018496245146,
0.05956582352519035,
0.044849053025245667,
0.012638374231755733,
0.026190517470240593,
0.006767744198441505,
-0.0244308989495039,
0.016797104850411415,
0.06010752171278,
-0.006776469759643078,
-0.017545364797115326,
-0.04540717601776123,
-0.015399357303977013,
-0.03570134565234184,
0.004917084705084562,
0.04635075107216835,
-0.012049674987792969,
-0.0021509232465177774,
-0.00873943604528904,
0.007927214726805687,
-0.0013860691105946898,
0.053886301815509796,
0.07072385400533676,
0.009256657212972641,
-0.008324633352458477,
-0.03671897202730179,
-0.05266566574573517,
-0.05545513331890106,
-0.015016536228358746,
0.03460404649376869,
0.01256369985640049,
-0.008291762322187424,
0.0013010521652176976,
0.04334978014230728,
0.019165154546499252,
-0.028155021369457245,
0.017199253663420677,
-0.023253407329320908,
0.03154494985938072,
0.004227947909384966,
0.008982324972748756,
0.00808054581284523,
0.023555340245366096,
0.03859585151076317,
-0.01840163581073284,
-0.026985466480255127,
-0.07324802875518799,
-0.03899606317281723,
0.0038097978103905916,
0.0347789004445076,
0.00746922055259347,
0.025388963520526886,
-0.05954677239060402,
-0.04161073639988899,
0.03656165301799774,
-0.02754751779139042,
0.014013233594596386,
-0.020062770694494247,
0.018807334825396538,
-0.007929140701889992,
-0.05128949135541916,
-0.04637452960014343,
-0.014487581327557564,
0.004302637651562691,
0.02159743756055832,
0.0022882376797497272,
-0.012460869736969471,
0.04140809178352356,
-0.005472003016620874,
0.0009665262186899781,
0.020049598067998886,
0.025796880945563316,
-0.04728533327579498,
-0.02140108495950699,
0.009278395213186741,
-0.04535014182329178,
-0.05376731976866722,
0.008063298650085926,
-0.04510080814361572,
-0.008131428621709347,
0.019325710833072662,
-0.04809850454330444,
-0.07144065201282501,
0.050744444131851196,
0.0058212485164403915,
0.024005405604839325,
0.0020134232472628355,
-0.01904730126261711,
0.048560138791799545,
0.059989944100379944,
-0.01608281023800373,
0.033238936215639114,
0.01842336170375347,
-0.0178444292396307,
-0.0199065413326025,
-0.03649168834090233,
0.00472260219976306,
-0.0346856489777565,
-0.003712198929861188,
-0.033790528774261475,
0.01950824074447155,
-0.04605846107006073,
0.04115358740091324,
-0.008635119535028934,
-0.001767680048942566,
-0.040288180112838745,
-0.05819880589842796,
0.03428042307496071,
0.0009526975336484611,
0.025602106004953384,
0.011929387226700783,
0.0031739254482090473,
0.019474605098366737,
0.020401079207658768,
-0.029402490705251694,
0.01633228361606598,
-0.05279174819588661,
0.02662929706275463,
-0.014725184999406338,
-0.0347021110355854,
-0.011995771899819374,
-0.00957721471786499,
-0.010748821310698986,
-0.015660414472222328,
-0.061573319137096405,
0.07677366584539413,
-0.018347101286053658,
0.04214904457330704,
0.021706338971853256,
-0.03909445181488991,
-0.00954462867230177,
0.016220347955822945,
0.033219173550605774,
0.0070469919592142105,
-0.06848848611116409,
0.043895967304706573,
0.03328017517924309,
0.025120532140135765,
-0.04999465495347977,
-0.023689264431595802,
0.05248253047466278,
-0.010534249246120453,
-0.03338433429598808,
0.008944148197770119,
-0.034448571503162384,
-0.012010700069367886,
-0.021378539502620697,
-0.004564243834465742,
0.03181114420294762,
-0.003814250696450472,
-0.06076018884778023,
0.019003985449671745,
0.00921926461160183,
0.04910699650645256,
-0.004748353734612465,
0.01089134905487299,
-0.00001739312028803397,
-0.022897975519299507,
0.0016783061437308788,
-0.02278747409582138,
0.039748698472976685,
-0.03718290105462074,
-0.024134596809744835,
-0.026120616123080254,
0.0062470040284097195,
0.04077896475791931,
-0.016628442332148552,
0.021176569163799286,
0.009534357115626335,
-0.00504394993185997,
-0.015497350133955479,
-0.02306465245783329,
0.011022118851542473,
0.010858320631086826,
0.013597782701253891,
0.002307458780705929,
0.01122056134045124,
0.009919446893036366,
-0.02516862191259861,
-0.008288058452308178,
-0.020826905965805054,
-0.0404302217066288,
0.009155449457466602,
0.09079558402299881,
-0.015566710382699966,
-0.009921119548380375,
-0.007157520856708288,
-0.03475058451294899,
0.031555671244859695,
-0.01655225269496441,
-0.02332109585404396,
0.04799681901931763,
0.0017016680212691426,
-0.07145161181688309,
-0.02476164698600769,
-0.04493780434131622,
0.04376426339149475,
0.07243194431066513,
-0.00896750669926405,
0.046498045325279236,
0.0002478614333085716,
0.006426362320780754,
0.015876388177275658,
-0.01358031015843153,
-0.008415298536419868,
-0.012495755217969418,
0.0021725711412727833,
0.03476959839463234,
-0.04137592017650604,
-0.01503288559615612,
0.010015185922384262,
0.032350070774555206,
-0.02017841301858425,
-0.01855781488120556,
0.055654723197221756,
-0.01714594103395939,
-0.002493305131793022,
0.002731971675530076,
-0.03433392941951752,
0.041495371609926224,
-0.014405795373022556,
0.028641829267144203,
-0.016108717769384384,
-0.02077407017350197,
0.03165900707244873,
0.021949252113699913,
0.007951474748551846,
-0.04451911896467209,
0.015740329399704933,
-0.05470353364944458,
0.006920886225998402,
0.01529028732329607,
0.01645074225962162,
0.009655945934355259,
0.004240961279720068,
0.005579457152634859,
0.005549557041376829,
0.009940911084413528,
-0.03690698742866516,
-0.04740210250020027,
0.0067130327224731445,
-0.010233169421553612,
-0.022481044754385948,
0.04657171294093132,
0.010347230359911919,
-0.009048596024513245,
0.03069429285824299,
-0.05090261623263359,
0.008147254586219788,
-0.020524874329566956,
0.03011268936097622,
0.009418526664376259,
0.09202847629785538,
-0.05616643279790878,
0.014236128889024258,
-0.004381753969937563,
-0.011197640560567379,
0.12239285558462143,
0.028530262410640717,
0.015579876489937305,
-0.037690430879592896,
0.04103443771600723,
0.025007043033838272,
0.005531010217964649,
-0.0030321215745061636,
0.032723598182201385,
-0.02566470205783844,
-0.0015142152551561594,
0.0071554710157215595,
0.08387506753206253,
-0.04739244654774666,
0.012824582867324352,
0.047321513295173645,
-0.04354563355445862,
-0.04218169301748276,
-0.01579466089606285,
0.011751694604754448,
-0.01873611845076084,
0.013872815296053886,
-0.00030268216505646706,
0.026757266372442245,
-0.03026510961353779,
-0.0028696274384856224,
-0.015186352655291557,
-0.017570573836565018,
0.013964259997010231,
-0.0038519904483109713,
-0.06771605461835861,
0.04164011403918266,
0.018639566376805305,
-0.00034170722938142717,
-0.08222052454948425,
0.05907907709479332,
-0.012995682656764984,
0.006354235112667084,
-0.013368678279221058,
0.00792421493679285,
-0.001258558826521039,
-0.007261311635375023,
0.029534390196204185,
-0.02331775426864624,
-0.0215179193764925,
0.007518364116549492,
-0.00435499707236886,
0.02558530494570732,
0.013184910640120506,
-0.026641476899385452,
-0.004856632091104984,
0.0039057021494954824,
-0.008735631592571735,
-0.03009437397122383,
-0.02299090474843979,
0.0017353779403492808,
0.02444796822965145,
-0.00924621894955635,
-0.040049221366643906,
-0.00840807892382145,
0.015786372125148773,
0.013651116751134396,
0.0006144371582195163,
-0.018748324364423752,
-0.0015936725540086627,
0.007632906083017588,
-0.0467989481985569,
0.07246900349855423,
0.0008582346490584314,
-0.0004081490624230355,
-0.0270982813090086,
0.030634913593530655,
-0.04429689422249794,
-0.00017483574629295617,
-0.025106677785515785,
0.05355110391974449,
0.03443671762943268,
0.048098113387823105,
0.011346191167831421,
-0.010118349455296993,
-0.06116963550448418,
0.04697621241211891,
-0.00448062876239419,
-0.0058160205371677876,
-0.042742062360048294,
-0.023479318246245384,
-0.012127503752708435,
0.0519193559885025,
-0.00447817100211978,
0.01524594146758318,
0.012247322127223015,
0.06700658053159714,
0.03022783249616623,
-0.01620439812541008,
-0.03609798476099968,
0.00020862485689576715,
-0.03834199905395508,
-0.03885463997721672,
0.01262629684060812,
0.033062566071748734,
0.011979692615568638,
0.03079833835363388,
-0.0026877515483647585,
0.007155818399041891,
-0.01900448277592659,
-0.011451778002083302,
0.003000478958711028,
-0.03223498538136482,
0.02188827469944954,
0.0322534516453743,
0.016142243519425392,
-0.04314142093062401,
0.0015412054490298033,
-0.037466783076524734,
-0.030874712392687798,
-0.015054363757371902,
0.011863062158226967,
-0.0027541257441043854,
0.0347222164273262,
-0.010248923674225807,
-0.0026840297505259514,
-0.04363759607076645,
-0.008694375865161419,
-0.028355726972222328,
-0.05662975460290909,
0.044127143919467926,
-0.005639608483761549,
-0.018379755318164825,
0.042432140558958054,
-0.015942886471748352,
0.008032938465476036,
0.008630247786641121,
0.018971526995301247,
0.010970748029649258,
-0.054470062255859375,
0.05605827271938324,
0.0031527436804026365,
0.05060333386063576,
-0.03471263498067856,
-0.05045618861913681,
0.0024662327487021685,
0.010380216874182224,
-0.02289802022278309,
0.023434901610016823,
-0.009641422890126705,
0.025697769597172737,
-0.005028305109590292,
-0.02237536571919918,
-0.009806646034121513,
0.05378346145153046,
-0.013842059299349785,
-0.02613736502826214,
-0.024912545457482338,
-0.045457642525434494,
0.029950793832540512,
-0.03541480004787445,
0.007965532131493092,
0.04049283638596535,
0.03628072887659073,
0.032940447330474854,
0.04009031876921654,
0.02201293408870697,
-0.0009460001019760966,
-0.008011464960873127,
-0.002807484706863761,
0.03252685070037842,
0.017035454511642456,
0.010440792888402939,
0.043554436415433884,
0.010425110347568989,
-0.02600196562707424,
-0.007329214364290237,
-0.006308996584266424,
-0.0015567959053441882,
-0.12439381331205368,
-0.005553539842367172,
0.023861724883317947,
0.025663893669843674,
0.057560160756111145,
-0.060320090502500534,
0.008986610919237137,
0.022414546459913254,
-0.07113587856292725,
-0.03911508247256279,
-0.03675633668899536,
-0.032050758600234985,
-0.03307272121310234,
-0.0033757719211280346,
0.000602885615080595,
0.03799193352460861,
-0.0018912861123681068,
0.035956498235464096,
0.03832308575510979,
-0.0020450977608561516,
-0.025590429082512856,
-0.031382061541080475,
0.013048266060650349,
0.04800523817539215,
0.01943102851510048,
-0.021485406905412674,
0.053824689239263535,
-0.025120345875620842,
-0.007505877874791622,
0.03646305575966835,
-0.023899449035525322,
0.02189856953918934,
-0.014902164228260517,
-0.01991528831422329,
-0.021538900211453438,
0.03274769335985184,
-0.008567734621465206,
0.01586282253265381,
-0.054196517914533615,
-0.001127202296629548,
0.01021331362426281,
0.018253503367304802,
-0.0039180428721010685,
-0.014162413775920868,
0.014665660448372364,
-0.004078560974448919,
-0.041794776916503906,
0.02703617885708809,
-0.029445592314004898,
0.0035869639832526445,
-0.007454712875187397,
-0.00854924414306879,
0.012511677108705044,
-0.037552040070295334,
-0.018417084589600563,
-0.028867073357105255,
0.02918454259634018,
0.05264081805944443,
-0.0005827759159728885,
-0.007241183891892433,
-0.019263550639152527,
0.05495815724134445,
-0.028271889314055443,
-0.023502519354224205,
-0.02134949527680874,
-0.02665759064257145,
-0.022792918607592583,
0.015614612959325314,
-0.029883703216910362,
-0.0326894149184227,
0.005896406248211861,
-0.029802611097693443,
-0.01181455422192812,
0.05620019510388374,
0.013083120808005333,
0.02501307614147663,
0.03260223940014839,
-0.043854180723428726,
-0.04468819499015808,
-0.08869553357362747,
0.021485714241862297,
-0.0095903929322958,
-0.05282626301050186,
0.014418154023587704,
-0.012933948077261448,
-0.006586667615920305,
0.03264477476477623,
0.022330543026328087,
0.00519576808437705,
0.005627126898616552,
0.01903535984456539,
-0.007818087935447693,
-0.009955652058124542,
-0.02499687485396862,
0.0009255279437638819,
-0.020083623006939888,
0.010293572209775448,
0.026969971135258675,
0.019506283104419708,
0.04324992001056671,
-0.0009906936902552843,
0.023650767281651497,
-0.02268666960299015,
0.04467027261853218,
0.016140306368470192,
-0.02192317694425583,
0.005540344398468733,
0.017264654859900475,
-0.000797061831690371,
0.11570275574922562,
0.0024637142196297646,
-0.01826712116599083,
0.012814022600650787,
-0.010934785008430481,
-0.07213617116212845,
0.04406927525997162,
-0.015651831403374672,
-0.023094283416867256,
-0.027279889211058617,
-0.01782822795212269,
-0.021109318360686302,
-0.06127595901489258,
-0.0012315057683736086,
0.03341688960790634,
-0.020141463726758957,
-0.018356937915086746,
0.0298940259963274,
0.03851698711514473,
0.047361552715301514,
-0.027743909507989883,
0.03188198059797287,
0.008717075921595097,
-0.0024451452773064375,
0.004100406542420387,
-0.012121492065489292,
0.08000782132148743,
0.05347573012113571,
0.009878027252852917,
0.041023630648851395,
-0.0431092232465744,
0.008798873983323574,
-0.017599325627088547,
-0.005466862116008997,
0.007192706689238548,
-0.03258669748902321,
0.0061805411241948605,
-0.00598861975595355,
0.02655031345784664,
0.029988877475261688,
0.03619742766022682,
0.05487072467803955,
-0.028865063562989235,
-0.026679523289203644,
-0.03948502987623215,
-0.0026576442178338766,
-0.026394540444016457,
0.03269171714782715,
0.0179385207593441,
-0.01304490678012371,
-0.0003335151122882962,
0.015074660070240498,
-0.009122451767325401,
-0.02423340268433094,
0.0037453940603882074,
0.020174603909254074,
0.0017395407194271684,
0.01593802496790886,
-0.0008329649572260678,
-0.03338034451007843,
-0.05661420524120331,
-0.054585520178079605,
-0.047972310334444046,
0.05346067249774933,
0.02784392237663269,
-0.00913555920124054,
-0.016067037358880043,
-0.007617757190018892,
-0.04007836803793907,
0.0547478087246418,
-0.05114278197288513,
-0.03390692174434662,
0.013636265881359577,
-0.011240720748901367,
0.03532378375530243,
-0.051463011652231216
] |
<p>My question is fairly simple, but I do need clarification on how to get the inverse of the <a href="http://en.wikipedia.org/wiki/Lennard-Jones_potential" rel="nofollow">Lennard-Jones</a> potential V(x).</p>
<p>I am working with the following expression:
$$
V(x) = e\times[(R/x)^{12} -2\times(R/x)^6]
$$</p>
<p>So given a value $V$, how can I find $x(V)$ ?</p> | 1,558 | [
0.01949658989906311,
-0.011715295724570751,
-0.012336638756096363,
-0.01964467577636242,
-0.025504885241389275,
0.000757089292164892,
-0.054533399641513824,
-0.00958583876490593,
0.012649341486394405,
-0.028392035514116287,
0.05099325254559517,
0.03478202596306801,
0.07458768039941788,
-0.0097573883831501,
0.03829134628176689,
0.01807383820414543,
-0.034699007868766785,
0.0007626783335581422,
0.027536964043974876,
-0.0281623937189579,
0.00040998696931637824,
-0.025616541504859924,
0.010054705664515495,
-0.017062023282051086,
-0.021619699895381927,
0.05071340873837471,
0.03141630068421364,
-0.04020880162715912,
0.017121518030762672,
0.047917623072862625,
-0.005058917682617903,
-0.04906703531742096,
0.04402489960193634,
0.037731293588876724,
0.0005999092245474458,
0.037121959030628204,
0.0035685328766703606,
-0.056327275931835175,
-0.030346501618623734,
0.04726923629641533,
-0.03495015576481819,
0.0026204613968729973,
0.009913718327879906,
0.05438099801540375,
-0.010374055244028568,
0.018892157822847366,
0.007069532293826342,
-0.0323595367372036,
0.022809844464063644,
-0.05730307102203369,
0.0897083431482315,
0.03371976315975189,
0.03164932131767273,
0.02792065218091011,
-0.001075579784810543,
-0.01609233021736145,
0.047585926949977875,
0.06782439351081848,
0.029283545911312103,
-0.003946411423385143,
-0.012528741732239723,
0.009033633396029472,
-0.0477849543094635,
-0.008970399387180805,
-0.03329702094197273,
-0.02049865573644638,
-0.008896972984075546,
0.022823791950941086,
0.03529706969857216,
0.008308601565659046,
0.024681011214852333,
0.053511276841163635,
0.01639053039252758,
0.014665961265563965,
0.0376594141125679,
-0.0396529920399189,
0.01584075577557087,
0.015613355673849583,
0.005744510795921087,
-0.03156010061502457,
-0.0372358001768589,
0.010382959619164467,
0.021343089640140533,
0.061433982104063034,
-0.03165213391184807,
-0.02279849536716938,
0.04165639355778694,
-0.032899126410484314,
0.034597620368003845,
0.046358320862054825,
-0.028148973360657692,
0.010428004898130894,
0.030811423435807228,
-0.03374073654413223,
-0.05065888538956642,
0.03957582265138626,
-0.00436435779556632,
0.05917058512568474,
-0.03685632348060608,
-0.025901664048433304,
0.00771974166855216,
-0.03834580257534981,
-0.013332244008779526,
0.06579911708831787,
-0.026972612366080284,
-0.02761865220963955,
-0.013795754872262478,
-0.0014212721725925803,
0.021221794188022614,
-0.0006040624575689435,
-0.04230745509266853,
0.02543460950255394,
-0.003121450077742338,
-0.030124114826321602,
0.04058973491191864,
-0.01160466019064188,
-0.053563546389341354,
-0.03738837316632271,
0.043645791709423065,
0.03035961277782917,
0.01362326368689537,
-0.01318676769733429,
0.07500159740447998,
-0.061420343816280365,
-0.059794407337903976,
-0.0073879617266356945,
-0.0068412646651268005,
0.022224750369787216,
0.0009364928118884563,
0.02627674862742424,
0.035688597708940506,
-0.034295160323381424,
0.00476390914991498,
0.040023721754550934,
0.016132328659296036,
-0.03722724691033363,
-0.06206849589943886,
-0.04715503007173538,
0.041145600378513336,
-0.0007157974177971482,
-0.01769798994064331,
-0.07230362296104431,
0.007772395852953196,
0.04444195702672005,
0.039751119911670685,
0.02246280200779438,
0.014703039079904556,
0.007965115830302238,
0.03018753044307232,
-0.009444075636565685,
0.025416063144803047,
-0.030619945377111435,
-0.0031629877630621195,
-0.05443231761455536,
0.013889914378523827,
-0.02011319436132908,
0.016323696821928024,
0.002518970053642988,
-0.040476758033037186,
-0.03029436431825161,
0.07670816034078598,
-0.036557942628860474,
-0.036928437650203705,
0.010295139625668526,
0.007739913649857044,
-0.026716740801930428,
0.09495775401592255,
0.022255590185523033,
-0.01476257387548685,
-0.01974870078265667,
-0.0011723749339580536,
0.0008280560723505914,
0.0030702308285981417,
0.022721316665410995,
0.08419036865234375,
-0.006665833294391632,
0.009121539071202278,
-0.024699734523892403,
0.05900326371192932,
-0.0020042939577251673,
-0.05363619700074196,
-0.022952336817979813,
0.019964732229709625,
0.0021577647421509027,
0.030072249472141266,
0.043579746037721634,
-0.017857005819678307,
-0.010560576803982258,
-0.004426911007612944,
-0.04087793081998825,
-0.0121272262185812,
-0.03771696984767914,
0.02562059462070465,
0.01965242624282837,
-0.03173024207353592,
0.04192042723298073,
0.018685340881347656,
0.035788070410490036,
0.009274699725210667,
-0.02270258590579033,
-0.007656339555978775,
0.022235337644815445,
0.017842257395386696,
-0.0058136917650699615,
-0.002368486486375332,
0.0650717094540596,
0.06263813376426697,
-0.008699306286871433,
0.041736822575330734,
-0.019851867109537125,
0.014766458421945572,
-0.009009486064314842,
-0.04161636158823967,
0.01668952777981758,
-0.022367751225829124,
-0.014164824970066547,
0.03895077854394913,
-0.0002124009479302913,
-0.004498912021517754,
0.030228663235902786,
-0.010276242159307003,
0.05353759229183197,
0.07151218503713608,
0.029159007593989372,
-0.009991753846406937,
0.040394607931375504,
-0.011790667660534382,
0.05987337604165077,
0.022175265476107597,
-0.05986347794532776,
-0.034690193831920624,
-0.0031844822224229574,
0.022926371544599533,
-0.003347138874232769,
-0.05525907874107361,
0.01604212261736393,
0.04428030923008919,
-0.020017094910144806,
0.03133976832032204,
0.060385122895240784,
-0.012638261541724205,
-0.003279394470155239,
0.03323394060134888,
0.00642937608063221,
0.008301051333546638,
0.022124040871858597,
0.020733505487442017,
0.035768017172813416,
0.037265848368406296,
-0.023362986743450165,
-0.004229424986988306,
0.03317246958613396,
-0.023946458473801613,
-0.009727911092340946,
-0.02754419669508934,
-0.01363939419388771,
0.03259366750717163,
-0.012860622256994247,
0.02608298324048519,
0.04251779615879059,
-0.01217604149132967,
0.025193357840180397,
-0.009671839885413647,
-0.00014403411478269845,
0.032897137105464935,
-0.014939658343791962,
-0.025790786370635033,
-0.012351270765066147,
0.02137165702879429,
-0.03901607170701027,
-0.007511982694268227,
-0.030168019235134125,
0.019792551174759865,
-0.035219378769397736,
0.02163805440068245,
-0.014722900465130806,
-0.006649491377174854,
-0.036370016634464264,
0.00808263011276722,
0.0011636004783213139,
0.010848446749150753,
-0.009204862639307976,
0.005922951269894838,
0.03925641253590584,
-0.025360185652971268,
0.01311332918703556,
-0.016372287645936012,
-0.023566478863358498,
0.002796979621052742,
0.013134841807186604,
-0.040729768574237823,
0.014083380810916424,
-0.0217476487159729,
-0.08344528079032898,
0.016547352075576782,
-0.030263928696513176,
0.02499997615814209,
-0.018730463460087776,
-0.0072259907610714436,
0.05655871704220772,
-0.004577274434268475,
-0.036104194819927216,
0.018090393394231796,
-0.0501069612801075,
-0.02453436329960823,
-0.055414196103811264,
-0.028654249384999275,
0.06696674227714539,
-0.0039564878679811954,
0.043569616973400116,
0.04697291925549507,
-0.00823551882058382,
0.003150263102725148,
-0.08342088013887405,
-0.048507872968912125,
0.01449974998831749,
0.016252603381872177,
0.007214354816824198,
0.02025400660932064,
-0.04108405113220215,
0.08190378546714783,
0.0025531051214784384,
-0.05219327285885811,
-0.025086086243391037,
0.009333319962024689,
-0.003205488435924053,
-0.0046126823872327805,
-0.013026425614953041,
0.03653785213828087,
-0.036878231912851334,
-0.0026742375921458006,
-0.041227418929338455,
0.041342634707689285,
0.020768694579601288,
-0.047716908156871796,
-0.03204928711056709,
0.002613844582810998,
0.009169790893793106,
-0.00579605158418417,
0.06886076927185059,
-0.03389238193631172,
0.013289593160152435,
0.020624374970793724,
-0.006998111493885517,
0.0199727825820446,
0.017317401245236397,
-0.011166871525347233,
0.005530539900064468,
0.002787573030218482,
0.02590033784508705,
-0.0005103103467263281,
0.026300042867660522,
-0.010014810599386692,
-0.019806766882538795,
0.018643902614712715,
0.0137128671631217,
0.043614134192466736,
-0.034542955458164215,
-0.028333541005849838,
0.04627778008580208,
0.011989044956862926,
-0.024957530200481415,
-0.03216773271560669,
0.006583124399185181,
0.007481860462576151,
0.03703182563185692,
0.023304501548409462,
0.003417977597564459,
0.07153571397066116,
0.04282805696129799,
0.042531535029411316,
-0.04728129506111145,
-0.04673459380865097,
0.006733778398483992,
-0.005389584228396416,
-0.002518747001886368,
-0.013245094567537308,
0.04109477996826172,
-0.0020111259073019028,
0.03084736131131649,
0.02892570197582245,
0.010133541189134121,
-0.009424686431884766,
0.014550057239830494,
-0.06870874762535095,
0.032359231263399124,
-0.010646945796906948,
0.004367039538919926,
-0.05629374831914902,
0.008168725296854973,
0.011827177368104458,
0.011278165504336357,
-0.04328273981809616,
0.01489876676350832,
-0.03697394207119942,
-0.04061640053987503,
-0.011918440461158752,
-0.05379253625869751,
0.0034173098392784595,
-0.03820185735821724,
0.04059690982103348,
0.04449378699064255,
-0.05052576959133148,
0.0016314571257680655,
0.03395359218120575,
-0.021918464452028275,
-0.0057515413500368595,
-0.015569819137454033,
-0.01325241755694151,
0.017099326476454735,
0.046429961919784546,
0.0018030848586931825,
0.00944567658007145,
0.036632783710956573,
0.017694735899567604,
-0.014500531367957592,
0.03361200541257858,
0.00549551285803318,
0.013344692066311836,
0.004676714073866606,
-0.04346553981304169,
-0.02773827314376831,
-0.025269094854593277,
0.018546096980571747,
-0.023703305050730705,
0.05535230413079262,
0.0049249958246946335,
-0.0031454055570065975,
-0.02264581061899662,
0.039095330983400345,
0.07560630887746811,
0.007192044053226709,
-0.0077269491739571095,
-0.04628724977374077,
0.019650695845484734,
-0.025706816464662552,
-0.0353911928832531,
0.04824668914079666,
0.0053725456818938255,
-0.03433849662542343,
-0.0265736635774374,
0.020901203155517578,
0.04654868319630623,
-0.002309118863195181,
-0.016116559505462646,
-0.04451821371912956,
0.02554456889629364,
-0.04278170317411423,
-0.03700432553887367,
-0.02025630511343479,
0.0001499480422353372,
0.03971943259239197,
-0.01814587041735649,
0.020035281777381897,
-0.10051354765892029,
-0.007345991209149361,
0.02620605193078518,
0.05104006826877594,
-0.04239848256111145,
-0.006112886127084494,
-0.04748111590743065,
-0.00971154123544693,
0.04631916806101799,
-0.04055013135075569,
-0.029621200636029243,
-0.015094449743628502,
0.0017528778407722712,
0.006566727068275213,
-0.010826686397194862,
-0.01653251238167286,
0.0005171883967705071,
-0.017163816839456558,
0.022560149431228638,
-0.036447204649448395,
0.01670669950544834,
-0.036204129457473755,
0.006753695663064718,
-0.006652945186942816,
0.08261584490537643,
0.023495368659496307,
-0.009343787096440792,
0.007375938817858696,
0.0179252028465271,
-0.03396796062588692,
-0.0625874474644661,
-0.013603458181023598,
0.0013786220224574208,
0.005285404156893492,
0.04950879514217377,
-0.023162759840488434,
-0.04015704616904259,
0.03527185320854187,
0.0035574387293308973,
-0.0006662856321781874,
0.00861101970076561,
0.008515693247318268,
0.018681600689888,
0.03545575961470604,
0.031076636165380478,
0.08837849646806717,
0.06103895604610443,
0.01167086511850357,
-0.029629547148942947,
-0.0008500593830831349,
0.006269005127251148,
-0.024656789377331734,
-0.03191579133272171,
-0.023946065455675125,
-0.004286246374249458,
-0.0021486161276698112,
0.009542608633637428,
-0.05037005990743637,
0.04584750160574913,
-0.008388216607272625,
-0.017970135435461998,
0.005365826655179262,
0.008774181827902794,
0.01614825613796711,
-0.010994567535817623,
0.0004692623333539814,
0.017678655683994293,
0.03808891400694847,
-0.0417335219681263,
-0.003516905475407839,
0.03767932951450348,
-0.013293287716805935,
0.01024103257805109,
-0.019712205976247787,
0.04556754603981972,
-0.004894664976745844,
-0.0032873842865228653,
0.032904282212257385,
-0.04419940710067749,
0.026602480560541153,
-0.005048756487667561,
-0.026152990758419037,
0.010890630073845387,
-0.06361164152622223,
-0.0021247505210340023,
0.0010367347858846188,
-0.008215410634875298,
-0.0013138717040419579,
-0.060181859880685806,
0.026715833693742752,
0.008863394148647785,
-0.0020572023931890726,
-0.0899384543299675,
-0.06303652375936508,
0.008569256402552128,
0.011115552857518196,
-0.01366169098764658,
-0.03348133713006973,
-0.009276054799556732,
0.025860659778118134,
0.02264869399368763,
-0.008114872500300407,
0.017359670251607895,
-0.005952995270490646,
-0.012892491184175014,
0.010427886620163918,
0.04039338231086731,
0.04149773716926575,
-0.0031868861988186836,
-0.005591507535427809,
0.039498232305049896,
-0.004111109301447868,
-0.004862796049565077,
0.009761243127286434,
0.02791869454085827,
-0.03160550072789192,
0.0033478052355349064,
0.0003649599093478173,
-0.01967756450176239,
0.034177266061306,
-0.03532891720533371,
0.006515305023640394,
0.026487616822123528,
0.027539249509572983,
-0.0010788709623739123,
-0.021334180608391762,
-0.020692193880677223,
-0.008699873462319374,
0.040194109082221985,
0.006589304190129042,
-0.0010019794572144747,
-0.04868698492646217,
-0.01890968158841133,
0.011791422963142395,
-0.016319938004016876,
-0.005539583507925272,
0.0012355647049844265,
0.10152510553598404,
-0.021927112713456154,
-0.0006165231461636722,
0.01488347165286541,
-0.020452119410037994,
-0.014249135740101337,
0.012102427892386913,
-0.03866080939769745,
0.024074530228972435,
-0.021500783041119576,
-0.02914438210427761,
-0.05070722848176956,
-0.06306309998035431,
0.020769676193594933,
0.06303568184375763,
-0.054482318460941315,
0.05492027476429939,
-0.016865529119968414,
0.025235330685973167,
0.03493889421224594,
-0.029428550973534584,
-0.00018526645726524293,
-0.0116898063570261,
0.0035827404353767633,
0.06420442461967468,
-0.013838300481438637,
0.028065327554941177,
0.02099691890180111,
0.010779389180243015,
0.011679408140480518,
0.0060584889724850655,
0.0342259518802166,
0.04029923304915428,
0.018171923235058784,
-0.012701278552412987,
-0.013786458410322666,
0.04395618662238121,
-0.0058527421206235886,
0.036522939801216125,
-0.020699620246887207,
-0.034826572984457016,
0.06027127429842949,
-0.014062645845115185,
-0.01602022349834442,
-0.06279308348894119,
-0.05864657461643219,
-0.008275543339550495,
0.01219913363456726,
0.002782400930300355,
0.0007945221150293946,
0.0016656920779496431,
0.038493234664201736,
-0.002607099711894989,
0.02796465903520584,
0.04955802485346794,
-0.019036347046494484,
-0.07487768679857254,
-0.002496204571798444,
-0.014672043733298779,
-0.024783765897154808,
0.02567601203918457,
0.038991935551166534,
-0.03266089782118797,
0.04859285429120064,
-0.027851635590195656,
0.03664923459291458,
0.017200246453285217,
0.01792987436056137,
0.0009271989692933857,
0.08200796693563461,
0.002715393900871277,
0.046709220856428146,
0.0022044649813324213,
0.01952965371310711,
0.10034910589456558,
0.07235737890005112,
0.018262039870023727,
-0.061106935143470764,
-0.01055583544075489,
-0.02565707266330719,
-0.004459585528820753,
-0.001422132714651525,
0.016987266018986702,
-0.026839707046747208,
-0.013922855257987976,
-0.0036358716897666454,
0.0325898714363575,
0.02603130042552948,
0.006510380655527115,
0.03456005081534386,
-0.013852161355316639,
-0.027053892612457275,
-0.006335211452096701,
0.019418776035308838,
-0.005490606650710106,
0.0037768820766359568,
-0.05722600221633911,
0.0429672934114933,
-0.06797918677330017,
0.001203098683618009,
-0.03798748180270195,
-0.058591872453689575,
0.006370179355144501,
0.03775691241025925,
-0.0022990801371634007,
0.05382149666547775,
0.0072873979806900024,
-0.004910924471914768,
-0.006345205008983612,
0.02207225002348423,
0.0478680394589901,
0.006591948214918375,
-0.0011773144360631704,
0.028800731524825096,
-0.005874190479516983,
0.012666420079767704,
0.024706169962882996,
0.02384997345507145,
-0.06549248844385147,
-0.00959614384919405,
0.008033012971282005,
0.032795537263154984,
-0.015923265367746353,
-0.00782535970211029,
-0.009504729881882668,
-0.003430179785937071,
-0.011281426064670086,
-0.042916055768728256,
-0.027150580659508705,
-0.0227434691041708,
0.019776001572608948,
-0.02648443728685379,
-0.0171363465487957,
-0.0070256926119327545,
0.023456744849681854,
-0.029886215925216675,
0.031928591430187225,
-0.02837451919913292,
-0.029926978051662445,
0.017970887944102287,
-0.01474909670650959,
0.03989652171730995,
-0.027614809572696686,
-0.036468010395765305,
-0.017238972708582878,
-0.01871349662542343,
-0.008253592066466808,
-0.037050094455480576,
0.027544451877474785,
0.03698398545384407,
0.039379000663757324,
-0.006767809856683016,
-0.001825369312427938,
-0.010901103727519512,
-0.08665989339351654,
0.033042870461940765,
-0.01797560229897499,
0.020757051184773445,
-0.021690605208277702,
0.006129339803010225,
0.02247127704322338,
0.03179733827710152,
-0.02712748944759369,
0.002922231564298272,
0.022831948474049568,
0.02265009470283985,
0.016653090715408325,
-0.027424277737736702,
-0.017617370933294296,
0.0018541398458182812,
-0.04026779532432556,
0.023912107571959496,
0.006701733451336622,
0.02295575477182865,
0.019192852079868317,
0.015842728316783905,
-0.047007966786623,
0.03757108375430107,
-0.02617037668824196,
0.008565325289964676,
-0.012126319110393524,
-0.019033219665288925,
0.003153747646138072,
-0.0048765754327178,
0.008391516283154488,
-0.04104875400662422,
-0.010724227875471115,
-0.013445133343338966,
-0.008355983532965183,
0.014961031265556812,
0.008607672527432442,
-0.04592724144458771,
-0.053371772170066833,
-0.035126663744449615,
0.016163917258381844,
-0.004421547520905733,
0.0012353678466752172,
-0.0002431796892778948,
-0.02228056825697422,
0.009986174292862415,
-0.0029316735453903675,
-0.048086293041706085,
0.030202969908714294,
-0.0048876069486141205,
-0.004058648366481066,
0.021180789917707443,
0.048356056213378906,
0.028322607278823853,
-0.027074430137872696,
0.028556687757372856,
-0.009904895909130573,
0.06102745234966278,
-0.026888534426689148,
-0.052706025540828705,
0.07302876561880112,
-0.07892309874296188,
-0.035070329904556274,
0.025629455223679543,
0.022806363180279732,
0.028884107246994972,
0.02779299207031727,
-0.002787091536447406,
-0.005419053137302399,
0.04994268715381622,
-0.006152572110295296,
0.02415696531534195,
0.006999232806265354,
-0.04554156959056854,
-0.024295274168252945,
-0.006949395872652531,
-0.0078060985542833805,
-0.03715391084551811,
0.006125741638243198,
0.028281202539801598,
0.038686834275722504,
-0.024923987686634064,
-0.015449363738298416,
0.023964576423168182,
0.04585634544491768,
0.03449404239654541,
0.022378655150532722,
-0.007497360929846764,
0.045777417719364166,
0.020390907302498817,
-0.006739791017025709,
0.04100826382637024,
0.0035194922238588333,
-0.01532068196684122,
-0.08545026183128357,
-0.027706513181328773,
-0.0096352593973279,
-0.025156501680612564,
0.05347751826047897,
-0.06266715377569199,
-0.01617182046175003,
0.03551679477095604,
-0.028126448392868042,
-0.0024876089300960302,
-0.005994219798594713,
0.00916717667132616,
-0.008986501954495907,
-0.02070649527013302,
-0.0026734943967312574,
0.02286120317876339,
0.018837399780750275,
0.0458405576646328,
0.03624867647886276,
0.0075116027146577835,
-0.012298166751861572,
-0.038227710872888565,
0.029042214155197144,
0.02336580492556095,
0.004217769484966993,
-0.026224244385957718,
0.04200564697384834,
0.0017596366815268993,
-0.04577458277344704,
0.028314659371972084,
-0.02658175118267536,
0.03368864580988884,
-0.007558147888630629,
-0.018353383988142014,
-0.020289650186896324,
0.056746914982795715,
0.004504603799432516,
-0.01273823156952858,
-0.01750847138464451,
0.013488802127540112,
0.0008874746854417026,
0.004445810802280903,
0.023898068815469742,
0.011357092298567295,
0.02220182865858078,
-0.011658028699457645,
-0.04445670172572136,
0.016207832843065262,
-0.015333219431340694,
-0.02258313074707985,
-0.01928797736763954,
-0.018198270350694656,
0.019661972299218178,
-0.05299210548400879,
-0.0017405155813321471,
-0.048757895827293396,
-0.009059637784957886,
0.02545125223696232,
-0.013705948367714882,
0.01212808396667242,
0.03339923545718193,
-0.04527481272816658,
-0.04176978021860123,
0.03791385516524315,
-0.00039047159953042865,
-0.009553496725857258,
-0.05751877278089523,
-0.030395301058888435,
0.028979239985346794,
-0.01603083126246929,
0.008900395594537258,
-0.0064978511072695255,
-0.026701416820287704,
0.025241773575544357,
0.03562399372458458,
0.03182153031229973,
0.011872067116200924,
-0.026446819305419922,
0.002156605711206794,
-0.028332116082310677,
0.017270971089601517,
0.015660423785448074,
-0.06783133000135422,
-0.018133243545889854,
-0.005046733655035496,
0.01079464890062809,
-0.014508163556456566,
0.042091138660907745,
-0.030175361782312393,
-0.006936320103704929,
-0.018287193030118942,
0.009548180736601353,
0.02224978432059288,
-0.04962100461125374,
-0.017792893573641777,
-0.00042232227860949934,
0.017478860914707184,
-0.0023996673990041018,
0.006968670058995485,
-0.023106610402464867,
0.005594728048890829,
-0.02611897513270378,
-0.0038509422447532415,
-0.016580497846007347,
0.000553179532289505,
-0.0176670104265213,
0.008454867638647556,
-0.0007318490534089506,
0.027157459408044815,
0.06899821758270264,
0.0007813392439857125,
0.0029426277615129948,
-0.00937574077397585,
-0.0003821987775154412,
0.00014123786240816116,
0.030894970521330833,
-0.07012806087732315,
-0.05683697760105133,
0.02302178554236889,
-0.05486215651035309,
0.058723531663417816,
-0.04279936105012894,
-0.03493458032608032,
0.0550338439643383,
-0.0267924964427948,
-0.011223695240914822,
0.03589509055018425,
0.03283001482486725,
0.05499197542667389,
-0.013278904370963573,
0.026021962985396385,
0.038922492414712906,
0.004197720903903246,
-0.016267329454421997,
-0.015730148181319237,
0.02281387895345688,
-0.0007451885030604899,
-0.01596781797707081,
0.05040192976593971,
-0.02035425789654255,
0.04314003139734268,
0.045256201177835464,
0.02913554385304451,
-0.009324388578534126,
0.004531793296337128,
0.010002613998949528,
-0.02880924753844738,
0.03683294728398323,
-0.04676499590277672,
-0.012911423109471798,
0.053609445691108704,
-0.007636913564056158,
0.004136040341109037,
-0.03852938488125801,
-0.0033341050148010254,
-0.03455061465501785,
-0.018733756616711617,
0.010739886201918125,
-0.01213903445750475,
-0.03168347477912903,
-0.0018821058329194784,
-0.039426855742931366,
-0.00526057742536068,
0.036451179534196854,
-0.016077101230621338,
0.019169827923178673,
-0.011078557930886745,
-0.03430646285414696,
-0.03829776868224144,
-0.026904290542006493,
0.007624227553606033,
-0.010995812714099884,
-0.014033596031367779,
0.05818924307823181,
0.030685145407915115,
0.03637203201651573,
0.008791406638920307,
-0.017677221447229385,
0.058096304535865784,
-0.05971498787403107,
-0.016583895310759544,
-0.029283108189702034,
-0.017898237332701683,
0.0028822720050811768,
-0.0030965253245085478
] |
<p>I'm currently consuming a course on QFT where we need to define the unitary time-evolution to get the time evolution of the wave function in the interaction picture:</p>
<p>$\hat{U}(t_1,t_0) = \exp\left(\frac{i}{\hbar}\hat{H}_0t_1\right)\exp\left(-\frac{i}{\hbar}\hat{H}(t_1-t_0)\right)\exp\left(-\frac{i}{\hbar}\hat{H}_0t_0\right)$ .</p>
<p>Now one can show that this operator follows a Schrödinger equation by simply taking the derivative to time:</p>
<p>$i\hbar\frac{d}{dt}\hat{U}(t,t_0) = \hat{H}_1^I(t)\hat{U}(t,t_0)$ .</p>
<p>Where $\hat{H}_1^I$ is the perturbation to our free-field Hamiltonian $\hat{H}_0$.</p>
<p>Now I started wondering whether $\hat{U}(t_1,t_0)$ shouldn't also follow a Heisenberg equation since it's an operator.</p>
<p>I believe it shouldn't since $\hat{U}(t_1,t_0)$ gives a unitairy time-evolution which is a transformation, while the Heisenberg equation applies to observables. I was woundering if someone could confirm my reasoning or disprove it?</p> | 1,559 | [
0.006081259343773127,
-0.033317066729068756,
0.042659129947423935,
-0.01231129840016365,
-0.00017456903879065067,
-0.00989222340285778,
-0.037645258009433746,
-0.02400067076086998,
0.01659507490694523,
-0.0351581908762455,
0.00017300060426350683,
0.01860661990940571,
0.03946631774306297,
0.0002660758327692747,
-0.0011036930372938514,
0.02509964071214199,
0.0034890894312411547,
-0.02148240990936756,
-0.03406781703233719,
-0.016520129516720772,
0.004642318934202194,
0.06541583687067032,
0.003924287389963865,
-0.006428224965929985,
-0.011321671307086945,
0.008480860851705074,
0.004584405105561018,
0.047451794147491455,
0.0009162635542452335,
0.10061508417129517,
-0.019893048331141472,
-0.05690803378820419,
0.01350812241435051,
0.046577759087085724,
0.0001519943034509197,
0.004288679454475641,
-0.03618024289608002,
-0.0558917261660099,
0.004304120782762766,
-0.00017197668785229325,
-0.03109218366444111,
-0.029607824981212616,
-0.005265113897621632,
0.04289313405752182,
0.024907192215323448,
0.01924893632531166,
-0.013252339325845242,
-0.026415878906846046,
0.04723189398646355,
-0.04424392059445381,
0.06302889436483383,
0.01984817534685135,
0.03579014912247658,
0.01967799849808216,
-0.03487812727689743,
-0.005250456742942333,
0.07897258549928665,
0.06350576132535934,
0.0015365567523986101,
-0.0434744767844677,
-0.005821553058922291,
-0.03992079943418503,
-0.001391847268678248,
-0.032771430909633636,
-0.015810329467058182,
0.010048823431134224,
0.02243843488395214,
-0.0016644949791952968,
0.018544137477874756,
-0.0409034863114357,
0.01743868924677372,
-0.0456589050590992,
0.06101933866739273,
-0.013381891883909702,
0.02084050141274929,
-0.020908109843730927,
0.015394536778330803,
0.036298613995313644,
0.0473962277173996,
0.033579446375370026,
-0.011746310628950596,
0.0037801507860422134,
0.035220932215452194,
0.010325409471988678,
-0.009044278413057327,
0.01360976230353117,
0.0555901937186718,
0.006959037855267525,
0.0013550405856221914,
0.05097934231162071,
-0.03996315598487854,
0.019517438486218452,
0.034430477768182755,
-0.008784359320998192,
-0.006983764935284853,
0.031850624829530716,
0.02230665646493435,
0.04732585325837135,
-0.007740708068013191,
-0.04125967249274254,
0.0004152358160354197,
-0.07246928662061691,
0.012756259180605412,
0.04111306741833687,
0.020734449848532677,
0.008852748200297356,
-0.05499640107154846,
0.02492132969200611,
-0.03724613040685654,
-0.036370083689689636,
-0.059898167848587036,
0.000761530187446624,
-0.04530362784862518,
0.0007733964594081044,
-0.053716495633125305,
-0.04226890951395035,
0.02713944762945175,
-0.00021322474640328437,
0.07574701309204102,
0.0650642141699791,
0.04512203857302666,
-0.040566857904195786,
0.019853418692946434,
-0.028299175202846527,
-0.10159631818532944,
0.010237041860818863,
0.03652838617563248,
-0.007753689307719469,
-0.03698379918932915,
0.01728713884949684,
0.010041599161922932,
-0.0303255133330822,
0.030690273270010948,
0.006588428746908903,
0.02364593930542469,
-0.027440430596470833,
-0.11124007403850555,
-0.06471280753612518,
0.0031273835338652134,
-0.025044623762369156,
0.005938035435974598,
-0.09120788425207138,
-0.018697859719395638,
0.04517826810479164,
0.09082210063934326,
-0.03153587505221367,
0.010742554441094398,
-0.008414153009653091,
0.022360816597938538,
0.02411688305437565,
-0.014210292138159275,
-0.029305970296263695,
-0.0116732781752944,
-0.04613065347075462,
0.004139102064073086,
-0.04026033729314804,
0.021913448348641396,
0.023654764518141747,
-0.010692196898162365,
0.026633545756340027,
0.11084581166505814,
0.00801803171634674,
0.02357478067278862,
0.03128383308649063,
-0.00857564713805914,
-0.05451960116624832,
0.07825639098882675,
0.014750502072274685,
0.05597912147641182,
0.05201224610209465,
0.0107372235506773,
0.010297066532075405,
0.007574441842734814,
0.03846953436732292,
-0.013193923979997635,
-0.03645928204059601,
-0.016637831926345825,
-0.03174601495265961,
-0.023235125467181206,
-0.00906402338296175,
-0.007558328565210104,
-0.025127286091446877,
-0.03700190782546997,
0.0006568424869328737,
-0.004859637003391981,
0.008355396799743176,
-0.014746279455721378,
0.032751526683568954,
-0.014195132069289684,
-0.04140831530094147,
-0.006668663118034601,
-0.05698041617870331,
-0.0008662124164402485,
0.031180936843156815,
0.03517603874206543,
0.05937853083014488,
-0.017515359446406364,
0.016374720260500908,
-0.013328444212675095,
-0.05832914263010025,
-0.0045949118211865425,
0.01616048626601696,
0.006468098144978285,
0.0006581906927749515,
0.02861296944320202,
0.028434649109840393,
0.039630744606256485,
0.02108071930706501,
0.025875961408019066,
-0.052935268729925156,
-0.026371169835329056,
0.022908443585038185,
0.006704800296574831,
0.022983836010098457,
-0.003957303240895271,
0.012085029855370522,
0.0067680273205041885,
-0.04177611693739891,
-0.010935710743069649,
0.013328569009900093,
-0.00942782312631607,
0.03141944855451584,
0.0425630584359169,
0.005028720013797283,
0.007200821302831173,
0.04533405974507332,
0.01237711776047945,
0.021406179293990135,
-0.00458214757964015,
-0.035422228276729584,
-0.032798994332551956,
0.020977411419153214,
0.042892925441265106,
0.025371331721544266,
-0.026438366621732712,
-0.00501887034624815,
0.008816431276500225,
0.056140635162591934,
0.018035613000392914,
0.01735781878232956,
-0.0024802638217806816,
-0.018908793106675148,
0.015599820762872696,
-0.0013831759570166469,
0.0068169548176229,
-0.024806145578622818,
0.024575917050242424,
-0.013118415139615536,
0.03145056962966919,
0.007197197992354631,
-0.04363342374563217,
0.0209523756057024,
-0.04725673049688339,
0.0065176161006093025,
0.009353242814540863,
-0.004742121789604425,
-0.013136173598468304,
-0.030581768602132797,
0.021744774654507637,
-0.0009493522811681032,
-0.0362996943295002,
-0.023673566058278084,
-0.028865324333310127,
-0.029258187860250473,
0.029458582401275635,
-0.02018001675605774,
-0.017013927921652794,
-0.013452677056193352,
0.006290195509791374,
-0.017632082104682922,
-0.023700756952166557,
-0.01619766466319561,
-0.00765133835375309,
-0.016632094979286194,
-0.0012590483529493213,
0.04046864062547684,
0.04768398776650429,
0.023145442828536034,
-0.043772291392087936,
-0.041691750288009644,
0.0018988697556778789,
-0.022207990288734436,
0.06675650924444199,
0.026166701689362526,
-0.030903154984116554,
0.04895466938614845,
-0.055030714720487595,
-0.030049869790673256,
0.04469779133796692,
-0.008639061823487282,
0.029069334268569946,
-0.01611929200589657,
-0.014512184076011181,
-0.03721615672111511,
-0.04064547270536423,
-0.059222228825092316,
0.019685233011841774,
-0.012909074313938618,
-0.006106057669967413,
0.04031852260231972,
-0.0007230241899378598,
-0.02873469702899456,
0.06163033843040466,
-0.003682682989165187,
-0.05052106827497482,
-0.008211469277739525,
0.006672369781881571,
0.06978697329759598,
-0.01259134616702795,
0.03275131434202194,
0.029521124437451363,
-0.032316431403160095,
-0.04913526773452759,
-0.05582495778799057,
-0.030088001862168312,
0.051794979721307755,
0.04685474932193756,
0.029309667646884918,
0.008672570809721947,
-0.030070966109633446,
0.06987481564283371,
0.020374272018671036,
-0.02809593454003334,
-0.025673383846879005,
0.009568649344146252,
0.013044700026512146,
-0.008539176546037197,
0.016649052500724792,
-0.010922316461801529,
0.002976331626996398,
0.035173941403627396,
-0.008569004014134407,
0.013154090382158756,
0.04292101413011551,
0.0017588145565241575,
-0.0062430137768387794,
0.009419044479727745,
-0.0038533746264874935,
0.0024014580994844437,
0.07377062737941742,
-0.008253117091953754,
0.002611267613247037,
0.008303895592689514,
-0.016242051497101784,
0.01740729995071888,
0.009465557523071766,
-0.03559839725494385,
0.07370693981647491,
0.0009773052297532558,
0.008826235309243202,
-0.01353746559470892,
0.02879280224442482,
-0.02761455625295639,
-0.025856973603367805,
-0.03313454985618591,
0.027324814349412918,
0.0378103107213974,
-0.026213953271508217,
0.038053009659051895,
0.03910849988460541,
0.014209778048098087,
-0.03422877937555313,
-0.01534191332757473,
-0.008376975543797016,
-0.036993544548749924,
0.03370506316423416,
-0.041885197162628174,
-0.06534227728843689,
0.03428453952074051,
0.027371998876333237,
0.016586607322096825,
-0.04373607411980629,
-0.06354385614395142,
-0.040815968066453934,
-0.04373905062675476,
0.021823465824127197,
-0.009627388790249825,
0.064883753657341,
0.017859289422631264,
0.062440138310194016,
0.03890209645032883,
0.009385079145431519,
0.02326921932399273,
0.021878557279706,
-0.050994787365198135,
0.027539556846022606,
-0.02279023453593254,
-0.020575106143951416,
-0.004067520145326853,
-0.00868950504809618,
0.03628703951835632,
-0.020421726629137993,
0.0025906632654368877,
-0.011967619881033897,
-0.06340420246124268,
-0.03859617933630943,
0.017504973337054253,
-0.007313649170100689,
-0.033071476966142654,
-0.007723627611994743,
-0.00024305858823936433,
0.015289564616978168,
0.013394396752119064,
0.005914779379963875,
0.039080116897821426,
-0.019271045923233032,
0.030089084059000015,
-0.01748187094926834,
-0.004228407982736826,
0.027762847021222115,
0.00460238941013813,
0.0271218940615654,
-0.0005380514776334167,
-0.03821781650185585,
0.01940060965716839,
0.002973671304062009,
0.0600125826895237,
-0.007109771016985178,
-0.057068146765232086,
0.0014793394366279244,
-0.05224313214421272,
-0.0008359956555068493,
0.03637318313121796,
0.0691172182559967,
0.016362546011805534,
0.009750603698194027,
0.05102214962244034,
0.00770017271861434,
0.00048411256284452975,
0.029765836894512177,
0.03152104839682579,
0.006841826718300581,
-0.000829746772069484,
-0.034217704087495804,
0.0225457064807415,
0.0007556573254987597,
-0.03406378626823425,
-0.013275333680212498,
0.00004051841824548319,
-0.01372894924134016,
0.007109398487955332,
0.015769287943840027,
0.04527448117733002,
-0.015876999124884605,
-0.0197089035063982,
0.02527696080505848,
0.007540876977145672,
0.00026272996910847723,
0.004502229392528534,
0.032085906714200974,
0.046921830624341965,
0.013795528560876846,
-0.012612421065568924,
0.02215062640607357,
-0.05193072557449341,
-0.016861435025930405,
0.04331960901618004,
0.02961687184870243,
-0.012017560191452503,
0.0007249524351209402,
-0.01990317367017269,
-0.029243186116218567,
0.05618744716048241,
-0.01864778995513916,
0.02561067044734955,
0.03261006996035576,
-0.032896384596824646,
0.005543578881770372,
-0.050292015075683594,
-0.03279699757695198,
0.03983105346560478,
0.007745593786239624,
-0.002344253472983837,
-0.018028106540441513,
0.0037059984169900417,
0.013064099475741386,
0.010082940571010113,
0.0065683359280228615,
0.06593362987041473,
0.0011610053479671478,
-0.004692161455750465,
0.012681743130087852,
0.04088231548666954,
-0.05091821402311325,
-0.07969486713409424,
-0.0005936892703175545,
0.005524164531379938,
-0.010966992937028408,
0.024480203166604042,
-0.01549964863806963,
-0.06797446310520172,
0.02595919743180275,
0.036866605281829834,
0.006336606573313475,
-0.004134303890168667,
-0.04723822697997093,
0.05954364314675331,
0.01931426115334034,
-0.015134060755372047,
0.03712034970521927,
0.06289626657962799,
0.01795007288455963,
-0.009137662127614021,
-0.025617562234401703,
0.012451820075511932,
-0.025626854971051216,
0.027610210701823235,
-0.041991136968135834,
-0.004705930128693581,
-0.023718612268567085,
0.02157697267830372,
-0.02413555607199669,
0.00883825495839119,
-0.02426256611943245,
-0.028169894590973854,
0.010921270586550236,
0.03176714479923248,
-0.01903461664915085,
-0.020497815683484077,
-0.04207824915647507,
-0.009819546714425087,
0.022906772792339325,
-0.021003467962145805,
-0.036099936813116074,
0.00023070820316206664,
-0.015568770468235016,
0.05553056299686432,
0.009549274109303951,
0.02979486994445324,
-0.021350406110286713,
-0.03498683124780655,
-0.025562260299921036,
-0.06592465937137604,
0.014577014371752739,
-0.018875285983085632,
-0.0030410371255129576,
-0.0008874948252923787,
-0.0053199343383312225,
0.013837898150086403,
0.007039058953523636,
-0.0023628855124115944,
0.0032240967266261578,
-0.028454242274165154,
0.004199661314487457,
0.03039788268506527,
-0.005957239307463169,
-0.09814532101154327,
-0.04755037650465965,
-0.018333295360207558,
0.005534295924007893,
-0.01670275628566742,
-0.010518821887671947,
0.029997888952493668,
-0.03084607422351837,
-0.019482702016830444,
0.03516153618693352,
0.03163577616214752,
0.0023288652300834656,
-0.02679336816072464,
0.015416000038385391,
0.055070217698812485,
0.053795211017131805,
-0.0016992862801998854,
0.006859302520751953,
-0.00204916438087821,
-0.010221822187304497,
-0.049537543207407,
0.04077685996890068,
0.0661064088344574,
-0.002453562803566456,
-0.012119900435209274,
0.006849643774330616,
-0.02313951589167118,
0.025601522997021675,
-0.007390244398266077,
-0.007540433201938868,
0.027492957189679146,
0.00475914916023612,
0.013558746315538883,
-0.03035685606300831,
0.0034187783021479845,
-0.0035527932923287153,
0.014020413160324097,
0.03357604146003723,
0.0247515756636858,
-0.011940088123083115,
-0.03494487702846527,
0.026630820706486702,
-0.018351783975958824,
-0.020897628739476204,
0.03965459764003754,
0.03253508731722832,
0.0041750455275177956,
0.00100125081371516,
0.03564002737402916,
-0.0321352556347847,
0.0016468961257487535,
-0.003010691376402974,
-0.006216424982994795,
0.009972243569791317,
-0.00677326088771224,
-0.022190239280462265,
-0.018596192821860313,
-0.05918028950691223,
0.02367996796965599,
0.034503087401390076,
-0.007648789323866367,
0.03514191880822182,
-0.004737145733088255,
0.0032759876921772957,
-0.0365387499332428,
-0.016358667984604836,
-0.020894918590784073,
0.02054278366267681,
-0.00024822860723361373,
0.02936478704214096,
-0.012996386736631393,
-0.013788215816020966,
0.022077176719903946,
0.021660665050148964,
-0.023442091420292854,
0.012219330295920372,
0.037944238632917404,
0.024377670139074326,
0.031074391677975655,
0.018983783200383186,
-0.0698651671409607,
0.045161787420511246,
-0.03947194293141365,
0.03263816982507706,
0.007670384831726551,
-0.001538193435408175,
0.004641216713935137,
0.03007342480123043,
-0.002007732167840004,
-0.02134210802614689,
-0.02128499560058117,
-0.046883225440979004,
0.010442996397614479,
0.010103017091751099,
0.009177527390420437,
0.002090088091790676,
-0.0064612324349582195,
0.031167346984148026,
0.011408369056880474,
0.025081505998969078,
0.00652842503041029,
-0.04283946380019188,
0.01266151387244463,
-0.07218767702579498,
-0.02359393797814846,
0.04491889849305153,
-0.018105976283550262,
0.0006147121894173324,
-0.021570036187767982,
-0.02070588245987892,
0.0019951886497437954,
-0.021777885034680367,
0.03307092562317848,
-0.021774865686893463,
0.06760916858911514,
0.001162857748568058,
0.015657346695661545,
-0.011484798043966293,
0.001822866266593337,
0.11606879532337189,
0.041766293346881866,
0.0485321544110775,
-0.03591134399175644,
-0.022742554545402527,
-0.01559828408062458,
-0.0055297305807471275,
-0.03214263916015625,
0.037271685898303986,
-0.005304461345076561,
-0.030506953597068787,
-0.016686540096998215,
0.045844223350286484,
0.03277428820729256,
0.006819381378591061,
0.06322221457958221,
-0.060045208781957626,
-0.02122628316283226,
0.014145195484161377,
0.012353251688182354,
-0.011211507953703403,
-0.002782679395750165,
-0.033468373119831085,
0.000488330377265811,
-0.03573783114552498,
0.028013477101922035,
0.0013386638602241874,
-0.033225104212760925,
0.02563236653804779,
-0.005344476085156202,
-0.06398609280586243,
-0.007108860649168491,
-0.021404657512903214,
-0.01818881742656231,
-0.04827539250254631,
0.01917165331542492,
-0.012742952443659306,
-0.012721629813313484,
0.041050318628549576,
0.039203088730573654,
0.024669183418154716,
-0.019498640671372414,
0.039080455899238586,
-0.005393668077886105,
-0.01364540122449398,
0.01865965686738491,
-0.021545879542827606,
0.05615207180380821,
-0.036284834146499634,
-0.024612925946712494,
-0.006773634813725948,
-0.024739859625697136,
0.014192922040820122,
-0.05871642008423805,
-0.013634155504405499,
-0.0019996187184005976,
0.0358411930501461,
0.01610398478806019,
0.03164993226528168,
-0.04391275346279144,
-0.004444924648851156,
-0.005689589772373438,
0.015280487015843391,
0.0028524259105324745,
-0.024511633440852165,
-0.006295245140790939,
0.006493636406958103,
0.014695017598569393,
-0.026629837229847908,
-0.010144231840968132,
0.00806258525699377,
-0.002900416497141123,
-0.05993998050689697,
-0.027938252314925194,
0.05920223519206047,
-0.003507317742332816,
0.08078029751777649,
-0.012060550041496754,
0.020223647356033325,
-0.044734422117471695,
-0.08909402042627335,
0.017204247415065765,
0.02524620294570923,
-0.03277033194899559,
-0.007033293601125479,
0.0021979159209877253,
0.03406643494963646,
0.06647011637687683,
-0.0402534157037735,
0.009018688462674618,
0.005411648191511631,
0.014296342618763447,
0.02652657963335514,
-0.01579444669187069,
-0.0022556642070412636,
0.046355050057172775,
0.0017689487431198359,
0.003658402245491743,
-0.02311887964606285,
-0.03098699077963829,
0.03090091235935688,
0.02301640622317791,
-0.018131516873836517,
0.029819495975971222,
0.010926799848675728,
0.006248088087886572,
0.009721627458930016,
-0.012753366492688656,
0.033949438482522964,
-0.001100099296309054,
0.03163726627826691,
-0.025740930810570717,
-0.06410329788923264,
-0.024295615032315254,
0.017805052921175957,
-0.011996828950941563,
0.006327266339212656,
-0.03639785200357437,
-0.0006072903051972389,
-0.019037457183003426,
0.06749962270259857,
-0.03339768573641777,
0.002327434252947569,
-0.08236396312713623,
0.022944362834095955,
0.03208491578698158,
-0.010241284035146236,
0.006083996966481209,
0.028013482689857483,
-0.00599147193133831,
-0.0412302128970623,
0.04373108595609665,
0.04815471172332764,
-0.027122532948851585,
0.008522248826920986,
0.005074162967503071,
0.027330361306667328,
0.008200223557651043,
0.004720126278698444,
-0.026225920766592026,
0.0260042492300272,
-0.018246758729219437,
-0.022290602326393127,
0.026629215106368065,
0.015129291452467442,
0.03676098957657814,
0.04038434103131294,
-0.02489376813173294,
-0.023045308887958527,
0.024054206907749176,
-0.03827150538563728,
0.01567010208964348,
0.03172178566455841,
-0.04568038880825043,
-0.015425873920321465,
-0.031565047800540924,
0.022596275433897972,
0.009156737476587296,
-0.013118615373969078,
0.025547537952661514,
0.00460791727527976,
-0.010467245243489742,
-0.00434735557064414,
-0.016546720638871193,
0.013068807311356068,
0.037905868142843246,
0.013823510147631168,
-0.011512192897498608,
0.03795254975557327,
0.07485371083021164,
-0.039917562156915665,
0.0180372204631567,
0.025311017408967018,
0.021126972511410713,
-0.09713420271873474,
-0.03024488314986229,
0.023018909618258476,
0.02490374818444252,
0.035067424178123474,
-0.01664470136165619,
0.01624174974858761,
0.013144996017217636,
-0.04104214906692505,
0.037908829748630524,
-0.06467010825872421,
-0.011485612019896507,
0.008205296471714973,
0.024958519265055656,
-0.02192770130932331,
0.02437298558652401,
0.00916344951838255,
0.030577361583709717,
0.006158734206110239,
0.03591150790452957,
0.014580635353922844,
-0.0024059892166405916,
-0.02601597085595131,
0.008568151853978634,
0.015494892373681068,
-0.025887535884976387,
0.07841776311397552,
-0.014774276874959469,
-0.023628268390893936,
0.02611386775970459,
0.01686258427798748,
-0.026097793132066727,
-0.028281820937991142,
0.02769223228096962,
0.010709380730986595,
-0.0029303289484232664,
0.0472545325756073,
-0.04882367327809334,
-0.006381871644407511,
0.016350487247109413,
0.016590438783168793,
0.028198927640914917,
0.005319542251527309,
-0.0007574775954708457,
-0.013356621377170086,
-0.03909517824649811,
-0.05022256448864937,
0.05465700849890709,
0.002663219813257456,
-0.013031329028308392,
-0.035158317536115646,
-0.0337519608438015,
-0.01089967880398035,
-0.0008908026502467692,
0.025701232254505157,
-0.03058771602809429,
-0.029294820502400398,
-0.005751059390604496,
0.013799598440527916,
-0.008017918094992638,
0.003330383449792862,
-0.030606713145971298,
-0.03496599197387695,
0.023358622565865517,
0.020924706012010574,
-0.01274515688419342,
-0.05770519748330116,
-0.005281099583953619,
-0.0036282131914049387,
-0.02346489392220974,
-0.02017999440431595,
-0.030759060755372047,
-0.03573472425341606,
-0.0005953643703833222,
-0.0012021773727610707,
0.01947098784148693,
-0.04944930225610733,
-0.04222645238041878,
-0.03109898418188095,
-0.03858962655067444,
0.056888800114393234,
0.015493764542043209,
-0.0075479368679225445,
-0.021420583128929138,
-0.04193636029958725,
-0.0290683563798666,
0.012090694159269333,
0.07210687547922134,
-0.01645331270992756,
-0.03768661618232727,
0.01620086096227169,
-0.025566164404153824,
0.001917043817229569,
-0.02757323905825615,
0.0038940778467804193,
-0.03200148791074753,
0.001622597686946392,
-0.003625755198299885,
-0.011910495348274708,
-0.016430294141173363,
0.05951004475355148,
0.013355176895856857,
-0.014893301762640476,
0.021696003153920174,
0.006387106142938137,
-0.06435699760913849,
0.050529416650533676,
0.011319980956614017,
0.012057703919708729,
0.06630831956863403,
-0.007527633104473352,
0.01846066117286682,
0.04375585541129112,
-0.016866223886609077,
-0.030738141387701035,
0.021777763962745667,
-0.02952651120722294,
-0.03187509998679161,
-0.004470901098102331,
0.009153277613222599,
0.024646535515785217,
-0.02178405411541462,
-0.023349083960056305,
0.005074298474937677,
-0.03145651891827583,
-0.005266867112368345,
0.023908836767077446,
0.013843008317053318,
0.015698183327913284,
0.0043049524538218975,
0.008201565593481064,
0.05533161759376526,
0.043157439678907394,
0.01834462583065033,
0.04353565350174904,
0.010151791386306286,
-0.003614790504798293,
0.027640532702207565,
0.001272437977604568,
-0.0067769004963338375,
0.005086265504360199,
0.028946299105882645,
0.029052836820483208,
-0.02073083259165287,
-0.03033866547048092,
0.033026158809661865,
-0.01079653576016426,
-0.03514382615685463,
0.013280026614665985,
-0.043215312063694,
0.049085505306720734,
-0.0028853064868599176,
0.028283776715397835,
-0.01876802369952202,
0.015246412716805935,
-0.030094975605607033,
0.010246051475405693,
0.060249265283346176,
0.0671980082988739,
-0.04635598137974739,
-0.024353140965104103,
-0.031982358545064926,
-0.012339635752141476,
-0.018370693549513817,
-0.06342588365077972,
-0.027546025812625885,
0.03217540681362152,
-0.046966537833213806,
-0.0028240513056516647,
-0.020420648157596588,
-0.009845197200775146,
-0.010297585278749466,
0.018173154443502426,
0.05832295119762421,
0.022318758070468903,
-0.025757266208529472,
-0.008523531258106232,
-0.020244982093572617,
0.0639212429523468,
-0.05712464079260826,
0.013820609077811241,
0.005263796541839838,
0.005924456287175417,
0.010724306106567383,
-0.004665149841457605
] |
<p>In the 19th century, most astronomers adopted an island universe model, in which our galaxy was the only object in an infinite space. They didn't know that the "spiral nebulae" were other galaxies. This model had the advantage of being dynamically stable (unlike Newton's infinite and uniform cosmology), and of avoiding the fact that Poisson's equation doesn't have unique solutions for an infinite and uniform universe. Ca. 1830, the geologist Lyell advocated a theory of uniformitarianism, in which the universe would have had uniform conditions going back infinitely far in time. There was some debate between Lyell and physicists such as Kelvin, who objected that the sun would have run out of energy, the earth would have lost its internal heat, and so on, but this was inconclusive because they didn't know enough thermodynamics and didn't know about the atomic nucleus.</p>
<p>But by 1850, the second law of thermodynamics had been formulated, and this would seem to have been solid proof that the universe could not possibly have existed for an infinite time in the past. (This level of understanding of thermodynamics would also, I'd imagine, allow them to show that stars would gradually evaporate out of the galaxy, since the velocity distribution would have a high-velocity tail.) Kelvin did attack Lyell with the second law, but it doesn't sound like people at the time appreciated that this was a decisive argument.</p>
<p>With the benefit of hindsight, we can say that it was decisive, and from 1850 to 1905, people should have been considering only cosmological models that used Newtonian mechanics and that stretched back a finite time into the past. Are such models possible?</p>
<p>For example, I suppose you could make a Newtonian big bang, in which, as many students today imagine, there was an explosion at a specific point in otherwise empty space. Extrapolating the motion of all particles back in time using the laws of physics, one would find their trajectories all converging on a point, then diverging from it again on the other side, i.e., it would look like a big crunch/big bang "singularity," -- it would be a singularity of the matter density, temperature, etc. Thermodynamically, it would look like an extreme thermodynamic fluctuation, which is no worse than the thermodynamic implausibility of the low-entropy big bang in modern GR-based theories. There would be an upper bound on ages of objects in today's universe, because everything was destroyed in the singularity.</p>
<p>Another possibility I can imagine is that you could start off with a universe containing an infinite amount of matter and an infinite amount of energy thermodynamically available to do work. After an infinite time, you would have expended an infinite amount of energy to do work, but you would still have an infinite amount left. The modern counterpart of this kind of thinking would be calculations of whether you can do an infinite calculation in various cosmological models (Dyson 1979, Krauss 1999).</p>
<p>Related: <a href="http://physics.stackexchange.com/questions/6897/why-didnt-newton-have-a-cosmological-constant">Why didn't Newton have a cosmological constant</a></p>
<p><em>References</em></p>
<p>Dyson, Time without end: Physics and biology in an open universe, Reviews of Modern Physics 51 (1979), pp. 447–460, doi:10.1103/RevModPhys.51.447; described in <a href="http://math.ucr.edu/home/baez/end.html">http://math.ucr.edu/home/baez/end.html</a></p>
<p>Krauss and Starkman, 1999, Life, The Universe, and Nothing: Life and Death in an Ever-Expanding Universe, <a href="http://arxiv.org/abs/astro-ph/9902189">http://arxiv.org/abs/astro-ph/9902189</a></p> | 1,560 | [
-0.05172962695360184,
-0.018235934898257256,
0.034969985485076904,
-0.023662352934479713,
0.08341432362794876,
-0.036356549710035324,
-0.057248685508966446,
0.0012981760082766414,
-0.051153361797332764,
-0.032079510390758514,
0.011131681501865387,
0.013679266907274723,
0.03607369214296341,
0.008570271544158459,
0.021147072315216064,
0.001991709228605032,
0.01428813487291336,
-0.029003674164414406,
0.005694881081581116,
-0.010774816386401653,
0.035808153450489044,
0.006713951006531715,
-0.043235618621110916,
0.010131683200597763,
-0.046301815658807755,
0.014644167385995388,
0.014963870868086815,
-0.006275425665080547,
-0.002292454242706299,
0.058721110224723816,
-0.036912430077791214,
-0.003924340009689331,
0.024146948009729385,
0.025191212072968483,
0.03919260948896408,
0.023526523262262344,
0.006927094422280788,
-0.04115762561559677,
-0.011482917703688145,
0.00881167408078909,
-0.031773511320352554,
-0.012170476838946342,
0.00668248999863863,
-0.007585826329886913,
-0.072872593998909,
0.05429822579026222,
-0.0008057357044890523,
-0.016427095979452133,
0.034939322620630264,
-0.01270554680377245,
0.026917099952697754,
-0.010279642418026924,
0.013908881694078445,
0.028216062113642693,
-0.009916874580085278,
-0.00825199019163847,
0.09605387598276138,
0.05153852328658104,
-0.007022124249488115,
-0.04925074055790901,
-0.002533219987526536,
0.028306638821959496,
-0.02071021869778633,
-0.023091860115528107,
0.026592504233121872,
-0.010927172377705574,
0.03426409140229225,
-0.03781195357441902,
0.004691873677074909,
-0.021281862631440163,
0.028453459963202477,
0.027497712522745132,
0.019728345796465874,
0.019800962880253792,
0.023718807846307755,
0.0060894242487847805,
0.02165672369301319,
-0.01693924330174923,
-0.005308283492922783,
0.015091201290488243,
-0.030654849484562874,
-0.004384705331176519,
0.039329394698143005,
0.03970954939723015,
0.010742825455963612,
0.016838841140270233,
0.0572136789560318,
-0.016597682610154152,
0.003963015042245388,
0.0505346804857254,
-0.012401629239320755,
0.001908796140924096,
0.011257844977080822,
-0.014044460840523243,
-0.010943067260086536,
0.037421006709337234,
-0.007603174541145563,
0.0012457522097975016,
0.022292504087090492,
-0.0038807387463748455,
-0.005978303030133247,
-0.024625418707728386,
0.0038430376444011927,
0.0886940285563469,
0.041565731167793274,
-0.015555440448224545,
-0.056285712867975235,
0.01100869569927454,
-0.04955907166004181,
0.0012770683970302343,
-0.05575249344110489,
0.03831356018781662,
0.001931556616909802,
0.027297193184494972,
-0.0006259196088649333,
0.0034007206559181213,
-0.02558915875852108,
-0.030591027811169624,
0.09844619780778885,
0.062034972012043,
0.04087456688284874,
0.021829860284924507,
-0.001594420406036079,
-0.002768161939457059,
-0.06987053900957108,
0.018551785498857498,
0.051200930029153824,
-0.02139080874621868,
-0.004242280498147011,
-0.003090613055974245,
0.01545992773026228,
0.01904015801846981,
-0.026743242517113686,
0.014843416400253773,
0.05788610130548477,
0.0017282450571656227,
-0.08034121990203857,
-0.0579342320561409,
0.0380217544734478,
0.029428815469145775,
0.00537697970867157,
-0.03888779878616333,
0.024713464081287384,
0.03792586922645569,
0.06554839760065079,
-0.012598900124430656,
-0.011630288325250149,
-0.052636221051216125,
0.07993091642856598,
-0.04614654555916786,
-0.03798927739262581,
-0.0252623800188303,
0.011166607029736042,
-0.004574493505060673,
0.013449465855956078,
-0.10072360187768936,
0.03391486033797264,
0.04534459859132767,
0.01308242604136467,
-0.006884381175041199,
0.05637916177511215,
-0.04067602381110191,
0.01160887349396944,
-0.03539985418319702,
-0.007012771442532539,
-0.03089139796793461,
0.09779031574726105,
0.000284634210402146,
0.01382432784885168,
0.03287516534328461,
-0.011608281172811985,
0.034877389669418335,
0.010631049983203411,
-0.006672654300928116,
0.00014123135770205408,
-0.020699264481663704,
0.004654384683817625,
-0.02972770668566227,
-0.02028212510049343,
-0.0026907152496278286,
-0.025518126785755157,
0.01951550506055355,
0.018433749675750732,
-0.011433983221650124,
0.02268144302070141,
0.039234429597854614,
0.021484719589352608,
0.008398707956075668,
0.028415773063898087,
-0.033860065042972565,
-0.03747423738241196,
-0.06188344955444336,
0.017079370096325874,
0.0036732901353389025,
0.020684976130723953,
0.0046221669763326645,
-0.019262954592704773,
0.02367638796567917,
-0.02677413634955883,
-0.02836858294904232,
0.006479847710579634,
0.04160119965672493,
0.04117698594927788,
-0.008621037006378174,
0.028329873457551003,
0.07617821544408798,
0.04033036157488823,
0.0030350908637046814,
0.011716751381754875,
-0.011547603644430637,
-0.025431698188185692,
0.02163231186568737,
-0.021444540470838547,
0.029984764754772186,
0.0326804593205452,
0.026999270543456078,
-0.007652336731553078,
0.04379541426897049,
-0.0065788524225354195,
0.018842196092009544,
-0.03701868653297424,
0.04727393761277199,
-0.0027235462330281734,
0.024531027302145958,
-0.024943426251411438,
0.06859714537858963,
0.002222379669547081,
0.006042210850864649,
-0.010789104737341404,
-0.026623958721756935,
-0.07479911297559738,
-0.019464340060949326,
0.028543565422296524,
0.05677396431565285,
-0.004175417125225067,
0.008394967764616013,
0.00005056018562754616,
0.07037436962127686,
0.015485625714063644,
-0.015669405460357666,
0.006095547694712877,
-0.02300708368420601,
0.002772658597677946,
-0.030657000839710236,
0.03032691217958927,
0.040167853236198425,
0.04481028392910957,
-0.011490986682474613,
-0.03247876092791557,
-0.012058993801474571,
-0.006328443996608257,
0.0007301517762243748,
0.053763218224048615,
-0.013050343841314316,
0.004549195058643818,
-0.03442090004682541,
0.020927943289279938,
0.034222815185785294,
0.04029930382966995,
0.02005925215780735,
0.01912836730480194,
0.005562643054872751,
-0.08983509242534637,
0.008190878666937351,
-0.0024794014170765877,
0.020327270030975342,
-0.01127544417977333,
-0.018274446949362755,
0.043745316565036774,
-0.02324148640036583,
-0.028568904846906662,
-0.006111960858106613,
-0.004511483013629913,
-0.03419684246182442,
-0.011062843725085258,
-0.007894933223724365,
0.03191334009170532,
0.006418764591217041,
-0.020454872399568558,
-0.021166127175092697,
0.0115570779889822,
0.0030098322313278913,
0.0035466679837554693,
0.03310791403055191,
-0.02061470039188862,
0.016608331352472305,
0.010199636220932007,
0.014975710771977901,
0.03232663497328758,
0.00152356899343431,
0.03782109543681145,
0.0011441350216045976,
-0.002557831583544612,
-0.037616051733493805,
0.01870892010629177,
-0.03780760616064072,
0.0025243093259632587,
-0.01619938388466835,
0.008136814460158348,
0.05747109651565552,
-0.016216250136494637,
-0.07875040173530579,
0.015318663790822029,
-0.07515238970518112,
-0.024597028270363808,
-0.044516660273075104,
-0.03606561943888664,
-0.011382694356143475,
-0.0121600441634655,
-0.0027993610128760338,
0.021735722199082375,
-0.027893193066120148,
-0.026515891775488853,
-0.03465094789862633,
-0.061705783009529114,
0.027786478400230408,
-0.001935077947564423,
0.04602451249957085,
-0.03470180928707123,
-0.015300496481359005,
0.03763238340616226,
0.01953796111047268,
0.004778580274432898,
-0.01870349794626236,
0.026700647547841072,
0.004494646564126015,
0.0011456445790827274,
-0.002207490848377347,
-0.004533472470939159,
-0.01773785427212715,
0.0006735757924616337,
-0.01870749332010746,
0.04197454825043678,
-0.0011535856174305081,
-0.007868476212024689,
0.013933262787759304,
0.031428661197423935,
0.0021780093666166067,
0.027705006301403046,
0.027643447741866112,
0.03874257206916809,
-0.020656758919358253,
0.010298360139131546,
-0.05341164022684097,
0.06509053707122803,
0.040206167846918106,
-0.06933097541332245,
0.03808979317545891,
0.02043677680194378,
0.013889431953430176,
-0.0259893499314785,
0.03499417006969452,
-0.03389793634414673,
-0.0010620832908898592,
-0.004215728025883436,
-0.00634346017614007,
0.03417972847819328,
0.019757026806473732,
0.015305086970329285,
-0.006051621399819851,
0.023959076032042503,
-0.012925089336931705,
0.015006424859166145,
0.003982972353696823,
-0.008216720074415207,
0.010250769555568695,
-0.02946762926876545,
-0.011028352193534374,
0.01905285380780697,
0.0023114504292607307,
-0.014744734391570091,
0.027796732261776924,
-0.024512140080332756,
-0.016054105013608932,
-0.060008250176906586,
0.006591382436454296,
-0.03869647905230522,
0.044619668275117874,
-0.0018477726262062788,
0.01718795858323574,
-0.002830660669133067,
0.029269322752952576,
-0.0034138886258006096,
-0.024280739948153496,
-0.08095297962427139,
-0.00701154675334692,
-0.03415397182106972,
-0.03781841695308685,
-0.017766956239938736,
0.030384128913283348,
-0.011415437795221806,
0.025982597842812538,
0.010625956580042839,
-0.04024830460548401,
0.005353954154998064,
-0.05824604630470276,
0.01979449763894081,
-0.03411252796649933,
-0.07561244815587997,
-0.028084129095077515,
0.02781909517943859,
0.04711078852415085,
-0.009437826462090015,
0.04461822658777237,
-0.005394634325057268,
-0.010048194788396358,
-0.009229377843439579,
-0.015479333698749542,
-0.007554191164672375,
0.004300987347960472,
-0.004202037118375301,
-0.0005733509315177798,
0.026543516665697098,
-0.01354229636490345,
0.0033229547552764416,
0.0646064355969429,
-0.0032140370458364487,
0.01626480557024479,
0.014862575568258762,
-0.014741434715688229,
-0.011103765107691288,
-0.02369680441915989,
0.02627100981771946,
0.04668262600898743,
-0.0059522646479308605,
0.017110193148255348,
-0.008837469853460789,
0.0007631147163920105,
0.027555635198950768,
0.04433585703372955,
0.009855310432612896,
-0.05339708924293518,
-0.02371104620397091,
0.013570861890912056,
-0.015069050714373589,
-0.00948267336934805,
0.0035070765297859907,
0.0022484532091766596,
0.029585275799036026,
-0.026820406317710876,
0.02311878837645054,
-0.016778675839304924,
0.04082931578159332,
-0.01175000611692667,
0.0043961051851511,
-0.02351001277565956,
0.03444616496562958,
-0.04871787875890732,
-0.005334843415766954,
0.027272820472717285,
0.0160187017172575,
0.03448497876524925,
-0.019017405807971954,
-0.020170345902442932,
-0.04356107860803604,
-0.020863013342022896,
-0.004013737663626671,
-0.0035575400106608868,
-0.01938369683921337,
0.0028679203242063522,
-0.08745865523815155,
-0.04938367009162903,
0.025587929412722588,
-0.02599027380347252,
0.013594594784080982,
-0.03642474487423897,
0.005238864570856094,
0.00572382565587759,
-0.06290936470031738,
0.0039046111050993204,
0.03250737488269806,
-0.008140349760651588,
0.013383070006966591,
0.002940482459962368,
0.014214916154742241,
-0.033900756388902664,
-0.019476113840937614,
-0.004427126608788967,
0.01955774798989296,
0.002674933522939682,
0.0014782933285459876,
-0.028867747634649277,
0.011967156082391739,
-0.03393112123012543,
-0.05118580162525177,
0.013270454481244087,
0.005265361629426479,
-0.011693092994391918,
0.019652822986245155,
-0.029723968356847763,
-0.0555705763399601,
0.04413945972919464,
-0.0030887729953974485,
-0.035013388842344284,
0.013023130595684052,
-0.026247292757034302,
0.036566752940416336,
-0.008264316245913506,
0.008153386414051056,
0.016887780278921127,
0.04200102761387825,
-0.03353508934378624,
0.031040769070386887,
-0.041442375630140305,
-0.005087331403046846,
-0.014569263905286789,
-0.0038365772925317287,
-0.060080818831920624,
-0.00012149497342761606,
-0.040352676063776016,
-0.006591463461518288,
0.019430045038461685,
0.016640091314911842,
-0.027104293927550316,
-0.030518367886543274,
0.015284785069525242,
0.0042539676651358604,
0.03362124785780907,
0.01386354025453329,
-0.06958974152803421,
0.022259647026658058,
0.003390904748812318,
-0.04106978327035904,
0.03586120158433914,
0.02032247744500637,
0.017588192597031593,
0.022004075348377228,
0.019507596269249916,
0.026860548183321953,
-0.0033164629712700844,
-0.019418450072407722,
0.006331244017928839,
-0.013346120715141296,
0.05332719162106514,
-0.003719207365065813,
0.00317069492302835,
0.031522780656814575,
-0.034138087183237076,
-0.04423493146896362,
0.01869991049170494,
-0.061691075563430786,
-0.009906873106956482,
-0.026269733905792236,
-0.005746706388890743,
0.013375435955822468,
-0.002606055699288845,
-0.08231843262910843,
0.0008444030536338687,
0.049101199954748154,
-0.004945829045027494,
-0.06240145489573479,
0.0027455633971840143,
0.007191114127635956,
-0.03886476531624794,
-0.009088076651096344,
0.026996763423085213,
0.03695254400372505,
0.009624614380300045,
-0.017154237255454063,
-0.007360665127635002,
0.03501607105135918,
0.05227122828364372,
-0.013016358017921448,
-0.017329787835478783,
-0.006379192229360342,
-0.01254880428314209,
0.006820557173341513,
-0.004454281646758318,
0.043646439909935,
-0.027619069442152977,
-0.00025411354727111757,
-0.015907902270555496,
0.02732706256210804,
-0.006635547615587711,
-0.03121240623295307,
-0.054093945771455765,
0.06221870705485344,
-0.036406952887773514,
-0.009718810208141804,
0.007190675009042025,
0.03637060150504112,
-0.007470133248716593,
0.03332923352718353,
-0.022759582847356796,
-0.014846841804683208,
0.03719515725970268,
-0.06895226985216141,
0.04109082743525505,
-0.01058982964605093,
0.01783604733645916,
0.014005061239004135,
0.059545159339904785,
-0.0026548304595053196,
-0.004998960066586733,
0.022389279678463936,
-0.007932664826512337,
0.025218268856406212,
-0.010604927316308022,
-0.03350521996617317,
-0.00023411883739754558,
0.019831731915473938,
-0.043463606387376785,
-0.027666276320815086,
-0.02154172770678997,
0.01679639331996441,
0.053439706563949585,
-0.005730010103434324,
0.039738062769174576,
0.005756550934165716,
0.014687422662973404,
-0.02308044023811817,
-0.030624380335211754,
-0.013295985758304596,
-0.00046636239858344197,
-0.012414727360010147,
0.027879996225237846,
-0.06934771686792374,
-0.0032190156634896994,
0.04419814795255661,
0.006146645173430443,
-0.015668505802750587,
-0.0005410771700553596,
0.007194459903985262,
0.008661073632538319,
0.013209972530603409,
-0.03731028735637665,
-0.03294384852051735,
0.003971656318753958,
-0.05438919737935066,
0.01744833029806614,
0.02567603625357151,
-0.0003309814492240548,
0.015204641968011856,
0.0179681945592165,
-0.030344858765602112,
-0.057139478623867035,
-0.031921710819005966,
-0.0712532252073288,
-0.0032435439061373472,
0.03350946307182312,
0.042408961802721024,
-0.0009772138437256217,
-0.003928590565919876,
-0.016796639189124107,
-0.0006604645750485361,
-0.005383723881095648,
0.006681838072836399,
-0.06386955082416534,
-0.03174177557229996,
-0.036127056926488876,
-0.03746390715241432,
0.014422768726944923,
-0.006581552792340517,
-0.018185431137681007,
-0.04076468199491501,
-0.008813525550067425,
0.0039853183552622795,
0.029950445517897606,
0.01165616326034069,
-0.021795619279146194,
0.05758092179894447,
-0.022604558616876602,
0.005293007008731365,
-0.05709091201424599,
0.022781237959861755,
0.1547631323337555,
0.05906692147254944,
0.01985909976065159,
-0.034028906375169754,
0.018921272829174995,
-0.0006444429745897651,
-0.017793087288737297,
-0.01652367226779461,
-0.0017934865318238735,
0.011436652392148972,
0.006125185173004866,
0.01659010536968708,
0.015638025477528572,
-0.025273580104112625,
-0.045104868710041046,
0.029997246339917183,
-0.024180637672543526,
-0.008083290420472622,
0.022396588698029518,
-0.009437144733965397,
-0.03545575588941574,
0.0239611454308033,
-0.023503024131059647,
-0.010714317671954632,
-0.015454316511750221,
0.023055613040924072,
-0.0068278443068265915,
-0.032258108258247375,
-0.0012518352596089244,
0.03539925068616867,
-0.08137574791908264,
0.03468521684408188,
0.04744461923837662,
-0.019510304555296898,
-0.027175674214959145,
-0.021749919280409813,
0.00815402902662754,
0.010615047998726368,
0.040362581610679626,
0.029193930327892303,
0.033421967178583145,
0.011910698376595974,
-0.004581248387694359,
0.0071885245852172375,
-0.02293531969189644,
-0.01823302172124386,
-0.025669986382126808,
0.03263721615076065,
-0.008044137619435787,
0.0013739651767536998,
0.01824614591896534,
-0.011042185127735138,
0.020975712686777115,
-0.010951327160000801,
-0.01741732843220234,
0.0073459879495203495,
0.035204194486141205,
-0.024739233776926994,
-0.02066519483923912,
0.0451422780752182,
-0.018696188926696777,
0.017666975036263466,
0.04278678447008133,
0.0014888555742800236,
0.012280377559363842,
-0.02274581976234913,
0.01803743466734886,
0.05053358152508736,
-0.006165147293359041,
0.014573603868484497,
-0.054669711738824844,
-0.0200345441699028,
-0.07736103981733322,
0.02657860703766346,
0.009719230234622955,
0.04823771119117737,
0.039002425968647,
0.01438642293214798,
-0.015621375292539597,
-0.058124229311943054,
-0.03089858591556549,
0.023353399708867073,
0.01675032265484333,
-0.006314459722489119,
0.008298564702272415,
0.02261071279644966,
0.011165483854711056,
0.011452498845756054,
-0.04764997586607933,
-0.0017630992224439979,
0.01835145242512226,
0.030961785465478897,
0.03607206791639328,
-0.0040915487334132195,
-0.015479423105716705,
-0.02036350965499878,
-0.06189892441034317,
0.010635203681886196,
-0.023996418341994286,
0.038947753608226776,
0.07228212058544159,
-0.00834085326641798,
0.033950477838516235,
0.014961718581616879,
-0.015885774046182632,
0.007792099379003048,
0.03925807401537895,
-0.06507129222154617,
0.0005653296248055995,
0.002787373960018158,
0.03778424859046936,
-0.02146149054169655,
-0.03869302570819855,
-0.04343986511230469,
0.014691522344946861,
-0.0021371133625507355,
-0.01876472681760788,
-0.012016784399747849,
0.0067826732993125916,
-0.025116708129644394,
0.03267969191074371,
-0.031966760754585266,
-0.00047069991705939174,
-0.032537490129470825,
-0.012341299094259739,
0.0048077902756631374,
0.018449166789650917,
-0.0035564093850553036,
0.03687781095504761,
0.002270527882501483,
-0.05859078839421272,
0.025321530178189278,
-0.00200685509480536,
-0.057330016046762466,
-0.044091589748859406,
-0.030376261100172997,
0.015521020628511906,
0.041730113327503204,
-0.019712384790182114,
0.014146000146865845,
0.002949650166556239,
0.01877819187939167,
-0.0720527321100235,
0.0037813300732523203,
-0.012763026170432568,
-0.00543876551091671,
0.016837328672409058,
0.0012285604607313871,
-0.03374440222978592,
0.08510690927505493,
-0.04806731268763542,
-0.006787903141230345,
0.020640423521399498,
0.014211347326636314,
0.0036493411753326654,
0.010287926532328129,
0.05054539442062378,
-0.001501000951975584,
0.003917849622666836,
0.02803937718272209,
0.030185796320438385,
-0.028575267642736435,
-0.026172980666160583,
-0.011637585237622261,
-0.059981152415275574,
0.01211867481470108,
-0.01804172433912754,
0.014098786748945713,
0.04732383415102959,
0.03809279948472977,
-0.06125711649656296,
0.016013607382774353,
0.05917453393340111,
0.00382901169359684,
-0.08009135723114014,
0.01874483749270439,
0.0021466484759002924,
0.007142812944948673,
0.06933485716581345,
-0.05593555420637131,
0.009117120876908302,
0.022595252841711044,
-0.09558473527431488,
0.020913008600473404,
-0.019211111590266228,
-0.008004777133464813,
-0.040075015276670456,
-0.01674541085958481,
-0.039794471114873886,
0.029548250138759613,
0.04861292615532875,
0.04700828343629837,
-0.011895155534148216,
0.03926569223403931,
-0.005959243047982454,
0.02038615755736828,
0.0057662175968289375,
0.016160236671566963,
-0.0387512668967247,
0.037729207426309586,
0.051329273730516434,
-0.03179366886615753,
-0.022037388756871223,
0.04903462529182434,
0.007400738075375557,
0.045629557222127914,
-0.051482733339071274,
-0.006490905303508043,
0.03351152688264847,
0.02818293310701847,
0.009476563893258572,
0.0021695273462682962,
0.0022418901789933443,
0.05084555968642235,
0.01671767793595791,
-0.019574614241719246,
0.0015386695740744472,
-0.025461068376898766,
0.03651618957519531,
-0.0868803858757019,
-0.001724555273540318,
0.03778892010450363,
0.0252470001578331,
0.036237917840480804,
0.031226277351379395,
0.021517585963010788,
0.006045349407941103,
0.015490934252738953,
-0.026000596582889557,
-0.039042189717292786,
-0.03135684132575989,
0.03347598761320114,
-0.0019460472976788878,
-0.009110902436077595,
-0.00655705900862813,
-0.015192501246929169,
-0.03732139617204666,
0.025152727961540222,
-0.020681066438555717,
-0.002993730129674077,
-0.03593350201845169,
-0.022570008412003517,
-0.011000063270330429,
0.0019998219795525074,
0.008426781743764877,
-0.025146353989839554,
-0.05292871594429016,
0.03951964154839516,
0.031858328729867935,
0.043104492127895355,
-0.028865717351436615,
-0.06844512373209,
-0.027741001918911934,
-0.04037131369113922,
0.026448765769600868,
-0.007432157173752785,
0.0570199079811573,
-0.04867615923285484,
-0.04572092369198799,
0.011558075435459614,
0.00974044669419527,
0.05676664039492607,
-0.00891912542283535,
0.00698080426082015,
-0.0011726426891982555,
-0.014571268111467361,
0.030497947707772255,
-0.027086500078439713,
0.0146779241040349,
-0.00765865808352828,
0.0010833179112523794,
0.02679329551756382,
0.0022080703638494015,
0.005351560655981302,
-0.01637822762131691,
0.04027152806520462,
0.004115676507353783,
0.004892751574516296,
0.05112236738204956,
-0.038831137120723724,
0.021876348182559013,
0.032281093299388885,
-0.012842036783695221,
0.033740658313035965,
0.002109814900904894,
0.020931284874677658,
0.005391397513449192,
-0.0006988632958382368,
-0.053921520709991455,
0.0024182829074561596,
-0.03671343997120857,
-0.004866789560765028,
-0.04133616387844086,
-0.00017350222333334386,
-0.0054826075211167336,
-0.032444484531879425,
-0.008137957192957401,
0.04715362563729286,
-0.000837828847579658,
0.017389193177223206,
-0.00715582724660635,
-0.046211566776037216,
0.05305139720439911,
-0.04711885377764702,
-0.01846940815448761,
0.009989629499614239,
0.02603413723409176,
0.0020524996798485518,
0.024561284109950066,
0.07648231089115143,
-0.0067191049456596375,
0.012246393598616123,
0.02477310411632061,
0.006157660391181707,
0.029481498524546623,
-0.0237334743142128,
0.02719244360923767,
-0.0776384100317955,
0.027582671493291855,
0.02800780162215233,
-0.008605152368545532,
0.02464814856648445,
0.07047747820615768,
0.01762811653316021,
0.07969705015420914,
0.005808334331959486,
0.034358520060777664,
-0.004746776539832354,
-0.022007739171385765,
0.011269709095358849,
0.033285170793533325,
0.009695697575807571,
0.019127054139971733,
-0.025185465812683105,
-0.008668376132845879,
-0.005031762178987265,
0.024351609870791435,
0.027342818677425385,
-0.0025985296815633774,
-0.017325470224022865,
-0.012340392917394638,
0.015020949766039848,
-0.013922234997153282,
0.032017782330513,
-0.04324350506067276,
-0.008804471231997013,
0.028679290786385536,
0.04291620850563049,
0.01567920669913292,
0.016679814085364342,
0.013394084759056568,
-0.04444762319326401,
0.02873269096016884,
-0.0374557189643383,
0.04718188941478729,
0.002472350839525461,
0.055005934089422226,
0.006552345585078001,
-0.0243039820343256
] |
<p>In the last 40 years (approximately) people have been "discovering", "rediscovering" and "studying" SUSY as a powerful tool and "symmetry principle". </p>
<p>Question: </p>
<p>What if SUSY is not realized in Nature at the end? Is SUSY the only path to "relate" fermions and bosons or what else? Remark: SUSY has not been discovered yet, so keep you totally conservative. What if there is no SUSY?</p>
<p>Bonus:</p>
<p>What are the merits of SUSY? What are its main issues? I do know some answers to this, but I think it could very enlightening if we "listed" pros and contras of current supersymmetric theories to see where we are NOW. </p> | 1,561 | [
-0.017456432804465294,
-0.00476693082600832,
0.015533367171883583,
-0.026766248047351837,
0.023860450834035873,
0.04092251881957054,
-0.008606232702732086,
-0.04588554427027702,
0.019422128796577454,
-0.04307400807738304,
0.019324395805597305,
0.01108572818338871,
0.0190750565379858,
0.020556839182972908,
0.003962440881878138,
0.025835227221250534,
-0.01556113176047802,
-0.02189941145479679,
-0.03496550768613815,
0.010386965237557888,
0.0232135858386755,
0.03495407477021217,
0.00038773048436269164,
0.017778098583221436,
-0.008187881670892239,
0.036131542176008224,
-0.020877819508314133,
0.0016012791311368346,
0.017156455665826797,
0.06933824717998505,
0.00219123438000679,
-0.018409959971904755,
0.026471832767128944,
0.026008373126387596,
0.0325908437371254,
0.011419227346777916,
0.00038473561289720237,
-0.050774283707141876,
-0.010242924094200134,
0.01631142571568489,
-0.004657589830458164,
-0.016590652987360954,
-0.01783633418381214,
0.058603379875421524,
-0.01843142881989479,
0.01747133582830429,
-0.011866607703268528,
-0.0023508877493441105,
0.05363064631819725,
-0.08860514312982559,
0.04615913704037666,
0.04585837200284004,
-0.012833056971430779,
0.008526825346052647,
0.006071625277400017,
-0.024813633412122726,
0.06400342285633087,
0.0729401707649231,
0.030012818053364754,
-0.06957535445690155,
-0.04082444682717323,
-0.039903271943330765,
0.03273673728108406,
-0.02464214526116848,
-0.06302662193775177,
0.05370428040623665,
-0.010550694540143013,
0.023462088778614998,
0.031400129199028015,
0.022385450080037117,
0.0020687084179371595,
0.019608041271567345,
0.06248733773827553,
0.02913030982017517,
0.02634262479841709,
-0.033923856914043427,
0.0025863000191748142,
-0.012691791169345379,
0.013492705300450325,
0.05369356647133827,
-0.020665625110268593,
0.015627533197402954,
-0.009383587166666985,
0.04273879900574684,
0.01910543069243431,
-0.021809076890349388,
0.03887869790196419,
-0.008331822231411934,
-0.01663016527891159,
0.022244764491915703,
0.015550632029771805,
-0.01625833474099636,
0.0602787509560585,
-0.015406287275254726,
-0.02819986268877983,
0.040214572101831436,
0.015308873727917671,
0.05702153593301773,
0.012654244899749756,
-0.014107421971857548,
0.019435282796621323,
0.013554958626627922,
0.014703810214996338,
0.07055506855249405,
-0.011254998855292797,
-0.013856043107807636,
-0.03635306656360626,
0.00881190411746502,
-0.0384134016931057,
-0.025983009487390518,
-0.03265380859375,
-0.0020037430804222822,
-0.013411195948719978,
-0.01399228349328041,
0.014537334442138672,
-0.03477625176310539,
0.008629042655229568,
-0.022105496376752853,
0.04975767806172371,
0.08012598752975464,
0.04415053501725197,
0.00782567448914051,
0.003384915180504322,
-0.008636683225631714,
-0.06461838632822037,
-0.0021396433003246784,
0.040533192455768585,
0.009114164859056473,
-0.03699854388833046,
0.030526526272296906,
0.01274785865098238,
0.023457175120711327,
0.0019876209553331137,
-0.04397307708859444,
0.05255753546953201,
-0.01093029323965311,
-0.0946882888674736,
-0.07531717419624329,
0.05942027270793915,
0.0130776297301054,
-0.0562179833650589,
-0.03786621615290642,
0.0008970872731879354,
0.021866818889975548,
0.08767015486955643,
-0.02819686196744442,
-0.02940535731613636,
0.03896615654230118,
0.04279458895325661,
0.02970314957201481,
-0.002263362053781748,
-0.01920665241777897,
-0.006623242981731892,
-0.020003199577331543,
-0.02245383709669113,
-0.03816959634423256,
-0.008258807472884655,
-0.015557540580630302,
0.01867455057799816,
-0.018880363553762436,
0.09038421511650085,
-0.002997056348249316,
0.04778432473540306,
-0.008087826892733574,
-0.03018064610660076,
-0.02474566549062729,
0.07599426060914993,
-0.006903947331011295,
0.019695155322551727,
0.025950802490115166,
-0.011084694415330887,
0.012146763503551483,
0.018144700676202774,
0.025225941091775894,
0.03706260770559311,
-0.0359511524438858,
-0.040150873363018036,
-0.005860504694283009,
-0.0014265478821471334,
-0.034525301307439804,
-0.028689730912446976,
-0.04865459352731705,
-0.012859100475907326,
0.04181907698512077,
-0.021633507683873177,
0.041171878576278687,
-0.028442569077014923,
-0.023565098643302917,
0.05909192934632301,
-0.0748986303806305,
-0.04508362337946892,
-0.0800628587603569,
-0.03614550828933716,
0.00034140923526138067,
-0.002662752289324999,
0.05488268658518791,
0.04055442288517952,
0.0030507829505950212,
-0.05685573071241379,
-0.03624730557203293,
0.0033895259257405996,
0.06237311661243439,
0.04929327592253685,
0.03735208511352539,
0.018857652321457863,
0.01580413617193699,
0.019481446593999863,
-0.030618708580732346,
0.0110838133841753,
-0.01265251636505127,
-0.07451637089252472,
0.02004530280828476,
-0.0255545973777771,
0.012813418172299862,
0.01906348578631878,
0.02802138589322567,
0.006948062218725681,
-0.019664211198687553,
-0.02397690713405609,
0.046653956174850464,
-0.023699132725596428,
0.08490179479122162,
0.008341066539287567,
0.009482179768383503,
0.011885039508342743,
0.011941011063754559,
-0.0001392416888847947,
0.018597953021526337,
-0.0321829617023468,
-0.016918689012527466,
-0.06927358359098434,
-0.004500301089137793,
0.045212432742118835,
0.05961481109261513,
-0.01396054495126009,
0.04268459230661392,
-0.011000464670360088,
0.010818722657859325,
0.037675000727176666,
-0.006136748939752579,
-0.03496197238564491,
-0.06275143474340439,
0.023970847949385643,
0.002520985435694456,
0.0031579250935465097,
0.03131599351763725,
0.004181345924735069,
0.027184490114450455,
-0.0069525339640676975,
0.00038042603409849107,
-0.02563629299402237,
0.06023203954100609,
0.029164312407374382,
-0.013366480357944965,
0.018361683934926987,
-0.02860797382891178,
0.024536389857530594,
-0.0228726863861084,
0.04115835577249527,
0.01619921810925007,
-0.013637484051287174,
0.012501999735832214,
-0.0354808047413826,
-0.02742302604019642,
0.010321145877242088,
-0.006222326308488846,
-0.04938086122274399,
-0.03456100821495056,
0.010341733694076538,
-0.04815564677119255,
-0.0153042646124959,
-0.016282089054584503,
-0.00038408118416555226,
-0.017671747133135796,
-0.00034148688428103924,
-0.008617346175014973,
-0.02271825075149536,
0.04873618111014366,
-0.019831117242574692,
-0.027753621339797974,
0.026119938120245934,
-0.008058629930019379,
0.011740798130631447,
0.05216740071773529,
-0.06436152011156082,
-0.02000204101204872,
-0.05133381858468056,
-0.024431589990854263,
0.021921761333942413,
0.011627217754721642,
0.029539072886109352,
-0.0011722230119630694,
-0.003914371132850647,
-0.05491169914603233,
-0.02637789212167263,
-0.00781505648046732,
0.027669470757246017,
-0.037720292806625366,
-0.005168315023183823,
0.033350709825754166,
0.0002531699137762189,
0.015563294291496277,
-0.027042808011174202,
-0.0143299400806427,
-0.061026837676763535,
-0.008522805757820606,
0.0006968755624257028,
0.034840818494558334,
-0.05219455808401108,
0.016380514949560165,
0.020731821656227112,
-0.062234148383140564,
0.030866704881191254,
-0.05211695283651352,
-0.049978408962488174,
-0.007412816863507032,
-0.0009159839246422052,
0.02373620681464672,
-0.00016051536658778787,
-0.03701947256922722,
0.09815573692321777,
0.028204794973134995,
-0.03167983889579773,
-0.013993269763886929,
-0.01854882203042507,
0.014941733330488205,
-0.01981501281261444,
-0.012307974509894848,
0.006708147935569286,
0.024400124326348305,
-0.0006951924879103899,
0.01584404706954956,
0.05476239323616028,
0.00456705829128623,
0.03425586223602295,
-0.06197002902626991,
-0.009673798456788063,
-0.0072980113327503204,
-0.016040988266468048,
0.014802399091422558,
-0.0015353548806160688,
0.0077051687985658646,
0.000703563797287643,
-0.0003515159769449383,
0.04215218499302864,
0.026257287710905075,
-0.024165287613868713,
0.06090318039059639,
-0.000052218874770915136,
0.03755993768572807,
-0.02456575632095337,
0.012054443359375,
0.003052801825106144,
-0.020948760211467743,
-0.01919572427868843,
0.022789204493165016,
0.05051808804273605,
-0.01470144372433424,
0.01940787024796009,
0.02356930635869503,
0.04567790776491165,
-0.046715036034584045,
-0.03324613347649574,
-0.0035081738606095314,
0.003444257890805602,
-0.01228239294141531,
-0.0068488274700939655,
-0.012784579768776894,
0.019458573311567307,
0.060151342302560806,
0.015116904862225056,
-0.017494747415184975,
-0.0341566726565361,
-0.015947528183460236,
-0.011087778955698013,
-0.005778144113719463,
-0.01904168725013733,
0.04715440794825554,
0.025573089718818665,
0.024357745423913002,
0.019920235499739647,
0.0011248413939028978,
-0.02302093431353569,
0.01577189192175865,
-0.07789860665798187,
0.022813457995653152,
-0.07271181046962738,
0.02179579623043537,
-0.012059259228408337,
0.008826307952404022,
0.020430881530046463,
-0.010652699507772923,
-0.04091857373714447,
-0.038851961493492126,
-0.01949038729071617,
-0.0311014074832201,
0.013876120559871197,
-0.03827783837914467,
-0.03544440120458603,
-0.003204432548955083,
0.001752743381075561,
0.07173297554254532,
-0.015380826778709888,
0.01674601063132286,
0.006321932189166546,
-0.03531099110841751,
0.0032351610716432333,
-0.03308354690670967,
0.03359583020210266,
-0.0022253410425037146,
0.023631805554032326,
0.056311365216970444,
0.027610989287495613,
-0.05339707061648369,
0.006065752822905779,
0.025669019669294357,
0.056327544152736664,
-0.0073918625712394714,
0.020769700407981873,
0.008306761272251606,
-0.04506170004606247,
-0.03516369313001633,
-0.0003445800393819809,
0.04279034212231636,
-0.0016395112033933401,
-0.0005929603357799351,
0.06048685312271118,
0.005838402081280947,
-0.05232839658856392,
0.04964078962802887,
0.046684812754392624,
0.023620029911398888,
-0.0355813167989254,
-0.0471007265150547,
-0.05280289798974991,
-0.028091425076127052,
-0.004269850440323353,
0.03688701242208481,
-0.014099747873842716,
-0.039353303611278534,
-0.017677631229162216,
0.00831900630146265,
0.028985215350985527,
-0.03267143294215202,
0.006672468967735767,
-0.022093309089541435,
0.014974790625274181,
0.00013502224464900792,
-0.012688558548688889,
-0.012821421958506107,
0.03688742592930794,
0.027310363948345184,
-0.025156604126095772,
0.012985168024897575,
-0.053294628858566284,
0.025795403867959976,
0.055490586906671524,
0.058144498616456985,
-0.017190489917993546,
-0.0179599579423666,
-0.06944412738084793,
-0.008397323079407215,
0.06080714985728264,
-0.03389762341976166,
0.011486375704407692,
-0.029147818684577942,
-0.017750343307852745,
-0.015523316338658333,
-0.01114970538765192,
-0.005269311834126711,
0.027114974334836006,
0.010874373838305473,
0.027210360392928123,
-0.012863341718912125,
-0.018105559051036835,
-0.03194025531411171,
0.026598460972309113,
0.003089095000177622,
0.04375334084033966,
0.0268311258405447,
0.02641885168850422,
0.01670362614095211,
0.003146269591525197,
0.0043901544995605946,
-0.09987550228834152,
0.018451277166604996,
0.005258462857455015,
-0.045360613614320755,
0.029039768502116203,
-0.013771159574389458,
-0.07325460016727448,
0.0003005416365340352,
-0.0008864466217346489,
-0.035221926867961884,
0.0018364927964285016,
-0.029670244082808495,
0.0518462248146534,
0.06976179778575897,
0.004297844134271145,
0.0044357008300721645,
0.03223244473338127,
-0.046463221311569214,
0.001934715430252254,
-0.036690667271614075,
0.017992854118347168,
-0.0014680916210636497,
0.022139469161629677,
-0.014012177474796772,
0.019203169271349907,
-0.032865457236766815,
0.0616743378341198,
-0.01934938319027424,
0.0037971674464643,
-0.0030382166150957346,
0.004151766654103994,
-0.01795700564980507,
0.01630242168903351,
0.00691229710355401,
-0.0031282196287065744,
0.02493312954902649,
0.02155948430299759,
-0.027289750054478645,
-0.04342953860759735,
0.01245207991451025,
0.003407862037420273,
0.0026759475003927946,
0.021208683028817177,
-0.009230540134012699,
0.01679505966603756,
0.004826842807233334,
-0.03596284240484238,
0.036000534892082214,
-0.05344686657190323,
0.033449847251176834,
-0.018425140529870987,
0.00715124374255538,
0.03255032002925873,
-0.054719094187021255,
-0.022487835958600044,
0.026039497926831245,
-0.032870568335056305,
-0.03243149071931839,
-0.0326838381588459,
0.037979964166879654,
0.015633193776011467,
0.003651950741186738,
-0.08365552127361298,
-0.032135654240846634,
-0.011770646087825298,
-0.013464822433888912,
-0.002789771882817149,
-0.03442162275314331,
-0.0017858596984297037,
-0.034137897193431854,
-0.009385178796947002,
0.021301817148923874,
0.046584755182266235,
-0.024539554491639137,
-0.037489891052246094,
0.004872067365795374,
-0.016521204262971878,
0.06765685230493546,
-0.029722247272729874,
-0.017981847748160362,
0.00009597872121958062,
0.003929284401237965,
0.025309355929493904,
0.007472663652151823,
0.043471015989780426,
0.006728834938257933,
-0.051869794726371765,
0.0029113658238202333,
-0.024025749415159225,
0.03575597703456879,
-0.010188051499426365,
-0.02798660844564438,
0.02264365740120411,
0.005407177843153477,
0.024342281743884087,
-0.01875559240579605,
0.01932850293815136,
-0.015249090269207954,
0.013149542734026909,
-0.004215781111270189,
0.028928061947226524,
-0.01846834272146225,
-0.04579290747642517,
0.044600050896406174,
-0.009370947256684303,
-0.00006785128789488226,
0.02689880132675171,
0.030155619606375694,
0.0030048969201743603,
0.025508178398013115,
0.008628994226455688,
-0.021096033975481987,
-0.011255363002419472,
0.0034176043700426817,
0.04157363995909691,
0.0007776913116686046,
0.028821496292948723,
0.0075202034786343575,
-0.041456129401922226,
0.015597918070852757,
0.0033470673952251673,
0.06648485362529755,
-0.056570492684841156,
0.02203211560845375,
0.013691695407032967,
-0.021288635209202766,
0.010901892557740211,
-0.0069320183247327805,
0.014004646800458431,
0.019938036799430847,
-0.006572007201611996,
-0.0023066727444529533,
-0.010827124118804932,
0.009728576056659222,
0.03283924236893654,
0.049503471702337265,
-0.01783864013850689,
0.03559812903404236,
0.035915229469537735,
0.025685107335448265,
0.08397172391414642,
-0.04606097191572189,
-0.03869819641113281,
0.02887042425572872,
-0.052363891154527664,
0.028356071561574936,
0.01577446050941944,
-0.02536923997104168,
0.0386928953230381,
0.005886788014322519,
0.003785495413467288,
0.013665877282619476,
-0.005797777324914932,
-0.03225325793027878,
0.03366047143936157,
0.011069981381297112,
0.012639088556170464,
0.0010497327893972397,
0.030152995139360428,
-0.00023089612659532577,
0.00503426231443882,
0.020921319723129272,
-0.013793372549116611,
-0.10047641396522522,
-0.04602758213877678,
-0.04079506918787956,
-0.016057204455137253,
0.08556543290615082,
0.0065169548615813255,
-0.007440983317792416,
-0.009170285426080227,
0.006449474487453699,
0.006089114584028721,
-0.006454449612647295,
0.026033421978354454,
-0.033470235764980316,
0.03815777227282524,
-0.022811971604824066,
0.03417620435357094,
0.009689977392554283,
0.02617545612156391,
0.1106901541352272,
0.03154716268181801,
0.006591893266886473,
-0.05983935296535492,
0.04534585028886795,
-0.017276408150792122,
-0.022941989824175835,
0.014570837840437889,
0.024737393483519554,
-0.00017705104255583137,
-0.01797613874077797,
-0.013281142339110374,
0.024605613201856613,
0.0089341402053833,
-0.017078250646591187,
0.07993976771831512,
-0.029713481664657593,
-0.030750157311558723,
-0.018287641927599907,
0.03098132647573948,
-0.009062448516488075,
0.00937314797192812,
-0.00941768940538168,
0.009407986886799335,
-0.011967113241553307,
0.009445142932236195,
-0.028538953512907028,
-0.052030619233846664,
0.004745043348520994,
0.023065902292728424,
0.02142367511987686,
-0.028409570455551147,
0.03638233616948128,
-0.0033631122205406427,
-0.06047577038407326,
-0.0036733048036694527,
0.015662869438529015,
0.006188711151480675,
0.0246498491615057,
0.05121985450387001,
0.011250939220190048,
-0.002013849327340722,
0.007156295236200094,
0.038784198462963104,
-0.06459783017635345,
-0.01337017584592104,
0.0023645006585866213,
0.05986051261425018,
-0.02928258664906025,
-0.04311888664960861,
-0.002442670986056328,
0.023059798404574394,
0.05214185640215874,
-0.009721281938254833,
-0.03336329758167267,
-0.004980182740837336,
0.06439968198537827,
-0.05287912115454674,
-0.018428605049848557,
0.01213855855166912,
0.043193984776735306,
-0.00030212156707420945,
0.030189672484993935,
-0.014755464158952236,
-0.03312794119119644,
-0.018357347697019577,
0.014443906024098396,
0.00869076233357191,
0.011495414189994335,
-0.010737084783613682,
-0.03762790188193321,
-0.000961862679105252,
-0.031459253281354904,
0.027960652485489845,
0.02068905346095562,
0.03488479554653168,
0.016174746677279472,
0.0037563869263976812,
-0.0202821996062994,
-0.041527919471263885,
-0.018203293904662132,
0.049195680767297745,
-0.009675169363617897,
-0.001883464166894555,
-0.02184571698307991,
-0.005495973862707615,
0.031065354123711586,
0.03356118127703667,
-0.05348984897136688,
0.019425341859459877,
-0.00011549619375728071,
0.023428121581673622,
0.005112393293529749,
-0.026899196207523346,
-0.016029132530093193,
-0.029322555288672447,
-0.037045396864414215,
0.015927588567137718,
0.0013539792271330953,
0.007319765165448189,
0.001124407397583127,
-0.01039754319936037,
0.02534438669681549,
0.02464308775961399,
0.0011026517022401094,
-0.013836540281772614,
0.04170360788702965,
-0.04163847491145134,
0.017504585906863213,
0.028282850980758667,
0.03540673106908798,
-0.013533264398574829,
-0.022624606266617775,
-0.021445298567414284,
-0.010442804545164108,
0.009267463348805904,
0.001154823461547494,
-0.04825906082987785,
0.02911020815372467,
-0.019912902265787125,
0.02831641212105751,
-0.04087032005190849,
-0.02519161067903042,
-0.059066291898489,
0.014968403615057468,
-0.007329650688916445,
-0.016934476792812347,
0.026549462229013443,
0.00007838810415705666,
-0.0021969429217278957,
-0.047576338052749634,
-0.01781260035932064,
0.029794208705425262,
-0.03093283623456955,
0.006164442747831345,
0.01837196759879589,
0.017179079353809357,
0.034952159970998764,
-0.008031352423131466,
-0.0002482061681803316,
0.040479741990566254,
-0.010669803246855736,
-0.04674244299530983,
0.04262364283204079,
-0.0051797847263514996,
0.021424461156129837,
0.008783550933003426,
-0.01574423722922802,
-0.04474128410220146,
-0.006312001962214708,
-0.03174721822142601,
0.026881229132413864,
-0.004939606878906488,
0.014671137556433678,
-0.03595495596528053,
-0.015625733882188797,
-0.036110877990722656,
0.0065862569026649,
-0.030293330550193787,
0.026056207716464996,
0.017591262236237526,
-0.012939329259097576,
0.013746131211519241,
-0.028886213898658752,
-0.05500904098153114,
-0.006559721194207668,
-0.013271667063236237,
-0.006907956674695015,
-0.009459343738853931,
0.022820420563220978,
-0.03802969306707382,
0.036099839955568314,
0.0053039249032735825,
0.003094766288995743,
-0.055325038731098175,
0.010514197871088982,
0.013986082747578621,
-0.0028034828137606382,
0.01850365474820137,
-0.021064486354589462,
-0.004923191387206316,
0.01809062995016575,
-0.03998170047998428,
0.04728296399116516,
-0.023708105087280273,
-0.052857618778944016,
-0.020602934062480927,
0.005744457710534334,
-0.034398771822452545,
0.07036098092794418,
0.0010648915776982903,
0.022404788061976433,
-0.004819735884666443,
-0.012159528210759163,
0.0321546271443367,
-0.009774450212717056,
-0.0558583065867424,
-0.0034929309040308,
-0.008540189824998379,
-0.023087168112397194,
0.06444742530584335,
-0.017253786325454712,
-0.01601567305624485,
0.0004458980110939592,
0.01930094324052334,
-0.011314474046230316,
0.031766150146722794,
-0.016187302768230438,
-0.040835414081811905,
0.02670498564839363,
0.031609006226062775,
-0.0074582453817129135,
0.007264458108693361,
0.023037176579236984,
0.004543855786323547,
0.051815345883369446,
-0.0043926178477704525,
0.031202349811792374,
-0.012062259018421173,
-0.004007826559245586,
-0.01482755783945322,
0.02433711662888527,
-0.023544857278466225,
-0.025525543838739395,
-0.0003193517040926963,
-0.000520556524861604,
-0.0004912613658234477,
0.006416112184524536,
-0.012916643172502518,
-0.03499891236424446,
-0.013058407232165337,
0.025190064683556557,
0.011696132831275463,
-0.0050317975692451,
0.04060816764831543,
-0.02880058065056801,
-0.02983757294714451,
-0.009992554783821106,
0.013541383668780327,
0.0017569606425240636,
-0.001255727605894208,
-0.01361324917525053,
0.02866411954164505,
0.04180581495165825,
-0.015046770684421062,
-0.023015769198536873,
-0.025104522705078125,
0.06900893151760101,
0.040409449487924576,
0.053209338337183,
-0.007954314351081848,
-0.0432279147207737,
-0.0026729970704764128,
-0.03716646507382393,
0.05774516239762306,
0.0012824602890759706,
0.016816623508930206,
0.0020191529765725136,
-0.0009057729039341211,
0.014016306959092617,
-0.00669962028041482,
0.028359215706586838,
-0.05006719008088112,
-0.02409905567765236,
0.030050231143832207,
0.03873741626739502,
0.014387947507202625,
-0.0005063595017418265,
-0.01896069198846817,
0.020059172064065933,
-0.017438633367419243,
-0.0390685573220253,
-0.03862388804554939,
-0.01905861124396324,
0.024946395307779312,
0.04884172976016998,
-0.015583962202072144,
-0.005652217194437981,
0.0051780627109110355,
-0.014763152226805687,
0.06832388788461685,
-0.015763157978653908,
-0.04712298884987831,
0.059150710701942444,
-0.018269045278429985,
0.012086094357073307,
-0.0047486331313848495,
-0.014521682634949684,
-0.017675375565886497,
0.03201720491051674,
-0.029344210401177406,
0.010847014375030994,
-0.014033892191946507,
-0.007963411509990692,
0.033554621040821075,
-0.06512410193681717,
0.019921626895666122,
0.06343954056501389,
-0.04199190065264702,
-0.015752216801047325,
0.0453961119055748,
-0.004873035475611687,
0.01784084551036358,
-0.0002068123867502436,
-0.02398630976676941,
0.02211185172200203,
0.010470686480402946,
0.02041039429605007,
0.05406811088323593,
0.01614493876695633,
0.00027326284907758236,
-0.004096046555787325,
0.011257320642471313,
-0.022074440494179726,
0.027318045496940613,
-0.002241076435893774,
0.028529267758131027,
-0.06765574216842651,
0.0005727518582716584,
0.046910256147384644,
0.012560335919260979,
0.03490482270717621,
0.00909954123198986,
-0.010714458301663399,
0.10137145221233368,
-0.012532920576632023,
0.0030252798460423946,
-0.02055692858994007,
-0.03428981080651283,
-0.020253069698810577,
-0.0015854293014854193,
-0.004850294440984726,
0.06675603985786438,
-0.019452355802059174,
-0.0018083403119817376,
-0.024634944275021553,
0.02845594845712185,
0.06429603695869446,
-0.02877669781446457,
0.0022877997253090143,
-0.02758469060063362,
-0.00452369125559926,
-0.002476621652022004,
-0.01972212642431259,
-0.053493935614824295,
-0.00804218091070652,
0.04256557673215866,
0.01602027751505375,
-0.017324894666671753,
0.017626527696847916,
-0.0246924739331007,
-0.009137162007391453,
0.039542827755212784,
-0.039482444524765015,
-0.0033763812389224768,
-0.03281387314200401,
0.00693632522597909,
-0.0483555942773819,
-0.023204920813441277
] |
<p>So electrons of specific atoms have a minimum amount of energy needed to escape the atom, called the work function, W. Now let's say that you emit a certain frequency of light, and $hf<W$. However, from my understanding, this work function is just a form of kinetic energy, and if an electron has enough kinetic energy, its inertia will be greater than the centripetal force and the electron will escape. So even though $hf<W$, the object being illuminated will still heat up from the light. This heating up means that the material is gaining internal energy, which means that the electrons are gaining kinetic energy. If the material gets hot enough and the electrons keep gaining speed, couldn't the they escape anyway even though $hf<W$? Thanks! </p> | 1,562 | [
-0.04040832817554474,
-0.03633640334010124,
0.020337440073490143,
-0.018632084131240845,
0.008189334534108639,
0.010597559623420238,
-0.03191186487674713,
0.005089513957500458,
0.017802469432353973,
-0.03281967341899872,
0.015842657536268234,
0.04652087017893791,
0.036191780120134354,
-0.01129505131393671,
0.023750903084874153,
0.028452865779399872,
-0.005708782467991114,
-0.018603170290589333,
-0.006151869893074036,
-0.024773096665740013,
-0.027829565107822418,
0.02724410966038704,
0.019251739606261253,
-0.004543346352875233,
-0.07113217562437057,
-0.0036808864679187536,
0.007159115746617317,
0.01995912194252014,
0.05254846438765526,
0.018147040158510208,
0.006229791324585676,
0.010451226495206356,
-0.0003865526814479381,
0.024605434387922287,
0.013310716487467289,
0.0239974707365036,
-0.035741183906793594,
-0.060264553874731064,
-0.024577859789133072,
0.011611034162342548,
-0.024507826194167137,
0.029172729700803757,
0.012702366337180138,
0.05094487592577934,
-0.008715619333088398,
-0.017983995378017426,
-0.013130350969731808,
-0.005007242318242788,
0.03709983825683594,
-0.06336704641580582,
0.05116325244307518,
-0.04602495953440666,
0.02398008294403553,
0.012767372652888298,
0.00222104717977345,
0.0072882710956037045,
0.08358239382505417,
0.06101815775036812,
-0.01753877103328705,
-0.01054077036678791,
-0.03777238354086876,
-0.035241950303316116,
-0.02108931727707386,
-0.013874058611690998,
-0.023221055045723915,
0.004099991638213396,
-0.011764983646571636,
-0.040213070809841156,
0.03420769423246384,
0.027365785092115402,
0.024155501276254654,
-0.010043714195489883,
0.0437113381922245,
-0.016720496118068695,
0.0205578301101923,
-0.017185594886541367,
0.014915326610207558,
0.029711177572607994,
0.03248358890414238,
0.06351038068532944,
-0.025028234347701073,
-0.015529000200331211,
0.010083955712616444,
0.03978191316127777,
0.006785778794437647,
0.023791002109646797,
0.07214416563510895,
-0.000316996214678511,
0.022473689168691635,
0.043170951306819916,
-0.023016002029180527,
0.0013487969990819693,
0.04146827757358551,
0.01281316764652729,
-0.0245758555829525,
0.010509300976991653,
0.003967082593590021,
0.04242542013525963,
0.017612893134355545,
-0.0022056822199374437,
0.04481786489486694,
0.008020234294235706,
0.03664984181523323,
0.04067321494221687,
0.0265842042863369,
-0.04193674772977829,
-0.004435222130268812,
-0.020531002432107925,
0.016267990693449974,
-0.00942087359726429,
-0.04187973588705063,
0.020372014492750168,
-0.014597121626138687,
0.011036805808544159,
-0.014122428372502327,
-0.003806702559813857,
-0.018243858590722084,
-0.036242421716451645,
0.020763326436281204,
0.049211155623197556,
-0.00977173913270235,
-0.01749502867460251,
0.054947927594184875,
-0.015513270162045956,
-0.011882660910487175,
0.007687518373131752,
-0.004977538716048002,
-0.002626745030283928,
-0.019607150927186012,
0.02091359905898571,
-0.004793005995452404,
-0.054517973214387894,
-0.003870525164529681,
-0.019427314400672913,
0.012405980378389359,
-0.02522893063724041,
-0.08233052492141724,
-0.0435110405087471,
0.02577139623463154,
-0.02752133272588253,
-0.0328318290412426,
-0.07986951619386673,
0.0046957493759691715,
0.017182139679789543,
0.0830765962600708,
-0.01964920200407505,
-0.024704571813344955,
-0.0689743235707283,
0.048689987510442734,
-0.014448287896811962,
-0.030814064666628838,
-0.017239661887288094,
0.01161904726177454,
-0.03618348017334938,
0.006803585682064295,
-0.09662926942110062,
0.019635135307908058,
0.00706107635051012,
0.03785480186343193,
-0.03711073845624924,
0.03705396130681038,
-0.012843639589846134,
0.02534983679652214,
0.0007387174409814179,
0.013249436393380165,
-0.03159182891249657,
0.0965297743678093,
0.018554409965872765,
0.009627596475183964,
0.016548097133636475,
0.05184067785739899,
0.03489529713988304,
-0.003942332696169615,
0.03241566941142082,
0.013549979776144028,
-0.030142713338136673,
0.007232148200273514,
-0.05590073764324188,
0.0397748127579689,
0.007646439131349325,
-0.04311268776655197,
-0.0456220842897892,
0.01816963590681553,
-0.0012230610009282827,
0.009579094126820564,
0.07489258795976639,
0.0073515973053872585,
-0.024737268686294556,
0.0005664746859110892,
-0.016481677070260048,
0.015160706825554371,
-0.04787645488977432,
0.0245943795889616,
0.023575112223625183,
0.0015669951681047678,
0.020922372117638588,
0.022946568205952644,
0.03746861591935158,
-0.006848219782114029,
-0.004177838563919067,
-0.030630310997366905,
0.022808555513620377,
-0.01852705515921116,
-0.014340751804411411,
0.018677683547139168,
0.014386871829628944,
0.030838128179311752,
0.05623260512948036,
0.018947066739201546,
-0.02681666612625122,
-0.03592318668961525,
0.007356859277933836,
-0.06339617818593979,
0.006371139548718929,
0.03918834775686264,
-0.00632357457652688,
0.008746872656047344,
-0.015602466650307178,
0.02878107689321041,
0.0422847718000412,
0.029373645782470703,
0.07982563227415085,
0.021440453827381134,
0.009226791560649872,
-0.025739213451743126,
0.06391777098178864,
-0.035736341029405594,
0.0072217071428895,
-0.010051405057311058,
-0.04097376763820648,
-0.02114136330783367,
0.023267023265361786,
0.026180308312177658,
-0.006019804626703262,
-0.07887954264879227,
0.012617734260857105,
0.016135139390826225,
0.020309891551733017,
0.058671608567237854,
0.047272004187107086,
-0.028067491948604584,
0.0049832286313176155,
0.0461670383810997,
-0.00393415242433548,
0.03183524310588837,
0.015357368625700474,
0.030507517978549004,
0.05120687559247017,
-0.018771998584270477,
0.005603260826319456,
0.01068498007953167,
0.027686050161719322,
0.03758128732442856,
0.005490454379469156,
-0.032494354993104935,
-0.0340520516037941,
0.01879635639488697,
-0.015178658068180084,
0.015264315530657768,
0.020676208660006523,
-0.011440886184573174,
0.028981663286685944,
-0.026281384751200676,
-0.03303374722599983,
0.013511947356164455,
-0.029639314860105515,
-0.002471155719831586,
-0.01923934556543827,
0.021675467491149902,
-0.056989386677742004,
0.017536232247948647,
0.008060356602072716,
-0.017207281664013863,
0.0012623467482626438,
-0.023505959659814835,
-0.014070454053580761,
0.025743337348103523,
0.04972666874527931,
-0.03434973955154419,
-0.05246457830071449,
-0.023906715214252472,
-0.06977351754903793,
0.015988217666745186,
-0.006735506001859903,
-0.003692363388836384,
0.004945869091898203,
-0.012579078786075115,
-0.07294895499944687,
0.04212251678109169,
-0.012826268561184406,
0.014136465266346931,
0.029145166277885437,
-0.029628632590174675,
-0.04750258848071098,
0.042276088148355484,
-0.011312337592244148,
-0.032882705330848694,
-0.01724616065621376,
-0.0029883303213864565,
0.08273392170667648,
-0.05716399475932121,
-0.008930372074246407,
0.01485154964029789,
-0.03207512944936752,
-0.08280403167009354,
-0.02114453911781311,
-0.010437478311359882,
0.015759969130158424,
-0.006031631957739592,
0.03248235955834389,
0.020991839468479156,
-0.07042978703975677,
-0.01098681427538395,
-0.06515538692474365,
-0.057866305112838745,
-0.007580526638776064,
-0.021797901019454002,
0.016241129487752914,
-0.027984492480754852,
-0.039255689829587936,
0.053812380880117416,
0.04560471698641777,
-0.018437480553984642,
-0.0061788177117705345,
-0.05656585097312927,
-0.016334230080246925,
-0.07653726637363434,
0.013921673409640789,
0.039544861763715744,
-0.01345470454543829,
0.017707111313939095,
-0.0013762983726337552,
0.017688127234578133,
0.04236025735735893,
-0.011823977343738079,
-0.0044040437787771225,
0.017808055505156517,
-0.008074498735368252,
-0.00974755734205246,
0.022405462339520454,
0.02297823876142502,
-0.014522641897201538,
0.0633622258901596,
0.0198069978505373,
0.06276746094226837,
0.034338705241680145,
-0.027096426114439964,
0.03536241501569748,
-0.005376356188207865,
0.012420964427292347,
-0.0619247704744339,
0.07681575417518616,
0.028202397748827934,
0.0015338921220973134,
0.00717764301225543,
0.017122909426689148,
0.06628172844648361,
-0.011909430846571922,
0.03450508788228035,
0.012624602764844894,
0.03751005604863167,
-0.007278542034327984,
-0.004710129462182522,
-0.026197489351034164,
0.012788751162588596,
-0.0014003789983689785,
0.012913831509649754,
-0.010264142416417599,
0.021210873499512672,
0.026997046545147896,
0.022697465494275093,
0.02170897275209427,
-0.010561550967395306,
-0.03215685486793518,
-0.04223201423883438,
-0.027173412963747978,
0.014979459345340729,
0.06137830391526222,
-0.00029970845207571983,
0.05834662541747093,
0.07728076726198196,
0.06383728981018066,
0.0029458003118634224,
-0.01213250495493412,
-0.10059885680675507,
0.028674833476543427,
-0.004566495772451162,
-0.023707788437604904,
-0.041782233864068985,
-0.0007553745526820421,
-0.0003508484805934131,
-0.03892594948410988,
-0.013474879786372185,
0.0015664421953260899,
-0.01762455515563488,
-0.03309407830238342,
0.00007806577195879072,
-0.017118066549301147,
-0.03567686676979065,
-0.019842607900500298,
0.020362451672554016,
0.059153079986572266,
-0.03190557658672333,
-0.013401252217590809,
0.05222209542989731,
-0.07233160734176636,
0.018879245966672897,
-0.021965881809592247,
-0.01525669265538454,
0.0121298898011446,
0.0063812462612986565,
0.03463622182607651,
0.013637767173349857,
-0.011147965677082539,
-0.006956496275961399,
0.02538512460887432,
0.03454964980483055,
0.021102556958794594,
0.002713319379836321,
-0.05528925359249115,
-0.05712103471159935,
-0.00009811147901928052,
-0.0021391522604972124,
0.04009268432855606,
-0.026494845747947693,
0.014191648922860622,
0.03791738301515579,
-0.011691474355757236,
-0.013098658062517643,
-0.007134970743209124,
0.003312827320769429,
0.007310874760150909,
-0.01795237697660923,
-0.027791282162070274,
-0.009597511030733585,
-0.025128260254859924,
-0.016322586685419083,
-0.02202671580016613,
-0.02164328098297119,
-0.029752608388662338,
0.011673646047711372,
-0.007616001646965742,
0.00007991310849320143,
-0.005013632122427225,
-0.003825242631137371,
-0.007376571651548147,
0.05135468393564224,
-0.010060695931315422,
-0.00687751779332757,
0.006961515638977289,
0.011925674974918365,
0.036635104566812515,
-0.00386217562481761,
0.03013610653579235,
-0.07480639219284058,
-0.026837699115276337,
0.01885376125574112,
0.03603031113743782,
-0.001449371105991304,
-0.01674468442797661,
-0.050904516130685806,
0.0042648776434361935,
0.01826169714331627,
-0.008276939392089844,
0.033442456275224686,
0.01732322759926319,
-0.012608103454113007,
0.008664130233228207,
-0.03908321261405945,
-0.023555895313620567,
0.010563728399574757,
-0.008016935549676418,
-0.007892951369285583,
-0.033064961433410645,
-0.008693519048392773,
0.022256355732679367,
-0.0020974332001060247,
0.041380222886800766,
0.01607757993042469,
-0.03698546066880226,
0.00015149738464970142,
0.029404599219560623,
-0.0074047669768333435,
0.0050720288418233395,
-0.08335154503583908,
-0.01938200369477272,
0.01397947408258915,
0.016236580908298492,
0.046630680561065674,
-0.047242045402526855,
-0.0326525904238224,
0.03262532874941826,
0.022612683475017548,
0.01582011766731739,
-0.020506015047430992,
-0.005845149513334036,
0.06602086126804352,
-0.0011754387523978949,
-0.009819970466196537,
0.02569769322872162,
0.033133238554000854,
-0.011340350843966007,
0.029628099873661995,
-0.030382568016648293,
0.04487483575940132,
-0.020114274695515633,
0.004373097326606512,
-0.06659367680549622,
-0.001768065500073135,
-0.012972126714885235,
0.059819210320711136,
0.016680991277098656,
-0.011705078184604645,
-0.01770949736237526,
-0.029743505641818047,
0.03653548285365105,
-0.0005701024201698601,
-0.0020832079462707043,
0.001890154555439949,
-0.031544845551252365,
0.03114253841340542,
-0.026716656982898712,
-0.01107179094105959,
-0.009318109601736069,
0.007224483415484428,
0.004865592811256647,
0.03047889471054077,
0.010257672518491745,
0.016172032803297043,
-0.03891538828611374,
0.00955167692154646,
-0.003556362120434642,
-0.04320172965526581,
0.03967243432998657,
-0.009802659973502159,
-0.009059048257768154,
-0.006255512125790119,
-0.013282900676131248,
0.010121947154402733,
0.006564119830727577,
-0.011257053352892399,
0.018259957432746887,
-0.01495247334241867,
0.0403984971344471,
-0.017102690413594246,
-0.006614833604544401,
-0.06919175386428833,
-0.019814003258943558,
0.0004379061865620315,
0.04061459004878998,
-0.02782619372010231,
-0.00369269005022943,
0.0025658109225332737,
-0.030936261638998985,
-0.0373649038374424,
0.00933984573930502,
0.013139245100319386,
-0.03836042806506157,
0.031205378472805023,
0.01819724403321743,
0.0032274294644594193,
0.03577173873782158,
-0.0015921673038974404,
-0.04130344092845917,
-0.0012065019691362977,
0.009768222458660603,
-0.014571423642337322,
0.022282948717474937,
0.03443579748272896,
-0.00010070393909700215,
-0.027122443541884422,
0.0037271580658853054,
-0.00988826435059309,
0.018010994419455528,
0.010228155180811882,
-0.017159251496195793,
0.056906603276729584,
0.02962358482182026,
-0.005779361817985773,
0.0024078544229269028,
0.04139178246259689,
-0.0038898023776710033,
0.05337979272007942,
0.02783804200589657,
0.010080411098897457,
-0.03973976895213127,
-0.03698491305112839,
0.03356846049427986,
-0.006127152591943741,
0.042176224291324615,
0.025078557431697845,
0.05455220863223076,
-0.04247669130563736,
0.03275002911686897,
0.004139164462685585,
0.0016691117780283093,
0.04526190832257271,
-0.027325022965669632,
0.00875866785645485,
0.0028466000221669674,
0.039356064051389694,
-0.04467500001192093,
-0.019130101427435875,
-0.04148060455918312,
-0.033767350018024445,
0.048731740564107895,
-0.03132017329335213,
0.0521354041993618,
-0.0061934944242239,
0.0021405774168670177,
0.045399896800518036,
-0.03182758018374443,
-0.0288978423923254,
0.009343188256025314,
-0.00584502425044775,
0.01052810437977314,
0.03317955136299133,
0.008218025788664818,
0.05383593589067459,
0.04931458458304405,
-0.042968861758708954,
0.013942491263151169,
0.014541303738951683,
0.018570134416222572,
0.006975995842367411,
-0.004156739450991154,
-0.03665047138929367,
0.010506398975849152,
-0.019268980249762535,
0.04212641716003418,
0.0032702931202948093,
-0.0029224655590951443,
0.03706929087638855,
0.0002242083864985034,
0.010925540700554848,
-0.03761283680796623,
-0.04710831493139267,
-0.0374082513153553,
0.05344685539603233,
-0.010479404591023922,
0.0066513726487755775,
-0.0251105148345232,
0.024397805333137512,
0.026616860181093216,
0.007610791828483343,
-0.00522712292149663,
-0.03525695949792862,
-0.03149258717894554,
-0.04393135383725166,
-0.050777167081832886,
0.0004769048828165978,
-0.0018008011393249035,
-0.015628773719072342,
-0.014033837243914604,
0.010680205188691616,
-0.03660356253385544,
0.016692714765667915,
-0.011009639129042625,
0.061108436435461044,
-0.0007746257469989359,
0.06351079791784286,
-0.00468806829303503,
0.012881380505859852,
-0.03389381617307663,
0.07096241414546967,
0.11594629287719727,
0.05791696161031723,
0.030438274145126343,
-0.031637027859687805,
-0.0213326346129179,
-0.04539235308766365,
0.006389111280441284,
-0.05297769233584404,
0.020433174446225166,
-0.010177789255976677,
0.02754339762032032,
0.022839834913611412,
0.08164935559034348,
0.003821459598839283,
0.02566939778625965,
0.02241259440779686,
-0.031177936121821404,
-0.0016930431593209505,
0.011696457862854004,
-0.007888245396316051,
0.008457225747406483,
0.013758203014731407,
-0.032174888998270035,
-0.010380423627793789,
-0.03761494532227516,
0.010621300898492336,
0.0012161278864368796,
-0.04585244506597519,
0.03229517489671707,
-0.02685154601931572,
-0.02716199867427349,
-0.007426906377077103,
0.0034879916347563267,
-0.008723151870071888,
-0.011949027888476849,
0.012859071604907513,
0.05842236429452896,
-0.0018168415408581495,
0.008956332691013813,
0.02811054326593876,
0.03554540127515793,
0.023245589807629585,
0.01480318047106266,
0.006924699526280165,
-0.019056720659136772,
0.00466263247653842,
-0.012432298623025417,
0.021346470341086388,
-0.0384272038936615,
0.019967898726463318,
0.019232140854001045,
-0.020388683304190636,
-0.010712036862969398,
-0.027826160192489624,
0.024175453931093216,
-0.03663700819015503,
-0.0068394155241549015,
0.02004026249051094,
0.0012575940927490592,
-0.08212427794933319,
0.03323177620768547,
0.030901169404387474,
-0.03041260316967964,
0.031403180211782455,
-0.002893011085689068,
0.02752537652850151,
0.013389778323471546,
0.041479211300611496,
-0.014566769823431969,
-0.07442820817232132,
0.00590673740953207,
-0.02283354289829731,
-0.012178770266473293,
-0.030522698536515236,
0.028089841827750206,
0.017015472054481506,
0.004400287754833698,
-0.02337365597486496,
0.0033810778986662626,
-0.05308939516544342,
-0.07807367295026779,
0.005696408450603485,
0.01895548216998577,
-0.05803957208991051,
-0.015254360623657703,
0.0037935920991003513,
0.03304746374487877,
0.048958346247673035,
-0.06012894585728645,
-0.009782075881958008,
0.021556980907917023,
-0.000040607388655189425,
0.016569282859563828,
-0.05157552659511566,
-0.013540762476623058,
0.02223973721265793,
0.025163840502500534,
-0.009472294710576534,
-0.0015000380808487535,
0.05582832172513008,
0.013191862031817436,
0.0089891217648983,
0.028446396812796593,
0.028868762776255608,
-0.03973713889718056,
0.026359518989920616,
0.02319510653614998,
-0.029900318011641502,
-0.0077452934347093105,
0.025468837469816208,
-0.008021586574614048,
-0.009535168297588825,
-0.05170305445790291,
-0.02764611504971981,
0.005645000841468573,
-0.01568750850856304,
0.06832507252693176,
-0.023518031463027,
0.022427214309573174,
-0.011928033083677292,
0.042591385543346405,
-0.04188809543848038,
-0.006594777572900057,
-0.046401847153902054,
0.014645212329924107,
0.02114861272275448,
0.0035762176848948,
0.006585974246263504,
0.02461419068276882,
-0.029427144676446915,
-0.026853129267692566,
0.01938491314649582,
0.020099768415093422,
-0.0283539779484272,
-0.007240409031510353,
-0.007871308363974094,
-0.010152621194720268,
0.03702345862984657,
-0.02554134465754032,
-0.029407303780317307,
0.04480694234371185,
-0.021147357299923897,
-0.055882979184389114,
0.014323800802230835,
-0.011327208019793034,
0.031925272196531296,
0.029123978689312935,
-0.010720616206526756,
0.009720233269035816,
0.06999772787094116,
0.017941031605005264,
0.004789791069924831,
-0.0038388085085898638,
-0.04935383051633835,
0.00971815176308155,
-0.020090917125344276,
0.028202004730701447,
-0.022545579820871353,
0.03283742070198059,
0.05261733755469322,
0.010172097012400627,
-0.011353173293173313,
-0.010315938852727413,
-0.0018179549369961023,
-0.011117007583379745,
-0.013888507150113583,
0.012908007949590683,
-0.00006527738878503442,
0.021241534501314163,
0.06450557708740234,
-0.0064125098288059235,
0.023150844499468803,
0.0076170992106199265,
-0.001955194165930152,
-0.10378776490688324,
-0.01828174479305744,
-0.010257681831717491,
0.013276123441755772,
-0.00904801208525896,
-0.059830013662576675,
0.03674640506505966,
0.025837475433945656,
-0.09235968440771103,
0.010800388641655445,
-0.03905176371335983,
-0.020345252007246017,
-0.0625980794429779,
0.008500643074512482,
-0.04647012799978256,
0.007805604487657547,
0.04505183920264244,
0.07409902662038803,
0.012984724715352058,
0.013584913685917854,
-0.03279460594058037,
-0.021726923063397408,
0.0141598554328084,
0.05599343404173851,
-0.004148880951106548,
-0.004362434148788452,
0.10230941325426102,
-0.026135319843888283,
-0.022635849192738533,
0.0004818422021344304,
-0.011527984403073788,
-0.01161948312073946,
-0.02976045571267605,
0.0009259857470169663,
0.007271696347743273,
0.006369527895003557,
0.02974475920200348,
-0.02424623630940914,
-0.025918127968907356,
0.026205629110336304,
0.029108019545674324,
0.010366830043494701,
-0.03192547336220741,
0.03355829790234566,
0.026538588106632233,
-0.03578979894518852,
-0.024773648008704185,
0.02248992957174778,
0.0065844180062413216,
-0.007237276993691921,
0.04440348967909813,
0.04295605793595314,
0.041400980204343796,
-0.016945507377386093,
-0.006584492512047291,
-0.06834419071674347,
-0.013512348756194115,
-0.02426004596054554,
0.02461867779493332,
-0.007966920733451843,
-0.021127665415406227,
-0.034194380044937134,
-0.005420559551566839,
0.03696918487548828,
-0.004399014636874199,
-0.009640167467296124,
-0.0504453182220459,
0.015555895864963531,
0.010546090081334114,
0.023852717131376266,
-0.028664927929639816,
-0.03553508594632149,
-0.013113804161548615,
-0.0017673216061666608,
-0.01073338370770216,
0.021213511005043983,
0.009431689977645874,
-0.06268561631441116,
-0.06444957107305527,
-0.06549255549907684,
0.02124885655939579,
-0.027880236506462097,
-0.009145863354206085,
-0.01883838325738907,
-0.024944374337792397,
0.0036018991377204657,
0.007694269996136427,
0.0430227629840374,
-0.009193952195346355,
-0.02554166316986084,
0.042826924473047256,
-0.02932639978826046,
-0.002322408137843013,
-0.04361792653799057,
0.015546497888863087,
-0.03401460126042366,
-0.011251796036958694,
-0.032606106251478195,
0.01283326931297779,
-0.029748961329460144,
0.0007100174552761018,
-0.0044836727902293205,
0.009521801955997944,
0.02175544574856758,
-0.0342494398355484,
-0.034750960767269135,
0.03341144695878029,
0.01606343872845173,
-0.019582223147153854,
0.0754721537232399,
-0.007808956317603588,
0.02777417190372944,
0.02207822911441326,
-0.023963404819369316,
-0.026824502274394035,
0.047827064990997314,
0.013132330030202866,
0.004701713565737009,
-0.012506588362157345,
-0.010605205781757832,
0.046763669699430466,
-0.03852148354053497,
-0.0010155447525903583,
0.02785945124924183,
-0.02962484583258629,
-0.0026168967597186565,
0.007187725510448217,
0.049386534839868546,
0.03733006864786148,
0.007565714418888092,
-0.015615880489349365,
-0.013872718438506126,
0.013305705972015858,
-0.006652439013123512,
0.0803040936589241,
-0.014531019143760204,
-0.03853967413306236,
0.057501450181007385,
0.006257023196667433,
-0.019788822159171104,
-0.016360461711883545,
0.002333965850993991,
0.040599167346954346,
-0.004563947208225727,
-0.02291269041597843,
-0.0000840573848108761,
0.023621078580617905,
-0.009303459897637367,
0.021465471014380455,
-0.03500238433480263,
0.05583501234650612,
-0.0028481888584792614,
0.040749888867139816,
-0.01488831639289856,
0.028699083253741264,
-0.013787630014121532,
0.01775711588561535,
0.015279721468687057,
0.0499337799847126,
-0.006341228261590004,
-0.0351639948785305,
-0.024514848366379738,
0.009642384946346283,
0.0240725576877594,
-0.02266572043299675,
0.036883726716041565,
-0.0207117460668087,
-0.02943497896194458,
-0.012755493633449078,
-0.0037220169324427843,
-0.032812755554914474,
-0.003014498157426715,
-0.0019507048418745399,
0.050430018454790115,
0.011692052707076073,
-0.008471271954476833,
-0.019589435309171677,
0.0005741140921600163,
0.02784670516848564,
-0.05445590242743492,
0.03635795786976814,
0.010868663899600506,
0.017966682091355324,
-0.02529551088809967,
-0.03531822934746742
] |
<p>I have this problem. I have an ideal gas that goes through an irreversible adiabatic decompression. I have the initial state (P,T,V), and the final pressure, and I have to calculate the entropy difference of the proccess. So, what I know is that I can make up any reversible proces bewteen the initial and final state because entropy is a state function, and integrate the heat over that process, but I can't solve it. I'm aplying $P_1V_1^\lambda=P_2V_2^\lambda$ to get the final state, but as I am creating the final point of the adiabatic, I get entropy difference of $0$ for an invented reversible path. That way of getting the final state is not correct, right? I have $PV=nRT$ but I only have the final $P$ so I need another equation.</p>
<p>EDIT: I have tried also to use $\Delta U=W\Rightarrow C_v\Delta T=P_{ext}\Delta V$, get $T_{final}$, and go on, but I don't get the correct result either. I thought this was general: $dU=C_vdT$, when can I apply that equation?</p> | 1,563 | [
0.020484935492277145,
0.001961108762770891,
-0.045855727046728134,
0.008967485278844833,
0.01425357349216938,
-0.007552050054073334,
-0.04216323420405388,
0.0013275790261104703,
-0.011830728501081467,
0.020293695852160454,
0.034090179949998856,
0.035735685378313065,
0.04468118026852608,
0.018381573259830475,
0.04157405346632004,
0.0046642557717859745,
-0.007582147605717182,
-0.007238317281007767,
0.007900831289589405,
-0.01218924205750227,
-0.00910150445997715,
-0.002011863049119711,
0.0029438172932714224,
-0.03949703276157379,
-0.03332255780696869,
0.06392841786146164,
0.003588542342185974,
0.007223190274089575,
-0.0005140855791978538,
0.04715342819690704,
-0.025609098374843597,
-0.038858864456415176,
0.010547163896262646,
0.048837337642908096,
-0.01286893617361784,
0.004926418885588646,
-0.014300744980573654,
-0.010320382192730904,
-0.02231583558022976,
0.01515300665050745,
-0.04019763693213463,
0.00154494505841285,
-0.021693378686904907,
0.031511444598436356,
0.012041319161653519,
0.016616512089967728,
0.022819243371486664,
-0.005739656742662191,
0.011877075769007206,
-0.05085228011012077,
0.049301233142614365,
0.021690836176276207,
0.05201556906104088,
0.02872147411108017,
-0.022050408646464348,
-0.0030947658233344555,
0.05357944965362549,
0.09290356934070587,
0.002283997368067503,
0.008948465809226036,
-0.024017291143536568,
0.008841898292303085,
0.0050569092854857445,
-0.004595727659761906,
-0.02459692396223545,
0.04364887997508049,
0.0018265749095007777,
-0.0043227276764810085,
0.033876683562994,
-0.007131066173315048,
-0.0004535903863143176,
-0.011910836212337017,
0.0246477909386158,
-0.007613907568156719,
0.020734230056405067,
-0.008129632100462914,
0.022382298484444618,
0.010259654372930527,
0.030636833980679512,
0.04857517406344414,
-0.011930624023079872,
0.04587661474943161,
0.01832985132932663,
0.0429929681122303,
-0.025316763669252396,
-0.01291483175009489,
0.08574125170707703,
-0.0178284402936697,
0.026479601860046387,
0.08230777829885483,
0.0009783586720004678,
-0.01422492042183876,
0.01914079673588276,
-0.036474645137786865,
0.015560736879706383,
-0.02022465318441391,
-0.020136212930083275,
0.04961760714650154,
-0.02230488695204258,
-0.027717016637325287,
-0.01913307048380375,
-0.023538393899798393,
0.017262686043977737,
0.06610731035470963,
-0.010404321365058422,
-0.02653946541249752,
-0.0617164745926857,
0.021117517724633217,
-0.01162094995379448,
-0.03369516134262085,
-0.039435483515262604,
0.0025956956669688225,
-0.01873321644961834,
-0.013818341307342052,
-0.0012792587513104081,
-0.03047715313732624,
0.0016641118563711643,
-0.038344595581293106,
0.06988449394702911,
0.05275590717792511,
0.054029740393161774,
-0.020599476993083954,
0.05091077834367752,
-0.012449742294847965,
-0.06720243394374847,
-0.006535636261105537,
0.04913610219955444,
-0.014782072976231575,
-0.025697387754917145,
0.0002487598394509405,
-0.025719275698065758,
-0.03847207501530647,
0.022169077768921852,
-0.014419770799577236,
0.019497768953442574,
-0.024274595081806183,
-0.0725880116224289,
-0.05792481452226639,
0.012035929597914219,
-0.031016521155834198,
-0.04378777742385864,
-0.03837449476122856,
0.04209943115711212,
0.036838989704847336,
0.0836925283074379,
-0.025221217423677444,
0.029924442991614342,
-0.018112635239958763,
0.024530204012989998,
0.00914809387177229,
-0.027295498177409172,
-0.04398064687848091,
-0.00018918603018391877,
-0.0077740796841681,
-0.012000508606433868,
-0.05231630429625511,
0.03284512460231781,
0.07322824746370316,
-0.013507592491805553,
0.016089409589767456,
0.06794237345457077,
-0.028437992557883263,
-0.02560262195765972,
0.008171655237674713,
0.016863783821463585,
-0.041263677179813385,
0.07105863839387894,
0.023587442934513092,
-0.0063568283803761005,
0.011758510954678059,
0.04774743318557739,
0.007231029216200113,
-0.016478093340992928,
-0.00420402130112052,
0.05660503730177879,
-0.0014118454419076443,
-0.014440763741731644,
-0.016045130789279938,
-0.00731029873713851,
0.0320814847946167,
0.006157316733151674,
-0.041926074773073196,
0.02177741564810276,
-0.019094746559858322,
0.014079042710363865,
0.01228976622223854,
0.009037826210260391,
0.0038897115737199783,
-0.01078013889491558,
-0.05608797445893288,
0.01323419064283371,
-0.033723071217536926,
0.021588928997516632,
0.038040436804294586,
0.005002980120480061,
0.021910931915044785,
0.008202713914215565,
0.04763204604387283,
-0.006244848016649485,
-0.02563539147377014,
-0.009435406886041164,
0.02299683913588524,
0.0060174232348799706,
-0.01732461526989937,
0.011381992138922215,
0.05278395861387253,
0.06775058060884476,
0.021259205415844917,
0.05072314664721489,
-0.004275592043995857,
-0.0004306031623855233,
0.00894777849316597,
-0.013932205736637115,
0.011500981636345387,
-0.04840987175703049,
-0.014663968235254288,
0.01890191063284874,
-0.022024963051080704,
0.016689788550138474,
0.01737702451646328,
-0.025521371513605118,
0.07137254625558853,
0.08371535688638687,
0.03694707900285721,
-0.0231415294110775,
0.026484686881303787,
-0.010259215719997883,
0.034068506211042404,
-0.030904125422239304,
-0.03580991178750992,
-0.022023998200893402,
-0.0062698195688426495,
0.013916593044996262,
0.015478064306080341,
-0.06403777748346329,
0.023393865674734116,
0.043027810752391815,
0.007733281701803207,
0.0419711172580719,
0.028207870200276375,
0.01307936105877161,
-0.00957425031810999,
0.035464778542518616,
0.0011941114207729697,
0.010254554450511932,
0.009196831844747066,
0.015445070341229439,
0.0016573232132941484,
0.013544208370149136,
0.00391349196434021,
-0.03777308762073517,
0.04371808469295502,
-0.00012697097554337233,
-0.00023321724438574165,
-0.04085719957947731,
-0.0029610316269099712,
0.0402800589799881,
-0.007895877584815025,
0.028475143015384674,
0.016996346414089203,
0.012180537916719913,
0.012320312671363354,
-0.00008741512283449993,
-0.006417406722903252,
0.018292339518666267,
0.0007637733942829072,
-0.006892225705087185,
0.022133100777864456,
0.033336248248815536,
-0.022157929837703705,
0.0026387081015855074,
-0.016350409016013145,
0.027327662333846092,
-0.05969370901584625,
0.012707189656794071,
0.02900417521595955,
-0.004157102666795254,
0.005123293027281761,
-0.02716526761651039,
-0.060409098863601685,
-0.01039206888526678,
-0.005534280091524124,
0.014570715837180614,
0.01369830034673214,
-0.05036383494734764,
0.03670916333794594,
-0.026297757402062416,
-0.05859268084168434,
0.02662944421172142,
0.02354549616575241,
-0.004224209580570459,
-0.00941489078104496,
-0.03190381079912186,
-0.07223746925592422,
-0.023122912272810936,
-0.03751809895038605,
-0.0017494478961452842,
-0.026462387293577194,
-0.006975522264838219,
0.04865333065390587,
0.0014764124061912298,
-0.030633650720119476,
0.0018600724870339036,
-0.0643811747431755,
-0.05626513808965683,
-0.012770875357091427,
-0.012192980386316776,
0.0418107770383358,
-0.006246832199394703,
0.06915795803070068,
0.056695837527513504,
-0.026634754613041878,
-0.007131614722311497,
-0.06008507311344147,
-0.045747626572847366,
0.04173271730542183,
-0.014713580720126629,
0.025535613298416138,
-0.017349345609545708,
-0.04023684188723564,
0.049962423741817474,
0.022429538890719414,
-0.04560721665620804,
0.012349478900432587,
0.007412048522382975,
-0.00586749566718936,
0.013514569960534573,
-0.0460035540163517,
-0.025190262123942375,
-0.042747803032398224,
0.04432410001754761,
-0.005159181077033281,
0.03412634879350662,
0.03354732692241669,
-0.010018367320299149,
-0.025529872626066208,
0.04998460039496422,
0.03168138116598129,
0.03911450132727623,
0.019579315558075905,
-0.010614677332341671,
0.0014218480791896582,
0.050780341029167175,
-0.013117141090333462,
0.038111113011837006,
0.03640226647257805,
-0.059813790023326874,
0.05739559978246689,
0.02394353225827217,
-0.0016230542678385973,
-0.0384715311229229,
0.023925824090838432,
-0.0407116673886776,
-0.0090170968323946,
-0.009628042578697205,
0.01683485321700573,
0.007462732493877411,
-0.04329438507556915,
-0.01176932081580162,
0.028536761179566383,
0.017278846353292465,
-0.008302219212055206,
-0.053591761738061905,
0.02511494979262352,
-0.022686833515763283,
0.012875804677605629,
0.03280119597911835,
-0.01030948106199503,
0.03579205274581909,
0.05108128860592842,
0.03669232502579689,
-0.035462841391563416,
-0.03531467542052269,
0.007975454442203045,
-0.04193386062979698,
0.004440580494701862,
-0.0011135906679555774,
0.06733693927526474,
-0.0007138867513276637,
0.06025911495089531,
0.028923429548740387,
0.03150003030896187,
0.02582855336368084,
0.014823372475802898,
-0.09672772884368896,
0.0385633260011673,
-0.0027525904588401318,
-0.04273587465286255,
0.014096302911639214,
0.011117820627987385,
0.022749170660972595,
-0.04664578661322594,
-0.06052163243293762,
0.017512328922748566,
0.001784043968655169,
-0.07302555441856384,
0.00871240720152855,
-0.03983669355511665,
-0.006701665930449963,
0.0014944139402359724,
0.035803910344839096,
0.04974692314863205,
-0.016162222251296043,
0.013091647066175938,
0.06263662129640579,
-0.014649702236056328,
0.04516984522342682,
-0.031078986823558807,
0.0074665965512394905,
0.033096324652433395,
0.02859710529446602,
0.06909017264842987,
-0.004718489944934845,
0.019749630242586136,
0.021745042875409126,
-0.016046348959207535,
0.04175351932644844,
-0.000898017839062959,
-0.017227889969944954,
-0.008164987899363041,
-0.04415645822882652,
-0.0009898390853777528,
0.008607564494013786,
0.030730511993169785,
-0.010832587257027626,
0.05495547503232956,
-0.018575578927993774,
0.017357176169753075,
-0.02635321393609047,
0.01817762665450573,
0.0387999527156353,
-0.04406282678246498,
-0.02252809703350067,
0.011851802468299866,
-0.013820715248584747,
-0.041126783937215805,
-0.028432009741663933,
0.0020058786030858755,
-0.0023510074242949486,
-0.042957644909620285,
-0.025159886106848717,
0.005756678991019726,
0.015333946794271469,
0.00875097420066595,
-0.007670925930142403,
-0.0002721704076975584,
0.026314660906791687,
0.013018148019909859,
-0.01898140273988247,
0.04074804112315178,
0.01795862801373005,
-0.021333182230591774,
-0.011157690547406673,
0.0023944652639329433,
-0.06661299616098404,
0.004387558903545141,
0.006001512054353952,
0.042385391891002655,
-0.02513742446899414,
-0.020532116293907166,
-0.05642635002732277,
-0.02750917337834835,
0.049247972667217255,
-0.011912268586456776,
0.016520828008651733,
0.015673400834202766,
-0.013251672498881817,
0.03876648470759392,
-0.01960962638258934,
-0.031133512035012245,
0.03811105340719223,
0.014791431836783886,
-0.004929033108055592,
0.006299182772636414,
-0.007514363620430231,
-0.001423915266059339,
-0.015302160754799843,
0.011288484558463097,
0.04182639718055725,
-0.04918714985251427,
-0.05073811858892441,
0.010566308163106441,
0.02876346930861473,
-0.02528518997132778,
-0.06848511099815369,
-0.02059040777385235,
0.0035339584574103355,
-0.00922857690602541,
0.012507384642958641,
-0.04615733027458191,
-0.0519377663731575,
0.057367537170648575,
-0.004102317616343498,
0.0003429891658015549,
0.011296401731669903,
0.002277393825352192,
0.06711063534021378,
0.004757576156407595,
-0.010073963552713394,
0.0661836564540863,
0.053344305604696274,
-0.004520990885794163,
-0.02679361402988434,
-0.024203062057495117,
0.028809107840061188,
-0.02124829962849617,
0.006413688417524099,
-0.06256090104579926,
0.01724899373948574,
-0.0026934542693197727,
0.040609799325466156,
-0.022451594471931458,
0.012165753170847893,
-0.015407322905957699,
-0.0353253073990345,
0.016231359913945198,
0.027737675234675407,
0.014448784291744232,
0.014470632188022137,
-0.0014256314607337117,
0.015631427988409996,
0.011468582786619663,
-0.01888967677950859,
-0.008497434668242931,
0.0038563136477023363,
-0.0023362145293504,
0.011474781669676304,
-0.0006452644593082368,
0.0452006459236145,
-0.01130166556686163,
-0.029539572075009346,
0.02613821066915989,
-0.035980936139822006,
0.034752435982227325,
-0.010493424721062183,
0.006567800417542458,
0.010664040222764015,
-0.029659142717719078,
0.009768364019691944,
-0.024510841816663742,
0.009267337620258331,
0.004929309710860252,
-0.058637700974941254,
0.021791987121105194,
0.0034261555410921574,
-0.004222129005938768,
-0.07907011359930038,
-0.03340725600719452,
0.024013208225369453,
-0.001091160112991929,
-0.0460147000849247,
-0.0502033457159996,
0.020291797816753387,
-0.014380188658833504,
-0.05502190440893173,
-0.012050626799464226,
0.0649171695113182,
0.029647303745150566,
-0.02638358809053898,
0.031663957983255386,
0.05641753226518631,
0.022448226809501648,
-0.011989636346697807,
0.008489246480166912,
-0.00518327159807086,
-0.0071076867170631886,
-0.023719102144241333,
0.04699918255209923,
0.030826063826680183,
-0.03266054391860962,
-0.028015507385134697,
0.012076369486749172,
0.006837106309831142,
0.05982351303100586,
-0.02499079704284668,
0.01635744981467724,
0.005690067540854216,
0.012726874090731144,
-0.02499864250421524,
-0.013511386699974537,
-0.0005148242926225066,
-0.015428004786372185,
0.020801417529582977,
-0.007779889740049839,
0.0020609479397535324,
0.006415827199816704,
-0.04927777498960495,
0.008438154123723507,
-0.01540698204189539,
0.025481151416897774,
-0.005109301768243313,
0.06804076582193375,
0.005710851866751909,
0.007047457154840231,
-0.00419158348813653,
-0.023348243907094002,
0.03456959128379822,
0.011866595596075058,
-0.017370518296957016,
0.0222938135266304,
-0.011411471292376518,
-0.046576932072639465,
-0.057049091905355453,
-0.059470128268003464,
0.033243004232645035,
0.07455500215291977,
-0.020078914240002632,
0.05682504549622536,
0.0005472953198477626,
0.018771952018141747,
0.01046491228044033,
-0.022389234974980354,
-0.04740786924958229,
0.02767316997051239,
-0.008498003706336021,
0.05053179711103439,
0.023103579878807068,
-0.025164654478430748,
0.02205479145050049,
0.027382200583815575,
-0.019235849380493164,
0.026129718869924545,
-0.004536925349384546,
-0.013647760264575481,
-0.007805219851434231,
-0.025376979261636734,
-0.0015445161843672395,
0.025159871205687523,
-0.015002215281128883,
0.032764799892902374,
-0.0060812365263700485,
0.001345342374406755,
0.0540178120136261,
-0.014910638332366943,
-0.022866809740662575,
-0.06726677715778351,
-0.021339068189263344,
-0.04471433535218239,
0.023900022730231285,
0.0066400389187037945,
0.003767285030335188,
0.042312994599342346,
0.01330123282968998,
0.04585693031549454,
-0.009522723965346813,
0.02204238250851631,
0.01389844249933958,
-0.030063994228839874,
-0.0035253851674497128,
-0.03414221853017807,
-0.044770315289497375,
0.03171103820204735,
-0.0034849762450903654,
-0.02689526416361332,
0.01568005047738552,
0.005684292409569025,
0.01878996379673481,
0.032133799046278,
0.04391741380095482,
0.020555874332785606,
0.08562013506889343,
-0.015411914326250553,
0.03346440568566322,
-0.015445681288838387,
0.0094856983050704,
0.12555408477783203,
0.04471917077898979,
0.03221509978175163,
-0.03879715874791145,
-0.0069017717614769936,
-0.0015283540124073625,
-0.0076313200406730175,
-0.01463324110955,
0.07189895212650299,
-0.006402414292097092,
-0.009016710333526134,
0.031866442412137985,
0.030129767954349518,
-0.042749203741550446,
-0.005528338253498077,
0.0032414894085377455,
-0.06075838580727577,
-0.03481237590312958,
0.03598180413246155,
0.0037940270267426968,
-0.027525508776307106,
-0.009240629151463509,
0.010527104139328003,
0.00058841920690611,
-0.013979850336909294,
0.011656377464532852,
-0.03638143464922905,
-0.049248840659856796,
0.019335584715008736,
-0.007674334105104208,
-0.016234658658504486,
0.012768360786139965,
0.024666672572493553,
0.014435929246246815,
-0.020550021901726723,
-0.004308057948946953,
0.015472381375730038,
-0.013240283355116844,
0.02842547558248043,
0.023445680737495422,
0.014156490564346313,
0.014376094564795494,
0.030149808153510094,
0.0032759434543550014,
-0.03692811354994774,
-0.0247669480741024,
-0.018247023224830627,
0.06437549740076065,
-0.015334093011915684,
0.0050890021957457066,
-0.027235889807343483,
-0.005874167196452618,
0.0074367765337228775,
-0.03477134928107262,
-0.010653210803866386,
-0.013270070776343346,
0.037680499255657196,
0.016575168818235397,
-0.033599723130464554,
-0.043078236281871796,
-0.00027725391555577517,
0.029614264145493507,
0.013694368302822113,
-0.02633623033761978,
-0.019335025921463966,
0.026939794421195984,
0.004624567925930023,
0.05030803382396698,
-0.03297948092222214,
-0.029346158728003502,
-0.0387834794819355,
-0.017202498391270638,
-0.028969863429665565,
-0.015335245989263058,
0.00886054988950491,
-0.042828936129808426,
0.04480794444680214,
0.006080001592636108,
-0.03976684808731079,
-0.023319074884057045,
-0.09860111773014069,
0.02837265096604824,
-0.01636640727519989,
-0.015288997441530228,
-0.003567800624296069,
0.03277156502008438,
0.0005319556221365929,
0.07176342606544495,
0.00033955229446291924,
0.00920652411878109,
0.04836010932922363,
0.02995493821799755,
0.019025249406695366,
-0.013942535035312176,
-0.017328033223748207,
-0.0019999006763100624,
-0.052086710929870605,
0.010381480678915977,
-0.01203067321330309,
0.042633235454559326,
0.014004246331751347,
0.0011365566169843078,
-0.04652786999940872,
0.016492944210767746,
-0.015216750092804432,
0.03057468682527542,
-0.027982285246253014,
-0.011714586988091469,
-0.015676073729991913,
0.013741240836679935,
0.015609555877745152,
-0.006898439023643732,
-0.026682129129767418,
-0.019538093358278275,
0.009604998864233494,
-0.02032615803182125,
-0.022281967103481293,
-0.031392600387334824,
0.002483505755662918,
-0.04366596043109894,
0.008010072633624077,
-0.05051906779408455,
-0.039039742201566696,
-0.026801014319062233,
0.0022315578535199165,
0.04239794984459877,
0.01796434447169304,
-0.019786762073636055,
-0.01090340968221426,
0.009408026933670044,
-0.030794229358434677,
0.007919021882116795,
0.04845374822616577,
-0.021755671128630638,
-0.05831054970622063,
0.03292681649327278,
0.019587181508541107,
0.07382547855377197,
-0.010464445687830448,
-0.04200087487697601,
0.009191754274070263,
-0.031427379697561264,
-0.06799210608005524,
0.024712318554520607,
0.03187558054924011,
0.05586404353380203,
0.020825130864977837,
0.00742357550188899,
-0.013215841725468636,
0.045324113219976425,
-0.007444979157298803,
-0.013820554129779339,
-0.01230823714286089,
-0.05456291884183884,
-0.03180583938956261,
-0.009840002283453941,
0.02161051332950592,
-0.010308975353837013,
-0.006700920406728983,
0.021609218791127205,
-0.00295591470785439,
-0.0048254202120006084,
0.020061137154698372,
0.0010654865764081478,
-0.0038751859683543444,
0.03647744283080101,
0.03164924681186676,
-0.015147439204156399,
0.03791920095682144,
0.05818962678313255,
-0.007703644689172506,
-0.012811807915568352,
0.049594003707170486,
0.029316609725356102,
-0.09954966604709625,
0.010066509246826172,
-0.01176119688898325,
-0.007671973202377558,
0.022242527455091476,
-0.04402608424425125,
0.0629599541425705,
0.020152874290943146,
-0.0044909450225532055,
0.0034079791512340307,
-0.03724111616611481,
0.018318627029657364,
-0.019239848479628563,
0.004059974104166031,
-0.034515105187892914,
0.06604111939668655,
0.038550518453121185,
0.028619641438126564,
0.01021020207554102,
-0.00880319532006979,
0.005209773313254118,
-0.037277985364198685,
-0.002164913807064295,
0.01112341694533825,
-0.02658391371369362,
-0.02654908411204815,
0.041474081575870514,
-0.029176346957683563,
-0.025816187262535095,
0.0066038621589541435,
-0.07341726124286652,
-0.02606523036956787,
-0.02630814164876938,
0.0319899246096611,
-0.015310674905776978,
0.007703874725848436,
0.05009760707616806,
-0.018571356311440468,
0.011148421093821526,
0.04136458784341812,
0.004930025897920132,
-0.023338625207543373,
-0.0003232368326280266,
0.000629512476734817,
0.026735220104455948,
-0.01732211746275425,
-0.03723837062716484,
0.059723109006881714,
-0.036358851939439774,
-0.039463747292757034,
0.0026463221292942762,
-0.03183801472187042,
-0.008399955928325653,
-0.029610322788357735,
0.009142370894551277,
-0.054907187819480896,
-0.006138170603662729,
0.02627493627369404,
-0.00492935860529542,
-0.036667920649051666,
-0.012300945818424225,
-0.016132105141878128,
-0.054850995540618896,
0.04769713431596756,
0.016231002286076546,
0.009960892610251904,
-0.04439583048224449,
-0.05941423773765564,
-0.01360311359167099,
-0.02299274317920208,
-0.02756175398826599,
-0.03379940986633301,
-0.0211960319429636,
0.047680702060461044,
-0.003791565541177988,
-0.0025677254889160395,
-0.030200643464922905,
-0.044074103236198425,
-0.022939519956707954,
-0.04361123591661453,
0.009715140797197819,
-0.020719630643725395,
-0.009161601774394512,
-0.017851820215582848,
-0.026336729526519775,
-0.007725208066403866,
0.036368049681186676,
0.06942860782146454,
0.006702806800603867,
-0.027544135227799416,
0.03571010008454323,
0.010975169017910957,
0.02553229033946991,
-0.047943469136953354,
-0.017798863351345062,
-0.019176701083779335,
-0.0027896109968423843,
-0.0010521291987970471,
0.01362761203199625,
-0.006536270026117563,
0.03286711871623993,
0.019138449802994728,
-0.024408679455518723,
-0.030121391639113426,
-0.006631426513195038,
0.024000316858291626,
0.05793372541666031,
0.007498341146856546,
-0.0067185815423727036,
0.05514146760106087,
-0.013159315101802349,
0.05974435806274414,
0.01078172866255045,
-0.00899041909724474,
-0.0459502674639225,
0.01875706948339939,
-0.02144724689424038,
-0.04154248535633087,
-0.025720050558447838,
-0.031381960958242416,
-0.001059172092936933,
-0.04147553816437721,
-0.021204669028520584,
0.0028479767497628927,
-0.086219422519207,
0.010125378146767616,
0.016390852630138397,
-0.019101876765489578,
0.04464384540915489,
-0.022341854870319366,
0.03974076360464096,
0.03553285449743271,
-0.004090147092938423,
0.023836256936192513,
0.061697330325841904,
0.03631852939724922,
0.032559242099523544,
0.008071926422417164,
0.002686435589566827,
-0.06833019107580185,
0.012776297517120838,
0.01249845139682293,
0.005746075417846441,
-0.0033433549106121063,
-0.008661597967147827,
-0.004755938891321421,
-0.015408378094434738,
-0.02176414430141449,
-0.011285685934126377,
-0.02209305949509144,
0.05883448198437691,
0.010814687237143517,
0.028819654136896133,
-0.02970951609313488,
-0.006308676674962044,
-0.010857036337256432,
-0.018750056624412537,
0.009945974685251713,
0.0467442125082016,
-0.00290671456605196,
0.007146635092794895,
-0.02535330504179001,
0.020169269293546677,
-0.01198684610426426,
-0.030581064522266388,
0.0025350998621433973,
0.010043540969491005,
-0.02309209108352661,
-0.02262742631137371,
-0.06345371156930923,
-0.007670820690691471,
-0.05561789125204086,
0.021991996094584465,
0.035096943378448486,
0.043736811727285385,
0.0196064505726099,
-0.008120711892843246,
0.015945235267281532,
0.06419219821691513,
-0.03520900011062622,
-0.05191238597035408,
0.014342419803142548,
0.0019708748441189528,
0.004026640206575394,
0.014705870300531387
] |
<p>I am having trouble understanding electromagnetic radiation (or waves in general, be it EM or sound). If I have a 1 Watt speaker, is it infinitely divided and spread out so that everyone in every direction around the speaker can hear it?</p>
<p>I do not believe they have "height", to reach more than one person at once, but if they did they would probably collide at one point. How do sound waves travel "backwards" (i.e. you are behind a speaker), are they scattered by air particles or itself so that people behind could hear it (at reduced amplitude)?</p>
<p>I am just unsure how to wrap my head around it.</p> | 1,564 | [
-0.017827846109867096,
-0.05271162837743759,
0.02157675102353096,
-0.055142827332019806,
0.031184306368231773,
-0.005343416705727577,
-0.01516417134553194,
0.00795656070113182,
-0.008669774048030376,
-0.008269640617072582,
0.03019135631620884,
0.04017012193799019,
0.07508928328752518,
-0.00508200004696846,
0.057091519236564636,
0.0021915610413998365,
-0.009866374544799328,
0.014668146148324013,
0.016568368300795555,
-0.021223071962594986,
-0.021291403099894524,
0.0135443564504385,
-0.02613585814833641,
0.0073917885310947895,
-0.0331253744661808,
0.01030739489942789,
0.03499748185276985,
0.030736438930034637,
0.03981149569153786,
0.03096754476428032,
0.028625981882214546,
-0.04833610728383064,
-0.009098919108510017,
0.02126140706241131,
0.03982184827327728,
-0.019783809781074524,
-0.025480814278125763,
-0.025115087628364563,
-0.03982238098978996,
-0.0027077023405581713,
-0.0036260653287172318,
-0.031811270862817764,
-0.010212209075689316,
0.03770877793431282,
-0.07130900770425797,
-0.004044319503009319,
0.019421637058258057,
-0.020817752927541733,
0.03493008390069008,
-0.08980048447847366,
0.10260462760925293,
-0.011355999857187271,
0.03849251568317413,
0.04208032041788101,
0.024945808574557304,
0.04017053171992302,
0.06841892004013062,
0.06534299999475479,
0.0165245421230793,
-0.05510258302092552,
0.016498850658535957,
0.02987627685070038,
-0.043813757598400116,
-0.002804029267281294,
-0.01794753037393093,
0.02282002381980419,
-0.012407766655087471,
-0.004205562639981508,
0.013695082627236843,
0.010061721317470074,
0.008778411895036697,
0.03498593717813492,
0.04286346584558487,
-0.02208312228322029,
0.008296948857605457,
-0.014907537028193474,
0.036860186606645584,
0.0013643797719851136,
0.04032309353351593,
0.03596971929073334,
0.0005766234244219959,
0.0006086141220293939,
0.018576551228761673,
0.03115071915090084,
-0.00014768306573387235,
-0.0359538234770298,
0.06787164509296417,
-0.03622892126441002,
-0.002146216342225671,
0.02024270035326481,
-0.02821440063416958,
0.016295185312628746,
0.0440763495862484,
0.007832393050193787,
-0.020910853520035744,
0.038074418902397156,
0.0004751743108499795,
0.055641643702983856,
0.03112694062292576,
-0.062017109245061874,
0.03198535367846489,
0.026550253853201866,
0.02531353384256363,
0.029090523719787598,
-0.015839669853448868,
-0.04307756572961807,
-0.06101764738559723,
0.04395350441336632,
-0.031712085008621216,
-0.01035743672400713,
-0.023749925196170807,
0.029672084376215935,
0.018435509875416756,
-0.024424392729997635,
0.03536401316523552,
-0.00493976566940546,
0.008543364703655243,
-0.03728312999010086,
0.06049463525414467,
0.09047211706638336,
0.037054650485515594,
-0.038078486919403076,
0.03801202028989792,
-0.02282683365046978,
-0.07296306639909744,
-0.010799705050885677,
-0.009410218335688114,
0.01661614514887333,
-0.049720603972673416,
0.06688486784696579,
0.011242907494306564,
-0.0027476446703076363,
0.04906520992517471,
-0.01939333975315094,
0.03496190905570984,
-0.02558175101876259,
-0.08438855409622192,
-0.02830248884856701,
0.024225058034062386,
-0.010506028309464455,
-0.01755046844482422,
-0.07028821110725403,
-0.0017332060961052775,
0.018269823864102364,
0.06610468029975891,
-0.005572222638875246,
0.01842719502747059,
-0.015341798774898052,
0.052542366087436676,
0.02097122184932232,
-0.02782052382826805,
0.01075877994298935,
-0.022037504240870476,
0.0017278335290029645,
0.0490066222846508,
-0.04751104116439819,
0.040464553982019424,
0.04779284447431564,
0.01619347743690014,
-0.04352261871099472,
0.055791109800338745,
-0.007974066771566868,
-0.013021761551499367,
0.035993900150060654,
-0.04632962867617607,
-0.02575545199215412,
0.07350046187639236,
0.013608013279736042,
-0.03426314517855644,
0.04267364367842674,
0.036982178688049316,
-0.022836368530988693,
-0.027986083179712296,
-0.00474343728274107,
0.030771439895033836,
-0.038047708570957184,
-0.012833607383072376,
-0.01565234176814556,
0.021923445165157318,
0.01568431220948696,
-0.060160331428050995,
-0.04455841705203056,
0.02126634120941162,
0.029956454411149025,
0.01199529878795147,
0.0442018061876297,
-0.0148299066349864,
-0.01997128687798977,
-0.02201448380947113,
-0.015677060931921005,
-0.0172075554728508,
-0.02234470471739769,
0.05238472670316696,
-0.021684948354959488,
0.009641295298933983,
0.003590298118069768,
0.01940700225532055,
0.02735770493745804,
-0.05268534645438194,
-0.010061428882181644,
0.010487101040780544,
0.04560565575957298,
0.004608488641679287,
-0.008971642702817917,
-0.0067446609027683735,
0.09350784122943878,
0.02262686751782894,
0.007017154712229967,
0.04870948567986488,
-0.0015658690826967359,
-0.03419354557991028,
-0.0014805520186200738,
-0.058962203562259674,
0.04747745022177696,
0.011340664699673653,
-0.005791599862277508,
0.01635248214006424,
-0.01714620366692543,
-0.0005295077571645379,
0.015350321307778358,
-0.010264964774250984,
0.04170982912182808,
0.037728503346443176,
-0.01171121932566166,
-0.01765848882496357,
0.010458678007125854,
0.011767463758587837,
-0.02738790214061737,
0.003068992169573903,
-0.022737914696335793,
-0.0662819966673851,
0.03191661462187767,
0.038552965968847275,
-0.012434067204594612,
-0.002086926018819213,
0.013053903356194496,
0.004040643107146025,
0.032120298594236374,
0.06649217009544373,
0.03184483200311661,
-0.05634310841560364,
-0.021527156233787537,
0.02206658385694027,
0.010636799968779087,
0.010391264222562313,
-0.0034652480389922857,
0.012178772129118443,
0.007159024942666292,
-0.01054698321968317,
-0.0055871158838272095,
-0.015077906660735607,
0.02290934883058071,
0.022144189104437828,
0.012050743214786053,
-0.025443363934755325,
-0.059744641184806824,
-0.0010209261672571301,
-0.03946409747004509,
0.006172624882310629,
-0.015619778074324131,
-0.03734557703137398,
-0.01542599592357874,
-0.028991278260946274,
0.003716318868100643,
0.004364721477031708,
0.018639439716935158,
-0.027836838737130165,
-0.0038103475235402584,
0.0339568555355072,
-0.02297833003103733,
0.024899842217564583,
-0.02349265292286873,
-0.03193479776382446,
0.00006526702782139182,
-0.02539249137043953,
0.07409264892339706,
0.03155125305056572,
0.04500699043273926,
-0.0491425059735775,
-0.05407248064875603,
-0.013493754900991917,
-0.05868976190686226,
0.018254457041621208,
0.0113745192065835,
-0.02853735350072384,
0.02222428284585476,
-0.0439927764236927,
-0.013415204361081123,
0.046686530113220215,
0.014869903214275837,
-0.010945980437099934,
0.03296975791454315,
-0.018231555819511414,
-0.06735921651124954,
-0.04367323964834213,
-0.03574296087026596,
0.03431970998644829,
-0.014576351270079613,
0.0003850759821943939,
0.04067575931549072,
-0.01918218843638897,
-0.0344192199409008,
0.01404059398919344,
-0.07190663367509842,
-0.025116493925452232,
-0.016470329836010933,
-0.026688694953918457,
0.020417775958776474,
-0.02603762596845627,
-0.009259918704628944,
0.009789790958166122,
-0.07112068682909012,
0.009634188376367092,
-0.021160051226615906,
-0.05575995519757271,
0.032824646681547165,
-0.0042741126380860806,
0.03495866805315018,
0.013576645404100418,
-0.014226088300347328,
0.05882168188691139,
0.027749404311180115,
-0.015350563451647758,
0.008732772432267666,
-0.00955036748200655,
0.016417033970355988,
-0.03750529885292053,
0.050454478710889816,
0.05286039784550667,
-0.040446627885103226,
0.031046070158481598,
0.03697895631194115,
0.01559338066726923,
0.010439855046570301,
-0.0018671088619157672,
-0.009633191861212254,
-0.02708769589662552,
-0.011738531291484833,
0.0028860431630164385,
0.035583801567554474,
-0.0011056814109906554,
-0.023169921711087227,
0.01060660369694233,
-0.027243683114647865,
0.033959321677684784,
0.023757442831993103,
-0.02943713217973709,
0.0013275841483846307,
-0.0018796088406816125,
0.007565596606582403,
-0.08726146817207336,
0.0371931716799736,
0.0020010885782539845,
-0.004217696841806173,
-0.0017159259878098965,
0.011495727114379406,
0.034145161509513855,
-0.02304253913462162,
-0.0035977200604975224,
0.005743454676121473,
0.06994365900754929,
-0.03902898728847504,
-0.06821554899215698,
-0.008237725123763084,
0.01379254087805748,
-0.011097338981926441,
0.02717095986008644,
-0.010971658863127232,
0.06295130401849747,
0.051304612308740616,
0.022580284625291824,
0.011133382096886635,
-0.03864862024784088,
-0.023065835237503052,
-0.039396632462739944,
0.03292682766914368,
-0.007138896733522415,
0.02227521874010563,
0.006785697769373655,
0.09822028875350952,
0.01746509037911892,
0.02037419192492962,
0.029789751395583153,
-0.011462611146271229,
-0.0721440389752388,
0.015993978828191757,
-0.020720642060041428,
-0.023869944736361504,
-0.04602112993597984,
-0.010369852185249329,
-0.04229428991675377,
0.006519722286611795,
-0.04518074914813042,
0.013687912374734879,
-0.010063842870295048,
-0.07505510002374649,
0.006951082032173872,
-0.049440648406744,
-0.02144625224173069,
-0.014988348819315434,
0.03697725385427475,
-0.008011684753000736,
-0.03864084184169769,
0.009528466500341892,
0.03886636719107628,
-0.025017865002155304,
-0.008500576950609684,
-0.006555858068168163,
0.011365760117769241,
0.01924903318285942,
0.020450420677661896,
0.060851581394672394,
-0.0013592634350061417,
-0.04900982975959778,
0.030325861647725105,
0.03270571306347847,
0.06016277149319649,
-0.011989912018179893,
0.009488528594374657,
-0.020638806745409966,
-0.00474470155313611,
-0.023173509165644646,
-0.011411961168050766,
0.02002684399485588,
0.008243363350629807,
-0.0057532344944775105,
0.0241316556930542,
0.013608557172119617,
-0.013689023442566395,
0.03655530512332916,
0.017007896676659584,
-0.010921277105808258,
-0.02713361196219921,
-0.049824487417936325,
-0.010066266171634197,
-0.023545531556010246,
0.008151369169354439,
0.0007651597261428833,
0.004098999314010143,
0.01759449951350689,
0.02322041243314743,
0.033569540828466415,
0.027553195133805275,
-0.018555302172899246,
0.03086235746741295,
0.0007146249990910292,
-0.036923691630363464,
-0.007665857672691345,
-0.029275551438331604,
-0.01696869358420372,
0.025199001654982567,
0.05282651633024216,
0.006880827248096466,
-0.029076136648654938,
-0.08197325468063354,
-0.00557707017287612,
0.004584453999996185,
0.030819803476333618,
-0.008882843889296055,
0.04362422972917557,
-0.02440420351922512,
-0.033184781670570374,
0.011059381067752838,
0.0072443666867911816,
0.03306419774889946,
-0.031900208443403244,
-0.014170867390930653,
0.002674882998690009,
-0.009837149642407894,
-0.009975805878639221,
0.022562140598893166,
-0.01921241730451584,
-0.005414209328591824,
-0.00874131079763174,
-0.00521253515034914,
-0.029449449852108955,
0.04424504563212395,
0.04652617871761322,
0.05007562413811684,
0.009187480434775352,
0.006599928718060255,
0.012047386728227139,
0.04126818850636482,
0.008982310071587563,
-0.03124328702688217,
-0.01793646439909935,
0.006372867152094841,
-0.025732463225722313,
0.07868219166994095,
-0.033535294234752655,
-0.031925126910209656,
0.018766440451145172,
0.04928228631615639,
0.010605999268591404,
-0.023389006033539772,
-0.001321099349297583,
0.045541614294052124,
-0.020753029733896255,
0.01931764930486679,
0.044059284031391144,
0.014310861006379128,
-0.005940877832472324,
-0.006788247264921665,
0.017635149881243706,
0.05348024517297745,
-0.020206958055496216,
0.006437554024159908,
-0.004075098782777786,
-0.004723105579614639,
-0.029814710840582848,
0.04244045168161392,
-0.011853615753352642,
-0.0043592266738414764,
0.0032497537322342396,
-0.05225096642971039,
-0.013225274160504341,
0.04632975906133652,
-0.0297696590423584,
-0.010034030303359032,
-0.008547598496079445,
0.038049619644880295,
-0.019045889377593994,
-0.012560105882585049,
0.011134836822748184,
-0.017419127747416496,
0.019921885803341866,
0.007227725349366665,
0.002676476025953889,
0.010975615121424198,
-0.024601489305496216,
-0.02399528957903385,
0.035308804363012314,
-0.020529724657535553,
0.04316091910004616,
-0.019528992474079132,
0.001986344810575247,
0.04618051275610924,
-0.0801675021648407,
-0.05066283047199249,
0.00997018814086914,
0.005526991561055183,
0.059893570840358734,
-0.04562361165881157,
0.019763251766562462,
0.008640325628221035,
0.01656220853328705,
-0.04287206009030342,
-0.010214593261480331,
0.0026790478732436895,
0.04151725023984909,
0.0008223868790082633,
-0.032452087849378586,
-0.00480416277423501,
-0.02820981666445732,
-0.024096598848700523,
0.007998855784535408,
-0.010066571645438671,
-0.03183261305093765,
0.04051152616739273,
0.037031691521406174,
-0.004343495704233646,
0.03972354531288147,
0.02595369704067707,
-0.03785444796085358,
0.014081833884119987,
0.005086184944957495,
0.007021029945462942,
-0.031926751136779785,
0.04526446387171745,
-0.021492399275302887,
-0.02929217554628849,
-0.006049441173672676,
-0.009898649528622627,
0.042766693979501724,
-0.04982280358672142,
-0.010827002115547657,
0.011364545673131943,
0.025370685383677483,
-0.010163027793169022,
-0.009133496321737766,
0.029950646683573723,
-0.013565254397690296,
0.024969223886728287,
-0.03399449586868286,
-0.040959637612104416,
-0.06586043536663055,
-0.021187806501984596,
0.02203710749745369,
-0.0005969092017039657,
0.045274704694747925,
-0.00961227621883154,
0.037113986909389496,
-0.013336547650396824,
0.004866900388151407,
0.02103421464562416,
-0.031477153301239014,
0.0365663580596447,
-0.022991133853793144,
-0.010513190180063248,
-0.0020323973149061203,
0.019017579033970833,
0.01957867667078972,
-0.0098808528855443,
-0.03464223071932793,
-0.00708867097273469,
0.06980898976325989,
-0.017101291567087173,
0.03631060570478439,
0.02018352784216404,
0.01108466275036335,
-0.019520888105034828,
-0.02021303027868271,
-0.0034321260172873735,
0.007570152170956135,
-0.016894347965717316,
0.0014933194033801556,
-0.04613791033625603,
-0.01358809694647789,
0.0361408069729805,
0.03035794384777546,
-0.005049609113484621,
-0.007010787259787321,
0.005853200331330299,
0.0187901072204113,
-0.0101012596860528,
0.024336447939276695,
-0.011214728467166424,
0.04021664336323738,
-0.06910204142332077,
-0.008437626995146275,
-0.006703953258693218,
0.02300489880144596,
0.03257521986961365,
0.020902248099446297,
-0.007717467378824949,
-0.046972163021564484,
-0.003155851038172841,
-0.02459503710269928,
0.017118137329816818,
0.0019855275750160217,
0.031440477818250656,
-0.025470823049545288,
-0.012454166077077389,
0.02152959443628788,
-0.011330821551382542,
0.0037701211404055357,
0.03488490357995033,
-0.07199081033468246,
-0.05400382727384567,
0.0020920608658343554,
-0.05900440365076065,
0.031218593940138817,
0.029143884778022766,
-0.033088281750679016,
0.014876621775329113,
-0.06279845535755157,
0.04231083765625954,
-0.008308803662657738,
0.025558076798915863,
0.02021355740725994,
0.04791087657213211,
0.022866783663630486,
0.015481912530958652,
-0.02208600752055645,
-0.004288744647055864,
0.09798416495323181,
0.013778256252408028,
0.015381421893835068,
-0.024046624079346657,
-0.007760220672935247,
-0.038205280900001526,
0.006177797913551331,
-0.049852658063173294,
0.011032147333025932,
-0.039210982620716095,
0.052686575800180435,
0.021976016461849213,
0.0540078729391098,
0.03758557140827179,
0.009605773724615574,
0.06153159961104393,
-0.005917866714298725,
-0.05888548493385315,
0.013399559073150158,
0.021155353635549545,
0.021952643990516663,
0.043307799845933914,
-0.08373332768678665,
0.0050775716081261635,
-0.04919809475541115,
-0.011735438369214535,
-0.02164003625512123,
-0.03190039470791817,
0.04450921341776848,
-0.015884561464190483,
-0.026860708370804787,
0.0016037136083468795,
0.01023035403341055,
-0.016771158203482628,
-0.03104219399392605,
0.02073753997683525,
0.04848162829875946,
-0.02229328639805317,
-0.00951254740357399,
0.02018100395798683,
0.014681598171591759,
0.00004719023854704574,
0.014095619320869446,
0.029566170647740364,
-0.028948990628123283,
-0.008449005894362926,
0.013654472306370735,
0.029114553704857826,
-0.008555075153708458,
0.015303270891308784,
-0.004286117386072874,
0.0305735245347023,
0.002432915149256587,
-0.056580811738967896,
0.0037695940118283033,
0.017205258831381798,
0.02384444884955883,
-0.010021213442087173,
0.0049892314709723,
-0.03675047308206558,
0.013877766206860542,
-0.02239200845360756,
-0.011368014849722385,
-0.011152221821248531,
0.0008178470889106393,
0.000918395584449172,
-0.027607709169387817,
0.01937919296324253,
-0.014845863915979862,
-0.03678906336426735,
-0.04496176540851593,
-0.02039973996579647,
-0.021436024457216263,
0.022102585062384605,
0.03526582568883896,
0.041980065405368805,
-0.0008930650074034929,
0.031817249953746796,
-0.007415309082716703,
-0.026097971946001053,
-0.048838645219802856,
0.03210368752479553,
-0.01765032671391964,
-0.04730811342597008,
0.02336505427956581,
-0.01916113682091236,
0.01615719310939312,
0.024594273418188095,
-0.01768684573471546,
0.0007032587891444564,
-0.007368683815002441,
0.014012864790856838,
-0.015478543937206268,
-0.018080025911331177,
-0.024887418374419212,
0.04103507101535797,
-0.010548007674515247,
0.001680893823504448,
0.013647159561514854,
0.04243762791156769,
0.01221553236246109,
-0.039147112518548965,
-0.003940038848668337,
0.029531942680478096,
-0.04727788642048836,
-0.018724316731095314,
0.010658824816346169,
-0.04150581732392311,
0.02026459574699402,
0.008779560215771198,
0.006850394420325756,
-0.0356038473546505,
-0.03656397759914398,
-0.004075192846357822,
0.01455391850322485,
-0.014030355960130692,
0.022823862731456757,
0.011190176010131836,
0.017219113186001778,
0.006237335968762636,
0.002060301136225462,
-0.028322208672761917,
-0.008604156784713268,
-0.016654545441269875,
0.017699867486953735,
0.0007892673602327704,
-0.030249105766415596,
-0.03751865401864052,
0.031187385320663452,
-0.06463246047496796,
-0.005840560421347618,
0.011200272478163242,
0.03585966303944588,
-0.004437319468706846,
-0.004322201479226351,
0.02434086985886097,
-0.00011928100138902664,
0.05862648785114288,
0.0035345822107046843,
-0.03644787147641182,
0.05250095948576927,
-0.017699917778372765,
-0.06881774216890335,
0.01561274379491806,
0.0072656129486858845,
0.05236749351024628,
0.012703437358140945,
0.002701897406950593,
-0.024300599470734596,
0.07146216183900833,
-0.0074860816821455956,
0.011040586046874523,
-0.013418972492218018,
-0.03895966336131096,
-0.019915081560611725,
0.007089268881827593,
0.023815428838133812,
-0.020877482369542122,
-0.01709543913602829,
0.026327185332775116,
0.03930021449923515,
0.010667026042938232,
0.02391872927546501,
0.0020626699551939964,
-0.025888653472065926,
0.013164582662284374,
0.009736300446093082,
0.0021315678022801876,
0.0163287241011858,
0.10225572437047958,
-0.04962797835469246,
0.042842522263526917,
0.010161535814404488,
-0.006435399875044823,
-0.086978480219841,
0.0018449603812769055,
0.03844286501407623,
-0.010376837104558945,
0.017792701721191406,
-0.05412592366337776,
-0.02509388141334057,
0.0387866273522377,
-0.0631229504942894,
0.03168772533535957,
-0.0007605170249007642,
-0.02480098232626915,
-0.02162834443151951,
0.025763630867004395,
0.012544432654976845,
0.06587429344654083,
0.02810921147465706,
0.07014840841293335,
-0.005776288919150829,
0.011946159414947033,
-0.004201438743621111,
-0.032780181616544724,
-0.028670744970440865,
0.020871935412287712,
0.006917820777744055,
0.026378879323601723,
0.08172117918729782,
-0.01299839373677969,
-0.0013548522256314754,
0.06275784224271774,
-0.04421894624829292,
0.024132559075951576,
0.011885222978889942,
0.003879572730511427,
0.004995788913220167,
0.025875650346279144,
-0.009339318610727787,
0.004631068091839552,
0.0037438429426401854,
0.034238316118717194,
0.022439422085881233,
-0.007564804051071405,
0.017707746475934982,
-0.013495185412466526,
0.041388727724552155,
-0.044845934957265854,
-0.0370558425784111,
0.04186657443642616,
-0.021629484370350838,
-0.029463401064276695,
-0.016441000625491142,
0.003993674647063017,
0.01847377046942711,
-0.028007933869957924,
0.011260731145739555,
-0.06048918142914772,
-0.053219810128211975,
-0.009799481369554996,
0.01578466035425663,
-0.0037851370871067047,
0.03946720436215401,
0.004316768608987331,
-0.0160372257232666,
0.026041092351078987,
0.00693915830925107,
0.011407073587179184,
-0.054231852293014526,
-0.022120345383882523,
0.0038460036739706993,
-0.002888393122702837,
0.02745342068374157,
-0.036368321627378464,
-0.01691814698278904,
0.007677189540117979,
0.028911562636494637,
0.01609250158071518,
0.01890667714178562,
-0.01632675528526306,
-0.0334533154964447,
-0.04659654200077057,
0.03129395470023155,
0.003840284887701273,
-0.01110922358930111,
-0.06615794450044632,
-0.03147924691438675,
-0.0011074300855398178,
0.0216075386852026,
0.051370713859796524,
-0.0007547928253188729,
0.014272133819758892,
0.019013911485671997,
-0.02908976748585701,
0.019774017855525017,
-0.04182932898402214,
-0.03483523428440094,
0.03237398713827133,
-0.03643152490258217,
-0.03870580717921257,
-0.012974527664482594,
-0.01903454028069973,
0.0010800607269629836,
0.022398492321372032,
-0.02228516712784767,
0.020492877811193466,
-0.02358400449156761,
-0.03679167106747627,
0.027109302580356598,
0.04948262497782707,
-0.021217210218310356,
0.0152091970667243,
-0.05355945602059364,
-0.0099738584831357,
0.026107581332325935,
-0.05084861069917679,
-0.05617501959204674,
-0.0031857681460678577,
-0.023439154028892517,
0.024546323344111443,
-0.0176040381193161,
0.011246036738157272,
0.05955474078655243,
-0.03798941895365715,
-0.042966414242982864,
0.039066433906555176,
-0.0590905025601387,
0.008739008568227291,
0.04573110118508339,
0.02699861116707325,
-0.009379846043884754,
-0.004966514650732279,
-0.001372140017338097,
0.02242986671626568,
-0.018508460372686386,
-0.0004380623868200928,
0.05954499542713165,
0.004222692921757698,
-0.008671051822602749,
0.011754265055060387,
0.03732181712985039,
0.0022781919687986374,
0.016304101794958115,
-0.026683645322918892,
0.024713262915611267,
-0.031283870339393616,
0.009183557704091072,
0.008532010950148106,
-0.013353305868804455,
-0.036995548754930496,
0.026456186547875404,
-0.015826957300305367,
0.06983259320259094,
-0.010866777040064335,
0.023010378703475,
0.02323424071073532,
-0.008663353510200977,
0.004735137801617384,
-0.015470080077648163,
0.006128400098532438,
0.0261158999055624,
-0.014452792704105377,
-0.04065624997019768,
-0.02257249504327774,
-0.0166726466268301,
0.040520716458559036,
-0.03740905597805977,
0.02245987206697464,
-0.03592361509799957,
-0.028611576184630394,
-0.022112052887678146,
-0.026533449068665504,
-0.025766009464859962,
-0.01854037120938301,
0.035351354628801346,
0.032169852405786514,
-0.00540984096005559,
0.015298730693757534,
0.0023080911487340927,
-0.05023437738418579,
0.045455314218997955,
-0.0450272262096405,
0.01691375859081745,
-0.035651952028274536,
0.04008421301841736,
0.0017299540340900421,
0.019022813066840172
] |
<p>I often see the term "net mechanical efficiency" used in literature, but I am not quite sure what it means, and what the difference is between it and "normal" efficiency. Take this sentence for example: <code>... increased the effectiveness, while reducing net mechanical efficiency.</code> What does exactly does this mean?</p> | 1,565 | [
-0.01411642786115408,
-0.016379062086343765,
-0.048048827797174454,
-0.013826251029968262,
-0.0014960933476686478,
0.042721234261989594,
0.0042162612080574036,
-0.03179330751299858,
0.013854963704943657,
-0.0216252189129591,
0.02862451784312725,
0.0366910919547081,
0.0543234758079052,
-0.007101540919393301,
0.030004063621163368,
-0.02702956460416317,
-0.010213677771389484,
0.016685163602232933,
0.032277729362249374,
-0.046516165137290955,
-0.034181706607341766,
-0.017810622230172157,
0.009474704973399639,
0.010815362446010113,
0.004968162626028061,
0.037081606686115265,
0.018329378217458725,
-0.040174782276153564,
-0.009673493914306164,
0.019475076347589493,
-0.014474970288574696,
-0.014086810871958733,
-0.006649952847510576,
0.032907310873270035,
-0.01583021692931652,
0.007786764297634363,
-0.08126477152109146,
-0.03187035396695137,
0.008085687644779682,
0.024983765557408333,
-0.020114434882998466,
0.007022338919341564,
-0.004415298346430063,
0.02198060229420662,
-0.012815698981285095,
0.04650786891579628,
-0.015838470309972763,
-0.021298671141266823,
0.004358385223895311,
-0.042910002171993256,
0.05130332335829735,
0.015752242878079414,
0.05381258204579353,
0.005352920852601528,
0.01109318807721138,
0.029679054394364357,
0.053021762520074844,
0.07559996098279953,
-0.007212161552160978,
-0.06292680650949478,
-0.027219178155064583,
-0.03609296679496765,
-0.004941422492265701,
-0.029748590663075447,
-0.016922662034630775,
0.061794545501470566,
-0.022578764706850052,
-0.03107944130897522,
0.08152653276920319,
0.012908867560327053,
0.01235711108893156,
0.012472063302993774,
0.005082232411950827,
-0.003932772669941187,
0.012390672229230404,
-0.05967172235250473,
0.006717825774103403,
0.009267749264836311,
-0.013057040050625801,
0.05292428284883499,
-0.00988371204584837,
0.0011559095000848174,
0.0343174934387207,
0.05309619754552841,
-0.003328523598611355,
-0.013411516323685646,
0.06566908210515976,
-0.03401627764105797,
0.0412273108959198,
0.01399309653788805,
0.01049116998910904,
0.0028960395138710737,
0.048607997596263885,
0.0067679788917303085,
-0.023284081369638443,
0.0023790125269442797,
0.006517650559544563,
0.01744415983557701,
0.0267971009016037,
-0.024727942422032356,
-0.005268959794193506,
-0.04096181318163872,
0.03691203147172928,
0.06939432770013809,
-0.002091588219627738,
-0.01800466887652874,
-0.07273708283901215,
0.021596845239400864,
0.011152164079248905,
0.009120470844209194,
-0.03272060677409172,
-0.0367932952940464,
-0.013710696250200272,
0.007290629204362631,
0.02774200774729252,
-0.022637031972408295,
0.00009255051554646343,
0.010385530069470406,
0.055347591638565063,
0.055033180862665176,
0.019409939646720886,
-0.006724516861140728,
0.04491457715630531,
-0.015878951177001,
-0.04183286428451538,
0.036990731954574585,
0.004909039940685034,
-0.020456643775105476,
-0.02642231248319149,
-0.0032935338094830513,
-0.026898035779595375,
0.003382541937753558,
-0.0026193144731223583,
-0.003180915955454111,
0.013913454487919807,
-0.02103249542415142,
-0.04517176374793053,
-0.011340792290866375,
0.09373801946640015,
0.007015470881015062,
0.020692264661192894,
-0.07172874361276627,
0.0025481567718088627,
0.045833125710487366,
0.04667549207806587,
0.05423354357481003,
-0.01072405930608511,
0.00016900729679036885,
0.02674049697816372,
-0.0049261674284935,
-0.006726880557835102,
-0.016859909519553185,
0.0228208489716053,
-0.022132862359285355,
-0.01938175968825817,
-0.0923503115773201,
0.059473223984241486,
0.030642006546258926,
-0.0029310856480151415,
-0.042895883321762085,
0.05460624024271965,
-0.01619374006986618,
-0.0047753313556313515,
-0.004931313917040825,
0.006331951357424259,
-0.03656865283846855,
0.030412469059228897,
0.007981184870004654,
0.01752040721476078,
0.04940401017665863,
0.02332867868244648,
0.02372734807431698,
0.019402211531996727,
0.03421252220869064,
0.04061039537191391,
0.0011162072187289596,
0.022478889673948288,
-0.017952360212802887,
-0.0008353216107934713,
0.004634884186089039,
-0.048984628170728683,
-0.03092457726597786,
-0.01742822490632534,
0.026325348764657974,
0.0384083054959774,
0.05001627281308174,
-0.019968902692198753,
-0.006379300262778997,
0.003184444969519973,
-0.025672949850559235,
-0.061395883560180664,
-0.09718446433544159,
0.015197749249637127,
-0.008020867593586445,
-0.04052393138408661,
0.014083056710660458,
-0.012934578582644463,
0.03810988366603851,
-0.004476391710340977,
-0.010282120667397976,
-0.017478177323937416,
0.012264872901141644,
0.015702765434980392,
-0.020065730437636375,
0.0027026061434298754,
0.010647997260093689,
0.03669818490743637,
0.002043433953076601,
0.03347112983465195,
-0.011633179150521755,
-0.06829029321670532,
0.016709253191947937,
-0.02828146331012249,
0.0016519998898729682,
0.007099148351699114,
-0.025975260883569717,
0.024122091010212898,
-0.0002268442331114784,
0.005763860419392586,
0.009660003706812859,
-0.02680625021457672,
0.05483856424689293,
0.0674830824136734,
0.006250263657420874,
-0.031223129481077194,
-0.004198568873107433,
-0.03699001669883728,
-0.0033314572647213936,
0.007431341800838709,
-0.01754821091890335,
-0.044187575578689575,
-0.0498623251914978,
0.03474505618214607,
0.03714461997151375,
-0.07673594355583191,
0.012953895144164562,
0.056810636073350906,
-0.015648197382688522,
0.043127965182065964,
0.024254804477095604,
-0.011585341766476631,
-0.01732500083744526,
0.057601988315582275,
0.07009876519441605,
0.039144884794950485,
0.023586684837937355,
0.02190430462360382,
0.06301268935203552,
0.009953523054718971,
0.016363637521862984,
0.0062077846378088,
0.06301014125347137,
0.010642103850841522,
-0.0008960754494182765,
-0.009558591060340405,
-0.02880442701280117,
0.024707529693841934,
-0.022175755351781845,
0.026734761893749237,
0.054640740156173706,
0.0033096622209995985,
0.03936369717121124,
-0.040586430579423904,
0.0022908677347004414,
0.015028840862214565,
0.020295582711696625,
0.036656077951192856,
-0.022924164310097694,
0.010017789900302887,
-0.03351091593503952,
0.025350255891680717,
-0.012870620004832745,
0.011780915781855583,
-0.04420924559235573,
-0.02320324070751667,
0.0003901355667039752,
0.004764690063893795,
0.054774314165115356,
-0.005503463558852673,
-0.0010181006509810686,
-0.005273650400340557,
-0.031244885176420212,
-0.018608536571264267,
-0.0036283559165894985,
-0.04359358921647072,
-0.03710504248738289,
-0.011814682744443417,
-0.045504264533519745,
0.06699946522712708,
-0.05146690830588341,
-0.011300846934318542,
0.039591673761606216,
-0.00387202063575387,
-0.05872488021850586,
0.017549874261021614,
-0.030706079676747322,
0.004923180676996708,
0.007979709655046463,
-0.019946448504924774,
0.08571659028530121,
-0.007832949981093407,
-0.03315846249461174,
-0.0032947163563221693,
-0.019260544329881668,
-0.058047570288181305,
-0.0357784740626812,
-0.009278915822505951,
0.007016459945589304,
-0.026329874992370605,
0.021157873794436455,
0.02650238759815693,
-0.05068357661366463,
0.0029511747416108847,
-0.045364733785390854,
-0.05170653387904167,
-0.009762431494891644,
-0.028608247637748718,
0.0285195279866457,
-0.026443205773830414,
-0.04151425510644913,
0.08421837538480759,
0.0038782916963100433,
-0.03484825789928436,
0.010120066814124584,
-0.028609514236450195,
0.006992867682129145,
-0.024762609973549843,
-0.009036759845912457,
0.0362316332757473,
0.002590901218354702,
0.027341751381754875,
0.006692735943943262,
0.03652830794453621,
0.044605035334825516,
-0.005077762063592672,
0.014071420766413212,
-0.0015004408778622746,
-0.004753235727548599,
-0.035055045038461685,
-0.01483085285872221,
-0.00886993296444416,
-0.031612712889909744,
0.026302674785256386,
-0.000037494821299333125,
0.015590347349643707,
0.0268532894551754,
-0.023770883679389954,
0.07773641496896744,
-0.002956687705591321,
-0.024025369435548782,
-0.01517276931554079,
0.023429248481988907,
-0.020033782348036766,
-0.027229320257902145,
-0.0015386800514534116,
0.017866091802716255,
0.008950241841375828,
-0.020455406978726387,
-0.007496057078242302,
0.009673208929598331,
0.06512008607387543,
-0.03497486561536789,
-0.009652790613472462,
-0.01758630760014057,
-0.011140911839902401,
-0.008141321130096912,
-0.010996505618095398,
-0.017893368378281593,
0.03543436899781227,
0.03478322550654411,
0.027882607653737068,
0.024966469034552574,
0.00478878291323781,
0.021058563143014908,
-0.0690704882144928,
-0.0017077766824513674,
-0.016840994358062744,
0.020881101489067078,
-0.002189567545428872,
-0.002462743315845728,
0.0113754253834486,
0.006950274109840393,
0.04373364895582199,
-0.025977903977036476,
-0.07069951295852661,
0.04537603631615639,
-0.03176553547382355,
-0.045243315398693085,
0.025386666879057884,
-0.05016250163316727,
0.011170115321874619,
-0.038631636649370193,
-0.062391526997089386,
0.01720283180475235,
0.04008978605270386,
-0.03566179424524307,
0.023582452908158302,
-0.00179771997500211,
-0.04454132542014122,
-0.008521527983248234,
0.017843833193182945,
-0.0029539086390286684,
-0.021619291976094246,
-0.014190216548740864,
0.0291945468634367,
-0.03763645514845848,
-0.0022406205534934998,
-0.028565675020217896,
-0.0038075176998972893,
-0.021771859377622604,
-0.006455445196479559,
0.019516590982675552,
0.0416167750954628,
0.008173318579792976,
0.030700592324137688,
0.04993032291531563,
0.06488654762506485,
0.009392364881932735,
-0.010887132957577705,
-0.053759317845106125,
0.001134134246967733,
-0.004443696700036526,
0.04335942491889,
0.02154281921684742,
0.012061922810971737,
0.03298351168632507,
-0.010035434737801552,
0.031723495572805405,
-0.03621245548129082,
0.027362100780010223,
0.05592150613665581,
0.025515535846352577,
-0.005318441893905401,
-0.08800303936004639,
-0.013821786269545555,
-0.004149836953729391,
-0.0010451655834913254,
0.048676736652851105,
0.016485469415783882,
-0.004600487183779478,
0.00929128285497427,
0.020871054381132126,
-0.05275935307145119,
-0.01884312368929386,
-0.00793426763266325,
-0.010175109840929508,
-0.0006727626314386725,
0.019287461414933205,
0.0022659539245069027,
0.027830252423882484,
0.02371702902019024,
0.03293215110898018,
0.01804867573082447,
0.020316870883107185,
-0.09969069063663483,
-0.028145156800746918,
0.04600859433412552,
0.01882505603134632,
-0.053179558366537094,
-0.016204239800572395,
-0.008759093470871449,
0.03118685819208622,
0.0016748667694628239,
-0.03751850128173828,
0.020985223352909088,
-0.04192812368273735,
0.010323555208742619,
-0.03844912350177765,
0.016476301476359367,
-0.03306376561522484,
0.027338651940226555,
0.011434896849095821,
0.022396741434931755,
-0.00047390058171004057,
-0.008125979453325272,
-0.040154796093702316,
-0.028243450447916985,
0.0052508083172142506,
0.03502688184380531,
-0.04155787453055382,
-0.03530823439359665,
-0.011713388375937939,
0.041869524866342545,
-0.004682841245085001,
-0.07212144881486893,
-0.0023696084972471,
0.02381518855690956,
0.0017672147369012237,
-0.0072168391197919846,
-0.028279976919293404,
-0.024731991812586784,
0.040654100477695465,
0.014941333793103695,
-0.034136079251766205,
-0.03621302917599678,
-0.03738431632518768,
0.047959402203559875,
0.029396673664450645,
-0.005737380590289831,
0.028635039925575256,
0.011962753720581532,
-0.029883502051234245,
0.02328779362142086,
-0.023021787405014038,
0.0219478290528059,
-0.034905098378658295,
-0.005106960888952017,
-0.04432103782892227,
0.014987576752901077,
-0.012164456769824028,
0.05905095487833023,
-0.005015464499592781,
0.05807996913790703,
-0.040356945246458054,
-0.06167945638298988,
-0.0360708087682724,
0.02336367964744568,
0.032532013952732086,
-0.061156708747148514,
0.01054234616458416,
-0.0011388869024813175,
-0.003614734625443816,
-0.005893050692975521,
-0.01685723289847374,
0.009592796675860882,
0.003987689036875963,
0.030643846839666367,
0.004716621711850166,
0.019730808213353157,
0.004663643427193165,
-0.017606783658266068,
0.041546184569597244,
0.014220028184354305,
0.043417613953351974,
0.024551689624786377,
0.011738274246454239,
0.0066931843757629395,
-0.058737363666296005,
-0.040173664689064026,
0.02934672124683857,
0.0007320816512219608,
-0.0007312318193726242,
-0.011964607052505016,
0.024637185037136078,
0.009896223433315754,
0.027140121906995773,
-0.035060711205005646,
-0.036437757313251495,
0.02174987830221653,
-0.013617117889225483,
0.03389514610171318,
0.0005512045463547111,
-0.027295777574181557,
-0.007443868089467287,
-0.0639365017414093,
0.01568138413131237,
0.03934217244386673,
-0.05078786984086037,
-0.004483474418520927,
0.04362231120467186,
-0.005795272067189217,
0.05633791163563728,
-0.003468054812401533,
-0.0454217828810215,
0.005458534695208073,
-0.005702340975403786,
-0.028766948729753494,
-0.019108373671770096,
0.03495165705680847,
-0.01387910544872284,
-0.007620886899530888,
-0.03707893565297127,
-0.01089768297970295,
0.07065675407648087,
0.013028796762228012,
0.009952270425856113,
0.038418013602495193,
-0.008798155002295971,
-0.0025685203727334738,
-0.004610905889421701,
0.003245412837713957,
-0.009371317923069,
0.09105319529771805,
0.01576313003897667,
0.009656384587287903,
-0.0021329999435693026,
-0.04646012559533119,
0.057110950350761414,
-0.015806179493665695,
-0.026729756966233253,
0.02155236154794693,
0.0687074214220047,
-0.05048837140202522,
0.03995669633150101,
-0.01755329966545105,
-0.027182359248399734,
0.006781351286917925,
0.03893377259373665,
0.06195072457194328,
-0.004399341531097889,
-0.005204011686146259,
-0.008657017722725868,
-0.02516431175172329,
-0.03805287554860115,
-0.001879109418950975,
0.021921226754784584,
-0.034906353801488876,
0.057754937559366226,
0.044873856008052826,
-0.007895822636783123,
0.009192438796162605,
-0.05173880606889725,
-0.018812701106071472,
0.01611284725368023,
0.01068294420838356,
0.0791606530547142,
0.014345257543027401,
-0.01403756532818079,
0.08171791583299637,
0.018851090222597122,
-0.010442453436553478,
0.012242782860994339,
0.022458858788013458,
0.03621741756796837,
-0.03907158598303795,
-0.02356143482029438,
-0.049312133342027664,
0.03088269755244255,
-0.058320339769124985,
0.02295866422355175,
-0.024503188207745552,
0.01433709729462862,
0.02537279576063156,
0.015576506033539772,
-0.03281794488430023,
-0.051949601620435715,
-0.0017888356233015656,
-0.03571945056319237,
-0.003541518934071064,
-0.00855328794568777,
-0.0709003284573555,
0.04260215163230896,
0.0020213669631630182,
0.01732114516198635,
-0.006068378686904907,
0.03475456312298775,
0.019087471067905426,
-0.047529637813568115,
-0.025042708963155746,
-0.025587569922208786,
-0.03805837035179138,
0.018437489867210388,
-0.02610977739095688,
-0.02877153269946575,
0.024487413465976715,
-0.002127210609614849,
0.013274351134896278,
0.010524692945182323,
-0.00818451214581728,
-0.004848003853112459,
0.0799650177359581,
0.010966295376420021,
0.04242860525846481,
0.015733705833554268,
-0.013120496645569801,
0.11746735870838165,
0.044125888496637344,
0.014338945969939232,
-0.047242023050785065,
0.0011863033287227154,
-0.012022712267935276,
-0.006477858871221542,
-0.014630408957600594,
-0.022893665358424187,
-0.006008312571793795,
-0.0019000741885975003,
0.03790699690580368,
0.0028818214777857065,
0.010714216157793999,
0.012263267301023006,
0.020035112276673317,
-0.038145069032907486,
-0.016996990889310837,
0.04537278786301613,
0.012214242480695248,
-0.022634590044617653,
-0.010258438065648079,
-0.05326204374432564,
0.004499946255236864,
0.008383824490010738,
-0.03437133878469467,
-0.0018611268606036901,
-0.019180648028850555,
0.02520098350942135,
0.005174258258193731,
-0.02220904640853405,
0.0016046077944338322,
-0.022230403497815132,
0.013704290613532066,
0.011085765436291695,
-0.029944434762001038,
0.028585240244865417,
0.006153522990643978,
-0.00871420931071043,
0.029238833114504814,
0.03917577490210533,
-0.01597868651151657,
0.031116753816604614,
0.022207818925380707,
-0.0833296850323677,
0.003110298654064536,
-0.004134014714509249,
0.006330719217658043,
0.0008976447861641645,
0.006090092938393354,
-0.00962410494685173,
0.002740807831287384,
-0.003305546473711729,
-0.02626444585621357,
-0.009091953746974468,
-0.022520368918776512,
0.017132798209786415,
-0.017897140234708786,
-0.020566150546073914,
-0.0029641680885106325,
0.005594415124505758,
0.009176230058073997,
0.03626395761966705,
-0.037955593317747116,
0.01786685921251774,
0.03374094143509865,
0.008641599677503109,
0.013926368206739426,
-0.026341520249843597,
-0.04239221662282944,
0.0006726155406795442,
-0.0028072705026715994,
-0.029871750622987747,
-0.004168196581304073,
-0.01064227893948555,
0.005457544699311256,
0.016547074541449547,
-0.007441017311066389,
-0.002468496561050415,
-0.02249680832028389,
-0.08971042931079865,
0.07533463090658188,
-0.004016352351754904,
0.015998205170035362,
-0.045475978404283524,
0.015309491194784641,
0.022207945585250854,
0.026522312313318253,
0.006845453288406134,
0.03422677516937256,
-0.016349148005247116,
0.03074171207845211,
0.03474819287657738,
-0.01181035302579403,
-0.05354555696249008,
0.042444292455911636,
-0.043049830943346024,
-0.021160786971449852,
-0.006052222102880478,
0.02564406208693981,
0.03367166593670845,
-0.03214944899082184,
-0.014929041266441345,
0.00984652154147625,
-0.002431407803669572,
0.014509276486933231,
0.008975675329566002,
-0.033350758254528046,
-0.012445512227714062,
0.008689920417964458,
-0.002010166645050049,
-0.0442870557308197,
0.007140820845961571,
-0.029049215838313103,
-0.02432798035442829,
-0.0007709249039180577,
0.04770253598690033,
0.009158013388514519,
-0.004479299299418926,
-0.04382219910621643,
0.018719347193837166,
-0.03234225884079933,
-0.03166170045733452,
-0.03793628513813019,
0.006492485757917166,
0.021407751366496086,
0.003228358458727598,
-0.03373359143733978,
0.025967394933104515,
0.0026261236052960157,
0.004492797423154116,
0.005731792654842138,
0.026621753349900246,
0.011569651775062084,
-0.016322579234838486,
-0.013583212159574032,
-0.012853299267590046,
0.0510302297770977,
-0.022705916315317154,
-0.008804814890027046,
0.037830520421266556,
-0.021669901907444,
-0.032171133905649185,
0.0229177363216877,
-0.0039010951295495033,
0.028051873669028282,
0.029185069724917412,
-0.004029725678265095,
-0.045901816338300705,
0.06794325262308121,
-0.050029754638671875,
-0.00875887181609869,
-0.036858342587947845,
-0.021802667528390884,
-0.02537849359214306,
-0.025980530306696892,
-0.015701884403824806,
-0.012606640346348286,
-0.03763942793011665,
0.0430932343006134,
0.0385298877954483,
-0.0034676864743232727,
-0.03065023384988308,
0.03308384120464325,
0.008628001436591148,
0.035439569503068924,
0.01680063270032406,
0.030772387981414795,
0.03656536340713501,
0.040977708995342255,
-0.0297744981944561,
0.019880050793290138,
-0.011037202551960945,
-0.0018163849599659443,
-0.08135490119457245,
0.0017638367135077715,
-0.035523686558008194,
-0.010704566724598408,
0.023846512660384178,
-0.03326023742556572,
0.015578013844788074,
-0.03164597973227501,
-0.030513638630509377,
0.00027786503778770566,
-0.03198827803134918,
-0.033068109303712845,
-0.07649292796850204,
0.00941470731049776,
0.0027459801640361547,
0.03017500415444374,
0.027249135076999664,
-0.01192630734294653,
0.022095192223787308,
0.023852162063121796,
-0.029857058078050613,
0.017963329330086708,
0.011511318385601044,
0.013105317018926144,
0.0068486537784338,
-0.038716331124305725,
0.024309666827321053,
-0.02416716143488884,
-0.06376978009939194,
0.04655741527676582,
-0.03303530067205429,
0.02020253613591194,
-0.0011012188624590635,
0.03215530142188072,
0.0015557908918708563,
-0.010287691839039326,
0.02240116149187088,
0.014283726923167706,
-0.02169898711144924,
0.0003284006379544735,
0.035722676664590836,
0.009684600867331028,
-0.012972068041563034,
0.028388196602463722,
0.006835244130343199,
-0.014324897900223732,
-0.04989368095993996,
0.03452986478805542,
-0.03171180188655853,
-0.03607131540775299,
0.005960421171039343,
0.002355757402256131,
0.056459203362464905,
-0.015937987715005875,
0.018398109823465347,
-0.029002832248806953,
-0.021891003474593163,
0.040457986295223236,
-0.007863047532737255,
-0.007683679927140474,
0.044754527509212494,
0.02644256502389908,
0.01985129341483116,
-0.016049806028604507,
0.030598923563957214,
-0.02371068112552166,
-0.07887869328260422,
0.009661320596933365,
-0.01745341159403324,
-0.019537271931767464,
-0.016282623633742332,
-0.015780555084347725,
-0.005606686696410179,
0.04236062616109848,
0.0408848375082016,
-0.010624288581311703,
0.01886470429599285,
-0.018967172130942345,
-0.007798982784152031,
-0.05905270576477051,
0.0486472025513649,
0.012419264763593674,
-0.03335222601890564,
-0.04177962988615036,
-0.02038959413766861,
-0.027241088449954987,
0.014553839340806007,
0.07972654700279236,
-0.010088049806654453,
-0.019360419362783432,
-0.004926699213683605,
0.04273127019405365,
0.019965512678027153,
-0.033840131014585495,
0.050963565707206726,
-0.04281897842884064,
-0.055677447468042374,
0.011642970144748688,
-0.026307158172130585,
-0.030278507620096207,
0.019200051203370094,
0.009551563300192356,
-0.015013136900961399,
-0.02804497443139553,
-0.024938691407442093,
0.005452100653201342,
0.034487415105104446,
0.028593821451067924,
0.009588145650923252,
0.055920857936143875,
-0.025464650243520737,
0.04189939424395561,
0.0035356436856091022,
0.020024096593260765,
-0.053559742867946625,
0.034540798515081406,
-0.018806910142302513,
0.029054339975118637,
-0.010170499794185162,
-0.014072395861148834,
0.021632475778460503,
-0.029806815087795258,
0.0028117394540458918,
0.021586479619145393,
-0.028255034238100052,
0.000532365869730711,
0.043007053434848785,
0.05934881418943405,
0.04697548598051071,
-0.0020089824683964252,
-0.006668278016149998,
-0.022041279822587967,
0.01698153279721737,
0.0013921951176598668,
0.048472922295331955,
0.04316384345293045,
-0.0018312075408175588,
-0.01131156925112009,
0.031864140182733536,
-0.0326656848192215,
0.03529761731624603,
0.013010766357183456,
0.043682657182216644,
-0.024974610656499863,
-0.06456892192363739,
0.030866988003253937,
0.015582699328660965,
0.018207723274827003,
0.041694652289152145,
-0.0034138918854296207,
0.03761778771877289,
-0.017560699954628944,
0.008591028861701488,
-0.0638439878821373,
-0.026555249467492104,
-0.005558602511882782,
-0.049191392958164215,
-0.00937043596059084,
0.043085191398859024,
0.022224485874176025,
0.003918394912034273,
0.026502098888158798,
-0.016887672245502472,
0.023018671199679375,
0.009340566582977772,
0.06165418401360512,
-0.024037698283791542,
0.02722383849322796,
-0.013999983668327332,
0.018110524863004684,
-0.017975561320781708,
-0.009808083064854145,
0.014735113829374313,
0.056165557354688644,
0.04405847191810608,
0.02605077251791954,
-0.044213153421878815,
0.014149729162454605,
0.05090591683983803,
-0.05401063710451126,
-0.036655839532613754,
-0.018886668607592583,
0.012920280918478966,
0.01072382740676403,
-0.0026156743988394737
] |
<p>It is usually said that existence of discrete spacetime violates Lorentz symmetry. What quantity is used to quantify such violation? I mean could someone points a reference for a derivation that shows such analysis.</p>
<p>My other question is that: if, and this is a big fat if, OPERA result was true (and I believe it is not) would that prove that spacetime is discrete?
(this is like the inverse to the 1st part of this post, if space-time is discrete then Lorentz symmetry is violated, what if Lorentz symmetry is violated, does that imply space-time is discrete? or not necessarily?)</p> | 1,566 | [
-0.029971439391374588,
-0.03788851201534271,
-0.0073812901973724365,
-0.05353164300322533,
0.059454891830682755,
0.03061552345752716,
-0.031189730390906334,
-0.01977909356355667,
-0.007153569720685482,
-0.010670769028365612,
0.042961180210113525,
0.00613818597048521,
0.05567573010921478,
-0.004038156941533089,
0.0215409304946661,
0.01965484395623207,
-0.007474460639059544,
-0.0043404786847531796,
-0.019217360764741898,
-0.054620515555143356,
-0.0011576471151784062,
0.030119944363832474,
0.021586785092949867,
-0.03437618538737297,
-0.038951098918914795,
0.02877195179462433,
0.04552575945854187,
0.03390858322381973,
0.006336888298392296,
0.06958940625190735,
-0.029969433322548866,
-0.04880070313811302,
0.020716385915875435,
0.04562489688396454,
-0.001033076667226851,
0.0016602086834609509,
-0.0458495207130909,
-0.03986452892422676,
0.00031524928635917604,
-0.0024111014790832996,
-0.027828726917505264,
-0.030848229303956032,
-0.015565927140414715,
0.042879197746515274,
-0.017511526122689247,
0.04002631828188896,
0.010211228393018246,
-0.004598052706569433,
0.07929494976997375,
-0.05389184132218361,
0.0883975476026535,
-0.011271360330283642,
0.05142247676849365,
-0.00014220201410353184,
-0.015450329519808292,
-0.010017270222306252,
0.10945863276720047,
0.04853011295199394,
-0.006981968879699707,
-0.0492573156952858,
-0.04822876304388046,
-0.04846915602684021,
0.042761966586112976,
-0.03208126127719879,
-0.007857084274291992,
0.030863670632243156,
-0.026472825556993484,
0.005701177287846804,
0.0015921533340588212,
-0.0010890631237998605,
-0.010327443480491638,
-0.010044149123132229,
0.030443252995610237,
-0.019316617399454117,
0.016134191304445267,
-0.003382846713066101,
0.04641149193048477,
-0.035518910735845566,
0.06177090108394623,
0.012460241094231606,
-0.006265630014240742,
0.002964541781693697,
0.006947043817490339,
0.04568595066666603,
-0.004677010700106621,
-0.04189647361636162,
0.04494108632206917,
0.009315350092947483,
0.006568045821040869,
0.009538907557725906,
-0.005304211750626564,
-0.021762939170002937,
0.038705334067344666,
-0.029680946841835976,
-0.040311239659786224,
0.03899393975734711,
-0.007847283966839314,
0.05346906930208206,
-0.0073224627412855625,
-0.02351514808833599,
-0.015080190263688564,
-0.04554305970668793,
0.030230935662984848,
0.09918687492609024,
-0.014473293907940388,
0.006337468978017569,
-0.0348539873957634,
0.04619688540697098,
-0.020283197984099388,
0.009574996307492256,
-0.02589690126478672,
0.009972315281629562,
-0.004249355755746365,
-0.013173114508390427,
0.015378808602690697,
-0.0014924454735592008,
-0.015217415988445282,
-0.007316499948501587,
0.05142897740006447,
0.09038504213094711,
0.05285079404711723,
-0.03375899791717529,
0.010709569789469242,
-0.01502298004925251,
-0.08349666744470596,
-0.004353058524429798,
0.02609974704682827,
-0.007984325289726257,
-0.02851499803364277,
0.03630813956260681,
-0.032019127160310745,
-0.029681261628866196,
0.03345539793372154,
-0.01730608567595482,
0.0517805814743042,
-0.026701446622610092,
-0.09243012219667435,
-0.05452536419034004,
0.017161138355731964,
0.020737437531352043,
-0.03379509225487709,
-0.061719994992017746,
0.01711576245725155,
-0.03271316736936569,
0.09152399003505707,
-0.020336110144853592,
0.052221719175577164,
0.021389752626419067,
0.031033026054501534,
0.01038049254566431,
-0.039559245109558105,
0.018731333315372467,
0.033190589398145676,
-0.032271116971969604,
-0.0021510045044124126,
-0.03426264226436615,
-0.013044076971709728,
0.031032215803861618,
-0.00031341562862508,
-0.04152629151940346,
0.05267324671149254,
0.002743709832429886,
-0.024056753143668175,
0.0534370057284832,
0.002333811717107892,
-0.017533978447318077,
0.059678807854652405,
-0.0020389161072671413,
-0.000979534350335598,
0.020011527463793755,
0.0046117533929646015,
0.02339092083275318,
0.0262138769030571,
0.034543827176094055,
0.017373260110616684,
-0.04239922761917114,
-0.02402176707983017,
-0.014951374381780624,
0.005141518544405699,
-0.009835818782448769,
-0.03957004472613335,
-0.022883377969264984,
-0.013960901647806168,
-0.004181602504104376,
-0.03632483631372452,
0.027423806488513947,
-0.0068778605200350285,
0.019153868779540062,
0.003810723079368472,
-0.029296088963747025,
0.01404820941388607,
-0.08913210779428482,
-0.006637689657509327,
0.018284829333424568,
-0.028304196894168854,
0.012571487575769424,
0.00833156704902649,
0.005610637366771698,
-0.06494469940662384,
-0.027635568752884865,
-0.006858162581920624,
0.028720328584313393,
-0.007682637311518192,
-0.017816275358200073,
0.0375213623046875,
0.04828590527176857,
0.05592423304915428,
0.012574045918881893,
-0.004851462785154581,
0.019430171698331833,
-0.012964834459125996,
0.004253159277141094,
-0.01154369581490755,
0.023416195064783096,
-0.03354712948203087,
-0.01822070963680744,
0.005581617821007967,
-0.017749525606632233,
-0.03872601315379143,
0.04609321057796478,
-0.016542868688702583,
0.05868348479270935,
0.05418096482753754,
0.0210234597325325,
0.0118943490087986,
0.0212808046489954,
0.00745004415512085,
-0.012041257694363594,
-0.012150801718235016,
-0.03822515904903412,
-0.03514961898326874,
0.008012713864445686,
0.08570358902215958,
0.04152793064713478,
-0.023076722398400307,
0.024235401302576065,
-0.0019995146431028843,
0.060810431838035583,
0.019024977460503578,
0.013406017795205116,
-0.05951850861310959,
-0.041473500430583954,
0.008031916804611683,
-0.01369380485266447,
0.04835832118988037,
0.013791115954518318,
0.038092855364084244,
0.004456053022295237,
0.009481645189225674,
-0.0046793934889137745,
-0.023133710026741028,
0.033063072711229324,
-0.0190963726490736,
0.004528076853603125,
-0.021651145070791245,
-0.03383265808224678,
0.02181226760149002,
-0.00781263317912817,
0.028879031538963318,
0.025723710656166077,
-0.013188679702579975,
0.010325792245566845,
-0.023480167612433434,
-0.015260662883520126,
0.008234537206590176,
0.011093216948211193,
-0.0454925112426281,
-0.02348225563764572,
0.004688485991209745,
-0.02895263582468033,
-0.01007133349776268,
-0.0027735091280192137,
0.0007780917221680284,
-0.013138661161065102,
-0.02196742594242096,
0.04542676359415054,
-0.003673197701573372,
0.023412995040416718,
-0.038071583956480026,
0.006556470412760973,
-0.003016343107447028,
-0.012961864471435547,
-0.002588504459708929,
0.026306120678782463,
-0.039943136274814606,
0.03657282888889313,
-0.021453605964779854,
-0.030911622568964958,
0.0144478315487504,
-0.012124786153435707,
0.035509418696165085,
0.026310795918107033,
-0.008054996840655804,
-0.057341303676366806,
-0.01994949020445347,
0.0052709695883095264,
0.0019950876012444496,
-0.04472890496253967,
0.014977363869547844,
0.05524195358157158,
0.0023572761565446854,
-0.020945139229297638,
-0.006090749986469746,
-0.021684089675545692,
-0.03360506147146225,
-0.031224319711327553,
-0.0033214588183909655,
0.02806761860847473,
-0.05902562662959099,
0.025038868188858032,
0.010685378685593605,
-0.03373922407627106,
0.01693466491997242,
-0.046992525458335876,
-0.040928542613983154,
0.012800763361155987,
-0.006608809344470501,
0.041232023388147354,
-0.02327783964574337,
-0.06026129052042961,
0.07309144735336304,
0.04834409058094025,
-0.0314590260386467,
-0.01207362487912178,
0.007312259171158075,
0.015614056028425694,
-0.010644529014825821,
-0.005542949307709932,
0.01326641533523798,
0.013096687383949757,
0.03695840761065483,
0.06410931050777435,
0.01991856098175049,
-0.021807346493005753,
0.02288649044930935,
-0.0477278046309948,
-0.00704490439966321,
0.010294517502188683,
0.018326779827475548,
0.04023759812116623,
0.06179487705230713,
-0.0437726192176342,
0.007098884787410498,
-0.010620705783367157,
0.029786502942442894,
0.0017635629046708345,
-0.06195658817887306,
0.02536192536354065,
0.007148140575736761,
0.00471665570512414,
0.008503129705786705,
0.03383541479706764,
0.019551649689674377,
-0.023495003581047058,
0.0037022694014012814,
0.003651394508779049,
0.024465210735797882,
-0.03580709919333458,
-0.005033858586102724,
0.04594334214925766,
0.046249788254499435,
-0.0482119545340538,
-0.002430856926366687,
-0.01529052946716547,
0.016261598095297813,
0.02122892625629902,
-0.017452454194426537,
-0.019620198756456375,
0.03803100436925888,
0.04313226416707039,
0.051693178713321686,
-0.013073472306132317,
-0.036834705621004105,
-0.008752352558076382,
-0.049401409924030304,
-0.007147184573113918,
-0.008423457853496075,
0.04635521396994591,
0.005618618801236153,
0.048052411526441574,
0.012663669884204865,
0.0027699077036231756,
0.00007243258733069524,
-0.01645500771701336,
-0.0758076012134552,
-0.0009886047337204218,
-0.04609965160489082,
-0.022334935143589973,
-0.006853098049759865,
-0.003900825046002865,
-0.015827668830752373,
-0.03719549998641014,
-0.011884883977472782,
-0.01695016399025917,
-0.0061045363545417786,
-0.0736270323395729,
-0.005205424502491951,
-0.029686816036701202,
-0.013144262135028839,
-0.00940551795065403,
0.011792159639298916,
0.04304751753807068,
-0.020523246377706528,
-0.0042924280278384686,
0.00798084121197462,
-0.03008541651070118,
-0.026271017268300056,
-0.029660910367965698,
0.011753645725548267,
0.0044450294226408005,
0.01727692037820816,
0.0190061554312706,
0.0014737780438736081,
-0.011693446896970272,
-0.0001071746664820239,
0.0239570252597332,
0.08418187499046326,
-0.004694636445492506,
0.002855813829228282,
-0.06239417567849159,
-0.042237523943185806,
-0.03236771374940872,
-0.015270350500941277,
0.05849909409880638,
-0.007030079141259193,
0.02807985059916973,
0.048198264092206955,
0.026203960180282593,
-0.043122973293066025,
0.02987651526927948,
0.04530855640769005,
-0.013441236689686775,
-0.026739761233329773,
-0.03189551830291748,
-0.042274221777915955,
-0.03747335076332092,
-0.0044064028188586235,
0.014131373725831509,
0.0032215076498687267,
0.013359715230762959,
0.03653925657272339,
0.01980595476925373,
-0.022234881296753883,
-0.025400154292583466,
-0.007080938201397657,
0.013081740587949753,
0.005534420721232891,
0.005388210993260145,
0.016071531921625137,
-0.003456014208495617,
0.05861110985279083,
0.0498378686606884,
0.026180503889918327,
-0.01681048609316349,
-0.0864105224609375,
0.01810539700090885,
0.021259503439068794,
0.012608016841113567,
0.017855204641819,
-0.0292877908796072,
-0.05219880864024162,
0.0005374999018386006,
0.0264884140342474,
-0.01440364494919777,
0.018349744379520416,
0.00186371139716357,
0.006230099126696587,
-0.027163639664649963,
-0.006730090826749802,
0.011331550776958466,
0.019670134410262108,
0.029148409143090248,
0.016321305185556412,
-0.04501199349761009,
0.0044427672401070595,
-0.00942701194435358,
0.035327520221471786,
0.039439428597688675,
0.014675677753984928,
0.007332226727157831,
0.026315726339817047,
-0.007042051758617163,
0.03289761766791344,
-0.030685115605592728,
-0.08212722092866898,
0.0042447373270988464,
0.03976171463727951,
-0.003371883649379015,
0.04366841912269592,
-0.057701703161001205,
-0.013592620380222797,
0.008145577274262905,
0.004981192760169506,
-0.0011612894013524055,
0.02958350069820881,
-0.05259190499782562,
0.030067479237914085,
0.002540644956752658,
0.0010091783478856087,
0.020245814695954323,
-0.003048751736059785,
-0.008318555541336536,
0.0028378900606185198,
0.0007486232207156718,
0.03946734592318535,
-0.021830491721630096,
0.0029710361268371344,
-0.04381479695439339,
-0.014835604466497898,
-0.040405988693237305,
0.055232346057891846,
-0.003392694517970085,
-0.011928290128707886,
0.02756180427968502,
-0.020939184352755547,
-0.009225870482623577,
0.038299236446619034,
0.022511957213282585,
0.008551464416086674,
-0.03322451934218407,
0.019372906535863876,
-0.009167267940938473,
-0.010240933857858181,
0.05166240036487579,
0.022653914988040924,
-0.02792217768728733,
0.021365903317928314,
0.009622203186154366,
0.035870540887117386,
-0.02670631930232048,
-0.01954076997935772,
0.028346212580800056,
-0.012839863076806068,
0.020685680210590363,
-0.035859595984220505,
-0.025772206485271454,
0.00013688710168935359,
-0.06036146730184555,
-0.01741013675928116,
-0.002716696821153164,
-0.012099875137209892,
0.052289001643657684,
-0.03040924482047558,
-0.004698113538324833,
0.008373084478080273,
0.012099266052246094,
-0.09078676998615265,
-0.052715003490448,
0.046301648020744324,
-0.007213314529508352,
-0.03278080001473427,
-0.020852727815508842,
0.00392128387466073,
-0.06520577520132065,
-0.046225372701883316,
0.04132800176739693,
0.05142269283533096,
-0.03194049745798111,
-0.02929290384054184,
-0.023127824068069458,
-0.017430365085601807,
0.04022334888577461,
-0.026788612827658653,
-0.02739592455327511,
-0.02689155749976635,
0.015003034844994545,
0.001334533328190446,
0.018348652869462967,
0.06541887670755386,
-0.019603503867983818,
-0.010529295541346073,
-0.015522774308919907,
-0.005575786344707012,
-0.013686037622392178,
-0.02581547386944294,
-0.0069754840806126595,
0.015786992385983467,
-0.028997691348195076,
0.02036409080028534,
-0.042545586824417114,
0.027776304632425308,
0.011908985674381256,
0.025379721075296402,
-0.017333215102553368,
0.0041004568338394165,
-0.04126431420445442,
-0.015915051102638245,
0.03174663335084915,
0.01730109192430973,
0.01746106706559658,
0.0014727984089404345,
0.04002625495195389,
0.009091348387300968,
-0.015242119319736958,
0.009805073030292988,
-0.02635522000491619,
-0.013655018992722034,
-0.0090683838352561,
0.0004019562911707908,
0.022505704313516617,
0.013012303970754147,
-0.06346896290779114,
-0.02370956540107727,
-0.028210317716002464,
0.03282441198825836,
0.041031647473573685,
0.013109234161674976,
0.04839072376489639,
0.05831479653716087,
-0.0011356512550264597,
-0.01681804284453392,
0.019308509305119514,
0.006958617363125086,
0.04274022579193115,
0.020296446979045868,
0.02607651613652706,
-0.020982522517442703,
-0.009504913352429867,
0.037336770445108414,
0.026808740571141243,
-0.019499942660331726,
0.023403964936733246,
0.04756557196378708,
-0.00027451218920759857,
0.034343160688877106,
-0.013043861836194992,
-0.028191206976771355,
0.04644092917442322,
-0.01663612201809883,
0.025353487581014633,
0.005968057084828615,
0.024540264159440994,
0.0413852259516716,
0.02010442316532135,
0.020218288525938988,
-0.012541239149868488,
-0.03147318586707115,
-0.06598583608865738,
0.002098497934639454,
0.002015727572143078,
0.03173336014151573,
0.014134279452264309,
-0.007307105232030153,
0.040920231491327286,
-0.004759112372994423,
0.0170558150857687,
0.03978091850876808,
-0.04328272119164467,
-0.029821783304214478,
-0.03690391406416893,
-0.034676648676395416,
0.03671589866280556,
0.02648688107728958,
-0.022558577358722687,
-0.01948551833629608,
-0.047628577798604965,
0.05369074270129204,
0.025906814262270927,
0.03852491080760956,
-0.03984834998846054,
0.05101947486400604,
-0.029783843085169792,
0.02722538262605667,
-0.009155131876468658,
0.017081953585147858,
0.09020080417394638,
0.06043701991438866,
-0.028279047459363937,
-0.063731350004673,
0.026669690385460854,
0.0030146646313369274,
0.027921371161937714,
-0.059442512691020966,
0.06236324459314346,
0.001988282660022378,
0.012344589456915855,
0.023421118035912514,
0.027009285986423492,
0.007672873325645924,
-0.05397973209619522,
0.025218892842531204,
-0.045719295740127563,
-0.045242492109537125,
0.02291642688214779,
0.04327496513724327,
0.03064366802573204,
0.008689431473612785,
-0.03188880905508995,
0.025217147544026375,
-0.01988118700683117,
-0.008661258965730667,
-0.03362055495381355,
-0.02383996732532978,
0.015545405447483063,
0.027451390400528908,
-0.02949756756424904,
-0.0068665253929793835,
0.03005116619169712,
-0.024977905675768852,
-0.08308308571577072,
-0.011648698709905148,
-0.008364468812942505,
0.007660087198019028,
0.029457082971930504,
0.0472114160656929,
-0.014957711100578308,
0.019479872658848763,
0.0001622431300347671,
0.023283688351511955,
-0.055223722010850906,
-0.005629191640764475,
-0.029950357973575592,
0.048086978495121,
-0.01667497493326664,
0.022073183208703995,
0.007254520431160927,
0.008640074171125889,
-0.027971133589744568,
-0.08697707206010818,
-0.04578838869929314,
-0.03183429315686226,
0.027179021388292313,
0.014518101699650288,
-0.023077988997101784,
-0.019887588918209076,
0.022480379790067673,
-0.015095187351107597,
0.0026231310330331326,
-0.0274449922144413,
-0.01751401275396347,
-0.005161887966096401,
0.0139851626008749,
0.029376763850450516,
-0.005717885214835405,
-0.03232628479599953,
-0.04627937451004982,
-0.01095450110733509,
-0.025337375700473785,
-0.000712625274900347,
0.023658353835344315,
0.020041460171341896,
0.023653607815504074,
0.03629286587238312,
0.005892869085073471,
0.029401831328868866,
-0.04702587425708771,
0.0034150502178817987,
-0.05143053084611893,
-0.033892594277858734,
-0.02165304310619831,
0.024798361584544182,
0.030204199254512787,
0.04041994735598564,
-0.032974500209093094,
0.03634917363524437,
0.0072737098671495914,
0.008205882273614407,
0.01416116300970316,
-0.009207356721162796,
0.02720465138554573,
0.010844778269529343,
-0.0010830532992258668,
-0.0010060531785711646,
-0.04310696944594383,
0.021144503727555275,
0.029514238238334656,
0.0004244391748216003,
0.03253423795104027,
0.038601864129304886,
-0.022359512746334076,
0.00021954771364107728,
0.02168613113462925,
-0.039759937673807144,
0.016879739239811897,
0.014743615873157978,
0.006343884859234095,
-0.044985927641391754,
-0.04651767387986183,
-0.01501243095844984,
0.007240024860948324,
0.013741981238126755,
-0.004464392084628344,
-0.014226227067410946,
-0.021983014419674873,
-0.03742826357483864,
-0.012532636523246765,
-0.03012283332645893,
-0.02550480142235756,
-0.02768542617559433,
0.016412194818258286,
-0.005193623714148998,
-0.02575477957725525,
-0.0003733047051355243,
0.006620687432587147,
0.014172903262078762,
-0.023122400045394897,
0.02956956811249256,
0.021304816007614136,
-0.011164877563714981,
-0.024091701954603195,
0.06206049770116806,
0.032331958413124084,
0.04132726043462753,
-0.01583450473845005,
-0.03739513084292412,
0.04584489390254021,
-0.05101706460118294,
-0.029557928442955017,
0.06384547799825668,
-0.05758105590939522,
0.004287098068743944,
0.015950137749314308,
-0.009213787503540516,
-0.02537364885210991,
0.052754491567611694,
-0.025281932204961777,
-0.002009080955758691,
-0.002469512866809964,
-0.035684939473867416,
0.0034356971736997366,
-0.026052476838231087,
0.045267678797245026,
0.00054427474969998,
-0.02135395258665085,
0.014780516736209393,
0.012521539814770222,
0.0028985070530325174,
0.00702392403036356,
0.009499384090304375,
-0.017617614939808846,
0.01248667947947979,
0.04119554162025452,
0.017117450013756752,
-0.018970487639307976,
0.053187295794487,
-0.004646555054932833,
-0.011571326293051243,
0.022533610463142395,
-0.00903812050819397,
-0.10266406834125519,
0.028950277715921402,
0.026856811717152596,
0.033066462725400925,
0.03908766806125641,
-0.04435425251722336,
0.011987755075097084,
0.0270284041762352,
-0.04421156272292137,
0.027713768184185028,
-0.03457389399409294,
-0.037385184317827225,
-0.0372270904481411,
-0.03641894832253456,
-0.02870987541973591,
0.05420082062482834,
0.03825637698173523,
0.04823730140924454,
0.030484052374958992,
0.01142002921551466,
-0.026353679597377777,
-0.04575124755501747,
-0.005450971890240908,
0.015097768977284431,
-0.022747047245502472,
-0.02888304367661476,
0.05998304486274719,
0.012092151679098606,
-0.030563879758119583,
0.041208308190107346,
0.006629144307225943,
-0.016597336158156395,
0.010690043680369854,
0.03550314903259277,
0.0016867663944140077,
0.03985479101538658,
0.023602478206157684,
0.024323755875229836,
0.0017903584521263838,
0.047785013914108276,
-0.0007842950290068984,
0.034734997898340225,
-0.010333286598324776,
-0.007713804021477699,
-0.00018826003361027688,
-0.05116792768239975,
-0.011321715079247952,
0.023837581276893616,
-0.012405693531036377,
0.006800564471632242,
-0.014625894837081432,
-0.01277963351458311,
0.01833389326930046,
-0.015200966037809849,
0.0019367651548236609,
-0.027872053906321526,
-0.018284959718585014,
0.04746905341744423,
-0.0014045553980395198,
-0.006034513004124165,
-0.014358154498040676,
0.0018336436478421092,
-0.03272351250052452,
0.028107641264796257,
0.011922487989068031,
0.005312989000231028,
-0.06821665167808533,
-0.0007563853869214654,
0.02586638182401657,
0.006685427390038967,
0.024962663650512695,
-0.023503577336668968,
0.005469030234962702,
0.044879019260406494,
0.023837603628635406,
-0.01708444580435753,
0.004946547094732523,
-0.02674778364598751,
-0.002115030074492097,
-0.07304465770721436,
0.02144281379878521,
0.013664977625012398,
0.019660213962197304,
-0.04219253733754158,
0.01882866770029068,
-0.0213871281594038,
0.015207124873995781,
0.040009986609220505,
0.020416168496012688,
-0.05183997005224228,
0.028368383646011353,
-0.0035680164583027363,
0.012258538976311684,
-0.04104457423090935,
-0.03398241475224495,
-0.032553885132074356,
-0.02776402235031128,
-0.021488429978489876,
-0.010581827722489834,
-0.03973455727100372,
-0.01188464742153883,
-0.000551302102394402,
0.0006742330733686686,
0.014038937166333199,
-0.002488279715180397,
-0.05220437049865723,
0.06635964661836624,
-0.0176125206053257,
0.010809618979692459,
0.062056124210357666,
0.00824002455919981,
0.021069033071398735,
0.036111824214458466,
-0.013085794635117054,
-0.01020797248929739,
0.009913627989590168,
-0.011310289613902569,
0.008360396139323711,
-0.013566250912845135,
0.027732349932193756,
0.02005774714052677,
0.007655237335711718,
0.004049546550959349,
0.07082900404930115,
-0.01581253856420517,
-0.01974424161016941,
0.031964607536792755,
0.012216438539326191,
0.03817415609955788,
-0.034150976687669754,
0.023506030440330505,
0.049823254346847534,
-0.0004352835239842534,
-0.006459789350628853,
0.049207575619220734,
0.011865216307342052,
0.003624167526140809,
0.0018496026750653982,
0.030694982036948204,
-0.019353369250893593,
0.013148467987775803,
0.039481427520513535,
0.03742239251732826,
-0.024091238155961037,
0.019351303577423096,
0.003957873210310936,
-0.011991137638688087,
0.016572222113609314,
0.008504015393555164,
-0.04333217069506645,
0.09963899850845337,
0.0011862667743116617,
0.01435418613255024,
-0.03009200654923916,
-0.017378048971295357,
-0.01985052600502968,
0.0018178584286943078,
0.04195496439933777,
0.0641610324382782,
-0.04658692330121994,
0.0023693204857409,
0.0021670563146471977,
0.004948719404637814,
0.024938104674220085,
-0.06354328989982605,
0.030168509110808372,
-0.011085041798651218,
-0.012201528996229172,
-0.027643973007798195,
-0.005622071214020252,
-0.03089253418147564,
-0.010187855921685696,
0.042527228593826294,
0.006976655218750238,
0.05177164077758789,
-0.0117960125207901,
-0.009236815385520458,
-0.015783147886395454,
0.03171508014202118,
-0.05160677433013916,
-0.017329461872577667,
-0.053525522351264954,
0.049096591770648956,
-0.04182730242609978,
-0.012248835526406765
] |
<p>I'm having some trouble calculating the 2nd order energy shift in a problem.
I am given the pertubation:</p>
<p>$\hat{H}'=\alpha \hat{p}$,</p>
<p>where $\alpha$ is a constant, and $\hat{p}$ is given by:</p>
<p>$p=i\sqrt{\frac{\hbar m\omega }{2}}\left( {{a}_{+}}-{{a}_{-}} \right)$,</p>
<p>where ${a}_{+}$ and ${a}_{-}$ are the usual ladder operators.</p>
<p>Now, according to my book, the 2nd order energy shift is given by:</p>
<p>$E_{n}^{2}=\sum\limits_{m\ne n}{\frac{{{\left| \left\langle \psi _{m}^{0} \right|H'\left| \psi _{n}^{0} \right\rangle \right|}^{2}}}{E_{n}^{0}-E_{m}^{0}}}$</p>
<p>Now, what I have tried to do is to calculate the term inside the power of 2. And so far I have done this:</p>
<p>$\begin{align}
& E_{n}^{1}=\alpha i\sqrt{\frac{\hbar m\omega }{2}}\int{\psi _{m}^{*}\left( {{{\hat{a}}}_{+}}-{{{\hat{a}}}_{-}} \right)}\,{{\psi }_{n}}\,dx=\alpha i\sqrt{\frac{\hbar m\omega }{2}}\left( \int{\psi _{m}^{*}\,{{{\hat{a}}}_{+}}{{\psi }_{n}}\,dx-\int{\psi _{m}^{*}\,{{{\hat{a}}}_{-}}{{\psi }_{n}}\,dx}} \right) \\
& =\alpha i\sqrt{\frac{\hbar m\omega }{2}}\left( \sqrt{n+1}\int{\psi _{m}^{*}\,{{\psi }_{n+1}}\,dx-\sqrt{n}\int{\psi _{m}^{*}\,{{\psi }_{n-1}}\,dx}} \right)
\end{align}
$</p>
<p>As you can see, I end up with the two integrals. But I don't know what to do next ? 'Cause if $m > n$, and only by 1, then the first integral will be 1, and the other will be zero. And if $n > m$, only by 1, then the second integral will be 1, and the first will be zero. Otherwise both will be zero.
And it seems wrong to have to make two expressions for the energy shift for $n > m$ and $m > n$.</p>
<p>So am I on the right track, or doing it totally wrong ?</p>
<p>Thanks in advance.</p>
<p>Regards</p> | 1,567 | [
0.028159096837043762,
-0.03513241559267044,
0.03311594948172569,
-0.009993690997362137,
0.053335823118686676,
0.013355603441596031,
-0.03463482856750488,
-0.04533246159553528,
0.009357853792607784,
-0.034095946699380875,
0.046985454857349396,
0.002678169868886471,
0.0565633699297905,
0.02499595656991005,
0.017284732311964035,
0.02179439552128315,
-0.011225367896258831,
-0.0014004765544086695,
-0.003121651941910386,
-0.022952048107981682,
0.00892331637442112,
0.028133517131209373,
-0.007497353944927454,
-0.01251352857798338,
-0.06090148165822029,
0.0504886731505394,
0.03062102012336254,
0.007618144154548645,
0.009335675276815891,
0.05645031854510307,
-0.03820129111409187,
-0.02738824114203453,
0.04347819834947586,
0.04895728826522827,
0.01147642731666565,
0.028954938054084778,
-0.03974548727273941,
-0.06236566603183746,
0.008023963309824467,
0.028506645932793617,
-0.03561168536543846,
-0.033871378749608994,
-0.001958211651071906,
0.0482478067278862,
-0.004971550777554512,
-0.006851791869848967,
0.006338829640299082,
-0.0329255685210228,
0.03740759193897247,
-0.031543437391519547,
0.0810914859175682,
0.003935300279408693,
0.03304492309689522,
0.01882045529782772,
-0.03795173019170761,
-0.02273692563176155,
0.04817810654640198,
0.07435671985149384,
0.030656030401587486,
-0.06116129457950592,
-0.007851827889680862,
-0.02825520932674408,
-0.02883494831621647,
-0.023057548329234123,
-0.006421003025025129,
-0.014613103121519089,
0.00681338319554925,
-0.005443522706627846,
0.0150747150182724,
-0.007458580192178488,
0.021347125992178917,
-0.036152470856904984,
0.026826664805412292,
-0.05172896757721901,
-0.000754519016481936,
-0.02187572792172432,
-0.024178117513656616,
0.013228473253548145,
0.03972265124320984,
0.031814176589250565,
0.013889330439269543,
0.02048245258629322,
0.04284263402223587,
0.01601080782711506,
-0.032352592796087265,
-0.012548012658953667,
0.06634677201509476,
0.005197275895625353,
0.013692092150449753,
0.03912288695573807,
-0.030391249805688858,
0.021287675946950912,
0.04439320042729378,
-0.017138030380010605,
0.014420881867408752,
0.02765054814517498,
0.014598768204450607,
0.04639723151922226,
0.013675631955265999,
-0.025965556502342224,
-0.02679215371608734,
-0.042174406349658966,
0.00826354045420885,
0.07174910604953766,
0.006241764407604933,
-0.006529925391077995,
-0.01853683963418007,
-0.008526026271283627,
-0.03969231992959976,
-0.03948397561907768,
-0.004437711555510759,
0.02067759819328785,
-0.01976197585463524,
0.012752268463373184,
-0.03496432676911354,
-0.06510335206985474,
0.008453389629721642,
-0.007407402154058218,
0.04508855938911438,
0.06798526644706726,
0.008529450744390488,
-0.005131980869919062,
-0.001518435194157064,
-0.005955877248197794,
-0.07371403276920319,
0.017254378646612167,
0.015520618297159672,
0.0018138578161597252,
-0.056205302476882935,
0.0006017817067913711,
0.0433950275182724,
-0.006325813941657543,
0.0033562693279236555,
-0.0378042496740818,
0.01129169575870037,
0.013810570351779461,
-0.09533552080392838,
-0.04306024685502052,
0.02349572815001011,
-0.04039386659860611,
0.008713658899068832,
-0.05991094186902046,
0.004229780286550522,
0.04380151256918907,
0.10311216861009598,
0.012566487304866314,
-0.0008022083784453571,
-0.0027544971089810133,
0.02510196529328823,
0.006166449747979641,
0.011744154617190361,
-0.028844764456152916,
-0.0278274267911911,
-0.013634934090077877,
0.013287350535392761,
-0.022135106846690178,
0.0004544888506643474,
0.03304223716259003,
-0.026154765859246254,
0.025915512815117836,
0.08563631772994995,
-0.0014150243951007724,
-0.005565093830227852,
0.005307634826749563,
-0.009982730261981487,
-0.020765982568264008,
0.08956986665725708,
0.03124254383146763,
0.009734043851494789,
0.0450325533747673,
0.00995886791497469,
0.02918505296111107,
-0.05182657763361931,
0.026421742513775826,
0.02627466432750225,
-0.03463614359498024,
-0.005489146802574396,
-0.0581241138279438,
0.011870069429278374,
0.036924369633197784,
-0.02166040614247322,
-0.03128811717033386,
-0.022005140781402588,
0.019675778225064278,
0.03982929885387421,
-0.012774946168065071,
0.00021741489763371646,
-0.00845908373594284,
-0.03188624978065491,
-0.03809200972318649,
-0.013901598751544952,
-0.027379117906093597,
0.026476668193936348,
-0.0017408413114026189,
-0.018609249964356422,
0.013673237524926662,
-0.0333319790661335,
-0.0011902471305802464,
0.014074577949941158,
-0.04324498027563095,
0.02048633247613907,
0.014752037823200226,
0.006331011652946472,
-0.04001971334218979,
0.04750966653227806,
0.05497681349515915,
0.020891547203063965,
0.025614552199840546,
0.05356934294104576,
-0.04966343566775322,
-0.026297621428966522,
0.015108841471374035,
0.003250690409913659,
0.03124397248029709,
-0.014471345581114292,
0.0047156489454209805,
-0.007375585846602917,
-0.03820875659584999,
0.017076371237635612,
0.01654859445989132,
-0.029136676341295242,
0.050473399460315704,
0.0707712396979332,
0.013178479857742786,
0.01929585076868534,
-0.006363230291754007,
-0.03442835062742233,
0.04775024205446243,
-0.019214440137147903,
-0.027082325890660286,
-0.03806806728243828,
-0.006507284939289093,
0.01743881031870842,
0.02901024930179119,
-0.06789892166852951,
-0.005126813426613808,
0.06007654592394829,
0.028170952573418617,
0.030793651938438416,
-0.00093309540534392,
-0.03041691519320011,
-0.020472027361392975,
0.007276478223502636,
0.012264306657016277,
-0.02837494947016239,
0.03718799352645874,
0.027446426451206207,
-0.006519895512610674,
0.04827611520886421,
-0.011597908101975918,
-0.013915159739553928,
0.04121892526745796,
-0.04441940039396286,
0.0027610657270997763,
-0.011027272790670395,
-0.018208378925919533,
0.0187597144395113,
-0.020903604105114937,
0.02687768079340458,
0.0428585521876812,
-0.023558970540761948,
0.003486910369247198,
-0.011099682189524174,
-0.04326177388429642,
0.01954135298728943,
0.013252262026071548,
0.011065537109971046,
-0.022301089018583298,
0.007997201755642891,
-0.026397742331027985,
-0.00002960969868581742,
-0.0024159762542694807,
-0.0063316780142486095,
-0.004855178762227297,
-0.026309827342629433,
0.03532509505748749,
0.040273044258356094,
0.02011861838400364,
-0.04696580767631531,
-0.007173658348619938,
0.01374361477792263,
0.0033436533994972706,
0.01986115798354149,
-0.017260247841477394,
-0.059136487543582916,
0.0033891370985656977,
-0.060855016112327576,
0.0006916694692336023,
0.06405341625213623,
0.016869179904460907,
-0.026627859100699425,
-0.0047417557798326015,
0.013995028100907803,
-0.05991414561867714,
-0.036480292677879333,
-0.008581997826695442,
0.0023128159809857607,
-0.035514749586582184,
-0.041136734187603,
0.06984008103609085,
0.013212015852332115,
-0.02963714860379696,
0.032338473945856094,
0.010121009312570095,
-0.029500411823391914,
-0.02947080507874489,
-0.0021499115973711014,
0.022744089365005493,
-0.0200498029589653,
0.037859316915273666,
-0.004761194810271263,
0.027045296505093575,
-0.00812479481101036,
-0.04427707567811012,
-0.032125551253557205,
0.01117038819938898,
0.014684515073895454,
-0.01101652905344963,
-0.0027809690218418837,
-0.03186650574207306,
0.11318860203027725,
0.02833518758416176,
0.007043226156383753,
-0.005624425131827593,
0.014017202891409397,
0.004662777297198772,
-0.02611038088798523,
0.0020256165880709887,
0.05173535272479057,
-0.018136601895093918,
0.01283312402665615,
-0.028808167204260826,
0.05274860933423042,
0.05479250103235245,
-0.017936792224645615,
-0.01207916159182787,
0.05973323807120323,
0.002964696614071727,
0.02488451823592186,
0.062344666570425034,
-0.03244936093688011,
-0.03250700980424881,
0.028888918459415436,
-0.00989411398768425,
-0.036737751215696335,
-0.029193159192800522,
-0.02182161621749401,
0.035446297377347946,
-0.035880569368600845,
-0.02681565098464489,
-0.013794277794659138,
0.061200592666864395,
0.019582757726311684,
-0.021130481734871864,
-0.03928928077220917,
0.036491263657808304,
0.04174948111176491,
-0.013812770135700703,
0.03968742862343788,
0.044674236327409744,
0.029729943722486496,
0.021643707528710365,
-0.028861060738563538,
-0.025953540578484535,
0.009060184471309185,
0.024801848456263542,
-0.03212897852063179,
-0.05933412164449692,
0.03723129630088806,
0.046183232218027115,
0.0034508719108998775,
-0.014959609135985374,
-0.03241659328341484,
-0.006838562432676554,
-0.014835857786238194,
-0.020387951284646988,
-0.026877395808696747,
0.07708463072776794,
-0.024082966148853302,
0.0685461238026619,
0.011446245945990086,
0.026725219562649727,
0.010772810317575932,
0.025215471163392067,
-0.06286708265542984,
0.018474102020263672,
-0.008792635053396225,
-0.019551189616322517,
0.024088487029075623,
0.012555621564388275,
0.004516003653407097,
-0.031201843172311783,
-0.007385066244751215,
-0.019821379333734512,
-0.023037133738398552,
-0.026722749695181847,
0.019041353836655617,
-0.04132663086056709,
-0.008710671216249466,
-0.02755224145948887,
0.04518027976155281,
0.0365925207734108,
-0.03948875144124031,
-0.026458412408828735,
0.01791945844888687,
-0.04367135837674141,
0.01189674437046051,
-0.004455960355699062,
0.011060883291065693,
0.03515873849391937,
0.04711703583598137,
0.028917761519551277,
0.028381692245602608,
-0.02104751020669937,
-0.01957686059176922,
-0.004864634480327368,
0.04249199479818344,
0.000022646290744887665,
-0.02839837782084942,
0.03329436480998993,
0.01135476678609848,
-0.00891090091317892,
-0.008275823667645454,
0.06464837491512299,
-0.02181299589574337,
0.03712927922606468,
-0.0024977815337479115,
-0.0006712276372127235,
-0.0382266528904438,
0.04024020954966545,
0.04924965649843216,
-0.0013253135839477181,
0.026761479675769806,
-0.07236968725919724,
0.01337468158453703,
-0.04104020446538925,
0.0032660351134836674,
-0.0334693044424057,
-0.03587489202618599,
-0.03585558384656906,
0.002384173683822155,
0.004402642138302326,
0.027353495359420776,
-0.012894630432128906,
0.010288630612194538,
0.006953115575015545,
-0.0008823501993902028,
0.021350622177124023,
0.008795383386313915,
0.02099449746310711,
0.009204750880599022,
0.016165832057595253,
-0.024073339998722076,
0.031383272260427475,
-0.05812562257051468,
-0.011357592418789864,
0.020231902599334717,
0.06196880713105202,
0.022450804710388184,
-0.0038059651851654053,
-0.06112973019480705,
-0.06193496659398079,
0.006188446655869484,
-0.04500015079975128,
0.058499448001384735,
0.014392140321433544,
0.02074512280523777,
-0.0020203045569360256,
-0.05502147227525711,
-0.06961783766746521,
0.008739677257835865,
0.002095480915158987,
0.008661599829792976,
-0.043998926877975464,
-0.002578450134024024,
-0.03814343363046646,
0.007534912787377834,
0.03737156093120575,
0.06427399814128876,
-0.04012313485145569,
-0.019345281645655632,
-0.013041027821600437,
0.025059111416339874,
-0.01687690243124962,
-0.0985475555062294,
0.0026997311506420374,
-0.00746653787791729,
-0.03989427909255028,
0.022980451583862305,
-0.04231547936797142,
-0.008574170060455799,
0.004992909263819456,
0.031860172748565674,
0.02753015235066414,
-0.03429388627409935,
-0.013555629178881645,
0.06963551044464111,
0.03244340419769287,
-0.008092294447124004,
0.06980664283037186,
0.04292414337396622,
-0.021354978904128075,
0.014550772495567799,
-0.030343305319547653,
0.019787034019827843,
-0.012152932584285736,
0.004859486594796181,
-0.03781018406152725,
-0.02127104625105858,
-0.047842491418123245,
0.04749544709920883,
-0.019892223179340363,
0.05315004661679268,
0.03453972190618515,
-0.0041666352190077305,
0.007340067531913519,
0.034943703562021255,
-0.04457109421491623,
0.01827099919319153,
0.015257230959832668,
0.025676850229501724,
0.04232754558324814,
-0.002755363704636693,
0.05012912303209305,
-0.01511362660676241,
0.002793916966766119,
0.0521702878177166,
-0.030643880367279053,
-0.008911839686334133,
-0.02331918478012085,
-0.04143480956554413,
0.01820092275738716,
-0.06115938723087311,
0.016646303236484528,
-0.019542936235666275,
0.02949792519211769,
-0.013659211806952953,
-0.019877003505825996,
-0.041372403502464294,
0.020555268973112106,
-0.018330223858356476,
-0.007733985781669617,
-0.022943168878555298,
-0.023596879094839096,
0.04560285061597824,
0.009958960115909576,
-0.060952454805374146,
-0.02762933075428009,
-0.0223647803068161,
0.0019090641289949417,
0.007080782204866409,
0.0012955714482814074,
-0.033924199640750885,
0.015498880296945572,
-0.0374956838786602,
0.008979936130344868,
0.03030085191130638,
-0.015149884857237339,
0.007991640828549862,
0.029108187183737755,
0.020747818052768707,
0.01273795124143362,
0.01325911097228527,
-0.03368307277560234,
0.01008859183639288,
-0.005627715028822422,
-0.040854714810848236,
0.027821017429232597,
0.04058000445365906,
-0.023722834885120392,
-0.0274784155189991,
-0.018559273332357407,
0.03634267300367355,
0.03894296661019325,
-0.004786388017237186,
-0.02483735978603363,
0.0169380996376276,
0.03170792758464813,
0.03429083153605461,
-0.030783336609601974,
-0.007518621627241373,
0.012660671956837177,
-0.0027307511772960424,
-0.015149435959756374,
-0.02916543558239937,
-0.046937014907598495,
-0.03067159280180931,
-0.01900385692715645,
0.023989858105778694,
-0.01700010523200035,
-0.008526168763637543,
0.06647440791130066,
-0.021623151376843452,
0.012909682467579842,
0.04988744482398033,
-0.015863556414842606,
-0.009341094642877579,
-0.0030461912974715233,
-0.0005791204748675227,
-0.020220857113599777,
-0.014853677712380886,
-0.031146666035056114,
-0.02723005972802639,
-0.06271813064813614,
0.02348928712308407,
0.029204130172729492,
0.04796471819281578,
0.04521328955888748,
-0.01807839423418045,
0.01808146946132183,
-0.030040422454476357,
-0.010884135961532593,
-0.031689491122961044,
0.03212221711874008,
-0.03493403643369675,
0.03498460724949837,
-0.04296796768903732,
0.003841693513095379,
0.029608391225337982,
0.03796940669417381,
-0.05189347267150879,
0.0048444271087646484,
0.01799311861395836,
0.05225405469536781,
-0.016687581315636635,
-0.010527968406677246,
-0.02317480556666851,
0.045071978121995926,
-0.019629627466201782,
0.04331091418862343,
-0.0036208212841302156,
-0.02635093405842781,
0.027969785034656525,
0.04273831844329834,
0.010267131961882114,
-0.05268747732043266,
-0.012475642375648022,
-0.04225464537739754,
-0.008935549296438694,
0.014651819132268429,
-0.023155750706791878,
0.012364559806883335,
0.03090006113052368,
0.008034498430788517,
-0.032691456377506256,
0.02247576043009758,
0.011646684259176254,
-0.03000364452600479,
0.0005971974460408092,
-0.04307723790407181,
-0.07439640164375305,
0.021339453756809235,
-0.02542312815785408,
-0.0015897199045866728,
0.026944657787680626,
-0.021493172273039818,
0.007259057369083166,
0.02886147052049637,
-0.0009163403883576393,
0.007319948170334101,
0.07621064782142639,
0.019419124349951744,
-0.004501871298998594,
0.015586001798510551,
-0.023545121774077415,
0.13084213435649872,
0.06499188393354416,
0.013559511862695217,
-0.0732915848493576,
0.0023119559045881033,
-0.02733377367258072,
0.03557918220758438,
-0.035571303218603134,
-0.006008862983435392,
-0.03193820267915726,
-0.021454446017742157,
-0.031188849359750748,
0.0854995921254158,
0.03850502148270607,
-0.0007069333223626018,
0.028635071590542793,
-0.009555697441101074,
-0.037632886320352554,
0.0346267931163311,
0.020893163979053497,
-0.028964897617697716,
0.022787882015109062,
-0.015928301960229874,
0.015970692038536072,
-0.011146665550768375,
-0.008543339557945728,
-0.050541337579488754,
0.005074072163552046,
0.015590065158903599,
-0.03673696890473366,
-0.049961015582084656,
0.015779506415128708,
-0.010647905059158802,
-0.0029079774394631386,
0.014474312774837017,
0.026258716359734535,
0.02867106720805168,
-0.0010541281662881374,
0.04218469560146332,
0.03749767318367958,
-0.012237743474543095,
-0.006834403146058321,
0.01677475869655609,
-0.002739165211096406,
-0.040096577256917953,
-0.04014244303107262,
-0.01956445723772049,
0.08911725878715515,
0.030214030295610428,
-0.04438658803701401,
0.03403501585125923,
-0.024725977331399918,
-0.009078457951545715,
-0.039591241627931595,
-0.004855745006352663,
0.014737292192876339,
0.02212712913751602,
-0.020707042887806892,
-0.012871808372437954,
0.003185293171554804,
0.019656937569379807,
0.030567161738872528,
-0.004667212255299091,
-0.0015902456361800432,
0.008838506415486336,
-0.004927345085889101,
0.03414599224925041,
0.014884824864566326,
-0.00356107740662992,
-0.02241094596683979,
0.003049630206078291,
0.017981678247451782,
-0.05652424320578575,
-0.03359394520521164,
-0.005493946373462677,
-0.005745482165366411,
0.0325188972055912,
0.0034480902832001448,
-0.034924253821372986,
-0.05584229528903961,
-0.054420389235019684,
0.006206600461155176,
0.006004459224641323,
-0.0002969884080812335,
0.019741201773285866,
-0.014357310719788074,
0.024719463661313057,
0.05162878334522247,
0.005601122044026852,
0.000782956019975245,
0.03296755999326706,
0.013310009613633156,
0.06713248044252396,
-0.03816237673163414,
-0.016020212322473526,
0.031303513795137405,
-0.04019436985254288,
-0.0002325537207070738,
-0.014549934305250645,
-0.012631679885089397,
-0.002596201142296195,
-0.021685143932700157,
0.011574849486351013,
0.01038071233779192,
-0.022290382534265518,
-0.028287513181567192,
-0.0004597892693709582,
0.0058617740869522095,
0.006781509146094322,
0.020289907231926918,
-0.0026740722823888063,
-0.002373947063460946,
0.0039031216874718666,
0.001992020523175597,
-0.004501484800130129,
-0.01801205240190029,
0.0519137866795063,
-0.0007621231488883495,
-0.024139922112226486,
0.005264873616397381,
0.0006972845876589417,
-0.01363139133900404,
0.028065679594874382,
0.0010171683970838785,
0.03136672452092171,
-0.010390108451247215,
-0.0029380074702203274,
-0.02791259065270424,
0.02671997994184494,
-0.023298144340515137,
-0.011804173700511456,
0.042584046721458435,
0.05505339056253433,
-0.011265751905739307,
-0.01249382272362709,
0.008807755075395107,
-0.0038920692168176174,
0.012791698798537254,
0.027091190218925476,
-0.02286435104906559,
0.02194567769765854,
-0.0383160263299942,
-0.0274759940803051,
0.043397385627031326,
0.026847438886761665,
0.046078357845544815,
0.016918649896979332,
-0.005996680818498135,
-0.021740920841693878,
0.04116848483681679,
-0.0273295771330595,
-0.05811766907572746,
-0.026162492111325264,
-0.037469249218702316,
0.0050620026886463165,
-0.00942264124751091,
-0.0038076003547757864,
-0.015001797117292881,
0.0499570332467556,
0.02292993851006031,
0.003229018533602357,
-0.017777588218450546,
-0.02839556522667408,
-0.013457552529871464,
-0.009670617990195751,
0.04300440102815628,
0.03499031439423561,
0.00009014772513182834,
0.0049574971199035645,
0.04629487171769142,
-0.01365566998720169,
0.029504327103495598,
0.002292715013027191,
0.025462420657277107,
-0.0711291953921318,
-0.015449993312358856,
-0.03241073340177536,
0.02161060832440853,
0.09569421410560608,
-0.05519743263721466,
0.03984619304537773,
0.012694264762103558,
-0.037676312029361725,
0.031211353838443756,
-0.028540002182126045,
0.020656030625104904,
0.008323024027049541,
0.013813240453600883,
-0.024768495932221413,
0.04291141778230667,
0.045826733112335205,
0.046294912695884705,
0.015845730900764465,
0.0033848388120532036,
-0.00033600590541027486,
-0.01989113539457321,
0.0022710219491273165,
0.03501481935381889,
0.0008623386383987963,
-0.004987331572920084,
0.04654340445995331,
-0.01789373718202114,
-0.027006160467863083,
0.026173489168286324,
-0.07484126836061478,
-0.0006054805126041174,
-0.01432658638805151,
0.05392969399690628,
-0.004608956165611744,
0.062150273472070694,
0.010085313580930233,
-0.0032053396571427584,
0.01587638258934021,
-0.020665593445301056,
0.03422927111387253,
-0.0006439067074097693,
-0.02015998400747776,
-0.00944775715470314,
-0.0002356045733904466,
-0.032073307782411575,
-0.04677240550518036,
0.05501239001750946,
-0.015046939253807068,
0.021905293688178062,
0.033573608845472336,
-0.023580443114042282,
-0.0017348643159493804,
-0.024960365146398544,
0.013814937323331833,
-0.037482090294361115,
-0.015231161378324032,
0.0014111152850091457,
0.027471603825688362,
-0.0042631481774151325,
-0.0033301569055765867,
-0.0026944433338940144,
-0.06197778508067131,
0.03944215923547745,
-0.011139693669974804,
-0.04832180216908455,
-0.05299782752990723,
-0.019382720813155174,
-0.026024453341960907,
0.0371546745300293,
-0.009752599522471428,
0.010155496187508106,
-0.04681524634361267,
0.00384328281506896,
0.01573498360812664,
-0.0021957873832434416,
-0.02987997606396675,
-0.044706977903842926,
-0.012996494770050049,
-0.08527828752994537,
0.02117612026631832,
0.018616368994116783,
-0.03522379323840141,
-0.013374067842960358,
-0.006331645883619785,
-0.006162089761346579,
0.015883471816778183,
0.06081084907054901,
-0.023475462570786476,
-0.035589832812547684,
-0.02778886817395687,
-0.02754989266395569,
0.01606033928692341,
-0.04776972904801369,
-0.01944804936647415,
0.007999426685273647,
-0.005774823483079672,
0.004731558728963137,
0.0179037693887949,
-0.018194537609815598,
0.05903499573469162,
-0.0027459010016173124,
0.0026024614926427603,
0.020524857565760612,
0.013514158315956593,
-0.01979524828493595,
0.03122490644454956,
-0.03158692270517349,
-0.014591534622013569,
0.060159508138895035,
-0.011699219234287739,
-0.007919399067759514,
0.037921320647001266,
-0.026422252878546715,
-0.04487696290016174,
-0.010228331200778484,
0.01892426609992981,
-0.0005035818903706968,
0.009449473582208157,
-0.0037830646615475416,
0.020017653703689575,
0.0010715130483731627,
0.00264105387032032,
0.04134683683514595,
-0.02028142288327217,
-0.034963592886924744,
0.02114979363977909,
0.01309880055487156,
0.011793770827353,
0.03450501710176468,
0.019822489470243454,
0.00006446354382205755,
-0.007028196472674608,
0.01977008953690529,
0.03882240131497383,
-0.002388742519542575,
0.007823910564184189,
0.05939720943570137,
0.019612615928053856,
-0.0032561502885073423,
-0.022907912731170654,
-0.006429988890886307,
-0.01703418791294098,
-0.035254642367362976,
-0.004390100482851267,
0.05618887022137642,
-0.04235536977648735,
-0.018907466903328896,
0.037599656730890274,
-0.04820017144083977,
0.04474693164229393,
-0.012186986394226551,
0.04722379148006439,
-0.015173631720244884,
0.015986425802111626,
-0.01652914099395275,
0.012335766106843948,
0.022719554603099823,
0.020419903099536896,
-0.007106298115104437,
0.017513878643512726,
-0.019672533497214317,
-0.020293639972805977,
-0.00981322955340147,
-0.07528679072856903,
-0.0071654715575277805,
0.025507314130663872,
-0.009779849089682102,
-0.03361184895038605,
-0.04440001770853996,
-0.013619444333016872,
-0.03500312194228172,
0.02484165132045746,
0.02437608689069748,
0.008878175169229507,
0.009480593726038933,
0.02350628934800625,
-0.026721131056547165,
0.027178281918168068,
-0.04119166359305382,
-0.005173435900360346,
-0.015507133677601814,
-0.006808019243180752,
-0.018320610746741295,
0.0017780613852664828
] |
<p>In Statistical Mechanics, we often postulate that for an isolated system, the phase-space density of all accessible microstates (i.e all microstates consistent with the energy) is the same. This is equivalent to assuming that the system is ergodic. This postulate leads us to the assertion that at any given time, the system is most likely to be found in that macrostate which has the maximum number of consistent microstates, and from then on, we calculate the entropy for this macrostate and get the fundamental relation for entropy, and hence, other thermodynamic quantities.
My question now is: Is this assumption of equal a-priori probabilities too strong to obtain the second assertion? In other words, can we not say that the macrostate with the maximum number of microstates <em>is</em> the observed thermodynamic state, while being non-committal as to whether indeed they are all equally probable or not? Or am I losing some information by not considering their probability distribution (maybe, say fluctuations)?</p> | 1,568 | [
-0.025488819926977158,
0.019427021965384483,
-0.002284236252307892,
-0.030661996454000473,
0.02219303511083126,
0.013908428139984608,
-0.017647072672843933,
0.010850466787815094,
-0.012039552442729473,
-0.010311623103916645,
0.034478895366191864,
0.013017693534493446,
0.04344798997044563,
0.01110401377081871,
0.020440248772501945,
-0.026130488142371178,
-0.00566168362274766,
-0.007252222392708063,
-0.010418903082609177,
-0.00768157048150897,
0.0034609658177942038,
0.019282637163996696,
0.0033477749675512314,
-0.06157860532402992,
-0.06110909953713417,
0.008928485214710236,
-0.009143354371190071,
0.0068649244494736195,
0.037361953407526016,
0.07237153500318527,
-0.015268760733306408,
-0.0325920432806015,
0.026365481317043304,
0.060635387897491455,
0.05451897904276848,
0.01187093649059534,
-0.049131013453006744,
-0.010473765432834625,
-0.02869579568505287,
0.03990403190255165,
-0.08585803955793381,
-0.012362225912511349,
-0.018211575224995613,
0.015299152582883835,
-0.004220098722726107,
0.028673283755779266,
0.016150323674082756,
-0.016461441293358803,
0.02860892564058304,
-0.05445561930537224,
0.05849554389715195,
-0.00043522357009351254,
0.0381704680621624,
0.05526572838425636,
-0.03482075035572052,
-0.04381332919001579,
0.07244538515806198,
0.07359692454338074,
-0.0067274002358317375,
-0.05476219207048416,
-0.02613217756152153,
-0.011792853474617004,
-0.013133802451193333,
-0.031206121668219566,
-0.02154923975467682,
0.04852458834648132,
0.018286030739545822,
-0.019546104595065117,
0.03828100115060806,
0.013929074630141258,
0.0008975040982477367,
-0.01162334717810154,
0.06801708787679672,
0.00043664066470228136,
-0.004463601391762495,
0.0046062590554356575,
0.04770950600504875,
-0.010066356509923935,
0.006416609976440668,
0.039419472217559814,
-0.0026541342958807945,
0.024908384308218956,
0.021777700632810593,
0.02771534025669098,
0.03401348367333412,
-0.013670693151652813,
0.04217171296477318,
-0.030927985906600952,
0.012679566629230976,
0.028965260833501816,
-0.03386467322707176,
0.010985746048390865,
0.05513358116149902,
0.005684596486389637,
-0.0655585303902626,
0.010151827707886696,
-0.016608158126473427,
0.025300007313489914,
-0.06122220307588577,
-0.01997743546962738,
-0.00775713287293911,
-0.04754367470741272,
0.033137790858745575,
0.050142187625169754,
-0.014519833028316498,
0.0005722667556256056,
-0.06949556618928909,
0.03074635937809944,
-0.00983739085495472,
0.0047004371881484985,
-0.01555036660283804,
0.02322137914597988,
0.014895978383719921,
0.011538306251168251,
-0.003154281061142683,
-0.01518710982054472,
-0.010287056677043438,
-0.029424753040075302,
0.03127645328640938,
0.07740380614995956,
0.0248060692101717,
-0.022823428735136986,
0.019357437267899513,
-0.035435017198324203,
-0.057209212332963943,
0.015693098306655884,
0.050372447818517685,
-0.005518397316336632,
-0.05802066996693611,
0.04292137175798416,
-0.016618462279438972,
0.03358633443713188,
0.03777174651622772,
0.003673612605780363,
0.020807234570384026,
-0.03695736825466156,
-0.10666590183973312,
-0.04238276556134224,
0.07671742886304855,
-0.016007350757718086,
-0.04923368617892265,
-0.05385638400912285,
0.01787785068154335,
0.0565958172082901,
0.06695989519357681,
-0.021999329328536987,
0.02205338142812252,
-0.028106220066547394,
0.06897220015525818,
-0.007386521436274052,
-0.04008158668875694,
-0.022835029289126396,
0.00457255681976676,
-0.05630948022007942,
0.015447050333023071,
-0.056235525757074356,
0.0528770387172699,
0.023983579128980637,
0.0035729126539081335,
-0.003101564012467861,
0.0013862114865332842,
0.00030175576102919877,
-0.009753560647368431,
-0.00390875106677413,
0.018058432266116142,
-0.02481856197118759,
0.06511340290307999,
-0.008729705587029457,
0.02622540481388569,
-0.0006131007103249431,
0.010218186303973198,
0.005911197513341904,
0.007746207062155008,
0.02986779250204563,
0.05210873857140541,
-0.04227020591497421,
-0.017755944281816483,
-0.015554388985037804,
0.035831768065690994,
0.007672313135117292,
-0.02361668460071087,
-0.003281691111624241,
-0.0329897403717041,
-0.026509014889597893,
-0.0017813934246078134,
0.018780842423439026,
-0.012243585661053658,
-0.02898930385708809,
-0.0000538119456905406,
-0.046265859156847,
-0.029007242992520332,
-0.06117776036262512,
-0.02141447924077511,
-0.015742722898721695,
-0.021761806681752205,
0.06438963860273361,
0.003787605557590723,
0.022100985050201416,
-0.01894450932741165,
-0.014147193171083927,
-0.028199130669236183,
-0.02288839779794216,
-0.00025828456273302436,
-0.005629903171211481,
0.024922702461481094,
0.05501185357570648,
0.03377964347600937,
-0.013600507751107216,
0.02566717006266117,
-0.0037792848888784647,
-0.06280826032161713,
-0.017417307943105698,
-0.027230868116021156,
0.0313371978700161,
0.005953694693744183,
-0.002947048284113407,
-0.0004966491833329201,
-0.033513497561216354,
-0.024157073348760605,
0.01594788394868374,
-0.05872730538249016,
0.06312611699104309,
0.04765402898192406,
0.006066013593226671,
-0.019498856738209724,
0.041082922369241714,
0.042284317314624786,
0.010709990747272968,
0.0003458006540313363,
-0.01756385900080204,
-0.09406350553035736,
-0.002316717291250825,
0.05326532572507858,
0.07381194829940796,
-0.05081822723150253,
0.0054115476086735725,
0.030029188841581345,
0.05113673210144043,
-0.006319503299891949,
0.052188873291015625,
-0.011677566915750504,
-0.03535819798707962,
0.030809205025434494,
-0.005929340608417988,
0.01959139108657837,
0.005891839507967234,
0.03465370088815689,
0.003654017811641097,
-0.02544860914349556,
0.0011846640845760703,
-0.006003654096275568,
0.003944031894207001,
-0.006147298030555248,
0.023432603105902672,
0.0039956532418727875,
-0.009966638870537281,
0.015057619661092758,
-0.015338600613176823,
0.04801802709698677,
-0.022476788610219955,
-0.006299137137830257,
0.009452419355511665,
-0.024683604016900063,
-0.023434584960341454,
-0.02498652972280979,
0.00297593604773283,
-0.04592796042561531,
-0.008740372955799103,
0.03221326693892479,
-0.025566739961504936,
-0.023385876789689064,
0.008832675404846668,
-0.02866557240486145,
0.03009852021932602,
0.005881042685359716,
0.02159506268799305,
-0.027992764487862587,
0.016260355710983276,
-0.031611550599336624,
0.009346903301775455,
0.01412008237093687,
0.005367921199649572,
-0.005156636703759432,
0.03671516478061676,
-0.05244973301887512,
-0.0006621930515393615,
-0.016689017415046692,
-0.0326782688498497,
-0.00021216021559666842,
-0.021721618250012398,
-0.0006229591090232134,
-0.010450671426951885,
0.005529029760509729,
-0.03956855088472366,
0.024737391620874405,
0.022021459415555,
-0.01600365713238716,
-0.041125088930130005,
0.0019072837894782424,
0.049608949571847916,
-0.016176478937268257,
-0.07575903832912445,
-0.0226532481610775,
-0.04645310342311859,
-0.03829524666070938,
0.014448730275034904,
-0.008067904971539974,
0.0328669548034668,
-0.009535585530102253,
0.053611256182193756,
0.0894264504313469,
-0.03101334348320961,
-0.04332071542739868,
-0.05506759509444237,
-0.07325395941734314,
0.05699930712580681,
-0.025763290002942085,
0.050714001059532166,
-0.027074705809354782,
-0.023954251781105995,
0.05672794580459595,
0.03871612623333931,
-0.04150821268558502,
0.011194738559424877,
-0.00710443127900362,
-0.007294660899788141,
0.007043242920190096,
-0.0216518621891737,
-0.004225161857903004,
-0.02935708314180374,
0.045874856412410736,
0.049810219556093216,
0.04398547485470772,
0.021168502047657967,
-0.01347377523779869,
0.010256140492856503,
0.03528519347310066,
0.039336178451776505,
0.0064842854626476765,
0.02678585797548294,
0.016570262610912323,
-0.018295517191290855,
0.01505979709327221,
0.004561782348901033,
0.04049444571137428,
0.0026523147244006395,
-0.057854603976011276,
0.07219801843166351,
0.0150043535977602,
0.03425832837820053,
-0.06972625106573105,
0.03873664513230324,
0.007839511148631573,
0.0011532478965818882,
0.01073087751865387,
0.03306251019239426,
0.02112940140068531,
0.007244258187711239,
0.0019512487342581153,
0.05485299974679947,
0.030764412134885788,
0.010883464477956295,
0.007664418313652277,
-0.01374103594571352,
-0.013913903385400772,
0.010752682574093342,
-0.003086936427280307,
-0.028674017637968063,
0.02561679482460022,
0.03532486408948898,
0.04260591045022011,
-0.024892354384064674,
-0.03356434032320976,
0.0020252037793397903,
-0.06763122975826263,
-0.017930760979652405,
-0.024459928274154663,
0.025000886991620064,
0.0032478112261742353,
0.05207972973585129,
-0.008265742100775242,
-0.01878557726740837,
-0.0022238779347389936,
0.02498549595475197,
-0.07340729981660843,
0.006464809644967318,
-0.025930779054760933,
0.006206362508237362,
0.005971034523099661,
-0.026919465512037277,
0.07124970108270645,
-0.04805511608719826,
-0.0237492136657238,
0.015276433899998665,
0.02057957462966442,
-0.07724331319332123,
-0.023471342399716377,
-0.05964887887239456,
-0.04087142273783684,
-0.04388265311717987,
0.01917274296283722,
0.031797826290130615,
-0.015346655622124672,
0.04930751398205757,
0.03337535634636879,
-0.05252191424369812,
0.019056379795074463,
-0.012000286020338535,
0.04988441243767738,
0.009360289201140404,
0.0108760641887784,
0.0005011616158299148,
0.03435909003019333,
-0.012642819434404373,
0.03201794624328613,
0.030550293624401093,
0.048760805279016495,
0.020039314404129982,
-0.03871504217386246,
-0.03783384710550308,
-0.017645200714468956,
-0.048003602772951126,
0.02479473687708378,
0.03695432469248772,
0.016178928315639496,
0.0005906324950046837,
0.015231125056743622,
0.01295242365449667,
-0.016096511855721474,
0.03977159783244133,
0.030291272327303886,
-0.02192697860300541,
-0.054072242230176926,
-0.019571412354707718,
-0.018735116347670555,
-0.017358366400003433,
0.031230369582772255,
0.0001873122964752838,
-0.011003060266375542,
-0.022935785353183746,
-0.007831954397261143,
-0.017575474455952644,
0.02959265187382698,
-0.03261324018239975,
-0.022736279293894768,
-0.0036710165441036224,
0.017530493438243866,
-0.00665881484746933,
-0.006153471302241087,
0.030941491946578026,
-0.008249808102846146,
0.012806981801986694,
0.034235212951898575,
0.0075873322784900665,
-0.04435490071773529,
0.0014125092420727015,
0.029201697558164597,
0.022592095658183098,
-0.006292107980698347,
0.0119510842487216,
-0.03313331678509712,
-0.019076557829976082,
0.06438717991113663,
0.010371977463364601,
0.03453874960541725,
0.009553516283631325,
-0.006664442829787731,
-0.024524129927158356,
-0.05374998226761818,
0.0003440303262323141,
-0.013884826563298702,
0.00728056114166975,
0.008303094655275345,
-0.007907637394964695,
-0.025965875014662743,
-0.047788675874471664,
-0.01428090501576662,
0.011428158730268478,
0.05494304746389389,
-0.01901601254940033,
-0.009930324740707874,
-0.018051214516162872,
-0.0014927191659808159,
-0.012347579002380371,
-0.060351625084877014,
0.0007280547870323062,
-0.020647140219807625,
-0.012547820806503296,
0.03382866829633713,
-0.048638176172971725,
-0.06213188171386719,
0.016376914456486702,
0.0012862661387771368,
-0.03396135941147804,
0.007270941510796547,
-0.006514440756291151,
0.06325496733188629,
0.02006160095334053,
0.0097169429063797,
0.02275504171848297,
0.0059804171323776245,
0.022924315184354782,
0.008832540363073349,
-0.008055731654167175,
0.02111990377306938,
-0.042903076857328415,
0.03147237375378609,
-0.03765934333205223,
0.019727138802409172,
0.006383070722222328,
0.04308224469423294,
0.002560368971899152,
0.02401774562895298,
0.0014260985190048814,
-0.043823130428791046,
-0.013861767016351223,
0.028001539409160614,
0.023001668974757195,
0.01256504561752081,
-0.014742140658199787,
0.027243446558713913,
-0.0098521513864398,
-0.014824035577476025,
0.004734623245894909,
0.01324026845395565,
0.00892806425690651,
0.03764822334051132,
-0.003549160435795784,
0.05541745200753212,
-0.052800241857767105,
-0.04289591312408447,
0.010547936893999577,
-0.03126072883605957,
0.04055275022983551,
-0.007703607436269522,
0.043984998017549515,
0.014877391047775745,
-0.042470186948776245,
-0.04007633030414581,
0.014599302783608437,
-0.02503129094839096,
0.03255447372794151,
-0.01024204958230257,
0.005353357642889023,
0.01247005257755518,
0.006789174396544695,
-0.08996384590864182,
-0.013036888092756271,
-0.009598231874406338,
0.044688496738672256,
-0.028624756261706352,
-0.059455905109643936,
0.026975037530064583,
-0.006454417482018471,
0.00023464459809474647,
0.007089614402502775,
0.017127184197306633,
0.026382889598608017,
-0.01180536299943924,
-0.00329898321069777,
0.049130089581012726,
0.0551142543554306,
-0.026116304099559784,
-0.014602220617234707,
0.023488545790314674,
0.025718986988067627,
0.0018998333252966404,
0.010723508894443512,
0.03205055370926857,
-0.020435871556401253,
-0.007762127090245485,
0.001069985912181437,
0.008275074884295464,
0.027667319402098656,
-0.006830411963164806,
-0.01684591919183731,
0.047595664858818054,
-0.020948896184563637,
0.004966938402503729,
-0.011202238500118256,
-0.003951697610318661,
-0.004719745833426714,
0.013159563764929771,
0.003926822450011969,
0.002607928588986397,
0.020580004900693893,
-0.037655625492334366,
0.043663833290338516,
0.006272050552070141,
-0.02113048918545246,
0.01018671877682209,
0.06534235924482346,
0.0004959280486218631,
-0.01898043043911457,
-0.006647096015512943,
-0.015033171512186527,
0.008411619812250137,
-0.015419794246554375,
0.018607119098305702,
-0.022436654195189476,
0.005201542284339666,
-0.03427518159151077,
-0.030613865703344345,
-0.054949723184108734,
0.01858530007302761,
0.041864339262247086,
-0.006744012236595154,
0.00643450953066349,
0.022203601896762848,
-0.00907869916409254,
-0.003004648955538869,
-0.032230671495199203,
-0.0017849638825282454,
0.0107101546600461,
-0.016839906573295593,
0.03268617019057274,
-0.030478639528155327,
-0.04290210083127022,
0.03571576997637749,
0.02476256713271141,
-0.03255145624279976,
0.027464671060442924,
0.0001130651799030602,
0.0056219385005533695,
0.028841586783528328,
-0.023928822949528694,
-0.023155638948082924,
0.06035958603024483,
-0.07928863912820816,
0.04646110162138939,
-0.016018962487578392,
-0.010670249350368977,
-0.005194803699851036,
0.011615701019763947,
-0.009394307620823383,
-0.02406267262995243,
-0.03814159333705902,
-0.004675648175179958,
0.05353110656142235,
-0.012380053289234638,
0.04587804153561592,
0.04730885103344917,
-0.01023164764046669,
0.022257160395383835,
0.014631904661655426,
-0.004214727319777012,
0.024875415489077568,
-0.07835284620523453,
-0.014174630865454674,
-0.006244005169719458,
-0.05024855211377144,
0.012866230681538582,
-0.013820257037878036,
-0.021026544272899628,
0.0019929350819438696,
-0.01915675774216652,
0.01789797469973564,
0.0060760402120649815,
0.048811234533786774,
0.004073210991919041,
0.09255930036306381,
0.0049437410198152065,
0.0536804124712944,
-0.005797892343252897,
0.014801722019910812,
0.1161595806479454,
0.0592384934425354,
0.012537667527794838,
-0.02475127764046192,
0.04348524287343025,
-0.011573233641684055,
-0.015761513262987137,
0.004708744119852781,
0.034215763211250305,
0.02468225546181202,
-0.005184984300285578,
-0.007316339295357466,
0.024124283343553543,
0.0015682801604270935,
-0.04200597479939461,
0.03146315738558769,
-0.046911802142858505,
-0.013304857537150383,
0.013535396195948124,
0.04249388352036476,
0.0019957993645220995,
-0.01616685837507248,
0.008289621211588383,
-0.01343577541410923,
0.0025711653288453817,
0.011477525345981121,
0.01987718977034092,
-0.033419787883758545,
0.013765571638941765,
0.014142005704343319,
-0.000040346010791836306,
-0.009651828557252884,
0.035337530076503754,
-0.01615874283015728,
-0.01927514746785164,
-0.018953433260321617,
0.013373170047998428,
0.016462424769997597,
0.041482701897621155,
0.014547081664204597,
0.007200540974736214,
0.03364037722349167,
0.023856520652770996,
0.010597368702292442,
-0.009860266000032425,
-0.0024946187622845173,
-0.013179942965507507,
0.042680513113737106,
-0.03452533483505249,
0.01096036285161972,
-0.007828463800251484,
-0.023275963962078094,
-0.0035286236088722944,
-0.021197693422436714,
0.0001838395546656102,
-0.020954737439751625,
0.034592967480421066,
-0.018419185653328896,
-0.02913166955113411,
-0.039887625724077225,
-0.007462465204298496,
0.022157035768032074,
0.008653963916003704,
-0.022084563970565796,
-0.008806581608951092,
-0.008809085935354233,
-0.0030897308606654406,
0.04244275763630867,
0.018162662163376808,
-0.003204272361472249,
-0.01433668751269579,
-0.033449139446020126,
-0.07331885397434235,
-0.028770674020051956,
-0.01736748404800892,
-0.05410250648856163,
0.07027608901262283,
0.04537699744105339,
-0.00437958212569356,
0.004033105447888374,
-0.04209556430578232,
-0.01897791400551796,
-0.03795694559812546,
-0.00137841806281358,
0.003919124137610197,
0.005723400041460991,
0.02179325744509697,
0.06007678434252739,
0.0075637781992554665,
-0.0019607353024184704,
0.008912565186619759,
0.014306117780506611,
-0.0014260405441746116,
-0.025791067630052567,
0.0006854747189208865,
-0.04907006770372391,
-0.053376466035842896,
-0.0006752853514626622,
0.016115546226501465,
0.012613280676305294,
0.0203515887260437,
0.03899117559194565,
0.022696664556860924,
0.025993872433900833,
0.030349131673574448,
0.021987559273838997,
0.0009097132133319974,
-0.028151480481028557,
-0.03342966362833977,
0.015481327660381794,
0.008036122657358646,
-0.03128919005393982,
-0.050745755434036255,
-0.05297738313674927,
0.006087885238230228,
0.02087508887052536,
-0.0056753866374492645,
-0.0027860805857926607,
-0.0005864389822818339,
-0.001169089344330132,
0.0021833842620253563,
-0.025409406051039696,
-0.024355662986636162,
0.00188727758359164,
0.0039170063100755215,
0.004418945871293545,
0.020385103300213814,
-0.020269114524126053,
0.05233610421419144,
0.003076916793361306,
-0.03218685835599899,
0.016145670786499977,
0.03095831349492073,
-0.035342127084732056,
-0.06281387805938721,
0.05546969175338745,
-0.011176035739481449,
0.08098385483026505,
-0.06417392194271088,
-0.0327797569334507,
0.02587752602994442,
-0.013247456401586533,
-0.043116435408592224,
-0.0006839765701442957,
-0.005513705313205719,
0.019514063373208046,
0.05164515599608421,
0.0018886193865910172,
-0.019124608486890793,
0.015639565885066986,
-0.02378653921186924,
0.002873034216463566,
0.003882667748257518,
0.008470557630062103,
0.002538183704018593,
-0.010437332093715668,
0.02189585193991661,
0.00601799925789237,
0.006645014509558678,
0.044512614607810974,
0.031058304011821747,
0.02619812823832035,
-0.020479584112763405,
0.018046965822577477,
-0.017572706565260887,
0.01530354842543602,
0.012959946878254414,
0.00332091492600739,
0.05330866575241089,
0.044000525027513504,
-0.03873058035969734,
0.004689659457653761,
0.05087340623140335,
-0.012698941864073277,
-0.06899165362119675,
-0.02516256459057331,
0.024676084518432617,
0.0012092316756024957,
0.01843474619090557,
-0.0196642205119133,
0.03191136568784714,
0.0228529404848814,
-0.07638488709926605,
-0.0001615501823835075,
-0.0008553224033676088,
-0.005073017906397581,
-0.04887079820036888,
0.01440732553601265,
-0.041659314185380936,
0.03951079398393631,
0.05312814563512802,
0.049390364438295364,
0.02354682981967926,
0.01358900498598814,
-0.024223430082201958,
-0.0033030633348971605,
-0.005585239268839359,
0.053735069930553436,
0.007965072989463806,
-0.021888479590415955,
0.06414997577667236,
-0.03847457468509674,
-0.042220573872327805,
0.041037678718566895,
-0.002164758974686265,
-0.018721221014857292,
-0.0255103912204504,
-0.0008259293390437961,
-0.01563955284655094,
0.02818291448056698,
0.03218977898359299,
-0.023035956546664238,
-0.004408875480294228,
0.01804957538843155,
-0.015383360907435417,
0.03273412585258484,
-0.022568197920918465,
-0.013446523807942867,
0.031869176775217056,
-0.019044358283281326,
-0.057318441569805145,
0.048485543578863144,
-0.0024511865340173244,
0.018795432522892952,
0.036445774137973785,
-0.00203381828032434,
0.0011052796617150307,
-0.023849116638302803,
0.02579059638082981,
-0.05298515036702156,
-0.0015252201119437814,
0.017990803346037865,
0.05348575487732887,
-0.0014837076887488365,
-0.030294936150312424,
0.0071160816587507725,
-0.034427460283041,
0.00512412004172802,
0.01607532985508442,
-0.02781275287270546,
-0.07355383038520813,
-0.015304850414395332,
-0.008019767701625824,
-0.03182279318571091,
-0.024085717275738716,
-0.05926431342959404,
-0.06028259918093681,
0.027167899534106255,
0.018559344112873077,
0.023898696526885033,
-0.004974722862243652,
-0.04279275983572006,
-0.029052799567580223,
-0.062271200120449066,
0.009809705428779125,
-0.00750726880505681,
0.024240707978606224,
-0.04667600989341736,
-0.0016123679233714938,
-0.002348804846405983,
-0.012785062193870544,
0.027980739250779152,
0.016356511041522026,
-0.0005457700463011861,
0.030141564086079597,
0.017784491181373596,
0.03971744328737259,
-0.0355306938290596,
0.009458641521632671,
-0.039827171713113785,
-0.03517254441976547,
-0.012283711694180965,
-0.01928701624274254,
0.007970319129526615,
0.013223311863839626,
0.03981691971421242,
-0.044564057141542435,
0.0027620946057140827,
0.0430908277630806,
-0.0012828678591176867,
0.09259825199842453,
-0.04621849209070206,
-0.01000872254371643,
0.03816606476902962,
-0.012699369341135025,
0.026221562176942825,
0.029278209432959557,
-0.055551063269376755,
-0.027965165674686432,
0.030272452160716057,
-0.027814671397209167,
-0.03429149091243744,
0.011617301031947136,
0.029071366414427757,
-0.009955170564353466,
-0.02151334285736084,
0.002386481035500765,
0.023200951516628265,
-0.05423351377248764,
-0.002886441769078374,
0.03472869470715523,
0.012731121852993965,
0.0708065778017044,
-0.0023897788487374783,
0.020880745723843575,
0.0059937904588878155,
0.015186210162937641,
-0.030899319797754288,
0.04011912643909454,
0.05641167610883713,
-0.014500046148896217,
0.026425808668136597,
0.007369083818048239,
-0.04615865647792816,
0.010849937796592712,
-0.006138375960290432,
0.03976136073470116,
-0.038844186812639236,
-0.01908654347062111,
0.016957826912403107,
-0.006820676848292351,
-0.007973246276378632,
0.0018504266627132893,
0.01393901463598013,
0.0630773976445198,
-0.008984852582216263,
0.002547997049987316,
-0.04045569524168968,
0.0023306086659431458,
-0.011849929578602314,
-0.01797584816813469,
0.018657933920621872,
0.011624298058450222,
0.0016950786812230945,
0.010820209048688412,
-0.0077299028635025024,
0.025837138295173645,
0.02562892436981201,
-0.03854811564087868,
-0.013620587065815926,
-0.011071966029703617,
-0.0178404301404953,
-0.02231590449810028,
0.010971066541969776,
-0.03297317028045654,
-0.04273127764463425,
0.00787210650742054,
0.05598001182079315,
0.03531598672270775,
0.003379659028723836,
-0.062438856810331345,
-0.02790789306163788,
0.0676773339509964,
-0.018909720703959465,
-0.004778825677931309,
-0.04517155885696411,
0.04070602357387543,
-0.007500706240534782,
-0.005672731436789036
] |
<p>I'm wondering if there is more than the empty theory (no local fields, identically vanishing stress energy tensor) that can have central charge $c$ equals to $0$?</p>
<p>My intuition tells me no, the stress energy tensor would transform as a primary field and so would only contain primary fields but there are none except for the identity operator. So there could only be (topological) degrees of freedom on the boundary. Is this reasoning wrong?</p>
<p>ps: I'm only thinking at unitary theories, otherwise, sure it could be possible to combine in a balanced way fields carrying positive and negative central charge.</p> | 1,569 | [
-0.013704454526305199,
0.03774407133460045,
0.011190874502062798,
-0.00739963399246335,
0.022509997710585594,
-0.004141837824136019,
-0.05423899367451668,
-0.02739374339580536,
-0.005670181475579739,
-0.08919288963079453,
0.016592081636190414,
0.013543075881898403,
0.028805231675505638,
0.024720551446080208,
-0.017232675105333328,
0.018955601379275322,
-0.010073890909552574,
-0.014762014150619507,
-0.023883763700723648,
-0.03208976611495018,
0.012295045889914036,
0.06018767133355141,
0.02127055823802948,
0.03768230974674225,
0.005523237865418196,
0.010326656512916088,
-0.005578464362770319,
0.0052172476425766945,
0.027135808020830154,
0.07862809300422668,
-0.03386945277452469,
-0.03316260874271393,
-0.050941161811351776,
-0.007112130057066679,
0.00906831119209528,
-0.020089082419872284,
-0.016880450770258904,
-0.02344934642314911,
-0.005608130246400833,
-0.01513234805315733,
-0.024528896436095238,
-0.02515120804309845,
-0.010381584987044334,
0.06402088701725006,
-0.0068697878159582615,
-0.006261721719056368,
0.014298388734459877,
-0.0009617129690013826,
0.05545800179243088,
-0.041697002947330475,
0.04013267531991005,
-0.009130330756306648,
0.02965819276869297,
0.021811209619045258,
0.015169280581176281,
-0.024989569559693336,
0.053685855120420456,
0.035482823848724365,
0.0035612108185887337,
-0.011996911838650703,
-0.03130558133125305,
-0.002127988962456584,
-0.0044365874491631985,
-0.04230954498052597,
-0.026183640584349632,
0.027205316349864006,
0.007227058056741953,
-0.0004089805588591844,
0.020278021693229675,
-0.025201423093676567,
-0.03298049792647362,
0.03215232491493225,
0.012836731970310211,
-0.03279430791735649,
0.027073998004198074,
-0.015481087379157543,
0.011705332435667515,
0.018007544800639153,
0.011999376118183136,
0.018397172912955284,
-0.03949786722660065,
0.0035626825410872698,
0.002490515122190118,
0.04292423650622368,
0.0220225490629673,
0.0015603770734742284,
0.02617427334189415,
-0.013442695140838623,
0.007954319007694721,
0.03892374411225319,
-0.014059385284781456,
-0.04711326211690903,
0.023448320105671883,
-0.022644463926553726,
-0.05139956995844841,
0.024115461856126785,
0.035854894667863846,
0.056201547384262085,
0.004571089055389166,
-0.0017594877863302827,
-0.01085198950022459,
0.0013481809291988611,
0.01616435870528221,
0.07879523187875748,
0.025568371638655663,
-0.0007802587351761758,
-0.061933260411024094,
0.010790272615849972,
-0.019532931968569756,
0.009845015592873096,
-0.048414088785648346,
-0.02061912976205349,
-0.004868005868047476,
-0.034794896841049194,
-0.013558783568441868,
0.00024049948842730373,
0.01156429573893547,
-0.03732598200440407,
0.044131893664598465,
0.030490074306726456,
0.0715671107172966,
-0.021816551685333252,
0.009933003224432468,
-0.041459277272224426,
-0.10216376185417175,
-0.00917973555624485,
0.013975943438708782,
0.0006060347077436745,
-0.02645365707576275,
-0.008242293260991573,
0.0023500267416238785,
-0.003770349780097604,
-0.0061072735115885735,
0.024713413789868355,
0.05036880820989609,
-0.012183381244540215,
-0.10383234918117523,
-0.05337041988968849,
0.006568300537765026,
-0.057042770087718964,
-0.03139244392514229,
-0.051105402410030365,
-0.00891033187508583,
0.023562148213386536,
0.0618562251329422,
-0.03771660476922989,
-0.004660742823034525,
0.01639743521809578,
0.033088359981775284,
0.03520067781209946,
0.03899753838777542,
-0.020542312413454056,
-0.056864235550165176,
-0.04934794083237648,
-0.020766861736774445,
-0.07154114544391632,
0.03901029750704765,
0.00982596818357706,
0.0051391287706792355,
-0.013843439519405365,
0.07029184699058533,
-0.032215870916843414,
0.042257845401763916,
0.003694870276376605,
-0.014919954352080822,
-0.024047210812568665,
0.08648937940597534,
0.012857047840952873,
0.009518647566437721,
0.027140893042087555,
0.031253792345523834,
0.012544495053589344,
0.04265400767326355,
0.0460299514234066,
0.03230401501059532,
-0.035917069762945175,
-0.0028221486136317253,
0.0024528149515390396,
0.033855587244033813,
0.001249090302735567,
-0.01964685134589672,
0.01059652678668499,
-0.010101919062435627,
0.024536069482564926,
-0.04323999956250191,
0.05356890708208084,
-0.03265116736292839,
-0.014413991943001747,
-0.016200073063373566,
-0.022328078746795654,
0.0412055067718029,
-0.027009202167391777,
0.0051408265717327595,
0.018009793013334274,
-0.004956246819347143,
0.046487245708703995,
0.03445999696850777,
0.016770679503679276,
-0.05600115284323692,
-0.051963839679956436,
0.004554840736091137,
0.03370688483119011,
-0.01463478896766901,
0.011853685602545738,
0.053334154188632965,
-0.006894147489219904,
0.06841512769460678,
0.007972984574735165,
0.02667548507452011,
0.021667221561074257,
-0.016485953703522682,
0.030928611755371094,
-0.010316530242562294,
0.038616832345724106,
-0.010178674012422562,
0.016583796590566635,
-0.009718294255435467,
0.018460718914866447,
0.013363933190703392,
0.06859074532985687,
-0.005691448226571083,
0.041570764034986496,
0.0031490016262978315,
-0.006737211253494024,
0.020774461328983307,
0.06208857521414757,
0.018746068701148033,
0.014688060618937016,
-0.002516548614948988,
-0.02138553559780121,
-0.054914068430662155,
-0.009443116374313831,
0.03203615918755531,
0.017014937475323677,
-0.04801378399133682,
0.0185688603669405,
0.03029623255133629,
0.037557944655418396,
-0.0010561556555330753,
-0.013257316313683987,
-0.013614892959594727,
-0.05188659206032753,
0.040278978645801544,
0.03729835897684097,
0.030180638656020164,
-0.00620593037456274,
0.02721945010125637,
0.005474703852087259,
0.02355232462286949,
-0.0014422880485653877,
0.0010086611146107316,
0.010183245874941349,
-0.028001707047224045,
0.005155418999493122,
-0.0024963312316685915,
-0.018098080530762672,
0.02095646597445011,
0.001038702786900103,
0.08064529299736023,
0.051988109946250916,
-0.021987393498420715,
-0.0017134805675595999,
-0.008594896644353867,
0.015517765656113625,
0.02080877311527729,
-0.011779657565057278,
-0.019063521176576614,
0.009228921495378017,
0.019014084711670876,
-0.029796116054058075,
0.002406290965154767,
0.008816896937787533,
0.006992040202021599,
-0.012879830785095692,
0.012137212790548801,
0.045951053500175476,
-0.01048310101032257,
0.0545678585767746,
-0.032841186970472336,
-0.005477813072502613,
0.02992302179336548,
-0.01872050203382969,
0.014310059137642384,
0.0330871157348156,
-0.03437093272805214,
0.052787162363529205,
-0.09133048355579376,
-0.02821444720029831,
0.008451211266219616,
0.00345612782984972,
0.019938359037041664,
0.0288542527705431,
-0.04843471944332123,
-0.022102249786257744,
-0.012137717567384243,
-0.024348074570298195,
0.015129226259887218,
-0.045239198952913284,
-0.005279576871544123,
0.03780674561858177,
0.006563444621860981,
-0.04511484503746033,
-0.012845140881836414,
-0.01043945923447609,
-0.03899755701422691,
-0.009190719574689865,
-0.01446071732789278,
0.04897035285830498,
-0.04413381963968277,
0.05521794781088829,
0.012952864170074463,
-0.04683021456003189,
0.010681962594389915,
-0.03402483090758324,
-0.014102424494922161,
0.028203804045915604,
-0.020724929869174957,
0.04471585154533386,
-0.013522033579647541,
-0.04396546632051468,
0.05149756371974945,
0.017279159277677536,
-0.04286019876599312,
0.006953701842576265,
-0.020684512332081795,
-0.009166586212813854,
-0.0032360439654439688,
-0.019602354615926743,
0.02385691925883293,
-0.037817761301994324,
-0.017201576381921768,
0.04818737879395485,
0.03191237151622772,
-0.0181815717369318,
0.03188573196530342,
-0.018552230671048164,
0.03480622544884682,
0.01644282042980194,
0.006637199316173792,
0.05457514896988869,
-0.01601898856461048,
0.028199106454849243,
-0.012161221355199814,
0.009240955114364624,
0.019163642078638077,
0.00909299124032259,
-0.043048836290836334,
0.07789822667837143,
0.007969978265464306,
0.03165612742304802,
-0.009768419899046421,
0.002174502471461892,
0.025060048326849937,
-0.03384507820010185,
0.00048177162534557283,
0.03300895541906357,
0.021189630031585693,
-0.03476914390921593,
0.00039433574420399964,
-0.015825076028704643,
-0.0033928470220416784,
-0.04553304985165596,
-0.024628914892673492,
0.0005191013333387673,
0.005057767033576965,
0.013280578888952732,
-0.021694011986255646,
-0.039857007563114166,
0.013288711197674274,
0.0798095092177391,
0.05925022065639496,
0.03622877970337868,
-0.03928269073367119,
0.036183249205350876,
-0.034836363047361374,
0.00044993567280471325,
-0.0011366949183866382,
0.032661210745573044,
0.012195756658911705,
0.02306184358894825,
0.015029337257146835,
0.011021089740097523,
-0.007576529402285814,
0.009168090298771858,
-0.051669251173734665,
-0.018367093056440353,
-0.019960157573223114,
0.01430561114102602,
0.0009212582954205573,
-0.044707704335451126,
0.025718873366713524,
0.012347323819994926,
-0.04476553574204445,
-0.03129645437002182,
-0.02336084470152855,
-0.038886960595846176,
0.016050701960921288,
-0.013040795922279358,
-0.023332929238677025,
0.013496268540620804,
0.02887682430446148,
0.022415444254875183,
-0.038837678730487823,
-0.020295439288020134,
0.015105506405234337,
-0.006691440008580685,
-0.00019670250185299665,
-0.024971507489681244,
0.01710641011595726,
0.0071694557555019855,
0.021699903532862663,
0.049682728946208954,
0.018807068467140198,
-0.05280887708067894,
-0.03176910802721977,
0.03634270653128624,
0.07260365039110184,
-0.009598031640052795,
-0.06813175231218338,
-0.021573297679424286,
-0.0649438351392746,
-0.043990105390548706,
0.010582422837615013,
0.0668519139289856,
0.020604334771633148,
0.018901582807302475,
0.0267847441136837,
0.0107157276943326,
-0.02019302174448967,
0.029250647872686386,
0.0788278803229332,
0.01516101136803627,
-0.04827501252293587,
-0.03459235653281212,
0.018962658941745758,
-0.019545555114746094,
0.0013607157161459327,
0.006487340200692415,
-0.031509339809417725,
-0.021785369142889977,
-0.02528558112680912,
0.015000549145042896,
0.039190977811813354,
-0.023572873324155807,
-0.00479075126349926,
0.004295297898352146,
0.019767412915825844,
-0.013904599472880363,
-0.013880336657166481,
0.013962389901280403,
0.019523294642567635,
0.052808620035648346,
0.03334086388349533,
-0.029027000069618225,
-0.04217424988746643,
0.007296309806406498,
0.028312617912888527,
0.03614433482289314,
0.009880367666482925,
-0.02702360600233078,
-0.04712137207388878,
-0.004433279857039452,
0.022036941722035408,
-0.005800916347652674,
0.02519132010638714,
-0.013381632044911385,
0.010388367809355259,
0.01310762856155634,
-0.03615395352244377,
-0.02962520718574524,
0.0452737994492054,
-0.006281827110797167,
-0.004919146653264761,
-0.03349129483103752,
0.02808704972267151,
0.007582306396216154,
0.020168663933873177,
-0.013887481763958931,
0.028637517243623734,
-0.017533179372549057,
0.024988343939185143,
0.028656654059886932,
0.06053021550178528,
-0.006634866818785667,
-0.07100481539964676,
-0.016965970396995544,
0.016044529154896736,
0.009600856341421604,
0.02459678053855896,
-0.017586136236786842,
-0.047908008098602295,
-0.0007235395023599267,
0.01832909695804119,
-0.01219844352453947,
0.041528116911649704,
-0.03794132173061371,
0.0399371013045311,
0.020873498171567917,
-0.009927391074597836,
0.03438566252589226,
0.034805960953235626,
-0.009279433637857437,
-0.033120978623628616,
-0.03885374590754509,
0.02115315943956375,
-0.01919158361852169,
0.027592096477746964,
-0.02106817066669464,
0.025461135432124138,
-0.02714373916387558,
0.01467294804751873,
-0.043376218527555466,
-0.00850079394876957,
-0.006504912860691547,
-0.03279715031385422,
-0.01443620678037405,
-0.002928992034867406,
-0.014430807903409004,
0.0005254388670437038,
-0.01782490499317646,
0.006094413343816996,
-0.0029407022520899773,
-0.012334298342466354,
-0.012378837913274765,
0.00015023548621684313,
0.005690682679414749,
0.0011844368418678641,
-0.0004622923443093896,
0.025080103427171707,
-0.008982962928712368,
-0.012272745370864868,
-0.015239547938108444,
-0.06268631666898727,
0.061428993940353394,
-0.003050905652344227,
-0.02413870207965374,
-0.04298285394906998,
-0.014491673558950424,
-0.023055441677570343,
0.016918018460273743,
-0.007024729158729315,
0.016609277576208115,
-0.017669904977083206,
0.024177951738238335,
0.02728547714650631,
0.011296982876956463,
-0.06376687437295914,
-0.05320476368069649,
0.016639580950140953,
0.040435295552015305,
-0.0016212079208344221,
-0.03626985475420952,
-0.02259586565196514,
-0.00396346440538764,
-0.00265315780416131,
0.00036770847509615123,
0.06850384920835495,
-0.02186528407037258,
-0.0037166792899370193,
0.02252504788339138,
0.03224840387701988,
0.008799206465482712,
0.010894563049077988,
-0.0031931300181895494,
0.05024522915482521,
-0.028949152678251266,
-0.005615699104964733,
0.0011252142721787095,
0.06586412340402603,
-0.026328055188059807,
-0.023009900003671646,
0.0007989348378032446,
-0.02049281634390354,
0.05443606898188591,
-0.029219791293144226,
-0.03591761365532875,
0.022048193961381912,
0.021377118304371834,
-0.042165666818618774,
-0.012957456521689892,
-0.0035659917630255222,
-0.011443976312875748,
0.024877825751900673,
-0.010063772089779377,
0.019703760743141174,
-0.04836214706301689,
-0.08586889505386353,
0.0300289336591959,
-0.015460340306162834,
-0.009113440290093422,
-0.018606973811984062,
0.07175493240356445,
0.06240685284137726,
-0.03893539682030678,
-0.014510015025734901,
-0.021393831819295883,
-0.027081703767180443,
0.02194281667470932,
0.0004253365332260728,
0.010584353469312191,
-0.021801689639687538,
-0.032729700207710266,
-0.01981370337307453,
-0.02031835727393627,
0.033679161220788956,
0.04948312044143677,
0.01280718483030796,
0.040374573320150375,
0.019228188320994377,
-0.03035670518875122,
-0.025377808138728142,
0.0205078162252903,
-0.041511740535497665,
0.02362770587205887,
0.01956959068775177,
0.04204406589269638,
-0.03582136332988739,
-0.019692301750183105,
0.03261023387312889,
0.0464981310069561,
-0.015948308631777763,
0.05373749881982803,
0.025356030091643333,
0.0171500276774168,
0.020757976919412613,
-0.02703072875738144,
-0.06010621413588524,
0.051465246826410294,
-0.023048968985676765,
0.029001358896493912,
0.03995351865887642,
-0.019653111696243286,
0.012812015600502491,
0.008718053810298443,
0.03636355325579643,
-0.0027813727501779795,
-0.07228285819292068,
-0.05453484505414963,
0.03328092396259308,
-0.002959897043183446,
0.03615637868642807,
-0.06199636310338974,
-0.030521312728524208,
0.023199668154120445,
-0.0007884512306191027,
-0.001104844151996076,
0.007564187981188297,
-0.04602789506316185,
-0.038140881806612015,
-0.040584392845630646,
-0.021819625049829483,
0.040719516575336456,
0.00044044488458894193,
-0.016090501099824905,
0.03202606365084648,
-0.0021443685982376337,
0.04774470999836922,
0.002628948772326112,
0.031643085181713104,
0.0016783099854364991,
-0.006855552084743977,
0.021461840718984604,
0.018782246857881546,
-0.0324593186378479,
0.011599804274737835,
0.14303359389305115,
0.06557735055685043,
0.016645075753331184,
-0.07104408740997314,
-0.004078382160514593,
-0.01612675003707409,
-0.006447220221161842,
-0.033342644572257996,
0.07824007421731949,
-0.004109617322683334,
-0.0019042530329898,
-0.013748085126280785,
0.054780203849077225,
-0.01503503043204546,
-0.03577438369393349,
0.06166199594736099,
-0.015745222568511963,
-0.05292821675539017,
-0.045871105045080185,
0.04816385731101036,
-0.01586643047630787,
-0.010681111365556717,
-0.02420813776552677,
0.00872025452554226,
-0.007839350029826164,
0.04277391359210014,
-0.038318898528814316,
-0.02118643932044506,
0.03293348476290703,
0.011636040173470974,
-0.021614085882902145,
-0.008033440448343754,
-0.00459087872877717,
-0.012345967814326286,
-0.0707973912358284,
-0.027393614873290062,
0.04372056946158409,
-0.011156508699059486,
0.0028229213785380125,
0.008804047480225563,
-0.0030964172910898924,
0.01828484982252121,
0.01169853750616312,
0.008847112767398357,
-0.041549839079380035,
0.005669622682034969,
-0.006076702382415533,
0.025486670434474945,
-0.031033020466566086,
0.018972858786582947,
0.0064541795291006565,
-0.03553381934762001,
0.018788060173392296,
0.0014979204861447215,
-0.025305133312940598,
-0.02563617378473282,
0.03871748596429825,
0.02285999245941639,
0.018451295793056488,
-0.01876516081392765,
0.062091290950775146,
0.018715795129537582,
-0.03009156323969364,
0.006907446775585413,
-0.02978513389825821,
-0.0014229953521862626,
-0.02592291869223118,
0.05700726434588432,
0.02156238816678524,
-0.019829703494906425,
0.002556628780439496,
-0.03873228654265404,
-0.03718799352645874,
0.003284886246547103,
-0.014495635405182838,
0.020987331867218018,
0.07355368882417679,
0.006697687320411205,
-0.021190382540225983,
0.0030297045595943928,
-0.012391537427902222,
-0.01691499911248684,
-0.028178242966532707,
-0.0058739702217280865,
0.002932520816102624,
0.016013581305742264,
-0.0034169007558375597,
0.10408610850572586,
-0.020875193178653717,
-0.019955547526478767,
0.04485403001308441,
0.006742467172443867,
0.0010922093642875552,
0.001773074734956026,
-0.02132432721555233,
-0.028690900653600693,
-0.05725403130054474,
0.03962590545415878,
-0.008635036647319794,
-0.011228619143366814,
-0.002881679218262434,
-0.004396790638566017,
0.013692530803382397,
0.06090981513261795,
-0.005260665435343981,
0.0000777020541136153,
0.055686671286821365,
-0.05292384326457977,
0.028739038854837418,
0.037187617272138596,
0.032762762159109116,
-0.04419717192649841,
-0.07968539744615555,
-0.0017856884514912963,
0.00838578213006258,
-0.004579099826514721,
0.050543755292892456,
-0.048729050904512405,
-0.045391764491796494,
-0.0004020396445412189,
0.0007876959280110896,
-0.05235082656145096,
-0.002811231417581439,
-0.08003561198711395,
0.0020667517092078924,
0.030606316402554512,
-0.014486167579889297,
0.023314520716667175,
0.02476416528224945,
-0.016678418964147568,
-0.0055276211351156235,
0.0247870571911335,
0.0129398163408041,
-0.04370928555727005,
-0.0026837403420358896,
0.013705835677683353,
0.05705758556723595,
0.038317061960697174,
0.016646236181259155,
-0.010899651795625687,
0.02412792108952999,
-0.03618163987994194,
-0.04916516691446304,
0.015602190047502518,
-0.010358540341258049,
0.012960745953023434,
0.012604020535945892,
-0.008212911896407604,
-0.020236069336533546,
0.02865370735526085,
-0.0029171518981456757,
0.02444489300251007,
-0.0010002785129472613,
-0.017770741134881973,
-0.0008270941325463355,
-0.027094263583421707,
0.0440901517868042,
0.022115325555205345,
-0.011543949134647846,
0.012776680290699005,
0.007851776666939259,
0.00876596663147211,
-0.04718422517180443,
-0.009992913343012333,
-0.019236009567975998,
0.017450537532567978,
0.022877085953950882,
0.0267719067633152,
-0.020161591470241547,
0.031484171748161316,
-0.04492296278476715,
0.009534469805657864,
0.020885050296783447,
0.03519142419099808,
-0.0934491902589798,
-0.05761220306158066,
0.030089041218161583,
0.016709668561816216,
0.003918115980923176,
-0.016367217525839806,
0.015198756009340286,
0.002248126780614257,
-0.08145158737897873,
-0.000551114440895617,
-0.014448965899646282,
-0.021762581542134285,
-0.03186861053109169,
-0.0020287742372602224,
-0.06704233586788177,
0.011976741254329681,
0.03758925199508667,
0.06279972195625305,
-0.02046540379524231,
0.006127812433987856,
-0.0028749965131282806,
-0.00005021143442718312,
-0.04137032479047775,
-0.0066354419104754925,
0.011345353908836842,
-0.0008178339921869338,
0.050330936908721924,
-0.03383995592594147,
-0.03689943253993988,
0.020506583154201508,
-0.004031992983072996,
-0.0372283011674881,
-0.010744367726147175,
0.004333734046667814,
0.006457812152802944,
0.03251156583428383,
0.021849414333701134,
-0.020457327365875244,
-0.018505092710256577,
0.020286552608013153,
0.003754161298274994,
0.032477013766765594,
-0.020348943769931793,
-0.009711502119898796,
0.009546308778226376,
-0.0389949306845665,
-0.032211679965257645,
0.04847739264369011,
-0.0375327542424202,
-0.011221380904316902,
0.00312524545006454,
-0.015596074052155018,
0.009816030971705914,
-0.003079462330788374,
0.00001642348615860101,
-0.054206423461437225,
0.024210026487708092,
-0.00465438375249505,
0.014421443454921246,
-0.011800413951277733,
0.03610588237643242,
0.014171196147799492,
-0.0095469756051898,
0.03900410979986191,
0.04850924015045166,
-0.016802987083792686,
-0.02825438231229782,
-0.009636171162128448,
-0.013856885023415089,
-0.013390072621405125,
0.006771158892661333,
-0.04384010657668114,
-0.03687993064522743,
0.015896962955594063,
-0.0019656354561448097,
0.029977038502693176,
-0.004423148464411497,
-0.040783945471048355,
-0.0004273233935236931,
-0.0774114727973938,
0.017670035362243652,
-0.0035314939450472593,
0.059110842645168304,
-0.0050498503260314465,
-0.019903983920812607,
-0.016529850661754608,
-0.003618846880272031,
0.03856834024190903,
-0.013155248947441578,
-0.01530630886554718,
0.004937345627695322,
0.007672347128391266,
0.024699117988348007,
-0.02488107420504093,
-0.022340204566717148,
-0.0008527986938133836,
-0.02646377868950367,
-0.00885186716914177,
-0.012682156637310982,
-0.025592777878046036,
0.019645750522613525,
0.028493372723460197,
-0.021482225507497787,
-0.0319194458425045,
-0.03263898193836212,
-0.02301236242055893,
0.05309080705046654,
0.0059334347024559975,
0.01778385043144226,
0.09892117977142334,
0.0003669546276796609,
0.033013150095939636,
0.006997673772275448,
-0.044988419860601425,
0.020520959049463272,
0.03890427574515343,
-0.03250851854681969,
-0.03120729699730873,
-0.04236263409256935,
0.02587440051138401,
0.047183647751808167,
-0.0013724204618483782,
-0.001713962061330676,
0.05286842957139015,
-0.014348544180393219,
-0.019526811316609383,
0.0372641459107399,
0.00256158784031868,
0.03482743725180626,
0.03201742097735405,
-0.04441440477967262,
0.0265128742903471,
-0.004958990961313248,
0.03492940589785576,
0.022306187078356743,
0.015680989250540733,
0.011778511106967926,
-0.0054503995925188065,
0.020953461527824402,
-0.030679326504468918,
0.015400324948132038,
-0.012749830260872841,
0.018901821225881577,
-0.012296861968934536,
-0.009531567804515362,
0.03493642434477806,
0.005284197628498077,
0.04401347413659096,
-0.03321143984794617,
-0.02961118146777153,
0.07228389382362366,
0.010562260635197163,
0.012271955609321594,
-0.05831895023584366,
0.005655804183334112,
0.028629058972001076,
0.03028753772377968,
-0.0013308590278029442,
0.07434161007404327,
-0.047544438391923904,
-0.05135471001267433,
-0.03983144462108612,
-0.002266629133373499,
0.015583448112010956,
-0.03179037198424339,
0.01017528772354126,
0.005605998449027538,
0.016660962253808975,
0.016476992517709732,
-0.025658510625362396,
-0.0005217250436544418,
-0.02986178547143936,
0.004831874743103981,
0.047170836478471756,
0.049556657671928406,
-0.0013609539018943906,
-0.008959381841123104,
-0.03268839791417122,
0.03921221196651459,
0.0020544202998280525,
0.008657007478177547,
-0.027528295293450356,
0.0012332798214629292,
-0.004085997585207224,
-0.012449963949620724
] |
<p>Why does production of white light using a LED require combining a short wavelength LED such as blue or UV, and a yellow phosphor coating?</p>
<p>Why can't a single LED produce pure white light?</p> | 1,570 | [
-0.05738348141312599,
-0.0008178962743841112,
0.016133006662130356,
-0.0015025038737803698,
0.036183565855026245,
-0.023520171642303467,
-0.04628967493772507,
-0.02883615903556347,
0.0020721445325762033,
-0.00638652965426445,
0.043286699801683426,
0.03964260220527649,
0.03095335140824318,
0.028597097843885422,
0.0020211469382047653,
0.01846732385456562,
0.02310076542198658,
-0.0015207174001261592,
-0.027414731681346893,
-0.012897335924208164,
-0.04479160159826279,
0.009581711143255234,
0.026094775646924973,
0.010388368740677834,
-0.002592601114884019,
-0.020187873393297195,
0.03951223939657211,
0.026845859363675117,
0.05485935136675835,
0.036765191704034805,
-0.0027932189404964447,
-0.0016380335437133908,
-0.014854037202894688,
0.04451311007142067,
0.00484215933829546,
-0.0236646868288517,
-0.031116297468543053,
-0.014413072727620602,
-0.02555120550096035,
0.01650637947022915,
-0.005404348485171795,
0.01608462817966938,
-0.014136983081698418,
0.007600425276905298,
-0.013623619452118874,
0.0416388213634491,
-0.05110219866037369,
-0.018328910693526268,
0.05756795033812523,
-0.05657757818698883,
0.03337900713086128,
-0.021556107327342033,
0.0491415373980999,
0.02363717369735241,
-0.015605250373482704,
0.01722070202231407,
0.051060277968645096,
0.07018712162971497,
-0.012374704703688622,
0.003614873858168721,
0.0013527404516935349,
0.016277587041258812,
0.007969660684466362,
-0.015949970111250877,
-0.0364009253680706,
0.02480713464319706,
0.0003788647009059787,
-0.012159794569015503,
-0.018969766795635223,
0.02982425130903721,
0.034064438194036484,
-0.007749950513243675,
0.023484885692596436,
-0.008302913047373295,
-0.019701583310961723,
-0.02011769451200962,
0.012572801671922207,
0.025366606190800667,
0.026793213561177254,
0.01854073815047741,
-0.005452346056699753,
-0.016798727214336395,
-0.0001963214745046571,
0.009422007016837597,
0.002954314462840557,
-0.005895755719393492,
0.08834955096244812,
-0.007158529944717884,
0.01692076213657856,
-0.0035742581821978092,
0.012181857600808144,
0.04169578477740288,
0.07091333717107773,
0.057739607989788055,
-0.010153945535421371,
0.02493423968553543,
-0.019955622032284737,
0.034402694553136826,
0.0013333925744518638,
-0.0068535758182406425,
0.021355364471673965,
-0.007203663233667612,
0.06013266369700432,
0.02740621194243431,
-0.013227125629782677,
-0.026081640273332596,
0.020126158371567726,
0.0032337584998458624,
0.01961292326450348,
0.0047582038678228855,
-0.06538497656583786,
-0.021701307967305183,
0.0031302180141210556,
0.0023419945500791073,
-0.017849307507276535,
0.010471954941749573,
-0.00734684756025672,
0.016332903876900673,
0.051281049847602844,
0.05238361656665802,
-0.014077737927436829,
-0.02272142842411995,
-0.002499606227502227,
-0.021576374769210815,
-0.0730421170592308,
0.005928459577262402,
-0.05925971269607544,
-0.0019962626975029707,
-0.03895648568868637,
0.014823513105511665,
0.03568844869732857,
-0.024441972374916077,
0.013602950610220432,
0.01654154807329178,
0.009611108340322971,
-0.03033750131726265,
-0.09846422076225281,
-0.07544714957475662,
0.021371429786086082,
-0.01862306147813797,
-0.002552771009504795,
-0.0742248073220253,
0.021493129432201385,
0.00995282456278801,
0.06383414566516876,
-0.01120498776435852,
-0.001962358830496669,
-0.0066644586622715,
0.008796675130724907,
-0.034139033406972885,
-0.0029494718182832003,
-0.035250935703516006,
0.02440246008336544,
-0.02582174725830555,
0.03878839686512947,
-0.07888202369213104,
0.02992071397602558,
0.030592795461416245,
-0.008603857830166817,
-0.04717929661273956,
0.026087502017617226,
-0.017221124842762947,
0.003607511054724455,
0.03410138562321663,
0.04333677142858505,
-0.04124101623892784,
0.04028525948524475,
0.01167318969964981,
0.019057754427194595,
0.058134522289037704,
-0.023926973342895508,
0.023387756198644638,
-0.01360023207962513,
0.02620062418282032,
-0.012595185078680515,
-0.028878744691610336,
-0.023888923227787018,
-0.0029063161928206682,
0.06245042011141777,
-0.015374732203781605,
-0.05226511135697365,
-0.027786632999777794,
-0.015552745200693607,
0.036092452704906464,
0.024578507989645004,
0.03729523718357086,
-0.009287528693675995,
-0.0012817314127460122,
-0.008920013904571533,
-0.05628183111548424,
-0.021024420857429504,
-0.04223870486021042,
-0.016997266560792923,
0.010035389102995396,
-0.03432353213429451,
0.015501673333346844,
-0.009009310975670815,
0.04008954018354416,
0.017839990556240082,
-0.02310372330248356,
-0.04354086145758629,
-0.00362952146679163,
0.023378746584057808,
0.006306941621005535,
0.044095683842897415,
0.053089071065187454,
0.04705357551574707,
0.0022958212066441774,
0.04214297980070114,
-0.03028522990643978,
-0.04888732358813286,
0.002277282765135169,
-0.02721782959997654,
0.034998819231987,
-0.01220741681754589,
0.013033319264650345,
0.005478691775351763,
0.0018997736042365432,
0.005288140848278999,
0.039427924901247025,
-0.00019310216885060072,
0.0771242305636406,
0.05770958587527275,
-0.044106028974056244,
-0.016039205715060234,
0.025496741756796837,
0.017635837197303772,
-0.0033805666025727987,
0.006737754680216312,
-0.031643908470869064,
-0.055188681930303574,
0.00964668020606041,
0.03520110249519348,
0.006948326248675585,
-0.031401291489601135,
0.030725611373782158,
0.006752087268978357,
0.044134825468063354,
0.00856701098382473,
0.04689465090632439,
-0.004931304603815079,
-0.016491036862134933,
0.04893708601593971,
0.03756562992930412,
-0.01867029257118702,
0.02621864341199398,
0.011132070794701576,
0.008835367858409882,
0.04177342355251312,
-0.018546035513281822,
-0.03605007380247116,
0.048978693783283234,
-0.05059420317411423,
-0.008126279339194298,
0.0038912207819521427,
-0.028936251997947693,
0.03383553400635719,
-0.04571790620684624,
0.03377050906419754,
0.02886820212006569,
-0.007573307957500219,
0.026280468329787254,
0.0015290084993466735,
-0.0489497147500515,
0.020407160744071007,
0.020664479583501816,
-0.048252735286951065,
-0.0038478735368698835,
0.03700445219874382,
-0.033873628824949265,
0.03319038450717926,
-0.03957636281847954,
-0.017308354377746582,
-0.034929607063531876,
-0.01445081178098917,
0.04240201413631439,
-0.0004589335585478693,
0.04124194011092186,
-0.08428943902254105,
-0.06100614368915558,
-0.0029860485810786486,
-0.03766583278775215,
-0.0158291794359684,
0.0008954143850132823,
-0.026813870295882225,
0.012882492505013943,
-0.016374018043279648,
-0.031422749161720276,
-0.010146541520953178,
-0.021643882617354393,
-0.0034582840744405985,
0.0058182720094919205,
0.004087056498974562,
-0.05058520287275314,
-0.040298014879226685,
-0.015114580281078815,
0.016867289319634438,
0.002268592594191432,
0.0020381200592964888,
0.008010465651750565,
-0.015391414053738117,
-0.06386569142341614,
-0.013073127716779709,
-0.03976942226290703,
-0.03486541286110878,
0.016933484002947807,
-0.01972733624279499,
0.02746136114001274,
-0.050493597984313965,
0.024673787876963615,
0.02558574080467224,
-0.04726409912109375,
-0.014744480140507221,
-0.017656613141298294,
-0.04130563512444496,
-0.006908084265887737,
-0.004555013496428728,
0.03876946493983269,
-0.0038885020185261965,
0.01168789528310299,
0.07495004683732986,
0.015924671664834023,
-0.003257506061345339,
-0.05608443170785904,
-0.049499914050102234,
-0.03508037328720093,
-0.06252951174974442,
0.021724548190832138,
0.04550184682011604,
-0.016215309500694275,
0.020327460020780563,
0.0008474913774989545,
-0.002798275323584676,
0.0499577522277832,
0.026702584698796272,
-0.0068692052736878395,
-0.008566157892346382,
0.008032482117414474,
-0.00753110321238637,
-0.012469692155718803,
0.0013298304984346032,
-0.027130387723445892,
-0.003114169230684638,
0.02154114842414856,
0.053099870681762695,
-0.001630238490179181,
-0.03799610212445259,
0.05527111142873764,
-0.0032032120507210493,
0.013089289888739586,
-0.08918846398591995,
0.01670638658106327,
0.03568543866276741,
0.0011786590330302715,
0.009320548735558987,
0.008161825127899647,
0.049305401742458344,
-0.03924424573779106,
-0.013889176771044731,
0.040936704725027084,
0.05254796892404556,
0.0003192867443431169,
-0.030253693461418152,
0.027602482587099075,
0.006871599238365889,
-0.0020915172062814236,
0.010150857269763947,
-0.0015326517168432474,
0.03702498972415924,
0.04806150496006012,
0.052858997136354446,
-0.0012133775744587183,
-0.005897440481930971,
-0.026785647496581078,
-0.06973277032375336,
0.006528270430862904,
-0.02050826884806156,
0.04012082889676094,
0.013274514116346836,
0.057594750076532364,
0.032643985003232956,
0.009237905032932758,
-0.024911990389227867,
-0.010671189054846764,
-0.10701694339513779,
0.03368663787841797,
-0.029438655823469162,
0.02293775975704193,
-0.038243748247623444,
-0.02636941522359848,
-0.012154297903180122,
-0.03760209307074547,
-0.04649459570646286,
-0.02294815145432949,
0.02062065899372101,
-0.00242786668241024,
-0.007393747568130493,
0.0013351746601983905,
-0.04858431965112686,
-0.01928791031241417,
0.0027778244111686945,
0.004025301430374384,
0.016146773472428322,
0.009972959756851196,
0.019952550530433655,
-0.02660088613629341,
0.0005223069456405938,
-0.011876452714204788,
0.053039681166410446,
-0.02343725599348545,
0.029659001156687737,
0.01944670081138611,
0.08983449637889862,
-0.016290340572595596,
-0.016280772164463997,
0.034260064363479614,
0.0471372976899147,
-0.0008161237346939743,
-0.013933978974819183,
-0.030092759057879448,
-0.06973978132009506,
-0.004335321951657534,
0.058892883360385895,
0.02327018417418003,
-0.0202205590903759,
0.012809217907488346,
0.04536648094654083,
-0.0008100456325337291,
-0.004515166860073805,
0.02382591925561428,
0.02485894039273262,
-0.00986823346465826,
-0.007075245957821608,
-0.021343911066651344,
-0.007489009294658899,
0.001407019211910665,
0.03555398806929588,
0.03421257063746452,
0.008515158668160439,
-0.00047702324809506536,
-0.026311853900551796,
0.011012660339474678,
0.000592652999330312,
-0.025309531018137932,
0.008360461331903934,
-0.01596129685640335,
0.006270917132496834,
0.029644036665558815,
-0.005015807691961527,
-0.022441009059548378,
0.05328873172402382,
0.008992725983262062,
0.021149901673197746,
-0.029375141486525536,
-0.07717497646808624,
-0.013750545680522919,
0.02062610536813736,
0.046153951436281204,
-0.0017245610943064094,
-0.01740008033812046,
-0.06677460670471191,
-0.03200526535511017,
0.009314822033047676,
-0.0046219672076404095,
0.028284626081585884,
-0.028406508266925812,
-0.005422038026154041,
0.005423517897725105,
-0.031062737107276917,
-0.01411385927349329,
0.024565236642956734,
0.004567897412925959,
0.025777768343687057,
-0.009301016107201576,
-0.036021359264850616,
-0.001184548600576818,
0.03789660707116127,
0.03763771802186966,
0.058066826313734055,
-0.023376479744911194,
0.0002555485116317868,
0.012533146888017654,
0.02944863960146904,
0.005300094373524189,
-0.08931495249271393,
-0.007762507535517216,
0.019071955233812332,
-0.00014008569996804,
0.03641633689403534,
-0.041510310024023056,
-0.07334265112876892,
0.058530282229185104,
0.05404367670416832,
-0.022322768345475197,
-0.010465173982083797,
-0.013720729388296604,
-0.003495060373097658,
0.02089339680969715,
-0.0008210192900151014,
0.05687955021858215,
0.0063612493686378,
-0.040074221789836884,
-0.008062341250479221,
-0.016444770619273186,
0.04830120503902435,
-0.058808259665966034,
0.004506814293563366,
0.0010844864882528782,
-0.009508742950856686,
0.008016989566385746,
0.07986431568861008,
0.016943149268627167,
-0.007041578646749258,
0.012206971645355225,
-0.05379164218902588,
-0.0026962319388985634,
0.02060154266655445,
-0.01654108054935932,
-0.027604490518569946,
-0.007895142771303654,
0.03615332394838333,
0.028184883296489716,
0.022530987858772278,
0.01611950807273388,
-0.006038866005837917,
0.021883225068449974,
0.006921546999365091,
0.025532161816954613,
0.029070822522044182,
-0.034613631665706635,
0.010910139419138432,
-0.006817518267780542,
-0.0210603978484869,
0.059726130217313766,
0.004764200188219547,
0.05839875712990761,
0.052034247666597366,
-0.0765671581029892,
-0.01743055135011673,
-0.004720525816082954,
-0.0007033756701275706,
0.04450063034892082,
-0.047642216086387634,
0.04272497817873955,
-0.002249294426292181,
-0.00972004421055317,
-0.06472311913967133,
-0.037772588431835175,
-0.005293561145663261,
0.05750375986099243,
0.004251550883054733,
-0.04939347505569458,
0.007268805522471666,
-0.005895982496440411,
0.0020231541711837053,
0.0034232386387884617,
-0.021414589136838913,
-0.009115951135754585,
-0.013339975848793983,
-0.0005485399160534143,
0.00269686128012836,
0.0027455417439341545,
0.008289927616715431,
-0.01186345610767603,
-0.00922202505171299,
-0.04671896994113922,
-0.013584866188466549,
-0.01847253181040287,
0.034849632531404495,
-0.011684886179864407,
-0.04945734888315201,
0.016517220064997673,
-0.010511981323361397,
0.04439099505543709,
-0.03221617639064789,
-0.007681469898670912,
0.02905326336622238,
0.05490444228053093,
-0.048272136598825455,
-0.021608207374811172,
0.03651488944888115,
0.01947813108563423,
0.0300902146846056,
0.026927556842565536,
-0.010337530635297298,
-0.04113808274269104,
-0.018321579322218895,
0.03839520364999771,
0.000251323013799265,
0.015196661464869976,
-0.009997241199016571,
0.07444899529218674,
-0.017835838720202446,
0.0005932916537858546,
0.011706412769854069,
-0.009069298394024372,
0.02113313414156437,
-0.04076237231492996,
0.026580769568681717,
0.0298654492944479,
-0.00019919047190342098,
-0.011806356720626354,
-0.023912843316793442,
0.005579244811087847,
-0.0013860899489372969,
0.035815462470054626,
-0.02692249044775963,
0.03859400004148483,
0.015075079165399075,
-0.010060558095574379,
-0.01981409266591072,
-0.03541862592101097,
-0.017650427296757698,
-0.01054801419377327,
-0.016074271872639656,
0.043717220425605774,
-0.0026939453091472387,
-0.04164166375994682,
0.01760653406381607,
0.046456534415483475,
0.027595531195402145,
0.0013414928689599037,
0.08295725286006927,
0.01732255518436432,
0.005068812519311905,
-0.02606271021068096,
-0.0440979078412056,
0.04742096737027168,
-0.018405549228191376,
0.010730861686170101,
-0.01153702475130558,
-0.012871215119957924,
0.043656814843416214,
-0.0571647509932518,
-0.002363990293815732,
-0.028719985857605934,
-0.003526488784700632,
-0.025573164224624634,
0.02518194541335106,
0.013941050507128239,
0.0031669081654399633,
0.004862253088504076,
-0.013956788927316666,
0.011729568243026733,
0.0291894618421793,
0.011659529991447926,
-0.03953887149691582,
-0.06053038313984871,
-0.07061991095542908,
-0.024318544194102287,
-0.01086670346558094,
0.021839715540409088,
-0.027059253305196762,
-0.016593454405665398,
0.0087441923096776,
-0.02283027581870556,
0.012152262963354588,
-0.015465600416064262,
0.053077127784490585,
0.006469159387052059,
-0.0280588548630476,
0.02534654550254345,
0.08206041902303696,
-0.015687210485339165,
0.022922683507204056,
0.14388811588287354,
0.026523282751441002,
-0.0005245771608315408,
-0.06180454418063164,
-0.005188088398426771,
-0.03284623846411705,
-0.004553601611405611,
-0.014567219652235508,
0.032253000885248184,
-0.0009288059081882238,
0.045845694839954376,
0.005703749600797892,
0.05363031476736069,
-0.010740835219621658,
-0.0067497724667191505,
0.0182237196713686,
-0.037924300879240036,
-0.028865156695246696,
0.025935878977179527,
0.0007026849780231714,
-0.000017019630831782706,
0.02867194265127182,
-0.0425700880587101,
-0.01588258147239685,
-0.021680710837244987,
-0.042854782193899155,
0.003954843617975712,
-0.019793402403593063,
0.04830745980143547,
0.004120392259210348,
-0.03149523586034775,
-0.00397955346852541,
0.03098595328629017,
-0.0158089492470026,
-0.03695196658372879,
0.03339168056845665,
0.02150895819067955,
-0.008037412539124489,
0.022558515891432762,
0.009590765461325645,
0.04654546454548836,
-0.03098495677113533,
0.006303115747869015,
-0.006220977753400803,
-0.042284026741981506,
-0.0016611486207693815,
-0.010359521023929119,
0.021981460973620415,
-0.0334172397851944,
0.03826627507805824,
-0.0074958172626793385,
-0.029626142233610153,
0.003379669040441513,
-0.041997309774160385,
0.007322587538510561,
0.005511509254574776,
0.033650655299425125,
-0.03944573178887367,
-0.021922091022133827,
0.0029644083697348833,
0.02116016484797001,
-0.0031336776446551085,
0.008513297885656357,
0.017159616574645042,
0.019074374809861183,
0.007930727675557137,
0.0254841186106205,
0.014979793690145016,
0.02375750243663788,
-0.045551784336566925,
-0.037068404257297516,
0.011317462660372257,
-0.03451235964894295,
-0.03221244737505913,
0.027769487351179123,
0.009977436624467373,
0.019347339868545532,
-0.003683156566694379,
-0.005577919539064169,
-0.02738242782652378,
-0.07740338146686554,
0.0419779010117054,
0.03609062731266022,
-0.04185349866747856,
-0.0013195191277191043,
-0.010490676388144493,
0.05177145451307297,
0.04366472363471985,
-0.0013559645740315318,
0.012926879338920116,
-0.006492401007562876,
0.04176051542162895,
0.02062530256807804,
-0.01618671976029873,
-0.03540678694844246,
0.023162707686424255,
-0.007147186901420355,
0.005760082975029945,
-0.019988704472780228,
0.007134623359888792,
-0.00461536506190896,
0.035362064838409424,
0.023554880172014236,
0.011849273927509785,
-0.0445878766477108,
-0.016709070652723312,
0.010075747966766357,
-0.007355656940490007,
0.0003308819723315537,
0.009919809177517891,
0.033837903290987015,
-0.008937411941587925,
-0.06279632449150085,
-0.01934005506336689,
-0.020257504656910896,
0.05764227733016014,
0.024268342182040215,
0.007928051054477692,
-0.010834718123078346,
0.010009466670453548,
0.05192670226097107,
-0.021239740774035454,
-0.01874229870736599,
-0.030716225504875183,
0.01369657926261425,
-0.02494172751903534,
-0.015188006684184074,
0.01767301745712757,
0.020409537479281425,
0.003494186792522669,
0.001898562884889543,
0.04489506408572197,
0.05037250369787216,
-0.005676828324794769,
0.03147817403078079,
0.002727607963606715,
0.013076046481728554,
0.03778151050209999,
-0.009172757156193256,
-0.04151185229420662,
0.04613181948661804,
-0.0025332856457680464,
-0.06787528842687607,
0.004113831557333469,
-0.02827494405210018,
0.04713812470436096,
0.02657151408493519,
-0.032785266637802124,
-0.007010601460933685,
0.05200664699077606,
-0.0030716843903064728,
-0.03640032932162285,
0.015996750444173813,
0.012086782604455948,
0.01648331992328167,
0.01206023246049881,
-0.031214671209454536,
-0.03714124485850334,
0.005139480344951153,
0.05298447608947754,
-0.0011690042447298765,
-0.0023547890596091747,
-0.0070688193663954735,
-0.016062898561358452,
0.014640855602920055,
0.035667646676301956,
0.04223771020770073,
0.03964463248848915,
-0.0009363822173327208,
0.0022965753450989723,
0.00665071327239275,
0.03170542046427727,
-0.0068276370875537395,
-0.015199088491499424,
-0.10060180723667145,
-0.015769071877002716,
-0.01840919815003872,
-0.02516387216746807,
-0.011303703300654888,
-0.038169313222169876,
0.02127167209982872,
0.008898314088582993,
-0.10526007413864136,
-0.026872947812080383,
-0.01803784817457199,
-0.03895992785692215,
-0.04132603108882904,
0.01190864946693182,
-0.017160097137093544,
0.03484654799103737,
0.033520717173814774,
0.07060764729976654,
-0.01631145551800728,
0.013905050233006477,
-0.011434752494096756,
-0.008950533345341682,
-0.00981198064982891,
0.004341976251453161,
-0.02608432248234749,
-0.0032479127403348684,
0.06946275383234024,
-0.021967533975839615,
0.01294216513633728,
-0.01937570422887802,
-0.011919091455638409,
0.018881844356656075,
0.01241016574203968,
0.004752211272716522,
-0.013163176365196705,
0.0068326774053275585,
0.01886393316090107,
-0.012349627912044525,
-0.038673777133226395,
0.012582008726894855,
0.04210595414042473,
0.006657836958765984,
0.0008493588538840413,
-0.016444914042949677,
0.02469225786626339,
-0.03212061524391174,
-0.0536152645945549,
0.0023702478501945734,
-0.02972920797765255,
-0.017115393653512,
0.027418138459324837,
0.06446985900402069,
0.02948164939880371,
-0.034300319850444794,
-0.013165113516151905,
-0.06073644012212753,
-0.03587684407830238,
-0.012166380882263184,
0.04262138903141022,
-0.002894841367378831,
0.01079093012958765,
-0.01651703752577305,
-0.030126549303531647,
0.016883784905076027,
0.0061370874755084515,
0.009253038093447685,
-0.03859037160873413,
0.02594263292849064,
0.03363792225718498,
0.008645189926028252,
0.030034717172384262,
-0.005728831514716148,
-0.05522996187210083,
0.01578247919678688,
-0.0325540266931057,
0.043163273483514786,
-0.010093389078974724,
-0.0689418762922287,
-0.022242333739995956,
-0.041206300258636475,
0.05949186161160469,
0.007937705144286156,
-0.009219751693308353,
-0.04552079364657402,
-0.039299048483371735,
-0.011137280613183975,
0.02738862670958042,
0.05835457518696785,
0.025146735832095146,
-0.02552812546491623,
0.012523575685918331,
0.03962911292910576,
0.024994170293211937,
-0.01935199275612831,
0.03663722425699234,
0.0009545303182676435,
0.003048157086595893,
-0.05581730231642723,
-0.013106749393045902,
-0.029245885089039803,
-0.0059450361877679825,
0.02184026502072811,
-0.009295988827943802,
-0.015993960201740265,
-0.009341331198811531,
-0.007090530823916197,
0.07355093955993652,
-0.02533038705587387,
-0.022700155153870583,
0.06499481201171875,
-0.006120122969150543,
0.019034020602703094,
0.027228616178035736,
-0.007195527199655771,
-0.07710348814725876,
0.022854769602417946,
-0.020181309431791306,
0.0028757192194461823,
-0.018088987097144127,
0.005508683156222105,
0.05216280743479729,
-0.04755190759897232,
0.019881175830960274,
-0.021603107452392578,
-0.006958506070077419,
-0.015221123583614826,
0.06494472175836563,
0.005679478403180838,
0.03714023530483246,
-0.004178657196462154,
-0.016555678099393845,
-0.005986613687127829,
0.04675593972206116,
-0.013285821303725243,
0.027150413021445274,
-0.023346493020653725,
0.008089606650173664,
0.04228239506483078,
0.005057479254901409,
0.023302597925066948,
0.016383841633796692,
0.00015231201541610062,
0.03447150066494942,
-0.020416637882590294,
-0.039381805807352066,
0.014552673324942589,
0.008725897409021854,
0.0007633026689291,
0.03012809343636036,
-0.01025341171771288,
0.09042249619960785,
-0.024882571771740913,
0.027903109788894653,
-0.020272811874747276,
0.0031793417874723673,
-0.02662580832839012,
0.02181665413081646,
0.006762530189007521,
0.06352443993091583,
0.001663824892602861,
-0.017904264852404594,
-0.042258121073246,
-0.009372641332447529,
0.018128566443920135,
-0.03860370069742203,
0.026790818199515343,
0.01923319511115551,
-0.02706044353544712,
0.009941763244569302,
-0.012276224792003632,
-0.0034504125360399485,
-0.030907191336154938,
-0.01068838033825159,
0.05260481685400009,
0.006987841334193945,
0.013672754168510437,
0.0035843083169311285,
-0.03157951310276985,
0.03617256134748459,
-0.046790190041065216,
-0.029334258288145065,
-0.0133201964199543,
-0.02127612754702568,
-0.03891666606068611,
-0.003850402543321252
] |
<p>Suppose you have a U tube filled with a liquid. The height of the liquid column in both the arms of the U tube is not the same. Will the pressure be the same at two points in the two arms of the U tube which are at the same height from the base of the U tube or will it vary depending on height of liquid column above these two points?</p> | 1,571 | [
-0.0006160929333418608,
-0.0274746585637331,
-0.03465903922915459,
-0.04010254889726639,
0.01970701292157173,
-0.0074242474511265755,
0.005055525805801153,
-0.041686881333589554,
0.02566174790263176,
-0.03070090524852276,
0.044543687254190445,
0.025914477184414864,
0.05761270225048065,
-0.044870611280202866,
0.00966363213956356,
0.028087304905056953,
-0.0020238638389855623,
-0.008975229226052761,
0.011168355122208595,
-0.00864436849951744,
-0.009866411797702312,
0.015744538977742195,
-0.0002903193235397339,
-0.008672170341014862,
-0.03622919321060181,
0.053191110491752625,
0.032869454473257065,
-0.014050643891096115,
0.02272413671016693,
0.03121638484299183,
-0.015650954097509384,
-0.004457689821720123,
-0.005696147680282593,
0.057314299046993256,
0.06407530605792999,
0.016260121017694473,
-0.045759085565805435,
-0.023387368768453598,
-0.06293999403715134,
0.03366157412528992,
-0.0051345969550311565,
-0.03557949885725975,
0.006301534827798605,
0.008176584728062153,
-0.024880560114979744,
0.03890136256814003,
0.02397257648408413,
-0.02865707315504551,
0.029372552409768105,
-0.06220414489507675,
0.013844774104654789,
-0.0027263308875262737,
0.02487960085272789,
0.06025839224457741,
-0.012376510538160801,
0.008041110821068287,
0.058285050094127655,
0.03845972940325737,
-0.032492414116859436,
-0.04262406378984451,
0.005945257842540741,
0.04996342584490776,
-0.012002077884972095,
-0.0142538882791996,
-0.026934782043099403,
0.03019934706389904,
-0.023274432867765427,
-0.026791445910930634,
-0.008764753118157387,
-0.0254837479442358,
-0.012283096089959145,
0.008023478090763092,
0.024052487686276436,
-0.028419729322195053,
0.03337838500738144,
-0.041790351271629333,
0.007773421239107847,
0.020937345921993256,
0.010060442611575127,
0.036845576018095016,
0.0011010970920324326,
0.02772482857108116,
0.04875202849507332,
0.016223110258579254,
-0.02762993983924389,
-0.01769864559173584,
0.033156171441078186,
0.022715900093317032,
-0.0010661169653758407,
0.06789358705282211,
-0.01897633820772171,
0.018927834928035736,
0.008171243593096733,
-0.007931205444037914,
0.018437357619404793,
-0.020694226026535034,
-0.018301883712410927,
0.04812506213784218,
0.01626117341220379,
-0.021183501929044724,
0.06509359925985336,
-0.0229649655520916,
0.005746978335082531,
0.11217324435710907,
0.03287019208073616,
-0.049521636217832565,
-0.018755724653601646,
-0.0013894655276089907,
-0.017527597025036812,
-0.007206520065665245,
-0.03107207454741001,
-0.0185996163636446,
-0.03232673555612564,
-0.011394675821065903,
0.005297685973346233,
-0.013181312941014767,
0.02418648824095726,
-0.013757463544607162,
0.04658704251050949,
0.031080329790711403,
0.05046989023685455,
-0.018345508724451065,
0.03796100243926048,
0.015112767927348614,
-0.07524164766073227,
0.014242099598050117,
0.009157348424196243,
-0.02019253559410572,
-0.06041640788316727,
0.029305804520845413,
-0.007484209258109331,
0.026888489723205566,
-0.02194380573928356,
0.008611425757408142,
0.0659860372543335,
0.024746941402554512,
-0.11142301559448242,
-0.05826324224472046,
0.014865756966173649,
-0.012977496720850468,
-0.026866978034377098,
-0.049464765936136246,
0.020322149619460106,
0.030688945204019547,
0.06435514986515045,
-0.009259344078600407,
-0.018243422731757164,
-0.012794050388038158,
0.022254126146435738,
0.011866860091686249,
0.01658915914595127,
0.01242621336132288,
-0.02945280633866787,
-0.05418120697140694,
0.028267541900277138,
-0.06477337330579758,
0.030699867755174637,
0.03495199233293533,
-0.009123134426772594,
-0.008915979415178299,
0.05753167346119881,
-0.04226093739271164,
0.031187212094664574,
-0.02510720118880272,
-0.013292423449456692,
-0.02130158618092537,
0.031034313142299652,
0.009934395551681519,
-0.01477509830147028,
0.030756182968616486,
0.00029670351068489254,
0.030392566695809364,
-0.032194700092077255,
-0.003778052981942892,
0.06001690775156021,
-0.014167950488626957,
-0.008862699382007122,
-0.04307575151324272,
0.0487588606774807,
0.039912622421979904,
-0.03256479278206825,
-0.0325818695127964,
-0.023230478167533875,
0.0011820930521935225,
-0.010136695578694344,
0.03603144735097885,
0.008410665206611156,
0.0045919278636574745,
0.002741912379860878,
-0.028782030567526817,
-0.004997356794774532,
-0.059890203177928925,
0.029720401391386986,
-0.052094005048274994,
-0.0005708369426429272,
0.013180802576243877,
0.030671052634716034,
-0.005512559320777655,
-0.06614196300506592,
-0.021824168041348457,
0.015684276819229126,
0.032395679503679276,
0.03455120325088501,
0.0028757068794220686,
0.03171258047223091,
0.040506262332201004,
0.02666397951543331,
0.008258228190243244,
0.04512786865234375,
-0.030629131942987442,
-0.00824176985770464,
0.0459350124001503,
-0.005555715411901474,
0.01460025180131197,
-0.006359801162034273,
0.02223065495491028,
0.0007356880814768374,
0.010794914327561855,
0.00953839160501957,
0.043335262686014175,
-0.08370529115200043,
0.0888122171163559,
0.09128357470035553,
-0.0065940264612436295,
0.04105484113097191,
-0.002337565878406167,
0.013411631807684898,
0.036470577120780945,
0.020834214985370636,
-0.02989473007619381,
-0.046490754932165146,
0.0011199899017810822,
0.014480083249509335,
0.009740441106259823,
-0.021609317511320114,
-0.007912901230156422,
0.05434797704219818,
0.0026114564388990402,
0.03645873814821243,
0.03095097281038761,
-0.010583518072962761,
-0.05544115975499153,
0.009101212956011295,
0.05613717436790466,
0.006174846086651087,
-0.014313668012619019,
0.02329716458916664,
0.05209895968437195,
0.03627108782529831,
-0.04305942729115486,
0.0013991894666105509,
0.007907610386610031,
-0.006849297322332859,
-0.00508270924910903,
-0.018129535019397736,
-0.010587919503450394,
0.03521279618144035,
-0.02522936463356018,
0.0016638505039736629,
0.021660741418600082,
-0.022871343418955803,
-0.018256885930895805,
-0.027526861056685448,
0.008814861997961998,
0.0197402685880661,
0.032348137348890305,
-0.045996375381946564,
-0.017107412219047546,
0.026674814522266388,
-0.028501585125923157,
-0.005084725562483072,
-0.06903842091560364,
-0.0037622738163918257,
-0.035252895206213,
-0.0013412719126790762,
0.029087960720062256,
-0.003993208985775709,
0.04008857533335686,
-0.03787152096629143,
-0.05061793699860573,
-0.009407893754541874,
-0.00006624656816711649,
-0.011636882089078426,
-0.0154732009395957,
-0.0296054445207119,
0.014123007655143738,
-0.029391949996352196,
-0.015029759146273136,
0.04298198223114014,
0.026062026619911194,
0.017133086919784546,
0.015680212527513504,
0.002288606483489275,
-0.02673584595322609,
-0.02188235893845558,
-0.027784833684563637,
0.03274216502904892,
0.014681283384561539,
0.006520003080368042,
0.04775967821478844,
0.0018784640124067664,
-0.03192998096346855,
0.011571566574275494,
-0.05968140438199043,
-0.019245773553848267,
-0.024115046486258507,
0.021452784538269043,
0.02919490449130535,
-0.04179995507001877,
0.023401737213134766,
0.018087146803736687,
-0.06210966035723686,
-0.033556949347257614,
-0.0310949869453907,
-0.03608090430498123,
0.03705403953790665,
-0.006116589531302452,
0.05181095749139786,
0.011755231767892838,
-0.025201847776770592,
0.05581951513886452,
-0.03160286322236061,
-0.06774790585041046,
-0.00979361217468977,
-0.022338522598147392,
-0.0003602194192353636,
0.008075172081589699,
0.023875324055552483,
0.04353735223412514,
-0.03043139912188053,
0.020120063796639442,
0.06983760744333267,
0.04294464737176895,
0.04367586597800255,
0.06588012725114822,
0.02412167377769947,
-0.01557379961013794,
0.05368151143193245,
-0.009279551915824413,
0.06517864018678665,
0.00407966785132885,
0.02099316567182541,
0.004100799094885588,
-0.012539359740912914,
0.019763117656111717,
0.014599546790122986,
-0.04025707766413689,
0.05117613822221756,
0.026327138766646385,
-0.01927613466978073,
-0.04384662210941315,
0.03575674071907997,
-0.017150936648249626,
0.0037997225299477577,
-0.01853965036571026,
0.0257203858345747,
0.04302743077278137,
-0.010802156291902065,
-0.02865849807858467,
0.046838756650686264,
0.06726256012916565,
-0.04131030663847923,
-0.05250528082251549,
0.01626056618988514,
-0.022323323413729668,
0.051657721400260925,
-0.0356464721262455,
-0.038778576999902725,
0.06878457218408585,
0.023199906572699547,
-0.0191778764128685,
0.026465844362974167,
-0.046008169651031494,
0.027490505948662758,
-0.07813116908073425,
-0.017374632880091667,
-0.0032115457579493523,
0.05303715169429779,
-0.015231424011290073,
0.05347811430692673,
0.012513475492596626,
0.02669554017484188,
0.030735483393073082,
0.019344434142112732,
-0.06911050528287888,
-0.004453004337847233,
-0.012666387483477592,
0.013781107030808926,
-0.014159725978970528,
-0.022106964141130447,
-0.013986796140670776,
-0.025138776749372482,
-0.0025419914163649082,
0.010823975317180157,
0.0143237030133605,
-0.04660198092460632,
0.05658908933401108,
-0.0011872267350554466,
-0.00038088628207333386,
-0.02272014133632183,
0.04298204928636551,
0.03477725759148598,
-0.008293169550597668,
0.05285423621535301,
0.012854536063969135,
-0.005203592590987682,
-0.009529738686978817,
0.009359538555145264,
0.037247996777296066,
0.033344816416502,
0.06117936223745346,
0.030741866677999496,
0.011437845416367054,
0.0013359534787014127,
0.0014669024385511875,
0.024764634668827057,
0.053626835346221924,
-0.011168827302753925,
-0.029767362400889397,
-0.008361799642443657,
-0.04217353090643883,
-0.00019269400218036026,
-0.002486694138497114,
0.03897786885499954,
-0.020341962575912476,
0.026197079569101334,
-0.0005013281479477882,
-0.015596090815961361,
-0.02532881312072277,
0.04701720178127289,
0.0724293515086174,
0.01719076745212078,
-0.01671617664396763,
-0.0642983615398407,
-0.006008368916809559,
-0.03700999543070793,
-0.00186737475451082,
0.036190882325172424,
0.0034114718437194824,
-0.04184678569436073,
0.005433387588709593,
0.01779196411371231,
0.02305346354842186,
-0.050744056701660156,
0.004986843094229698,
0.023580392822623253,
0.01549350842833519,
-0.01685594581067562,
0.0025693275965750217,
0.03301549702882767,
-0.004627017304301262,
0.011069736443459988,
0.028611810877919197,
-0.04226674139499664,
-0.05615874007344246,
-0.025421783328056335,
0.03167682886123657,
0.029464546591043472,
-0.019485680386424065,
0.005621553864330053,
-0.027841530740261078,
-0.016169870272278786,
0.05457032099366188,
-0.017328651621937752,
0.01505818497389555,
-0.010726767592132092,
0.0014362387591972947,
0.002437032526358962,
-0.03933406621217728,
-0.026727786287665367,
-0.032781828194856644,
-0.0352863147854805,
0.00485609844326973,
-0.011584466323256493,
-0.00887503381818533,
-0.016263965517282486,
0.005379822105169296,
0.046463724225759506,
0.04833914339542389,
0.013462004251778126,
-0.014604784548282623,
-0.03923190012574196,
0.03719576448202133,
-0.02610434964299202,
-0.06530632078647614,
-0.014278477057814598,
0.006782148033380508,
0.028767334297299385,
0.045230768620967865,
-0.01568988710641861,
-0.03960529342293739,
0.080292709171772,
-0.007521411869674921,
-0.008620832115411758,
-0.0046571288257837296,
0.01482287235558033,
0.022716207429766655,
0.053275205194950104,
-0.0009927514474838972,
0.03781111165881157,
0.011183845810592175,
-0.0044828057289123535,
-0.04280119761824608,
-0.024692291393876076,
0.023247823119163513,
-0.013822791166603565,
-0.038195595145225525,
-0.03282631188631058,
0.009479891508817673,
0.009076520800590515,
0.03920872136950493,
-0.018039697781205177,
0.01673095114529133,
-0.008735771290957928,
-0.03519931435585022,
0.016760477796196938,
0.034424398094415665,
0.022510075941681862,
-0.002158088143914938,
-0.0024339829105883837,
0.009493520483374596,
0.02522295154631138,
-0.033528316766023636,
-0.0022777270060032606,
-0.02248888835310936,
0.024338535964488983,
-0.013395970687270164,
-0.030372973531484604,
0.006148445885628462,
-0.005638927686959505,
-0.019281815737485886,
-0.00023673733812756836,
-0.020463833585381508,
0.04496040195226669,
0.02016719989478588,
0.03527763485908508,
0.020424362272024155,
-0.024734463542699814,
-0.016938162967562675,
0.045095764100551605,
-0.0033758843783289194,
0.023628538474440575,
-0.037849340587854385,
0.049737028777599335,
0.007409803569316864,
0.008489198051393032,
-0.06342045217752457,
-0.02577134221792221,
0.06159146875143051,
0.029719693586230278,
-0.003458081977441907,
0.006770366337150335,
-0.01873682253062725,
-0.010185256600379944,
-0.027658196166157722,
-0.008201862685382366,
0.047189757227897644,
-0.009801426902413368,
-0.0540832094848156,
0.02164587937295437,
0.015298549085855484,
0.08008646219968796,
0.017984814941883087,
-0.023437807336449623,
-0.0021160198375582695,
-0.022647792473435402,
-0.007530245464295149,
-0.02430015057325363,
0.03728886693716049,
-0.03266062214970589,
-0.023017609491944313,
-0.012083794921636581,
-0.016892464831471443,
0.048920441418886185,
-0.038021236658096313,
0.009234566241502762,
0.01672525145113468,
0.022086285054683685,
0.0008136862888932228,
-0.014764828607439995,
0.012088474817574024,
-0.029127297922968864,
0.038708265870809555,
0.03194462135434151,
-0.04355071112513542,
-0.02525601163506508,
-0.016422616317868233,
-0.03903476893901825,
-0.0046243430115282536,
-0.04423636943101883,
-0.0068882545456290245,
0.06558328121900558,
0.005686089396476746,
-0.017376527190208435,
-0.004501840565353632,
-0.04570307582616806,
-0.0005139579880051315,
0.0021527158096432686,
-0.03559132665395737,
0.03974256291985512,
0.027617625892162323,
-0.03069121576845646,
-0.04956355318427086,
-0.00454519921913743,
0.029011469334363937,
0.046156421303749084,
-0.012825364246964455,
0.04853949323296547,
0.02958027459681034,
-0.00041644272278063,
0.01790679804980755,
-0.038049500435590744,
-0.03403473645448685,
0.0031045908108353615,
-0.041287921369075775,
0.05862574279308319,
-0.02463015541434288,
-0.01029454730451107,
0.030432872474193573,
0.03700537979602814,
-0.008413559757173061,
0.0022934519220143557,
0.06200609356164932,
0.03015092760324478,
-0.0032080933451652527,
0.00833770353347063,
-0.04789278283715248,
0.043575335294008255,
-0.055976010859012604,
0.015323255211114883,
-0.00935694482177496,
-0.023552587255835533,
0.020999569445848465,
0.023099152371287346,
0.004524578806012869,
-0.053904514759778976,
0.005962876137346029,
-0.037714406847953796,
0.01446483377367258,
-0.012990412302315235,
0.03242340311408043,
-0.03552982956171036,
0.04781196638941765,
0.02569078840315342,
-0.017535915598273277,
0.009837339632213116,
0.008622128516435623,
-0.051051728427410126,
-0.024848373606801033,
0.002515021711587906,
-0.027808066457509995,
0.036524537950754166,
0.009516449645161629,
-0.018846457824110985,
0.026985986158251762,
-0.02797687239944935,
0.0037957809399813414,
-0.01309859286993742,
0.04087498039007187,
-0.014061464928090572,
0.08808056265115738,
0.0033516352996230125,
0.03681523725390434,
0.009692644700407982,
0.005733960773795843,
0.11617615073919296,
0.04562012478709221,
0.04600581154227257,
-0.06647711992263794,
0.017134344205260277,
0.009658416733145714,
-0.0042721787467598915,
-0.00754805700853467,
0.02322700060904026,
0.007090045139193535,
-0.0019347845809534192,
-0.005985047202557325,
0.04932301118969917,
-0.029041467234492302,
0.02522306889295578,
0.08476752042770386,
-0.05218225717544556,
0.005536602344363928,
-0.025162693113088608,
0.0029647089540958405,
-0.036532510071992874,
0.03793735057115555,
-0.020360341295599937,
0.03201829642057419,
-0.013468273915350437,
0.003159075044095516,
-0.025281328707933426,
-0.02947854995727539,
0.06640651077032089,
-0.0014539568219333887,
-0.05579797551035881,
0.001741318148560822,
-0.014032877050340176,
-0.0198222566395998,
-0.0676422044634819,
0.039043184369802475,
0.004396941978484392,
-0.03067580983042717,
-0.0001936164335347712,
0.025387737900018692,
-0.006177753675729036,
-0.004730392247438431,
-0.015266180969774723,
0.014135573990643024,
-0.03768397122621536,
0.028088567778468132,
-0.006982846651226282,
0.002104444894939661,
0.001922295312397182,
-0.033848829567432404,
-0.0019656859803944826,
0.02079634927213192,
0.013173152692615986,
-0.0379205122590065,
-0.058663032948970795,
0.012094482779502869,
0.013078835792839527,
0.0003816914977505803,
-0.02632979489862919,
-0.03121309168636799,
0.0188523530960083,
-0.014048140496015549,
0.007225039415061474,
-0.024433890357613564,
0.009654039517045021,
-0.009380803443491459,
-0.009366639889776707,
0.04683421924710274,
-0.015956459566950798,
-0.010737203061580658,
-0.03397490456700325,
0.002089981222525239,
-0.06326253712177277,
0.006286608055233955,
-0.009331082925200462,
0.011422846466302872,
0.0611509345471859,
0.022314518690109253,
0.0058907633647322655,
0.0043456777930259705,
-0.061718281358480453,
0.02947884239256382,
-0.02122926525771618,
0.030359741300344467,
-0.027707120403647423,
0.019984131678938866,
0.012652574107050896,
0.071378193795681,
0.002074382035061717,
-0.024422354996204376,
0.0007109276484698057,
0.027428150177001953,
0.030641982331871986,
-0.05794334411621094,
-0.04566206783056259,
-0.01419062353670597,
-0.041283901780843735,
-0.00870093610137701,
-0.020810924470424652,
-0.0021331030875444412,
0.041671641170978546,
0.02331085503101349,
-0.02502639777958393,
-0.0032341855112463236,
-0.04781464487314224,
0.004527765326201916,
-0.007109105587005615,
-0.03722064569592476,
0.016218017786741257,
0.04063531756401062,
0.00954452995210886,
-0.01038016751408577,
-0.03803509473800659,
0.010595154017210007,
-0.03617141768336296,
0.0009421321447007358,
-0.0026492848992347717,
-0.004425886087119579,
0.0052815512754023075,
-0.00887482799589634,
-0.010941941291093826,
-0.031134137883782387,
0.011654586531221867,
-0.03888625651597977,
-0.03157859668135643,
0.022975672036409378,
-0.0010848924284800887,
-0.037854477763175964,
0.014980470761656761,
-0.049162399023771286,
-0.018174346536397934,
-0.02144855633378029,
0.015862520784139633,
0.014270289801061153,
-0.016855502501130104,
0.06194043532013893,
0.0013268032344058156,
0.03993351757526398,
-0.0004451742279343307,
-0.01591031439602375,
0.010224460624158382,
-0.007540207821875811,
-0.02506253868341446,
0.030769485980272293,
-0.01177240815013647,
0.020570477470755577,
0.01684480533003807,
-0.016430342569947243,
-0.00703453179448843,
0.07401297986507416,
-0.03343161940574646,
-0.0003367382741998881,
-0.0324479378759861,
-0.01621435023844242,
0.0032457830384373665,
0.004446896258741617,
0.010110744275152683,
-0.016270536929368973,
-0.01115508284419775,
0.019061654806137085,
0.06404337286949158,
-0.003906926605850458,
-0.02517933025956154,
0.02853783592581749,
0.02584194950759411,
0.044721078127622604,
0.017061589285731316,
-0.02493332326412201,
0.03109140507876873,
0.05206679925322533,
-0.023986710235476494,
0.04248308390378952,
0.007762304041534662,
-0.01524911168962717,
-0.09765803813934326,
-0.02410072833299637,
-0.008462448604404926,
-0.023956622928380966,
0.01696866936981678,
-0.016644198447465897,
-0.0213975477963686,
0.03793342784047127,
-0.03294704109430313,
-0.028453651815652847,
-0.023046137765049934,
0.0038577490486204624,
-0.0060785310342907906,
-0.010343418456614017,
-0.019343946129083633,
0.07033423334360123,
-0.00015091296518221498,
0.010693931952118874,
0.011821365915238857,
-0.01505353581160307,
0.023157691583037376,
0.012119689024984837,
0.012965680100023746,
0.016503555700182915,
-0.02167806401848793,
-0.02482737973332405,
0.038384370505809784,
-0.039470333606004715,
-0.023358670994639397,
0.02091118134558201,
-0.015861915424466133,
0.0009592872229404747,
-0.011745188385248184,
-0.04624614864587784,
-0.02308766543865204,
0.04987930878996849,
-0.019382968544960022,
0.019824571907520294,
-0.00469096889719367,
0.00854832399636507,
-0.002683917060494423,
0.008626352064311504,
-0.0036084051243960857,
-0.00960876140743494,
0.00879270862787962,
-0.03108428232371807,
0.005914631765335798,
0.03707641735672951,
-0.023710519075393677,
0.014056391082704067,
0.0017210718942806125,
-0.005190225783735514,
0.0130809610709548,
-0.025904620066285133,
0.01239551417529583,
-0.05082264915108681,
0.007554998621344566,
0.046665821224451065,
0.03436749055981636,
-0.008014191873371601,
-0.0034078394528478384,
0.024236569181084633,
-0.019131068140268326,
0.00008085901208687574,
0.003205335233360529,
-0.038081392645835876,
-0.05665280297398567,
-0.0026458697393536568,
-0.032556165009737015,
-0.03713778033852577,
-0.001623111660592258,
-0.08303869515657425,
-0.01647905260324478,
0.018347203731536865,
0.01848701387643814,
0.013369803316891193,
0.008991041220724583,
-0.003503791755065322,
-0.002910386770963669,
-0.05993910878896713,
0.02826162800192833,
-0.011205494403839111,
-0.012084812857210636,
-0.023348785936832428,
-0.029792599380016327,
0.004653151612728834,
0.04032191261649132,
0.041432399302721024,
0.027187231928110123,
-0.015108512714505196,
-0.010243929922580719,
0.0007693519000895321,
0.02764284424483776,
-0.022623909637331963,
-0.005921012256294489,
0.017072094604372978,
-0.048489801585674286,
0.010737955570220947,
-0.028425365686416626,
0.01192984264343977,
0.027322392910718918,
0.006619027815759182,
-0.027031930163502693,
0.007501525338739157,
0.006178210023790598,
0.004861883819103241,
-0.0160438884049654,
0.030040007084608078,
-0.007419596426188946,
0.06035785377025604,
0.030892271548509598,
-0.0035691356752067804,
0.0011521175038069487,
-0.00873885303735733,
-0.06022856757044792,
0.042379189282655716,
-0.04859825596213341,
-0.0059076277539134026,
-0.033895477652549744,
-0.017100900411605835,
-0.002392319031059742,
-0.04699143022298813,
0.005217754747718573,
0.031564049422740936,
-0.06404940038919449,
-0.022426694631576538,
0.03295828774571419,
0.031072232872247696,
0.028924206271767616,
-0.04067573323845863,
0.01286536455154419,
0.030914636328816414,
0.016462275758385658,
0.008487285114824772,
0.018568232655525208,
0.04592938721179962,
0.022667285054922104,
-0.010996172204613686,
0.03382815793156624,
-0.030195575207471848,
0.00592912919819355,
-0.002472657710313797,
-0.011887658387422562,
-0.032389797270298004,
-0.05691353231668472,
0.017116904258728027,
-0.03466345742344856,
0.026288006454706192,
0.05386364832520485,
-0.013738338835537434,
0.03732910007238388,
-0.03391152247786522,
0.004684480372816324,
-0.060428328812122345,
-0.00740910554304719,
0.008752061054110527,
0.009033584967255592,
0.0059186797589063644,
0.012253486551344395,
0.006351296789944172,
-0.012080325745046139,
-0.003301439341157675,
-0.027529902756214142,
0.03647991642355919,
-0.01824047788977623,
0.019102005288004875,
-0.02305210940539837,
0.009703736752271652,
-0.07488196343183517,
-0.026806268841028214,
-0.05432835966348648,
-0.007023445796221495,
0.05744851380586624,
0.014581939205527306,
0.03689028322696686,
0.0474376305937767,
-0.012566149234771729,
-0.02527606301009655,
0.04262567684054375,
-0.07186125963926315,
-0.0364362932741642,
-0.02552955038845539,
-0.004791357088834047,
0.03191255033016205,
-0.03902925178408623
] |
<p>If I try to add up neutrino masses (let's assume 1 eV rest mass equivalent each) to count as DM, do I use the rest mass or relativistic mass?</p> | 1,572 | [
0.009963893331587315,
-0.0394359827041626,
-0.02753465808928013,
-0.03813027963042259,
0.031308211386203766,
0.01907939463853836,
-0.050693344324827194,
-0.04346705973148346,
0.020698804408311844,
0.0021472915541380644,
0.03809439018368721,
0.01144345197826624,
0.05811547860503197,
0.006303235422819853,
0.04144476354122162,
0.034969404339790344,
0.007105829659849405,
-0.011122760362923145,
0.021025389432907104,
-0.05754219740629196,
-0.006247243843972683,
0.023369362577795982,
0.022344956174492836,
-0.009550893679261208,
0.0023437635973095894,
0.06971242278814316,
0.022144462913274765,
0.0024211450945585966,
-0.0013452240964397788,
0.01876741461455822,
-0.002429383108392358,
-0.04428203031420708,
0.04743626341223717,
0.03448687121272087,
0.03509259223937988,
0.024133756756782532,
0.00512963579967618,
-0.017600813880562782,
-0.023614756762981415,
0.024781187996268272,
-0.03549230098724365,
-0.04049206152558327,
0.002315848134458065,
0.02867063879966736,
-0.03592570871114731,
0.020224208012223244,
0.020792150869965553,
-0.018990326672792435,
0.06699799001216888,
-0.0805802196264267,
0.0841103345155716,
0.0540083684027195,
0.050518639385700226,
-0.00580966379493475,
-0.018900984898209572,
-0.00942421518266201,
0.09733625501394272,
0.05496133118867874,
-0.01898663118481636,
-0.018489783629775047,
-0.03725685924291611,
-0.032311610877513885,
0.012648829258978367,
-0.017545824870467186,
0.0038766227662563324,
0.06022265553474426,
-0.019060740247368813,
0.01630525104701519,
0.016124432906508446,
0.018491940572857857,
0.022901242598891258,
-0.004818481858819723,
0.026008162647485733,
-0.013626566156744957,
0.02732716128230095,
-0.03271091729402542,
0.031002018600702286,
0.019255241379141808,
0.01462207455188036,
0.05369997024536133,
-0.02441963367164135,
0.01993025653064251,
0.046341679990291595,
0.031855467706918716,
0.003917076624929905,
-0.009377362206578255,
0.041535381227731705,
0.019324976950883865,
-0.004538862966001034,
0.05879313498735428,
-0.031107880175113678,
-0.004833641462028027,
0.021728042513132095,
-0.010936028324067593,
-0.03214866667985916,
0.030705248937010765,
-0.0054680160246789455,
0.03916081041097641,
-0.012159147299826145,
-0.002529110526666045,
-0.04086443781852722,
0.005596045404672623,
0.03952860087156296,
0.07533973455429077,
0.002152280416339636,
-0.02029997669160366,
-0.03418689966201782,
0.021801700815558434,
-0.01664414256811142,
-0.024467894807457924,
-0.031359706073999405,
0.013392528519034386,
-0.046123940497636795,
-0.016514135524630547,
0.0368618480861187,
-0.00859065167605877,
0.0076424251310527325,
-0.02607949636876583,
0.06065826863050461,
0.03502703830599785,
0.026866555213928223,
-0.015361765399575233,
0.0013186046853661537,
-0.035734087228775024,
-0.04402826353907585,
0.02154364623129368,
0.035142119973897934,
0.00018960148736368865,
-0.019883742555975914,
0.004585052840411663,
-0.003676646389067173,
-0.04388686269521713,
-0.020406493917107582,
-0.030545493587851524,
0.043315339833498,
-0.002080038655549288,
-0.06159284710884094,
-0.06131812930107117,
0.02278505265712738,
-0.008077416568994522,
-0.0400695838034153,
-0.0622236393392086,
-0.01754654198884964,
0.013668123632669449,
0.06873088330030441,
0.05223317816853523,
0.008638691157102585,
-0.008826085366308689,
0.04846785590052605,
-0.003390308702364564,
0.010959479957818985,
-0.0503966361284256,
0.012856201268732548,
-0.0616900697350502,
0.0055920775048434734,
-0.07657475769519806,
-0.007505769841372967,
0.03618338331580162,
-0.016853870823979378,
0.022522497922182083,
0.05570956692099571,
-0.0018687868723645806,
0.014430987648665905,
0.014007175341248512,
0.004841766320168972,
-0.01300241518765688,
0.03898303583264351,
-0.00804515928030014,
0.005368224810808897,
0.036004438996315,
0.016141751781105995,
0.03232375159859657,
0.04802059382200241,
0.049699220806360245,
0.07675863802433014,
-0.0019816304557025433,
-0.026286110281944275,
-0.04106972739100456,
0.03481386974453926,
0.016783280298113823,
-0.05361669510602951,
-0.03144610673189163,
-0.002377532422542572,
0.007581720128655434,
0.028569547459483147,
0.008034156635403633,
-0.012790998443961143,
-0.004405450075864792,
-0.003774910466745496,
-0.0008826322155073285,
-0.005046353209763765,
-0.04190345108509064,
-0.01782122068107128,
-0.016255876049399376,
0.004896154627203941,
-0.006671218667179346,
0.016907820478081703,
0.030010076239705086,
-0.032300904393196106,
-0.03923449292778969,
-0.024522889405488968,
0.035978104919195175,
0.011927619576454163,
-0.013085873797535896,
0.0032675147522240877,
0.028992243111133575,
0.04916641116142273,
-0.023141101002693176,
-0.009566843509674072,
-0.0117796640843153,
-0.017177512869238853,
-0.03771229460835457,
0.001623264979571104,
0.009798863902688026,
-0.020792219787836075,
-0.0009158164029940963,
0.023123160004615784,
0.00004382557381177321,
-0.017387205734848976,
0.06881280988454819,
0.003299446078017354,
0.09072592854499817,
0.020223252475261688,
0.0023269925732165575,
-0.02194967120885849,
0.006241389084607363,
0.015082819387316704,
0.03032626211643219,
-0.02816486544907093,
-0.017357423901557922,
-0.02725973352789879,
0.01520033460110426,
0.044164955615997314,
-0.000820169982034713,
-0.04564520716667175,
0.042458102107048035,
0.05921148508787155,
0.02909179963171482,
0.0180188175290823,
0.015551305375993252,
-0.03260243311524391,
-0.0652274563908577,
0.004096431192010641,
0.0478748120367527,
-0.0031463608611375093,
-0.0006157163297757506,
0.034140221774578094,
0.0045233373530209064,
-0.0006937783909961581,
-0.00854477845132351,
-0.007709920406341553,
0.011307552456855774,
-0.004010447766631842,
-0.028902646154165268,
-0.005421086680144072,
-0.05282855033874512,
0.03837438300251961,
-0.025725867599248886,
0.027620185166597366,
0.05096998065710068,
-0.01968456245958805,
-0.03843735158443451,
0.009670179337263107,
-0.013191615231335163,
0.04957257956266403,
0.006586960516870022,
-0.003390469355508685,
-0.02409534715116024,
0.029471423476934433,
-0.035132892429828644,
0.0388849675655365,
-0.04356337711215019,
-0.025821177288889885,
-0.02437424659729004,
0.022047890350222588,
0.011389724910259247,
-0.02062671072781086,
0.032178714871406555,
-0.02235221303999424,
-0.015646109357476234,
-0.007829532027244568,
-0.023506909608840942,
-0.04453866556286812,
0.05409751459956169,
-0.04940962418913841,
0.03338770195841789,
-0.03757195174694061,
-0.06594474613666534,
0.005920297931879759,
0.027957910671830177,
0.006912109907716513,
0.02726178802549839,
0.005101191345602274,
-0.030476020649075508,
-0.04989071562886238,
-0.008791252039372921,
-0.014598844572901726,
-0.03221331536769867,
0.015119560994207859,
0.0406990684568882,
0.006897591054439545,
-0.03786330670118332,
-0.010786638595163822,
-0.04043087735772133,
-0.04632854089140892,
-0.008753742091357708,
-0.0062090675346553326,
0.015072450041770935,
-0.07760345190763474,
0.02841041050851345,
0.00491125276312232,
-0.052734971046447754,
0.019260581582784653,
-0.03490138798952103,
-0.07754308730363846,
0.06128789111971855,
0.0021726363338530064,
0.021975936368107796,
0.05321453884243965,
-0.0509677454829216,
0.07973375916481018,
0.04853786528110504,
-0.011818218976259232,
-0.025342034175992012,
-0.010811230167746544,
0.017755625769495964,
-0.026353413239121437,
-0.009396031498908997,
0.01640130952000618,
-0.02164543606340885,
0.008199995383620262,
0.03518500551581383,
0.011849951930344105,
0.013395749032497406,
-0.017368584871292114,
0.01492341049015522,
0.021655896678566933,
0.01858595572412014,
-0.002574008656665683,
0.06821832805871964,
0.005702546797692776,
0.008110487833619118,
0.009817875921726227,
0.0185534805059433,
0.09159588813781738,
-0.010927119292318821,
-0.06505745649337769,
0.03753940761089325,
-0.0023028897121548653,
0.005394555162638426,
0.005629540886729956,
0.0073658740147948265,
0.027720149606466293,
-0.012000135146081448,
0.018632175400853157,
0.007406020071357489,
0.014504780061542988,
-0.05760903283953667,
-0.022922109812498093,
0.041875943541526794,
0.051219210028648376,
0.013689462095499039,
-0.05618297681212425,
-0.003908257465809584,
0.011525005102157593,
0.007683236617594957,
-0.0014084030408412218,
-0.008365757763385773,
0.060361750423908234,
0.02572096697986126,
0.03785115107893944,
-0.007081298623234034,
-0.031779468059539795,
-0.024994689971208572,
-0.08499156683683395,
0.01688329316675663,
-0.00403704633936286,
0.028942031785845757,
-0.010250823572278023,
0.035861436277627945,
0.014094476588070393,
-0.01497286930680275,
-0.01011948473751545,
-0.0184430293738842,
-0.048367299139499664,
0.054794374853372574,
-0.07318474352359772,
-0.02643037959933281,
-0.0072259544394910336,
-0.003930805251002312,
-0.026028256863355637,
-0.02326143905520439,
0.0034271725453436375,
-0.0446559302508831,
-0.02706730365753174,
-0.025056982412934303,
0.030363809317350388,
0.004335267469286919,
-0.03099442459642887,
0.020619580522179604,
0.04988286271691322,
0.01614304631948471,
-0.017170296981930733,
-0.03925381228327751,
0.053446535021066666,
-0.006729462184011936,
-0.012218363583087921,
-0.022070124745368958,
0.03305107355117798,
-0.014570455066859722,
0.017396893352270126,
0.05202450975775719,
0.007576769683510065,
-0.023540420457720757,
0.032231949269771576,
0.019313950091600418,
0.02468603476881981,
-0.008374952711164951,
-0.05105264484882355,
-0.05859363079071045,
-0.03181658685207367,
-0.0007907681283541024,
0.019083172082901,
0.0519232340157032,
-0.02677883207798004,
0.025065036490559578,
0.021913504227995872,
0.007558575365692377,
-0.008115306496620178,
0.048044491559267044,
0.03913642093539238,
-0.026548245921730995,
-0.05410744249820709,
-0.08624450862407684,
-0.0034137661568820477,
0.004291888792067766,
0.0005970552447251976,
0.0376303531229496,
0.056528739631175995,
-0.025350093841552734,
-0.02833370864391327,
-0.029289133846759796,
-0.041786447167396545,
-0.028503697365522385,
-0.011582070961594582,
0.0249312873929739,
0.017509980127215385,
-0.02957705594599247,
-0.011443392373621464,
-0.015232726000249386,
0.04509738087654114,
0.014476660639047623,
-0.022581059485673904,
0.023228546604514122,
-0.0807478278875351,
0.021459931507706642,
0.0624709278345108,
0.042715489864349365,
-0.035453323274850845,
-0.018060162663459778,
-0.04857521504163742,
-0.006148208398371935,
0.040917348116636276,
-0.046324603259563446,
0.011902834288775921,
0.017209766432642937,
0.011947883293032646,
-0.01577533408999443,
-0.02120126225054264,
-0.006579020991921425,
0.030896229669451714,
0.029803656041622162,
0.036262646317481995,
-0.01583792082965374,
-0.004053480923175812,
-0.00920417532324791,
0.011935506947338581,
0.05393289029598236,
0.0287715382874012,
-0.004026575479656458,
0.015276213176548481,
0.006287242751568556,
0.0136006660759449,
-0.002211676212027669,
-0.08960665017366409,
-0.026724226772785187,
0.02419203706085682,
0.003486290341243148,
0.04654889553785324,
-0.01731659099459648,
-0.06873838603496552,
0.04591459780931473,
-0.0016315083485096693,
0.00374040799215436,
-0.015074828639626503,
-0.0346556082367897,
0.0860815942287445,
0.03850133717060089,
-0.00666741793975234,
0.033158622682094574,
0.0020328809041529894,
-0.0043411520309746265,
0.0020261199679225683,
-0.013349205255508423,
0.03179051727056503,
-0.047579098492860794,
-0.034666091203689575,
-0.0011673560366034508,
-0.01707710325717926,
-0.030129121616482735,
0.020252497866749763,
-0.0060114143416285515,
0.044280242174863815,
0.037022124975919724,
-0.04390518367290497,
-0.018841998651623726,
0.04758721590042114,
0.03314462676644325,
0.0047142342664301395,
-0.003648466896265745,
-0.015068640932440758,
0.017776668071746826,
-0.01802966371178627,
0.034104276448488235,
0.016565846279263496,
-0.023448757827281952,
0.01902121677994728,
-0.022552354261279106,
0.05279446765780449,
0.02629537135362625,
-0.023605138063430786,
0.03914763033390045,
-0.03970896080136299,
0.009844105690717697,
-0.00757297407835722,
0.010741675272583961,
-0.00493848929181695,
-0.06653836369514465,
-0.022530192509293556,
-0.028789853677153587,
-0.012773597612977028,
0.04209169000387192,
-0.056070443242788315,
0.019784940406680107,
0.021054254844784737,
0.035894956439733505,
-0.06986719369888306,
-0.047661300748586655,
0.006848612334579229,
-0.00003465414192760363,
0.0065749394707381725,
-0.00896565429866314,
0.008305186405777931,
-0.03411298617720604,
-0.008394508622586727,
0.0016764503670856357,
0.11541031301021576,
-0.023935159668326378,
-0.022292133420705795,
-0.0095481863245368,
0.016377046704292297,
0.06513986736536026,
-0.0418853759765625,
-0.01724546030163765,
0.01906488835811615,
-0.022357240319252014,
0.017427954822778702,
0.03328588977456093,
0.03155152499675751,
-0.02489318698644638,
-0.020394504070281982,
-0.030319930985569954,
0.00415260111913085,
0.04232899844646454,
-0.027935929596424103,
0.004730443935841322,
0.08011190593242645,
-0.003245365573093295,
-0.012828209437429905,
-0.03307393938302994,
0.04258329048752785,
-0.0006148731918074191,
0.02061609737575054,
0.023248959332704544,
-0.011576483026146889,
-0.017378339543938637,
-0.009058047086000443,
0.04354880377650261,
-0.016392771154642105,
0.04336031153798103,
-0.007113945670425892,
0.05039072036743164,
0.016692165285348892,
-0.02191268466413021,
0.019599607214331627,
-0.027155129238963127,
0.01334767509251833,
-0.03023039922118187,
0.020472949370741844,
0.010073062032461166,
-0.006519090849906206,
-0.04534706473350525,
-0.04397399351000786,
-0.04024286940693855,
0.0055043743923306465,
0.07441560924053192,
-0.007671252358704805,
0.04071882367134094,
-0.00990256667137146,
0.006544761825352907,
0.03106595389544964,
-0.038100458681583405,
-0.0009396974928677082,
0.013854160904884338,
-0.02057204395532608,
0.0466657429933548,
-0.025918880477547646,
-0.02036368101835251,
0.005566657055169344,
0.038687340915203094,
0.0016486623790115118,
0.011882014572620392,
0.041356611996889114,
0.03917832300066948,
-0.002322645392268896,
0.01937517337501049,
-0.02733142115175724,
-0.003280270379036665,
-0.011260873638093472,
0.00951298139989376,
-0.00806425791233778,
-0.02417933940887451,
0.03215328976511955,
-0.010952766984701157,
0.010549946688115597,
-0.0014201825251802802,
-0.033642880618572235,
-0.00947736669331789,
-0.0024308315478265285,
0.026837019249796867,
0.029882920905947685,
-0.03147986903786659,
0.03721939027309418,
0.045828595757484436,
-0.00375880254432559,
0.0036387767177075148,
-0.004660835023969412,
-0.07300266623497009,
-0.022568412125110626,
0.0054858080111444,
-0.06625791639089584,
0.04195728152990341,
-0.018779544159770012,
-0.0004901518113911152,
-0.024536004289984703,
0.0006181849748827517,
0.004261916037648916,
0.022462252527475357,
0.026458166539669037,
-0.04461481794714928,
0.03573447838425636,
0.016798092052340508,
0.010707181878387928,
0.003799288999289274,
0.008420770056545734,
0.10644135624170303,
0.005130365490913391,
0.04098004847764969,
-0.055537402629852295,
-0.006378821562975645,
-0.010292427614331245,
0.032709039747714996,
0.0016330558573827147,
0.01289348490536213,
-0.02562122419476509,
0.01947486214339733,
0.0121897729113698,
0.02959594689309597,
0.006721487268805504,
0.013514094986021519,
0.024653587490320206,
-0.00007288355845957994,
-0.04565929248929024,
0.02941271848976612,
0.033967964351177216,
0.005716967862099409,
0.02109907567501068,
-0.03393455967307091,
0.05095938965678215,
0.005229664500802755,
0.016949493438005447,
-0.021038183942437172,
-0.0010638664243742824,
0.0005000585224479437,
0.002263997681438923,
-0.04623320698738098,
-0.010157814249396324,
-0.002190927043557167,
0.0006233538151718676,
-0.046458933502435684,
0.013297556899487972,
-0.004798842594027519,
0.008433113805949688,
0.030518783256411552,
0.009184375405311584,
0.02437894232571125,
0.031776707619428635,
-0.03135043755173683,
-0.019232913851737976,
-0.08894702047109604,
0.03137629106640816,
0.005494799464941025,
0.03398041054606438,
-0.02023431658744812,
-0.012201461009681225,
0.025302331894636154,
0.007668561302125454,
-0.008988435380160809,
-0.06022699177265167,
-0.02523071877658367,
-0.004859337583184242,
0.013769709505140781,
0.018669024109840393,
0.016825981438159943,
-0.04394685477018356,
0.05480049178004265,
-0.016150174662470818,
0.047309692949056625,
-0.005002578254789114,
0.012838482856750488,
0.00305059808306396,
-0.051977429538965225,
-0.015267142094671726,
-0.00817194115370512,
-0.02908635325729847,
-0.012678018771111965,
-0.020027773454785347,
-0.04496818408370018,
-0.012182828038930893,
0.014688740484416485,
0.028928270563483238,
0.05065968260169029,
-0.0029712242539972067,
0.022281266748905182,
-0.04035250470042229,
-0.05784124881029129,
0.03732074052095413,
-0.01840140111744404,
-0.02929590828716755,
-0.027583954855799675,
0.006765132304280996,
-0.005032113287597895,
0.0412156917154789,
-0.03985808044672012,
0.01530004758387804,
0.014766523614525795,
0.00471000699326396,
-0.010190030559897423,
-0.03588744252920151,
0.03381410986185074,
0.010184426791965961,
-0.02358078770339489,
0.010452650487422943,
-0.03808652237057686,
-0.008764974772930145,
0.01682777889072895,
-0.00014931750774849206,
0.008470292203128338,
0.032993875443935394,
-0.007722124923020601,
0.006114166229963303,
-0.03522434085607529,
-0.02412460185587406,
0.01090401690453291,
-0.02014276385307312,
-0.012696956284344196,
-0.026629382744431496,
-0.018760086968541145,
-0.0680580735206604,
-0.013053376227617264,
-0.0051566604524850845,
0.017876384779810905,
-0.05344855412840843,
0.023489931598305702,
-0.008999794721603394,
0.01109013520181179,
0.00025128910783678293,
0.019203586503863335,
-0.05459251254796982,
0.019670933485031128,
-0.009589551016688347,
-0.015869390219449997,
-0.007302222773432732,
0.0004054471501149237,
-0.008375696837902069,
0.010336015373468399,
0.027805760502815247,
0.02078341133892536,
-0.04180469363927841,
-0.01750120520591736,
0.016950367018580437,
-0.016796233132481575,
0.031425587832927704,
-0.01954801194369793,
-0.019230300560593605,
0.027636229991912842,
-0.0357196144759655,
-0.04082241281867027,
0.042511485517024994,
0.0007459524204023182,
0.029131799936294556,
0.040016058832407,
-0.0010881712660193443,
0.00036555182305164635,
0.07035419344902039,
-0.043712981045246124,
-0.056259654462337494,
0.003630170365795493,
-0.023722989484667778,
-0.010911666788160801,
-0.01409949827939272,
-0.0034134446177631617,
-0.017304429784417152,
-0.006727149244397879,
0.022471871227025986,
0.01340933796018362,
-0.04990175738930702,
0.02953134849667549,
0.0024344990961253643,
-0.03644554689526558,
0.01923871785402298,
0.046646565198898315,
0.014459550380706787,
-0.012469790875911713,
0.05212483927607536,
-0.025998244062066078,
0.013131930492818356,
0.01452780980616808,
0.009507374837994576,
-0.07528626918792725,
-0.029993021860718727,
-0.03315110504627228,
-0.00391667103394866,
-0.0015091367531567812,
-0.03206692263484001,
0.003310770494863391,
0.003936744760721922,
-0.03394581750035286,
-0.002033648546785116,
-0.03997180983424187,
-0.03295226767659187,
-0.004027658607810736,
0.005579581018537283,
0.018256185576319695,
0.03520800918340683,
0.056810323148965836,
0.04824954271316528,
0.03807101771235466,
-0.01432991586625576,
-0.0031648585572838783,
-0.04781609773635864,
-0.03207369148731232,
0.01810225285589695,
0.02786196768283844,
-0.0364045687019825,
0.04750273376703262,
-0.027731865644454956,
-0.015581452287733555,
0.0435497872531414,
0.03607810288667679,
0.018237965181469917,
-0.006803479976952076,
0.01702767238020897,
0.015728391706943512,
0.009485782124102116,
0.006112216506153345,
-0.03256788104772568,
-0.018229400739073753,
-0.00021971056412439793,
0.031608112156391144,
0.042981717735528946,
-0.0566362701356411,
-0.00557815283536911,
-0.00027867822791449726,
-0.021714260801672935,
-0.02838495932519436,
0.03478528559207916,
-0.017224624752998352,
-0.051043372601270676,
0.0017495955107733607,
-0.0034127263352274895,
0.0240314994007349,
-0.04199610650539398,
-0.013727863319218159,
-0.043836433440446854,
0.015804437920451164,
0.034301888197660446,
-0.004765782505273819,
-0.01279210764914751,
0.02719992958009243,
0.022690143436193466,
-0.015631498768925667,
-0.024293506518006325,
0.011132643558084965,
-0.03389371931552887,
-0.03962765634059906,
0.01430309284478426,
0.03912341967225075,
0.017829284071922302,
0.010510621592402458,
-0.023341096937656403,
-0.03857484087347984,
0.07372250407934189,
0.006297003943473101,
0.02155161090195179,
-0.019062571227550507,
-0.050770409405231476,
0.020736444741487503,
-0.06499850749969482,
0.003480001352727413,
-0.0025652789045125246,
-0.011902456171810627,
-0.029079241678118706,
-0.00240297126583755,
0.014752392657101154,
-0.0073863910511136055,
0.0571591816842556,
0.016296718269586563,
-0.03166339918971062,
-0.0017248645890504122,
-0.016980597749352455,
0.001210022484883666,
-0.05970664322376251,
-0.019430529326200485,
-0.02174564264714718,
-0.022112363949418068,
0.010239739902317524,
0.016637777909636497,
-0.017920108512043953,
0.009250316768884659,
0.0392720028758049,
0.0052991947159171104,
0.011231780052185059,
-0.004674470517784357,
0.009507260285317898,
0.044671040028333664,
0.011914094910025597,
0.0033096924889832735,
0.046151526272296906,
-0.02323930896818638,
0.012418277561664581,
0.05897751450538635,
-0.025356117635965347,
-0.05419312044978142,
0.03024262934923172,
-0.004457977134734392,
-0.009709225967526436,
-0.013770005665719509,
0.019135983660817146,
0.020108496770262718,
-0.04200102016329765,
0.005535219796001911,
0.07028864324092865,
-0.01017535850405693,
-0.028120828792452812,
0.03354794532060623,
0.00022016552975401282,
0.04008084163069725,
0.013047954998910427,
0.0385795533657074,
0.01762521266937256,
-0.0038243921007961035,
0.02670653723180294,
0.04960900545120239,
0.030259517952799797,
0.03250996023416519,
-0.011559159494936466,
0.0003874313260894269,
0.002011867705732584,
0.029866749420762062,
-0.027833957225084305,
0.0232254546135664,
-0.014777102507650852,
-0.025660017505288124,
0.021391520276665688,
-0.02605755627155304,
0.04759961739182472,
0.014397460967302322,
-0.003301043761894107,
0.0669117122888565,
-0.012744838371872902,
0.016452277079224586,
-0.01891384646296501,
-0.05258765444159508,
-0.01668415404856205,
0.03375383839011192,
-0.0026494809426367283,
0.02986866794526577,
-0.020115964114665985,
0.008904504589736462,
-0.04438294097781181,
-0.009924233891069889,
0.03291521593928337,
-0.0810401663184166,
0.011312210001051426,
0.00755847105756402,
0.015624266117811203,
-0.03120802529156208,
-0.010334577411413193,
-0.013213587924838066,
-0.015564478002488613,
0.0068506039679050446,
0.022859832271933556,
0.00808448065072298,
-0.032915979623794556,
-0.02838505059480667,
-0.019970083609223366,
0.012640639208257198,
-0.014166036620736122,
-0.05545857921242714,
-0.04227656498551369,
-0.009893328882753849,
-0.010679787956178188,
-0.010906215757131577
] |
<p>About the meta questions <a href="http://meta.physics.stackexchange.com/questions/1193/full-migration-of-theoretical-physics-se-questions-to-physics-se">1193</a> and <a href="http://meta.physics.stackexchange.com/questions/2609/why-theoretical-physics-has-been-closed">2609</a>, I've heard parallelly, that the complete branch <a href="http://en.wikipedia.org/wiki/Theoretical_physics" rel="nofollow">theoretical physics</a> is already done and that there isn't any thing else to do in this field, how true is it?</p> | 1,573 | [
-0.01200191956013441,
-0.020052488893270493,
0.00018265502876602113,
-0.009302722290158272,
0.017767485231161118,
0.020775001496076584,
0.008450386114418507,
-0.04533535614609718,
0.011753756552934647,
-0.04665278643369675,
0.014438992366194725,
0.04310392215847969,
0.03803805261850357,
0.017557404935359955,
0.024759169667959213,
0.022435834631323814,
0.0002744059602264315,
-0.01924373395740986,
0.013915052637457848,
-0.008043790236115456,
-0.012481316924095154,
0.01031208224594593,
0.004329141229391098,
0.019966306164860725,
-0.015809953212738037,
-0.004865502007305622,
0.0007350785308517516,
0.011881580576300621,
0.0007716758991591632,
0.03661816939711571,
-0.008554410189390182,
-0.0345047265291214,
0.02286604978144169,
-0.0119332792237401,
-0.025360284373164177,
0.005992301274091005,
-0.033954862505197525,
-0.040110666304826736,
0.002954739611595869,
0.0009663659729994833,
-0.0629546269774437,
-0.006142905913293362,
-0.03914838284254074,
0.0185224786400795,
-0.012129067443311214,
0.0039874170906841755,
-0.027239255607128143,
0.013779781758785248,
0.04790257290005684,
-0.07152168452739716,
0.04782227426767349,
0.0065369210205972195,
0.014201249927282333,
0.005419410299509764,
-0.0059660361148417,
0.010460942052304745,
0.08013493567705154,
0.07821637392044067,
-0.007989508099853992,
-0.06894860416650772,
-0.00717967888340354,
-0.019265582785010338,
0.022539732977747917,
0.02009880542755127,
-0.0548163466155529,
0.07524718344211578,
0.009262297302484512,
-0.027030136436223984,
0.03390262648463249,
-0.025899477303028107,
-0.002389639848843217,
0.036401309072971344,
0.010065361857414246,
-0.02475062385201454,
0.008910570293664932,
-0.03757201507687569,
0.01937631331384182,
0.01190098188817501,
-0.003042706521227956,
0.057653963565826416,
0.0002845242852345109,
0.016969187185168266,
0.015993190929293633,
0.044957127422094345,
-0.0095316581428051,
0.00216337526217103,
0.09630510956048965,
-0.02679537795484066,
-0.027252916246652603,
0.010640266351401806,
0.027383938431739807,
-0.01668713428080082,
0.046501196920871735,
0.0018437606049701571,
-0.046389371156692505,
0.04926502704620361,
0.011450139805674553,
0.044106487184762955,
-0.00019213027553632855,
-0.03853972628712654,
0.013308335095643997,
0.011676928959786892,
0.02648322656750679,
0.03285156562924385,
-0.0024603817146271467,
-0.04149036854505539,
-0.025160379707813263,
0.005555450450628996,
-0.031193168833851814,
-0.009532129392027855,
-0.03667803481221199,
0.012918018735945225,
-0.006405262742191553,
-0.0044822096824646,
-0.0036120624281466007,
-0.025275837630033493,
0.02562670037150383,
0.0027824670542031527,
0.06728748232126236,
0.07504600286483765,
0.03300606086850166,
-0.04836780205368996,
0.03869529068470001,
-0.011694262735545635,
-0.09824447333812714,
-0.01916501484811306,
0.05514837056398392,
-0.0399516336619854,
-0.0798187255859375,
-0.012496929615736008,
-0.00992397591471672,
0.021070163697004318,
0.011946650221943855,
-0.0014945698203518987,
0.026811663061380386,
-0.021912124007940292,
-0.08549855649471283,
-0.05896715447306633,
0.03271513804793358,
-0.0022687441669404507,
-0.017659083008766174,
-0.06460975855588913,
-0.00891245249658823,
0.02189067006111145,
0.10582085698843002,
-0.007948442362248898,
0.018179962411522865,
-0.019273286685347557,
0.04265028238296509,
0.003326273988932371,
-0.030556218698620796,
-0.013344821520149708,
-0.00537197245284915,
0.01702537201344967,
-0.01822066865861416,
-0.07692661881446838,
0.02645975723862648,
0.01589832827448845,
-0.00679133553057909,
-0.0045637148432433605,
0.08090910315513611,
0.0001605775614734739,
0.015437058173120022,
-0.013314403593540192,
0.003496031742542982,
0.0017114540096372366,
0.06404488533735275,
0.03609279543161392,
0.0036725166719406843,
0.022155584767460823,
-0.00789579190313816,
0.0013537604827433825,
-0.003699597669765353,
0.005608568899333477,
0.0280016902834177,
-0.03828040510416031,
-0.019666507840156555,
0.0009683399111963809,
0.013907785527408123,
-0.025390591472387314,
-0.0038319590967148542,
-0.004488829523324966,
0.004384985193610191,
0.000340140686603263,
0.019641496241092682,
0.07462265342473984,
-0.022548798471689224,
0.013286271132528782,
0.02967287041246891,
-0.04557230323553085,
-0.007472797762602568,
-0.05462780222296715,
-0.005231054965406656,
-0.005153343081474304,
0.015930958092212677,
0.03009440004825592,
-0.00300010247156024,
-0.005161787383258343,
-0.018003081902861595,
-0.020676221698522568,
0.014741471037268639,
0.04881005734205246,
0.033309388905763626,
0.04197997599840164,
0.019988292828202248,
0.0453803688287735,
0.02723032608628273,
-0.02844136208295822,
0.023778453469276428,
-0.02087537758052349,
-0.07385686039924622,
0.008602914400398731,
-0.01216459833085537,
0.05451452359557152,
0.01888938806951046,
-0.011876789852976799,
-0.0024391128681600094,
0.03234429657459259,
-0.019499680027365685,
0.03721078485250473,
-0.03329990431666374,
0.027963612228631973,
0.019085774198174477,
0.026334980502724648,
0.014344568364322186,
0.04016992077231407,
0.02449715882539749,
0.019072316586971283,
0.028803443536162376,
-0.006583389360457659,
-0.05688181146979332,
0.0017925651045516133,
0.042049746960401535,
0.014092071913182735,
-0.07105426490306854,
0.02851950190961361,
-0.03779828920960426,
0.031147006899118423,
0.04068588465452194,
0.009788397699594498,
-0.05573789402842522,
-0.054517630487680435,
0.029578138142824173,
0.03173574060201645,
-0.010919669643044472,
-0.0011644497280940413,
-0.011309821158647537,
0.029798835515975952,
-0.03131949156522751,
0.024374693632125854,
0.00002547751137171872,
0.06061256304383278,
0.014814002439379692,
-0.011407030746340752,
0.020892253145575523,
-0.027608947828412056,
0.06482309103012085,
-0.03811635076999664,
0.00427667610347271,
0.007775869686156511,
0.011974643915891647,
-0.00316149671562016,
-0.0286784116178751,
-0.01027960516512394,
0.0026691455859690905,
0.03281195089221001,
-0.008719373494386673,
-0.016187801957130432,
0.012744066305458546,
-0.04875306785106659,
-0.02334301546216011,
-0.03329950198531151,
0.01169484481215477,
-0.01830284669995308,
0.02105814591050148,
0.019469378516077995,
0.0037641613744199276,
0.053755536675453186,
-0.03064214438199997,
-0.0018357466906309128,
0.03091970831155777,
-0.024567104876041412,
-0.001477062818594277,
0.02877693809568882,
-0.023999366909265518,
-0.010209714062511921,
-0.04718315973877907,
-0.03605422377586365,
0.037142615765333176,
-0.07290812581777573,
0.048870719969272614,
0.018870966508984566,
0.0069910394959151745,
-0.025635384023189545,
-0.01346474140882492,
-0.022730322554707527,
0.022185657173395157,
-0.03138750419020653,
0.0010726932669058442,
0.006803895812481642,
0.005298265255987644,
-0.022580459713935852,
0.0035787788219749928,
-0.027598576620221138,
-0.0685783177614212,
-0.02178574539721012,
0.02178071066737175,
0.018052861094474792,
-0.03687605634331703,
0.006781137082725763,
0.027419719845056534,
-0.06159641221165657,
0.03450114652514458,
-0.07093065977096558,
-0.011684686876833439,
0.03517251834273338,
-0.009825472719967365,
0.04584885761141777,
0.004482334479689598,
-0.02650652639567852,
0.05300265550613403,
0.026255212724208832,
-0.04533623903989792,
-0.014639380387961864,
-0.00963208731263876,
-0.030651815235614777,
-0.028174370527267456,
-0.019756430760025978,
0.0058854431845247746,
0.023753158748149872,
0.02936306968331337,
0.04051554948091507,
0.040547292679548264,
0.010681092739105225,
0.05749130994081497,
-0.014088237658143044,
0.011920144781470299,
0.02306944690644741,
0.003946462646126747,
0.03546418622136116,
0.004417054820805788,
-0.036712367087602615,
0.009224445559084415,
-0.0445685088634491,
0.011989476159214973,
0.01868170127272606,
-0.018942784518003464,
0.08573650568723679,
0.028024248778820038,
-0.0008055575890466571,
-0.020316442474722862,
0.05026722326874733,
0.0005553629016503692,
-0.03370077162981033,
0.011802183464169502,
0.01982920803129673,
0.046711843460798264,
0.023963581770658493,
-0.022228406742215157,
0.009608651511371136,
0.05856798216700554,
-0.0434589758515358,
-0.01783379726111889,
-0.03984585776925087,
-0.011330455541610718,
0.018823254853487015,
-0.010516239330172539,
-0.04858717322349548,
0.03850400075316429,
0.054368507117033005,
0.02889569289982319,
0.009662286378443241,
-0.015842953696846962,
-0.02915329299867153,
-0.05896218866109848,
-0.007709507830440998,
-0.0364389531314373,
0.0769737958908081,
0.003300693118944764,
0.007601387798786163,
0.03550378605723381,
0.0010154295014217496,
-0.017344778403639793,
0.048007216304540634,
-0.1001816838979721,
0.018440797924995422,
-0.05075843632221222,
0.016074225306510925,
0.0026436273474246264,
0.013476784341037273,
-0.012622982263565063,
0.0035437888000160456,
-0.053618304431438446,
-0.019389856606721878,
-0.0037540625780820847,
-0.05689002946019173,
-0.0041504232212901115,
-0.06797381490468979,
-0.04184882342815399,
-0.01278744637966156,
0.03101831115782261,
0.031119374558329582,
-0.04055747017264366,
0.027713831514120102,
0.029962902888655663,
-0.042934127151966095,
-0.009122855961322784,
-0.004388492088764906,
0.02520703338086605,
-0.0029753597918897867,
0.02669541724026203,
0.06678151339292526,
0.027614202350378036,
-0.03900379315018654,
0.02614571526646614,
0.03355427831411362,
0.028887547552585602,
0.04639489948749542,
-0.025391926988959312,
0.003957017790526152,
-0.06778617948293686,
-0.024727577343583107,
0.0057044257409870625,
0.031960904598236084,
0.0050672497600317,
-0.0034628654830157757,
0.026953615248203278,
0.0031402562744915485,
-0.02429642528295517,
0.06373921781778336,
0.0667097419500351,
-0.02714681066572666,
-0.049296148121356964,
-0.02783578634262085,
-0.015216313302516937,
-0.0020242007449269295,
-0.008005231618881226,
0.013842148706316948,
0.02483205683529377,
0.011066692881286144,
0.02549666538834572,
0.01618000864982605,
0.006247371900826693,
-0.0456819012761116,
0.037485044449567795,
-0.0040204329416155815,
0.021764254197478294,
-0.022381069138646126,
-0.016662318259477615,
-0.014762062579393387,
0.041079096496105194,
0.04488001763820648,
-0.01780726946890354,
0.01118050329387188,
-0.07076502591371536,
0.01819942146539688,
0.050039391964673996,
0.053383711725473404,
-0.0076351831667125225,
-0.012922333553433418,
-0.04547637328505516,
-0.003720198292285204,
0.017036400735378265,
-0.03217994049191475,
0.004960373975336552,
-0.043277811259031296,
-0.004551304504275322,
-0.03363817185163498,
-0.04186715930700302,
0.038029301911592484,
0.029732858762145042,
0.014514886774122715,
0.02373727224767208,
-0.045176248997449875,
-0.001371414982713759,
0.0015681548975408077,
0.02748299576342106,
0.02354852482676506,
0.06259583681821823,
0.013621973805129528,
-0.013968177139759064,
-0.003326680511236191,
-0.008208109997212887,
-0.04925936087965965,
-0.07429878413677216,
-0.014699002727866173,
0.007685995195060968,
-0.04340377449989319,
0.051767610013484955,
-0.04999677091836929,
-0.042638521641492844,
0.03501143306493759,
0.013577546924352646,
-0.03122769109904766,
0.005474181845784187,
-0.04769446328282356,
0.04199419543147087,
0.03805768862366676,
0.006942334584891796,
0.03217095509171486,
0.05158524215221405,
-0.054396774619817734,
0.011957885697484016,
0.013674124144017696,
0.019039316102862358,
0.012470793910324574,
0.024569960311055183,
-0.012888936325907707,
0.006631807424128056,
-0.05589699000120163,
0.0319233238697052,
-0.01155642420053482,
0.007788308430463076,
-0.03277869150042534,
-0.010884729214012623,
-0.03948964551091194,
0.00392611138522625,
-0.01881697215139866,
-0.019624462351202965,
0.04027937725186348,
0.04613710567355156,
-0.0008453719783574343,
-0.03474293649196625,
0.02040618471801281,
0.01472829096019268,
-0.0024687685072422028,
0.041367240250110626,
0.013531506061553955,
0.01806359738111496,
-0.03790723532438278,
-0.03333195298910141,
-0.01539262942969799,
-0.021032121032476425,
0.015483051538467407,
-0.0035132491029798985,
-0.009738151915371418,
0.039245862513780594,
-0.06480273604393005,
-0.01341225765645504,
0.028571320697665215,
-0.0046863858588039875,
-0.006208361126482487,
-0.03139963373541832,
0.05055905133485794,
0.016876770183444023,
0.019069084897637367,
-0.04674554243683815,
-0.011178144253790379,
0.031029336154460907,
0.009942356497049332,
-0.021674420684576035,
-0.0356525257229805,
0.01467227190732956,
-0.054397206753492355,
-0.010947264730930328,
-0.0278441421687603,
0.05344896391034126,
-0.04889517277479172,
0.004835295490920544,
0.006470807362347841,
0.025497259572148323,
0.043607890605926514,
-0.004051498137414455,
-0.01964465342462063,
-0.009182031266391277,
0.01495369616895914,
-0.00830339640378952,
0.004147403407841921,
0.029227349907159805,
-0.026453394442796707,
-0.03448024392127991,
-0.0036750156432390213,
-0.005124012473970652,
0.04261869564652443,
-0.0056849936954677105,
0.0027653800789266825,
0.018319178372621536,
-0.0227520689368248,
-0.004719711374491453,
-0.03860516846179962,
0.01712309755384922,
0.011431590653955936,
0.03914497047662735,
-0.01689104177057743,
0.048779506236314774,
0.012404464185237885,
-0.012318356893956661,
0.020191781222820282,
-0.00816920306533575,
0.02555866539478302,
-0.008838125504553318,
0.021705156192183495,
-0.00864281877875328,
0.015253082849085331,
0.01939055137336254,
-0.03118119388818741,
0.01564427837729454,
0.009555192664265633,
0.045215144753456116,
0.0013879385078325868,
-0.008197211660444736,
0.012434234842658043,
-0.05134361609816551,
-0.03386227414011955,
-0.01995505951344967,
0.04886151850223541,
-0.01936829835176468,
0.053997814655303955,
0.008036578074097633,
-0.03791200369596481,
-0.03391382470726967,
-0.004312656819820404,
0.004567006137222052,
0.021047882735729218,
0.03394162654876709,
-0.016714483499526978,
-0.04020772501826286,
0.002062680199742317,
0.0429360456764698,
0.026219841092824936,
0.02600652351975441,
-0.0018039067508652806,
0.03173188865184784,
0.04375811293721199,
0.012653931975364685,
-0.0615924708545208,
-0.03416259214282036,
0.055789411067962646,
-0.06779810041189194,
0.030706148594617844,
0.04192188009619713,
-0.02787948027253151,
0.028802070766687393,
0.015249219723045826,
0.021084332838654518,
0.0033226674422621727,
-0.015162724070250988,
-0.0486585907638073,
0.021148424595594406,
-0.03379983454942703,
0.031245816498994827,
-0.002039064886048436,
-0.009497147984802723,
-0.002804458374157548,
0.03237780183553696,
0.03217800706624985,
0.0058123026974499226,
-0.06626374274492264,
-0.02366526424884796,
-0.040491849184036255,
-0.04928596690297127,
0.06192393600940704,
-0.02240007370710373,
-0.03172989562153816,
0.03638853877782822,
-0.02127229794859886,
0.008763816207647324,
-0.004316875245422125,
0.0352618470788002,
-0.0634775385260582,
0.058369431644678116,
-0.008783753030002117,
0.030753877013921738,
0.004118827171623707,
-0.013878557831048965,
0.11430540680885315,
0.051723383367061615,
0.03018440306186676,
-0.06466593593358994,
0.010621433146297932,
-0.022135725244879723,
0.016399724408984184,
-0.0473950020968914,
-0.005054459907114506,
-0.009542716667056084,
0.0030836474616080523,
0.010322538204491138,
0.09264516830444336,
0.04245651140809059,
0.00439177080988884,
0.03907592222094536,
-0.02208021469414234,
-0.05814092606306076,
-0.0004911018768325448,
0.03300997242331505,
-0.019336994737386703,
-0.008698849007487297,
-0.031242789700627327,
0.006974626332521439,
-0.020106926560401917,
0.024440590292215347,
-0.03468422219157219,
-0.024569712579250336,
0.026128435507416725,
-0.01802549883723259,
-0.06162990257143974,
0.00024224385560955852,
-0.006520180497318506,
-0.020060274749994278,
-0.03795383870601654,
0.02504521794617176,
0.0225065965205431,
-0.040344931185245514,
0.03165782243013382,
0.06249161437153816,
0.014474608935415745,
-0.007439216133207083,
-0.012080272659659386,
0.002157296985387802,
-0.040358636528253555,
0.02835606224834919,
-0.009526483714580536,
0.016523078083992004,
-0.01202558446675539,
0.00281284237280488,
-0.012992605566978455,
-0.018846113234758377,
-0.02739342860877514,
-0.011192785575985909,
-0.018692679703235626,
-0.004109131172299385,
0.04624497517943382,
-0.01191701553761959,
0.001356707769446075,
-0.03869512304663658,
0.02181783691048622,
-0.00431812135502696,
0.030260847881436348,
-0.016920069232583046,
-0.029549026861786842,
-0.01951451040804386,
-0.010200773365795612,
0.018635515123605728,
-0.008958442136645317,
-0.0069589572958648205,
-0.04306638240814209,
0.0313129723072052,
-0.03903478756546974,
-0.017652155831456184,
0.0013928038533776999,
0.018292462453246117,
0.057977914810180664,
0.0038075123447924852,
0.00948663055896759,
-0.02079099230468273,
-0.0414900965988636,
0.004172631539404392,
-0.0073926798067986965,
-0.014491000212728977,
-0.02775155007839203,
0.003634592518210411,
0.022630101069808006,
0.026012824848294258,
-0.009107111021876335,
0.0013867595698684454,
-0.01820209063589573,
0.020185653120279312,
0.010830225422978401,
-0.0392046794295311,
-0.02136472798883915,
0.009027308784425259,
-0.03637954592704773,
0.02793194353580475,
-0.007224162109196186,
0.0010962424566969275,
0.018578439950942993,
0.0003005261532962322,
0.025366926565766335,
0.01657707616686821,
-0.0029836820904165506,
0.003817324060946703,
0.036488037556409836,
-0.044346362352371216,
-0.015664448961615562,
0.01450529508292675,
0.004561225418001413,
-0.04412725567817688,
-0.02476002834737301,
-0.009230772033333778,
-0.003020548727363348,
0.04399971291422844,
0.026117388159036636,
-0.043264150619506836,
0.03534429520368576,
-0.0386783666908741,
0.011855910532176495,
-0.06290438026189804,
-0.009446535259485245,
-0.07151757925748825,
-0.010060442611575127,
-0.009114599786698818,
-0.011556396260857582,
-0.0064954026602208614,
0.039275873452425,
0.009894010610878468,
-0.0367741733789444,
0.022588742896914482,
0.03896253556013107,
-0.05205725133419037,
0.03662216290831566,
-0.009834660217165947,
0.012237222865223885,
0.028985466808080673,
-0.01555092167109251,
-0.027383947744965553,
0.059802647680044174,
-0.018085671588778496,
-0.0462782084941864,
0.03254576772451401,
-0.029322393238544464,
0.005615824833512306,
0.006705509033054113,
-0.0254234466701746,
-0.02375882677733898,
0.06618477404117584,
-0.009900657460093498,
0.0020307220984250307,
0.011947373859584332,
-0.014703853987157345,
-0.007883335463702679,
-0.022278446704149246,
0.030341964215040207,
0.0006207575788721442,
-0.016176987439393997,
0.025971008464694023,
0.049842365086078644,
-0.012069804593920708,
-0.011603293940424919,
-0.017823562026023865,
-0.0363493338227272,
0.018098266795277596,
0.011463613249361515,
0.010711615905165672,
0.0326433926820755,
0.04557665064930916,
-0.073126882314682,
0.009933851659297943,
-0.015244191512465477,
0.0063858311623334885,
-0.09323722869157791,
0.00036828481825068593,
0.02050425112247467,
-0.008199856616556644,
0.0282073263078928,
-0.012587867677211761,
0.04086359962821007,
0.02502681128680706,
-0.08808279782533646,
0.03405824303627014,
-0.008701616898179054,
-0.06529219448566437,
-0.022709233686327934,
0.0015110303647816181,
-0.031009269878268242,
0.03612096980214119,
-0.01828852668404579,
0.030684614554047585,
-0.003788728266954422,
0.0024109480436891317,
-0.009120186790823936,
-0.005032472778111696,
-0.03198615461587906,
-0.007201800588518381,
-0.015220937319099903,
-0.0005405473639257252,
0.07042429596185684,
-0.011084342375397682,
-0.07388970255851746,
0.01692359521985054,
0.019181201234459877,
0.027444614097476006,
-0.021828360855579376,
0.0025731499772518873,
0.0030090410728007555,
-0.013050049543380737,
0.05730561167001724,
-0.000382941507268697,
-0.004475285764783621,
0.00787317380309105,
0.027774987742304802,
0.04201845824718475,
0.017638538032770157,
0.03669999912381172,
-0.010639547370374203,
-0.03647314012050629,
-0.0166213009506464,
0.02464793436229229,
-0.044343505054712296,
-0.0030318843200802803,
-0.01764143817126751,
0.012471389956772327,
0.0053446595557034016,
-0.029301267117261887,
-0.021455099806189537,
-0.048697806894779205,
-0.024388661608099937,
0.03207530826330185,
0.01381239015609026,
0.04674781113862991,
0.005567752756178379,
0.007566951680928469,
-0.027300400659441948,
-0.0062574283219873905,
-0.02117101661860943,
-0.006233516614884138,
-0.04823189973831177,
-0.021571394056081772,
0.02054089494049549,
-0.001241217483766377,
0.0013044701190665364,
-0.03383448347449303,
-0.025276491418480873,
0.025067424401640892,
0.01940501667559147,
0.025736089795827866,
-0.00770464027300477,
-0.029245860874652863,
-0.0178830586373806,
-0.04284629970788956,
0.025113673880696297,
0.007645281031727791,
0.036009542644023895,
-0.01775769144296646,
-0.028826190158724785,
-0.003959972877055407,
0.006717569660395384,
0.03019561991095543,
-0.01077031809836626,
-0.008132562041282654,
0.0017984813312068582,
-0.012887129560112953,
0.021607812494039536,
-0.056661367416381836,
-0.0370650514960289,
-0.032781168818473816,
-0.0054013472981750965,
0.013324340805411339,
-0.03804532811045647,
-0.004566127434372902,
0.0034928065724670887,
0.03862304985523224,
-0.00409074267372489,
0.017532791942358017,
0.015492398291826248,
-0.009925191290676594,
0.04162180423736572,
0.005504676606506109,
0.002822451526299119,
0.06059064716100693,
0.0018762585241347551,
0.03575700893998146,
0.04035944491624832,
0.0011150676291435957,
0.024828756228089333,
0.05098234489560127,
-0.034726470708847046,
0.005271784029901028,
-0.01234133169054985,
-0.03125404193997383,
0.011324824765324593,
-0.012108059599995613,
0.016249138861894608,
0.04767478257417679,
-0.022682735696434975,
0.002509272424504161,
0.04389544576406479,
0.059004489332437515,
0.027661079540848732,
0.01912241242825985,
-0.011926360428333282,
0.016109881922602654,
-0.04034401848912239,
0.004988015163689852,
0.06246667727828026,
0.030559737235307693,
0.003917081747204065,
0.010139700025320053,
0.00907858181744814,
0.005902347154915333,
0.0060228388756513596,
0.020100541412830353,
0.04820961132645607,
-0.019204502925276756,
-0.014255347661674023,
0.02625887282192707,
0.011776570230722427,
0.01647184230387211,
0.0428963266313076,
-0.025368310511112213,
0.07485538721084595,
-0.016404828056693077,
0.027070295065641403,
0.021313928067684174,
-0.03154941648244858,
-0.0032621605787426233,
-0.0004951343289576471,
0.010482355952262878,
0.04215475171804428,
-0.02511187456548214,
-0.0215750839561224,
-0.01992136985063553,
0.06217968836426735,
0.015342449769377708,
-0.053142204880714417,
0.0013834181008860469,
-0.023003309965133667,
0.007851753383874893,
-0.0021412610076367855,
-0.005736973136663437,
-0.0324508436024189,
-0.014205699786543846,
0.019979294389486313,
0.035656798630952835,
0.001166075118817389,
-0.02513439580798149,
0.003561520017683506,
-0.04398868978023529,
0.031269725412130356,
-0.00315741915255785,
0.00705720717087388,
-0.02047920413315296,
0.02388491854071617,
-0.022340981289744377,
-0.03940664976835251
] |
<p><strong>The Setup</strong>: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric </p>
<p>$ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$. </p>
<p>It seems to me that in the usual discussion (e.g. di Francesco, Ginsparg, Polchinski), one proceeds to consider an analytic continuation of the CFT to $\mathbb C^2$ with coordinates $z^1, z^2$ and complex metric</p>
<p>$ds^2 = (dz^1)^2+(dz^2)^2$</p>
<p>and then, one performs the coordinate transformation $z = z^1+iz^2$ and $\bar z = z^1-iz^2$. In this way the coordinates $z$ and $\bar z$ can be considered "independent" because they are coordinates on a complex two-dimensional manifold. Also, in these coordinates the metric becomes</p>
<p>$ds^2 = dz\,d\bar z$</p>
<p>and it becomes clear that conformal mappings consist of mappings: $(z, \bar z)\to (f(z), g(\bar z))$.</p>
<p><strong>My confusion is this</strong>: Since our original theory was on $\mathbb R^2$, books say that when we do calculations, we should consider the physical theory as living on the copy of $\mathbb R^2$ embedded in $\mathbb C^2$ given by the condition $\bar z = z^*$. But consider the mapping $(z, \bar z)\to (z^2, \bar z)$. This is a conformal mapping on $\mathbb C^2$, but it does not map the surface $\bar z = z^*$ to itself; for example the point $(z, \bar z)=(2,2)$ gets mapped to the point $(z^2, \bar z) =(4,2)$ and $2$ is clearly not equal to $4^*$. In particular, it seems to me that analytic continuation to a CFT on $\mathbb C^2$ enlarges the set of mappings one can have, so what relevance does it really have to the original CFT on $\mathbb R^2$? (my apologies for the long post)</p> | 1,574 | [
0.030179694294929504,
0.007645116653293371,
0.033336300402879715,
-0.05308401584625244,
0.02080649882555008,
-0.0014218637952581048,
-0.02401955984532833,
-0.044379353523254395,
-0.014015348628163338,
-0.05177169665694237,
0.013029214926064014,
0.0047927191480994225,
0.06477613747119904,
0.003831462701782584,
0.011349032633006573,
-0.008714750409126282,
-0.020021256059408188,
-0.01195675041526556,
-0.05565110966563225,
0.018320387229323387,
0.04918593913316727,
0.021070584654808044,
-0.013838996179401875,
-0.020746583119034767,
-0.00035424705129116774,
0.016107909381389618,
-0.02759413793683052,
-0.003391276579350233,
-0.02689727209508419,
0.060023076832294464,
-0.04143914580345154,
-0.04104984179139137,
0.010851738043129444,
0.009466825984418392,
-0.005676256492733955,
-0.013524897396564484,
-0.05192860588431358,
-0.015919040888547897,
0.007852091453969479,
0.003062227740883827,
-0.044965919107198715,
-0.02983846515417099,
-0.03465808182954788,
0.060797616839408875,
-0.011765921488404274,
0.0070630875416100025,
-0.016044221818447113,
-0.012196533381938934,
0.0519280880689621,
-0.04192834720015526,
0.043600570410490036,
0.002867715433239937,
0.009900291450321674,
0.009045562706887722,
-0.007430291268974543,
-0.012323890812695026,
0.06655579060316086,
0.019474590197205544,
0.025241170078516006,
-0.04444519430398941,
-0.04002083092927933,
-0.0004928765702061355,
0.009616684168577194,
-0.03593892231583595,
-0.011220098473131657,
0.037817973643541336,
0.0190380048006773,
0.008623704314231873,
0.016889600083231926,
-0.0015357364900410175,
0.009495260193943977,
0.010451085865497589,
0.01709412783384323,
-0.04139496013522148,
0.04236505180597305,
0.008527036756277084,
-0.013727677054703236,
0.007929523475468159,
0.056942183524370193,
-0.005399717018008232,
0.014365549199283123,
0.012721703387796879,
0.02290554903447628,
0.006652896758168936,
0.00945206731557846,
-0.02100859209895134,
0.055130042135715485,
0.025303339585661888,
0.002002848545089364,
0.03697168081998825,
0.01688636839389801,
-0.009834641590714455,
0.025377079844474792,
-0.05531613528728485,
-0.021998625248670578,
0.06064398214221001,
0.020645160228013992,
0.03064478188753128,
-0.04826381057500839,
-0.004049370530992746,
-0.029106270521879196,
-0.03808772191405296,
0.003224130254238844,
0.07032347470521927,
0.001678423024713993,
0.021019382402300835,
-0.037302713841199875,
0.02156534045934677,
-0.05794692784547806,
-0.03977758064866066,
-0.024771753698587418,
0.024043522775173187,
-0.03196078538894653,
0.0366678461432457,
-0.011410246603190899,
-0.0026920612435787916,
-0.01654941216111183,
-0.00654251966625452,
0.04263950139284134,
0.04010884463787079,
0.030032707378268242,
-0.01233102846890688,
-0.0169123113155365,
-0.03399771824479103,
-0.05132296681404114,
0.025004597380757332,
0.07697559893131256,
0.017137737944722176,
-0.03504963964223862,
-0.01535340491682291,
0.0635213702917099,
0.00030414608772844076,
0.006815603002905846,
0.05561544746160507,
0.0035082101821899414,
-0.00925125740468502,
-0.06954505294561386,
-0.03543929383158684,
0.023309459909796715,
0.008599471300840378,
0.01175332348793745,
-0.07885592430830002,
-0.001885942998342216,
0.015335208736360073,
0.08992785960435867,
-0.02466459572315216,
0.02993607707321644,
0.03978133574128151,
0.03038729354739189,
-0.013087240979075432,
-0.010627202689647675,
0.005739941727370024,
-0.026431996375322342,
-0.0415763221681118,
-0.04951810464262962,
-0.030882421880960464,
0.024875987321138382,
0.04212285950779915,
0.01624506525695324,
-0.021504459902644157,
0.05805445834994316,
-0.02147533744573593,
0.016360847279429436,
0.0029490222223103046,
-0.0027165838982909918,
-0.0005078382673673332,
0.050454095005989075,
0.012737859971821308,
0.020159007981419563,
0.027775242924690247,
-0.020050542429089546,
0.03289332985877991,
-0.01273076981306076,
0.03102518990635872,
0.0054669566452503204,
-0.03136417642235756,
-0.04445963725447655,
0.004584581591188908,
-0.02905452437698841,
-0.00003590143023757264,
0.014281637966632843,
-0.03495042398571968,
-0.02457418106496334,
0.02344556525349617,
-0.01367836445569992,
0.055531710386276245,
0.01410911325365305,
-0.016745854169130325,
0.02171057090163231,
-0.06466225534677505,
0.015106307342648506,
-0.049210235476493835,
0.0065424018539488316,
0.020774517208337784,
-0.016076767817139626,
0.03010903112590313,
-0.017918502911925316,
-0.008269836194813251,
0.04111335054039955,
-0.04034382849931717,
-0.0009750468307174742,
0.026118522509932518,
0.02511480264365673,
0.010526391677558422,
0.03112872689962387,
0.040311917662620544,
0.05327833071351051,
0.030227189883589745,
0.01280150655657053,
-0.031513869762420654,
-0.014126474037766457,
0.012433594092726707,
0.00785348005592823,
0.025583483278751373,
0.017203936353325844,
0.0028094265144318342,
-0.01358169224113226,
0.0007737474516034126,
-0.03509476035833359,
0.01885957457125187,
-0.05539573356509209,
0.04787527397274971,
0.06141263619065285,
-0.012922504916787148,
-0.006217262241989374,
0.06224565953016281,
0.0032144507858902216,
0.007568371947854757,
0.021506380289793015,
-0.027306485921144485,
-0.037172358483076096,
-0.010523518547415733,
0.05722664296627045,
0.08857809752225876,
-0.038289874792099,
-0.024958636611700058,
0.03711285442113876,
0.05200519040226936,
-0.011749512515962124,
0.0016757179982960224,
-0.018139386549592018,
-0.05504874140024185,
0.029383916407823563,
-0.044173527508974075,
0.038378309458494186,
0.0016483751824125648,
0.0317995585501194,
0.008386877365410328,
-0.0325065478682518,
-0.013893012888729572,
-0.019796667620539665,
0.04374856874346733,
-0.0469607375562191,
-0.01561069767922163,
0.011250784620642662,
0.02772293984889984,
0.022029051557183266,
0.003102221991866827,
0.002375893760472536,
0.03159623593091965,
0.03340437263250351,
-0.030812950804829597,
-0.044186726212501526,
0.011656724847853184,
0.01880156248807907,
0.019558073952794075,
-0.014603779651224613,
-0.014712844975292683,
0.009353493340313435,
-0.02556215599179268,
-0.00465324567630887,
-0.013002834282815456,
-0.03156444430351257,
0.020111234858632088,
0.002237627748399973,
0.02173020876944065,
0.0034149102866649628,
-0.001003054203465581,
-0.03997117280960083,
-0.03766448050737381,
0.004971134010702372,
0.004107361659407616,
0.004460022784769535,
0.03839012235403061,
-0.018445389345288277,
0.027159541845321655,
-0.06524933874607086,
0.01617816649377346,
0.04031977429986,
-0.0048939548432827,
0.005410688929259777,
-0.008980299346148968,
0.012468243017792702,
-0.033000946044921875,
-0.055856700986623764,
-0.034824881702661514,
0.04919636622071266,
-0.04545889422297478,
0.016690626740455627,
0.10489166527986526,
0.037571121007204056,
-0.006474069319665432,
0.009747907519340515,
-0.0005744890659116209,
-0.027132688090205193,
0.011377827264368534,
-0.026033727452158928,
0.008497553877532482,
-0.020924553275108337,
0.015360221266746521,
-0.002061529317870736,
-0.058093637228012085,
0.0027414194773882627,
-0.047399409115314484,
-0.06641885638237,
0.01784888282418251,
-0.005034938454627991,
0.01031141635030508,
-0.002524112816900015,
-0.060714300721883774,
0.08855132758617401,
-0.014815311878919601,
-0.027001280337572098,
-0.0018862847937271,
0.033255696296691895,
-0.005321752279996872,
-0.020689038559794426,
-0.027682004496455193,
0.024737780913710594,
-0.021556252613663673,
0.028812631964683533,
0.00958305411040783,
-0.006439832970499992,
0.0461159311234951,
0.008028348907828331,
-0.019806042313575745,
0.0323810912668705,
0.01685735583305359,
0.006762536242604256,
0.0255745816975832,
0.01303355023264885,
-0.008009806275367737,
0.00230482779443264,
0.01787036471068859,
-0.005746102891862392,
0.03430827334523201,
-0.05651768296957016,
0.03853581100702286,
-0.014769069850444794,
0.010081463493406773,
-0.002400212222710252,
0.03905051201581955,
-0.013186447322368622,
-0.05352141708135605,
-0.012332936748862267,
0.0026590763591229916,
0.04916377365589142,
-0.019554587081074715,
-0.014654632657766342,
0.008315100334584713,
0.03831684589385986,
-0.057175736874341965,
-0.017970385029911995,
-0.0026365050580352545,
0.0019362162565812469,
0.03778313845396042,
-0.02372688241302967,
-0.0028424577321857214,
0.036066506057977676,
0.04169106483459473,
0.03595975413918495,
-0.011331229470670223,
-0.023201588541269302,
0.025995898991823196,
-0.058551620692014694,
0.003729631192982197,
-0.01382205355912447,
0.036774538457393646,
-0.019001008942723274,
0.05033250153064728,
0.014353275299072266,
0.008501154370605946,
-0.00040914444252848625,
0.001694675418548286,
-0.06460683792829514,
-0.03902801126241684,
-0.011497629806399345,
-0.021337656304240227,
-0.011192775331437588,
-0.03550124540925026,
0.018111014738678932,
-0.018832551315426826,
-0.02300078608095646,
-0.025998050346970558,
-0.010120710358023643,
-0.03137848526239395,
0.011182006448507309,
-0.043319568037986755,
-0.055378373712301254,
-0.020060203969478607,
0.07114965468645096,
0.0826951116323471,
-0.018081193789839745,
-0.019168345257639885,
0.05580254644155502,
-0.022245557978749275,
0.01979910582304001,
-0.02409440651535988,
0.027064349502325058,
-0.00041866747778840363,
0.03758985176682472,
-0.007319679018110037,
0.04312804713845253,
0.01339016668498516,
0.0241620484739542,
0.032470013946294785,
0.03515029326081276,
0.0028275263030081987,
-0.037267860025167465,
0.00376428896561265,
-0.05819685757160187,
-0.0153929078951478,
-0.025789570063352585,
0.07856500148773193,
0.018028292804956436,
-0.0007753808749839664,
0.05205356329679489,
-0.015079324133694172,
0.03383335843682289,
0.01466656569391489,
0.05679614096879959,
-0.014434433542191982,
-0.0743795856833458,
-0.036707352846860886,
-0.05527863651514053,
-0.013871056027710438,
-0.0061051566153764725,
0.023840073496103287,
-0.000906130182556808,
-0.02107054553925991,
-0.0018747970461845398,
0.022850146517157555,
0.031867168843746185,
-0.002516578184440732,
-0.022889049723744392,
-0.011410597711801529,
-0.012308345176279545,
0.01958608813583851,
0.019994234666228294,
0.0003085891657974571,
0.045715779066085815,
0.03302996605634689,
0.0032013896852731705,
-0.03913445398211479,
-0.031204592436552048,
0.008924976922571659,
0.021393343806266785,
0.007269012276083231,
-0.004193718079477549,
0.0016570099396631122,
-0.037929266691207886,
-0.008678071200847626,
0.04453222453594208,
0.008329336531460285,
0.04230228438973427,
0.018965264782309532,
0.010314111597836018,
-0.029777398332953453,
-0.01968422345817089,
-0.005472231190651655,
0.01869918592274189,
0.013450142927467823,
0.0023559918627142906,
-0.04662401229143143,
0.0327952578663826,
-0.006044834386557341,
0.013984238728880882,
-0.0005483448621816933,
0.037908099591732025,
0.00030545765184797347,
0.036605995148420334,
-0.0038431633729487658,
0.030925199389457703,
-0.02331194095313549,
-0.06006838008761406,
-0.00550668453797698,
-0.008950341492891312,
-0.022220714017748833,
0.02647203579545021,
-0.04843493551015854,
-0.03210494667291641,
0.016605760902166367,
0.02298220619559288,
0.02053012140095234,
0.04496483877301216,
-0.058608997613191605,
0.04873831942677498,
0.05246369168162346,
0.01097183208912611,
0.015652362257242203,
0.009233606047928333,
-0.05450501665472984,
0.01623135805130005,
-0.018843999132514,
0.008266034536063671,
-0.013375788927078247,
0.0013485277304425836,
-0.0390961579978466,
0.013173793442547321,
-0.018703073263168335,
0.026161666959524155,
-0.01408558338880539,
0.007203536108136177,
-0.02058172971010208,
-0.010773025453090668,
0.0034001723397523165,
0.039414919912815094,
-0.02322811260819435,
0.052072711288928986,
0.0050887614488601685,
0.05136661231517792,
-0.025078115984797478,
-0.04932251200079918,
0.011051331646740437,
-0.011407915502786636,
-0.014430763199925423,
0.003605143167078495,
-0.01862124353647232,
0.022510433569550514,
-0.04198639839887619,
-0.026408422738313675,
0.04225444421172142,
-0.049505848437547684,
0.04679679125547409,
-0.01274846214801073,
-0.00821001548320055,
0.010059492662549019,
-0.052147723734378815,
-0.0190579816699028,
-0.00501217832788825,
0.0037453072145581245,
-0.03972720727324486,
-0.04232022166252136,
0.011688207276165485,
0.06650670617818832,
0.00048224179772660136,
-0.08121512830257416,
-0.02348300628364086,
-0.011023380793631077,
-0.018704403191804886,
-0.04621397331357002,
-0.02787075564265251,
0.036083705723285675,
-0.04055720567703247,
-0.03313281387090683,
-0.029170790687203407,
0.07495289295911789,
-0.008805399760603905,
-0.028304388746619225,
0.030184265226125717,
0.05235949903726578,
-0.007772345561534166,
-0.0207046028226614,
-0.006297308020293713,
0.017562994733452797,
0.013915449380874634,
0.004194349981844425,
0.012691736221313477,
0.03226504102349281,
-0.005114230327308178,
0.002320427680388093,
-0.003508881665766239,
-0.013487033545970917,
0.012330018915235996,
0.00037780270213261247,
-0.00822598859667778,
0.003338723676279187,
-0.0016218844102695584,
-0.007076676469296217,
-0.004258436616510153,
-0.03650546073913574,
0.005507214926183224,
0.053246498107910156,
-0.039119526743888855,
0.0055899773724377155,
-0.007675627712160349,
-0.029744828119874,
-0.004626475274562836,
0.03846586123108864,
-0.011428202502429485,
0.0032564059365540743,
0.03362326696515083,
0.027015483006834984,
-0.04036664962768555,
-0.035660501569509506,
-0.007386236917227507,
-0.005845267791301012,
0.0008136143442243338,
0.04329332709312439,
0.010017752647399902,
-0.002787899225950241,
-0.008033409714698792,
-0.018402526155114174,
-0.03096182458102703,
0.0179610475897789,
0.06828577071428299,
0.03317500278353691,
0.040429066866636276,
0.010598298162221909,
-0.029060110449790955,
0.0385863222181797,
-0.02573959156870842,
-0.0014245671918615699,
0.007516319863498211,
-0.0013863054336979985,
0.03282979130744934,
-0.055924057960510254,
-0.027462944388389587,
0.037245362997055054,
0.0180599894374609,
-0.012683626264333725,
-0.01309296116232872,
0.019270850345492363,
-0.0074572148732841015,
0.024367423728108406,
-0.03764469921588898,
-0.06802647560834885,
0.06772885471582413,
-0.04941536486148834,
0.03772653639316559,
0.0015588784590363503,
0.020386844873428345,
0.007993249222636223,
0.04582081362605095,
-0.012765421532094479,
-0.033417630940675735,
-0.02194277010858059,
-0.03348177671432495,
0.009339012205600739,
0.014811582863330841,
0.0011759218759834766,
0.012623166665434837,
-0.03172501549124718,
0.03286602720618248,
-0.030922194942831993,
0.0006413203664124012,
0.03417826443910599,
-0.05032564327120781,
0.020394684746861458,
-0.02856425940990448,
-0.05610773712396622,
0.08699734508991241,
-0.018400069326162338,
-0.02267691306769848,
-0.005154029466211796,
-0.02795000933110714,
0.01671593077480793,
0.031623728573322296,
0.020761655643582344,
-0.0272060614079237,
0.08161801844835281,
-0.013647870160639286,
0.017024416476488113,
-0.021454565227031708,
-0.0014962226850911975,
0.1396627128124237,
0.058681830763816833,
-0.014329764991998672,
-0.07162044197320938,
0.033085208386182785,
-0.013632064685225487,
0.015294174663722515,
-0.023727230727672577,
0.05919471010565758,
0.0053587923757731915,
-0.0018262335797771811,
0.015042521059513092,
0.04961061105132103,
0.03137839585542679,
-0.027201876044273376,
0.01050643716007471,
-0.041481368243694305,
-0.03885171189904213,
-0.01047289464622736,
-0.006978476420044899,
-0.09053204208612442,
-0.0029104917775839567,
-0.004257982596755028,
-0.0029991043265908957,
-0.01781347393989563,
0.014872836880385876,
-0.010848832316696644,
-0.031359460204839706,
0.006800027098506689,
0.032224029302597046,
-0.0616958811879158,
0.004355153534561396,
0.008856398053467274,
-0.027517156675457954,
-0.02826741896569729,
0.04128624498844147,
0.020370792597532272,
0.004825526382774115,
0.00212483131326735,
0.03636966645717621,
-0.01869197003543377,
0.028943950310349464,
-0.010446692816913128,
0.0035540068056434393,
-0.04174339398741722,
-0.010795109905302525,
-0.033659305423498154,
0.06171588972210884,
-0.035090528428554535,
-0.000049081078032031655,
0.010839925147593021,
0.024417465552687645,
0.06131858751177788,
-0.017661696299910545,
0.04839147627353668,
-0.008386095054447651,
-0.0015530841192230582,
-0.013595149852335453,
-0.005521203391253948,
-0.02012000046670437,
0.04244687408208847,
0.011257539503276348,
0.0101210568100214,
-0.0166457686573267,
-0.02068142779171467,
-0.025496387854218483,
0.007365045603364706,
0.03751770779490471,
0.015915341675281525,
0.007713162340223789,
-0.026779718697071075,
0.027683023363351822,
-0.018059389665722847,
-0.042733170092105865,
-0.016714205965399742,
0.003219516947865486,
0.07365196198225021,
0.031076574698090553,
0.00288123800419271,
-0.04556035250425339,
-0.029520271345973015,
0.003085378324612975,
-0.024440309032797813,
-0.002821381902322173,
-0.01811409741640091,
-0.006967946887016296,
0.02945035696029663,
0.036123670637607574,
0.015268075279891491,
0.0005377316265366971,
-0.022699179127812386,
0.012529214844107628,
0.038910865783691406,
-0.026780955493450165,
-0.02535773627460003,
0.01021197997033596,
-0.03328191488981247,
-0.007420672103762627,
-0.02019701898097992,
-0.0064690615981817245,
0.010295769199728966,
0.03787943348288536,
-0.060572221875190735,
0.02470928430557251,
0.005880067590624094,
0.01942558027803898,
0.03562231361865997,
-0.021145634353160858,
-0.003338030306622386,
0.017378220334649086,
0.020243873819708824,
-0.005546498112380505,
-0.015500721521675587,
0.001250842702575028,
-0.010935687460005283,
-0.0037731402553617954,
0.0022435602732002735,
-0.03566865622997284,
0.018886765465140343,
-0.003349984297528863,
0.002922980347648263,
-0.04798666760325432,
-0.04131406173110008,
-0.03647826611995697,
0.026059305295348167,
0.01792498119175434,
0.03221422806382179,
-0.0013460101326927543,
0.011683469638228416,
-0.02188420295715332,
-0.052080363035202026,
0.000246728042839095,
0.003065640339627862,
-0.01042842771857977,
0.010002901777625084,
0.008023945614695549,
-0.021583670750260353,
0.034289635717868805,
0.01583906263113022,
-0.004304335452616215,
-0.002538264263421297,
-0.01626657322049141,
-0.05590720474720001,
0.029415667057037354,
-0.027886483818292618,
0.029334010556340218,
-0.004389882553368807,
-0.025408366695046425,
-0.042381882667541504,
-0.020035570487380028,
-0.02436409704387188,
-0.01763514056801796,
-0.02000255323946476,
-0.04645433649420738,
0.008309985511004925,
-0.020510369911789894,
0.04741736873984337,
-0.014993308112025261,
0.015407370403409004,
0.0032193688675761223,
0.008605239912867546,
-0.014284510165452957,
-0.017308613285422325,
-0.02210645005106926,
-0.04278494045138359,
-0.00818278081715107,
-0.01735563948750496,
0.010306448675692081,
0.06578449159860611,
0.030975157395005226,
-0.01848176307976246,
0.006840705405920744,
0.00576145900413394,
0.012386792339384556,
-0.09611143916845322,
-0.009263766929507256,
0.04810621216893196,
0.0348375104367733,
0.05969169735908508,
-0.036261849105358124,
-0.018959593027830124,
-0.030929550528526306,
-0.07690410315990448,
0.019816581159830093,
-0.03742239624261856,
-0.023441525176167488,
-0.009080122224986553,
-0.008680514991283417,
-0.06600768119096756,
0.04705698415637016,
0.041996896266937256,
0.03505490720272064,
-0.030487120151519775,
0.0109852384775877,
0.01884325221180916,
-0.001135075930505991,
-0.05108228325843811,
-0.014029967598617077,
-0.0128350043669343,
-0.014564596116542816,
0.05701352283358574,
0.002140449360013008,
-0.008179343305528164,
-0.025015991181135178,
-0.01670917682349682,
-0.0035104085691273212,
-0.009712154045701027,
-0.0005264725768938661,
0.0475243516266346,
-0.00012784307182300836,
0.017946086823940277,
-0.014749187044799328,
-0.022143686190247536,
-0.01898360066115856,
0.017215682193636894,
0.027944415807724,
-0.019934648647904396,
-0.010631303302943707,
-0.033163491636514664,
-0.02119670808315277,
-0.010156110860407352,
0.024495746940374374,
-0.03263362869620323,
-0.022314507514238358,
-0.0040808082558214664,
0.0050817811861634254,
0.0020418590866029263,
-0.019474992528557777,
0.02519172988831997,
-0.05988913029432297,
-0.003997440449893475,
0.030225621536374092,
0.012880070134997368,
0.04379350692033768,
0.047241661697626114,
0.012312760576605797,
-0.02966533601284027,
0.035450469702482224,
0.012699844315648079,
0.013136661611497402,
-0.037107933312654495,
-0.05591292679309845,
0.007416474167257547,
-0.009554695338010788,
0.03265722841024399,
-0.01756482757627964,
0.033734820783138275,
0.009032750502228737,
0.023774631321430206,
-0.008556162938475609,
-0.08330820500850677,
-0.05914224684238434,
0.03397027775645256,
-0.05288120359182358,
0.035951245576143265,
-0.02013104222714901,
-0.01098265778273344,
0.0017703931080177426,
-0.03488236293196678,
-0.0004097722703590989,
0.017934327945113182,
0.045919906347990036,
-0.01979982666671276,
0.009195906110107899,
-0.015635769814252853,
0.01977204717695713,
0.058480650186538696,
-0.05017196759581566,
-0.006554898340255022,
0.04102382808923721,
0.01550154946744442,
0.006552164442837238,
0.010225599631667137,
-0.01610083505511284,
0.01930403895676136,
0.051371894776821136,
-0.027418103069067,
0.0707763060927391,
0.03429323807358742,
-0.06429850310087204,
0.04058278724551201,
0.019003110006451607,
-0.03502083942294121,
0.08894762396812439,
0.036800816655159,
0.02385466918349266,
0.06465301662683487,
-0.042674195021390915,
0.010191457346081734,
0.03663495182991028,
-0.012331104837357998,
-0.0010502288350835443,
-0.0062468103133141994,
0.015914015471935272,
0.023504983633756638,
-0.0092381052672863,
-0.0015982708428055048,
0.043730925768613815,
-0.04670095443725586,
-0.03630218282341957,
0.06896265596151352,
0.011487062089145184,
0.01134882215410471,
0.011217325925827026,
-0.0022215715143829584,
0.01010922435671091,
0.013632399030029774,
0.014864707365632057,
0.021649226546287537,
0.033890124410390854,
0.04251594841480255,
-0.01700006239116192,
0.02986546978354454,
-0.024766363203525543,
-0.01973346248269081,
0.0010282257571816444,
0.08421661704778671,
-0.01167638972401619,
-0.017819151282310486,
0.006462882272899151,
-0.015121472999453545,
-0.016156107187271118,
0.006268808152526617,
-0.0199188981205225,
0.08380303531885147,
-0.017993243411183357,
0.00012212994624860585,
-0.04540100693702698,
-0.0017147718463093042,
-0.04623157158493996,
0.0580284483730793,
0.04163341969251633,
0.046543654054403305,
0.003593011759221554,
0.03323139622807503,
-0.03733610361814499,
-0.011452266946434975,
0.00010427913366584107,
-0.02689659409224987,
-0.007934966124594212,
-0.00186709885019809,
0.016623981297016144,
0.016451792791485786,
-0.014417306520044804,
-0.015580161474645138,
-0.012366845272481441,
0.033435456454753876,
0.02812650240957737,
0.0189669169485569,
-0.02729783207178116,
0.006026123650372028,
-0.025117212906479836,
0.030223265290260315,
-0.05695931985974312,
-0.004747485741972923,
0.02053152024745941,
0.047307249158620834,
-0.009874709881842136,
0.009276357479393482
] |
<p>I'm trying to learn how to apply WKB. I asked a <a href="http://physics.stackexchange.com/questions/90157/how-to-apply-the-wkb-approximation-in-this-case">similar question</a> already, but that question was related to finding the energies. Here, I would like to understand how to find the wave functions using WKB.</p>
<blockquote>
<p><em>An electron, say, in the nuclear potential</em>
$$U(r)=\begin{cases}
& -U_{0} \;\;\;\;\;\;\text{ if } r < r_{0} \\
& k/r \;\;\;\;\;\;\;\;\text{ if } r > r_{0}
\end{cases}$$
<em>What is the wave function inside the barrier region ($r_{0} < r < k/E$)?</em></p>
</blockquote>
<p>Shouldn't the wave function have the following form?</p>
<p>$$\psi(r)=\frac{A}{\sqrt{2m(E-U(r))}}e^{\phi(r)}+\frac{B}{\sqrt{2m(E-U(r))}}e^{-\phi(r)}$$
where
$$\phi(r)=\frac{1}{\hbar}\int_{0}^{r} \sqrt{2m(E-U(r))} dr'$$</p> | 1,575 | [
0.00463062385097146,
-0.01727604866027832,
0.034086525440216064,
0.012766966596245766,
-0.004488176666200161,
-0.011608395725488663,
-0.01111728884279728,
-0.05288056284189224,
0.008818097412586212,
-0.0174418892711401,
0.063720703125,
0.0024123420007526875,
0.06338223814964294,
-0.0137531952932477,
0.029983045533299446,
0.00945785827934742,
-0.022775011137127876,
-0.06329606473445892,
-0.0036541037261486053,
-0.021351536735892296,
-0.0031801112927496433,
0.017337234690785408,
0.013105516321957111,
-0.0010855429572984576,
-0.03902442753314972,
0.03825780004262924,
0.010754586197435856,
-0.007732716389000416,
0.04125520586967468,
0.035574108362197876,
-0.012968817725777626,
-0.04597336798906326,
0.04931953549385071,
0.01758267730474472,
0.034459151327610016,
0.027231944724917412,
-0.04856092482805252,
-0.051186490803956985,
-0.014217658899724483,
0.03190764784812927,
-0.03123454377055168,
-0.03589106723666191,
0.03185456246137619,
0.037982240319252014,
0.015232432633638382,
0.005039428360760212,
0.003637762274593115,
-0.03184736147522926,
0.03300926834344864,
-0.04756941646337509,
0.047929417341947556,
0.03671964257955551,
0.00704067712649703,
0.007683722302317619,
0.001929277554154396,
-0.02200491540133953,
0.06631673872470856,
0.09055040776729584,
0.009643414057791233,
-0.016017697751522064,
-0.019351337105035782,
-0.029390977695584297,
-0.034008778631687164,
-0.008058969862759113,
-0.021484270691871643,
0.013298756442964077,
0.0032635703682899475,
-0.019808998331427574,
0.004451978486031294,
-0.014645449817180634,
0.028937995433807373,
0.0014290697872638702,
0.00700396578758955,
-0.02987731248140335,
0.031864527612924576,
-0.01834952086210251,
0.000244928669417277,
0.023018499836325645,
0.008213014341890812,
0.03602240979671478,
-0.033128850162029266,
0.028632624074816704,
0.03673802688717842,
0.016958875581622124,
-0.0056060804054141045,
-0.0014061990659683943,
0.07242137938737869,
0.020624034106731415,
-0.03311694413423538,
0.02038305439054966,
-0.025523392483592033,
0.011271326802670956,
0.04561890661716461,
-0.031168576329946518,
-0.04314451292157173,
0.02763970196247101,
-0.023915335536003113,
0.05578077211976051,
0.01660115085542202,
-0.028304919600486755,
0.002774609951302409,
-0.03443324565887451,
0.05037383735179901,
0.07919825613498688,
-0.010226879268884659,
-0.014246415346860886,
-0.03232767432928085,
0.018114032223820686,
0.03211940452456474,
-0.014033176936209202,
-0.03520646691322327,
0.048053670674562454,
-0.012159701436758041,
-0.0009607048705220222,
0.010142046958208084,
-0.02162867970764637,
-0.03132054954767227,
0.003320499788969755,
0.02826446108520031,
0.02525879628956318,
0.0663006529211998,
-0.02039858140051365,
0.03337465971708298,
-0.04109203815460205,
-0.060933638364076614,
0.008474396541714668,
0.004326655063778162,
0.010955454781651497,
-0.030554547905921936,
0.01759597472846508,
0.03721855953335762,
0.00016852114640641958,
0.013603095896542072,
0.0008398168138228357,
0.04637899622321129,
-0.029523814097046852,
-0.09914717823266983,
-0.06040169298648834,
0.01016146969050169,
-0.027335723862051964,
-0.014915787614881992,
-0.0778055191040039,
-0.00758175877854228,
0.03018808737397194,
0.07312984019517899,
0.013839758932590485,
-0.0023008750285953283,
-0.005832488648593426,
0.02405312843620777,
0.01831643097102642,
-0.01668410561978817,
-0.03303057700395584,
-0.027222519740462303,
-0.01654992811381817,
0.028006605803966522,
-0.05476604774594307,
0.013146071694791317,
0.025932552292943,
-0.016247928142547607,
-0.010100621730089188,
0.10510526597499847,
-0.016670284792780876,
0.0008760595810599625,
-0.003223579376935959,
-0.020925771445035934,
0.007746784016489983,
0.09675136208534241,
0.020792057737708092,
-0.009022951126098633,
0.0581362247467041,
0.01910756528377533,
0.02408617176115513,
-0.024849437177181244,
0.01611120067536831,
0.03451719880104065,
-0.049770090728998184,
-0.003209388814866543,
-0.05736245587468147,
0.023406896740198135,
0.00669395225122571,
-0.05698573961853981,
-0.01918710395693779,
0.017227599397301674,
-0.003208397887647152,
0.016528144478797913,
0.01789013296365738,
0.032174333930015564,
-0.011010847054421902,
-0.052852898836135864,
-0.03981490805745125,
-0.011119470931589603,
-0.07528071105480194,
0.016946200281381607,
-0.009519696235656738,
-0.019602898508310318,
0.036771856248378754,
-0.03534472733736038,
0.02949563041329384,
0.012916930951178074,
-0.05370490998029709,
0.01757650449872017,
0.029254617169499397,
-0.013276489451527596,
0.00870203971862793,
0.02254147082567215,
-0.01083808671683073,
0.03048883005976677,
-0.009771431796252728,
0.025964535772800446,
-0.03150629624724388,
-0.004280293360352516,
-0.0004780407471116632,
-0.02184910885989666,
0.029606133699417114,
0.007167493924498558,
-0.020768241956830025,
-0.004819741006940603,
-0.018174944445490837,
0.010970664210617542,
-0.016385627910494804,
-0.05311962962150574,
0.022801091894507408,
0.04430341348052025,
0.03585490956902504,
-0.014368006959557533,
0.03788292035460472,
0.01578345336019993,
0.023799555376172066,
-0.005792848765850067,
-0.03727804124355316,
-0.027036072686314583,
-0.0037442001048475504,
0.05227021872997284,
-0.006320975720882416,
-0.06632272899150848,
0.0060295891016721725,
0.017650114372372627,
0.00932358205318451,
0.0178510881960392,
0.03313786908984184,
-0.036297693848609924,
-0.006077424623072147,
0.024555670097470284,
0.016195377334952354,
-0.012887770310044289,
0.009541911073029041,
0.018515383824706078,
0.013713983818888664,
0.018297141417860985,
-0.0012088450603187084,
-0.030192099511623383,
0.059235356748104095,
-0.07332023233175278,
0.021120695397257805,
-0.018220581114292145,
-0.033891577273607254,
0.037029195576906204,
-0.028219804167747498,
0.0271597933024168,
0.026636788621544838,
-0.04470955953001976,
-0.016668781638145447,
-0.041061822324991226,
-0.02125328592956066,
0.05005619302392006,
-0.013632884249091148,
0.0016399811720475554,
0.002429978922009468,
-0.00036405824357643723,
-0.05403256043791771,
-0.01833069510757923,
-0.028446925804018974,
0.009312170557677746,
-0.021221691742539406,
-0.026565728709101677,
0.02628469653427601,
0.053709376603364944,
-0.006026329472661018,
-0.045774754136800766,
-0.03142697364091873,
-0.0021117248106747866,
-0.011228125542402267,
0.03470788151025772,
-0.013351622968912125,
-0.016024481505155563,
-0.00013556597696151584,
-0.02936428226530552,
0.02448846399784088,
0.042011916637420654,
-0.009816267527639866,
-0.024701766669750214,
-0.028391007333993912,
0.02445872314274311,
-0.04044358804821968,
-0.013210802339017391,
-0.0007027485407888889,
0.00819937139749527,
-0.012485479936003685,
0.023755254223942757,
0.022762229666113853,
-0.012566586956381798,
0.00921016838401556,
0.020502254366874695,
-0.02441052906215191,
-0.024835897609591484,
-0.015422633849084377,
-0.012794413603842258,
0.023055151104927063,
-0.01363103836774826,
0.025896811857819557,
0.010326286777853966,
-0.04173561558127403,
-0.0025277489330619574,
-0.06298545747995377,
-0.007422959432005882,
0.025232812389731407,
0.003767942078411579,
0.005833189003169537,
-0.000687619496602565,
-0.036139748990535736,
0.09348715841770172,
-0.005456043407320976,
-0.046068914234638214,
-0.011971378698945045,
0.015744375064969063,
-0.020486583933234215,
-0.018433459103107452,
-0.013426349498331547,
0.050668369978666306,
-0.015172334387898445,
0.022481925785541534,
0.001902547082863748,
0.04060583934187889,
0.05288265272974968,
-0.008701405487954617,
0.015988338738679886,
0.035427019000053406,
-0.02883215807378292,
-0.022760124877095222,
0.09373954683542252,
-0.028875095769762993,
0.026106873527169228,
0.036520954221487045,
-0.02832791768014431,
0.0010486338287591934,
0.06179292872548103,
-0.049568742513656616,
0.0635642483830452,
0.00279742362909019,
0.01781879924237728,
-0.03140147775411606,
0.05586666613817215,
0.005093684419989586,
-0.02274247072637081,
-0.012727471999824047,
-0.006378622259944677,
0.035146940499544144,
-0.007874706760048866,
0.013171214610338211,
0.04698660224676132,
0.026203662157058716,
-0.010870574042201042,
-0.03922600299119949,
-0.0005229584639891982,
0.02096259593963623,
0.015201618894934654,
-0.0002453736960887909,
-0.046368956565856934,
0.0484936386346817,
0.03223595768213272,
0.0005028779269196093,
-0.03543737903237343,
-0.033685412257909775,
-0.010846580378711224,
-0.052253421396017075,
-0.050541382282972336,
-0.010808050632476807,
0.06836114078760147,
0.003966258838772774,
0.04882977902889252,
0.04823911935091019,
0.017467975616455078,
0.011058802716434002,
0.007406879682093859,
-0.03380727767944336,
0.0277528278529644,
-0.029141515493392944,
0.008189920336008072,
-0.03430650010704994,
-0.016017651185393333,
-0.006681995000690222,
0.011045276187360287,
-0.03929428383708,
0.010492609813809395,
-0.028885619714856148,
-0.005984297022223473,
0.012894457206130028,
0.00033681272179819643,
-0.022602463141083717,
-0.05509835109114647,
0.028775781393051147,
0.012230997905135155,
0.011193047277629375,
-0.004396539647132158,
0.07681876420974731,
-0.04926690831780434,
0.008282200433313847,
-0.0076785036362707615,
0.007694229483604431,
-0.003941744100302458,
0.043158791959285736,
0.036544010043144226,
-0.00457725627347827,
0.008248412981629372,
-0.004049730021506548,
0.03814603388309479,
0.06882967054843903,
0.025610212236642838,
-0.010354110971093178,
-0.014021290466189384,
-0.026315679773688316,
0.006392657291144133,
-0.023444121703505516,
0.03763944283127785,
-0.013032643124461174,
0.04071727767586708,
0.032190851867198944,
-0.004894500598311424,
-0.01657033897936344,
0.01703931950032711,
0.03519544005393982,
0.011676991358399391,
-0.0020701715257018805,
-0.054998695850372314,
0.019872279837727547,
-0.030555110424757004,
-0.010906078852713108,
0.005379158537834883,
0.0035937633365392685,
-0.0012611798010766506,
0.015987565740942955,
0.031099481508135796,
0.03435526043176651,
-0.0005928712198510766,
0.0002942653081845492,
-0.012361866421997547,
0.008065132424235344,
-0.016885066404938698,
-0.007087331730872393,
0.018438491970300674,
0.026983890682458878,
0.0184908639639616,
-0.029121289029717445,
0.0008764928206801414,
-0.0414942242205143,
-0.01191715057939291,
0.03559484705328941,
0.030754325911402702,
0.012623896822333336,
0.007243918254971504,
-0.07998178899288177,
-0.008907614275813103,
0.07139942049980164,
-0.01947709359228611,
0.01807548478245735,
-0.02677101269364357,
0.016453050076961517,
-0.014781228266656399,
-0.041724298149347305,
-0.028033200651407242,
-0.009949158877134323,
-0.009863504208624363,
0.005754666402935982,
-0.03456709161400795,
-0.0012676723999902606,
-0.039261139929294586,
-0.0035684523172676563,
0.033082664012908936,
0.10326354205608368,
-0.02138959802687168,
-0.007300056517124176,
0.0015141774201765656,
0.016871310770511627,
-0.026470648124814034,
-0.0724010020494461,
-0.010827713645994663,
-0.02880636788904667,
0.003673683386296034,
0.03023516945540905,
-0.05340806394815445,
-0.04123968258500099,
0.06303151696920395,
0.03902839496731758,
-0.00039718946209177375,
0.006618954241275787,
-0.023017968982458115,
0.07035335153341293,
0.04174012318253517,
-0.011168252676725388,
0.07223592698574066,
0.01520264707505703,
0.00313696195371449,
0.004086041357368231,
-0.05931767076253891,
0.00823076069355011,
0.004229212645441294,
0.002556194318458438,
-0.030713997781276703,
-0.029546882957220078,
-0.02920336090028286,
0.01982550509274006,
-0.025639692321419716,
0.03364061564207077,
-0.05493956059217453,
-0.025006653741002083,
0.014770197682082653,
-0.02481902204453945,
-0.05909358710050583,
-0.026676718145608902,
0.01902773045003414,
-0.012927147559821606,
0.036982204765081406,
-0.04217498004436493,
0.010093394666910172,
0.003538574790582061,
-0.004494262393563986,
0.038110122084617615,
-0.0061719901859760284,
0.01800699159502983,
-0.016450699418783188,
-0.03228277340531349,
-0.003387976437807083,
-0.054004088044166565,
0.03166251257061958,
-0.032609935849905014,
-0.011849990114569664,
0.002410764805972576,
-0.04013874754309654,
-0.01479411218315363,
0.012663557194173336,
-0.011357585899531841,
0.0009166122763417661,
-0.034553803503513336,
0.024378975853323936,
0.03438124433159828,
-0.0029333713464438915,
-0.07476434856653214,
-0.01282903179526329,
0.010869096964597702,
0.003919543698430061,
-0.02508755959570408,
-0.011289802379906178,
0.010958450846374035,
-0.014696155674755573,
-0.010765992105007172,
0.022898193448781967,
0.031812138855457306,
-0.02017124556005001,
0.01162782497704029,
-0.007894027046859264,
0.009343559853732586,
0.0430961437523365,
0.017081668600440025,
-0.016269346699118614,
0.050290871411561966,
-0.04350735992193222,
-0.008470860309898853,
0.02852310612797737,
0.03324577584862709,
-0.022875366732478142,
-0.009730445221066475,
-0.0207154992967844,
-0.02265082858502865,
0.019715307280421257,
-0.007534053176641464,
-0.02704889513552189,
0.027495868504047394,
0.015375361777842045,
0.03081141784787178,
0.004679779056459665,
-0.01363301556557417,
0.004296496976166964,
0.018535496667027473,
-0.00019746219913940877,
-0.008545774035155773,
-0.05952391400933266,
-0.024375662207603455,
0.02629213221371174,
-0.027555786073207855,
-0.0008169352659024298,
0.007762033026665449,
0.06257826089859009,
-0.022146139293909073,
0.021592890843749046,
0.003957392647862434,
-0.042804766446352005,
0.0005899184616282582,
-0.019492389634251595,
0.00335492892190814,
0.01842641830444336,
-0.004947602283209562,
-0.028653347864747047,
-0.04067474976181984,
-0.06957193464040756,
0.010497940704226494,
0.051958389580249786,
-0.005865355487912893,
0.046281371265649796,
-0.010870486497879028,
-0.007478334475308657,
-0.0201562512665987,
-0.055336616933345795,
-0.04448575899004936,
-0.005575062707066536,
0.018231496214866638,
0.05374753475189209,
-0.011214918456971645,
0.017971618101000786,
0.020273519679903984,
0.02687447890639305,
-0.006941838655620813,
0.013069765642285347,
0.028732648119330406,
0.05827596038579941,
0.030937358736991882,
0.0011803609086200595,
-0.0039889877662062645,
0.04088858515024185,
-0.008834129199385643,
0.02264202944934368,
0.020541086792945862,
-0.00781491119414568,
0.0652981549501419,
0.00016355754632968456,
0.0010064884554594755,
-0.017538581043481827,
-0.026905963197350502,
-0.013187498785555363,
0.03772294148802757,
0.016602154821157455,
-0.008616193197667599,
0.000244995579123497,
0.0358792282640934,
0.031330108642578125,
0.015445479191839695,
0.006497415713965893,
0.009133545681834221,
-0.054279156029224396,
-0.024873262271285057,
-0.05376620963215828,
-0.04671849310398102,
0.000884353939909488,
0.012857077643275261,
-0.014172891154885292,
0.024669522419571877,
-0.03072150982916355,
0.021456226706504822,
-0.0032133404165506363,
0.01819540746510029,
-0.022764045745134354,
0.07610780000686646,
0.0019719123374670744,
0.01634613424539566,
-0.006785789504647255,
0.005682719871401787,
0.1328231245279312,
0.05828113853931427,
0.033808253705501556,
-0.06742321699857712,
-0.012177687138319016,
-0.027618497610092163,
0.007824529893696308,
0.0009825034067034721,
-0.01639765314757824,
0.010917372070252895,
-0.0056734527461230755,
0.0038821252528578043,
0.07529715448617935,
0.034267377108335495,
0.044606879353523254,
0.045637305825948715,
-0.006737433839589357,
-0.05367297679185867,
0.04285037890076637,
0.0010509336134418845,
-0.0001139513187808916,
0.004507843405008316,
-0.002455543726682663,
0.01770136132836342,
-0.0564521960914135,
-0.010227191261947155,
-0.056685689836740494,
-0.014279547147452831,
0.033086422830820084,
-0.027780456468462944,
-0.014156688936054707,
0.04813188314437866,
-0.0369107723236084,
-0.0046552615240216255,
0.02609546296298504,
0.016186416149139404,
0.06149876117706299,
-0.027474911883473396,
0.03372136130928993,
0.014886761084198952,
-0.013835614547133446,
-0.011165114119648933,
0.015441383235156536,
0.026282966136932373,
-0.021531423553824425,
-0.013145198114216328,
-0.019214307889342308,
0.07565608620643616,
-0.014492690563201904,
-0.034543827176094055,
-0.007776965852826834,
0.016051756218075752,
0.019274935126304626,
-0.04145270586013794,
0.007666178047657013,
0.005251457914710045,
0.0009506377973593771,
-0.020111965015530586,
0.006530677899718285,
-0.032336391508579254,
0.010721204802393913,
-0.0013234905200079083,
0.016008025035262108,
-0.01707419566810131,
-0.016118910163640976,
0.006603945046663284,
-0.0192450862377882,
0.012828961946070194,
-0.02702917344868183,
-0.008865171112120152,
0.0017752593848854303,
-0.005493276286870241,
-0.05156611651182175,
-0.02912640944123268,
0.023634061217308044,
-0.0010323200840502977,
0.07046391069889069,
-0.023404184728860855,
0.014080185443162918,
-0.02740337885916233,
-0.12042240798473358,
0.010457180440425873,
-0.0006345493602566421,
-0.03347112238407135,
-0.00983244739472866,
-0.01432725414633751,
0.04680296778678894,
0.046252213418483734,
-0.014931950718164444,
-0.010359169915318489,
-0.007016978692263365,
0.018385116010904312,
0.02957800216972828,
-0.04622642323374748,
-0.014812448993325233,
0.0047371117398142815,
-0.010626210831105709,
0.03516611084342003,
-0.00957899447530508,
0.01209944486618042,
0.012026142328977585,
0.006264109630137682,
-0.0020015330519527197,
0.026657264679670334,
-0.05118784308433533,
-0.011802843771874905,
-0.008098234422504902,
-0.019452454522252083,
-0.016389600932598114,
-0.00718982657417655,
0.0081990547478199,
-0.011460079811513424,
0.00286965467967093,
-0.03712136298418045,
-0.01407827902585268,
0.002994511043652892,
0.008021597750484943,
0.0007472200086340308,
0.019347479566931725,
-0.012827813625335693,
-0.02928655967116356,
-0.011181368492543697,
-0.001524425344541669,
-0.013784613460302353,
0.011334124952554703,
-0.012284956872463226,
-0.013209682889282703,
-0.000756608962547034,
0.029771381989121437,
0.01714221015572548,
-0.004197803325951099,
0.014304859563708305,
0.052180152386426926,
-0.030236154794692993,
0.021042175590991974,
0.002477981150150299,
-0.004877688828855753,
0.03038996458053589,
0.02091239020228386,
0.009690448641777039,
0.01694655232131481,
-0.05885301157832146,
-0.029274223372340202,
-0.0027945528272539377,
0.042277466505765915,
0.02766599878668785,
0.03411240875720978,
-0.023217784240841866,
0.0025930595584213734,
0.050791673362255096,
-0.01546137873083353,
-0.0009655465837568045,
0.01598086953163147,
-0.035973213613033295,
0.01705915480852127,
-0.04143466055393219,
0.010933876037597656,
-0.021274009719491005,
0.036513254046440125,
0.0476369708776474,
-0.00010305445903213695,
-0.019675200805068016,
0.01942628063261509,
0.023590579628944397,
-0.008171229623258114,
0.02839110977947712,
0.007963473908603191,
-0.007150295656174421,
0.016282016411423683,
0.05921551585197449,
-0.013613099232316017,
0.043355800211429596,
0.0015551928663626313,
0.003533724695444107,
-0.08239549398422241,
-0.042021263390779495,
-0.017155207693576813,
-0.004085721913725138,
0.06450766324996948,
-0.05889863520860672,
0.014712431468069553,
0.04226662218570709,
-0.08004569262266159,
0.01553287636488676,
-0.015473218634724617,
0.011976744048297405,
-0.01817135326564312,
-0.008860524743795395,
-0.05195239558815956,
0.03985381871461868,
-0.021392161026597023,
0.037012308835983276,
0.018872320652008057,
0.014348074793815613,
-0.002951274625957012,
-0.0319383330643177,
0.0011601216392591596,
0.04365931451320648,
-0.0021793488413095474,
-0.04575550928711891,
0.08464960753917694,
0.008453595452010632,
-0.01741660386323929,
0.021185893565416336,
-0.047727055847644806,
0.03076121397316456,
-0.03290775790810585,
0.0201799925416708,
0.007362967357039452,
0.04409214109182358,
0.024755142629146576,
-0.005710550118237734,
-0.02627163752913475,
0.0011785624083131552,
0.05440890043973923,
0.0054198154248297215,
0.005857732146978378,
0.011765425093472004,
0.017547516152262688,
-0.029884150251746178,
-0.04224889725446701,
0.09278135746717453,
-0.014863364398479462,
0.003801829181611538,
-0.01812850311398506,
-0.005591742228716612,
0.03190821781754494,
-0.06357556581497192,
0.023594064638018608,
-0.04517379775643349,
0.007145804353058338,
-0.008259949274361134,
0.027200739830732346,
0.010691472329199314,
0.00972126703709364,
-0.021585451439023018,
-0.04160144925117493,
0.05568422004580498,
-0.005000843666493893,
-0.019390463829040527,
-0.06383543461561203,
-0.007232514675706625,
-0.020747825503349304,
0.017494818195700645,
0.010165371000766754,
-0.019437972456216812,
-0.038289230316877365,
-0.013644241727888584,
-0.012670240364968777,
0.003388302866369486,
0.00407832209020853,
-0.007981128990650177,
-0.023840783163905144,
-0.06026941537857056,
0.024461654946208,
0.011895513162016869,
-0.00021769112208858132,
-0.021125158295035362,
-0.019795533269643784,
0.005652689374983311,
-0.006952220574021339,
0.07809609919786453,
0.001314062043093145,
-0.01800675503909588,
0.033807605504989624,
0.006786228157579899,
-0.0031115924939513206,
-0.055748533457517624,
-0.001700509455986321,
0.008077669888734818,
0.03080892749130726,
0.011846419423818588,
0.00965153332799673,
-0.008290683850646019,
0.05706031993031502,
-0.020216437056660652,
0.01642974093556404,
-0.012141767889261246,
0.003439361695200205,
-0.03730960935354233,
0.020608069375157356,
-0.009498054161667824,
-0.024191176518797874,
0.05821435526013374,
-0.005042541306465864,
0.018938183784484863,
0.0373673215508461,
-0.03467554599046707,
-0.017526153475046158,
0.026728760451078415,
-0.03097139485180378,
-0.05033176392316818,
0.01564810238778591,
-0.01835923083126545,
0.035134222358465195,
-0.05827539414167404,
-0.04025181382894516,
0.019521920010447502,
-0.06004421040415764,
0.00940154679119587,
0.061591293662786484,
0.014403602108359337,
0.05232631415128708,
0.056433916091918945,
-0.005934440065175295,
0.008170630782842636,
-0.0020777443423867226,
0.01492760144174099,
-0.017271380871534348,
0.0029119912069290876,
0.018047356978058815,
0.04199427366256714,
0.060598161071538925,
-0.03840303793549538,
-0.0009677206398919225,
0.017958026379346848,
0.017597166821360588,
-0.047778237611055374,
-0.004389775451272726,
0.0394834540784359,
-0.0334872342646122,
-0.006705186795443296,
-0.005188917275518179,
-0.05382062867283821,
0.08057066053152084,
-0.0480731762945652,
0.013673555105924606,
-0.014283682219684124,
0.003972632810473442,
-0.001961704343557358,
0.03803333267569542,
0.03838779404759407,
0.0011529132025316358,
-0.015130938962101936,
-0.021254532039165497,
-0.05355968698859215,
0.026210343465209007,
0.026727333664894104,
-0.046304862946271896,
0.010012853890657425,
0.0070990025997161865,
-0.07265733182430267,
-0.035132359713315964,
-0.03728875890374184,
0.006081751547753811,
0.003079185029491782,
0.01729593053460121,
0.040848441421985626,
0.02033121883869171,
-0.027588767930865288,
0.0071893418207764626,
-0.021587049588561058,
0.07643529772758484,
-0.03461296856403351,
0.014151022769510746,
-0.00976130086928606,
0.006347118876874447,
-0.013767244294285774,
-0.02519114874303341
] |
<p>Is there any temperature dependence of relaxation time in impurity scattering of conducting electrons? It seems to me that there is none. But, some people claim that there is.</p>
<p>So if you could explain, how temperature dependence comes into play if it does at all?</p> | 827 | [
-0.0030970564112067223,
-0.019670071080327034,
0.016615215688943863,
-0.06726961582899094,
-0.0011336369207128882,
-0.00014036288484930992,
-0.03783245384693146,
0.001185871777124703,
0.016333898529410362,
-0.02834787219762802,
0.07319532334804535,
0.039198704063892365,
0.0493491105735302,
-0.013104534707963467,
-0.011603624559938908,
0.026637379080057144,
-0.008990234695374966,
-0.001628887141123414,
0.00409656809642911,
0.011801416054368019,
0.007634463254362345,
0.004222664050757885,
-0.007433801423758268,
-0.01710245944559574,
-0.04011101648211479,
0.009328433312475681,
-0.018157610669732094,
0.012521648779511452,
0.03950033336877823,
0.05961136147379875,
-0.02528635412454605,
-0.01244029775261879,
0.00270856823772192,
0.006587625946849585,
0.02350871078670025,
-0.008615212514996529,
-0.01448378898203373,
-0.07014800608158112,
-0.009245586581528187,
0.012999082915484905,
-0.01997935026884079,
-0.011066492646932602,
0.007736463099718094,
0.017738303169608116,
0.023450560867786407,
-0.015858426690101624,
0.013871407136321068,
-0.045321185141801834,
0.05073418468236923,
-0.055988457053899765,
0.008391418494284153,
-0.06270566582679749,
0.02931361459195614,
0.024652451276779175,
0.0005778828053735197,
-0.0019389123190194368,
0.07137077301740646,
0.0709681361913681,
-0.017672883346676826,
-0.008528275415301323,
0.03731890022754669,
-0.03261749446392059,
0.017120959237217903,
-0.0012576993321999907,
-0.01639176346361637,
0.007220839150249958,
0.017101768404245377,
-0.04274958372116089,
0.03087129443883896,
-0.008767461404204369,
0.000035898247006116435,
-0.024175062775611877,
0.0014270942192524672,
-0.0034619062207639217,
0.029692107811570168,
-0.028061946853995323,
0.04106371849775314,
0.031281303614377975,
0.0329812653362751,
0.05854786932468414,
-0.04555770754814148,
0.002273916732519865,
0.03075828030705452,
-0.004332175012677908,
-0.03657990321516991,
-0.013741287402808666,
0.05331253260374069,
-0.034442346543073654,
-0.0020720649044960737,
0.028718529269099236,
0.012648165225982666,
0.06497807800769806,
0.011803839355707169,
0.0140476543456316,
-0.012624604627490044,
-0.012616375461220741,
0.025131836533546448,
0.07842881232500076,
-0.03797009959816933,
-0.03745162487030029,
-0.0029794317670166492,
-0.029666177928447723,
0.016815314069390297,
0.0638255774974823,
-0.014321615919470787,
-0.009317497722804546,
-0.014505450613796711,
-0.008822769857943058,
-0.03127991035580635,
-0.040015146136283875,
-0.054312460124492645,
0.0033669685944914818,
-0.023834064602851868,
0.030912727117538452,
0.01285090297460556,
-0.02868928574025631,
0.004885500762611628,
-0.013853493146598339,
0.059317078441381454,
0.04084378480911255,
0.015916243195533752,
-0.04851215332746506,
0.017581628635525703,
-0.023018643260002136,
-0.043082933872938156,
0.04828285425901413,
0.015182875096797943,
0.02231949381530285,
0.0013863671338185668,
0.0273048784583807,
0.011640075594186783,
-0.037871602922677994,
0.036558859050273895,
-0.041282907128334045,
0.020989403128623962,
0.006704059895128012,
-0.07731001824140549,
-0.0636349692940712,
0.0315772108733654,
-0.024291066452860832,
0.026154011487960815,
-0.08415613323450089,
0.008603321388363838,
0.010913096368312836,
0.07197604328393936,
-0.017023392021656036,
0.020614663138985634,
-0.024305587634444237,
0.029298346489667892,
0.02551899291574955,
-0.0014867396093904972,
-0.032511427998542786,
0.0378144346177578,
0.004088537767529488,
0.014419292099773884,
-0.02676727995276451,
0.07088138163089752,
0.03699539229273796,
0.025573261082172394,
-0.017225099727511406,
0.026301328092813492,
-0.01040711160749197,
0.009310498833656311,
0.010069034993648529,
0.01426684483885765,
-0.0056684259325265884,
0.10429095476865768,
0.012747935019433498,
0.0356520339846611,
0.016581660136580467,
-0.016983505338430405,
0.01677647978067398,
0.03655162826180458,
0.02256493642926216,
0.048861220479011536,
-0.05491374060511589,
-0.013263256289064884,
-0.00019201324903406203,
-0.027014324441552162,
0.004183073528110981,
-0.05812598392367363,
-0.03356090188026428,
0.011175853200256824,
0.009553526528179646,
0.0030553718097507954,
0.021497070789337158,
0.013820174150168896,
-0.006315712817013264,
-0.00792228989303112,
-0.05463390052318573,
-0.03071364387869835,
-0.0525486022233963,
0.017024027183651924,
0.0212569497525692,
-0.030356066301465034,
0.028430553153157234,
-0.006185866426676512,
0.024384744465351105,
0.0037170089781284332,
-0.06212631240487099,
0.010746084153652191,
-0.012969063594937325,
-0.011998018249869347,
-0.016126981005072594,
0.024427097290754318,
0.044082172214984894,
0.036385729908943176,
-0.020290033891797066,
0.019673971459269524,
-0.02849125675857067,
-0.04308447241783142,
-0.03979332372546196,
-0.0442076101899147,
0.03786899149417877,
0.02846207469701767,
-0.0184338316321373,
-0.00543628865852952,
-0.03937218338251114,
-0.03625735640525818,
0.0132079953327775,
-0.012361236847937107,
0.08521534502506256,
0.021484792232513428,
0.010033450089395046,
-0.017841700464487076,
0.014172381721436977,
-0.0042624762281775475,
-0.0150788938626647,
0.01408587396144867,
-0.040617842227220535,
-0.023062383756041527,
-0.01316945068538189,
0.033626947551965714,
0.030830059200525284,
-0.03186921775341034,
0.031173616647720337,
0.015227410942316055,
0.033533792942762375,
0.06095287948846817,
0.02676156535744667,
-0.02312428317964077,
-0.01920638233423233,
0.04334442690014839,
-0.005161024630069733,
-0.03284420818090439,
-0.002335725584998727,
0.005079685244709253,
-0.03565983846783638,
0.03635439649224281,
-0.03309919685125351,
-0.04492142051458359,
0.002065780572593212,
0.010758830234408379,
-0.01423642598092556,
-0.048632316291332245,
-0.03093426115810871,
-0.003153744852170348,
-0.018141860142350197,
0.02836800552904606,
-0.01342490129172802,
-0.007078939117491245,
0.06325718760490417,
-0.03503233566880226,
-0.045037344098091125,
0.036210402846336365,
-0.012104438617825508,
-0.020412102341651917,
-0.030041499063372612,
0.032797545194625854,
-0.018964819610118866,
0.0384506992995739,
-0.04084811732172966,
0.003143648849800229,
-0.0034962452482432127,
0.01174929179251194,
0.044397637248039246,
0.007539219688624144,
-0.00023863621754571795,
-0.03862375020980835,
-0.020807795226573944,
0.0012727509019896388,
-0.042901840060949326,
0.021702900528907776,
0.005272362381219864,
-0.02204718254506588,
-0.002674899762496352,
-0.013111689127981663,
-0.032229192554950714,
0.030266722664237022,
-0.01953100971877575,
-0.01685420610010624,
-0.02161366678774357,
-0.005317543167620897,
-0.07796887308359146,
-0.01604033075273037,
0.014273720793426037,
0.01290592085570097,
-0.07174983620643616,
0.01042137946933508,
0.024891838431358337,
-0.028644884005188942,
0.017423506826162338,
0.013292962685227394,
-0.017614450305700302,
-0.017312048003077507,
0.019796548411250114,
-0.023503011092543602,
0.019122948870062828,
-0.03416156768798828,
0.021606694906949997,
0.030106071382761,
-0.0332939550280571,
-0.015550348907709122,
-0.030104290693998337,
-0.04206511378288269,
0.02646138146519661,
-0.011093193665146828,
0.010512509383261204,
-0.030284054577350616,
-0.03053847700357437,
0.07419440150260925,
0.008771473541855812,
0.019731568172574043,
-0.025618741288781166,
-0.03451524302363396,
-0.052828941494226456,
-0.0013703418662771583,
0.009963810443878174,
0.04297340661287308,
-0.03446231037378311,
-0.008482028730213642,
0.01218817662447691,
0.03768385946750641,
0.05841667205095291,
0.0003195164317730814,
0.002605827059596777,
0.029932910576462746,
0.002543404931202531,
0.007491257041692734,
0.047925062477588654,
0.010286855511367321,
-0.03789727762341499,
-0.0033307347912341356,
-0.014428033493459225,
0.053420692682266235,
0.03575087711215019,
-0.06614597886800766,
0.06121121346950531,
-0.01592261716723442,
0.033378683030605316,
-0.02375674806535244,
0.0235454048961401,
-0.0034364485181868076,
0.010931371711194515,
-0.016182608902454376,
0.040528442710638046,
-0.002633044496178627,
0.011986423283815384,
0.0030502842273563147,
0.04419812560081482,
0.04884282499551773,
-0.01619195193052292,
-0.02789328619837761,
0.01713055744767189,
-0.049051932990550995,
0.016445228829979897,
-0.01341030653566122,
-0.01993052288889885,
0.00460316427052021,
-0.01062942948192358,
0.052233580499887466,
0.016534870490431786,
-0.034051764756441116,
-0.023961417376995087,
-0.04764490947127342,
-0.015332885086536407,
0.0138350585475564,
0.05714019015431404,
0.019789885729551315,
0.03416156768798828,
0.027912238612771034,
0.015407520346343517,
-0.019444050267338753,
-0.00002807236887747422,
-0.08118626475334167,
-0.022023295983672142,
-0.018110554665327072,
-0.04440881684422493,
-0.025704963132739067,
0.008717489428818226,
-0.01900559477508068,
-0.023416176438331604,
0.0019362719031050801,
-0.012386035174131393,
-0.004401992540806532,
-0.018574783578515053,
0.04423662647604942,
-0.026915468275547028,
-0.04589471220970154,
-0.019443253055214882,
-0.0019033922581002116,
-0.016474023461341858,
-0.03716564178466797,
0.01568005047738552,
0.030273472890257835,
-0.006712868809700012,
-0.012893668375909328,
-0.02356892265379429,
0.025638844817876816,
-0.00040840942529030144,
0.029192592948675156,
0.052403759211301804,
0.035323452204465866,
-0.05435745418071747,
0.02181272767484188,
0.02461838908493519,
0.05745145305991173,
0.01320241205394268,
-0.03301709517836571,
-0.023795029148459435,
-0.07385239750146866,
-0.03120880201458931,
0.04373898729681969,
0.04369775578379631,
0.003919916693121195,
-0.007725799921900034,
0.025193730369210243,
-0.005847052671015263,
-0.006685119587928057,
-0.027852896600961685,
0.025287454947829247,
-0.007503007538616657,
-0.01974029466509819,
-0.04217951372265816,
-0.0041045574471354485,
0.0025227952282875776,
0.04244828596711159,
0.00764212803915143,
0.011592306196689606,
0.026255788281559944,
0.002441367832943797,
0.030512694269418716,
-0.013495692983269691,
0.007655016612261534,
-0.036042455583810806,
0.00845118798315525,
0.007437470834702253,
0.02185734361410141,
0.034358467906713486,
0.026705684140324593,
0.024482741951942444,
0.002457316964864731,
0.030544554814696312,
0.008168363943696022,
-0.042404334992170334,
-0.012796259485185146,
0.02960352413356304,
0.03557759150862694,
-0.030865991488099098,
-0.0036802419926971197,
-0.06613627821207047,
0.01456022821366787,
0.05297745391726494,
0.04575492441654205,
0.02590275928378105,
-0.029980666935443878,
-0.03675820305943489,
-0.032152239233255386,
-0.01850372925400734,
0.028883356600999832,
0.03211178258061409,
0.06853929162025452,
0.03282170370221138,
-0.03333078324794769,
-0.030126890167593956,
0.032787732779979706,
-0.005765227135270834,
0.0338849239051342,
0.06846978515386581,
-0.005803554318845272,
0.05473443120718002,
-0.009898241609334946,
0.008690876886248589,
-0.00865108985453844,
-0.10997649282217026,
-0.01220661960542202,
-0.019614487886428833,
0.02075253613293171,
0.0340396873652935,
-0.015505197457969189,
-0.04454389959573746,
0.036545511335134506,
0.02879904955625534,
0.003206351539120078,
0.019283536821603775,
-0.03114360198378563,
0.06110613793134689,
0.01967129483819008,
-0.01842302829027176,
0.03899678215384483,
0.02371821738779545,
0.02092120423913002,
0.006871599704027176,
-0.01858033426105976,
0.08921750634908676,
-0.04799753800034523,
0.02856222167611122,
-0.015164373442530632,
0.016979411244392395,
-0.016281018033623695,
0.07081662118434906,
0.006975191179662943,
0.0048358747735619545,
-0.007938047870993614,
-0.035000670701265335,
-0.012819924391806126,
0.006228224374353886,
0.0049171168357133865,
0.0052371094934642315,
-0.01050302293151617,
0.012257694266736507,
-0.025776630267500877,
-0.006569516845047474,
0.017725862562656403,
0.03431866690516472,
0.04389636963605881,
0.02506396546959877,
-0.02479477971792221,
0.050255440175533295,
-0.07687926292419434,
0.00836144294589758,
-0.012954880483448505,
-0.034785471856594086,
0.053308434784412384,
0.014961238950490952,
-0.013673663139343262,
0.020263761281967163,
-0.045112624764442444,
0.035221803933382034,
0.0435456857085228,
-0.009713809005916119,
0.04820305109024048,
-0.07649888098239899,
-0.009761473163962364,
0.020589472725987434,
0.013374541886150837,
-0.11532919853925705,
-0.06569011509418488,
-0.019947560504078865,
0.025102604180574417,
-0.03485732898116112,
-0.04578789323568344,
-0.012049802578985691,
-0.024033082649111748,
-0.03976195678114891,
0.04443899914622307,
0.046217456459999084,
0.03393685445189476,
-0.005409569479525089,
-0.009654691442847252,
0.018676703795790672,
0.056473247706890106,
0.03511843457818031,
0.003666448872536421,
-0.001585157704539597,
-0.05936222895979881,
-0.034761879593133926,
-0.027267104014754295,
0.05447416752576828,
-0.014334769919514656,
-0.011497248895466328,
-0.005108182784169912,
-0.015277309343218803,
0.015039595775306225,
0.033127814531326294,
-0.0419941246509552,
0.04662168771028519,
0.01203848421573639,
0.00275193783454597,
0.001644700882025063,
0.031154051423072815,
0.026743337512016296,
0.03092513233423233,
0.03250668942928314,
-0.004321938846260309,
-0.027282847091555595,
-0.033333297818899155,
0.009623599238693714,
0.008583755232393742,
-0.008230049163103104,
0.01393884513527155,
0.06693343818187714,
-0.027754168957471848,
-0.02531396597623825,
0.040341079235076904,
0.0035179860424250364,
0.0027648836839944124,
-0.02112383022904396,
-0.016276715323328972,
-0.0027581313624978065,
-0.02598610147833824,
-0.0348203144967556,
-0.04622264951467514,
-0.04867779463529587,
-0.0005643093027174473,
0.029538866132497787,
-0.02285514958202839,
0.03708726912736893,
0.0016238224925473332,
-0.02196776680648327,
-0.012264187447726727,
-0.04695378616452217,
-0.011860103346407413,
0.007596674375236034,
-0.04827691242098808,
0.018238933756947517,
-0.008331453427672386,
-0.024519041180610657,
0.011579526588320732,
0.05837620794773102,
-0.019280020147562027,
0.013427607715129852,
-0.002095684641972184,
-0.004244043026119471,
0.02410322241485119,
-0.009521160274744034,
-0.02636205218732357,
0.03456931188702583,
-0.04576230049133301,
0.04704103618860245,
-0.021747613325715065,
-0.028011079877614975,
0.06281590461730957,
-0.007850917056202888,
0.02487371489405632,
-0.02785753272473812,
-0.019992316141724586,
-0.024372244253754616,
0.012894854880869389,
0.003758265171200037,
-0.0033675082959234715,
0.006554279010742903,
0.021603159606456757,
0.030551496893167496,
0.021258831024169922,
0.013131821528077126,
0.0073023526929318905,
-0.010968607850372791,
-0.0029611370991915464,
-0.023990364745259285,
-0.019063593819737434,
0.006198362447321415,
-0.016984151676297188,
-0.02001800574362278,
0.010628893971443176,
-0.0185103639960289,
0.025830432772636414,
-0.0012165773659944534,
0.012398554012179375,
-0.008994994685053825,
0.06011050567030907,
-0.0070827919989824295,
0.03511298820376396,
-0.020832128822803497,
0.03312854468822479,
0.10780194401741028,
0.04143529012799263,
0.041132260113954544,
-0.047254741191864014,
-0.003957175184041262,
0.01211682241410017,
0.014410789124667645,
-0.05175519362092018,
-0.026599686592817307,
-0.019057517871260643,
-0.009103958494961262,
0.021050570532679558,
0.01556103490293026,
0.005241766106337309,
-0.002653965260833502,
-0.0006956608267500997,
-0.026840971782803535,
-0.025843262672424316,
0.04037168622016907,
0.025207994505763054,
0.00002703312384255696,
0.022175349295139313,
-0.04407353699207306,
0.014041117392480373,
-0.03053382597863674,
0.02684512548148632,
-0.034661486744880676,
-0.013014981523156166,
0.025903694331645966,
-0.03935633599758148,
-0.006278357468545437,
-0.007673285435885191,
0.03704475983977318,
0.02005646377801895,
-0.05031374841928482,
0.004611372947692871,
0.0044565279968082905,
-0.017375322058796883,
0.03610018268227577,
0.025656115263700485,
0.01636568270623684,
-0.010787252336740494,
0.011389381252229214,
0.01671941950917244,
-0.04236004501581192,
0.003144597401842475,
0.010736348107457161,
0.018335171043872833,
0.017408939078450203,
-0.006207385566085577,
0.0058098481968045235,
0.002675937255844474,
0.03972180187702179,
-0.016648009419441223,
0.01173304207623005,
-0.0007780355517752469,
0.0037122408393770456,
-0.01550234667956829,
0.00417775334790349,
-0.013986969366669655,
0.020628497004508972,
0.006006852723658085,
-0.00276469555683434,
-0.013605499640107155,
-0.020693480968475342,
0.018736768513917923,
-0.001908518373966217,
0.011323066428303719,
0.006271461956202984,
-0.031654778867959976,
-0.048128511756658554,
0.017864324152469635,
-0.022955114021897316,
-0.015892429277300835,
0.0006690070731565356,
0.0014846366830170155,
0.036777447909116745,
0.003880877047777176,
-0.034786008298397064,
-0.010249468497931957,
-0.09546049684286118,
0.042015187442302704,
0.0057204426266252995,
0.0032074686605483294,
-0.016658427193760872,
0.006600917782634497,
0.027897588908672333,
0.020572178065776825,
-0.0267934687435627,
0.016180671751499176,
0.006635852158069611,
0.029291480779647827,
0.04158468917012215,
-0.044833954423666,
-0.0005378864007070661,
0.017079466953873634,
-0.05953880399465561,
0.0184719767421484,
-0.034889765083789825,
0.020913349464535713,
-0.00444188853725791,
-0.004615921527147293,
0.0031275649089366198,
-0.010522270575165749,
-0.008529897779226303,
0.005337489768862724,
0.010358433239161968,
-0.04043644666671753,
0.0224541574716568,
-0.0172068253159523,
0.003929090686142445,
-0.0061393920332193375,
-0.03391046077013016,
-0.049729932099580765,
0.041878052055835724,
-0.011591099202632904,
-0.0012919656001031399,
-0.027030479162931442,
0.024896590039134026,
0.0023845380637794733,
0.00968773290514946,
-0.05890853703022003,
0.026478391140699387,
-0.025959542021155357,
-0.0017984056612476707,
-0.011550109833478928,
0.01339077390730381,
0.0530877523124218,
0.039561886340379715,
-0.01570594124495983,
-0.002968995599076152,
0.05285809189081192,
0.04223853722214699,
0.02008092775940895,
0.00566768879070878,
-0.005974444095045328,
0.0011067058658227324,
0.046768270432949066,
-0.05386815220117569,
-0.02861815132200718,
0.07712950557470322,
-0.06137792393565178,
-0.04173075780272484,
0.023041484877467155,
-0.005362336523830891,
0.01010320708155632,
0.042580828070640564,
0.029281334951519966,
-0.01201830804347992,
0.0849558413028717,
-0.01300846692174673,
-0.014587299898266792,
0.006036370061337948,
-0.051238998770713806,
0.022916769608855247,
-0.005140862427651882,
-0.01384417712688446,
-0.01369206327944994,
-0.001849723281338811,
0.05736249312758446,
0.02739224024116993,
-0.007437570486217737,
-0.015051360242068768,
-0.011232002638280392,
0.002325517125427723,
0.0192426610738039,
0.03925994411110878,
0.007620242424309254,
0.03851104527711868,
0.06039770692586899,
-0.021316779777407646,
0.030817566439509392,
0.021706702187657356,
-0.000002375179747104994,
-0.11092034727334976,
-0.01954709179699421,
0.006484413519501686,
0.03816830366849899,
0.006858756300061941,
-0.012136590667068958,
0.04522626847028732,
0.010252943262457848,
-0.08585605025291443,
0.05164652317762375,
-0.013373186811804771,
-0.059832070022821426,
-0.07558141648769379,
0.0037664095871150494,
-0.01985059306025505,
0.038842976093292236,
0.0409281961619854,
0.05020478367805481,
0.014301813207566738,
0.0281631238758564,
-0.01154195424169302,
-0.0121936509385705,
-0.03360069915652275,
0.017528077587485313,
0.01974225789308548,
-0.022120296955108643,
0.019298000261187553,
-0.008485650643706322,
0.0010601829271763563,
0.032018087804317474,
0.011606278829276562,
0.03019305132329464,
0.00399453891441226,
0.032299887388944626,
0.018601836636662483,
-0.006956016644835472,
0.03553717955946922,
-0.06457102298736572,
0.019809866324067116,
-0.010716593824326992,
0.0268815029412508,
0.02741570584475994,
-0.013342542573809624,
0.019875189289450645,
0.0035101643297821283,
-0.04445431008934975,
-0.026025928556919098,
0.03518835827708244,
-0.029219286516308784,
-0.018522139638662338,
0.01806875504553318,
0.0004592406621668488,
0.006050337105989456,
0.01335239689797163,
0.024249374866485596,
-0.0408695787191391,
-0.020108001306653023,
0.024255624040961266,
0.030979691073298454,
0.01831684820353985,
0.006786376237869263,
-0.020604019984602928,
-0.008392156101763248,
-0.015198200941085815,
0.014119379222393036,
0.026895781978964806,
-0.005294805392622948,
-0.04761844128370285,
0.01016188133507967,
0.027590202167630196,
-0.02935265749692917,
-0.027119765058159828,
-0.03166636452078819,
0.012101331725716591,
-0.009691828861832619,
0.020048679783940315,
-0.04617905616760254,
-0.04571942985057831,
-0.018496308475732803,
-0.038697026669979095,
0.009917299263179302,
-0.05607980489730835,
-0.01857454515993595,
-0.0568605400621891,
-0.023962808772921562,
-0.04069448262453079,
0.03068552352488041,
0.059506986290216446,
0.0266510471701622,
-0.004447209183126688,
0.0047449991106987,
-0.021617738530039787,
0.018247542902827263,
-0.04764119163155556,
0.023426193743944168,
-0.01147020235657692,
0.01840820349752903,
-0.019281864166259766,
-0.018145300447940826,
-0.0037364244926720858,
0.03615235164761543,
0.008142143487930298,
0.007876046933233738,
-0.011371703818440437,
0.014502538368105888,
-0.03973379358649254,
0.07646030932664871,
0.041040606796741486,
-0.010901514440774918,
0.07166998833417892,
-0.0484524630010128,
0.02112690359354019,
0.01054913830012083,
-0.015438510105013847,
-0.04653521999716759,
0.012317701242864132,
-0.044674258679151535,
-0.03499472513794899,
0.01682116463780403,
0.016794225201010704,
-0.003432905301451683,
-0.047392621636390686,
0.006901084445416927,
0.016910819336771965,
-0.05159282684326172,
-0.02147757261991501,
0.03792646899819374,
0.036684948951005936,
0.046682339161634445,
0.008445397950708866,
-0.0044030495919287205,
-0.012036408297717571,
0.02594597637653351,
-0.01706036366522312,
0.050822239369153976,
0.012304901145398617,
0.019181041046977043,
0.0362313874065876,
-0.020027311518788338,
0.015256350859999657,
0.004746745340526104,
0.016486484557390213,
0.015634823590517044,
-0.032717954367399216,
-0.015381471253931522,
0.035886265337467194,
-0.01872139237821102,
0.01070760004222393,
0.03294358402490616,
-0.008843175135552883,
0.0693749338388443,
-0.03648574650287628,
0.00361637189052999,
-0.02233048714697361,
0.02451471798121929,
0.009500598534941673,
0.02832009643316269,
0.050057925283908844,
0.02992917411029339,
-0.0441700704395771,
-0.027650918811559677,
-0.026783868670463562,
0.020389800891280174,
0.03688530623912811,
-0.09426137804985046,
0.004546141251921654,
-0.03032948635518551,
-0.022723015397787094,
-0.02911532297730446,
-0.019632473587989807,
-0.04162324219942093,
0.034290432929992676,
-0.004402574617415667,
0.027531756088137627,
0.011819645762443542,
-0.0022152576129883528,
-0.01618075743317604,
-0.001603534328751266,
0.04000265151262283,
-0.0364496186375618,
-0.01604633592069149,
-0.0354766920208931,
0.03748168423771858,
-0.004157644230872393,
-0.010777372866868973
] |
<p>The problem I am working on is:</p>
<blockquote>
<p><em>Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure below). Calculate the total rotational kinetic energy of the two hands about the axis of rotation. (You may model the hands as long, thin rods rotated about one end. Assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 minutes, respectively.)</em></p>
</blockquote>
<p>(Converted) Angular Speed of Clock Hands:</p>
<p>Hour Hand $1.45\cdot10^{-4}~rad/s$</p>
<p>Minute Hand $1.75\cdot10^{-3}~rad/s$</p>
<p>Rotational Moment of Inertia:</p>
<p>Hour Hand $I=1/3(300~kg)(2.70~m)^2=729~kg\cdot m^2$</p>
<p>Minute Hand $I=1/3(100~kg)(4.20~m)^2=243~kg\cdot m^2$</p>
<p>Rotational Kinetic Energy:</p>
<p>$K_{rot}=1/2(729~kg\cdot m^2)(1.45\cdot10^{-4}~rad/s)^2+1/2(243~kg\cdot m^2)(1.75\cdot10^{-3}~rad/s)^2$</p>
<p>When I calculate this, it comes out incorrect, what has happened?</p> | 1,576 | [
-0.02959422394633293,
-0.04648013412952423,
-0.03625759482383728,
0.01289007905870676,
0.015514585189521313,
-0.04115801304578781,
-0.03787233307957649,
-0.016791317611932755,
0.0036369613371789455,
-0.017309678718447685,
0.05245889350771904,
0.05225053429603577,
0.0647866502404213,
0.05079315975308418,
0.011087624356150627,
-0.01209163386374712,
-0.004566790536046028,
-0.013172417879104614,
-0.002223706804215908,
-0.017164994031190872,
-0.0017331262351945043,
0.001702087465673685,
0.01876254566013813,
-0.022834867238998413,
-0.021237991750240326,
0.024012580513954163,
0.04879371449351311,
-0.01907280832529068,
0.00563983665779233,
0.04247706010937691,
-0.014863325282931328,
-0.01938508078455925,
0.04042663425207138,
0.026520712301135063,
0.007134432438760996,
0.032503705471754074,
-0.020696524530649185,
-0.030348865315318108,
-0.03360031172633171,
0.04870210587978363,
-0.03385956585407257,
0.014631192199885845,
-0.0070991734974086285,
0.03747320920228958,
0.0018967257346957922,
0.027035173028707504,
-0.022645018994808197,
-0.001720739179290831,
0.04035850986838341,
-0.059916622936725616,
0.10407567024230957,
0.02023213542997837,
0.0481991283595562,
-0.015542724169790745,
-0.01829596608877182,
-0.04339239373803139,
0.029086533933877945,
0.045687656849622726,
-0.0020815576426684856,
-0.0610068179666996,
0.00016175064956769347,
-0.009629725478589535,
-0.001851058448664844,
-0.02277141623198986,
0.024337323382496834,
-0.012284920550882816,
-0.007900784723460674,
0.010711973533034325,
0.044758301228284836,
-0.012519494630396366,
0.07914406061172485,
0.029594777151942253,
0.06967202574014664,
-0.03724515065550804,
-0.013702950440347195,
-0.03198960795998573,
0.010685705579817295,
0.025481758639216423,
0.02473955973982811,
0.03228135034441948,
-0.01824236288666725,
-0.006631570402532816,
0.06539303809404373,
0.04152325913310051,
0.02690117433667183,
-0.013431057333946228,
0.064353808760643,
-0.007510045543313026,
0.0184284970164299,
0.009687764570116997,
0.03826800361275673,
-0.00533033674582839,
0.01680239476263523,
0.006266285665333271,
-0.0009253642638213933,
0.061234887689352036,
-0.019415423274040222,
0.0623328760266304,
0.022810760885477066,
-0.0031962187495082617,
0.008059309795498848,
-0.00427299365401268,
0.04308741167187691,
0.05222485959529877,
0.01244061253964901,
-0.00411587068811059,
-0.02946595475077629,
0.0002306670357938856,
-0.011049214750528336,
-0.037555135786533356,
-0.04055760055780411,
0.004686770960688591,
-0.048688922077417374,
-0.00011443608673289418,
-0.007322658319026232,
-0.05841412767767906,
-0.03966307267546654,
-0.003950356971472502,
0.05234542116522789,
0.032913994044065475,
0.05423332005739212,
-0.06480288505554199,
-0.015267516486346722,
-0.05964626744389534,
-0.060708001255989075,
0.02486421912908554,
0.019295481964945793,
-0.01913677155971527,
-0.04221975430846214,
0.03533750772476196,
0.016216345131397247,
-0.005051284097135067,
-0.028310047462582588,
-0.012094780802726746,
0.03118174895644188,
-0.018271418288350105,
-0.13103514909744263,
-0.047674957662820816,
0.0726710632443428,
0.009015030227601528,
-0.022602995857596397,
-0.0913001298904419,
-0.01006141398102045,
0.008452343754470348,
0.06461551040410995,
0.015211925841867924,
-0.002079831436276436,
-0.011568188667297363,
0.02621181681752205,
-0.01465095765888691,
-0.025567935779690742,
0.005234513897448778,
0.013098271563649178,
-0.016652947291731834,
-0.0031634755432605743,
-0.049235984683036804,
0.04124138504266739,
0.00128973089158535,
0.026819221675395966,
-0.03581713140010834,
-0.00490201823413372,
0.0036771795712411404,
0.006657200399786234,
0.03400447219610214,
0.0024023610167205334,
-0.018992239609360695,
0.085512176156044,
0.056503795087337494,
-0.00017240540182683617,
0.03403518721461296,
0.04223022982478142,
0.00660669757053256,
-0.006565054878592491,
0.0059355078265070915,
0.047199368476867676,
-0.01747949980199337,
0.0176178477704525,
0.006682624574750662,
0.0060795508325099945,
-0.001411988865584135,
-0.0601062998175621,
-0.04933498799800873,
-0.010644350200891495,
-0.010811964981257915,
-0.0021685839165002108,
0.06288189440965652,
-0.024619897827506065,
0.0045448229648172855,
-0.023392489179968834,
-0.025904938578605652,
-0.02194122038781643,
-0.07240675389766693,
0.027181070297956467,
-0.0007386613870039582,
-0.007992001250386238,
-0.008692041039466858,
-0.0006355592049658298,
0.05060065910220146,
-0.01797834038734436,
0.0122788455337286,
-0.033648401498794556,
0.00994428526610136,
0.03370989114046097,
0.01603863574564457,
-0.007471523247659206,
0.017234617844223976,
0.03226233646273613,
-0.013905270025134087,
0.025236530229449272,
-0.011624379083514214,
-0.0033022805582731962,
-0.018722228705883026,
-0.0384673997759819,
-0.020539384335279465,
0.055649325251579285,
-0.014951031655073166,
-0.00010615306382533163,
0.00818948820233345,
-0.002745561534538865,
0.009985378012061119,
0.019994718953967094,
0.05591391772031784,
0.011106591671705246,
0.008024926297366619,
0.02969665825366974,
0.07011967152357101,
0.020217683166265488,
0.011563335545361042,
-0.022390248253941536,
-0.0457041971385479,
-0.005418709013611078,
-0.010219286195933819,
0.019145609810948372,
0.021646926179528236,
-0.04475969076156616,
0.014709091745316982,
0.030140887945890427,
0.05233149975538254,
0.020623167976737022,
-0.006773742381483316,
0.004310412332415581,
-0.030456548556685448,
-0.003806985914707184,
0.006197542417794466,
-0.01025138609111309,
-0.020592842251062393,
0.019456567242741585,
0.0258979219943285,
-0.010942387394607067,
0.035044342279434204,
-0.03414999321103096,
0.022067168727517128,
0.004423337522894144,
0.0433337464928627,
0.02414843440055847,
-0.01892411708831787,
0.05252402648329735,
-0.013753415085375309,
-0.006063147913664579,
0.044215936213731766,
-0.007242036052048206,
0.03230185806751251,
-0.009351435117423534,
-0.03644625470042229,
-0.009187783114612103,
0.014714998193085194,
0.0024758544750511646,
0.005328427534550428,
0.0022557831835001707,
0.004015455022454262,
-0.013568839058279991,
-0.0009195681195706129,
-0.019656550139188766,
-0.021334649994969368,
-0.009371639229357243,
0.011357069946825504,
0.03941792994737625,
0.026081321761012077,
-0.021984923630952835,
-0.027907056733965874,
-0.03947519510984421,
-0.031314343214035034,
0.004335511475801468,
0.0017656335840001702,
-0.04276353120803833,
0.032221175730228424,
0.011728090234100819,
-0.007326742168515921,
0.02689005434513092,
0.012480084784328938,
-0.0035701957531273365,
-0.009184424765408039,
0.0119320685043931,
-0.021194953471422195,
-0.009052685461938381,
-0.03822782635688782,
0.012240131385624409,
-0.04514773190021515,
0.02363576367497444,
0.04041806608438492,
0.0177976805716753,
-0.01776563562452793,
0.039621658623218536,
-0.06906025856733322,
-0.023557540029287338,
-0.007478285580873489,
0.027898235246539116,
0.03778739273548126,
-0.004092229530215263,
-0.00031479718745686114,
0.0006725158891640604,
0.030527343973517418,
-0.02801731415092945,
-0.07365764677524567,
-0.018469570204615593,
-0.0036791409365832806,
0.03568496182560921,
0.0610303096473217,
0.020725255832076073,
-0.019532738253474236,
0.07128933817148209,
0.03284649923443794,
-0.040006548166275024,
-0.0032294299453496933,
-0.012868087738752365,
0.016975607722997665,
-0.052608996629714966,
0.00817596260458231,
0.02905283495783806,
-0.04979900270700455,
0.000705236685462296,
0.020013825967907906,
0.004640330094844103,
0.04012691602110863,
-0.022701773792505264,
0.007038536947220564,
-0.004771148320287466,
-0.014177660457789898,
-0.01117390301078558,
0.048295680433511734,
-0.046820808202028275,
-0.04348384216427803,
-0.015254978090524673,
-0.017153602093458176,
0.0043222359381616116,
0.008246302604675293,
-0.07477965950965881,
0.03339062258601189,
-0.02877853997051716,
0.008489743806421757,
-0.03892570361495018,
0.04960670322179794,
-0.007951916195452213,
-0.0602324903011322,
0.002267370466142893,
0.024708110839128494,
0.09533106535673141,
0.026672031730413437,
0.02913789078593254,
0.04587550461292267,
0.04452919587492943,
0.026133976876735687,
-0.032282400876283646,
-0.04934247210621834,
-0.01314510591328144,
0.02676492929458618,
-0.02294159308075905,
-0.00782807171344757,
0.039882659912109375,
0.01627962663769722,
0.026948463171720505,
-0.03368627279996872,
-0.03597072884440422,
-0.018907366320490837,
-0.08669766783714294,
-0.019072789698839188,
-0.03215474262833595,
0.04264803230762482,
0.019468015059828758,
0.025648007169365883,
0.007224837318062782,
0.0016307239420711994,
0.013872717507183552,
0.03264370560646057,
-0.06824598461389542,
0.08985874801874161,
-0.011517606675624847,
-0.016008581966161728,
0.018852591514587402,
-0.015808777883648872,
0.01396959275007248,
-0.01809435337781906,
0.005392623133957386,
0.03169000521302223,
-0.02016083151102066,
-0.027745507657527924,
0.029378103092312813,
-0.03344995900988579,
-0.015687881037592888,
0.009085496887564659,
0.038593590259552,
0.026362434029579163,
-0.015855589881539345,
0.00780940568074584,
0.042761340737342834,
-0.03066817671060562,
0.008478136733174324,
-0.039022717624902725,
-0.022914284840226173,
-0.02793039381504059,
0.052942611277103424,
0.01481983345001936,
0.009686898440122604,
-0.003620564006268978,
0.03240165114402771,
0.029772697016596794,
0.0319603756070137,
0.01345987617969513,
-0.01148271095007658,
-0.026288429275155067,
-0.05739393085241318,
0.025568922981619835,
0.017053382471203804,
0.03295370563864708,
-0.0020441138185560703,
0.007524792104959488,
0.03460400924086571,
0.02946353144943714,
0.022008756175637245,
0.02722407877445221,
0.05132165551185608,
0.006734216120094061,
-0.028154611587524414,
-0.054702140390872955,
-0.004405552521348,
0.0039995997212827206,
-0.028436144813895226,
-0.004546106792986393,
0.014734091237187386,
-0.013723217882215977,
0.004019862040877342,
0.051873523741960526,
0.027966376394033432,
-0.007666788995265961,
0.08543845266103745,
0.01914641633629799,
0.046089060604572296,
-0.0005390028236433864,
-0.015480311587452888,
0.029090946540236473,
0.0024186393711715937,
0.04136599227786064,
-0.02184009552001953,
-0.038489386439323425,
-0.0788353979587555,
-0.012096035294234753,
0.02116360515356064,
0.07071742415428162,
-0.024728478863835335,
0.020098740234971046,
-0.05375536158680916,
0.0018274453468620777,
0.05095681548118591,
-0.054764844477176666,
0.06383167207241058,
0.0005076407687738538,
0.0487893708050251,
-0.012192104011774063,
-0.03658849000930786,
-0.03653382882475853,
0.012968654744327068,
-0.02326774410903454,
0.010577243752777576,
-0.027900902554392815,
-0.011980513110756874,
-0.01212124340236187,
-0.012437624856829643,
0.06230951473116875,
0.013078948482871056,
-0.015610264614224434,
-0.01116785779595375,
0.00962516013532877,
0.01804078184068203,
-0.026938043534755707,
-0.04869338870048523,
-0.01099612470716238,
0.011811971664428711,
-0.04594527557492256,
0.03387922793626785,
-0.03111237660050392,
-0.06311377137899399,
0.04961225762963295,
0.01860783062875271,
0.0048224362544715405,
0.005098631605505943,
-0.023434147238731384,
0.00784938782453537,
0.03478124365210533,
-0.016966674476861954,
0.05476269870996475,
0.06985539197921753,
-0.013911183923482895,
0.011131489649415016,
-0.018724272027611732,
0.00003550452311174013,
0.01629435457289219,
0.007833126001060009,
-0.04334891960024834,
0.013055210933089256,
-0.002251029945909977,
0.014278524555265903,
-0.03926984220743179,
0.05267869308590889,
-0.035427190363407135,
-0.015253638848662376,
-0.02043677680194378,
0.001986386487260461,
0.018621474504470825,
-0.004496071953326464,
-0.008393813855946064,
0.004633460659533739,
-0.022172529250383377,
-0.02452833205461502,
-0.002084403531625867,
-0.014284306205809116,
0.0035131273325532675,
0.01573730818927288,
-0.005193751305341721,
0.021112805232405663,
-0.039595670998096466,
-0.0062022702768445015,
-0.003133945632725954,
-0.035485927015542984,
0.02867080830037594,
-0.05614330992102623,
0.021179795265197754,
-0.0015366643201559782,
-0.03468092903494835,
-0.02547905035316944,
-0.029626650735735893,
0.026460980996489525,
0.00234858226031065,
-0.012267187237739563,
0.023448646068572998,
0.029662013053894043,
-0.020994549617171288,
-0.034831225872039795,
-0.03636515140533447,
0.043732576072216034,
0.031433530151844025,
-0.013862538151443005,
-0.01871594600379467,
-0.02884092926979065,
-0.016548722982406616,
-0.028756890445947647,
-0.012901108711957932,
0.04403599351644516,
-0.04164427891373634,
0.01629633642733097,
0.022373463958501816,
0.035873156040906906,
0.06964586675167084,
0.015427201986312866,
-0.025788655504584312,
-0.010868004523217678,
-0.0010193861089646816,
-0.07405457645654678,
0.015303842723369598,
0.0671771839261055,
-0.027455326169729233,
-0.02493036724627018,
0.014590450562536716,
0.014209534972906113,
0.07390613853931427,
-0.01477030199021101,
0.006932477001100779,
0.02099175751209259,
0.018237613141536713,
0.036940284073352814,
-0.01838020235300064,
0.059964947402477264,
0.009297550655901432,
0.056227944791316986,
-0.011214764788746834,
-0.008775186724960804,
-0.030723843723535538,
-0.03111143596470356,
0.017165139317512512,
0.008161832578480244,
-0.015297536738216877,
0.008465166203677654,
0.08306784182786942,
-0.020392704755067825,
0.004765264689922333,
0.03618635982275009,
-0.009022408165037632,
0.034840136766433716,
-0.02351834438741207,
0.0003815133241005242,
0.008642742410302162,
0.0023175941314548254,
-0.013271233066916466,
-0.03415699303150177,
-0.00003345031655044295,
-0.016880081966519356,
0.06211886554956436,
-0.01257339771836996,
0.06900426745414734,
0.008012761361896992,
0.027908388525247574,
0.03643103316426277,
-0.023662570863962173,
-0.007665381301194429,
-0.004676645155996084,
0.01967206597328186,
0.032484062016010284,
-0.00473346933722496,
0.0031294520013034344,
0.024386774748563766,
0.03263293579220772,
-0.0062666903249919415,
0.028636367991566658,
0.04223637655377388,
0.007147383876144886,
-0.0016682782443240285,
-0.005786788649857044,
-0.023961123079061508,
-0.0019753356464207172,
-0.012596379965543747,
0.05241657793521881,
-0.03532518446445465,
0.006183822639286518,
0.01724374108016491,
0.06139323115348816,
-0.01149623841047287,
-0.01296955719590187,
0.015312516130506992,
-0.03088979981839657,
0.008063878864049911,
-0.008944218046963215,
-0.021457599475979805,
-0.03337586671113968,
-0.01297038421034813,
0.03440399095416069,
0.0006270807352848351,
0.026835685595870018,
-0.07482872903347015,
-0.05060930550098419,
0.003517131321132183,
-0.02428407222032547,
-0.050283148884773254,
0.05616549029946327,
-0.0076431953348219395,
-0.04604215547442436,
0.05862489342689514,
-0.030460262671113014,
-0.006279348861426115,
-0.025951532647013664,
0.02507687546312809,
-0.03623703867197037,
0.10046008974313736,
0.031208984553813934,
-0.000013950111679150723,
-0.013474354520440102,
0.045534346252679825,
0.12934660911560059,
0.05332754924893379,
0.03117278590798378,
-0.02452574297785759,
0.02719353884458542,
-0.021113090217113495,
0.008849581703543663,
-0.027054045349359512,
0.005804584361612797,
-0.03913269564509392,
0.010580932721495628,
0.01600365899503231,
0.02015228383243084,
0.02881600707769394,
-0.015619923360645771,
0.0047762468457221985,
-0.004715918097645044,
-0.0394735112786293,
0.0006633909652009606,
0.00776378158479929,
0.005514032673090696,
-0.004806625656783581,
-0.039360128343105316,
0.037369418889284134,
-0.036975786089897156,
-0.037709884345531464,
-0.0269013624638319,
-0.04287146031856537,
0.01195975486189127,
-0.006268971133977175,
-0.056365493685007095,
0.010214284993708134,
-0.0077248928137123585,
-0.04448525235056877,
-0.01958862692117691,
0.0364549495279789,
0.014787852764129639,
-0.0009288613218814135,
0.03265304118394852,
0.02513631246984005,
-0.016445808112621307,
0.018024330958724022,
0.034427251666784286,
0.027387745678424835,
-0.07378777116537094,
-0.0032609188929200172,
-0.058121051639318466,
0.02406470477581024,
-0.014440612867474556,
-0.008622872643172741,
-0.007242576219141483,
-0.02828190289437771,
-0.019023606553673744,
-0.03150774911046028,
0.023973975330591202,
-0.013436981476843357,
0.011788000352680683,
-0.010076996870338917,
-0.04617076739668846,
-0.0227519478648901,
0.016304170712828636,
0.0146201616153121,
0.007234868127852678,
-0.0005795459146611392,
0.02010439708828926,
0.02272423356771469,
0.012953657656908035,
0.013841180130839348,
-0.03496738150715828,
-0.027608543634414673,
-0.004361864645034075,
-0.021204832941293716,
-0.022107750177383423,
-0.0005686396034434438,
0.006700999569147825,
0.0193378534168005,
0.04428354650735855,
-0.03649195283651352,
-0.004310435149818659,
-0.050165146589279175,
-0.021402690559625626,
0.016507107764482498,
0.021885009482502937,
-0.03843546658754349,
-0.004728085361421108,
-0.023829560726881027,
-0.005940018221735954,
0.03799901157617569,
-0.03846548870205879,
0.0048982687294483185,
-0.027996113523840904,
0.03160778060555458,
-0.014844680204987526,
-0.03053460456430912,
-0.03860120847821236,
0.013805662281811237,
0.0016513150185346603,
0.008701719343662262,
-0.025421656668186188,
0.02684205025434494,
0.03884438797831535,
0.01569175347685814,
0.014901667833328247,
0.03151300549507141,
-0.029693014919757843,
0.0023327148519456387,
0.005800379905849695,
-0.059877123683691025,
0.009782669134438038,
0.009998170658946037,
-0.012647041119635105,
-0.0390097051858902,
-0.007686240132898092,
-0.023394329473376274,
0.00798717513680458,
-0.015333752147853374,
0.027559058740735054,
-0.03695855662226677,
0.02047998271882534,
-0.07724440842866898,
0.014191882684826851,
-0.01926627941429615,
0.006394912488758564,
-0.06006837263703346,
0.004901578184217215,
0.014739724807441235,
-0.002647574059665203,
-0.022389791905879974,
0.06261403113603592,
0.01077851839363575,
-0.01854405179619789,
0.013652618043124676,
0.02536170929670334,
-0.028940735384821892,
0.016161050647497177,
-0.009466963820159435,
-0.02167198620736599,
0.0255376398563385,
-0.014901532791554928,
-0.015545811504125595,
0.024912502616643906,
-0.04750953987240791,
-0.03759882226586342,
0.02893139235675335,
0.013894962146878242,
0.0060614352114498615,
0.0034271758049726486,
-0.0222158320248127,
0.006880354136228561,
0.07363804429769516,
-0.06317475438117981,
0.0015648711705580354,
0.017720462754368782,
0.0033165444619953632,
0.01436672080308199,
-0.005086061544716358,
0.019866427406668663,
-0.0003546392254065722,
-0.02672463096678257,
0.06750909239053726,
0.03635444864630699,
-0.0505470372736454,
0.02465406246483326,
0.0038050697185099125,
0.026682715862989426,
-0.022559935227036476,
-0.009279814548790455,
0.03793259710073471,
0.031220946460962296,
0.040922682732343674,
-0.060628898441791534,
0.027815425768494606,
-0.016753042116761208,
0.009055675938725471,
-0.0844075009226799,
-0.01642913557589054,
-0.007505621295422316,
0.021472038701176643,
0.0612020306289196,
-0.0785645991563797,
-0.018174709752202034,
0.01580149494111538,
-0.044953539967536926,
-0.03373442217707634,
-0.04175519570708275,
-0.010733363218605518,
-0.020153481513261795,
-0.04307150840759277,
-0.0013258077669888735,
0.0039047161117196083,
-0.007112998515367508,
0.03803214430809021,
0.006971950642764568,
0.01628737896680832,
-0.014196280390024185,
-0.012711647897958755,
0.0261825080960989,
0.023893335834145546,
-0.0019813752733170986,
-0.011588250286877155,
0.04161995276808739,
-0.03877084329724312,
-0.02908768504858017,
0.02982098050415516,
-0.044181134551763535,
0.041340459138154984,
-0.030133666470646858,
0.012068703770637512,
-0.015752431005239487,
0.03853558376431465,
0.008920043706893921,
-0.012988568283617496,
-0.015016014687716961,
-0.019630001857876778,
0.023712318390607834,
0.010196777991950512,
-0.021953260526061058,
0.01070888340473175,
0.03890484571456909,
-0.03732208535075188,
-0.032851442694664,
-0.004227235447615385,
-0.01975540816783905,
0.009023457765579224,
0.01765500195324421,
0.013592326082289219,
0.004503350239247084,
-0.042764537036418915,
0.013160137459635735,
-0.01602478325366974,
0.02456814981997013,
0.05230439454317093,
-0.047720834612846375,
0.02557014673948288,
-0.005904048215597868,
0.008032303303480148,
0.00947500392794609,
0.005457391031086445,
0.002357066608965397,
-0.05230720341205597,
-0.033366598188877106,
-0.026702482253313065,
0.008418222889304161,
0.01718795672059059,
-0.03018615022301674,
-0.019538477063179016,
-0.052912112325429916,
0.024280672892928123,
0.02236747555434704,
0.03714394569396973,
-0.021184071898460388,
0.00555392587557435,
-0.026082029566168785,
-0.08011417090892792,
0.0011742440983653069,
0.035798221826553345,
-0.03913752734661102,
-0.03939651697874069,
-0.029857942834496498,
0.00001640118716750294,
0.00270825601182878,
0.049579471349716187,
0.012393875978887081,
-0.02335585281252861,
0.005883500911295414,
-0.013964270241558552,
-0.0056648519821465015,
-0.018484482541680336,
0.016932938247919083,
0.0031919856555759907,
-0.013138731941580772,
0.007133601699024439,
-0.024057593196630478,
-0.028607593849301338,
-0.03622664511203766,
0.009739217348396778,
-0.001796344411559403,
-0.003496428718790412,
-0.01504160650074482,
-0.02163485251367092,
0.04550526291131973,
-0.015452585183084011,
-0.008601555600762367,
0.01953072100877762,
0.024695824831724167,
0.016987549141049385,
0.03188994526863098,
-0.047062862664461136,
-0.029809854924678802,
0.06885235011577606,
-0.04095081984996796,
0.0117605896666646,
-0.006433009635657072,
-0.04752593860030174,
0.048544082790613174,
-0.03569968044757843,
-0.021943049505352974,
0.027999956160783768,
-0.02467428334057331,
-0.01448205765336752,
0.017439082264900208,
0.07092450559139252,
0.03989500179886818,
-0.0173109769821167,
-0.0032383876387029886,
0.031096335500478745,
-0.0047592781484127045,
0.02611382305622101,
-0.005377849098294973,
0.015759585425257683,
-0.010730359703302383,
-0.011397290974855423,
0.015443256124854088,
-0.018379274755716324,
0.015845712274312973,
0.002212967025116086,
0.012886738404631615,
-0.0032684821635484695,
-0.031046412885189056,
0.0076894634403288364,
-0.023096276447176933,
-0.005966522730886936,
0.02133977971971035,
-0.02512325346469879,
0.05574513599276543,
0.018034515902400017,
0.01198410801589489,
-0.0303792804479599,
-0.009141476824879646,
-0.0010045506060123444,
0.00293108937330544,
-0.0011205653427168727,
0.03686876222491264,
0.0094100721180439,
-0.014126055873930454,
-0.028064921498298645,
-0.008095894008874893,
0.010194460861384869,
-0.03185013681650162,
-0.01817493885755539,
-0.013745516538619995,
0.019725942984223366,
-0.024394752457737923,
-0.029046719893813133,
-0.007076536770910025,
-0.030706416815519333,
0.03726109117269516,
0.015748189762234688,
0.03343909978866577,
-0.017030326649546623,
-0.025567209348082542,
0.015073259361088276,
0.05716817453503609,
-0.08258642256259918,
-0.010024839080870152,
0.0067412517964839935,
0.04588748514652252,
0.023049840703606606,
0.011604995466768742
] |
<p>I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (self-adjoint operator) in quantum mechanics? </p>
<p>E.g. an operator $A$ with the Hamiltonian $H$?</p> | 651 | [
-0.02966451272368431,
0.008808820508420467,
0.009358307346701622,
-0.03647273778915405,
0.028076112270355225,
0.014287102036178112,
-0.02824513241648674,
-0.015384950675070286,
0.00846758484840393,
-0.02518540620803833,
0.0007615399663336575,
0.023961639031767845,
0.06276815384626389,
-0.013317171484231949,
0.036030616611242294,
0.007438681088387966,
-0.02315543405711651,
-0.03802599012851715,
-0.0066311475820839405,
0.03023766726255417,
0.005284405779093504,
0.028160689398646355,
0.04387739673256874,
-0.013390024192631245,
0.023132048547267914,
0.026211656630039215,
0.016763027757406235,
0.026121366769075394,
0.05540827289223671,
0.04963674768805504,
0.007780127227306366,
-0.034538231790065765,
-0.0038066627457737923,
0.06026635318994522,
0.0008359650382772088,
0.0005988145712763071,
0.0005565789178945124,
-0.035101309418678284,
-0.0037853482645004988,
0.015771115198731422,
-0.05403779447078705,
-0.030751913785934448,
0.0019277225947007537,
0.05039922520518303,
-0.02252039685845375,
-0.007245553191751242,
-0.027982238680124283,
-0.021802842617034912,
0.03355304151773453,
-0.05238858982920647,
0.08403147011995316,
0.020488286390900612,
0.054094284772872925,
0.027734845876693726,
-0.026745803654193878,
0.0365043506026268,
0.08302848041057587,
0.05967748910188675,
0.001876573427580297,
-0.055712949484586716,
-0.02668112702667713,
-0.027433177456259727,
-0.029939841479063034,
-0.03426864743232727,
-0.017251597717404366,
0.02433423325419426,
0.015035598538815975,
-0.03757186233997345,
0.01477007381618023,
0.0011036478681489825,
-0.0065380907617509365,
0.008008419536054134,
0.05072006583213806,
-0.05358729511499405,
0.041782673448324203,
-0.02117440104484558,
0.0164073184132576,
0.034978631883859634,
0.07895742356777191,
0.006608195137232542,
-0.012431597337126732,
0.016069242730736732,
-0.011004786938428879,
0.023759782314300537,
0.011435245163738728,
-0.0017600164283066988,
0.06216803565621376,
0.005201539024710655,
0.012294447980821133,
0.02276306413114071,
-0.03698286786675453,
0.02399665303528309,
0.012046554125845432,
-0.00672112824395299,
0.0008980829734355211,
0.03786061331629753,
0.00697049405425787,
0.05982726812362671,
0.0017828153213486075,
-0.039401449263095856,
0.0074048275128006935,
-0.02407214045524597,
0.016262559220194817,
0.06372521072626114,
0.000031003059120848775,
-0.02286565862596035,
-0.016217809170484543,
0.021280815824866295,
-0.009233927354216576,
-0.009013327769935131,
-0.02321682684123516,
0.02294856682419777,
0.003122009104117751,
0.025171512737870216,
0.023086989298462868,
-0.010048175230622292,
0.023507826030254364,
-0.005308022256940603,
0.032482270151376724,
0.06401856988668442,
0.04036521539092064,
-0.03620428964495659,
0.01309524942189455,
-0.010169935412704945,
-0.03782831132411957,
-0.011979048140347004,
0.03812452778220177,
0.007466379553079605,
-0.04751133918762207,
0.014226695522665977,
-0.0014351486461237073,
-0.04344252496957779,
-0.010804516263306141,
-0.008847539313137531,
0.007032151333987713,
-0.039306070655584335,
-0.12331075221300125,
-0.061603207141160965,
0.024910546839237213,
-0.024119718000292778,
-0.05155934393405914,
-0.08156413584947586,
0.007607480976730585,
0.037375450134277344,
0.07068603485822678,
-0.0042743380181491375,
-0.019378161057829857,
0.014707865193486214,
0.015409670770168304,
0.02709163725376129,
0.015109057538211346,
-0.050208620727062225,
0.0285793486982584,
-0.042768362909555435,
-0.0005140771390870214,
-0.04773908108472824,
0.008463330566883087,
0.026680855080485344,
-0.009379331022500992,
-0.04340597987174988,
0.06937111914157867,
-0.03596669062972069,
-0.004879343789070845,
0.01448829472064972,
0.01515140663832426,
-0.045183759182691574,
0.05654078349471092,
0.03324321284890175,
0.0017042327672243118,
0.03919589892029762,
0.020476648584008217,
0.023635365068912506,
0.01765754446387291,
0.05886152386665344,
-0.0034471082035452127,
-0.01505298912525177,
-0.02898116037249565,
-0.0292471032589674,
-0.007455434650182724,
-0.004343713168054819,
-0.024008776992559433,
-0.06111442297697067,
0.010832132771611214,
0.03050299547612667,
-0.01924065686762333,
0.015978505834937096,
-0.005367151461541653,
0.01665293611586094,
0.0018893785309046507,
-0.04004649072885513,
-0.0024215716402977705,
-0.062377896159887314,
0.0223920326679945,
-0.004135744646191597,
-0.012280266731977463,
0.05050100386142731,
0.05022812262177467,
0.004568639677017927,
-0.02151554450392723,
-0.060472868382930756,
-0.014919638633728027,
0.011115394532680511,
-0.0006872348603792489,
-0.01768769510090351,
0.03749440237879753,
0.047432269901037216,
0.03568003699183464,
0.028512943536043167,
0.04613732546567917,
-0.03632820025086403,
-0.04193481430411339,
0.006944685243070126,
-0.0041921851225197315,
0.010458559729158878,
0.016467995941638947,
0.008952468633651733,
-0.0012204438680782914,
-0.0486062727868557,
-0.011784568428993225,
0.026833200827240944,
-0.026462892070412636,
0.067178875207901,
0.035086944699287415,
-0.024563021957874298,
-0.016624657437205315,
0.07298723608255386,
0.006686625070869923,
-0.0061684902757406235,
-0.02168736234307289,
-0.02716062404215336,
-0.03150906041264534,
0.02456141822040081,
0.020098045468330383,
0.009687731973826885,
-0.029440168291330338,
0.011716468259692192,
-0.010875782929360867,
0.053643450140953064,
0.03604671731591225,
0.022179648280143738,
-0.03854724019765854,
-0.008700319565832615,
0.00930652767419815,
0.0021959629375487566,
0.0038709850050508976,
-0.013525284826755524,
0.015559971332550049,
0.017029326409101486,
0.04794768616557121,
0.01165421400219202,
-0.05240515619516373,
0.07554941624403,
-0.057507921010255814,
0.025520935654640198,
0.006759707350283861,
-0.04419245570898056,
0.009905190207064152,
-0.02944265492260456,
0.025657247751951218,
0.024472137913107872,
-0.017698626965284348,
0.003850894048810005,
-0.02545541524887085,
-0.04029656946659088,
0.007473838981240988,
-0.00672657135874033,
-0.0394868440926075,
-0.009143803268671036,
0.006140731740742922,
-0.005705994088202715,
0.013049491681158543,
-0.01398183312267065,
0.005239536985754967,
-0.010769299231469631,
-0.029285533353686333,
0.02533879689872265,
0.011181472800672054,
0.04509648680686951,
-0.026506034657359123,
-0.0605388805270195,
-0.018057340756058693,
-0.054999515414237976,
0.042328108102083206,
0.007127220742404461,
-0.045267507433891296,
0.044534701853990555,
-0.07463282346725464,
-0.037337493151426315,
0.04328344762325287,
-0.02518707513809204,
0.022024203091859818,
0.012039737775921822,
-0.023183217272162437,
-0.04376872628927231,
-0.0207335464656353,
-0.006603897083550692,
0.019592825323343277,
-0.032659754157066345,
0.015588851645588875,
0.03949781507253647,
-0.046253979206085205,
-0.02557731233537197,
-0.012601794674992561,
-0.001582499360665679,
-0.04236459359526634,
-0.004731640685349703,
-0.041318390518426895,
0.019726576283574104,
-0.03037531115114689,
0.025126086547970772,
0.056518469005823135,
-0.04726811870932579,
-0.014965836890041828,
-0.0438101701438427,
-0.048109184950590134,
0.021477624773979187,
0.023975413292646408,
0.01756485551595688,
0.008831326849758625,
-0.005302093457430601,
0.07680686563253403,
-0.0008037843508645892,
-0.039264533668756485,
-0.0006206013495102525,
0.010210772976279259,
-0.017556600272655487,
-0.03159342333674431,
0.03224032744765282,
0.04605412855744362,
-0.007512354291975498,
0.04665721207857132,
0.04395733028650284,
0.001359113841317594,
0.016610026359558105,
0.020202644169330597,
-0.0337323322892189,
0.0032194945961236954,
0.014901573769748211,
0.03666584938764572,
0.01690388098359108,
-0.02667272463440895,
-0.030083121731877327,
0.010255125351250172,
0.01780194789171219,
0.005864149425178766,
0.004628658760339022,
-0.030758311972022057,
0.07056684792041779,
0.002049320377409458,
0.01080425176769495,
-0.03579339757561684,
0.0595148466527462,
-0.0023756963200867176,
0.011443703435361385,
-0.0039847902953624725,
0.011859564110636711,
0.025640076026320457,
-0.034409139305353165,
0.014523040503263474,
0.051952049136161804,
0.008850764483213425,
-0.02626039832830429,
-0.023511024191975594,
-0.004900655243545771,
-0.01544121466577053,
0.007011128589510918,
0.004871353507041931,
-0.05325058475136757,
0.019111348316073418,
-0.0018759274389594793,
0.00807720236480236,
-0.007102109957486391,
-0.040535181760787964,
-0.011290856637060642,
-0.0686974748969078,
-0.002314726123586297,
0.027300246059894562,
0.02682792954146862,
-0.006187121849507093,
0.0780048742890358,
0.013958743773400784,
0.031235845759510994,
0.026563160121440887,
-0.009898198768496513,
-0.05308954790234566,
0.0315629243850708,
-0.035808220505714417,
-0.02234809100627899,
-0.010890381410717964,
-0.025437572970986366,
0.01529297512024641,
-0.029421763494610786,
-0.04229869320988655,
-0.019375931471586227,
-0.018157994374632835,
-0.04991926997900009,
-0.013383900746703148,
-0.04751518368721008,
-0.03905946761369705,
-0.03776581585407257,
0.00425777118653059,
0.036706775426864624,
0.0014332206919789314,
0.03928898647427559,
0.02130287140607834,
-0.048218876123428345,
-0.0010574507759884,
-0.02348381280899048,
-0.0024490526411682367,
0.032642658799886703,
0.004061203449964523,
0.051399409770965576,
0.03405226022005081,
-0.022299624979496002,
0.007451506331562996,
0.003418657463043928,
0.07396690547466278,
0.01033703237771988,
-0.03099357895553112,
0.006507922429591417,
-0.044886697083711624,
-0.008181657642126083,
-0.005793226882815361,
0.06445999443531036,
-0.004293571691960096,
0.009955811314284801,
0.029427867382764816,
0.010995768941938877,
-0.032764315605163574,
0.03089638240635395,
0.06119300425052643,
0.04752778634428978,
-0.03117620199918747,
-0.02496153675019741,
0.0046545336954295635,
-0.03706829622387886,
0.00041566090658307076,
0.027209343388676643,
-0.026588303968310356,
-0.016077635809779167,
0.033074840903282166,
0.000003544603259797441,
0.05092361569404602,
-0.02104572393000126,
-0.02783253788948059,
-0.0035604937002062798,
0.01340272556990385,
0.022101769223809242,
-0.015703370794653893,
-0.0006591116543859243,
0.059196047484874725,
0.04230552166700363,
-0.0008144142921082675,
0.021813848987221718,
-0.06256955862045288,
-0.00048405598499812186,
0.03107149340212345,
-0.008059002459049225,
-0.011213415302336216,
-0.010748052038252354,
-0.0026657504495233297,
-0.03446555882692337,
0.04273150861263275,
-0.018629183992743492,
0.06578424572944641,
-0.024908514693379402,
-0.020975949242711067,
-0.013117694295942783,
-0.023606076836586,
-0.026961982250213623,
0.061448145657777786,
0.013508569449186325,
-0.0014016448985785246,
-0.026899080723524094,
-0.018468698486685753,
-0.029341289773583412,
0.004780927207320929,
0.013813483528792858,
0.04449794068932533,
0.006304780952632427,
-0.010659406892955303,
-0.00545464875176549,
0.08166282624006271,
0.008517183363437653,
-0.07783876359462738,
-0.009506704285740852,
0.029195675626397133,
-0.02545362338423729,
0.044864535331726074,
-0.022823024541139603,
-0.030752284452319145,
0.004077963996678591,
-0.0006235272740013897,
0.009625740349292755,
0.01657276600599289,
-0.03392772376537323,
0.05159943923354149,
0.011640781536698341,
-0.02176631987094879,
0.026721421629190445,
-0.013810623437166214,
-0.023101620376110077,
-0.029735779389739037,
-0.03179958462715149,
0.06002793088555336,
-0.012297111563384533,
0.011143488809466362,
-0.042684029787778854,
-0.01242610439658165,
-0.02898343838751316,
0.02864980883896351,
-0.014062193222343922,
0.002031651558354497,
-0.0010781342862173915,
-0.03527076542377472,
-0.0293401088565588,
0.042641859501600266,
-0.029961926862597466,
-0.013215819373726845,
-0.003931380342692137,
0.03091711550951004,
0.0027390136383473873,
-0.021649427711963654,
-0.00871158018708229,
-0.02724538929760456,
-0.007694304920732975,
0.03708048537373543,
-0.0349438339471817,
0.03229047358036041,
-0.038639482110738754,
-0.02668553590774536,
0.028526803478598595,
-0.061890386044979095,
0.019654449075460434,
-0.03594883531332016,
-0.009196080267429352,
0.01023002341389656,
-0.04321059584617615,
-0.0611337348818779,
0.00869879499077797,
-0.014266238547861576,
0.036651208996772766,
-0.03818809613585472,
0.0330103300511837,
0.01833338662981987,
-0.022261496633291245,
-0.06693945825099945,
-0.05365903675556183,
0.012318091467022896,
0.017813917249441147,
-0.010060920380055904,
-0.0075903395190835,
0.05439979210495949,
-0.022246655076742172,
-0.013224822469055653,
-0.012571815401315689,
0.03128970041871071,
-0.04219326376914978,
-0.006048338953405619,
0.006390159483999014,
0.007686427794396877,
0.0227881520986557,
0.0013518170453608036,
-0.0183767918497324,
0.00459810858592391,
-0.03327569738030434,
0.0008607954951003194,
0.02992173098027706,
0.054249487817287445,
-0.015351051464676857,
-0.03312580659985542,
-0.01702645979821682,
-0.013573181815445423,
0.05763370916247368,
-0.026348182931542397,
0.0037752888165414333,
0.022017981857061386,
0.034668706357479095,
0.018134471029043198,
-0.0013552928576245904,
0.017944658175110817,
0.006842025090008974,
0.043345607817173004,
0.02202015556395054,
-0.0036005915608257055,
-0.04807687923312187,
-0.05323062837123871,
0.022525642067193985,
0.011303259991109371,
0.006670584436506033,
0.01913081668317318,
0.05593720078468323,
0.0009589946712367237,
0.0362740121781826,
0.004700267221778631,
-0.007643023040145636,
-0.004705789033323526,
-0.04376811906695366,
0.02242724783718586,
0.009302578866481781,
0.0007531913579441607,
-0.047577377408742905,
-0.02296573296189308,
-0.037479422986507416,
0.0004400887992233038,
0.051269322633743286,
-0.03671148046851158,
0.07686332613229752,
0.03450856730341911,
0.006708539556711912,
-0.0030556865967810154,
0.007051733788102865,
-0.008855781517922878,
0.018406400457024574,
0.0007911416469141841,
0.019268808886408806,
-0.01008785329759121,
0.009361778385937214,
0.03847718611359596,
0.06044137850403786,
-0.01368226669728756,
-0.013686509802937508,
0.02534000761806965,
0.049675509333610535,
0.0030285483226180077,
0.003750745439901948,
-0.042953044176101685,
0.024750983342528343,
-0.028285251930356026,
0.015681002289056778,
-0.02408275566995144,
-0.028353268280625343,
0.012907602824270725,
0.00224805879406631,
-0.010012615472078323,
-0.01333230547606945,
-0.025873443111777306,
-0.045819781720638275,
0.03026401996612549,
0.006132814101874828,
0.02639606222510338,
0.012352698482573032,
0.019956601783633232,
0.01987985335290432,
0.012774677947163582,
0.025144172832369804,
0.00583232007920742,
-0.06511681526899338,
-0.01312270388007164,
-0.016101611778140068,
-0.050648096948862076,
0.023153360933065414,
-0.017588229849934578,
-0.021394234150648117,
0.010756796225905418,
-0.015373735688626766,
0.02211187593638897,
0.014847148209810257,
0.029336707666516304,
-0.04515809938311577,
0.05687657743692398,
-0.0012793631758540869,
0.017223823815584183,
0.023293163627386093,
0.03609948977828026,
0.09349485486745834,
0.0467398464679718,
0.029048645868897438,
-0.06677337735891342,
-0.0043196058832108974,
0.0063847689889371395,
-0.004097010940313339,
-0.03238540515303612,
0.04999435320496559,
0.02866307832300663,
0.03150337561964989,
-0.010748554021120071,
0.0214878860861063,
0.013037888333201408,
-0.008975902572274208,
0.06869830191135406,
-0.04090620204806328,
-0.04276435077190399,
-0.0014457624638453126,
-0.000468901707790792,
0.003026018850505352,
0.0010069195413962007,
-0.05140005052089691,
-0.0009796909289434552,
-0.030919229611754417,
0.017886878922581673,
-0.02010047249495983,
-0.03385256603360176,
0.028845105320215225,
-0.003510688664391637,
-0.00016416270227637142,
0.0017063687555491924,
0.0002710543922148645,
-0.01959039643406868,
-0.06028986722230911,
0.04115258902311325,
0.026706187054514885,
0.009492716751992702,
0.027111563831567764,
0.005036267451941967,
0.0022403495386242867,
0.0018504410982131958,
0.01368903648108244,
-0.002376592019572854,
-0.040696609765291214,
-0.019402774050831795,
-0.009692839346826077,
0.06319032609462738,
0.009858742356300354,
0.030538707971572876,
0.010577564127743244,
-0.012155125848948956,
-0.023677675053477287,
-0.01967533305287361,
0.00256544747389853,
-0.014092858880758286,
0.04407690092921257,
-0.022484784945845604,
-0.014834034256637096,
-0.04547494649887085,
0.0048836469650268555,
-0.026752183213829994,
0.035784535109996796,
0.00007584650302305818,
-0.00890352949500084,
0.024389944970607758,
-0.008519507944583893,
0.024342071264982224,
-0.0011700064642354846,
-0.036616791039705276,
0.005631235893815756,
-0.0254511795938015,
-0.021798228845000267,
-0.05016043782234192,
0.029387440532445908,
0.0016827688086777925,
0.058053407818078995,
0.01431322656571865,
0.004209634382277727,
-0.00940527394413948,
-0.08734072744846344,
0.010957478545606136,
-0.016097228974103928,
-0.0156983882188797,
-0.015172215178608894,
-0.0031637821812182665,
0.06003246456384659,
0.0513504296541214,
-0.008449077606201172,
0.014114266261458397,
-0.005237056408077478,
-0.005117319989949465,
0.023260237649083138,
-0.002897310769185424,
-0.012787655927240849,
0.059263404458761215,
-0.039286449551582336,
-0.00405891751870513,
-0.006952363532036543,
-0.0036986544728279114,
0.03588569164276123,
-0.005288401618599892,
-0.002670265967026353,
0.03840859979391098,
-0.016728274524211884,
-0.003173615550622344,
0.010507418774068356,
-0.02972760796546936,
0.01603596843779087,
0.001729992451146245,
0.023331264033913612,
-0.04434455931186676,
-0.06049047037959099,
-0.02648397907614708,
0.03050857037305832,
0.005181366577744484,
0.019406350329518318,
-0.023967280983924866,
-0.023411991074681282,
0.013976175338029861,
0.06047093868255615,
-0.013055838644504547,
-0.0075587499886751175,
-0.06543602794408798,
0.017982715740799904,
0.024253947660326958,
-0.00912263710051775,
-0.012561801820993423,
0.04444115608930588,
0.022826634347438812,
-0.04015231877565384,
0.022122547030448914,
0.04072370380163193,
-0.013272576034069061,
0.0018598524620756507,
0.02959982305765152,
-0.029628505930304527,
0.04814618453383446,
0.020311139523983,
-0.04356861487030983,
0.04103275388479233,
-0.04996837303042412,
-0.012576439417898655,
0.04701978713274002,
-0.03862256556749344,
0.06162087619304657,
0.033352095633745193,
-0.03409279137849808,
-0.009340204298496246,
0.028071576729416847,
-0.02512606792151928,
0.004546741023659706,
-0.005650936160236597,
-0.054225414991378784,
-0.05424175411462784,
0.013543658889830112,
0.026214567944407463,
0.010087188333272934,
-0.005944933742284775,
0.014228487387299538,
0.04640941321849823,
0.001121428096666932,
-0.000607892929110676,
-0.003253488801419735,
0.03200875222682953,
0.022515716031193733,
0.022979160770773888,
-0.011870375834405422,
0.020555133000016212,
0.03634724020957947,
-0.054043881595134735,
0.04635177552700043,
0.028833560645580292,
0.012466782703995705,
-0.11349929869174957,
-0.01052805408835411,
0.012478477321565151,
-0.008197691291570663,
0.04275655746459961,
-0.05237128585577011,
0.029141947627067566,
0.02832045592367649,
-0.058511748909950256,
0.028599170967936516,
-0.03917602449655533,
-0.024094345048069954,
-0.008800255134701729,
0.00722049456089735,
-0.03752957284450531,
0.08396757394075394,
0.01686367392539978,
0.011430070735514164,
-0.0037028465885668993,
0.0029963681008666754,
-0.017056701704859734,
-0.034146517515182495,
-0.04410317540168762,
0.016660217195749283,
0.020597830414772034,
-0.006384817883372307,
0.056100763380527496,
-0.023407770320773125,
-0.0297060776501894,
0.03863520920276642,
-0.056124795228242874,
-0.012219865806400776,
-0.0086913350969553,
0.012400009669363499,
0.012246486730873585,
0.012152258306741714,
0.03809557110071182,
-0.01984163001179695,
-0.03802764043211937,
0.03175226226449013,
0.04136805981397629,
0.036217860877513885,
-0.029031388461589813,
-0.015125281177461147,
-0.0005900817923247814,
-0.06372719258069992,
-0.05701320990920067,
0.007380036171525717,
0.014500048942863941,
0.0035349836107343435,
0.002407791092991829,
-0.008417160250246525,
0.013183225877583027,
0.001682021887972951,
0.021030088886618614,
-0.02104177698493004,
-0.025716878473758698,
0.014665646478533745,
0.00009744989074533805,
0.004459989257156849,
0.021559860557317734,
-0.0356532447040081,
-0.031026137992739677,
0.05322453752160072,
0.016969896852970123,
-0.017726054415106773,
-0.07654374837875366,
-0.03208264708518982,
0.03948710113763809,
-0.015486640855669975,
0.003982983995229006,
-0.03500252589583397,
-0.031446199864149094,
0.041282396763563156,
0.012688606977462769,
0.028411269187927246,
-0.026000317186117172,
-0.05321153625845909,
-0.053430210798978806,
-0.053564250469207764,
0.03235771879553795,
0.017678679898381233,
-0.0052060713060200214,
-0.027507435530424118,
0.004508907441049814,
-0.008044338785111904,
-0.011267445981502533,
0.03309157118201256,
0.009916197508573532,
-0.03880372643470764,
0.015125335194170475,
0.005199413280934095,
0.0055120596662163734,
-0.03534916043281555,
0.0035927766002714634,
-0.02103675901889801,
0.003295870963484049,
-0.02826593816280365,
-0.004598562140017748,
-0.025545604526996613,
0.014484347775578499,
0.011808468960225582,
-0.03254600986838341,
0.008579266257584095,
0.0029403383377939463,
-0.05376604571938515,
0.06628776341676712,
0.02328207530081272,
0.01891045831143856,
0.06744185835123062,
0.0005797594203613698,
0.021346842870116234,
0.05361256003379822,
-0.03629148378968239,
-0.042574696242809296,
0.034988705068826675,
-0.010577542707324028,
0.015171332284808159,
0.011219010688364506,
-0.004405080806463957,
0.02137739397585392,
-0.029050543904304504,
-0.025649430230259895,
0.02814893051981926,
-0.024982357397675514,
-0.010913969948887825,
0.055227406322956085,
0.02558082528412342,
0.01484489906579256,
0.013991772197186947,
0.01884995587170124,
0.02761496603488922,
0.03397933021187782,
0.0015323309926316142,
0.05198988690972328,
0.0158099178224802,
-0.011608394794166088,
0.030721869319677353,
0.02306913211941719,
0.014414429664611816,
0.030355188995599747,
0.026131125167012215,
0.027900077402591705,
-0.0461672879755497,
0.008494238369166851,
0.02496040053665638,
-0.025236481800675392,
-0.006797320209443569,
0.012769034132361412,
-0.033899858593940735,
0.06585005670785904,
-0.04682640731334686,
0.0036116158589720726,
-0.03350560739636421,
0.03320937976241112,
-0.01337752677500248,
-0.03486446663737297,
0.026510506868362427,
0.049912046641111374,
-0.024156944826245308,
0.025383079424500465,
-0.018449816852808,
0.0005930912448093295,
-0.011201552115380764,
-0.03993765637278557,
0.01797398179769516,
0.021352600306272507,
-0.016278423368930817,
-0.04228176176548004,
-0.021930841729044914,
-0.03499108552932739,
-0.031389154493808746,
0.01278343703597784,
0.06534877419471741,
0.012199128977954388,
0.032206885516643524,
-0.020513031631708145,
-0.02447938546538353,
0.013795441016554832,
-0.04658928140997887,
-0.025327332317829132,
-0.026530668139457703,
0.03168056160211563,
-0.021068954840302467,
0.02674657292664051
] |
<p>Please can anyone explain the concepts of <a href="http://en.wikipedia.org/wiki/Electromagnetically_induced_transparency" rel="nofollow">electromagnetic induced transparency</a>? I am having problem with the technicality of the explanation on wikipedia. Please I am an engineer with a physics background though and would love if this can be explained with little to no jargons . I am working on optical buffers and studying recent technologies and would love and explanation on this.</p> | 1,577 | [
0.005126648116856813,
-0.048206135630607605,
0.003970958758145571,
-0.06788505613803864,
0.025144387036561966,
0.04943288862705231,
-0.00728720985352993,
-0.007424826733767986,
0.014827576465904713,
-0.03307640179991722,
0.035136427730321884,
0.040167659521102905,
0.04351281002163887,
-0.029212303459644318,
0.020234668627381325,
0.013140877708792686,
-0.0011120641138404608,
0.03628557547926903,
0.01621498540043831,
-0.03136304020881653,
-0.03797895833849907,
0.034485939890146255,
-0.02610279992222786,
0.019952520728111267,
-0.031131381168961525,
0.0014774501323699951,
0.03521618992090225,
0.0016399422893300653,
0.03719894587993622,
0.03632918745279312,
-0.03413008153438568,
-0.025220884010195732,
-0.028106791898608208,
0.024294603615999222,
-0.02084038220345974,
-0.015155068598687649,
-0.03451735898852348,
-0.042860809713602066,
0.018023792654275894,
0.016108477488160133,
-0.03317994624376297,
0.005567272659391165,
-0.021261660382151604,
0.04415018856525421,
-0.021684998646378517,
-0.036619044840335846,
0.021460896357893944,
-0.014650347642600536,
0.025497663766145706,
-0.030511334538459778,
0.07940955460071564,
-0.0706784650683403,
0.024521460756659508,
0.013361938297748566,
-0.014079191721975803,
0.03047342225909233,
0.08514062315225601,
0.06749430298805237,
-0.029895756393671036,
-0.04361509159207344,
-0.003310312982648611,
-0.004981331527233124,
-0.000199943853658624,
-0.007485964801162481,
-0.01394304633140564,
0.0467105433344841,
0.02275744080543518,
-0.012727157212793827,
0.06883177161216736,
0.0006148713873699307,
-0.010166526772081852,
-0.022620510309934616,
0.03153305873274803,
-0.025992069393396378,
0.025866176933050156,
-0.06391630321741104,
0.045568108558654785,
0.011669105850160122,
0.005351162515580654,
0.025682872161269188,
-0.009575244970619678,
-0.001091135200113058,
0.008874124847352505,
0.041227344423532486,
-0.012454918585717678,
-0.009003160521388054,
0.08274118602275848,
-0.033879633992910385,
0.042981501668691635,
0.0034659618977457285,
-0.04330241307616234,
0.03047308512032032,
0.026116589084267616,
0.0006122158956713974,
-0.04818086326122284,
0.013483652845025063,
-0.015939045697450638,
0.0801704153418541,
-0.01645008847117424,
-0.03031747415661812,
0.010514860041439533,
0.03308062255382538,
0.02930169552564621,
0.053510431200265884,
-0.020756205543875694,
-0.03834117203950882,
-0.02177528850734234,
0.029105082154273987,
-0.009775569662451744,
0.010483372956514359,
-0.023229893296957016,
-0.010299592278897762,
0.01801365055143833,
0.016573701053857803,
0.02639247477054596,
-0.019277941435575485,
0.007738563697785139,
0.00858994945883751,
0.0718386098742485,
0.08961105346679688,
0.031761907041072845,
-0.05700685828924179,
0.02793181873857975,
-0.0035000150091946125,
-0.07835250347852707,
0.019200574606657028,
0.03615045174956322,
0.026388196274638176,
-0.03726628050208092,
0.027355490252375603,
-0.02102743461728096,
-0.05868147313594818,
0.023483801633119583,
-0.003976927138864994,
0.04831012710928917,
-0.03635869920253754,
-0.105536088347435,
-0.06589710712432861,
0.030233437195420265,
0.005436431150883436,
-0.020106809213757515,
-0.0911661759018898,
0.01936597190797329,
0.023742083460092545,
0.11786683648824692,
0.04221377149224281,
0.00026654842076823115,
-0.011986544355750084,
0.027225898578763008,
0.025856126099824905,
-0.005409873090684414,
0.0012133106356486678,
0.040759384632110596,
0.006223349831998348,
0.02542976103723049,
-0.062305230647325516,
0.020272275432944298,
0.04213722050189972,
-0.033543869853019714,
-0.02838716469705105,
0.0669802874326706,
-0.00042393209878355265,
-0.012571237981319427,
0.025980474427342415,
-0.009098701179027557,
-0.03480269014835358,
0.09212712198495865,
-0.005910859443247318,
-0.0007799348095431924,
0.03720865771174431,
0.01075058151036501,
0.045130208134651184,
0.003558761440217495,
0.044068969786167145,
-0.02078268863260746,
-0.040076229721307755,
0.0050310613587498665,
-0.009125623852014542,
0.015533354133367538,
-0.014579332433640957,
-0.04982484504580498,
-0.0498821921646595,
0.010236036032438278,
0.0326213575899601,
0.002411540597677231,
-0.0023562712594866753,
-0.011520208790898323,
-0.008842525072395802,
0.020173147320747375,
-0.0881885290145874,
0.008790251798927784,
-0.04026763141155243,
0.03502100706100464,
-0.0013249559560790658,
-0.017216255888342857,
0.023676283657550812,
-0.012087980285286903,
-0.03271535411477089,
-0.018086029216647148,
-0.047729380428791046,
-0.020878538489341736,
-0.0032148053869605064,
0.015532304532825947,
-0.029841775074601173,
0.020709415897727013,
0.042707689106464386,
0.03479921817779541,
-0.00906449742615223,
-0.0029417078476399183,
-0.03749912604689598,
-0.039715155959129333,
0.014035197906196117,
-0.022873250767588615,
0.05852093547582626,
-0.017106426879763603,
-0.003301129676401615,
0.0031268286984413862,
0.012173057533800602,
0.008633545599877834,
0.01464034989476204,
-0.045814596116542816,
0.05861429497599602,
0.047417279332876205,
0.052646391093730927,
-0.023017290979623795,
0.021567102521657944,
-0.006010754965245724,
-0.011875014752149582,
-0.025091055780649185,
-0.04295243322849274,
-0.021783189848065376,
-0.0006111178663559258,
0.03546328470110893,
-0.0041662901639938354,
-0.048418790102005005,
0.03849827125668526,
-0.01865503191947937,
0.06078645959496498,
0.06475301086902618,
0.07024402916431427,
-0.03958833962678909,
-0.017146112397313118,
0.01450788602232933,
0.005612339358776808,
-0.021502401679754257,
0.05091891065239906,
0.0007825648644939065,
-0.00036636897129938006,
0.029697474092245102,
-0.0048475321382284164,
0.017066488042473793,
0.034167371690273285,
-0.031703487038612366,
-0.005438799969851971,
-0.015756791457533836,
-0.01775825023651123,
-0.011926860548555851,
-0.05368276312947273,
-0.006371736526489258,
0.034633997827768326,
0.001102311653085053,
0.021076224744319916,
-0.043450284749269485,
-0.014032859355211258,
-0.0013900670455768704,
-0.031038522720336914,
-0.034722473472356796,
-0.02022239752113819,
0.0016719081904739141,
-0.012431108392775059,
0.032009005546569824,
-0.002143915044143796,
0.0031271888874471188,
-0.06745991855859756,
-0.020575860515236855,
0.010873173363506794,
0.019546570256352425,
0.03713866323232651,
-0.04046888276934624,
-0.04487978667020798,
-0.03520509973168373,
-0.04364728555083275,
0.011070826090872288,
0.011382651515305042,
-0.014379576779901981,
0.015471325255930424,
-0.022935738787055016,
-0.02615746669471264,
0.07911211252212524,
-0.03137775883078575,
-0.029188167303800583,
-0.01381929311901331,
-0.004220493137836456,
-0.04805974289774895,
-0.026406025514006615,
0.009717023931443691,
-0.012204219587147236,
0.0014582228614017367,
-0.03451179713010788,
0.04661096632480621,
-0.016513893380761147,
-0.030828513205051422,
0.003030194900929928,
-0.045759931206703186,
-0.016015009954571724,
-0.004565471317619085,
-0.020362794399261475,
-0.008603808470070362,
-0.05043865367770195,
0.028229987248778343,
0.021992512047290802,
-0.03329595923423767,
0.01160205714404583,
-0.025127656757831573,
-0.07503221184015274,
0.03541800379753113,
-0.022170046344399452,
0.025848407298326492,
0.0007366631762124598,
-0.02347666583955288,
0.05855097249150276,
0.02172376587986946,
-0.018032873049378395,
-0.015070635825395584,
-0.005461389664560556,
0.018850984051823616,
-0.05019812285900116,
0.01796751469373703,
0.044327493757009506,
-0.013632207177579403,
0.020930970087647438,
0.0360058918595314,
0.012193476781249046,
0.03933331370353699,
-0.0037298304960131645,
-0.014631646685302258,
-0.005352790933102369,
-0.024366306141018867,
-0.027910714969038963,
0.037341855466365814,
0.04398706182837486,
-0.056614141911268234,
0.002643257612362504,
-0.016553111374378204,
0.039694663137197495,
0.043639108538627625,
-0.003935975022614002,
0.036111894994974136,
-0.006088485941290855,
-0.010381552390754223,
-0.015213975682854652,
0.04172251746058464,
-0.03950856626033783,
0.011441187933087349,
0.0022036386653780937,
0.013921527191996574,
0.0031116767786443233,
-0.02598755806684494,
-0.009298553690314293,
0.03460099920630455,
0.03958170488476753,
-0.02093752846121788,
0.011724456213414669,
-0.004894237499684095,
-0.017642373219132423,
0.04374505579471588,
-0.026718206703662872,
-0.0124433021992445,
0.07344456017017365,
0.03509623929858208,
0.02438540942966938,
-0.016832105815410614,
-0.010025698691606522,
-0.03518570959568024,
-0.019525766372680664,
0.038906022906303406,
0.008633890189230442,
0.03400165215134621,
0.011316732503473759,
0.06647619605064392,
0.04186493903398514,
0.022717196494340897,
0.013624622486531734,
-0.014433690346777439,
-0.07608073204755783,
0.009340409189462662,
-0.031983207911252975,
-0.008396623656153679,
-0.05066749453544617,
0.00799919106066227,
-0.020512867718935013,
-0.016374699771404266,
-0.06245777755975723,
-0.02457554265856743,
0.02535647712647915,
-0.059452466666698456,
-0.010564746335148811,
-0.024373406544327736,
0.012976955622434616,
-0.04683157429099083,
0.020694073289632797,
0.022248288616538048,
0.002095322823151946,
0.011906009167432785,
0.006113579496741295,
-0.042987558990716934,
-0.004109643399715424,
-0.010321971029043198,
-0.016437185928225517,
0.04457101598381996,
0.01956598274409771,
0.06900902837514877,
0.004623623564839363,
-0.016999781131744385,
0.012788786552846432,
0.013703119941055775,
0.06649791449308395,
0.026563512161374092,
0.007835503667593002,
-0.019818155094981194,
-0.03348173573613167,
-0.014713370241224766,
-0.03774566948413849,
0.052202705293893814,
-0.0087468596175313,
0.02654152363538742,
0.03398749232292175,
0.004764553625136614,
-0.03812309354543686,
0.03195927292108536,
0.0021350972820073366,
0.013763380236923695,
-0.00788332149386406,
-0.05452762544155121,
-0.006168990861624479,
-0.0004828961391467601,
0.012337901629507542,
-0.000827651412691921,
0.024791769683361053,
0.009655135683715343,
0.012536187656223774,
0.006490753497928381,
-0.010621454566717148,
-0.009445508010685444,
-0.0299728661775589,
0.0012866246979683638,
-0.016634033992886543,
-0.015038501471281052,
0.023322703316807747,
-0.0009036269620992243,
0.036878690123558044,
0.02779652178287506,
0.03003019094467163,
-0.014668523333966732,
-0.07970080524682999,
0.008793365210294724,
0.025843070819973946,
0.03129229322075844,
0.006323344074189663,
0.001777704688720405,
-0.039548687636852264,
-0.00678358506411314,
-0.00439721392467618,
-0.005035004112869501,
0.036203403025865555,
-0.0004501899238675833,
-0.0032504189293831587,
-0.052754584699869156,
0.007988741621375084,
0.03321821242570877,
0.03419831022620201,
0.015417670831084251,
0.040614061057567596,
-0.030856160447001457,
-0.008351253345608711,
-0.010869301855564117,
-0.0008616066770628095,
0.009896138682961464,
0.07997618615627289,
-0.009480634704232216,
-0.011401389725506306,
0.029586637392640114,
0.03919168561697006,
-0.03808973357081413,
-0.05998535826802254,
0.00556208984926343,
-0.010102223604917526,
-0.011924505233764648,
0.04219147562980652,
-0.03797733038663864,
-0.00809667631983757,
0.012194802984595299,
0.05820697918534279,
-0.011296196840703487,
-0.005100174807012081,
-0.01139040756970644,
0.024739988148212433,
0.009461048059165478,
-0.058642126619815826,
0.06228215619921684,
0.04078255593776703,
-0.04271456226706505,
0.0010991949820891023,
-0.0043291617184877396,
0.06200181692838669,
-0.05222528055310249,
0.013694397173821926,
-0.023432951420545578,
0.014864041469991207,
-0.055147603154182434,
0.05093364045023918,
-0.007193618919700384,
-0.011259262450039387,
-0.009879038669168949,
-0.022988414391875267,
0.0009243765380233526,
0.035761017352342606,
-0.052193641662597656,
-0.005959129426628351,
-0.023274054750800133,
0.010909798555076122,
-0.02209673635661602,
-0.02727961726486683,
0.022643936797976494,
0.006184655707329512,
0.02266545221209526,
0.015979230403900146,
0.013735012151300907,
0.02358374558389187,
-0.0432342067360878,
-0.02456100471317768,
0.016108764335513115,
-0.03384797275066376,
0.05762958526611328,
-0.018248451873660088,
0.024157850071787834,
0.01284338440746069,
-0.05659554526209831,
-0.019350690767169,
0.018062829971313477,
-0.05376529321074486,
0.04760248214006424,
-0.029046328738331795,
0.031809259206056595,
0.01882014237344265,
0.023459553718566895,
-0.04536140710115433,
-0.0713702067732811,
0.017920229583978653,
-0.004391020629554987,
-0.024415364488959312,
0.00870167650282383,
-0.03637165576219559,
-0.019356727600097656,
-0.044465385377407074,
0.024755526334047318,
0.01620241068303585,
-0.02251737006008625,
0.0019455000292509794,
0.01699565164744854,
-0.01375294104218483,
0.024130133911967278,
0.006713924929499626,
-0.06689120829105377,
-0.01923264190554619,
-0.04231243580579758,
-0.012263642624020576,
0.006078888662159443,
0.028016619384288788,
-0.017610622569918633,
-0.04026845097541809,
-0.014907050877809525,
0.02727820724248886,
0.025221262127161026,
-0.007710812147706747,
-0.0011015527416020632,
0.04593520238995552,
0.047929663211107254,
0.025272542610764503,
-0.05180477723479271,
-0.005657992325723171,
-0.004173890687525272,
0.040334030985832214,
0.03363627567887306,
-0.034929003566503525,
-0.021968061104416847,
-0.04428204521536827,
0.03156609833240509,
0.008540365844964981,
0.028553510084748268,
-0.006336911115795374,
0.08316706866025925,
-0.02084568329155445,
0.03592585027217865,
-0.011600060388445854,
-0.01336345449090004,
0.00867185927927494,
-0.02159806713461876,
0.0071327039040625095,
0.013552139513194561,
0.013083608821034431,
-0.03389495238661766,
-0.05187005549669266,
-0.03254874423146248,
0.018195513635873795,
0.049424909055233,
-0.06032729148864746,
0.040561649948358536,
0.03874773904681206,
-0.013711376115679741,
-0.009200194850564003,
-0.032086245715618134,
-0.00866772886365652,
0.03793010860681534,
-0.022605685517191887,
0.01338252890855074,
0.0009585895459167659,
0.0020625938195735216,
-0.0011578126577660441,
0.0758754312992096,
-0.023619046434760094,
0.025663059204816818,
0.045086950063705444,
0.04731258004903793,
0.028297651559114456,
0.004350379109382629,
-0.028411120176315308,
0.037502188235521317,
-0.04788097366690636,
0.020428093150258064,
0.03858056664466858,
0.02134876139461994,
0.027734702453017235,
-0.012769363820552826,
0.03830487281084061,
-0.047085050493478775,
-0.014113426208496094,
-0.03991898521780968,
0.030097991228103638,
-0.013288149610161781,
-0.017671670764684677,
0.016705552116036415,
-0.004268566612154245,
0.030157797038555145,
0.01081657875329256,
0.030903836712241173,
0.01165527943521738,
-0.06953098624944687,
-0.04019308090209961,
-0.02782686986029148,
-0.007457439787685871,
0.027928225696086884,
-0.007020424585789442,
-0.03582875803112984,
0.030845224857330322,
-0.02359466627240181,
0.030567806214094162,
0.022942133247852325,
0.022382857277989388,
-0.03949772194027901,
0.04585665091872215,
-0.01715950295329094,
0.029262391850352287,
-0.0018532209796831012,
-0.02337045595049858,
0.09287072718143463,
0.037221722304821014,
-0.003998757805675268,
-0.09317879378795624,
-0.008242953568696976,
-0.0033936500549316406,
0.00656117545440793,
-0.020415540784597397,
0.021821510046720505,
-0.01678898185491562,
0.03253288194537163,
0.018375232815742493,
0.01748204044997692,
0.03556862100958824,
0.028247853741049767,
0.028422927483916283,
-0.039571285247802734,
-0.04213342443108559,
0.023037897422909737,
0.026343127712607384,
-0.03925520181655884,
0.01905253529548645,
-0.09559481590986252,
0.010888359509408474,
-0.0393378920853138,
-0.025222402065992355,
-0.016118701547384262,
-0.015530996955931187,
0.050564851611852646,
0.002654008101671934,
-0.030910316854715347,
-0.01109156385064125,
-0.012921796180307865,
-0.0003989384858869016,
-0.02216232568025589,
0.02527242712676525,
0.029086919501423836,
0.017295440658926964,
-0.0015629393747076392,
0.02217887155711651,
0.040378082543611526,
-0.027616964653134346,
0.010281427763402462,
0.021920502185821533,
-0.040047500282526016,
0.008976653218269348,
-0.013635873794555664,
0.04652131348848343,
-0.020041698589920998,
-0.01884177327156067,
-0.0048646749928593636,
0.006676777731627226,
-0.006702312733978033,
-0.022701900452375412,
0.019803237169981003,
0.03828178346157074,
-0.0020646629855036736,
0.001913954969495535,
0.007166670169681311,
0.012373648583889008,
0.04638560116291046,
-0.030346402898430824,
0.01591925509274006,
-0.027407707646489143,
-0.011877160519361496,
0.01798480749130249,
0.00009355325164506212,
0.011680646799504757,
-0.020828261971473694,
-0.044227756559848785,
-0.05411272495985031,
-0.0037760366685688496,
-0.015592767857015133,
-0.02194342017173767,
0.012247252278029919,
0.013643762096762657,
0.010636024177074432,
-0.016004834324121475,
0.0013873104471713305,
0.020625896751880646,
-0.05233016237616539,
0.041546616703271866,
0.0013050212292000651,
-0.041709017008543015,
-0.019049618393182755,
-0.00005141044675838202,
0.048897016793489456,
0.008976197801530361,
0.014491706155240536,
0.032436810433864594,
0.005146631505340338,
-0.010128982365131378,
0.02579144947230816,
-0.03631170839071274,
-0.017567740753293037,
0.04265913367271423,
-0.02360597439110279,
-0.0037990882992744446,
-0.0002273846184834838,
0.05945780500769615,
0.0039112865924835205,
0.013564406894147396,
0.00925240758806467,
0.0022016626317054033,
-0.016636742278933525,
-0.027288438752293587,
0.003422559006139636,
-0.015713604167103767,
-0.010194316506385803,
-0.017906274646520615,
0.00878281332552433,
-0.019273821264505386,
-0.015079999342560768,
0.0007658023969270289,
-0.007485257927328348,
0.023060372099280357,
0.006127810571342707,
0.0034954047296196222,
0.003116633975878358,
-0.026312585920095444,
0.0021710700821131468,
-0.02019522711634636,
-0.035891566425561905,
-0.03654443472623825,
0.00009256148769054562,
0.006067556794732809,
0.0009026189218275249,
-0.01066960021853447,
0.004101295955479145,
-0.009439343586564064,
0.003002970479428768,
0.01847236603498459,
0.04273572936654091,
0.010530795902013779,
0.019762814044952393,
0.03905262053012848,
-0.01353009045124054,
0.0471370704472065,
-0.00968389306217432,
-0.036248330026865005,
0.03873099759221077,
-0.03837060555815697,
-0.03875140845775604,
0.013972281478345394,
0.00016096154286060482,
0.042986687272787094,
-0.005906322505325079,
-0.027149129658937454,
-0.033095307648181915,
0.06079231947660446,
-0.010742219164967537,
-0.0060341800563037395,
-0.00959262065589428,
-0.019162114709615707,
0.019223419949412346,
0.000560424814466387,
-0.00525106955319643,
-0.02761770784854889,
0.007227088324725628,
0.02266990765929222,
0.037214938551187515,
0.012171118520200253,
-0.033154211938381195,
-0.0005171396187506616,
0.010275101289153099,
0.009720499627292156,
0.0060991025529801846,
0.004303252790123224,
0.01401449739933014,
0.05031596124172211,
0.005644368007779121,
0.04915012791752815,
0.017315151169896126,
-0.015856321901082993,
-0.08413979411125183,
0.01965390145778656,
0.0021102859172970057,
0.00755341025069356,
0.04289839789271355,
-0.027260251343250275,
0.04792400076985359,
0.03719933331012726,
-0.0556652694940567,
-0.02654399536550045,
-0.016341175884008408,
-0.04447413608431816,
-0.023550041019916534,
0.024070408195257187,
-0.00017723161727190018,
0.02040752023458481,
0.04046054929494858,
-0.010276651941239834,
0.01506507396697998,
-0.010811427608132362,
-0.03733925521373749,
-0.0011224240297451615,
-0.015688158571720123,
0.03588001802563667,
-0.003441364038735628,
-0.002674355637282133,
0.042410898953676224,
0.02234429307281971,
-0.026644360274076462,
0.0380987785756588,
-0.01592474803328514,
0.018845677375793457,
-0.0035897342022508383,
-0.0001531005691504106,
0.000432418251875788,
-0.0057665337808430195,
0.011889705434441566,
0.001273437519557774,
-0.017349878326058388,
-0.004045519977807999,
0.04981723800301552,
0.042590439319610596,
0.03369859978556633,
0.008506176993250847,
-0.006172502879053354,
-0.04082677885890007,
-0.01866729184985161,
0.011632482521235943,
0.0021460670977830887,
0.004600015468895435,
0.008070362731814384,
0.0006583505892194808,
0.036428630352020264,
-0.034085772931575775,
0.03874584287405014,
-0.05534105375409126,
-0.04841257631778717,
0.0058799791149795055,
0.032407909631729126,
0.006009750533849001,
0.0019856481812894344,
-0.0034281471744179726,
-0.046610184013843536,
0.022932106629014015,
0.028509797528386116,
0.010135426186025143,
-0.032514434307813644,
-0.03250680863857269,
0.011705119162797928,
-0.03237077593803406,
0.014219948090612888,
-0.02341543324291706,
-0.04614310339093208,
0.026464344933629036,
0.027903517708182335,
-0.03830369561910629,
-0.007906830869615078,
-0.06834965199232101,
-0.019445868209004402,
-0.03323863446712494,
0.06797239184379578,
-0.0500975027680397,
-0.0024806938599795103,
-0.04019571840763092,
-0.003831914160400629,
-0.0025756913237273693,
0.0511673241853714,
0.05233732610940933,
-0.006200746167451143,
-0.0399790033698082,
-0.011799942702054977,
0.006325877271592617,
0.016153983771800995,
-0.04385209083557129,
0.01097614411264658,
0.01765035092830658,
-0.039126988500356674,
-0.0022850316017866135,
-0.004854497965425253,
-0.02399347722530365,
0.012593148276209831,
0.005636692047119141,
0.015175600536167622,
0.02194920927286148,
-0.003373613813892007,
-0.018861783668398857,
0.0390465147793293,
0.005336678586900234,
-0.011890677735209465,
0.04858893156051636,
-0.020209085196256638,
0.020128097385168076,
0.02007964998483658,
0.03650812432169914,
-0.059141021221876144,
0.022049041464924812,
-0.018657229840755463,
0.0076921661384403706,
-0.02428542822599411,
-0.02508408948779106,
0.026779672130942345,
-0.04100588709115982,
-0.01004788652062416,
0.010125470347702503,
-0.06267568469047546,
0.006242999341338873,
0.0759669840335846,
-0.01580478623509407,
0.017257943749427795,
0.005311090499162674,
0.03408883139491081,
-0.0404944121837616,
-0.03178809583187103,
-0.031405020505189896,
0.06388120353221893,
0.019171064719557762,
0.028458064422011375,
0.0632271021604538,
0.024815723299980164,
-0.015414953231811523,
0.010630002245306969,
0.0009317368967458606,
0.037078969180583954,
-0.010097559541463852,
-0.011284241452813148,
0.007625549100339413,
0.0015110314125195146,
0.015075895003974438,
0.04777384176850319,
0.00007354687841143459,
0.061370596289634705,
-0.04841095581650734,
0.04661829024553299,
-0.016928818076848984,
0.016552528366446495,
-0.01308109425008297,
0.005798360798507929,
0.006009411532431841,
0.01831447333097458,
0.0036721164360642433,
-0.015410622581839561,
-0.022623512893915176,
-0.003762645646929741,
0.042600326240062714,
-0.03154116868972778,
0.027752423658967018,
-0.019050633534789085,
-0.0401335209608078,
0.020862318575382233,
-0.022453410550951958,
0.013105887919664383,
-0.03230566903948784,
0.007216841913759708,
0.017441753298044205,
0.0015552976401522756,
0.005122326780110598,
-0.014855961315333843,
-0.028789758682250977,
0.05099108815193176,
-0.07521025091409683,
0.02804688550531864,
-0.026691561564803123,
0.03522159904241562,
-0.03378281369805336,
0.02595834992825985
] |
<p>Photons have no mass but they can push things, as evidenced by <a href="https://en.wikipedia.org/wiki/Laser_propulsion">laser propulsion</a>. </p>
<p>Can photons push the source which is emitting them? If yes, will a more intense flashlight accelerate me more? Does the wavelength of the light matter? Is this practical for space propulsion? Doesn't it defy the law of momentum conservation?</p>
<p><em>Note: As John Rennie mentioned, all in all the wavelength doesn't matter, but for a more accurate answer regarding that, see the comments in <a href="http://physics.stackexchange.com/a/112870/46604">DavePhD's answer</a> .</em></p>
<p><em>Related Wikipedia articles: <a href="https://en.wikipedia.org/wiki/Ion_thruster">Ion thruster</a>, <a href="https://en.wikipedia.org/wiki/Spacecraft_propulsion">Space propulsion</a></em></p> | 483 | [
-0.01255178451538086,
-0.03337344527244568,
-0.03988764435052872,
-0.0466744564473629,
0.04855739325284958,
-0.004456238821148872,
-0.044638168066740036,
-0.015460891649127007,
-0.003105110488831997,
-0.04757150262594223,
0.049601905047893524,
0.05307905375957489,
0.04872092232108116,
-0.0016124076209962368,
0.009825488552451134,
0.033403389155864716,
0.0264187753200531,
-0.009233364835381508,
-0.0057498011738061905,
-0.001989005832001567,
-0.027752524241805077,
0.012276382185518742,
0.010332887060940266,
0.015714135020971298,
-0.046313945204019547,
0.03466004133224487,
0.017755357548594475,
-0.014890474267303944,
-0.018398908898234367,
0.018828870728611946,
0.022954337298870087,
0.012021970935165882,
-0.006183059886097908,
0.005037411116063595,
0.003681817790493369,
0.000965785002335906,
-0.019807705655694008,
-0.032031282782554626,
0.007489912211894989,
0.012564391829073429,
-0.03172715753316879,
0.024563081562519073,
0.009813902899622917,
0.021774567663669586,
-0.01636292226612568,
0.029214810580015182,
-0.013739338144659996,
0.0021141869947314262,
0.064220130443573,
-0.07546176761388779,
0.03173470497131348,
-0.01012159138917923,
0.05417395010590553,
0.02303602360188961,
-0.0363486222922802,
-0.050895873457193375,
0.07334845513105392,
0.07870595902204514,
0.0030576351564377546,
-0.018660083413124084,
0.026840919628739357,
0.01572609506547451,
-0.002521623158827424,
-0.028139779344201088,
-0.02470293454825878,
0.04734145104885101,
-0.020930184051394463,
0.019265485927462578,
0.03134739771485329,
0.03561462089419365,
0.02438739500939846,
-0.004283423535525799,
0.03317101299762726,
0.015358734875917435,
-0.009553426876664162,
-0.02751476690173149,
0.04077694192528725,
0.023617379367351532,
0.04138508811593056,
0.05848786234855652,
-0.021390605717897415,
-0.019198132678866386,
0.007553014438599348,
0.023156864568591118,
0.026366975158452988,
0.001405292539857328,
0.07792554795742035,
0.00022053411521483213,
-0.003621563548222184,
0.007380379363894463,
0.015389589592814445,
0.038418326526880264,
0.012387556955218315,
0.006661301478743553,
0.021254241466522217,
0.04070264473557472,
-0.004395380616188049,
0.0287016611546278,
-0.015508097596466541,
-0.0017860017251223326,
0.01022043265402317,
0.037701431661844254,
0.033001672476530075,
0.05213172361254692,
-0.011002466082572937,
-0.019922010600566864,
-0.014282084070146084,
0.023571940138936043,
-0.04768919199705124,
0.00572805292904377,
-0.056914445012807846,
0.001653331913985312,
0.015519270673394203,
-0.013928830623626709,
0.0075110020115971565,
-0.04126004874706268,
0.005061717703938484,
-0.011909493245184422,
0.08220401406288147,
0.06317055970430374,
0.0138951875269413,
-0.033591631799936295,
0.05071460083127022,
-0.034410182386636734,
-0.03343464806675911,
-0.003104680683463812,
0.03610755503177643,
-0.007020608056336641,
-0.021252620965242386,
0.005846219602972269,
-0.0049010105431079865,
-0.025613637641072273,
-0.01049590203911066,
-0.032080747187137604,
0.02193640172481537,
-0.026241954416036606,
-0.08445027470588684,
-0.0666082575917244,
0.046020686626434326,
0.013584212400019169,
0.00005430883538792841,
-0.06471565365791321,
-0.008028221316635609,
0.025563061237335205,
0.09243651479482651,
-0.027098428457975388,
-0.00214802916161716,
-0.026780301705002785,
0.07244130969047546,
-0.0402788445353508,
-0.05746827274560928,
0.004332822747528553,
0.0012668515555560589,
-0.044138532131910324,
0.04096226766705513,
-0.084206722676754,
0.016116011887788773,
0.013266360387206078,
0.038227446377277374,
-0.020984528586268425,
0.049401722848415375,
-0.05108070373535156,
0.02125440537929535,
0.024009130895137787,
0.03227078914642334,
-0.024945784360170364,
0.0840788185596466,
0.06658212840557098,
-0.024857396259903908,
0.0470159575343132,
0.005425129551440477,
0.015244568698108196,
0.004676575772464275,
-0.02462867647409439,
0.03585101664066315,
-0.04608349874615669,
-0.03382899612188339,
-0.035829007625579834,
0.03411203995347023,
-0.0315057635307312,
-0.039366886019706726,
-0.08268077671527863,
-0.04447556287050247,
-0.013061746023595333,
0.027590062469244003,
0.03125792741775513,
0.011492584832012653,
0.017492549493908882,
-0.01731872744858265,
-0.0013926217798143625,
0.002244125120341778,
-0.02885648049414158,
0.04352976754307747,
0.021632257848978043,
0.0105691934004426,
0.028383592143654823,
-0.04033192992210388,
0.0285001490265131,
-0.014199146069586277,
0.002514762571081519,
-0.0007734400569461286,
0.04510758817195892,
-0.011132471263408661,
0.005000850185751915,
-0.013185949996113777,
0.05877699702978134,
0.019639072939753532,
-0.018448542803525925,
-0.017888780683279037,
0.005557154770940542,
-0.01545696146786213,
0.008226566016674042,
-0.01312014739960432,
0.02230427972972393,
0.004367217421531677,
0.02749534696340561,
0.02391834929585457,
0.010319174267351627,
-0.004954000934958458,
0.011764523573219776,
0.009209987707436085,
0.09355398267507553,
0.044277891516685486,
-0.021716283634305,
0.019261503592133522,
0.025801843032240868,
-0.0029796345625072718,
0.00024648563703522086,
0.015560065396130085,
-0.023411618545651436,
-0.03129302337765694,
-0.017293913289904594,
0.0114336172118783,
-0.0020148586481809616,
-0.058061081916093826,
0.04051103815436363,
0.030534688383340836,
0.02465912140905857,
0.014602361246943474,
0.033618539571762085,
-0.06549301743507385,
-0.011075888760387897,
0.036193348467350006,
0.03843028098344803,
-0.0020369719713926315,
0.022258814424276352,
0.023364370688796043,
0.005669071804732084,
0.011020820587873459,
0.009269182570278645,
0.024550780653953552,
0.0026962142437696457,
-0.006644163280725479,
-0.022390859201550484,
-0.006346415262669325,
-0.008673050440847874,
0.06105361878871918,
-0.03699115663766861,
0.02105199731886387,
0.007577250711619854,
-0.012629161588847637,
0.008744042366743088,
-0.026180844753980637,
-0.015766365453600883,
-0.03060823120176792,
-0.01783115416765213,
-0.000316218618536368,
-0.003987596835941076,
0.022713124752044678,
-0.0637814998626709,
0.04328577220439911,
-0.021116428077220917,
0.006840462330728769,
-0.042629875242710114,
-0.0334419310092926,
0.01255523320287466,
0.023886017501354218,
0.047173500061035156,
-0.05368586257100105,
-0.04168093577027321,
-0.014969670213758945,
-0.037758246064186096,
-0.01997188851237297,
-0.009443435817956924,
-0.02405506744980812,
0.014799252152442932,
-0.04748348891735077,
-0.03243253007531166,
0.05388132482767105,
-0.0017284337664023042,
-0.005914236884564161,
0.02179037034511566,
-0.007175210863351822,
-0.05462691932916641,
0.002446400001645088,
-0.014009334146976471,
0.0043766493909060955,
-0.03094988502562046,
0.015519460663199425,
0.027893906459212303,
-0.02791225165128708,
-0.06512961536645889,
-0.005891794804483652,
-0.05207354202866554,
-0.05640594661235809,
-0.005127338692545891,
-0.003482704283669591,
-0.013512058183550835,
-0.03075605072081089,
0.0042748646810650826,
0.010692053474485874,
-0.05664879083633423,
0.01869094930589199,
-0.048386506736278534,
0.010645407252013683,
0.028014609590172768,
-0.000921596132684499,
0.04231351986527443,
-0.01189903263002634,
-0.03838886693120003,
0.039126522839069366,
0.0575704351067543,
-0.02582104690372944,
-0.04310731217265129,
-0.020382819697260857,
-0.010189108550548553,
-0.02839621528983116,
0.003509249771013856,
0.03525102883577347,
-0.013350890949368477,
-0.005981407593935728,
0.017658434808254242,
0.03319746255874634,
0.005691102240234613,
0.028402740135788918,
-0.0072832247242331505,
-0.00017819767526816577,
0.03430159017443657,
-0.006403428502380848,
0.06701670587062836,
0.05216430500149727,
-0.02694017067551613,
0.036010149866342545,
-0.027118487283587456,
0.02272983081638813,
0.00247805193066597,
-0.03304513543844223,
0.05623693764209747,
0.039998311549425125,
0.007936484180390835,
-0.006327423732727766,
0.023151518777012825,
0.02778366208076477,
-0.014893670566380024,
0.0036834299098700285,
0.01727760024368763,
0.026770303025841713,
-0.004329158458858728,
-0.015570440329611301,
-0.015033530071377754,
0.05758748948574066,
-0.004553924314677715,
-0.01867225207388401,
0.021710192784667015,
-0.004684837535023689,
-0.010846942663192749,
0.006083982065320015,
-0.01865137182176113,
0.053206492215394974,
0.0339743010699749,
0.011509346775710583,
-0.014360511675477028,
-0.0016890682745724916,
0.013703732751309872,
-0.05749087408185005,
0.03422858193516731,
-0.037506647408008575,
0.05462511256337166,
0.03903402388095856,
0.06880955398082733,
0.017266996204853058,
0.024402856826782227,
0.019413845613598824,
-0.013237078674137592,
-0.11777715384960175,
0.009949463419616222,
-0.02275743894279003,
-0.01481822319328785,
-0.004671571310609579,
-0.017842596396803856,
-0.07438942790031433,
-0.032130151987075806,
0.002300117863342166,
-0.011213377118110657,
0.00037211610469967127,
-0.019882353022694588,
-0.002678515622392297,
-0.05601130425930023,
-0.05593407154083252,
0.000590883253607899,
-0.013593821786344051,
0.005282336380332708,
-0.050171807408332825,
-0.006733723450452089,
0.01176571287214756,
-0.022144420072436333,
0.0028865106869488955,
-0.012363388203084469,
0.00843044277280569,
-0.01351104024797678,
0.023782584816217422,
0.014440152794122696,
0.015599025413393974,
-0.005648894235491753,
0.012754274532198906,
0.02515486627817154,
0.021983763203024864,
-0.009677626192569733,
-0.05651791766285896,
-0.06167826056480408,
-0.009167271666228771,
0.009830912575125694,
0.009847011417150497,
0.04274234548211098,
-0.005266432650387287,
0.02448783628642559,
0.01837397739291191,
-0.028261180967092514,
0.022986482828855515,
0.03706701099872589,
0.020861083641648293,
-0.025732990354299545,
-0.0035648748744279146,
-0.0401727557182312,
-0.006424912251532078,
-0.0017547269817441702,
-0.0038331132382154465,
0.010866533033549786,
0.007218960672616959,
-0.007981741800904274,
-0.014528190717101097,
-0.010296624153852463,
0.033199913799762726,
-0.03329792991280556,
-0.001040418166667223,
0.012230828404426575,
-0.0032670528162270784,
-0.03841492533683777,
0.017172813415527344,
-0.00751203577965498,
0.01881536655128002,
0.02365841716527939,
-0.010165990330278873,
-0.0022083919029682875,
-0.07479840517044067,
-0.017043346539139748,
0.023152178153395653,
0.060793325304985046,
-0.02670702524483204,
-0.008355852216482162,
-0.03208266943693161,
-0.018107738345861435,
0.02314431592822075,
-0.029858233407139778,
0.03017100691795349,
-0.016823606565594673,
0.0008262652554549277,
0.00992149580270052,
-0.026152562350034714,
-0.004308005329221487,
0.03398237004876137,
0.011030744761228561,
-0.0020561018027365208,
-0.006203767843544483,
-0.014454919844865799,
0.017894890159368515,
0.04755878821015358,
0.04231986775994301,
0.028756801038980484,
-0.04883889853954315,
-0.028693124651908875,
0.0006070715608075261,
-0.0014874397311359644,
-0.008743922226130962,
-0.10037247091531754,
-0.027588045224547386,
0.03379695862531662,
-0.025742456316947937,
0.036294810473918915,
-0.04659326374530792,
-0.043807435780763626,
0.031742583960294724,
0.018928006291389465,
-0.03132098913192749,
-0.014994797296822071,
-0.028960518538951874,
-0.01618102565407753,
0.03914453461766243,
-0.00013555878831539303,
0.02700452320277691,
0.07764171063899994,
-0.05570461228489876,
-0.004735778085887432,
-0.028259487822651863,
0.05386057123541832,
-0.0328955352306366,
-0.028478218242526054,
-0.016755614429712296,
0.010903490707278252,
-0.028566665947437286,
0.07609742134809494,
0.00868310034275055,
-0.010961497202515602,
0.017101885750889778,
-0.012792919762432575,
0.010567638091742992,
0.03415507450699806,
-0.008714827708899975,
-0.0008273590356111526,
-0.028947096318006516,
0.04885951429605484,
-0.0020410949364304543,
-0.01682625338435173,
0.002206523437052965,
0.025215940549969673,
0.02740645781159401,
0.0246327742934227,
0.003489959752187133,
0.015816286206245422,
-0.024758553132414818,
0.015667293220758438,
-0.0076661924831569195,
-0.013864420354366302,
0.07198230177164078,
0.017164740711450577,
0.0021084791515022516,
0.005023491568863392,
-0.058764152228832245,
-0.030919257551431656,
-0.005935775116086006,
-0.022984836250543594,
0.02051958255469799,
-0.06049427017569542,
0.03599546477198601,
-0.008262823335826397,
0.028838569298386574,
-0.03842969611287117,
-0.029863711446523666,
-0.023743849247694016,
0.01856754720211029,
0.02165505662560463,
-0.024520210921764374,
0.0060112918727099895,
-0.053522948175668716,
-0.03898877277970314,
0.00953579880297184,
0.051830727607011795,
-0.02939743921160698,
-0.015326564200222492,
0.0017710146494209766,
-0.02425185590982437,
0.034054335206747055,
-0.004431318026036024,
-0.047958359122276306,
-0.007419028785079718,
0.020947931334376335,
0.008253933861851692,
-0.03555193170905113,
0.06540937721729279,
-0.034520700573921204,
-0.06007101386785507,
-0.002306652255356312,
-0.017305215820670128,
0.022378241643309593,
-0.016163615509867668,
0.028425810858607292,
0.0666457936167717,
0.017163842916488647,
-0.012874777428805828,
-0.014675483107566833,
0.02563801407814026,
-0.008110622875392437,
0.02847343496978283,
0.017707062885165215,
-0.007094905711710453,
-0.04762799292802811,
-0.04026710242033005,
0.0421949103474617,
-0.007588115520775318,
0.024822337552905083,
0.00007294675742741674,
0.033315662294626236,
0.013281315565109253,
0.008639509789645672,
0.025939524173736572,
0.009368082508444786,
-0.0022111120633780956,
-0.04872460663318634,
-0.003240958321839571,
0.0030682715587317944,
-0.010201280005276203,
-0.009515324607491493,
-0.02796577848494053,
-0.02431316114962101,
-0.021527066826820374,
0.07897083461284637,
-0.014141054823994637,
0.026348212733864784,
-0.00231567001901567,
-0.024238694459199905,
0.01307291816920042,
-0.045010775327682495,
0.010296632535755634,
-0.007469198200851679,
0.019201619550585747,
-0.005403459072113037,
-0.012416031211614609,
-0.00661011878401041,
0.050613660365343094,
0.019837619736790657,
0.006565105635672808,
-0.018758226186037064,
0.04213428124785423,
0.021224023774266243,
0.006145097780972719,
-0.04769023880362511,
-0.016270481050014496,
0.020564740523695946,
-0.0573689229786396,
0.016293993219733238,
0.03049848973751068,
0.013670033775269985,
0.03367322310805321,
-0.0013847713125869632,
-0.03375740721821785,
-0.018987778574228287,
0.004303961060941219,
-0.04176381602883339,
0.009817489422857761,
-0.006519806571304798,
0.014242153614759445,
0.0014623007737100124,
-0.007417698856443167,
0.021761879324913025,
0.007965045981109142,
-0.004193258937448263,
-0.03147321566939354,
-0.06597485393285751,
-0.061708349734544754,
-0.032349586486816406,
-0.041739944368600845,
0.05586004629731178,
0.008698712103068829,
-0.016675718128681183,
0.017523977905511856,
-0.04104302078485489,
0.015539240092039108,
0.024357866495847702,
0.04623032361268997,
0.005437346640974283,
0.04939741641283035,
-0.028537699952721596,
-0.011825387366116047,
-0.028888117522001266,
0.027107464149594307,
0.11611423641443253,
0.045139130204916,
0.05312217026948929,
-0.03950042650103569,
-0.011262485757470131,
-0.04480898007750511,
0.026060760021209717,
-0.029622217640280724,
0.014223892241716385,
-0.051312897354364395,
0.022626029327511787,
-0.001927457982674241,
0.0376908965408802,
-0.018565833568572998,
0.0038747640792280436,
0.02352730557322502,
-0.023142382502555847,
-0.031161310151219368,
0.04203874617815018,
0.0017578251427039504,
0.009726298041641712,
0.041792452335357666,
-0.019498879089951515,
0.00270937941968441,
-0.029362088069319725,
-0.015116031281650066,
-0.015958521515130997,
-0.03892255201935768,
0.042870886623859406,
-0.02038385346531868,
-0.012885509058833122,
-0.02184530533850193,
0.0009114203276112676,
-0.030955327674746513,
-0.03771381452679634,
0.026253454387187958,
0.03372972458600998,
-0.018177691847085953,
-0.0025548662524670362,
-0.022825276479125023,
0.0016459018224850297,
0.041799865663051605,
-0.0012862703297287226,
0.011345871724188328,
-0.0454217903316021,
0.0406242199242115,
-0.019037118181586266,
0.02504109777510166,
0.00921600591391325,
0.02628793567419052,
-0.004526757635176182,
0.008905328810214996,
0.0026465198025107384,
-0.08641020208597183,
-0.030758393928408623,
0.02696407586336136,
0.06185033544898033,
0.0330948643386364,
-0.036166347563266754,
-0.01914065331220627,
0.013687015511095524,
0.014449347741901875,
0.02043343149125576,
-0.011401711963117123,
0.014734597876667976,
-0.002642321400344372,
-0.011952613480389118,
0.029019799083471298,
-0.0022040014155209064,
-0.033694423735141754,
-0.017632892355322838,
0.015769222751259804,
-0.06431572884321213,
-0.04146303981542587,
0.02631409838795662,
0.05475470423698425,
-0.014977294020354748,
0.018049398437142372,
0.025423429906368256,
-0.06296584755182266,
-0.08484037220478058,
0.03570760041475296,
-0.008937587030231953,
-0.03235693275928497,
0.01789206452667713,
-0.015083995647728443,
0.039829183369874954,
0.0334491953253746,
0.001648736302740872,
-0.014279637485742569,
-0.019849400967359543,
0.03515331447124481,
0.03958188369870186,
-0.004730540327727795,
-0.04651307687163353,
0.012639740481972694,
0.00528893806040287,
0.0064163957722485065,
-0.03361092135310173,
0.017310339957475662,
0.009765646420419216,
-0.04012644663453102,
-0.000022753420125809498,
0.00788827333599329,
-0.051673922687768936,
0.008044114336371422,
0.003364239353686571,
-0.00017546671733725816,
-0.023160401731729507,
0.027025088667869568,
0.026456745341420174,
-0.019013715907931328,
-0.04251039773225784,
-0.017836255952715874,
-0.003667711978778243,
0.0190935879945755,
-0.0046830084174871445,
-0.019279802218079567,
0.021039430052042007,
-0.022668933495879173,
0.055087246000766754,
-0.04006199166178703,
0.0016893722349777818,
-0.008737558498978615,
0.013919239863753319,
-0.021615101024508476,
-0.02407546155154705,
-0.014217681251466274,
0.03625308349728584,
-0.032528262585401535,
-0.003942625597119331,
0.04060909152030945,
0.024704063311219215,
-0.007029521279036999,
-0.004625044297426939,
0.03168803080916405,
-0.014949049800634384,
0.04454312101006508,
0.004050350748002529,
-0.014780093915760517,
0.027584299445152283,
-0.011638672091066837,
-0.036092836409807205,
0.0525427907705307,
-0.05862519517540932,
0.02679191343486309,
0.029964473098516464,
-0.005328560248017311,
-0.006882609333842993,
0.06949172914028168,
-0.006086644250899553,
-0.01736624538898468,
-0.015991179272532463,
-0.0440538227558136,
0.022202301770448685,
0.013063053600490093,
0.006055544596165419,
-0.029048636555671692,
-0.021574022248387337,
0.047497715801000595,
0.005151804070919752,
0.0028517418541014194,
0.014032737351953983,
0.010693810880184174,
0.006050157826393843,
-0.0006843835581094027,
0.008259745314717293,
-0.010477696545422077,
0.01781275123357773,
0.00803929939866066,
0.0066912537440657616,
0.020008930936455727,
0.033072974532842636,
-0.03194224834442139,
-0.11051088571548462,
0.018379544839262962,
-0.019467687234282494,
0.012482122518122196,
0.029162371531128883,
-0.03492599353194237,
0.04055396467447281,
0.025355959311127663,
-0.07867279648780823,
0.05031895264983177,
-0.03378860279917717,
-0.02462105266749859,
-0.03224338963627815,
0.03426409512758255,
0.017259541898965836,
0.019367650151252747,
-0.011002641171216965,
0.07255908101797104,
-0.014437282457947731,
0.031188536435365677,
0.004632717929780483,
-0.04444675147533417,
0.04115208983421326,
0.03508180379867554,
-0.015916423872113228,
0.04973151907324791,
0.06156979873776436,
-0.03655301034450531,
0.0049996646121144295,
0.03673648089170456,
0.047518305480480194,
0.0473768375813961,
-0.029093412682414055,
0.008884869515895844,
-0.01263922918587923,
0.04485683515667915,
0.008050915785133839,
0.00890728272497654,
-0.025645429268479347,
0.023208536207675934,
-0.00012650535791181028,
0.019187139347195625,
-0.0039458563551306725,
0.027463411912322044,
0.049817174673080444,
-0.041544653475284576,
0.023894865065813065,
0.02873326651751995,
-0.014517842791974545,
0.013591640628874302,
0.03629517927765846,
-0.00046520770411007106,
0.0009753810591064394,
-0.01747848093509674,
0.005504357162863016,
-0.10316933691501617,
-0.005322839133441448,
-0.005719700362533331,
-0.017883138731122017,
0.007655077613890171,
-0.012735947035253048,
0.037123262882232666,
-0.010993445292115211,
0.008992772549390793,
-0.030126472935080528,
0.0069764344953000546,
-0.04591207578778267,
0.011123268865048885,
0.016803711652755737,
-0.0010939675848931074,
0.02156396582722664,
-0.04292590171098709,
-0.03820078447461128,
0.045458171516656876,
-0.02058846689760685,
0.028475619852542877,
0.03551790863275528,
-0.01559725496917963,
-0.007946196012198925,
-0.06678694486618042,
0.013391724787652493,
0.03066299669444561,
0.02888713963329792,
-0.0889965295791626,
-0.03388521075248718,
0.027452221140265465,
0.027970530092716217,
0.034335460513830185,
-0.010359352454543114,
-0.00386839103884995,
0.026324288919568062,
-0.03750184550881386,
-0.01168648898601532,
-0.053146328777074814,
-0.005010093096643686,
0.005556443240493536,
-0.02792748250067234,
-0.04320653900504112,
0.02338579297065735,
-0.06021223962306976,
0.016912302002310753,
0.044933099299669266,
0.023974988609552383,
0.005592250265181065,
-0.02159959077835083,
-0.03776393085718155,
0.04866830259561539,
0.016614507883787155,
0.00027510421932674944,
0.042425259947776794,
0.017177021130919456,
0.03531651571393013,
0.00221495539881289,
-0.0236488189548254,
-0.010092124342918396,
0.049179334193468094,
-0.011453665792942047,
-0.011159601621329784,
0.0003468042123131454,
-0.0020999303087592125,
0.04042086750268936,
-0.04822897911071777,
0.002968091983348131,
0.04029861465096474,
-0.00872102752327919,
-0.002311856020241976,
0.041440144181251526,
0.016632890328764915,
0.034264810383319855,
0.016719283536076546,
0.05096593499183655,
0.015000669285655022,
-0.03921860083937645,
-0.052270229905843735,
0.0011140038259327412,
-0.00924514140933752,
0.0004727115447167307,
0.018860474228858948,
0.01669294387102127,
0.028126051649451256,
-0.00801769271492958,
0.021306732669472694,
0.03242834657430649,
-0.028609182685613632,
-0.022532993927598,
0.006294735707342625,
0.03453528508543968,
0.01436016708612442,
0.039563391357660294,
-0.00795632041990757,
0.07392860949039459,
-0.03516647219657898,
0.021794185042381287,
-0.03194607049226761,
0.014566022902727127,
-0.005142987705767155,
0.013259433209896088,
-0.041635531932115555,
0.03498924896121025,
0.01588228903710842,
-0.031941596418619156,
-0.031842976808547974,
-0.02143596112728119,
0.03448319062590599,
-0.04019027203321457,
0.03258723393082619,
0.016511186957359314,
-0.02048969455063343,
0.0015228284755721688,
-0.026840923354029655,
-0.007891291752457619,
-0.02822919189929962,
-0.005086772609502077,
0.02858695015311241,
0.00028368024504743516,
-0.01870165392756462,
0.005448292009532452,
-0.020484499633312225,
0.04542454704642296,
-0.030897848308086395,
0.004293575417250395,
0.0029699960723519325,
-0.008968065492808819,
-0.019517548382282257,
-0.006433481350541115
] |
<p>I'm reading that general relativity let's us describe physics from the point of view of both inertial and accelerated observers. What does that actually mean in terms of doing actual physics? For example, say a physicist performed Millikan's oil drop experiment or Young's double slit experiment or decomposed white light with a prism:
(1) in deep space, far from any gravitational field,
(2) on Earth,
(3) near a black hole.
I'm assuming she would get different results, and I'm assuming that in some way this is near the heart of what's important regarding GTR, but how exactly? In other words, what are the implications of GTR for understanding these experiments?</p>
<p>Thank you</p> | 1,578 | [
0.02146768383681774,
-0.04751846566796303,
0.011847302317619324,
-0.03260859102010727,
0.029055971652269363,
0.021861203014850616,
-0.02371104434132576,
-0.029091810807585716,
-0.036889612674713135,
0.017992602661252022,
0.015524814836680889,
0.008711491711437702,
0.012735866010189056,
-0.018691012635827065,
0.014915206469595432,
-0.003785352688282728,
-0.030929436907172203,
0.0005258852615952492,
0.00908022839576006,
-0.0341503731906414,
0.0065719932317733765,
0.019371215254068375,
0.009012984111905098,
-0.001118341344408691,
-0.017989592626690865,
-0.0005318847252056003,
0.024945128709077835,
-0.013200253248214722,
0.034754492342472076,
0.01939077489078045,
0.009143823757767677,
0.015670008957386017,
-0.05791280418634415,
0.035036616027355194,
0.006655177567154169,
0.0027814069762825966,
-0.03824152424931526,
0.003500342834740877,
0.006936861667782068,
0.006915682461112738,
-0.058888014405965805,
-0.014454874210059643,
-0.016109269112348557,
0.04597293585538864,
-0.05130539834499359,
-0.002251294907182455,
-0.01515444926917553,
-0.006631532218307257,
0.038321174681186676,
-0.04665406793355942,
0.038881223648786545,
0.027138493955135345,
0.004117809701710939,
0.01591658964753151,
-0.0019357794662937522,
0.039285775274038315,
0.10490381717681885,
0.05991177633404732,
-0.037955354899168015,
-0.0354221947491169,
-0.020601043477654457,
-0.02447379007935524,
-0.03171413764357567,
-0.005477822385728359,
0.018171364441514015,
-0.010146054439246655,
-0.009115788154304028,
-0.013699201866984367,
-0.0051955608651041985,
0.011970825493335724,
0.013107440434396267,
0.03735439479351044,
0.003139202017337084,
0.018789716064929962,
-0.00011661013559205458,
-0.026110289618372917,
0.010298553854227066,
-0.008156877011060715,
0.04905946925282478,
0.0073512340895831585,
-0.03675425425171852,
-0.01575833559036255,
0.010504130274057388,
0.03336457535624504,
-0.008456063456833363,
-0.01573087088763714,
0.0912122055888176,
0.005341183859854937,
-0.000323175685480237,
0.02260393276810646,
-0.03943925350904465,
-0.0002975751121994108,
0.003525107866153121,
0.004088796209543943,
-0.04927027225494385,
0.00391756184399128,
-0.01602264493703842,
0.0459839403629303,
-0.01523469015955925,
0.009029261767864227,
0.02115829475224018,
-0.0027960604056715965,
0.015191290527582169,
0.07080996036529541,
0.0036379164084792137,
0.0039937677793204784,
-0.004595896229147911,
0.033129677176475525,
-0.024456636980175972,
-0.03612952306866646,
-0.02476092241704464,
0.023977985605597496,
-0.007449747063219547,
-0.000004855191946262494,
0.027390722185373306,
-0.02896878309547901,
-0.0019864297937601805,
-0.01792221888899803,
0.06777963042259216,
0.08049819618463516,
0.0738505870103836,
-0.03180639445781708,
0.014981442131102085,
-0.001186011591926217,
-0.07233861088752747,
0.002439243718981743,
0.018354138359427452,
-0.04499446973204613,
-0.0007333067478612065,
0.012908315286040306,
0.02456408366560936,
0.007169986143708229,
-0.010053815320134163,
0.025059502571821213,
0.009079992771148682,
-0.02887263149023056,
-0.1133846566081047,
-0.054527681320905685,
0.037924788892269135,
0.030895601958036423,
-0.011086767539381981,
-0.07327759265899658,
-0.010406921617686749,
0.033814311027526855,
0.07781615108251572,
0.006768934428691864,
0.03920329734683037,
0.006840276997536421,
0.021119844168424606,
-0.04102342948317528,
-0.056831423193216324,
0.013135906308889389,
-0.017681878060102463,
-0.03502322733402252,
-0.004856104496866465,
-0.10271557420492172,
0.0029994980432093143,
0.028737641870975494,
-0.015530330128967762,
-0.053029678761959076,
0.06894449889659882,
-0.03337864950299263,
0.01068456657230854,
0.030208926647901535,
-0.0070420741103589535,
0.011069574393332005,
0.08552104979753494,
0.01965976133942604,
-0.013253912329673767,
0.027104832231998444,
0.040590304881334305,
0.04993908107280731,
0.028857868164777756,
0.029226824641227722,
0.013492578640580177,
-0.024288391694426537,
0.018041159957647324,
0.0236581452190876,
0.0017444025725126266,
-0.027725810185074806,
-0.01552813220769167,
-0.03548552468419075,
0.009131189435720444,
-0.030153870582580566,
-0.012906866148114204,
0.025326356291770935,
-0.000014382445442606695,
0.017976634204387665,
-0.02117294818162918,
-0.04007425904273987,
0.0002787023549899459,
-0.059356432408094406,
0.005147148389369249,
-0.00042388838483020663,
0.02271273545920849,
0.02625965140759945,
0.016568658873438835,
0.028722036629915237,
-0.020606432110071182,
-0.021128486841917038,
-0.007328736130148172,
0.03675975650548935,
-0.025271892547607422,
-0.007385853677988052,
-0.016648834571242332,
0.03186982497572899,
0.009165586903691292,
-0.00892630685120821,
-0.010466041043400764,
0.018648626282811165,
-0.00846487283706665,
0.021576927974820137,
-0.017546415328979492,
0.01320512406527996,
0.016789857298135757,
-0.008085554465651512,
0.00304537289775908,
0.021749170497059822,
-0.014518268406391144,
0.052838873118162155,
-0.031245579943060875,
0.07666454464197159,
0.013200823217630386,
-0.007535426877439022,
-0.026036923751235008,
0.044956617057323456,
0.012011470273137093,
-0.022423291578888893,
0.010600409470498562,
-0.002855278318747878,
-0.0387754812836647,
-0.038163356482982635,
0.027299080044031143,
0.01111869141459465,
-0.03528985753655434,
0.03139948844909668,
0.03837788477540016,
0.051117658615112305,
0.027766317129135132,
0.04438966140151024,
-0.006208215840160847,
-0.04090739041566849,
0.02052314765751362,
0.0032413837034255266,
0.016564132645726204,
0.029682910069823265,
0.036387719213962555,
0.034473493695259094,
0.009090309962630272,
0.003484908025711775,
-0.0024539604783058167,
0.04291289672255516,
-0.016625607386231422,
0.0189866553992033,
0.014004740864038467,
0.0026738804299384356,
0.023111840710043907,
-0.027489926666021347,
0.00871616043150425,
0.024170486256480217,
-0.006016225554049015,
-0.008496842347085476,
-0.036165300756692886,
0.02366785518825054,
0.025230364874005318,
0.0029293023981153965,
-0.037212811410427094,
-0.044633492827415466,
0.029138965532183647,
-0.08436134457588196,
0.03625490888953209,
-0.021000105887651443,
-0.01949065737426281,
-0.06824754178524017,
0.001181605621241033,
0.003063864540308714,
0.02298995666205883,
0.020459212362766266,
-0.02407943643629551,
-0.0667094737291336,
0.0009417845867574215,
-0.03679802268743515,
0.01187214907258749,
0.022868186235427856,
-0.04025775566697121,
0.061270397156476974,
-0.05507593974471092,
-0.03420274332165718,
0.02951826900243759,
-0.03428101912140846,
0.03889714926481247,
0.021184397861361504,
-0.01792174018919468,
-0.04090137034654617,
-0.00394942332059145,
-0.034771185368299484,
-0.004266025498509407,
-0.026991739869117737,
-0.008504052646458149,
0.08260995149612427,
-0.008935325779020786,
0.002323631662875414,
-0.022374870255589485,
-0.013772904872894287,
-0.048142917454242706,
0.008832046762108803,
0.011079232208430767,
-0.009220977313816547,
-0.002601486863568425,
0.019246885553002357,
0.035643789917230606,
-0.058352112770080566,
-0.033127255737781525,
-0.02852087840437889,
-0.0677134320139885,
0.038474731147289276,
0.028944918885827065,
0.016592398285865784,
0.004314131569117308,
-0.010347606614232063,
0.06519436091184616,
0.019465211778879166,
-0.02640051208436489,
-0.04340004920959473,
0.0012593239080160856,
0.00840274803340435,
0.0023859788198024035,
0.014088671654462814,
0.01872350089251995,
-0.007584353443235159,
0.03244081512093544,
0.02505229040980339,
0.02606074884533882,
0.03960537537932396,
0.04374375939369202,
0.0001437799510313198,
-0.010298839770257473,
0.02587258256971836,
0.023045502603054047,
-0.009547458961606026,
0.0243771281093359,
-0.07841324806213379,
0.01035781018435955,
-0.012869575060904026,
0.023413293063640594,
0.016309164464473724,
-0.03365929052233696,
0.05834318697452545,
0.015880467370152473,
0.0031733515206724405,
-0.0019392777467146516,
0.009146242402493954,
-0.021524576470255852,
-0.0030162245966494083,
0.02871415764093399,
0.0003691734455060214,
0.05455225333571434,
-0.012677265331149101,
0.007166313473135233,
0.025900250300765038,
0.037392862141132355,
-0.035977426916360855,
-0.015325112268328667,
0.00007877282041590661,
-0.03321920335292816,
0.05915819853544235,
-0.0014818425988778472,
0.010128614492714405,
0.04581374675035477,
-0.0065512084402143955,
-0.014179066754877567,
0.0037640745285898447,
-0.02145019732415676,
-0.026480715721845627,
-0.0594114325940609,
0.0181720107793808,
0.002246926072984934,
0.007678896654397249,
0.009790503419935703,
0.008777941577136517,
0.03603384643793106,
0.008683566004037857,
-0.0068578473292291164,
-0.007949710823595524,
-0.07515113055706024,
0.03552424535155296,
-0.04375166818499565,
-0.02203177846968174,
-0.011454134248197079,
-0.0016053240979090333,
0.031064629554748535,
-0.02367391809821129,
-0.022608352825045586,
-0.016189927235245705,
0.007278569508343935,
-0.06533730775117874,
0.014509618282318115,
-0.014923826791346073,
-0.04717588797211647,
-0.03425949811935425,
0.03808049112558365,
0.03946084529161453,
0.02123090624809265,
0.0035073808394372463,
0.036516278982162476,
-0.01715966872870922,
-0.017096932977437973,
-0.0013948631240054965,
-0.012533684261143208,
-0.00018024432938545942,
0.04637693241238594,
0.05035410448908806,
0.004599618725478649,
-0.016322966665029526,
0.06772158294916153,
0.05138814449310303,
0.06821875274181366,
-0.023274347186088562,
-0.038646649569272995,
-0.0319756455719471,
-0.041835587471723557,
-0.027250736951828003,
-0.0041715167462825775,
0.040937408804893494,
-0.010539070703089237,
-0.014468720182776451,
0.02722018212080002,
0.010979852639138699,
0.011933701112866402,
0.02632034569978714,
0.030497586354613304,
-0.026784492656588554,
-0.022684387862682343,
-0.07450772076845169,
-0.02451295778155327,
-0.01003155019134283,
0.003290308639407158,
0.04048480838537216,
0.01136777549982071,
-0.023300793021917343,
-0.0003235641634091735,
-0.003970206715166569,
0.013921884819865227,
-0.03606195002794266,
-0.01105521246790886,
0.0040052421391010284,
0.023801999166607857,
0.02050918899476528,
0.015923388302326202,
-0.02868754230439663,
0.05784691125154495,
0.058742307126522064,
0.015605495311319828,
-0.004075514152646065,
-0.03606770560145378,
0.003862483659759164,
0.011276639997959137,
0.022475654259324074,
0.0059287589974701405,
-0.009005695581436157,
-0.042031530290842056,
-0.0184880793094635,
0.06326520442962646,
-0.02477237768471241,
0.026812491938471794,
-0.004942778963595629,
-0.015040435828268528,
-0.032758332788944244,
0.007953771390020847,
-0.006017234176397324,
0.011685405857861042,
-0.04909222945570946,
-0.023049702867865562,
-0.033738646656274796,
0.00024018950352910906,
-0.004286144860088825,
0.000609146780334413,
0.005473198369145393,
0.03906303644180298,
0.04242551699280739,
0.0446292981505394,
0.019269727170467377,
0.031149502843618393,
-0.02267586626112461,
-0.06334961205720901,
0.02899686060845852,
0.02147347293794155,
-0.01916818507015705,
0.07270359992980957,
-0.015789465978741646,
-0.0470636710524559,
0.04752487689256668,
0.011233271099627018,
0.0020661510061472654,
-0.017624177038669586,
-0.044851358979940414,
-0.006821247283369303,
0.003518447047099471,
-0.026839271187782288,
0.02691434696316719,
-0.02738877758383751,
-0.004592609591782093,
0.006207609549164772,
-0.002358880126848817,
0.03715842217206955,
-0.04514102265238762,
0.0119453901425004,
0.002576525555923581,
-0.024281801655888557,
0.003067250130698085,
0.05709291994571686,
-0.005846464075148106,
0.014807465486228466,
0.004473810084164143,
-0.06459098309278488,
-0.0004210250044707209,
0.030200697481632233,
0.013098596595227718,
-0.017950711771845818,
-0.0366351455450058,
0.004214633721858263,
-0.0004391841939650476,
-0.04849971458315849,
0.0045742760412395,
0.012104571796953678,
0.006331514101475477,
0.0555318146944046,
0.004719413351267576,
0.04786728695034981,
-0.025130141526460648,
0.02586347796022892,
0.030588867142796516,
-0.030390581116080284,
0.05114155262708664,
-0.020089799538254738,
0.021389057859778404,
0.026360517367720604,
-0.03990551456809044,
-0.051487457007169724,
0.005886326543986797,
-0.0075626131147146225,
0.06408130377531052,
-0.0680396556854248,
0.01281705778092146,
0.01556850504130125,
0.02663373202085495,
-0.0833510309457779,
-0.04554862156510353,
0.033856820315122604,
0.019774308428168297,
0.0032207744661718607,
-0.01759910397231579,
0.03186492249369621,
-0.04752905294299126,
-0.01838432252407074,
0.0077581387013196945,
0.03185475617647171,
-0.03821305185556412,
-0.025616100057959557,
-0.009964517317712307,
0.01228838786482811,
0.04823597893118858,
-0.0335577167570591,
-0.006314755417406559,
0.0005973453517071903,
-0.0018951671663671732,
0.006874739658087492,
0.004082954954355955,
0.03729124739766121,
-0.02200891263782978,
-0.004348850343376398,
-0.049027130007743835,
0.013583811931312084,
-0.025657497346401215,
-0.005503104534000158,
0.04454987123608589,
0.03018854185938835,
-0.009875600226223469,
0.003946763463318348,
-0.02135692909359932,
0.0048399437218904495,
0.00004475576133700088,
0.004894600249826908,
-0.009082703851163387,
-0.002054402604699135,
0.021873105317354202,
-0.02971874549984932,
0.04535350948572159,
0.010500207543373108,
0.009706594049930573,
0.0208846814930439,
0.04861864820122719,
-0.007224019151180983,
0.004970085807144642,
-0.01361743826419115,
-0.012704843655228615,
0.010026796720921993,
-0.03372123837471008,
0.04838123545050621,
0.023592449724674225,
-0.0007044475059956312,
-0.011146779172122478,
-0.025967497378587723,
-0.030956216156482697,
-0.012480707839131355,
0.07477539777755737,
0.0013896137243136764,
0.05673007667064667,
0.021781018003821373,
-0.007249129936099052,
-0.025523073971271515,
-0.032305292785167694,
0.020695000886917114,
0.02052180841565132,
-0.012241356074810028,
0.014336323365569115,
-0.005854705348610878,
-0.04792429879307747,
0.009112261235713959,
0.05518021062016487,
-0.024069959297776222,
0.027816971763968468,
0.01702558808028698,
0.06927219778299332,
0.002968908753246069,
-0.012156970798969269,
-0.05077854543924332,
0.06287720054388046,
-0.02866089902818203,
0.03203233331441879,
-0.010884342715144157,
0.0036257861647754908,
0.03945630416274071,
0.03590875864028931,
0.007689737249165773,
-0.024526527151465416,
-0.015438036061823368,
-0.08582358062267303,
0.0044650062918663025,
0.02503017522394657,
-0.0016185095300897956,
-0.0354195311665535,
-0.007242653984576464,
0.0406942181289196,
0.008724919520318508,
0.03340912610292435,
0.016871487721800804,
-0.0788322165608406,
-0.024617115035653114,
-0.048201803117990494,
-0.024524834007024765,
0.04999115690588951,
0.00818906631320715,
-0.015963174402713776,
-0.004712244495749474,
-0.016784654930233955,
0.004948965739458799,
0.029570385813713074,
0.07557092607021332,
-0.03040943667292595,
0.08119091391563416,
-0.012156166136264801,
0.008125919848680496,
-0.006166697479784489,
0.043212953954935074,
0.09913318604230881,
0.06252174824476242,
-0.02241169661283493,
-0.08057069778442383,
-0.012322443537414074,
-0.03420300409197807,
0.02804644964635372,
-0.013058868236839771,
0.01544173713773489,
0.03337804973125458,
0.0354386568069458,
0.02408262901008129,
0.0355670191347599,
0.0005935012013651431,
-0.015288998372852802,
0.06857949495315552,
-0.04572329670190811,
-0.049114517867565155,
-0.0253271646797657,
0.014745227061212063,
0.00321848108433187,
-0.007303294725716114,
-0.051242828369140625,
0.016634365543723106,
-0.030459821224212646,
0.006842233240604401,
-0.013533113524317741,
-0.0272306427359581,
0.000027744683393393643,
0.0012647053226828575,
-0.042673081159591675,
0.019486498087644577,
-0.010683080181479454,
0.0037493740674108267,
-0.07473110407590866,
0.046148765832185745,
0.022758465260267258,
-0.03281039372086525,
0.022739849984645844,
0.010416237637400627,
0.017513930797576904,
-0.022176584228873253,
0.005954579450190067,
0.004862014204263687,
-0.038759030401706696,
-0.013952854089438915,
-0.021097345277667046,
0.04855877906084061,
-0.012644362635910511,
-0.05123693868517876,
-0.01766042970120907,
-0.023846352472901344,
0.005856411065906286,
-0.0617062933743,
-0.0006701522506773472,
-0.001933674793690443,
-0.0013764438917860389,
-0.00883039552718401,
-0.009204169735312462,
-0.0220070481300354,
0.01736079342663288,
-0.014734949916601181,
0.0299279373139143,
-0.014899061992764473,
0.026243850588798523,
0.007785237859934568,
-0.05389877408742905,
0.02098657190799713,
-0.008320145308971405,
-0.03990310803055763,
-0.048563357442617416,
-0.011887955479323864,
-0.049633100628852844,
-0.017754634842276573,
0.021332480013370514,
0.018360476940870285,
0.01463976688683033,
-0.004136084113270044,
0.021287115290760994,
0.0021126498468220234,
-0.03616375848650932,
0.03495290130376816,
-0.02871982753276825,
-0.03563573211431503,
0.01573239266872406,
0.008044378831982613,
0.024159740656614304,
0.02210467867553234,
0.007500818930566311,
0.010225269012153149,
0.004553642123937607,
0.008875547908246517,
0.03402243182063103,
0.024251144379377365,
0.01015002466738224,
0.024755200371146202,
-0.02212394028902054,
-0.031670741736888885,
-0.01773000694811344,
0.04888198897242546,
0.007272533606737852,
-0.03233826160430908,
0.002926621586084366,
0.012918077409267426,
-0.023525821045041084,
-0.0009921176824718714,
0.0051346756517887115,
-0.01281479001045227,
0.01857772283256054,
0.011348678730428219,
0.04183434322476387,
-0.02633323334157467,
-0.012923743575811386,
-0.04364372789859772,
-0.0168592669069767,
0.00752745196223259,
0.00902004074305296,
0.018388688564300537,
0.025915760546922684,
0.02163884788751602,
0.026783350855112076,
0.0005359630449675024,
0.009518750943243504,
-0.04261926934123039,
0.04134739935398102,
0.0021693746093660593,
-0.014587124809622765,
0.010886399075388908,
0.025130311027169228,
0.004793486557900906,
-0.03260275349020958,
0.01992066204547882,
0.027957294136285782,
-0.03291529417037964,
-0.012820524163544178,
0.038323067128658295,
-0.05781028792262077,
0.03843090310692787,
0.014735477045178413,
-0.04729869216680527,
0.021203791722655296,
-0.046777237206697464,
-0.026227861642837524,
0.06335831433534622,
-0.01002931222319603,
0.02995547093451023,
-0.005859732627868652,
-0.058184944093227386,
-0.01971430517733097,
0.07236237078905106,
0.019143708050251007,
-0.005741842556744814,
0.003635570639744401,
-0.04490279406309128,
-0.04216959327459335,
-0.021068476140499115,
0.058857306838035583,
-0.03229765594005585,
-0.03214128315448761,
0.03256392106413841,
0.008980169892311096,
-0.030690260231494904,
0.036399222910404205,
-0.00943233072757721,
0.013295497745275497,
-0.036767493933439255,
-0.005306826438754797,
-0.01228155754506588,
0.04497331753373146,
0.057712920010089874,
-0.04370603337883949,
0.028356214985251427,
0.02095385082066059,
0.0402626134455204,
-0.08656327426433563,
-0.0025002555921673775,
0.013230632990598679,
-0.023620842024683952,
0.04308522865176201,
-0.022907208651304245,
0.01919616013765335,
0.021062694489955902,
-0.06635617464780807,
-0.00492899352684617,
-0.021258540451526642,
-0.010893351398408413,
-0.016724904999136925,
0.01536653470247984,
0.0053352974355220795,
0.024678312242031097,
0.04849310964345932,
0.0020686108618974686,
-0.011672241613268852,
0.01945408806204796,
-0.01943921111524105,
-0.007073001470416784,
-0.00514694768935442,
0.023127896711230278,
-0.004407590255141258,
0.009318210184574127,
0.07344405353069305,
-0.011958439834415913,
-0.020262375473976135,
0.0015473469393327832,
-0.0047759609296917915,
0.0041617900133132935,
0.016627777367830276,
0.01258044969290495,
0.013862001709640026,
0.010783758014440536,
-0.0025468869134783745,
-0.01316380687057972,
-0.03331901505589485,
0.02841499261558056,
0.022489719092845917,
0.023201273754239082,
-0.014645375311374664,
0.007101431023329496,
-0.007555985823273659,
-0.059068817645311356,
-0.012719114311039448,
0.013823413290083408,
0.019173169508576393,
-0.023191427811980247,
0.027281323447823524,
0.03618718683719635,
0.030754804611206055,
-0.03380690515041351,
0.018917551264166832,
-0.05053848773241043,
-0.0033866611775010824,
0.017886804416775703,
0.0225402619689703,
-0.01551956869661808,
-0.012443771585822105,
-0.03743874281644821,
-0.018160715699195862,
-0.016854507848620415,
-0.007849439047276974,
0.019637709483504295,
-0.038562338799238205,
-0.025123707950115204,
-0.0018416197272017598,
-0.013727984391152859,
0.011540470644831657,
-0.050948332995176315,
-0.014785939827561378,
0.0307835154235363,
0.018138248473405838,
0.017831893637776375,
-0.01442759670317173,
-0.031885985285043716,
-0.022523541003465652,
-0.09944743663072586,
0.022483497858047485,
-0.0027505229227244854,
-0.011017910204827785,
-0.04228527471423149,
0.01210514921694994,
-0.004995304625481367,
0.015496022067964077,
0.015686172991991043,
0.004227392841130495,
-0.01578100584447384,
0.04952426999807358,
-0.005834898911416531,
-0.015240021981298923,
-0.03174836188554764,
0.025097128003835678,
-0.038364410400390625,
-0.041591670364141464,
-0.04983920976519585,
-0.020321398973464966,
-0.04750024154782295,
-0.0009077759459614754,
0.000801646092440933,
0.0010609650053083897,
0.09069200605154037,
-0.017836065962910652,
-0.02283240295946598,
0.07495926320552826,
0.0074828932993113995,
0.006007521878927946,
0.0517682209610939,
-0.03360475227236748,
0.02040489949285984,
0.06352272629737854,
-0.0318431593477726,
-0.03857753053307533,
0.048887528479099274,
-0.018038934096693993,
0.012317031621932983,
0.006023809313774109,
-0.005596080794930458,
0.004301984794437885,
-0.023226844146847725,
0.0029325876384973526,
-0.0153820114210248,
-0.04423048719763756,
0.004081308376044035,
0.04623859003186226,
0.0392337441444397,
0.037181656807661057,
-0.019651293754577637,
-0.017846623435616493,
0.012441311962902546,
0.0052497354336082935,
-0.03460140898823738,
0.054878175258636475,
0.021150100976228714,
0.026755835860967636,
-0.002597394399344921,
0.0321163535118103,
0.008568691089749336,
0.01704084873199463,
0.03308882564306259,
0.0553131140768528,
-0.03430958837270737,
0.013730681501328945,
-0.002446576952934265,
-0.03348078578710556,
0.02565232291817665,
0.0418318547308445,
-0.00239682849496603,
0.06221044808626175,
-0.041978444904088974,
-0.04899735748767853,
0.008973782882094383,
0.007666603196412325,
-0.012428190559148788,
0.023007119074463844,
0.019134314730763435,
0.06644676625728607,
0.021293122321367264,
0.016665851697325706,
-0.057108547538518906,
-0.021231452003121376,
0.024626191705465317,
0.0026042982935905457,
0.00323711009696126,
-0.013646441511809826,
-0.020993614569306374,
0.0229945071041584,
-0.03876297175884247,
-0.04197869077324867,
-0.030148951336741447,
0.012824833393096924,
0.01731652021408081,
0.038437217473983765,
-0.05396144837141037,
-0.018203524872660637,
-0.03314010426402092,
0.0654677078127861,
-0.08098147809505463,
-0.011354210786521435,
-0.020450560376048088,
0.03675520047545433,
0.001750592957250774,
-0.007972140796482563
] |
<p>The anthropic principle has become a very popular explanation among theoretical physicists lately. Life is unlikely, but only life can observe, so we find ourselves in an unlikely position, so to speak. What I would like to ask is just how unlikely is life? Is the evolution of life generic for most laws of physics, or extremely unlikely with extreme fine-tuning? What is so controversial about the anthropic principle? No one is surprised to find themselves on an Earth-like planet orbiting a long lived star at just about the right distance from the star with plenty of liquid water, a thick atmosphere and plenty of carbon amidst the sterile antiseptic reaches of space. What are the major pros and cons? String theory conveniently provides a multiverse and a landscape.</p> | 1,579 | [
0.020119592547416687,
-0.04644853249192238,
0.04491884261369705,
-0.07304041087627411,
0.023018933832645416,
0.0067033241502940655,
0.00012064705515513197,
-0.021115005016326904,
-0.0050597661174833775,
-0.03146405890583992,
0.005598646122962236,
0.040536168962717056,
0.023195520043373108,
0.046729136258363724,
0.0034684832207858562,
-0.007014350965619087,
-0.004864071495831013,
-0.025035478174686432,
-0.05210655555129051,
0.00498872809112072,
0.059810228645801544,
0.007725787349045277,
0.04581598937511444,
0.008295685984194279,
-0.028795422986149788,
0.0028126088436692953,
-0.019709806889295578,
-0.004031287040561438,
0.014623585157096386,
0.0576414056122303,
-0.011258990503847599,
-0.0012358452659100294,
0.01911589317023754,
0.013641731813549995,
0.018359269946813583,
-0.00831686146557331,
-0.012539326213300228,
-0.030155101791024208,
0.007757852785289288,
0.011026781983673573,
-0.030240656808018684,
-0.03481137380003929,
-0.005728543270379305,
0.034877534955739975,
-0.0279771126806736,
0.003805493703112006,
-0.004466645419597626,
-0.010547667741775513,
0.08360176533460617,
-0.04763776436448097,
0.021810030564665794,
0.0066938805393874645,
0.00885082595050335,
0.016397355124354362,
0.017703842371702194,
-0.012681137770414352,
0.08870173990726471,
0.05164168030023575,
0.004081333056092262,
-0.053980257362127304,
-0.06683329492807388,
-0.0361749492585659,
0.013086103834211826,
-0.001281565404497087,
-0.04359004646539688,
0.04979333654046059,
-0.015605430118739605,
-0.005653471685945988,
0.04950452968478203,
0.008190899156033993,
0.005277732852846384,
0.006709194742143154,
0.010819986462593079,
0.03664402291178703,
-0.010614107362926006,
-0.01828130893409252,
0.010114898905158043,
-0.0025266450829803944,
0.031710706651210785,
0.05526646226644516,
0.012519760057330132,
0.02945883572101593,
0.018455225974321365,
0.03446338698267937,
0.03045138716697693,
-0.0056404839269816875,
0.036446064710617065,
-0.0412575826048851,
0.0142200393602252,
0.021902207285165787,
0.013380948454141617,
0.025633351877331734,
0.04438791051506996,
0.0072440532967448235,
-0.04398006200790405,
0.05694719776511192,
-0.0003922261530533433,
0.06481407582759857,
-0.016854776069521904,
-0.0071685295552015305,
-0.013432073406875134,
-0.01971893571317196,
0.030790025368332863,
0.042200177907943726,
0.019351432099938393,
-0.026928365230560303,
-0.045694004744291306,
0.016457470133900642,
-0.010907107964158058,
-0.004888718947768211,
-0.029381901025772095,
0.03508363291621208,
0.004624457564204931,
0.006884140893816948,
-0.0015547098591923714,
-0.011457865126430988,
0.008626479655504227,
-0.023057349026203156,
0.08833836019039154,
0.04687434807419777,
0.04078271985054016,
0.011776984669268131,
0.035163383930921555,
0.0024989719968289137,
-0.026130566373467445,
0.019106527790427208,
0.008278709836304188,
0.0017266140785068274,
-0.030998267233371735,
-0.0028935568407177925,
-0.02523859217762947,
0.004727471154183149,
0.007412782870233059,
0.040979474782943726,
0.08816394209861755,
-0.018177848309278488,
-0.11158474534749985,
-0.05701422691345215,
0.04450168088078499,
0.00283762882463634,
-0.009525373578071594,
-0.06149214878678322,
0.00032557491795159876,
0.028233878314495087,
0.09970424324274063,
-0.010138140991330147,
0.00607044342905283,
0.05288584157824516,
0.022007808089256287,
0.04529770463705063,
-0.04667895659804344,
0.01977691426873207,
-0.04862361028790474,
-0.04589105397462845,
0.002385352971032262,
-0.053352080285549164,
0.030187567695975304,
0.0213342122733593,
0.034508224576711655,
-0.017948271706700325,
0.07787859439849854,
-0.03501763567328453,
-0.006890791468322277,
0.013956592418253422,
-0.02462482638657093,
-0.014627785421907902,
0.08904581516981125,
0.03049550950527191,
-0.009032163769006729,
0.0420205220580101,
0.01409519836306572,
0.021364450454711914,
0.027324626222252846,
0.034116167575120926,
0.0006250277510844171,
-0.048996876925230026,
-0.006955401971936226,
-0.0006773254135623574,
0.017965570092201233,
0.0018854987574741244,
-0.030195267871022224,
-0.0018771375762298703,
-0.0003055502602364868,
-0.0012757359072566032,
0.0046545774675905704,
0.006816844455897808,
-0.05532931163907051,
-0.03592366725206375,
0.026991713792085648,
-0.0234104935079813,
-0.02713807299733162,
-0.052193447947502136,
-0.006595374085009098,
0.06480281054973602,
0.02430248260498047,
0.007636480964720249,
0.03947783634066582,
0.0019805734045803547,
-0.059751275926828384,
0.0016192131442949176,
0.00804948154836893,
0.05353045463562012,
0.015600518323481083,
0.018765350803732872,
0.032875608652830124,
0.05289766564965248,
0.01931610330939293,
-0.01603950746357441,
-0.009023506194353104,
0.009787916205823421,
-0.08866289258003235,
0.010790569707751274,
-0.0255325585603714,
0.040024533867836,
0.036861781030893326,
0.018319064751267433,
0.010866637341678143,
-0.033254873007535934,
-0.00015357782831415534,
0.040731217712163925,
-0.007469152566045523,
0.06289143860340118,
-0.011407943442463875,
0.005503022111952305,
-0.006259371060878038,
0.02333436906337738,
0.004655579105019569,
-0.04896363615989685,
-0.002889810362830758,
-0.04041633754968643,
-0.0641556903719902,
0.0008358311606571078,
0.036672379821538925,
0.06206187978386879,
-0.0009077791473828256,
0.03265109658241272,
-0.00790711585432291,
0.04387301206588745,
0.02123745158314705,
0.028303585946559906,
-0.049305353313684464,
-0.01527256891131401,
0.013652813620865345,
0.01976487785577774,
0.0186191126704216,
0.014222138561308384,
0.02304035983979702,
0.029548009857535362,
-0.00012856864486820996,
-0.010608678683638573,
-0.006673506926745176,
0.012101680971682072,
-0.01638900116086006,
0.028243886306881905,
0.0021855407394468784,
-0.01022949256002903,
-0.015958089381456375,
-0.0532134510576725,
-0.025992359966039658,
0.05143687129020691,
0.00976741686463356,
0.02070758305490017,
-0.0504683293402195,
0.010371415875852108,
-0.031100232154130936,
0.011609217151999474,
-0.051510848104953766,
-0.007288794498890638,
0.029479490593075752,
-0.042035046964883804,
-0.015566571615636349,
-0.019973281770944595,
-0.013873681426048279,
-0.009095137007534504,
0.005873416550457478,
-0.013324358500540257,
-0.033547766506671906,
0.015526875853538513,
-0.01007208414375782,
-0.03064602054655552,
0.011121949180960655,
-0.012733157724142075,
-0.036414727568626404,
0.027223195880651474,
-0.04178875684738159,
0.002725103870034218,
-0.01630568690598011,
-0.020777758210897446,
0.04163799434900284,
-0.0003855346003547311,
0.027809742838144302,
-0.009911526925861835,
0.01066504791378975,
-0.020230842754244804,
0.009531189687550068,
0.0010746800107881427,
0.009069545194506645,
-0.006078625097870827,
-0.00011002182145603001,
0.036295972764492035,
-0.0420738123357296,
-0.0028810519725084305,
0.04383862391114235,
-0.049297671765089035,
-0.08710671216249466,
0.016668617725372314,
0.041420575231313705,
0.0018282067030668259,
-0.04568120464682579,
0.012003347277641296,
0.0348062738776207,
-0.06154530495405197,
-0.002117745578289032,
-0.04643219709396362,
-0.08109091967344284,
-0.0035928485449403524,
-0.017007144168019295,
0.023311875760555267,
-0.007251075003296137,
-0.03698642924427986,
0.027952106669545174,
0.06157434731721878,
-0.006697065196931362,
-0.004500905051827431,
-0.014071845449507236,
-0.017986956983804703,
0.011037353426218033,
0.01951993629336357,
0.023205162957310677,
0.010965297929942608,
0.019577324390411377,
0.02985384315252304,
0.015588754788041115,
-0.0035208165645599365,
-0.0038184085860848427,
-0.04296109080314636,
0.006531425751745701,
0.005945212673395872,
-0.009134044870734215,
0.022572048008441925,
0.033259909600019455,
0.021527737379074097,
0.021446136757731438,
-0.047271911054849625,
0.002364386571571231,
0.026942739263176918,
-0.02211892232298851,
0.04663447290658951,
-0.0011092191562056541,
0.018347783014178276,
-0.035698242485523224,
0.052268777042627335,
0.003323633223772049,
0.036238182336091995,
0.011234886012971401,
-0.01197392214089632,
0.041318267583847046,
-0.0023329867981374264,
-0.00833724532276392,
0.020872812718153,
0.03843118995428085,
-0.0111269885674119,
-0.018117111176252365,
0.006675183307379484,
0.019041016697883606,
-0.010112765245139599,
-0.02383059449493885,
-0.042934712022542953,
0.03247430920600891,
0.04573986679315567,
0.018316514790058136,
-0.013508402742445469,
-0.0219094417989254,
0.026384906843304634,
-0.0372629314661026,
-0.009420063346624374,
-0.006131836678832769,
0.04399671033024788,
0.0013339081779122353,
0.01847071200609207,
0.0032327515073120594,
-0.02655775472521782,
-0.0010811161482706666,
-0.01247492153197527,
-0.06358366459608078,
0.019957194104790688,
-0.045478396117687225,
0.01772340014576912,
0.0023759405594319105,
-0.0004091687733307481,
0.016175411641597748,
-0.014317507855594158,
-0.04495280608534813,
-0.03207709267735481,
0.019505521282553673,
-0.05949319899082184,
-0.0013154704356566072,
-0.058681387454271317,
-0.03949454054236412,
-0.03581769019365311,
0.029799072071909904,
0.04399707913398743,
0.0015840624691918492,
0.004445186350494623,
0.027715908363461494,
-0.049844250082969666,
-0.004841943737119436,
-0.0025982775259763002,
-0.0146047817543149,
-0.018776822835206985,
0.06476650387048721,
0.05033260956406593,
-0.010154216550290585,
-0.012482098303735256,
-0.009984160773456097,
-0.0018129065865650773,
0.03651603311300278,
-0.003083392046391964,
0.01740054227411747,
-0.002031620591878891,
-0.002189301885664463,
-0.04194394871592522,
-0.01003476232290268,
0.006115684285759926,
-0.0012796224327757955,
0.0030044480226933956,
0.06479589641094208,
-0.0008537127287127078,
-0.03529789671301842,
0.05866881459951401,
0.027212131768465042,
-0.01695365272462368,
-0.02234727330505848,
-0.02928476594388485,
-0.05712087079882622,
-0.030696414411067963,
0.006718458607792854,
0.029343634843826294,
-0.016653025522828102,
-0.022033270448446274,
-0.005651761312037706,
-0.0075501506216824055,
0.007464872673153877,
-0.030182963237166405,
0.00999126024544239,
-0.03730160742998123,
0.020322881639003754,
-0.0012930161319673061,
-0.013172084465622902,
-0.016281232237815857,
0.010567596182227135,
0.03370649367570877,
0.02867795340716839,
-0.04289988428354263,
-0.0480843186378479,
0.005252729635685682,
0.024573924019932747,
0.03426268324255943,
0.012830544263124466,
0.0020433308091014624,
-0.06406202167272568,
-0.03224668651819229,
0.050868429243564606,
-0.0394432470202446,
0.019098447635769844,
-0.03281626105308533,
-0.035157669335603714,
-0.0014934897189959884,
-0.039608150720596313,
0.022713547572493553,
0.007386980578303337,
0.005143620539456606,
0.011815786361694336,
-0.02653343975543976,
0.0036563610192388296,
0.008517088368535042,
0.05654442310333252,
-0.010495815426111221,
0.0517444871366024,
0.012154900468885899,
-0.005334050860255957,
0.02212805487215519,
-0.0091573316603899,
-0.0008832583553157747,
-0.03853501006960869,
0.018585175275802612,
-0.005411764606833458,
-0.03185351938009262,
0.02017635479569435,
-0.010206527076661587,
-0.03065969981253147,
0.022429104894399643,
-0.020363343879580498,
-0.02800975926220417,
0.00955077912658453,
-0.02616654895246029,
-0.030382784083485603,
0.019736124202609062,
0.0109034338966012,
0.027811134234070778,
0.025061963126063347,
-0.012794137932360172,
0.00471237488090992,
-0.027843939140439034,
0.025178756564855576,
0.005288533866405487,
0.016885610297322273,
-0.03725875914096832,
-0.022123299539089203,
-0.04639827460050583,
0.016450917348265648,
0.007828674279153347,
-0.03077811747789383,
0.00122050940990448,
-0.011589914560317993,
-0.03145482391119003,
-0.005738067906349897,
-0.005237902514636517,
0.011593975126743317,
0.02950652688741684,
0.04247206822037697,
-0.012251395732164383,
0.0066112796775996685,
0.031729862093925476,
-0.03384950011968613,
0.011705082841217518,
0.03845443204045296,
0.007888589054346085,
0.04794052615761757,
-0.01101539097726345,
-0.04159291833639145,
0.008600104600191116,
-0.08506398648023605,
0.039435986429452896,
-0.013861240819096565,
0.015704771503806114,
-0.014856928028166294,
-0.07576450705528259,
-0.032894376665353775,
-0.026913844048976898,
-0.011034826748073101,
0.034906934946775436,
-0.02841271460056305,
0.027194209396839142,
-0.010762895457446575,
0.009046443738043308,
-0.05361755192279816,
-0.007637809030711651,
-0.006681966595351696,
0.05687352642416954,
-0.024459345266222954,
-0.013241983018815517,
-0.007389528676867485,
-0.03912399709224701,
0.01975991576910019,
-0.0073919701389968395,
0.033004578202962875,
-0.014789024367928505,
-0.0027269581332802773,
-0.012062408030033112,
0.02482723817229271,
0.061854854226112366,
-0.028506729751825333,
0.0014667873037979007,
0.0569143183529377,
-0.004724558442831039,
0.04236821085214615,
-0.05394643172621727,
0.03144686669111252,
-0.044120363891124725,
-0.04396607354283333,
0.015680452808737755,
-0.0025477763265371323,
-0.022094696760177612,
-0.03653287515044212,
-0.01991872303187847,
0.03741506114602089,
-0.008672479540109634,
-0.014476963318884373,
-0.017354194074869156,
0.04097441956400871,
-0.03781357780098915,
0.013375502079725266,
0.020985664799809456,
0.011683514341711998,
0.014478449709713459,
-0.07421615719795227,
0.007919959723949432,
0.004325338639318943,
-0.010551223531365395,
0.021804075688123703,
0.02357272431254387,
0.004408684559166431,
-0.04034245014190674,
0.006890750024467707,
-0.03769390285015106,
0.01477466244250536,
0.004326409660279751,
0.019118646159768105,
0.03491218760609627,
0.005889579653739929,
-0.030402574688196182,
-0.033020973205566406,
-0.0408695749938488,
0.03409603610634804,
0.03612664341926575,
-0.04935769364237785,
0.025256339460611343,
0.029199963435530663,
-0.00017622706945985556,
-0.00521324947476387,
-0.012301896698772907,
-0.01374774519354105,
0.01103141251951456,
0.006494287401437759,
0.015902070328593254,
-0.035163216292858124,
-0.0046481117606163025,
0.06707935780286789,
0.037495020776987076,
-0.021835384890437126,
0.04320541024208069,
0.014445599168539047,
0.02020801417529583,
0.02776297554373741,
-0.006939619313925505,
-0.012669749557971954,
0.011144828051328659,
-0.06871368736028671,
0.06806249171495438,
0.01267912331968546,
-0.025379398837685585,
0.009917711839079857,
-0.007556510157883167,
-0.00039955732063390315,
-0.030918706208467484,
-0.041461579501628876,
-0.010668749921023846,
0.018970945850014687,
0.013430812396109104,
0.04125174507498741,
0.05302860587835312,
-0.01850946620106697,
-0.004641547333449125,
0.010809500701725483,
-0.006404799874871969,
0.012731743045151234,
-0.1015726700425148,
-0.007986294105648994,
-0.030322371050715446,
-0.06479116529226303,
0.07011964172124863,
0.03228338062763214,
-0.04921267181634903,
0.027857204899191856,
-0.011287721805274487,
0.01999415084719658,
0.012277737259864807,
0.04162980988621712,
-0.01552390493452549,
0.04740982502698898,
0.009152591228485107,
0.012213553301990032,
-0.02465079352259636,
0.03678775206208229,
0.15024180710315704,
0.06491599977016449,
0.005432601552456617,
-0.05758317559957504,
0.03369723632931709,
-0.038782279938459396,
0.008825937286019325,
0.019317401573061943,
0.0024896564427763224,
0.024053486064076424,
0.007880370132625103,
0.007762930355966091,
-0.01669483259320259,
0.01264297217130661,
-0.03791248798370361,
0.029063615947961807,
-0.05894128233194351,
-0.010020196437835693,
-0.02721795253455639,
-0.009951937012374401,
0.009502093307673931,
-0.0009196418686769903,
0.001465623383410275,
-0.036500751972198486,
-0.012614172883331776,
0.0003675792249850929,
-0.0006756716757081449,
-0.06471297144889832,
0.025533584877848625,
0.011257121339440346,
-0.02311154641211033,
-0.02432839386165142,
-0.0013182144612073898,
-0.011802433989942074,
0.014265445061028004,
-0.00658850371837616,
0.003997109364718199,
0.0006039487780071795,
-0.00875850673764944,
0.017012104392051697,
0.03787081316113472,
0.02044345624744892,
0.01095407735556364,
0.0014558621915057302,
-0.0443253368139267,
-0.0040718261152505875,
0.005090293940156698,
0.023520085960626602,
0.007593933492898941,
0.027666769921779633,
-0.03624458238482475,
0.01505914144217968,
0.03367152810096741,
-0.014826394617557526,
-0.014464261010289192,
-0.011871508322656155,
0.05649750679731369,
-0.0045481519773602486,
-0.07607313990592957,
0.03791625797748566,
-0.004021394532173872,
-0.03213001415133476,
0.030261971056461334,
0.006935763638466597,
0.0002604690089356154,
-0.040302928537130356,
0.032322339713573456,
0.03109755925834179,
-0.02946670912206173,
-0.010938677936792374,
-0.0734851285815239,
-0.006437353789806366,
-0.0664825290441513,
0.027956340461969376,
0.038899995386600494,
0.04405028373003006,
0.013108929619193077,
0.02671775408089161,
0.005756563972681761,
-0.03294432908296585,
-0.020337987691164017,
-0.011125465855002403,
-0.029297763481736183,
-0.005176750477403402,
-0.027249811217188835,
-0.01318279653787613,
0.054340485483407974,
-0.009014836512506008,
-0.009974093176424503,
0.015411747619509697,
-0.02138764038681984,
0.026152659207582474,
-0.00876309908926487,
-0.0005893245688639581,
0.0022214557975530624,
-0.035602252930402756,
-0.01695948652923107,
-0.031060049310326576,
-0.012889864854514599,
0.03862134367227554,
0.01224016584455967,
0.01258865837007761,
0.01539447158575058,
0.012177154421806335,
-0.013316014781594276,
0.0014589146012440324,
0.04175633192062378,
-0.012073307298123837,
-0.01842881366610527,
0.03798498213291168,
0.017125993967056274,
-0.028762739151716232,
-0.01740712858736515,
-0.021975820884108543,
-0.04776386916637421,
-0.0252140574157238,
0.018759142607450485,
-0.0235856045037508,
0.013593579642474651,
-0.006227126810699701,
-0.026874355971813202,
-0.05015280097723007,
-0.0013688228791579604,
-0.03665203973650932,
0.032278403639793396,
0.012203307822346687,
-0.004897396545857191,
-0.017316855490207672,
-0.00008726714440854266,
-0.021924233064055443,
-0.06683484464883804,
0.00617867661640048,
0.003888328094035387,
-0.0008461886900477111,
0.046552225947380066,
0.024014277383685112,
-0.019507277756929398,
0.024577487260103226,
-0.04479711875319481,
-0.029458986595273018,
0.003975809086114168,
-0.028532546013593674,
-0.07008395344018936,
0.025389844551682472,
-0.06346848607063293,
0.02499666064977646,
-0.0015871310606598854,
-0.028828201815485954,
0.002090183785185218,
0.04183149337768555,
-0.01754016801714897,
0.016532298177480698,
0.013374853879213333,
-0.009048040956258774,
-0.05906638130545616,
0.01663224771618843,
-0.013412374071776867,
0.010289058089256287,
-0.027178240939974785,
0.027907144278287888,
0.02839278243482113,
0.00822749175131321,
0.027084972709417343,
-0.023732008412480354,
-0.06986038386821747,
-0.005403248127549887,
0.039018359035253525,
0.005930754821747541,
0.032889168709516525,
0.04709678143262863,
0.009800164960324764,
0.0557064525783062,
0.012617578729987144,
0.0289585180580616,
-0.06985244899988174,
0.03872044011950493,
0.06128993630409241,
-0.0022271533962339163,
0.01644650660455227,
-0.014102499932050705,
0.010486798360943794,
0.048107318580150604,
-0.056633058935403824,
0.039275746792554855,
-0.017820633947849274,
-0.012108167633414268,
-0.036974694579839706,
-0.00741757545620203,
-0.05232788622379303,
0.04565858095884323,
0.01202958170324564,
0.012901094742119312,
0.008159063756465912,
0.020042242482304573,
-0.02478681318461895,
-0.0445820689201355,
-0.007651105988770723,
0.06915917247533798,
-0.047750093042850494,
0.04309632256627083,
0.0320218987762928,
0.015123678371310234,
-0.05614281818270683,
0.01796756312251091,
-0.009602569974958897,
0.026456492021679878,
0.028150931000709534,
0.009675799869000912,
0.03163762763142586,
-0.007221458479762077,
0.022347724065184593,
-0.04327242448925972,
-0.025401148945093155,
0.02209695242345333,
0.026994476094841957,
0.013891201466321945,
-0.004175124224275351,
0.007771479897201061,
-0.0255852360278368,
-0.0064786700531840324,
-0.01781376823782921,
0.023657796904444695,
-0.002066470915451646,
0.007317019626498222,
-0.012705768458545208,
0.03601450100541115,
-0.011599701829254627,
-0.011043397709727287,
0.006012990605086088,
-0.06582609564065933,
-0.015420057810842991,
0.031557850539684296,
0.06121613830327988,
0.02120085619390011,
0.00508095882833004,
-0.02200920134782791,
-0.01825353130698204,
0.002815086394548416,
-0.0035782072227448225,
-0.012055031023919582,
0.005261478014290333,
0.011603839695453644,
-0.020251065492630005,
0.03336029499769211,
0.0006528020021505654,
-0.021618271246552467,
-0.005767295137047768,
0.03382844850420952,
0.001354898326098919,
0.045566122978925705,
-0.012249625287950039,
-0.07185032963752747,
-0.008011572062969208,
-0.07455793023109436,
0.06849906593561172,
-0.03154974430799484,
0.0909661203622818,
-0.0590926930308342,
-0.032318513840436935,
0.014646652154624462,
0.04051615670323372,
-0.0022416196297854185,
-0.004938604310154915,
0.024947939440608025,
0.001386995310895145,
0.022934667766094208,
0.00026884989347308874,
-0.026686595752835274,
-0.014114435762166977,
0.008322887122631073,
-0.0433964729309082,
0.009874971583485603,
-0.01791842095553875,
0.006914490833878517,
-0.007275823969393969,
0.04663054272532463,
-0.054753080010414124,
0.015993798151612282,
0.052114952355623245,
-0.033515237271785736,
0.0773317813873291,
-0.015533867292106152,
-0.018362419679760933,
0.04948180541396141,
-0.014748319052159786,
0.02531464211642742,
-0.00014206234482116997,
-0.0021468568593263626,
0.024252325296401978,
0.04149888455867767,
0.0020071729086339474,
-0.033816732466220856,
0.0011682939948514104,
0.0313170924782753,
-0.012815513648092747,
-0.025264058262109756,
0.011455787345767021,
0.03842557966709137,
-0.029102424159646034,
0.0006620523054152727,
0.03187303617596626,
-0.014463134109973907,
0.05451268330216408,
-0.008153261616826057,
-0.016937432810664177,
-0.001445505185984075,
0.03587727248668671,
-0.053596995770931244,
-0.009253878146409988,
0.00807553343474865,
-0.03833578899502754,
0.0459393672645092,
-0.00408752029761672,
-0.04326687380671501,
0.021956870332360268,
0.015257627703249454,
0.02707679010927677,
-0.043108779937028885,
0.00903387926518917,
0.005945012904703617,
0.00503158662468195,
0.020559607073664665,
0.007857357151806355,
-0.006181264761835337,
0.11094930022954941,
0.036105990409851074,
0.012496409937739372,
0.01700194738805294,
-0.044727224856615067,
-0.023937052115797997,
0.003673550905659795,
-0.04157238453626633,
0.029863480478525162,
0.015140784904360771,
0.025686709210276604,
-0.007651516702026129,
0.0360163077712059,
0.04730474203824997,
-0.056477244943380356,
0.01705607958137989,
-0.03205243498086929,
0.008461643010377884,
0.0097854845225811,
-0.021850522607564926,
-0.020811347290873528,
-0.022643262520432472,
0.00007106125849531963,
0.0045311604626476765,
0.004728829022496939,
-0.010815760120749474,
-0.016751402989029884,
-0.00030985387274995446,
0.022451722994446754,
-0.029023462906479836,
0.022737819701433182,
-0.03987570106983185,
0.03596162050962448,
-0.0001669073972152546,
-0.0584229901432991
] |
<p>I was recently reading <a href="http://en.wikipedia.org/wiki/Siphon#Explanation_using_Bernoulli.27s_equation" rel="nofollow">the explanation for the behaviour of a siphon</a> on Wikipedia, which uses Bernoulli's equation in its proof. The argument is generally pretty easy to follow, except for one key point: how can we assume that the velocity of the water is constant at all points throughout its flow through the tube? This tacit assumption is made at various point, not least in the terming of "the siphon velocity" (implying there's only one). I would be grateful if someone could clarify this.</p>
<p>Note: I've done a hefty amount of classical mechanics in my time, but barely any fluid mechanics I'm afraid. First principles explanations would be appreciated.</p> | 1,580 | [
-0.015663648024201393,
0.00023499340750277042,
-0.006985816638916731,
-0.024627935141324997,
0.04717906564474106,
-0.032350413501262665,
0.01670263148844242,
0.0151119539514184,
-0.016211360692977905,
-0.021790336817502975,
0.015853920951485634,
0.07210534811019897,
0.04445141181349754,
-0.0108772162348032,
0.029302533715963364,
0.0004520876391325146,
0.004912679549306631,
-0.03183767944574356,
0.03668113425374031,
-0.035344261676073074,
-0.014581496827304363,
0.007535965647548437,
0.02580198273062706,
0.022204145789146423,
0.0062010218389332294,
-0.015060622245073318,
0.029468171298503876,
-0.004802719224244356,
0.011087731458246708,
0.009838547557592392,
-0.008018537424504757,
-0.011954477988183498,
-0.03842031583189964,
0.03209376335144043,
0.017797458916902542,
0.003463095985352993,
-0.056681156158447266,
0.00480665871873498,
-0.020256388932466507,
0.03030308336019516,
-0.038386594504117966,
0.023249279707670212,
-0.009000441059470177,
0.024192307144403458,
-0.031464774161577225,
0.03294572979211807,
0.0334150493144989,
-0.006315065547823906,
0.04950429126620293,
-0.067699134349823,
0.02021857723593712,
0.03689968213438988,
0.05996481329202652,
0.05095493793487549,
0.011410316452383995,
0.0056503042578697205,
0.0649016872048378,
0.049175042659044266,
-0.040025800466537476,
-0.06077992171049118,
-0.023699836805462837,
0.002033582655712962,
-0.0016735595418140292,
-0.007503872737288475,
0.00022636677022092044,
0.008777749724686146,
0.013106036931276321,
-0.047122739255428314,
0.03343946114182472,
-0.003677951404824853,
-0.0009924311889335513,
-0.012968962080776691,
0.03529013320803642,
-0.006492792163044214,
0.005229292903095484,
0.004578052554279566,
0.024568408727645874,
0.018806032836437225,
0.01298251748085022,
0.0301798228174448,
-0.021382315084338188,
0.016555851325392723,
0.05148365721106529,
0.05933675915002823,
-0.013011615723371506,
-0.007404937408864498,
0.09342671930789948,
0.008095132187008858,
0.03727435693144798,
0.005354470573365688,
0.02090456709265709,
0.012757360003888607,
0.014134606346487999,
0.015265158377587795,
0.00228338735178113,
0.01580224372446537,
-0.016344472765922546,
0.0710550919175148,
0.03674919158220291,
-0.051887109875679016,
0.00819569081068039,
-0.029581891372799873,
0.005980122368782759,
0.08341052383184433,
-0.020912406966090202,
-0.0254160538315773,
-0.05074170231819153,
0.041792746633291245,
-0.036216333508491516,
-0.013641352765262127,
-0.05391542240977287,
-0.006943205837160349,
0.0006037737475708127,
0.00013475395098794252,
-0.024839621037244797,
-0.012998641468584538,
-0.01689884252846241,
-0.005290535278618336,
0.07426857948303223,
0.037049490958452225,
0.052723824977874756,
-0.044187214225530624,
0.03460899367928505,
-0.02499890886247158,
-0.06503325700759888,
0.03441325202584267,
-0.016250262036919594,
-0.035486526787281036,
-0.03137555345892906,
0.01068268995732069,
0.02584313601255417,
0.013847127556800842,
-0.016733361408114433,
0.025570809841156006,
0.05629023164510727,
-0.007881906814873219,
-0.09881795197725296,
-0.06265122443437576,
0.04860442131757736,
-0.009935562498867512,
-0.023032283410429955,
-0.07756997644901276,
0.02178337797522545,
0.031056171283125877,
0.12052001804113388,
-0.04855269566178322,
-0.026956209912896156,
-0.010429998859763145,
0.012697589583694935,
-0.013290165923535824,
-0.03888772055506706,
-0.01294140238314867,
0.041126053780317307,
-0.025466548278927803,
-0.011623663827776909,
-0.06569012999534607,
0.029798856005072594,
0.019355250522494316,
0.03135840222239494,
-0.06453637033700943,
0.02435869537293911,
-0.02936583198606968,
-0.010974186472594738,
0.0007204457651823759,
0.002399524673819542,
-0.030310461297631264,
0.067288838326931,
0.028089143335819244,
-0.0031791538931429386,
0.013917354866862297,
0.03597818687558174,
0.020668573677539825,
-0.025061577558517456,
0.02576509304344654,
0.03908006474375725,
-0.041193053126335144,
-0.014484129846096039,
0.006704979110509157,
0.00621009198948741,
0.027138439938426018,
-0.022165916860103607,
-0.03034142032265663,
-0.006578447297215462,
0.0344238243997097,
-0.022389601916074753,
0.014060266315937042,
-0.01836109533905983,
0.016905494034290314,
0.01820474863052368,
-0.04690522328019142,
0.008417490869760513,
-0.07530374825000763,
0.031302519142627716,
-0.03975856676697731,
0.005516450386494398,
0.004303902853280306,
-0.004087007604539394,
0.021569015458226204,
-0.06290524452924728,
0.0031347693875432014,
-0.013989129103720188,
0.0025262099225074053,
0.00848786998540163,
-0.008217944763600826,
0.00035085066338069737,
0.02307385765016079,
0.024587856605648994,
0.01603825017809868,
0.029825497418642044,
0.01590942032635212,
-0.012332267127931118,
-0.0028042555786669254,
-0.034874673932790756,
0.02468491531908512,
-0.03266361728310585,
-0.01779399812221527,
-0.0013527162373065948,
-0.030784346163272858,
0.03666948154568672,
0.02529303915798664,
-0.05833273008465767,
0.1324673295021057,
0.04602612182497978,
0.03635832294821739,
-0.0032922562677413225,
0.03149276226758957,
0.017894485965371132,
-0.008356385864317417,
0.003815330332145095,
-0.036836400628089905,
-0.05327729508280754,
-0.008729187771677971,
0.004066205117851496,
0.04603112116456032,
-0.003027124796062708,
-0.02714948169887066,
0.003245811676606536,
0.03754744678735733,
0.028963647782802582,
-0.0008439964149147272,
-0.010885131545364857,
0.0029657857958227396,
0.0032002090010792017,
0.027249615639448166,
-0.007224420551210642,
0.03042851760983467,
0.03595637157559395,
0.024052990600466728,
0.0532086156308651,
-0.025385824963450432,
-0.025379370898008347,
0.001786884036846459,
-0.02011050097644329,
0.023083897307515144,
-0.00015266206173691899,
0.0041609569452703,
0.026286568492650986,
-0.028205202892422676,
0.005885327234864235,
0.015910880640149117,
0.0035886839032173157,
0.00897992867976427,
-0.040900301188230515,
0.01192747987806797,
0.018502317368984222,
-0.009173213504254818,
-0.03593675047159195,
-0.02010861039161682,
0.01995866186916828,
-0.03688142076134682,
0.0151258809491992,
-0.0421333909034729,
-0.02078329399228096,
0.0061421082355082035,
0.02164803445339203,
-0.0021749373991042376,
0.01382247731089592,
0.028703829273581505,
-0.034461040049791336,
-0.03336812183260918,
-0.0034661705140024424,
-0.010492433793842793,
-0.03837156668305397,
0.026569854468107224,
-0.045920684933662415,
0.016796499490737915,
-0.01947791688144207,
0.005822503473609686,
0.07279107719659805,
0.003899779636412859,
0.022326521575450897,
0.014972088858485222,
0.019696906208992004,
-0.04540513455867767,
0.007546655368059874,
-0.03557923063635826,
0.023897508159279823,
-0.003907050006091595,
0.02138814702630043,
0.04678338021039963,
-0.032083071768283844,
-0.030498642474412918,
0.027830323204398155,
-0.06069796159863472,
-0.0532698929309845,
-0.04372502118349075,
0.022495107725262642,
0.024599075317382812,
-0.008493756875395775,
0.006122438237071037,
0.027135904878377914,
-0.06461729109287262,
-0.016339793801307678,
-0.030447712168097496,
-0.06019163131713867,
0.023293470963835716,
0.014607375487685204,
0.05474787577986717,
0.010620891116559505,
-0.040020618587732315,
0.0454501174390316,
-0.000193690400919877,
-0.06745095551013947,
0.0017442387761548162,
0.019270408898591995,
-0.01951705478131771,
-0.02142799086868763,
0.017594758421182632,
0.0392073430120945,
-0.041053012013435364,
-0.002365139778703451,
-0.0014385709073394537,
0.026758288964629173,
0.037325646728277206,
0.003918241709470749,
0.015949426218867302,
-0.022874530404806137,
0.030000971630215645,
0.009656365029513836,
0.024022208526730537,
0.01654893532395363,
-0.033181965351104736,
0.016228601336479187,
-0.0245850570499897,
0.06183357164263725,
0.016028763726353645,
-0.03985867276787758,
0.06705476343631744,
0.013151021674275398,
-0.03508472070097923,
-0.06103590503334999,
0.015053404495120049,
-0.025708582252264023,
-0.0110468165948987,
0.034564949572086334,
0.026586659252643585,
0.03442372754216194,
0.01704014465212822,
0.0067052822560071945,
0.017623674124479294,
0.04549382999539375,
-0.02704319916665554,
-0.029575863853096962,
-0.026253199204802513,
-0.03821037709712982,
0.025485169142484665,
-0.0006077898433431983,
-0.004763072356581688,
0.04484190419316292,
0.0043126316741108894,
0.013224142603576183,
-0.0033456392120569944,
-0.03488369286060333,
0.02443675883114338,
-0.08366512507200241,
-0.0038018974009901285,
0.021762996912002563,
0.0282912477850914,
-0.010447841137647629,
0.05161067470908165,
0.012089675292372704,
0.04923636093735695,
0.007146821357309818,
0.02099011279642582,
-0.07750040292739868,
0.007576917763799429,
-0.039852965623140335,
-0.0003458534483797848,
-0.015543871559202671,
-0.022077208384871483,
0.0075572170317173,
-0.05541549250483513,
-0.0570782832801342,
-0.000025420753445359878,
0.004034365061670542,
-0.046875759959220886,
0.01744822785258293,
-0.04153679683804512,
-0.02407377026975155,
-0.013302815146744251,
0.03347204253077507,
0.03550820052623749,
-0.03196074441075325,
0.03197504207491875,
0.03232463449239731,
-0.00888972170650959,
-0.006603294052183628,
-0.00456429086625576,
0.01423901878297329,
0.04427703469991684,
0.016419336199760437,
0.043033748865127563,
0.033362843096256256,
-0.007833820767700672,
0.025433305650949478,
0.003530501388013363,
0.03691025450825691,
-0.01173735223710537,
-0.005991090554744005,
-0.027663111686706543,
-0.07408833503723145,
0.02476171776652336,
0.023557450622320175,
0.02410665899515152,
0.0030721472576260567,
0.005715625360608101,
0.024991653859615326,
0.0034164623357355595,
-0.013341517187654972,
0.06636780500411987,
0.02965337596833706,
0.014039064757525921,
-0.022153645753860474,
-0.04897821694612503,
0.005701745394617319,
-0.008141408674418926,
0.020391032099723816,
0.014454225078225136,
0.03631100431084633,
-0.013564998283982277,
-0.004972956143319607,
0.003656273242086172,
-0.0011556637473404408,
-0.031210513785481453,
-0.0015003130538389087,
0.022085044533014297,
0.04717777669429779,
-0.008460045792162418,
-0.011748302727937698,
0.019771020859479904,
0.01396888867020607,
0.004900410771369934,
0.0073413304053246975,
-0.014316744171082973,
-0.049043189734220505,
-0.027157122269272804,
0.027227554470300674,
0.04377938061952591,
-0.0015314193442463875,
0.017992032691836357,
-0.04565921053290367,
-0.01451516430824995,
0.05122203752398491,
-0.005132308229804039,
0.009144301526248455,
0.004464242607355118,
0.005261179991066456,
0.0050823199562728405,
-0.032744571566581726,
0.012038031592965126,
-0.00433082040399313,
-0.0419096015393734,
-0.007223621942102909,
-0.02467346377670765,
0.0011704687494784594,
-0.04090571403503418,
-0.019312871620059013,
0.022771835327148438,
0.05333301052451134,
0.022684235125780106,
0.0026555981021374464,
-0.0018334576161578298,
0.03498624265193939,
-0.01427517645061016,
-0.06665085256099701,
0.003057439113035798,
-0.029894642531871796,
0.020754238590598106,
-0.0015121555188670754,
-0.033016372472047806,
-0.04467944800853729,
0.026675591245293617,
0.01896749436855316,
-0.027599917724728584,
0.03994821384549141,
-0.03546145558357239,
-0.0025858129374682903,
0.018345266580581665,
0.006642035208642483,
0.005477621220052242,
0.02517051249742508,
-0.039339691400527954,
-0.03254192695021629,
-0.013485684059560299,
0.011114892549812794,
-0.012306620366871357,
-0.015400951728224754,
-0.06200769543647766,
0.032158538699150085,
0.002751440042629838,
0.040426645427942276,
0.0056111752055585384,
0.008871624246239662,
0.006741909310221672,
-0.025983845815062523,
0.0006515688146464527,
0.034683965146541595,
0.0014588215854018927,
0.020588986575603485,
0.03058655932545662,
0.024407729506492615,
0.023638958111405373,
-0.06341579556465149,
0.012563783675432205,
-0.012452814728021622,
-0.005296568386256695,
0.034026093780994415,
0.017383474856615067,
0.0074846562929451466,
-0.015197194181382656,
-0.03381899371743202,
0.034785982221364975,
-0.032624468207359314,
0.039001140743494034,
-0.036255575716495514,
0.028736839070916176,
-0.007856632582843304,
-0.03636037930846214,
-0.02029471844434738,
0.03422175347805023,
-0.00826386921107769,
0.01055597048252821,
-0.05216074362397194,
0.008708667941391468,
0.027556853368878365,
0.01927242800593376,
-0.06481326371431351,
-0.05589773878455162,
0.057655300945043564,
0.0006101666367612779,
-0.023253630846738815,
-0.03670912981033325,
-0.015383998863399029,
-0.011737301014363766,
-0.05504662171006203,
0.025844477117061615,
0.04472026228904724,
0.00069924391573295,
-0.01642622798681259,
-0.008266668766736984,
0.03103051520884037,
0.08198967576026917,
0.000022968510165810585,
-0.019580885767936707,
-0.02158542163670063,
-0.058728501200675964,
0.0004989829030819237,
-0.011101259849965572,
0.06714171171188354,
-0.008083533495664597,
0.016785625368356705,
-0.0050253476947546005,
0.01531141810119152,
0.03790805861353874,
-0.03794848546385765,
-0.004125979728996754,
0.007207638118416071,
0.007813291624188423,
-0.016796531155705452,
-0.024206098169088364,
-0.009358614683151245,
0.016901368275284767,
0.056463975459337234,
-0.0033238762989640236,
-0.020916828885674477,
-0.026846319437026978,
-0.05080211162567139,
0.025171803310513496,
-0.014302583411335945,
-0.02094096690416336,
-0.020498573780059814,
0.05603352561593056,
-0.021476473659276962,
-0.010071173310279846,
0.007708250544965267,
-0.004987383261322975,
0.02800748124718666,
0.0176897831261158,
-0.009820655919611454,
-0.028895366936922073,
-0.005364719312638044,
-0.01715649850666523,
-0.035790782421827316,
-0.05003726854920387,
0.06585032492876053,
0.0586874894797802,
-0.025817178189754486,
0.030360981822013855,
0.004078106954693794,
-0.014792783185839653,
0.013682096265256405,
-0.0045545026659965515,
-0.05088295787572861,
-0.007185047958046198,
-0.019527481868863106,
0.03606845438480377,
-0.03292619436979294,
-0.029550883919000626,
0.008890759199857712,
0.05462970584630966,
-0.0067845797166228294,
-0.018617896363139153,
0.04334624856710434,
-0.004283631220459938,
0.008489386178553104,
0.008118337951600552,
-0.018861789256334305,
0.03348574787378311,
-0.019496049731969833,
0.05369913950562477,
-0.002937139244750142,
-0.01662437431514263,
0.04059069976210594,
-0.008538447320461273,
-0.001303992117755115,
-0.05573660507798195,
0.005133419297635555,
-0.04138314351439476,
0.023511618375778198,
0.011814369820058346,
0.02370770089328289,
-0.012292535044252872,
0.01506197638809681,
0.0076361591927707195,
0.012597071938216686,
0.027393639087677002,
-0.01778700388967991,
-0.008342619985342026,
-0.020919540897011757,
-0.017467359080910683,
-0.011928419582545757,
0.02043943479657173,
0.003557812422513962,
-0.04325481131672859,
-0.008505355566740036,
-0.022027328610420227,
-0.00734164472669363,
0.029312673956155777,
0.013798685744404793,
-0.008970835246145725,
0.0641949325799942,
0.012169448658823967,
0.02168133296072483,
-0.014159461483359337,
0.005153148900717497,
0.10956218093633652,
0.04630323871970177,
0.017835892736911774,
-0.062587670981884,
-0.0037236646749079227,
-0.01702190190553665,
0.0014032158069312572,
-0.02727564051747322,
0.02915983833372593,
0.03356018662452698,
0.0009884826140478253,
0.004888198804110289,
0.026659639552235603,
0.008077537640929222,
0.015972590073943138,
0.06246139854192734,
-0.053537726402282715,
-0.016297781839966774,
-0.0070704128593206406,
0.01735168881714344,
-0.05854349210858345,
0.02563253790140152,
-0.06844869256019592,
0.01860879175364971,
-0.03700442239642143,
-0.04174133390188217,
-0.003737257095053792,
-0.026375489309430122,
0.022090639919042587,
0.000030426212106249295,
-0.057909682393074036,
0.00266233435831964,
-0.014685983769595623,
-0.03731558844447136,
-0.03497800976037979,
0.0411972776055336,
0.030981315299868584,
-0.02717977948486805,
0.026006506755948067,
0.024124545976519585,
0.026226527988910675,
-0.005112490151077509,
0.004871085751801729,
0.05319922789931297,
-0.01918533816933632,
-0.009593022055923939,
-0.008008639328181744,
0.034825410693883896,
-0.007028000894933939,
-0.010255366563796997,
-0.005419617518782616,
-0.03170393407344818,
0.0012321271933615208,
-0.08373215794563293,
-0.02092367224395275,
-0.005581967532634735,
0.045670464634895325,
-0.006431434769183397,
-0.025992807000875473,
0.008374401368200779,
-0.009203024208545685,
-0.013700556941330433,
-0.0029146315064281225,
0.0007818257436156273,
-0.014714526943862438,
-0.036972612142562866,
-0.008153603412210941,
0.008967429399490356,
-0.00900768768042326,
-0.04190690815448761,
-0.01077339705079794,
-0.01636543683707714,
-0.09440147131681442,
0.02759031020104885,
0.018566500395536423,
0.001826647319830954,
0.06031985208392143,
-0.003064193297177553,
0.001621511415578425,
0.01166252326220274,
-0.0709100142121315,
0.03277800604701042,
0.003307004924863577,
-0.01989157125353813,
-0.012621022760868073,
0.004813972860574722,
0.015537275932729244,
0.07430890202522278,
-0.02819555252790451,
-0.019206814467906952,
-0.04190494120121002,
0.0030935273971408606,
0.014321878552436829,
-0.04980969801545143,
-0.039878521114587784,
0.009420079179108143,
-0.03047659434378147,
-0.03322024270892143,
-0.019063139334321022,
0.03781934082508087,
0.06479918956756592,
0.024085909128189087,
-0.028190163895487785,
-0.0005234176642261446,
-0.01905953884124756,
0.02656317874789238,
0.002696624957025051,
-0.04625292494893074,
-0.03205765038728714,
0.032476216554641724,
0.005637821275740862,
-0.026653410866856575,
-0.03760853782296181,
-0.05033909156918526,
0.02410222589969635,
-0.010934583842754364,
0.012194228358566761,
-0.026332003995776176,
-0.012981405481696129,
-0.008781172335147858,
0.018778227269649506,
-0.02944205515086651,
-0.003386810189113021,
-0.04585372284054756,
-0.01193839218467474,
-0.0022256432566791773,
0.0267751794308424,
-0.028149140998721123,
0.016790449619293213,
-0.03313388302922249,
-0.053788550198078156,
0.029340481385588646,
-0.019003335386514664,
-0.0036998512223362923,
0.003017500275745988,
0.05540897324681282,
-0.009014767594635487,
0.028745152056217194,
-0.02268468588590622,
-0.017279885709285736,
0.02803288772702217,
-0.005715430714190006,
-0.02828933857381344,
0.010746295563876629,
0.005110161378979683,
-0.019382186233997345,
0.003330558305606246,
-0.0035518105141818523,
0.009065931662917137,
0.08302893489599228,
-0.031019069254398346,
0.043232325464487076,
-0.005734387785196304,
-0.03961198031902313,
-0.009155236184597015,
-0.029488515108823776,
0.03373751789331436,
-0.03307383507490158,
0.008356676436960697,
0.05124658718705177,
0.044951315969228745,
0.01719304546713829,
-0.025888655334711075,
0.0232815220952034,
-0.005625105928629637,
-0.023138178512454033,
0.015835080295801163,
0.018955625593662262,
0.014948492869734764,
0.057582952082157135,
-0.04717402160167694,
0.045284613966941833,
0.01913098432123661,
0.00013404736819211394,
-0.10503214597702026,
0.04152200371026993,
-0.020116697996854782,
0.00683900061994791,
0.021417997777462006,
-0.047102972865104675,
0.01503395102918148,
0.047774046659469604,
-0.03998051956295967,
-0.025628283619880676,
-0.03839436173439026,
0.0009779715910553932,
-0.04734604060649872,
-0.02195833809673786,
0.0012225311947986484,
0.07628463208675385,
0.03807082027196884,
0.03467195853590965,
0.026571737602353096,
0.009949345141649246,
0.012611236423254013,
0.005187275819480419,
-0.0159579087048769,
0.03300116956233978,
-0.030289454385638237,
0.0179902371019125,
0.024069443345069885,
-0.018132664263248444,
-0.028803864493966103,
0.03186537325382233,
-0.002193039283156395,
0.023966064676642418,
-0.007551414892077446,
0.019563423469662666,
-0.002799566136673093,
0.05198494344949722,
0.032247111201286316,
0.014664781279861927,
0.006618870422244072,
0.03943286091089249,
0.030075877904891968,
0.03925315663218498,
-0.024328386411070824,
-0.006140078883618116,
0.011695283465087414,
-0.05033280327916145,
-0.01921815052628517,
0.011356925591826439,
-0.00502910977229476,
0.010670196264982224,
-0.0022988978307694197,
-0.044301193207502365,
0.02345600165426731,
-0.006398831028491259,
0.029208434745669365,
-0.0317942313849926,
0.0017093170899897814,
0.05630666762590408,
0.009941226802766323,
-0.019450001418590546,
-0.005071735940873623,
0.022611424326896667,
-0.015111311338841915,
-0.018179992213845253,
-0.022120708599686623,
-0.0031070143450051546,
-0.05406568571925163,
-0.02434208057820797,
0.02652687206864357,
-0.029570577666163445,
-0.008428176864981651,
-0.04651116207242012,
-0.011813266202807426,
0.04345330595970154,
0.06884564459323883,
0.03142378851771355,
0.00466596893966198,
-0.03364822641015053,
-0.0012935184640809894,
-0.03883045166730881,
0.05066453292965889,
0.003477575723081827,
0.01139632798731327,
-0.02720107138156891,
-0.012216438539326191,
0.008577721193432808,
0.012485005892813206,
0.06849798560142517,
-0.05277632176876068,
0.007097920868545771,
0.012647373601794243,
0.003921933472156525,
0.03394215926527977,
-0.01663208194077015,
-0.006539599969983101,
-0.012785693630576134,
-0.05659325048327446,
-0.001559780677780509,
-0.019713405519723892,
-0.017334477975964546,
0.01572878658771515,
0.014220135286450386,
-0.017828049138188362,
0.033734455704689026,
0.010418209247291088,
-0.03257090598344803,
0.02978830598294735,
0.03205209970474243,
-0.023228885605931282,
0.07040062546730042,
-0.03697346895933151,
0.009667228907346725,
0.006772801745682955,
-0.001273751724511385,
-0.06332273036241531,
0.04382658749818802,
-0.012833144515752792,
0.004565070848912001,
-0.012265835888683796,
-0.05811963602900505,
0.035404983907938004,
-0.04390326142311096,
0.01972111128270626,
0.01734894886612892,
-0.023880815133452415,
-0.029814954847097397,
0.03398910164833069,
0.011160043999552727,
0.051924556493759155,
-0.01905791275203228,
-0.009148110635578632,
0.014632640406489372,
0.0038972734473645687,
-0.003874349407851696,
0.01720598340034485,
0.038622695952653885,
0.013317383825778961,
0.012988337315618992,
0.021086301654577255,
0.010830679908394814,
0.021290617063641548,
0.015468858182430267,
0.02027948573231697,
-0.023648668080568314,
-0.04479417949914932,
0.0064752777107059956,
-0.05902481824159622,
-0.015179676003754139,
0.00773911876603961,
0.00531460577622056,
0.07485125958919525,
-0.005298111587762833,
0.04328816011548042,
-0.025897439569234848,
0.029342960566282272,
-0.003038454335182905,
-0.015286333858966827,
0.022213701158761978,
0.03408127650618553,
0.006098911166191101,
-0.021300118416547775,
0.005271575879305601,
-0.005953019019216299,
0.02995762787759304,
-0.014332386665046215,
0.03587799891829491,
0.021456172689795494,
-0.022944094613194466,
-0.04925176128745079,
-0.013943441212177277,
0.006930883973836899,
-0.017092492431402206,
0.045313604176044464,
0.06934356689453125,
-0.004970234353095293,
0.028670083731412888,
-0.012340954504907131,
-0.02501724660396576,
0.08239580690860748,
-0.07929586619138718,
0.008962788619101048,
-0.02102658711373806,
0.019536690786480904,
-0.009465854614973068,
-0.009740451350808144
] |
<p>Amorphous metals are often referred to as metallic glasses due to their quenched atomic disorder. Do they fracture in the same fashion as silicate glasses? If not, what failure mode(s) do they have?</p> | 1,581 | [
-0.047185253351926804,
-0.03775688633322716,
0.03525036945939064,
-0.04000477120280266,
0.04941749572753906,
0.05806208774447441,
-0.04276040196418762,
-0.03157157823443413,
-0.000053484411182580516,
-0.03747592493891716,
0.060318607836961746,
0.01874617673456669,
0.012719953432679176,
0.0077344924211502075,
0.01315785851329565,
-0.007764967158436775,
0.030173897743225098,
-0.0411439910531044,
0.007961881347000599,
-0.005515845958143473,
-0.007234674412757158,
-0.023212091997265816,
-0.0230597872287035,
0.012398876249790192,
-0.02111409418284893,
-0.01853174902498722,
0.008014167658984661,
0.018097491934895515,
0.02571258507668972,
0.012143420986831188,
-0.03007071278989315,
-0.019590312615036964,
0.022733360528945923,
0.02246527187526226,
0.00008506705489708111,
-0.006862441543489695,
-0.02986169420182705,
-0.030977660790085793,
-0.055931463837623596,
0.0077583822421729565,
-0.038905128836631775,
0.0006022847373969853,
0.018926935270428658,
0.05018632486462593,
-0.01608891971409321,
-0.0388682596385479,
0.0000072632506089576054,
-0.042720381170511246,
-0.005383440293371677,
-0.020318299531936646,
0.04214485362172127,
-0.03796279802918434,
0.0398549884557724,
0.026383258402347565,
0.005398911889642477,
0.005778325721621513,
0.06972074508666992,
0.06438294053077698,
0.0027324333786964417,
-0.06397359073162079,
-0.040276963263750076,
-0.04109804332256317,
0.0015235323226079345,
-0.017345380038022995,
-0.04823528602719307,
0.042785122990608215,
-0.03375036269426346,
-0.08574646711349487,
0.00150208396371454,
0.05690159648656845,
0.01595170423388481,
0.02734800986945629,
0.02561773918569088,
-0.027489716187119484,
0.01405106671154499,
-0.009486195631325245,
-0.014298456721007824,
-0.004379067569971085,
0.057463087141513824,
0.05959734693169594,
0.01479332149028778,
0.033597543835639954,
0.0039035070221871138,
0.017689766362309456,
-0.024771209806203842,
-0.020692327991127968,
0.10106305032968521,
-0.011590532958507538,
0.009328966960310936,
-0.0019952936563640833,
-0.004559303633868694,
0.013321206904947758,
-0.010432153940200806,
0.025209682062268257,
-0.04021530970931053,
-0.015525707975029945,
-0.015367786400020123,
0.05828496441245079,
-0.010223421268165112,
0.013715500943362713,
0.0062022581696510315,
0.0031769410707056522,
0.046159353107213974,
0.06498155742883682,
0.009359579533338547,
-0.06697001308202744,
0.004197238478809595,
0.01776839978992939,
-0.009670519270002842,
0.0033880469854921103,
-0.0012241981457918882,
0.021965162828564644,
0.019531456753611565,
-0.008342539891600609,
0.038372986018657684,
-0.004226530436426401,
-0.00521090067923069,
-0.041071951389312744,
0.03349629044532776,
0.11379758268594742,
0.029006963595747948,
-0.018223557621240616,
-0.002263816772028804,
-0.012817255221307278,
-0.06790447980165482,
0.0010174065828323364,
-0.006528390571475029,
-0.010195404291152954,
-0.014027618803083897,
0.019767900928854942,
-0.03133416548371315,
0.0035042620729655027,
0.023676177486777306,
-0.03123621828854084,
0.050151973962783813,
-0.018220020458102226,
-0.0988735631108284,
-0.03950849547982216,
0.04844851419329643,
0.012487863190472126,
-0.007924780249595642,
-0.042414531111717224,
0.060199882835149765,
-0.005626987665891647,
0.05999812111258507,
0.029694514349102974,
0.01952514238655567,
-0.005202712491154671,
0.025519927963614464,
0.020965930074453354,
-0.04851241782307625,
-0.0033179710153490305,
0.04571394622325897,
-0.021313413977622986,
0.02631189115345478,
-0.0668448954820633,
0.00950452871620655,
0.03255552425980568,
0.01720922812819481,
-0.047312505543231964,
0.046309396624565125,
-0.0337216779589653,
0.0027886393945664167,
0.028615009039640427,
0.023459656164050102,
0.008211448788642883,
0.04550741985440254,
0.020780079066753387,
0.05473233386874199,
0.04954708367586136,
0.021954337134957314,
-0.0025502427015453577,
0.0476350411772728,
0.048938021063804626,
0.02644946798682213,
-0.005405434872955084,
0.004586110357195139,
-0.018824735656380653,
0.027902288362383842,
0.03608519583940506,
-0.02457812801003456,
0.007997089996933937,
-0.003282971680164337,
0.017933521419763565,
0.0019022244960069656,
0.06879846751689911,
0.03624901920557022,
-0.012818267568945885,
-0.024665994569659233,
-0.04118168726563454,
-0.018676893785595894,
-0.03684989735484123,
0.05524398386478424,
-0.004008352290838957,
-0.006331842392683029,
0.026080774143338203,
0.012123466469347477,
0.0057561094872653484,
0.000467020261567086,
-0.06270361691713333,
-0.009523777291178703,
0.023478494957089424,
-0.012567467987537384,
-0.027575388550758362,
0.030653607100248337,
0.07059729099273682,
0.008667048066854477,
-0.012434977106750011,
0.025032300502061844,
-0.04750695824623108,
-0.018252113834023476,
-0.0006046592607162893,
-0.022059669718146324,
-0.006048421375453472,
-0.013464407064020634,
-0.05530979111790657,
0.031563371419906616,
-0.00700866524130106,
0.0020150579512119293,
0.025848116725683212,
0.008403509855270386,
0.046956658363342285,
0.023555759340524673,
0.037421610206365585,
0.004175607580691576,
0.023056449368596077,
-0.012609055265784264,
-0.022820310667157173,
-0.042152952402830124,
0.002405986888334155,
-0.06580094248056412,
-0.013411962427198887,
0.059713974595069885,
0.04397202283143997,
-0.0350743792951107,
0.041183024644851685,
0.0015660848002880812,
0.03832366690039635,
0.0438263900578022,
0.00676434300839901,
-0.06360521912574768,
-0.013859909027814865,
0.013971556909382343,
0.0017701108008623123,
0.017001362517476082,
0.010251987725496292,
-0.04199749231338501,
0.0250692218542099,
-0.0024910890497267246,
-0.01282197330147028,
0.01405415777117014,
0.05163362994790077,
-0.006453963462263346,
-0.010258819907903671,
0.018095701932907104,
-0.0951666310429573,
0.03125875070691109,
-0.02269960194826126,
-0.03801312670111656,
0.035544559359550476,
0.02150573581457138,
0.007214595563709736,
-0.016184786334633827,
-0.005339824128895998,
0.0201078113168478,
0.031930964440107346,
-0.023509535938501358,
-0.03978555276989937,
0.023526350036263466,
-0.001500026206485927,
-0.010355371981859207,
-0.05672275647521019,
0.029193906113505363,
0.015685435384511948,
0.016851963475346565,
0.012439592741429806,
-0.0405876524746418,
0.032011669129133224,
-0.01763680949807167,
-0.025921527296304703,
0.00948286522179842,
-0.03740957751870155,
-0.029538718983530998,
-0.012738737277686596,
-0.02457541599869728,
0.009972857311367989,
0.021784264594316483,
-0.01550096832215786,
0.00816923938691616,
0.030937423929572105,
-0.0011882546823471785,
-0.012481972575187683,
0.008917590603232384,
-0.04166347160935402,
0.018923716619610786,
0.0030536935664713383,
-0.023150814697146416,
-0.03780386969447136,
0.022852638736367226,
-0.003727592760697007,
0.013175921514630318,
0.010574434883892536,
-0.02500709518790245,
-0.01974453777074814,
-0.01477513462305069,
-0.010822859592735767,
-0.010047330521047115,
0.010690758936107159,
-0.03314432129263878,
0.018419764935970306,
0.06892476230859756,
-0.07283909618854523,
0.017574438825249672,
-0.03957469016313553,
-0.041044682264328,
0.013647879473865032,
-0.08722952008247375,
-0.0091781010851264,
-0.013530016876757145,
-0.003927378449589014,
0.03503083437681198,
0.00633849436417222,
-0.04872279614210129,
0.018147779628634453,
-0.04186826944351196,
-0.0023418136406689882,
-0.022547302767634392,
0.023994607850909233,
0.047435462474823,
0.0054206629283726215,
0.005313406698405743,
0.028445851057767868,
0.028001436963677406,
0.008998102508485317,
0.019686870276927948,
-0.02443377487361431,
-0.0017320469487458467,
0.055356405675411224,
-0.037494957447052,
0.002995177870616317,
0.03856955096125603,
-0.025485755875706673,
0.008652164600789547,
0.001300245407037437,
0.05660761147737503,
0.054853424429893494,
-0.03516257926821709,
0.04528833553195,
-0.042426954954862595,
-0.015607200562953949,
-0.06146647781133652,
0.0351412408053875,
-0.00018018181435763836,
-0.043330300599336624,
-0.0008717853343114257,
0.02408616431057453,
0.03877294063568115,
-0.003367027034983039,
-0.0027741300873458385,
0.023494428023695946,
0.021338647231459618,
-0.03789632394909859,
-0.019462011754512787,
0.003301171585917473,
-0.026882853358983994,
0.014525885693728924,
-0.01790943183004856,
0.002994330832734704,
0.0233480054885149,
0.003027200698852539,
0.04938726872205734,
-0.02160562388598919,
-0.036615706980228424,
0.008833324536681175,
-0.06409955024719238,
0.0033805265557020903,
0.006893012672662735,
0.03125296160578728,
0.0007000908371992409,
0.03267630934715271,
0.054306838661432266,
0.011430162936449051,
0.02028551697731018,
-0.04048685356974602,
-0.07785466313362122,
0.0006560533074662089,
-0.036601703613996506,
-0.027143431827425957,
-0.02639489434659481,
0.008674253709614277,
-0.013094395399093628,
-0.05050291121006012,
-0.02727915160357952,
-0.018014958128333092,
-0.028969183564186096,
-0.031403228640556335,
0.002893970813602209,
-0.04492605850100517,
-0.04959099367260933,
0.00712073827162385,
-0.021496305242180824,
0.027537744492292404,
-0.02726029045879841,
0.02538912184536457,
0.000970390799921006,
0.011497682891786098,
0.00965513102710247,
0.008265510201454163,
0.005587254650890827,
0.00584873603656888,
0.048064060509204865,
0.008460098877549171,
-0.027432482689619064,
0.007524622138589621,
-0.016140077263116837,
0.020074184983968735,
0.03060307167470455,
0.03740008547902107,
-0.0018583853961899877,
-0.03341056406497955,
-0.04345027729868889,
-0.02152458392083645,
-0.015532959252595901,
0.016658637672662735,
-0.009937538765370846,
0.007448805961757898,
0.012497637420892715,
-0.027497177943587303,
-0.05145400017499924,
0.036059390753507614,
0.01622709631919861,
0.02998333051800728,
-0.008794574066996574,
-0.03312671184539795,
-0.06042838096618652,
-0.024424826726317406,
-0.00584061723202467,
0.029101327061653137,
0.032596223056316376,
-0.02193235233426094,
0.06248610094189644,
0.03342865779995918,
-0.018888328224420547,
-0.035576846450567245,
-0.004436274990439415,
0.00007002813799772412,
0.03209488093852997,
0.020063310861587524,
-0.009835532866418362,
0.014201639220118523,
0.04763379693031311,
0.05208052322268486,
0.037269897758960724,
-0.009672713465988636,
-0.09314355999231339,
0.057890161871910095,
0.03205905854701996,
0.0353732630610466,
-0.02671010047197342,
-0.022326037287712097,
-0.03369676321744919,
-0.05707474797964096,
0.04237227514386177,
-0.031738266348838806,
0.007265676744282246,
-0.027569154277443886,
0.019772257655858994,
-0.0701884776353836,
-0.039714932441711426,
-0.015506649389863014,
-0.001305416808463633,
0.03383580595254898,
0.01976419985294342,
-0.04028144106268883,
0.01186249777674675,
-0.026763828471302986,
0.03908291086554527,
0.00995439663529396,
0.022189436480402946,
0.010531255044043064,
0.000613766664173454,
-0.034326791763305664,
0.017044764012098312,
0.0004034528974443674,
-0.058637212961912155,
-0.0036857682280242443,
-0.014154222793877125,
-0.003938770387321711,
0.028602425009012222,
-0.03244113549590111,
-0.023516124114394188,
0.055242870002985,
0.0018469833303242922,
-0.015319055877625942,
0.014921512454748154,
-0.0054977149702608585,
0.010940401814877987,
0.003354485146701336,
0.00003715790808200836,
0.04542621225118637,
0.025285225361585617,
0.0025429250672459602,
0.0023334643337875605,
-0.0473552905023098,
0.04376088082790375,
-0.050746023654937744,
0.01761813275516033,
-0.012382586486637592,
0.00036681588971987367,
-0.01973104104399681,
0.03955942019820213,
0.009547736495733261,
0.02889385260641575,
-0.021532805636525154,
-0.019581817090511322,
0.007803978864103556,
-0.007508177775889635,
0.02779555134475231,
-0.03460137918591499,
-0.008214988745748997,
0.043292976915836334,
-0.030356358736753464,
0.006519398186355829,
0.004636554047465324,
-0.029755644500255585,
0.02421870455145836,
0.029098307713866234,
-0.02112891711294651,
0.017771946266293526,
-0.05730719119310379,
-0.015578236430883408,
0.01243791077286005,
-0.06076845899224281,
0.0328669436275959,
-0.019660502672195435,
0.006096756551414728,
0.005442311055958271,
-0.024300379678606987,
0.04996195808053017,
-0.011181307025253773,
-0.022507600486278534,
0.033111099153757095,
-0.044731318950653076,
0.06423593312501907,
-0.01301503460854292,
-0.026012511923909187,
-0.08684609085321426,
-0.029514163732528687,
-0.000892761570867151,
0.01646355725824833,
-0.04604418948292732,
-0.015582296065986156,
0.00950299110263586,
-0.0015731198946014047,
-0.04053247720003128,
0.008814333006739616,
0.03265353664755821,
-0.04431046172976494,
-0.0004564464034046978,
-0.015115979127585888,
-0.0022011527325958014,
0.07292205095291138,
0.0016259686090052128,
-0.021949654445052147,
0.0065924618393182755,
-0.033054083585739136,
-0.024196941405534744,
-0.034135669469833374,
0.041670750826597214,
-0.018506983295083046,
0.006733826827257872,
-0.010876340791583061,
-0.027507303282618523,
0.03614797443151474,
-0.006844759453088045,
0.00911527406424284,
0.018817882984876633,
-0.004127807915210724,
-0.010623076930642128,
-0.008155524730682373,
0.025164641439914703,
0.042072635143995285,
0.0331278033554554,
0.004578062333166599,
0.02153223752975464,
-0.01831187680363655,
0.01719254069030285,
0.04172913730144501,
0.011818289756774902,
0.024461135268211365,
0.043665267527103424,
0.07458969205617905,
-0.04207205772399902,
0.040915630757808685,
0.006035025231540203,
-0.06387808173894882,
0.012855938635766506,
-0.0262936782091856,
0.005644102580845356,
0.006173698231577873,
0.003466955153271556,
-0.028063518926501274,
-0.04727470129728317,
-0.0022320435382425785,
-0.030898822471499443,
0.04616059735417366,
-0.011565797962248325,
0.016152746975421906,
0.010285848751664162,
-0.03017314523458481,
0.01005809847265482,
-0.040134262293577194,
-0.0006027990020811558,
0.04068310558795929,
-0.02673180028796196,
0.04925788566470146,
-0.0009797585662454367,
0.015113148838281631,
0.027406634762883186,
0.0452316552400589,
-0.04076419770717621,
0.01351348776370287,
0.016608359292149544,
0.0037383507005870342,
0.01618213951587677,
-0.05712403729557991,
-0.05060611665248871,
0.04890723153948784,
-0.08970777690410614,
0.028658533468842506,
-0.02534169889986515,
-0.010185514576733112,
0.016453873366117477,
0.002714816015213728,
0.04257101193070412,
-0.013160099275410175,
-0.014061550609767437,
-0.040288060903549194,
0.02458200603723526,
-0.0004281908622942865,
0.03188126161694527,
0.010411451570689678,
0.020867062732577324,
-0.009105770848691463,
0.01197809912264347,
0.003098418703302741,
0.013861614279448986,
-0.07831811159849167,
-0.02535952441394329,
0.015509190037846565,
-0.0005362433148548007,
0.028943346813321114,
-0.017341138795018196,
-0.03331983461976051,
0.025607002899050713,
-0.014470318332314491,
0.024957651272416115,
0.002111930400133133,
0.03228328004479408,
0.00760289141908288,
0.055232442915439606,
-0.03735604137182236,
0.02720257267355919,
0.02934916317462921,
0.019251542165875435,
0.12090715765953064,
0.07635734975337982,
0.02614164911210537,
-0.045088160783052444,
-0.002090411027893424,
-0.027328282594680786,
0.00801415741443634,
-0.016077235341072083,
0.0055063338950276375,
-0.007828754372894764,
0.02895042672753334,
0.04508528485894203,
0.04211728274822235,
-0.017370281741023064,
0.0028688355814665556,
0.04272764176130295,
-0.004782362375408411,
0.022646650671958923,
-0.014078709296882153,
0.03526591509580612,
-0.006253599189221859,
0.005168667994439602,
-0.002030649222433567,
0.020866088569164276,
-0.02988441288471222,
-0.030430898070335388,
-0.03881467878818512,
-0.019849279895424843,
0.03548535704612732,
0.017887311056256294,
-0.014547869563102722,
-0.02509419433772564,
0.032312992960214615,
0.03189804032444954,
-0.005010073538869619,
-0.014658907428383827,
0.019239775836467743,
0.020586537197232246,
0.023888835683465004,
0.0017980351112782955,
0.01687483675777912,
0.0013295805547386408,
-0.0023174581583589315,
0.05484778434038162,
-0.06235072389245033,
-0.01734127849340439,
-0.016327276825904846,
-0.011857968755066395,
-0.019356001168489456,
0.00754254637286067,
-0.024924132972955704,
-0.0046887085773050785,
0.022038176655769348,
0.022028794512152672,
-0.02120332419872284,
0.003130268771201372,
0.018651189282536507,
-0.029306380078196526,
-0.0489080585539341,
-0.007467938121408224,
0.002648691413924098,
-0.006174345500767231,
0.01843876577913761,
-0.014407151378691196,
-0.01343569066375494,
0.025514179840683937,
-0.006304888054728508,
-0.0052162110805511475,
-0.039585407823324203,
-0.012061401270329952,
-0.06453438103199005,
-0.0027277616318315268,
-0.013982213102281094,
0.024480417370796204,
0.013808269053697586,
0.04853257164359093,
0.07896407693624496,
0.0042260512709617615,
0.003451506607234478,
-0.003991483245044947,
-0.03300091624259949,
0.05865338072180748,
-0.031670212745666504,
-0.006408250890672207,
-0.03478078916668892,
-0.014081096276640892,
0.037441641092300415,
-0.0010335649130865932,
-0.009248806163668633,
0.017950749024748802,
-0.013003679923713207,
0.015642020851373672,
0.03841370716691017,
-0.01618683896958828,
-0.0008496033260598779,
-0.0043470351956784725,
-0.03756338730454445,
0.0064668008126318455,
-0.027520107105374336,
0.03572673723101616,
0.024107061326503754,
-0.0065566967241466045,
0.013445230200886726,
0.024238023906946182,
-0.018375586718320847,
0.008078619837760925,
0.023922909051179886,
-0.008157041855156422,
-0.02646789140999317,
0.006708845961838961,
0.024236585944890976,
-0.004585782531648874,
-0.054088182747364044,
-0.0156887024641037,
-0.01064504124224186,
0.00561129953712225,
0.019411146640777588,
-0.021208958700299263,
0.010126275941729546,
-0.024493899196386337,
0.014554904773831367,
-0.02092001959681511,
-0.011483930982649326,
-0.035981763154268265,
-0.018451854586601257,
0.02744300849735737,
-0.00733905378729105,
-0.00749894417822361,
0.0171023178845644,
0.007112625986337662,
-0.000364607636583969,
0.026637325063347816,
0.021477369591593742,
0.006001764442771673,
0.009378723800182343,
0.021856574341654778,
-0.03380529209971428,
0.04986536502838135,
-0.03184458985924721,
-0.012763136066496372,
0.03556963801383972,
-0.00738913519307971,
-0.062393587082624435,
0.01412874087691307,
-0.03166364133358002,
0.008902361616492271,
0.020824609324336052,
-0.004256086889654398,
-0.0007353540859185159,
0.06956836581230164,
-0.02914665825664997,
-0.014685326255857944,
0.027272190898656845,
-0.00035624534939415753,
0.014307204633951187,
0.01482613105326891,
0.00396388117223978,
0.004431559704244137,
-0.0077949934639036655,
0.061322715133428574,
0.03652464970946312,
0.01472428347915411,
0.03961901739239693,
0.03315292298793793,
-0.006150965578854084,
0.005922092590481043,
0.026218507438898087,
0.05074872821569443,
0.021220318973064423,
0.004323923494666815,
0.020318802446126938,
0.06454252451658249,
0.04534522071480751,
0.0012232178123667836,
-0.07437590509653091,
-0.0033955101389437914,
0.01649126224219799,
0.03230476379394531,
-0.003551787231117487,
-0.02071157842874527,
0.016244791448116302,
0.03334207832813263,
-0.046105049550533295,
-0.01008802093565464,
-0.05487404018640518,
-0.08397961407899857,
-0.06001955643296242,
-0.005195662844926119,
-0.0102692237123847,
0.02925865352153778,
0.016179412603378296,
0.03442346677184105,
0.04161302372813225,
0.038453347980976105,
-0.042287737131118774,
-0.002270401455461979,
-0.004693931434303522,
0.01251248735934496,
-0.004787753336131573,
-0.010091155767440796,
0.06657740473747253,
-0.01990092732012272,
-0.047928307205438614,
0.01831125281751156,
0.0016289318446069956,
0.021814141422510147,
0.061791401356458664,
-0.020820898935198784,
0.00008559189882362261,
-0.014537069015204906,
-0.040091414004564285,
-0.027368534356355667,
-0.0270547978579998,
0.015007425099611282,
-0.009614577516913414,
0.03773123025894165,
-0.02212325856089592,
0.0021331452298909426,
0.009816358797252178,
-0.014314993284642696,
-0.00969485379755497,
0.008737997151911259,
-0.016395462676882744,
-0.0032468202989548445,
-0.033998120576143265,
0.021109899505972862,
0.04677153751254082,
0.0011400820221751928,
-0.009696017019450665,
-0.0237362552434206,
-0.02097729966044426,
0.014530411921441555,
0.014761077240109444,
0.0022756317630410194,
0.01565835066139698,
-0.006075428333133459,
0.0029961937107145786,
-0.021678289398550987,
0.04116570204496384,
-0.06340637803077698,
-0.011379355564713478,
-0.00971527025103569,
0.0061154114082455635,
-0.0007936375914141536,
-0.02563335932791233,
0.019012657925486565,
0.0019187834113836288,
0.08300077170133591,
0.008636131882667542,
0.0355985164642334,
0.03626289963722229,
-0.05300780013203621,
-0.04318604618310928,
-0.0650886669754982,
0.016671234741806984,
-0.05752742290496826,
-0.031863536685705185,
-0.011014857329428196,
-0.04596194624900818,
-0.018274007365107536,
0.016018588095903397,
0.0441860668361187,
-0.015641581267118454,
0.03649669140577316,
-0.0026604807935655117,
-0.007410464342683554,
0.02483934722840786,
-0.06115034967660904,
-0.0059262351132929325,
0.0006724034319631755,
0.002104708459228277,
-0.0211214330047369,
0.016724856570363045,
-0.001207987079396844,
0.003183971857652068,
0.05775342136621475,
-0.01165755558758974,
-0.028194237500429153,
0.01285806018859148,
-0.012245574966073036,
0.058916520327329636,
0.01784376986324787,
-0.019861888140439987,
0.10112535208463669,
-0.05928346887230873,
-0.0011319038458168507,
0.0062570711597800255,
0.012795811519026756,
-0.014351299032568932,
0.03973068669438362,
-0.024185936897993088,
0.013424118049442768,
-0.005922012962400913,
-0.00936434417963028,
0.010629692114889622,
-0.0376945398747921,
0.020102370530366898,
0.0024730197619646788,
-0.0444503054022789,
-0.007212159689515829,
-0.01310058869421482,
0.0014470824971795082,
0.04784008860588074,
-0.006909704767167568,
-0.01527944952249527,
0.03185025975108147,
0.01932304911315441,
-0.04056013748049736,
0.05212847888469696,
0.02222900651395321,
0.02219776250422001,
0.014677462168037891,
0.019744455814361572,
-0.04860306158661842,
-0.003163207322359085,
-0.023541055619716644,
0.010305093601346016,
-0.05215064436197281,
-0.03225662559270859,
0.02193213254213333,
-0.012515908107161522,
0.032115887850522995,
0.023306241258978844,
-0.015699222683906555,
0.08363961428403854,
-0.020200110971927643,
0.008514754474163055,
-0.033406101167201996,
0.006376034114509821,
0.0073331790044903755,
0.027194179594516754,
0.019923288375139236,
0.006556963548064232,
0.020604314282536507,
0.015441848896443844,
0.002962138270959258,
0.06265892088413239,
0.06645648181438446,
-0.04579150676727295,
0.018999332562088966,
-0.012779123149812222,
-0.010089355520904064,
-0.05595275014638901,
-0.01989390142261982,
-0.06109737977385521,
0.0032868636772036552,
-0.037492912262678146,
0.006691275164484978,
0.0017840178916230798,
-0.021875858306884766,
0.03899601474404335,
-0.012006907723844051,
0.010391968302428722,
-0.07723559439182281,
0.004722184967249632,
-0.04126984253525734,
0.023171285167336464,
-0.035704270005226135,
0.024227892979979515
] |
<p>When comparing two light sources, for example, a light bulb at 20W and a light bulb at 100W, what is it about the incoming light that makes the latter look brighter than the former? Are there different reasons why different light sources looks different in brightness (High five for cramming three instances of "different" in the same sentence)? For example, in <a href="http://physics.stackexchange.com/questions/3145/sensitivity-of-eye">this</a> thread, it is stated that the human eye is most sensitive around 555nm, something that I guess translates to meaning that given a light of the same intensity (whatever that means, hence my question), it is going to be perceived as most bright when hitting 555nm. Does this question have different answers depending on if you're seeing light as a particle vs a wave?</p> | 1,582 | [
-0.0534416101872921,
-0.05945034325122833,
0.01423085667192936,
-0.022615110501646996,
0.030856924131512642,
0.020802149549126625,
-0.004969482775777578,
-0.055483244359493256,
0.023975500836968422,
-0.021664541214704514,
0.04864929988980293,
0.06399065256118774,
0.06463180482387543,
0.03957032784819603,
0.028746388852596283,
-0.010668713599443436,
0.021130787208676338,
-0.03135880455374718,
-0.031359534710645676,
0.0091391047462821,
0.007727654650807381,
0.029960984364151955,
0.03123554401099682,
-0.010140679776668549,
-0.052622389048337936,
0.031146332621574402,
0.02663382515311241,
0.03823113441467285,
0.01549615804105997,
0.010478605516254902,
0.005953483749181032,
-0.031142927706241608,
-0.0017704026540741324,
0.0332021564245224,
0.020554441958665848,
-0.0032298380974680185,
0.006822946481406689,
-0.0014622262679040432,
-0.036250922828912735,
0.013674275018274784,
-0.014413679018616676,
-0.028105759993195534,
0.01623900979757309,
0.02096673473715782,
-0.04459020867943764,
-0.016608653590083122,
0.004655104596167803,
-0.05961328744888306,
0.0250544473528862,
-0.07389876991510391,
0.051515430212020874,
0.03196931630373001,
0.02512574940919876,
0.04191270098090172,
-0.026765398681163788,
0.006535270716995001,
0.057348135858774185,
0.07208709418773651,
-0.020180851221084595,
-0.06236150115728378,
-0.016031643375754356,
0.015303706750273705,
-0.02763446979224682,
-0.00284515880048275,
-0.017278889194130898,
0.02415965311229229,
-0.011005513370037079,
-0.02166266180574894,
0.03639816492795944,
0.023843074217438698,
0.002624851418659091,
0.010354515165090561,
0.06287538260221481,
-0.016384871676564217,
-0.015503904782235622,
-0.03881709650158882,
0.04054122045636177,
0.0292891226708889,
0.059497665613889694,
0.04000312089920044,
-0.01460333913564682,
-0.012761128135025501,
-0.035342056304216385,
0.04366309568285942,
0.025770112872123718,
0.010279785841703415,
0.08269952982664108,
-0.01970108039677143,
0.005495269782841206,
0.045537203550338745,
-0.012864100746810436,
0.05095527321100235,
0.018646152690052986,
0.01977638155221939,
0.0034702590201050043,
0.01341161411255598,
-0.027941828593611717,
0.027396198362112045,
0.0027358352672308683,
-0.005688478704541922,
0.027064120396971703,
0.02536160871386528,
0.0492560938000679,
0.03390060365200043,
-0.022429214790463448,
-0.017735933884978294,
-0.013647893443703651,
0.011172490194439888,
-0.005375316832214594,
0.018032962456345558,
-0.02676134929060936,
0.004055745434015989,
-0.004047652240842581,
0.010764716193079948,
0.02244557812809944,
-0.041273973882198334,
0.004496395122259855,
-0.027806073427200317,
0.07541001588106155,
0.037759583443403244,
0.017838692292571068,
-0.03009018488228321,
0.03526122495532036,
-0.02604367397725582,
-0.037388816475868225,
-0.00512212747707963,
0.019556747749447823,
0.005102729424834251,
-0.04526597633957863,
0.03641366586089134,
-0.034763239324092865,
-0.004856076557189226,
0.004494620952755213,
-0.011373136192560196,
0.0339035801589489,
-0.011010278947651386,
-0.09374041855335236,
-0.052796922624111176,
0.03029446303844452,
0.015875760465860367,
-0.05301763117313385,
-0.06849715858697891,
0.025999663397669792,
0.031211400404572487,
0.04846353456377983,
-0.02207198552787304,
-0.006647962145507336,
-0.028646603226661682,
0.029338188469409943,
0.005792876705527306,
-0.036045484244823456,
-0.008829869329929352,
0.0058599840849637985,
-0.017604131251573563,
0.02729042060673237,
-0.054925061762332916,
-0.006238583009690046,
0.02815210074186325,
0.00002472423693689052,
-0.017289983108639717,
0.049412306398153305,
0.015514876693487167,
0.012593675404787064,
0.037636999040842056,
0.028134876862168312,
-0.006028522737324238,
0.08560696244239807,
0.01942894048988819,
0.01157530676573515,
0.05367959290742874,
-0.012941047549247742,
0.012732157483696938,
0.00624045729637146,
-0.003141683991998434,
0.03537314385175705,
-0.03656955063343048,
-0.011287014931440353,
-0.013574964366853237,
0.019032493233680725,
0.0009064820478670299,
-0.037004243582487106,
-0.032833050936460495,
-0.00998062826693058,
-0.025911662727594376,
0.020656760782003403,
0.0556921623647213,
-0.01376612950116396,
-0.001378806191496551,
0.007955314591526985,
-0.01798502542078495,
-0.022276621311903,
-0.036945220082998276,
0.007187800481915474,
-0.005346918944269419,
-0.004766146652400494,
0.045885298401117325,
-0.03048788569867611,
-0.01856662519276142,
0.014456674456596375,
-0.0064726052805781364,
0.004791317041963339,
0.03281528875231743,
0.008113810792565346,
0.01420534122735262,
0.024328917264938354,
0.05397171154618263,
0.034481387585401535,
-0.009996063075959682,
0.0029566106386482716,
-0.04659922793507576,
-0.07324623316526413,
0.01034970860928297,
-0.033046361058950424,
0.05559365823864937,
0.03277689218521118,
-0.017254730686545372,
-0.007699084002524614,
0.009234482422471046,
-0.008199095726013184,
0.04221278056502342,
-0.020686788484454155,
0.038581375032663345,
0.01965252310037613,
-0.01686008647084236,
0.0025482308119535446,
0.03705349937081337,
-0.027736974880099297,
-0.011880348436534405,
0.004777930211275816,
-0.007951200008392334,
-0.054604422301054,
0.0074249254539608955,
0.052860189229249954,
-0.02055388316512108,
-0.053281817585229874,
-0.0006031760131008923,
-0.00443114060908556,
0.059695787727832794,
0.03766471892595291,
0.029361488297581673,
-0.051507748663425446,
-0.04542951285839081,
0.007888775318861008,
0.054414551705121994,
0.007216968573629856,
0.05170537903904915,
0.02036525495350361,
0.028566718101501465,
0.0345899797976017,
-0.026526421308517456,
-0.0014258973533287644,
0.061852939426898956,
-0.019704287871718407,
0.015561298467218876,
-0.03261563181877136,
0.00364206125959754,
0.01743713766336441,
-0.04713495820760727,
0.001864942954853177,
0.04358194023370743,
-0.019724562764167786,
-0.022127658128738403,
-0.034979160875082016,
-0.0133565878495574,
0.001994975609704852,
0.01777713932096958,
-0.033227697014808655,
0.03585522994399071,
0.029308581724762917,
-0.02035422995686531,
0.032975565642118454,
0.005419180728495121,
0.020895758643746376,
-0.06597480177879333,
-0.010309209115803242,
0.0038508682046085596,
0.025021620094776154,
0.031345125287771225,
-0.05692439153790474,
-0.07069173455238342,
-0.022392159327864647,
-0.05355605110526085,
0.0009137520100921392,
-0.015488826669752598,
-0.04611390456557274,
0.02583795040845871,
-0.03199481591582298,
-0.026782294735312462,
0.05032983794808388,
-0.012203703634440899,
0.012524563819169998,
0.025944096967577934,
-0.003808918409049511,
-0.0561707504093647,
0.019996827468276024,
-0.008509723469614983,
0.022468529641628265,
-0.0138138672336936,
-0.011678879149258137,
0.03972432017326355,
-0.016692645847797394,
-0.031207673251628876,
0.02561192587018013,
-0.023428047075867653,
-0.031957149505615234,
0.0027044822927564383,
-0.009340066462755203,
0.021671149879693985,
-0.01361828576773405,
-0.008214780129492283,
0.030070748180150986,
-0.0419558584690094,
0.028987014666199684,
-0.03224717825651169,
-0.047313377261161804,
0.004661331884562969,
0.00402664253488183,
0.0662364512681961,
0.016295436769723892,
-0.012956148944795132,
0.045289892703294754,
0.04667671024799347,
-0.04368719458580017,
-0.026415465399622917,
0.014750256203114986,
-0.02639804594218731,
-0.02605138160288334,
0.013648927211761475,
0.05807735025882721,
-0.03566693887114525,
0.038214586675167084,
0.03572604060173035,
0.04500915855169296,
0.03873090445995331,
0.033248260617256165,
0.0033926679752767086,
0.018100690096616745,
-0.024684173986315727,
-0.03466374799609184,
0.009422516450285912,
0.003364551579579711,
-0.06156241521239281,
0.0456618070602417,
-0.0009601297788321972,
0.015068172477185726,
0.015220166184008121,
-0.0015706154517829418,
0.08224425464868546,
0.007736251689493656,
-0.012756950221955776,
-0.08378812670707703,
0.039752814918756485,
-0.0058691296726465225,
0.035290610045194626,
-0.01573559083044529,
0.025234341621398926,
0.025323254987597466,
-0.033845387399196625,
-0.015516703948378563,
0.03287224844098091,
0.050335366278886795,
-0.017505396157503128,
-0.02537696436047554,
0.008164312690496445,
-0.012835507281124592,
0.014292838983237743,
-0.025388546288013458,
-0.03433360531926155,
0.054609514772892,
0.014245323836803436,
0.026327181607484818,
0.001980014145374298,
-0.02945614606142044,
-0.008066000416874886,
-0.07367308437824249,
-0.013642290607094765,
-0.03942544758319855,
0.06275486201047897,
-0.013401767238974571,
0.0682646632194519,
0.03022228181362152,
0.024627957493066788,
0.01305650919675827,
0.0044618528336286545,
-0.10776447504758835,
0.029065532609820366,
-0.030110256746411324,
-0.00008939894905779511,
-0.0186824519187212,
-0.03213691711425781,
-0.02782117761671543,
-0.03671429678797722,
0.013675889000296593,
-0.015830352902412415,
0.03244998678565025,
-0.041752107441425323,
-0.007143366616219282,
-0.036807965487241745,
-0.02837926335632801,
-0.03728709742426872,
0.040559593588113785,
-0.028723739087581635,
-0.0029160615522414446,
0.025335388258099556,
0.024903487414121628,
-0.05386349931359291,
0.011103140190243721,
-0.015982968732714653,
0.04450611397624016,
0.010971068404614925,
0.05593899264931679,
0.03222496435046196,
0.03414393961429596,
-0.03676333278417587,
0.01952504552900791,
0.01094977930188179,
0.007583383470773697,
0.008398599922657013,
-0.05468561500310898,
-0.03222183883190155,
-0.04730181768536568,
-0.029498722404241562,
-0.033870432525873184,
0.03889584168791771,
0.011725356802344322,
0.011012514121830463,
0.027281146496534348,
0.010845804587006569,
0.00866694189608097,
0.030389774590730667,
-0.00578278535977006,
-0.036903150379657745,
-0.012575516477227211,
-0.04660272225737572,
0.015059547498822212,
-0.023183155804872513,
0.035208143293857574,
0.007146777119487524,
0.027885712683200836,
0.01635279506444931,
-0.006731247995048761,
0.022947460412979126,
-0.03106592409312725,
-0.005251012742519379,
-0.003651364939287305,
0.00013570683950092643,
0.008770445361733437,
0.010762428864836693,
-0.007984151132404804,
-0.027023332193493843,
0.029317758977413177,
0.054019782692193985,
-0.008364073932170868,
-0.036665286868810654,
-0.06975314021110535,
-0.02457546815276146,
0.03641341254115105,
0.02420194074511528,
-0.0021526459604501724,
0.0039016923401504755,
-0.04087590426206589,
0.01612059958279133,
0.01924259401857853,
0.0023491778410971165,
0.047730736434459686,
-0.030873138457536697,
-0.00798704568296671,
-0.03335227072238922,
-0.016547473147511482,
0.0002297513565281406,
0.02001037448644638,
0.010146955028176308,
0.039646659046411514,
-0.0025530080311000347,
-0.027126792818307877,
-0.02680276893079281,
0.027454344555735588,
0.033192336559295654,
0.03326376900076866,
-0.0000963653001235798,
-0.048679571598768234,
-0.020421328023076057,
0.027973057702183723,
-0.02062791958451271,
-0.04643366485834122,
0.0012813364155590534,
0.02038896270096302,
-0.02662872150540352,
0.0726761594414711,
-0.03693635016679764,
-0.0375918373465538,
0.046847764402627945,
-0.001896039815619588,
-0.023625271394848824,
-0.0011004514526575804,
-0.002636626595631242,
0.0408097468316555,
0.03022807091474533,
0.017805248498916626,
0.05445793271064758,
0.019633399322628975,
-0.0365612767636776,
-0.006639154627919197,
-0.00010235229274258018,
0.06402750313282013,
-0.05340497940778732,
-0.02859332598745823,
-0.013322360813617706,
-0.033800676465034485,
-0.02801794372498989,
0.06223040074110031,
-0.0036505775060504675,
0.041575174778699875,
-0.01289738342165947,
-0.062270887196063995,
-0.014874624088406563,
0.031850747764110565,
0.014459333382546902,
0.0003092125407420099,
0.007405772339552641,
0.0006236957269720733,
0.01275038905441761,
-0.008634185418486595,
0.024973945692181587,
-0.022767001762986183,
0.024723786860704422,
0.01812148466706276,
-0.004419326316565275,
0.02733459323644638,
-0.03821450099349022,
0.03583260998129845,
0.014386883936822414,
-0.011820263229310513,
0.0740857943892479,
0.015842508524656296,
0.020677238702774048,
0.038996580988168716,
-0.07690391689538956,
-0.0438801534473896,
0.02002144791185856,
-0.021081537008285522,
0.04925718531012535,
-0.03956189751625061,
0.035102374851703644,
0.0003042172465939075,
-0.026734882965683937,
-0.06272158771753311,
-0.02076694369316101,
-0.007152656093239784,
0.05199132859706879,
0.025821628049016,
0.005533183459192514,
0.031090283766388893,
-0.02184109203517437,
-0.02952718548476696,
0.0018733835313469172,
0.025679834187030792,
0.010800905525684357,
-0.0330442450940609,
0.0005477307131513953,
0.006127151660621166,
0.050041720271110535,
-0.011525590904057026,
-0.02400030381977558,
-0.028525544330477715,
-0.011231957003474236,
0.012270626612007618,
-0.019329383969306946,
0.07884315401315689,
-0.02185249701142311,
-0.034952398389577866,
-0.0037700466345995665,
-0.024363888427615166,
0.04672091826796532,
-0.0017807258991524577,
-0.003940774593502283,
0.0354178361594677,
-0.008797791786491871,
-0.014235845766961575,
-0.021165624260902405,
0.02151414379477501,
-0.0008005098206922412,
0.02926122397184372,
0.014677518047392368,
-0.032335568219423294,
-0.015900105237960815,
-0.04425797984004021,
0.05094694718718529,
0.025620877742767334,
0.03210797905921936,
0.017500143498182297,
0.05003559589385986,
-0.045399848371744156,
0.009286030195653439,
0.03491833806037903,
-0.006224231794476509,
0.057760581374168396,
-0.05841689184308052,
0.021810749545693398,
0.012154601514339447,
0.010227314196527004,
-0.013043203391134739,
-0.02588656172156334,
-0.031759656965732574,
-0.04254988580942154,
0.05055912584066391,
-0.016071567311882973,
0.03381584212183952,
0.02906312420964241,
-0.03361405059695244,
0.0028616017661988735,
-0.05432337895035744,
-0.02436378039419651,
-0.0019172619795426726,
-0.03684396296739578,
0.03148207813501358,
-0.04887134209275246,
0.006181515287607908,
0.031961265951395035,
0.07338438183069229,
-0.004071177449077368,
0.01126740500330925,
0.015777025371789932,
0.03972708061337471,
0.01996222697198391,
-0.01687469519674778,
-0.019536450505256653,
0.025697505101561546,
-0.02635800465941429,
-0.014278343878686428,
-0.007594912312924862,
-0.028388643637299538,
0.040422797203063965,
-0.0014687784714624286,
0.007207009010016918,
-0.03732457756996155,
-0.004115905612707138,
-0.041708555072546005,
0.0015686708502471447,
0.03963909298181534,
0.018009284511208534,
-0.01555266510695219,
0.017936529591679573,
0.009430098347365856,
0.02722896635532379,
0.010465594939887524,
-0.011787204071879387,
-0.052419185638427734,
-0.08076806366443634,
-0.02395610511302948,
-0.029521487653255463,
0.020359044894576073,
-0.015650784596800804,
-0.036299239844083786,
0.028395041823387146,
-0.07728897035121918,
0.014574278146028519,
-0.01842961460351944,
0.020164091140031815,
0.0029056272469460964,
0.0186231080442667,
-0.031074997037649155,
0.01998813822865486,
-0.005417403299361467,
0.01137534249573946,
0.08691506087779999,
0.047933340072631836,
0.03755456209182739,
-0.03523356840014458,
0.015477640554308891,
-0.01522811222821474,
-0.0000073165851972589735,
-0.02987072616815567,
0.025536369532346725,
-0.017833102494478226,
0.045556116849184036,
0.028532370924949646,
0.05264974758028984,
0.043971944600343704,
-0.00287258205935359,
0.023121459409594536,
-0.037711117416620255,
-0.020916419103741646,
0.04211747646331787,
0.0228100772947073,
0.018543044105172157,
0.014763260260224342,
-0.026963701471686363,
0.0022744950838387012,
-0.011251021176576614,
0.00024671986466273665,
0.018942823633551598,
-0.0352322943508625,
0.03672121837735176,
-0.010960600338876247,
-0.007982340641319752,
0.014849078841507435,
0.007299421820789576,
-0.015742579475045204,
-0.056109920144081116,
0.04478819668292999,
0.0460062250494957,
-0.006194040644913912,
0.01462678611278534,
-0.0022751621436327696,
0.03448096662759781,
-0.006734306458383799,
-0.024025993421673775,
0.01727430336177349,
-0.03203705698251724,
-0.021568723022937775,
-0.0286108311265707,
-0.015412598848342896,
0.005374451167881489,
-0.01933402754366398,
0.005386923439800739,
0.017067801207304,
-0.0059313396923244,
-0.06221805885434151,
0.0177043154835701,
0.0038762101903557777,
0.02838464267551899,
0.00524900620803237,
-0.021574417129158974,
-0.036225009709596634,
0.04647466167807579,
-0.0035304802004247904,
0.038355205208063126,
-0.02044621855020523,
0.015611864626407623,
-0.023976700380444527,
-0.0075072115287184715,
0.02858634665608406,
-0.0025333671364933252,
-0.04235482215881348,
-0.0055370028130710125,
0.01908450573682785,
-0.03155452385544777,
-0.052812427282333374,
0.02678619883954525,
0.024706672877073288,
0.02118765190243721,
0.013606811873614788,
-0.002228402066975832,
-0.02955678291618824,
-0.06714191287755966,
0.013449300080537796,
0.03306018188595772,
-0.023371633142232895,
-0.028983846306800842,
-0.0018284698016941547,
0.016694599762558937,
0.003068102989345789,
0.03847884759306908,
0.027972934767603874,
-0.013986458070576191,
0.012587525881826878,
0.022113323211669922,
-0.05197535455226898,
-0.011430163867771626,
0.045940056443214417,
0.003228389425203204,
-0.00880917627364397,
-0.0029203318990767,
0.02788015455007553,
-0.0205885861068964,
0.0017838679486885667,
0.0345502607524395,
0.01514474581927061,
-0.029856029897928238,
-0.003019900992512703,
0.002818279666826129,
-0.031031910330057144,
-0.012601999565958977,
0.01069945003837347,
0.011806413531303406,
0.04823511466383934,
-0.035488080233335495,
-0.037375904619693756,
-0.018440768122673035,
-0.004016639664769173,
-0.017949208617210388,
0.05293426290154457,
-0.005371624603867531,
0.010736675933003426,
-0.015009071677923203,
-0.034220609813928604,
-0.04383150860667229,
-0.04012545943260193,
0.03722093626856804,
0.024386946111917496,
-0.027652084827423096,
0.01849798858165741,
0.01495237834751606,
-0.030213389545679092,
-0.029440632089972496,
0.006676589138805866,
0.04413589462637901,
0.014585825614631176,
-0.009281870909035206,
-0.008410795591771603,
-0.013800354674458504,
0.04249740391969681,
-0.014645274728536606,
-0.044777754694223404,
0.04058936610817909,
-0.02065669186413288,
-0.03831372782588005,
0.014951489865779877,
-0.0218327809125185,
0.016041530296206474,
-0.0030121158342808485,
0.003068416379392147,
-0.018787728622555733,
0.0601804256439209,
0.0014247035142034292,
-0.016317427158355713,
0.0052541508339345455,
0.00008259084279416129,
0.009119085036218166,
0.004468164406716824,
0.017468910664319992,
-0.03296871483325958,
0.011549470946192741,
0.0658358633518219,
-0.016179652884602547,
-0.02130310609936714,
0.011052378453314304,
-0.026673929765820503,
-0.04659256711602211,
-0.00795631855726242,
0.019369155168533325,
0.023656802251935005,
0.03275926783680916,
0.00690421974286437,
-0.012794354930520058,
0.05232313275337219,
-0.015750475227832794,
-0.01592121087014675,
-0.0829460471868515,
0.01316805463284254,
0.009655836969614029,
-0.029479850083589554,
0.014739823527634144,
-0.05204980820417404,
0.06286198645830154,
0.017816923558712006,
-0.079302579164505,
0.026667794212698936,
0.00974737573415041,
-0.0030160057358443737,
-0.04384765774011612,
0.019516702741384506,
-0.004348443821072578,
0.005229967646300793,
0.015116910450160503,
0.026312610134482384,
0.007151748985052109,
0.011742927134037018,
-0.012057037092745304,
-0.021330060437321663,
0.0056263660080730915,
0.07534316927194595,
0.0004539663786999881,
-0.053572382777929306,
0.047013115137815475,
0.0014315812150016427,
-0.011110298335552216,
0.031621500849723816,
0.016266191378235817,
0.0018421706045046449,
-0.029973356053233147,
-0.009045200422406197,
0.01126733236014843,
0.0344245508313179,
0.03621227666735649,
-0.03946520388126373,
-0.04088630527257919,
0.015836132690310478,
0.023079918697476387,
0.011554231867194176,
0.006364011205732822,
0.019379748031497,
0.044757869094610214,
-0.045209139585494995,
-0.06153402850031853,
0.019871417433023453,
0.011904352344572544,
-0.0321003757417202,
0.02840055339038372,
0.024866145104169846,
0.07243332266807556,
-0.021283136680722237,
0.03337457776069641,
-0.10246413201093674,
-0.017535502091050148,
-0.003987194504588842,
-0.031113775447010994,
0.010435210540890694,
-0.012896822765469551,
-0.013796131126582623,
-0.029540134593844414,
-0.007605907507240772,
0.00467677740380168,
-0.008348285220563412,
-0.025816557928919792,
-0.013049133121967316,
0.005795476492494345,
0.014120894484221935,
0.005087411031126976,
-0.045259054750204086,
-0.07172638177871704,
0.017591601237654686,
-0.028856635093688965,
-0.001856527291238308,
0.023009654134511948,
-0.047705426812171936,
-0.06831855326890945,
-0.05453843995928764,
0.016275184229016304,
0.0008176373667083681,
-0.004282188601791859,
-0.049408309161663055,
0.004885716363787651,
-0.04025375097990036,
0.05162591487169266,
0.04295159876346588,
0.0032177018001675606,
-0.04699230566620827,
0.02468831092119217,
-0.02023634873330593,
0.013182693161070347,
-0.04517944157123566,
0.036650218069553375,
0.02169976942241192,
-0.024396371096372604,
-0.06696412712335587,
0.007801818195730448,
0.015660379081964493,
-0.002109146909788251,
0.015134227462112904,
0.0003954345593228936,
0.030092347413301468,
-0.051375966519117355,
-0.015576442703604698,
0.05997757241129875,
0.009937015362083912,
-0.03335656225681305,
0.05496585741639137,
-0.008356400765478611,
0.023679398000240326,
0.03363104164600372,
-0.0023143156431615353,
-0.039457906037569046,
0.011661921627819538,
0.02159871533513069,
-0.01927361637353897,
-0.004813923966139555,
0.013898959383368492,
0.02854740433394909,
-0.05579057335853577,
-0.010969345457851887,
0.016273606568574905,
-0.025619039312005043,
-0.04716920480132103,
0.05334959179162979,
0.020417001098394394,
0.01870672032237053,
0.025739500299096107,
0.024298645555973053,
0.0023216705303639174,
-0.01932252198457718,
-0.026675386354327202,
0.01714625582098961,
0.039297327399253845,
0.02769128419458866,
0.03499045968055725,
0.026882659643888474,
-0.0019277534447610378,
0.013823972083628178,
-0.025243615731596947,
0.01594937965273857,
-0.01764717511832714,
-0.045743804425001144,
0.02452671527862549,
0.012727068737149239,
-0.026658426970243454,
0.009998410940170288,
0.01535949669778347,
0.05721234902739525,
-0.02768518403172493,
-0.004677214659750462,
-0.0058810957707464695,
0.020452730357646942,
-0.023647664114832878,
-0.004784016404300928,
0.015527511015534401,
0.04081958532333374,
0.014904447831213474,
-0.0012365769362077117,
-0.01497814804315567,
-0.007812547497451305,
0.026185767725110054,
-0.046019915491342545,
0.015339002944529057,
-0.013219203799962997,
-0.04151565954089165,
-0.013491662219166756,
0.00048001177492551506,
-0.03708967566490173,
-0.028034910559654236,
0.007333999965339899,
0.01941336877644062,
0.04382374882698059,
0.026803171262145042,
-0.03801523521542549,
-0.005712845828384161,
0.02675984427332878,
-0.06305410712957382,
-0.01373799704015255,
-0.0014713204000145197,
0.003813499817624688,
-0.003479538019746542,
-0.040939368307590485
] |
<p>Does the internal structure of a neutron star resemble anything like that of an atomic nucleus? I.e., are the neutrons arranged in a shell like structure with different energy levels, and without a distinct location for each neutron?</p>
<p>I know that the force holding a neutron star is gravity, compared to the strong interaction inside atomic nuclei, but does this matter?</p> | 1,583 | [
-0.02804763987660408,
-0.023196730762720108,
-0.022909987717866898,
-0.05279988422989845,
0.04340562969446182,
0.024263756349682808,
-0.042182520031929016,
-0.044888775795698166,
0.013391685672104359,
-0.04965908080339432,
0.054324131458997726,
0.0205735694617033,
0.05258934199810028,
-0.018965521827340126,
0.0024092383682727814,
0.017306067049503326,
-0.008896250277757645,
-0.03317565470933914,
-0.003922448027879,
-0.0008088659378699958,
-0.008693155832588673,
0.007427275646477938,
-0.03060602769255638,
-0.0066912672482430935,
-0.012349299155175686,
0.049691036343574524,
0.027463797479867935,
0.0006755805225111544,
0.038565486669540405,
0.05500105395913124,
0.027884095907211304,
-0.02544602006673813,
0.028544750064611435,
0.054391659796237946,
0.05121215805411339,
-0.01528573501855135,
-0.04420188441872597,
-0.038515038788318634,
-0.007091905456036329,
0.045925531536340714,
-0.023951958864927292,
-0.04740610346198082,
-0.012357211671769619,
-0.011132586747407913,
-0.009073547087609768,
0.0013010174734517932,
0.03162092715501785,
-0.004611961077898741,
0.03165564313530922,
-0.023258686065673828,
0.04484174773097038,
0.01564236730337143,
0.023497004061937332,
0.030103018507361412,
-0.029656706377863884,
-0.016622129827737808,
0.07424990832805634,
0.05099572613835335,
-0.011611646972596645,
-0.06057555228471756,
-0.028085514903068542,
0.0026092983316630125,
-0.04033733159303665,
-0.010025245137512684,
-0.027979400008916855,
0.06683848798274994,
-0.035726241767406464,
-0.04682449623942375,
-0.011442579329013824,
0.021089522168040276,
0.010791786015033722,
0.03446364402770996,
0.007954402826726437,
-0.004952923860400915,
-0.022265851497650146,
-0.023046979680657387,
0.03504229336977005,
-0.005689616315066814,
0.03423992171883583,
0.019747719168663025,
-0.01886473409831524,
0.0010269932681694627,
0.002393364906311035,
0.021427452564239502,
0.0193476602435112,
0.016301436349749565,
0.07255776226520538,
-0.019420431926846504,
0.0024597947485744953,
0.057755306363105774,
-0.0007415668806061149,
0.027427848428487778,
0.032681904733181,
-0.017372723668813705,
-0.04034401848912239,
-0.0005196131533011794,
0.012068365700542927,
0.056959353387355804,
-0.014476414769887924,
0.00795909482985735,
0.036864273250103,
-0.0004110429435968399,
0.01569436490535736,
0.08279358595609665,
0.07016369700431824,
-0.052849192172288895,
-0.03429064527153969,
0.023231642320752144,
-0.04033805429935455,
0.013631999492645264,
-0.02194356359541416,
0.025256382301449776,
0.004018399398773909,
-0.027659786865115166,
0.04160398989915848,
-0.03171605244278908,
0.01490525621920824,
-0.017468668520450592,
0.0246562696993351,
0.07064532488584518,
0.026522906497120857,
0.004568453412503004,
0.0084792235866189,
-0.062431078404188156,
-0.04639416188001633,
0.006913468707352877,
0.04783269762992859,
0.01595199480652809,
-0.04105003550648689,
0.016669483855366707,
-0.02334422431886196,
0.007672162726521492,
0.010977678000926971,
-0.02367020770907402,
0.04093072935938835,
-0.000035224362363805994,
-0.1191069558262825,
-0.03921381011605263,
0.024935513734817505,
0.0006641193176619709,
-0.05181862413883209,
-0.07531046867370605,
-0.0023040729574859142,
0.025116559118032455,
0.06373994052410126,
-0.011329389177262783,
-0.04277825355529785,
0.026036061346530914,
0.06514131277799606,
0.00030999811133369803,
0.0052099283784627914,
0.009285430423915386,
-0.011889910325407982,
-0.06775860488414764,
-0.0021221647039055824,
-0.06504007428884506,
0.00972358975559473,
0.006233580876141787,
0.022703932598233223,
-0.024993520230054855,
0.05587190389633179,
-0.04241327941417694,
0.029921410605311394,
-0.011068404652178288,
-0.012349803932011127,
-0.024982066825032234,
0.014377281069755554,
0.001411129953339696,
-0.013626305386424065,
0.05990326404571533,
-0.01659708470106125,
-0.0038460136856883764,
0.023960361257195473,
0.013639956712722778,
0.04745941981673241,
-0.04629763215780258,
-0.04520563408732414,
-0.02239033952355385,
-0.014062532223761082,
0.021811196580529213,
-0.053529322147369385,
-0.025534598156809807,
-0.014371329918503761,
0.02925664372742176,
0.00425789225846529,
0.05130646005272865,
0.009727771393954754,
-0.032731588929891586,
-0.025760872289538383,
-0.031221898272633553,
0.005589770153164864,
-0.03989952802658081,
0.011939817108213902,
-0.01868707686662674,
-0.026253001764416695,
0.023556329309940338,
0.045918017625808716,
0.006779620423913002,
-0.014082561247050762,
-0.008318227715790272,
-0.021644270047545433,
0.053361840546131134,
-0.021500395610928535,
-0.0038084336556494236,
0.027040861546993256,
0.02127884514629841,
-0.008962146006524563,
-0.0102039510384202,
0.026340292766690254,
-0.021727176383137703,
-0.05147463083267212,
-0.02068229392170906,
0.010035323910415173,
-0.0021022679284214973,
0.004142509773373604,
0.021988609805703163,
0.04369278624653816,
0.0074118273332715034,
-0.014740923419594765,
0.02145986072719097,
-0.00569846760481596,
0.09130222350358963,
-0.004039154388010502,
0.010713774710893631,
0.012257038615643978,
0.03130842745304108,
0.03818117454648018,
0.02079627476632595,
0.012004590593278408,
-0.018749691545963287,
-0.06942388415336609,
-0.02113545499742031,
0.043490003794431686,
0.024123461917042732,
-0.039732564240694046,
0.04041944071650505,
0.011226858012378216,
0.059570539742708206,
0.015399467200040817,
0.004975152667611837,
-0.06270381808280945,
-0.04291294887661934,
0.028590422123670578,
-0.0003198436461389065,
-0.012163223698735237,
0.0008568966295570135,
0.0065636057406663895,
0.05182819068431854,
0.006611811462789774,
-0.023809073492884636,
-0.004913001786917448,
0.010325663723051548,
-0.021234286949038506,
-0.010934882797300816,
-0.015143427066504955,
-0.0724095031619072,
0.068486787378788,
-0.0077356635592877865,
0.01244049146771431,
0.024213822558522224,
-0.016883084550499916,
0.000015986139260348864,
-0.032893311232328415,
-0.016455184668302536,
-0.0002527309115976095,
0.018460601568222046,
-0.0023663996253162622,
-0.0026286672800779343,
0.015539408661425114,
-0.03201226517558098,
0.02971777133643627,
-0.04724901169538498,
0.029776528477668762,
-0.026809481903910637,
0.020740555599331856,
0.031995709985494614,
0.016962923109531403,
0.013293973170220852,
-0.003964389208704233,
-0.01875051110982895,
0.021093834191560745,
-0.04281996563076973,
-0.003455765312537551,
0.02628418430685997,
-0.06748833507299423,
0.03824330493807793,
-0.048660390079021454,
0.0011030887253582478,
0.014931795187294483,
-0.022307423874735832,
0.026252159848809242,
-0.017120439559221268,
-0.0324050672352314,
-0.07532535493373871,
0.03955446556210518,
0.0012570058461278677,
0.0003536340082064271,
-0.02618570812046528,
0.025256482884287834,
0.06394916772842407,
0.008758215233683586,
-0.02242675982415676,
-0.012699859216809273,
-0.0027031023055315018,
-0.02260022796690464,
0.003787074238061905,
0.022048786282539368,
0.03580411151051521,
-0.01888551563024521,
0.023102981969714165,
0.08844830840826035,
-0.05713168904185295,
0.024376092478632927,
-0.05689068138599396,
-0.025887249037623405,
0.033567510545253754,
-0.0250376109033823,
0.026909340173006058,
0.009596717543900013,
0.004516826011240482,
0.08380419760942459,
0.03112185373902321,
-0.04187352582812309,
-0.026225222274661064,
0.005342360585927963,
0.0032836005557328463,
0.011374309659004211,
-0.00027068675262853503,
0.02252010628581047,
0.04000231996178627,
-0.03025207854807377,
0.05189182236790657,
0.053468115627765656,
-0.006087007001042366,
-0.0032942472025752068,
-0.009440754540264606,
0.008007584139704704,
0.05233507975935936,
-0.02141811139881611,
0.03810515254735947,
0.006236511282622814,
-0.02022234909236431,
0.01966824382543564,
0.02630649507045746,
0.011669617146253586,
0.010584325529634953,
-0.019343968480825424,
0.06868024915456772,
-0.021600261330604553,
0.0062931678257882595,
-0.04938017576932907,
0.03158331289887428,
-0.019715726375579834,
0.003394623752683401,
0.033183082938194275,
0.01968824490904808,
0.040211137384176254,
0.008165242150425911,
-0.009713657200336456,
0.022775012999773026,
0.042389266192913055,
-0.026240456849336624,
-0.011503523215651512,
0.005151296034455299,
-0.015169807709753513,
-0.00374224572442472,
-0.003583422861993313,
0.001812431961297989,
0.009555798023939133,
0.01388254202902317,
0.04471616819500923,
0.0072046020068228245,
-0.020184125751256943,
0.009419704787433147,
-0.07545135915279388,
-0.029822269454598427,
0.017887787893414497,
0.0382465198636055,
-0.0022669327445328236,
0.018274860456585884,
0.025582170113921165,
0.02581370621919632,
0.0009383814758621156,
-0.014541068114340305,
-0.09503327310085297,
0.017085643485188484,
-0.05490357056260109,
-0.005654096603393555,
-0.018419036641716957,
-0.012201628647744656,
-0.0318133682012558,
-0.017775898799300194,
0.0021733685862272978,
-0.003222019411623478,
-0.017323287203907967,
-0.015199367888271809,
0.04013536497950554,
-0.06155259907245636,
-0.02223423682153225,
0.0023405696265399456,
0.0339568592607975,
0.04870704934000969,
-0.009043572470545769,
0.009792058728635311,
0.0013772653182968497,
-0.028278512880206108,
-0.01071447879076004,
0.01969563402235508,
0.014939362183213234,
0.002881688065826893,
0.026845287531614304,
0.04451798275113106,
0.025878284126520157,
0.0039670467376708984,
-0.016368979588150978,
0.02451026812195778,
0.026616910472512245,
0.008743377402424812,
-0.04828843101859093,
0.003887713886797428,
-0.05165582150220871,
-0.017673898488283157,
0.007980727590620518,
0.03839440643787384,
-0.03748803958296776,
0.008912341669201851,
0.013851047493517399,
-0.009910495951771736,
-0.02848668210208416,
0.038553446531295776,
0.05621748045086861,
0.011142995208501816,
-0.0622512623667717,
-0.04387451708316803,
-0.02225770242512226,
-0.04763498157262802,
0.001108658849261701,
0.022732118144631386,
-0.03418014198541641,
-0.05480903387069702,
0.0629473626613617,
0.004952526185661554,
-0.02371067740023136,
-0.06151599436998367,
-0.030015336349606514,
-0.027333633974194527,
0.01921544224023819,
-0.03143630176782608,
0.028994178399443626,
0.0300311129540205,
0.029245007783174515,
0.0658889040350914,
-0.004587100353091955,
0.00813304539769888,
-0.07159607112407684,
-0.027725903317332268,
0.07305742055177689,
0.0252995565533638,
0.002136052818968892,
-0.024038558825850487,
-0.08763635158538818,
-0.019344275817275047,
0.051000505685806274,
-0.011135621927678585,
0.0012251930311322212,
0.0004161713586654514,
-0.025785008445382118,
0.0026530532632023096,
-0.04362070932984352,
-0.003073490923270583,
0.0033928444609045982,
-0.014477874152362347,
-0.0030087647028267384,
-0.07192132622003555,
0.010751639492809772,
-0.02094804123044014,
0.046690843999385834,
0.01982952281832695,
-0.009155540727078915,
0.02211477980017662,
0.014020154252648354,
-0.019350135698914528,
0.009798693470656872,
-0.007074476685374975,
-0.09593567997217178,
-0.015653831884264946,
0.009289192035794258,
-0.028424061834812164,
0.026344114914536476,
-0.03835485130548477,
-0.07479187101125717,
-0.0043505290523171425,
0.028145547956228256,
0.01496672723442316,
-0.019256874918937683,
-0.0470527820289135,
0.03564954549074173,
0.0017829862190410495,
-0.02186634950339794,
0.018902266398072243,
0.03187244385480881,
-0.01788025163114071,
-0.02247694320976734,
-0.04464413598179817,
0.04425358399748802,
-0.03732433170080185,
0.00005502701969817281,
0.004892363678663969,
-0.002468990394845605,
-0.03980095684528351,
0.04031654819846153,
-0.0023563839495182037,
0.023166894912719727,
0.03294680267572403,
-0.009227176196873188,
0.014146625995635986,
0.03537346050143242,
0.013635375536978245,
-0.020374875515699387,
0.001739470288157463,
0.018861575052142143,
-0.004421320278197527,
-0.041137535125017166,
0.01592833735048771,
-0.008972342126071453,
0.016939526423811913,
0.03827594593167305,
-0.015394878573715687,
0.009598007425665855,
-0.02485037036240101,
-0.06423369795084,
0.023086512461304665,
-0.05608654022216797,
0.047393664717674255,
-0.01755395531654358,
-0.006436524912714958,
0.053075194358825684,
-0.007924367673695087,
-0.003097758861258626,
-0.010068380273878574,
-0.030168715864419937,
0.008332086727023125,
-0.011078327894210815,
0.04474175348877907,
0.003886670805513859,
-0.0019704108126461506,
-0.10342388600111008,
-0.009762326255440712,
0.03389303758740425,
0.006123120430856943,
-0.022581513971090317,
-0.0488288588821888,
0.02661188319325447,
-0.009666270576417446,
0.014187761582434177,
-0.020353246480226517,
0.01326968427747488,
-0.050964854657649994,
-0.024460630491375923,
0.006482042837888002,
-0.00033520912984386086,
0.06522379070520401,
-0.008001911453902721,
-0.01442745327949524,
0.005194602068513632,
0.009221052750945091,
0.03271791338920593,
-0.01086761150509119,
0.05498760938644409,
-0.012282217852771282,
-0.06311164051294327,
-0.048628244549036026,
-0.000055721422540955245,
0.02095753140747547,
-0.011810635216534138,
-0.0031303432770073414,
0.07456856220960617,
-0.01624136045575142,
0.013291455805301666,
-0.018510963767766953,
0.000053267518524080515,
-0.001249923137947917,
0.026020726189017296,
-0.01753203570842743,
-0.010297754779458046,
-0.016360027715563774,
-0.0420612171292305,
0.04017484188079834,
-0.03256349265575409,
0.004717494361102581,
0.02729925699532032,
0.04072289913892746,
0.005508298985660076,
0.010793464258313179,
0.007053495850414038,
-0.016816526651382446,
0.012276686728000641,
-0.02046862803399563,
-0.0011639742879197001,
-0.005468158051371574,
0.018404990434646606,
-0.01987704262137413,
-0.01547958329319954,
-0.05037728324532509,
-0.016265712678432465,
0.033946696668863297,
-0.0027527662459760904,
0.03300131857395172,
0.01866684854030609,
0.004286617506295443,
-0.018884247168898582,
-0.035895198583602905,
-0.0024807669688016176,
0.007691476959735155,
-0.00035491446033120155,
0.03530900180339813,
-0.005649931728839874,
-0.013587938621640205,
0.036676954478025436,
0.09132543951272964,
-0.009542513638734818,
0.03429963439702988,
0.01969350501894951,
0.00946386344730854,
0.02198123186826706,
-0.003986771684139967,
-0.04595433920621872,
0.035235967487096786,
-0.023605801165103912,
0.045482899993658066,
-0.002705598482862115,
-0.004078985191881657,
-0.00029207009356468916,
-0.0033761165104806423,
0.056326184421777725,
-0.01446202490478754,
-0.033133625984191895,
-0.010287576355040073,
0.02111455798149109,
0.03872569277882576,
0.024176890030503273,
-0.05113176256418228,
0.012873907573521137,
0.01693364977836609,
0.022655878216028214,
-0.0001092779784812592,
0.022194666787981987,
-0.07230030745267868,
-0.02183140628039837,
-0.020643774420022964,
-0.06202269718050957,
0.007609724532812834,
-0.009644881822168827,
-0.045967843383550644,
0.028082173317670822,
-0.013383857905864716,
0.061734989285469055,
0.023119330406188965,
0.03272521123290062,
-0.009568953886628151,
0.0565350316464901,
-0.04408588260412216,
-0.019240111112594604,
-0.009103497490286827,
-0.004173704423010349,
0.10208269208669662,
0.02444029413163662,
0.011969675309956074,
-0.05587400123476982,
-0.01166701503098011,
-0.010380477644503117,
0.025462299585342407,
0.006972602568566799,
0.00534818135201931,
-0.0012405342422425747,
-0.008611601777374744,
-0.0043047829531133175,
0.03745412826538086,
-0.003600446041673422,
-0.01099062617868185,
0.05286729708313942,
-0.023725567385554314,
-0.029206929728388786,
-0.0015885153552517295,
0.017168506979942322,
0.013047011569142342,
0.012268027290701866,
-0.054157450795173645,
0.030696293339133263,
-0.009056232869625092,
0.035887669771909714,
-0.02864283137023449,
-0.03437623009085655,
0.022507503628730774,
0.02133863791823387,
-0.03898749500513077,
-0.012859436683356762,
-0.010293551720678806,
-0.025710908696055412,
-0.0178841520100832,
0.0012904080795124173,
0.01181674376130104,
-0.02489064447581768,
0.01365954615175724,
0.0007916152244433761,
0.02259018085896969,
0.0123136630281806,
0.01816410943865776,
-0.00696935597807169,
-0.04872960224747658,
-0.010740499012172222,
-0.012749248184263706,
0.026249568909406662,
0.006390675436705351,
-0.008939741179347038,
-0.014565447345376015,
0.00893592182546854,
0.015833057463169098,
-0.012673042714595795,
0.008293628692626953,
-0.020220817998051643,
0.00930002611130476,
-0.02457173354923725,
-0.03078920766711235,
-0.03676900267601013,
0.03827831894159317,
-0.02661179192364216,
0.02547537535429001,
-0.013423395343124866,
-0.0015113555127754807,
0.05233430489897728,
-0.017575008794665337,
0.017507564276456833,
-0.006345463916659355,
0.02300899662077427,
-0.021321408450603485,
0.0009426982142031193,
-0.02426598034799099,
-0.015797602012753487,
0.015498129650950432,
0.022584030404686928,
0.03610002249479294,
0.05152817815542221,
0.011639694683253765,
-0.011816682294011116,
-0.055217258632183075,
0.06639814376831055,
0.006836500950157642,
-0.03115793690085411,
-0.00021740653028246015,
0.00949572492390871,
0.024798091500997543,
0.04722362384200096,
-0.02282015234231949,
0.013770866207778454,
0.0010052191792055964,
-0.010184060782194138,
-0.015091062523424625,
-0.024216365069150925,
0.0041853273287415504,
0.019847458228468895,
-0.051434893161058426,
0.008984198793768883,
-0.026616062968969345,
0.00885979924350977,
0.035585667937994,
-0.022760983556509018,
0.023333294317126274,
0.03639138489961624,
-0.02564733289182186,
-0.02053879387676716,
0.0022463523782789707,
-0.024743560701608658,
0.00039842899423092604,
-0.009466739371418953,
-0.006564776413142681,
-0.05851989984512329,
-0.03556440398097038,
-0.04162080958485603,
-0.02065262757241726,
-0.012180188670754433,
0.049199819564819336,
-0.014145905151963234,
0.020727569237351418,
-0.015713436529040337,
0.006334183271974325,
-0.020772146061062813,
0.027508186176419258,
-0.05354311689734459,
-0.028491191565990448,
0.009939277544617653,
-0.02937486581504345,
-0.01576678827404976,
0.01658186875283718,
0.005690874997526407,
0.00929831713438034,
0.025556892156600952,
-0.005880176555365324,
-0.021075939759612083,
0.02996157482266426,
0.032958731055259705,
-0.014863417483866215,
0.03275660052895546,
-0.005902915261685848,
-0.013546213507652283,
0.029932212084531784,
-0.009820100851356983,
-0.04669210687279701,
0.04686111956834793,
-0.04287675768136978,
-0.0033754827454686165,
0.014875494875013828,
-0.04399196803569794,
-0.009507961571216583,
0.07884842157363892,
0.008617066778242588,
-0.00806210283190012,
0.0018965185154229403,
-0.0008431464666500688,
0.011661858297884464,
-0.006756111513823271,
0.011125107295811176,
-0.018849806860089302,
-0.04768023267388344,
0.03790341317653656,
0.021052712574601173,
-0.024100033566355705,
-0.006485494785010815,
-0.031983450055122375,
-0.0069078863598406315,
0.02494230680167675,
0.0097225746139884,
0.04846508428454399,
0.031384795904159546,
0.021136758849024773,
-0.053068459033966064,
0.07600680738687515,
0.02425856702029705,
-0.004900737665593624,
-0.09355764091014862,
-0.02269226685166359,
-0.009046626277267933,
-0.00782030913978815,
0.013846535235643387,
-0.0394606739282608,
0.028124447911977768,
0.020096736028790474,
-0.05568847805261612,
0.034845467656850815,
-0.01616855151951313,
-0.0319107249379158,
-0.02451767772436142,
-0.01773073896765709,
-0.002343242522329092,
0.06470555067062378,
0.03915804997086525,
0.04467048496007919,
-0.002139924094080925,
0.005392155144363642,
0.00494787935167551,
0.014976462349295616,
-0.027322430163621902,
0.024456024169921875,
0.006206138990819454,
-0.018806831911206245,
0.04123426228761673,
-0.014650681987404823,
-0.026113996282219887,
0.02803954854607582,
-0.005000435747206211,
0.005022626835852861,
0.013844666071236134,
-0.014040160924196243,
-0.0066668801009655,
0.033626776188611984,
0.001683223876170814,
-0.022052781656384468,
-0.01973775029182434,
0.04948138818144798,
0.00023175908427219838,
0.05713089555501938,
0.01088126190006733,
0.01608223281800747,
0.021080316975712776,
-0.02149396389722824,
-0.0050232610665261745,
0.021672945469617844,
-0.025630908086895943,
0.004688558634370565,
-0.054371193051338196,
-0.003196894656866789,
0.023797623813152313,
-0.010799543000757694,
-0.004674226976931095,
-0.06481987237930298,
0.0214685071259737,
-0.0010480423225089908,
0.004610149655491114,
0.0016391891986131668,
0.04038320109248161,
0.025238920003175735,
-0.006110199727118015,
-0.02373708412051201,
0.026997841894626617,
-0.013569788075983524,
-0.011767803691327572,
0.02305850200355053,
0.040762536227703094,
-0.011856654658913612,
0.019255349412560463,
-0.034082889556884766,
-0.020909490063786507,
0.056356653571128845,
0.03932121396064758,
0.03270816057920456,
0.027187326923012733,
-0.05528097227215767,
-0.03547164797782898,
-0.05822677165269852,
0.022066500037908554,
0.003255719318985939,
-0.005815758835524321,
-0.0008838134235702455,
0.0031192500609904528,
0.0011652966495603323,
0.004994244780391455,
0.019766753539443016,
0.01720181480050087,
-0.0014774207957088947,
0.0378090925514698,
-0.0306254830211401,
0.030480679124593735,
-0.03987119346857071,
-0.007838474586606026,
-0.008179837837815285,
-0.017851628363132477,
0.0032175483647733927,
-0.010254540480673313,
-0.05213451012969017,
0.03803149610757828,
0.021194832399487495,
-0.0040185353718698025,
0.008513306267559528,
0.016485726460814476,
0.0047838627360761166,
0.07192195951938629,
0.015734564512968063,
0.003344554454088211,
0.0781649649143219,
0.0019587832503020763,
-0.01618463359773159,
0.04698527976870537,
-0.03666536137461662,
0.00023594999220222235,
-0.0037924028001725674,
-0.010930693708360195,
-0.011378433555364609,
-0.007938431575894356,
-0.042562391608953476,
0.013307670131325722,
-0.02298601344227791,
-0.006719270255416632,
0.050306536257267,
-0.03146001696586609,
-0.018413303419947624,
0.03088894858956337,
0.04968605935573578,
0.03430112078785896,
0.01814742013812065,
-0.017886707559227943,
0.02792767621576786,
0.011455527506768703,
-0.022469306364655495,
0.05827323719859123,
0.052490685135126114,
0.030832896009087563,
0.020006230100989342,
0.016490580514073372,
0.012209899723529816,
0.001477635931223631,
-0.004968544002622366,
0.023512179031968117,
-0.04151691123843193,
-0.014126861467957497,
0.05322665721178055,
-0.0020966283045709133,
0.04046302288770676,
0.006751152686774731,
-0.030794283375144005,
0.0859227254986763,
-0.024245066568255424,
0.017885860055685043,
-0.013230322860181332,
0.01235080137848854,
-0.009527457877993584,
0.018894601613283157,
0.02471611090004444,
0.03650330752134323,
0.0007117030909284949,
-0.0291686300188303,
-0.019422035664319992,
0.024621769785881042,
0.05068056657910347,
-0.04188275337219238,
-0.008467845618724823,
-0.015835067257285118,
0.02001638524234295,
-0.036617621779441833,
0.00410544965416193,
-0.06092667579650879,
-0.038210976868867874,
0.009051123633980751,
0.026062678545713425,
0.044260650873184204,
0.001779211568646133,
0.0036169353406876326,
-0.03072243183851242,
0.0695486068725586,
-0.0876794308423996,
-0.012257403694093227,
-0.0489736907184124,
0.004729923326522112,
-0.030136028304696083,
-0.02290598675608635
] |
<p>While watching the first 4 seconds of <a href="http://www.gizmodo.com.au/2011/11/driving-at-745kmh-is-ludicrous-from-any-angle/" rel="nofollow">driving at 745 km/h is ludicrous from any angle</a>
wondered </p>
<p>1)If we knew the curvature of the earth in a "flat" desert, what would be the speed of the car?</p>
<p>2)Assuming we don't know the curvature of the earth, how long would it take for the car to go around the earth ( assuming a "flat" desert all the way travelling on a great arc)?</p>
<p>Using my ninja pause skills it seemed it took 2 seconds from the time the car appeared ( as a dot ) in horizon to the time it passed by the camera, although 2 second window of observation seems to lead to a great error in overall estimates, using the 745 as the value for 1 and 2 the error of human observation could be calculated (?) </p> | 1,584 | [
-0.037793755531311035,
-0.02988995425403118,
0.018226947635412216,
0.02046736516058445,
0.07069121301174164,
-0.006709219887852669,
-0.07134151458740234,
-0.015302833169698715,
-0.022944414988160133,
0.0016835912829264998,
0.0074539449997246265,
0.044134434312582016,
0.02035972848534584,
0.0612853579223156,
0.03526876121759415,
0.025497328490018845,
0.023432081565260887,
0.005890093743801117,
-0.012872765772044659,
-0.035569071769714355,
0.03323037549853325,
0.018479645252227783,
0.00323162111453712,
-0.006947229616343975,
-0.003772519528865814,
0.002127142157405615,
0.023487797006964684,
-0.02199273742735386,
0.03403003513813019,
0.031233564019203186,
-0.008059958927333355,
-0.015359891578555107,
0.021671630442142487,
0.009349790401756763,
0.009251000359654427,
0.015767492353916168,
-0.026897596195340157,
-0.02487759292125702,
-0.0042412462644279,
0.03087029606103897,
0.028683219105005264,
0.007888680323958397,
0.010631202720105648,
0.07168743759393692,
-0.04525786265730858,
0.01878892257809639,
-0.009370233863592148,
-0.026500923559069633,
0.062073320150375366,
-0.05419408157467842,
0.061626266688108444,
-0.0009825400775298476,
-0.009419675916433334,
0.02034766599535942,
-0.012251718901097775,
-0.002089541172608733,
0.02789357304573059,
0.030140675604343414,
-0.01854829303920269,
-0.039845872670412064,
-0.026775166392326355,
-0.039595212787389755,
0.014444737695157528,
0.023529112339019775,
-0.011173234321177006,
0.0038255886174738407,
-0.02752365916967392,
-0.03303414583206177,
0.030261388048529625,
0.05966911464929581,
0.007869257591664791,
0.011480673216283321,
0.015308246947824955,
0.016834476962685585,
0.03386591747403145,
-0.05404888093471527,
0.010079431347548962,
0.00431283563375473,
0.035609666258096695,
0.029005974531173706,
0.01836320385336876,
0.00340844364836812,
0.045947302132844925,
0.02725278213620186,
0.08135867118835449,
0.031442128121852875,
0.06130654364824295,
0.006793156266212463,
0.01528357807546854,
0.011916679330170155,
0.022252710536122322,
0.020085791125893593,
0.017639154568314552,
-0.005459559615701437,
0.01032766792923212,
0.03917426988482475,
-0.00830187276005745,
0.03212864696979523,
0.014638411812484264,
-0.015112926252186298,
-0.00790808629244566,
-0.02087114006280899,
0.039806004613637924,
0.030868228524923325,
0.036204952746629715,
-0.005354112014174461,
-0.008563610725104809,
-0.0012190119596198201,
-0.019509118050336838,
-0.02345684915781021,
-0.03675393760204315,
-0.006635672878473997,
0.011694248765707016,
0.019850876182317734,
-0.02674274891614914,
-0.005851192865520716,
-0.0006797351525165141,
-0.0177437923848629,
0.07705570012331009,
0.011358112096786499,
0.024929342791438103,
-0.030819270759820938,
-0.0007496751495637,
-0.052095331251621246,
-0.06517709046602249,
0.014497149735689163,
0.02863391488790512,
0.007641069125384092,
-0.05713650584220886,
0.01540849357843399,
0.010240129195153713,
-0.013137996196746826,
0.011802833527326584,
0.018292998895049095,
0.031007923185825348,
0.0360678993165493,
-0.09324256330728531,
-0.08338650315999985,
0.015114886686205864,
0.04461023211479187,
0.023491322994232178,
-0.07127710431814194,
0.0393025279045105,
0.030333247035741806,
0.07126536220312119,
-0.004292414057999849,
0.015837334096431732,
0.013749227859079838,
0.024004027247428894,
-0.025942986831068993,
-0.015095872804522514,
-0.016713814809918404,
0.02604600042104721,
-0.052767232060432434,
-0.015823643654584885,
-0.05626225471496582,
0.0367983803153038,
0.022196922451257706,
0.03109930269420147,
-0.03149959817528725,
0.0061231316067278385,
0.02457948960363865,
-0.00011201242887182161,
-0.009863318875432014,
-0.03172285482287407,
-0.008533872663974762,
0.06096687912940979,
0.02853202633559704,
-0.0025209698360413313,
-0.0029430589638650417,
0.03447733819484711,
0.034126535058021545,
-0.03614599630236626,
-0.018682990223169327,
0.04537541791796684,
-0.07187263667583466,
-0.004569884389638901,
0.012464795261621475,
-0.000390673172660172,
-0.012098600156605244,
-0.03628595918416977,
-0.017695073038339615,
0.012600335292518139,
0.005399156827479601,
0.04113011062145233,
0.056975506246089935,
-0.045680347830057144,
0.025744788348674774,
0.023224586620926857,
-0.04151846840977669,
-0.03598236292600632,
0.008256715722382069,
-0.005192261189222336,
0.006233883555978537,
0.004803902469575405,
-0.013330318965017796,
-0.05429866537451744,
0.012342541478574276,
-0.018724540248513222,
-0.007078536320477724,
-0.018834276124835014,
0.04566100984811783,
0.04419618472456932,
-0.002491127233952284,
-0.008412019349634647,
0.09669137001037598,
0.010593217797577381,
-0.007311186753213406,
-0.00793470162898302,
-0.012319333851337433,
-0.009392705745995045,
-0.014305108226835728,
-0.006564382929354906,
0.019633376970887184,
-0.021600838750600815,
0.014242012053728104,
-0.026760892942547798,
0.010274330154061317,
0.013510755263268948,
-0.000008395707482122816,
-0.04598288610577583,
0.07921163737773895,
0.02975860983133316,
0.01095044519752264,
0.00827284436672926,
0.02530919946730137,
0.01011613942682743,
-0.02663804218173027,
0.012242589145898819,
-0.031096026301383972,
-0.07542047649621964,
-0.009804286062717438,
0.03001614846289158,
-0.003072143532335758,
-0.0016232662601396441,
-0.010837527923285961,
0.042492110282182693,
0.03680172935128212,
0.01523829810321331,
-0.02478114515542984,
-0.0032006222754716873,
-0.035342298448085785,
0.004976751748472452,
0.013693462125957012,
0.01656040921807289,
-0.000008610441000200808,
0.004173679742962122,
-0.015988599509000778,
-0.002182372845709324,
-0.02096150815486908,
-0.0051069557666778564,
0.01867634989321232,
-0.021310046315193176,
0.02515025995671749,
-0.015523367561399937,
0.025950348004698753,
0.03616864234209061,
-0.008870752528309822,
-0.0025294111110270023,
0.06231863796710968,
0.019370678812265396,
0.0067994012497365475,
-0.06901907920837402,
-0.004713936243206263,
-0.009878016076982021,
0.02465352602303028,
-0.038365792483091354,
-0.0015873424708843231,
0.05036487057805061,
-0.012475552037358284,
-0.009288931265473366,
-0.005532767158001661,
0.002465541008859873,
-0.01929447613656521,
-0.007787143345922232,
0.030812587589025497,
0.01648828200995922,
-0.02238592877984047,
-0.030266636982560158,
0.0022056957241147757,
0.00508376257494092,
0.007158832624554634,
-0.01055576466023922,
0.023730410262942314,
-0.04771210625767708,
0.01264245342463255,
0.01683499664068222,
0.002803030190989375,
0.04741736501455307,
0.012729126028716564,
0.017247915267944336,
0.08509539812803268,
-0.012087437324225903,
-0.051714710891246796,
-0.02994203194975853,
-0.03677042946219444,
0.008684525266289711,
-0.04667043685913086,
-0.019788343459367752,
0.014936726540327072,
-0.026583479717373848,
-0.0008871251484379172,
0.06500599533319473,
-0.04227864742279053,
-0.02302670106291771,
-0.037345122545957565,
0.01893330179154873,
0.030073393136262894,
-0.025601884350180626,
0.04778138920664787,
-0.008529664017260075,
0.005563242826610804,
0.009577823802828789,
-0.042826879769563675,
-0.06011670455336571,
0.03568480536341667,
-0.025435302406549454,
0.029366569593548775,
-0.033953748643398285,
-0.021146267652511597,
0.04291760176420212,
0.01629062369465828,
-0.02399415522813797,
-0.057429395616054535,
0.007046121172606945,
-0.016042817384004593,
-0.01314469613134861,
-0.01771640218794346,
0.01817769557237625,
-0.03609096631407738,
0.019189611077308655,
0.002648134483024478,
0.057048097252845764,
0.028477977961301804,
-0.014203018508851528,
-0.0118650421500206,
-0.008927347138524055,
-0.029874835163354874,
0.03040187619626522,
0.010096931830048561,
0.06733116507530212,
0.0002274388971272856,
0.03597327694296837,
-0.01818099431693554,
0.05169805884361267,
-0.0012153876014053822,
-0.04286390542984009,
0.030588354915380478,
-0.004122218117117882,
-0.0289422869682312,
-0.021328333765268326,
0.02091611921787262,
0.014542867429554462,
-0.01735536940395832,
-0.04122646898031235,
0.04174300283193588,
0.057800665497779846,
0.02207891456782818,
-0.013745317235589027,
0.02931489236652851,
0.05349520593881607,
-0.007232418283820152,
-0.0355832539498806,
-0.0359036847949028,
0.005428995005786419,
0.042742226272821426,
-0.02784690260887146,
-0.010853893123567104,
0.05985991284251213,
0.05235665291547775,
0.008288872428238392,
-0.005549079738557339,
-0.03591418266296387,
-0.02054538205265999,
-0.07717527449131012,
-0.01808757707476616,
-0.025603072717785835,
-0.003726764814928174,
0.017254019156098366,
0.0275934636592865,
0.009847397916018963,
0.03403078392148018,
0.011678124777972698,
0.02381959557533264,
-0.06570251286029816,
0.00865072850137949,
-0.0319082997739315,
-0.06238344684243202,
-0.0024230650160461664,
-0.015651727095246315,
0.026093976572155952,
-0.03502253443002701,
0.054855573922395706,
-0.02533244714140892,
0.00787428393959999,
-0.04122646898031235,
-0.03142267465591431,
-0.012394296005368233,
-0.030132543295621872,
-0.00798756629228592,
0.016440007835626602,
0.04229472205042839,
0.017637019976973534,
0.04663409665226936,
0.02678758278489113,
-0.010460831224918365,
-0.022591261193156242,
-0.032955002039670944,
-0.004883619025349617,
-0.025977490469813347,
0.020049942657351494,
-0.015090030618011951,
0.010180894285440445,
-0.052232496440410614,
0.00875747948884964,
0.008961563929915428,
0.0165302362293005,
0.0123826889321208,
0.020999908447265625,
-0.052137430757284164,
-0.0077718887478113174,
-0.022644901648163795,
0.033335354179143906,
0.04324846342206001,
-0.03867195546627045,
0.03926319628953934,
0.02217436581850052,
-0.006351116579025984,
0.04265090450644493,
0.03282326087355614,
0.04187645763158798,
-0.023003511130809784,
0.026638032868504524,
-0.05660445615649223,
-0.057968348264694214,
-0.020852943882346153,
0.00707846088334918,
0.036391593515872955,
0.02295495755970478,
-0.006248805671930313,
-0.01850040629506111,
0.04601558670401573,
-0.009816941805183887,
0.01550635602325201,
0.0398854985833168,
-0.005317521281540394,
0.030414540320634842,
0.021813586354255676,
0.014589273370802402,
0.022360337898135185,
0.0399145670235157,
0.06048876419663429,
0.02568923681974411,
-0.07471729069948196,
-0.11029376834630966,
-0.022763201966881752,
-0.02572294883430004,
0.043038226664066315,
-0.022668790072202682,
-0.016642030328512192,
-0.06389796733856201,
-0.02501659095287323,
0.03746439144015312,
-0.01688273437321186,
0.04022003710269928,
-0.04391786828637123,
0.055457953363657,
0.0041656154207885265,
-0.0033259866759181023,
-0.016388671472668648,
0.012155097909271717,
-0.008078434504568577,
0.036377888172864914,
-0.001497299992479384,
-0.024323616176843643,
0.006160211283713579,
0.01206500455737114,
0.0278379637748003,
0.06011776626110077,
0.045101348310709,
0.0368194654583931,
-0.02384370006620884,
0.0005662902258336544,
-0.04641528055071831,
-0.05212783440947533,
0.0005014161579310894,
-0.01577123999595642,
-0.04299934580922127,
0.040187109261751175,
-0.032790131866931915,
-0.027124494314193726,
0.02245239168405533,
-0.0073877074755728245,
-0.009744850918650627,
-0.0018441224237903953,
-0.06467465311288834,
-0.01452457532286644,
0.024736978113651276,
-0.006895707920193672,
0.021395064890384674,
0.012508008629083633,
0.00010426731023471802,
0.04238198325037956,
0.0004070383438374847,
0.005883785896003246,
-0.004656078759580851,
-0.03429731726646423,
0.013358999975025654,
0.0029352724086493254,
-0.06155025213956833,
0.0025669471360743046,
0.02857036143541336,
0.01287683006376028,
-0.0494074821472168,
-0.044551458209753036,
-0.007386339828372002,
0.013986608944833279,
0.013621997088193893,
0.026438796892762184,
-0.058701593428850174,
0.006902806460857391,
0.012961099855601788,
-0.004115188028663397,
-0.0017581781139597297,
-0.037176381796598434,
0.015383947640657425,
0.023966729640960693,
0.01364397257566452,
0.006312579847872257,
-0.02134653553366661,
-0.00821769330650568,
0.026315728202462196,
-0.06874196976423264,
0.06732739508152008,
-0.036208827048540115,
0.009938635863363743,
0.03327304869890213,
-0.0502701997756958,
-0.024725131690502167,
0.028596999123692513,
-0.013542314060032368,
0.05574082210659981,
-0.03363051265478134,
0.017217213287949562,
0.038006674498319626,
-0.014819835312664509,
-0.03820248320698738,
-0.0327305905520916,
0.02219465747475624,
0.006894718389958143,
-0.032129012048244476,
0.013961722142994404,
-0.019564969465136528,
-0.02267995849251747,
-0.01914217323064804,
-0.018108384683728218,
0.047400735318660736,
0.0013514936435967684,
0.007701626978814602,
-0.030565664172172546,
-0.007474670186638832,
0.06014377996325493,
-0.015183229930698872,
-0.01716919057071209,
0.025078492239117622,
0.002994704293087125,
-0.04699304699897766,
-0.018040407449007034,
0.06669490784406662,
-0.02570834569633007,
-0.027306776493787766,
-0.022072087973356247,
0.002999914111569524,
0.005970444995909929,
-0.024053925648331642,
0.003604533150792122,
0.039955802261829376,
-0.00795962568372488,
-0.01335201133042574,
0.015929022803902626,
0.035739753395318985,
-0.012292103841900826,
0.011483684182167053,
-0.017521806061267853,
-0.0012064536567777395,
-0.00995578058063984,
-0.054210126399993896,
0.056930847465991974,
0.0025536431930959225,
-0.03623562678694725,
-0.03718815743923187,
0.07029952108860016,
0.015317046083509922,
-0.02742103859782219,
0.049181148409843445,
-0.016759928315877914,
0.03326089680194855,
-0.007484808564186096,
-0.002385522238910198,
0.02006230503320694,
-0.014746771194040775,
-0.04785199463367462,
-0.022700784727931023,
-0.021827969700098038,
0.03206701949238777,
0.08216927945613861,
-0.03589767590165138,
0.0011439950903877616,
-0.00039383035618811846,
0.006765701808035374,
-0.007169548887759447,
-0.03808828443288803,
0.00471532391384244,
0.019659901037812233,
0.010029833763837814,
0.05979981645941734,
-0.009944234974682331,
0.02104617841541767,
0.010926643386483192,
0.03515676409006119,
0.035098254680633545,
-0.008038865402340889,
0.020379742607474327,
0.03697161376476288,
0.026336567476391792,
-0.03865019604563713,
-0.010504295118153095,
-0.0028315980453044176,
0.0161080751568079,
0.016194036230444908,
-0.008008860982954502,
0.0280660018324852,
0.07449014484882355,
0.0029493500478565693,
0.03164133429527283,
-0.024005508050322533,
-0.02252992056310177,
-0.06844716519117355,
-0.019318848848342896,
0.0072967857122421265,
0.0026915022172033787,
0.002078714082017541,
-0.019729625433683395,
0.03511374816298485,
-0.01570381224155426,
0.04445184767246246,
-0.026441188529133797,
-0.062220629304647446,
-0.025667158886790276,
-0.01567663624882698,
-0.04342173784971237,
0.07046825438737869,
0.026674924418330193,
0.002574026584625244,
0.026271341368556023,
-0.03485411778092384,
0.0031018161680549383,
0.05540773272514343,
0.06136655807495117,
-0.039584044367074966,
0.05262844264507294,
-0.012064466252923012,
0.029422147199511528,
-0.05939137563109398,
-0.022906143218278885,
0.11038011312484741,
0.022803552448749542,
-0.028559932485222816,
-0.007886885665357113,
0.01648132875561714,
-0.016590364277362823,
0.013485563918948174,
-0.015591071918606758,
-0.021468769758939743,
-0.0005787314148619771,
-0.005359019618481398,
0.05694682523608208,
0.0056488425470888615,
0.009828144684433937,
-0.03581082448363304,
-0.02807139791548252,
-0.01073109358549118,
0.018806220963597298,
-0.004209335893392563,
0.024957461282610893,
0.010392049327492714,
0.02306005358695984,
0.004388731438666582,
0.020605212077498436,
-0.051352448761463165,
0.007707553915679455,
-0.0031664399430155754,
-0.015097578056156635,
0.04105952009558678,
-0.014617422595620155,
-0.06962893903255463,
0.05469097942113876,
0.04250657930970192,
-0.0862368643283844,
-0.03438568860292435,
0.01620587520301342,
0.0163442250341177,
-0.008058769628405571,
-0.005101827904582024,
0.05920103192329407,
-0.00464123347774148,
0.021170025691390038,
0.009687060490250587,
0.0040682596154510975,
-0.044538404792547226,
-0.028434818610548973,
-0.020426567643880844,
0.038820698857307434,
-0.012360996566712856,
0.02835839055478573,
-0.014667648822069168,
-0.0014956254744902253,
-0.016331862658262253,
-0.07551325112581253,
0.0016457680612802505,
0.007004698738455772,
0.015030952170491219,
0.008573018945753574,
-0.04362912476062775,
0.021267738193273544,
-0.008347341790795326,
0.06493278592824936,
0.027646970003843307,
0.03523651883006096,
0.005782528780400753,
-0.02509857714176178,
-0.019274737685918808,
0.057548638433218,
-0.045341745018959045,
-0.01334721315652132,
-0.029531389474868774,
-0.014716986566781998,
-0.051715463399887085,
0.04295283928513527,
0.026460859924554825,
-0.014208844862878323,
-0.004124919883906841,
0.0070519824512302876,
0.03096669167280197,
-0.05063338950276375,
-0.01746271178126335,
0.0016215660143643618,
0.014347339980304241,
-0.015287631191313267,
-0.0546850748360157,
-0.011161341331899166,
0.05673752725124359,
-0.03239474818110466,
0.005118411034345627,
0.0072132679633796215,
0.01899876818060875,
0.02180057018995285,
-0.00500549515709281,
-0.0072949728928506374,
-0.008112642914056778,
0.017970655113458633,
-0.016916880384087563,
-0.004256892949342728,
-0.005225225817412138,
0.04979928582906723,
0.013629095628857613,
-0.01703673042356968,
0.007209931965917349,
0.02416137047111988,
0.0033006833400577307,
0.02298508584499359,
0.03959471732378006,
-0.021405339241027832,
-0.03684172034263611,
0.011565806344151497,
0.016378551721572876,
-0.04715833440423012,
-0.03280844911932945,
-0.05136614292860031,
-0.01136818528175354,
-0.0016248427564278245,
0.005462306551635265,
-0.005858880002051592,
0.0634857639670372,
-0.02159050852060318,
0.026165828108787537,
-0.0430322028696537,
0.024358877912163734,
-0.00910959579050541,
0.015993649140000343,
-0.01886371336877346,
0.007894734852015972,
-0.022079413756728172,
0.024774760007858276,
-0.017909884452819824,
-0.02919214591383934,
0.01625930145382881,
0.03217143565416336,
-0.005850211251527071,
-0.044568032026290894,
-0.007148585747927427,
0.0007148109725676477,
-0.007084071636199951,
-0.049955274909734726,
-0.03279615938663483,
0.025674644857645035,
-0.0312841422855854,
-0.03318614885210991,
0.06015780568122864,
-0.00030997206340543926,
0.012544285506010056,
0.005831557791680098,
-0.03970000892877579,
0.018290527164936066,
0.03427900746464729,
-0.04941234365105629,
-0.006294063292443752,
0.03282508999109268,
0.023136623203754425,
-0.04695307835936546,
-0.01416857074946165,
0.017902890220284462,
-0.036975957453250885,
-0.007230059709399939,
0.0543268546462059,
0.025701072067022324,
-0.032326068729162216,
0.012797298841178417,
0.008639125153422356,
-0.04032641649246216,
-0.003971754107624292,
-0.00762245524674654,
0.0137482900172472,
0.035687174648046494,
0.01668447256088257,
-0.04162808880209923,
0.013723104260861874,
-0.0027491135988384485,
-0.01070709154009819,
-0.06262803822755814,
0.003813068615272641,
0.04281154274940491,
0.020634640008211136,
0.0637950748205185,
-0.05893396586179733,
0.004128654021769762,
0.04602205753326416,
-0.05497965216636658,
0.012526703998446465,
-0.01743629015982151,
-0.004207008518278599,
-0.04948946833610535,
-0.017329171299934387,
0.019842177629470825,
0.00967694167047739,
0.05386264622211456,
0.017338113859295845,
0.03521373122930527,
0.02616616152226925,
-0.05624745786190033,
-0.050347503274679184,
0.012317594140768051,
0.0407300740480423,
0.0007864744402468204,
0.017143364995718002,
0.061292074620723724,
-0.01994876191020012,
0.006540970411151648,
0.04516739398241043,
-0.035336047410964966,
0.05402878671884537,
-0.00808013416826725,
0.012775198556482792,
0.018308158963918686,
-0.011734024621546268,
0.024503985419869423,
-0.01976211555302143,
0.0031319172121584415,
-0.020671498030424118,
0.027808096259832382,
0.024286925792694092,
0.009519909508526325,
-0.02251449227333069,
-0.022593433037400246,
0.0024865977466106415,
-0.027275079861283302,
0.04069375991821289,
-0.001374237472191453,
-0.005330503452569246,
0.02138235606253147,
0.03306766226887703,
-0.02235618233680725,
-0.0772237628698349,
-0.020932672545313835,
-0.00030276388861238956,
0.020674578845500946,
-0.003386219497770071,
-0.0010790128726512194,
-0.04706789180636406,
0.01254530344158411,
-0.012581858783960342,
-0.0030604524072259665,
0.01283614244312048,
-0.03748786076903343,
-0.014640544541180134,
-0.021000493317842484,
0.003843181300908327,
0.002239570952951908,
-0.006768306251615286,
0.02992315962910652,
-0.020444277673959732,
-0.017255712300539017,
0.05551573634147644,
0.018571432679891586,
-0.026420805603265762,
0.023699119687080383,
-0.02262783981859684,
-0.015532328747212887,
-0.06733490526676178,
-0.004324169363826513,
-0.020672472193837166,
-0.028836987912654877,
-0.01103281881660223,
-0.02321825735270977,
-0.018627792596817017,
-0.014763535931706429,
0.06490173190832138,
-0.03483836352825165,
0.0025339743588119745,
-0.007967878133058548,
-0.013641437515616417,
0.00646879430860281,
-0.03518727049231529,
0.025043979287147522,
0.003273020964115858,
-0.05550464242696762,
-0.02997887320816517,
-0.0066345371305942535,
0.007336846552789211,
-0.009486514143645763,
0.03301341086626053,
0.007381313480436802,
0.05781238153576851,
0.015856092795729637,
-0.014653662219643593,
0.0214894637465477,
0.0007812705589458346,
-0.00680624321103096,
0.03981892764568329,
0.03920232132077217,
0.0033847594168037176,
0.01408130768686533,
-0.03432203456759453,
-0.05091405659914017,
-0.01935959793627262,
-0.0056858789175748825,
-0.02446901984512806,
-0.04478004202246666,
-0.02411407046020031,
0.046076271682977676,
-0.052105896174907684,
-0.017107946798205376,
0.030930211767554283,
-0.009718307293951511,
-0.011681812815368176,
0.027197808027267456,
-0.016032768413424492,
0.04585440829396248,
-0.010125573724508286,
0.04949670657515526,
0.020244479179382324,
-0.002626052824780345,
-0.0036690987180918455,
0.03271513804793358,
0.01775568351149559,
0.0067933090031147,
0.02265562117099762,
0.012332017533481121,
-0.00343888346105814,
0.029158025979995728,
-0.007497695740312338,
0.0747939795255661,
-0.014816286973655224,
-0.018058381974697113,
-0.01917552575469017,
-0.012683059088885784,
-0.03482774272561073,
0.023566270247101784,
0.005793973337858915,
0.06769934296607971,
0.010513589717447758,
-0.013903643004596233,
0.0061285169795155525,
-0.007529017049819231,
-0.07588329911231995,
0.022242112085223198,
-0.0001413112913724035,
-0.004403467755764723,
0.021083710715174675,
-0.046655021607875824,
-0.026415828615427017,
0.029309388250112534,
0.020015912130475044,
-0.015210236422717571,
0.01218750886619091,
-0.03845209255814552,
-0.028615683317184448,
-0.025151139125227928,
-0.028376959264278412,
-0.0151607571169734,
-0.012642505578696728,
0.04915963485836983,
0.030893491581082344,
-0.016938956454396248,
-0.024011019617319107,
0.007112850435078144,
-0.010288930498063564,
0.0498664453625679,
-0.08605092018842697,
-0.050309207290410995,
-0.02408768981695175,
0.05541657283902168,
0.008402476087212563,
-0.03766605257987976
] |
<p>The book I'm reading about optics says that an anti-reflective film applied on glass* makes the glass <em>more</em> transparent, because the air→film and film→glass reflected waves (originated from a <a href="http://en.wikipedia.org/wiki/Paraxial_approximation" rel="nofollow">paraxial</a> incoming wave) interfere destructively with each other, resulting on virtually no reflected light; therefore the "extra" light that would normally get reflected, gets transmitted instead (to honor the principle of conservation of energy, I suppose?).</p>
<p>However, <a href="http://physics.stackexchange.com/questions/10410/why-dont-waves-erase-out-each-other-when-looking-onto-a-wall/10439#10439">this answer</a> states that <em>"Superposition is the principle that the amplitudes due to two waves incident on the same point in space at the same time can be naively added together, but the waves do not affect each other."</em></p>
<p>So, how does this fit into this picture? If the reflected waves actually continue happily travelling back, where does the extra transmitted light come from?</p>
<p><sub>* the film is described as (1) having an intermediate index of refraction between those of air and glass, so that both the air-film and film-glass reflections are "hard", i.e., produce a 180º inversion in the phase of the incoming wave, and (2) having a depth of 1/4 of the wavelength of the wave in the film, so that the film-glass reflection travels half its wavelength back and meets the air-film reflection in the opposite phase, thus cancelling it.</sub></p> | 1,585 | [
-0.041270527988672256,
-0.024395247921347618,
0.026910828426480293,
0.013954066671431065,
0.014141942374408245,
0.015044519677758217,
0.018484631553292274,
-0.023059044033288956,
-0.01924941875040531,
-0.0036698447074741125,
0.010834796354174614,
0.019774392247200012,
0.050627823919057846,
0.02416040375828743,
-0.011973222717642784,
-0.003898024559020996,
0.003958951216191053,
-0.0054102190770208836,
0.00966601725667715,
-0.05457356572151184,
-0.05050310865044594,
0.028927752748131752,
-0.03027261607348919,
-0.014152919873595238,
-0.06239410117268562,
0.055321525782346725,
0.02166910469532013,
0.0003630633873399347,
0.048707276582717896,
-0.010318244807422161,
0.01047081220895052,
0.008970837108790874,
-0.012981606647372246,
0.012337484396994114,
0.025280112400650978,
0.009171899408102036,
-0.01350821740925312,
-0.030300991609692574,
0.01642225868999958,
-0.004938086029142141,
-0.002511795377358794,
0.02139544114470482,
-0.0003933292755391449,
0.028410308063030243,
-0.01666811853647232,
-0.025620583444833755,
-0.00760628841817379,
0.002557699102908373,
0.04975248500704765,
-0.08507692813873291,
0.050236377865076065,
-0.01172251719981432,
0.04932352527976036,
0.027982836589217186,
0.006039612460881472,
0.003693728242069483,
0.06629320234060287,
0.06355297565460205,
-0.02864886075258255,
-0.04302036017179489,
0.017582733184099197,
-0.016984984278678894,
-0.04251790791749954,
0.0018511483212932944,
-0.016661647707223892,
-0.00708131305873394,
0.013671666383743286,
-0.014042157679796219,
0.055374082177877426,
0.01949327625334263,
-0.017497343942523003,
-0.0002115039387717843,
0.050042275339365005,
-0.015325334854424,
0.0042463489808142185,
-0.02119445987045765,
0.02693818137049675,
0.037202466279268265,
0.058764662593603134,
0.01833200640976429,
0.01748434081673622,
-0.005327057559043169,
0.018658660352230072,
0.06860492378473282,
-0.003966495394706726,
0.024539677426218987,
0.09187650680541992,
0.005187491420656443,
0.021542027592658997,
0.02115478180348873,
0.00477837398648262,
0.03440525755286217,
0.01930759660899639,
0.04635683074593544,
-0.018877463415265083,
0.04141663387417793,
-0.02819785475730896,
0.07726424187421799,
0.024869972839951515,
-0.01221118401736021,
-0.01723061129450798,
0.006901530548930168,
0.013364424929022789,
0.07752936333417892,
0.0012961968313902617,
-0.06146874651312828,
-0.028008971363306046,
0.04859541356563568,
0.025996550917625427,
0.029703205451369286,
-0.023528942838311195,
0.033108361065387726,
0.024983694776892662,
-0.012762479484081268,
0.006611889693886042,
-0.014149387367069721,
0.04042752459645271,
0.004567013122141361,
0.06655308604240417,
0.08900713920593262,
0.027550728991627693,
-0.024356547743082047,
0.0012506915954872966,
-0.003998547792434692,
-0.09096753597259521,
0.011821458116173744,
0.013922559097409248,
-0.017857220023870468,
-0.025928707793354988,
0.030811557546257973,
0.0269504114985466,
-0.011126690544188023,
-0.000752790889237076,
-0.025547537952661514,
0.03666605055332184,
-0.004971285816282034,
-0.09927111864089966,
-0.05826524272561073,
0.03413942828774452,
-0.03853754699230194,
-0.0314469113945961,
-0.0764048844575882,
-0.01733257994055748,
0.011427299119532108,
0.12685351073741913,
-0.04172094538807869,
0.01740359328687191,
-0.029631204903125763,
0.013648160733282566,
0.010241424664855003,
0.014903638511896133,
0.007324737962335348,
0.028911318629980087,
-0.06092909723520279,
-0.006094931159168482,
-0.06634180247783661,
0.012896062806248665,
0.035745907574892044,
-0.01641426980495453,
-0.024801956489682198,
0.06833905726671219,
-0.018669433891773224,
-0.009883636608719826,
0.02439744956791401,
-0.0077077834866940975,
-0.0619407556951046,
0.06175646558403969,
0.025486981496214867,
0.0065628476440906525,
0.028875039890408516,
0.0016454551368951797,
0.022955581545829773,
-0.04867962747812271,
0.010980679653584957,
0.00721120135858655,
0.0003416234103497118,
0.004312305245548487,
-0.02148284949362278,
0.0003654587490018457,
0.003553945105522871,
0.010974057950079441,
-0.05437935143709183,
0.01484790351241827,
0.01387503556907177,
0.028894051909446716,
0.023617321625351906,
-0.027277665212750435,
-0.0019585832487791777,
0.01389331929385662,
-0.04989280551671982,
-0.033596958965063095,
-0.04106545448303223,
0.03502073884010315,
-0.013412355445325375,
0.002178011229261756,
0.005532818380743265,
0.016347698867321014,
0.009392229840159416,
-0.003419684013351798,
-0.04782160371541977,
0.0014946444425731897,
0.029321692883968353,
0.03754440322518349,
-0.007735277526080608,
0.010192030109465122,
0.039367616176605225,
0.06387604773044586,
0.020882006734609604,
0.021983081474900246,
-0.019467787817120552,
-0.0009615895105525851,
-0.008720280602574348,
-0.020539959892630577,
0.004527052864432335,
-0.03800022229552269,
-0.011962516233325005,
0.010319426655769348,
0.022799106314778328,
0.026944922283291817,
0.010494724847376347,
-0.029463622719049454,
0.028049707412719727,
0.051277175545692444,
0.00836180243641138,
-0.009004832245409489,
0.05826751887798309,
0.019233420491218567,
0.021478043869137764,
0.000623135594651103,
-0.03661733493208885,
-0.03914637118577957,
-0.014606229960918427,
0.020548732951283455,
-0.026494614779949188,
-0.023299770429730415,
0.006783104036003351,
-0.010223234072327614,
0.049174826592206955,
0.03914232552051544,
0.06774401664733887,
-0.007621080614626408,
-0.04845566302537918,
-0.00400159228593111,
0.007399896625429392,
0.011071710847318172,
0.012806066311895847,
0.0013492212165147066,
0.01796010509133339,
-0.00008919537503970787,
-0.03802070766687393,
-0.03524462878704071,
0.011201710440218449,
-0.0025207814760506153,
0.08317109197378159,
0.00180658302269876,
-0.015284150838851929,
-0.006830195430666208,
-0.01698477752506733,
0.02807311899960041,
0.03263162821531296,
-0.0024046560283750296,
0.009500286541879177,
-0.06112726777791977,
-0.010636083781719208,
-0.019483374431729317,
0.001720158034004271,
-0.03701309859752655,
-0.018679458647966385,
0.02254827506840229,
-0.03295257315039635,
0.019765010103583336,
-0.028631115332245827,
-0.0010959439678117633,
-0.010006205178797245,
-0.013975274749100208,
0.007117173634469509,
0.028345618396997452,
0.0666421502828598,
-0.05809466168284416,
-0.0849374309182167,
-0.01845431886613369,
-0.03576403856277466,
0.011133749969303608,
0.01185514684766531,
-0.02278423309326172,
0.02286224439740181,
-0.045279085636138916,
-0.010515616275370121,
0.061001233756542206,
-0.0018150531686842442,
0.0012372335186228156,
-0.017494913190603256,
-0.05502747371792793,
-0.042250894010066986,
-0.027121907100081444,
-0.046045225113630295,
0.000488405697979033,
-0.022811176255345345,
0.002359169302508235,
0.038292691111564636,
0.014328021556138992,
-0.036829546093940735,
0.01573154143989086,
-0.04354974254965782,
-0.03795367851853371,
0.03235570341348648,
-0.020019711926579475,
0.02063777483999729,
-0.03955366834998131,
-0.004480332136154175,
0.0274436566978693,
-0.03838394209742546,
-0.008317096158862114,
-0.037661679089069366,
-0.08344770222902298,
0.03096122294664383,
0.030072741210460663,
0.013531025499105453,
0.009669885970652103,
-0.0014138069236651063,
0.04685501381754875,
0.03211710974574089,
-0.02077704668045044,
0.00965014100074768,
-0.012214462272822857,
0.04928799718618393,
-0.02501591295003891,
0.002906107110902667,
0.049396634101867676,
0.013251329772174358,
0.0716894194483757,
-0.015079670585691929,
-0.010752759873867035,
0.0417923778295517,
0.04687795788049698,
-0.0007348485523834825,
-0.024251015856862068,
0.021679284051060677,
-0.006409699097275734,
0.017444822937250137,
0.0005659254384227097,
-0.03179532289505005,
0.013020872138440609,
0.008242784067988396,
0.017881814390420914,
0.030470890924334526,
-0.026073915883898735,
0.0352516733109951,
-0.011543519794940948,
0.016587266698479652,
-0.04489880055189133,
0.054339271038770676,
-0.018640097230672836,
0.033744119107723236,
-0.028113072738051414,
0.0033686263486742973,
0.033125147223472595,
-0.009802150540053844,
0.017405986785888672,
0.027456218376755714,
0.06807304173707962,
0.00015801457630004734,
-0.021795915439724922,
-0.01913542114198208,
0.012691754847764969,
-0.014386877417564392,
-0.025342948734760284,
-0.006075182929635048,
0.06488826125860214,
0.028552452102303505,
-0.004978665150702,
0.00595438526943326,
-0.03873557224869728,
-0.008275950327515602,
-0.035812705755233765,
0.028320958837866783,
-0.03815999627113342,
0.03587798401713371,
-0.011728421784937382,
0.07585017383098602,
-0.00009228739509126171,
0.03615179657936096,
0.033646270632743835,
0.014800476841628551,
-0.05171967297792435,
-0.0048523456789553165,
-0.00800243392586708,
-0.018174173310399055,
-0.011849215254187584,
0.00120639824308455,
0.01846938580274582,
-0.035816341638565063,
-0.04357561841607094,
0.021166203543543816,
-0.02403654158115387,
-0.059574998915195465,
-0.020333576947450638,
-0.025938762351870537,
-0.0390901081264019,
-0.04093565791845322,
0.04478444531559944,
0.016320055350661278,
-0.018262125551700592,
0.007679057773202658,
0.049512676894664764,
-0.016843978315591812,
-0.004808828700333834,
-0.034978944808244705,
0.0076006194576621056,
0.015248491428792477,
0.01858176290988922,
0.05556899681687355,
0.0012685076799243689,
-0.01435707975178957,
0.01205039955675602,
0.03721531480550766,
0.022221889346837997,
-0.013718807138502598,
-0.004967796616256237,
-0.04621139168739319,
-0.01331416331231594,
-0.007835044525563717,
-0.030615417286753654,
0.06211073324084282,
-0.012999510392546654,
-0.007370621431618929,
-0.01529255323112011,
0.03490624949336052,
-0.037118520587682724,
0.04088795185089111,
0.012758217751979828,
0.012504572048783302,
0.03339261934161186,
-0.040169619023799896,
-0.008316322229802608,
-0.022060483694076538,
0.002228879602625966,
0.043577611446380615,
0.02055390179157257,
-0.02541847713291645,
-0.004995087161660194,
0.04380226507782936,
0.0023593921214342117,
-0.010506306774914265,
0.03902750462293625,
-0.05841284990310669,
-0.03258981183171272,
0.014848670922219753,
-0.019407784566283226,
-0.013588972389698029,
0.04620955139398575,
0.03976311534643173,
0.03229343518614769,
-0.0029221659060567617,
-0.06087956950068474,
-0.010033749043941498,
0.03527427837252617,
0.05128229409456253,
0.00629241531714797,
0.005762438289821148,
-0.04533766955137253,
-0.023305531591176987,
0.0007871678099036217,
-0.019087161868810654,
0.018772892653942108,
-0.03012821078300476,
0.008450326509773731,
-0.02244335412979126,
-0.036625444889068604,
-0.005350773222744465,
0.014756782911717892,
-0.005117590539157391,
0.0006050830706954002,
0.027892805635929108,
-0.0003349394828546792,
-0.01819012686610222,
-0.00023343331122305244,
0.012995094992220402,
0.044312067329883575,
-0.031527306884527206,
-0.009356343187391758,
-0.02373209036886692,
0.04868265613913536,
-0.04864486679434776,
-0.03106289729475975,
0.007292634807527065,
-0.008915871381759644,
-0.029125966131687164,
0.03253239020705223,
-0.03584589436650276,
0.02484080009162426,
0.02057025209069252,
0.028970956802368164,
-0.02067890204489231,
-0.005110342521220446,
-0.0463348850607872,
0.0164474006742239,
0.03995523974299431,
0.008150449022650719,
0.0453723780810833,
0.040498632937669754,
-0.011988089419901371,
0.002509883139282465,
-0.003848067484796047,
0.06294835358858109,
-0.037965886294841766,
0.010786496102809906,
-0.014960289001464844,
-0.0254340972751379,
-0.033982161432504654,
0.05349316820502281,
-0.004234503023326397,
-0.0033495156094431877,
-0.016789482906460762,
-0.03878870606422424,
-0.015941690653562546,
-0.008241133764386177,
-0.013546002097427845,
-0.0007315903785638511,
-0.0076391133479774,
0.040736231952905655,
0.023840902373194695,
0.003584634279832244,
0.0025544550735503435,
0.009817540645599365,
0.001212048577144742,
0.027854491025209427,
0.028725439682602882,
0.03978521749377251,
-0.07077854871749878,
-0.00005873272311873734,
-0.001335951848886907,
-0.02576209232211113,
0.013628114014863968,
-0.019182808697223663,
0.013649305328726768,
0.007985295727849007,
-0.05127864331007004,
-0.013949713669717312,
0.01705559343099594,
-0.04986736923456192,
0.015918301418423653,
-0.056018587201833725,
0.06367328017950058,
0.033689528703689575,
0.0008239394519478083,
-0.07009359449148178,
-0.04453502595424652,
0.02161872200667858,
0.014393151737749577,
-0.01661207154393196,
-0.030232785269618034,
-0.014350619167089462,
-0.03427703678607941,
-0.05483691766858101,
0.02225501462817192,
-0.03343990445137024,
-0.029021594673395157,
-0.027659807354211807,
0.03183193877339363,
-0.005844359751790762,
0.01821930892765522,
-0.011438344605267048,
-0.03931889310479164,
0.010444102808833122,
-0.030882567167282104,
-0.017253177240490913,
-0.0023185217287391424,
0.03933698683977127,
0.004997098818421364,
-0.038422394543886185,
-0.0032097529619932175,
-0.00032398587791249156,
0.014185911044478416,
-0.036508746445178986,
0.04238877817988396,
-0.013458413071930408,
0.023442206904292107,
-0.0072625200264155865,
-0.0214214026927948,
0.021060772240161896,
0.0053498949855566025,
0.043900325894355774,
0.023222461342811584,
0.004718521609902382,
-0.026339782401919365,
-0.011315658688545227,
0.015084885060787201,
0.010050851851701736,
0.00959525816142559,
-0.020639851689338684,
0.07913880795240402,
-0.009085508063435555,
-0.023098628968000412,
0.01469678245484829,
-0.02773955650627613,
0.00946080219000578,
-0.0072732120752334595,
-0.009757212363183498,
0.04261988401412964,
0.009198112413287163,
-0.03705764561891556,
-0.020042989403009415,
-0.010236763395369053,
0.00033833805355243385,
0.06209443137049675,
-0.07924746721982956,
0.024137351661920547,
0.006261469330638647,
-0.01780591532588005,
-0.007687807083129883,
-0.030100934207439423,
0.007190584205091,
0.04779281094670296,
-0.03183659166097641,
0.036314789205789566,
-0.037453871220350266,
-0.0006634979508817196,
-0.0077453297562897205,
0.07645914703607559,
0.014008554629981518,
-0.0002218881418230012,
0.034882254898548126,
0.05699043720960617,
0.01242879405617714,
-0.02255650795996189,
-0.024225294589996338,
0.05568806454539299,
-0.03960128501057625,
0.013595462776720524,
0.011537054553627968,
-0.004032592289149761,
0.05224209278821945,
0.0030319218058139086,
0.019563322886824608,
-0.07715427130460739,
-0.022175263613462448,
-0.014340467751026154,
-0.01890718564391136,
-0.012444918975234032,
0.039307259023189545,
0.008024726994335651,
-0.005630221217870712,
0.010190198197960854,
0.00860326923429966,
0.025306005030870438,
-0.0017699211603030562,
-0.06915328651666641,
-0.04396180808544159,
-0.0201437845826149,
-0.016907649114727974,
0.030071822926402092,
-0.04026598855853081,
-0.011070501059293747,
0.03194699436426163,
-0.06012943759560585,
0.009765489026904106,
0.003326710546389222,
0.0012668224517256021,
-0.013500249944627285,
0.029803737998008728,
0.014292499981820583,
0.05472433567047119,
-0.012090442702174187,
-0.011270815506577492,
0.12496118992567062,
0.04607649892568588,
-0.005001412238925695,
-0.05384228378534317,
-0.01561887376010418,
-0.017946137115359306,
-0.0037741484120488167,
-0.05278526246547699,
0.023278269916772842,
-0.03479764983057976,
0.010345051996409893,
0.0012956107966601849,
0.05315760523080826,
0.012298215180635452,
0.0009956971043720841,
0.006924154702574015,
-0.07023221999406815,
0.0056093246676027775,
0.014060186222195625,
-0.025976257398724556,
-0.004142416175454855,
0.025697972625494003,
-0.028073923662304878,
-0.006243295036256313,
-0.012422045692801476,
-0.028387606143951416,
0.00730166444554925,
-0.06308677792549133,
0.01804398186504841,
0.033512379974126816,
-0.006664727348834276,
0.018831999972462654,
-0.004784790333360434,
-0.01252702996134758,
-0.0518365241587162,
0.019237279891967773,
0.04783504828810692,
-0.00279262475669384,
0.00579748535528779,
0.011181908659636974,
0.03204021975398064,
-0.026173613965511322,
0.03600902855396271,
0.047226205468177795,
-0.048141323029994965,
0.005743206012994051,
0.010333629325032234,
0.05815624073147774,
0.00262049725279212,
-0.003721873974427581,
-0.001576049136929214,
-0.021034816280007362,
0.020677724853157997,
-0.0695902481675148,
-0.024732431396842003,
-0.010439318604767323,
0.037269771099090576,
0.026676757261157036,
-0.03816842660307884,
0.02561112493276596,
0.018114328384399414,
-0.003954571671783924,
0.010497654788196087,
0.001105493283830583,
0.005793641321361065,
-0.04006766155362129,
-0.027057506144046783,
0.016548899933695793,
-0.007871286943554878,
-0.02780160680413246,
-0.05150274187326431,
0.012542430311441422,
0.0038562333211302757,
-0.006425839848816395,
0.012077835388481617,
0.012093085795640945,
0.03205087035894394,
0.008645230904221535,
0.0008321204222738743,
-0.0474972166121006,
-0.03945739567279816,
0.03270173445343971,
-0.04413013905286789,
-0.01201524306088686,
0.0023669118527323008,
-0.03218403831124306,
0.029213638976216316,
0.01912826858460903,
-0.01981775276362896,
0.0065368651412427425,
0.00984339788556099,
0.030784497037529945,
0.007451368495821953,
-0.008233797736465931,
-0.07208379358053207,
0.0045370119623839855,
0.012787027284502983,
-0.022762630134820938,
-0.027248069643974304,
0.01941555179655552,
0.01273912563920021,
0.02953227609395981,
0.04558182507753372,
0.04452674463391304,
-0.019612161442637444,
-0.026370950043201447,
-0.028906315565109253,
-0.041332926601171494,
0.033107414841651917,
0.0071479822508990765,
0.038192518055438995,
0.0010309381177648902,
-0.014449112117290497,
0.01007600873708725,
0.011825572699308395,
-0.00824916921555996,
0.051263477653265,
-0.006263707298785448,
0.00789869949221611,
-0.026067128404974937,
0.015685204416513443,
-0.028350774198770523,
-0.011748525314033031,
-0.03537002578377724,
0.012055786326527596,
0.0041174981743097305,
-0.009953264147043228,
-0.03569483757019043,
0.05031988397240639,
-0.017234602943062782,
-0.03093099594116211,
-0.006570559460669756,
0.02923610620200634,
-0.047418057918548584,
0.019296711310744286,
0.01788208819925785,
-0.006598307751119137,
0.009344971738755703,
-0.004454474896192551,
-0.020977674052119255,
0.04878126457333565,
-0.023786142468452454,
-0.06768806278705597,
0.029836229979991913,
-0.00013109597784932703,
0.03383505716919899,
0.015841331332921982,
0.001442821230739355,
-0.03185395896434784,
0.061337511986494064,
-0.007818374782800674,
-0.012918157503008842,
-0.02935958467423916,
-0.021840393543243408,
0.023453475907444954,
-0.02461307868361473,
-0.0017904187552630901,
-0.006810186430811882,
0.01831189915537834,
0.04624981805682182,
0.0158770103007555,
-0.009294959716498852,
0.048170074820518494,
0.007475777063518763,
-0.03315963223576546,
-0.03389604762196541,
-0.006888536736369133,
-0.009884214028716087,
-0.0006563097704201937,
0.013127717189490795,
0.010435972362756729,
0.05092019587755203,
0.033895108848810196,
-0.026193173602223396,
-0.08419407159090042,
0.031986068934202194,
0.006733364425599575,
0.019006740301847458,
0.01537245698273182,
-0.05713079124689102,
0.036171797662973404,
0.01692836917936802,
-0.08229419589042664,
0.03073865734040737,
-0.029306607320904732,
-0.021140675991773605,
-0.04035930708050728,
0.03707026317715645,
-0.029914001002907753,
0.03752924129366875,
0.023232324048876762,
0.03210559859871864,
0.009809554554522038,
-0.0026098391972482204,
-0.009087054058909416,
-0.02150636725127697,
0.008518585935235023,
0.012153947725892067,
-0.020464954897761345,
0.01254926435649395,
0.08270405977964401,
0.013866877183318138,
0.008113374933600426,
0.028794875368475914,
-0.02400297299027443,
0.009107035584747791,
-0.024047940969467163,
-0.0172974094748497,
-0.029560670256614685,
0.0026184723246842623,
-0.026226667687296867,
0.01149849034845829,
-0.011263295076787472,
0.029245207086205482,
0.08234398066997528,
-0.008890671655535698,
0.012342512607574463,
-0.014599418267607689,
-0.010386618785560131,
-0.022204315289855003,
-0.042013708502054214,
-0.003160757478326559,
0.00920042023062706,
0.025082457810640335,
-0.009514162316918373,
0.023566538468003273,
0.04567702114582062,
-0.001806359738111496,
-0.011864736676216125,
-0.053885042667388916,
-0.03170146048069,
0.009111671708524227,
0.010753406211733818,
-0.010445375926792622,
0.03231111168861389,
-0.012835611589252949,
-0.04652894660830498,
0.0002726935490500182,
-0.0161292627453804,
-0.0086286636069417,
-0.03725537657737732,
-0.05427064374089241,
0.0006014431128278375,
-0.022765956819057465,
0.014500594697892666,
-0.010681617073714733,
-0.07189758121967316,
-0.00686298543587327,
0.016544245183467865,
0.015884267166256905,
-0.016309157013893127,
-0.08596832305192947,
-0.015432621352374554,
-0.055304817855358124,
0.049127720296382904,
-0.00025789925712160766,
-0.03345528990030289,
-0.04225356876850128,
0.012730645947158337,
0.003652887884527445,
0.04676748067140579,
0.046998247504234314,
-0.007572040893137455,
-0.015287475660443306,
-0.008307889103889465,
-0.0006365909357555211,
0.031105320900678635,
-0.04498552158474922,
-0.0032323014456778765,
0.022733071818947792,
-0.03208548203110695,
-0.025306886062026024,
-0.00024300107907038182,
-0.009647052735090256,
0.019776003435254097,
0.001425751717761159,
-0.015126856043934822,
0.013827820308506489,
-0.012082180939614773,
-0.024669747799634933,
0.018436115235090256,
-0.005662618204951286,
0.006924012675881386,
0.07598081976175308,
-0.004883082117885351,
0.004254520870745182,
0.05938847362995148,
-0.0031076734885573387,
-0.06689871102571487,
0.01771189644932747,
-0.004184401594102383,
0.002190203405916691,
-0.02930808812379837,
-0.00918840803205967,
0.06600865721702576,
-0.0448324978351593,
0.01981498673558235,
0.03198615089058876,
-0.02138361893594265,
-0.0544007234275341,
0.06421906501054764,
-0.00012402170978020877,
0.023074854165315628,
-0.010097884573042393,
0.025871139019727707,
-0.03258495777845383,
0.020728154107928276,
-0.01606745459139347,
0.0663549154996872,
-0.012776368297636509,
0.02564433589577675,
0.026297204196453094,
0.03801248222589493,
0.03174243122339249,
0.014191958121955395,
-0.011256355792284012,
0.020465785637497902,
-0.006589445285499096,
-0.009101398289203644,
-0.007714709732681513,
-0.006870404351502657,
-0.00039203520282171667,
0.05336379632353783,
0.011239386163651943,
0.05749358981847763,
-0.009120897389948368,
0.023653216660022736,
0.017152776941657066,
-0.01690635457634926,
-0.011435745283961296,
-0.00640407670289278,
0.06124703586101532,
0.043995656073093414,
-0.009728101082146168,
-0.0319557823240757,
-0.03224029764533043,
0.003001125995069742,
-0.010224954225122929,
-0.06325531005859375,
0.01403171569108963,
-0.0477193221449852,
-0.039906974881887436,
-0.00991961918771267,
0.0073257749900221825,
-0.014518163166940212,
-0.012417321093380451,
0.017195401713252068,
0.028484856709837914,
-0.04244714230298996,
0.016910452395677567,
-0.001142350840382278,
0.019043439999222755,
0.05753970891237259,
-0.060947246849536896,
0.010534606873989105,
0.02151601016521454,
0.028894459828734398,
-0.006219014059752226,
-0.011140784248709679
] |
<p>For some electric devices, like a fan or air conditioner, I read about their power consumption in watts on their specification guide.</p>
<p>Does it tell about the power at normal or full speed? or Does the speed even affect the power consumption? Can I find the consumption at different speeds?</p> | 1,586 | [
-0.02326570823788643,
-0.047659825533628464,
-0.0010342899477109313,
-0.03190120682120323,
0.0390593446791172,
0.016728229820728302,
-0.021354708820581436,
0.005777111742645502,
0.0036118521820753813,
-0.0044971490278840065,
0.021665580570697784,
0.06847938895225525,
0.031106289476156235,
0.029152698814868927,
0.02308553270995617,
-0.01426367275416851,
-0.011168252676725388,
0.001262014382518828,
-0.004789349157363176,
-0.002846269868314266,
-0.031572919338941574,
-0.014922278001904488,
0.010814052075147629,
-0.019468404352664948,
-0.02753264829516411,
0.013517791405320168,
0.003972047008574009,
-0.013713800348341465,
0.007312321569770575,
0.002600952284410596,
0.0030535657424479723,
-0.01457369327545166,
0.019841434434056282,
0.04244952276349068,
0.03850417584180832,
-0.002260987414047122,
-0.028182733803987503,
-0.05620918795466423,
0.001168257207609713,
0.07474550604820251,
-0.010555960237979889,
0.020529145374894142,
0.01726960577070713,
-0.02020162157714367,
-0.01082749105989933,
0.06878944486379623,
0.014082226902246475,
-0.01611967757344246,
-0.006391084287315607,
-0.07856671512126923,
0.07157817482948303,
0.0021891670767217875,
0.03293230012059212,
-0.004383984487503767,
0.003041698131710291,
0.049016132950782776,
0.07093574106693268,
0.035001982003450394,
-0.039657432585954666,
-0.04788553714752197,
0.009738091379404068,
0.010656217113137245,
-0.006562696769833565,
-0.045487791299819946,
-0.031276412308216095,
0.029816143214702606,
-0.012742164544761181,
-0.04725373908877373,
0.0683879479765892,
0.001960909925401211,
0.022648761048913002,
0.014616638422012329,
0.03683503344655037,
0.0010101273655891418,
-0.013313488103449345,
-0.034187253564596176,
0.04639916494488716,
0.0482645258307457,
0.06603366136550903,
0.07568880170583725,
-0.03349652886390686,
0.01477004773914814,
0.022121714428067207,
0.03282276168465614,
0.027629757300019264,
-0.023321937769651413,
0.04722680523991585,
0.022358035668730736,
-0.012674927711486816,
0.017670543864369392,
0.014022450894117355,
0.0020317379385232925,
0.013230130076408386,
-0.012121524661779404,
-0.013914758339524269,
0.02323726750910282,
-0.05052292346954346,
0.015217447653412819,
0.015703171491622925,
-0.011844538152217865,
0.02867184765636921,
0.016929298639297485,
0.05727621912956238,
0.017006846144795418,
-0.03498784452676773,
-0.009528236463665962,
-0.010994319804012775,
-0.013016280718147755,
-0.008436070755124092,
0.02916974574327469,
-0.03295263648033142,
-0.014452869072556496,
0.004731140565127134,
0.006220292299985886,
0.015485266223549843,
0.0031573285814374685,
0.014955096878111362,
-0.011258075013756752,
0.06869679689407349,
0.04772108048200607,
0.03858112916350365,
-0.0072038136422634125,
-0.0005642313044518232,
-0.0049364143051207066,
-0.013579203747212887,
0.04144955426454544,
0.009535795077681541,
-0.03046364337205887,
-0.043865177780389786,
0.02895725518465042,
-0.02197371982038021,
-0.018390562385320663,
0.007823036052286625,
-0.05729250609874725,
0.02547239512205124,
-0.01146342046558857,
-0.04121026769280434,
-0.040158744901418686,
0.024967625737190247,
0.003517228877171874,
-0.012285573408007622,
-0.060363758355379105,
0.0013132966123521328,
0.011499530635774136,
0.05170882120728493,
-0.01405792310833931,
-0.002243999857455492,
-0.011755870655179024,
0.014763313345611095,
0.007413473445922136,
-0.04253475368022919,
-0.011959475465118885,
0.02574087493121624,
-0.03119709901511669,
0.03777508810162544,
-0.04100741073489189,
-0.003729966003447771,
0.04577236622571945,
0.0027294475585222244,
-0.003772518364712596,
0.01171712577342987,
0.009588328190147877,
-0.04034307971596718,
0.017691805958747864,
-0.029791323468089104,
-0.014109245501458645,
0.025193320587277412,
-0.02957719936966896,
0.03716589882969856,
-0.008771387860178947,
0.014377287589013577,
0.016577094793319702,
0.0010872510029003024,
-0.019824592396616936,
0.05866509675979614,
0.026463819667696953,
-0.027545085176825523,
-0.05311281234025955,
0.006533520761877298,
-0.02849786914885044,
-0.06133416295051575,
-0.051429446786642075,
0.020452052354812622,
0.026881977915763855,
0.01755443774163723,
0.05796457454562187,
0.004416512791067362,
-0.007802112493664026,
0.009500306099653244,
-0.03771354258060455,
-0.04094557464122772,
-0.0563548244535923,
0.055361416190862656,
-0.02725905179977417,
-0.01352327223867178,
0.017869215458631516,
-0.0005318323383107781,
0.04706059396266937,
-0.024702390655875206,
-0.004839552566409111,
0.0524664930999279,
0.032792072743177414,
-0.009300049394369125,
-0.050508320331573486,
-0.015804804861545563,
0.02460004948079586,
0.03384483605623245,
-0.030405526980757713,
0.0041814036667346954,
0.0037374517414718866,
-0.07574395835399628,
0.004940942395478487,
-0.058388758450746536,
-0.015315406024456024,
0.03530704230070114,
0.015804506838321686,
-0.016185691580176353,
0.017944157123565674,
-0.020413335412740707,
0.027872515842318535,
0.03710374981164932,
0.019009772688150406,
0.06907472014427185,
-0.020367203280329704,
0.026446187868714333,
0.015065768733620644,
-0.037141796201467514,
-0.021337268874049187,
-0.011073939502239227,
-0.01291254535317421,
-0.049488089978694916,
-0.02129821479320526,
0.036165863275527954,
-0.000011796501894423272,
-0.05021517723798752,
-0.014734294265508652,
0.06679483503103256,
0.00041866215178743005,
0.04566057026386261,
0.00033376793726347387,
-0.0064844656735658646,
-0.03652232885360718,
0.020487455651164055,
0.020543258637189865,
-0.0018825166625902057,
0.02061229944229126,
0.0076647354289889336,
0.05233481898903847,
0.036138035356998444,
0.005825039464980364,
-0.01935478486120701,
0.08775214105844498,
0.011410797014832497,
0.03458086773753166,
0.01251165196299553,
-0.05176788568496704,
0.04161206632852554,
-0.042798738926649094,
0.019374825060367584,
-0.016552481800317764,
-0.002806704957038164,
0.029425596818327904,
0.021587669849395752,
-0.00785931758582592,
-0.006625962443649769,
-0.019702648743987083,
0.005016015376895666,
-0.04649273306131363,
0.025110112503170967,
-0.037558287382125854,
0.07155781239271164,
-0.03938215970993042,
0.0057601649314165115,
-0.03545338287949562,
0.00899501983076334,
0.01677442342042923,
-0.005353766027837992,
0.05335034802556038,
-0.04783941060304642,
-0.045631181448698044,
-0.005562650505453348,
-0.06728768348693848,
0.02087445929646492,
-0.008169456385076046,
-0.035304877907037735,
0.017176641151309013,
-0.04552535340189934,
-0.03628184273838997,
0.022877583280205727,
-0.005693389102816582,
0.029675360769033432,
0.034444209188222885,
0.007477347273379564,
-0.07025465369224548,
0.035530172288417816,
-0.007769299671053886,
0.003686951007694006,
-0.015424161218106747,
0.023415159434080124,
0.04188312590122223,
-0.00950546283274889,
-0.058829888701438904,
-0.005032438784837723,
-0.03424916788935661,
-0.030594058334827423,
-0.0026794075965881348,
-0.06127258390188217,
0.036464642733335495,
-0.011472173035144806,
0.007582952734082937,
0.036106981337070465,
-0.08120645582675934,
0.0015788540476933122,
-0.03915909305214882,
-0.05810828134417534,
0.032217636704444885,
-0.009457279928028584,
0.07412101328372955,
-0.010755319148302078,
-0.04643837735056877,
0.032700445502996445,
0.03540714457631111,
-0.020524747669696808,
-0.03038203716278076,
-0.0390317365527153,
-0.016507554799318314,
-0.06596270948648453,
-0.004097703378647566,
0.06899170577526093,
-0.03902008756995201,
-0.007078639697283506,
-0.003454306861385703,
0.02391110733151436,
0.058987900614738464,
0.016391616314649582,
-0.009685681201517582,
-0.011413431726396084,
-0.020579617470502853,
0.02375812828540802,
0.03673991933465004,
0.01014441717416048,
-0.003990283701568842,
0.03328894078731537,
-0.04079341143369675,
0.05186799168586731,
0.02100021205842495,
-0.02880445308983326,
0.03935142233967781,
-0.016329044476151466,
0.021258879452943802,
-0.06499187648296356,
0.033473242074251175,
0.055566076189279556,
0.010647660121321678,
-0.03428434953093529,
0.046338215470314026,
0.023940743878483772,
0.01324114203453064,
-0.016603829339146614,
0.02912614308297634,
0.05304709076881409,
-0.022180132567882538,
-0.0643334910273552,
-0.019633691757917404,
-0.01857113093137741,
-0.02276637777686119,
0.003954498562961817,
-0.0564323253929615,
0.04127327725291252,
0.014277689158916473,
0.0003489964874461293,
0.029710210859775543,
-0.01585984043776989,
0.0026083369739353657,
-0.08098204433917999,
-0.03482259809970856,
-0.007733043283224106,
0.035952914506196976,
-0.021360337734222412,
0.07202309370040894,
0.011313858442008495,
0.008567866869270802,
-0.004883733112365007,
-0.016098875552415848,
-0.0587858110666275,
0.055790096521377563,
-0.03638794273138046,
-0.024500982835888863,
-0.013609286397695541,
-0.0006052461103536189,
-0.02618931420147419,
-0.03918039798736572,
0.00249979249201715,
-0.017757751047611237,
-0.027148829773068428,
-0.041646573692560196,
0.02027931623160839,
0.009261077269911766,
-0.014896927401423454,
-0.005357969086617231,
0.015599741600453854,
0.02670200914144516,
-0.04211689531803131,
0.023790715262293816,
0.04023642838001251,
0.00071446638321504,
-0.014412282966077328,
0.01526555698364973,
0.00020301018957979977,
-0.029091915115714073,
0.03146885335445404,
0.04042407497763634,
-0.020465737208724022,
-0.02836124412715435,
0.024937724694609642,
-0.01573042944073677,
0.032568927854299545,
0.01699085719883442,
-0.046149056404829025,
-0.03915364295244217,
0.0002689679677132517,
-0.027875615283846855,
-0.020156556740403175,
0.021766306832432747,
-0.005278872326016426,
-0.006554624997079372,
0.012377158738672733,
0.011520170606672764,
-0.008106435649096966,
0.03539108484983444,
0.029492177069187164,
-0.010312769562005997,
-0.030043603852391243,
-0.08211414515972137,
0.010731176473200321,
0.010069204494357109,
-0.004808355122804642,
-0.006712115835398436,
0.018313860520720482,
-0.01950179599225521,
0.030706113204360008,
-0.0018649683333933353,
-0.009995082393288612,
-0.03670689836144447,
0.05344327539205551,
0.03922730311751366,
-0.009827551431953907,
0.02145666629076004,
-0.021014777943491936,
0.023926861584186554,
0.04455201327800751,
-0.004950513131916523,
0.0026100575923919678,
-0.008766764774918556,
-0.07730231434106827,
-0.012951366603374481,
0.038615524768829346,
0.03521868959069252,
0.011302206665277481,
0.0057801189832389355,
-0.0007556542987003922,
0.008940239436924458,
0.03894302248954773,
-0.00856680329889059,
0.039224669337272644,
-0.022163257002830505,
-0.0021287095732986927,
-0.05072399601340294,
-0.020835034549236298,
-0.006989538669586182,
0.027943080291152,
-0.027419596910476685,
0.011981251649558544,
-0.023002300411462784,
-0.016503626480698586,
-0.021013103425502777,
0.0212546493858099,
0.03250247985124588,
0.05509117990732193,
-0.014734712429344654,
0.005339392926543951,
0.00924464501440525,
0.03864424303174019,
-0.018478022888302803,
-0.04043576493859291,
0.011510016396641731,
-0.008780212141573429,
0.005391325801610947,
0.04363907873630524,
-0.01834133081138134,
-0.026521459221839905,
0.011680458672344685,
-0.013383968733251095,
-0.02486005611717701,
-0.022382086142897606,
-0.06395043432712555,
0.06695400923490524,
-0.004844715818762779,
0.02375827543437481,
0.03306056559085846,
0.04576420411467552,
-0.0319848395884037,
-0.01663942262530327,
0.010216752998530865,
0.050141118466854095,
-0.023692145943641663,
-0.01682029291987419,
-0.01589672826230526,
-0.041553057730197906,
-0.04704977199435234,
0.042121563106775284,
-0.02389918453991413,
0.06480029970407486,
-0.0050439550541341305,
-0.039279207587242126,
-0.030139239504933357,
0.008598840795457363,
-6.8358883709152e-7,
-0.021707583218812943,
-0.007403814699500799,
0.0339253805577755,
-0.021566197276115417,
-0.020381532609462738,
-0.01139778271317482,
-0.019731156527996063,
0.027251770719885826,
0.03354156017303467,
0.011244487017393112,
0.028188493102788925,
-0.019400067627429962,
0.02206132374703884,
-0.003325347788631916,
0.0032447180710732937,
0.0291255135089159,
-0.002022295258939266,
0.0022190178278833628,
0.0014378504129126668,
-0.07026723772287369,
-0.019889462739229202,
0.04614616930484772,
0.003185960929840803,
-0.001724847941659391,
-0.015795715153217316,
0.03262978419661522,
0.01644352823495865,
-0.008597346022725105,
0.004254000261425972,
-0.03668811544775963,
0.017708128318190575,
0.024689752608537674,
-0.007193786092102528,
-0.008900949731469154,
0.014743901789188385,
-0.04501984640955925,
-0.038838569074869156,
0.009348589926958084,
0.021034233272075653,
-0.03107699751853943,
-0.02253904938697815,
0.02482086420059204,
-0.0075791142880916595,
0.07001393288373947,
0.00030282975058071315,
-0.05584866553544998,
0.002166909631341696,
-0.011568822897970676,
-0.012937582097947598,
-0.023367928341031075,
0.01952841877937317,
-0.020549185574054718,
0.020199306309223175,
0.013837701641023159,
-0.02764919586479664,
0.04451659321784973,
-0.0000313387718051672,
0.03277552127838135,
0.0218896996229887,
-0.014072746969759464,
-0.0020966583397239447,
0.008448737673461437,
0.03922678157687187,
-0.0038853920996189117,
0.02760653756558895,
0.026528550311923027,
-0.034743137657642365,
-0.0326819084584713,
-0.007345640100538731,
0.030549924820661545,
0.03261521831154823,
0.00955385435372591,
-0.002560460241511464,
0.05702105164527893,
-0.02866790071129799,
0.013823502697050571,
-0.011360949836671352,
-0.025463975965976715,
0.030395280569791794,
0.014530569314956665,
0.013135015033185482,
-0.038567181676626205,
-0.013994276523590088,
0.007299288176000118,
0.00682805385440588,
-0.043169450014829636,
-0.08781000971794128,
0.06076274439692497,
0.01581701450049877,
0.05944303050637245,
0.028703274205327034,
-0.02290048636496067,
0.0011601467849686742,
-0.05623938515782356,
-0.0004774109984282404,
-0.005555385258048773,
-0.008419574238359928,
-0.009283052757382393,
0.02440667897462845,
-0.04027839004993439,
0.05990590527653694,
-0.004006638191640377,
0.013642369769513607,
0.008369176648557186,
0.06553938239812851,
0.030763505026698112,
0.016602404415607452,
0.00716477632522583,
-0.014806038700044155,
0.009708932600915432,
-0.013809547759592533,
0.006419191136956215,
-0.008851820603013039,
0.012790937907993793,
0.043120596557855606,
0.02368639037013054,
-0.019689757376909256,
-0.053486403077840805,
0.032862547785043716,
-0.04208016395568848,
-0.011741269379854202,
0.006286707706749439,
-0.027392908930778503,
0.010007400065660477,
0.025230539962649345,
0.05057583749294281,
-0.04063146933913231,
0.040831755846738815,
0.012043642811477184,
-0.02726767025887966,
0.0026206637267023325,
-0.014539281837642193,
-0.05071836709976196,
0.032509397715330124,
-0.005751244258135557,
-0.003907515201717615,
0.001513294642791152,
-0.0018580112373456359,
0.024237781763076782,
0.00440934719517827,
0.03266207501292229,
0.018549486994743347,
0.07252757251262665,
0.01177440956234932,
-0.019150372594594955,
-0.011243290267884731,
0.0048700557090342045,
0.11792433261871338,
0.016417739912867546,
0.0199795663356781,
-0.045489534735679626,
0.005703614093363285,
-0.02613501250743866,
0.015570411458611488,
-0.019100302830338478,
-0.0002626078203320503,
-0.018444906920194626,
0.01633031666278839,
0.034978415817022324,
0.035539064556360245,
0.02329479157924652,
0.007128202356398106,
0.04489731788635254,
-0.02801622450351715,
-0.007918553426861763,
0.05303084850311279,
0.06475389748811722,
-0.023981798440217972,
0.016064485535025597,
-0.03282822668552399,
-0.005935369990766048,
-0.013405867852270603,
-0.028423702344298363,
0.006971533410251141,
-0.05196942761540413,
0.04399089142680168,
-0.03814522549510002,
-0.05620695650577545,
0.03490186110138893,
0.04665710777044296,
0.004502172581851482,
-0.04089070111513138,
-0.015679866075515747,
0.03266202658414841,
-0.00107931112870574,
-0.03056466393172741,
0.051609788089990616,
0.015655184164643288,
-0.020467495545744896,
-0.018735358491539955,
0.003891419619321823,
-0.06016857549548149,
-0.01897278241813183,
-0.0202935840934515,
-0.030391329899430275,
0.02307385765016079,
0.0068014636635780334,
-0.00139857386238873,
0.057947173714637756,
-0.021416470408439636,
-0.058308206498622894,
0.015486657619476318,
0.00880251545459032,
0.03825229033827782,
-0.028773346915841103,
-0.01802484691143036,
-0.0815928727388382,
0.010177483782172203,
-0.018924981355667114,
0.020846648141741753,
0.011966564692556858,
-0.020205533131957054,
0.04576066508889198,
0.01061485055834055,
-0.004107873421162367,
-0.01037344429641962,
-0.041871052235364914,
0.008320414461195469,
-0.021051524206995964,
-0.0281115360558033,
0.020094990730285645,
0.040260039269924164,
-0.0013957149349153042,
0.005835672840476036,
-0.029608018696308136,
-0.015716785565018654,
-0.05307277664542198,
-0.1094321608543396,
0.038589462637901306,
0.006182408891618252,
0.007249907590448856,
-0.007819769904017448,
0.003935119602829218,
0.044950347393751144,
0.03342205658555031,
0.00735387671738863,
0.019874319434165955,
-0.02156912162899971,
0.046066753566265106,
0.030125770717859268,
-0.019757937639951706,
-0.005207054316997528,
0.04277940094470978,
-0.0193224735558033,
0.029442233964800835,
-0.0067800236865878105,
0.05113162472844124,
0.048720356076955795,
-0.007245295215398073,
-0.03208966180682182,
-0.0014337722677737474,
0.0005198428989388049,
-0.008341610431671143,
0.0076581272296607494,
-0.05598045885562897,
-0.0047984556294977665,
0.00604486558586359,
-0.025485197082161903,
-0.015694839879870415,
-0.031335990875959396,
-0.06388077139854431,
0.0180357675999403,
-0.042158447206020355,
0.007650239393115044,
0.013679347932338715,
0.036132752895355225,
-0.051488492637872696,
0.027650048956274986,
-0.030011175200343132,
-0.017406905069947243,
-0.026335638016462326,
-0.005372083280235529,
0.0327211394906044,
0.015586434863507748,
0.01481206901371479,
0.03387919068336487,
-0.04674597457051277,
0.030669182538986206,
0.01981186307966709,
0.011014941148459911,
0.02102517895400524,
0.00821719504892826,
-0.011273522861301899,
-0.03715522214770317,
0.039621636271476746,
-0.03599498048424721,
-0.03280285745859146,
0.07298655807971954,
0.0022726061288267374,
0.013379989191889763,
0.03996623679995537,
-0.0033546555787324905,
-0.005945228971540928,
-0.002554855775088072,
-0.003880215808749199,
0.014482531696557999,
0.0037092729471623898,
-0.033632099628448486,
0.04472760856151581,
0.01120769139379263,
0.011712067760527134,
0.008723150007426739,
0.038708366453647614,
-0.003582586767151952,
-0.016750140115618706,
0.013293031603097916,
0.029355879873037338,
0.028813686221837997,
-0.030120164155960083,
-0.003760233521461487,
-0.005026699975132942,
-0.003161525819450617,
0.036279719322919846,
0.035781003534793854,
-0.0007336916169151664,
0.059477921575307846,
0.01724790222942829,
-0.025454562157392502,
0.016369521617889404,
-0.022360803559422493,
-0.02682545594871044,
-0.07384620606899261,
-0.015219531953334808,
-0.011853878386318684,
0.0011324364459142089,
0.024673735722899437,
-0.03909154608845711,
-0.008932958357036114,
0.02854163944721222,
-0.07690916210412979,
-0.010151827707886696,
-0.003516155993565917,
0.006163781508803368,
-0.0667552500963211,
0.025141365826129913,
0.013453560881316662,
0.03478066623210907,
0.03536013886332512,
0.03414962440729141,
0.0013460046611726284,
0.01601518504321575,
-0.009364211931824684,
-0.05360308662056923,
0.017758119851350784,
0.03687615320086479,
0.002001668093726039,
-0.036755964159965515,
0.017158005386590958,
-0.03414391353726387,
-0.02271359972655773,
0.008437925018370152,
-0.012073925696313381,
0.04207899793982506,
-0.051165301352739334,
0.012559153139591217,
0.01379418559372425,
0.05967945605516434,
0.07994579523801804,
-0.022380955517292023,
-0.03463257476687431,
-0.011460821144282818,
-0.005319593474268913,
0.05364443361759186,
-0.000519541441462934,
0.011346611194312572,
0.02461867593228817,
-0.038507428020238876,
-0.014294459484517574,
0.005573467817157507,
-0.022472264245152473,
-0.038216717541217804,
0.02886979468166828,
-0.009277279488742352,
0.012289957143366337,
-0.008541501127183437,
0.007531342562288046,
-0.04618529975414276,
-0.041732095181941986,
0.03652206435799599,
-0.025873368605971336,
0.008446617051959038,
0.006094480399042368,
-0.0071467929519712925,
-0.011060488410294056,
0.045089494436979294,
0.01709861122071743,
-0.007399424910545349,
-0.0712360069155693,
-0.017403051257133484,
0.009801993146538734,
-0.007829714566469193,
-0.044643208384513855,
-0.01725463755428791,
-0.0014453635085374117,
0.010798773728311062,
0.045324407517910004,
-0.015662914142012596,
0.027207382023334503,
-0.04251953959465027,
0.002100748708471656,
-0.0249550249427557,
0.02553004026412964,
0.03862009197473526,
-0.008501579985022545,
-0.03935391083359718,
-0.008661279454827309,
0.001342569594271481,
0.008402426727116108,
0.04515837877988815,
0.014285416342318058,
-0.024812813848257065,
-0.016215553507208824,
-0.026517823338508606,
0.033242326229810715,
-0.04024007171392441,
0.02267538569867611,
-0.015092768706381321,
-0.060203563421964645,
0.002845484297722578,
-0.009166228584945202,
-0.03978029638528824,
0.01698807254433632,
0.04650850594043732,
-0.01192678976804018,
-0.003257715841755271,
-0.016136350110173225,
-0.0005905155558139086,
0.062397733330726624,
0.057966139167547226,
-0.006628241389989853,
0.04755643382668495,
-0.04441554844379425,
0.03434867039322853,
0.062345512211322784,
-0.0006645238609053195,
-0.06190463900566101,
-0.004482263699173927,
-0.025309443473815918,
0.005604395642876625,
0.015668852254748344,
0.010284951888024807,
0.05364535376429558,
-0.045443013310432434,
-0.029033740982413292,
0.02800736576318741,
0.0019017001613974571,
-0.01406349241733551,
0.03963901102542877,
0.045176196843385696,
-0.009109360165894032,
-0.0007863678620196879,
-0.00015453767264261842,
0.021069426089525223,
-0.0421271026134491,
-0.01699393428862095,
0.05154932290315628,
0.03155210614204407,
-0.010481217876076698,
-0.0019501863280311227,
0.033974260091781616,
0.010982274077832699,
0.017128655686974525,
-0.015065744519233704,
0.053726255893707275,
-0.026138564571738243,
-0.026832476258277893,
-0.01064729318022728,
0.0012648673728108406,
0.03369845449924469,
0.030179481953382492,
-0.03265805542469025,
0.0497545562684536,
-0.034679509699344635,
0.012894509360194206,
-0.022318297997117043,
0.0002712512796279043,
-0.015024556778371334,
-0.04919920116662979,
0.02743448130786419,
0.03889290243387222,
-0.01149019319564104,
-0.0013482312206178904,
-0.013184626586735249,
-0.01812019571661949,
0.045573584735393524,
-0.06145671010017395,
0.035762906074523926,
-0.026886437088251114,
-0.011815858073532581,
-0.021090615540742874,
-0.017242148518562317,
-0.04698498919606209,
-0.01563587598502636,
0.01662142015993595,
0.03306503966450691,
-0.015964414924383163,
-0.018506405875086784,
-0.01556653343141079,
-0.012298393063247204,
0.04092518612742424,
-0.06597122550010681,
0.0005655667628161609,
0.006719264667481184,
0.011115903966128826,
0.0390731543302536,
0.000834137958008796
] |
<p>Why is electricity not transmitted wirelessly such that we don't need to span cables on the earth's surface? As in: electricity is transmitted wirelessly from the power plant to the household.</p> | 1,587 | [
-0.0381939522922039,
-0.018276507034897804,
0.021976180374622345,
-0.01594957709312439,
0.0024814438074827194,
-0.006705472711473703,
-0.020981060341000557,
0.0001523168321000412,
0.02652956172823906,
-0.019025668501853943,
0.023006262257695198,
0.0744522288441658,
0.03659558668732643,
0.00007469188130926341,
0.03466079756617546,
0.017460064962506294,
0.0005036807269789279,
0.0032885128166526556,
-0.0037969963159412146,
-0.024693334475159645,
-0.025238441303372383,
0.005954836029559374,
-0.01863056607544422,
0.03148498013615608,
0.009990694001317024,
-0.013595178723335266,
0.036282021552324295,
0.0018798247911036015,
0.03220444917678833,
0.04539381340146065,
0.0018186679808422923,
-0.034700796008110046,
0.0016042920760810375,
0.04045005142688751,
0.023538436740636826,
-0.008972574956715107,
-0.06532865762710571,
-0.03360104560852051,
-0.016268694773316383,
-0.002929872600361705,
0.014791835099458694,
-0.025386745110154152,
-0.0033191402908414602,
0.020888036116957664,
-0.052621375769376755,
0.037407416850328445,
0.027952872216701508,
-0.02933064103126526,
0.04749104008078575,
-0.053780242800712585,
0.026057172566652298,
-0.04347127303481102,
0.022589121013879776,
0.013030724599957466,
-0.004740023519843817,
0.04228940233588219,
0.11057201772928238,
0.0484749898314476,
-0.02624508924782276,
-0.02655591070652008,
-0.04214866831898689,
-0.005989700090140104,
-0.015070656314492226,
-0.04266700893640518,
-0.03639087453484535,
0.04988056793808937,
-0.0072211092337965965,
-0.0420459508895874,
0.023355737328529358,
-0.004776610992848873,
-0.000036696557799587026,
0.013842272572219372,
0.010188860818743706,
-0.0059724305756390095,
-0.025605084374547005,
-0.011492494493722916,
0.0014946877490729094,
0.012378893792629242,
0.06619758158922195,
0.027286287397146225,
-0.030152790248394012,
-0.013778218068182468,
0.011936166323721409,
0.03554628789424896,
-0.006388360168784857,
-0.0256086103618145,
0.038512054830789566,
-0.006171629298478365,
0.015688447281718254,
-0.00137148960493505,
-0.01881979964673519,
-0.013181994669139385,
0.043776415288448334,
-0.010060235857963562,
0.03121221251785755,
0.03568777069449425,
-0.0028710949700325727,
0.005822720471769571,
0.012043500319123268,
-0.05339252948760986,
0.04840254783630371,
-0.0037415497936308384,
0.026524873450398445,
0.060050997883081436,
0.05091841146349907,
-0.05376394838094711,
-0.020084485411643982,
0.00694144144654274,
0.014087353833019733,
0.0023351481650024652,
-0.03407198563218117,
-0.0009693884640000761,
0.035404615104198456,
0.00119210802949965,
0.016962798312306404,
-0.04329928010702133,
0.030257979407906532,
-0.02505115047097206,
0.0292693879455328,
0.08671054244041443,
0.0009407366742379963,
-0.018545271828770638,
0.06505746394395828,
-0.046318620443344116,
-0.03375084325671196,
0.034430790692567825,
-0.018669556826353073,
0.0048776473850011826,
-0.022443974390625954,
0.0004505125107243657,
-0.015674512833356857,
-0.007430541329085827,
0.02945118583738804,
-0.010440459474921227,
0.0705854743719101,
-0.030844345688819885,
-0.15026907622814178,
-0.0600062720477581,
0.016949046403169632,
0.0042417715303599834,
0.025186147540807724,
-0.05925946310162544,
0.02978573925793171,
0.021421819925308228,
0.08228068053722382,
-0.005857204552739859,
0.0011962578864768147,
-0.008837118744850159,
0.022881977260112762,
-0.007646057289093733,
-0.010988522320985794,
-0.031934455037117004,
0.03342508524656296,
-0.013734321109950542,
0.044305115938186646,
-0.03094329871237278,
0.028817545622587204,
0.03687739372253418,
0.018132580444216728,
-0.014303061179816723,
0.010845119133591652,
0.005355841480195522,
-0.04064265638589859,
0.0003110110992565751,
-0.04376569762825966,
-0.03793647885322571,
0.047330357134342194,
0.03498905897140503,
0.03393486887216568,
0.048518579453229904,
0.016935031861066818,
0.014757080934941769,
-0.0009725782438181341,
0.031471189111471176,
0.006443986669182777,
-0.035952527076005936,
0.005385866854339838,
-0.0006637785118073225,
0.014937612228095531,
0.010937858372926712,
-0.03140406683087349,
-0.02303961291909218,
0.05449121817946434,
0.05320372432470322,
0.0104873301461339,
0.054644182324409485,
-0.02511955052614212,
0.000009020629477163311,
0.01923086866736412,
-0.032925866544246674,
-0.03294748067855835,
0.0354483462870121,
0.05660437047481537,
0.01389814168214798,
0.004297598730772734,
-0.04710959643125534,
0.013787799514830112,
-0.009090176783502102,
-0.03733756020665169,
-0.02623964473605156,
0.010682215914130211,
0.04593378305435181,
0.03676844760775566,
-0.003112026257440448,
0.012181578204035759,
0.05759670212864876,
0.06493079662322998,
0.018649693578481674,
0.04504230618476868,
0.020697223022580147,
-0.050162021070718765,
-0.011478050611913204,
-0.04399093985557556,
0.024223435670137405,
0.04849720746278763,
-0.015619834885001183,
0.019159434363245964,
-0.02331281267106533,
-0.008787428960204124,
0.04714536294341087,
-0.010121691040694714,
0.0762922614812851,
0.03507039323449135,
0.022755064070224762,
-0.012100158259272575,
0.025945434346795082,
0.01583312824368477,
0.0027293297462165356,
-0.01240758690983057,
-0.04762185364961624,
-0.08672512322664261,
0.023107312619686127,
0.026351729407906532,
-0.0007271305075846612,
-0.030044615268707275,
0.0024067971389740705,
0.013731017708778381,
0.07821424305438995,
0.01617630384862423,
0.023611344397068024,
-0.01498276088386774,
-0.0258911345154047,
0.030208153650164604,
0.01293889433145523,
-0.023672282695770264,
0.028234077617526054,
-0.0023223143070936203,
-0.0009868387132883072,
-0.0053671482019126415,
-0.019372466951608658,
-0.015870168805122375,
0.048102498054504395,
-0.03253401443362236,
0.01746290922164917,
0.018236679956316948,
-0.028583591803908348,
0.03384370356798172,
-0.07839999347925186,
0.017115239053964615,
-0.019813939929008484,
-0.0013984485995024443,
0.006209892220795155,
-0.0064903730526566505,
-0.01136124785989523,
0.03888659551739693,
0.003945436328649521,
-0.027956560254096985,
-0.013350581750273705,
0.03579643368721008,
-0.03612436726689339,
0.03976746276021004,
-0.03676598519086838,
0.020180219784379005,
-0.005256962031126022,
0.0009462606976740062,
0.043979935348033905,
-0.006389266811311245,
0.049449075013399124,
-0.021865947172045708,
-0.04120149463415146,
-0.016123328357934952,
-0.04262116178870201,
-0.004240780603140593,
0.017324505373835564,
-0.0046132816933095455,
-0.011393699795007706,
-0.01405665185302496,
-0.016870994120836258,
0.07197516411542892,
0.002499526599422097,
0.017481928691267967,
-0.010759534314274788,
0.01581696607172489,
-0.04196343943476677,
0.00033221300691366196,
-0.0072357673197984695,
0.03779714182019234,
0.0013150982558727264,
-0.004683002829551697,
0.045453865081071854,
-0.01337098702788353,
-0.034812211990356445,
-0.00848382618278265,
-0.07282397896051407,
-0.041005514562129974,
0.008910814300179482,
-0.038231395184993744,
0.014294265769422054,
-0.05589810013771057,
0.028803348541259766,
0.009680664166808128,
-0.09990309178829193,
-0.013286963105201721,
-0.024746013805270195,
-0.07913011312484741,
0.024208208546042442,
-0.02645554207265377,
0.026873188093304634,
-0.00005147330739418976,
-0.03704504296183586,
0.04371055215597153,
0.026880992576479912,
-0.010738592594861984,
-0.011450627818703651,
-0.03670882061123848,
-0.024060582742094994,
-0.04104473814368248,
0.006624607369303703,
0.06123949587345123,
0.004571747034788132,
-0.012505164369940758,
0.044860370457172394,
0.0038472814485430717,
0.01965460553765297,
-0.013897632248699665,
-0.008409712463617325,
-0.01717907190322876,
-0.00661600474268198,
-0.021761897951364517,
0.036301176995038986,
0.006265155039727688,
-0.05058905482292175,
-0.000985422171652317,
0.0033114845864474773,
0.02266063168644905,
0.004924639128148556,
-0.019632399082183838,
0.02065398171544075,
-0.010287647135555744,
0.03543706238269806,
-0.05858882516622543,
0.0390300415456295,
-0.006609425414353609,
-0.004194997251033783,
0.011191243305802345,
0.007591748610138893,
0.05504196882247925,
-0.0168807040899992,
-0.015278717502951622,
0.025032438337802887,
0.07081711292266846,
-0.03426659107208252,
-0.02940051257610321,
-0.011725279502570629,
0.017486058175563812,
-0.026470819488167763,
0.045302268117666245,
-0.05646225064992905,
0.03524186089634895,
0.028112448751926422,
0.026513058692216873,
0.03734979033470154,
0.00015352011541835964,
-0.013191267848014832,
-0.02997170016169548,
0.009699943475425243,
0.002777641639113426,
0.04592584818601608,
-0.010971369221806526,
0.0393332839012146,
0.04132584109902382,
0.032518163323402405,
-0.015668807551264763,
-0.0014313854044303298,
-0.0413362979888916,
-0.0006976498407311738,
-0.04306583106517792,
-0.007771618198603392,
0.0047598411329090595,
-0.023707207292318344,
-0.06939292699098587,
-0.008497496135532856,
-0.04737086966633797,
-0.02435995452105999,
-0.02500319294631481,
-0.058420952409505844,
-0.0007247839239425957,
0.008262824267148972,
-0.02105364389717579,
-0.021546009927988052,
-0.01771572045981884,
0.037625327706336975,
-0.033323828130960464,
0.014640853740274906,
0.03876715153455734,
-0.020472919568419456,
0.010883595794439316,
-0.005802225321531296,
-0.017870157957077026,
0.007345304358750582,
0.0006852889782749116,
0.0641808807849884,
-0.003060670802369714,
-0.021190881729125977,
-0.024217942729592323,
0.01344236172735691,
0.037409815937280655,
-0.014345293864607811,
-0.022264059633016586,
-0.007492179051041603,
-0.03830241784453392,
-0.03137718141078949,
0.012859649024903774,
0.017077811062335968,
-0.01573285274207592,
0.015370486304163933,
0.03003954328596592,
-0.021965330466628075,
0.005610164720565081,
-0.005733069963753223,
0.012220781296491623,
-0.014194326475262642,
-0.034119874238967896,
-0.019644269719719887,
-0.02689635567367077,
-0.02397419512271881,
-0.012584892101585865,
0.020290497690439224,
-0.021048078313469887,
0.02459668554365635,
-0.026487061753869057,
0.06417176872491837,
-0.0042860559187829494,
-0.014637228101491928,
0.028945880010724068,
0.013467401266098022,
-0.006425495725125074,
0.0045232283882796764,
-0.030563412234187126,
-0.006761603057384491,
-0.006422597449272871,
0.0065938630141317844,
0.014561534859240055,
-0.040781766176223755,
-0.09647416323423386,
-0.014304173178970814,
0.009389056824147701,
0.03776290640234947,
-0.012848630547523499,
-0.026674890890717506,
-0.05963733047246933,
0.005762412212789059,
0.03544187173247337,
-0.005210044793784618,
0.03396672010421753,
-0.04942518472671509,
-0.025414250791072845,
-0.03850444033741951,
-0.049993209540843964,
0.004497178830206394,
0.007330288179218769,
0.011131097562611103,
0.03106210194528103,
0.009651010856032372,
-0.016425088047981262,
-0.0024706367403268814,
0.011528333649039268,
0.05793549865484238,
0.07090862095355988,
0.020549172535538673,
0.02311042882502079,
-0.006181778851896524,
0.040822532027959824,
-0.029947953298687935,
-0.04847995564341545,
-0.0011574197560548782,
-0.0044196839444339275,
-0.028201298788189888,
0.033717118203639984,
-0.006235203705728054,
-0.0595950111746788,
0.010191178880631924,
0.028557851910591125,
-0.009645466692745686,
0.0034506856463849545,
-0.018648868426680565,
0.03300647810101509,
0.007193371187895536,
0.018824897706508636,
0.0738111361861229,
0.04619476571679115,
-0.046129610389471054,
0.015434143133461475,
-0.007250446826219559,
0.058799657970666885,
-0.022127564996480942,
-0.00505578238517046,
0.020491493865847588,
0.01376459188759327,
-0.020824521780014038,
0.0330696776509285,
-0.019184447824954987,
-0.013620354235172272,
-0.013269065879285336,
-0.04291791841387749,
-0.026513099670410156,
0.012150725349783897,
-0.005027529783546925,
-0.03404663875699043,
-0.040726061910390854,
0.041917771100997925,
-0.018832175061106682,
-0.03629273176193237,
0.0020373109728097916,
-0.018304971978068352,
-0.0023083325941115618,
0.012368995696306229,
0.008566662669181824,
-0.02179313451051712,
-0.05926208570599556,
-0.015077406540513039,
0.022515378892421722,
-0.034597333520650864,
0.046586643904447556,
-0.0010357728460803628,
-0.020914128050208092,
-0.010165468789637089,
-0.1010625883936882,
-0.04068936035037041,
-0.0002536119136493653,
0.007197408005595207,
0.044774457812309265,
-0.018452804535627365,
0.007178258616477251,
-0.031124146655201912,
-0.03801366686820984,
-0.03856956958770752,
-0.041120387613773346,
0.034489259123802185,
0.06557518988847733,
0.01526093389838934,
-0.02409287355840206,
0.0077452585101127625,
-0.0186421200633049,
-0.027022935450077057,
-0.02671254612505436,
0.015667874366044998,
-0.026009662076830864,
0.020600294694304466,
0.015771817415952682,
0.006960498634725809,
0.024364838376641273,
-0.02112971991300583,
-0.013253838755190372,
0.022376224398612976,
-0.04853980243206024,
0.014832056127488613,
-0.0679931566119194,
0.036937616765499115,
-0.022004539147019386,
-0.04726629704236984,
0.0013124799588695168,
-0.016338834539055824,
0.025030100718140602,
-0.01673251949250698,
-0.03068877011537552,
0.02798527292907238,
0.006877226755023003,
-0.03127341717481613,
0.008301028981804848,
0.045084547251462936,
0.019156284630298615,
0.032139260321855545,
-0.016197379678487778,
0.012876947410404682,
-0.048266202211380005,
-0.0422426275908947,
0.02969942055642605,
-0.005780207458883524,
0.014991938136518002,
0.005056325346231461,
0.04953620955348015,
-0.027533002197742462,
0.007166913710534573,
0.03648914769291878,
0.018574317917227745,
0.029071468859910965,
-0.013201446272432804,
-0.0010082167573273182,
-0.01755003072321415,
0.016196878626942635,
0.009032895788550377,
-0.011464708484709263,
-0.002264861948788166,
0.024753201752901077,
0.05293910950422287,
-0.03996484354138374,
0.042434778064489365,
-0.0002511304628569633,
-0.01963881030678749,
0.008392268791794777,
0.0038723896723240614,
-0.02239898033440113,
0.02503165230154991,
-0.010759166441857815,
0.0036384377162903547,
0.012668712064623833,
-0.00827109720557928,
0.039935752749443054,
0.06463249772787094,
0.005231489893049002,
0.023549100384116173,
0.03443329036235809,
0.023857876658439636,
0.01161728985607624,
0.007481485139578581,
-0.04253673180937767,
0.01924561895430088,
-0.04159339517354965,
-0.003499408485367894,
0.018228020519018173,
-0.025060826912522316,
0.04882706329226494,
-0.05932527035474777,
-0.01023399829864502,
-0.009593944065272808,
-0.0022273031063377857,
-0.05605426803231239,
0.041296038776636124,
-0.0024249600246548653,
0.02047443762421608,
-0.0007239715196192265,
-0.01269492506980896,
0.016571203246712685,
-0.02981565333902836,
0.012262019328773022,
0.012229999527335167,
-0.07697298377752304,
-0.036421164870262146,
-0.023155923932790756,
-0.028868891298770905,
0.07001148164272308,
0.03809080645442009,
-0.022400500252842903,
0.005935758352279663,
-0.01501381304115057,
0.023158106952905655,
0.020162269473075867,
0.037195149809122086,
-0.028690114617347717,
0.057986754924058914,
0.001299300347454846,
0.029541965574026108,
-0.013333040289580822,
-0.008801532909274101,
0.09600646793842316,
0.0053023057989776134,
0.036648496985435486,
-0.03999892249703407,
0.02562359906733036,
-0.049243830144405365,
-0.0066645038314163685,
-0.03165328875184059,
0.029339168220758438,
-0.007808181457221508,
0.012139850296080112,
0.03946004807949066,
0.016023537144064903,
0.031575847417116165,
0.020821593701839447,
0.09289320558309555,
-0.07601752877235413,
-0.0431022010743618,
0.011665113270282745,
-0.007716154679656029,
-0.012455137446522713,
-0.000718330149538815,
-0.05994154140353203,
0.0191815085709095,
-0.06127892807126045,
-0.03145280480384827,
0.029075955972075462,
-0.019337642937898636,
0.0583709217607975,
0.013256063684821129,
-0.05491199344396591,
-0.02152998000383377,
0.03347714617848396,
-0.027099737897515297,
-0.04215100407600403,
0.018932998180389404,
0.05137621611356735,
0.011674104258418083,
0.0020960757974535227,
-0.010239120572805405,
0.031918372958898544,
-0.01596428081393242,
0.02226215787231922,
0.036223623901605606,
-0.05917399004101753,
-0.009409088641405106,
-0.03651042282581329,
0.015077217482030392,
0.0034930852707475424,
-0.00706776138395071,
0.015000976622104645,
0.020935026928782463,
-0.007226079702377319,
-0.01843339204788208,
0.014916304498910904,
-0.009621747769415379,
0.01620478369295597,
-0.0046144770458340645,
-0.0009770223405212164,
-0.012067068368196487,
0.02821311540901661,
-0.011883973143994808,
0.03312398120760918,
0.02391594462096691,
0.01719188317656517,
0.026354718953371048,
0.01253634411841631,
0.007006857078522444,
-0.032077446579933167,
-0.017969803884625435,
-0.017014306038618088,
-0.013043954037129879,
-0.01769942045211792,
-0.016401154920458794,
0.025411125272512436,
0.020268931984901428,
0.008846666663885117,
-0.016491724178195,
0.010354040190577507,
0.005807079374790192,
-0.03637136518955231,
0.04903542250394821,
0.015346242114901543,
-0.016419826075434685,
-0.017246456816792488,
-0.005300140008330345,
0.012263021431863308,
0.03252342343330383,
-0.010392875410616398,
0.0085865817964077,
-0.05271283909678459,
0.01513100229203701,
0.010965470224618912,
-0.025157198309898376,
-0.012656887993216515,
-0.0011293659918010235,
-0.03962739184498787,
-0.01811022125184536,
-0.0014024075353518128,
0.02120891399681568,
0.05680099502205849,
-0.0034901159815490246,
-0.011951383203268051,
0.010308397002518177,
-0.04902161657810211,
-0.009868083521723747,
0.013882226310670376,
-0.026871705427765846,
-0.030713818967342377,
0.020989878103137016,
-0.002422340912744403,
-0.0035576079972088337,
-0.03555285930633545,
-0.03161628916859627,
0.01324132177978754,
0.011471942998468876,
0.026921510696411133,
0.002549243625253439,
-0.006709179375320673,
-0.03927662968635559,
0.03265947103500366,
-0.041494764387607574,
-0.008814588189125061,
-0.0854988545179367,
-0.007885009981691837,
-0.018698198720812798,
-0.01828000880777836,
0.01619761623442173,
0.01849515736103058,
-0.0567098967730999,
0.014949015341699123,
0.03492623567581177,
0.019309353083372116,
0.010995332151651382,
0.03012409433722496,
-0.0006738294032402337,
0.003692737314850092,
0.03773179277777672,
-0.04485907405614853,
-0.03124416247010231,
0.05986981838941574,
-0.02128295972943306,
-0.04367561265826225,
0.007994068786501884,
-0.03900507837533951,
0.034168168902397156,
0.01527715940028429,
-0.06230948865413666,
-0.0027329844888299704,
0.04226505011320114,
-0.015805892646312714,
0.013672122731804848,
0.038785796612501144,
0.010923170484602451,
0.0008909421740099788,
0.011268623173236847,
-0.016040800139307976,
-0.041511863470077515,
0.008623153902590275,
0.028696205466985703,
0.0311525147408247,
0.03621663898229599,
-0.01629265397787094,
0.0038155000656843185,
-0.013221337459981441,
0.05977281555533409,
0.05609891563653946,
0.023333445191383362,
-0.01423371210694313,
0.04720710590481758,
-0.03762957453727722,
0.03844622150063515,
0.01119988039135933,
0.0036055005621165037,
-0.07607980817556381,
-0.0021273752208799124,
-0.01698901690542698,
-0.004215001594275236,
0.025177014991641045,
-0.048283740878105164,
0.0006676072371192276,
0.013989190571010113,
-0.11056597530841827,
0.012102777138352394,
0.012122044339776039,
-0.04340578243136406,
-0.024127960205078125,
0.018023842945694923,
-0.023868761956691742,
0.043145518749952316,
0.05560813844203949,
0.06121090427041054,
0.01503764372318983,
0.0042406488209962845,
-0.02498668059706688,
-0.005721989553421736,
-0.047427672892808914,
0.014674910344183445,
-0.01883998140692711,
-0.008527741767466068,
0.03016374446451664,
-0.005750170908868313,
0.017813608050346375,
0.019526777788996696,
-0.0277064498513937,
0.013385103084146976,
0.0000742463962524198,
0.02436358667910099,
0.04278264194726944,
0.0182512067258358,
0.021879037842154503,
-0.01659056916832924,
-0.021181127056479454,
0.01114639826118946,
0.03488120436668396,
0.009445320814847946,
0.010805778205394745,
0.02116965875029564,
0.019106470048427582,
-0.024740464985370636,
-0.012428944930434227,
0.0020699782762676477,
-0.029250605031847954,
-0.003911011386662722,
-0.010702409781515598,
0.05142294242978096,
0.03808744624257088,
-0.033617764711380005,
-0.03908419981598854,
-0.025163384154438972,
-0.05438661947846413,
0.03878458961844444,
0.010123890824615955,
0.0038226942997425795,
0.000005991147190798074,
-0.019113995134830475,
-0.02318127080798149,
0.0019081500358879566,
0.03265320882201195,
0.007091275416314602,
-0.046639423817396164,
-0.023165030404925346,
0.004209398757666349,
0.018326299265027046,
0.012187774293124676,
-0.03391338512301445,
-0.004882480949163437,
0.023599470034241676,
0.031199214980006218,
0.028134630993008614,
0.03849009424448013,
-0.03640120476484299,
-0.021851632744073868,
-0.019244978204369545,
0.07657726109027863,
-0.032642558217048645,
0.028678519651293755,
-0.02497061714529991,
-0.05585045740008354,
0.009645356796681881,
0.02998177893459797,
0.07912051677703857,
-0.005723700392991304,
-0.005368911661207676,
0.016159934923052788,
0.004997020121663809,
0.02986699342727661,
-0.026047252118587494,
0.026480453088879585,
0.014158159494400024,
-0.04313162341713905,
-0.0011239572195336223,
-0.05043653026223183,
0.018323779106140137,
0.015438565984368324,
0.014045847579836845,
0.0072957053780555725,
0.0014017540961503983,
-0.019790519028902054,
-0.007415833417326212,
0.010661927983164787,
0.04145488888025284,
-0.0445345938205719,
0.06039969250559807,
-0.035689156502485275,
0.025973742827773094,
-0.00046645087422803044,
-0.0063650659285485744,
-0.02316305600106716,
0.038642048835754395,
-0.051192495971918106,
0.04251469671726227,
-0.012358913198113441,
0.01604018174111843,
0.02261466160416603,
-0.04260791093111038,
-0.018170174211263657,
0.027928361669182777,
-0.03773411363363266,
-0.005485148634761572,
0.06686779111623764,
0.006976796314120293,
-0.01062589231878519,
0.02563086338341236,
-0.009189939126372337,
-0.01277232076972723,
0.028889520093798637,
-0.0155458003282547,
0.02611417882144451,
0.022490492090582848,
-0.03558934107422829,
0.05236054211854935,
0.014847795478999615,
-0.001990061718970537,
0.03091413341462612,
-0.013493245467543602,
0.031282756477594376,
-0.027942543849349022,
-0.06169141083955765,
0.00925239734351635,
0.02107895351946354,
-0.03318043425679207,
0.024842580780386925,
-0.019232966005802155,
0.08399689197540283,
-0.006341983564198017,
0.018285995349287987,
0.022012291476130486,
0.0034639565274119377,
0.03803693503141403,
0.012140938080847263,
0.010561458766460419,
0.030252989381551743,
-0.029614673927426338,
-0.004855578299611807,
-0.009910253807902336,
-0.011691011488437653,
0.04889442026615143,
0.00006286185816861689,
0.01172824576497078,
-0.042317263782024384,
-0.03009907342493534,
-0.03634371608495712,
-0.001866531907580793,
0.002426929771900177,
0.018799902871251106,
0.02749905176460743,
0.030171100050210953,
0.008488542400300503,
-0.0023329174146056175,
-0.021235313266515732,
-0.018109256401658058,
0.04824042320251465,
-0.06843603402376175,
0.03639936074614525,
-0.026319772005081177,
0.008271404542028904,
0.0029604157898575068,
0.014340001158416271
] |
<p>The book I'm reading about optics says at some point that "each color (wavelength) contained in the white light interferes only with itself". But why is this so?</p>
<p>Edit: I moved the rest of the question <a href="http://physics.stackexchange.com/q/12208/4283">elsewhere</a>.</p> | 1,588 | [
-0.04098756983876228,
-0.014924288727343082,
0.022476449608802795,
-0.03131226450204849,
0.05106158182024956,
0.024773111566901207,
-0.008225596509873867,
-0.0011374420719221234,
-0.01620597019791603,
0.006461189594119787,
0.019492514431476593,
0.062197037041187286,
0.06703899055719376,
0.013145795091986656,
0.020916251465678215,
0.0026355222798883915,
-0.007914603687822819,
-0.004220439121127129,
0.001990914111956954,
-0.019430484622716904,
-0.024653123691678047,
0.03521880507469177,
0.01614675112068653,
-0.002400533528998494,
-0.05324966460466385,
0.015205875039100647,
0.023031266406178474,
0.01307433657348156,
0.06376922130584717,
0.032740939408540726,
-0.012621131725609303,
0.021251725032925606,
-0.033691469579935074,
0.05296540632843971,
0.0001744240871630609,
-0.014380045235157013,
-0.015682101249694824,
-0.04129841551184654,
-0.018266627565026283,
0.012322910130023956,
-0.014934496954083443,
-0.0082040224224329,
-0.02203282341361046,
0.06444807350635529,
-0.021475739777088165,
0.018706578761339188,
-0.02223837561905384,
-0.022065984085202217,
0.0546041876077652,
-0.04605114087462425,
0.08093652129173279,
-0.00918260682374239,
0.05965031310915947,
0.015783322975039482,
-0.025395089760422707,
0.04092264175415039,
0.07760035246610641,
0.08577136695384979,
-0.039953455328941345,
-0.017215877771377563,
-0.01272553764283657,
-0.01322607696056366,
-0.010987138375639915,
0.00006331318581942469,
-0.03576721251010895,
0.021636152639985085,
-0.0027412427589297295,
-0.03208070993423462,
0.025773175060749054,
0.019365811720490456,
-0.008341910317540169,
0.030397363007068634,
0.05002878978848457,
-0.021277280524373055,
-0.011923784390091896,
-0.031438276171684265,
0.02540138177573681,
0.014155518263578415,
0.046692874282598495,
-0.0006596713792532682,
-0.013644837774336338,
-0.014248745515942574,
-0.012235449627041817,
-0.0009933182736858726,
0.012598320841789246,
-0.019279003143310547,
0.09363263845443726,
0.00562981516122818,
-0.0012728404253721237,
-0.011585505679249763,
-0.011983835138380527,
0.032027751207351685,
0.00927522499114275,
0.01751621626317501,
-0.018323717638850212,
0.03252135217189789,
-0.03633793815970421,
0.04983207583427429,
-0.007547341752797365,
-0.029130425304174423,
0.017344940453767776,
-0.007520975079387426,
0.028415154665708542,
0.04263569042086601,
-0.01839620992541313,
-0.054590094834566116,
-0.023347865790128708,
0.0313093401491642,
0.03141366317868233,
0.005389240104705095,
-0.007421582937240601,
0.01746574603021145,
0.0322083905339241,
-0.008032798767089844,
0.015577035024762154,
-0.013646574690937996,
0.030917391180992126,
0.02420680597424507,
0.06094779819250107,
0.07631529122591019,
0.0233754999935627,
-0.03538187965750694,
0.02493668720126152,
-0.009392742067575455,
-0.05060955509543419,
0.01676187291741371,
0.005645641125738621,
0.022845078259706497,
-0.011927424930036068,
0.024852575734257698,
0.011589283123612404,
-0.03268328681588173,
0.005563531070947647,
0.012950888834893703,
-0.002215926768258214,
-0.035365164279937744,
-0.10111737996339798,
-0.06560280174016953,
0.028585417196154594,
-0.03442615643143654,
-0.01807330548763275,
-0.05805061385035515,
0.007925421930849552,
0.010958125814795494,
0.11720147728919983,
-0.009054754860699177,
-0.012220333330333233,
0.0009352098568342626,
0.015463161282241344,
-0.014988545328378677,
-0.020300524309277534,
-0.01865977793931961,
0.0272431168705225,
-0.026249554008245468,
0.043030329048633575,
-0.07539328187704086,
0.010149379260838032,
0.024149244651198387,
0.014316588640213013,
-0.04100826382637024,
0.04904710873961449,
-0.014112644828855991,
0.009078794158995152,
0.03014034405350685,
-0.0003697071224451065,
-0.03416828811168671,
0.10765042901039124,
0.018364720046520233,
0.012109429575502872,
0.03613126650452614,
0.007000736426562071,
0.028886999934911728,
-0.01864437200129032,
0.03534067049622536,
0.003644455224275589,
0.0017386864637956023,
0.0011670856038108468,
-0.02262641303241253,
0.04109399393200874,
-0.023361897096037865,
-0.011754374019801617,
-0.05367908626794815,
0.008206341415643692,
0.03423718735575676,
0.0027569022495299578,
0.04737607762217522,
-0.019236616790294647,
0.00021704594837501645,
-0.007053806446492672,
-0.02827559970319271,
-0.003617578186094761,
-0.02664259448647499,
0.013612760230898857,
0.0006207679398357868,
-0.025832198560237885,
0.03499544411897659,
0.017503133043646812,
0.020521489903330803,
-0.008588513359427452,
-0.03948010876774788,
-0.02801969088613987,
0.0191033948212862,
0.002966160885989666,
-0.0007743624155409634,
0.036527715623378754,
0.046680551022291183,
0.034273579716682434,
0.004950360860675573,
0.033762142062187195,
-0.03963889926671982,
-0.036101266741752625,
0.03860512003302574,
-0.017461005598306656,
0.04460488632321358,
0.0007144574774429202,
0.004431155044585466,
0.012626610696315765,
0.01572708785533905,
0.011916464194655418,
0.017722148448228836,
0.001702588051557541,
0.027903582900762558,
0.029948219656944275,
-0.005005864892154932,
-0.019953325390815735,
0.0332379974424839,
-0.007845950312912464,
0.021583450958132744,
0.021577004343271255,
-0.023314252495765686,
-0.03440498933196068,
0.005345883313566446,
0.019275691360235214,
0.006597633007913828,
-0.032665472477674484,
-0.003769236383959651,
-0.003059949027374387,
0.046202391386032104,
0.022808613255620003,
0.029481738805770874,
-0.018074458464980125,
-0.039948418736457825,
0.007746133487671614,
0.045958925038576126,
0.03625873476266861,
0.02713017910718918,
0.01617087796330452,
0.0008836816996335983,
0.043314751237630844,
-0.03811277449131012,
-0.03381902724504471,
0.03785279393196106,
-0.019275564700365067,
0.046167727559804916,
0.0004660750273615122,
-0.01673615351319313,
0.017146466299891472,
-0.030450718477368355,
0.02594050206243992,
0.023567259311676025,
-0.01867675967514515,
0.00030692570726387203,
-0.037093691527843475,
-0.01334143616259098,
0.0023887157440185547,
-0.008619837462902069,
-0.06436998397111893,
-0.007182039320468903,
0.017517641186714172,
-0.04924027621746063,
0.011538594029843807,
-0.015802009031176567,
-0.01249381247907877,
-0.04265638068318367,
-0.014896192587912083,
0.01562352105975151,
0.029820315539836884,
0.047011230140924454,
-0.06301058828830719,
-0.06598153710365295,
-0.020559893921017647,
-0.03612658381462097,
-0.013233899138867855,
-0.015833871439099312,
-0.04098737984895706,
0.013643471524119377,
-0.04327131062746048,
-0.023879555985331535,
0.01957741752266884,
-0.01829048991203308,
0.005331067834049463,
-0.00005040936594014056,
-0.009217668324708939,
-0.045212291181087494,
-0.018372705206274986,
-0.003044119803234935,
-0.011746736243367195,
-0.018718915060162544,
-0.016104329377412796,
0.021187206730246544,
-0.021682720631361008,
-0.04627871513366699,
0.003280641743913293,
-0.05190213397145271,
-0.05716787278652191,
-0.010191498324275017,
-0.0008648451184853911,
0.022827444598078728,
-0.04620499163866043,
-0.04491665959358215,
0.013791194185614586,
-0.035118117928504944,
0.004147069528698921,
-0.026656191796064377,
-0.07572808861732483,
-0.0015035709366202354,
0.0007831768016330898,
0.05673842504620552,
-0.016218585893511772,
0.016571249812841415,
0.04360703006386757,
0.023379309102892876,
-0.02246086113154888,
-0.03322870284318924,
-0.022044088691473007,
-0.030480265617370605,
-0.06334931403398514,
0.048538822680711746,
0.031761180609464645,
-0.010529804043471813,
0.04182665795087814,
0.006482867524027824,
0.018678365275263786,
0.041440945118665695,
0.030142968520522118,
-0.01535335648804903,
-0.012615439482033253,
-0.0046002729795873165,
-0.021867884323000908,
0.010452446527779102,
0.022168008610606194,
-0.019770901650190353,
-0.007486315909773111,
0.033555932343006134,
0.046720393002033234,
0.028128838166594505,
-0.009334806352853775,
0.06967482715845108,
-0.009925469756126404,
0.03644604608416557,
-0.02498728409409523,
0.05560727044939995,
-0.003416135674342513,
0.029819916933774948,
0.021685006096959114,
-0.00409234082326293,
0.04302321374416351,
-0.016778649762272835,
-0.012217085808515549,
0.03967961296439171,
0.014125114306807518,
-0.008595779538154602,
-0.01521003246307373,
-0.001298838877119124,
-0.006806378252804279,
0.01366503071039915,
-0.0020033898763358593,
-0.009896200150251389,
0.06389795988798141,
0.042456842958927155,
-0.005580555647611618,
-0.017203129827976227,
-0.02832648903131485,
-0.002012537093833089,
-0.05591612681746483,
-0.012201953679323196,
0.009479820728302002,
0.016156399622559547,
-0.004070911090821028,
0.06356612592935562,
0.021062718704342842,
0.03763047978281975,
0.0010926994727924466,
-0.005908053833991289,
-0.061448268592357635,
0.010924933478236198,
-0.02596406079828739,
-0.006803723983466625,
-0.03997081518173218,
-0.0301371980458498,
-0.00663432152941823,
-0.03801461309194565,
-0.04830125719308853,
-0.011766527779400349,
-0.018142903223633766,
-0.026792490854859352,
-0.0045324587263166904,
-0.01268322765827179,
-0.040967077016830444,
-0.0105603551492095,
0.05187042057514191,
0.013798179104924202,
-0.007826738059520721,
0.02043321169912815,
0.04154063016176224,
-0.028456076979637146,
-0.016865791752934456,
-0.0038384476210922003,
0.0316142812371254,
0.03182047978043556,
0.0307810977101326,
0.047211773693561554,
0.05001969262957573,
-0.03528420627117157,
-0.0005500916158780456,
0.0028522657230496407,
0.04143429175019264,
0.01293841004371643,
-0.018767913803458214,
-0.011788526549935341,
-0.053378451615571976,
-0.006638129707425833,
-0.03163145110011101,
0.03770757094025612,
-0.03918151929974556,
0.0067831408232450485,
0.05015774071216583,
0.014928934164345264,
-0.047069255262613297,
0.03259510546922684,
0.024147164076566696,
0.002326755318790674,
-0.03222084417939186,
-0.013726118952035904,
0.0037946461234241724,
-0.02246558852493763,
0.034054335206747055,
0.0018347558798268437,
0.011351415887475014,
-0.0036509940400719643,
-0.011618881486356258,
0.007331077009439468,
0.015508820302784443,
-0.008946804329752922,
0.009032193571329117,
-0.04848778620362282,
-0.030292175710201263,
-0.025201689451932907,
-0.00861397385597229,
-0.007863635197281837,
0.037515293806791306,
0.044518835842609406,
0.023269694298505783,
-0.01350485347211361,
-0.0579758957028389,
0.0055402712896466255,
0.016070101410150528,
0.028413251042366028,
-0.005324817728251219,
-0.004511632490903139,
-0.06691119819879532,
-0.010143882595002651,
0.035245515406131744,
-0.020103000104427338,
0.051585279405117035,
-0.05051930993795395,
0.004525597207248211,
-0.03561931475996971,
-0.002044384367763996,
-0.006056509912014008,
0.006287390366196632,
0.024016723036766052,
0.00028583387029357255,
-0.02303527668118477,
-0.01752992905676365,
-0.04199804738163948,
0.03319338336586952,
0.03877117857336998,
0.056828100234270096,
-0.024393230676651,
-0.010802296921610832,
-0.001058397931046784,
0.032577577978372574,
-0.015866000205278397,
-0.06524018943309784,
0.023869335651397705,
0.004742514807730913,
0.00459080096334219,
0.06461817026138306,
-0.03604934364557266,
-0.0388033501803875,
0.025197036564350128,
0.04958469048142433,
-0.008584048599004745,
0.008651841431856155,
-0.04088466614484787,
0.02945377118885517,
0.004540989175438881,
0.0023399244528263807,
0.059949036687612534,
0.019444366917014122,
-0.02315335161983967,
-0.003888204460963607,
-0.028170723468065262,
0.07999027520418167,
-0.0444694347679615,
-0.006193033419549465,
-0.0036445558071136475,
-0.01657280884683132,
-0.024488026276230812,
0.067632757127285,
-0.0007182600675150752,
-0.02121405303478241,
-0.01878967322409153,
-0.0538463294506073,
0.0044985609129071236,
-0.013795202597975731,
0.0013890049885958433,
0.014864303171634674,
0.008044332265853882,
0.020558446645736694,
0.02186448872089386,
0.02705688215792179,
0.029691558331251144,
-0.003448772244155407,
-0.011169387958943844,
0.02232535183429718,
0.0441724918782711,
0.0378570593893528,
-0.06881808489561081,
-0.014565329067409039,
-0.015889175236225128,
-0.03110538050532341,
0.01668539270758629,
-0.018153127282857895,
0.028028687462210655,
0.03630375862121582,
-0.06730256974697113,
-0.0536779947578907,
0.006331608165055513,
-0.0414050929248333,
0.05062297359108925,
-0.03892633318901062,
0.03594690561294556,
0.02623842842876911,
0.007400860544294119,
-0.07504305243492126,
-0.053628645837306976,
-0.014445438049733639,
0.020275261253118515,
0.009666652418673038,
-0.019923733547329903,
0.035075075924396515,
0.004169140476733446,
-0.023809190839529037,
-0.007829653099179268,
-0.0019557385239750147,
-0.0033159456215798855,
-0.03396286442875862,
0.009363933466374874,
0.003319981275126338,
0.019943738356232643,
0.01103589590638876,
-0.011097049340605736,
-0.003231505397707224,
-0.05568350851535797,
-0.0275495033711195,
-0.002808771561831236,
0.04574105888605118,
-0.01050629187375307,
-0.024194512516260147,
-0.008433324284851551,
-0.01224800106137991,
0.04561280831694603,
-0.04869677871465683,
-0.015445368364453316,
0.008889022283256054,
0.021498197689652443,
-0.01691550388932228,
-0.020498476922512054,
0.014269418083131313,
0.01319059357047081,
0.008047950454056263,
0.036003921180963516,
-0.01371247973293066,
-0.05346404388546944,
-0.03668233007192612,
0.02148263528943062,
0.020309504121541977,
0.01256976742297411,
-0.01483890600502491,
0.0972808226943016,
0.003260652767494321,
-0.01081031933426857,
-0.023762864992022514,
-0.03199655935168266,
-0.004751260858029127,
-0.011446718126535416,
-0.015818508341908455,
0.029137026518583298,
0.035405173897743225,
-0.014115139842033386,
-0.032521817833185196,
-0.008346808142960072,
0.027722174301743507,
0.059986360371112823,
-0.057825714349746704,
0.041792094707489014,
0.05312448740005493,
-0.026990050449967384,
-0.021229734644293785,
-0.02674054354429245,
-0.006069528870284557,
0.001692123361863196,
-0.0078053646720945835,
0.03859195485711098,
-0.017297808080911636,
-0.011233427561819553,
-0.007889490574598312,
0.043280553072690964,
0.022563721984624863,
-0.009763702750205994,
0.038376305252313614,
0.020942730829119682,
-0.0066911811009049416,
-0.004750317428261042,
-0.06069400534033775,
0.05837308615446091,
-0.031110960990190506,
0.004284898284822702,
0.0008479726384393871,
-0.010231721214950085,
0.0271559190005064,
-0.026391388848423958,
0.013171840459108353,
-0.02166379615664482,
-0.033153269439935684,
-0.01188566628843546,
0.01144892442971468,
-0.03149798512458801,
0.04173661768436432,
0.013060199096798897,
-0.0027545273769646883,
0.016033051535487175,
0.03556426614522934,
0.03721994906663895,
-0.02256203070282936,
-0.08753526955842972,
-0.065268874168396,
-0.041102807968854904,
-0.025294825434684753,
0.06034740433096886,
-0.010332503356039524,
-0.033330827951431274,
0.013784310780465603,
-0.04898950085043907,
0.027812723070383072,
0.011272329837083817,
0.03306901082396507,
0.0005670352838933468,
-0.003928328398615122,
0.011814028024673462,
0.05573200434446335,
0.004017910920083523,
0.011091012507677078,
0.10810701549053192,
0.058159515261650085,
0.01209169626235962,
-0.07449420541524887,
0.0075384993106126785,
-0.06755267083644867,
-0.007947718724608421,
-0.03689086437225342,
0.04348886013031006,
-0.02868666686117649,
0.04029383882880211,
0.010329733602702618,
0.053184255957603455,
0.05276348814368248,
-0.021089231595396996,
0.03753180056810379,
-0.03470885753631592,
-0.03812170401215553,
0.014865441247820854,
0.012536956928670406,
-0.02179752290248871,
0.02577812969684601,
-0.04077976942062378,
0.011733375489711761,
-0.023412995040416718,
-0.01508555468171835,
0.004707643762230873,
-0.03400309756398201,
0.024752948433160782,
0.0053946757689118385,
-0.01755474880337715,
0.007677898742258549,
0.009054201655089855,
-0.009235294535756111,
-0.0756472572684288,
0.02959945611655712,
0.053511206060647964,
-0.013208465650677681,
0.050459519028663635,
-0.022128134965896606,
0.020133113488554955,
0.0015467682387679815,
0.0038515375927090645,
0.025053348392248154,
-0.031702473759651184,
-0.022418662905693054,
0.0014804304810240865,
0.05287569388747215,
0.007291434332728386,
0.008110570721328259,
-0.02538025937974453,
-0.005927986465394497,
0.01954314485192299,
-0.07371780276298523,
-0.016306133940815926,
-0.002678344026207924,
0.018215665593743324,
-0.03016495890915394,
-0.019448036327958107,
-0.008071952499449253,
0.01852591335773468,
-0.021822316572070122,
0.00805443711578846,
0.02930949628353119,
-0.008573539555072784,
-0.009770355187356472,
-0.0021235025487840176,
0.004134200979024172,
0.046927984803915024,
-0.032857563346624374,
-0.03578973934054375,
-0.016460860148072243,
-0.02792937494814396,
-0.031068049371242523,
0.022751014679670334,
0.024939609691500664,
0.03418824076652527,
-0.03670896217226982,
-0.008836105465888977,
-0.02031313069164753,
-0.06347982585430145,
0.021104183048009872,
-0.007411859929561615,
-0.018529249355196953,
-0.006987112574279308,
-0.005832327529788017,
0.059427253901958466,
0.031912900507450104,
0.005279624834656715,
0.015564745292067528,
-0.008462331257760525,
0.012409273535013199,
0.021056270226836205,
0.005280699115246534,
-0.031041931360960007,
0.03519489988684654,
-0.017706524580717087,
0.001449216273613274,
0.008019126951694489,
0.015554806217551231,
-0.015236524865031242,
0.00838377233594656,
0.0359380878508091,
0.01707451418042183,
-0.04949622228741646,
-0.012955546379089355,
-0.008047537878155708,
-0.049249134957790375,
0.01709635555744171,
0.030906835570931435,
0.028546523302793503,
-0.009938828647136688,
-0.044887054711580276,
-0.021988732740283012,
0.010633314959704876,
0.02021965943276882,
0.03974119573831558,
-0.0005813641473650932,
-0.0010374290868639946,
0.0017817484913393855,
0.01940671168267727,
-0.03582844138145447,
-0.03266473487019539,
-0.06070037931203842,
-0.0016808172222226858,
-0.013440859504044056,
-0.029896261170506477,
-0.016205625608563423,
0.03529530391097069,
-0.004990146495401859,
-0.040414001792669296,
0.014671510085463524,
0.023086629807949066,
0.01775316894054413,
-0.001705928472802043,
0.0246565043926239,
0.0027938871644437313,
0.0595027394592762,
-0.003358642105013132,
-0.023413479328155518,
0.06912870705127716,
-0.03037247061729431,
-0.03957225754857063,
0.007675939239561558,
-0.02863568253815174,
0.043027639389038086,
0.011350665241479874,
0.003048987127840519,
-0.022246355190873146,
0.049806222319602966,
-0.0058814771473407745,
-0.007251009810715914,
0.00849920604377985,
-0.040046557784080505,
0.01699174754321575,
0.007608423009514809,
-0.017152391374111176,
-0.008538969792425632,
-0.007766609080135822,
0.042814724147319794,
-0.0013790555531159043,
0.022875448688864708,
-0.017591632902622223,
-0.005428500473499298,
-0.009674380533397198,
-0.0003701191453728825,
0.031197216361761093,
-0.014308049343526363,
-0.02169680967926979,
0.022848157212138176,
-0.016581080853939056,
0.06638740748167038,
0.013046568259596825,
-0.014628388918936253,
-0.11346765607595444,
0.014201912097632885,
-0.00006908332579769194,
0.03233597055077553,
0.04089920222759247,
-0.026030102744698524,
0.0031788977794349194,
0.03397585451602936,
-0.09968128055334091,
-0.0005184700130484998,
-0.03119761496782303,
-0.031910356134176254,
-0.04775771498680115,
0.02940816432237625,
-0.02988891303539276,
0.015116841532289982,
0.03402029722929001,
0.03570070117712021,
0.03537427634000778,
0.001118282089009881,
-0.03267978876829147,
-0.0198004562407732,
0.008564181625843048,
0.02874816209077835,
-0.019489513710141182,
0.022051550447940826,
0.028516188263893127,
-0.0076767448335886,
-0.038699932396411896,
0.0001695372920949012,
-0.017722977325320244,
0.009887713007628918,
-0.011934841051697731,
-0.002264769747853279,
-0.006660517305135727,
0.0021447371691465378,
0.015081125311553478,
-0.003678040113300085,
-0.023517394438385963,
0.0024910317733883858,
0.049946218729019165,
0.00797518715262413,
0.017978716641664505,
-0.003975333645939827,
0.007552056107670069,
-0.078107550740242,
-0.07578346133232117,
-0.0030132164247334003,
-0.00433352729305625,
0.008807030506432056,
0.016601940616965294,
0.04543804004788399,
0.023692646995186806,
-0.055302027612924576,
0.014840038493275642,
-0.06015792861580849,
-0.008946185000240803,
-0.002168989973142743,
0.041915472596883774,
0.012727941386401653,
0.00915620382875204,
0.010880333371460438,
-0.046364810317754745,
0.023081127554178238,
0.019178101792931557,
0.01795079931616783,
-0.02517976239323616,
0.009981990791857243,
0.014142505824565887,
-0.01163182221353054,
0.02157244272530079,
-0.005315870977938175,
-0.03604762628674507,
-0.0013485376257449389,
-0.01776796765625477,
-0.015012950636446476,
0.014364667236804962,
-0.08803810179233551,
-0.04311502352356911,
-0.03674542158842087,
0.06469624489545822,
0.0008172111120074987,
0.000944189669098705,
-0.06751589477062225,
-0.006251655984669924,
-0.023743223398923874,
0.05116451904177666,
0.01902129501104355,
-0.005765751004219055,
-0.027830004692077637,
-0.004389072302728891,
0.03321342542767525,
0.03375141695141792,
-0.031836509704589844,
0.01706467941403389,
-0.0010735838441178203,
-0.020262738689780235,
-0.03053872473537922,
-0.007213952019810677,
-0.018250426277518272,
0.02152637019753456,
0.0008943708380684257,
-0.0014049633173272014,
0.017175748944282532,
-0.004468019586056471,
-0.023668784648180008,
0.06428414583206177,
-0.0177029836922884,
0.0005007869331166148,
0.07791228592395782,
-0.005770088639110327,
0.0253213532269001,
0.044867102056741714,
-0.010096968151628971,
-0.06145089492201805,
0.024755792692303658,
-0.016471736133098602,
-0.003267650492489338,
0.002099777339026332,
0.055532779544591904,
0.03950206935405731,
-0.03526601567864418,
0.03510558232665062,
0.02320563979446888,
0.0012531999964267015,
-0.0317530520260334,
0.03882215917110443,
-0.0008046873845160007,
0.04181361570954323,
0.024289656430482864,
-0.014686878770589828,
0.00811938475817442,
-0.012992177158594131,
-0.015880035236477852,
0.06180513650178909,
-0.006196523550897837,
0.017783137038350105,
0.044961195439100266,
0.030182084068655968,
0.021951623260974884,
-0.001029113307595253,
0.017051029950380325,
0.03137284517288208,
-0.01599058322608471,
-0.009466229937970638,
-0.002201352035626769,
0.02463974803686142,
0.013507063500583172,
0.0354151651263237,
-0.01190548948943615,
0.07001795619726181,
-0.05378652364015579,
0.05787214636802673,
-0.03297248110175133,
0.017954032868146896,
-0.03614027053117752,
0.005630319472402334,
0.020254462957382202,
0.03765196353197098,
-0.03555232286453247,
-0.027184924110770226,
-0.019802242517471313,
0.009313889779150486,
0.019065458327531815,
-0.055807217955589294,
0.04229040816426277,
-0.004706348292529583,
-0.0345626063644886,
-0.013272902928292751,
-0.0025687627494335175,
-0.004245269577950239,
-0.014636225067079067,
0.012197520583868027,
0.03976576402783394,
-0.005145099014043808,
0.0013698321999982,
0.018490944057703018,
-0.052493613213300705,
0.062097832560539246,
-0.06389852613210678,
0.008638801984488964,
0.012418502010405064,
0.03393881767988205,
-0.05626146122813225,
-0.0005232141120359302
] |
<p>Could anyone suggest a recent review article or book on gas chromatography instrumentation? My interest is in the devices themselves, rather than using them for a particular application.</p>
<p><a href="http://rsi.aip.org/resource/1/rsinak/v61/i11/p3317_s1" rel="nofollow">This article</a>, "Gas Chromatography" in Review of Scientific Instruments is the sort of thing I'm going for; I'm just checking to see if there's a more recent or superior introduction.</p> | 1,589 | [
0.005840005818754435,
-0.037778861820697784,
0.018399951979517937,
0.0025453476700931787,
0.03798694908618927,
0.01972702331840992,
-0.005626773927360773,
-0.025045102462172508,
0.012640722095966339,
-0.029998039826750755,
0.034599464386701584,
0.05119093134999275,
0.027346041053533554,
0.021254580467939377,
-0.016541872173547745,
-0.03545703366398811,
0.005116162355989218,
-0.02214955724775791,
0.012005073018372059,
-0.014860853552818298,
-0.031689684838056564,
-0.009068652056157589,
-0.006248950958251953,
0.003295295173302293,
-0.003118606051430106,
0.03297561779618263,
-0.031394895166158676,
-0.02606017142534256,
0.012912929989397526,
0.020761119201779366,
-0.08626773208379745,
0.008842935785651207,
-0.04292481020092964,
-0.019121134653687477,
-0.01834418997168541,
-0.03632710501551628,
-0.015129695646464825,
-0.06462402641773224,
-0.02060156874358654,
0.03016790933907032,
-0.07247143238782883,
-0.02739647589623928,
0.01558657456189394,
0.0049242000095546246,
-0.0009163171052932739,
0.0024254133459180593,
-0.044302262365818024,
-0.021015524864196777,
0.045798346400260925,
-0.10937377065420151,
0.04920593276619911,
0.018538380041718483,
0.049803704023361206,
0.033818796277046204,
0.00037611628067679703,
0.08047033101320267,
0.04817183315753937,
0.05288884416222572,
-0.024259421974420547,
-0.04541705548763275,
-0.007432227488607168,
-0.044007133692502975,
0.022988609969615936,
-0.004687673412263393,
-0.06308849900960922,
0.006881055422127247,
-0.011439966969192028,
-0.049970898777246475,
0.04274744167923927,
-0.0028906946536153555,
0.02443300560116768,
0.010719656944274902,
0.008082112297415733,
0.014943305402994156,
-0.015340768732130527,
-0.011657155118882656,
-0.007465207017958164,
-0.0021340176463127136,
0.05949942395091057,
0.02383612096309662,
0.027328506112098694,
0.02302905172109604,
-0.009582857601344585,
-0.010321244597434998,
-0.025916393846273422,
-0.030365299433469772,
0.09951673448085785,
-0.02999577857553959,
-0.03297310695052147,
-0.007679645903408527,
0.00021407328313216567,
0.013627893291413784,
0.020117303356528282,
0.019252978265285492,
-0.014134292490780354,
0.021136073395609856,
-0.011139689944684505,
0.06407328695058823,
-0.029583478346467018,
-0.026187147945165634,
-0.006246544420719147,
-0.0033984719775617123,
0.023844491690397263,
0.1025671735405922,
-0.016651980578899384,
-0.041873499751091,
-0.030795684084296227,
0.03320040926337242,
0.02131621167063713,
-0.014161091297864914,
-0.009454522281885147,
-0.014437263831496239,
0.023971596732735634,
0.019391246140003204,
0.000599671620875597,
0.025071827694773674,
0.00837699230760336,
-0.0052235983312129974,
0.05750737711787224,
0.055961787700653076,
0.02445773035287857,
-0.01890472136437893,
0.02856495976448059,
-0.01236267201602459,
-0.0750032588839531,
0.01958395354449749,
0.024921216070652008,
-0.03133925050497055,
-0.013551194220781326,
0.017812887206673622,
0.003421052824705839,
-0.007381309289485216,
0.017370594665408134,
0.0018695222679525614,
0.011754071339964867,
-0.017384398728609085,
-0.08444379270076752,
-0.05121760815382004,
0.0713689774274826,
-0.03159511089324951,
0.034522492438554764,
-0.061147142201662064,
-0.009095946326851845,
-0.0007336884154938161,
0.057001858949661255,
0.02826065756380558,
-0.021043406799435616,
-0.046106934547424316,
0.0461113341152668,
-0.0051447544246912,
-0.03347450867295265,
-0.025085411965847015,
0.031031446531414986,
-0.010098283179104328,
0.005176943261176348,
-0.04919467493891716,
0.022058628499507904,
0.03420319780707359,
0.021617047488689423,
-0.0330423004925251,
0.06315305829048157,
0.019468875601887703,
-0.028347061946988106,
0.0004335090343374759,
-0.024103423580527306,
-0.04176224395632744,
0.04306836053729057,
-0.011516289785504341,
0.007980610243976116,
-0.0056886738166213036,
0.010216932743787766,
0.04108911380171776,
0.01739969663321972,
-0.00023931414762046188,
0.05620356276631355,
-0.0012208467815071344,
0.020288435742259026,
0.019754936918616295,
0.016667796298861504,
0.015726281329989433,
0.006128828506916761,
-0.015315748751163483,
0.009313035756349564,
0.027178160846233368,
0.025712864473462105,
0.004990026354789734,
-0.015421622432768345,
-0.006225296761840582,
0.021881844848394394,
-0.05313267558813095,
-0.022244803607463837,
-0.05473504960536957,
0.0066648200154304504,
0.00025562182418070734,
-0.018831973895430565,
0.06027783825993538,
0.017964167520403862,
0.01693342626094818,
-0.01733366772532463,
-0.0781264528632164,
0.007348949089646339,
-0.0009819560218602419,
0.026464911177754402,
-0.04187855124473572,
-0.015999775379896164,
0.014346413314342499,
-0.0031886340584605932,
-0.0005994046223349869,
0.03218018263578415,
0.008002761751413345,
-0.0495787151157856,
0.030112484470009804,
-0.013286069966852665,
0.005836154334247112,
-0.03684541955590248,
-0.04098522290587425,
0.004535536747425795,
-0.01981743425130844,
-0.001942819682881236,
0.03804587572813034,
-0.028059786185622215,
0.02734207734465599,
0.03628699854016304,
0.039418529719114304,
0.010812400840222836,
0.02161497250199318,
0.023241570219397545,
0.010790855623781681,
0.006506949197500944,
-0.013156844303011894,
-0.025671010836958885,
-0.025606753304600716,
0.025040825828909874,
0.06244576349854469,
-0.01376283634454012,
0.010532894171774387,
0.02138628624379635,
0.03777169808745384,
0.01666208729147911,
0.019228892400860786,
-0.012891481630504131,
-0.052121710032224655,
-0.02063900977373123,
0.03742722049355507,
-0.011365850456058979,
0.025191467255353928,
0.0164670217782259,
0.02312343567609787,
0.03127191588282585,
0.008794276975095272,
0.000051941689889645204,
0.029788747429847717,
0.0042677875608205795,
-0.007338198367506266,
0.022440915927290916,
0.008935772813856602,
0.05553390830755234,
-0.013977350667119026,
0.014508940279483795,
0.009565147571265697,
0.033126357942819595,
0.04537370428442955,
0.005607042461633682,
-0.016589781269431114,
-0.006943422835320234,
0.0008152129012160003,
-0.01664409227669239,
0.009100372903048992,
0.007375504355877638,
-0.07114462554454803,
0.05958689749240875,
-0.0593341626226902,
0.03359119966626167,
-0.0315365269780159,
-0.0010715759126469493,
-0.03108045645058155,
0.022588957101106644,
0.04363049939274788,
-0.010167880915105343,
-0.035323821008205414,
-0.03489570692181587,
-0.037023283541202545,
0.02879459410905838,
0.0002071335620712489,
-0.028477052226662636,
-0.0031778747215867043,
-0.03840838372707367,
-0.0022894549183547497,
0.03476151078939438,
-0.02963811531662941,
-0.0558832548558712,
0.004771133419126272,
0.024575017392635345,
-0.03279433399438858,
0.010611969977617264,
0.052837271243333817,
-0.0112602598965168,
0.0005149481003172696,
-0.013427299447357655,
0.0020914110355079174,
-0.037535861134529114,
0.02062511071562767,
0.008424058556556702,
-0.03246571123600006,
-0.023683469742536545,
-0.03177347034215927,
0.02543889731168747,
0.011361823417246342,
-0.025163400918245316,
-0.010768262669444084,
0.0371558777987957,
-0.05039086565375328,
-0.04167209193110466,
-0.021465428173542023,
-0.03490237146615982,
0.018635055050253868,
0.026812830939888954,
0.04241463541984558,
0.00039854549686424434,
-0.0069146850146353245,
0.03900982812047005,
0.0018690993310883641,
-0.006391676142811775,
-0.005949700716882944,
-0.043409693986177444,
-0.008090700022876263,
-0.021267777308821678,
-0.004843246191740036,
0.002899883082136512,
0.015189013443887234,
0.017749935388565063,
0.005307562183588743,
-0.008265296928584576,
0.0488402433693409,
0.02267502434551716,
-0.02341035194694996,
0.02661639265716076,
0.001842292957007885,
-0.0015660523204132915,
0.01628785952925682,
0.03511221334338188,
-0.037270449101924896,
0.010951417498290539,
0.005050639156252146,
0.023972006514668465,
0.04634949564933777,
-0.030931685119867325,
0.046529412269592285,
0.0028959771152585745,
-0.009633198380470276,
0.002821146510541439,
-0.020572738721966743,
0.012461092323064804,
-0.02370787039399147,
0.019708096981048584,
0.045087628066539764,
-0.00003832230868283659,
0.006285327486693859,
-0.025935309007763863,
0.050402235239744186,
0.028811173513531685,
-0.038667768239974976,
-0.022798806428909302,
0.014249074272811413,
-0.030349986627697945,
0.043701786547899246,
-0.014895649626851082,
-0.00809144414961338,
0.04907691851258278,
0.020285477861762047,
0.015215124003589153,
-0.024906806647777557,
-0.04244738817214966,
0.0035737629514187574,
-0.07820659130811691,
-0.0001226492749992758,
-0.00829076487571001,
0.02937353029847145,
0.0021099215373396873,
0.046453703194856644,
0.00832341518253088,
-0.006364080589264631,
0.033521294593811035,
-0.011950813233852386,
-0.08729185163974762,
0.015373566187918186,
-0.038022954016923904,
0.020276132971048355,
0.008983842097222805,
0.02063700743019581,
0.011786453425884247,
0.009502715431153774,
-0.013356192968785763,
-0.006180020049214363,
0.047764599323272705,
-0.050273094326257706,
0.027567047625780106,
-0.024002371355891228,
-0.029701219871640205,
-0.030750831589102745,
0.020477352663874626,
0.0075307018123567104,
0.005655005108565092,
0.00566002307459712,
-0.004022317007184029,
-0.011030995287001133,
-0.010850322432816029,
-0.013724996708333492,
0.015691466629505157,
0.007554769981652498,
0.018556153401732445,
0.036088619381189346,
0.013608263805508614,
-0.017473867163062096,
0.000570177158806473,
0.01131539698690176,
0.050299592316150665,
-0.0387461893260479,
-0.04483504220843315,
-0.0179001297801733,
-0.0178513303399086,
-0.02241475321352482,
0.02011382021009922,
0.04631350189447403,
0.01574580930173397,
0.01957201026380062,
-0.009280222468078136,
-0.02287975326180458,
-0.04513269662857056,
0.03857545554637909,
0.01085422933101654,
0.01560857892036438,
-0.004115893505513668,
0.0213572159409523,
-0.007706684526056051,
-0.029883868992328644,
0.0005870872410014272,
0.03117445483803749,
0.026127280667424202,
-0.01023833453655243,
-0.03250488266348839,
-0.0014350805431604385,
0.03837762773036957,
-0.04004347696900368,
-0.0015978547744452953,
0.038442887365818024,
0.04266940429806709,
-0.025057237595319748,
-0.012372665107250214,
-0.008130266331136227,
0.035630002617836,
0.0455188974738121,
0.015584876760840416,
-0.022341035306453705,
-0.08106547594070435,
-0.0015073252143338323,
0.0439249649643898,
-0.0016540255164727569,
-0.06401107460260391,
-0.0011838075006380677,
-0.04941068962216377,
-0.009129581972956657,
0.021717151626944542,
-0.03964397683739662,
0.022717271000146866,
-0.08100001513957977,
-0.0308850035071373,
-0.028607038781046867,
0.0002083931613015011,
-0.00931994803249836,
-0.018629608675837517,
0.03006076253950596,
-0.0010440185433253646,
-0.023972170427441597,
-0.016116149723529816,
-0.04502744972705841,
-0.018019994720816612,
-0.006446471903473139,
0.05367029458284378,
0.024042721837759018,
-0.0006561712943948805,
0.04146426543593407,
0.058094464242458344,
-0.04031048342585564,
-0.04705597832798958,
0.013498552143573761,
-0.003053748281672597,
0.0017953149508684874,
0.047586314380168915,
-0.02019975334405899,
-0.06167230382561684,
0.023755082860589027,
-0.009909452870488167,
-0.037483204156160355,
-0.04053955152630806,
-0.022498976439237595,
0.02231621742248535,
0.028785327449440956,
-0.01580384001135826,
0.08837193995714188,
0.03135065734386444,
-0.01737852208316326,
0.04385063797235489,
0.01532700750976801,
0.039930559694767,
-0.06295926868915558,
-0.028975678607821465,
-0.026453876867890358,
-0.0071662068367004395,
-0.03794596716761589,
0.04159729927778244,
0.005496716592460871,
0.02600390650331974,
-0.011354773305356503,
-0.03299521282315254,
0.03909187391400337,
0.028554685413837433,
0.009850775822997093,
-0.007951861247420311,
0.020238343626260757,
0.013857044279575348,
0.014405208639800549,
-0.021626750007271767,
-0.0023015968035906553,
0.014966140501201153,
-0.01366901770234108,
0.0073953671380877495,
0.002255704952403903,
0.018772557377815247,
-0.07422377914190292,
-0.012170017696917057,
-0.014085418544709682,
-0.0073634120635688305,
0.09751292318105698,
0.01496435608714819,
-0.002681716112419963,
0.01759571023285389,
-0.04350768029689789,
-0.036055199801921844,
0.04339402914047241,
0.004974965937435627,
-0.00017788566765375435,
-0.09959261864423752,
0.057204872369766235,
-0.029294854030013084,
0.008490914478898048,
-0.0718696340918541,
-0.013145074248313904,
0.02488703653216362,
-0.02057741768658161,
-0.01322413794696331,
-0.056274719536304474,
0.03874798119068146,
0.009488840587437153,
-0.029898788779973984,
0.003021199954673648,
0.0285070538520813,
-0.014901090413331985,
-0.010402140207588673,
0.020401116460561752,
0.035212866961956024,
0.0562313087284565,
-0.02416168712079525,
-0.0006844832096248865,
-0.007383961230516434,
-0.015709497034549713,
-0.02331775240600109,
-0.0031478519085794687,
-0.028964504599571228,
-0.016574140638113022,
-0.013040393590927124,
-0.0011915632057935,
0.028396764770150185,
0.02162630297243595,
-0.042028822004795074,
0.02075100690126419,
0.03594200685620308,
-0.008735427632927895,
-0.007698667235672474,
-0.03472686931490898,
0.0186057947576046,
-0.04118742421269417,
0.02835695818066597,
-0.015222519636154175,
0.011212429031729698,
-0.006463212892413139,
-0.029940472915768623,
-0.010570387355983257,
0.007223952561616898,
-0.012913593091070652,
0.014026404358446598,
0.03147107735276222,
-0.007513910531997681,
0.020061301067471504,
0.04838516190648079,
-0.037677206099033356,
0.020421942695975304,
0.002274692989885807,
0.045408327132463455,
0.0431525781750679,
-0.019131876528263092,
-0.030493732541799545,
-0.06942003965377808,
-0.008843951858580112,
-0.018171265721321106,
0.01734735444188118,
0.042903341352939606,
0.03530449792742729,
0.04125499725341797,
-0.04154124855995178,
-0.013570455834269524,
-0.037888363003730774,
-0.008834071457386017,
0.027450792491436005,
0.0019923709332942963,
0.046401333063840866,
-0.029131971299648285,
-0.001689603552222252,
0.0033690843265503645,
0.013402217999100685,
-0.006277834065258503,
-0.007341913413256407,
0.007264304906129837,
0.05047473683953285,
-0.014853195287287235,
-0.020945033058524132,
-0.06891792267560959,
0.03999091312289238,
-0.03380489721894264,
0.04552645981311798,
-0.009025315754115582,
0.013961120508611202,
0.004058497026562691,
0.030623508617281914,
0.018468480557203293,
-0.06242537871003151,
-0.02024335227906704,
-0.028017880395054817,
0.006808147765696049,
0.0377475805580616,
-0.055668193846940994,
0.006634617689996958,
-0.0036890986375510693,
0.024926230311393738,
-0.007238131947815418,
0.033255234360694885,
0.007687347941100597,
-0.054876383394002914,
-0.007031171582639217,
0.012198043055832386,
-0.028048425912857056,
0.04815268516540527,
-0.022082244977355003,
-0.03249185532331467,
0.005471524782478809,
-0.023848803713917732,
0.029732372611761093,
-0.0041755447164177895,
-0.008966367691755295,
-0.006472027860581875,
0.09718106687068939,
-0.0624622106552124,
0.018357830122113228,
0.04102630168199539,
-0.019871003925800323,
0.1242443323135376,
0.009351101703941822,
0.02269729971885681,
-0.08234117925167084,
0.04058852046728134,
-0.008170733228325844,
0.02314332127571106,
-0.010025808587670326,
0.0004811991238966584,
-0.012072618119418621,
0.022694416344165802,
0.0006943080225028098,
0.06156935170292854,
-0.02496136724948883,
0.03784172236919403,
0.04649210721254349,
-0.005914051551371813,
-0.01763494871556759,
-0.019200537353754044,
0.009506422095000744,
-0.060073498636484146,
0.02222282811999321,
-0.03555615246295929,
0.021243931725621223,
-0.004927696194499731,
-0.023340115323662758,
-0.031568415462970734,
-0.03715452551841736,
0.03856620937585831,
0.002929958049207926,
-0.04974183812737465,
-0.021553970873355865,
-0.01378682628273964,
0.006018346641212702,
-0.017172837629914284,
0.025570521131157875,
0.02495802938938141,
0.039800435304641724,
-0.004192291293293238,
0.006404215004295111,
0.018279248848557472,
0.0041451058350503445,
0.03715210780501366,
0.02023441344499588,
-0.026670344173908234,
-0.004491127096116543,
0.020011212676763535,
0.027490967884659767,
-0.033398546278476715,
-0.02440209873020649,
-0.03737732395529747,
0.015097571536898613,
0.0003506836073938757,
-0.028834789991378784,
-0.06553210318088531,
0.009354772977530956,
0.04852829873561859,
-0.05384465679526329,
-0.041286908090114594,
-0.034858282655477524,
0.03802758455276489,
-0.036894798278808594,
0.009134570136666298,
-0.023055506870150566,
-0.016499411314725876,
0.0039707669056952,
-0.04097510501742363,
0.033626195043325424,
0.0023090625181794167,
-0.021915912628173828,
-0.038823723793029785,
0.03518860042095184,
-0.05277252569794655,
-0.019932948052883148,
-0.006792434025555849,
0.030241938307881355,
0.028344469144940376,
-0.015625301748514175,
-0.013075154274702072,
0.006833246909081936,
-0.07119917869567871,
0.044545628130435944,
-0.020024169236421585,
-0.001160505460575223,
-0.007117719855159521,
-0.014619562774896622,
0.03479762375354767,
0.012907817028462887,
-0.009267165325582027,
0.05316128581762314,
-0.007854257710278034,
0.002534956205636263,
0.05269452556967735,
-0.010470578446984291,
0.0031208868604153395,
0.02289140410721302,
-0.04361315444111824,
-0.005315842572599649,
-0.00535227544605732,
0.04524066671729088,
0.012328148819506168,
-0.0065050432458519936,
0.004889451898634434,
-0.01970817893743515,
-0.008427957072854042,
-0.004102984443306923,
0.028858253732323647,
0.026509243994951248,
-0.0256554763764143,
0.009506408125162125,
0.06921688467264175,
-0.04034426063299179,
-0.06193728372454643,
-0.03448152169585228,
0.010572277009487152,
-0.014642504043877125,
0.024703189730644226,
0.0027895281091332436,
0.03886488825082779,
-0.019454555585980415,
0.029149644076824188,
-0.042123544961214066,
0.00940241664648056,
-0.07067444920539856,
0.007772461511194706,
0.003348343539983034,
0.027755767107009888,
0.009567866101861,
0.030920447781682014,
-0.015152931213378906,
-0.015178241766989231,
0.044376831501722336,
0.02871548943221569,
0.019165165722370148,
0.005499967839568853,
-0.0005800244980491698,
-0.03913358971476555,
0.054572172462940216,
-0.036168552935123444,
0.004126775544136763,
0.050990257412195206,
-0.021370306611061096,
-0.04723263531923294,
0.04173315316438675,
-0.006173213478177786,
-0.0012910704826936126,
-0.012584682554006577,
0.0006097774021327496,
-0.0011500355321913958,
0.02673751302063465,
0.016139421612024307,
-0.0255505982786417,
-0.0033227726817131042,
-0.00006984620995353907,
-0.01929193176329136,
-0.029823344200849533,
0.009782269597053528,
-0.003416377352550626,
-0.02864815481007099,
0.03860682621598244,
0.010014952160418034,
0.037601154297590256,
0.04544251039624214,
0.010212267749011517,
-0.03340939059853554,
0.04180367290973663,
0.03176749497652054,
-0.009963154792785645,
0.05597788468003273,
0.07672953605651855,
-0.05699466913938522,
0.015355239622294903,
0.02237977460026741,
0.01196985226124525,
-0.05927611514925957,
0.005064106080681086,
-0.02423853427171707,
-0.0018955921987071633,
0.05351777747273445,
-0.03590398654341698,
-0.014426478184759617,
0.039593834429979324,
-0.0718780905008316,
-0.01598205789923668,
0.0014682636829093099,
-0.01986119896173477,
-0.014456073753535748,
-0.021282263100147247,
0.02317829243838787,
0.0020281532779335976,
0.0023595886304974556,
0.02046160213649273,
0.021222658455371857,
0.03995681181550026,
-0.006273398641496897,
-0.02837810292840004,
0.0021247249096632004,
0.03179234266281128,
-0.015647096559405327,
-0.05710751935839653,
0.024491334334015846,
-0.03935455530881882,
-0.0008372191223315895,
0.020342739298939705,
0.0051429723389446735,
0.028318800032138824,
-0.004176571033895016,
-0.02136613428592682,
-0.04683885723352432,
0.04966019466519356,
0.02702847123146057,
-0.010522214695811272,
-0.013035537675023079,
0.02483614906668663,
0.010995070450007915,
0.034680046141147614,
0.018164154142141342,
0.021537071093916893,
-0.009644734673202038,
-0.018033139407634735,
-0.014769029803574085,
0.011018973775207996,
-0.03433587774634361,
-0.03642448037862778,
0.024458209052681923,
0.006899373605847359,
-0.006394516211003065,
-0.023471897467970848,
-0.0019928249530494213,
-0.03309306502342224,
-0.012053701095283031,
0.041525546461343765,
0.018240004777908325,
0.03564374893903732,
-0.009022516198456287,
-0.012018847279250622,
-0.021734721958637238,
0.0061818077228963375,
0.025060774758458138,
0.02351832389831543,
-0.01395415235310793,
0.0018733924953266978,
0.009146139025688171,
-0.006326151080429554,
0.00009535766730550677,
-0.019442783668637276,
-0.02907397225499153,
0.045760657638311386,
-0.026078274473547935,
0.0007649509934708476,
-0.03497815877199173,
-0.020682442933321,
0.02011093869805336,
-0.028598075732588768,
0.054327648133039474,
0.023431148380041122,
0.01564551331102848,
-0.00282560964114964,
-0.0357959121465683,
0.005716641433537006,
0.01722719892859459,
0.08070357888936996,
-0.027108702808618546,
-0.03862271085381508,
-0.0030039832927286625,
0.055270615965127945,
0.026688499376177788,
-0.031852900981903076,
0.06645142287015915,
0.016485262662172318,
-0.04519665613770485,
0.003198321210220456,
-0.043440207839012146,
-0.02218475751578808,
0.019974812865257263,
0.0018664952367544174,
0.014291519299149513,
0.003361515933647752,
-0.031518179923295975,
0.0016633995110169053,
0.07984768599271774,
0.016731305047869682,
0.004636985249817371,
0.07223258167505264,
-0.038835734128952026,
0.03677408769726753,
0.024264758452773094,
-0.0006959102465771139,
-0.02261669561266899,
0.017574969679117203,
-0.011610637418925762,
-0.01088341511785984,
-0.032757192850112915,
-0.0024016050156205893,
-0.011996426619589329,
-0.02909666672348976,
0.044771838933229446,
-0.030262775719165802,
-0.036751020699739456,
0.0043782382272183895,
0.05546901375055313,
0.008425909094512463,
0.03834071755409241,
-0.006399084813892841,
0.014405089430510998,
0.039442867040634155,
0.04076968878507614,
-0.034010253846645355,
0.05268222466111183,
0.02889595739543438,
0.04475996643304825,
0.01591070555150509,
0.02092372253537178,
-0.011459814384579659,
0.030475370585918427,
0.006623811088502407,
0.02910597436130047,
-0.024541044607758522,
-0.02546561509370804,
0.013156999833881855,
-0.012857530266046524,
-0.005580596160143614,
0.053082987666130066,
-0.029976531863212585,
0.08868642151355743,
-0.07406634092330933,
-0.03702878952026367,
-0.023309769108891487,
-0.014542859047651291,
-0.0065572550520300865,
-0.029396867379546165,
-0.023680882528424263,
0.04604879766702652,
-0.006566622294485569,
0.06426813453435898,
-0.036077409982681274,
0.013917418196797371,
0.01846437342464924,
-0.0023901548702269793,
0.027564777061343193,
-0.003059044014662504,
0.014900361187756062,
-0.013381373137235641,
-0.04748670011758804,
-0.0086549436673522,
-0.031798481941223145,
0.012976046651601791,
0.06429703533649445,
-0.008443623781204224,
0.014251147396862507,
-0.004080456215888262,
-0.01228255219757557,
0.0584636889398098,
-0.04602314159274101,
0.01938922144472599,
-0.0012010924983769655,
-0.009089771658182144,
-0.04045090824365616,
0.024607984349131584
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.