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<p>I just found this news article: <a href="http://www.nature.com/nature/journal/v481/n7379/full/nature10695.html" rel="nofollow">http://www.nature.com/nature/journal/v481/n7379/full/nature10695.html</a></p>
<p>What did those researchers actually do? The article itself doesn't sound to me like it can be taken seriously, so... what was the experiment and what was observed?</p> | 4,636 | [
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<p>Is spacetime moving in general relativity?</p>
<p>If not, how does spacetime retain its past, while moving toward future?</p> | 4,637 | [
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<p>In his <em>Principles of Quantum Mechanics</em> Dirac writes: $$\int \langle \phi \frac{d}{dq}|q'\rangle dq' \psi(q')=\int \phi(q') dq' \frac{d\psi(q')}{dq'}.$$</p>
<p>To me it is rather strange, and it seems as if he was treating the operator $\frac{d}{dq}$ as a function of the observable canonical coordinate $q$, beacuse for functions of observables he gave the definition: $$f(\xi)|\xi'\rangle=f(\xi')|\xi'\rangle,$$ where $|\xi'\rangle$ is an eigenket of the observable $\xi$. Using this analogy, taking $f(q)=\frac{d}{dq}$ one could write $$\frac{d}{dq}|q'\rangle=\frac{d}{dq'}|q'\rangle$$ but then we would also need to differentiate $|q'\rangle$, since it is a function in $q'$.</p>
<p>So what happens here? Please explain!</p>
<p>Also, as a side question: why does $$\int \langle \phi \frac{d}{dq}|q'\rangle dq' \psi(q')=-\int \frac{d\phi(q')}{dq'} dq' \psi(q')$$ imply $$\langle \phi \frac{d}{dq}|q'\rangle=-\frac{d\phi(q')}{dq'}~?$$ Simply because the results of the integrations equal, that doesn't mean that their arguments also equal.</p>
<p>The book can be accessed <a href="http://www.fulviofrisone.com/attachments/article/447/Principles%20of%20Quantum%20Mechanics%20-%20Dirac.pdf" rel="nofollow">here</a>. The formulas are on page 90, using the books original numbering.</p> | 4,638 | [
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<p>Acceleration due to mechanical force will lessen due to relativistic mass increase as kinetic energy becomes significant near c.</p>
<p>But if acceleration is gravitational, the gain in relativistic mass will produce a corresponding gain in gravitational attraction, so acceleration should be constant (for large M and small m), even as m nears c.</p>
<p>But that would imply that c could be approached and exceeded.</p>
<p>What slows the acceleration to prevent m exceeding c?</p> | 153 | [
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] |
<p>I was informed that:</p>
<blockquote>
<p>There is a maximum density at which we can store information. For a sphere with surface area A, the maximum information that can be contained
within is equivalent to the maximum entropy of a sphere of size A, which is given by S_max = A/(4 L^2), where L is the Planck length [Boltzmann constant set to 1].
Incidentally, that's the equation for the entropy of a black hole.</p>
</blockquote>
<p>Is this true? If so, why or how does it work? Why is the Boltzmann constant set to 1, and how does that relate to the Planck length?</p> | 4,639 | [
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<p>What about considering the microwave background radiation (2.7K if I remember well) as a reference system with some absolute character? Please explains if this question make sense and possible answers.
Thank you.</p> | 4,640 | [
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<p>I am looking for an exact or approximate solution to a statistical lattice-particle problem:</p>
<p>Given a lattice of size $L\times L$ where $\rho\cdot L^2$ particles are randomly distributed, calculate the probability distribution function for $M$ defined as number of pair interactions, i.e. number of edges between adjacent occupied cells. Interactions can be horizontal or vertical, and system has open boundaries (i.e. particle on the edge only has 3 or 2 neighbors to interact with).</p>
<p>My final aim is to design an <a href="http://en.wikipedia.org/wiki/Null_hypothesis" rel="nofollow">$H_0$</a> statistics, given a single realization of the $L\times L$ lattice, and estimate the probability this is a non-random distributed set of particles.</p> | 4,641 | [
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] |
<p>Its difficult to put this into the title.</p>
<p>I was watching the Redbull Jump and noticed that the height of this is at 39 kilometres (24 mi) the atmosphere pressure is at I believe about 0.4% of that at sea-level. I was imagining, what if a large satellite dragged a cable (bungie cord, rope) below it into the atmosphere and the person grabbed onto the cord that is below the satellite, from the position of the Redbull jump altitude. The satellite may or may not be geo-stationary.
Since the atmosphere pressure is low, even if the cable was moving through the atmosphere, its air friction would be relatively low and therefore its movement through the atmosphere wouldn't be much of a concern. Maybe there would be a lower chance of the cable breaking, also less cable length and therefore less weight could be used.</p>
<p>Would this be a better way to get an object into space when compared with a full cable from the satellite to earth as in the traditional space elevator idea <a href="http://en.wikipedia.org/wiki/Space_elevator" rel="nofollow">http://en.wikipedia.org/wiki/Space_elevator</a>.
Can you compare and contrast the two options against each other?</p>
<p>Photo of Red Bull Jump
<a href="http://i.imgur.com/thjAO.jpg" rel="nofollow">http://i.imgur.com/thjAO.jpg</a></p> | 4,642 | [
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<p>In his book "Einstein's mistakes" H. C. Ohanian, the author, holds that Einstein delivered 7 proofs for $E=mc^2$ in his life that all were in some way incorrect. This despite the fact that correct proves had been published and mistakes in his proofs were sometimes pointed out to him. </p>
<p>The first proof e.g. contains a circular line of thought in that it falsely assumes special relativity to be compatible with rigid bodies.<br>
EDIT: Reference: stated by V. Icke, prof. theoretical astronomy at Leiden University in his (Dutch) book 'Niks relatief': "Einstein made an error in his calculation of 1906".</p>
<p>Do you think Ohanian's statement is true or was/is he biased in his opinion?</p> | 4,643 | [
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<p>Here we have electron gas and some other stuff. We expand the Hamiltonian to the 1st order of one single harmonic oscillator's displacement $\vec{u}$. Its equilibrium position is at the origin. Then we get an effective coupling Hamiltonian $\vec{j}(\vec{r})\times\vec{f}(\vec{r})\cdot \vec{u}$, wherein $\vec{j}(\vec{r})$ is the electron density, $\vec{f}(\vec{r})$ is some effective potential.</p>
<p><img src="http://i.stack.imgur.com/hu3t7.jpg" alt="enter image description here"></p>
<p>I assumed a particular mode (frequency $\Omega$ for x,y,z) of $\vec{u}$. And I tried to work out the above diagram. It's doable. </p>
<ol>
<li>In this electron Green's function calculation, do we take into account of the interaction's influence on the oscillator? Is it damped or not?</li>
<li>I'm confused about where the momentum transfer $q$ come from. Potential $\vec{f}(\vec{r})$ or oscillator's motion $\vec{u}$? I only Fourier transform $\vec{j}(\vec{r})$ and $\vec{f}(\vec{r})$ in the Hamiltonian, therefore this $q$ merely appears in terms that come from $\vec{j}(\vec{r})\,,\vec{f}(\vec{r})$. So I suppose this momentum transfer $q$ comes from the potential. Is this correct?</li>
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<p>I saw this <a href="http://www.ted.com/talks/woody_norris_invents_amazing_things.html">TED talk</a> and I am curious as to how the sound is focused on the general level. Can anyone explain this or does anyone have any good articles?</p> | 4,645 | [
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<p>I am having difficulty of finding more basic information on warped geometries. All the standard textbooks are not covering it.</p>
<p>In the <a href="http://en.wikipedia.org/wiki/Warped_geometry" rel="nofollow">wiki article</a> it's only said that warped geometry is the one which can be decomposed in a certain way, but there are no details. All the articles mentioning warped AdS geometry refers to topological massive gravity.</p>
<p>If someone can tell me where I could find some introduction to warped geometries and it's uses, that would be great. </p> | 4,646 | [
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] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/312/particle-physics-getting-started">Particle physics getting started</a> </p>
</blockquote>
<p>I'm looking for a book that introduces the building blocks refer to the standard model for a course in nuclear physics. There are good books on this?</p> | 154 | [
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<p>Question shortly:
How far would a hockey puck slide in two different cases:</p>
<ol>
<li>The puck is sliding (translation) on ice and spinning on its flat surface. </li>
<li>The puck is sliding on ice without spinning. </li>
</ol>
<p>Other conditions are the same in both cases. </p>
<p>Simplifications: no air resistance, the coefficient of friction is const while sliding(spinning)<br>
Let's formalize the problem: </p>
<p>Given a disc with diameter D = 8 cm, mass m=170 g, the coefficient of friction on ice let be $\mu=0.02$
Initial values: </p>
<ol>
<li>$v_0=10 \frac{m}{s}$ and $\omega_0=100 \frac{rad}{s}$ </li>
<li>$v_0=10 \frac{m}{s}$ and $\omega_0=0 \frac{rad}{s}$ </li>
</ol>
<p>Obviously the part 2) is trivial. I am working currently on part 1). This seems to be very difficult. Instead of a solid disc i took a thin ring at first. But even in that case the solution seems to be an integro-differential equation. If you have some ideas let us know.</p> | 4,647 | [
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<p>If a butterfly did not flap its wings some time ago, but instead decided to slide for that millisecond, can this cause a tornado on the other side of the earth if we just wait long enough? Does this perturbation die out, or average out in short time, or does it propagate and have grander and grander consequences?<br>
(Clearly there are cases where it propagates, ie if its wings were artificially connected to trigger some nuclear bomb, but is it always so that it propagates?)</p>
<p>Is there some clear-cut criteria to determine whether a perturbation propagates or dies out?</p>
<p>Is the answer different if the world was purely classical versus QM? </p> | 4,648 | [
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<p>I'm using a game engine that has a ton of physics stuff built in. What I am currently trying to do is to simulation an explosion with F force in an x,y coordinate system and figure out how other items in the world are affected by it (they each have x,y as well).</p>
<p>The ultimate function I call is applyForce and it takes an x,y vector in Newtons for the force and a point to act on (the other objects in this case).</p>
<p>Currently I am doing the following:</p>
<ol>
<li>Determining the distance of the explosion point for each of the objects' x,y coordinates</li>
<li>If the distance is less than the force F (my total explosion force) then I proceed</li>
<li>I subtract the distance from F and assign that back to F - so this effectively becomes the total force that can act on the object based on distance</li>
<li>I find the angle of the explosion point from the object by atan2(x1-x2,y1-y2)*180/PI</li>
<li>Find the resulting X force by F * cos(angle)</li>
<li>Find the resulting Y force by F * sin(angle)</li>
<li>Use these to assign the Force vector and apply it to the object</li>
</ol>
<p>In general I think this okay but I feel like I am missing something as right now the forces are still a bit sporadic. I think I am making the assumption that the signs of the force (- or +) will be handled by the Trig functions above but I have a feeling that is not the case. From my logs sometimes the angle is -167 and I'm wondering if that shouldn't just be based on a 360 degree system instead? I'm assuming if that's the case then I have to do some logic to assign the correct - or + signs to the forces so it moves in a direction away from the explosion point. Can anyone point me in the right direction? I am a developer so this could be completely off :)</p> | 4,649 | [
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<p>I'm trying to determine the viscous dampening coefficient of a spring $c$. Read about it on Wikipedia <a href="http://en.wikipedia.org/wiki/Damping" rel="nofollow">here</a>.</p>
<p>The two equations which I have are:
$f=-cv$ and $ma+cv = -kx$</p>
<p>I know the spring constant $k=5$, the mass is $50\text{ }\mathrm{g}$ and the initial amplitude of the spring is $10\text{ }\mathrm{cm}$.</p> | 4,650 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/556/what-is-the-fallacy-in-this-infinite-motion-machine">What is the fallacy in this infinite motion machine?</a> </p>
</blockquote>
<p>Most of the "troll physics" images I can figure out, but this one has me stumped. What is broken about the following machine's physics?</p>
<p><img src="http://i.stack.imgur.com/VbmLW.jpg" alt="infinite electricity machine"></p> | 155 | [
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<p>I'm reading Cardy's notes on CFT. He states the following in section 4.3:</p>
<p>$$\hat L_n\left(\hat L_{-2}|\phi_j\rangle-(1/g)\hat{L^2}_{-1}|\phi_j\rangle\right)=0.$$</p>
<p>I tried to work this out explicitly and I managed to prove it for $n=1$ and $n=2$, but I can't figure this out for general $n$. After some manipulations I get stuck here:</p>
<p>$$((n+2)\hat L_{n-2}-(n+1)(1/g)\hat{L}_{n-1})\hat L_{-1}|\phi_j\rangle+(n+1)\hat L_{-1}\hat L_{n-1}|\phi_j\rangle.$$</p>
<p>How is this zero?</p> | 4,651 | [
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<p>For example... If I had a 2W green laser, a 2W red laser, and a 2W blue laser, could I combine them using crystals to form a 6W white laser? Or is that now how it works? If not what would be the output in watts of such a laser?</p> | 4,652 | [
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<p>I had previously asked <a href="https://physics.stackexchange.com/questions/117172/how-to-calculate-gravity-path-integrals-about-an-ads-background">this question</a>. This is kind of a continuation of that. </p>
<p>I recently found this expression which seems to be called the "Fierz-Pauli action" which is apparently the quadratic action for gravitons about $AdS_{d+1}$, </p>
<p>$S = \frac{c }{2 l_p ^{d-1} }\int d^{d+1}x \sqrt{-g} \left ( \frac{1}{4} \nabla_\mu h_{\rho \lambda}( \nabla^{\mu} h^{\rho \lambda} - 2\nabla^\rho h^{ \mu \lambda}) + \frac{1}{2}\nabla_\mu h^{\mu \nu}\nabla_\nu h - \frac{1}{4} \nabla_\mu h \nabla^\mu h - \frac{d(d-1) }{2L^2} ( h^{\mu \nu}h_{\mu \nu} - \frac{1}{2} h^2 ) + O(h^3) \right )$</p>
<ul>
<li>Can someone help derive (or reference) this? </li>
</ul>
<hr>
<p>I am aware of general expressions for curvature invariants expanded to second order in metric fluctuation about some chosen background. But its not clear to me as to how does one covariantly impose that the background is some $AdS$... </p> | 4,653 | [
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<blockquote>
<p><em>A completely isolated neutral conducting sphere of radius $R$ is kept such that its center is at a distance of $r\left(>R\right)$ from a
point charge $+Q$.</em></p>
</blockquote>
<p>How can I find the force of interaction of the induced charges and the point charge, or at least the energy?
I can't use "method of images" because the sphere is not grounded.</p>
<p><strong>Note:</strong> The actual question has a sphere already charged with $+Q$ charge and it asks for the $r$ at which the point charge is in equilibrium. I thought of breaking the force down into a superposition of two forces, one from the $+Q$ of sphere and the other from the induced charges. If there is some other way to solve this, I would like to know that too.</p> | 4,654 | [
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<p>we recently took a tour to a radio telescope and recorded some spectra, one of them being Cassiopeia A. Looking at the difference in on-source and off-source spectra, we find sharp absorption and emission lines in the spectrum for the 21 cm line. Where do they come from? We have different theories:</p>
<ol>
<li>The absorption lines come from the exploding shell and are more redshifted for the part of the cloud moving away from us relative to the part moving to us.</li>
<li>The absorption lines come from hydrogen clouds between Cas A and us and the remaining emission lines are those from the explosing shell which don't correspond to any hydrogen cloud in between.</li>
</ol>
<p>The problem with 2. is -- in my opinion -- that the difference of on- and off-source measurements should cancel out the hydrogen clouds in between. I've attached the measured spectrum below.</p>
<p><img src="http://i.stack.imgur.com/U9ddy.png" alt="Measured Cassiopeia A spectrum"></p> | 4,655 | [
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<p>I'm currently trying to figure out the following in the simplest possible way:</p>
<p>Say we have a nozzle in a vacuum environment.
A gas of a certain pressure is emitted through the nozzle, which has a certain diameter, int the vacuum. The question is now how high is the pressure at a certain distance away from the nozzle exit? </p>
<p>Any help would be greatly appreciated!</p> | 4,656 | [
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<p>How do you tell the difference between a gamma-ray burst and a star just from a picture of a nebula, in which it cannot flash on and off here and there?</p> | 4,657 | [
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<p>I am trying to get my head around why would and silicon engineer care about the minority life time carrier and how does the minority carrier affect the switching speed of PN junction. Why is it so much about minority and not majority carriers?</p> | 4,658 | [
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<p>Given 10-1000 Watts of electrical power (and no other consumables), what is the current best way to turn it into thrust? Just running it through a heater on an insulating pad would result in an IR thruster, but has bad focus. A laser has good focus but only for a small percentage of the energy. </p> | 4,659 | [
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<p>In theories with extended supersymmetry, both short and long multiplets exist. For some reason or other, short multiplets are studied more often. Why? What's wrong with long multiplets?</p> | 4,660 | [
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<p>Let's say 10 kg block is sliding on a frictionless surface at a constant velocity, thus its acceleration is 0. </p>
<p>According to Newton's second law of motion, the force acting on the block is 0:</p>
<p>$a = 0$</p>
<p>$F = ma$</p>
<p>$F=0$</p>
<p>So let's say that block slid into a motionless block on the same surface, the motionless block would move.</p>
<p>Wouldn't the first block need force to be able to move the initially motionless block? I understand that it has energy due its constant velocity, but wouldn't it be its force that causes the displacement?</p> | 4,661 | [
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<p>Eventually, we are going to reach our limits in particle physics, or maybe find the theory of everything. Particle physics isn't easy by any means. It requires at the minimum years of graduate school and more to master. The main motivation of learning is to come up with original research later. But if there is no more research to do in the future, hardly anyone would be motivated to learn particle physics given its intrinsic difficulty. What would happen then? Would knowledge of particle physics disappear because no one would be around to remember it? Or would it become a scholastic tradition passed down dogmatically from generation to generation.</p> | 4,662 | [
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<p>Suppose that an electron with spin up emits a photon in the field of an ion (<a href="http://en.wikipedia.org/wiki/Bremsstrahlung" rel="nofollow">bremsstrahlung</a>). What is the spin of the emitted photon? Is it correct to say that the photon is circularly polarized if the spin of the electron flips down and linearly polarised if it remains up?</p> | 4,663 | [
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<p>How should we put two converging lens in order for parallel rays passing between both lens to remain parallel?</p> | 4,664 | [
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<p>I'm working on a 2D He superfluid system with vortices. I was asked to calculate the kinetic energy of vortex-(anti-)vortex pairs and compare the two situations. One finds in literature that the vortex-vortex situation is unstable, and the vortex-antivortex pair can be stable. This is a crucial observation in what follows.</p>
<p>In the calculation of the energies, I came across a striking fact, which may or may not have any physical implications: the (kinetic) energy of the vortex-vortex situation had an imaginary component, while in the vortex-antivortex energy, everything imaginary nicely cancelled. It seems my results are consistent with what is expected, and certainly scale as they should for the system (energy logarithmically in the size of the system, and in the distance between the vorteces).</p>
<p>For now, I just "forgot" about the imaginary part of the energy, but my question is this:
Can the imaginary part of the energy be interpreted as the lifetime of an unstable state in the case of a vortex-vortex situation (comparable to the lifetime of resonances in S-wave scattering, which also comes into play as the complex part of the energy of the resonance). Or is it merely a remnant of my approximate calculation and the result of logarithms in the complex plane and have I been staring at this too long?</p>
<p>Thanks!</p>
<p>PS: for those interested, the integration I performed can be viewed as a question on math.stackexchange.com. Please ignore the question itself, because it is not really an example of my intellect in this field, just some conjectures/"fleeting hope" <code>;)</code> <a href="http://math.stackexchange.com/questions/32286/choosing-the-branch-of-a-logarithm">http://math.stackexchange.com/questions/32286/choosing-the-branch-of-a-logarithm</a></p> | 4,665 | [
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<p>Related to my other misguided question, D-branes are equivalent to p-branes. D-branes are described by a sheet in topologically trivial spacetime. p-branes are extremal black branes. They have an event horizon which is infinitely far away along spatial geodesics. However, we may cross the event horizon in a finite affine time for null and timelike geodesics. So, we need to extend spacetime, and if we do that, the Penrose diagram consists of an infinite chain of universes, ordered by time. Each universe has its own null infinity. Causal information is "created" in the past null infinity of each universe. So, a universe in the "future" contains information which is causally independent from and inaccessible to "our universe". All this is invisible if we work with D-branes. Where did all the other universes go to? Where is all the information contained within them encoded?</p> | 4,666 | [
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<p>I am trying to decipher what decibels are:</p>
<p><a href="http://en.wikipedia.org/wiki/Decibel" rel="nofollow">http://en.wikipedia.org/wiki/Decibel</a></p>
<p>It seems to be a log ratio of audio amplitude multiplied by a constant. I am confused by what this means though.</p>
<p>If my original volume is X, what does say increasing the volume by Y decibels mean? </p>
<p>Does it mean <code>New Volume = 10 log ( Y / X )</code>?</p> | 4,667 | [
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] |
<p>Taken from <a href="http://www.feynmanlectures.caltech.edu/I_06.html#Ch6-S3" rel="nofollow">Volume 1, Chapter 6, Section 3</a> of the Feynman Lectures on Physics.</p>
<p>Feynman says that in describing random, equally-probable-backwards-or-forwards motion, that,</p>
<blockquote>
<p>We might therefore ask what is his average distance travelled in <em>absolute value</em>, that is, what is the average of $|D|$. It is, howevermore convenient to deal with another measure of "progress", the square of the distance: $D^2$ is positive for either positive or negative motion, and is therefore a reasonable <em>measure</em> of such random wandering.</p>
<p>We can show that the expected value of $D^2_N$ is just $N$, the number of steps taken.....</p>
</blockquote>
<p>He seems to provide a reason that applies just the same to using absolute value. From there, beginning with that next paragraph, he doesn't make any sense at all, so I think this is central to his point. Why does he use squares of the distances instead of absolute value? And how does $D^2_N = N$?</p> | 4,668 | [
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<p>I want to solve a problem of plane wave diffraction by a large sphere. There is a formula that I found from papers, but I think needs numerical solution. please help me to solve it The formula is below:
<img src="http://i.stack.imgur.com/98WnS.jpg" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/tblGM.jpg" alt="enter image description here"></p>
<p>Here $U$ is total field (incident and diffracted).</p> | 4,669 | [
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<p>I am currently studying this problem: <a href="http://aforrester.bol.ucla.edu/comprobs/F06prob14.pdf" rel="nofollow">14 b)</a></p>
<p>There you see an integral $$A(r) = \int f(\theta) (-\sin(\phi), \cos(\phi),0) d \Omega$$ where $f$ is the function containing all the rest of the integrand that you see there and I don't see why this integral is not zero? (I am especially referring to the integral in the second row of part b) . I mean clearly: $$\int_{0}^{2\pi} (-\sin(\phi), \cos(\phi),0) d\phi = 0$$ so why does this integral not vanish completely?</p>
<p>Also I don't get why there is this $\phi'$ in the denominator? I mean, don't we have $$||r-r'||= \sqrt{r^2+r'^2-2rr'\cos(\theta-\theta')}$$ so this should not depend on $\phi'$? (This is the reason why I said that $f$ only depends on $\theta$.)</p> | 4,670 | [
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<p>Why does current return to its source?</p> | 4,671 | [
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<p>Jupiter has about twice the density of Saturn (1.33 versus 0.69 g/cm^3) because it apparently has a higher mass percentage of rocky core and of metallic hydrogen in its interior. Available density references of this hydrogen state differ widely from 0.3 - 2.8 g/cm^3. Is there a theoretical density of metallic hydrogen, and would its density remain relatively constant given the varyng high pressures and temperatures found in these planetary interiors?</p> | 4,672 | [
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<p>Suppose we have a quantum state, well described by its time-independent wave function $\Psi$. And we have a well-defined Hermitian (self-adjoint) operator $\hat{A}$. We successfully evaluate the expectation value of the operator $\hat{A}$. Next we derive the general formula for the higher moments of $\hat{A}$ (i.e. the expectation value of $\hat{A^n}$ for $n=2,3,4…$). Finally we scale the operator $\hat{A}$ appropriately, in order to make the result dimensionless and to remove a possible growth factor (of type $C^n$) in the moments. We obtain:</p>
<p>$$ <\hat{A^n}> = Cn + D $$</p>
<p>for $n=1,2,3,...$ and where $C$ and $D$ are constants.</p>
<p>Let us now define a new operator $\hat{B}$ as follows:</p>
<p>$$ \hat{B} = \hat{A^{n+1}} - \hat{A^n} $$</p>
<p>We can easily verify that the first and second moment of B are given by: </p>
<p>$$ < \hat{B} > = C $$</p>
<p>$$ < \hat{B^2} > = 0 $$</p>
<p>Therefore the variance of operator $\hat{B}$ is negative! In violation of statistical laws.</p>
<p>Should we conclude from this example that the results derived for the moments of $\hat{A}$ must be flawed? Or should we conclude that the new operator $\hat{B}$ is not a proper operator after all and therefore its strange properties are insignificant with respect to questions about the validity of $\hat{A}$?</p>
<p>$$\begin{align}
<\hat{B}> &= <\hat{A^{n+1}}> - <\hat{A^n}> \\
&= C(n+1) + D - Cn - D = C
\end{align}$$</p>
<p>$$\begin{align}
<\hat{B^2}> &= <\hat{A^{2n+2}}> - 2<\hat{A^{2n+1}}> + <\hat{A^{2n}}> \\
&= C(2n+2) + D - 2C(2n+1) - 2D + C(2n) + D \\
&= 0
\end{align}$$</p>
<p>$$\begin{align}
\text{Variance of }\hat{B} &= <\hat{B^2}> - \left(<\hat{B}>\right)^2 \\
&= -C^2
\end{align}$$</p> | 4,673 | [
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<p>What is the meaning of the text quoted below?</p>
<blockquote>
<p>In the physical world, if a system is described by an equation that is
first order in time, the system is general dissipative (has energy
loss). If the equation is second order in time, the system may be non
dissipative. Such a system has time-reversal symmetry.</p>
</blockquote>
<p>Can somebody explain what it really means to be first order and second order in plain English?</p> | 4,674 | [
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<p>What factors affects the size of a shadow and how would you derive the diameter of a shadow of a circular object on a flat screen?</p> | 4,675 | [
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<p>The mass-energy equivalence, first established by Einstein is an important and highly discussed phenomenon in physics. Without claiming much knowledge about high-end discussions on this topic, I would like to ask a question on this. </p>
<blockquote>
<p><strong>Does the equivalence allow "energy" to exhibit gravitational
interactions with other masses and energy?</strong></p>
</blockquote>
<p>Furthermore, how can an intangible thing like energy be localized in space which is necessary, atleast according to the classical view, for gravity? This could help solve a related question that </p>
<blockquote>
<p>does a matter-annihilation event between two particles also ceases the
gravitational effect the original particles might be having on
adjacent (and far-off) particles? </p>
</blockquote>
<p>I recently <a href="http://www.vijyoshi.in/" rel="nofollow">attended a lecture</a> by <a href="http://en.wikipedia.org/wiki/Ashoke_Sen" rel="nofollow">Ashoke Sen</a> where he probably hinted towards gravitational interaction by energy, but I might be mistaken as it was only a passing reference.</p> | 4,676 | [
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<p>In Weinberg's <em>Gravitation,</em> </p>
<p>the formula for the volume element in curviliniar coordinates is given by
$$dV=h_1 h_2 h_3 dx^1 dx^2 dx^3.$$ </p>
<p>The metric is given by $ds^2=h_1^2 dx_1^2+h_2^2 dx_2^2+h_3^2 dx_3^2.$</p>
<p>I am totally confused by this, I know that $\sqrt{g^{\prime}}=|\frac{\partial x}{\partial x^{\prime}}|\sqrt{g}$. If I take the initial metric to be euclidean, then clearly $\sqrt{g^{\prime}}=\det(J)$. The change in volume element is given by $dV=\det(J)^{-1}dV_{euclidean}$, which gives $dV=\frac{1}{h_1 h_2 h_3}dx_1 dx_2 dx_3.$</p>
<p>Where am I going wrong?</p>
<p>Also, the expression for curl, divergence etc have a factor of $\det(g)^{-\frac{1}{2}}$.</p>
<p>Why is this so? How do I prove it?</p> | 4,677 | [
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<p>Earth rotates on its axis and revolves around the sun, <a href="http://www.universetoday.com/18028/sun-orbit/">the sun revolves around the galaxy</a>, the galaxy is also moving. So Earth's net rotation as observed from a fixed inertial frame consists of all these contributions (and is rather complex).</p>
<p>Now a <a href="http://en.wikipedia.org/wiki/Foucault_pendulum">Foucault pendulum</a> on earth is supposed to tell the experimenter whether the earth is rotating or not. See a recent question on this forum <a href="http://physics.stackexchange.com/questions/66234/proof-that-the-earth-rotates/66235#66235">Proof that the Earth rotates?</a> Basically for a Foucault's pendulum, the plane of the oscillation of the bob rotates, as the Earth rotates. But, the Foucault's pendulum does not single out one type of rotation, it gets affected by all. Therefore the rotation of plane of oscillation can be used to measure rotation of Earth around its own axis, around the sun, everything. </p>
<p>But the question is, around what is the Foucault pendulum measuring Earth's rotation with respect to? That is, finally <strong><em>what is the Earth rotating around/revolving around?</em></strong> Isn't it intriguing that the effect of the entire Universe on Earth can be measured by a <em>pendulum</em>?</p>
<p><em>I understand that the effect on the pendulum due to say the revolution of solar system around the galaxy is going to be small, but still, it can be measured say in an experiment going on for 10 years. You can keep on increasing the accuracy by measuring for longer periods.</em></p> | 995 | [
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] |
<p>Why is quantum physics needed to explain photosynthesis?</p>
<p>In what aspect does the corresponding classical theories for photosynthesis fail?</p> | 4,678 | [
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<p>The below is the sixth question of the very first chapter from halliday and resnicks fundamentals of physics text,which i'am not able to comprehend.</p>
<p><strong>Harward Bridge,which connects MIT with its fraternities accross the Charles River,has a length of 364.4 Smoots plus one ear.The unit of one Smoot is based on the length of Oliver Reed Smoot,Jr.,class of 1982,who was carried or dragged length by length across the bridge so that other pledge members of the Lambda Chi Alpha fraternity could mark off (with paint) 1-Smoot lengths along the bridge.The marks have been repainted biannually by fraternity pledges since the initial measurement,usually during times of traffic congestion so that the police cannot easily interfere.(Presumably,the police were originally upset because the Smoot is not an SI unit,but these days they seem to have accepted the unit.) the below figure shows three prallel paths,measured in Smoots (S),Willies (W),and Zeldas (Z).What is the length of 50.0 Smoots in (a) Willies and (b) Zeldas?</strong></p>
<p><img src="http://i.stack.imgur.com/5d4pY.jpg" alt="enter image description here"></p>
<p>The method used in this text to solve these kind of problems is <strong>chain link conversion</strong> where in you set up the problem in such a way the unwanted units cancel.I would be glad if someone could help me in setting it up so that i can work through it.</p> | 156 | [
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<p>Consider a piece of metal of length $L$ and linear thermal expansion coefficient $\alpha$. We eat the metal $\Delta T$ degrees, causing the metal to increase to length
$$ L' = L + L \alpha \Delta T$$
Now, cool the object back to the original temperature. This causes the metal to decrease in length to
$$L'' = L' - L'\alpha\Delta T \\ = L + L \alpha \Delta T - (L + L \alpha \Delta T)\alpha \Delta T \\
=L (1 - \alpha^2 \Delta T^2)$$</p>
<p>My intuition would lead me to believe that heating up and then recooling an object would cause it to return to the same size it began at (if it did not, then bridges which repeatedly warmed and cooled would continually shrink) but this is not true according to my mathematics, which indicates that warming and recooling an object leaves it slightly smaller than it was before.</p>
<p><strong>Do objects really not return to their original size when recooled? If so, then why do objects which warm and cool on a daily basis not slowly shrink?</strong></p>
<p>I suspect that this may be related to $\alpha$ varying over the range of temperatures, but I didn't think that was a significant effect for solids.</p> | 4,679 | [
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<p>I have the following exercise:</p>
<p><strong>Use Heisenberg's uncertainty principle and the relation $\Delta u = \sqrt{\langle u^2 \rangle - \langle u \rangle^2}$ to find the range of energy an electron has in an atom of diameter 1 amstrong.</strong></p>
<p>This is the attempt at a solution:</p>
<ul>
<li><p>From the uncertainty principle: $\Delta p \Delta x \geq \hslash / 2 $. Therefore $\Delta p \geq \hslash / 2\Delta x$.</p></li>
<li><p>Without considering relativistic corrections (don't know if this is OK), $E_c = p^2/2m$</p></li>
<li><p>From the definition of standard deviation $\Delta p = \sqrt{\langle p^2 \rangle - \langle p \rangle^2}$. Then $\Delta p^2 = \langle p^2 \rangle - \langle p \rangle^2$. Therefore $\langle p^2 \rangle = \Delta p^2 + \langle p \rangle^2$</p></li>
<li><p>The energy of the electron will be the kinetic energy minus the potential energy:</p></li>
</ul>
<p>$E = p^2/2m - e^2/r$</p>
<p>And so the average energy will be</p>
<p>$\langle E \rangle = \langle p^2\rangle/2m - e^2/\langle r \rangle = (\Delta p^2 + \langle p \rangle^2)/2m - e^2/\langle r \rangle$</p>
<p>Here I don't know how to continue. Do I have to assume $\langle p \rangle = 0$? Why? And even when I assume that, replacing $\langle r\rangle$ with $\Delta x$, which I suppose is $1 * 10^{-10} m$ (why?) I don't get a value of energy similar to the ground level energy of a hydrogen atom (which has roughly the same diameter than this one).</p>
<p>What am I doing wrong?</p> | 4,680 | [
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<p>Based on the transfer length method (TLM), one can accurately calculate the contact resistivity for an <a href="http://en.wikipedia.org/wiki/Ohmic_contact" rel="nofollow">ohmic contact</a>, by evaluating the absolute resistance measured through the test structure and plotting it as a function of the gap spacing between the two ohmic contacts. By extrapolation, the contact resistance and transfer length (and thus, the contact resistivity) can be calculated. </p>
<p>However, what if a measurement of the contact resistivity of a Schottky contact was desired? In this case, the forward biased current is non-linear (does not follow Ohm's law), and thus the absolute resistance measured is a function of voltage. Is there another way to measure the contact resistivity in this case?</p>
<p>On the flip side of the coin, I have only seen the Schottky barrier height calculated for Schottky contacts. However, some ohmic contacts (e.g. tunneling ohmic contacts) still have a positive Schottky barrier height. How is the height measured in this case?</p> | 4,681 | [
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<p>Does entanglement not immediately contradict the theory of special relativity? Why are people still so convinced nothing can travel faster than light when we are perfectly aware of something that does?</p> | 4,682 | [
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] |
<p>The following <a href="https://www3.amherst.edu/~rhromer/MISC/Spin-Statistics-AJP.pdf">link</a> provides a letter to the editor by Robert H. Romer who writes, </p>
<blockquote>
<p>In a 1994 "question" in this journal,
Neuenschwander asked whether anyone
had yet met Feynman’s challenge of pro-
viding an elementary proof of the spin-
statistics theorem... In spite of the importance of the spin-
statistics theorem and the attention that
has been devoted to it, the physics commu-
nity still waits—probably in vain—for an
elementary proof.</p>
</blockquote>
<p>I currently face mixed answers on our understanding of the elementary proof of the spin-statistics theorem. Romer's letter suggests to me that we still do not fully understand how to prove the spin-statistics theorem from first principles. Does Romer's letter still stand true today, or has there been a recent publication that out-dates Romer's letter?</p> | 4,683 | [
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<p>Every space show I watch mentions that anti-matter used to exist, or still does and we just can't detect it. I think some shows even say we can create a small amount of anti-matter. It is not presented as an unproven conjecture like string theory, but rather as a fact.</p>
<p>In terms someone without a PhD might understand, what is the strongest and simplest evidence that anti-matter used to exist, or still does?</p> | 4,684 | [
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<p>If the curvature of the universe is zero, then $$Ω = 1$$ and the Pythagorean Theorem is correct. If instead $$Ω> 1$$ there will be a positive curvature, and if $$Ω <1$$ there will be a negative curvature, in either of these cases, the Pythagorean theorem would be wrong (but the discrepancies are only detectable in the triangles whose lengths its sides are of a cosmological scale). but could think of a curvature of the universe such that $$Ω= a+ib$$ is a complex number? that would mean physically?</p> | 4,685 | [
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<p>I have mass, $g$, and luminosity of each of the stars in a binary system, extracted from a model. I calculated the individual radii from $g$ and the mass. I am trying to compute $a$, but I seem to be stuck or I'm just missing something obvious. I can't think any method that does not involve the period.</p>
<p>How do I get the semi-major axis? </p> | 4,686 | [
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<p>I know roughly <em>how</em> a turbine engine (let's say a gas turbine producing no jet thrust) is supposed to work:</p>
<blockquote>
<p>The compressor forces fresh air into a combustion chamber, where it reacts with fuel to become hot exhaust gas. On its way out of the engine, the exhaust gas drives a turbine, and the turbine <em>both</em> makes the compressor go, <em>and</em> has enough leftover torque to do useful work.</p>
</blockquote>
<p>However, how do the exhaust gases know they're supposed to push on the turbine blades to drive the shaft, rather than push back on the compressor blades to <em>retard</em> the drive shaft in equal measure?</p>
<p>In a piston engine there are valves that force things to flow in the correct direction at the right times. But with the turbine engine everything is openly connected all the time. Shouldn't that mean that the pressure differential the compressor must work against is exactly the same as that which is available to drive the turbine?</p>
<p>Something magical and irreversible seems to happen in the combustion chamber.</p>
<p>The descriptions I can find that go deeper than the three-step explanation above all seem to jump directly to a very detailed model with lots of thermodynamics and fluid dynamics that make my head spin. Is there an idealized system with fewer variables that I could think of to convince myself we're not getting something for nothing here (e.g., might the working fluid be incompressible, or massless, or have infinite heat capacity or whatever)?</p> | 4,687 | [
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<p>Is it possible to take a tensor to the other side of the equation, and the tensor becomes its inverse(i.e contravariant becomes covariant and vice versa)? It is a stupid question, but It confuses me.</p>
<p>For example, if</p>
<p>$A_{ij} = B_{ij},$</p>
<p>Can I write</p>
<p>$A_{ij}B^{ij} = \delta_{j}^{i}$, (though I think it should be $A^2$) </p>
<p>Or is it only valid for the metric tensor?</p>
<p>Also, is there a difference in the matrix representations of a tensor's contravariant and covariant form, or only the transformation rules differ? </p> | 4,688 | [
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<p>In J.D. Jackson's first chapter, he says the proper equation connecting $\textbf E$ and $\textbf D$</p>
<p>$$ D_\alpha = \sum_\beta \int d^3x'\int dt' \epsilon_{\alpha\beta}(\textbf x',t')E_\beta(\textbf x - \textbf x',t-t') $$</p>
<p>He suggests that this is because the connection between these two can be non-local. What is author referring to here ? The direct relation is given in the momentum space,</p>
<p>$$ D_\alpha(\textbf k,\omega) = \sum_\beta \epsilon_{\alpha\beta}(\textbf k,\omega) E_\beta(\textbf k,\omega) $$</p> | 4,689 | [
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<p>I think,</p>
<p>$$\sigma_{ij}\sigma^{ij} = \sigma^2.$$</p>
<p>However,
on the Wikipedia page on <a href="http://en.wikipedia.org/wiki/Raychaudhuri_equation" rel="nofollow">Raychaudhuri equation</a>,
It was mentioned:</p>
<p>$$\sigma^2=\frac{1}{2}\sigma^{ij}\sigma_{ij}$$</p>
<p>I am confused, but I think the first equation is only valid for tensors whose inverse is the same as the tensor itself. Which is the correct one?</p>
<p>Also, IF (and only if),</p>
<p>$$\sigma_{ij}\sigma^{ij}= \sigma^2,$$ then is this true:</p>
<p>$$\sigma_{ij}\sigma_{ij}=\sigma^2 ~?$$</p>
<p>Please explain in detail. </p> | 4,690 | [
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<p>I am trying to understand how complex numbers made their way into QM. Can we have a theory of the same physics without complex numbers? If so, is the theory using complex numbers easier?</p> | 4,691 | [
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<p>I'm working on a sample problem and it asks on how steep of an incline can a car park? From what I learned the friction is in the opposite direction if there was motion in said friction-less environment. Is this the right way to think of friction? </p>
<p>In the case of the car; it would move down the hill and the friction would be up the hill. Why is the friction pointing down the incline and not up the incline?</p>
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<p>The Wikipedia says on the page for the <a href="http://en.wikipedia.org/wiki/Uncertainty_principle" rel="nofollow">uncertainty principle</a>:</p>
<blockquote>
<p><em>Mathematically, the uncertainty relation between position and momentum arises because the expressions of the wave function in the two corresponding bases are Fourier transforms of one another (i.e., position and momentum are conjugate variables).</em> </p>
</blockquote>
<p>Does that mean that position and momentum are just 2 different measurements of the same wave function? I.e., it is the same thing that is being measured, just in two different ways? Meaning, they are not really two different things, but two different views on the same thing?</p> | 4,693 | [
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<p>Suppose a person is walking in rain carrying an umbrella. He is tilting his umbrella at some angle with the vertical so as to protect himself from the rain. But a neutral observer who is standing still will find it really absurd because he will find the rain falling vertically downward, how come there are two realities for the same event?</p> | 4,694 | [
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<p>I listened to Christoph Weniger present his results at SLAC today. See his paper is here: <a href="http://arxiv.org/abs/1204.2797">http://arxiv.org/abs/1204.2797</a> and also see a different analysis here: <a href="http://arxiv.org/abs/1205.1045">http://arxiv.org/abs/1205.1045</a>. The data seems convincing to me! Is this result consistent with theoretical expectations for DM candidates? In particular is the reported estimate cross section for annihilation into photons consistent with estimated cross sections for the various WIMP dark matter candidate particles (like LSP dark matter candidates)? Are there any other reasonable astrophysical mechanisms that would produce this 130 GeV photon line?</p>
<p>The summary for the talk claims: Using 43 months of public gamma-ray data from the Fermi Large Area Telescope, we find in regions close to the galactic center at energies of 130 GeV a 4.6 sigma excess that is not inconsistent with a gamma-ray line from dark matter annihilation. When taking into account the look-elsewhere effect, the significance of the observed signature is 3.3 sigma. If interpreted in terms of dark matter particles annihilating into a photon pair, the observations imply a partial annihilation cross-section of about $10^{-27} cm^3 s^{-1}$ and a dark matter mass around 130 GeV.</p> | 4,695 | [
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<p>In real-space renormalization group how does one find the complete RG flow exactly, (not schematically)? I understand it needs to be done on a computer. For example, I have the ising model on a triangular lattice and I also get the RG recursion relations by blocking ( as done in Nigel Goldenfeld's book). Now how do I get the smooth RG flow over the full parameter space?</p> | 4,696 | [
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<p>I am long been confused by these entropy terms. Would be obliged if an explanation is provided in less technical jargon</p>
<ol>
<li>What are the differences between Shannon's entropy, topological entropy and source entropy?</li>
<li>What exactly is the significane of Kolgomorov complexity. Is it same as Kolgomorov entropy. How is it related to Shannon's entropy?</li>
<li>What information does the complexity number convey? It is known that source entropy=kolgomorov entropy , so what does this imply from the point of view of infomation theory?</li>
</ol>
<p>Thank you</p> | 4,697 | [
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<p>In CFT, when we have an OPE:
$$O_1(z)O_2(w)=\frac{O_2(w)}{(z-w)^2}+\frac{\partial O_2(w)}{(z-w)}+...$$
this holds inside a time-ordered correlation function, so $O_1(z)O_2(w)=O_2(w)O_1(z)$. Does it mean that
$$O_1(z)O_2(w)=\frac{O_1(z)}{(w-z)^2}+\frac{\partial O_1(z)}{(w-z)}+...$$
?</p> | 4,698 | [
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<p>Here is a problem on diffraction -
Diffraction pattern of single slit of width 0.5 cm is formed by a lens of focal length of 40 cm. calculate the distance between first dark and next bright fringe from the axis. Wavelength of the light used is 4890 Angstrom.</p>
<p>I am confused by following statement of the problem:
"distance between first dark and next bright fringe from the axis"</p>
<p>it is like saying calculate distance between x and y from m. Here x and y are bands and y is a line.</p>
<p>My first hunch was - do not first dark and next bright lie next to each other? what is the point in asking distance between them? Looks like the problem is asking us to calculate width of first bright fringe (what is pretty straight forward).</p>
<p>Referring to one of earlier post - what is the point in asking distance between fringes?</p> | 4,699 | [
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<p>I came upon this while wondering whether the friction of a rolling cylinder on an inclined plane depends on the value of friction coefficient.</p>
<p><img src="http://i.stack.imgur.com/wC0Lz.png" alt="enter image description here"></p>
<p>now,
$$f\leqq\upsilon N$$</p>
<p>Again after calculating I found that the
$$f=\frac{mg\sin\theta}{3}$$
So,$$\frac{mg\sin\theta}{3}\leqq \upsilon mg\cos\theta$$
$$\Rightarrow \tan\theta\leqq 3\upsilon$$
But, I can set the angle and mu to be such that this relation does not hold!</p>
<p>What will happen then? Please explain.</p> | 4,700 | [
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<p>I am wondering if an extension of <a href="http://en.wikipedia.org/wiki/Noether%27s_theorem" rel="nofollow">Noether theorem</a> to <a href="http://en.wikipedia.org/wiki/Supergroup_%28physics%29" rel="nofollow">supergroups</a> exists.
In particular the analogy with the usual case should be that supersymmmetries are in 1 to 1 correspondence to certain "currents" whose charge is the supersymmetric spinor charge $Q_{\alpha}$.</p>
<p>Has this topic been studied at all?</p> | 4,701 | [
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<p>I was watching the men's <a href="http://en.wikipedia.org/wiki/Luge">luge</a> ride with my dad. My dad said, the mass of the athlete must be at an optimum level so that he wins. I said, his volume should be minimum, but it has nothing to do with the mass, as the acceleration is independent of mass.</p>
<p>Is it just like any other "block on an incline" problem? Or am I wrong?</p> | 4,702 | [
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<p><img src="http://i.stack.imgur.com/xyeuE.jpg" alt="Image 1"></p>
<p>Imagine that there is a car and it is not moving but its headlights are on. There is a wall in front of the car but is very far away. Right now energy is being used only in switching on the headlights. Now the car starts moving at a very high speed.</p>
<p><img src="http://i.stack.imgur.com/265ho.jpg" alt="image 2"></p>
<p>As I have shown in the picture, there is a blueshift of light and so the energy of light emitted per unit time has increased. Now my question is that from where does this extra energy come from.</p>
<p>Some arguments that prove that extra energy is generated. If the car was moving without the headlights off but at the same speed, the energy would have been used in the movement of the car. Now if the car was not moving and only the headlight was on, the energy would have been used in powering the headlight. But when we take both the cases simultaneously, then we see that there is an increase in the net energy. For further explanation I will give some equations.</p>
<p><strong>Case 1 when the car is moving but the headlights are off</strong></p>
<p>$Q_1 = \frac{dE}{dt} = \frac{d\sqrt{p^2c^2 + m^2c^4}}{dt} = 0;$</p>
<p><strong>Case 2 when the car is not moving but the headlights are on</strong></p>
<p>$Q_2 = \frac{dE}{dt} = \frac{d(mc^2)}{dt} < 0$ since energy is being radiated by the lights on;</p>
<p><strong>Case 3 when the car is moving and the headlights are on</strong></p>
<p>$Q_3 = \frac{dE}{dt} = \frac{d\sqrt{p^2c^2 + m^2c^4}}{dt} < Q_2$, because the power of radiation is higher than in Case 2. This is because the light is blue-shifted and its quanta have higher energy.</p>
<p>So from where does this extra energy of light come from?</p> | 4,703 | [
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<p>I've read that electrons in Graphene behave 'pseudo-relativistically'; what does this mean? how do they behave differently from electrons in other materials?</p> | 4,704 | [
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<p>I'm studying quantum mechanics in its most basic level (I don't even know if Physicists call this already quantum mechanics) and I have one doubt in Schrodinger's equation. The book presents the equation for the special case where the solution is of the form $\Psi(x,t)=\psi(x)e^{-i\omega t}$ and says that Schrodinger's equation (in one dimension) is</p>
<p>$$\dfrac{d^2\psi}{dx^2}+\dfrac{8\pi^2 m}{h^2}(E-U(x))\psi(x)=0$$</p>
<p>Where $m$ is the mass of the particle, $E$ it's total energy and $U$ it's potential energy function.</p>
<p>The first doubt that arises is the following: the book says that $E$ is the "constant total energy" of the particle. But wait, since $E = K + U$ and $U$ varies, clearly $E$ should vary. How can $E$ be constant if $U$ is not?</p>
<p>Also, when we write $E-U(x)$ isn't this simply $K$, the kinectic energy? Why do we bother then writing explicitly $E-U$?</p>
<p>I feel that the potential $U(x)$ on the equation and the one that is part of $E$ are different, but I'm not understanding how.</p> | 4,705 | [
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<p><a href="http://arxiv.org/abs/1003.6023" rel="nofollow">http://arxiv.org/abs/1003.6023</a> Gauge Higgs unification .</p>
<p>Does gauge higgs unification has been proved ？
If so , what is it exactly meaning ?</p> | 157 | [
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<p>I was researching a question for another post and it occurred to me that you might expect to see Hawking radiation at the mouth of wormholes. </p>
<hr>
<p>Given the mechanism of Hawking radiation at the event horizon of black holes: virtual partial pairs forming at the edge and being separated by the event horizon; would virtual particles at the edge of wormholes likewise be divided? As I understand it, the trip is one way, which should cause the spontaneous formation of electrons and separation of positrons. </p>
<hr>
<ol>
<li>Am I on the right track or is this a ridiculous assumption?</li>
<li>I don't see this in the literature on Hawking radiation or wormholes. Can you point me to any resources?</li>
<li>If this wouldn't occur, why not?</li>
</ol> | 4,706 | [
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<p>Some years ago, I heard a talk about a an Irish or Scottish physicist named McCullough who had formulated Maxwell's equations several years before Maxwell. This fellow was recognized for his work, according to the talk, by systematically discounted by other luminaries of the day like Stokes and Hamilton in favor of Maxwell. At some point, he was found with his throat cut for no apparent reason.</p>
<p>I can find no mention of McCullough anywhere and I am wondering if this story is at all true. I may have some details wrong; the talk was several years ago. If anyone knows anything, please let me know.</p> | 4,707 | [
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<p>I am interested in <a href="http://en.wikipedia.org/wiki/Shor%27s_algorithm" rel="nofollow">Shor's algorithm</a>, and I am reading several papers that related to the quantum Fourier transform (<a href="http://en.wikipedia.org/wiki/Quantum_Fourier_transform" rel="nofollow">QFT</a>). </p>
<p>I know the there is a difference between the output of QFT and DFT (<a href="http://en.wikipedia.org/wiki/Discrete_Fourier_transform" rel="nofollow">DFT</a>). But I do not know how to derive QFT from DFT. I do not know how to link from QFT and DFT, and maybe I have not comprehend all the differences between QFT and DFT.</p> | 4,708 | [
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<p>Simple power counting tells you that a scalar field coupled to some fermions at one-loop picks up a correction to the mass of the order $\Lambda^2$.</p>
<p>Based on this people say things like "it's natural to expect that the mass of the scalar is roughly the cut-off scale", which in this case is some GUT/Planck scale.</p>
<p>My question is this: is this really the right interpretation?
If I'm doing perturbation theory and it's telling me that I have a correction as big as the largest scale in my problem (cut-off scale), it means I cannot trust the answer. It does not meant the answer is $m_\phi^2 \propto \Lambda^2$.
The renormalized mass could still be far below $\Lambda$, but the current approach cannot see that. The correct and finite answer might emerge only after adding up all diagrams.
There's no reason to try to fine-tune anything such that already at one-loop the mass is small. One must simply concede that the one-loop answer is not correct.</p>
<p>What is the correct interpretation?</p>
<p>EDIT: corrected "far beyond $\Lambda$" with "far below $\Lambda$"</p> | 4,709 | [
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<p>I am reading a online tutorial about Lagrangian mechanics. In one section, it states that if the kinetic term in Lagrangian has no explicit time dependence, the Hamiltonian does not explicitly depends on time, so $H=T+V$. I just wonder if it is always true that $H=T+V$, why require it has no explicit time dependence?</p> | 4,710 | [
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<p>According to Peierls and Landau, 2D crystals were thermodynamically unstable. They can't exist!
Of course, this theory was disapproved in 2004 (example: graphene).</p>
<p>What is the general definition of stability of a general system?</p>
<p>What is the thermodynamics' stability?</p> | 4,711 | [
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<p>I have read most of the supernova article on wikipedia, and there are a lot of numbers and different types of supernovae so I am confused.</p>
<p>What I need to know is how much energy is released from some very powerful supernovae in any form (EM radiation, kinetic energy.. etc) other than neutrinos. </p>
<p>Also please take a look at <a href="http://books.google.com.eg/books?id=VlfSviM9eIIC&pg=PA144&lpg=PA144&dq=1052%20supernova%20ergs%20kinetic%20energy&source=bl&ots=JqgIQVqkf4&sig=C-5E6HEkVCvRjCDlIrcDvw_cgwE&hl=ar&sa=X&ei=zBLPUoflHrGp0AX724DIBQ&ved=0CFIQ6AEwBA#v=onepage&q=1052%20supernova%20ergs%20kinetic%20energy&f=false" rel="nofollow">this</a> and tell me what you think about this 10^52 ergs of kinetic energy.</p> | 4,712 | [
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<p>I'm looking to compute the pitch and roll of a device fitted with a three axis accelerometer when it is not at rest or moving at a constant velocity. Most applications I've seen so far are for stationary tilt sensing... genuinely stuck on this one! Aiming to use it for a python program I'm working on.</p>
<p>For a stationary case I have the following:</p>
<pre><code>roll = np.arctan2(a_y, a_z) * 180/np.pi
pitch = np.arctan2(a_x, np.sign(a_z)*np.sqrt(np.power(a_y,2) + np.power(a_z,2)))*180/np.pi
</code></pre>
<p>Essentially I have a case where I need to find the linear vertical acceleration of a device with g subtracted from it. My initial idea was to use something along the lines of the following:</p>
<pre><code>a_linear_z = a_measured_z - g*R
R = [-np.sin(pitch),np.cos(pitch)*np.sin(roll),np.cos(pitch)*np.cos(roll)]
</code></pre>
<p>Because of the nature of the gestures being investigated I am able to set yaw = 0. I thought with this I would be able to find a work around for a method of subtracting $g$ and obtaining linear acceleration. </p> | 4,713 | [
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<p>The topological ground state degeneracy(g.s.d.) provides useful information for a topological field theory(TQFT), such as <a href="http://physics.stackexchange.com/questions/92809/topological-ground-state-degeneracy-of-sun-son-spn-chern-simons-theory">this post</a> shows some example.</p>
<p>To <strong>count g.s.d.</strong>, it seems to be equivalent to <strong>count the volume of the symplectic phase space</strong>. As I have heard, it is known that a gauge theory with a non-compact gauge group the g.s.d. is infinity:
$$
\text{g.s.d.}=\infty
$$
(specifically, my interest can be 2+1D Chern-Simons theory; or other cases). </p>
<p>Question 1: Are there some explicit ways to demonstrate this $
\text{g.s.d.}=\infty
$? </p>
<p>Question 2: Does <strong>non-compact</strong> gauge group necessarily(only if)/sufficiently(if) leads to a <strong>non-unitary theory</strong>?</p>
<p>Many thanks. </p> | 4,714 | [
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<p>Related to: <a href="http://physics.stackexchange.com/questions/5456/the-speed-of-gravity">The speed of gravity?</a></p>
<p>In the related question and in many other questions here, it seems as if the propagation speed of the gravitational interaction is $c$. To my understanding, the only axioms of relativity is that the propagation speed of <em>light</em> (read here EM waves) in vacuum is $c$, and that the laws of physics must be the same in every inertial reference frame.</p>
<p>How can we conclude that the propagation speed of the gravitational interaction is the same as the propagation speed of the EM interaction?</p> | 158 | [
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<p>I came across an interesting article by Montesinos (J. Geom. Phys. 2 (1985), no. 2, 145–153.). In it, he finds that spin structures (as lifts of $SO(4)$) are not compatible with all Riemannian metrics on a four-manifold. In other words, he finds there are no "universal spinors" which are compatible with all the possible Riemannian metrics.</p>
<p>I don't completely understand the article (specifically he is doing some spinor variations to prove his results which I am still working out), but I'm wondering if anyone is familiar with this result (or similar results) and can tell me about their physical significance.</p>
<p>The first thing I am thinking is this implies something about the compatibility between GR and QFT, since there would be some metrics that may solve the classical Einstein equations but which do not admit some kinds of quantum matter described by spinors.</p>
<p>Is that a shot in the dark? Can anyone give me a more concrete explanation of what this paper means?</p>
<p>Here is an INSPIRE link to the paper (<a href="http://inspirehep.net/record/232859?ln=en" rel="nofollow">http://inspirehep.net/record/232859?ln=en</a>) but unfortunately I cannot find an open source one.</p> | 4,715 | [
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<p>From what I've learned so far, it appears that all models that attempt to explain the expansion of the universe are either based on Lambda-CDM or quintessence. The former support a big bang with rapid expansion, then deceleration of the expansion and then expansion again (non accelerated expansion) with $w=-1$. The latter (quintessence) do not support big bang, but support accelerated expansion with $w<-1$. The two schools of thought appear to box you in one way or the other, depending whether $w=-1$ or $w<-1$. </p>
<p>Why doesn't Lambda-CDM have a model that explain an accelerated expansion (i.e. $w < -1$) ? Or do they have one? Does Lambda-CDM maintain that $\Lambda$ has to be constant and so you're stuck with quintessence whenever $w<-1$? If that is the case, why couldn't $\Lambda$ increase with time?</p>
<p>In summary, is there any model that support a universe with:</p>
<ol>
<li><p>Big Bang</p></li>
<li><p>Inflationary period with rapid expansion</p></li>
<li><p>Deceleration of expansion </p></li>
<li><p>Linear Expansion</p></li>
<li><p><strong>Future acceleration of expansion</strong>? </p></li>
</ol>
<p>That is, we should be able to see in that model that $H_t > H_0$ for any $t_i >> t_0$ when $w<-1$. </p> | 4,716 | [
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<p>Is there any way to tell how far away a lightning strike is by how its thunder sounds? I thought one way might be by using the fact that higher frequencies travel faster than lower frequencies. Would you have to correct for the fact that thunder may not take a straight path? (If so, this would affect the distance calculation based on the time between lightning and thunder as well.)</p> | 4,717 | [
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<p>My brother and I built a wood burning, convection based, thermal circulating hot-tub. (With and oxyacetylene torch, lots of 1.5" pipe, a brake drum, and a thirty year old jacuzzi). Our design is similar to that of what is manufactured and sold for $7000 by the name of a Dutchtub: </p>
<p><img src="http://i.stack.imgur.com/0qxCA.jpg" alt="enter image description here"></p>
<p>Now As I'm sure you can figure out from the picture, The wood burns inside the coils, heating the water, cold water is sucked in from the bottom and hot water is pushed out the top. Our Version is using a fiberglass luvtub from the 80s or so, that holds approx. 500 gallons of water. After completion of construction and filling we decided to go ahead and test our creation. We knew it would be slow. (given not only that we were heating close to 1,900 litres by convection but that it also happened to only be a couple degrees above freezing. We Started the fire at 17:00 and kept it burning until after 21:00 in the first 20 minutes we already noticed a difference, after an hour or two, the top was steamy and the first six-eight inches or water was ready. however at 21:00 when it was make or break time, we had to call it day. Unfortunately the tub was only up the temperature about a foot down. My brother feels we need to install some sort of pump to increase circulation because he feels the tub temperature is reaching a plateau and our heat loss is too great. I think that install a pump defeats the whole purpose of the tub in the first place.
<strong>Here's my question(s).</strong></p>
<p>Would Stirring the tub help? Based on my understanding, this would slow the circulation as the difference in temperature would be lower. However the average temperature of the water would be consistent. Therefore the stove would not only not have to change the temperature of the incoming water as greatly, but the warmer water would not cool the stove as quickly as the frigid water sitting in the bottom waiting to be sucked in. There's also the joule effect to be considered which, would make an extremely minimal impact in this instance I would think. Nevertheless, would this, stirring, not make a huge difference in the overall heating of the tub?</p>
<p><em>A few things to also consider.</em></p>
<p><strong>1. The Lid</strong>
Our lid is made of 3/4 plywood that does not make a perfect cover. The wood is also perforated with 3/8" holes every square foot.</p>
<p><strong>2. The Tub</strong>
It's dug into the ground but only about half way. That is to say that only half the of the tub is subterranean with some dirt packed around the sides. I am under the understanding, correct me if I'm wrong, but packing dirt all around the edges of the tub would help retain heat. As the dirt will act as a heatsink at first but in the long-run it will help maintain the temperature of the tub. As opposed to bleeding that heat out the side of the tub, for the cold air to wisp away.</p>
<p><strong>3. The fire</strong>
We started with a pretty solid fire inside the stove, then we surrounded the coils with brick (with hole opens so the bottom of the fire/coalbed would still get oxygen and could still be billowed) There was also a chiminea top that we set on top of the coils/bricks, to hold more heat in. (At any given time there was close to a 8-18inch flame shooting out of the top) After some time we changed tactics. We pulled the top and set the bricks about 6 inches away from the coils and made a bigger fire. We knew we wouldn't be retaining as much heat, but there would be so much more produced and the coils would be heating from inside the stove and from out.
*Our Stove is less than a yard from the tub but we installed a sheet of galvanized steel to act as a heat shield so the tub won't catch on fire. </p>
<p>In conclusion, how dramatic would our gains be if we, packed dirt all the way up to the lip of the tub, started with the style fire we ended with, and I think, most importantly, stirred the water in the tub?</p> | 4,718 | [
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<p>When choosing a self-adjoint extension of a Hamiltonian, in general one can obtain domains in which
(i) the probabilities teleport* between points on the boundary
and
(ii) boundary conditions locally conserve probabilities.</p>
<p>The ones which locally conserve probability currents somehow seems nicer to me. But this is not at all an argument especially since tunneling is allowed in quantum mechanics.</p>
<p>Is there any fundamental physical reasoning one can use to discard teleporting boundary conditions?</p>
<p>Thanks in advance for any useful inputs.</p>
<p>*I have used terminology from discussion about a related question :
<a href="http://physics.stackexchange.com/questions/27119/physical-interpretation-of-different-selfadjoint-extensions/27120#27120">Physical interpretation of different selfadjoint extensions</a></p> | 4,719 | [
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<p>The surface of a running track (i.e. cinder or rubber) has an effect on a runner's performance. I would like to get some device for measuring how much energy a runner loses on each surfaces. I've tried to rig up a system with a ball and measuring how high it bounces on both surfaces, but this hasn't worked out well.</p>
<p>Is there a device I could get that I get which would measure how much energy is lost when a body strikes a surface which would work on a cinder and rubberized surface?</p> | 4,720 | [
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<p><a href="https://en.wikipedia.org/wiki/Gravitational_wave" rel="nofollow">Gravitational waves</a> are a yet unproven idea... The lack of positive results from <a href="https://en.wikipedia.org/wiki/LIGO" rel="nofollow">LIGO</a> indicates these are still theoretical constructs not yet supported by experimental data. Is not the explanation of the <a href="https://en.wikipedia.org/wiki/BICEP_and_Keck_Array#BICEP2" rel="nofollow">BICEP2</a> analysis as primordial gravitational waves from <a href="https://en.wikipedia.org/wiki/Inflation_%28cosmology%29" rel="nofollow">inflation</a> presuming the existence of a purely theoretical facet?</p>
<hr>
<p>EDIT: </p>
<p>No one likes this... So it breaks down to the fact that it seems gravitational radiation is being used as an observational/experimental tool similar to <a href="https://en.wikipedia.org/wiki/Electromagnetic_radiation" rel="nofollow">electromagnetic radiation</a> (EM) when the evidence of gravitational radiation is as of yet lacking (failure of LIGO's).</p>
<p><a href="http://www.scientificamerican.com/article/gravitational-wave-finding-causes-spring-cleaning-in-physics/?WT.mc_id=SA_Facebook" rel="nofollow">http://www.scientificamerican.com/article/gravitational-wave-finding-causes-spring-cleaning-in-physics/?WT.mc_id=SA_Facebook</a></p> | 4,721 | [
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] |
<p>Vacuum cementing apparently is far more likely in space than on a planetary surface in atmosphere. How long must two surfaces be kept in contact with each other in a vacuum for vacuum weld/cementing to 'take'? </p> | 4,722 | [
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<p>What is the difference between a battery and a charged capacitor? </p>
<p>I can see lot of similarities between capacitor and battery. In both these charges are separated and When not connected in a circuit both can have same Potential difference <code>V</code>.</p>
<p>The only difference is that battery runs for longer time but a capacitor discharges almost instantaneously. Why this difference? What is the exact cause for the difference in the discharge times? </p> | 4,723 | [
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<p>I've written a program which simulates the motions of planets and other bodies. I'd like to run it on our own solar system, but to do so I need to know the current positions (preferably in heliocentric coordinates) of the planets as well as their current velocities. Is there a website where I can find this?</p>
<p>I've found all the positions of the planets <a href="http://www.planetary-aspects.com/curr_asp/curr_posns.php" rel="nofollow">here</a>, and I can find their average orbital speed fairly easily, but for some planets (e.g. Mercury) the orbital speed varies a fair amount.</p> | 4,724 | [
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<p>By looking at this picture:</p>
<p><a href="http://earthspacecircle.blogspot.com/2013/01/earths-location-in-universe.html" rel="nofollow">http://earthspacecircle.blogspot.com/2013/01/earths-location-in-universe.html</a></p>
<p>The earth is near the center of the universe. I've read that the universe look the same no matter where the observer is located. It is the same distance everywhere.</p>
<p>So I understand that for general relativity the universe need to be homogeneous and isotropic, so it will <strong>look the same</strong> no matter where I am.</p>
<p>But what if I'm on one of the planets near the right or left of the image, then if I draw the same picture of the universe, but from my perspective, then I would be also located in the center? If that's not the case (I'm actually near an <em>edge</em>), then part of my sky would be completely dark, and all the sky that way won't be isotropic?</p> | 725 | [
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<p>The Weyl tensor equates the Riemann tensor in vacuum</p>
<p>$$ C_{\mu \nu \eta \lambda} = R_{\mu \nu \eta \lambda} $$</p>
<p>So it makes me wonder about the tensor</p>
<p>$$T_{\mu \nu \eta \lambda} = C_{\mu \nu \eta \lambda} - R_{\mu \nu \eta \lambda} $$</p>
<p>and how it relates to the 2nd-rank stress-energy tensor $T_{\mu \nu}$. In particular, both tensors are zero and non-zero in the same domains, so they must be related. In the other hand, general relativity says that matter affects geometry only through the 2nd-rank tensor, so in theory no higher rank tensor should contain more information about the matter fields than what it (the 2nd-rank tensor) already does</p>
<p>I'm trying to figure out if the 4th rank tensor can be interpreted or not as containing more information about the energy-matter fields or if the extra degrees of freedom are strictly geometric. The question is relevant for considering alternative formulations of the matter curvature relationship that tend to the Einstein equation in some sensible limit</p> | 4,725 | [
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<p>atom has well defined spin(up and down) and orbital(s,p,d,etc) momentum, but when forming crystals, why the spin degree continues to be good quantum number while orbital momentum is quenched?</p> | 4,726 | [
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<p>When building models people typically gauge $SU(N)$ but rarely try to gauge $SO(N)$ (the only example I know about is $SO(10)$, but even that isn't quite $SO(10)$ but actually its double cover). At least with $SO(2) $ and $SO(3)$ one could choose to gauge these groups or their isomorphisms, $U(1)$ and $SU(2)$. </p>
<p>Is there a good reason why working with the $SO(N)$ is more difficult? Furthermore, could there be some new physics that's hiding in an orthogonal group and not inside a unitary one?</p> | 4,727 | [
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