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<p>I am confused in one question in general relativity, why we can always express a space-time geometry only by metric. It means a metric, which is just about distance in tangent space, can tell us all the information about the manifold.</p>
<p>I know there are standard proofs, for instance, we can express connection by metric, and so the Riemann curvature. However, I am not very satisfied by these answers. I still want a more direct reason for that.</p>
<p>To my understanding, a metric just defines the distance, the length of tangent vectors, however, Riemann curvature, in my eyes, tell us more, for instance, how a line differ from a direct line and how a vector travel along a closed path. </p>
<p>I believe there must be some neat and beautiful argument show that metric is enough, is everything.</p>
<p>This question is quite vague, so please just feel like a chatting.</p> | 4,094 | [
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<p>Does the universe obey the holographic principle due to Stokes' theorem?</p>
<p>\begin{equation}
\int\limits_{\partial\Omega}\omega = \int\limits_{\Omega}\mathrm{d}\omega.
\end{equation}</p>
<p>Can this theorem be enough proof of our Universe being a hologram – the choice of $\omega$ and $\Omega$ is completely arbitrary!</p> | 4,095 | [
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<p>Lets say, I have a fluid in a rectangular enclosure (2D). I apply electric potential $U=U_1$ at left boundary and $U_2$ at right boundary. In the lower and upper boundaries, the potential varies linearly from $U_1$to $U_2$.</p>
<p>I am simulating this problem. So what initial condition should I take for potential of the fluid (inside the four boundaries)?
Also how will the potential develop?</p> | 4,096 | [
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<p>In a question I am doing it says:</p>
<blockquote>
<p><em>Show explicitly that the function $$y(t)=\frac{-gt^2}{2}+\epsilon t(t-1)$$ yields an action that has no first order dependency on $\epsilon$.</em></p>
</blockquote>
<p>Also my textbook says that</p>
<blockquote>
<p><em>[...] if a certain function $x_0(t)$ yields a stationary value of $S$ then any other function very close to $x_0(t)$ (with the same endpoint values) yields essentially the same $S$, up to first order of any deviations.</em></p>
</blockquote>
<p>I am confused about the first order bit? In the first case does it mean that $\frac{\partial S}{\partial \epsilon}=0$ or that it does not depend of $\epsilon$ but may take some other constant value. In the second case does it mean likewise or something different, please explain?</p> | 4,097 | [
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<p>In Landau & Lifshitz's book, <em>Classical theory of fields,</em> the action for a free particle is defined as: </p>
<p>$$\tag{8.1} S= \int ^b _a {-mc \ \text d s}=0,$$</p>
<p>where $$\text d s=c\,\text d t\sqrt{1-\frac {v^2}{c^2}}$$
is the the invariant space-time interval beetween points along the particles worldline.
From the latter expression of the Lagrangian, it's easy to obtain the expressions of the momentum and the energy of the particle.</p>
<p>However, after a "classical" derivation, the author repeats the calculations with a different notation (I'll post the derivation from the "particle in a electromagnetic field" case omitting the 4-potential terms, because I think that my book contains an error in the free particle case):</p>
<blockquote>
<p>Since $\text d s= \sqrt {\text dx^i \text dx_i}$: $$\delta S = -mc \int ^b _a\dfrac{\text dx_i \text d\delta x_i}{\text ds}.$$
Integrating by part, introducing the 4-velocity $u_i =dx_i/ds$, we get: </p>
</blockquote>
<p>$$\tag{9.10}\delta S =-mcu_i\delta x^i|^b _a+\int_a ^bmc\dfrac{\text d u_i}{\text d s} \delta x^i \,\text ds.$$</p>
<p>I'm very puzzled about the meaning of these two lines; I have three questions: </p>
<p><strong>1)</strong> What does the notation $\text d \delta x_i$ mean?</p>
<p><strong>2)</strong> How does he obtain the $\delta S$ expression?</p>
<p><strong>3)</strong> How does he pass from the first integral to the second?</p>
<p>If someone could explain in detail I'd be very grateful.</p>
<p>Note, I have no problem in getting the result, I can obtain it by replacing $\text d s =c\text d t \sqrt {...}$ and doing the variation on $v$.</p> | 4,098 | [
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<p>Based on the concept that energy can never be destroyed and is only transferred. Does it mean that energy since the formation of literally everything still here today?</p> | 4,099 | [
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<p>I have been told that $$[\hat x^2,\hat p^2]=2i\hbar (\hat x\hat p+\hat p\hat x)$$ illustrates <strong><em>operator ordering ambiguity</em></strong>.</p>
<p>What does that mean?
I tried googling but to no avail.</p> | 4,100 | [
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<p>When there is a charged conducting object near an another charged conducting object the charges on these objects accumulate to the sides where the closest points between these objects are. However, since these objects are conductors the charges also have to move on these objects. For a perfect conductor(~superconductors)would the charges still move on the object because to my mind it should accumulate on the sides and be static. I am pretty confused at this point so I hope someone could explain it to me: Would the charges on a superconductor near an another charged conductor move and produce magnetic field?</p> | 4,101 | [
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<p>People sometimes talk about KeV mass sterile neutrinos as a warm dark matter candidate. I think they call them <em>KeVins</em> (horrible name btw). Now, In order for it to be a good dark matter candidate it must be quasi-stable, so the mixing with active neutrinos must be quite small. Can anybody give me the upper bound on the active-sterile mixing? Thanks</p> | 4,102 | [
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<p>A circuit has a self-induction of 1 H and carries a current of 2 A. To prevent sparking when the circuit is witched off, a capacitor of which can withstand a voltage of 400 V is used. The least capacitance of the capacitor connected across the switch must be?</p>
<p>I have no idea how to go about this question.</p> | 4,103 | [
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<p>Let's say a room is filled with butane, I then throw a cigarette into the room. What happens to the atoms/molecules of the butane when they are in contact with the heat from the cigarette?</p> | 4,104 | [
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<p>Lets say you have a plank is you hit it once and get t time if you hit is 2x as hard will it travel t/2? will it be the same or will it travel only slightly faster?</p> | 4,105 | [
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<p>I am totally confused about the Hilbert Space formalism of Quantum Mechanics. Can somebody please elaborate on the following points: </p>
<ol>
<li><p>The observables are given by self-adjoint operators on the Hilbert Space. </p></li>
<li><p>Gelfand-Naimark Theorem implies a duality between states and observables </p></li>
<li><p>What's the significance of spectral decomposition theorem in this context? </p></li>
<li><p>What do the Hilbert Space itself corresponds to and why are states given as functionals on the Hilbert space. </p></li>
</ol>
<p>I need a real picture of this.
I posted in <a href="http://math.stackexchange.com/q/271548/11127">Math.SE</a> but got no answer. So I am posting it here.</p> | 783 | [
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<p>I was doing an exercise in physics and I noted that the <a href="http://en.wikipedia.org/wiki/Angular_acceleration" rel="nofollow">angular acceleration</a> was negative. What does that mean?</p> | 4,106 | [
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<p><strong>A clarification please</strong></p>
<p>The following scheme to measure <strong>linear</strong> polarization states (a single polarizing beam splitter and two photo counters) orientation (as $arctan \sqrt{\frac{v}{h}}$) of <strong>coherent</strong> light pulses cannot discriminate two states which make the same angle with the measuring bases. $\langle n \rangle$ is the average number os photons per pulse.</p>
<p><img src="http://s14.postimage.org/evo2hbpzl/g4322.png" alt="a"></p>
<p>In the example, the $+45^o$ and $-45^o$ polarized pulses will result on the same output.</p>
<p>I'd like to know if it is OK to do the following setup and what would be change in precision of the polarization angle, if any:</p>
<p><img src="http://s2.postimage.org/xsyztz1g9/g4361.png" alt="b"></p> | 4,107 | [
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<p>In looking at the answers to this question regarding light from distant galaxies ever being visible to us:</p>
<p><a href="http://physics.stackexchange.com/questions/129980/expansion-of-the-universe-will-light-from-some-galaxies-never-reach-us">Expansion of the Universe, will light from some galaxies never reach us?</a></p>
<p>I came across a few concepts that were quite surprising to me. In particular:</p>
<ul>
<li><p>Movement faster than the speed of light</p></li>
<li><p>The big bang was not an explosion outwards from a single point.</p></li>
</ul>
<p>Granted I am just a rank beginner and self-studier, yet I did study a QM course from Oxford, have read several sets of notes on SR, and readily went through the first hundred pages of "Student Friendly QFT."</p>
<p>Yet I have never encountered these notions.</p>
<p>My question is where does one acquire this type of information. Not necessarily the technicalities (of, e.g., GR); but just a correct awareness.</p> | 4,108 | [
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<p>I know that there is theory that strings are the most fundamental particles. But if it is a string, then it can be 'cut' into pieces, and if it can be 'cut', then it can be cut at infinitely many places. Then does this makes the strings fundamental? If not, then what is ultimately <em>the</em> fundamental piece of matter? </p> | 4,109 | [
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<p>In string theory, it is assumed that all particles can be described as quanta corresponding to the excitations of only one kind of fundamental string. </p>
<p>How can in principle the different motion patterns of one kind of string give rise to the whole particle zoo in the standard model? How are the different properrties, that characterize an elementary particle such as their</p>
<ul>
<li>mass</li>
<li>spin</li>
<li>charges</li>
</ul>
<p>encoded in the allowed motion pattterns of the string?</p>
<p>(I know that the vacuum corresponding to our standard model can not be uniquely identified at present, but I am interested in the general concepts and ideas that should in principle give rise to the different characteristics of the particles we observe.)</p>
<p><strong>Note</strong></p>
<p><em>This is just an attempt to extract and reask the useful part of <a href="http://physics.stackexchange.com/q/44300/2751">this</a> now a bit too overloaded original question.</em></p> | 4,110 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/1030/what-is-the-evidence-for-inflation-of-the-early-universe">What is the evidence for Inflation of the early universe?</a> </p>
</blockquote>
<p>I am reading some public science books on inflationary universe, e.g. <a href="http://www.google.com.hk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=11&ved=0CCEQFjAAOAo&url=http://www.amazon.com/Inflationary-Universe-Alan-Guth/dp/0201328402&ei=-iCqUJz8DK6jiAfg6oDYAQ&usg=AFQjCNFaGrv71HsWgfYTcLmvk8-RAGxkrw&sig2=yDBnfDzP6Mm_hz8m5Sqknw" rel="nofollow">The Inflationary Universe</a> by A. Guth.</p>
<p>Both in this book and the Wiki page mention briefly how this theory of inflation can possibly solve Flatness Problem, Horizon Problem and Monopole Problem. But their explanations are too sketchy for me. </p>
<p>Can somebody give a detailed explanation? But I do not want something too technical. I am doing this for a presentation in my general education class. The professor is a prominent physicist so I need some more details to satisfy him, but most of the audience are just <em>average</em> college students.</p>
<p>How does an inflationary universe solve the Flatness Problem, Horizon Problem and Monopole Problem?</p> | 123 | [
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<p>What is the electric current $I_{12}$ and voltage $U_{12}$ in following electric circuit? $I_{12}$ and $U_{12}$ are between points 1 and 2. </p>
<p><img src="http://i.stack.imgur.com/FldEO.jpg" alt="picture of electric circuit of the question">. </p>
<p>I have used <a href="http://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab" rel="nofollow">this</a> in constructing this electric circuit and as you can see simulator shows wrong electric current($I_{12}=0,34 A$) between points 1 and 2, but why? I mean, because both bulbs has resistivity of $10 \Omega$ and Cell has voltage as 10 V, then should be $I_{12}=0 A$.</p>
<p><img src="http://i.stack.imgur.com/nm86W.jpg" alt="Another configuration showing another value of $I_{12}$"></p>
<p>Now $ I_{12} \approx 0$ so I think something is wrong with this simulator. </p> | 4,111 | [
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<p>Recently, I was pondering over the thought that is most of the elementary particles have intrinsic magnetism, then can gravity be just a weaker form of electromagnetic attraction? But decided the idea was silly. </p>
<p>But I then googled it and found <a href="http://theuniverseandman.wordpress.com/2012/09/04/how-and-why-gravity-is-electromagnetic-attraction/#comment-28">this</a> article. Is this idea really compatible with other theories as the article mentions? Is there any chance of this proposition being true?</p> | 4,112 | [
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<p>The usual Lagrangian for a relativistically moving charge, as found in most text books, doesn't take into account the self force from it radiating EM energy. So what is the Lagrangian for a relativistic charge that includes the self-force?</p> | 4,113 | [
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<p>Is it really possible to walk on water or levitate in air. If not then how do some magician,s like dynemo do it simply while walking on street? And i have asked for possibility of walking on water so please exclude the high velocity concept.</p> | 4,114 | [
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<p>As I understand, to an observer well outside a black hole, anything going towards it will appear to slow down, and eventually come to a halt, never even touching the event horizon. </p>
<p>What happens if you (theoretically) wait long enough? Would you see the black hole vaporize before you see the object even reach it?</p> | 4,115 | [
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<p>Question: How can I find physics papers, articles and preprints decades ago?</p>
<p>Description: The search of articles and papers is for the purpose of finding interesting phenomenon for a science project. Where can I find a website where physics papers, articles and preprints in the 80's or older could be found?</p> | 4,116 | [
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<p>What's so ingenious in diffractive lenses?</p>
<p>To my naive eye they seem to be just Fresnel lenses with smaller features.</p>
<p>What makes it so magic and why all the fuss about it?</p> | 4,117 | [
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<p>muon neutrino momentum distribution </p>
<p>I have read the public data of T2K ,KEK to find this subject, I'm curiously that it's coincides with my prediction perfectly: The neutrino get its momemtum by its effect-partner, which is obvious in the reactional formula, especialy that by me. You can find the figures<a href="http://blog.sciencenet.cn/home.php?mod=space&uid=595492&do=blog&id=462424" rel="nofollow"> Here </a>( htis link is a blog including the detialed idea) the first is the radium function of e, the second cut from paper from the lab, the third is the momemtum spectrum. Do any one find the simlar distribution of other particle? I just work on Hep just for a few months.</p> | 4,118 | [
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<p>If lasers are collimated, what causes them to decollimate? Their production system seems to suggest a completely linear, collimated light source, but they do spread out over large distances. The same holds for synchrotrons. Why does this happen?</p> | 4,119 | [
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<p>I am referring to <a href="http://physics.stackexchange.com/questions/30105/is-qcd-free-from-all-divergences">this question</a>, and especially <a href="http://physics.stackexchange.com/a/30150/605">this answer</a>. </p>
<blockquote>
<p>In addition, QCD has - like all field theories - only an asymptotic
perturbation series, which means that the series itself will also
diverge if all terms are summed.</p>
</blockquote>
<p>What does it mean? From what I know, if the sum over a series diverge, that means that the summation doesn't work, which means that the quantity you are trying to calculate, you can't get answer for that, for any quantity that comes back from your calculation must be of finite value.</p>
<p>But in QCD and QED things seem a lot more complicated, <a href="http://physics.stackexchange.com/a/30114/605">since some divergences are allowed</a>:</p>
<blockquote>
<p>This doesn't mean that QCD perturbation theory doesn't have
ultraviolet divergences, it has those like any other unitary
interacting field theory in 4d. These ultraviolet divergences though
are not a sign of a problem with the theory, since the lattice
definition works fine. This is in contrast to, say, QED, where the
short lattice spacing limit requires the bare coupling to blow up, and
it is likely that the theory blows up to infinite coupling at some
small but finite distance. This is certainly what happens in the
simplest interacting field theory, the quartically self-interacting
scalar</p>
</blockquote>
<p>My questions:</p>
<ol>
<li>How many kinds of divergence there are in QCD and QED?</li>
<li>And how do we know what kind of divergence is acceptable ( in the sense that we can still extract values out for prediction after some renormalization process)?</li>
<li>If the sum diverge, then we won't be able to calculate the series's sum. Isn't that is defeating the purpose of the series? For any series, if the sum diverge after summing all the terms, then we know that the formula must be wrong or the series have no physical meaning. But why is it that for QCD series, the formula is still correct ( because it is used to extract coupling constants) and has physical meaning ( QCD series must correspond to something in reality)?</li>
<li>The fact that QCD has non-convergent series means that it cannot be the fundamental theory of nature, right?</li>
</ol> | 4,120 | [
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<p>Consider the particle in a box problem in QM. The crux of the reason why QM is able to explain the physical phenomenon is not just the theory but also able to impose boundary conditions which eventually result in quantization. Now in the particle in a 1-d box problem, the wave function is assumed to be zero at the boundaries. It has been said that it is imposed, so that the wave function is continuous. Okay, but what about differentiability? In order for the wave function to satisfy Schrodinger equation,we also need differentiability right? Okay if we assume only left (from one side) derivative to exit, we could have as well assumed only left continuity (from one side). For continuity, we assume it should be from both sides, but for differentiability we need only one side? They also say the slope also must be continuous. I don't see any rationale behind these quantizations!</p> | 4,121 | [
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<p>The most basic situation, water at room temperature, has dissolved oxygen, CO2, and more. Why is this? How would one calculate how much gas <em>should</em> be dissolved in any given liquid?</p> | 4,122 | [
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<p>Why we don't see any <a href="http://en.wikipedia.org/wiki/Gibbs_phenomenon" rel="nofollow">Gibb's phenomenon</a> in quantum mechanics?</p>
<p><strong>EDIT</strong></p>
<p>At sharp edges (discontinuities), we usually find ringing. This cane be observed in many physical phenomenon (eg. shock waves). Naturally, whenevr there is a shrp discontinuity in wave functions, i'd expect a ringing in the probability of finding a particle around that edge.</p> | 4,123 | [
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<blockquote>
<p>A heavy particle is projected at speed $U$ at an angle $\alpha$ to the horizontal. The particle is subject to air resistance which is experimentally found to vary proportionally to the square of the speed. Show that</p>
<p>$$\vec{\dot{v}} = -\frac{g}{V^2}\lvert\vec{v}\rvert\vec{v} - g\vec{j},$$</p>
<p>where $V$ is the terminal velocity of the particle. If $\alpha = \frac{\pi}{2}$ (so that the particle is projected directly upwards), find the maxium height reached and the time taken to reach it. What is the speed of the particle when it returns to the horizontal?</p>
</blockquote>
<p>I'm having troubles solving this question, firstly I have some fundamental mis-understandings,</p>
<ul>
<li><p>if the particle is subject to air resistance which is proportional to the square of the speed then do we model newton second law as:</p>
<p>$$\vec{\ddot r} = \vec{g} - k|\vec{v}|^2\dfrac{\vec{v}}{|\vec{v}|}$$</p>
<p>or $$\vec{\ddot r} = \vec{g} - k|\vec{v}|^2$$?</p>
<p>I'm assuming the former by looking as what's required but <em>why</em>? The question says it's just proportional to speed, why in the direction of the velocity?</p></li>
<li><p>Secondly, why do we have to artificially put a negative sign? Does this mean that $k>0$ from now on?</p></li>
</ul>
<p>As for my attempt of the question I done it as follows:</p>
<p>$$\vec{\ddot r} = \vec{g} - k|\vec{v}|^2\dfrac{\vec{v}}{|\vec{v}|} = -g\vec{j} - k|\vec{v}|\vec{v} $$</p>
<p>so we have, $\vec{\dot v} = -g\vec{j} - k|\vec{v}|\vec{v}$</p>
<p>solving this I get the solution of $$ \vec{v} = \dfrac{-g}{k|\vec{v}|} + \vec{c}e^{-kt|\vec{v}|} $$ where $\vec{c}$ is a constant vector, </p>
<p>now from here I get terminal velocity as $\dfrac{-g}{k|\vec{v}|} \vec{j}$ but I am unsure how to get $V^2$ from here.</p>
<p>on second thoughts if $|\underline{v}| = V$ then I get the required result, but <em>why</em> would the speed be the same as the terminal speed</p> | 4,124 | [
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<p><strong>The problem statement</strong></p>
<p>Vehicle A and Vehicle B are moving in opposite directions on the NJTP. Vehicle A is heading south toward atlantic city while vehicle B is heading north towards Hoboken. In situation 1 and 2 described below, at t = 0s both vehicles are at a distance of separation of 400m and are moving towards each other.</p>
<p>Situation 1: When vehicle A is moving at a constant velocity of 30 m/s and travels a distance of 120 m, the vehicles pass each other on the turnpike.</p>
<p>Situation 2: When vehicle A is moving at a constant velocity of 80 m/s and after a time of 3s, the vehicles pass each other on the turnpike.</p>
<p>For vehicle A label variables as: Via, Vfa, aa, da,ta
For vehicle B label variables as: Vib, Vfb, ab,db, tb</p>
<p>In the ORDER INDICATED:</p>
<p>(a) Calculate the initial velocity of vehicle B or Vib; and </p>
<p>(b) Then calculate the acceleration of vehicle B or ab</p>
<p>Show all work in DETAIL and keep all numerical values to the nearest hundredth value. Draw and label all pictures</p>
<p>Note: You will receive NO CREDIT if you first calculate part (b) and then part (a)</p>
<p>For situations 1 and 2</p>
<p>vib = constant ; vfb ≠ a constant value since its value changes w/ time</p>
<p>ab = constant</p>
<p><strong>My Work</strong></p>
<p>Situation 1:
Da + Db = 400</p>
<p>Via = 30 m/s
Vfa = 30 m/s
a = 0 m/s2
da = 120 m
ta = ?</p>
<p>Vave = d/ t = vf + vi /2
Vave = da/ta
ta = 4s</p>
<p>db = 280
ta = 4s</p>
<p>Situation 2:
Via = 80 m/s
aa = 0 m/s2
vfa = 80 m/s
ta = 3s = tb
da = ?</p>
<p>Using same equation as in situation 2,</p>
<p>da = 240</p>
<p>db=160
tb = 3s</p>
<p>Situation 1
db = vibtb + 1/2abtb^2
280 = vib(4) + 1/2 (ab)(4)^2</p>
<p>Situation 2
db = vibtb + 1/2abtb2
160 = vib(3) + 1/2 (ab)(3)^2</p>
<p>Solving for ab I get ab = 11.85 / vib</p>
<p>Plugging that back into the equation I get Vib = .34 m/s and plugging that into the 280 = (.34)(4) + 1/2 (ab)(4)^2 = ab = 34.82 m/s^2.</p>
<p>I'm sorry if I'm new and breaking the rules, but this problem has really been bothering me for the last week. My friend says it's correct, but it just seems too low of an initial velocity.</p> | 4,125 | [
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<p>I'm studying for a course in electromagnetism, and I've been given an electric field for which I need to find the associated scalar potential. The field is the field generated by a sphere of radius $R$ with constant charge density $\rho$ throughout its volume, so that the total charge $Q=\dfrac{4\pi r^3 \rho}{3}$contained in the sphere is constant.</p>
<p>The electric field is given by $\vec{E}_{\text{in}}(\vec{r})=\dfrac{Q}{4\pi \epsilon_0 R^3}r$ and $\vec{E}_{\text{out}}(\vec{r})=\dfrac{Q}{4\pi \epsilon_0 r^2}$, where the former is valid for $r\leq R$ and the latter for $r\geq R$. This I've calculated before and I do not have trouble with. The scalar potential $\phi(\vec{r})$ is defined by $\vec{E}=-\vec{\nabla}\phi$. The provided solutions to the problem are hand written but I'll type them here using the exact same notation:</p>
<p>$\phi_{\text{in}}=-\int \vec{E}_{\text{in}}d\vec{r}=-\dfrac{Qr^2}{8\pi \epsilon_0 R^3} + C_1$</p>
<p>$\phi_{\text{out}}=-\int \vec{E}_{\text{out}}d\vec{r}=\dfrac{Q}{4\pi \epsilon_0 r} +C_2$</p>
<p>This is literally all the information I've been given. I really don't know what these integrals are, nor how they follow from the above equation. I can see that the result of the first integral for example is just the indefinite integral $-\int \dfrac{Q}{4\pi \epsilon_0 R^3}r dr$ but I can't see how this stage was reached. I think my professor intended this to be a $\cdot$ in the integrals but has missed them out. Even so I can't figure out where these integrals come from (i.e. why they give the potential), what these integrals mean, or (if they are indeed surface integrals) how to evaluate them.</p>
<p>Any clarification would be much appreciated!</p> | 4,126 | [
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<p>I have the following circuit:</p>
<p><img src="http://i.stack.imgur.com/Ss7Iv.jpg" alt="enter image description here"></p>
<p>It is subject to a steady, time-invariant magnetic field which points out of the paper. At $t = 0$, the switch closes.</p>
<p>I thought that the magnetic flux would decrease at the moment the switch closes and, by Faraday's law, cause the voltmeter to change its reading. However, my textbook says that the voltmeter won't change. How does one arrive at this conclusion?</p> | 4,127 | [
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<p>When i read about how the concept works, it looks pretty solid. But in reality accelerometers are just so imprecise that they need to be configured with alternative ways to correct their positions.</p>
<p>I am talking about using accelerometer to measure position. Sounds very solid, but then fails to be practical for other than very limited uses. </p> | 4,128 | [
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<p>I'm redoing the calculations of "Point Canonical Transformations in the path integral", by Gervais and Jevicki; while doing so I stumbled in integrals like
$$
\int \mathrm{d}t \, \Delta_F^3(t) = -\frac{1}{12} \frac{i}{\omega^4}, \\
\int \mathrm{d}t \, \dot{\Delta}_F^2(t) \Delta_F(t) = \frac{1}{12} \frac{i}{\omega^2}
$$
where
$$
\Delta_F(t) = \int \frac{\mathrm{d}\nu}{2\pi} \, e^{i\nu t} \frac{i}{\nu^2-\omega^2+i \varepsilon}.
$$</p>
<p>I tried various methods, without success. For instance, I integrated explicitly $\Delta_F(t)$ and after some calculations I found $\Delta_F(t) = \frac{1}{2\omega} \cos(\omega t)$; but this expression, inserted in the previous ones, does not make the integrals converge. Maybe in these integrals it's important to integrate in $\mathrm{d}t$ before doing the $\mathrm{d}\nu$ integration; but when trying to do so what I obtain is terribly complicated.</p> | 4,129 | [
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<p>This comes from Electromagnetic Fields and Waves by Lorrain et al, page 77 on a Hollow, <em>ungrounded</em> conductor enclosing a charged body:</p>
<blockquote>
<p>The surface charge density at a given point on the <em>outside</em> surface of the conductor is independent of the distribution of Q in the cavity. It is the same as if the conductor were solid and carried a net charge Q.</p>
</blockquote>
<p>1) I don't believe this. As I move +Q around the inside of the cavity, this will affect the distribution of $-Q$ on the inside surface, which must also affect $+Q$ on the outside surface to keep $E=0$ inside the cavity conductor.</p>
<blockquote>
<p>Inversely, the field inside the cavity is independent of the field outside the conductor. The conductor then acts as an *electrostatic shield.</p>
</blockquote>
<p>2) I don't believe this either for similar reasons. The external fields will affect the distribution of $+Q$ on the outer surface, which must affect the distribution of $-Q$ on the inner surface and therefore the electrostatic field inside the cavity, to maintain $E = 0$ inside the conductor.</p>
<p>So am I correct to disbelieve that an ungrounded conductive cavity can provide electrostatic shielding for the reasons 1. and 2. above?</p> | 4,130 | [
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<p>I am curious what causes the charge build up in a cloud before lightning occurs. I have seen in a few places such as <a href="http://www.regentsprep.org/Regents/physics/phys03/alightnin/default.htm" rel="nofollow">this</a>, that the process is not fully understood. Is this some form of static electricity? Here are a few of my thoughts:</p>
<ul>
<li><p>It seems that rain or ice particles occur are present in the clouds where this happens since thunderstorms are usually accompanied by rain.</p></li>
<li><p>These clouds tend to be cumulus or cumulonimbus clouds which are much taller than other types that are commonly encountered. Is the physical size of the cloud related to this type of buildup of charge or is it a result of the moisture content? </p></li>
<li><p>If the charge buildup is caused by static electricity which two surfaces are contacting to create the charge? Is this just rain and ice particles? Can it be something else? (I think I recall something about lightning storms without rain in the desert) Why do some clouds with lightning have rain and others do not if the rain drops are the source of the static?</p></li>
<li><p>Is there a minimum solid or liquid particle density needed for static electricity within a cloud? </p></li>
</ul>
<p>Any thoughts would be interesting to hear! </p> | 4,131 | [
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<p>I want to calculate the matrix elements of the operator $\hat{x} \hat{p}$ in momentum and position basis, that is the two quantities ($p,q$ - momenta, $x,y$ - positions):</p>
<p>$$\langle p|\hat{x} \hat{p}|q\rangle$$
$$\langle x|\hat{x} \hat{p}|y\rangle$$</p>
<p>I don't know how to do this. I write $\hat{p}|q\rangle = q | q \rangle$. And $\hat{x} |q \rangle = -i\hbar \frac{d}{dp} | q\rangle$, so </p>
<p>$$\langle p|\hat{x} \hat{p}|q\rangle = -i\hbar q \frac{d}{dp} \delta(p-q)$$</p>
<p>This is nonsensical.</p>
<p>How do I proceed?</p> | 4,132 | [
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<p>Why can't we use fissions products for electricity production ?</p>
<p>As far has I know fissions products from current nuclear power plants create enough 'waste' heat to boil water; and temperature decreases too slowly for an human life. So why can't we design a reactor to use this energy.</p> | 4,133 | [
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<p>I used to live in Italy, and when it was sunny, well, as expected it was pretty hot. Both under the direct light of the sun through the atmosphere, and in the shade, where the temperature was of course lower. I would formalise this saying that in Italy I experienced a certain $\Delta T_{it}$ between shady and exposed outdoor surfaces.
Now I live in England, and I have always noticed that the difference is way bigger. In general, when it's sunny (sure, UK doesn't help such observations) the sun seems to warm more, and in general I experience a bigger $\Delta T_{UK}>\Delta T_{it}$. </p>
<p>I do not know (because I haven't had the opportunity to actually measure the temperature) whether:</p>
<ul>
<li><p>It is only a perception-effect;</p></li>
<li><p>Sun radiation is effectively less filtered, and this results in a higher temperature under its direct light;</p></li>
<li><p>The air is cold and the air ventilation doesn't allow it to warm to a point such that its presence would "mitigate" the difference $\Delta T$</p></li>
<li><p>What is the reason for this? How much is the Latitude relevant?</p></li>
</ul> | 4,134 | [
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<p>Let's say that there is a circular conical section that has diameter $D=.25x$ without any heat generation and I need to find the temperature distribution.</p>
<p>Originially I thought I could use the heat diffusivity equation at steady state to find the temperature distribution. The differential equation would be:</p>
<p>$$\frac{d}{dx}(k\frac{dT}{dx})=0$$</p>
<p>I am looking at the solution to the example in the book and they use Fourier's Law
$$q_{x}=-kA\frac{dT}{dx}$$
and their result is $T(x)=T_{1}-\frac{4q}{\pi a^{2}k}(\frac{1}{x_{1}}-\frac{1}{x_{2}})$</p>
<p>Why do they use one as opposed to the other? Will the two methods produce the same result?</p>
<p>The reason I ask is because they also provide a derivation for the temperature distribution of a plane wall with no heat generation and they use the heat diffusivity equation</p> | 4,135 | [
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<p>I am developing a numerical algorithm to find the ground state of a Hermitian matrix. Obvious applications are quantum many-body systems and particles in various potentials. I am a little stuck with the comparison for the latter example. Could anyone recommend a numerical package to find a ground state of a particle in a simple 3D domain, say, L-shape?</p>
<p>UPDATE: Having read the rules of phys.SE more accurately, I want to emphasise that the question is not about numerical algorithms, but about tools of the trade that people in physics community use and recommend.</p> | 4,136 | [
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<p>If I have an optical transparent slab with refractive index $n$ depending on the distance $x$ from the surface of the slab, the refractive index can be described by:
$$n(x)=f(x)$$ where $f(x)$ is a generic function of $x$. so, we can write:
$$\dfrac{dn(x)}{dx}=f'(x)$$
The snell law of refraction states:
$$n_1\sin(\theta_1)=n_2\sin(\theta_2)$$ How can I write the equation of the ray tracing through the slab? Thanks</p> | 4,137 | [
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<p>The question is: if I were to insert a brass plate between two charges, what will happen to the force between the charges? Would it increase, decrease or stay the same?
<br><br>
Does the brass plate increase the value of permittivity of the medium and therefore the force decreases?
<br><br>
The correct answer is that it will increase. But I do not understand how. </p> | 4,138 | [
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<p>I'm a math student who's dabbled a little in physics, and one thing I'm a little confused by is separation of variables. Specifically, consider the following simple example: I have a Hamiltonian $H$ which can be written as $H_x + H_y + H_z$ depending only on $x,y$, and $z$ , respectively, and I want to find the eigenfunctions. Now, it is clear that the product of eigenfunctions of $H_x, H_y$, and $H_z$ will be eigenfunctions for $H$. But why can <em>all</em> eigenfunctions be expressed this way?</p>
<p>I suspect this is not even strictly true, but can somebody give a physics-flavored plausibility argument for why we only need to concern ourselves with separable eigenfunctions?</p> | 4,139 | [
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<p>My problem is the following: I'm trying to model a dust (pressure-less relativistic gas) in the presence of electromagnetic field using colisioness vlasov-equation (relativistic version of boltzmann equation). Please note that I'm in flat minkowski spacetime with signature $(+,-,-,-)$.</p>
<p>So, I have the following:</p>
<p>Colision-less Vlasov Equation:</p>
<p>$ p^\mu \partial_\mu f_k + q_k\left(p^0\vec E +\vec p \times \vec B\right)\cdot \frac{\partial f_k}{\partial \vec p} = 0$</p>
<p>Everything is in the mass shell, so, $p^0=\sqrt{\vec p^2+m^2}$</p>
<p>Now, I know that the current and the stress tensor are given by:</p>
<p>$j^\mu = m \int \frac{d^3\vec p}{p^0} p^\mu f_k(x^\mu,\vec p)$</p>
<p>$T^{\mu\nu} = m \int \frac{d^3\vec p}{p^0} p^\mu p^\nu f_k(x^\mu,\vec p)$</p>
<p>Using the vlasov equation directly I arrive at:</p>
<p>$\partial_\mu j^\mu = 0$</p>
<p>$\partial_\mu T^{\mu\nu} = q_k F^{\nu\mu}j_\mu$</p>
<p>And I also know that the stress tensor for dust is:</p>
<p>$T^{\mu\nu}= \rho u^\mu u^\nu$</p>
<p>where $\rho$ would be the mass density of the dust. I wanted to find the $f_k$, the probability density in phase space that would give me the above stress energy tensor and also would satisfy the vlasov-equation.</p>
<p>My guess was:</p>
<p>$f_k = \frac{p^0}{m^2} n_k(x^\mu) \delta (\vec p - \vec p_k(x^\mu))$</p>
<p>With $n_k$ being a proper number density in space, because, when I plug this in the definition of stress tensor, I arrive at:</p>
<p>$T^{\mu\nu}_k = \frac{n_k}{m} p^\mu p^\nu$</p>
<p>Which is pretty much what I was looking for. The problem starts when I try to get this to satisfy the vlasov equation, what I do is to derivate the above equation, separate the term in $\delta$ and the one in $\delta'$, and whatever end in each term equals to zero by itself. Doing this I arrive here:</p>
<p>$p^\mu_k \partial_\mu \vec p_k = q_k (p^0_k \vec E + \vec p_k \times \vec B)$</p>
<p>$p^\mu_k \partial_\mu n_k = -n_k q_k \frac{\vec p}{p^0} \cdot \vec E$</p>
<p>So, the first equation is ok, I can convert it to $p^\mu_k \partial_\mu p_k^\nu = q_k F^{\nu\mu}p_{k\ \mu}$ and I get a nice covariant equation for $p^\mu_k$. My headache is on the second one. The right hand side, as far as I could imagine, is not Lorentz invariant, and so spoils all the merit of my former guess.</p>
<p>Just to complicate things even more, when I try to derive $T^{\mu\nu}_k$ and I use the equations for $n_k$ and for $p^\mu_k$, I get the following:</p>
<p>$\partial_\mu T^{\mu\nu} = q_k n_k F^{\nu\mu} p_{k\ \mu} + n_k \left[\partial_\mu p^\mu_k - n_k q_k \frac{\vec p}{p^0} \cdot \vec E \right] p^\nu_k$</p>
<p>Which is what I wanted plus a trash in the end which I haven't found how to to get rid of, thus messing the original equation that I had in the first place. Also I have a similar situation when I try to calculate $\partial_\mu j^\mu_k$.</p>
<p>So, my questions are the following:</p>
<p>1) Do anyone know the right probability density in phase-space to recover the dust stress-tensor? If not, is there anything obviously wrong with my guess?</p>
<p>2) If my guess is reasonable, have I done any miss calculation along the way that would make me have the above problems? (What bothers me is not only that ugly non-covariant term but also the $\partial_\mu p^\mu_k$ which I don't have any idea how to deal with).</p> | 4,140 | [
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<p>General relativity tells us that there is no absolute frame of reference (actually, it tells us that all frames are relative, which is close but not the same as there is no absolute frame).</p>
<p>Special relativity demonstrates that there <em>is</em> an absolute: the speed of light.</p>
<p>Notwithstanding the impracticality of the issues, is it possible to determine an absolute frame of reference based on minuscule difference in the wave length of light (measured by doppler shift)?</p>
<p>In effect, can we measure our (Earth's) compound frame of reference by measuring the doppler shift / compression of light in our own frame of reference. Or would any relativistic compression be undetectable within that same frame of reference? Or would it be practically infeasible?</p>
<p>If practically impossible, is it theoretically possible; how would multiple frames of reference affect our ability to examine this question? </p>
<p>Here is another way of looking at it:<br/>
We know a moving sound source (such as a train) creates doppler shift, irrespective of whether or not anyone is in the "stationary" frame of reference. So, is it a reasonable conjecture to say that the Sun is creating doppler shift in light, irrespective of any specific observer or frame of reference? If so, that would seem to indicate that we could measure motion respective to an absolute frame of reference.</p> | 4,141 | [
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<p><a href="http://en.wikipedia.org/wiki/Future_of_an_expanding_universe#Matter_decays_into_iron" rel="nofollow">Wikipedia</a> says that all matter should decay into iron-56. But it also says <a href="http://en.wikipedia.org/wiki/Nickel-62" rel="nofollow">Nickel-62</a> is the most stable nucleus.</p>
<p>So could this mean that in the far future, everything could (through quantum tunneling) fuse and/or decay into nickel-62 rather than iron-56?</p>
<p>Question inspired by an interesting comment made on a post here: <a href="http://www.quora.com/Do-atoms-ever-deteriorate-over-time/answer/Alex-K-Chen/comment/574730" rel="nofollow">http://www.quora.com/Do-atoms-ever-deteriorate-over-time/answer/Alex-K-Chen/comment/574730</a></p> | 4,142 | [
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<p>I am teaching myself basic mechanics from a standing start. I am trying to understand Angular Acceleration and have set myself a problem to solve. My answer 'feels' wrong, so I'd like some help to understand if I've misunderstood, or miscalculated anything. I've taken many liberties with rounding, please ignore, this is more about the basic process/theory than accuracy. Thanks in advance!!</p>
<p><strong>Problem</strong></p>
<blockquote>
<p><em>An object is travelling around a circle with a radius of 40m. It's speed at (A) is calculated as 50mph. 5 seconds later, it's speed at (B) is calculated as 40mph. Determine the Angular Acceleration.</em></p>
</blockquote>
<p><strong>Basic conversions</strong></p>
<p>Circumference = $2\pi r = 251\text{ m}$</p>
<p>Velocity (A) = $22\text{ m/s}$</p>
<p>Velocity (B) = $18\text{ m/s}$</p>
<p><strong>Angular Velocity at (A)</strong></p>
<p>251 / 22 = 11.4. Therefore one full revolution would take 11.4 seconds.</p>
<p>$$\omega = \theta/t$$</p>
<p>$$\omega = 2\pi /t$$</p>
<p>$$\omega = 2\pi/11.4$$</p>
<p>$$\omega = 0.55 \text{ rad/s}$$</p>
<p><strong>Angular Velocity at (B)</strong></p>
<p>$251/18 = 13.9$. Therefore one full revolution would take $13.9$ seconds.</p>
<p>$$\omega = \theta/t$$</p>
<p>$$\omega = 2\pi /t$$</p>
<p>$$\omega = 2\pi/13.9$$</p>
<p>$$\omega = 0.45\text{ rad/s}$$</p>
<p><strong>Angular Acceleration</strong></p>
<p>$$\alpha = \frac{d\omega}{dt} $$</p>
<p>$$\alpha = \frac{0.45 - 0.55}{5 - 0}$$</p>
<p>$$\alpha = -0.1 / 5$$</p>
<p><strong>Answer to Problem</strong></p>
<p>$\alpha = -0.02\text{ }\mathrm{rad/s^2}$</p> | 4,143 | [
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<p>I still don't know what mathematicians mean by <a href="http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations" rel="nofollow">Navier-Stokes</a> existence and smoothness. Since there is a <a href="http://www.claymath.org/millennium/Navier-Stokes_Equations/" rel="nofollow">reward</a> for proving it, it seems important to them. (in past several months I've read online articles on this topic). </p>
<p>Physically, what do we get from such a proof? Is it possible that we <em>don't</em> have existence and uniqueness mathematically, but that our physics still "works" somehow? Also, is there a consensus on whether, based on physical intuition (we are modelling real things after all), there <em>must</em> be existence and uniqueness to the pure math problem?</p> | 4,144 | [
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<p>I always heard that three atomic force in small scale structure (Strong, weak and electromagnetic) are unified through the <a href="http://en.wikipedia.org/wiki/Standard_Model" rel="nofollow">standard model</a>, but I've never seen its unified equation. What is single unified equation that describes these three forces?</p>
<hr>
<p>As the Motl answer is not really answer but kidding, I'm still wait.</p> | 4,145 | [
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<p>Apologies if this is a little vague. It might not have a good answer.</p>
<p>Given the interpretation of $|\psi(x)|^2$ as a probability distribution it's unsurprising that a wave function that is concentrated around a point $x$ should behave at least a little like a classical particle at the point $x$.</p>
<p>Is there a similarly intuitive explanation for why a plane wave function $\exp(ik\cdot x)$ behaves somewhat like a classical particle with momentum $\hbar k$? I'm not looking for the standard explanation in terms of eigenstates of the momentum operator, but something that can be used pedagogically for people whose linear algebra isn't sophisticated enough for that.</p>
<p>For example it's not hard to see that a plane wave in n-dimensions has a direction associated with it but it's not intuitively obvious to me that a higher frequency wave should have a higher momentum (unless I reason via the Schrödinger equation which I don't want to do). It's also not surprising that a plane EM wave carries momentum, after all it can interact with charged matter via the Lorentz force and transfer momentum to it, but wave functions don't have such a straightforwardly interpretable interaction.</p>
<p>So how can we make it unsurprising that a plane wave function has a definite momentum?</p> | 4,146 | [
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<p>I'm a bit confused on the topic of refraction, some starting premises:</p>
<p>1) When light refracts from exiting a medium with a low n and entering a medium with high n the light bends. </p>
<p>2) The index of refraction, n, supposedly is lower for longer wavelengths than others (why exactly this is, is difficult to understand) which is why we have chromatic dispersion of white light. I.e. although we're given n for certain substances, n is actually wavelength dependent</p>
<p>3) The speed of light slows down when traveling in media with higher index than 1 (vacuum).</p>
<p>4) Frequency of a light wave doesn't change as it enters a new medium</p>
<p>====</p>
<p>Because of 3 and 4, wavelength must decrease if the speed light travels in a medium decreases. what does this mean for the color of light? wavelength has changed but the frequency hasn't. E.g. do we perceive red colored light in the air the same as red if we view it underwater?? (maybe another way of asking this is, does the color change as light passes through different media)</p>
<p>If light underwent refraction from air to water for instance (1), what happens if there's another medium? From 2, n would differ with different "wavelengths" but would you use the new wavelength after it passed through the water or would you use the wavelength from the light as if it were in a vacuum?? (i.e. is it really "wavelengths" that determine these differing n's or is it the frequency)</p>
<p>If someone can give an easy to understand explanation WHY n would differ with different wavelengths ie #2 (also why isn't it said that n differs with frequency??)</p>
<p>If this sounds confusing please ask me to clarify or restate my questions</p>
<p>THANKS!</p> | 4,147 | [
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<p>Suppose I have a large 2D flat rubber sheet of a given stiffness. I mark a point on the sheet at polar coordinates $(\rho, \theta)$. Then I insert a pencil in the center of the sheet and I leave the pencil there. The pencil creates a round hole of radius $r$ centered at $(0, 0)$. Assuming the sheet does not fold into the third dimension, the point that I marked at the beginning has moved away from the center and is now at ($\rho'$, $\theta$). What is the value of $\rho'$ as a function of $\rho$? I don't care about the special case where $\rho = 0$.</p> | 4,148 | [
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] |
<p><strong>EDIT</strong>: Additional question at the end</p>
<p>I am trying to illuminate how the "unphysical" gauge bosons $W^{1}_{\mu},W^{2}_{\mu},W^{3}_{\mu},B_{\mu}$ will be the "physical" $W^{\pm},Z_{\mu},A_{\mu}$ when diagonalizing the mass matrix. Notice that it is in Euclidean time, so we do not have to care about the Lorentz indices. Furthermore $\sigma(x)$ is the Higgs field and $v$ is the vacuum expectation value.</p>
<p>After the symmetry breaking
$$
SU(2)_L\times U(1)_Y \rightarrow U(1),
$$</p>
<p>and inserting the vacuum expecation value, I got the following Lagrangian (just the dynamical part):</p>
<p>$$
\frac{1}{2}D_{\mu}\phi^{\dagger}D_{\mu}\phi = \frac{1}{2}\partial_{\mu}\sigma \partial_{\mu} \sigma + \frac{(v+\sigma)^2}{8}(g^2W^{1}_{\mu}W^{1}_{\mu} + g^2W^{2}_{\mu}W^{2}_{\mu} + (gW^{3}_{\mu} - g'B_{\mu})(gW^{3}_{\mu} - g'B_{\mu})) .
$$
$W^{\pm}=W^{1}_{\mu}\pm W^{2}_{\mu}$ is clear, but retrieving $Z_{\mu}$ and $A_{\mu}$ not. I tryied the following, since the last part of the Lagrangian can be written like:<br>
$$
(W^{3}_{\mu},B_{\mu}) \begin{pmatrix}g^2 & -gg'\\-gg'& g'^{2} \end{pmatrix} \begin{pmatrix}W^{3}_{\mu}\\B_{\mu} \end{pmatrix}
$$
The diagonlized matrix reads
$$
M_D=\begin{pmatrix}0 & 0\\0& g^2 +g'^{2} \end{pmatrix}
$$
and does not give the right linear combinations of $Z_{\mu}$ and $A_{\mu}$, which are given in my literature as
$$
A_{\mu} = \frac{g'W^{3}_{\mu} + g B_{\mu}}{\sqrt{g^2+g'^2}},\qquad Z_{\mu} = \frac{gW^{3}_{\mu} - g' B_{\mu}}{\sqrt{g^2+g'^2}}
$$
My question is now, how to get these combinations, it looks like I am close, but only close. And the other question where comes the normalization conditions for the field from?</p>
<p>Cheers!</p>
<p><strong>EDIT</strong>: </p>
<p>I finally found the linear combinations, mass eigenstates, like they are in the literature, by inserting not only the diagonlized mass matrix $M_D$, but by inserting $M = PM_DP^{-1}$
As I was looking at the covariant derivative to find out how the fields couple to the Higgs doublet I was wondering how I could possibly turn the following matrix into mass eigenstates of the gauge fields:</p>
<p>$$
\frac{i}{2}\begin{pmatrix}gW^{3}_{\mu} + g'B_{\mu} & 0\\
0& g W^{3}_{\mu} + g'B_{\mu}\end{pmatrix}
$$</p>
<p>again, cheers!</p> | 4,149 | [
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<p>I'm having some trouble doing an easy computation with the AdS space. I'm considering $\text{AdS}_3$ space with the Poincaré coordinates, so the metric reads</p>
<p>$$ds^2 = \frac{R^2}{z^2}(dz^2 - dt^2 + dx^2)$$</p>
<p>I want to compute the geodesics for a $t=\text{const.}$ slice, in order to obtein the holographic entanglement entropy for the region $x\in[-l/2,+l/2]$, as described in <a href="http://arxiv.org/abs/1204.2450" rel="nofollow">this</a> paper (eq. 12 to 14).</p>
<p>So, I set $t = \text{const.}$ and I compute the geodesics equations:</p>
<p>$$\ddot{z} + \frac{1}{z}(-\dot{z}^2 + \dot{x}^2) = 0$$</p>
<p>$$\ddot{x} - \frac{2}{z}\dot{z}\dot{x}=0$$</p>
<p>As the paper says, the solution should be the semicircunference $x = \sqrt{(\frac{l}{2})^2-z^2}$, or written in parametric form:</p>
<p>$$x = - \frac{l}{2}\cos \pi\lambda$$</p>
<p>$$z = \frac{l}{2}\sin \pi\lambda$$</p>
<p>with $\lambda\in[0,1]$.</p>
<p>But if I substitute this solution into the geodesics equations I don't get they are satisfied. So, what do you suggest is my problem?</p> | 4,150 | [
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<p>I'm beginner and amateur interested by the quantum physics.</p>
<p>I would like to know if it exists entanglements systems at natural state or it requires mandatory an human intervention ?</p>
<p>Is it possible ? Either no or yes, Why ?</p>
<p>Thanks</p> | 4,151 | [
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] |
<p>If you see through small enough aperture, you can see things without glasses. </p>
<p>How does this trick work?</p> | 4,152 | [
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<p>I have been looking in to alternating current and I am confused. If the voltage reverses doesn't the flow of electrons also reverse? I am aware of another fair answer on this site <a href="http://physics.stackexchange.com/q/28036/">here</a>. That answer, however, confused me just a bit. I gathered that the electrons do not per se "flow." Is this true? How is the electrical current moving? </p> | 124 | [
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<p>The theory of Inflation explains the apparent consistency of the universe by proposing that the early universe grew exponentially for a 1E-36 seconds. Isn't a simpler explanation that the universe is just older and so the homogeneousness comes from a slower more steady growth? Is there any evidence that rules out a slow growing universe and supports Inflation theory?</p> | 123 | [
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<p>I understand how telescope, microscope and glasses work.<br>
But how do contact lenses work?</p> | 4,153 | [
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<p>I've been working with some dust solutions in General Relativity, practicing calculating the Riemann curvature tensor, and I came across an odd metric: the Tolman-Bondi-de Sitter metric. A quick internet search (to supplement the book I'm reading) can tell you that it describes spherical dust, while accounting for a cosmological constant. It's a pretty simple solution, with a line element of the form</p>
<p>$$ds^2=dt^2-e^{-2\Psi(t,r) } dr^2-R^2 (t,r)d\theta^2-R^2 (t,r) \sin^2\theta d\phi^2$$</p>
<p>There's one term in there that has me a bit befuddled, and that I can't find an explanation for in a book or on the Internet: $\Psi(t,r)$</p>
<p>At first, I thought it had to be a simple wavefunction, but after looking at it more, I'm not quite sure. What is it, and what is its significance in the metric?</p> | 4,154 | [
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<p>This is a very cool, and highly beneficial problem in my opinion. I feel as though truly understanding this proof would broaden anyone's conceptual understanding of electric potential.</p>
<p>My textbook asks me to utilize the identity: </p>
<p>$\bigtriangledown(\phi\bigtriangledown\phi) = (\phi\bigtriangledown)^2 + \phi\bigtriangledown^2\phi$ </p>
<p>and the divergence theorem to prove that the potential energy of a system of charges $U_E = \cfrac \pi8\int_{entire-field}E^2dv$ and the work that it takes to assemble a charge distribution $U_w = \cfrac 12\int \rho\phi dv$ are "not different" for all charge distributions of finite values.</p>
<p>So far, I have decided to substitute $-\bigtriangledown^2\cfrac{1}{8\pi}$ in for $\rho$ so that I can use the given identity [ I also had to rearrange the ordering to $\phi\bigtriangledown^2\phi = \bigtriangledown(\phi\bigtriangledown\phi) -(\phi\bigtriangledown)^2 $] and ascertain that $U = \cfrac \pi8\int \bigtriangledown(\phi\bigtriangledown\phi)dv - \cfrac \pi8\int \phi\bigtriangledown^2\phi dv, $ but now I am stuck. I know that the next step must have to do with using the divergence theorem to simplify this thing though. Any help would be greatly appreciated.</p> | 4,155 | [
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<p>This question concerns the physics behind the implementation of electronic compasses to find the orientation of a device.</p>
<p>In the robotics community, <strong>3-axis magnetometers</strong> are often used for this purpose. After some calibration, these provide a three-dimensional vector indicating the direction of the earth's magnetic field relative to the sensor.</p>
<p>As a second step, apparently a process called "tilt" detection is carried out. This uses a <strong>3-axis accelerometer</strong> to measure the vector of earths gravitational field relative to the sensor and use it to determine roll and pitch of the device.</p>
<p>The roll and pitch angles are then used to somehow "compensate" the magnetic measurement for the tilt of the device.</p>
<p><strong>What is the purpose of this tilt compensation? Why is it needed? Could it not be made obsolete by combining the position data from a gps with earth magnetic maps?</strong></p>
<p>Am I understanding correctly when concluding that at the equator no tilt correction is necessary while close to the poles the errors are large without tilt correction?</p>
<p>I am not looking for implementation details but a easy to understand physics reasoning of what the problems are that are being solved by the "tilt compensation" and what alternative solutions are to measuring the earthy gravity field.</p> | 4,156 | [
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<p>When describing the defining characteristics of bosons and fermions, I have a problem with the idea of "label switching" - whereby you have the wavefunction for two particles and the particles' labels in the wavefunction are switched and we look at the effect. The wavefunction remains the same: particles are bosons. If not, they are fermions. This is probably a silly question, but if the particles are indistinguishable how can we assign labels to them? </p> | 4,157 | [
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<p>Take a gravitational field (with all the field lines pointing inwards) and a perfectly circular curve as an object's trajectory. To find the work exerted by the force on the object, compute the line integral $\oint_C\overrightarrow{F} \cdot \overrightarrow{v}=Work=0$; which is to be expected as there is no tangential component to a conservative force, and $\overrightarrow{F} \cdot \overrightarrow{v}=0$ everywhere. </p>
<p>However, work <em>is</em> being done on the planet as it isn't moving in a straight line, and $\overrightarrow{F} $ is the only force around to provide this work.</p>
<p>Therfore, is perfect circular motion unphysical? Is the real motion more like Newton's 'infinitesimal pulling in' model pictured below, the downward pulls being the points where $\overrightarrow{F} \cdot \overrightarrow{v} \ne 0$, for instance? Have I misunderstood something?</p>
<p><img src="http://i.stack.imgur.com/4VFL9.png" alt="enter image description here"></p> | 4,158 | [
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<p>I'm learning some applications for equation of motion. But I'm failing to relate velocity, acceleration and position.</p>
<p>If $v=\frac{dr}{dt}$ and $a=\frac{dv}{dt}$, why $a$ is $\frac{d^2r}{dt^2}$ instead of $\frac{dr}{dt^2}$? Probably i'm lacking basic calculus or physics.</p> | 4,159 | [
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<p>In Feynman's simple QED book he talks about the probability amplitude P(A to B) ,where A and B are events in spacetime, and he says that it depends of the spacetime interval but he didn't put the expression. I would like to know what expression was he referring to.
He said then that the amplitudes for a photon to go faster or slower than c are very smaller than the contribution from speed c. How is that this contributions cancel out for long distances?</p>
<p>I would like also that you explain how it is related to the path integral of the form exp(iKL) of the question <a href="http://physics.stackexchange.com/questions/10967/how-is-the-path-integral-for-light-explained-or-how-does-it-arise">How is the path integral for light explained, or how does it arise?</a>
I think this path integral is very strange because it doesn't have spacetime fixed points but space fixed points. Its paths doesn't have the same time if we assume speed constant so they wont reach the same event.</p> | 4,160 | [
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<p>It is known that there is a famous quantum factorization algorithm by Peter Shor. The algorithm is thought to be suitable only for quantum gate computer.</p>
<p>But can a an adiabatic quantum computer especially that which is capable of quantum annealing be used for factorization?</p>
<p>I am asking this because it seems that Geordie Rose <a href="http://dwave.wordpress.com/2011/05/11/learning-to-program-the-d-wave-one/#comment-22008">claims</a> in his blog that they have a quantum factorization algorithm that is somehow "better than Shor". But the details are unavailable as of now.</p> | 4,161 | [
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] |
<p>In the <a href="http://en.wikipedia.org/wiki/NEAR_Shoemaker" rel="nofollow">wikipedia article about NEAR Shoemaker</a> it is mentioned that the craft stopped operating under these conditions:</p>
<blockquote>
<p>At 7 p.m. EST on February 28, 2001 the last data signals were received from NEAR Shoemaker before it was shut down. A final attempt to communicate with the spacecraft on December 10, 2002 was unsuccessful. This was likely due to the extreme -279 °F (-173 °C, 100 K) conditions the probe experienced while on Eros.[6]</p>
</blockquote>
<p>I could understand the lack of sunlight during the Eros night being a contributing factor, but that is not mentioned specifically. Are the conditions near an asteroid much harsher for spacecraft than interplanetary space?</p> | 4,162 | [
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<p>There is a <a href="http://io9.com/5811236/this-is-the-coolest-science-experiment-youll-see-all-week" rel="nofollow">video</a> of an experiment from University of Mexico using corn syrup (highly viscous) and water. They are "mixed together" in a container by turning a crank but when the crank is turned in the opposite direction they neatly un-mix.</p>
<p>I understand that the two liquids actually do not blend, but how can the syrup droplets be returned to very close to their initial state. It looks as if the entropy is greatly reduced. Is the increase in temperate of the liquids (through the turning of the crank) the answer?</p> | 4,163 | [
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<p>I've heard mentioned in various classes that neutron stars, like superconductors, are described by BCS theory. I know that in superconductors a key element in forming cooper pairs is a net attractive force between the electrons which would normally repel one another. That attractive force is accounted for via lattice vibrations (phonons) created and "absorbed" by electrons. </p>
<p>So my question is: what provides the attractive force between neutrons? just gravity? If it is true that neutron stars follow BCS theory, by what means was someone able to verify that?</p> | 4,164 | [
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<p>In the <a href="http://www.bipm.org/en/CGPM/db/3/2/" rel="nofollow">Resolution 2 of the 3rd meeting of the CGPM</a>, defining the <a href="http://www.bipm.org/en/si/si_brochure/chapter2/2-1/kilogram.html" rel="nofollow">kilogram</a>, “the International Service of Weights and Measures” is mentioned (the <a href="http://www.bipm.org/fr/CGPM/db/3/2/" rel="nofollow">French original text</a> reads “le Service international des Poids et Mesures”). I wonder which organization this should be, and I am unable to find any other mention on Google except quotations of the resolution.</p>
<p>(Sorry if this question is considered off-topic here, I thought Physics would be the best match.)</p> | 4,165 | [
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<p>I was blown away by the abundance of good info here, and I thought maybe you could help me out with this query. I am in the process of developing a product, and I need to find a clear plastic resin (visually clear) that is also transparent to x-rays (medical application). The only only other characteristic that I need is durability (scratch-resitant). Any advice?</p> | 4,166 | [
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<p>Consider an electron described by a wave packet of extension $\Delta x$ for experimentalist A in the lab. Now assume experimentalist B is flying at a very high speed with regard to A and observes the same electron. The extension of the wave packet will appear contracted, and the uncertainty on momentum will increase. What happens when the later become larger than the electron's rest mass?</p> | 4,167 | [
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<p>How can we define simply that velocity is a vector quantity without mentioning that velocity has vector properties. How can we simply say it needs both magnitude and direction for its complete description? Well for magnitude it is clear but for direction being a necessary for its complete description I found it hard clear the concept on the subject?</p> | 4,168 | [
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<p>After watching a few videos on <a href="http://en.wikipedia.org/wiki/Light" rel="nofollow">light</a> and <a href="http://en.wikipedia.org/wiki/Electromagnetic_radiation" rel="nofollow">electromagnetic radiation</a>, I am a little confused.</p>
<p>The way things are explained, is that light is just the same as electromagnetic radiation
I thought this would be strange as then microwaves and radios would also be called light.
Plus, I am not sure of the origin of the word photon, but in Japanese which I use it is 光子 which kind of translates to light molecule.</p>
<p>I found an answer to this:</p>
<blockquote>
<p><em>electromagnetic radiation to which the organs of sight react, ranging in wavelength from about 400 to 700 nm</em> (<a href="http://dictionary.reference.com/browse/light?s=t" rel="nofollow">http://dictionary.reference.com/browse/light?s=t</a>)</p>
</blockquote>
<p>However, after searching the web it seems that this is approximately the same spectrum for humans. So, is there a difference between light and visible light? If not, why use visible light?</p> | 125 | [
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] |
<p>I'm looking for guidance to choose material for a self-study of <a href="http://en.wikipedia.org/wiki/Photonics" rel="nofollow">photonics</a>, biased towards <a href="http://en.wikipedia.org/wiki/Optical_computing" rel="nofollow">optical computing</a> recent advances.</p>
<p>My background is of undergraduate level electrodynamics, quantum mechanics, statistical mechanics, and so on.</p> | 4,169 | [
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<p>Why is the anticommutator actually needed in the canonical quantization of free Dirac field?</p> | 4,170 | [
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<p>I had a left over coffee cup this morning, and tried to wash it out. I realized I always instinctively use hot water to clean things as it seems to work better. </p>
<p>A google search showed other people with similar results, but this yahoo <a href="https://answers.yahoo.com/question/index?qid=20120808093022AAeMKbL">answer</a> is a bit confusing in terms of hot water "exciting" dirt. </p>
<p>What is the physical interaction between hot water and oil or a material burnt onto another vs the cold water interaction?</p> | 4,171 | [
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<p>Consider the scenario where you measure the time it takes for light to travel to the left 10 meters and to the right 10 meters. Both measurements will take the same time, even though we are moving through space at crazy speeds. This must mean that light is not moving relative to "space" as a whole. What does it move relative to? The light emitter? If so, try shooting two beams of light 10 meters from the wall. The first time the emitter is stationary; the second time it is moving at 100 m/s. Am I mistaken in thinking that it would hit the wall slightly faster? Wouldn't this light be moving faster than the light emitted from the stationary source?</p> | 4,172 | [
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<h1>The Question</h1>
<p>If the three vector electric and magnetic fields come from the four component four-potential, then is there a fourth component to the electric and magnetic field?</p>
<h1>Related Question</h1>
<p>I posted the following question: <a href="http://physics.stackexchange.com/questions/103664/express-maxwells-equations-in-terms-of-dipole-field-equations">Express Maxwell's equations in terms of dipole field equations?</a> . I remember along time ago I wrote Maxwell's equations down and I crossed the fields with the position vector and I was able to transform Maxwell's equations from a monopole charge source to something that appeared to be a dipole sourced field equations. When I did this it revealed a bizarre fourth component in the field equations which I think might be related to this question, </p> | 4,173 | [
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<p>Mathematically, I'm having trouble understanding where we can use what with light. I read somewhere on this site that Huygen's Principle is effectively just taking an expansion of a wave onto the spherical harmonics, (<a href="http://physics.stackexchange.com/questions/89884/is-huygens-principle-axiomatic">Is Huygen's Principle Axiomatic?</a> comment by gatsu) and on another on of my question, I was told that the image produced from a lens is some how related to a fourier transform of the incoming light. That answer is here: <a href="http://physics.stackexchange.com/questions/80808/why-cant-we-perfectly-focus-light-abberations-aside">Why can't we perfectly focus light-abberations aside</a>
So my question is, why are these two ideas appropriate for light? What is the general statement for either of these? Does the fourier transform always have some relation with lenses, and why does an expansion on the spherical harmonics have a name, is it a fundamental quality of light?</p> | 4,174 | [
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<p>What would the properties of a particle be that would allow light to orbit it?</p>
<p>Light travels fast. <em>Really</em> fast. Almost to the point where we consider that it's instantaneous, and moves only in a straight line.</p>
<p>We know that's not true though. Light can be influenced in such a way so as to cause it to change course. "Bend" if you will.</p>
<p>Black holes influence light strongly enough as to cause the light to be pulled in without escaping. (at least, as far as we know. right?)</p>
<p>This gives me the fundamental basis for thinking that it would be possible to influence light enough to allow it to orbit a particle. I'm curious if anyone has an idea of what properties a particle like this would have, how it could be described, and whether or not it could exist in our physical reality.</p> | 126 | [
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<blockquote>
<p><em>Unlike mass, the charge on an object is said to be unaffected by the motion of the object.</em> </p>
</blockquote>
<p>This statement in my text book, is not yet understood by me. I don't know theory of relativity. On expressing my inability in understanding this particular line. My sir said that, the statement understanding needs knowledge about theory of relativity. Sir said that, according to theory of relativity, mass doesn't remain constant during object's motion. And sir expressed their inability to make me understand this particular line because of lack of knowledge on this topic. </p>
<p>I got a doubt from the statement made by my teacher. If mass varies during motion, why do charge remain constant. What I thought is, charge is the property of all the substances. If mass varies, charge should also vary. Because, electron and proton are the particles exhibiting charge property, and they are the part of that particular mass which varies during motion. Then, why is it said that charge remains unaffected during the motion of the object? </p>
<p><em>EDIT</em>: I tried to answer myself, if we consider a neutral body and assume mass varies discretely by the mass of atom, even though mass varies, net charge remains constant. So, here constancy of charge is maintained. But, if we consider a charged body in motion or uncharged body with variation of mass continuously, charge should also vary with change in mass. I don't know whether I am right in predicting this, but this what I have thought.</p> | 4,175 | [
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<p>When we define $\mathcal{N}=4$ SYM on flat Minkowski space, the supersymmetric vacua are parametrized by scalars living in the cartan subalgebra of the gauge group. A generic point in the moduli space breaks the SU(N) to $U(1)^r$ where r is the rank of the cartan subalgebra. This is called the Coulomb branch for obvious reasons. On page 59 of this review </p>
<p><a href="http://arxiv.org/pdf/hep-th/9905111v3.pdf" rel="nofollow">http://arxiv.org/pdf/hep-th/9905111v3.pdf</a></p>
<p>it is stated that when we put the theory on $\mathbb{R} \times S^3$ (so that the dual will live on global AdS instead of the Poincare patch), the Coulomb branch is lifted because the scalars are conformally coupled through a term
$\int d^4x Tr(\phi^2)R$. </p>
<p>Why is it that the scalars are conformally coupled? It makes some sense to me that putting a CFT on a sphere should introduce some scale (radius) and could lead to some conformal anomaly (ex central charge and cylinder in string theory). But I was under the impression there is no unique way to know, given the theory in flat space, what the covariantization should be. In other words, there are lots of terms I could use to couple fields to the curvature that would vanish in the flat space limit.</p>
<p>In strings for instance, I could take a free scalar. That defines one CFT. I could also consider a scalar with a background charge that couples to the curvature through a term like $Q\int \phi R$. This would give me the linear dilaton CFT, a totally different CFT with different primaries etc.</p>
<p>So my question is why do the authors assume that the scalars are conformally coupled? Is this a general principle in QFT in curved space or is it arbitrary?</p> | 4,176 | [
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<p>The stability group $G_\Sigma$ is a subgroup of the Poincare group $P(1;3)$. Its generators $X$ in the <strong>front form</strong> leave the hypersurface $\Sigma: x^+ = 0$ invariant. Phrased differently they satisfy the condition: $x'^{+} = x^+ + [x^+, X] = x^+ = 0$. So, for the generators $X$ of the stability group we have $$ [x^+, X]=0 . $$</p>
<p>How can I relate the matter of leaving the hypersurface invariant with the condition: $x'^{+} = x^+ + [x^+, X] = x^+ = 0$ ?</p> | 4,177 | [
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<p>I am trying to gain an intuitive picture of what is referred to by "electron-shell energy". I have read that outer electron shells have higher energy than inner electron shells, and this seemed to make sense to me by analogy to a wheel — a point on the rim of a wheel moves faster than a point on the hub. However, I have also read that electrons in inner shells move faster than those in outer shells, that in particularly heavy atoms, relativistic effects have to be taken into account for the inner shells to determine the chemical behavior of the element. And if inner shells are smaller, doesn't that mean that for an electron to be in such a shell, it would need a shorter wavelength, thus higher energy? Can anybody shed some light on my confusion?</p>
<p><strong>Edit:</strong> I posted my question because there is an aspect to this that I feel has not been addressed in that other question about the speed of electrons, but I did not express it clearly enough. I recognize that the billiard-ball picture of electrons is not right, and getting beyond that picture is not my difficulty. It is that for all I read that speed is not a relevant concept in this context, I nevertheless keep running into mention of electron "speed" in technical literature, like in a recent SA article, <a href="https://www.scientificamerican.com/article.cfm?id=cracks-in-the-periodic-table" rel="nofollow">Cracks in the Periodic Table</a> (Scientific American, June 2013), and in the Wikipedia article <a href="http://en.wikipedia.org/wiki/Electron_configuration#Other_exceptions_to_Madelung.27s_rule" rel="nofollow">Electron Configuration</a>:</p>
<blockquote>
<p>For the heavier elements, it is also necessary to take account of the effects of Special Relativity on the energies of the atomic orbitals, as the inner-shell electrons are moving at speeds approaching the speed of light.</p>
</blockquote>
<p>So, speed is not a relevant concept in the context of electron shell energies, except when it is? Can somebody help me sort out the conflicting messages here?</p> | 4,178 | [
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<p>What are <a href="http://en.wikipedia.org/wiki/Coherence_%28physics%29" rel="nofollow">coherent</a> and incoherent radiation?</p>
<p>I am a mathematician who is self-learning physics. In reading Jackson's electrodynamics and other books, I often hear that radiation is incoherent or coherent. What does this mean? Does it just mean that the phases are the same in coherent radiation and are different in incoherent radiation?</p> | 4,179 | [
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<p>I'm studying a circuit in AC. I use a function generator and set a waveform.
I have a solenoid and I put a small solenoid inner it.
Could you tell me if there is a relation between frequency and emf inducted on the second solenoid?</p> | 4,180 | [
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<p>I want to know what is the smallest device that can work on a few milli amps? I know a NE-2 neon bulb works on less than 10 mAmp but on 90 volts at least.</p>
<p>I need to find a small device that:
1- Consumes electricity
2- works independently (just by hooking it to a battery)
3- Operates on a few volts
4- Operates on very few amps
5- Preferably a device that works by ionizing air (like a neon bulb), not a direct resistance.</p> | 4,181 | [
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<p>When light from an object passes through a convex lense, it gets reconverged at a single real image. From there, the light rays presumabely begin diverging again, exactly as if there was a light-emitting object sitting at the real image point.</p>
<p>Why is it that if we look at the real image point, we don't see a hologram of the object sitting there?</p> | 4,182 | [
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<p>In the semi-classical model of a crystal in solid state physics, electrons and holes are assigned effective masses that account for their different mobilities. E.g. in silicon, holes have a bigger mass than electrons. This results in different electron/hole densities as the temperature increases.</p>
<p>Why do those different densities not violate conservation of charge? In what way do these imaginary electrons/holes correspond to real particles, in what way do they not?</p> | 4,183 | [
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<p>Has anyone done any research about the upwind vehicle <a href="http://www.popsci.com/cars/article/2012-07/wind-powered-car-travels-upwind-twice-speed-wind" rel="nofollow">http://www.popsci.com/cars/article/2012-07/wind-powered-car-travels-upwind-twice-speed-wind</a>?</p>
<p>I think it is impossible but get a surprising number of disputes from some pretty educated people. It seems to me that if it were possible for a wind powered vehicle to go into the wind at greater than the speed of the wind X, then it would follow that on a windless day, a Ford F-150 towing the same vehicle at speed X (equaling the relative wind), would allow the vehicle to accelerate and pass the Ford, which is absurd, especially considering that the towed vehicle only needs to overcome the rolling coefficient of friction while the self starting vehicle must overcome the static coefficient of friction. </p>
<p>Am I overlooking something?</p> | 127 | [
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<p>Would this be a valid equation to calculate kinetic energy created from a drop from a height:</p>
<p>$$E_{kinetic} ~=~ v_{vertical}tmg$$</p>
<p>Velocity multiplied by time gives distance. Distance multiplied by gravitational force acting on it provides kinetic energy. Would this equation be valid?</p> | 4,184 | [
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<p>I'm following the proof of <a href="http://electron6.phys.utk.edu/qm2/modules/m4/projection.htm" rel="nofollow">Wigner-Eckart projection theorem</a> which states that:</p>
<p>$$\langle \bf{A} \rangle ~=~ \frac{\langle \bf{A} \cdot \bf{J} \rangle}{\langle {\bf{J}}^2 \rangle} \langle \bf{J} \rangle $$</p>
<p>if ${\bf J}$ is conserved.</p>
<p>There is an equation:</p>
<p>$$ \langle k'jm | {\bf J} \cdot {\bf A} | k j m\rangle = m \hbar \langle k'jm | A_0 | k j m\rangle + \frac{\hbar}{2} \sqrt{j(j+1) - m(m-1)} \langle k'j(m-1) | A_{-1} | k j m\rangle - \frac{\hbar}{2} \sqrt{j(j+1) - m(m+1)} \langle k'j(m+1) | A_{+1} | k j m\rangle ~\stackrel{(1)}{=}~ c_{jm} \langle k'j \| {\bf A} \| k j \rangle$$</p>
<p>Now, why on the left of (1) there are components of the vector while on the right it is vector itself?
I suppose it may be due to:</p>
<p>$$\alpha \langle j \| A_0 \| j \rangle + \beta \langle j \| A_{-1} \| j \rangle + \gamma \langle j \| A_{+1} \| j \rangle ~\stackrel{(1)}{\equiv}~ c \langle j \| {\bf A} \| j \rangle $$
but what justifies this simplified notation?</p> | 4,185 | [
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<p>I have two sets of data (globular clusters), one for the Andromeda Galaxy and one for the Milky Way.</p>
<p>I want to compare the distribution of globular clusters between the two galaxies according to their distance from the galaxy's centre, but the measurements they use in each are different.</p>
<p>Andromeda has X-Y locations for the GCs in arcminutes, with R = sqrt(X^2 + Y^2)</p>
<p>The MW data has X-Y locations in kpc from the galactic centre. It also has a value for R_gc (distance from galactic centre) in kpc.</p>
<p>What's the easiest way to convert one of these sets so I can compare the two populations?</p>
<p>I would suspect it would be easier to convert the Milky Way data into arcminutes. I am aware of a way to get R_projected values, R_projected = Pi/4*R_gc but I'm not sure if that's what I need to do. Or is there something else I should be looking at? </p>
<p>Thanks.</p> | 4,186 | [
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