question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>Have a look at the following diagram:</p>
<p><img src="http://i.stack.imgur.com/zB8KY.png" alt="CMB measurements"></p>
<p>This shows measurements of the CMB by various experiments, with multipole moment $l$ on the x-axis and the temperature of the corresponding moment on the y-axis. (Please correct me if I have that wrong.)</p>
<p>Looking at the plot, I can see that WMAP's results extend to about $l=1000$, and they become poor as we go to higher values of $l$. Meanwhile, the other experiments can't measure the CMB at lower values of $l$ around $l < 500$. I'm guessing that a ground-based approach with a large collector is required to get the high resolutions needed to measure the power of the component at high values of $l$. Is this correct?</p>
<p>What I don't understand is, why can't the other experiments get measurements in the lower part of the plot?</p> | g13134 | [
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<p>How would you find an escape orbit which includes a given starting point (not assuming a circular starting orbit) and escapes the sphere of influence of the current body with a given remaining velocity?</p>
<p>A problem perhaps similar to Lambert's Problem, but instead of an arrival location and time, it is a final velocity.</p>
<p>I have a solution that someone suggested to me, that takes the final velocity as a hyperbolic excess velocity, uses that to calculate specific energy and semi major axis of the departure orbit. However they then assume that you're departure burn will occur at the periapsis of the new orbit and derive the eccentricity, and determine other elements of the departure orbit using that. The approach would work, though you have to use various guesses as the starting position until you find one that results in an orbit departing in the correct direction and the start is always at the periapsis of the departure orbit.</p>
<p>I am hoping that there is an answer to this problem that doesn't require starting at the periapsis of the escape orbit, as I think that would broaden the range of potential departure directions from a given point. However I don't know how I would begin to calculate that.</p> | g13135 | [
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<p>Could anyone tell me why the height is $2h$?, and is the total gpe in a system where the masses are balanced 0? </p>
<p><img src="http://i.stack.imgur.com/OcQae.png" alt="enter image description here"></p> | g13136 | [
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<p>I am trying to make sense to the issue of how does the <a href="http://en.wikipedia.org/wiki/Kac%E2%80%93Moody_algebra" rel="nofollow">Kac-Moody algebra</a> encode the symmetries of the non-truncated theory.</p>
<p>Let's contextualize a little bit. Ok, so in the 5 dimensional Kaluza-Klein we start with pure (5 dimensional) gravity. Then we assume a $M_4×S^1$ ground state where we have Minkowski space with a circle. The topology of this ground state breaks the 5D diffeomorphism invariance because now only periodic transformations are allowed. So considering a coordinate change</p>
<p>$$x\to{}x'=x+\xi,$$</p>
<p>we can Fourier expand</p>
<p>$$\xi(x,\theta)=\sum{}\xi(x)e^{in\theta}.$$</p>
<p>It is known that if we truncate at $n=0$ we get a theory of gravitation in 4 dimensional space-time, electromagnetism and a scalar field (sometimes called the Dilaton).</p>
<p>So, the remnants of the initial 5 dimensional diffeo invariance are 4 dimensinal diffeo invariance, $U(1)$ gauge and a scale invariance for the dilaton.</p>
<p>In the non truncated theory we will keep all the modes in the previous Fourier expansion and we will have more symmetries. The 4d diffeo and $U(1)$ gauge do survive in the non truncated version but not the scale invariance of the dilaton.</p>
<p>So far so good.</p>
<p>But, how to know the symmetries of the full theory? well, with Kac-Moody generalization of Poincaré algebras. For example in <a href="http://arxiv.org/abs/hep-th/9410046" rel="nofollow">http://arxiv.org/abs/hep-th/9410046</a> says this. But HOW exactly? I would like a clear explanation of how this Kac-Moody algebra encodes the remnant symmetries of the original diffeo 5 and also how the zero modes of this algebra correspond to diffeo4 and $U(1)$</p>
<p>EDIT:: this is the algebra I am talking about</p>
<p>$[P_{\mu}^{(n)},P_{\nu}^{(m)}]=0$</p>
<p>$[M_{\mu\nu}^{(m)},P_{\lambda}^{(n)}]=i(\eta_{\lambda\nu}P_{\mu}^{(m+n)}-\eta_{\lambda\mu}P_{\nu}^{(m+n)})$</p>
<p>$[M_{\mu\nu}^{(n)},M_{\rho\sigma}^{(m)}]=i(\eta_{\nu\rho}M_{\mu\sigma}^{(m+n)}+\eta_{\mu\sigma}M_{\nu\rho}^{(m+n)}-\eta_{\mu\rho}M_{\nu\sigma}^{(m+n)}-\eta_{\nu\sigma}M_{\mu\rho}^{(m+n)})$</p>
<p>$[Q^{(n)},Q^{(m)}]=(n-m)Q^{(n+m)}$</p>
<p>$[Q^{(n)},P^{(m)}_{\mu}]=-mP^{(n+m)}_{\mu}$</p>
<p>$[Q^{(n)},M^{(m)}_{\mu\nu}]=-mM^{(n+m)}_{\mu\nu}$</p> | g13137 | [
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<p>I have a problem with the calculus of magnetic moment of Li-6.</p>
<p>The configuration of protons is $1p_{3/2}$, and the neutrons' one is the same. </p>
<p>I have to add the magnetic moment of uncoupled proton and uncoupled neutron.</p>
<p>I use the following formula for $J=l+\frac{1}{2}$ (J is the particle spin):
$$ \frac{\mu}{\mu_N}=g_lJ+\frac{g_s-g_l}{2}$$</p>
<p>For the proton I have: $g_l=1; g_s=5.58 \rightarrow \frac{\mu}{\mu_N}=J+2.29=3.79$</p>
<p>For the neutron I have: $g_l=0; g_s=-3.82 \rightarrow \frac{\mu}{\mu_N}=-1.91$</p>
<p>So the total $\frac{\mu}{\mu_N}=3.79-1.91=1.88$, exactly 1 more than the correct value, 0.88!
What's wrong?</p> | g13138 | [
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<p>I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also like to go ahead and apologize for not knowing how to format correctly.</p>
<p>I was given that a particle is scattered with the given Hamiltonian:
$$
H = P^2 - g\delta(x)
$$
Where $\delta(x)$ is the <a href="http://en.wikipedia.org/wiki/Dirac_delta_function" rel="nofollow">Dirac delta function</a>. I was able to find the states in momentum representation, and was supposed to Fourier transform them to get the position representation states. Doing this leads to an integral with simple poles on the real axis, and can be solved by moving the poles above or below the real axis by some constant, applying the residue theorem, and taking the constant to zero. This leads to three different solutions, depending on if I move one pole up and one down (two possibilities), or both poles into a contour.</p>
<p>While I was talking to my professor, he mentioned that the solutions only work for certain values of $x$, and that the range of $x$ is given by what makes the arc in the contour go to zero. I'm actually having trouble seeing this, since that introduces an ambiguity in the solutions. If I shift the left pole up and the right pole down and close the contour in the upper plane, this means that x has to be positive, in order to get a decaying exponential in the integral. However there is nothing stopping me from moving the poles in the opposite way, and closing above to obtain a different solution for $x>0$.</p>
<p>Is there something wrong in the math, or is the way I move the poles governed by the physical situation I'm interested in? (Which would be no plane waves moving the left for $x>0$ d.)</p>
<p>I should mention that I am assuming:
$$
|\psi> = |p> + |\psi_{sc}>
$$ </p>
<p>Where p is the incoming momentum and $|\psi_{sc}>$ is the scattered portion of the wave function.</p>
<p>Working in momentum representation, I obtain:
$$
\psi_{sc}(k) = \frac{g - \frac{g^2 i}{2p+ g i}}{2\pi(k^2-p^2)}
$$</p>
<p>Where k is the momentum variable, and p is the fixed momentum of the incoming particle. The transform I obtain is:
$$
\psi_{sc}(x) = \eta \int_{-\infty}^{\infty} \frac{e^{i k x}}{k^2-p^2} dk
$$</p>
<p>This is where I run into the problem with the poles. I know there shouldn't be any waves traveling to the left for $x>0$. My final goal is to check my states by checking the reflection and transmission coefficients and confirming they add up to 1.</p> | g13139 | [
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<p>Why should adding a small amount of a stretchy material make an otherwise non-stretchy fabric stretch? Shouldn't the non-stretch fibres still constrain the maximum stretch of the fabric?</p> | g13140 | [
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<p>We have a tube (rigid or compliant) filled with a fluid (Newtonian or non-Newtonian). We apply a pressure drop and mobilize the fluid. What is the amount of energy required to transport a certain amount of fluid. I am looking for a general answer which takes into account both the type of fluid and type of tube otherwise it is straightforward to get an answer for the special cases.</p> | g13141 | [
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<p>I was revisiting some old popular science books a while ago and two statements struck me as incompatible.</p>
<ul>
<li><p>No-hair theorems: a black hole is fully-described by just a few numbers (mass, spin etc) irrespective of the type or configuration of the matter/energy within the event horizon.</p></li>
<li><p>Surface area measures entropy: you can't reduce the total entropy of the universe by throwing a box of hot gas into a black hole, its size/entropy will increase by the necessary amount.</p></li>
</ul>
<p>Suppose I have two black holes, A and B. They are identical and interchangeable, same mass, spin, charge...</p>
<p>I have two boxes, BoxA and BoxB. BoxA contains a kilogram of salt in the form of a single crystal and BoxB contains a kilogram of salt as loose powder. <strong>BoxA has less entropy than BoxB</strong> but is otherwise identical.</p>
<p>I throw BoxA into A and BoxB into B.</p>
<p>The no-hair theorems seem to imply that A and B will increase in size by the same amount. The entropy theorems seem to imply that B will end up larger than A.</p>
<p>What am I missing here?</p> | g13142 | [
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<p>Here's an intuitive problem which I can't get around, can someone please explain it?</p>
<p>Consider a proton P and an electron E moving through the electromagnetic field (or other particles for other forces, same argument). They exert a force upon one another. In classical mechanics this is expressed as their contributing to the field and the field exerts a force back upon them in turn. In quantum mechanics the model is the exchange of a particle.</p>
<p>Let's say one such particle X is emitted from P and heads towards E. In the basic scenario, E absorbs it and changes its momentum accordingly. Fine.</p>
<p>How does X know where E is going to be by the time it arrives? What's to stop E dodging it, or having some other particle intercept X en route?</p>
<p>Are P and E emitting a constant stream of force-carrying particles towards every other non-force-carrying particle in the universe? Doesn't this imply a vast amount of radiation all over the place?</p>
<p>I am tempted to shrug of the entire particle exchange as a mere numerical convenience; a discretization of the Maxwell equations perhaps. I am reluctant to say "virtual particle" because I suspect that term means something different to what I think it means.</p>
<p>Or is it a kind of observer effect: E "observes" X in the act of absorbing it, all non-intercepting paths have zero probability when the waveform collapses?</p>
<p>Or have I missed the point entirely?</p> | g13143 | [
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<p>1) How vwoulHow would I go about writing the time dependent wave function given the wavefunction at $t=0$?
go about writing the time dependent wave function given the wavefunction at $t=0$? </p>
<p>Suppose How would I go about writing the time dependent wave function given the wavefunction at $t=0$?
an electron is in a superposition state in the hydrogen atom at $t=0$ with normalized wavefunction:
How would How would I go about writing the time dependent wave function given the wavefunction at $t=0$?
I go about writing the time dependent wave function given the wavefunction at $t=0$? </p>
<p>$$\psi(r,\theta,\phi) ~=~ A(2R_{10}Y_{00}+4R_{21}Y_{1,-1}).$$</p>
<p>2) What woHow would I go about writing the time dependent wave function given the wavefunction at $t=0$?
uld the tiHow wouHow would I go about writing the time dependent wave function given the wavefunction at $t=0$?
ld I go about writing the time dependent wave function given the wavefunction at $t=0$?
me dependent wave function look like? </p>
<p>3) Also how couHow would I go about writing the time dependent wave function given the wavefunction at $t=0$?
ld I tell if the probabilities of measuring a certain energy, or angular momentum arHow would I go about writing the time dependent wave function given the wavefunction at $t=0$?
e time dependent?</p> | g13144 | [
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<p>I have been told that industrial mixing machines (say, for cake batter) switch directions periodically, first stirring in one direction, then the other, because this mixes the material more thoroughly.</p>
<p>I imagine (but don't know for sure) that stirring in only one direction will tend to create helical structures in the mixed material, where each helix is more or less uniform but two helices might be quite different from one another; and that switching directions tends to break up and mingle these helices. Is this at all correct?</p>
<p>Is there a way to quantify the effectiveness of different methods of stirring? If so, how much better is it to stir in alternating directions, and how often should one switch directions? </p> | g13145 | [
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<p>If you have a set amount of space, lets say 10 cubic centimeters, and you would be able to trap photons in there.<br>
If you would then add more and more photons to that space, could you then go on infinitely or would you eventually run into a maximum amount of photons that can be in that space?</p> | g13146 | [
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<p>I'm confused about the following problem.</p>
<blockquote>
<p>A ball is shot from the ground into the air. At a height of $9.1\text{ m}$, its velocity is $v = (7.6\hat{\imath}+ 6.1\hat{\jmath})\text{m/s}$, with $\hat{\imath}$ horizontal and $\hat{\jmath}$ upward. </p>
<ol>
<li>To what maximum height does the ball rise?</li>
<li>What total horizontal distance does the ball travel?</li>
<li>What is the magnitude and angle (below the horizontal) of the ball’s velocity just before it hits the ground?</li>
</ol>
</blockquote>
<p>The given answers are: (1) 11m, (2) 22.76m, (3) 16.57m/s, 62.69</p>
<p>We know $S=ut + 1/2 at^2$. So,</p>
<p>$$Y = Y_0 + V_{0y}t - 1/2gt^2$$</p>
<p>and,</p>
<p>$$X=X_0 + V_{0x}t$$</p>
<p>and $v=u+at$, so</p>
<p>$$V_x = V_{0x} - gt$$</p>
<p>and </p>
<p>$$V_y = V_{0y} - gt$$</p>
<p>and we're given that $V_x=7.6$ and $V_y=6.1$</p>
<p>I can realize that here $Y = 9.1\text{ m}$ but I cant find the $V_0$ and also the initial angle. How can I do that?</p> | g13147 | [
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<p>Since a magnetic field can induce a current in a coil, moving electrons from one side to another. Why isn't possible to use the same principle in a electrophorus using one magnet instead of charged body?</p>
<p>What's the difference between induction with magnetics and a negatively charged body? </p>
<p>P.S: I'm not asking for clarification about the difference about a magnetic field and a electric filed. Maybe it's related, but my point is that if both can induce charges, why it cannot act as a substitution on a electrophorus?</p> | g13148 | [
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<p>In QFT texts with $c=1$ units (most of them), D'Alembert operator is written as:</p>
<p>$$\Box ={\partial^2 \over \partial t^2} - \nabla^2$$</p>
<p>For pedagogical purposes, however, some texts don't set $c=1$, and then</p>
<p>$$\Box =\frac{1}{c^2} {\partial^2 \over \partial t^2} - \nabla^2$$</p>
<p>Is that right? I am a bit confused because Wikipedia uses the second form <a href="http://en.wikipedia.org/wiki/D%27Alembert_operator" rel="nofollow">here</a> despite the fact that, in the very next line it is stated </p>
<blockquote>
<p>We have assumed units such that the speed of light $c=1$</p>
</blockquote>
<p>Am I missing something very basic, or is that page in Wikipedia simply wrong?</p>
<hr>
<p>EDIT: In other words, when $c=1$ is assumed, $c$ NEVER appears in the equations. Is that correct in QFT, just as it happens in GR?</p> | g13149 | [
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<p>I am reading up on Chern-Simons matter theories in $d=3$. Here is the quote (from <a href="http://thesis.library.caltech.edu/7111" rel="nofollow">http://thesis.library.caltech.edu/7111</a> page 15) that I am having trouble with:</p>
<p><em>One could also add a supersymmetric Chern-Simons term for the gauge multiplet. This restricts one to at most N = 3 supersymmetry. However, in the presence of a Chern-Simons term alone (i.e., no Yang-Mills term), the gauge field is nonpropagating, and with a clever choice of matter content and superpotential, one can obtain very large amounts of supersymmetry</em></p>
<p>Context: The discussion is about possible supersymmetric constructions using vector multiplets. There are two things I do not understand:</p>
<ol>
<li><p>Is it true that in the presence of a CS term alone (No Yang-Mills, no matter), the supersymmetry is limited to ${\cal N}=3$. If so, why?</p></li>
<li><p>I understand that when we add matter in a clever way one can obtain extended supersymmetry (as in the ABJM paper <a href="http://arxiv.org/abs/0806.1218" rel="nofollow">http://arxiv.org/abs/0806.1218</a>). What I don't understand is that what does have to do with the gauge field being non-propagating??</p></li>
</ol>
<p>I guess that the answer to my second question lies in the answer to the first. Any help?</p> | g13150 | [
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... |
<p>Consider a hollow cylinder carrying a current $I$ and a wire outside the cylinder carrying a current $I'$.
Let's say the cylinder is symmetrical with even current distribution etc.. so the $\mathbf{B}$ field at any point (due to current in cylinder) within the cylinder is zero by Amperes Law. However, this doesn't mean the $\mathbf{B}$ field is zero within the cylinder entirely - there is a $\mathbf{B}$ field contribution from the wire. So my question is: What is the usefulness of Amperes Law?</p>
<p>Does Ampere's Law only tell me something about the $\mathbf{B}$ field from a particular source?</p>
<p>Also say we have a solid cylinder inside a hollow cylinder with radii $a$ and $b$ respectively. They have opposite current directions. Then by Ampere, the $\mathbf{B}$ field at some point $P$ where $a < P < b$ is given as $B = \frac{\mu I}{2\pi r}, I $ the current in the solid cylinder. Is it really? The $\mathbf{B}$ field from the hollow cylinder will be in the opposite direction at $P$ and so acts to cancel the $\mathbf{B}$ field at $P$ from the solid cylinder thus resulting in zero net $\mathbf{B}$ field, no? Yet the $\mathbf{B}$ field at $P$ is in fact nonzero?</p>
<p>I understand how the non zero $\mathbf{B}$ field was obtained using Ampere's Law, but the Amperian loop which coincides with $P$ does not simply shield the $\mathbf{B}$ field from the hollow cylinder. So I am struggling to see why the $\mathbf{B}$ field would be nonzero.</p>
<p>Many thanks.</p> | g13151 | [
-0.00849935319274664,
-0.005129408556967974,
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-0.009653660468757153,
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0.03561649098992348,
-0.04148897901177406,
0.04402759671211243,
-0.0438837930560112,
-0.039... |
<p>Do black holes have charges? If so, how would they be measured? Also, does electricity behave the same way? Black holes affect photons, which are carriers of EM radiation, so do black holes have any effect on the electric force?</p> | g13152 | [
-0.0009214181918650866,
0.007915902882814407,
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0.0018986309878528118,
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0.02409648895263672,
0.011242521926760674,
-0.0076116654090583324,
-0.041097525507211685,
... |
<p>How can electron spins in Iron at room temperature have ferromagnetic order even though they are travelling at very high speeds?</p>
<p>One could argue that spin and motion are completely uncorrelated and hence you can have superfast electrons that still somehow manage to orient their spins - but then how do you explain domains?</p> | g13153 | [
0.03047986514866352,
0.033050213009119034,
-0.006207687314599752,
0.045111507177352905,
0.09052912890911102,
0.010335516184568405,
0.047732844948768616,
0.0195445716381073,
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-0.012185863219201565,
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0.0075629050843417645,
0.026049872860312462,
-0.... |
<p>I've seen the other posts on this question, but unfortunately I'm still having difficulty understanding the meaning of the direction of the torque vector. It makes intuitive sense that the magnitude of the torque exerted on an object is dependent on the length of the lever arm and the angle between the lever arm and the applied force. </p>
<p>What I don't understand is what the direction of the torque vector is describing. How can I relate the direction of the torque vector to a real world example (that is not an example involving a wrench + screw and the screw "unscrewing" in the direction of the torque...which doesn't give me any more of an intuition on what torque means).</p>
<p>Thanks! </p> | g413 | [
0.020419592037796974,
-0.014988237991929054,
0.0009240862564183772,
-0.030071480199694633,
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0.08949322998523712,
0.01858959160745144,
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-0.02285078540444374,
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-0.03554657846689224,
0.07069958001375198,
-0.... |
<p>I am a layman and was wondering, the quantum observer effect. The regular notion to laymen seems to be literally "if you look at it", but as I am coming to understand the world I live in better I feel it means just coming in contact with something. </p>
<p>Is this an ongoing question? Whether a particle that is not interacting with anything undergoes changes in state? Though now that confuses me too, If it is in two states at once. What denote say spin to the left from spin to the right, what denotes the origins of the calculations we make?</p> | g13154 | [
0.013739386573433876,
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0.013153170235455036,
0.04317142069339752,
-0.009560... |
<p>Could <a href="http://en.wikipedia.org/wiki/High_Frequency_Active_Auroral_Research_Program" rel="nofollow">HAARP</a> (or any other secret device) really trigger an earthquake?
For example I've heard that U.S Trigger 6.3 magnitude earthquake in Kaki near Bushehr to destroy Iran's nuclear power plant!?</p>
<p>(<em>Earthquake killed 37 people and injured 850 until know.</em>)</p> | g414 | [
0.00711275078356266,
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0.032525449991226196,
-0.05... |
<p>I'm studying the problem of the radiation of an uniformly accelerated point charge:</p>
<p>$$x^{\mu}(\lambda)\to(g^{-1}\sinh g\lambda,0,0,g^{-1}\cosh g\lambda)$$</p>
<p>I found that when a point charge is moving along the $z$ axis with a constant acceleration $g$, the components of the 4-potential can be found using Rindler coordinates:</p>
<p>$$z=Z\cosh g\tau, \qquad t=Z\sinh g\tau \qquad \mathrm{I} $$
$$z=Z\sinh g\tau, \qquad t=Z\cosh g\tau \qquad \mathrm{II} $$
$$z=-Z\cosh g\tau, \qquad t=-Z\sinh g\tau \qquad \mathrm{III} $$
$$z=-Z\sinh g\tau, \qquad t=-Z\cosh g\tau \qquad \mathrm{IV} $$</p>
<p>with the metric</p>
<p>$$ds^{2}=\epsilon(-g^{2}Z{}^{2}\, d\tau^{2}+dZ^{2})+dx^{2}+dy^{2}$$</p>
<p>where $\epsilon=+1$ in regions I and III, and $\epsilon=-1$ in regions II and IV. And the numbers indicate the space-time region:
<img src="http://i.stack.imgur.com/LBqaG.png" alt="enter image description here"></p>
<p>Now, I understand that the potentials obtained with the Rindler coordinates must be equivalent to the Liénard-Wiechert potential, because the change of coordinates (Minkowski->Rindler) is equivalent to change from an inertial frame of reference to an accelerated one. The problem is, the article </p>
<blockquote>
<p>Radiation from a uniformly accelerated charge. D G Boulware. <a href="http://dx.doi.org/10.1016/0003-4916%2880%2990360-7" rel="nofollow"><em>Ann. Phys.</em> <strong>124</strong> no.1 (1980), pp. 169–188</a>. <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.205.5420" rel="nofollow">Available on CiteSeerX</a></p>
</blockquote>
<p>finds that the components of the 4-potential (Rindler coordinates) are:</p>
<p>$$A_{\tau}=-\frac{eg}{4\pi}\frac{\epsilon Z^{2}+\rho^{2}+g^{-2}}{\left[\left(\epsilon Z^{2}+\rho^{2}+g^{-2}\right)^{2}-4 \epsilon Z^{2}g^{-2}\right]^{1/2}}$$</p>
<p>where $\rho^{2}:=x^{2}+y^{2}$. $A_x=A_y=0$, and </p>
<p>$$A_{Z}=-\frac{e}{4\pi Z}$$</p>
<p>In regions I and II.</p>
<p>My <strong>question</strong> is: How can I conclude that this components are actually equivalent to the components of the Liénard-Wiechert potential?</p> | g13155 | [
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0.02... |
<p>I recently tumbled over a statement in a <a href="http://dx.doi.org/10.1190/1.3554411" rel="nofollow">geophysics paper</a> (<a href="http://www.cgg.com/technicalDocuments/cggv_0000009953.pdf" rel="nofollow">PDF here</a>). They have a wave equation which they formulate as</p>
<blockquote>
<p>$$
\frac{1}{v_0}\frac{\partial^2}{\partial t^2}
\begin{pmatrix}p \\ r\end{pmatrix}
=
\begin{pmatrix} 1+2\epsilon&\sqrt{1+2\delta}\\\sqrt{1+2\delta} &1\end{pmatrix}
\begin{pmatrix}G_{\bar x \bar x}+G_{\bar y \bar y}&0\\0&G_{\bar z \bar z} \end{pmatrix}
\begin{pmatrix} p\\r \end{pmatrix}\tag{20}
$$</p>
</blockquote>
<p>and they claim that</p>
<blockquote>
<p>To achieve stability, the rotated differential operators $G_{\bar x \bar x}$, $G_{\bar y \bar y}$, and $G_{\bar z \bar z}$ should be self-adjoint and nonpositive definite as are the second-order derivative operators ($\tfrac{\partial^2}{\partial x^2}$, $\tfrac{\partial^2}{\partial y^2}$ and $\tfrac{\partial^2}{\partial z^2}$).</p>
</blockquote>
<p>(see eq. 14 and statement under eq. 20). They also claim that self-adjointness and nonpositiveness of the differential operators of the wave equation are necessary to conserve the energy in this system, and that if they were not self-adjoint, numerical instabilities occur.</p>
<blockquote>
<p>We have solved the problem by introducing the self-adjointness to the operator matrices in equation 20 to make sure that energy is conserved during the wave propagation to avoid amplitude blowup in the modeling.</p>
</blockquote>
<p>In this case the wave equation consists of two coupled elliptical PDEs. What happens in general, when some operators are not bounded and linear?</p>
<p>Unfortunately I don't have the mathematical background to understand this statement.</p> | g13156 | [
0.02183983288705349,
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0.00033040280686691403,
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0.06098432093858719,
-0.016299249604344368,
0.... |
<p>How do we know superposition exists? Has it been observed, or has it been deduced, and how certain are we?</p>
<p>The Copenhagen Interpretation seems to imply that superposition collapses into one state once measurement has occurred, so I don't understand how we can observe it.</p>
<p>The reason I ask is I'm totally bewildered by the mainstream interpretations of Quantum Mechanics. I understand its probabilistic; I'm very accepting of the idea of there existing fundamentally stochastic scenarios where the initial state does not entirely determine the next state. What I don't understand is why superposition is so necessary to the theory. The two mainstream explanations are the Copenhagen Interpretation and the Many Worlds Theory, which both seem so incredibly farfetched and counterintuitive.</p>
<p>Thanks for any help or insight.</p> | g13157 | [
0.010729490779340267,
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-0.05411206930875778,
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0.022553550079464912,
0.030... |
<p>Coulomb's law is formally parallel to Newton's Law of Universal Gravitation, which is known to give way to General Relativity for very large masses. Does Coulomb's Law have any similar limits of applicability? What physics takes over then? Does the law hold for very large and very small charges?</p> | g13158 | [
0.011176844127476215,
0.08621755987405777,
0.004995372146368027,
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0.025384606793522835,
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0.028379295021295547,
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0.006331336218863726,
-0.014... |
<p><img src="http://i.stack.imgur.com/9zeX7.png" alt="enter image description here"></p>
<p>I'd like to calculate how polygons bounce off a plane. In this picture, the square doesn't bounce straight up, but instead it bounces somewhat to the right and starts spinning. But I have no idea what angle it bounces and how much energy is converted into rotational kinetic energy.</p> | g13159 | [
0.05881812050938606,
0.039405759423971176,
0.009435374289751053,
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0.04025901108980179,
0.027738235890865326,
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0.007537878584116697,
0.01746945083141327,
-0.... |
<p>Whatever happens in there is not falsifiable nor provable to the outside. If for (amusing) example the interior consisted of 10^100 Beatles clones playing "Number Nine" backwards, do we know how to unscramble the Hawking radiation to divine this? The same question applies to this new firewall furor. So of what use is a description of the interior to our physics on the outside?</p>
<p>The only possibility of usefulness I can see is if our own universe can be described as an interior up to the cosmic horizon in de Sitter space. But that's only an "if".</p> | g13160 | [
-0.013483728282153606,
0.09056299179792404,
0.004143719095736742,
-0.0497843436896801,
-0.026126757264137268,
0.0005818053614348173,
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0.010428449138998985,
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-0.09554000198841095,
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0.0018605230143293738,
0.01717967353761196,
0... |
<p>I have come across an article which talks about quantum discord (Observing the operational significance of discord consumption. M. Gu <em>et al. Nature Physics</em> <strong>8</strong>, 671–675 (2012) <a href="http://dx.doi.org/10.1038/nphys2376" rel="nofollow">doi:10.1038/nphys2376</a>), but I am struggling with the abstract, which says:</p>
<blockquote>
<p>The amount of extra information recovered by coherent interaction is quantified and directly linked with the discord consumed during encoding. <strong>No entanglement exists at any point of this experiment</strong>. Thus we introduce and demonstrate an operational method to use discord as a physical resource.</p>
</blockquote>
<p>So how can this happen? Usually quantum computations are thought to consume entanglement to perform calculations, and only pure states are involved. However, when quantum discord is discussed, the mixed state description makes it hard to understand where 'discordance' comes from.</p>
<p>Are there explicit (mathematical) examples that demonstrate whether it is possible to have</p>
<ul>
<li>(a) zero entanglement, non-zero discord;</li>
<li>(b) non-zero entanglement, zero discord; and</li>
<li>(c) non-zero entanglement, non-zero discord?</li>
</ul>
<hr>
<p>In classical information theory, the (Shannon) entropy is defined by
$ H(A) = -\sum p_i \log(p_i) $ for a given probability distribution $p_i$. The mutual information can be defined as</p>
<p>$$\mathcal{I}(A:B) = H(A)+H(B)-H(A,B)$$
or
$$\mathcal{J}(A:B) = H(A)+H(B|A),$$</p>
<p>where $H(A,B)$ and $H(B|A)$ are the entropy of joint system and the conditional entropy, respectively. These two expressions are equivalent in the classical case, and the second one can be derived from the first one using Bayes' rule.</p>
<p>Similar expressions can be defined in the quantum system, with the entropy replaced by the Von Neumann entropy,
$$H(\rho)=-Tr(\rho \ln \rho).$$</p>
<p>However, the expressions $\mathcal{I}(A:B)$ and $\mathcal{J}(A:B)$ are not always equivalent in quantum systems and the difference is called the quantum discord:</p>
<p>$$ \mathcal{D}(A:B) = \mathcal{I}(A:B) - \mathcal{J}(A:B).$$</p>
<p>Therefore, it can be treated as a measure for the non-classical correlations in a quantum system.</p> | g13161 | [
0.014851902611553669,
0.0002553282829467207,
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0.04646371304988861,
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0.028443217277526855,
0.0009776776423677802,
-0.021181518211960793,
-0.010707048699259758,
0.002798131201416254,
-0.030572030693292618,
... |
<p>I'm trying to show that the electromagnetic energy density and momentum density satisfy the inequality: $ u \geq c |\vec{\wp}| $, where $\wp$ is the momentum density and $u$ is the energy density.</p>
<p>I can at least show that $$|\wp|^2 = \epsilon_0 \mu_0 \vec{S}\cdot\vec{S} = \epsilon_0 ^2 (\vec{E}\times\vec{B})\cdot(\vec{E}\times\vec{B})$$ and therefore $$|\wp|^2 = \epsilon_0^2 (E^2+B^2-2 \vec{E}\cdot\vec{B})$$ but I do not know how to proceed. How do I even get the $\mu_0$ back into the momentum density equation, given that $$u= \frac{1}{2}(\epsilon_0 E^2+\frac{1}{\mu_0}B^2)$$</p> | g13162 | [
0.005786197260022163,
0.03252076357603073,
-0.016680097207427025,
-0.030819594860076904,
0.05789991840720177,
0.044187724590301514,
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0.04048667103052139,
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0.030167490243911743,
-0.020704880356788635,
0.011524788103997707,
-0.02845185622572899,
0.0... |
<p>The Large Hadron Collider (LHC) "remains one of the largest and most complex experimental facilities ever built" (<a href="http://en.wikipedia.org/wiki/Large_Hadron_Collider" rel="nofollow">Wikipedia</a>); it may even be the most complex project in humankind's history (?).</p>
<p>Such projects usually have impact beyond their original target and boost science and technology in a non-trivial way. </p>
<p>I wonder, then, what kind of impact it has or might have on other science and technology fields, in particular on mathematics (if any), and what specific impact has mathematics had (or might have) on the LHC project (if any)?</p>
<p>Cross-post on mathoverflow: <a href="http://mathoverflow.net/questions/114363/impact-of-lhc-on-math" rel="nofollow">Impact of LHC on math</a>.</p> | g13163 | [
0.019040176644921303,
0.07288146764039993,
0.0114686144515872,
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-0.03095013089478016,
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0.04565434902906418,
0.023... |
<p>I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in <a href="http://www.youtube.com/watch?v=H0P7efmz7CY&feature=g-subs-u">this</a> video. However, I wonder; is this actually a duality? At the most fundamental level, we 'know' that everything is made up out of particles, whether those are photons, electrons, or maybe even strings. That light for example, also shows wave-like properties, why does that even matter? Don't we know that everything is made up of particles? In other words, wasn't Young wrong and Newton right, instead of them both being right?</p> | g304 | [
0.04782665893435478,
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0.02403377741575241,
0.013158118352293968,
0.07903603464365005,
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0.032326437532901764,
0.03950458765029907,
-0.024090956896543503,
0.03979133442044258,
0.034945033490657806,
0.030389348044991493,
0.0205... |
<p>when we electric field between two conductors in certain direction the current density should pass in its direction why current density direction change at boundary although the direction of electric field is the same for both conductors </p>
<p><img src="http://i.stack.imgur.com/qOEiH.png" alt="enter image description here"></p> | g13164 | [
0.05389475077390671,
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0.06758060306310654,
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0.020130153745412827,
0.01995008811354637,
0.00004282028749003075,
-... |
<p>Is it possible to cool down a system in milliseconds?
And if so how can I? If I have a red hot metal at 773.15K can I dope it to 673.15K super fast?</p> | g13165 | [
0.06373351067304611,
0.0023653972893953323,
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0.027491427958011627,
0.023991936817765236,
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0.00728619983419776,
0.021328885108232498,
0.05708223208785057,
0.021609319373965263,
-0.000... |
<p>I need the derivation of Bethe formula for stopping power, but I can't see the corresponding paper to this matter.</p>
<blockquote>
<p>Application of Ordinary Space-Time Concepts in Collision Problems and Relation of Classical Theory to Born's Approximation. E. J. Williams. <a href="http://dx.doi.org/10.1103/RevModPhys.17.217" rel="nofollow"><em>Rev. Mod. Phys.</em> <strong>17</strong> no. 2-3 (1945) pp. 217-226</a>.</p>
</blockquote>
<p>Can anyone help me about this paper please?</p> | g13166 | [
0.006589797325432301,
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0.02249869517982006,
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0.02411237545311451,
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0.04996854439377785,
0... |
<p><em>Experimental alert:</em> Someone may be able to answer this question experimentally simply by going to a shopping mall and finding the right piece of holographic jewelry.</p>
<p>My question is whether the type of front-view "thick film" hologram often seen in jewelry can be used to create a true mirror, one in which you can see an image of yourself reflected in the hologram.</p>
<p>I'm afraid I messed up the terminology quite badly in my first try at this question! The type of hologram I was trying to ask about is correctly called a <a href="http://www.holo.com/holo/book/book5.html" rel="nofollow"><em>reflection</em> (or <em>thick film</em> or <em>volume</em>) hologram</a> because of its ability to reflect light back in the direction from which it came. It does that using only photographic emulsion, via a wave exclusion effect similar to the one that gives peacock feathers and opals their bright colors. (For the record, I was originally thinking, quite incorrectly, that "reflection holograms" meant the ones that use holes in a smooth metallic surface, such as those seen on almost any credit card. Now I'm unsure what those ones are called.)</p>
<p><a href="http://askville.amazon.com/transmission-hologram-mirror-reflect-images/AnswerViewer.do?requestId=125019" rel="nofollow">At least one non-SE site</a> correctly points out that you cannot create a holographic mirror by using a <em>transmission</em> hologram, which is the kind where the light source passes through a film and you view it from the other side. (Again, I was using this term incorrectly in my first version of this question.) That's not a very deep answer, however, since light from the viewer plays no role at all in what is being seen in a transmission hologram. You can't reflect something whose light plays no role in the image being shown!</p>
<p>So, my question is this: Can the wave exclusion effect that is used in volume holograms, which lack any true metallic surfaces despite their shiny appearance, be configured in a way that makes it possible to reflect true images of objects in front of the hologram?</p>
<p>I suspect it's possible for two reasons: (1) Somewhere I still have a thick-film hologram of the insides of a watch. I clearly recall watching a bright spot move left and right on the image of a curved metal part within the watch as I moved a background light move left and right in front of the hologram. While a moving bright spot is hardly a complete image, it does indicate that a hologram is capable of a visible response to an object not in the original hologram. (2) I'm not aware of anything from diffraction theory that says you <em>cannot</em> use multilayer diffraction patterns to create simple, mirror-like reflecting surfaces. (Nor am I aware of anything that says you <em>can</em> for sure, either.)</p>
<p>So, experimenters: Does anyone out there have a hologram in hand that seems to reflect non-trivial light patterns?</p>
<p>And theorists: Regardless of how one would create it in the lab, is it mathematically possible to create multilayer diffraction patterns that, like metallic mirrors, would reflect light in a way that depends on the incident angle of the light?</p> | g13167 | [
-0.012781919911503792,
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0.005709205288439989,
0.04058577120304108,
-... |
<p>I was looking at "Properties of Compressed Liquid Water" (Table A-5) in Fundamentals of Engineering Thermodynamics by Moran. Table A-5 shows that the specific internal energy $u$ of compressed liquid water decreases as as the pressure increases at a fixed temperature. For instance, $u=418.24$ kJ/kg at $T = 100$ F and $P = 2.5$ MPa. While $u=412.08$ kJ/kg at $T = 100$ F and $P = 25$ MPa. Also, this same trend in specific internal energy is shown in <a href="http://www.nist.gov/srd/upload/NISTIR5078-Tab3.pdf" rel="nofollow">Table 3. Compressed Water and Superheated Steam</a>. This trend that the specific internal energy decreases with increases pressure goes completely against my intuition and the numerous examples of compressing a gas or two phase mixture in a cylinder with a piston. Any thoughts on how the internal energy is decreasing?</p> | g13168 | [
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0.015781547874212265,
0.007021330762654543,
-... |
<p>I want to build the brightest lamp, for it to be seen at daylight, should I use 3 2500 mcd LEDs or 1 6000 mcd?</p>
<p>And also Why?</p> | g13169 | [
0.0075644515454769135,
0.014103378169238567,
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0.00494746956974268,
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... |
<p>Every now and then, I find myself reading papers/text talking about how <em>this</em> equation is a constraint but <em>that</em> equation is an equation of motion which satisfies <em>this</em> constraint.</p>
<p>For example, in the Hamiltonian formulation of Maxwell's theory, Gauss' law $\nabla\cdot\mathbf{E}=0$ is a constraint, whereas $\partial_\mu F^{\mu\nu}=0$ is an equation of motion. But why then isn't $\partial_\mu j^\mu=0$, the charge-conservation/continuity equation, called an equation of motion. Instead it is just a 'conservation law'.</p>
<p>Maybe first-order differentials aren't allowed to be equations of motion? Then what of the Dirac equation $(i\gamma^\mu\partial_\mu-m)\psi=0$? This is a first-order differential, isn't it? Or perhaps when there is an $i$, all bets are off...</p>
<p>So, what counts as an equation of motion, and what doesn't?
How can I tell if I am looking at a constraint? or some conservation law?</p> | g13170 | [
0.02561197429895401,
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0.004604102112352848,
0.0017708165105432272,
0... |
<p>By "Gross-Neveu like" I mean non-supersymmetric QFTs whose partition function/beta-function (or any n-point function) is somehow exactly solvable in the large $N_c$ or $N_f$ or 't Hooft limit. </p>
<p>(..supersymmetric examples would also be helpful to know of if in case there are no other theories like the above..) </p> | g13171 | [
0.006544892676174641,
0.008692973293364048,
0.02526675909757614,
0.02355143241584301,
0.000005276681804389227,
0.003878803690895438,
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-0.0032141886185854673,
0.0002782735391519964,
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0.0068984185345470905... |
<p>I was doing leg press at the gym today and was curious how much weight I actually lift when I do the exercise as compared to when I do a squat.</p>
<p>Suppose I load $w_L$ onto the machine, which has an angle of elevation $\theta$. I know that the actual weight I lift vertically is $w_L \sin(\theta)$, but could someone give me an explanation why this is so? </p>
<p>My intuition is to appeal to simple trigonometry, which tells me the vertical side of the triangle is $w_L \sin(\theta)$.</p> | g415 | [
0.04806631803512573,
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<p>If you observe a picture of a person hanging on a wall who seems to be looking directly towards you always seems to be looking at you even though you change your angle of observation to the extremes.
The same can be observed in a television. If a television is watched by many people from different angles all observe that a person on the screen is looking at them.</p>
<p>Why does it happen like that?</p>
<p>Update:
I First thought that it may be because of some data being lost due to conversion of 3D to 2D. But same is observed in a theater while watching a 3D movie.</p> | g13172 | [
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0.003689019475132227,
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0.0... |
<p>We know that $$ds^2 = g_{\mu\nu}dx^{\mu}dx^{\nu},$$
Can you say how to calculate $ds$?</p> | g13173 | [
-0.03890422359108925,
0.02828824333846569,
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<p>If we have a particle in a 3D infinite square well box, with length $L$, e.g. an electron in a conduction metal. </p>
<p>By solving the Time independent Schrodinger equation, we can get the formula of
$$k^2=(n_x^2+n_y^2+n_z^2)\pi^2 / L ^2$$</p>
<p>Now each state occupies a volume of $(\pi/L)^3$</p>
<p>I don't get why we need to use the density of states, considering that at the bottom of the infinite square well, the energy levels are discrete, and in higher energy levels, there are more states than the bottom. Does that mean we shouldn't use density of states for the lower energy levels region?</p>
<p>My professor split the the whole system into ($e^j$) levels, where each level ($e^j$) was individual energy level was smeared by ($g^j$) states i.e. there are $g^j$ number of them, where $j$ is the superscript denoting the number of level it is in.</p>
<p>E.g. 10 energy levels At $j=1$ there are $g^1=10$ levels where $g^1 = 10$
I still couldn't get why they can treat it using a continuum?</p> | g13174 | [
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... |
<p>As asked in the title, is Hamiltonian containing enough information to judge the existence of spontaneously symmetry breaking?</p>
<p>Any examples?</p> | g13175 | [
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<p>It is approximately 275km from WVWHS to Kingston corners. If your car gets 30.0 miles per gallon and gas costs 3.85 per gallon, how many cents of gas is burned from going from school to Kingston corners?</p> | g13176 | [
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0.053281012922525406,
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... |
<p>What kind of image would a transcient toroidial black hole merger produce from it's gravitalional lensing effect?</p>
<p><a href="http://arxiv.org/abs/gr-qc/9905039" rel="nofollow">http://arxiv.org/abs/gr-qc/9905039</a></p>
<p>What does a torus shaped lens actually look like?</p>
<p>Are there any other hypothesized transcient shapes for gravitational lenses that could arise from a merger or collapse?</p> | g13177 | [
0.012589366175234318,
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0.046424902975559235,
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0.09237347543239594,
0.01495... |
<p>I am trying to find the required specifications of an paul RF trap, in which a proton can be confined.(trap dimensions,voltage frequency and amplitude used, etc). I have to solve the equations of motion numerically because the potential doesn't have a closed form for this specific geometry and equations of motion can not be solved analytically (indeed , only a series solution can be obtained for potential using Legendre polynomials and this series is present in the system of equations of motion) .</p>
<p>for this purpose, I solve this system of ODEs numerically (Runge-Kutta) and see if the ion leaves the trap. you know, I can simulate the motion for a <strong>limited time span</strong> (typically about some milliseconds at most). So if the ion happen to leave the trap after a longer time span , I can't notice that.</p>
<p><strong>The question is that how and when I can claim that the ion is confined in the trap?(using numerical methods)</strong></p> | g13178 | [
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0.006070725154131651,
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<p>i had a physics exam yesterday, which was all in all pretty good except for this one question which i just don't get.:</p>
<p><code>
9) Two forces 4N and 6N act at a point. All of the following could be the magnitude of their resultant except.</p>
<p>A) 1N B) 6N C)10N D)4N E) 8N
</code></p>
<p>Could you please help me to understand the logic behind this question?</p> | g13179 | [
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0.027232451364398003,
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<p>I am a student in Mechanical department and I took today a lesson with a title of <em>Orbital motion.</em> I need a good mechanics reference that discusses this topic. </p> | g98 | [
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0.02614503540098667,
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0.03723352402448654,
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<p>Let $f(x)$ a solution of the wave equation $\square f(x) = 0$. I don't understand why the following operator
$$
\mathcal{D} \equiv \frac{1}{2}(\nabla^2)^{-1} (x_0\partial_0 - C)
$$
for arbitrary constant C, works as an inverse of the D'Alembert wave operator, namely:
$$
\square \mathcal{D} \ast f(x) = f(x)
$$</p> | g13180 | [
0.01645786687731743,
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0.05262313410639763,
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0.001... |
<p>I am looking for the formula to calculate how much energy it requires to create a vortex. Can anyone assist please?</p> | g13181 | [
0.009424164891242981,
0.08937738090753555,
0.004269117023795843,
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0.018932251259684563,
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0.027309568598866463,
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<p>I'm learning supersymmetry, supergravity and superstring. I want some problems books to have some idea in this area. Is there this kind of books? Or are there some papers that have many solved model?</p> | g13182 | [
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<p>Assume a pulley and a massless rope. On one end there is a 10.0kg mass. On the other there is a 34.5kg mass. What is the acceleration of the 34.5kg mass?</p>
<p>I created a free-body diagram with $m_1g_1$ pointing up and $m_2g_2$ pointing down, so the total tension is $m_1g_1 - m_2g_2$. This results in 240 N downwards, so I divide by 34.5kg to get $6.96 m/s^2$. However that is incorrect. What is my mistake?</p> | g13183 | [
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0.0008302161586470902,
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0.024813184514641762,
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0.006835293024778366,
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<p>It's known that at the center of an electromagnet/solenoid the magnetic field $B$ is strongest there. At the pole/edge of the solenoid/ or electromagnet is the magnetic field $B$ strong? Let's assume $B$ = $1$ $Tesla$ at the center, how different is $B$ at the edges? </p>
<p><img src="http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/imgmag/barsol.gif" width="600" height="300"></p>
<p>In general, is it simple to create a $1$ $Tesla$ magnetic field or higher?
MRI's use field's above $4$ $Tesla$ yet it seems very complex and requires massive power & cooling. </p> | g13184 | [
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0.03145648539066315,
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0.036805443465709686,
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<p>The "Ozma problem" was coined by Martin Gardner in his book <a href="http://en.wikipedia.org/wiki/The_Ambidextrous_Universe" rel="nofollow">"The Ambidextrous Universe"</a>, based on <a href="http://en.wikipedia.org/wiki/Project_Ozma" rel="nofollow">Project Ozma</a>. Gardner claims that the problem of explaining the humans left-right convention would arise if we enter into communication (by radio waves, no images allowed) with life on another planet. We can ask the aliens to perform any experiment they want. It is claimed that the classical experiments with magnets, electrical currents, light polarization, gyroscopes etc. can't solve the problem. The only simple experiment that solves the problem is the beta decay in which the parity is not conserved and this can be used to distinguish humans left-right spatial relations. But all this are quite old, the parity violation in weak interactions was experimentally proved in 50s by Chien-Shiung Wu. I was wondering if something has changed since then and if there are some other experiments (maybe some thought experiments) and theories that can solve the Ozma Problem.</p> | g13185 | [
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0.0... |
<p>I noticed this one day, a lightning/thunder occurred and my Fabulosa Spanish music died for a second. But not FM? </p> | g13186 | [
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-0.0031017812434583902... |
<p>In optics one of "diffraction-limited" criteria is wavefront tolerance: a textbook example is is optical system with 1/4 wavelength limits producing image of a point source with 68% of the energy contained in the airy disk. Some optics books, however introduce a "roughness" idea, implying that certain mirror surface pattern would imply light scattering, and supporting this idea with naive ray-trace diagram. Does it make any sense, I would think one can made quite strong assertion, namely that <em>any mirror surface shape within 1/8 wavelength tolerance of paraboloid would produce an of a point source with 68% of the energy contained in the airy disk area</em>. Any proofs/refutations?</p> | g13187 | [
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0.058466024696826935,
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0.01820387691259384,
... |
<p>The equations of motions for the <a href="http://en.wikipedia.org/wiki/Double_pendulum" rel="nofollow">double pendulum</a> is given by </p>
<p>$$\dot{\theta_1} = \frac{6}{ml^2}\frac{2p_{\theta1} - 3\cos(\theta_1 - \theta_2)p_{\theta2}}{16 - 9\cos^2(\theta_1 - \theta_2)}$$ </p>
<p>and similarly for the other pendulum. In respect to what does the change in angle for the first pendulum refer to? Is it with respect to time? So that $\dot{\theta_1} = \frac{d\theta}{dt}$? </p> | g13188 | [
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0.027509678155183792,
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0.06764417886734009,
0.04904642701148987,
-0.0... |
<p>Let, diameter of cylinder hole of height 30m and diameter 2m filled with water. In a book, when author tried to find out the power for lifting all of the water then he used average height. why is that.
I mean he wrote average height $ h = \frac{0+30}{2}$.
why is that?</p> | g13189 | [
0.060505468398332596,
-0.011836133897304535,
-0.016842905431985855,
-0.055802229791879654,
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0.05980867147445679,
0.07679262012243271,
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0.039692576974630356,
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0.02780887670814991,
0.... |
<p>I had read somewhere that if a person attains twice the speed of light, he can actually reach the future. </p>
<ol>
<li><p>But since the world belongs to one time and space, how will it change for one particular person? </p></li>
<li><p>And if a person actually attains that speed wouldnt his body burn out because of such high velocity?</p></li>
</ol> | g13190 | [
0.00680715125054121,
0.060950301587581635,
-0.006682170554995537,
0.025154344737529755,
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0.020671289414167404,
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-0.020071879029273987,
-0.03860020637512207,
0.018199879676103592,
0.010331966914236546,
-... |
<p>How can I derive that
$$\vec{E}=-\vec{\nabla}\phi-\frac{\partial \vec{A}}{\partial t}$$ where $\phi$ is the scalar potential and $\vec{A}$ the vector potential? </p> | g13191 | [
0.050829850137233734,
0.026617832481861115,
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0.004411902278661728,
0.0819452702999115,
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0.06515994668006897,
0.007327529136091471,
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0.05011903494596481,
-0.01932871714234352,
-0.011796072125434875,
0.002339316997677088,
0.068094... |
<p>How <strong>Triangle Law and
Parallelogram law of addition</strong> of
Vectors are different?<em>Ain't they.</em></p>
<p>Please don't tell me the things
written in book......give me the
appropriate reason.And how do i distinguish between the two while adding vectors,what am i trying to say is i get really confused where to use parallelogram law and where triangle law</p>
<p>P.s:my basics are really weak though!May be the question might not be right</p> | g13192 | [
0.03608148545026779,
0.013503373600542545,
0.008260141126811504,
0.03412453085184097,
0.06143256276845932,
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0.0004798352892976254,
0.02640547789633274,
-0.0... |
<p>I wonder what were the main experiments that led people to develop the concept of wave function collapse? (I think I am correct in including the Born Rule within the general umbrella of the collapse paradigm.) Are there any instances where cases once thought to be examples of collapse have since been explained as the normal time-evolution of the wave function? </p>
<p>EDIT: I'm going to have to make an objection to Ron Maimon's very excellent answer about particle tracks as evidence of collapse. I've been waiting for someone to suggest what I personally have always considered the prototype of the wave function collapse, namely the appearance of flecks of silver on a photographic plate when exposed to the light of a distant star. This has the essential elements of collapse in a way that ordinary photographic exposures do not. The mere appearance of dots on a photographic plate does not signal the collapse of anything: it is readily explainable as a consequence of the rate of silver-bromide reduction being proportional to light intensity. It is only when the intensity becomes so very low that the time taken to accumulate enough energy for a single conversion becomes unreasonable that we must consider the explanation of wave function collapse. </p>
<p>The tracks in the cloud chamber do not demonstrate this phenomenon since the energy needed for the creation of the tracks is already available in the supersaturated gas. It is not necessary for the incoming particle to supply energy for the creation of the track, so there is no need to collapse its wave function. The straightness of the tracks is explained by Mott as an ordinary consequence of time-evolution of the wave function. There is no experimental proof that a single "particle" cannot be responsible for multiple tracks in the cloud chamber, because the tracks are not tagged according to which particle created them.</p> | g13193 | [
0.04615744203329086,
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-0.04133503511548042,
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0.08700868487358093,
0.06734... |
<p>Why does an object sink when filled with water, even if the same object would float without water inside?</p>
<p>For example, put an empty glass cup into water, and it floats.</p>
<p>But if you put a plastic container filled with water in water, it'll sink. Why is that?</p> | g13194 | [
0.045939553529024124,
0.037136565893888474,
0.011694768443703651,
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0.056503068655729294,
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0.03929447382688522,
0.01199528481811285,
-0.01... |
<p>Please help me with the following. I want to know if there is an equation/set of equations to find out the projected area of a (3-D) cube when it is oriented at different angles of attack to the fluid flow, rendering the velocity vector of the impinging fluid on the cube surface to change with each angle of attack. In particular, what is the projected area when the cube is oriented at such an angle that the flow velocity vector passes through one of the vertex and the geometric centre of the cube? Thanks.</p> | g13195 | [
0.017155541107058525,
0.03192775323987007,
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0.006829113699495792,
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0.048135314136743546,
0.010828516446053982,
-... |
<p>The speed of light in a material is defined as $c = \frac{1}{\sqrt{\epsilon \mu}}$. There are metamaterials with negative permittivity $\epsilon < 0$ and permeability $\mu < 0$ at the same time. This leads to a negative refractive index of these materials. </p>
<p>But do (meta-) materials exist with only negative $\epsilon < 0$ and positive $\mu > 0$ or vice versa? This would lead to a complex speed of light inside such materials.</p>
<p>What would be the consequences of a complex speed of light? Could particles reach unlimited speed inside these materials? Would there still be Cherenkov radiation? </p> | g13196 | [
0.025097711011767387,
0.0686870738863945,
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0.03516380116343498,
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0.011141817085444927,
0.027151791378855705,
0.03543771058320999,
0.024983972311019897,
-0.0006626... |
<p>There is a linear electro-optic effect called Pockels Effect
The brief is that refractive index changes due to electric field.
If there is an anisotropy (like birefringence) and electric field is in perpendicular to optical axis then refractive index changes for different polarization of ordinary rays.
It gets eigendirections 45 degrees to electric field.
Why so? Why it gets min 45 degrees but not exactly towards direction of E?</p> | g13197 | [
0.016310937702655792,
0.028973372653126717,
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0.019631698727607727,
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0.04766344279050827,
0.0014500117395073175,
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<p>I am reading this paper on <a href="http://arxiv.org/abs/hep-th/9601085" rel="nofollow">Dyons and Duality in $\mathcal{N}=4$ super-symmetric gauge theory</a>. The author finds the zero modes or a dirac equation obtained by considering first order perturbations to the Bogolomony equation for bps monopoles. He finds out that when the simple root used for embedding the SU(2) monopole is simple then the bosonic zero modes which I believe is the solution for the higgs field transform as $1 \oplus 0$, and when it is not a simple root it transforms as two doublets. Hope this is not required for my question. </p>
<p><strong>Then he says that the zero modes are SENSITIVE to the center of SU(2), and hence the isometry group is SU(2)? What does sensitive to the center mean? Is center the subset which commutates with all elements of SU(2)? How can it tell me about the isometry group?</strong></p> | g13198 | [
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0.10753899067640305,
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0.003985641058534384,
0.004094358533620834,
0.004... |
<p>I have a chair like this(shown in figure). I was kneeling on the part where we sit. I just gave a sudden push to the part where we rest the back, without moving my legs. I found that the chair is moving little in the direction I applied the force. I couldn't find any reason why this chair would move forward because I am inside this system and no external force is coming from outside. When I apply the force on it , equal amount of force I am applying there on the seat in the opposite direction, so there should not be any movement.</p>
<p>I tried this experiment again right now. Now holding on the handles of the chair. Did the same thing. Again found the chair moving.</p>
<p>Where I am wrong and how does the chair move?</p>
<p><img src="http://i.stack.imgur.com/NxRe7.jpg" alt="X"></p> | g13199 | [
0.018908532336354256,
0.030923787504434586,
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0.03109673783183098,
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0.032107748091220856,
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0.0266781747341156,
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-0.... |
<p>I'm trying to split a high power laser (1064nm, 20W, beam diameter @ 1/e^2 intensity: 3.2mm) into two beams and couple them after some additional optics into two SMF's (single mode fiber). So far I tried a PBS (polarizing beam splitter) cube and a NPBS (non polarizing beam splitter) cube. I can split the beam but the cubes seem to destroy the mode in the reflected port at high power. I conclude this because I couple approx. 20% less efficient in the SMF.
Does anybody know how to split(50:50 would be sufficient although polarisation dependent would be preferred) a high power beam without aggravating the mode?</p>
<p>Note1:
Plate beam splitters are not preferable as they usually have the same dielectric beam splitter coating as cubes and the reflected port tends to interfere with reflections from the back side of the plate
Note2:
I'm aware of Glan-Laser Calcite, Glan-Thompson and Glan-Taylor polarizers but as they are, similar to PBS/NPBS cubes, two cemented prisms and I personally suspect this layer to be the reason. I would like to know if anybody has experience with them concerning high power.</p> | g13200 | [
-0.010459075681865215,
0.018840961158275604,
0.019315868616104126,
-0.0018667050171643496,
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0.0873919352889061,
0.042969342321157455,
-0.0001999716623686254,
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0.006834479980170727,
-0.06962872296571732,... |
<blockquote>
<p>The horizontal force P acts on the rim of the homogeneous cylinder of radius R and weight W. Determine the smallest coefficient of static friction that enables the cylinder to start rolling up the 30◦ incline.</p>
<p><img src="http://i.stack.imgur.com/4JquL.jpg" alt="image"></p>
</blockquote>
<p>Which FBD would be correct? should it be a vertical normal force with friction force going on left, or should it be the normal force facing perpendicularly the 30 degree include while the friction is along the 30 degree line also. which is the proper fbd?</p> | g13201 | [
0.052809614688158035,
0.012163849547505379,
0.007368138525635004,
0.025247924029827118,
0.04470536857843399,
0.018450740724802017,
0.08488912880420685,
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-0.050155118107795715,
0.012087767943739891,
0.00032398197799921036,
0.02360542304813862,
-0.0... |
<p>Do you know any simple explanation on the reason why the turn-on delay time on a laser diode is reducing while we increase the bias current?</p>
<p>Turn on delay,is the time that the laser needs from the time that one applies the current until the time that the light goes out of the laser.This time is strongly depended to the input current density,the higher the bias current it is the less the turn on delay it is. That I don’t understand is the physics behind it,how that interaction occurs.</p>
<p>Is it something obvious, because I am trying to find a simple explanation and I can not.
Best Regards,
George</p> | g13202 | [
0.048789892345666885,
0.004302676767110825,
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0.042160242795944214,
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0.04284587875008583,
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0.0068259043619036674,
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0.03322838246822357,
0.06312399357557297,
-0.... |
<p>I wanted to know if there is a physical theory that considers that the laws of physics undergo an evolutionary process. That see the law of physics or the absence of them, as something dynamic, and that with time they slowly converge to something we know today. A kind of simulated annealing of the physical laws.</p> | g13203 | [
0.03851018846035004,
0.05138542875647545,
0.009293186478316784,
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0.05245046317577362,
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0.0184331014752388,
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0.01652355119585991,
0.047687556594610214,
-0.046639662235975266,
0.03351285308599472,
0.011335... |
<p>Can Helium disappear?
As we know Helium is lighter than air, so basically Helium fly off from Earth.
Is it possible that in the future we will run out Helium?</p> | g13204 | [
0.026721294969320297,
0.05025504156947136,
0.019650785252451897,
0.00032288182410411537,
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0.08986186236143112,
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0.029022768139839172,
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-0.02020537480711937,
-0.020655570551753044,
0.016218405216932297,
-0.0389857143163681,
0.052... |
<p>How would you evaluate
\begin{equation}|iD\!\!\!\!/-m|\end{equation} Where $D_{\mu}=\partial_{\mu}-ieA_{\mu}$.
I have an idea of how to do this without the gauge field, because it's essentially
\begin{equation}|i\partial\!\!\!/-m|=|\partial^{2}-m^{2}|^{1/2}\end{equation}
and A. Zee's book covers this is some detail. From what I can tell, you use $\ln|A|=\mathrm{tr}\ln A$. The trace is in momentum space
\begin{equation}\frac{1}{2}\int \frac{d^{4}k}{(2\pi)^{4}} \ln (k^{2}-m^{2}-i\epsilon)+C\end{equation}
How do you do this in the presence of a gauge field?
I've gotten this far
\begin{equation}|iD\!\!\!\!/-m|=e^{\frac{1}{2}\mathrm{tr}\ln \left(D^{2}-(e/2)\sigma^{\mu\nu}F_{\mu\nu}+m^{2}\right)}\end{equation}
With $\sigma^{\mu\nu}=(i/2)[\gamma^{\mu},\gamma^{\nu}]$. But I have no idea how to proceed.</p> | g13205 | [
-0.032975465059280396,
-0.06376103311777115,
-0.02256770059466362,
-0.05925866216421127,
0.04394249618053436,
0.0010407367954030633,
0.07615897804498672,
0.025567183271050453,
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0.024473153054714203,
0.01381873432546854,
0.011960533447563648,
-0.014255835674703121,
0.0... |
<p>My question is about electrically nonconductor dielectrics. We know such materials don't possess free charges.They have atoms bound together and every atom has specific numbers of electrons turning around its nucleus.</p>
<p>When we make a dielectric charged:</p>
<p>where does this charge go? </p>
<p>what keeps the charge fixed on the structure? </p>
<p>Are they bound to specific atoms? If your answer is "yes",so What makes that atom specific to possess the charge?</p>
<p>(same questions about positively charging.) </p> | g13206 | [
0.011774563230574131,
0.05582207813858986,
-0.03108845092356205,
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0.07095695286989212,
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0.007475440390408039,
-0.00801793672144413,
-0.06524877995252609,
0.013505706563591957,
0.0047513279132544994,
-0.... |
<p>What are some applications to the <a href="http://en.wikipedia.org/wiki/Van_der_Pol_oscillator" rel="nofollow">Van der Pol equation</a>? Are there any physical examples?</p> | g13207 | [
-0.0027845632284879684,
0.007380495313555002,
-0.013223507441580296,
-0.060566071420907974,
0.03953508660197258,
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0.04637382552027702,
0.015606996603310108,
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0.0045170350931584835,
-0.02822941727936268,
-0.0036488273181021214,
0.024259690195322037,
... |
<p>Q:</p>
<p>We have a homogeneous charged ball with radius R which contains a ball-shaped hollow (with radius := r and distance from center of the bigger ball (M) to the center of the hollow (N) := b).</p>
<p>What’s now the field force inside the hollow, depending on b?</p>
<p>————</p>
<p>I first thought about calculating E(Ball R, without a hollow) - E(of the hollow r, displaced ) to use the superpostion principle, but then i would have no idea how to calculate the latter of those… would be happy about any hints! </p> | g13208 | [
0.059393949806690216,
0.021408049389719963,
-0.024922698736190796,
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0.039362695068120956,
0.02552996762096882,
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0.029149580746889114,
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0.01325171161442995,
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0.023616807535290718,
-0.013434264808893204,
... |
<p>Scientists today think the expansion of the universe is accelerating. </p>
<p>According to Hubble's law, objects further away are moving faster than objects closer to us. The further away an object is, the further back in time we are seeing, so in the past objects moved faster (is this sentence correct?).</p>
<p>So because objects moved faster before than they do now, surely that's deceleration not acceleration?</p>
<p>my textbook says "if Scientists today think the rate of expansion of the Universe were decreasing then distant objects should appear different to Hubble's Law predictions: universe is accelerating. More distant objects would seem to be receding faster (since expansion was faster in the past)"</p> | g13209 | [
0.05292670428752899,
0.042657166719436646,
0.015394874848425388,
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0.04613906890153885,
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0.04839253053069115,
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0.07098303735256195,
0.030964... |
<p>In most <a href="http://www.colgate.edu/portaldata/imagegallerywww/98c178dc-7e5b-4a04-b0a1-a73abf7f13d5/ImageGallery/gaussian-beams.pdf">introductory analysis of Gaussian beam optics</a>, Helmoltz scalar optics is assumed. Hence polarisation is ignored. But I'm not clear what are the possible orientations for the lower transverse mode $T_{00}$ when full vectorial electric and magnetic fields are allowed.</p>
<p>Assuming cylindrical coordinates, where the beam propagates in the axial coordinate z. The intensity of the fundamental mode is axially symmetric; but How does look the electric field orientation for a linearly polarized gaussian beam? is it always aligned toward a fixed direction? it has axial symmetry as well?</p> | g13210 | [
0.0004100167425349355,
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0.029163749888539314,
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0.01666386052966118,
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0.007941951043903828,
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... |
<p>In various types of stars, one can learn how they evolve differently, depending on factors such as their size and chemistry. Some stars have a short lifetime and others much longer. </p>
<p>But, what is known about the lifetime and evolution of gas giants. Do they just remain stable until some external source, such as the burn out of the sun, disrupts this?</p> | g13211 | [
-0.03476011008024216,
0.021802106872200966,
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0.06076282635331154,
0.04868406057357788,
-0... |
<p>Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the fluctuated action reads</p>
<p>$$S_{fl}=\int dt dx \sqrt{g} ~{\vec \xi}^T~{\tilde O}~{\vec \xi}$$</p>
<p>Where the differential operator ${\tilde O}$ is given by</p>
<p>$${\tilde O}=\begin{pmatrix}
\nabla^2+M_1(x) & -\frac{1}{\sqrt{g}}\partial_x +M_{12} \\
\frac{1}{\sqrt{g}}\partial_x +M_{12} & \nabla^2+M_2(x)
\end{pmatrix}$$</p>
<p>Following the standard procedure, one has to compute the functional determinant of ${\tilde O}$ to obtain the effective action for the fluctuations. Now, since the system is coupled (off-diagonal elements are present), the computation of $\det[{\tilde O}]$ will be rather hard, if not impossible:</p>
<p>$$\det[{\tilde O}]=\det\begin{pmatrix}
\nabla^2+M_1(x) & -\frac{1}{\sqrt{g}}\partial_x +M_{12} \\
\frac{1}{\sqrt{g}}\partial_x +M_{12} & \nabla^2+M_2(x)
\end{pmatrix}\\=\det\left(\left(\nabla^2+M_1(x)\right)\left(\nabla^2+M_2(x) \right)-\left(-\frac{1}{\sqrt{g}}\partial_x +M_{12}\right)\left(\frac{1}{\sqrt{g}}\partial_x +M_{12}\right)\right)$$</p>
<p>However, formally, before attempting to compute the determinant, one can multiply out all the terms in the fluctuation Lagrangian $L_{fl}={\vec \xi}^T~{\tilde O}~{\vec \xi}$, partially integrate once in the off-diagonal terms and rearrange the fields $\xi_1 \xi_2$ such that if one puts all the terms back into matrix notation, one finds:</p>
<p>$$S_{fl}=\int dt dx \sqrt{g} ~{\vec \xi}^T~{\tilde O}~'~{\vec \xi}$$</p>
<p>where now</p>
<p>$${\tilde O}~'=\begin{pmatrix}
\nabla^2+M_1(x) & 0 \\
\frac{2}{\sqrt{g}}\partial_x +2M_{12} & \nabla^2+M_2(x)
\end{pmatrix}$$</p>
<p>If one proceeds to compute the determinant now:</p>
<p>$$\det[{\tilde O}~']=\det\left(\left(\nabla^2+M_1(x)\right)\left(\nabla^2+M_2(x) \right)\right)\\=\det\left(\nabla^2+M_1(x)\right)\det\left(\nabla^2+M_2(x) \right)$$</p>
<p>one finds a much simpler problem to solve.
Now my question - is this "simplification" actually allowed, or did I miss some subtlety which forbids such a rearrangement of bosonic fields at the Lagrangian level?</p> | g13212 | [
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<p>First of all, this question is going to seem a a bit of philosophy but know that vague and purposeless wandering is certainly not what i'm trying to propose here.<br>
Also, the reason i didn't post in philosophy communities is that they certainly know a lot less ( if anything ) of quantum mechanics than most of you here. </p>
<p>My question :
I heard several times that the results of quantum mechanics (double-slit experiment for instance ) challenge our logic. One example of that is the famous physicist Lawrence Krauss. </p>
<p>He keeps saying that after our discoveries of quantum mechanics, "logic" is becoming flawed.He wears a 2 + 2 = 5 T-Shirt to support his case. </p>
<p>Does anyone know exactly are physics reffering to when they introduce the word "logic" to say it shouldnt be taked for granted ? Would "logic" be common-sense ? would "logic" be sensory experience ? if yes, then i'd highly agree. While we can't experience aurally frequencies out of 20-20khz range we are certain that they do exist. </p>
<p>On the other hand, if "logic" reffers to our deductive and inductive logic then i dont understand.<br>
How could we say that the result of lots of year of deductive and inductive logic ( from Thales to Newton to our modern Science ) points out that deductive and inductive logic is flawed.<br>
Mathematics also rely heavily on deductive logic.Mathematics is also the language in which physics is formally expressed.<br>
Denying or not taking for granted even our "deductive logic" would be not taking for granted Mathematics in which case would end Physics. </p> | g13213 | [
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<p>I have very little background in physics, and none in quantum physics, but I've been reading about how sub-atomic particles behave probabilistically, so I was wondering, is it possible (even though the probability would be unimaginably small) that all the particles which make up my body are located somewhere 100 light years away?</p>
<p>Or have I misunderstood the concept?</p> | g13214 | [
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<p>If you take Einstein's field equations,
\begin{equation}
R_{\mu\nu}-\tfrac{1}{2}g_{\mu\nu}R = -\kappa T_{\mu\nu},
\end{equation}
and you insert the metric
\begin{equation}
g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu},
\end{equation}
then you get a field theory in flat spacetime for the propagation of the perturbation $h_{\mu\nu}$. This is 'linearised GR' and it's a first place to start for a description of gravitational waves. </p>
<p>The equations result from the linearisation process are a set of wave equations of the form
\begin{equation}
\square^{2}\bar{h}_{\mu\nu} = - 2\kappa T_{\mu\nu}.
\end{equation}
Here, $\bar{h}_{\mu\nu} = h_{\mu\nu} - \tfrac{1}{2}\eta_{\mu\nu}h$ is called the 'trace-reversed' perturbation, and $h=\eta^{\mu\nu}h_{\mu\nu}$ is the trace. </p>
<p>If you want to solve this animal, then you can follow the analogous problem in electromagnetism and use a retarded Green's function. You can guess the form of the Green's function and with a little refinement; this is how I have solved it.</p>
<p>However, I recently read that one can solve this equation <em>without guesswork</em>. Apparently, you have to impose the boundary conditions, that
\begin{equation}
\displaystyle\lim_{t\to-\infty}\left[\frac{\partial}{\partial r} + \frac{\partial}{c\partial t}\right]\,r\bar{h}_{\mu\nu}=0
\end{equation}
where the limit is taken along any surface $ct + r = constant$, together with the condition that $r\,\bar{h}_{\mu\nu}$ and $r \partial_{\rho}\bar{h}_{\mu\nu}$ be bounded by this limit. The book I saw this in said that the physical meaning of this is that there's no incoming radiation from past null infinity. </p>
<p>What am I looking for?</p>
<ul>
<li>What exactly are these three conditions telling us,</li>
<li>Why these conditions have the form that they do, and</li>
<li>What is means that a surface has constant $ct + r$.</li>
</ul> | g13215 | [
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0.020037533715367317,
0.07470323145389557,
0.013282283209264278,
-0.016089... |
<p>A general solition equation can be obtaion from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{92.6}$$
where $x_0$ is a constant of integration when we drived this solution from Lagrangian.</p>
<p><strong>Comparing to the sine-Gordon theory <a href="http://pauli.uni-muenster.de/tp/fileadmin/lehre/NumMethoden/WS0910/ScriptPDE/SineGordon.pdf" rel="nofollow">with this article </a>, can we convert our equation to the sine-Gordon equation?</strong> </p>
<p>Because this equation represented for 2 dimensions (1 space dimension and 1 time dimension) then how will I get Kink solutions and domain wall equation from the above equation.
Any elaboration would be helpful for me.
This is a continuing post of <a href="http://physics.stackexchange.com/questions/61019/solving-the-soliton-equation-without-energy">Solving the soliton equation without energy</a>.</p>
<p><strong>ADDITION:
If I want to visualize the solition equation (92.6) by graph then what would be the best process?</strong></p> | g13216 | [
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0.0008177154813893139,
-0.02291925624012947,
-0.026275990530848503,
0.0428253635764122,
0.054073259234428406,
0.0310... |
<p>I would like to ask you if the question asked </p>
<blockquote>
<p><em>What is the minimum force parallel to the plane, which can be prevent the block from slipping down the plane?</em></p>
</blockquote>
<p>I just did the calculation and and got the answer correctly but I didnt understand why i calculate like that to get the minimum force for that situation. And also, for what situation should I use static friction coefficient and kinetic friction coefficient? That's all thanks. I am studying for my final now so I need clarification not just by doing it right, but also knowing what I'm doing. I'm hoping for further explanation. :)</p>
<p>So basically this is the plane and the block.(The drawing is quite epic as I'm using 'Paint'.)
<img src="http://i.stack.imgur.com/SLyeJ.png" alt="enter image description here"></p> | g13217 | [
0.06342069059610367,
0.05935341492295265,
0.006149740424007177,
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0.018017619848251343,
0.010938930325210094,
0.05456247180700302,
0.03841426968574524,
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-0.04547426849603653,
0.017943914979696274,
0.03126989305019379,
-0.016800960525870323,
0.03034... |
<p>In an article, when considering invariance of the Hilbert action under a general coordinate change this formula appears for how the metric changes</p>
<p>$$\delta{}g_{\mu\nu}=\partial_{\mu}\xi^{\rho}g_{\rho\nu}+\partial_{\nu}\xi^{\rho}g_{\rho\mu}+\xi^{\rho}\partial_{\rho}g_{\mu\nu}.$$</p>
<p>I have (maybe naively) tried using the tensor coordinate change formula considering $x^{\alpha}~\to~ x'^{\alpha}=x^{\alpha}+\xi^{\alpha}$ (formula I guessed, it isn't specified in the article I am reading) but I don't get there.</p>
<p>So, how does this formula come up?</p> | g13218 | [
0.005997558124363422,
-0.012279502116143703,
-0.026607733219861984,
-0.00543553102761507,
0.019279206171631813,
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0.0646192878484726,
0.029136670753359795,
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0.02229388803243637,
-0.008872946724295616,
0.029773732647299767,
0.029142674058675766,
-0.015... |
<p>An under water explosion creates a bubbly which quickly collapses on itself. The action takes less that 1/100 of a second for bubbles less than a foot across. This creates a point of extremely focused energy at the middle point where the bubble collapses. In theory, this point focuses enough energy to trigger nuclear fusion. </p>
<p>Could the same effect be achieved by suspending a metal sphere under water which contains a near complete vacuum. If the sphere were opened uniformly along all of its surface area, the water rushing should create the same effect as the explosion, focusing all of the energy on a point at the center of the sphere.</p>
<p>IF not, then what are the limiting factors (surface tension maybe?) In my mind, It seems the major limiting factor is the shrinking surface area of the bubble as it collapses. as the surface area shrinks, the water molecules along the surface of the bubble would resist the change of surface area (some would need move away from the surface, in the oppisit direction of the collapse), causing the collapse rate to slow.</p> | g13219 | [
-0.004701291676610708,
0.05909658223390579,
0.039442747831344604,
0.02946079522371292,
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-0.03925178572535515,
0.0026366007514297962,
0.03997069597244263,
0.008190411143004894,
0.0252... |
<p>I was reading an article on Huffington Post (<a href="http://www.huffingtonpost.com/2014/03/31/multiverse-gravitational-waves_n_5062376.html?utm_hp_ref=science" rel="nofollow">link to article</a>) about the Multiverse theory. In the article it said this: </p>
<blockquote>
<p>The big news last week came from the Background Imaging of Cosmic Extragalactic Polarization 2 (BICEP2) experiment at the South Pole, which saw imprints in the cosmic microwave background—<strong>the oldest light in the universe</strong>, dating from shortly after the big bang...</p>
</blockquote>
<p>I am far from scientific, actually just a web dev, but I have an interest in learning and reading about science, so please explain your answer in a way I can understand it. My question is in regards to the bold type in the quote. Does light ever actually end, go away, or just cease to exist once it is created? Will this "oldest light in the universe" ever completely cease to exist, or does light stay around indefinitely.</p> | g13220 | [
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0.011672909371554852,
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0.0... |
<p>I am an undergraduate student and I would like to approach the subject of topological order with focus on topological quantum computation, I know (very) little QFT and basic algebraic topology (if that matters...).</p>
<p>To give a reference frame, I'd like to understand papers like <a href="http://arxiv.org/abs/quant-ph/9707021v1" rel="nofollow">http://arxiv.org/abs/quant-ph/9707021v1</a> or Preskill's great presentations: <a href="http://online.kitp.ucsb.edu/online/exotic_c04/preskill/" rel="nofollow">http://online.kitp.ucsb.edu/online/exotic_c04/preskill/</a>, and later to take it as my field of research for a PhD.</p>
<p>So my questions are:</p>
<p>1) What kind of studies are useful/needed for this field? I assume Quantum Computation/Information are, but what else? Quantum Field Theories, Topology, Quantum Optics...?</p>
<p>2) Which are univerities or research centers active in the field (preferably in Europe)?</p>
<p>3) Any reference suggested? (Better if beginner-focused)</p> | g13221 | [
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0.008991530165076256,
0.0348396822810173,
0.014333139173686504,
0.08743198215961456,
-0.04177... |
<p>Is the acceleration of a free-falling observer at the Schwarzschild radius of a black hole the same regardless of the numerical value of the radius (i.e. outside of a black hole, is the acceleration of the free-falling observer only a function of his distance from the Schwarzschild radius)? </p> | g13222 | [
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0.035271745175123215,
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0.047... |
<p>I'm currently studying physics at University and struggling with the problem mentioned, it's on a past paper I'm trying to do.</p>
<p>I have calculated the B field on axis as (sorry don't know how to format this yet)</p>
<p>$$B = \mu \frac{Ia^2 }{2(a^2 + z^2)^{3/2}}$$</p>
<p>In the $z$ direction.</p>
<p>The question then asks:</p>
<blockquote>
<p>At a small distance ($\rho\ll a$) off axis near the point $A=(0,0,z)$, the diverging magnetic flux density has a component perpendicular to the axis. Find this'
<img src="http://i.stack.imgur.com/A9iqn.png" alt="Diangram of setup"></p>
</blockquote>
<p>Should I use $\nabla\cdot\mathbf B=0$ then try and solve? Not really sure where to go from here.</p> | g13223 | [
0.07147980481386185,
0.03211909905076027,
0.005006317514926195,
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0.1077093780040741,
0.03272959217429161,
-0.0387... |
<p>So... recently a Newtonian-mechanics related exercise has raised in me many questions basically ragarding which forces influence a given system and how, I know they might sound bit too "noobish" but I just had to get them out of my chest (yes it really gave me something to think about in the last day).</p>
<p>perhaps you should take a look at the above mentioned exercise to better understand what I am trying to figure out</p>
<p><img src="http://s21.postimg.org/ek3mmimw7/Nuova_immagine_bitmap.png" alt="image of the system"> </p>
<p>So, I'm trying to figure out how this system works...
the exercise says (please forgive me for all the grammatical errors you will eventually find):</p>
<blockquote>
<h1>Problem</h1>
<p>a cube with a mass $\ M=50Kg$ is standing on a plain surface and can move on it without
friction. On that cube is standing another cube with a mass $\ m=10Kg$, at a given
distance $\ d=0.5 m$ from the upper-left corner of the cube. Initially, when everything is stationary, a force $\ F=100N$ is applied to the bigger cube horizontally (I assume that the force $\ F$ is constant); at the moment $\ t=2s$ the smaller cube falls. Calculate the friction coefficient between the two cubes.</p>
</blockquote>
<h1>Variables used:</h1>
<blockquote>
<p>$\ μ$= friction coefficient</p>
<p>$\ g$= gravitational acceleration on earth =$\ 9.81 m/s^2$</p>
<p>$\ a_M$= acceleration of the bigger cube ($\ M$)</p>
<p>$\ a_m$= acceleration of the smaller cube ($\ m$)</p>
<p>$\ F_f$= friction force</p>
</blockquote>
<p>So, I assume that the bigger cube carries the smaller one which moves with a constant, negative acceleration until it falls (please correct me if I'm wrong), with equation of motion</p>
<p>$\ x(t)= x_0 + v_0t + 1/2 at^2$</p>
<p>so $\ 0.5m = - 1/2 at^2$ ------> $\ a= -0.25 m/s^2 $</p>
<p>now...</p>
<p>$\ F- μ mg = Ma_M$</p>
<p>in other terms (and again please correct me if I'm wrong): $\ F$ is partially dissipated by the friction between the cubes, and the bigger cube moves under the influence of a force which equals to the applied force $\ F$ minus the friction force $\ F_f= μ mg$</p>
<p>now the universe collapses: the solution says:</p>
<blockquote>
<p>$\ μmg = ma_m$</p>
<p>$\ a_r = a_M - a_m = [ μg (m + M) -F] / M$ which leads to $\ μ=0.15 $</p>
</blockquote>
<p>But... what leads to those last two equations?</p> | g13224 | [
0.03003665618598461,
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0.002691472414880991,
0.0006538305315189064,
0.034787412732839584,
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-0.04739755392074585,
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0.017725596204400063,
-0.013975890353322029,
0.... |
<p>I have a Lagrangian $L$, a momentum $p$ and a Hamiltonian $H$:</p>
<p>$$L=\frac m 2(\dot z + A\omega\cos\omega t)^2 - \frac k 2 z^2$$</p>
<p>$$p=m\dot z + mA\omega\cos\omega t$$</p>
<p>$$H=p\dot z - L=\frac m 2 \dot z^2 - \frac m 2 (A\omega\cos\omega t)^2 - \frac k 2z^2$$</p>
<p>And I want to calculate $\frac {\partial H} {\partial z}$ and $\frac {\partial H} {\partial p}$. I understand from <a href="http://physics.stackexchange.com/questions/119992/what-do-the-derivatives-in-these-hamilton-equations-mean">this question</a> that I need to algebraically manipulate $H$ to express it in terms of $p$ and $z$. The answers there suggested trying to express $\dot z$ in terms of $z$ and $p$, and presumably I need to express $t$ in terms of $z$ and $p$ as well. But that seems like its going to lead into very nasty territory... first of all, I've got quadratics, so that's not an invertible function. Second of all, for $t$, if I have to use inverse trigonometric functions, then it'll only be valid over a particular range of the variable.</p>
<p>Could I get some pointers on how to tackle this calculation? Is inverting the various relations really the way to go?</p> | g13225 | [
0.013405011966824532,
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-0.019535990431904793,
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0.039002180099487305,
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0.03675498068332672,
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0.03521163389086723,
0.0027340867090970278,
0.03819... |
<p>Trying to teach myself general relativity. I sort of understand the derivation of the geodesic equation $$\frac{d^{2}x^{\alpha}}{d\tau^{2}}+\Gamma_{\gamma\beta}^{\alpha}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau}=0.$$ which describes "how" objects move through spacetime. But I've no idea "why" they move along geodesics. </p>
<p>Is this similar to asking why Newton's first law works? I seem to remember reading Richard Feynman saying no one knows why this is, so maybe that's the answer to my geodesic question?</p> | g760 | [
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0.07927530258893967,
0.02237... |
<p>Regarding static granular mixtures (pile of sand - particles with different sizes), is there an expression that will give me the entropy of such a mixture? I am interested in finding the entropy of the system initially and once it has been screened ie once the larger particles get sorted out, giving two piles (I think that ths is a reversible process, correct me if I am wrong). Would this mixing entropy be consistent with a bulk entropy such as $\Delta S = m c_p ln(T)$ ? Could I use this bulk entropy and the mixing entropy together in some free energy expression? I have looked for some references but I get nothing that I can access.</p>
<p>Thanks</p> | g13226 | [
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0.0222266037017107,
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-... |
<p>In the case of a point charge $q$ at the origin, the flux of $\vec{E}$ through a sphere of radius r is,
\begin{equation}
\oint \vec{E}\cdot d\vec{a} = \int \frac{1}{4 \pi \epsilon_0 }(\frac{q}{r^2}\hat{r})\cdot (r^2 \sin\theta d\theta d\phi \hat{r})=\frac{1}{\epsilon_0}q.
\end{equation}
I want to know that, how the above equation has the value of $\frac{1}{\epsilon_0}q$?</p> | g13227 | [
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0.026597531512379646,
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0.08035384863615036,
0.08068332821130753,
0.0273796... |
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