question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>I got some naive questions on the ground states of <a href="http://arxiv.org/abs/cond-mat/0506438" rel="nofollow">honeycomb Kitaev model</a> (with open boundary conditions):</p>
<p>(1) Consider a simple case that $J_x=J_y=0$, then the model reduces to $$H=J_z\sum_{z\text{ }\text{links}}S_i^zS_j^z.$$ It's obvious that $H$ has highly degenerate GSs (degeneracy$=2^N$, where $N$ is the number of unit cells), and in each GS configuration, every two spins connected by a $z$ link are aligned parallel (if $J_z<0$) or antiparallel (if $J_z>0$). Thus, each of these GSs corresponds to a spin configuration and is <em>not</em> a spin liquid (SL).</p>
<p>On the other hand, the Majorana <strong>exact solution</strong> tells us that the GS of $H$ is a <em>gapped</em> SL.</p>
<p>So, does the <strong>exact solution</strong> just <em>single out</em> <strong>one</strong> of the highly degenerate GSs, which <strong>happens to be</strong> a SL (some certain manner of superposition of the above $2^N$ spin configurations) ?? </p>
<p>(2) Following question (1), if the <strong>exact solution</strong> does <em>single out</em> just <strong>one</strong> of the highly degenerate GSs of $H$, and how could this be?</p>
<p>According to Kitaev's discussion on P.19 in his paper, the GS is achieved by the vortex-free field configuration, which follows from a theorem proved by Lieb. </p>
<p>But shouldn't an <strong>exact solution</strong> gives <em>all</em> the $2^N$ GSs ? Why only <em>single out</em> <strong>one</strong> which strongly contradicts the obviously correct GS degeneracy$=2^N$ ? Is there something wrong with applying the Lieb's theorem here ? I'm confused....</p> | g14730 | [
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<p>I keep reading the same phrase about the very short life time of the top quark:</p>
<blockquote>
<blockquote>
<p>Because the t-quark decays on a shorter than the characteristic QCD interaction-time it cannot hadronize. Therefore it give to possibility to be seen as a bare quark.</p>
</blockquote>
</blockquote>
<p>I cannot find any more information beyond this simple phrase. There are however a few things that I would like to seen cleared out (sorry for the naive questions) :</p>
<ul>
<li>The first question is simple: I don't understand why this offers to opportunity to see a bare quark, since this quark decays that fast it must be very difficult te see it...</li>
<li>A bare quark?? I thought this was ruled to see colorful particles?</li>
</ul> | g14731 | [
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<p>So, objects are certain colors because they are absorbing every color except for that one. So why is it that if I take a projector and project a blue image on a red wall, the red wall still reflects the blue image rather than absorbing the blue light? I don't know if this is considered a dumb question, but I was thinking about it and it got me curious (also, I haven't taken any kinds of physics). </p> | g14732 | [
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<p>If I have these theoretical predictions:
\begin{align}
\omega_{p_1} = 4.5132 \pm 0.0003~\text{rad/s} && \omega_{p_2} = 4.5145 \pm 0.0002~\text{rad/s}\\
\omega_{b_1} = 0.0707 \pm 0.0003~\text{rad/s} && \omega_{b_2} = 0.0700 \pm 0.0002~\text{rad/s}
\end{align}</p>
<p>And I got these experimental results:
\begin{align}
\omega_{p_1} = 4.5148 \pm 0.0001~\text{rad/s} && \omega_{p_2} = 4.5147 \pm 0.0001~\text{rad/s}\\
\omega_{b_1} = 0.0702 \pm 0.0001~\text{rad/s} && \omega_{b_2} = 0.0707 \pm 0.0001~\text{rad/s}
\end{align}</p>
<p>Can I only say that the experimental measurements are incompatible with the theoretical predictions even if the discrepancy is in the order of $\sim 10^{-3}\text{ s}$? Or can I say something else more?</p> | g14733 | [
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<p>My mom and I were in a car accident. We are ok, but I want to know how fast the car that hit us was going. We were stopped at a light. The car that hit us from behind was a big GMC SUV. Our car was a Cadillac srx and mom looked it up it weighs 4,277 pounds. Then we hit a little car in front of us at 12mph and the air bag went off!</p>
<p>Mom says the car behind us must have going faster than that because she says our car absorbed some kinetic energy. I don't know what that means but I think it was going slower and the hit pushed us to go faster.</p>
<p>How can we figure out what actually happened?</p> | g14734 | [
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<p>We know that when a capacitor charges from a source $E$, it stores energy of $E=\frac{1}{2}QV $. <br> This is derived without taking into consideration any resistances present in the circuit.</p>
<p>We also know that the battery does work $W=QV$ to pump the charge $Q$.
It is explained that the remaining $\frac{1}{2}QV$ is dissipated as heat in the circuit resistance. And we can verify it to be true:</p>
<p>$\frac{1}{2}QV= \frac{1}{2}CV^{2} = {\displaystyle \int_0^\infty V_oe^\frac{-t}{RC} \cdot I_oe^\frac{-t}{RC} dt} $</p>
<p>What happens if there the resistance in the circuit is zero? Where will the energy go?</p> | g14735 | [
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<p>This is a question regarding Francesco, section 4.3.3. In this section, he considers the two-point function
$$
S_{\mu\nu\rho\sigma}(x) = \left< T_{\mu\nu}(x) T_{\rho\sigma}(0)\right>
$$
He then goes on to claim that symmetry of the stress-energy tensor implies $$S_{\mu\nu\rho\sigma}(x) = S_{\nu\mu\rho\sigma}(x)~~~(1)$$
Though he doesn't mention this, I presume this is true only when $x \neq 0$ since the EM tensor is symmetric in a correlation as long as the other fields in the correlator are not evaluated at the same point. </p>
<hr>
<p>EDIT: Due to some comments, I'll explain why I think so. If a theory is Poincare invariant, it has conserved currents $T^{\mu\nu}$ for translations and
$$
j^{\mu\nu\rho} = T^{\mu\nu} x^\rho - T^{\mu\rho} x^\nu
$$
for Lorentz transformations. For completeness, we also note that if the theory has scale invariance the dilation current is
$$
j^\mu_D = T^{\mu\nu} x_\nu
$$
In a classical theory, conservation of these currents implies symmetry and tracelessness of the stress-energy tensor. In a quantum theory, we have a Ward Identity, which for each of the currents reads
\begin{equation}
\begin{split}
\partial_\mu \left< T^\mu{}_\nu X \right> &= \sum\limits_{i=1}^n \delta^d(x-x_i) \frac{\partial}{\partial x_i^\nu} \left< X \right> \\
\partial_\mu \left< j^{\mu\nu\rho} X \right> &= \sum\limits_{i=1}^n \delta^d(x-x_i) \left( x_i^\rho\frac{\partial}{\partial x_i^\nu} - x_i^\nu\frac{\partial}{\partial x_i^\rho} - i S_i^{\mu\nu} \right) \left< X \right> \\
\partial_\mu \left< j^\mu_D X \right> &= - \sum\limits_{i=1}^n \delta^d(x-x_i) \left( x_i^\alpha \frac{\partial}{\partial x_i^\alpha} + \Delta_i \right) \left< X \right>
\end{split}
\end{equation}
where $X = \Phi_1(x_1) \cdots \Phi_n(x_n)$, $S^{\mu\nu}_i$ is the representation of the Lorentz algebra under which $\Phi_i(x_i)$ transforms and $\Delta_i$ is the scaling dimension of $\Phi_i(x_i)$. Now plugging in the exact forms of the currents $j^{\mu\nu\rho}$ and $j^\mu_D$, we find
\begin{equation}
\begin{split}
\partial_\mu \left< T^\mu{}_\nu X \right> &= \sum\limits_{i=1}^n \delta^d(x-x_i) \frac{\partial}{\partial x_i^\nu} \left< X \right> \\
\left< \left( T^{\mu\nu} - T^{\nu\mu} \right) X \right> &= i \sum\limits_{i=1}^n \delta^d(x-x_i) S_i^{\mu\nu} \left< X \right> \\
\left< T^\mu{}_\mu X \right> &= \sum\limits_{i=1}^n \delta^d(x-x_i) \Delta_i \left< X \right>
\end{split}
\end{equation}
Clearly, the EM tensor is not symmetric under correlation functions at the points $x = x_i$.</p>
<hr>
<p>Now, using these symmetry properties and certain other properties under parity, he argues that
$$
S^\mu{}_\mu{}^\sigma{}_\sigma(x) = \left< T^\mu{}_\mu(x) T^\sigma{}_\sigma(0)\right> = 0
$$
Following the above arguments, this should then only be true at $x \neq 0$. <strong>However, Francesco claims that this holds <em>everywhere</em> and therefore concludes that $\left< T^\mu{}_\mu(0)^2 \right> = 0$.</strong> How does this makes sense?</p> | g14736 | [
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<p>What is the best container material for heat transfer between ice and water?</p>
<p>this is a difficult question to ask without displaying a picture of what I'm meaning.</p> | g14737 | [
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<p>Why do neutrino account for 99% of the energy release for a SN II, while it is not expected to be the case for SN Ia?</p>
<p>Is it because the densities are not high enough to induce inverse beta-decay?</p>
<p>(The question came from reading Particle Astrophysics of Donald Perkins, section 7.14.1 last paragraph (it is on page 178 of the second edition).)</p> | g14738 | [
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<p>What is the proper format to ask debunking questions without being marked as off-topic, yet be able to step through the entire theory logically?</p>
<p>Specifically, I am looking at Wallace Kluck's claim on decuity.com that </p>
<p>"Light is an inertial particle not a wave"</p>
<p>A rotating electron is treated as a charged ring with its radius as the radius of gyration. </p>
<p>Total kinetic energy is divided equally into linear kinetic energy or rotational kinetic energy. </p>
<p>The total kinetic energy, linear and rotational, of each particle increases to mc^2 while the charge of the electron decreases to zero.</p>
<p>The overall theory looks simple, I just need better minds than mine to help elucidate...</p> | g14739 | [
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<p>Recently, I was taught by my sir that the Acceleration of an electron of Bohr Atom is equal to its frequency. I am confused and didnt understand why it turns out to be equal</p> | g14740 | [
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<p>When a conductor <strong>that's purpose is to carry current</strong> ,is laminated to reduce eddy currents, does it affect the current capacity for that same conductor? Will it reduce the current capacity?</p> | g14741 | [
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<p>I came across a line that said "an atom of heavy element is hit with a <strong>low velocity neutron</strong>, otherwise the required reaction would not achieve result". So, why not a neutron of high velocity is successful to achieve a nuclear fission ? </p> | g14742 | [
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<p>I know the derivation of Hubble time goes something like this (I am an a-level student so this may not be the actual derivation): Two galaxy that is moving away from each other at speed v are now D distance apart assuming the time when they where together is t=0 i.e. at the Big Bang the time since the Big Bang is given by $$T= \frac{D}{V}$$ $$V=\frac{D}{T}$$ Hubble's law is given by $$V=HD$$ therefore subbing the first expression into the latter gives $$\frac{1}{T}=H$$ and therefore $$T=\frac{1}{H}$$ The thing I do not understand is if we are assuming the rate of expansion is constant (as is required for this) why does that mean we can use $$t=\frac{d}{v}$$ Because as the galaxies get further apart together the space between them gets more and more hence they will move away from each other faster the further the are apart. This equation needs v to be constant which is not the case. Please can someone explain?</p>
<p>In the linked qestion they use the formula t=d/v just saying it is a linear extrapolation. This does not help me with my qestion as i can still not understand why this can be used as it assumes v is constant (i think) which it would not be. I am looking for this to be explained in more detail then the linked question. </p> | g452 | [
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<p>I am interested in solutions of the Schroedinger equation. For simplicity I started my studies with the $n=1$ ground state of the hydrogen atom. I was particularly interested in the higher moments of the kinetic energy operator $\mathbf{T}$. Much to my surprise I encountered serious problems as soon as I worked on the second moment. It turns out that $(\mathbf{T}\psi)(\mathbf{T}\psi)$ is not the same as $\psi(\mathbf{T}\mathbf{T}\psi)$. In other words, the operator $\mathbf{T}$ is not self-adjoint when acting on $\mathbf{T}\psi$, where $\psi(r) = \exp(-r)$.</p>
<p>On this forum, and previously on another physics forum, I had lengthy discussions about this peculiar result. One can talk about the operator $\mathbf{T}$ (for which stronger versions than the usual one can be constructed), about the domain of the operator, about boundary terms at $r=0$ that appear when performing partial integration, or about the fact that the Coulomb potential arises from a point charge and that therefore the wave function $\psi(r) = exp(-r)$ has a cusp at $r=0$.</p>
<p>It occurred to me, that the last comment was perhaps the most useful; well, I mean for me as a QM layman to use as starting point. It does not require specialistic mathematical skill to go from a point charge model for the Hydrogen atom to a model with a broader charge distribution. The idea is to soften the $1/r$ singularity in the potential $V(r)$ and hence make the wave function more analytic. In turn, this might solve the above mentioned problem with the kinetic energy operator. Or at least highlight the origin of the problem.</p>
<p>The simplest modification seemed to me to model the Hydrogen nucleus as a small conducting sphere of radius $R$ and with charge $+e$. Outside of the sphere ($r > R$) the potential $V(r)$ is exactly the same as in the point charge model [this is a well-known fact from electrostatics]. So we can write down the lowest energy solution as: $\psi(r) = exp(-\frac{r}{r_0})$ for $r > R$. Here $r_0$ is the Bohr radius. Note: the energy spectrum is discrete, because:</p>
<ol>
<li>one must balance three terms in the wave function which is difficult to accomplish, and</li>
<li>the solution must be bounded at infinity.</li>
</ol>
<p>Inside the sphere ($r < R$) the potential $V(r)$ is constant [another well-known fact from electrostatics]. Hence, by continuity, its value must be equal to the potential on the surface of the sphere: $V(r) = V(R)$. Inside the sphere, the electron is "free". Its oscillatory solution is the same as for a particle in a spherical box. The solution is the zeroth order Bessel function $j_0(r)$. So we obtain: $\psi(r) = \frac{A\sin(kr)}{r}$. The wave factor $k$ is fully determined by the energy $E$, potential $V$ and some physical parameters (Planck's constant ans electron mass). </p>
<p>At this stage we have only one adjustable parameter in our model, the amplitude $A$. Its value is determined by demanding continuity of the wave function. This leads to the result $A = \frac{R\exp(-\frac{R}{r_0})}{\sin(kR)}$. </p>
<p>My problem is that there are no adjustable parameters left. Therefore one can not demand smoothness of the wave function (continuity of the first derivative). On the other hand, from the continuity of the potential at $r=R$ one would expect the first derivative of the wave function to be not only continuous and but also smooth at $r=R$ ! So I feel something is wrong. But I don't see what. Hence my question in a previous thread about the admissibility of certain diverging terms (which would give one an extra parameter). </p> | g14743 | [
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<p>An electric motor draws 20 Amps, when at maximum load of x.
Can that value of current be applied even if the load was ten times less than x from a certain power source? </p> | g14744 | [
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<p>If an orifice is placed inside a pipe with a smaller diameter than the rest of the pipe, fluid will follow a curved path in order to enter the orifice, and then expand. </p>
<p>I was wondering at what distance would the diameter of the flow reach its minimum (the vena contracta) and at what distance after that would the diameter of the flow once again reach the diameter of the pipe.</p> | g14745 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/9898/the-density-of-clouds">The Density of Clouds</a> </p>
</blockquote>
<p>according to definition of cloud :</p>
<p>A visible mass of condensed water vapor floating in the atmosphere, typically high above the ground</p>
<p>as there's an enormous amount of gravitational force on earth why can't the cloud particles cant get attracted towards earth ,</p>
<p>my general question is if we threw an object which weighs even 1milligram to ground it gets attracted and falls down on earth,</p>
<p>As per the gravity definition:</p>
<pre><code>an attractive force that affects and is produced by all mass and other forms of energy as well as pressure and stress
</code></pre>
<p>so why can't the cloud's particle can't get attracted by gravitational force as the cloud is an form when they have tons of water particles in them?</p> | g260 | [
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0.017738... |
<p>From what I gather, a <a href="http://www.scholarpedia.org/article/Boltzmann_machine" rel="nofollow">Boltzmann machine</a> can be identified with a <a href="http://en.wikipedia.org/wiki/Spin_glass" rel="nofollow">spin glass</a>. Though I don't know the details yet (and would welcome any references within the last 5 years--not, e.g. MacKay, etc.), I also gather that a <a href="http://www.scholarpedia.org/article/Boltzmann_machine#Restricted_Boltzmann_machines" rel="nofollow">Restricted Boltzmann Machine</a> (RBM) corresponds to a particular type of spin glass, and it is well known that spin glasses have multiple decoupled timescales associated with their dynamics. Now, it would be of great interest to me if the spin glass corresponding to an RBM turned out to have a single well-defined characteristic timescale associated to it that is independent (i.e., any other timescales exhibit the same scaling under time reparametrization). So: is this true? In other words:</p>
<blockquote>
<p>Does a restricted Boltzmann machine correspond to a spin glass that
has a single well-defined characteristic timescale?</p>
</blockquote>
<p>(I will wait a while before doing so, but suspect this may be better asked at the theoretical physics site.)</p> | g14746 | [
0.0038011970464140177,
0.036715615540742874,
0.007421601563692093,
0.0029694214463233948,
0.03653493896126747,
-0.0345410481095314,
0.03358709439635277,
-0.006534842774271965,
0.022414138540625572,
0.030283309519290924,
-0.003529328154399991,
0.05909448117017746,
-0.0022215498611330986,
0.... |
<p>Everybody knows that sound cant travel through space, but is really valid? Here is my scenerio:</p>
<p>Given the size of a football field's length cubed, there are two objects at two opposing sides. the walls of the vacuum are nonexistent, so the only matter that exists are the two objects. Now if the Object A were to create a noise that were to be loud enough to be vibrate Object B on Earth, would there still be an affect in this theoretical vacuum?</p>
<p>Given that sound energy moves from one molecule to another, would this same energy from Object A travel to Object B to some affect event though the distance between the two in a vacuum is much greater than the distance between to molecules? </p> | g14747 | [
0.05566423386335373,
0.050332289189100266,
0.014952481724321842,
0.011896583251655102,
0.0002819900691974908,
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0.01230703480541706,
-0.0... |
<p>In many books, for a linear dielectric medium in which we have Maxwell's equations and the relationships
$${\mathbf D}=\varepsilon({\mathbf x}){\mathbf E}$$
and
$${\mathbf B}=\mu({\mathbf x}){\mathbf H}$$
we find formulae for the electromagnetic energy as
$$U=\int d{\mathbf x}\frac{1}{2}({\mathbf E}\cdot{\mathbf D}+{\mathbf B}\cdot{\mathbf H})$$
in e.g. J.D. Jackson's book. </p>
<p>Suppose, instead, we have Maxwell's equations and the ${\it general}$ linear relationship
$${\mathbf D}=\varepsilon({\mathbf x}){\mathbf E}+{\mathbf P}$$
and
$${\mathbf B}=\mu({\mathbf x})({\mathbf H}+{\mathbf M}).$$
We are willing to suppose that we know what the energy for making the polarization $\mathbf P$ and magnetization $\mathbf M$ appear are - but want to know what the electromagnetic energy is. Think for example that we are only moving a bunch of permanent magnets around and want to know how the energy changes when we do. We don't care about the condensed matter cost of making the magnets and the medium has no hysteresis and is linear as above. What then is the formula for the electromagnetic energy? Do you have a reference for this (likely) more than century old result?</p> | g14748 | [
0.015271876007318497,
0.01997993513941765,
-0.03713670372962952,
-0.012234359979629517,
-0.03139641880989075,
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0.04779508709907532,
0.07108711451292038,
-0.0502423532307148,
-0.013780927285552025,
0.002173930173739791,
0.009774082340300083,
0.014149480499327183,
-0.05... |
<p>In the derivation of Rutherford's scattering formula, for example, this one <a href="http://tinyurl.com/qxc6m6k" rel="nofollow">here</a> or this one <a href="http://www.personal.soton.ac.uk/ab1u06/teaching/phys3002/course/02_rutherford.pdf" rel="nofollow">here</a>, we conclude that:
$$\frac{db}{d\theta} < 0,$$ i.e., as the collision parameter increases, the scattering angle decreases.</p>
<p>The thing that bothers me is that the minus sign is merely dropped in what follows. In the first derivation I linked, it says (page 4):</p>
<blockquote>
<p>We omit the minus sign in the following, because it has no physical
meaning.</p>
</blockquote>
<p>And in the second derivation, it says (page 5):</p>
<blockquote>
<p>The minus sign has been dropped as it merely indicates that as b
increases, the scattering angle decreases - N must be positive.</p>
</blockquote>
<p>I understand the reasons... but I just feel extremely uncomfortable dropping the minus sign there, why is it acceptable, why should the "mathematically correct" way give an incorrect result in this case?</p> | g14749 | [
0.03563383221626282,
0.0032835884485393763,
0.015880420804023743,
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0.08229365199804306,
0.053258903324604034,
0.043899402022361755,
0.030064279213547707,
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-0.030881788581609726,
0.026429308578372,
0.011687315069139004,
0.04735226929187775,
0.02147... |
<p>Is there any book that provides an overview of <a href="http://en.wikipedia.org/wiki/Condensed_matter_physics" rel="nofollow">Condensed Matter Physics</a>? I have had a course in QM and statistical physics and some. I dont know anything about this field, so is there a readable introduction to this large field? One that provides an overview, instead of too much detail? </p>
<p>Edit: I am looking for something of a lower level than <a href="http://en.wikipedia.org/wiki/Condensed_matter_physics" rel="nofollow">this</a> Phys.SE question. Can we reopen?</p> | g453 | [
0.029304780066013336,
0.043220534920692444,
0.00108038738835603,
-0.03835282847285271,
0.004981688689440489,
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0.022970417514443398,
0.006115339696407318,
-0.008502627722918987,
0.008173118345439434,
0.036310795694589615,
0.033694781363010406,
0.05062151700258255,
-0.04... |
<p>Does the concept of strong coupling mean anything in a classical setting? If strong coupling means just an inability to apply perturbative methods to the Hamiltonian, then obviously yes, we can provide examples of "classical" systems that cannot be handled perturbatively, such as granular materials, dusty plasmas, etc.</p>
<p>I have only rudimentary QFT knowledge (and strong coupling is originally a QFT concept), but my intuition from my background in spectroscopy tells me that there is more to the term strong coupling than just the need for nonperturbative methods. The example I am most deeply familiar with is Forster energy transfer or FRET in biophysics. You're in weak coupling if the non-radiative rate is small compared to the radiative rate. But you're in strong coupling if the non-radiative rate is so large that you can get energy migration, where multiple energy transfer processes occur in series. In that case, the excitation is delocalized and you have to treat the network of interacting atoms as a single entity. I was under the understanding that delocalization was an essential feature of the term "strong coupling".</p>
<p>Now, back to the original question, to what degree is it appropriate to use the term strong-coupling in many-body classical systems, such as granular materials, dusty plasmas, and dense colloidal glasses? These systems are classical in the sense that there is complete decoherence, and hard sphere potentials are the rule. In one sense, I want to say yes, the kinetic energy terms carry little information and most of the energy is stored in potential energy terms, but I am still hung up on the issue of delocalization. Can anyone help set me straight?</p> | g14750 | [
0.04956454038619995,
0.038875482976436615,
0.009633996523916721,
0.001616465742699802,
0.00006414076779037714,
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0.008820360526442528,
0.05943167209625244,
-0.010098961181938648,
0.026367170736193657,
0.009324715472757816,
-0.017490040510892868,
... |
<p>In the book Quantum Gravity in 2+1 dimension by S. Carlip, in the second chapter (section 2.1), he comments that a compact 3-manifold with a flat time orientable Lorentzian metric and a purely spacelike boundary, necessarily has the topology $[0,1]\times \Sigma$, where $\Sigma$ is a closed surface that is homeomorphic to one of the boundary components. </p>
<p>Does this mean that all spacetime manifolds (flat) that we could allow in 2+1 dimension are necessarily of this topology (it seems to be a big restriction)?</p>
<p>Also, is it necessary for the boundary of a spacetime (for those that would have one) to be spacelike ? I have a rough argument (which I am not sure about) for this, that if we had a timelike boundary, in some coordinate system, we would have the boundary at some given value for the space co-ordinates which seems weird to me. </p> | g14751 | [
-0.008676797151565552,
0.04522634670138359,
0.00009136558946920559,
0.02551773376762867,
-0.015940183773636818,
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0.04296986758708954,
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-0.01542674284428358,
0.08260682970285416,
-0.0018615401349961758,
0.06817087531089783,
0.... |
<p>The principle conservation of energy is often taken as an obvious fact, or law of nature. But it seems to me the definition of energy is far from obvious, or natural: <a href="http://en.wikipedia.org/wiki/Energy" rel="nofollow">http://en.wikipedia.org/wiki/Energy</a> lists lots of different types of energy. </p>
<p>So if I want to apply this principle in some concrete experiment, I have to go through all the forms of energy and consider whether this form of energy is applicable to each particular entity in my experiment. This seems like a rather cookbook-oriented approach (and the wiki list doesn't even claim to be complete!).</p>
<p>Now I wonder:
---> to what extent can these different energies be derived from some single simpler definition?</p>
<p>For example, if my model is that everything is made up of atoms (I don't want to consider anything at a smaller scale, I fear that would muddle the discussion and miss the main point. Also, I'm considering only classical mechanics.) which are determined by their position, momentum, charge and mass (?), is there a clear and exhaustive definition of the energy of a such a system?</p>
<p>EDIT: In light of comments and answers, I think I need to clarify my question a bit.</p>
<ul>
<li><p>Is it true that the electric potential and gravitation potential (for atoms, say) will explain all instances of conservation of 'energy' occurring in classical mechanics?</p></li>
<li><p>If no, is there some modification of "electric potential and gravitation potential" above which will yield yes?</p></li>
<li><p>My question is not really about mathematics - Noether's theorem for example is a purely mathematical statement about mathematical objects. Of course mathematics and my question are related since they both involve similar kinds of reasoning, but I'm ultimately after a physical or intuitive explanation (which is <em>not possible</em> using only mathematics since this involves choice of a model, which needs to be explained intuitively) or assertion that all these energies (chemical, elastic, magenetic et.c. (possibly not including nuclear energy - let's assume we're in the times when we did not know about the inner workings of atoms)) come from some simple energy defined for atoms (for example).</p></li>
</ul> | g14752 | [
0.060745902359485626,
0.02827848680317402,
0.0038116825744509697,
-0.03607245534658432,
0.03449363261461258,
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0.04967371001839638,
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0.011122907511889935,
0.010368438437581062,
-0.06955070048570633,
-0.013020440936088562,
0.... |
<p>In Coulomb's law if the relation was as if electric field intensity was to vary inversely $1/r$ with distance rather than the inverse $1/r^2$ of square of distance, would the Gauss's law still be valid? This was asked in our university tests and I'm clueless about it.</p> | g14753 | [
0.005612410604953766,
-0.027762521058321,
0.014584282413125038,
0.0045065139420330524,
0.01683608815073967,
0.06457681953907013,
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0.037360742688179016,
0.015553264878690243,
0.024111580103635788,
-0.012602346017956734,
0.023596350103616714,
-0.02580917254090309,
-0.065... |
<p>On the one hand, classical electromagnetism tells us that light is a propagating wave in the electromagnetic field, caused by accelerating charges. Then comes quantum mechanics and says that light consists of particles of quantized energy, $hf$. Also, now these particles are modeled as probability waves obeying Shrodinger's equation, which gives the probability of observing a photon particle at some point in space at any given time.</p>
<p>My question is - how does that change our model of the classical electromagnetic field? Do we now view it as some sort of average, or expectation value, of a huge number of individual photons emitted from a source? If so, how are the actual $\vec{E}$ and $\vec{B}$ values at a point $(\vec r,t)$ calculated : how are they related-to/arise-from the probability amplitudes of observing individual photons at that point? Or put another way - how do the probability amplitude wavefunctions of the photons give rise to the electromagnetic vector field values we observe?</p>
<p>[In classical EM, if I oscillate a charge at frequency $f$, I create outwardly propagating light of that frequency. I'm trying to picture what the QM description of this situation would be - is my oscillation creating a large number of photons (how many?), with the $f$ somehow encoded in their wavefunctions?]</p>
<p>(Also, what was the answer to these questions before quantum field theory was developed?)</p> | g14754 | [
-0.006351956166327,
0.006876560393720865,
-0.03140488266944885,
0.0148181626573205,
0.07241048663854599,
0.030343355610966682,
0.09287051111459732,
0.04725252836942673,
-0.025062618777155876,
-0.01913689449429512,
0.003367523429915309,
0.001343588693998754,
0.07848837226629257,
0.028601346... |
<p>I have hit a roadblock in my simulation, where there are 2 authors with contradicting equations on the model.</p>
<p>So I have simulated both, and drew it out for a few diameters. My dish size is 40m.</p>
<p>I am unsure which model to use for laser transmission over 40,000km from space to Earth. The more intuitive/logical model is the 2nd author's.</p>
<p>But is the first one correct? I know Heisenberg's Uncertainty Principle is at play in causing the divergence on the non-parallel line photon paths from electron source emissions. But does light really take on this inverse pattern?</p>
<p>To me it also seems similar to the double slit experiment in QM, whereby decreasing the slit diameter decreases the diameter of the interference pattern, but it eventually reaches a point where the diameter of the interference pattern suddenly increases, and this is a phenomena to this date, from my knowledge. Could something similar be the case here? And any recommendations on which equation to use?</p>
<p><a href="http://i.stack.imgur.com/P39MM.jpg" rel="nofollow"><img src="http://i.stack.imgur.com/P39MM.jpg" alt=""></a></p>
<p>Where <code>d_t</code> = diameter of transmitter dish, and <code>d_r</code> = diameter of receiver dish</p>
<p>Edit: to make the question clear, "Does light emission truly behave like case 1, whereby the angle inverses proportionally at a certain point relative to increasing dish diameter, the same as the double slit experiment phenomena? Apparently yes, it does."</p> | g14755 | [
0.015814341604709625,
0.041195496916770935,
-0.01788722351193428,
-0.0323062539100647,
-0.04237611964344978,
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0.02342444285750389,
0.003856371622532606,
0.008660443127155304,
0.004383607767522335,
0.019467942416667938,
0.07664205133914948,
0.03467239439487457,
-0.0126667... |
<p>Just what the title states.</p>
<p>Assuming identical conditions, excellent visibility -
If a 1W monochromatic light source, and a 1W non-monochromatic light source were viewed at a location in deep space, which of the two would be visible from a greater distance? </p> | g14756 | [
0.030077466741204262,
0.023009290918707848,
-0.0006294839549809694,
-0.013325177133083344,
-0.04086235538125038,
0.006907739210873842,
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0.001414504018612206,
0.01987416483461857,
0.0001635320804780349,
0.04178936034440994,
0.08188601583242416,
0.019061779603362083,
0... |
<p>My possibly mistaken understanding is that <a href="http://en.wikipedia.org/wiki/Dark_energy" rel="nofollow">dark energy</a> changes with time, whereas a <a href="http://en.wikipedia.org/wiki/Cosmological_constant" rel="nofollow">cosmological constant</a> is, well, constant. What about gravitational clumping? Detecting relative motion?</p> | g14757 | [
0.042621295899152756,
0.013945057988166809,
-0.009935549460351467,
-0.05163156986236572,
0.023965321481227875,
0.013586671091616154,
0.025806963443756104,
0.03305300325155258,
-0.06903355568647385,
-0.010288049466907978,
0.036782603710889816,
0.02190212346613407,
0.05484588071703911,
0.015... |
<blockquote>
<p>A balloon with volume 2800 m³ is heated up to 60 °C.
If the outer temperature is 12 °C and the air has a pressure of 960 hPa, what is
the density of the air inside the balloon and on the outside?</p>
</blockquote>
<p>In the solutions they used the following formula: $ \rho_1 = \rho_0 \cdot \frac{P_1}{P_0} \cdot \frac{T_0}{T_1} $</p>
<p>However, I have no clue on how to get to this fomula. It is neither in my fomulary nor was I able to derive it from another formula.</p>
<p>My approach was to calculate the molar mass of the air which is $28.96 \frac{g}{mol}$ and then use it in this formula (which I derived from the $p\cdot V = n \cdot R \cdot T $):
$$ \rho = \frac{p\cdot M}{R\cdot T} $$
But that doesn't seem to be correct, since I get extremly high numbers and the correct value should be $1.17 \frac{kg}{m^3}$. Also, this approach only works for the outer density - I do not have the pressure inside the baloon.</p> | g14758 | [
0.017489252611994743,
0.01057218573987484,
0.01541856024414301,
0.008047773502767086,
-0.010149745270609856,
0.014114748686552048,
-0.03323585167527199,
0.00841886829584837,
-0.05945936590433121,
-0.03421342000365257,
-0.0590280219912529,
0.04808860644698143,
0.018712526187300682,
-0.01987... |
<p><a href="http://en.wikipedia.org/wiki/Ocean_thermal_energy_conversion" rel="nofollow">OTEC</a> (Ocean Thermal Energy Conversion) utilizes the temperature gradient between cold deep ocean water, and warmer water to do work. I understand the pressure in the depths may be as high as a couple of orders greater than surface atmospheric pressure. </p>
<p>I also remember, vaguely, that a fluid moves from an area of high pressure to low pressure; wouldn't a sealed pipe merely need valves at the top to control the flow? Does water need to be pumped up out of the deeps?</p> | g14759 | [
-0.0063906386494636536,
0.016666406765580177,
-0.030695175752043724,
-0.055059801787137985,
0.0031046990770846605,
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0.021642642095685005,
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-0.020029664039611816,
-0.02854812517762184,
0.051310375332832336,
0.05599720776081085,
... |
<p>The work function of any metal is no doubt constant for it is related to electromagnetic attraction between electrons and protons. However on increasing the intensity of any light source the kinetic energy of the emitting electrons must increase, mustn't it? Let us assume there is only 1 electron in a metal surface. Let hf be the energy required to expel it out with a velocity 'v'. Again let us increase the intensity of the source keeping frequency constant. Now ' hf ' will change to 'nhf' where n = no. of photons striking on electron at a same time. Since work function is constant the only variable must be 'v' letting it increase its K.E. This clearly shows Kinetic energy of emitting electrons is directly proportional to the intensity of light source. If kinetic energy depends upon the intensity, stopping potential for a particular frequency of light for a particular metal is a variable quantity. It is true that on increasing the intensity the no.of photo electrons will increase. But what if the no.of electrons in a metallic plate is constant. Suppose I have only two electrons in a metal, on increasing intensity i.e on increasing the no.of photons , the no.of photons colliding from different sides simultaneously may increase . So, K.E of emitted electron must increase on increasing intensity, mustn't it? But experimental data doesn't show this. What is wrong? Help me out</p> | g14760 | [
0.04458320885896683,
0.05178863927721977,
-0.010053093545138836,
0.01035956759005785,
0.02287798747420311,
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0.016950007528066635,
0.03537672385573387,
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0.016946295276284218,
0.00749619398266077,
0.07204432785511017,
0.003496310207992792,
-0.0185414... |
<p>I've always pictured EM radiation as a wave, in common drawings of radiation you would see it as a wave beam and that had clouded my understanding recently.</p>
<p>Illustration on the simplest level:</p>
<p><img src="http://i.stack.imgur.com/UEs0c.jpg" alt="EM wave from sun"></p>
<p>Which obviously would not make sense (to me), as electrons would collide more likely moving as such.</p>
<p>For example, in a 10 meter (kHz) radio wavelength, do <strike>particles</strike> electrons move forward and back ten meters? If so, in which direction, and if in one why not any others?</p>
<p>What does wavelength actually have to do with its movement? Does it change the polarity, make it go in reverse or does it continue the same as others, higher frequency just means "more energy"?</p> | g14761 | [
0.0035332657862454653,
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0.04560895264148712,
0.041300490498542786,
-0.0... |
<p>Hamilton's principle states that a dynamic system always follows a path such that its action integral is stationary (that is, maximum or minimum).</p>
<p>Why should the action integral be stationary? On what basis did Hamilton state this principle?</p> | g617 | [
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0.0011819996871054173,
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-0.07630988955497742,
0.... |
<p>I understand that an accurate determination of the bounds of the "habitable zone" for a given stellar system depends on a large number of factors, including many beyond characteristics of the parent star, such as details of planetary atmosphere and residual heat of formation, system age and dynamics, etc.; but is there a simple first approximation formula that is generally used?</p>
<p>Is there a simple formula for approximating the semimajor axis bounds of "habitable zone" using only the luminosity of the parent star? What is the next factor (metallicity, age?) that would come into play in calculating the habitable zone with the next level of accuracy?</p> | g14762 | [
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0.0... |
<p>It has always bugged me that tables for water (and other) properties have the capability to look up internal energy as a function of <em>both</em> temperature and pressure. If we limit the discussion to liquid below the saturation temperature, then what is the qualitative argument to say that $u(T)$ is inaccurate and that the multivariate function $u(P,T)$ is needed?</p>
<p>From Wikipedia Internal Energy:</p>
<blockquote>
<p>In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields.</p>
</blockquote>
<p>I understand that internal energy is not fully a proxy for temperature, so what thermodynamic property could we define (in $J/kg$) that <em>would</em> be a fully 1-to-1 relationship with temperature with <em>no</em> influence from pressure? If a liquid was fully incompressible would internal energy then not be a function of pressure?</p>
<p>If my physics understanding is correct, temperature has a definition that stems from the concept of thermal equilibrium. Quantitatively, I thought that temperature was proportional to the average kinetic energy the molecules, but I doubt that as well (in fact, I think this is wrong). The zeroth law of thermodynamics is necessary for formally defining temperature but it, alone, is not sufficient to define temperature. My own definitions for temperature and internal energy do not have the rigor to stand up to scrutiny. What qualitative arguments can fix this?</p>
<hr>
<p>Symbols</p>
<ul>
<li>$u$ - internal energy</li>
<li>$P$ - pressure</li>
<li>$T$ - temperature</li>
</ul> | g14763 | [
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0.04782350733876228,
0.03771372139453888,
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-0.01337310392409563,
-0.044... |
<p>Has Bose-Einstein theory been considered for dark matter?</p>
<p>The theory would explain why no measurable radiation is emitted due to zero temperature--its lack of interaction with other matter and its gravitational lensing. Yet I haven't seen it considered. Am I missing something or have I totally misunderstood dark matter and/or Bose-Einstein theory? </p> | g14764 | [
0.021884365007281303,
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0.05383394658565521,
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0.03795313835144043,
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0.06355206668376923,
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-0.06804034113883972,
0.07679077982902527,
0.00669340044260025,
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<p>In graphene, free electrons can have the following wavefunctions (there are other options, with minus signs in various places, but this will serve as an example): </p>
<p>$\psi(\vec{p})=A\left[\begin{array}&e^{-i\phi/2}\\e^{i\phi/2}\end{array}\right]$ </p>
<p>where $\phi=\tan(p_y/p_x)$ is the polar angle in momentum space and A is the normalization constant. Clearly $\phi^\dagger(\vec{p})\phi(\vec{p})=|\phi(\vec{p})|^2=2|A|^2$. </p>
<p>To normalize (ie find $A$) we would usually perform the integration over all of momentum space and set to unity:<br>
$\int|\phi(\vec{p})|^2d\vec{p}=2|A|^2\int d\vec{p}=1$<br>
however the integral will obviously blow up. </p>
<p>In similar situations within the position space picture, we would usually limit the 'size' of space, so that we integrate over some volume (that is $-\frac{L}{2}<x<\frac{L}{2}$ and similarly for $y$ and $z$). If we do the same here (where $V$ is the volume of momentum space) we obtain $A=\frac{1}{\sqrt{2V}}$. The usual practice is to then set $V=1$.</p>
<p>Question: The procedure for limiting the size of space from infinity to $V$ makes sense in the position space picture, but what is the justification in momentum space? It boils down to the assumption that there is some maximum momentum, and we only have to integrate up to that value, but what justification is there for assuming that this is true? Also, what is the justification for setting $V=1$? This is more of a recap: if I remember my undergraduate lectures correctly it is because the volumes will always cancel each other later.</p> | g14765 | [
0.06090621277689934,
0.03346296399831772,
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0.035571373999118805,
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0.016502665355801582,
0.026433955878019333,
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-0.003... |
<p>In all the houses of two levels where I have been, why I hear the sound from downstairs clearer when I am at the second level, than I hear sound from upstairs when I am at the first level?</p>
<p>Does sound travel upward more easily than downward?</p>
<p>Do the architectures of houses matter much?</p> | g14766 | [
0.001262389007024467,
0.027094237506389618,
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0.010913792066276073,
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0.093... |
<p>From my experiments with measuring how fast a coin falls, I have consistently measured a faster falling rate for a coin that flips as it falls.</p>
<p>As an example, a coin dropping on its edge from height of $45 \:\rm{cm}$ hits the ground $20 \:\rm{ms}$ later than a flipping coin falling from the same height.</p>
<p>Now here's the catch: I use a microphone to mark the events. I drop the coin off the edge of a table letting it slightly brush off it. The bang noise of this event combined with the noise the coin makes as it hits the hard ground let's me measure the fall duration accurately (I hope). I also take into account the time it takes the sound of coin hitting the ground to come back up to the mic.</p>
<p>Using $\approx340\:\rm{m/s}$ for speed of sound and $9.806\:\rm{m/s^2}$ for acceleration due to gravity, my measurement of height is dead accurate, BUT only for a coin dropped on its edge. A flipping coin constantly gives me a measurement less than correct value.</p>
<p>First I suspected the air resistance, but if that was the case, shouldn't the coin falling on its edge fall quicker?</p>
<p>Any ideas?</p> | g14767 | [
0.08056546747684479,
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0.006... |
<p>From my point of view, it seems that a soldier armed with a <strong>full metal plate armor</strong> was almost invulnerable at the time their opponents yielded swords, spears or bows. I understand that it couldn't be the case, but I'm not sure about the physics behind it.</p>
<p>More specifically:</p>
<ol>
<li><p>How could an archer beat this soldier? Would it matter whether the archer aimed at more vulnerable spots at the soldier, or any arrow shooted with full power would do?</p></li>
<li><p>How could a swordsman or a spearman beat this soldier? Would the impact of these weapons suffice?</p></li>
<li><p>Just out of curiosity, a modern gun would penetrate into the plates that easily? One headshot would do?</p></li>
</ol>
<p>I'm thinking on a soldier wearing an armor like this one below, or even more bulkier.</p>
<p><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/34/Italian_-_Sallet_-_Walters_51580.jpg/378px-Italian_-_Sallet_-_Walters_51580.jpg" alt="Italian suit of Armor, c.1450">[1]</p>
<p>[1] Courtesy of Wikipedia</p> | g14768 | [
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0.019535088911652565,
0.004451673943549395,
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<p>How can I prove that in the static spacetime, the extrinsic curvature of hypersurface $t=constant$ is zero? My efforts all are failed. Any hint would be greatly appreciated.</p> | g14769 | [
0.0588730052113533,
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0.0... |
<p>I have a problem regarding computation of spin connection in the case where One or more dimension is compactified. For example if we take a $D+1$ dimensional bosonic string action and write the $D+1$ dimensional metric in terms of $D$ dimensional fields,and we want to compute the spin connection then how to exactly do it.</p>
<p>I am mainly referring to calculation of 1.10 in the following <a href="http://people.physics.tamu.edu/pope/ihplec.pdf" rel="nofollow">paper about Kaluza-Klein Theory</a> by C. Pope.</p>
<p>Edit-I actually used Cartan's first structure equation with zero torsion to get something useful but it did not work. Like for $$\hat{\omega}^{ab}$$,I used
$$d\hat{e^a} + \hat{\omega}^a_b \hat{e}^b = 0$$ and then,
$$d\hat{e^a} = d(e^{\alpha \phi} e^a) = e^{\alpha \phi} d(e^a) + d(e^{\alpha \phi}) e^a \\ \ \ \ \ \ = e^{\alpha \phi} d(e^a) + \alpha e^{\alpha \phi} \partial_b \phi dx^b \wedge e^a \\
\ \ \ \ \ = - e^{\alpha \phi}\omega^a_b \wedge e^b + \alpha e^{\alpha \phi} \partial_b \phi dx^b \wedge e^a \\
\ \ \ \ \ = - \omega^a_b \wedge \hat{e}^b + \alpha \partial_b \phi dx^b \wedge \hat{e}^a \\
\ \ \ \ \ = -\hat{\omega}^a_b \hat{e}^b$$
But this is no good, not even slight nearer, After all the formula written in the answer below can be obtained from Cartan's structure equation.I have no idea how to get $$F^{ab}e^{\beta - 2 \alpha} \hat{e}^z$$ type term.I had actually calculated some spin connections before but there I always used there component form. </p> | g14770 | [
0.022320454940199852,
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<p>When a ball moves to the right, friction acts to oppose the motion, in other words, to the left. However, when a car travels around a bend, the friction acts in the perpendicular direction to the car's velocity and provides the centripetal force. I just cannot understand why friction would act in that direction.</p>
<p><img src="http://i.stack.imgur.com/yLgrh.gif" alt="enter image description here"></p> | g950 | [
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<p>I would like to know why scientists try to use deuterium and tritium for <a href="http://en.wikipedia.org/wiki/Fusion_power" rel="nofollow">fusion</a> and not just the ordinary <a href="http://en.wikipedia.org/wiki/Isotopes_of_hydrogen" rel="nofollow">isotope of Hydrogen</a> ${}^1H$? </p> | g14771 | [
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... |
<p>According to this calculator <a href="http://www.abecedarical.com/javascript/script_collision1d.html" rel="nofollow">http://www.abecedarical.com/javascript/script_collision1d.html</a> when low mass object hits high mass object it is reflected gaining opposite velocity almost the same as initial velocity. </p>
<p>If I jump onto the wall why my body is not reflected? I know that collision is not fully elastic but it should be at least similar.</p> | g14772 | [
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0.03433848172426224,
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0.06582089513540268,
0.0026037... |
<p>My question is the following: if we had the trajectory of a particle eventually reaching a point of a rotation axis $ \vec{u} $ (take that as being the z-axis for convenience) by an angle $ s $, would Noethers Theorem still give a conserved quantity?</p>
<p>More specifically (let me go through the calculations and details first)</p>
<ol>
<li>Statement of Noether's Theorem</li>
</ol>
<p>If a Lagrangian $ \mathcal{L}(\vec{q_i}, \dot{\vec{q_i}}, t) $ admits a one-parameter group of diffeomorphisms $ h^s : \mathcal{M} \rightarrow \mathcal{M} $ such that $ h^{(s=0)} (\vec{q_i})= \vec{q_i} $, then there is a conserved quantity locally given by $$I = \sum_{i} \frac{\partial \mathcal{L}}{\partial \dot{q_i}} \left.\frac{d}{ds}(h^s(q_i))\right\vert_{s=0}$$</p>
<ol>
<li>Applying to Simple Lagrangian</li>
</ol>
<p>Assume a potential-free Lagrangian $ \mathcal{L} = \frac{m}{2}( \dot{x}^2 + \dot{y}^2 + \dot{z}^2 ) $.
A suitable transformation can be given by $$ h^s (x,y,z)= \begin{pmatrix}
\cos(s) & -\sin(s) & 0 \\
\sin(s) & \cos(s) & 0 \\
0 & 0 & 1
\end{pmatrix} $$</p>
<p>Working out the conserved quantity, we get that the z-component of angular momentum $ L_z = m \dot{y}(t) x(t) - m \dot{x}(t) y(t) $ is conserved for any path $ (x(t),y(t),z(t)) $.</p>
<ol>
<li>The problem:
If this trajectory would include any point on the rotation axis z, $ h^s(q_i) $ would be 0 there and so by conservation, valued 0 all along the path.
However, we know that angular momentum is conserved.
So, in all rigor - is this inconsistency amendable or a sign of some bigger problem?</li>
</ol> | g14773 | [
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... |
<p>Suppose the linear size of everything is doubled overnight. Can you test the statement by measuring sizes by a meter stick? Can you test it by using the fact that the speed of light is a universal constant and has not changed? What will happen if all the clocks in the universe start running at half speed?</p> | g454 | [
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0... |
<p>I am studying magnetism and I am curious as to what happens in a transformer that has its secondary output wires connected through a circuit versus one that doesn't.</p>
<p>My main questions (in the case of the unconnected secondary) are:</p>
<p>Is there more or less resistance on the primary?</p>
<p>Are there equations that describe the heat losses (of the primary and secondary) in this scenario?</p> | g14774 | [
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0.... |
<p>Question #1: Why does speed have nothing to do with inertia?</p>
<p>Question #2: If a car hits a steel wall and stops, where did the momentum go?</p> | g14775 | [
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0.022... |
<p>I'm curious to know this. Neglect air friction and imagine a bullet that were shot normal to the Earth's surface, from the Equator. I will have to consider the Coriolis effect and so I expect the path of the bullet will follow a spiral rather that a straight line (relative to Earth's centre). The gravity will reduce with altitude as well and so it would be difficult to apply basic laws of motion, but I really need to know how this would look like and how long it will take for the bullet to reach around 36000 km above the Earth's surface. Will it come back, stay in that orbit, or escape (assuming that normal velocity reached 0 @ that orbit)? I expect if it comes back, then it will follow a similar path it traveled along during the shot. This is just a curiosity and thanks for help in advance.</p> | g14776 | [
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<p>If you have an electron moving in empty space, it will be represented by a wave packet. But packets can spread over time, that is, their width increases, with it's uncertainty in position increasing. Now, if I throw a basketball, why doesn't the basketball's packet spread as well? Wouldn't that cause its uncertainty in position to increase so much to the point it disappears?</p>
<p>EDIT: I realize I wasn't clear what I meant by disappear. Basically, suppose the wave packet is spread over the entire Solar System. Your field of vision covers only an extremely tiny part of the Solar System. Therefore, the probability that you will find the basketball that you threw in your field of vision is very small.</p> | g14777 | [
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-0.00358... |
<p>While a treatment of electron spin can be found in any introductory textbook, I've noticed that the electron's magnetic field seems to be treated classically. Presumably this is because a quantum treatment of the electromagnetic field would venture into the much more difficult topic of quantum electrodynamics. However, treating the magnetic field classically also seems to create conceptual difficulties. How can we write something like</p>
<p>$$\mathbf{\mu} = \frac{g_e \mu_b}{\hbar} \mathbf{S}$$</p>
<p>and treat the left-hand side as a vector, while treating the right-hand side as a vector-valued operator?</p>
<p>So... what really happens when we measure the magnetic field around an electron? For simplicity imagine that the electron is in the ground state of the hydrogen atom, where it has zero orbital angular momentum. It seems to me that we can't observe what looks like a classical dipole field, because such a field would have a definite direction for the electron's magnetic moment, which would appear to contradict the quantum-mechanical properties of spin.</p>
<p>My guess is that measuring any one component of the magnetic field at a point near an electron would collapse the spin part of the electron wave function, and in general the three components of the magnetic field will fail to commute so we cannot indeed obtain a definite direction for the electron magnetic dipole moment. However, I'm not even sure how to begin approaching this problem in a rigorous fashion without breaking out the full machinery of QED. For an electron <em>in</em> a magnetic field we have the Dirac equation. For the magnetic field <em>of</em> the electron I wasn't able to find an answer online or in the textbooks I have at hand.</p> | g14778 | [
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<p>I am trying to get a better understanding of the definition of temperature at the subatomic level. I have a background in molecular biology with some college physics, but no deep quantum mechanics background.</p>
<p>Everything I've found on the web (Wikipedia, Google Scholar) seems to use 'temperature' very loosely as just "<em>agitation of particles</em>": more movement/agitation of particles equals higher temperature. But what exactly does this mean?</p>
<p>The reason I'm asking is because the use of "particles" in relation to temperature seems to just mean <strong>atoms</strong>. The increase in agitation of <em>atoms</em> is equal to an increase in temperature. But I am asking because I don't know if this is true.</p>
<p>So atoms are made out of protons/neutrons/electrons. Protons and neutrons are <em>composite particles</em>, each made up of 3 <em>elementary particles</em>: quarks. Also, each of these examples I've mentioned are <em>matter</em> particles, but other particles like photons are massless. So how do they fit into temperature?</p>
<p>Basically, how do the different subatomic particles (both composite and elementary) relate to temperature?</p> | g14779 | [
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... |
<p>Could someone please explain this equation $$M\bf {\ddot{r}}=-\nabla \phi$$
Where $\bf r$ is a position vector and $\phi$ is the potential function.
Could someone brief explain the potential function and tell me why we've got <strong>minus sign</strong> before the nabla operator?</p> | g14780 | [
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<p>Wikipedia says yes but on Newtonian arguments. From general relativistic point of view Moon is not rotating but moving along geodesic trajectory. And like parallel transport of a vector (pointing to the direction of motion) on a surface of a sphere along equator, from outside it seems like rotation. So, would Moon still be rotating if we remove the Earth? Would Foucault pendulum on Moon detect its rotation?</p> | g14781 | [
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-0.021580321714282036,
-0.... |
<p>We have two identical massive metal spheres at the same temperature at rest in free space. Both have an identical charge and the Coulomb force [plus the black-body radiation pressure if the temperature is non-zero] exactly counteracts the gravitational force between them, resulting in no net forces on either object. They are electrostatically levitating at rest in space. It is my understanding that the charge distribution in each sphere exists only at the surface, and should be concentrated on the side facing away from the other sphere.</p>
<p>Now heat one of the spheres uniformly with an external energy source. What happens in the instant following?</p>
<p>Could it be: The increased mass-energy of the hot sphere increases the gravitational force, and the cold sphere starts to fall inward.</p>
<p>Or else: The increased temperature modifies the charge distribution on the hot sphere by giving it more variance and bringing it closer on average to the cold sphere, increasing the Coulomb force. The cold sphere starts to fall away. [Carl's answer says there is no effect on the charge distribution like I describe, but DarrenW points out that there will be an increased black-body radiation pressure between the spheres, similarly causing an outward force.]</p>
<p>Which direction is correct, and what is the best explanation? Does it depend on the amount
of temperature change or the initial conditions?</p> | g14782 | [
0.108212910592556,
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0.001865892787463963,
0.08507926017045975,
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0.0337553508579731,
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-0.004318818915635347,
-0.005639965180307627,
0.048508014529943466,
0.021655280143022537,
0.0163329... |
<p>This concerns the famous two-slit experiment. Electrons or photons or your favorite particle, doesn't matter. As we all know, the attempt to detect which slit the quanta pass through leads to loss of the diffraction pattern. </p>
<p>The interesting part of the experiment is describing what happens when neither slit has a particle detector. It is commonly said that each particle goes through both slits at the same time. At the popular level this makes QM seem weird and mystical, and at the professional level we might cite the Copenhagen Interpretation which boils down to: Don't ask questions about things you can't observe, and so we don't speak of such things, just do the math.</p>
<p>How sound this reasoning is at a fundamental level? Can we really conclude each quantum goes through both slits yet as a whole entity? Can we define a "it went through both slits" observable? Is there a proper Hermitian operator with (I suppose) eigenvalues 0 and 1, that can distinguish a quantum going through both slits vs. only one slit but without saying which one?</p>
<p>Perhaps it would make more sense to think about an N-slit experiment, and ask about a Hermitian operator that can report n, the number of slits a quantum takes?</p>
<p>I suspect I'm not asking this question quite right, but have an intuition there's something yet to be dug up from this age old gedankenexperiment. </p> | g14783 | [
0.01619420014321804,
0.006793534848839045,
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0.05194762349128723,
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0.025345608592033386,
0.05423779413104057,
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-0.007457703817635775,
0.03070239908993244,
0.030912160873413086,
0.03227629140019417,
0.038476... |
<p>Can someone please explain to me what <a href="http://www.google.com/search?as_q=&as_epq=euler+density" rel="nofollow">Euler Density</a> is? I have encountered it in <a href="http://en.wikipedia.org/wiki/Conformal_anomaly" rel="nofollow">Weyl anomaly</a> related issues in various articles. Most of them assumes that its familiar, but I couldn't find any accessible paper or a book discussing that. So, it would be nice if I can understand what it is physically and mathematically and also find a reference where I can look it up.</p>
<p>Also related to that it would be nice to find a reference where people have derived $\langle T_i^i\rangle$ in curved background which involves Euler Density, $W^i$ etc.</p> | g14784 | [
0.07902786135673523,
0.022902101278305054,
0.008279336616396904,
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0.03945977985858917,
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0.05127737298607826,
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0.027977073565125465,
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0.003243220504373312,
0.09721733629703522,
0.03... |
<p>After watching this video:</p>
<p><a href="http://www.youtube.com/watch?v=j1jIjx0XF_U" rel="nofollow">http://www.youtube.com/watch?v=j1jIjx0XF_U</a></p>
<p>The experience is made with a speaker that generates a sound wave or mechanic wave. Can you use this to establish a link to <a href="http://en.wikipedia.org/wiki/High_Frequency_Active_Auroral_Research_Program" rel="nofollow">HAARP</a> which I believe uses ELF EM radiation?</p>
<p>Thanks</p> | g414 | [
-0.022809816524386406,
0.07075755298137665,
-0.00436673266813159,
-0.06291648745536804,
0.06723334640264511,
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0.01300137396901846,
0.023180531337857246,
0.031316209584474564,
-0.04683585837483406,
0.03827640786767006,
0.03403495252132416,
0.03038978949189186,
0.0364099... |
<p>In various articles (I am here talking about specially the ones related to string theory etc.) I have seen the discussion on density and distribution of eigenvalues. I want to know why do we use them (why are they important to consider in some calculation, how to construct them), if there's any physical significances behind them etc. And anything else that you might want to mention. And again a reference could be useful.
Thanks!</p> | g14785 | [
0.017527109012007713,
0.04906388372182846,
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0.04316294193267822,
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0.008807351812720299,
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0.0890713557600975,
0.061... |
<p>Is it possible to find the true anomaly of an object in a Kepler orbit given the orbital period of the object, the orbital eccentricity and the time? Assuming a two body system and the mass of the orbiting body is negligible.</p>
<p>I'm doing this computationally so I'd like to be able to place an object on an orbital ellipse with as few evaluations as possible. I ask about these orbital elements specifically because at the time in the program that I need to calculate the true anomaly, I have these values on hand already.</p>
<h2>Edit</h2>
<p>I've been searching extensively for an answer to this, and found <a href="http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Position_as_a_function_of_time" rel="nofollow">these four steps</a> to solving position as a function of time. The thing I'm having most trouble with is solving Kepler's equation -- it seems like there should be a simpler way to do this -- I can find the velocity at each apsis, and the orbital period relatively easily. As the eccentricity approaches 1 the orbiting object would spend more time near apoapsis and less time near periapsis -- but I can't seem to put that into numbers. </p> | g14786 | [
0.021960550919175148,
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<p>I read in a book that at low temperature the hydrophobic effect (for example) is entropic but at high temperatures it is enthalpic. I thought that entropy should decrease at very low temperatures. Hypothetically, can you even have entropic effects at absolute zero?</p> | g14787 | [
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<p>I apologize if electro-optic material is not the correct word.</p>
<p>As I understand it, when an electric field is applied to an electro-optic material, the index of refraction changes in proportion to the applied field.</p>
<p>What is happening to the structure of the material for this to occur?</p> | g14788 | [
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<p>Recently I'm studying PSG and I felt very puzzled about two statements appeared in Wen's <a href="http://prb.aps.org/abstract/PRB/v65/i16/e165113" rel="nofollow">paper</a>. To present the questions clearly, imagine that we use the Shwinger-fermion $\mathbf{S}_i=\frac{1}{2}f_i^\dagger\mathbf{\sigma}f_i$ mean-field method to study the 2D spin-1/2 system, and get a mean-field Hamiltonian $H(\psi_i)=\sum_{ij}(\psi_i^\dagger u_{ij}\psi_j+\psi_i^T \eta_{ij}\psi_j+H.c.)+\sum_i\psi_i^\dagger h_i\psi_i$, where $\psi_i=(f_{i\uparrow},f_{i\downarrow}^\dagger)^T$, $u_{ij}$ and $\eta_{ij}$ are $2\times2$ complex matrices, and $h_i$ are $2\times2$ Hermitian matrices. And the projection to the spin subspace is implemented by projective operator $P=\prod _i(2\hat{n}_i-\hat{n}_i^2)$(Note here $P\neq \prod _i(1-\hat{n}_{i\uparrow}\hat{n}_{i\downarrow})$). My questions are:</p>
<p>(1)How to arrive at Eq.(15) ? Eq.(15) means that, if $\Psi$ and $\widetilde{\Psi}$ are the mean-field ground states of $H(\psi_i)$ and $H(\widetilde{\psi_i})$, respectively, then $P\widetilde{\Psi}\propto P\Psi$, where $\widetilde{\psi_i}=G_i\psi_i,G_i\in SU(2)$. How to prove this statement?</p>
<p>(2)The statement of translation symmetry above Eq.(16), which can be formulated as follows: Let $D:\psi_i\rightarrow \psi_{i+a}$ be the unitary translation operator($a$ is the lattice vector). If there exists a $SU(2)$ transformation $\psi_i\rightarrow\widetilde{\psi_i}=G_i\psi_i,G_i\in SU(2)$ <strong>such that</strong> $DH(\psi_i)D^{-1}=H(\widetilde{\psi_i})$, then the projected spin state $P\Psi$ has translation symmetry $D(P\Psi)\propto P\Psi $, where $\Psi$ is the mean-field ground state of $H(\psi_i)$. How to prove this statement?</p>
<p>I have been struggling with the above two puzzles for several days and still can't understand them. I will be very appreciated for your answer, thank you very much.</p> | g14789 | [
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<p>I barely know anything about optics, so I could use some help about how to go about solving this problem. </p>
<p>If I have a ray of light at a certain height from the optical axis, propagating at an angle, and the distance it travels before it comes in comes in contact with a mirror, can I find the angle and height of the ray after it reflects? </p>
<p>I know the mirror is concave and the radius of curvature, and I know the parameters listed above, but how should I write an equation to find the height and angle of a reflected ray?</p>
<p>EDIT: For example, I have a ray 5mm from the optical axis, and it propagates at 0.3 mrad to that axis. The ray travels a distance of 2cm and comes in contact with a concave mirror of R = 1. How can I find the height and angle of the ray 1m away from the point reflected? I've looked at three optics books, and I still can't find an easy explanation for calculating this.</p>
<p>I tried to use the matrix method to solve this problem, but I don't even know if this would work or not. Below is what I referred to. Can anyone tell me if this would work for my problem?</p>
<p><img src="http://i.stack.imgur.com/KTE7D.png" alt="Concave reflection"></p> | g14790 | [
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0.0036601321771740913,
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0.08810220658779144,
0.07301593571901321,
-... |
<p>I was trying to understand how paper batteries work and came across some explanations saying that the paper battery can also behave like a supercapacitor on account of its ability to discharge and to produce bursts of peak energy.</p>
<p>Why is a normal battery unable to do the same thing?</p> | g14791 | [
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0.04764058440923691,
0.003... |
<p>I have a 1D gas made of $N$ particles placed in a harmonic potential well, so the Hamiltonian is:</p>
<p>$$ \mathcal H = \sum_{j=1}^N \left ( \frac{p_j^2}{2m} + \frac{1}{2}m\omega^2 x_j^2 \right )$$</p>
<p>The first part of the exercise asked me to find the canonical partition at temperature $T$ if the particles are distinguishable, then to find the partition if the particles are indistinguishable, but the Maxwell-Boltzmann approximation applies. In both cases this was easy. But now the exercise asks me to find the partition if the particles are identical bosons, and then to show that this is equal to the Maxwell-Boltzmann approximation for large temperatures.</p>
<p>I don't know exactly how to set up the summation to count the states properly when you treat them as bosons. I know we have the states $\epsilon_j = \hbar \omega (j+\tfrac{1}{2})$ and that each of those states will be occupied by $n_j$ bosons and since it's 1D I don't have to worry about degeneracy...but I'm unsure how to continue.</p>
<p>From what I understand, it's nicer to work with fermions and boson in the grand canonical ensemble, but we haven't seen this in class yet.</p>
<p>Thanks!</p> | g14792 | [
0.012172588147222996,
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0.03061145916581154,
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0.0545303076505661,
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0.... |
<p><a href="http://www.physics4all.com/schrodingers-cat-sort-of-explained-by-perimeter-institute-physicists/" rel="nofollow">Erwin Schrödinger’s famous thought experiment's video</a> presented by Perimeter Institute for Theoretical Physics. From this video can we conclude that , in a macroscopic label we can not have a superposition. If we could have then, isn't it hard to comprehend that the cat is in both states and its a contradiction to our daily life? </p> | g14793 | [
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0.0442... |
<p>I have a question regarding the well known fact that General Relativity is not a conformal invariant theory or to put it in other words about the fact that it is conformal variant:</p>
<p>What are the physical assumptions in General Relativity about the gravitation that make the resulting formulation of gravity to be conformal variant?</p>
<p>I am not asking about a mathematical reasoning because that is obvious:</p>
<p>One performs a conformal transformation and he can check that the action and field equations are not invariant under this transformation. This mathematical part is obvious for me. </p>
<p>I am asking what is the physical assumption that make this happen? What physical property of gravity (which is absent in Electromagnetic interaction) makes it conformal variant (at least in GR)? is it weak equivalence principle? is it the requirement of the Corresponding principle? or what? there should be some physics behind this, it can't be a mere mathematical coincidence ...</p> | g14794 | [
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<p>According to <a href="http://en.wikipedia.org/wiki/List_of_particles" rel="nofollow">http://en.wikipedia.org/wiki/List_of_particles</a>, the list of elemetary particles includes more than 30 particles (bottom of the page). Does the Standard Model explain (if yes, then how) how many of elementary particles we should expect?</p> | g14795 | [
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<p>Suppose we have
$$\rho=p_1\rho_1+p_2\rho_2$$
Where $\rho_1$ and $\rho_2$ are density matrices with $p_1+p_2=1$</p>
<p>I'm trying to show this is also a <a href="http://en.wikipedia.org/wiki/Density_matrix" rel="nofollow">density matrix</a> </p>
<p>If we let
$$\rho_1=\sum_i^n p_{\psi_i} |\psi_i \rangle \langle\psi_i|$$
and
$$\rho_2=\sum_i^n p_{\phi_i} |\phi_i \rangle \langle\phi_i|$$
I'm assumsing these two denstiy matrices are of size $n$, otherwise adding them wouldn't make any sense. I'm having trouble seeing how this produces a density matrix, if it were too then it would want to be describing the probabilities of the combinations of combined quantum states, which would be a $n^2\times n^2$ matrix? That's all I can see as being an physical interpretation of this as.</p>
<p>Approaching it more mathematically, each $n\times n$ matrix in the sum over both $p_1\rho_1$ and $p_2\rho_2$ has a factor of $p_1p_{\psi_i}+p_2p_{\phi_i}$ and </p>
<p>$$\sum_i^n p_1p_{\psi_i}+p_2p_{\phi_i}=\sum_i^n p_1(p_{\psi_i}-p_{\phi_i})+p_{\phi_i}=1$$</p>
<p>Which is promising (and the only way i've found so far to use the condition on $p_1,p_2$), but as far as I can see this factor doesn't really mean anything. Any help would be greatly appreciated, I'm a little lost!</p> | g14796 | [
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0.043215394020080566... |
<p>So I was sitting and looked at a street lamp outside my house.</p>
<p>It is an ordinary lamp that looks something like that: <img src="http://i.stack.imgur.com/0KVsN.png" alt="enter image description here"></p>
<p>This lamp emits white light and it is about 20 meters from my house. It was very dark outside and the only light that was out there emerged from this lamp. </p>
<p>When I slightly closed my eyes, and made them look something like that : (not my eyes :) <img src="http://i.stack.imgur.com/XdqM8.png" alt="enter image description here"></p>
<p>I noticed something very peculiar - I saw two beams of light coming out from the main light source directed up and down, but what realy astonished me was that I was able to see the colors of the rainbow splitting from those beams.</p>
<ul>
<li>What is going on? </li>
<li>How the status of my eyes changes the look of the light emergin from the lamp?</li>
<li>Why almost closing my eyes creates two "beams" of lights from the lamp?</li>
<li>Why I can see the <strong>colors of the rainbow</strong> splitting out from those beams?</li>
</ul> | g14797 | [
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-0.014573689550161362,
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0.026026492938399315,
0... |
<p>Is the time of the collapse of the wave function empirical?</p>
<p>Suppose there is a very long von Neumann chain of observations of a quantum system. Suppose also practically irreversible decoherence happens very early along the chain. We can have an entire class of models parameterized by the point along the chain past the point of irreversible decoherence where the wave function "actually" collapses. Can we distinguish between these models empirically?</p>
<p>Is it even possible to push this point to the future of Jan 2013 so that as of Jan 2013, we are still in an uncollapsed superposition?</p> | g14798 | [
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0.034685976803302765,
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0.009... |
<p>In the paper <a href="http://arxiv.org/abs/1004.5489" rel="nofollow">arXiv:1004.5489</a> The origin of the hidden supersymmetry, the author use {Qa,Qa}={Qb,Qb}=2H, {Qa,Qb}=0 for N=2 hidden SUSY, which is different from what I was taught: {Qa,Qa}={Qb,Qb}=0, {Qa,Qb}=2H. I think they are controversially different. Is any of them wrong? If not, could anyone help by explaining some more?</p> | g14799 | [
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<p>I'm asking in terms of physics. Can powerful magnetic induction rearrange spins of my body in such way I will die? How? </p>
<p>Or maybe it can rip all iron from me, which would make my blood cells useless? How many teslas should such magnet have? Are there other ways to kill people with magnetic induction only? </p> | g14800 | [
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-0.0497... |
<p>I'm interested in how the <a href="http://en.wikipedia.org/wiki/Skin_effect" rel="nofollow">Skin Effect</a> and the <a href="http://en.wikipedia.org/wiki/Proximity_effect_(electromagnetism)" rel="nofollow">Proximity Effect</a> interact with each other. </p>
<p>From what I can understand:</p>
<ul>
<li>The Skin Effect is when AC current 'collects' on the skin of
conductors due to the counter-emf from its magnetic field. </li>
<li>The Proximity Effect is when the magnetic field of a wire induces eddy currents in adjacent wires, which 'push' the current away from conductors carrying current in the same direction.</li>
</ul>
<p>Now in the case of a transformer, the wires are close enough for the Proximity Effect to occur, so could the two effects average each other out (to create a uniform/close-to-uniform current density)?</p>
<p>Thanks in advance.</p> | g14801 | [
0.03397316485643387,
-0.010634655132889748,
-0.006805723998695612,
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0.005866887979209423,
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0.0436641089618206,
0.02567240037024021,
0.0177... |
<p>Recently-ish, I stumbled across <a href="http://www.archive.org/stream/Galaxy_Magazine_Volume_16_Number_5_/IA_Galaxy_Magazine_Volume_16_Number_5_#page/n71/mode/2up">an interesting short story</a> (by way of <a href="http://scifi.stackexchange.com/q/59555">Science Fiction & Fantasy Stack Exchange</a>) where a soccer referee is apparently incinerated by concentrated sunlight.</p>
<blockquote>
<p>Where the referee had been standing, there was a small, smoldering heap, from which a thin column of smoke curled up into the still air.</p>
</blockquote>
<p>This is accomplished in-story by some 50 000 reflective tinfoil program covers, each about the size of a tabloid sheet.</p>
<p>What got me interested (physics is one of my peripheral interests) is the feasibility of this method in the real world. <a href="https://en.wikipedia.org/wiki/Tabloid_%28paper_size%29#Loose_sizes">Wikipedia says</a> a tabloid sheet is $279\;\mathrm{mm} \cdot 432\;\mathrm{mm} = 120528\;\mathrm{mm}^2 \approx 0.121\;\mathrm{m}^2$, giving fifty thousand people with a program each a total of $6026.4\;\mathrm{m}^2$ to work with. (Adjusting for less-than-perfect aim, I'd say closer to about $5000\;\mathrm{m}^2$.) If you could redirect that much sunlight at about a person's surface area, how much power would that be? What damage could you cause?</p>
<blockquote>
<p>He couldn't have felt much; it was as if he had been dropped into a blast furnace...</p>
</blockquote>
<p>Could that amount of power actually incinerate someone?</p>
<hr>
<p>It occurs to me that the Wikipedia summary of the story (quoted on SciFi.SE) states only that the referee "collapsed and died". If incineration isn't possible, could the energy involved still be lethal by other means?</p> | g14802 | [
0.009330208413302898,
0.01975773088634014,
-0.0018896902911365032,
-0.0076002152636647224,
-0.008469310589134693,
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0.014981500804424286,
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-0.010790593922138214,
0.023909546434879303,
-0.002042859559878707,
0.05424471199512482,
... |
<p>Massive heat wave here and I don't have an air conditioner. I was investigating how commercial air conditioners work and to my surprise found that they use merely evaporation rather than a compressor/radiator cycle like fridges.</p>
<p>I have this fan on my desk so I did a quick test by putting a plastic shroud around it and funneling the air through a little damp sponge. To my surprise the effect was much better than expected, the air flow was rather low but the air that did come through was quite chilly!</p>
<p>Now I'm planning to make a bigger version. I got this 500w bigass fan that I'm going to leave outside, shroud it and run the air through a few layers of ~0.5m by 0.5m thin cotton, dapened(hopefully) by capillary action from a vat below. Do you think that will give any kind of tangible effect for cooling a single 5m by 5m room?</p>
<p>EDIT: Wait a minute, I had another thought. I checked the energy figures for air and water and came up with this: If I have a closed system with 1kg of dry air and 100g of water at 20C and sea level pressure and then if the water should spontaneously evaporate consuming 226000j of energy and expanding the volume by 0.18m3, it should suck that energy out of the air and give a mixture of</p>
<ol>
<li>0.18m3 of 100C water vapor</li>
<li>0.19m3 of -206C air</li>
</ol>
<p>for the temperature average by volume of -57C so the concept should still work or..? Obviously not all of the water will spontaneously evaporate but every bit that does should cool the overall system no?</p> | g14803 | [
0.006514828652143478,
0.04106675833463669,
-0.0023489517625421286,
0.05805845931172371,
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0.04493753984570503,
0.05414948612451553,
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0.037094149738550186,
0.04064803197979927,
0.0019862777553498745,
0.... |
<p>In lieu of recent research showing the possibility of obtaining the Bose-Einstein condensate Nq, in certain polymers is there any statistical mechanical way of figuring out the frequency with which the condensate would happen at random in say certain small regions of space with high gravitational fields ie stars, black holes? Can MKT/2pih^2 be represented using statistical mechanics by simply isolating Boltzman's constant under a set of restraints? Trying to find a way to approach this problem mathematically with a background in only physical chemistry is challenging. Thanks. J. Gray</p> | g14804 | [
-0.01708778366446495,
0.0294012613594532,
0.007107177283614874,
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0.04475327953696251,
0.0005690681864507496,
0.055803243070840836,
-0... |
<p>In an organic semiconductor, what is the average distance travelled by an exciton up to recombination? How is this value related to the morfology / structure of the organic semiconductor?</p> | g14805 | [
-0.058324385434389114,
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0.05849029868841171,
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-0... |
<p>I went to school one day, so I thought I was able to get this simple one.. but it looks like I'm not anymore. :(</p>
<p>One lonely little spaceship is resting into space. It has a small fuel capacity that it suddently burns to run away and finally reaches a speed $v$. Its tank is now empty, its kinetic energy $E = \frac{m v^2}{2}$ is exactly what it had in reserve, and it is equal to the work performed by the constant force $F$ it has just applied to itself over the run distance $d$ with $W = Fd = E$..</p>
<p>Now, instead of being free, it is tied with a rope to a wall. It does try to run away, burns its fuel.. But there is nothing to do, the rope is too strong. And it ends up with an empty tank and a null speed, a null kinetic energy, and the work $F$ has performed has been null all the time, for the rope's $-F$ has prevented any acceleration..</p>
<p>Where is its energy gone? The entire universe had energy $E$ all the time, the spaceship had $E$ initially (chemical potential) now $0$.. what is the system that had energy $0$ initially and now $E$, and why? what happened?</p>
<p>If it is only friction and heat within the rope and the wall, does it mean there is no way modeling a "perfect rope" without assuming that some energy is lost?</p> | g14806 | [
0.056616853922605515,
-0.013093954883515835,
-0.027099119499325752,
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0.03904331475496292,
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0... |
<p>Permittivity is a function of frequency from an existing EM wave. But permittivity in some ways describes how a wavelength of light interacts with a metal. Certain wavelengths, sense different densities of electrons more than others. </p>
<ol>
<li><p>Can I modify the permittivity of a conductor, by applying a current? Considering the equation, $J=I/A=q\times n\times v$ and $J=\sigma\times E$, could I back solve for permittivity? </p></li>
<li><p>Can one EM wave at freq1 effect the permitivity of a conductor at freq2 (considering cases of a magnitude of 100 or greater)? My initial guess is no, because you would need some kind of nonlinear interaction, but my classical picture of electromagnetics has got me stumbling.</p></li>
</ol>
<p>A separate but related question...</p>
<p>A peer of mine once stated the permittivity of a conductor that has a current passing through it, can be modified by performing a reverse calculation, assuming that the number of electrons in the conductor was increased. This interpretation is right or wrong? </p>
<p>Do more electrons exist in a conductor with an applied field, or less? I suppose it might make some sense in a semiconductor, there have been some models that hint towards this...I'll see if I can find the documents.</p>
<p>I've read through some similar questions: "How does electricity propagate in a conductor?", etc, but non seem to be answering my question.</p> | g14807 | [
-0.045493368059396744,
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0.001196409692056477,
0.01013254839926958,
-0.014428799040615559,
0.03186231106519699,
0.035836827009916306,
... |
<p>In Griffiths <em>Introduction to electrodynamics</em> it is said that Newton's third law is not valid in electrodynamics, but, in the example given, the it does not consider the retarded values for the fields and looks at the contradiction only on the magnetic force.</p>
<p>Just putting the books example: Two positive charges are moving along axes x and y towards the origin. The electric forces satisfy Newtons 3rd law, but the magnetic don't. </p>
<p>Below an image with the original example and a 'diagram' showing where my doubt comes from:
<img src="http://s12.postimg.org/jimbjlx4d/g9174.png" alt="1"></p>
<p><strong>Question:</strong> Does Newton's third law hold for Lorenz force with appropriate retarded fields? </p> | g14808 | [
0.05367182195186615,
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0.08696357905864716,
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0.0008804104872979224,
-0.0012441315921023488,
0.019676711410284042,
-0.033065300434827805,
-0.05... |
<p>A question on <a href="http://biology.stackexchange.com/q/21076/6166">Biology SE</a> got me thinking, ignoring <a href="http://biology.stackexchange.com/a/21092/6166">weight naturally lost during the night</a>, <em>"Do we weigh less in the morning?"</em></p>
<p>During the night, the sun is above us, and the earth below us. Conversely, at night, both the earth and the sun are "below" us. Our mass obviously stays the same, but would there be a greater gravitational pull on us since the added gravity from both the earth and the sun on the other side are acting on us?</p>
<p>Or do we not notice the gravitational pull from the sun, for the same reason astronauts aboard the ISS don't notice the gravitational pull from the earth?</p> | g455 | [
0.02786673605442047,
0.01566385291516781,
0.008842457085847855,
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-0.0680282935500145,
0.06660403311252594,
-0.006447615101933479,
0.001956816529855132,
0.042... |
<p>So the universe is expanding, rather space is expanding. By expanding we mean space is coming into existence at all points. </p>
<p>Is that an equal rate of expansion everywhere?</p>
<p>Now the expansion does not over come the force holding matter together, planetary systems, galaxies even galactic clusters to some extent. Larger scales than that and things are moving apart.</p>
<p>Is it that space is not expanding within the smaller structures or is space expanding through these structures?</p> | g456 | [
0.04739595949649811,
0.05854831635951996,
0.02930799499154091,
0.01507467683404684,
-0.00026480547967366874,
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0.019885478541254997,
-0.09898842871189117,
0.0827782154083252,
-0.038735974580049515,
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0.00... |
<p>Lets say you have a cylinder of length L, radius R, and mass M. How fast will it accelerate a mass of mass M2 that is entering the "throat" of the cylinder, considering the effects of gravitoelectromagnetism?</p>
<p>By Gravitoelectromagnetism, I'm specifically talking about the effect where a spinning body will pull an object through the "throat" of its spin.</p>
<p>Also, I'm wondering what the practical limit of this is: considering the strongest known materials, how fast could a cylinder be spun?</p> | g457 | [
-0.0006669096765108407,
0.09579050540924072,
0.015113781206309795,
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0.039979130029678345,
0.01704358123242855,
0.06217290088534355,
0.037124212831258774,
-... |
<p>Can you have a resistance less than one? Is this allowed? I've only ever seen circuits with one ohm resistance at least.</p> | g14809 | [
0.008349010720849037,
0.037640199065208435,
0.010198944248259068,
-0.012171361595392227,
0.03648833557963371,
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0.03225686401128769,
0.029378555715084076,
-0.0016168069560080767,
-0.03374052047729492,
0.017796844244003296,
-0.10212714970111847,
0.0... |
<p>If $1 / H_0 $ is about 14 billion years, then what happened when the universe was half its current age?</p>
<p>Is the empirically determined $H_0$ supposed to have been twice its current value?</p>
<p>And when the universe is twice its current age is Hubble's parameter half its current value?</p>
<p>That would predict expansion is slowing. But expansion is actually speeding up. That implies that $ H_0 $ is getting larger, and because $1 / H_0 $ gets smaller in that case, the universe is growing younger.</p>
<p>I asked this question already <a href="http://physics.stackexchange.com/q/78558/2451">here</a>, but it was marked a duplicate. I know that Hubble's Parameter is not a constant. That doesn't actually clarify the answers to these questions.</p> | g452 | [
0.021409234032034874,
-0.00018865773745346814,
-0.002572581171989441,
-0.01624167338013649,
0.0040616742335259914,
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0.02973630651831627,
... |
<p>Thermodynamical definition of <a href="http://en.wikipedia.org/wiki/Entropy" rel="nofollow">entropy</a> $$S(p)=-\int p\ln p~dx$$ is defined only on equilibrium system. But why can't we use it for non-equilibrium system? Is there a well-accepted definition for it? </p> | g14810 | [
-0.02123166248202324,
0.07554023712873459,
-0.008969979360699654,
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0.006471395958214998... |
<p>Suppose you're analyzing some 3 dimensional object of any sort of shape, and this object explodes from some internal force (e.g, like a grenade). How would you go about determining the average number of fragments that the shape would be broken up into upon the explosion created by this internal force? </p> | g14811 | [
0.011828497983515263,
-0.006352193187922239,
0.01830434240400791,
-0.05619383230805397,
0.007495378144085407,
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0.03695530444383621,
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-0.02798008732497692,
-0.005868950858712196,
-0.030678626149892807,
0.055489279329776764,
-... |
<p>I was reading a bit of Landau and Lifshitz's Mechanics the other day and ran into the following part, where the authors are about to derive the kinetic energy of a free particle. They use the fact that the Lagrangian of this particle must be the same (or at most, differ by the total time derivative of a function of co-ordinates and time) in different inertial frames.</p>
<blockquote>
<p><em>We have $L'=L(v'^2)=L(v^2+2\mathbf{v}\cdot\boldsymbol{\epsilon}+\boldsymbol{\epsilon}^2)$. Expanding this expression in powers of $\boldsymbol{\epsilon}$ and neglecting terms above the first order, we obtain</em>
$$L(v'^2)=L(v^2)+\frac{\partial L(v^2)}{\partial (v^2)}2\mathbf{v}\cdot\boldsymbol{\epsilon}.$$</p>
</blockquote>
<p>I think I'm ok with all the physics in this section. What I don't get is just the part I quoted above (so maybe this post is better suited for the math site, but since this is book is so physics-y I thought I'd post it here). My math is pretty rusty, so I'm not really sure- how do the authors expand the function to arrive at the above expression? It reminds me a bit of a Taylor expansion, but not very much. What's the process used to arrive at it? </p> | g14812 | [
0.08550048619508743,
0.03460834175348282,
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0.04057527706027031,
0.06663966923952103,
0.00... |
<p>Newton's second law of motion states that $f = ma$. However, in this equation, theoretically there could be a value of $f$ and $m$ that results in an acceleration that is enough to push an object past the speed of light. In my case I have a value of newtons that is large enough (I think) to accelerate an object past the speed of light if $f=ma$ held. Is there any way, knowing that value of newtons, and the mass of the object it is acting on to find the acceleration in an Einsteinian universe?</p> | g14813 | [
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0.04582945629954338,
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0.01251948345452547,
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0.05892452597618103,
0.02... |
<p>I am still unclear what the hamilitonian of a quantized field is, but what I do know is the hamilitonian of the boson field is defined as
\begin{align}
H_{\text{boson}} &=& \frac{1}{2}\sum_{\mathbf{k},\mu=-1,1} \hbar \omega_{\mathbf{k},\mu}
\Big({a^\dagger}^{(\mu)}(\mathbf{k})\,a^{(\mu)}(\mathbf{k}) + a^{(\mu)}(\mathbf{k})\,{a^\dagger}^{(\mu)}(\mathbf{k})\Big) \\
&=& \sum_{\mathbf{k},\mu} \hbar \omega_{\mathbf{k},\mu} \Big({a^\dagger}^{(\mu)}(\mathbf{k})a^{(\mu)}(\mathbf{k}) + \frac{1}{2}\Big)
\\
&=& \sum_{\mathbf{k},\mu} \hbar \omega_{\mathbf{k},\mu} \Big( N_{\mathbf{k},\mu} + \frac{1}{2}\Big)
,
\end{align}
however something that appears scarcely mentioned in the literature is the Hamiltonian of the fermion field. Interpolating from the boson field Hamilton, my guess is the Hamiltonian of the fermion field would be
\begin{align}
H_{\text{fermion}} &=& \frac{1}{2}\sum_{\mathbf{k},\mu=-1,1} \hbar \omega_{\mathbf{k},\mu}
\Big({b^\dagger}^{(\mu)}(\mathbf{k})\,b^{(\mu)}(\mathbf{k}) + b^{(\mu)}(\mathbf{k})\,{b^\dagger}^{(\mu)}(\mathbf{k})\Big)
\\
&=& \frac{1}{2}\sum_{\mathbf{k},\mu=-1,1} \hbar \omega_{\mathbf{k},\mu}
\Big({b^\dagger}^{(\mu)}(\mathbf{k})\,b^{(\mu)}(\mathbf{k}) - {b^\dagger}^{(\mu)}(\mathbf{k})\,b^{(\mu)}(\mathbf{k})+1\Big)
\\
&=& \sum_{\mathbf{k},\mu} \hbar \omega_{\mathbf{k},\mu} \Big( 0_{\mathbf{k},\mu} + \frac{1}{2}\Big)
.
\end{align}</p>
<p>I found $H_{\text{fermion}}$ to be very different from $H_{\text{boson}}$, because $H_{\text{boson}}$ depends on the number of bosons $N_{\mu,\boldsymbol{k}}$, however $H_{\text{fermion}}$ is independent of the number of fermions in each of its states, but rather seams to equal the vacuum energy only. Is $H_{\text{fermion}}$ real and what is its physical interpretation?</p> | g14814 | [
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0.03491147607564926,
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0.042446643114089966,
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0.005528360605239868,
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0.02956574596464634,
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-0.00227... |
<p>The concept of orbital velocity tells us that there must be a minimum velocity for a satellite to revolve around earth and the velocity should be such that the gravitational force of earth provides centripetal acceleration to that velocity. So how is it that even a stationary body like an astronaut outside his spaceship revolves around the earth?? i mean shouldn't he get pulled into its surface? (the concept of escape velocity is quite different.....that makes a body escape the gravitational field of earth).</p> | g14815 | [
0.009386909194290638,
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0.0056... |
<p>My question is a follow-up to <a href="http://physics.stackexchange.com/questions/80773/the-example-of-relativity-of-simultaneity-given-by-einstein">this question about simultaneity</a>. I would have posted it as a comment to the replies for that question, but I wasn't allowed to.</p>
<p>When Resnick introduces relativity of simultaneity, he gives the following example (see figure): S & S' are two inertial frames with a relative velocity v, and each with its own synchronised clocks and meter sticks. Two events leave marks, at A & B in reference frame S and at A' & B' in reference frame S'. The observers in the two frames are located at O (equidistant from A,B) and O'(equidistant from A',B'), respectively. When the event happens at A, A' coincides with A, and when the event happens at B, B' coincides with B.</p>
<p><img src="http://i.stack.imgur.com/Cada3.png" alt="Resnick example"></p>
<p>Resnick goes on to show that the events can't be simultaneous for both observers because, if the events are simultaneous for O, then O' will see the light pulses at slightly different times (viewed from the S frame).</p>
<p>I'm missing something in this argument: What basic inconsistency will arise if the events were simultaneous in both the frames? What will happen if the clocks in S at A,B show the same time for the events, <em>and</em> the clocks in S' at A', B' show the same time for the events? </p>
<p>Also, a related question: Will the synchronised clocks of S' appear unsynchronised (to each other) to the observer in S? How will the observer in S check this?</p> | g14816 | [
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<p>I've noticed that we have so-called 'black' clothes everywhere, I haven't seen so far any piece of clothes that would be <strong>really</strong> black, it's always some kind of lighter black.</p>
<p>For instance, if you take a 'black' shirt then put some water on it, the stain will look even darker.</p>
<p>Why is it so hard to make (nearly) totally black clothes?</p> | g14817 | [
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<p>Can anyone recommend a good reference for classical electrodynamics that goes over <a href="http://en.wikipedia.org/wiki/Maxwell%27s_equations_in_curved_spacetime" rel="nofollow">electrodynamics in curved spacetime</a> that doesn't assume much knowledge of GR -- that is it builds up the tensor calculus and GR principles itself?</p> | g14818 | [
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