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<p>Cold fusion is being mentioned a lot lately because of some new setup that apparently works. This is an unverified claim.</p>
<p>See for example:</p>
<ul>
<li><a href="http://hardware.slashdot.org/story/11/01/24/1550205/Italian-Scientists-Demonstrate-Cold-Fusion">http://hardware.slashdot.org/story/11/01/24/1550205/Italian-Scientists-Demonstrate-Cold-Fusion</a></li>
<li><a href="http://www.physorg.com/news/2011-01-italian-scientists-cold-fusion-video.html">http://www.physorg.com/news/2011-01-italian-scientists-cold-fusion-video.html</a></li>
<li><a href="http://www.wipo.int/pctdb/en/wo.jsp?WO=2009125444&IA=IT2008000532&DISPLAY=DOCS">http://www.wipo.int/pctdb/en/wo.jsp?WO=2009125444&IA=IT2008000532&DISPLAY=DOCS</a></li>
<li><a href="http://www.journal-of-nuclear-physics.com/files/Rossi-Focardi_paper.pdf">http://www.journal-of-nuclear-physics.com/files/Rossi-Focardi_paper.pdf</a></li>
</ul>
<p>While we should give the scientific community time to evaluate the set up and eventually replicate the results, there is undoubtedly some skepticism that cold fusion would work at all, because the claim is quite extraordinary.</p>
<p>In the past, after Fleischmann and Pons announced their cold fusion results, in perfectly good faith, they were proven wrong by subsequent experiments.</p>
<p>What are the experimental realities that make Fleischmann and Pons style cold fusions experiments easy to get wrong?</p>
<p>Would the same risks apply to this new set up?</p>
| 640 |
<p>Watching quantum mechanics lectures and it was mentioned that it is pointless/meaningless to try to talk/question things that can not be tested/measured.</p>
<p>Is this a principle? And if so what is it's name?</p>
<p>Also does this apply to questions other than Quantum mechanics? E.g. does it make sense to ask if earth was the only object in universe if gravity would still exist? Although it seems intuitive to answer yes, yet it is something that can never be tested/verified. It seems almost as meaningless as to ask if the universe was only made of a unicorn would it have gravity?</p>
<p>As an analogy consider glottogony, at some point it was banned as it seemed to be an unanswerable problem. <a href="http://en.wikipedia.org/wiki/Origin_of_language" rel="nofollow">http://en.wikipedia.org/wiki/Origin_of_language</a></p>
| 3,907 |
<p>The title says it all. Why are snowflakes <a href="http://en.wikipedia.org/wiki/Snowflake#Gallery">symmetrical in shape</a> and not a mush of ice? </p>
<p>Is it a property of water freezing or what? Does anyone care to explain it to me? I'm intrigued by this and couldn't find an explanation.</p>
| 521 |
<p>I was reading this interesting recent review on arxiv about particle identification:</p>
<p><a href="http://arxiv.org/pdf/1101.3276">Particle Identification</a></p>
<p>In figure 2, there is an interesting comparison between the CMS and ATLAS calorimeter performances. I hope the paper author won't mind if I reproduce the image here:</p>
<p><img src="http://img809.imageshack.us/img809/1180/calo.png" height="250"></p>
<p>You see that the CMS EM calorimeter has much better resolution than the ATLAS one, and I'm certain that this is due to the almost unfair comparison between an homogenous and a sampling calorimeter. No surprise here.</p>
<p>On the other hand, the ATLAS hadronic calorimeter has much better resolution than CMS's. </p>
<p>1) Why is that? Is this just a by-product of the reduced size of the CMS hadronic calorimeter?</p>
<p>2) Are those resolutions final or can the collaborations make them better when they have more data? How?</p>
| 3,908 |
<p>Whereas I can calculate the <strong>Chern number</strong> of a quantum state (or band) from the integration of the Berry curvature in all space.</p>
<p>How can I infer the topology of the quantum state from this result? What is the physical meaning of a quantum state with non-zero Chern number?</p>
| 3,909 |
<p>One morning I woke up to a text message and picked up my phone but I was not yet fully awake and my eyes had not really gotten its focus.
When I stared at the phone I saw two phones. Which is obviously just a depth perception and missed focus. There is even and art form called <a href="http://en.wikipedia.org/wiki/Stereogram" rel="nofollow">stereogram</a> and its fun to play with sometimes , which is what I was doing, because there was some interesting light coming through the window. In the corner of my eye I even caught a glimpse of the visible light band spectrum.</p>
<p>So I was looking at the two phones. One real and the other a recreation of the other, and they were exact copies of each other ( as they should be ). But when I titled my head, a light reflection would pass over the real one but not its doppelganger. However the original light reflection was still showing even though the real phone had tilted showing another reflection.</p>
<p>Does anyone know what this phenomenon this?</p>
| 3,910 |
<p>What are the current most important <em>theoretical</em> problems on quantum entanglement?
What is that we don't yet understand about how it works?
(Not considering interpretation etc problems)</p>
| 3,911 |
<p>I remember a while ago my father dropped a glass lid and it smashed. <a href="http://images.google.com/imgres?imgurl=http://www.webvert-cookware.co.uk/flatglasslid-300.jpg&imgrefurl=http://www.webvert-cookware.co.uk/flatglasslid.htm&usg=__dPS-9DaG0CrN-iOj0zLN8v15L9k=&h=300&w=300&sz=21&hl=no&start=0&sig2=3ETNZ53Jv3YGPd32e5Ng6g&zoom=1&tbnid=3YP3t6rszo9PVM%3a&tbnh=166&tbnw=180&ei=uxgSTdmEOIal8QOVqc2EBw&prev=/images%3Fq%3Dglass%2Blid%26hl%3Dno%26biw%3D1438%26bih%3D815%26gbv%3D2%26tbs%3Disch:1&itbs=1&iact=rc&dur=198&oei=uxgSTdmEOIal8QOVqc2EBw&esq=1&page=1&ndsp=24&ved=1t:429,r:0,s:0&tx=159&ty=107">It looked something like this.</a> When that happened, for about 5 minutes afterwards, the glass parts were splitting, kind of like popcorn, and you could hear the sound. I was just wondering why this happened, and the particles didn't just sit quietly in their own original parts?</p>
| 3,912 |
<p>I essentially have three questions concerning <a href="http://en.wikipedia.org/wiki/High-energy_radio-frequency_weapons" rel="nofollow">weapons based on EM waves</a> or more <a href="http://en.wikipedia.org/wiki/Directed-energy_weapon#Lasers" rel="nofollow">generally</a>.</p>
<ol>
<li><p>Focusing on the weapons using radio-waves and/or micro-waves, what power do these types of weapons need to radiate to generate the described effects?</p></li>
<li><p>How easy or difficult would it be to make your own weapon or to acquire one. As I understand it from the wikipage, only the US army is known to have such weapons, so I suppose it is not something you could easily make unless you have a physics lab at your disposition.</p></li>
<li><p>We live in a world where the "amount" of radio-waves and micro-waves that pervade our space is impressive. Isn't there any danger to be expected from these waves, considering that weapons can be built based solely on concentrated pulses of EM waves? Could something apparently as benign as a cell phone or a WiFi connection have the same effects, even though they would require longer exposition? I am aware that <a href="http://en.wikipedia.org/wiki/Wireless_electronic_devices_and_health" rel="nofollow">studies</a>, also this <a href="http://en.wikipedia.org/wiki/Electromagnetic_radiation_and_health" rel="nofollow">link</a> and this <a href="http://en.wikipedia.org/wiki/Electrical_sensitivity" rel="nofollow">one</a>, have been done, and they seem to be either inconclusive or answering in the negative. Yet, I have this nagging doubt.</p></li>
</ol>
<p>I am aware that the question is bordering on questions of medicine and physiology as well as engineering rather than pure physics, but I'm not sure where else to ask.</p>
| 3,913 |
<p>Laser beams are said to have high <a href="http://en.wikipedia.org/wiki/Laser">"spacial coherence"</a>. This means that the beam is highly concentrated even at long distances (low spread).</p>
<p>Can this be achieved with radio waves (much longer waves) or is it due to laser's <a href="http://en.wikipedia.org/wiki/Stimulated_emission"> stimulated emission</a>?</p>
| 3,914 |
<p>With regard to the recent arXiv article:</p>
<p>J. D. Shelton, <em>Eddy Current Model of Ball Lightening</em><br>
<a href="http://arxiv.org/abs/1102.1224" rel="nofollow">http://arxiv.org/abs/1102.1224</a></p>
<p>I wonder if this is a reasonable explanation of ball lightening, or if there is such an explanation. The paper is somewhat technical and E&M is one of my worst subjects.</p>
<p>Please feel free to edit this question to one better suited, or if you don't have the rep, add a comment suggesting changes.</p>
| 3,915 |
<p>Is it possible that the process of quantum entanglement creates new space time?</p>
<p>If two entangled particles' quantum states cannot be described individually, even if they are separated to us, is it possible that observation causes the space time they occupy to "separate"? Hence the near instantaneous information transfer?</p>
<p>Could this also cause inflation in some way?</p>
| 3,916 |
<p>I know that in string theory, D-branes are objects on which open strings are attached with Dirichlet boundary conditions. But what exactly is a brane? Are they equally fundamental objects like string? If so then do they also vibrate? If the visible universe itself is not a brane then what is the dynamics of these branes within the universe? Do individual D-Branes interact, collide? Can an open string tear itself off from the D-brane? If so what are the results?</p>
| 3,917 |
<p>Bell-type experiments look at the violation of this inequality: $|S|\leq 2$.</p>
<p>where $S=E(a,b)-E(a,b')+E(a',b)+E(a',b')$ and $E$ is the correlation function.</p>
<p>Mathematically, the maximal violation of the inequality is reached when $|S|=4$ (because the bounds of $\cos \theta_{ab}$ are $\pm 1$).</p>
<p>However, wherever I look in the literature it says that experimentally, quantum states produce a violation up to $|S|\leq 2\sqrt{2}$. That is Tsirelson's bound.</p>
<p>The detector settings are always given in intervals of $\frac{\pi}{8}$ radians. A very common set-up in degrees is: $a = 0$, $a' = 45$, $b = 22.5$, $b' = −22.5$.</p>
<p>They seem to take it for granted that this is THE configuration for maximal violation, without an explanation (I think I'm missing something). </p>
<p>Why can't the mathematical maximum be achieved experimentally?</p>
<p>Thanks in advance! :)</p>
| 3,918 |
<p>I have a 4' hose that is closed at one end and connected to a Airdata Test Set (precise control of pressure) and a high accuracy pressure monitor on the other end with a T and valve. The valve allows the Airdata Test Set connection to be closed off resulting in a hose connected to the pressure monitor and closed at the other end. The valve is a high quality needle valve. The pressure monitor is a a Druck DPI 142. Half the length of the hose is in a temperature chamber controlled to 70 C. The Druck connected end is outside the chamber at roughly 22 C. When the airdata test set is commanded to a pressure of 1300 mb and allowed to settle for 30 seconds or so, then the valve closed, the pressure reported by the Druck drops over 20 minutes or so with a decreasing rate of change. The airdata test set draws air from the room when operating. The hose is ~0.190" ID neoprene, Saint-Gobain P/N 06404-15. The temp chamber, hose, etc, are given 1 hour to thermally stabilize prior to commanding the pressure to 1300 mb. The difference between initial pressure and stable pressure is ~18 mb. Why does the pressure take 20 minutes to stabilize?</p>
| 3,919 |
<p>if the universe is a 0 energy universe, could the value of G be worked out through summing up the strong, weak and electromagnetic force strengths for an elementary particle up to an infinite distance, and take the value of the negative energy gravity provides as that value in reverse? </p>
<p>Or at the very least the value of the sum of the force of gravity and the cosmological constant?</p>
| 3,920 |
<p>What used to be functions in the context of classical mechanics like position, linear momentum, angular momentum, etc in quantum mechanics are operators (these operators act on the state to get results). So the question is: Historically, conceptually, and mathematically how functions become operators in quantum mechanics?</p>
| 118 |
<p>Do all planets have an electric charge? </p>
<p>If yes, is positive or negative?
And how much each magnitude? </p>
<p>I have read some articles which really confused me. Some of these articles said that all planets have a negative charge and the sun has a positive charge. Some other articles said the the exact opposite. </p>
| 3,921 |
<p>Most modern texts spend some time deriving the <a href="http://en.wikipedia.org/wiki/LSZ_reduction_formula" rel="nofollow">LSZ reduction formula</a> that connects S matrix elements to time ordered field correlation functions. It seems essential, and really helps clear up what you are calculating. Yet some earlier texts and even some modern texts (e.g. <a href="http://www.google.com/search?hl=en&as_q=student+friendly+quantum+field+theory" rel="nofollow">"Student Friendly Quantum Field Theory"</a> by R. Klauber) seem to skip right past this, working everything out in the "interaction" picture. It seems there must be something going wrong with this latter procedure, but I am not quite able to put it together. </p>
| 3,922 |
<p>Vaporization is an interesting engineering subject, but unfortunately much about it has always been unclear to me.</p>
<p>Recent research of mine has brought my mind to link <i>vapor pressure</i> to <i>boiling</i> and <i>partial pressure</i> to <i>evaporating</i>. So I would just like to confirm the following two understandings of mine:</p>
<ol>
<li><b>VAPOR PRESSURE</b> is the pressure needed to "mechanically" keep a liquid from <b>BOILING</b>. The composition of the air exerting the pressure doesn't matter.</li>
<li>When an evaporating substance's <b>PARTIAL PRESSURE</b> equals its <b>VAPOR PRESSURE</b>, "statistically" it stops <b>EVAPORATING</b>.</li>
</ol>
<p>Thank you.</p>
| 3,923 |
<p>It is more or less known that a given antisymmetric tensor $F$ in two indices can be written in terms of spinorial indices, splitting into self-dual and anti-self-dual parts
$$ F_{\mu\nu} =
F_{\alpha\beta}
(\sigma_\mu)^{\alpha\dot\alpha}(\sigma_\nu)^{\beta\dot\beta}
\varepsilon_{\dot\alpha\dot\beta} +
F_{\dot\alpha\dot\beta}
(\sigma_\mu)^{\alpha\dot\alpha}(\sigma_\nu)^{\beta\dot\beta}
\varepsilon_{\alpha\beta} .$$</p>
<p>My question is the following:
start from <a href="http://arxiv.org/abs/hep-th/9307158" rel="nofollow">(equations 5.3 and 5.4)</a>
$$ W_{\mu\nu}^{ij} = T_{\mu\nu}^{ij} -
R_{\mu\nu\lambda\rho}\theta^i\sigma_{\lambda\rho}\theta^j + \cdots $$
which is self-dual in Lorentz indices $\mu\nu$ and antisymmetric
in $\mathrm{SU}(2)$ indices $ij$.
Then it is squared to
$$W^2= \varepsilon_{ij}\varepsilon_{kl} W_{\mu\nu}^{ij}W_{\mu\nu}^{kl}.$$
How do I see (possibly using the first equation above) that this is the same as a tensor <a href="http://arxiv.org/abs/hep-th/9912123" rel="nofollow">(formula 4.1 and below)</a>
$W_{\alpha\beta}$ with self-dual $T$ as top component, where $\alpha$, $\beta$ denote symmetric spinor indices and
$$W^2=W_{\alpha\beta}W_{\alpha'\beta'}
\varepsilon^{\alpha\alpha'}\varepsilon^{\beta\beta'} ?$$</p>
| 3,924 |
<p>I come from a maths background and am struggling with some of the more physical texts on SUSY. In particular they claim that the fermionic generators $Q_A^i$ <strong>carry</strong> a representation of the Lorentz group. What does this mean? I have never heard the word 'carry' applied to representations in a mathematical framework. </p>
<p>I would appreciate it if someone could </p>
<ol>
<li>give me a general mathematical definition of this term</li>
<li>explain specifically why it is used in this context (see edit below)</li>
</ol>
<p><strong>Edit</strong>: most books I have read note that $$[Q_A, J_{ab}]= (b_{ab})_A^BQ_B$$ and use the super-Jacobi identity to conclude that the structure constant matrices $b_{ab}$ form a representation for the Lorentz algebra. </p>
<p>They <strong>use this</strong> to immediately conclude that $Q_A$ "carry a representation" of the Lorentz group. What is the logic here?</p>
| 3,925 |
<p>We know from conservation of momentum or energy that energy (lets think about one quantity at a time) is conserved before and after collision. But how the energy is distributed between the bodies? I mean $1+3=4$ otherwise we can say $2+2=4$. Which distribution would be preferable?</p>
| 3,926 |
<p>I recently got a more complete proof of photons having no mass. (I knew it before, but now I <em>really</em> know it.) But now, I'm curious how gravitational lensing can occur without a mass to act on.</p>
<p>I have heard that space is like a sheet and gravity works because the more massive an object is, the more it bends space. I heard that when I was five years old. When I got older I questioned how that would work, seeing as space is 3-dimensional. The answer I eventually cobbled together from a plethora of excellent resources was this: </p>
<blockquote>
<p>Gravity is like a point light source. At the center, you have the most intense light. As you move outward the intensity decreases with the square of the distance. Like light, gravity radiates in all directions simultaneously.</p>
</blockquote>
<p>This works well for me, and I still believe it to be accurate. However, when I was thinking about photons, I realized that you cannot apply a force to an object without mass. At least, you can't by standard Newtonian thinking. This is because $F=ma$. With no mass, you can have no force. Alternately, you could rearrange to $\frac{F}{m}=a$. With no mass, and no force, you can have no acceleration.</p>
<p><strong><em>Yet gravity is able to refract light.</em></strong> </p>
<p>How is this possible? Like $E=mc^2$, does this only apply to a specific set of conditions?</p>
| 3,927 |
<p><em>I've studied the AC circuit for an ideal inductor in many physics books. After deriving the final equation for current the integration constant $C$ is assumed to be $0$ by giving inadequate reasons. In this question I seek for an adequate reasons.</em> </p>
<p>Suppose an ideal AC voltage source is connected across a pure inductor as shown: </p>
<p><img src="http://i.imgur.com/aevwKxN.jpg" alt="i"></p>
<p>The voltage source is$$V=V_0\sin(\omega t).$$ From Kirchhoff’s loop rule, a pure inductor obeys
$$V_0 \sin(\omega t)=L\frac{di}{dt},$$ so
$$\frac{di}{dt}=\frac{V_0}{L} \sin(\omega t)$$
whose solution is
$$i=\frac{-V_0}{\omega L}\cos(\omega t)+C$$</p>
<p>Consider the (hypothetical) case where the voltage source has zero resistance and zero impedance.</p>
<blockquote>
<p>In most of elementary physics books $C$ is taken to be $0$ for the case of an ideal inductor. </p>
</blockquote>
<p>$$\text{Can we assume that } C \neq 0?$$</p>
<blockquote>
<ol>
<li><p>(To me this is one of the inadequate reasons). This integration constant has dimensions of current and is independent of time. Since source has an emf which oscillates symmetrically about zero, the current it sustain also oscillates symmetrically about zero, so there is no time independent component of current that exists. Thus constant $C=0$.</p></li>
<li><p>(Boundary condition) there might exist a finite DC current through a loop of wire having $0$ resistance without any Electric field. Hence a DC current is assumed to flow through the closed circuit having ideal Voltage source and ideal inductor in series if the voltage source is acting like a short circuit like a AC generator which is not rotating to produce any voltage. When the generator starts, it causes the current through the circuit to oscillate around $C$ in accordance with the above written equations. </p></li>
</ol>
</blockquote>
| 3,928 |
<p>I am trying to initialize a <strong>traveling</strong> wave for a 1d simulation as one can see from the attached figure.
<img src="http://i.stack.imgur.com/J0iOi.png" alt="enter image description here"></p>
<p>Such that it will be <strong>traveling to the right</strong>.
However, I cannot initialize the right velocity profile, and this makes the initial pressure distribution tends to be more uniform to reach the same pressure of the surrounding fluid !</p>
<p>Can any one provide some support?</p>
| 3,929 |
<p>By biot-savart:</p>
<p>$$\bar{H} = \frac{I}{4\pi} \oint \frac{d\bar{l} \times \bar{r}}{r^{3}}$$</p>
<p>so</p>
<p>$$\bar{H} = \frac{I}{2a} \hat{n}$$</p>
<p>Please, explain the last implication. I cannot find such integral to match the results. The radius of the loop is $a$. The current is $I$. $d\bar{l}$ is a vector along the perimeter.</p>
| 3,930 |
<p>I'm trying to find out if black holes could be created by focusing enough light into a small enough volume.</p>
<p>So far I have found (any or all may be incorrect):</p>
<ul>
<li>Maxwell's equations are linear, dictating no interaction of radiation.</li>
<li>The Kerr effect and self-focusing has been observed in mediums, but not vacuums.</li>
<li>Masses bending light have been observed per general relativity.</li>
<li>Photons are said to have no rest mass, just energy and momentum (???).</li>
<li>General relativity seems to provide for energy to energy interaction.</li>
</ul>
<p>This leads to a more specific question:</p>
<p>Does radiation or energy curve space like mass curves space?</p>
| 3,931 |
<p>I am trying to come up with everyday size objects comparisions of atomic scales items, e.g. if a proton probability cloud was of size basketball how far would the next atoms to it be?</p>
<p>reason being is to give an idea of the space in between the atoms and giving student some idea of relative atomic object sizes.</p>
<p>Looking for examples of how does dnsity of materials can be reflected in this comparsion scheme, for example comapring a dense material to a relatively far less dense material and much closer the basketball sized atomic cloulds would relatively be closer to each other.</p>
<p>PS : No models of everyday objects as analogy to atomic structure will be used, only relative distances of the structures is the main objective.</p>
| 3,932 |
<p>I am wondering if, for a particle moving close to the speed of light (so that we must examine things relativistically rather than classically) does the centripetal force equation $F_c=m\frac{v^2}{r}$ still hold? If not, what is the correct equation for centripetal force?</p>
| 119 |
<p>If I take two plane EM waves travelling in opposite direction e.g. $E = E_0 \sin(kx-\omega t)$ and $E=E_o \sin (kx + \omega t)$, they sum to give a standing wave with a time-averaged Poynting vector of zero.</p>
<p>If I use the appropriate special relativistic transformations to derive how these fields appear to an observer travelling at $v$ along the x-axis, I find that one E-field is diminished, one is boosted, whilst at the same time one wave is blue-shifted and the other red-shifted. These waves do not sum to give a standing wave in the moving frame of reference and have a non-zero time-averaged Poynting vector.</p>
<p>So, is the phenomenon of a standing wave dependent on the frame of reference of the observer?</p>
| 3,933 |
<p>Do Dyson's <a href="http://en.wikipedia.org/wiki/Bladeless_fan" rel="nofollow">bladeless fans</a> produce enough air pressure to cool say an air conditioning unit and do they produce a vortex pressure like a bladed fan?</p>
| 3,934 |
<p>I have a finite state ensemble with an energy functional (you can think of it as an ferromagnetic Ising model if you like), and I need very careful estimates of the partition function. What methods are available to me to get reasonable estimates (in reasonable temperature regimes) of $Z(\beta)$?</p>
| 3,935 |
<p>If you drop a proton and a neutron in a gravitational field, they both fall, but the proton has a charge and accelerating charges radiate energy, so that leaves less kinetic energy for the proton and by this reasoning, it should fall more slowly than a charge-free object.</p>
<p>The issue is discussed but not in the terms above in Peierls's "Surprises in Theoretical Physics" in the chapter "radiation in hyperbolic motion", but I didn't understand the chapter well enough (or at all) to apply it to my version of the question. Peirls also refers to Pauli's Relativity book (section 32 gamma) but while Pauli claims there is no radiation from uniform hyperbolic motion, he does say there is radiation when two uniform rectilinear motions are connected by a portion of hyperbolic motion. So I take it that would mean a proton at rest which falls for a second and then is somehow forced to maintain its newly acquired downward velocity from the fall without speeding up any further would have radiated.</p>
| 3,936 |
<p>I'll be teaching a seminar for first-year undergraduates next year. The idea of my university's first-year seminar program is to expose students to exciting ideas and important texts in a somewhat interdisciplinary way. My course will focus on three epochs in the history of cosmology in which our ideas about the size of the Universe underwent radical expansions: the Copernican revolution, the early 20th century, and the present / recent past. </p>
<p>I have a lot of ideas for good undergraduate-friendly readings on the first two topics, but not so many for the last one. One idea I want to get at with them is that recent theories suggest that the observable Universe is a small and perhaps not even typical fraction of the entire Universe. I'd even love to get them arguing about the anthropic principle while I'm at it.</p>
<p>So my question is this: Can you suggest good books, articles, etc. for me to consider in the syllabus for this course? Because of the interdisciplinary nature of the course, I'm happy to consider fiction, philosophy, and history as well as straight-up science. (For instance, Borges's story about the Library of Babel has a nice metaphorical connection to some of these ideas.) Just remember that these are kids fresh out of high school -- they're not ready for <em>Phys. Rev. D</em>!</p>
| 3,937 |
<p>At xmas, I had a cup of tea with some debris at the bottom from the leaves. With less than an inch of tea left, I'd shake the cup to get a little vortex going, then stop shaking and watch it spin. At first, the particles were dispersed fairly evenly throughout the liquid, but as time went on (and the vortex slowed, although I don't know if it's relevant) the particles would collect in the middle, until, by the time the liquid appeared to almost no longer be turning, all the little bits were collected in this nice neat pile in the center.</p>
<p>What's the physical explanation of the accumulation of particles in the middle?</p>
<p>My guess is that it's something to do with a larger radius costing the particles more work through friction...</p>
| 196 |
<p>Flux, as I understand it, is the amount of substance passing through a particular surface over some time. So, from a simple perspective, considering photons that go through some virtual surface $A$ (or $S$, doesn't matter). They have a fixed speed in vacuum, $v=299,792,458$ $\text m/\text s$. To simplify even further, they're all hitting the surface head-on. So, if we wanted to figure out how many photons go through the surface, we conclude that at a constant velocity they will only pass through the surface if they are in the volume bounded by sweeping the surface area along the velocity vector (perpendicular to the surface, the opposite of its normal) a distance $d$ in the alloted time $t$: $d = vt$</p>
<p>So the flux volume is well-defined as $V(t) = Avt$. We could just look for a period of unit time and "drop" the dependency on time. But even then, it's useless if we cannot sample photon volume density $\rho_p$ to determine how many photons occupy a unit volume in order to determine the actual flux. That makes sense:</p>
<p>$$\Phi = \rho_pV(t)$$</p>
<p>And now comes along the electric flux and thwarts my understanding of the whole notion completely. An electric field is generated when a charge is dropped somewhere in space. Any other charge, especially idealized point charges, placed in its vicinity would experience a force exerted on them by the source charge, its magnitude modulated by the amount of charge. So, the electric field maps points in space with force vectors (ie. a vector field) whose direction and magnitude is parametrized by the interaction between the source charge and the point charge.</p>
<p>And this electric flux is defined as $\Phi = E \cdot S$ (I'll use $\Phi = E \cdot A$) and I just cannot interpret the semantics of this dot product, the product's dimensionality is not what I've come to expect from the notion of flux ($\text{Vm}^{-1}$ or any other). <strong>How does this in any way show how much electric field flow goes through a surface? Furthermore, what is this vague thing called electric field flow? It seems like it is completely disconnected.</strong></p>
<p>I've tried expressing it in different ways from the derivation of the expression of an electric field, which makes sense (non-vector form, dropped unit vector):</p>
<p>$$E = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}$$</p>
<p>I've intentionally separated the inverse square of the distance and the $4\pi$ which is, I presume, a part of the normalization factor (steradians of sphere) -- but I noticed that together they forge the area of a sphere $A_r = 4\pi r^2$. This way, I could see the expression as the uniform charge density distribution on the surface of a sphere, scaled by the vacuum permittivity.</p>
<p>$$E = \frac{Q}{A_s\varepsilon_0}$$</p>
<p>And then, due to presumed uniformity, by multiplying by an arbitrary area, I could get the flux, the amount of charge(?) flowing through a particular surface in unit time(?):</p>
<p>$$\Phi = E \cdot A = \frac{Q}{A_s\varepsilon_0} A $$</p>
<p>I could see that as flux, but I'm really not sure can I really reinterpret parts of the normalization factor and the inverse-square of the distance into the area of a sphere. From the perspective of voltage over distance it makes absolutely no sense to me.</p>
<p>Any help would be appreciated.</p>
| 3,938 |
<p>I tried reading the Wikipedia article to no avail - I simply cannot understand the <a href="http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation" rel="nofollow">Schrödinger Equation</a> (what does each of the variables mean, especially the wave function), and the Schrödinger Model of the Atom. Could someone explain in simple words how this entire thing works and its consequences/conclusions in Physics?</p>
<p><img src="http://i.stack.imgur.com/wykwd.png" alt="enter image description here"></p>
| 3,939 |
<p>If a servant lifts 10 cubic meter of liquid from a tank, which is at a depth of 40m . If the work done by him is 1600J, then find the density of the liquid (g = 10 m/s^2)</p>
| 3,940 |
<p>Firstly apologies if this is not the correct place to post this but wasn't sure which site would be good to ask regarding about measurement uncertainty calculation.</p>
<p>I am trying to calculate the combined measurement uncertainty, however the uncertainties I want to combine are using different scales:</p>
<p>Carrier level uncertainty: ±0.5dB (logarithmic)</p>
<p>Modulation uncertainty: ±5% (linear)</p>
<p>Converting either from one format to another will not give me a simple ±value in the other format</p>
<p>What is the best way to combine these uncertainties?</p>
| 3,941 |
<p>In an interacting theory I expect there to be caustics, resonances, and other situations in which <em>some</em> observables would give an infinite experimental result. Of course, these are idealized states and observables -- if a real device's measurement results are quite accurately modeled by such an observable, and we created a state in which its expected value is large enough, the device would be destroyed.</p>
<p>An idealized world in which models never predict infinite results seems somehow different from the world we live in. Even though experiments never return the measurement result "infinity", they do return the measurement result "I'm so sorry, I'm breaking now, it's bigger than you thought it could be". The Wightman axioms do not require operators to be bounded, and to me seem much better for it. QFT as it's used in practice isn't constructed within the Wightman axioms, but it's much less constructed within the Haag-Kastler axioms, and, it seems to me, particularly for this reason.</p>
<p>I take boundedness to mean that all the eigenvalues of an operator in its action on a Hilbert space of idealized Physical states are required to be finite. This is much stronger than requiring the expected values of an operator to be finite for a dense subset of the Hilbert space (or other, relatively weaker, requirements).
It's certainly mathematically more convenient to use bounded operators (because we don't have to keep track of for which states we get a finite result for a given measurement, because they all do), but is that enough? At least, is this acceptable as part of a major attempt to axiomatize theoretical Physics? Is it obvious enough to be an axiom?</p>
<p>I'm prompted to ask this question in this way by a comment in Doplicher's "The principle of locality: Effectiveness, fate, and challenges" <a href="http://jmp.aip.org/resource/1/jmapaq/v51/i1/p015218_s1" rel="nofollow">J.Math.Phys. 51, 015218 (2010)</a>, <a href="http://arxiv.org/abs/0911.5136" rel="nofollow">http://arxiv.org/abs/0911.5136</a>, which I'm reading this morning, where he sets out on the first page (2nd page in the arXiv) that "In quantum mechanics the observables are given as bounded operators on a fixed Hilbert space", which seems a specially sanitized version of QM, insofar as it rules out position, momentum, and energy observables.</p>
<p>Finally, this question is asking, as always, have I got something (very) wrong?</p>
| 3,942 |
<p>Has it been observed that charged high capacitance capacitors do generate a strong positive electrostatic charge on their exterior insulating surfaces?</p>
<p>Has it been observed that charged high capacitance capacitors attract exterior negative electrostatic charges to their exterior insulated surfaces?</p>
| 3,943 |
<p>Title pretty much states the question. How much hotter do air conditioning units make it outside in a large city like NYC, Chicago, etc?</p>
| 3,944 |
<p><strong>What is the conversion factor for qubits (qudits) to bits/bytes in classical information theory/computation theory?</strong></p>
<p>I mean, how can we know how many "bits/bytes" process, e.g., a 60 qubit quantum computer (quamputer), are equivalent to classical bits (dits)?What about memories and velocities in "attaniable" quantum computers versus classical current memories and computer velocities(GHz)?</p>
| 3,945 |
<p>According to <a href="http://en.wikipedia.org/wiki/Noether%27s_theorem" rel="nofollow">Noether's theorem</a>, <em>Every continuous symmetry of the action leads to a conservation law.</em> For example, conservation of linear momentum corresponds to translational symmetry, conservation of angular momentum corresponds to rotational symmetry.</p>
<p>My question is on the conservation of baryon number, lepton number and strangeness. What type of symmetry does imply when the above mentioned quantities are conserved in a system?</p>
| 3,946 |
<p>Consider two parallel wires of finite radius. When a current is applied to one of the wire for a short period of time, what is the current induced in the other wire?</p>
<p>Applying Maxwell's equations, it seems that there is a change in magnetic field perpendicular to the second wire, and as a result, the induced current has a nontrivial distribution which averages somewhat to zero. Is this correct? Intuitively, I had instead expected a simpler result similar to the case of two coils of wires placed side by side.</p>
| 3,947 |
<p>In Morse & Feshbach (P512 - 514) they show how 10 different orthogonal coordinate systems (mentioned on <a href="http://mathworld.wolfram.com/HelmholtzDifferentialEquation.html" rel="nofollow">this page</a>) are derivable from the confocal ellipsoidal coordinate system $(\eta,\mu,\nu)$ by trivial little substitutions, derivable in the sense that we can get explicit expressions for our Cartesian $x$, $y$ & $z$ in terms of the coordinates of some coordinate system by simply modifying the expressions for $x$, $y$ & $z$ which are expressed in terms of ellipsoidal coordinates. Thus given that</p>
<p>$$x = \sqrt{\frac{(\eta^2 - a^2)(\mu^2 - a^2)(\nu^2 - a^2)}{a^2(a^2-b^2)}}, y = ..., z = ...$$</p>
<p>in ellipsoidal coordinates, we can derive, for instance, the Cartesian coordinate system by setting $ \eta ^2 = \eta' ^2 + a^2 $, $\mu^2 = \mu'^2 + b^2$, $\nu = \nu'$, $b = a\sin(\theta)$ & letting $a \rightarrow \infty$ to get that $x = \eta'$, $y = \mu'$ & $z = \nu'$. Substitutions like these are given to derive a ton of other useful coordinate systems.</p>
<p>I don't see why one shouldn't be able to use the exact same substitutions on the scale factors. Thus given</p>
<p>$$h_1 = \sqrt{\frac{(\eta^2 - \mu^2)(\eta^2 - \nu^2)}{(\eta^2 - a^2)(\eta^2 - b^2)}}$$</p>
<p>I don't see any reason why the exact same substitutions should not give the Cartesian scale factors, namely that $h_1 = 1$ in this case, yet I can't do it with the algebra - I can't get it to work. You get these $a^4$ factors which you just cannot get rid of, thus it seems like one can't derive the scale factors also by mere substitution... Now it might just be late & that I've worked too much, hence my question is: </p>
<p><strong>Is it possible to get the scale factors for orthogonal curvilinear coordinate systems by simple substitutions into the scale factor formulae for the ellipsoidal coordinate system, analogous to the way one can derive the formulae for Cartesian components in terms any 'standard' orthogonal coordinate system by substitutions into the formulae for them expressed in terms of ellipsoidal coordinates? If not, why not?</strong> </p>
<p>If there is then the gradient, divergence, Laplacian & curl become extremely easy to calculate in the standard orthogonal coordinate systems, & working separation of variables for all the standard pde's becomes immensely easier, if not I'd have to derive the scale factors by differentiation of completely crazy formulas (at least there's an easy way to remember any formula in $\vec{r}(u^1,u^2,u^3) = ...$ from which we can derive the scale factors thanks to Morse & Feshbach!!!)</p>
<p>Thanks for any help possible.</p>
| 3,948 |
<p>Why it's not explained just by Doppler redshift caused by faster movement of those galaxies billions of years ago when that light was emitted? </p>
<p>Would the speeds of the galaxies necessary for Doppler redshift to explain all of the observed galaxies redshift be unreasonable or is there something else that prevents such explanation to be sufficient?</p>
| 3,949 |
<p>This is a problem concerning covariant formulation of electromagnetism.</p>
<p>Given
$$\partial^{[\alpha} F^{\beta\gamma]}= 0 $$</p>
<p>how does one prove that $F$ can be obtained from a 4-potential $A$ such that</p>
<p>$$F^{\alpha \beta}=\partial^{\alpha} A^{\beta} - \partial^{\beta} A^{\alpha} $$</p>
| 3,950 |
<p>I am sure this is a silly question, but I was reading something that described the pre big-bang universe as having "nearly infinite mass."</p>
<p>How can something be "nearly" infinite? The term seems to make no sense. </p>
| 3,951 |
<p><a href="http://www.ted.com/speakers/brian_greene.html" rel="nofollow">Brian Greene</a> in this <a href="http://www.ted.com/talks/brian_greene_why_is_our_universe_fine_tuned_for_life.html" rel="nofollow">TED talk about possible multiverse</a>, claims tomwards the end (At around 18:00 mark) this statement. 'Because the expansion is speeding up, in the very far future, those galaxies will rush away so fast, we wont be able to see them, not because of technological limitations, but because of the law of physics.'</p>
<p>This seems to me against the basic premise of relativity, namely that two objects are moving so fast away from each other that their relative speed is greater than that of light. Can anybody explain whether he really meant what I understood, and if not what he really meant.</p>
| 3,952 |
<p>I have recently entered university — studying CS — and I have spoken to many physics students on campus. Most of these — when propmted — will gladly proclaim that QM is counterintuitive, and not something you are supposed to understand.</p>
<p>To my knowledge, no one proclaims similar things about, e.g. Relativity, that is just difficult mathematics; but we have the rubber sheet analogy and all that.</p>
<p>Do any professionals share this opinion? Are we purposefully imparting it on the students? Where does this meme originate, historically?</p>
| 3,953 |
<p>How would one show that the nonabelian ${F_{\mu\nu}}$ field strength tensor transforms as ${F_{\mu\nu}\to F_{\mu\nu}^{\prime}=UF_{\mu\nu}U^{-1}}$ under a local gauge transformation? Rather than going through this in a very manual manner (i.e., gauge transform ${A_{\mu}\to A_{nu}^{\prime}}$ and use the explicit expression for ${F_{\mu\nu}}$), it was suggested to me to show first that ${D_{\mu}\to D_{\mu}^{\prime}=UD_{\mu}U^{-1}}$ and then gauge transform the commutator relation ${\left[D_{\mu},D_{\nu}\right]}$ for ${F_{\mu\nu}}$: ${\left[D_{\mu},D_{\nu}\right]\psi\left(x\right)-gF_{\mu\nu}\psi\left(x\right)}$.</p>
| 3,954 |
<p>I am trying to understand the some of the properties of wakefields, namely the energy change. So, as a preface I am interested in primarily the wakefield due to electron beams as they progress through a curved section (the eletcrons radiate strongly when they are in circular motion). There are two main/simple regimes:</p>
<ol>
<li>When the wakefield is constant and not dependent on how far Δθ the electrons have traversed, we have a wakefield like so:</li>
</ol>
<p>$$\frac{dE}{sds}(z) $$</p>
<p>Which to my understanding (which I am very certain of) describes the $$\frac{dE}{ds}$$ (the change in energy per distance traveled along its curved trajectory) for a given z (position along the eletcron beam, where zero is defined as the certer of the eletcron beam which we can consider to be gaussian-ly distributed).</p>
<p>2 When the wakefield is not constant and is dependent on how far Δθ the eletcrons have traversed, we have the wakefield like so:</p>
<p>$$\frac{dE}{ds}(z,θ) $$</p>
<p>Where this describes the $$\frac{dE}{ds}$$ (the change in energy per distance traveled along the curved trajectory) for a given z (position along the eletcron beam) and θ (the amount the eletcrons have traversed). Now, the main difference between 1 and 2 is the fact that for two $$\frac{dE}{ds}$$ is changing wrt θ (is some function of theta).</p>
<p>If you were to integrate regime 1, wrt ds from 0 to L (the total path length), then you would get the total energy change through the curved region as a function of z: $$ Etotal(z,θ) $$.</p>
<p>Now this is where I start getting confused: If we turn our attention to regime two with θ dependence.</p>
<p>WHat do we have when:</p>
<ol>
<li><p>We integrate $$\frac{dE}{ds}(z,θ) $$ wrt to θ from 0 to θ (thet total travesrved angle of teh eletcron beam)? We would have something like $$\frac{dE}{ds}(z) $$ which is still a function of ds (the path travesersed).</p></li>
<li><p>We integrate $$\frac{dE}{ds}(z,θ) $$ wrt to the path ds? We would now have something like $$Etotal(z,θ) $$ which is still a function of θ.</p></li>
</ol>
<p>Any help on conceptually understanding this would be greatly appreciated! I have been at it for days!</p>
| 3,955 |
<p>If a body travelling at speed falls to the ground through an arc from a certain height (someone walking who trips, for example), how does friction of the ground surface affect the forces impacting upon the body (treating it as a point mass) when it reaches the ground? How can the net forces on the body and the net vertical impact velocity be calculated?</p>
| 3,956 |
<p>For a system of two interacting particles <code>1</code>, <code>2</code> we get from the conservation of momentum
$$ \dot{\bf{p_1}} + \dot{\bf{p_2}} = 0$$
and from conservation of angular momentum
$$ \bf{r_1} \times \dot{\bf{p_1}} + \bf{r_2} \times \dot{\bf{p_2}} = 0$$
so
$$ \bf{F_1} = -\bf{F_2} $$
and
$$ \bf{r_{12}} \times \bf{F_1} = 0 $$
where $ \bf{r_{12}} = \bf{r_1} - \bf{r_2} $ is the separation between particles. So basically only central forces $\bf{F}=\bf{F}\left(|\bf{r_{12}}|\right)$ are allowed.</p>
<p>But for a system of three and more interacting particles we don't have such restrictions. E.g. for 3 particles
$$ \bf{F_3} = -\bf{F_1}-\bf{F_2}$$
and
$$ \bf{r_{13}} \times \bf{F_1} + \bf{r_{23}} \times \bf{F_2} = 0 $$
(two more likewise expressions for <code>(21,31)</code> and <code>(12,32)</code>). And this is, I believe, as far as one can get in general case.</p>
<p>We can expand
$$ \bf{F_1} = \bf{F_{1,2}} + \bf{F_{1,3}} + \bf{R_1} $$
where $\bf{F_{1,2}}$ and $\bf{F_{1,3}}$ are for two-body interactions, but no one forbids the existence of 3-body force $\bf{R_1}\left(\bf{r_{12}}, \bf{r_{23}}, \bf{r_{31}}\right)$.</p>
<p>Are there any known examples or I am missing something?</p>
| 3,957 |
<p><strong>What I'm looking for:</strong></p>
<p>Let $\vec{W}$ be the vector of conserved variables for a 1-dimensional, adiabatic, (special) relativistic, electrically neutral fluid. (Yes, something that simple!) I'm looking for a paper that derives the form of the matrix $A$ that linearizes the evolution equation. That is,
$$ \partial_t \vec{W} \approx A \partial_x \vec{W}. $$
Alternatively, the matrix $B$ that does the same for the conserved variables will work:
$$ \partial_t \vec{U} \approx B \partial_x \vec{U}. $$</p>
<p>These matrices are useful in fluid computations for several reasons. I need more than just the eigenvalues (used in certain solvers) - I also need the eigenfunctions. I've found plenty of papers that treat the nonrelativistic case (for one of many, many examples, see the appendices of <a href="http://dx.doi.org/10.1086/588755" rel="nofollow">Stone et al. 2008, ApJS 178 137</a>) both with and without magnetism. I've found some papers that just quote a few eigenfunctions for relativistic MHD, but these are often the ones that are interesting only with magnetism in play.</p>
<p>I'm looking for whatever paper derives these matrices in the rather simple case I'm dealing with. An answer that gives the derivation would be nice, but I'm also trying to locate the relevant literature. In particular, I would like a paper addresses the physical reliability/usefulness of the linear approximation.</p>
<p><strong>Background:</strong></p>
<p>There are three primitive variables defining my fluid: rest-mass density $\rho$, velocity $v$, and pressure $p$. By convention, these variables are combined into a vector $\vec{W} = (\rho, v, p)^\mathrm{T}$.</p>
<p>Many approaches to evolving fluids deal with the equations in flux-conservative form. Here, the conserved variables are
\begin{align}
D & = \gamma\rho && \text{(lab-frame density),} \\
M & = Dh\gamma v && \text{(relativistic momentum),} \\
E & = Dh\gamma - p && \text{(relativistic energy).}
\end{align}
Here I define
\begin{align}
\gamma & = \frac{1}{\sqrt{1-v^2}} && \text{(standard Lorentz factor),} \\
h & = 1 + \frac{\Gamma}{\Gamma-1} \left(\frac{p}{\rho}\right) && \text{(enthalpy),}
\end{align}
where the ratio of specific heats $\Gamma$ is assumed to be constant. These are often combined as $\vec{U} = (D, M, E)^\mathrm{T}$.</p>
<p>Along with the vector of conserved quantities, we can define the vector of fluxes
$$ \vec{F} =
\begin{pmatrix}
Dv \\ Mv + p \\ M
\end{pmatrix}. $$
Then we have the relation
$$ \partial_t \vec{U} + \partial_x \vec{F} = 0, $$
which is used as the basis for most Riemann solvers and many fluid codes in general.</p>
| 3,958 |
<p>I was asked to think of a situation where a car driver only feels centripetal acceleration, but exerts no tangential acceleration.</p>
<p>The first thing that came to mind was orbit, where the satellite does not need to speed up but be caught by the gravity of Earth, and keeps orbiting around it.</p>
<p>So, my question is this.</p>
<p>I tried to consider a case where a car is driving towards a loop with no friction so that it will not need any tangential acceleration, but the centripetal acceleration is not constant due to gravity.</p>
<p>One of my friends told me that a banked road can do the same thing as orbit, but I did not understand his explanation at all. I cannot imagine a car moving in circles on a banked road without accelerating tangentially.</p>
<p>Can someone explain me this kinematics ?</p>
| 3,959 |
<p>I'm a tutor. This is a high school level problem. In high school, every one have might have solved a problem of <a href="http://www.crbond.com/papers/ent2-3.pdf">effective resistance of a ladder of resistors having infinite steps.</a> Now the problem is little different. what if it has <code>n</code> steps instead of infinite steps. How to calculate effective resistance in that case?<img src="http://i.stack.imgur.com/n1eIX.jpg" alt="enter image description here"></p>
| 3,960 |
<p>I have a test in a few hours, and my professor gave us a practice test, and I'm stuck. Could you give me a hint as to how to approach this problem, equations I could use.
It's an algebra based class so I'd avoid using calculus equations. Thank you.</p>
<p><em>Three thin infinite wires carrying currents I in the same direction go
perpendicularly to the paper sheet that they intersect at the points forming an
equilateral triangle of side L. Calculate the force acting on each wire per unit
length. What is the direction of the forces?</em></p>
| 3,961 |
<p>When does the total time derivative of the Hamiltonian equal the partial time derivative of the Hamiltonian? In symbols, when does $\frac{dH}{dt} = \frac{\partial H}{\partial t}$ hold?</p>
<p>In Thornton & Marion, there is an identity in one of the problems, for any function $g$ of the generalized momentum and generalized coordinates, the following is true:
$$ \frac{dg}{dt} = [g,H] + \frac{\partial g}{\partial t},$$
where H is the Hamiltonian.
It seems to me that if we let $g = H$, then, since the Hamiltonian clearly commutes with itself, then $\frac{dH}{dt} = \frac{\partial H}{\partial t}$ is always true. Is this the correct way to look at it?</p>
| 3,962 |
<p>The eigenfunctions of Laplace-Beltrami operator are often used as the basis of functions defined on some manifolds. It seems that there is some kind of connection between eigen analysis of Laplace-Beltrami operator and the natural vibration analysis of objects. I wonder, is my intuition true? What is the physical meaning of Laplace-Beltrami eigenfunctions?</p>
<p>For now, I only know that the eigenfunctions of the Laplace-Beltrami operator are real and orthogonal, thus they could be used as the basis of functions on the manifold where the functions are defined.</p>
| 3,963 |
<p><a href="http://en.wikipedia.org/wiki/Liquid_metal" rel="nofollow">http://en.wikipedia.org/wiki/Liquid_metal</a> describes some alloys which are liquid at room temperature containing gallium, and sodium-potassium. We are advised not to handle them, and mercury, with unprotected skin. Are there any which are safe (as safe as, say, alcohol or glycerine)?</p>
| 3,964 |
<p>When I was using ultrasonic horn in a beaker, I notice that there are convection currents in the beaker and stir up my substance. I don't understand why it produce water current, I thought that it will just vibrate like the ultrasonic bath. So why does ultrasonic horn create water currents? Thank you.</p>
| 3,965 |
<p>Can anyone explain in a simple manner why interacting noncommutative quantum field theories with space-time noncommutativity of the Moyal bracket sort are unitary?</p>
<p>Thanks.</p>
| 3,966 |
<p>I have been studying differential equations in RLC circuits: <strong><em>(a generator with fixed EMF $=E$,a capacitor $C$, an inductor with inductance $L$ and internal resistance $r$, and a separate resistor $R$)</em></strong>
with the elementary cases accounting for $q$ (the charge on the capacitor), $V_c$ its voltage or$i$ the current flowing through the circuit (such as $\ddot q+\frac{R+r}{L}\dot q+\frac{q}{LC}=E$). I've been trying to find such a differential equation for the compound voltage $V_{L,r}=V_L +V_r=ri+L\frac{di}{dt}$, which didn't seem to satisfy the criteria for a "regular ODE": $\fbox{$\ddot V_{L,r}+\frac{R}{L}\dot V_{L,r}+\alpha V_{L,r}=\frac{\alpha r}{L}e^{-rt/L}\int e^{rt/L} \ V_{L,r} \ dt$}$ with $\alpha=\frac{-Rr}{L^2}+\frac{1}{LC}$
I started with trying to express $i$ through $V_{L,r}$ as all relevant voltages are expressed in $i$ (resistor), $q$ (capacitor) and $\frac{di}{dt}$ ($V_{L,r}$). At first through this relation by applying regular ODE properties: $V_{L,r}=ri+L\frac{di}{dt} \rightarrow \fbox{$i=\frac{1}{L}e^{-rt/L} \int e^{rt/L} \ V_{L,r} \ dt$}$, and then replaced in : $E=V_{L,r}+Ri+\frac{q}{C} \rightarrow 0=\frac{dV_{L,r}}{dt}+R\frac{di}{dt}+\frac{i}{C}$ and obtained the aforementionned DE. Should I be using any other physical relation </p>
| 3,967 |
<p>I would like to abide by the site policies on not asking open-ended/chatty questions so if someone feels there is a better location or wording for this question, please feel free to modify it as appropriate.</p>
<p>I am normally a big fan of open source/open access work and I believe I have learned a great deal from such sources. There is an open-access journal question <a href="http://physics.stackexchange.com/questions/8942/what-are-the-best-open-access-journals-in-physics">here</a>. Nonetheless, there are times where I really do want a specific article that is not available through non-commercial means. I am currently studying to return to school (in other words I don't have access to an institutional subscription) for a physics PhD and reading published work is becoming increasingly important to me. As a result I am considering subscribing to one of the big publishing houses (Elsavier, ScienceDirect, Science, Nature, etc.).</p>
<p>Before I spend that kind of money, I would like to know what other physicists think of these organizations and who offers the best value. If I decided to opt for a subscription, which would be the best? Is a subscription even the best idea, or should I perhaps buy individual articles as needed?</p>
<p>PS - I know the answer to these questions depends on the area of interest, my interests lie in quantum field theories and the like, but feel free to answer for your particular area of expertise.</p>
| 3,968 |
<p>In a cavity of dimension L, the wave must give zero amplitude at the wall, means wave equation has zero amplitude. Why?
Answer from hyperphysics "since a non-zero value would dissipate energy and violate our supposition of equilibrium. To form a standing wave, the reflection path around the cavity must produce a closed path."
1) what is supposition of equilibrium?
2) in 3D, how do we know $$E=E_0sin\frac{n_1\pi x}{L}sin\frac{n_2\pi y}{L}sin\frac{n_3\pi z}{L}sin\frac{2\pi ct}{\lambda}$$
from link
<a href="http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html" rel="nofollow">http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html</a></p>
| 3,969 |
<p>How is it possible to demagnetize a magnet with a laser?</p>
<p>Source: <a href="http://www.helmholtz-berlin.de/pubbin/news_seite?nid=13657&sprache=en&typoid" rel="nofollow">http://www.helmholtz-berlin.de/pubbin/news_seite?nid=13657&sprache=en&typoid</a></p>
<p>And the paper: <a href="http://prb.aps.org/abstract/PRB/v88/i21/e214404" rel="nofollow">http://prb.aps.org/abstract/PRB/v88/i21/e214404</a></p>
<p>How does this work?</p>
| 3,970 |
<p>In the discussion of the amplituhedron paper (<a href="http://arxiv.org/abs/1312.2007" rel="nofollow">arXiv:1312.2007</a>), there is the following discussion in paragraph 14.outlook (page 28):</p>
<blockquote>
<p>Quantum mechanics forces us to divide the world in two pieces - an
infinite measuring apparatus and a finite system being observed. However for any
observations made in a finite region of space-time, gravity makes it impossible to
make the apparatus arbitrarily large, since it also becomes heavier, and collapses the
observation region into a black hole.</p>
</blockquote>
<p>Can one elaborate this point? Is this related to coordinate invariance?</p>
| 3,971 |
<p>My goal is to monitor the change in specific gravity of a liquid over a period of time. My question is: What are the appropriate formula for determining expected apparent weight of an object immersed in a liquid where the liquids specific gravity g/ml is expected to change?</p>
<p>EG. If I were to take an object who's density is 2.6 (average for glass) weighing 100 grams and plunk it into distilled water I believe I should expect an apparent weight should be roughly 61.53 grams. Please let me know if I am just horridly wrong.</p>
<p>So then if that distilled waters density/specific gravity were to change say to 1.010, would my new apparent weight of the object be 61.15 grams?</p>
<p>My math is not solid in this. I'm basically using ratios in order to produce these answers. Please for the sake of simplicity if you are to choose to answer leave out extenuating circumstances such as temperature of the liquid/object and possible compression of the object due to pressure.</p>
<p>If you do chose to add extenuating circumstances I would ask to add those concepts as tertiary answers.</p>
<p>I'm sure that my question is probably very basic, but grasping the concepts has proven perplexing to me. I am probably not using the correct search. Your help in this simple question is greatly appreciated.</p>
| 3,972 |
<p>I have just discovered that if I rotate my left spectacle lens about the vertical axis by 10 degrees in one direction, the vision in that eye becomes much crisper.</p>
<p>Note that the sphere and cylinder prescriptions in the (unrotated) lens were confirmed yesterday by an optometrist as being the best I could get -- but simply by yawing the lens I can see much better.</p>
<p>What is this rotation correcting? Is it physically possible to create a lens with the same correction but without the rotation?</p>
| 120 |
<p>I am trying to understand a line in the quantum mechanics book by Merzbacher, specifically the second line of equation 14.106.</p>
<p>The problem is a forced quantum harmonic oscillator. The Hamiltonian operator in the Schrodinger picture is</p>
<p>$H_S(t) = \hbar \omega_0 (a^{\dagger}a + 1/2) + \hat{x}f_x(t) +\hat{y}f_y(t)$</p>
<p>Here $\hat{x}$ and $\hat{y}$ are the quadratures of motion of the oscillator, ie. dimensionless position and momentum. In other words $a = (1/\sqrt{2})(\hat{x}+i\hat{y})$</p>
<p>If we define $f(t)\equiv -f_x(t)+if_y(y)$ we can rewrite the Hamiltonian as</p>
<p>$H_S(t) = \hbar \omega_0 (a^{\dagger}a + 1/2) + af(t) + a^{\dagger}f^*(t)$</p>
<p>The thing that I don't understand is that Merzbacher goes from the previous equation to</p>
<p>$\bar{H}(t) = \hbar \omega_0 (\bar{a}^{\dagger}(t)\bar{a}(t) + 1/2) + f(t)\bar{a}(t) + f^*(t)\bar{a}^{\dagger}(t)$</p>
<p>where the overbars indicate Heisenberg picture operators. The question is, how does he do this? Since the Schrodinger picture Hamiltonian is time dependent and doesn't commute with itself at different times, the conversion from Schrodinger to Heisenberg pictures isn't simple. Can someone explain how this is done?</p>
<p>My approach is to say that the propogator in the Schrodinger picture is some operator $T(t)$, ie. $T(t)$ propagates the Schrodinger picture state vector forward from time 0 to time $t$. Then I define the Heisenberg picture operators by</p>
<p>$\bar{A}(t) \equiv T^{\dagger}(t)A_S(t)T(t)$</p>
<p>Using $i\hbar \dot{T}(t) = H_S(t)T(t)$ you can show</p>
<p>$i\hbar \frac{d\bar{A}(t)}{dt} = \left[ \bar{A}(t), H_S(t) \right] + T^{\dagger}(t)(\partial A_S(t) / \partial t)T(t)$</p>
<p>Suppose we want to solve for $\bar{a}(t)$. The Schrodinger picture operator $a$ has no time dependence so the equation of motion is</p>
<p>$i\hbar \frac{d\bar{a}(t)}{dt} = \left[ \bar{a}(t), H_S(t) \right]$</p>
<p>If the Schrodinger picture Hamiltonian commuted with itself at different times this would be simple to work with, because <em>in that case</em> $H_S(t)=\bar{H}(t)$. We would then be able to use the fact that</p>
<p>$\left[\bar{a}(t), \bar{a}^{\dagger}(t) \right] = 1$</p>
<p>to evaluate the commutator on the right hand side of the equation of motion. However, in the present problem this is not the case so I don't know how to compute the commutator.</p>
| 3,973 |
<p>does anybody here know an analytical approximation of the bonding hydrogen orbital MOLECULE?</p>
<p>I am looking for a good approximation to this orbital, that might be in some textbooks to get an impression how this whole concept of bonding antibonding works?</p>
| 3,974 |
<p>This <em>should</em> be easy, but I think I have a mind-block... </p>
<p>For $\beta^-$-decay, what is the maximum possible momentum for the electron? The two equations I can use are conservation of energy and conservation of momentum, but I have three unknowns: Momentum of electron, nucleus and anti-neutrino, so what am I missing?</p>
<p>Could I just set the kinetic energy of the nucleus to zero and work from there?</p>
| 3,975 |
<p>Suppose I can solve time-dependent Schrödinger equation for several 1D particles (currently 3). I'd like to see, what an electronic hole is and how it behaves — in a series of numerical experiments.</p>
<p>I know that a hole is lack of electron in a sea of occupied electron states, but I think I don't quite understand, what it really is: do I need to have electron repulsion to see any useful effects? Do I need much more electrons for such a simulation than 3? What initial conditions should I use to <em>see</em> the hole? I'm thinking of using a model "crystal" potential with 3 cells — would this be enough?</p>
<p>As an example of what I'd like to actually see is exciton, namely how its wave packet wanders across the crystal. For an electron in conductivity band, taken as a wavepacket, I'd expect it to look like increase in probability density in the place where the wavepacket is located, and for hole it might be a similar decrease in charge density, so I guess the exciton should look like an increase of charge density in a wave packet and decrease around this wave packet. Is it right? Or is it actually invisible as a charge density?</p>
<p>Another example would be seeing excitonic states in band gap, but for this I don't really understand, what to compare it with — should I use some single-particle approximation to compute band structure without excitonic states, and then after computation of true energy states search for extra states in band gap, or how should I go about finding them?</p>
| 3,976 |
<p>I'm wondering if there are any free particle physics datasets out there, for use in teaching, demonstrations, developing analysis techniques etc.. I'm looking for data events e.g. as ROOT trees or in a similar format, together with a standard set of background events and postprocessing, or maybe even a simple framework with detector simulation to create my own events. I'm not looking for the very "raw" data, but something you could do a simple analysis on, like plot the dilepton mass and see resonances. The kind of experiment doesn't matter that much, as its for illustration purposes (can be e+e-, pp, medium or high energy).</p>
<p>Publishing raw data is common in other areas or fundamental (non-applied) research, especially in government-funded astronomy experiments. Imaging my astonishment when I started in this field that you couldn't just download "the data" from www.cern.ch as a torrent :-). For collaboration-political reasons, and because the data is considered too ununderstandable for laypersons, it is tightly controlled by the experiments. Yet, internally, especially on mature collaborations, you often have "the (processed) dataset", "the standard MC", "the standard corrections and uncertainties", and writing a simple analysis (for demonstration, not for publication) boils down to just writing custom code for event selection, so it should be entirely possible for a physics student or even an interested layperson to make a little sense of the data.</p>
<p>So, I believe that at least one of the now closed experiments (LEP, Tevatron, Hera, ...) might have published their framework and data, but I couldn't find anything on the net. Does anyone know of such a case?</p>
| 3,977 |
<p>I read about <a href="https://en.wikipedia.org/wiki/Vacuum_energy#Implications" rel="nofollow">vacuum energy</a>. It explains the Hawking radiation, the black hole necessary radiation:</p>
<blockquote>
<p>Physical insight into the process may be gained by imagining that
particle-antiparticle radiation is emitted from just beyond the event
horizon.
Vacuum fluctuations are always created as particle–antiparticle pairs.
The creation of these virtual particles near the event horizon of a
black hole has been hypothesized by physicist Stephen Hawking to be a
mechanism for the eventual "evaporation" of black holes.</p>
</blockquote>
<p>Is this "insight" supposed to make us to think that</p>
<ol>
<li><p>the virtual pair created is a part of black hole so that when half flies away then the BH mass is reduced? The article on vacuum energy says that <a href="https://en.wikipedia.org/wiki/Vacuum_energy#Implications" rel="nofollow">the vacuum energy is an underlying background energy that exists in space throughout the entire Universe</a>. So, it is not related to the black holes, though one particle of the couple may create the salute that you may consider as BH evaporation, it actually covers up the fact that the <strong>second particle flies into the BH, increasing its mass</strong>.</p></li>
<li><p>Why do we believe that the receding half of the couple does not fall back to the Black Hole? Yes, it has escaped the horizon but the (pretty strong) BH gravitation is still in action, and it is only <a href="https://en.wikipedia.org/wiki/Force#Units_of_measurement" rel="nofollow">few neutons</a> less than $\infty$ because we are still almost at the horizon initially. This means that to <a href="https://en.wikipedia.org/wiki/Escape_velocity" rel="nofollow">actually escape</a> and not to fall back into BH, the speed of the receding particle must be virtually infinite. I doubt that it is likely that you will have many such virtual particles right at the event horizon. It is much much (<a href="https://en.wikipedia.org/wiki/Almost_surely" rel="nofollow">Almost surely</a>) more likely that <strong>"escaped" half of the couple will also eventually fall onto the black hole, increasing its mass</strong>.</p></li>
</ol>
<p>So, considering the virtual particles of vacuum energy, we find two ways to add mass to the BH. Why do they call it BH (mass) evaporation?</p>
| 3,978 |
<p>In what part of the spectrum is it radiating? In the infrared, in the microwave? Or is not radiating anymore at all? </p>
<p>In russian:</p>
<p>Чему сейчас равна температура поверхности и ядра нейтронной звезды, которая образовалась 12 миллиардов лет назад?
В каком диапазоне она сейчас излучает? В инфракрасном, микроволновом? Или не излучает вообще?</p>
| 3,979 |
<p>Why is electric flux through any closed surface $q/\epsilon_0$? In schools we are only taught of its simplest case, i.e. flux through a sphere with charge centered at origin. And then it is generalised to all closed surfaces. Is there really any proof of flux through all closed surfaces.</p>
| 3,980 |
<p>I have naive question about Einstein action for field-free case:
$$
S = -\frac{1}{16 \pi G}\int \sqrt{-g} d^{4}x g^{\mu \nu}R_{\mu \nu}.
$$
It contains the second derivatives of metric. When we want to get the Einstein equation (which doesn't contain the third derivatives), we must use variational principle. The variation of "problematic" factor $R_{\mu \nu}$ (which contains the second derivatives) is equal to
$$
\delta R_{\mu \nu} = D_{\gamma}(\delta \Gamma^{\gamma}_{\mu \nu}) - D_{\nu}(\delta \Gamma^{\lambda}_{\mu \lambda}).
$$
So the corresponding variation of action may be rewritten in a form
$$
\delta_{R_{\mu \nu}} S = -\frac{1}{16 \pi G}\int d^{4}x \sqrt{-g}\partial_{\lambda}(g^{\mu \nu}\delta \Gamma^{\lambda}_{\mu \nu} - g^{\mu \lambda}\delta \Gamma^{\sigma}_{\mu \sigma}). \qquad (1)
$$
Then one likes to say that it is equal to zero. But why it must be equal to zero? It isn't obvious to me. After using the divergence theorem $(1)$ becomes
$$
\delta_{R_{\mu \nu}} S = -\frac{1}{16 \pi G}\int dS_{\lambda} \sqrt{-g}(g^{\mu \nu}\delta \Gamma^{\lambda}_{\mu \nu} - g^{\mu \lambda}\delta \Gamma^{\sigma}_{\mu \sigma}).
$$
Why it must be equal to zero? It is metric, not physical field, even if Christoffel symbols refer to the gravitational field, so I don't understand why it must be equal to zero at infinity.</p>
| 3,981 |
<p>If classical particles fall through a Galton Board they pile up in the limit of large numbers like a normal distribution, see e.g. <a href="http://mathworld.wolfram.com/GaltonBoard.html">http://mathworld.wolfram.com/GaltonBoard.html</a></p>
<p><img src="http://i.stack.imgur.com/ll7PE.gif" alt="Galton Board"></p>
<p>What kind of distribution would one see, if the particles would obey the laws of quantum mechanics (as a thought experiment) ? Wouldn't interference effects lead to a different distribution than the normal distribution?</p>
| 3,982 |
<p>I have been trying to do all the calculations in the Green, Schwarz and Witten Superstring Theory textbook. </p>
<p>At the end of chapter 3, the author did one-loop calculation for Weyl invariance for the bosonic string, in section 3.4.2 and 3.4.5. In the latter section more fields were included, and not much calculation detail was given.</p>
<p>The actions are</p>
<p>$S_1=\frac{-1}{4\pi\alpha'}\int d^2\sigma\sqrt h h^{\alpha \beta}\partial_\alpha X^\mu \partial_\beta X^\nu g_{\mu \nu}$</p>
<p>$S_2=\frac{-1}{4\pi\alpha'}\int d^2\sigma \epsilon^{\alpha \beta}\partial_\alpha X^\mu \partial_\beta X^\nu B_{\mu \nu}$</p>
<p>$S_3=\frac{1}{4\pi}\int d^2\sigma \sqrt h \Phi (X^\rho) R^{(2)}$</p>
<p>I consider those one-loop calculations to be very good exercise, but as a beginner in string theory I find myself not able to do them. </p>
<p>Therefore may I ask if there are some notes/papers in literature that give explicit calculation or point out key steps? Thank you very much!</p>
| 3,983 |
<p>For example, consider the following measurement: A sensor can measure a specific physical quantity, and has a range of $0$ to $100$. All values above $100$ will be shown as 100. We now take the following measurements: $78$, $100$, $82$, $94$, $100$, and we conclude that the average is $90.8$. However, the true values were $78$, $112$, $92$, $94$, $105$, resulting in the true average of $94.2$. Both end results are in the valid measurement rage, but individual measurements are not.</p>
<p>Can we call it saturation? It has a similar meaning in photography, but in mathematics it seems to have a completely different meaning.</p>
| 3,984 |
<p>When the pressure on the liquid surface is less than the vapor pressure of the liquid at a given temperature, the liquid will start to evaporate. This is common sense. </p>
<p>The problem is more difficult when the liquid and its vapor are heated inside a rigid container, with the specific volume of the mixture less than the critical specific volume:</p>
<p><img src="http://i.stack.imgur.com/ESHNv.png" alt="enter image description here"></p>
<p>According to my professor's notes, the level of the liquid in the container would fall. Why? What is the physics (or the thermodynamics) behind this? If a mixture is heated in a constant volume what happens to it? I know that it will not boil completely because it would attain equilibrium pressure with its vapor soon enough, but how do we fix the state when it would stop boiling? Why is it that if the specific volume of the mixture is less than the critical specific volume, the level of the liquid will fall when heated?</p>
| 3,985 |
<p>I was answering a question on proving the parallel axis thereom for angular momentum and came across this:
$$\int Yy'dm=Y\int y' dm=0$$
Where the position of the center of mass of an object is given by $(X,Y,Z)$, $(x',y',z')$ is a position relative to the centre of mass and m is the mass of the object. </p>
<p>My text book (Introduction to classical mechanics) says that this is due to the definition of the centre of mass. There are two things that I don't understand firstly why is $Y$ independent of mass whilst $y'$ is not? and secondly please can you explain what definition of the centre of mass they are using to get the reslut above? I really have no idea to the answer for either of these questions? </p>
| 3,986 |
<p>Are there any optical filters which filter the signal's frequency and not based on the wavelength of the light? So what I mean is, if I have a modulated/pulsating light signal riding on a large DC offset, is there some way I can filter out the DC offset using optics alone? I've tried searching the internet for this but this is obviously hard since I don't know which keywords to use... "optical filters" are always based on filtering the spectrum of light, not on the temporal signal.</p>
<p>Would appreciate any help and/or discussions/debates about this, thanks a lot!</p>
| 3,987 |
<p>Consider a cylinder filled partially with a liquid (e.g. water). The cylinder is sealed, and is at held at room temperature (e.g 298K). At equilibrium (or when no external disturbance is imparted to the system), the liquid in the cylinder exists in equilibrium with its vapor at the vapor pressure of the liquid, applicable at room temperature.</p>
<p>Suppose that the bottom of the cylinder is fitted with a piston. Note that the system is still sealed. Now imagine that the piston moves upwards. The liquid column moves upwards, the volume the vapor occupies decreases, but the vapor still exists at the vapor pressure of the liquid (assuming that thermodynamic equilibrium can be achieved fast enough).</p>
<p>What's interesting is when the piston move downwards. If the piston moves at a slow speed, the liquid column should stay "on top of" the piston (without any "gap" between the column and the piston). Now, if the piston moves downwards fast enough (or when the downward acceleration is high enough), the liquid column shall "leave" the piston, and a "packet" of vapor shall be formed between the piston and the liquid column. (Please refute the former claim if you think it's wrong.) Why? if the "friction" between the cylinder walls and the liquid column is negligible, and the liquid column is already in a state of free-falling, there is no mechanism to "pull" it downwards further anymore.</p>
<p>Now, imagine that the piston moves upwards again. Then the liquid column shall "collide" with the piston. Will it "stick" to the piston, as in an inelastic collision, or recoil, as in an elastic collision? </p>
<p><em>P.S. After thinking for a while, I think it is not at all an easy question to answer. Now whether the liquid will "recoil" (not "slosh", which implies that the liquid changes shape) depends on how momentum is transferred from the piston to the liquid column. Please refer to the youtube video for the "beer bottle trick". If the cavity formed at the bottom is a "vacuum", which is probably the case, then when the liquid "smash back", the atmospheric pressure shall press on the liquid column, and most probably it will not "recoil". On the other hand, if the cavity formed is gas-filled, then the kinetic energy from the liquid (which is trying to "smash back" on the glass bottle) may be dissipated to the gas (in the original gas-filled cavity), through the formation of many tiny cavitations (claim: the latter claim is not sound; I am just guessing). For as long as the impact is "dampened", a recoil will not happen.<br>
Indeed there are many ways in which a liquid may dissipate energy, because it's formless/shapeless, and there's viscosity in the picture. The more "flexible" it is to energy dissipation, the less likely it is to recoil.</em> </p>
| 3,988 |
<p>Does <a href="http://en.wikipedia.org/wiki/Redshift" rel="nofollow">redshift</a> depend on the
spatial orientation of <a href="http://www.sdss.org/" rel="nofollow">SDSS galaxies</a> with redshift in the range 0.19 to 0.20 ?</p>
| 3,989 |
<p>We know that linear speed of object going around a circle is $\omega * r $
Now let us take an elastic string and rotate a body of negligible mass with $\omega = 500 rad/s$
It is possible to further stretch this string while maintaining $\omega$ constant using a super powerful motor.</p>
<p>If we extend the chord length to say $1,000,000 m$ then the linear speed of the body should come out to be equal to $500,000,000 m/s $ which is greater than the speed of the light.
<img src="http://i.stack.imgur.com/p2uoX.jpg" alt="enter image description here"></p>
<p>Where is the fallacy in the above argument?</p>
| 121 |
<p>Suppose we have a rigid token-ring network. An observer at any node can seemingly determine the angular momentum of the network by measuring the time it takes for a packet to travel around the ring in each of the two directions. Is it possible by any means for an observer to determine whether the network is knotted?</p>
| 3,990 |
<p>One of the arguments in favor of TeV scale SUSY breaking is that it leads to the appropriate running of the gauge coupling strengths leading to grand unification, i.e. $k_Y = \frac{5}{3}$ instead of $k_Y = \frac{4}{3}$. With the LHC ruling out TeV scale SUSY breaking, what is the current consensus on grand unification? I know it's always possible to restore grand unification if you really insist upon it with contrived mechanisms like split SUSY, brane worlds with fine-tuned couplings, exotic fields, etc. but what would you say the current Bayesian posterior probability for grand unification is right now? How much would you be willing to bet on it? Isn't it kind of suspicious we've never detected proton decay or magnetic monopoles so far? The doublet-triplet splitting problem also makes you wonder...</p>
| 3,991 |
<p>I don't know if anyone else has noticed this but in most buildings and most rooms, radiators are predominantly placed under a window. </p>
<p>Now, in my eyes, that is the worst place to put them; hot air rises, reaches the window (which no matter how well insulated it's still letting out heat, in loose terms) and the thermal energy of the air disperses around the window area, thus not doing much to warm up the room. </p>
<p>Am I wrong to think this? I mean, I can hold my hand close to my window and feel that it is colder there than at the other end of my room, but then again, my room does warm up when the radiator is on.</p>
| 3,992 |
<p>The dominant method of neutron star cooling is neutrino emission. There are two regimes usually presented, the "direct Urca" and "modified Urca" processes, each of which are sequences of neutron decay and inverse reactions. The direct Urca looks like this:
$$n\rightarrow p+l+\overline{\nu_l},\quad p + l \rightarrow n + \nu_l$$
where $l$ is a lepton - either an electron or a muon. These processes cause continuous emission of neutrinos which cools a neutron star relatively quickly.</p>
<p>But below a density of $\rho\approx 10^{15}\mathrm{\,g\,cm^{-3}}$ (about three times the nuclear density) this process is suppressed, which means that the direct Urca process only occurs in the core. This is the reason according to a review of neutron star cooling from Pethick and Yakovlev (2004):</p>
<blockquote>
<p>The process can occur only if the
proton concentration is sufficiently
high. The reason for this is that, in
degenerate matter, only particles with
energies within ~$k_BT$ of the Fermi
surface can participate in reactions,
since other processes are blocked by
the Pauli exclusion principle. If the
proton and electron Fermi momenta are
too small compared with the neutron
Fermi momenta, the process is
forbidden because it is impossible to
satisfy conservation of momentum.
Under typical conditions one finds
that the ratio of the number density
of protons to that of nucleons must
exceed about 0.1 for the process to be
allowed.</p>
</blockquote>
<p>This makes some sense. But what surprises me is that this process can still work with a slight modification at lower densities. The <em>modified</em> Urca process can cool the star
$$n+N\rightarrow p+N+l+\overline{\nu_l},\quad p + N + l \rightarrow n + N + \nu_l$$
where $N$ is a nucleon - a proton or a neutron.</p>
<p>This process, I'm told, can work at much lower densities, but produces 7 orders of magnitude less emissivity. As a result, it's the dominant process in the superfluid outer core.</p>
<p>My question is why does the additional nucleon permit lower densities? How does an additional neutron or proton get us out of the conservation of momentum problem with the direct Urca process?</p>
| 914 |
<p>I was on my workshop lab today and had to <a href="http://en.wikipedia.org/wiki/Filing_%28metalworking%29" rel="nofollow">file</a> (rub on metal surface with rough surface to smooth-en it) an iron bar. It made iron dust fall of the surface. To mark some points on the bar I then had to hammer a pointed another Iron bar over the former. What I noticed is that the iron dust that had previously fallen off were clinging on the top circumference of the pointed bar. </p>
<p>I have two probable explanations for this</p>
<ol>
<li>The iron dust being small acted as magnets as there are fewer magnetic domains and they essentially align on single direction so that the dust were attracted.</li>
<li>Hitting the top of bar somehow could have magnetized the bar so that the dust were attracted</li>
</ol>
<p>Am I correct with one or both of these explanations?</p>
| 3,993 |
<p>Is there any way to produce food without sun, synthetically? I mean if we face solar winter. look at: <a href="http://physics.stackexchange.com/questions/30095/is-there-any-way-to-survive-solarwinter-like-in-sunshine-movie">Is there any way to survive solarwinter like in Sunshine - movie?</a></p>
| 3,994 |
<p>Reading about the spectacular Opera claim, I`m (again ;-P) wondering if a confirmation of superliminous neutrinos could help settle some still open quantum gravity issues ...?</p>
<p><a href="http://physics.stackexchange.com/questions/14973/what-would-be-the-immediate-effects-if-light-does-not-go-at-the-maximum-speed-pos">In this post</a>, Lumo explains why tachyons should better be bosonic if they exist, making use, among other things, of some string theoretical considerations.</p>
<p>So what would a confirmation of the claim mean for string theory?</p>
<p>On the other hand, would a confirmation of superluminal neutrinos and a corresponding incompleteness of GR (and allowance to violate Lorenz Invariance?) lend some "updraft" to other QG theories like LQG, spin foams, spin networks etc or even provide some positive hint of them?</p>
| 3,995 |
<p>There’s an interesting <a href="http://www.scientificamerican.com/article.cfm?id=raizen-entropy-cooling-experiment-interactive&posted=1" rel="nofollow">article on Scientific American</a>
that tells how to cool individual atoms to within a very tiny fraction of Absolute Zero.</p>
<p>It uses two laser beams acting on a very cold rarified gas in a magnetic trap. Initially, all of the atoms are in one state. The first laser beam (call it red) only affects atoms in a second stable state. A second laser (call it orange), offset and parallel to the first of a different color is turned on. This laser switches atoms to the previously mentioned second stable state when it hits an atom. </p>
<p>These excited atoms cannot pass the first laser beam (the excited atoms rebound from this beam). This leads to a concentration of the excited atoms on the side of the second beam. All of the atoms will eventually cross the two beams and move into the smaller area, being compressed without raising their temperature (supposedly). The lasers are then turned off, the gas is allowed to expand (and cool) into its original volume and you end up with a lower temperature gas.</p>
<p>I’ve left the following question there, but haven’t gotten an answer (I keep getting notices that the comments have been added to, but even when I clear my browser cache, or use a different browser, I still don’t see them). So here is my question. Can you help me understand?</p>
| 3,996 |
<p>Consider a magnetic spring as seen on this <a href="http://www.youtube.com/watch?v=jMeCbFX80W4" rel="nofollow">YouTube</a> video, but ignore gravity. If I wanted to calculate the effective spring rate (Force vs. Deflection) curve for the top magnet, how would I go by doing that?</p>
<p>Consider $N$ permanent magnets made of <a href="http://en.wikipedia.org/wiki/Neodymium_magnet" rel="nofollow">Neodymium</a> with known geometry (length, diameter etc). Space them equally such as the total span is $L=N\;\Delta x$ such that they can slide along a rod (1 <strong>DOF</strong> each). Finally apply a unit force $F$ on one end, while holding the other end fixed.</p>
| 3,997 |
<p>If a power source is supplying a current I and a voltage V, that travels to its destination through resistors of restance R is the power delivered at the destination = $VI - RI^2$, where $(Pi=) VI$ is the power input of the power source (i.e. the total power supplied) and $RI^2$ is the power wasted over the restance which also equals $Pi^2R/V^2$ is this correct??</p>
| 3,998 |
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