question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>How do I verify homogeneity and isotropy of space, for example for hyperbolic space? My idea is to verify that Lorentz transformations in 4-vectors can move any desired point on the hyperboloid into the origin, and can rotate the hyperboloid about the origin by an arbitrary angle. The problem is I do not know how to map these statements into a precise mathematical language. Can you please help me?</p> | g12856 | [
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<p>I'm trying to build a mathematical model of C. <em>elegans</em> locomotion under overdamped viscous environment. </p>
<p>In order to simplify this problem, I use six discrete pieces of rigid cylinders to represent worm body, and this chain of rigid pieces are connected by torsional springs this way:</p>
<pre><code> -----*-----*-----*-----*-----*-----
</code></pre>
<p>Notation: ------ is one piece of rigid body; * is torsional spring.</p>
<p>Suppose that 1) external drag force is applied on the center point of each piece, 2) we know the length of each piece, spring stiffness, and damping coefficient(which should be very small and negligible), and external viscous drag coefficients, 3) I input a periodically changing torque to the first torsional spring (counting from head), and supposedly posterior spring torque is coupled both to the angle displacement of the anterior spring and its current torque. </p>
<p>Can someone help me write a set of dynamics equations that describe the locomotion of the worm? Or I also appreciate if someone can suggest me some book or article to read about.</p>
<p>Thanks,</p>
<p>Frank</p> | g12857 | [
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<p>As far as I know the lightest gas is hydrogen due to low mass of its nucleus, but what if we were to somehow strip hydrogen atoms of electrons and enclose protons in a container made of teflon (high electronegativity).</p>
<p>Would such a proton-only gas be stable? And what would be its density under atmospheric pressure (assume teflon envelope around the gas)? Would electrostatic effects between positively charged protons contribute to lowering density of such gas?</p> | g12858 | [
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<p>Assuming that the black hole starts grow in the exact center of the planet and that the general structure of the planet does not degrade as it is eaten from the inside, would the gravity on the surface of the planet be affected by the black hole growing.</p>
<p>My uneducated guess is that as the matter becomes more compacted the gravity on the surface would actually decrease due to the fact that the distance to the mass, with respect to the surface, is increasing.</p>
<p>Also would the evaporation of the black hole actually decrease the total amount of mass in the center of the planet?</p> | g12859 | [
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<p>The gist of my query is in the title. </p>
<p>I have been searching for papers and studies that could provide transmission curves (in nematic liquid crystals) across the visible to near-IR range (or from 300 nm to 2200 nm). I would thus like to know if anyone has encountered, or happens to know, of how a layer of nematic liquid crystals (for example in an LCD) deals with incident infrared light - whether it allows the majority through, or if it absorbs/reflects most of the waves.</p> | g12860 | [
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<p>As a Mathematician reading about the Dirac equation on the internet, leaves me with a great deal of confusion, about it. So let me start with its definition:</p>
<p>The <strong>Dirac equation</strong>, is given by</p>
<p>$
i \hbar \gamma^\mu \partial_\mu \psi = m c\cdot \psi
$</p>
<p>where the Dirac matrices $\gamma^\mu$ are defined by
$\gamma^\mu\gamma^\nu + \gamma^\nu\gamma^\mu = \eta^{\mu\nu}$ and where
$\psi$ is a "solution". </p>
<p>Ok, the first deal of confusion already starts with the $\psi$'s. It seems that people freely see them as spinor valued functios or as "operator fields". </p>
<p>But if I understand this correctly, seeing them as operators, is not part of the
original picture, but was later added as the so called <strong>second quantization</strong>. Right?</p>
<p>Now my question is the following: Why do we need this second quantization of the
Dirac equation? What experiments can not be described by the original Dirac equation?</p>
<p>Maybe there is a list somewhere or such.</p> | g12861 | [
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<p>This question is based on an odd phenomenon I noticed last week. Since then, I've been collecting more data to try to get an accurate picture of the facts.</p>
<p>Each morning, I go to my bus stop. It's on a main road, and when I get there, there is a lot of traffic. Every couple minutes a large truck goes by, and I suddenly feel a breeze go by me. The catch here is that there is about a one-second delay between the truck passing by and the start of the breeze. What is causing this phenomenon?</p>
<p>Here's some more information: I'm about three meters from the road; The breeze begins roughly one second after the truck passes by, and last for one and a half seconds; The breeze seems to be blowing diagonally, from my rear left to my front right side (I'm in America, so the trucks go from left to right); The breeze does not seem to depend on truck size (although small vehicles do not cause it).</p>
<p>I do have two possible explanations for the breeze:</p>
<p>1) The truck goes by at about 30 mph. This could create a tiny, short-lived vacuum at the back as it moves forward, thereby drawing air towards the rear of the truck.</p>
<p>2) The breeze is the result of some sort of "bow shock" from the truck.</p>
<p>Neither of these explanations seem to satisfy me, though, because they seem a bit far-fetched, and I am certainly no expert in fluid mechanics. What could be the cause of the breeze?</p>
<p>As a last note, I have no idea what tags to use for this question, because I don't know what the cause of the breeze is. Suggestions for these and other edits are welcome.</p> | g12862 | [
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<p>Can someone please tell me why
$$4\int d^4x \, x^\mu x^\nu ~=~\int d^4x \, g^{\mu\nu}x^2 $$
by some rotational symmetry argument?</p> | g12863 | [
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<p>What are the most popular algorithms used to obtain a binodal curve
for the ternary mixture (starting from Flory-Huggins theory)? I would
like to obtain a plot similar to the one calculated here
<a href="http://physics.stackexchange.com/a/112972/46158">http://physics.stackexchange.com/a/112972/46158</a>.</p>
<p>I am aware that the binodal consists of pairs of points, say
$\phi=(\phi_A,\phi_B,\phi_C)$ and $\bar\phi=(\bar \phi_A,\bar
\phi_B,\bar \phi_C)$, for which the chemical potentials are equal</p>
<p>\begin{align}
\mu_A(\phi_A,\phi_B,\phi_C)=\mu_A(\bar \phi_A,\bar \phi_B,\bar \phi_C)\\
\mu_B(\phi_A,\phi_B,\phi_C)=\mu_B(\bar \phi_A,\bar \phi_B,\bar \phi_C)\\
\mu_C(\phi_A,\phi_B,\phi_C)=\mu_C(\bar \phi_A,\bar \phi_B,\bar \phi_C)
\end{align}</p>
<p>(here $\phi_A$, $\phi_B$ and $\phi_C$ are relative volumetric
concentrations of components $A$, $B$ and $C$).</p>
<p>Because the volumetric concentrations must sum to unity
($\phi_A+\phi_B+\phi_C=1$ and $\bar\phi_A+\bar\phi_B+\bar\phi_C=1$) so
we have a total of five conditions for six unknowns. To recover the
binodal it suffices to solve these five equations for pairs of points
$\phi$ and $\bar\phi$. This brute force approach was developed in
70s [1] but there is little to no information in more recent
experimental papers concerning the algorithms used by the authors. I
am unsure whether the algorithm from [1] is still used or some
alternative has been found.</p>
<p>[1] Hsu C C and Prausnitz J M 1974 Thermodynamics of Polymer Compatibility in Ternary Systems Macromolecules 7 320–4</p> | g12864 | [
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<p>When showing that the magnetic field derived from the curl being proportional to current and the divergence being zero is unique, Purcell says that at some sufficiently remote enclosing boundary the difference of two magnetic fields (two possible fields from the curl), D, would take a constant value. Why is this true?</p> | g12865 | [
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<p>With hyperopia, the focal point is behind the retina, shouldn't this mean that the image is flipped on the retina itself from what is usual?
I must be drawing my ray diagrams wrong.</p>
<p>A little something different from: <a href="http://physics.stackexchange.com/q/63883/24082">Optics, lenses and our eyes</a></p> | g12866 | [
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<p>I saw this picture on one of my social media sites with the caption, "I'd do this in a heart beat! Who's with me!"</p>
<p><img src="http://i.stack.imgur.com/GMzJi.jpg" alt="enter image description here"></p>
<p>I was about to go balls to the walls and say, "I'm in! When and where??" But then I got to thinking, how fast would I be going when I hit the water? If I were going too fast, would it hurt me?</p>
<p>SO I was trying to figure this out, and I'm not very good at physics so I was wondering if you guys could help me out.</p>
<p>I estimate the guy is 90 kg in mass, the wire is angled pi/6 from the horizontal and he's about 50 meters above the water when he starts (all estimates...).</p>
<p>What is the formulas I need to figure out the speed the guy will be going once he hits the water? I know there's some calculus in there, and I'm pretty good at calculus. </p> | g12867 | [
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0.00533868744969368,
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0.02788434736430645,
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<p>My data set of upper atmospheric cloud occurrences $N$ versus their thickness (or optical brightness, say $B$) show an exponential variation over more than two orders of magnitude - that is $N$ varies as $\mathrm{e}^{-cB}$. The quantity $c$ can vary from location to location. More than one first-principle model shows the identical exponential law. This behavior is clearly robust, but I have no idea as to what would cause such a beautiful distribution of such complicated animals, like clouds. Where would I start to try to understand the underlying physical principle? There must be something basic here that I am missing.</p> | g12868 | [
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<p>The optimum wheel diameter of cars and bikes appear to be roughly the same, certainly well within an order of magnitude. This is despite very different average speeds and propulsion mechanisms.</p>
<p>Can anyone come up with a dimensional analysis-type argument explaining why this is? </p> | g12869 | [
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<p>If we have a configuration of metal concentric spheres (each of negligible thickness) of radii $r_1,r_2,r_3$ respectively and $r_1<r_2<r_3$, and we are given the potentials of the spheres to be $0, constant,0$ respectively. How might we find the capacitance of the configuration?</p>
<p><em><strong>EDIT: My question: How is capacitance defined for such a system?</em></strong></p>
<p>Added: I think I have managed to find the charge on each shell :) What is missing now is just a definition of capacitance for such a system.</p> | g12870 | [
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<p>The thought randomly occurred to me that a circular particle accelerator would have to exert a lot of force in order to <em>maintain the curvature of the trajectory</em>. Many accelerators move particles at fully relativistic speeds, and I want to ask how that affects things.</p>
<p>Why does this matter? Well, if I understand correctly, a particle in the LHC moving at $0.999 c$ would be <em>dramatically</em> more difficult to keep moving in the circle than a particle moving at $0.99 c$. Reading Wikipedia, I was delighted to find a fully specified problem within a single paragraph.</p>
<p><a href="http://en.wikipedia.org/wiki/Large_Hadron_Collider">http://en.wikipedia.org/wiki/Large_Hadron_Collider</a></p>
<blockquote>
<p>The LHC lies in a tunnel <strong>27 kilometres</strong> (17 mi) in circumference, as deep as 175 metres (574 ft) beneath the Franco-Swiss border near Geneva, Switzerland. Its synchrotron is designed to collide opposing particle beams of either <strong>protons at up to 7 teraelectronvolts</strong> (7 TeV or 1.12 microjoules) per nucleon, or lead nuclei at an energy of 574 TeV (92.0 µJ) per nucleus (2.76 TeV per nucleon).</p>
</blockquote>
<p>I can (or Google can) <a href="https://www.google.com/search?q=sqrt%281-%28%28proton%20mass%29%2a%28speed%20of%20light%29%5E2/%287%20TeV%29%29%5E2%29">calculate</a> the proton case to come to $0.999999991 c$. In order to correctly calculate the force that the LHC must exert on it, do I need to start from $F=dp/dt$, or can I get by with $v^2/r$ times the relativistic mass? I'm not quite sure how to do the former.</p>
<p><strong>Question:</strong> Say I have 2 protons, both moving so fast they're going almost the speed of light but one has twice the energy of the other. They move side-by-side and enter either an electric or magnetic field that causes them to accelerate perpendicular to the velocity vector. Is the radius of curvature mostly the same for the two, or is it different by a major factor (like 0.5x, 1x, or 2x)?</p>
<p>I want to read some comments from people who understand these physics well. The particles beyond a certain energy are all going <em>almost exactly</em> the same speed. Is it still okay for me to say they have the same "acceleration" too? They just happen to have absurdly huge inertia compared to the same particle at a more modest fraction of the speed of light. Is this the correct perspective?</p> | g119 | [
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<p>I've noticed that snow seems to reflect red light more than any other wavelength at night. It's seen in the sky, as well as the snow itself, both of which take on a reddish tint. Why exactly does it do this? Additionally, why is this only noticeable under moonlight? If it's the moonlight that's tinted red, then alternatively, why is that? My apologies for the rather basic question, but I can't seem to find information on the matter elsewhere.</p> | g12871 | [
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<p>"When a current passes through an electric motor, the magnetic force on the motor causes a torque on the loop of wire causing it to turn". However, when the loop rotates, there should also be a change in magnetic flux causing an induced emf (Faraday's law). However, my book makes no such reference. </p>
<p>my questions:</p>
<ol>
<li>Is there going to be an induced emf opposing the applied emf of the DC source in the electric motor?</li>
<li>If yes, wouldn't the induced emf cancel the applied emf causing no magnetic force to be exerted and thus no longer converting electrical energy to mechanical energy?</li>
</ol> | g12872 | [
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<p>Does energy of light change when a light travels from a medium to another of different optical density?</p> | g12873 | [
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<p>If the quarks in a neutron are (up,down,down), why isn't it negatively charged? Excuse the silly question, just wondering.</p> | g12874 | [
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<p>In cavity QED for a 2-level atom, the revival time for oscillation b/w the states $\left|\ e\ 0\right\rangle$ and $\left|\ g\ 1\right\rangle$ (absorbing the same photon that is emitted) is said to be infinity because in general, Rabi oscillation revival time is proportional to the square root of the mean of the occupancies of Fock states. Why should the spread of the Fock states distribution go to large values or close to infinity in the spontaneous emission case, to make the revival time infinity ? Refer :- <a href="http://prl.aps.org/abstract/PRL/v94/i1/e010401" rel="nofollow">http://prl.aps.org/abstract/PRL/v94/i1/e010401</a> for a description of Rabi Oscillations Revival</p> | g12875 | [
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<p>I am trying to understand a calculation using Wick's theorem. Let $T(z)$ be the analytic part of a stress-energy tensor, and $\phi(z)$ a free boson field. </p>
<p>Now, $$T(z)\partial_{w}\phi(w)=-2\pi:\partial_{z}\phi(z)\partial_{z}\phi(z):\partial_{w}\phi(w).$$ Using Wick's theorem, we know that $$:\partial_{z}\phi(z)\partial_{z}\phi(z):\partial_{w}\phi(w)=:\partial_{z}\phi(z)\partial_{z}\phi(z)\partial_{w}\phi(w):+2\langle \partial_{z}\phi(z)\partial_{w}\phi(w)\rangle :\partial_{z}\phi(z):$$. Then why is this just equal to $$2\langle \partial_{z}\phi(z)\partial_{w}\phi(w)\rangle \partial_{z}\phi(z)?$$ as stated in many CFT books?</p> | g12876 | [
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0.030241239815950394,
-0.043663330376148224,
0.046417366713285446,
0.039473216980695724,
-0.035524796694517136,
0.026332112029194832,
-0.08115842193365097,
0.030712582170963287,
-0.006693888921290636,
... |
<p>This question is on the construction of the Einstein Field Equation.</p>
<p>In my notes, it is said that </p>
<blockquote>
<p>The most general form of the Ricci tensor $R_{ab}$ is $$R_{ab}=AT_{ab}+Bg_{ab}+CRg_{ab}$$
where $R$ is the Ricci scalar.</p>
</blockquote>
<p>Why is this the most general form (involving up to the second derivative of the metric --- by definition of $R_{ab}$)? I suppose there are symmetry and degrees of freedom arguments. But I can only see why the LHS is a <em>possible</em> form. I can't se why it is the most general form...</p>
<blockquote>
<p>Taking the covariant derivative $\nabla_a$ of the expression above gives $$C=\frac{1}{2}$$.</p>
</blockquote>
<p>This I understand.</p>
<blockquote>
<p>Compare the resulting expression with the Poisson equation gives $$A=\frac{8\pi G}{c^4}$$.</p>
</blockquote>
<p>This I <em>don't</em> understand --- perhaps I am being silly again... but still. </p>
<p>I assume the "Poisson equation" referred to here is $$E^i{}_i=4\pi\rho G$$
where $E^i{}_i$ is the tidal tensor and may be expressed as $$E^i{}_i=R^i{}_{aib}T^aT^b$$ where $T^a$ is the tangent vector of the geodesic.
So contracting $$R_{ab}=AT_{ab}+Bg_{ab}+CRg_{ab}$$ with $T^aT^b$ gives $$4\pi\rho G=AT_{ab}T^aT^b$$.</p>
<p>But then what? Or perhaps I have already made a mistake? I only know the energy-momentum tensor $T_{ab}$ to be of the form
$$\begin{pmatrix}H&\pi_i\\\frac{s_i}{c}&T_{ij}\end{pmatrix}$$ where $H$ is the energy density, $\pi_i$ is the momentum density, $s_i$ is the energy flux.</p>
<p>But I don't understand how it leads to $$A=\frac{8\pi G}{c^4}$$.</p> | g12877 | [
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0.007796776946634054,
0.018886476755142212,
-0.0... |
<p>A scammer got a hollow gold bar and fills it with a combination of lead and air, with the same average density as gold. </p>
<p>What's the simplest way of discovering the fraud? I know that x-rays will see it, but are there simple means for analyzing it? (without destroying it)</p> | g12878 | [
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0.06839339435100555,
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<p>What would be an intuitive way to damage objects in a physics game using impulses? Since momentum is conserved, so is impulse (the change in momentum for any two time periods) in a closed system.</p>
<p>So if I have the impulse of a collision (that is, the change in momentum during a time interval for one of the two bodies) what would be the intuitive way to damage both the objects. Should each object receive the same damage based on the impulse of the overall system, or should the damage incurred be split unevenly based on the relative mass of each object? My intuition is that objects with larger mass would have higher hit-points, and so would be less affected if the same damage was incurred to both the objects in the collision.</p> | g12879 | [
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<p>I've read many facts from NASA's webpage.. Sometimes they tell, (for example) "NASA's Chandra X-Ray Observatory discovered this ultra-luminous X-Ray source (about 15 million LY) which shows an extraordinary outburst..."</p>
<p>My question is.. Is it possible to obtain those electromagnetic radiation (Infra-red, Visible, UV or X-Rays) from such a long range? If so.. How?</p> | g12880 | [
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<p>In Heaviside-Lorentz units the Maxwell's equations are:</p>
<p>$$\nabla \cdot \vec{E} = \rho $$
$$ \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} = \vec{J}$$
$$ \nabla \times \vec{E} + \frac{\partial \vec{B}}{\partial t} = 0 $$
$$ \nabla \cdot \vec{B} = 0$$</p>
<p>From EM Lagrangian: $$\mathcal{L} = \frac{-1}{4} F^{\mu \nu}F_{\mu\nu} + J^\mu A_\mu$$ </p>
<p>I can derive the first two equations from the variation of the action integral: $S[A] = \int \mathcal{L} \, d^4x$. Is it possible to derive the last two equations from it?</p> | g12881 | [
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<p>I read that the definition of the chemical potential is, that it is the partial derivative of the Free energy with respect to the number of particles, $$\mu=\frac{\partial F}{\partial N}.$$ Unfortunately, I don't get this definition, wherefore I wanted to choose an example: Let me think of a system for example a water in oil emulsion. How would one evaluate the chemical potential of this mixture? There the chemical potential would definitely depend on the question: Where do you want to insert which sort of particles?</p> | g12882 | [
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<p>One of the postulates of quantum mechanics is that every physical observable corresponds to a Hermitian operator $H$, that the possible outcomes of the measurements are eigenvalues of the operator, and that after a measurement the state collapses into the eigenfunction corresponding to the observed eigenvalue. </p>
<p>Some authors state that this is the reason quantum mechanics is "built on" linear algebra. However from a linear algebra standpoint this postulate seems strange. In linear algebra operators are linear transformations that take vectors to vectors; hence I would expect an operator also be a linear transformation, physically realised by a black box that takes in a particle in a state $\psi$ and emits the particle in the transformed state $H \psi$.</p>
<p>In fact, if I look at the creation operator (from say an electron in a harmonic oscillator potential), this clearly can't correspond to an observable because it's not hermitian. I can imagine the black box to be implemented by a machine that fires a photon into the electron. I can also imagine operators that for example rotate the angular momentum of an electron without measuring it. Can I create a physical apparatus that "implements" the position operator (in position space, it takes a state $\psi(x)$ and returns $x \psi(x)$)? Why does QM use operators in these two different senses and how do I distinguish them?</p> | g12883 | [
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<p>The Hamiltonian for this system is given by
\begin{equation}
\mathcal{H} \{S\} = -H\sum_i S_i - \frac{J_0}{2} \sum_{ij} S_i S_j,
\end{equation}
where $H$ is the external magnetic field and there is no restriction to nearest neighbour interaction. The spin at each site, $S_i$, may take value $+1$ or $-1$. </p>
<p>Now my question is:</p>
<p><strong>Why does this model only make sense if $J_0 = J/N $, where $N$ is the number of spins in the system?</strong> </p> | g12884 | [
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<p>i've problem with the last terms of uncertainty principle:
1. are these equalities true:
$$\langle \{\Delta \hat A,\Delta \hat B\} \rangle=\langle \{\hat A, \hat B \}\rangle$$
$$\langle [\Delta \hat A,\Delta \hat B] \rangle=\langle [\hat A, \hat B] \rangle.$$</p>
<ol>
<li>what is result of product commutator with anti commutator?</li>
</ol> | g12885 | [
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0.02298753149807453,
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0.016159789636731148,
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... |
<p>this doubt is related to Generalized Hamiltonian Dynamics paper by Dirac.</p>
<p>Consider the set of $n$ equations : $p_i$ = $∂L/∂v_i$,</p>
<p>(where $v_i$ is $q_i$(dot) = $dq_i/dt$, or time derivative of $q_i$)($L$ is the lagrangian, $q$ represent degrees of freedom in configuration space)</p>
<p>Now Dirac says : "If the $n$ quantities $∂L/∂v_i$ on the right-hand side of the given equations are NOT independent functions of the velocities, we can eliminate the $v$'s from (the above-given) set of equations and obtain one or more equations:
$\phi_j(q, p) = 0$, ($j = 1, 2, ... , m$ if there are $m$ such constraints)"</p>
<p>Could anyone please explain how this comes about? I can't understand how the $v$'s can be necessarily eliminated, and if the $p$'s are not all independent, then we can simply obtain relations like $\sum_i a_ip_i = 0$ (where $a$'s are non-zero coefficients), not involving $q$'s at all.</p>
<p>Thanks (and apologies in case I'm missing something obvious).</p> | g12886 | [
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0.017657987773418427,
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0.04175... |
<p>I came across this problem. Please help me solve it. </p>
<blockquote>
<p>A radioactive sample S1 having an activity of $5\ \mathrm{\mu Ci}$ has twice the number of nuclei as another sample S2 which has an activity of $10\ \mathrm{\mu Ci}$. The half lives of S1 and S2 can be</p>
<p>(A) 20 years and 5 years, respectively</p>
<p>(B) 20 years and 10 years, respectively</p>
<p>(C) 10 years each</p>
<p>(D) 5 years each</p>
</blockquote>
<p>All through out my high school i was never introduced to the idea that radioactivity could change depending on the number of nuclei. Can someone throw some light on this?</p> | g12887 | [
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0.021800510585308075,
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0.03462723642587662,
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0.0016815860290080309,
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0.08018539100885391,
0.0066267079673707485,
-0.00... |
<p>I am trying to figure out how large of a mass and how quickly I need to spin said mass to keep a two-wheeled robot stable. Ideally, I am looking for a formula that relates <i>m</i><sub>1</sub>=mass of robot, <i>m</i><sub>2</sub>=mass of spinning disk, <i>v</i>=rotational speed of disk (rpm), and some sort of stability factor <i>s</i> (or amount of mass <i>m</i><sub>1</sub> that it can counteract). Is there any such formula, and what would it be?</p>
<p>Thanks!</p> | g12888 | [
0.002505667507648468,
0.0434940904378891,
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0.009159530512988567,
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0.0742553099989891,
-0.017221974208950996,
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-0.014658350497484207,
-0.02607034705579281,
0.01950814761221409,
0.08114320784807205,
0.008... |
<p>As we all know that light travels in rectilinear motion. But can we bend light in parabolic path? If not practically then is it possible in paper? Has anyone succeeded in doing that practically ?</p> | g806 | [
-0.002086704596877098,
0.024154365062713623,
0.0014758631587028503,
0.04644821584224701,
0.03916073590517044,
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0.0006200268398970366,
-0.006522030103951693,
0.03884054347872734,
-0.02364422380924225,
0.024428730830550194,
... |
<p>I have been reading about quantum entanglement, and I was wondering what quantum states can be "sent" using entanglement. I know you can measure the spin of one of the particles, and know the spin of the other, but can you also do this with other quantum states, such as polarization, or energy?</p>
<p>Also, could you theoretically entangle molecules, or even larger structures? What is happening in this field of physics?</p>
<p>Finally, if you were able to measure the energy levels of the entangled particles, when you changed the energy state of one of the particles, would the other? Could this violate the first law of thermodynamics, or is the change so small that it does not matter, since this is the quantum world?</p> | g12889 | [
-0.043154917657375336,
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0.011342115700244904,
0.014746171422302723,
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0.04010649770498276,
0.02652815729379654,
-0.00676910113543272,
-0.005535930395126343,
0.01849885657429695,
-0.0... |
<p>I was wondering if it would be possible to create an amount of positive energy out of a vacuum, in addition to an equal amount of negative energy, thus not violating the first law of thermodynamics, since the total amount of energy in the universe would remain the same. It could be like an "energy loan," with the positive energy being like the "loan money," and the negative energy being like the "debt." Is this theoretically (or even practically) possible?</p>
<p>For example, I am asking if you could create 200 units of positive energy out of a vacuum, as long as you also created 200 units of negative energy too, so as not to violate the second law of thermodynamics. By negative energy, I mean energy that is below 0 degrees Kelvin. </p>
<p>I came across the idea as I was reading about the zero-energy universe theory. It suggested that this mechanism was what made the universe, and that it could have been started by an unusually large quantum fluctuation. </p>
<p>Does this idea conflict with the second law of thermodynamics in any way? Would entropy have to be considered, since negative energy reduces entropy, violating the second law? If so, is there a way of changing the idea a bit so there as to avoid the problem? Could "quantum interest" account for the missing entropy?</p>
<p>Do any restrictions apply on the negative and positive energy, such as quantum inequalities? Can the positive and negative energy be separated? Is there a way to get around the restrictions, if there are any?</p>
<p>Finally, if all of this is possible, could it be done? Would a possible method be to recreate an unusually large quantum fluctuation, as described in the second paragraph? Are there other ways of making the "energy loan"? </p> | g12890 | [
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0.0006662377272732556,
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0.049391429871320724,
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-0.022944018244743347,
0.0140644870698452,
0.001650314312428236,
0.008904309943318367,
0.007... |
<p>Were there physics teaching aids used in the past? Or did professors just basically follow the textbook the students read?</p>
<p>In other words: How was physics was taught in the past?</p> | g12891 | [
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0.010380113497376442,
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0.023339366540312767,
0.055206771939992905,
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-0.018222421407699585,
0.040214654058218,
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0.012737846933305264,
0.0159... |
<p>I suspect this question has a simple answer, but I can't get my head around it.</p>
<p>The classic example of a person in orbit around the Earth at high speed experiencing a slower passage of time than the people on Earth is well known. I don't understand, however, what dictates that the person orbiting experiences less passage of time rather than more. Isn't the person on the ground moving relative to the person in orbit just as quickly? Why isn't it that the person comes back after a year in orbit to find that only five minutes have passed on Earth, instead of the other way around?</p>
<p>EDIT:</p>
<p>Sorry, this is a duplicate. I found the answer here:</p>
<p><a href="http://physics.stackexchange.com/questions/76726/if-i-travel-close-to-the-speed-of-light-and-come-back-why-is-everyone-else-dead?rq=1">If I travel close to the speed of light and come back, why is everyone else dead, and not me?</a></p>
<p>The explanation is that the person orbiting the Earth is required to accelerate and then decelerate, whereas no acceleration is required from the people on Earth.</p> | g84 | [
0.0629313662648201,
0.061497628688812256,
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0.056642841547727585,
0.02168092504143715,
0.05416710674762726,
0.06893713772296906,
0.0058074346743524075,
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-0.014573111198842525,
0.026076948270201683,
0.006223203148692846,
0.02862287126481533,
0.00007... |
<p>What is the origin of induced emf in a conductor which is produced by changing magnetic flux.I mean why changing magnetic flux causes the production of induced emf.
Is there some kind of energy involved?Is it.</p> | g12892 | [
0.07054367661476135,
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0.009033234789967537,
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0.03788548707962036,
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-0.015607958659529686,
-0.10413531213998795,
0.06069916859269142,
0.0032591496128588915,
0.01022... |
<p>I know I can use Gauss's law to find the Electric Field inside and outside the cylinder very easily. We can select Gaussian surfaces for different cases (i.e. $r \lt R$ and $r \gt R$, where $R$ is the radius of the cylinder and $r$ is the radius of Gaussian surface). </p>
<p>But I want to know Electric fields at the bottom and the upper circular surface of the cylinder.</p>
<p>Edit: Charge of the cylinder can be anything ($\lambda, \sigma, \rho$). For clarification there is one cylinder and I want to find the E field on the top and bottom circular surfaces rather than inside or outside.</p> | g12893 | [
-0.0026544490829110146,
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0.06631702929735184,
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0.007940869778394699,
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0.017222803086042404,
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0.02902793139219284,
0.008907651528716087,
-0.00... |
<p><a href="http://en.wikipedia.org/wiki/Ehrenfest_theorem" rel="nofollow">Ehrenfest theorem</a> is usually dubbed as the quantum mechanical equivalent of Newton's law and Griffiths states, in the first chapter of his textbook, that Ehrenfests theorem enables us to work with expectation values in quantum mechanics as <em>Ehrenfest theorem tells us that expectation values obey classical laws.</em></p>
<p>On the other hand, the <a href="http://en.wikipedia.org/wiki/Correspondence_principle" rel="nofollow">correspondence principle</a> states that <em>the behavior of systems described by the theory of quantum mechanics reproduces classical physics in the limit of large quantum numbers.</em></p>
<p>Are the two logically equivalent?</p>
<p>References:
<a href="http://farside.ph.utexas.edu/teaching/qm/lectures/node31.html" rel="nofollow">http://farside.ph.utexas.edu/teaching/qm/lectures/node31.html</a></p> | g12894 | [
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0.012764252722263336,
-0.029949989169836044,
... |
<p>I am not clear on that. </p>
<p>Is gravity repulsive during inflation?</p> | g12895 | [
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0.00435263616964221,
0.0211295448243618,
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0.01645... |
<p>It is well known that there exist mappings between operators in N = 4 Super Yang–Mills and spin chain states making the theory Bethe Ansatz integrable. Is integrability a necessity for the Amplituhedron? Most QFTs are not integrable.
Does Nima Arkani-Hamed, et al. claim to be able to extend the Amplituhedron to generic QFTs? Is then maybe integrability somehow hidden in the structure of all QFTs and the ones which are not integrable emerge as certain limits of the underlying Amplituhedron? </p> | g12896 | [
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-0.030016154050827026,
... |
<p>I am familiar with the basic ideas of quantum field theory but I feel uncomfortable when I have to derive Feynman rules by myself for a given action (for example in non-linear sigma models or electrodynamics). Could you provide a list of good books, articles, lecture notes and/or any other sources (except Peskin), where Wick's theorem and the Feynman rules are derived from the functional integral <strong>in detail</strong>, preferably with examples?</p> | g12897 | [
0.04172549024224281,
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0.014634789898991585,
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0.02705439366400242,
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0.003199664643034339,
-0.0504162460565567,
0.041... |
<p>The overly simplified explanation I'm giving myself right now is <a href="http://en.wikipedia.org/wiki/Dark_energy" rel="nofollow">dark energy</a> causes the opposite of what gravity does, that's why the universe is expanding. Now where gravity is a force, why dark energy is "energy"? Why it's not called "Dark Force" instead? I think I must be missing something here.</p> | g859 | [
0.06014944985508919,
0.0773928090929985,
-0.008285479620099068,
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0.04092108830809593,
-0.002907064976170659,
0.018971383571624756,
-0.02... |
<p>I am quite familiar with duality transformations for lattice spin systems (i.e. systems with global $O(n)$ symmetry) and pure gauge systems (i.e. local $SU(n)$). However, after searching for a bit, I can't seem to find literature on dual variables for lattice fermions (systems with inner products of grassmann fields). For the spin and gauge cases we do harmonic analysis and fourier expanded the exponential of the action (or a character expansion for the gauge case). Is there an analogous process for lattice actions with grassmann fields? Thanks.</p> | g12898 | [
0.02249131165444851,
0.014604100026190281,
0.0011344265658408403,
-0.02389269322156906,
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0.008984615094959736,
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0.0173... |
<p>Joule heating happens every time when the conduction electrons transfer kinetic energy to the conductor's atoms through collisions, causing these conductor's atoms to increase their kinetic and vibrational energy which manifests as heat. Then, why wouldn't it happen when no current is flowing through the conductor? When there is no current, the electrons are still moving randomly at a speed of $\mathrm{~10^5\ m/s}$, but at a zero average velocity.</p>
<p>Then, why don't these electrons collide with the atomic ions making up the system and transfer energy to them causing them to heat up even when no net current is flowing?</p> | g12899 | [
0.029886942356824875,
0.013229422271251678,
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0.0008847628487274051,
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0.0... |
<p>In many textbooks an illustration of a vibrating string at a fundamental mode shown (and wikipedia) shown like this <a href="http://en.wikipedia.org/wiki/File%3aStanding_waves_on_a_string.gif" rel="nofollow">http://en.wikipedia.org/wiki/File:Standing_waves_on_a_string.gif</a>). However if you watch youtube videos of string vibrating in slow motion you see something like this (<a href="http://projects.kmi.open.ac.uk/role/moodle/pluginfile.php/1239/mod_page/content/1/ta212_2_008i.jpg" rel="nofollow">http://projects.kmi.open.ac.uk/role/moodle/pluginfile.php/1239/mod_page/content/1/ta212_2_008i.jpg</a>)
So which one is this? Is the first one just a schematic version of the second? Also the notion of a wave propagation in a string sort of relevant only to the second pictire only? Or am I wrong? Please clarify, I think I am missing something fundamental here.</p>
<p>Thanks </p> | g12900 | [
0.03611624985933304,
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0.0133... |
<p>I've thought I had a good understanding how resolution enhancement tricks works for projection lithography, until I tried to understand if it's possible to get sub-diffraction performance for focused laser beam:</p>
<p>Let's assume we have a laser with nice and shiny perfect aspherical focusing lens (with performance greatly exceeding diffraction limit for it's NA). This system moves around and draw stuff.</p>
<p>The question is - can we get enhanced resolution if we apply usual lithography trick of annular/quadruple illumination? Obviously, we won't reduce aberrations thanks to off-axis illumination, as there are none. </p> | g12901 | [
0.0010330833029001951,
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<p>This is a continuation to my <a href="http://physics.stackexchange.com/questions/111063/casimir-forces-due-to-scalar-field-using-path-integrals">previous question</a>, in which I began an attempt solve the Casimir Force problem using path integrals. As one of the <a href="http://physics.stackexchange.com/questions/111063/casimir-forces-due-to-scalar-field-using-path-integrals/111105#111105">answers</a> there suggest I solve the Feynman propagator subject to the boundary conditions $x=0$ and $x=L$ at the plate boundaries. The equation for Feynman propagator is
$$ (\Box^2+m^2)\Delta_F(x-x') = -\delta(x-x') $$</p>
<p>The solution to the free field is </p>
<p>$$ \Delta_F(x-x') = \lim_{\epsilon\rightarrow0}\int \frac{d^4p}{(2\pi)^4}\frac{e^{ip_{\mu}(x^{\mu}-x'^{\mu})}}{p^2-m^2+i\epsilon} $$</p>
<p>What would be the boundary conditions that I have to exactly impose ?</p>
<p>Imposing a boundary condition would mean, I think we might have to introduce the a new function (I don't if am right, but this is in general true for Green's function I guess)
$$ \Delta_F(x-x') \rightarrow \Delta_F(x-x') + F(x-x') $$</p>
<p>where $F(x-x')$ is such that it satisfies the Boundary condition.</p>
<p>Now my question is in case I have boundary condition (like below) how do I solve the differential equation for the boundary conditions like, (take plates to be at $z=0$ and $z=L$)
$$ \Delta_F(x-x')\bigg|_{z=0} = \Delta_F(x-x')\bigg|_{z=L} = 0 $$</p>
<p>EDIT 1: It just occurred to me that there might be short route to this problem with some conceptual reasoning, I gave this a try..</p>
<p>Considering the region between the plates, I know the momentum is quantised in the z-direction, so I have (which is some sense imposed by the boundary condtions)
$$ p_z = \frac{n\pi}{L} $$
Now using the Feynman propagator in momentum representation, which is
$$\widetilde\Delta_F(p) = \frac{1}{(p^0)^2-(\textbf p^2+m^2)+i\epsilon}$$</p>
<p>In this I can substitute for, $p_z$, which will give me
$$ \widetilde\Delta_F(p) = \frac{1}{(p^0)^2-(p_x^2+p_y^2+\Big(\frac{n\pi}{L}\Big)^2)+m^2)+i\epsilon} $$</p>
<p>Now can I get back to position representation, but with integral on $p_z$ replaced by a sum over $n$. Am I right in doing this procedure ?</p>
<p>EDIT 2 :
Following the procedure that I have mentioned, for a simple (1+1) case of the Feynman propagator in position representation, I have</p>
<p>$$ \Delta_F(x-x') = \sum_{n=1}^\infty\int\frac{dp_0}{(2\pi)^2}\frac{e^{ip_0(x^0-x'^0)}e^{i\frac{n\pi}{L}(z-z')}}{(p^0)^2-\big(\big(\frac{n\pi}{L}\big)^2+m^2\big)} $$</p>
<p>EDIT 3 :
$$ \text{Tr}\log{\Delta} = - \sum_n \int dp_0 \log{\bigg(p_0^2 - \bigg(\frac{n\pi}{L}\bigg)^2 + m^2\bigg)} $$</p>
<p>But this term seems to diverge, how does one obtain a cutoff in the context of this problem. (A cutoff for $p_0$ integral is also needed I guess).</p> | g12902 | [
0.09111900627613068,
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0.029077444225549698,
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0.0280... |
<p>What is a simple bare-bones description of exchange interaction between two electrons?</p>
<p>For instance, it seems to me that the only necessary ingredients are the Coulomb interaction and the requirement that the total wavefunction be antisymmetric.</p> | g12903 | [
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-0.007335364352911711,
... |
<blockquote>
<p>Three masses $m_1 = 3\text{ kg}$, $m_2 = 9\text{ kg}$ and $m_3 = 6\text{ kg}$ hang from three identical springs in a motionless elevator. The elevator is moving downward with a velocity of $v = -2\text{ m/s}$ but accelerating upward with an acceleration of $a = 5\ \mathrm{m/s^2}$. (Note: an upward acceleration when the elevator is moving down means the elevator is slowing down.) What is the force the bottom spring exerts on the bottom mass? Take $g = 10\ \mathrm{m/s^2}$.</p>
</blockquote>
<p><strong>My argument</strong></p>
<p>The elevator is steadily slowing down and it get an upward acceleration. </p>
<p>So as it goes down the net force is</p>
<p>$$\begin{gather}F_s - mg = ma \\
F_s = 6(10 + 5) = 6(15) = 90\text{ N}\end{gather}$$</p>
<p>But this is the force the spring has. It is the same as the force EXERTED on the body attached? Is there a Newton's third law involved? </p>
<p><strong>Friend's argument</strong></p>
<p>He says that BECAUSE it has an upward acceleration and it is going down that we need to be concern with</p>
<p>$$Fs = mg - ma = 90 - 60 = 30\text{ N}$$</p> | g12904 | [
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0.012043568305671215,
-0.03958295285701752,
-0.0... |
<p>In the winter I am in the habit of opening my oven door once I am done baking so that I can add the heat to the house. However I recently thought about it and it would seem that even if the door is closed, and the oven insulated, the only way for the oven to cool would be to heat the house. So this would mean that there is no benefit to opening the door in the winter and keeping it closed in the summer.</p>
<p>So my question is: Does opening the door of a hot oven heat the house more effectively than allowing it to cool with the door closed? </p> | g12905 | [
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0.07159512490034103,
0.010964429937303066,
0.0... |
<p>I am a senior in High School who is taking the course AP Physics Electricity and Magnetism.</p>
<p>I was studying Gauss's laws and I found this problem: </p>
<blockquote>
<p>A solid insulating sphere of radius R contains a positive charge that is distrubuted with a volume charge density that does not depend on angle but does increase with distance from the sphere center. Which of the graphs below correctly gives the magnitude E of the electric field as a function of the distance r from the center of the sphere? </p>
<p><img src="http://i.stack.imgur.com/gR7kV.png" alt="Choices A through E"></p>
</blockquote>
<p>The correct answer is given to be choice D but I cannot see why the answer is D. Isn't the equation for electric field in this case just $E = \frac{q \cdot r}{4 \pi \epsilon _{0} \cdot R^{3} } $ if $r \le R$? </p>
<p>This formula occurs for spherical insulators as given by the textbook Fundamentals of Physics by Halliday/Resnick. According to this equation for the electric field, the graph should clearly be linear until $r=R$. </p>
<p>That is why I think the answer is C. I believe this is a problem with the textbook, am I correct?</p>
<p>If I am wrong can someone please explain why I am wrong?</p>
<p>Thank you very much for your time!</p> | g12906 | [
0.018027154728770256,
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0.0309588760137558,
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-... |
<p>So, I understand that quantum teleportation is the transfer of a quantum state from one particle or system of particles and its correlations to another receiving system consisting of particle(s). Can't this be used in a way to achieve teleportation as depicted in sci-fi?</p>
<p>You start out with a translationally entangled particle pair (position and momentum are correlated) as described by this paper:
<a href="http://pra.aps.org/abstract/PRA/v61/i5/e052104" rel="nofollow">http://pra.aps.org/abstract/PRA/v61/i5/e052104</a></p>
<p>Now according to these papers, you can theoretically teleport the position and momentum information of particle. Atomic teleportation of the external degrees of freedom, (Their position and momentum)</p>
<p><a href="http://pra.aps.org/abstract/PRA/v49/i2/p1473_1" rel="nofollow">http://pra.aps.org/abstract/PRA/v49/i2/p1473_1</a></p>
<p><a href="http://prl.aps.org/abstract/PRL/v86/i14/p3180_1" rel="nofollow">http://prl.aps.org/abstract/PRL/v86/i14/p3180_1</a></p>
<p><a href="http://iopscience.iop.org/0295-5075/75/6/847" rel="nofollow">http://iopscience.iop.org/0295-5075/75/6/847</a></p>
<p>Firstly, I need someone to help me understand <strong>exactly what is being teleported in regards to the papers I've listed</strong>. I understand completely the discrete case of quantum teleportation with spin or polarization, I'm not asking for that.</p>
<p>This is what I know:</p>
<p>1) Start out with a translationally entangled pair.
2) Interact an "input" particle with one of the pairs.
3) Make a measurement of the input particle with one of the pairs' position and momentum.
(This is the step I don't really understand) But I know that this is analogous to the Bell state measurement in discrete quantum teleportation that is widely described everywhere.
4) This result is communicated to the other laboratory where appropriate "shifts" of position and momenta are done to the entangled pair just like in the discrete case again.</p>
<p>So, if position and momentum information is teleported, then does this mean that if the input particle was propagating in the X-direction like a wave-packet, then after teleportation, the receiving particle will now move in the X-direction relative to its original position? This is quite confusing to me.</p>
<p>I want to understand this because I want to ask the trillion dollar question, "What if you are to replace the input particle with a input MOLECULE?"</p>
<p>For a diatomic molecule, its simply two atoms of the same type. According to this wikipedia article:
<a href="http://en.wikipedia.org/wiki/Linear_combination_of_atomic_orbitals" rel="nofollow">http://en.wikipedia.org/wiki/Linear_combination_of_atomic_orbitals</a></p>
<p>I know there are vibrational states in molecules which ARE essentially position and momenta information right?</p>
<p>If we are to set up TWO translationally entangled pairs of atoms of the same type...
And have them simultaneously interact with the molecule in step 3), <em>then can't we do the appropriate SHIFTS of the entangled pairs of atoms to make them turn into the input molecule?!</em></p>
<p>So, the overall effect is that if you start out with H2 in Lab A, and had a translationally entangled pair for each atom, then you'll end up with H2 in Lab B after teleportation which is exactly what we want if we want to stick close to the sci-fi sense.</p>
<p>If what I am saying makes sense, then can't this be in principle be extrapolated to larger molecules and eventually cells, and organs, to an entire human? I know that this is a large jump...</p>
<p>However, what I'm trying to say is that according to this kinda scheme I'm asking about, its sticking to real physics, and its essentially accomplishing teleportation in the sense people know about. Do I make sense?</p> | g12907 | [
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-... |
<p>To measure <a href="http://en.wikipedia.org/wiki/Velocity" rel="nofollow">velocity</a> we use derivative </p>
<p>$$v=\frac {dr}{dt}.$$ </p>
<p>Is the any other mathematical tool to do this?</p> | g12908 | [
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0.011935499496757984,
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0.06490492820739746,
0.043... |
<p>I am trying to get my head around a few concepts related to frame dragging and related physics. In regards to black holes that have no charge and all their mass is tied up in rotational kinetic energy then the ergosphere is a maximum size. By definition, as I see it defined, the outer boundary of the ergosphere is the point at which a photon becomes stationary with respect to outside observation if it is <strong>orbiting</strong> retrograde. The radius at the <strong>equator</strong> of this maximal case is $2GM$ making it twice the inner event horizon radius if I am understanding correctly. The innermost stable orbit for massive particles is at GM in a pro-grade direction. If any of this is incorrect please let me know. </p>
<p>So my questions are:</p>
<blockquote>
<ol>
<li><p>Pretty much by definition it is impossible for a massive particle to go slower than the speed of light relative to outside observers if it is within the ergosphere - true? What is the limit of this speed relative to outside observers? I'm looking for the limit before it passes into the inner horizon. </p></li>
<li><p>Since the frame dragging extends outward (presumably to infinity
with extremely negligible effect) what would happen in the case
where you had a ring of orbiting black holes equally spaced with
spin aligned such that the axis of rotation was tangential to the
circle? Without touching event horizons it would appear to be able
to pull massive particles through the center of the circle in a
straight line rather than a curved path as above - correct? And if
the holes were close enough would that allow the ergospheres to
merge (temporarily as I'd assume everything would merge eventually)
would that allow faster than light travel for massive particles in a
straight line? I'm neglecting that the orbits of the holes are
unstable and would radiate gravitational waves and that they are
massive enough so tidal forces are 'small' compared to the particle
or mass of particles.</p></li>
<li><p>If the holes above are arranged as stated would this extend the ergosphere inward toward the center if they are closely spaced at some distance? I've seen cases for general non-maximal spin cases of two holes and am unable to determine how this would play out. </p></li>
</ol>
</blockquote>
<p>Thanks for taking the time to read and if I put too much in a single question I apologize but didn't want to spam several closely related questions. </p> | g12909 | [
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-0.0... |
<p>I am interested simulating the evolution of an electronic wave packet through a crystal lattice which does not exhibit perfect translational symmetry. Specifically, in the Hamiltonian below, the frequency of each site $\omega_n$ is not constant.</p>
<p>Suppose the lattice is specified by a certain tight-binding Hamiltonian
$$
H = \sum_n \omega_n a^\dagger_n a_n + t \sum_{<n>} a^\dagger_n a_{n+1} +\text{all nearest neighbor interactions} + \text{h.c}.
$$
We prepare a wavepacket, and for simplicity, we express the wavepacket in the fock basis of each lattice site
$$
| \psi \rangle = \sum_i |b_1\rangle |b_2\rangle \ldots |b_n\rangle.
$$
Thus, there are $b_1$ electrons in the $1$st lattice site. Of course, electrons are fermions and $b_1$ may be either $0$ or $1$.</p>
<p>Suppose we treat this problem purely quantum mechanically. Then we will need to prepare a vector of length $2^n$, which is computationally intractable for any significant $n$.</p>
<p>I am interested in physical techniques that may be employed to simplify this problem. Is it possible to attempt the problem in a semiclassical manner?</p> | g12910 | [
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0.016317036002874374,
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-0.004... |
<p>I understand that adding/sprinkling, say NaCl, on a highway depresses the freezing point by making any moisture on the road harder to freeze as the NaCl molecules get in the way of phase transition. So now we need lower temperatures to freeze the moisture on the road.</p>
<p>However, why can I cool my drink "better" by placing it in a salt + ice bath instead of just an ice bath? It would seem that a salt + ice bath only keeps the water from freezing or in other words, the ice from melting for longer duration of time. Where does the lowering of temperature come into this picture? </p>
<p>I am not able to connect these two phenomenon although people tell me they are the same.</p>
<p>Links to what I have already seen:</p>
<p><a href="http://antoine.frostburg.edu/chem/senese/101/solutions/faq/why-salt-melts-ice.shtml" rel="nofollow">http://antoine.frostburg.edu/chem/senese/101/solutions/faq/why-salt-melts-ice.shtml</a></p>
<p><a href="http://revision3.com/forum/showthread.php?t=34351" rel="nofollow">http://revision3.com/forum/showthread.php?t=34351</a></p>
<p>I need someone to rephrase something and I cant put my finger on it.</p>
<h2>Edit:</h2>
<p>I was thinking more about it and here is what I can further add to my question:</p>
<ol>
<li><p>Sprinkling salt on the highway PREVENTS water to ice transition by intereference due to NaCl molecules. It is actually preventing the liquid-solid transition and it would seem to people that NaCl is <em>melting</em> the ice.</p></li>
<li><p>When I place my drink in a ice + salt (NaCl) mix, the NaCl molecules dissociate into Na+ and Cl- ions into the water and this is an endothermic reaction where the NaCl molecules remove heat from the water molecules decreasing the temperature of water molecules and converting them to ice. I am assuming that the NaCl molecules strip the ice of heat as well further decreasing their temperature.</p></li>
</ol>
<p>Any comments?</p> | g12911 | [
0.026664989069104195,
0.027661839500069618,
0.0023273848928511143,
-0.024778544902801514,
0.04330843687057495,
0.008415388874709606,
0.027576878666877747,
0.07451821863651276,
-0.0025935559533536434,
-0.021068604663014412,
-0.008696951903402805,
-0.0001721079897833988,
0.041483182460069656,
... |
<p>Lenny Susskind explains in <a href="http://www.youtube.com/watch?v=-BleG7PBwEA&list=ECA2FDCCBC7956448F&index=2" rel="nofollow">this</a> video at about 40min, as an extended object (for example a relativistic string) is boosted to the infinite momentum frame (sometimes called light cone frame), it has no non-relativistic degrees of freedom in the boost direction. Instead, these degrees of freedom are completely determined by the (non-relativistic) motions in the plane perpendicular to the boost direction.</p>
<p>I dont see why this is, so can somebody explain to me how the degrees of freedom are described in this infinite momentum frame?</p> | g12912 | [
0.03941601514816284,
0.0433211587369442,
0.0021708509884774685,
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-0.05038614943623543,
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0.001753... |
<p>On a sunny day an outdoor swimming pool will heat up fairly quickly. My question is, what is the exact mechanism for this and can we put numerical figures on it?</p>
<p>Given that water is clear and colorless, it seems that it will absorb very little direct radiation from the sun. The sides and the bottom of the pool can however heat it by conduction. </p>
<p>Is it possible to estimate the influence of radiation versus conduction in this process or in general to give a full explanation?</p> | g12913 | [
0.005614305846393108,
0.015588824637234211,
0.008712510578334332,
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0.008837134577333927,
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0.07262846827507019,
0.05431065708398819,
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-0.002503609750419855,
0.0006816639797762036,
0.08157332241535187,
0.10531449317932129,
0.028197... |
<p>Let's say there's a static fluid in an arbitrarily deep vessel with constant non-zero compressibility ($k=\frac{1}{B}=-\frac{dV}{Vdp}=\frac{d\rho}{\rho dp}$). Let $z$ be the vertical distance below the surface of the fluid. Then $dp=g\rho dz$ ($g$ here is positive and assumed to be constant). As $k$ is constant, $\rho$ can be expressed in terms of $p$: $\rho=C_{0}e^{kp}$. If $\rho=\rho_{0}$ and $p=p_{0}$ at $z=0$, then $C_{0}=\rho_{0}e^{-kp_{0}}$, which is a positive quantity. So $e^{-kp}dp=C_{0}gdz$, which can be solved to get $p(z)=-\frac{1}{k}\ln(C_{1}k-C_{0}kgz)$. This doesn't make sense, because the coefficient of $z$ is negative, so there exists a positive value of $z$ for which $p=\infty$. What did I do wrong?</p> | g12914 | [
0.005297932308167219,
-0.011196072213351727,
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0.06838121265172958,
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0.02522066980600357,
0.008396588265895844,
-0.003... |
<p>Water usually comes to mind when thinking about freezing. Once it reaches a certain temperature, water freezes, becoming a solid.</p>
<p>However could you make the same statement about a rock? Is a rock at room temperature considered frozen because it is in a solid state?</p> | g12915 | [
0.07537626475095749,
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0.016849173232913017,
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... |
<p>In a gauge theory like QED a gauge transformation transforms one mathematical representation of a physical system to another mathematical representation of the same system, where the two mathematical representations don't differ at all with respect to observables. Gauge transformations are therefore manifestations of a true redundandcy of the mathematical descriptions.</p>
<p>In GR the role of diffeomorphisms is different, a diffeomorphism represents a change of the reference frame. Different observers in different reference frames will of course have different results when they measure the same observable/event. In this sense I agree with Raymond Streater (see <a href="http://www.mth.kcl.ac.uk/~streater/lostcauses.html#XXII">Diff(M)</a>) that it is misleading to say that Diff(M) is a gauge group (if you disagree with me please explain).</p>
<p>In AQFT one associates observables (selfadjoint operators) with bounded open subsets of a spacetime, these observables represent what is observable in the given domain of space and time. A detector that is operated for two hours in a laboratory would be, for example, represented by such an observable (this is only approximately true, because the Reeh-Schlieder theorem says that it is not possible to use a truly localized observable, but one has to use an "approximately local observable" instead).</p>
<p>I think that this line of reasoning will stay true even if one day there is a theory of quantum gravitation. But from time to time I read statements like "local observables are not gauge invariant in a theory with (quantum) gravity and therefore cannot exist/ are not valid observables". (If my phrasing of the statement is wrong, please explain and correct it.)</p>
<p>I have never read about an explanation of this statement and would like to hear about one. Isn't a detector, for example, a (approximatly) local observable and won't detectors exist within a theoretical framework of (quantum) gravity?</p>
<p>Edit: A little of explanation of "observables" in GR: I am aware that in GR only "events" make sense as an observable, but of course not, for example, the spacetime coordinates of a point of spacetime, see the discussion of Einstein's hole argument on the nLab:</p>
<ul>
<li><a href="http://ncatlab.org/nlab/show/spacetime">spacetime</a>, see paragraph "Einstein's hole argument".</li>
</ul>
<p>When a detector detects a particle, I assume that this is an event that is observable because it is defined by the proximity of a localized field excitation and the detector, and the fact that the detecter makes "ping" is a fact that all observers in all reference frames agree upon.</p> | g12916 | [
0.0412481315433979,
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0.012474512681365013,
0.010673639364540577,
0.0397... |
<p>My question is the title of a 1991 paper by Richard Gott and Li-Xin Li:
<a href="http://arxiv.org/abs/astro-ph/9712344" rel="nofollow">http://arxiv.org/abs/astro-ph/9712344</a>
and is also a subject of his popular book, "Time Travel in Einstein's Universe"
Ultimately with cosmology, the chicken and egg question reduces to "How can something come from nothing?" Gott and Li use the concept of a "jinn" (or djinn-genie)---that is something that loops back in time in a closed timelike curve--In the movie, "Somewhere in Time", an elderly Jane Seymour places a pocket watch in young Christopher Reeve's jacket and tells him to come back to her Later, he travels back in time and gives her the watch. The watch is a djinn. Where did it come from? Gott argues that in say the first Planck time, the universe could have pulled a closed timeline curve and created itself. Other than the immense fun value of this thought, is using the concept of CLC in this way valid if it is done in less than the Planck time without violating causality?</p> | g12917 | [
-0.0007353915716521442,
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0.01385136041790247,
0.056914180517196655,
0.04... |
<p>This just started to bother me after reading yet another entangled particle question, so I hate to ask one myself, but...</p>
<p>If we have two entangled particles and take a measurement of one, we know, with certainty, what the outcome of same measurement of the other particle will be when we measure it. But, as with all fundamental QM, we also say the second particle does not have a definite value for the measurement in advance of making it.</p>
<p>Of course, the particle pairs are always described by an appropriate wave function, and measurement of half the pair changes the probabilities associated with each term. But, and this is the part that bothers me, with knowledge of the first measurement, we know the outcome of the second measurement. There's nothing strange or forbidden or anything about this, no non-local affects, no FTL communication, etc. </p>
<p>But does it still make sense to talk about the second particle <em>not</em> being in a definite state prior to the measurement? Or can we consider a local measurement of one half of an entangled pair to be a measurement of the other half? The latter option feels distasteful because it implies communication between the particles when communication is possible, which is obviously wrong, but I find it hard to pretend the second particle in the pair, whose state I know by correlation, is somehow not in that state before I confirm it by measurement.</p>
<p>I should clarify that my uneasiness comes from a comparison with the usual "large separation" questions of entangled particles, where our ignorance of the first measurement leads us to write an "incorrect" wavefunction that includes a superposition of states. Although this doesn't affect the measurement outcome, it seems there is a definite state the second particle is in, regardless of our ignorance. But in this more commonly used scenario, it seems more fair to say the second particle really isn't in a definite state prior to measurement.</p>
<p>As a side note, I realize there's no contradiction in two different observers having different descriptions of the same thing from different reference frames, so I could accept that a local measurement of half the pair does count as a measurement of the other half, while a non-local measurement doesn't, but the mathematics of the situation clearly point to the existence of a definite state for the second particle, whereas we always imply it doesn't have a well-defined state (at least in the non-local case) before measurement.</p>
<p>At this point, my own thinking is that the second particle is in a definite state, even if that state could, in the non-local separation case, be unknown to the observer. But that answer feels too much like a hidden variables theory, which we know is wrong. Any thoughts?</p> | g12918 | [
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-... |
<p>It is well know that we can measure the spinning of the Earth with a <a href="http://en.wikipedia.org/wiki/Foucault_pendulum">Foucault pendulum</a>.</p>
<p>But, is there a similar experiment for the rotation of the Earth around the Sun? I would like to know if we could prove that the Earth rotates the Sun without astronomical observation.</p> | g12919 | [
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... |
<p>Where is the Higgs Field? I get the idea of how it works but I couldn't find anything explaining where it is.</p> | g12920 | [
0.03272680193185806,
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0.020815324038267136,
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0.03797135502099991,
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<p>I am trying to derive the out-of-plane <a href="http://en.wikipedia.org/wiki/Phonon" rel="nofollow">phonon</a> <a href="http://en.wikipedia.org/wiki/Phonon#Dispersion_relation" rel="nofollow">dispersion relation</a> for a membrane. As far as I can tell, one of the simplest ways to do so is with a Lagrangian of the form:</p>
<p>$$L_{bending}=\frac{1}{2}\rho \dot{h}^2-\frac{1}{2}\kappa(\nabla^2h)^2$$</p>
<p>Where $h$ is the out-of-plane displacement, $\rho$ the mass density and $\kappa$ the bending rigidity.</p>
<p>I tried to proceed by using the Euler-Lagrange equations with the substitution:</p>
<p>$$h=h_o \exp\left[-i(\omega t + qa)\right]$$</p>
<p>as per standard-solid-state phonon treatments, but I don't know how to deal with the $(\nabla^2 h)$ term following the above substitution (perhaps that is the incorrect part).</p>
<p>I know the answer should turn out to be:</p>
<p>$$\omega^2=\frac{\kappa q^4}{\rho}$$</p>
<p>Note: Many of the papers I look at point to the following paper for the answer - but Google gives me nothing for it. But I feel the answer is simple and I am not doing the math correctly. There are various more complicated treatments in the literature, including QM formulations, none of which I can follow very well.</p>
<p>I. M. Lifshitz, Zh. Eksp. Teor. Fiz, vol. 22, p. 475, 1952.</p> | g12921 | [
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... |
<p>According to multiple sources the SI units for angular momentum are kg * m$^2$ / sec</p>
<p>I am confused about the derivation for this. Here is what I have done:</p>
<p>$$L = I \cdot \omega \\
= m \cdot r^2 \cdot r \cdot v(translational) \\
= kg \cdot m^3 \cdot m/s \\
= (kg \cdot m^4)/s$$</p>
<p>What are my doing wrong here</p> | g12922 | [
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<p>I read this post, <a href="http://physics.stackexchange.com/questions/86769/is-the-symmetry-group-of-two-spin-1-2-particles-su2-times-su2-or-su4">Is the symmetry group of two spin 1/2 particles $SU(2) \times SU(2)$ or $SU(4)$?</a></p>
<p>If the picked answer is correct, can I believe that an $N$-degenerate system respects $SU(N)$ symmetry? But if so, I am confused in this way: can we understand that a spin $j$ particle contains $2j+1$ internal degenerate states? Then the symmetry of this particle is $SU(2j+1)$, right? If $j>2$, then it is larger than $SU(2)$!</p>
<p>I must be wrong somehow since I know little about group theory. So, basically, what kind of system respects $SU(N)$?</p>
<hr>
<p><strong>Update 1</strong></p>
<p>Since I have not enough reputation, I could not add comment on the linked post, which I am still confused, so I may also post here(related to this issue):
There are $M\geq 2$ particles, if each particle respects $SU(N)$ symmetry, and if </p>
<ul>
<li>A. there is no interaction between them, then what is the symmetry group, if</li>
<li><ul>
<li>A1.they are non-identical particles?<br></li>
</ul></li>
<li><ul>
<li>A2. they are identical particles?<br></li>
</ul></li>
<li>B. there is pairwise interaction between them, and the interaction is $SU(N)$ invariant,</li>
<li><ul>
<li>B0. what do I mean by $SU(N)$ invariant?<br></li>
</ul></li>
<li><ul>
<li>B1. symmetry group for non-identical case?<br></li>
</ul></li>
<li><ul>
<li>B2. for identical case?</li>
</ul></li>
</ul> | g12923 | [
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0.02516940049827099,
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0.... |
<p>Newtonian gravity can be described by the equation:
$$ \nabla^2 \phi = 4 \pi \rho G $$
where $\rho$ is the mass density, $\phi$ is the gravitational potential, and G is the universal gravitational constant.
Of course, one of the shortcomings is that it is not consistent with special relativity. General relativity handles this shortfall but is a tensor theory. However,the above equation can be modified as follows:
$$ (\nabla^2 - \frac{1}{c^2}\frac{\partial^2}{{\partial t}^2}) \phi = 4 \pi \rho G $$
This would be consistent with special relativity. Would this model give results close to experiment? Would it give correct results in some observed situations where Newtonian gravity fails? Why or why not?</p> | g12924 | [
0.026430530473589897,
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<p>According to <a href="http://en.wikipedia.org/wiki/Hund%27s_rules" rel="nofollow">Hund's second rule</a>, the spin tends to be maximal.
That would, in my understanding, imply that, regarding the Stern-Gerlach experiment, the important electron in a silver atom has spin 1/2 (or "up"). This should hold for all atoms.</p>
<p>Every atom would have the same spin magnetic moment (<em>smm</em>) - because the smm points in direction of the spin - and thus be affected by the <strong>B</strong>-field just like any other atom.</p>
<p>But, if every electron has the same <em>smm</em> w.r.t. the magnetic field, why do we get two "blobs" on the screen and not just one "blob" above or below the z-axis?</p>
<p>Where is the error in my thought process?</p> | g12925 | [
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-0.0... |
<p>I already learned the Physics' basics like Newton Laws, Electricity, and Optics.
Can you recommend me a good book for advancing with my learning of physics(with some math)?</p> | g98 | [
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0.03718016296625137,
-0.019... |
<p>What is the exact $SU(2)$ representation to which these Hermitian generators belong?
\begin{equation}
t_a=\{t_1,t_2,t_3\}=\left\{\frac{1}{\sqrt{2}}\begin{pmatrix}
0 & 1 & 0 \\
1 & 0 & 1 \\
0 & 1 & 0
\end{pmatrix},\,\frac{1}{\sqrt{2}}\begin{pmatrix}
0 & -i & 0 \\
i & 0 & -i \\
0 & i & 0
\end{pmatrix},\,\begin{pmatrix}
1 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & -1
\end{pmatrix} \right\}
\end{equation}</p>
<p>I'm a bit puzzled with this, these are not the generators of the triplet representation of $SU(2)$ (the triplet in $SU(2)$ is the adjoint rep which is real and constructed with the structure constants), nevertheless they are used as if they were in much literature. What are really these generators? They seem like the extension to 3 dimensions of the Pauli matrices. The 3 dimensional fundamental rep (this does not make sense to me)? some kind of non-irreducible representation? </p> | g12926 | [
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0.053849052637815475,
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0.012722605839371681,
-0.022923866286873817,
... |
<p>I am looking at Griffiths introduction to Electrodynamics 3rd ED. Problem 2.10 asks for the flux of $E$ through the right face of the cube, when a charge $q$ is in the back left corner of the cube. The solution manual says it should be $\frac q {24\epsilon _0}$ but I think it should be $\frac q {6\epsilon _0}$ because each side should experience the same flux, and the face of the cube represents 1/6th of the cube.</p> | g12927 | [
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0.011... |
<p>I have a random point defined by:</p>
<pre><code>int x = rand.nextInt(9)-4;//-4 to +4
int y = rand.nextInt(4)+2;//+2 to +5
int z = rand.nextInt(9)-4;//-4 to +4
</code></pre>
<p>Y happens to be the "up" vector, but I suspect that's irrelevant.</p>
<p>I want to rotate this point so that it ends up relative to a vector that passes through (i,j,k) rather than relative to the vector that passes through (0,1,0).</p>
<p>Thus if (x,y,z) is (0,6,0) and (i,j,k) is (1,1,0) the result should be about (5,5,0).</p>
<p>Essentially I'm trying to draw a random deflection vector based on the initial input force vector. In this case, fractures through 3D voxel rock, but bullet deflection lines off armor make for a good visualization.</p> | g12928 | [
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-0.03749755024909973,
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0.00045853800838813186,
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0.011782560497522354,
0.05532702058553696,
0.030105246230959892,
0.02444523759186268,
-0.03... |
<blockquote>
<p>The resistance of a bulb filament is $100\Omega$ at a temperature of $100^\circ \text{C}$. If its temperature coefficient of resistance be $0.005 \space \text{per} ^\circ \text{C}$, its resistance will become $200\Omega$ at a temperature of </p>
<ol>
<li>$300^\circ\text{C}$</li>
<li>$400^\circ\text{C}$</li>
<li>$500^\circ\text{C}$</li>
<li>$200^\circ\text{C}$</li>
</ol>
</blockquote>
<p>Now the linear approximation is $R_t=R_0(1+\alpha T)$</p>
<p>Therefore
\begin{align*}
100\Omega &= R_0(1+0.005\times 100) \\
\therefore R_0 &= \frac{100}{1.5} \\
\text{Now } 200 &= \frac{100}{1.5}(1+0.005\times t_2) \\
0.005\times t_2 &= 2 \\
t_2 &=400^\circ\text{C}
\end{align*}</p>
<p>But there is also this formula $\alpha=\frac{R_2-R_1}{R_1(t_2-t_1)}$</p>
<p>\begin{align*}
0.005 &=\frac{200-100}{100(t_2-100)} \\
t_2 &= 1/0.005 + 100 \\
t_2 &= 300^\circ\text{C}
\end{align*}</p>
<p>Why are these answers differing?</p> | g12929 | [
0.040513332933187485,
-0.043355416506528854,
0.008733312599360943,
-0.0370430164039135,
0.04221051558852196,
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0.07424896210432053,
0.02558480016887188,
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0.008040395565330982,
-0.07312213629484177,
0.04183683544397354,
-0.01150678563863039,
0.02622... |
<p>When grabbing a typical tree branch of at least two feet, it's so easy to snap with a less than one inch circumference that even a toddler can do it.</p>
<p>However, after breaking it, the smaller halves with multiply from the center, going like this:</p>
<p>1 - BB (before break)</p>
<p>2 - AB (after break)</p>
<p>4 - AB (half of second break equals four)</p>
<p>8 - AB (continuing multiplication factors of two)</p>
<p>And so on....</p>
<p>But what I want to know is why this is ... in quantum physics.</p>
<p>I want to know why the more you break it, the harder it is to keep breaking it from the center of each half.</p>
<p>This applies to tearing as well ... if you tear a cardboard box in half down the middle it's easy, but if you turn it over and continue on it keeps getting harder as the pieces get smaller.</p> | g12930 | [
0.019526371732354164,
0.04639923572540283,
-0.0090363509953022,
-0.019244305789470673,
-0.013590625487267971,
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0.04165642336010933,
0.009452000260353088,
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-0.021093038842082024,
-0.05792246386408806,
-0.01622464321553707,
0.0028262226842343807,
-0.0... |
<p>Here's my question: if atoms have well defined energy levels and those differences correspond to the frequencies of light that can be absorbed, how is it that opaque objects absorb all or most visible light frequencies?, frequencies get absorbed and you basically don't have any visible light coming out on the other end. </p>
<p>Shouldn't only those frequencies that have to do with its energy levels get absorbed? Yes, I realize ordinary materials have many different compounds, but surely they don't add up to an infinite number of energy levels? Thanks.</p> | g407 | [
0.032987482845783234,
0.0359513983130455,
0.019147120416164398,
-0.022884780541062355,
0.024479759857058525,
0.024566924199461937,
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0.0651361495256424,
0.011073692701756954,
-0.017702696844935417,
-0.008707618340849876,
-0.03317638114094734,
0.03837034851312637,
-0.0087... |
<p>The terminology "topological charge" is frequent in lots of research papers related to optical vortex or optical OAM, it is used to represent the optical OAM. Why? How to comprehend it?</p> | g12931 | [
0.028127236291766167,
0.012616768479347229,
0.005898301023989916,
-0.027246546000242233,
0.08200148493051529,
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0.01255081407725811,
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0.08441615849733353,
0.034815236926078796,
0.014857796020805836,
0.00015470157086383551,
0.026203766465187073,
0.... |
<ol>
<li><p>Will Linear momentum be conserved in a non-inertial frame of reference? </p></li>
<li><p>In other words what is the fundamental condition for linear momentum to be conserved?</p></li>
<li><p>Also which is more fundamental- Newton's Third Law or Conservation of Linear Momentum? (as in Newton's third law does not hold true when we go to the quantum/atomic level or at relativistic speeds whereas linear momentum to my knowledge holds true)</p></li>
</ol> | g12932 | [
0.05683309957385063,
-0.021673396229743958,
0.027846241369843483,
0.0049022044986486435,
0.0741049200296402,
0.01650376245379448,
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0.019958268851041794,
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0.02364247292280197,
0.021340584382414818,
-0.04279470443725586,
-0.08385763317346573,
-0.0... |
<p>consider two identical charges moving with uniform velocity. There will be a magnetic force of attraction between them as two currents in the same direction attract each other. If I sit on one of the charges, according to me the other charge is not moving. So there wont be any magnetic attraction. How does changing the frame of reference change the outcome of the interaction? What is it that will actually happen?</p> | g12933 | [
0.041866760700941086,
0.012822551652789116,
0.005814129952341318,
-0.01264344435185194,
0.08375947922468185,
0.026238763704895973,
0.030096180737018585,
0.03042203187942505,
-0.03743286058306694,
-0.036042194813489914,
-0.018218418583273888,
-0.01596691831946373,
-0.02334222011268139,
-0.0... |
<p>My question is:
It is easy to balance a bicycle when it is moving at a fairly high velocity, say 7 m/s or 25 km/hr.
But when a bicycle slows down, it is hard to keep it upright, and the person riding it may thus fall down! Why?</p> | g408 | [
0.09024704992771149,
0.06238691136240959,
-0.009220018982887268,
0.04803312569856644,
0.06635792553424835,
0.02583952434360981,
0.07678443938493729,
0.023676928132772446,
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-0.020548664033412933,
-0.038401514291763306,
-0.05384349450469017,
-0.05458313226699829,
-0.0042... |
<p>I'm just brushing up on a bit of CFT, and I'm trying to understand whether conformal symmetry is local or global in the physics sense.</p>
<p>Obviously when the metric is viewed as dynamical then the symmetry is local, because essentially then we're dealing with a change of variables under which the metric transforms with a local scale factor $\Omega = \Omega(x)$.</p>
<p>Usually, however, we think of the metric as fixed. David Tong's excellent notes suggest that in this case the symmetry should be thought of as global. But I'm not sure I agree. </p>
<p>Say we work in 2D and have general conformal transformation given by holomorphic function $f(z)$. Under a conformal transformation $z\to w$ say, viewed actively, a general field $\Phi$ will transform to</p>
<p>$$(\frac{dw}{dz})^h \Phi$$</p>
<p>where the prefactor is clearly dependent on the spacetime point. This would suggest that the transformation is local in the physics sense.</p>
<p>Perhaps the distinction he is trying to make is between physical and gauge transformations. But then again I might be wrong because I thought that only global transformations had nonzero conserved quantities, and there's definitely a conserved current for conformal symmetry.</p>
<p>Could anyone help to clarify this for me?</p> | g12934 | [
0.05575048550963402,
-0.02333690971136093,
-0.011506869457662106,
-0.007027244661003351,
0.07398536056280136,
0.027512744069099426,
0.10315828770399094,
0.024500567466020584,
-0.046205632388591766,
-0.020212814211845398,
-0.0012945072958245873,
0.0043250396847724915,
0.001123302150517702,
... |
<p>What is
\begin{align}
\sum_{\mu=0}^{3}
\langle \sigma_{\mu} \rangle^2
=
?
\end{align}
$\sigma_{\mu}$ are the Pauli matrices. The Bra-Ket notation is used in this question:
\begin{align}
\langle \sigma_{\mu} \rangle
=
\langle \Psi \lvert \sigma_{\mu} \lvert \Psi \rangle
,
\end{align}
where $\Psi$ is the Pauli spinor of two complex components.</p> | g12935 | [
-0.007456333842128515,
-0.041722219437360764,
-0.02916303090751171,
-0.04192851856350899,
-0.010915162041783333,
-0.018923718482255936,
0.017688287422060966,
0.02943836711347103,
-0.02959844283759594,
0.059654753655195236,
-0.03313668072223663,
0.04647085443139076,
0.03142789378762245,
-0.... |
<p>In a holography set-up, as shown in the figure below, Illumination beam and reference beam both are in phase. The interference pattern generated at the detector contains the whole information about the object. When illumination beam will incident on to the object its phase and amplitude will change and further object beam will recombines with reference beam at the detector. Question is how the Interference pattern provides complete 3D information of the object ?</p>
<p><img src="http://i.stack.imgur.com/9SQa1.png" alt="Typical Holography setup"></p> | g12936 | [
-0.004887185525149107,
-0.027640381827950478,
0.021624542772769928,
0.011153395287692547,
-0.013462627306580544,
0.03290899842977524,
0.010652455501258373,
0.03654993698000908,
-0.007093209307640791,
-0.022812945768237114,
0.005169472191482782,
-0.03185924515128136,
-0.013815635815262794,
... |
<p>Given the electromagnetic Lagrangian density
$$
\mathcal{L}~=~-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}~=~\frac{1}{2}(E^2-B^2)
$$
is a Lorentz invariant, how many other electromagnetic invariants exists that can be incorporated into the electromagnetic Lagrangian?</p> | g12937 | [
0.03462008759379387,
0.01922581158578396,
-0.010017051361501217,
-0.044415488839149475,
0.006346187088638544,
0.0827847272157669,
0.007245166227221489,
0.00871592853218317,
-0.05166782811284065,
0.01937539130449295,
0.008195674978196621,
0.0015860035782679915,
-0.00014188411296345294,
0.05... |
<p>Electrical wires are relatively inefficient in transferring energy--especially when the place of production is quite far from communities.</p>
<p>Would it be possible to transfer that energy via photons? I realize that to some degree photons react with atoms, but might there be a specific condition in which this would be feasible and even more efficient--such as a specific wavelength of the electromagentic spectrum which encounters little resistance from the atoms in air (and thus low energy loss).</p>
<p>This is often a hurdle for utilities when the source of power is far away from the communities, such as hydro electric dams. I'm not speaking about removing metal wires altogether, just when it may be practical.</p> | g12938 | [
-0.010505138896405697,
0.04561718925833702,
0.027483904734253883,
-0.012953358702361584,
-0.038197439163923264,
-0.010852939449250698,
-0.025973722338676453,
0.05315258353948593,
-0.021688008680939674,
0.03277353569865227,
0.04103143513202667,
0.04606566205620766,
-0.013587599620223045,
-0... |
<p>In the <a href="http://en.wikipedia.org/wiki/Gupta%E2%80%93Bleuler_formalism" rel="nofollow">Gupta-Bleuler formalism</a> we have a problem with two states (scalar photons and longitudinal photons), because here $\langle \vec{k}_a|\vec{k}_b\rangle $ is negative or zero. However, I thought that only $|\langle \vec{k}_a|\vec{k}_b\rangle |^2$ corresponds to probabilities, a quantity which would be non-negative anyway.</p>
<p>What am I doing wrong?</p> | g12939 | [
0.04452134668827057,
0.00457868492230773,
-0.007681111339479685,
0.007815483957529068,
0.057430341839790344,
0.004237120505422354,
0.051810234785079956,
0.051490217447280884,
-0.04422394558787346,
0.01595817692577839,
0.044028423726558685,
0.008946960791945457,
0.010860763490200043,
0.0332... |
<p>I am self-studying this <a href="http://www.google.dk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&ved=0CEMQFjAC&url=http://ocw.mit.edu/courses/mechanical-engineering/2-25-advanced-fluid-mechanics-fall-2005/study-materials/06_viscous_flow.pdf&ei=W_W9Uqr4EsKY4wThyoBg&usg=AFQjCNGj6pKmX04DYEHf7e4q7HiCFfhBcg&sig2=K_GBxIh5Q2Zq_X-0E3lZhg&bvm=bv.58187178,d.bGE" rel="nofollow">note</a> and I am stuck in the derivation of the normal shear stress. Specifically I can't see how the relations (23) and (24) come about.</p>
<p>Specifically, what I don't understand is</p>
<p>$$
\tau'_{xx} = \frac{\tau_{xx}+\tau_{yy}}{2}+\tau_{yx} \tag{23}
$$
and
$$
\tau'_{yy} = \frac{\tau_{xx}+\tau_{yy}}{2}-\tau_{yx}\tag{24}
$$
Can someone elaborate on the note to make it clearer? </p> | g12940 | [
0.020105909556150436,
0.0013426776276901364,
-0.03386905789375305,
-0.0706460028886795,
0.05602193996310234,
-0.025134865194559097,
0.022914811968803406,
-0.02063916064798832,
0.01959679089486599,
-0.029149245470762253,
-0.05060124769806862,
0.05068936571478844,
-0.013971044681966305,
-0.0... |
<p>So I was curious about, what if we make a tunnel from one side of the earth, to the other side of the earth? Gravity is ofcourse always negative, which makes you "fall" and not "float".</p>
<p>If we take this image, let's imagine that the BLACK LINE in the midle of the earth, is a tunnel from one side of the earth, to the other side of the earth.</p>
<p>The red DOT is the midpoint, where something in theory, should happen to gravity that is out of our forces.</p>
<p>What would happen, if a human were to be in the red dot? Would the human just stay there for eternity?</p>
<p><strong>Notes</strong>: Imagine that the being in the center couldn't kill you, neither would it bring you in contact of any substance. Just a long tunnel with nothing but the tunnel itself.</p>
<p><img src="http://i.stack.imgur.com/FPC7p.png" alt="enter image description here"></p> | g76 | [
-0.0007398935849778354,
0.04011305794119835,
0.010329272598028183,
0.03474095091223717,
0.014423915185034275,
0.08337514847517014,
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0.013023734092712402,
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-0.060103874653577805,
0.03211238235235214,
-0.02347133494913578,
0.07290630787611008,
-0.022... |
<p>What makes Liouville theory subject to relatively intense research field?</p> | g12941 | [
0.0050377994775772095,
0.05454464629292488,
0.008923941291868687,
-0.05116776376962662,
0.003882697317749262,
0.016353420913219452,
0.03234783560037613,
-0.005271233152598143,
0.007119692862033844,
-0.012365906499326229,
-0.0264569278806448,
-0.048119839280843735,
0.03455420956015587,
-0.0... |
<p>On <a href="http://en.wikipedia.org/wiki/Quantum_chromodynamics" rel="nofollow">Wikipedia</a> it says that the two peculiar properties of quantum chromodynamics (QCD) are: <a href="http://en.wikipedia.org/wiki/Color_confinement" rel="nofollow">confinement</a> and <a href="http://en.wikipedia.org/wiki/Asymptotic_freedom" rel="nofollow">asymptotic freedom</a>.</p>
<p>Asymptotic freedom is the idea that at low energies we <em>cannot</em> use perturbation theory because the coupling becomes extremely strong. One the other hand, at sufficiently high energies, the coupling becomes very small and so we can use perturbation theory. This can all be determined by investigating the $\beta$-function. </p>
<p>My question is:</p>
<blockquote>
<p>Why is the asymptotic freedom of quarks not considered to be a sufficient explanation for confinement?</p>
</blockquote>
<p>My logic: </p>
<p>According to asymptotic freedom: at low energies the coupling becomes so strong that quarks cannot be isolated which explains confinement. If I am right (which I'm probably not), then why is confinement still considered to be such a mystery?</p> | g12942 | [
0.06117668002843857,
0.01106986403465271,
-0.008972272276878357,
-0.021297510713338852,
0.008317080326378345,
0.011606695130467415,
0.02631208300590515,
-0.0035730681847780943,
-0.026325048878788948,
-0.023779984563589096,
0.05080797150731087,
0.011627215892076492,
0.009634998627007008,
0.... |
<p>I was trying to do linear stability analysis of spring pendulum. I arrived at the differential equations which describe the system. But I am unable to proceed to linear stability analysis. Is it possible to do linear stability analysis on 2nd order differential equations by finding eigen values of Jacobian matrix? The equations are as below :</p>
<p>$mr'' - m(L+r)(\theta')^2-mgcos(\theta)+kr' = 0$ and</p>
<p>$(L+r)\theta''+2r'\theta'+gsin(\theta)=0$</p>
<hr>
<p>UPDATE : The fixed points are $(mg/k,0)$ and $(-mg/k,\pi)$</p> | g12943 | [
-0.0035421974025666714,
-0.03469203785061836,
0.011162430047988892,
-0.009442392736673355,
0.000048291549319401383,
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0.057195570319890976,
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-0.03449476882815361,
0.013062669895589352,
-0.061753641813993454,
0.050859205424785614,
0.025161493569612503... |
<p>First of all I'd like to point out that I'm a complete layman when it comes to physics and I apologise if this isn't the correct forum for this.</p>
<p>If I were to sit on an office chair on a laminated floor and fired a shotgun out in front of me roughly how far backwards would I <a href="http://en.wikipedia.org/wiki/Recoil" rel="nofollow">recoil</a>, imagine I weight 170lbs, I'll let you choose both the office chair and shotgun being used (I haven't got a shotgun to use as an example, this is purely hypothetical).</p>
<p>Also if I was to fire the shotgun in the same situation as above but facing a wall would I be projected further?</p> | g12944 | [
0.06089641898870468,
0.02096441201865673,
0.018065886572003365,
0.003719836939126253,
0.012338347733020782,
0.009256611578166485,
0.010197644121944904,
0.018649255856871605,
-0.06844217330217361,
-0.02738860622048378,
-0.037177134305238724,
0.05105213448405266,
-0.0500635989010334,
-0.0101... |
<p>I have seen in the in the Dirac equation $$\gamma_0,\gamma_1,\gamma_2,\gamma_3.$$ Then I have seen the definition of a new matrix $$\gamma_5=i\gamma_0\gamma_1\gamma_2\gamma_3.$$ Now my question is why the name of the new matrix has not been given as $$\gamma_4.$$ Is there any historical reason behind this or it is simply taken as $$\gamma_5$$ without any special reason skipping $$\gamma_4~?$$ </p> | g12945 | [
0.01960848644375801,
-0.07197467237710953,
0.004926695488393307,
-0.05882860720157623,
0.07225712388753891,
0.004053807817399502,
0.07297518849372864,
-0.0013380668824538589,
-0.07742731273174286,
0.011665735393762589,
-0.030177734792232513,
0.015952054411172867,
-0.008109047077596188,
0.0... |
<p>I was playing around with a battery, an ammeter, and a light bulb. The ammeter originally read 1.99 A, but after reversing the leads going into and out of the ammeter the ammeter read -1.98A. I know this was because the leads were reversed but I am not sure why reversing the leads led to the ammeter readind a negative value. Why?</p> | g12946 | [
0.044837586581707,
-0.04573157802224159,
-0.019097698852419853,
-0.002273250836879015,
0.06362885981798172,
0.06749458611011505,
0.020267970860004425,
0.03090607188642025,
-0.005432509817183018,
0.0035241199657320976,
0.04642453044652939,
0.07467532157897949,
-0.01901397295296192,
0.001224... |
<p>What happens to a photon shot straight into a black hole? Does it gain infinite momentum before it crosses the horizon? If it has a finite momentum going in, then it would seem that a photon of the same momentum could escape the BH by time reversal.</p>
<p>Does the photon enter the BH at the speed of light as we perceive it from the outside? Or does time dilation take place as the photon gains energy?</p>
<p>Does the photon add to the mass of the black hole an amount of mass m = e/c^2, where e is photon energy? If so, is it the energy the photon had at the beginning, or the energy the blue shifted photon has as it crosses the horizon?</p> | g12947 | [
0.02960502728819847,
0.02546650916337967,
0.008807537145912647,
0.03857727721333504,
0.03294597193598747,
0.022580420598387718,
0.005435326136648655,
0.057847533375024796,
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-0.0004985705600120127,
0.0006613573059439659,
0.03790971264243126,
-0.0462358221411705,
-0.002... |
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