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<p>I need to solve this problem as part of my review in college physics. The task is to find the value of 5 branch currents using Kirchhoff's laws and elimination method (or maybe called elimination by substitution BUT not using any matrix method).</p>
<p>The circuit is:
<img src="http://i.stack.imgur.com/DNVkI.png" alt="enter image description here"></p>
<p>I got the KCL equations:</p>
<p>a: $I_1 - I_2 - I_3 = 0$</p>
<p>b: $I_3- I_4- I_5 = 0$</p>
<p>and the KVL equations:</p>
<p>$\text{Loop 1}: 15 - 4I_1 - 6I_2 = 0$</p>
<p>$\text{Loop 2}: 6I_2 - I_3- 3I_4 = 0$</p>
<p>$\text{Loop 3}: 3I_4 - 2I_5 - 10 =0$</p>
<p>My problem is I can't get the correct answer by elimination method. Please help me to provide the solution if the given answers are:</p>
<blockquote>
<p>$I_1 = 1.89$<br>
$I_2 = 1.24$<br>
$I_3 = 0.65$<br>
$I_4 = 2.26$<br>
$I_5 = -1.61$</p>
</blockquote>
<p>Please show the solution and give tips on how to solve this type of problems using elimination method so other students can benefit and learn here.</p> | 5,001 | [
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<p>I have come across a very new idea for me concerning nuclear weapons effects, check <a href="http://en.wikipedia.org/wiki/Talk%3aEffects_of_nuclear_explosions#Units_and_blast_absorption_due_to_destructive_work" rel="nofollow">this</a> please.</p>
<p>In brief, that person states that blast overpressure attenuates/decays by causing damage for each individual building it crosses in a radial line, which makes some sense. But, the numbers this guy gave were really shocking, for example, he stated (calculated from data given by W.Penney) that 1% of the blast energy is lost for each wood-frame house the blast crosses, and about 5% for each concrete or brick building. If that is true, then by correcting the blast overpressure rings driven from the usual scaling laws we find that for example : for a 1 MT, the ideal 20 psi ground range is about 2.6 km, then by applying the decay/attenuation rate over say 50 concrete buildings in a modern city (just a rough estimate for buildings in 2.6 km radial line), we get 0.95^50 = 7.5% of the value of the overpressure expected for an ideal surface at 2.6 km, which is about 1.5 psi, so that makes nuclear weapons much much weaker than we ever imagined.</p>
<p>So now my back to my question. Is there a way to calculate how the buildings will affect the attenuation of the blast wave in a common urban area ?</p>
<p>Also, do the numbers of 1% and 5% makes sense for you ?</p>
<p>I am sorry if I can't express what I want in a better way, English is not my first language so I did my best and I hope that was enough to explain what I want to know. </p> | 5,002 | [
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<p>I tried deriving the expression for chemical potential of a Relativistic Fermi Gas using asymptotic expansion (for large z) in :</p>
<p>$$ N = \frac{V}{h^3}4\pi (KT)^3g_s \int \frac{p^2 dp}{e^{p-\nu}+1} $$
where $ z = e^\nu $ and $ \nu =\frac{\mu}{KT} $</p>
<p>After evaluating the integral by asymptotic expansion, I obtained the value (upto first order in T) :
$$ \mu(T) = \mu(0)\bigg[1-\frac{2\pi^2}{3} \frac{KT}{\mu} \bigg] $$</p>
<p>I am also able to obtain the energy for the system using this and expression for energy to be :</p>
<p>$$ E(T) = \frac{3}{4}N\mu(0)\bigg[1-\bigg(1-\frac{2\pi^2}{3}\bigg) \frac{4KT}{\mu} \bigg]$$</p>
<p>I am unable to check the correctness of these expressions. Although energy gives the right answer for the one at T=0K</p> | 5,003 | [
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<p>This is a quite specific question continuing the problems I have with computing the expectation value of intersecting Wilson loops I laid out <a href="https://physics.stackexchange.com/questions/119529/intersecting-wilson-loops-in-2d-yang-mills">here</a>. Using the tools from the answer there, I quite quickly arrive at the following expression for the local factor associated to a vertex, where two Wilson loops with reps $\alpha_1$ and $\alpha_2$ meet, and where the four surrounding regions have reps $\beta_1$ to $\beta_4$:</p>
<p>$$ G(\alpha_1,\alpha_2,\beta_{1,2,3,4})_{\mu\nu}^{\sigma\rho} := \epsilon_\mu^{ijk}(\alpha_1,\beta_1,\beta_4)\epsilon_\nu^{lmn}(\alpha_2,\beta_1,\beta_2){\epsilon^*}^\sigma_{ijk}(\alpha_1,\beta_2,\beta_3){\epsilon^*}^\rho_{lmn}(\alpha_2,\beta_3,\beta_4)$$</p>
<p>The Greek indices are the indices incurred from decomposing tensor products as $a^i \otimes b^j \otimes b^k = \epsilon_\mu^{ijk}e^\mu$, leading to integral results like </p>
<p>$$\int \alpha_i(V_b)^i_{i'} \beta_c(V_b)^j_{j'} \beta_{c'}(V_b)^k_{k'} \mathrm{d} V_b = {\epsilon^*}^\mu_{i'j'k'}\epsilon^{ijk}_\mu$$
(see <a href="http://physics.stackexchange.com/a/119657/50583">previous answer</a>). Since the $\epsilon^*$ that has the $\mu$ this is summed with lives on the opposite end of the (part of) the Wilson line, the Greek indices must necessarily remain open at the vertices. I am totally fine with this being the result of the computation, but I am still puzzled why the relation to the 6j symbol is so casually tossed about. </p>
<p>Let me first remark that the above equation is already suspiciously similar to the very first equation in the definition of <a href="https://en.wikipedia.org/wiki/6j_symbol" rel="nofollow">$6j$ symbols</a>, but the free indices are irritating me. If $\epsilon_\mu^{ijk}(\alpha_l,\beta_m,\beta_n)$ is the $3jm$ symbol (with $i,j,k$ playing the role of the $m$ and the reps corresponding to the $j$), what is the additional index $\mu$ doing here? If it is not the $3jm$ symbol (which I am currently thinking), then why would the $G$ defined above be the $6j$ symbol (and why has it free indices)? (If these are neither $3jm$ nor $6j$ symbols, then why do Witten, Ramgoolam, Moore, etc. insist they are?)</p>
<p>Note that the $6j$ symbol cannot arise after summing the Greek indices, since the $G$s the second index belongs to are, in general, at other vertices, and so have not exactly the same 6 reps as arguments.</p>
<p>Furthermore, the $3jm$ symbols are, if I understand them correctly, essentially the Clebsch-Gordan coefficients for expanding a tensor product of <em>two</em> irreducible reps in a third, and the $\epsilon$ above expand the tensor product of <em>three</em> irreducible reps in all possible fourths (which are then summed over in form of the Greek indices).</p>
<p>Something does not add up here, and I heavily suspect it is only in my understanding of the symbols, so I would really appreciate someone clearing up my confusion.</p>
<p><strong>EDIT</strong>:</p>
<p>Ok, I think I have found something, but I am still a far shot from solving this riddle, and it requires to think more carefully about the coefficients $\epsilon^{ijk}_\mu$:</p>
<p>Let $\alpha,\beta,\gamma$ be reps with basis elements $a^i,b^j,c^k$as before. Then, we can decompose the tensor product stepwise instead of at once as:</p>
<p>$$ a^i \otimes b^j \otimes c^k = \sum_{\rho \subset \alpha \otimes \beta} C(\alpha,\beta,\rho)^{ij}_\zeta e(\rho)^\zeta \otimes c^k = \sum_{\rho \subset \alpha \otimes \beta} \sum_{\sigma \subset \rho \otimes \gamma} C(\alpha,\beta,\rho)^{ij}_\zeta C(\rho,\gamma,\sigma)^{\zeta k}_\mu e(\sigma)^\mu$$</p>
<p>(I apologize for the abundance of symbols, but it really becomes clearer what's happening that way.)</p>
<p>Here, the $C(j_1,j_2,j_3)$ are now manifestly Clebsch-Gordan coefficients for $j_1,j_2$ in $j_3$, and thus essentially $3jm$ symbols, and the notation $\rho \subset \alpha \otimes \beta$ means that the irreducible rep $\rho$ occurs as a subrep in $\alpha \otimes \beta$. Since Clebsch-Gordan coefficients for reps not appearing in a given tensor product are zero, we can drop the constraint on the sums and sum over all irreducible reps. Thus, $\epsilon^{ijk}_\mu = \sum_\rho C(\alpha,\beta,\rho)^{ij}_\zeta C(\rho,\gamma,\sigma)^{\zeta k}_\mu$.</p>
<p>Now, in the integral result above, by the Peter-Weyl theorem (see also previous answer), the $\epsilon$ are only summed over the $\mu$ belonging to trivial subreps of $\alpha \otimes \beta \otimes \gamma$, i.e $\sigma = 0$, if we denote the trivial rep by $0$ in analogy to $j = 0$ in the spin case. Therefore, we have that the result of the integral is</p>
<p>$$I := \int \alpha(g)^i_{i'}\beta(g)^j_{j'}\gamma(g)^k_{k'} = \left(\sum_\rho C(\alpha,\beta,\rho)^{ij}_\zeta C(\rho,\gamma,0)^{\zeta k}_\mu C^*(\alpha,\beta,\rho)_{i'j'}^\eta C^*(\rho,\gamma,0)_{\eta k'}^\mu\right) $$</p>
<p>But the trivial irreducible rep has only one dimension, so the sum over the $\mu$ is just the multiplicity $n(\rho,\gamma,0)$ of $0$ in $\rho \otimes \gamma = \bigoplus_\sigma n(\rho,\gamma,\sigma)\sigma$, i.e.</p>
<p>$$ I = \sum_\rho n(\rho,\gamma,0)C(\alpha,\beta,\rho)^{ij}_\zeta C(\rho,\gamma,0)^{\zeta k} C^*(\alpha,\beta,\rho)_{i'j'}^\eta C^*(\rho,\gamma,0)_{\eta k'}$$</p>
<p>This gets rid of the annoying $\mu$, would lead to the $G$ from the beginning of the question to be comprised of the sum over a product of 8 $3jm$ symbols (the $C(\alpha,\beta,\gamma)$), of which 4 each are summed over their $m$ indices, yielding the product of two $6j$ symbols summed over one of their $j$s (the $\rho$). Also, the index structure in $e^{ijk}e^*_{ijk}$ in $G$ would translate to an index structure of the $C$ exactly matching that of the $3jm$ in a $6j$ symbol.</p>
<p>But before I work that out, can anybody tell me if this is the right track or if I butchered something along the way (I am not comfortable enough with my skills yet to fully trust my reasoning when it leads me to an answer whose shape I already know)? Or should I perhaps take this to the mathematicians, since the answer seems to be purely group theoretic so far?</p> | 5,004 | [
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<p>It is well known that in Schwarzschild space-time, a torque-free gyroscope in circular orbit at <em>any</em> permissible angular velocity at the photon radius will, if initially tangent to the circle, remain tangent to the circle everywhere along its world-line. This is usually explained as follows. Say I'm described by an arbitrary worldline in an arbitrary space-time and I orient a gyroscope and a photon gun along some direction at an initial event; there is a swarm of mirrors surrounding me in my infinitesimal neighborhood and at each instant of my proper time, I shoot out a photon in the direction of the gyroscope axis at that instant and reorient the gyroscope axis in the direction of the reflected photon when it arrives back to me, with the direction being relative to my worldline of course. In doing this, the gyroscope axis gets Fermi-Walker transported along my worldline; see section 2 of <a href="https://www.zarm.uni-bremen.de/uploads/tx_sibibtex/2001LaemmerzahlNeugebauer.pdf" rel="nofollow">https://www.zarm.uni-bremen.de/uploads/tx_sibibtex/2001LaemmerzahlNeugebauer.pdf</a> and problem 5 on p.161 of Geroch's general relativity notes <a href="http://home.uchicago.edu/~geroch/Links_to_Notes.html" rel="nofollow">http://home.uchicago.edu/~geroch/Links_to_Notes.html</a> and p.164 of said notes for the solution. </p>
<p>Coming back to the photon radius in Schwarzschild space-time, it is clear from the above prescription that Fermi-transport of the gyroscope implies the gyroscope always points tangent to the circle because a photon emitted from my photon gun will travel along this circle, and so will the reflected photon, irrespective of my angular velocity. I have two questions with regards to the above:</p>
<p>(1) I don't quite understand what constraints there are on the worldline of the mirror in the above operational procedure, which is basically Pirani's "bouncing photon" method. Certainly it cannot follow an arbitrary worldline in my infinitesimal neighborhood, so what kind of restrictions are there on said mirror's worldline? Consider for example an observer and a mirror at rest on a rigidly rotating disk in flat space-time that are separated by an infinitesimal radial amount. Then there exist both future and past directed radial null geodesics given by $\frac{dr}{dt} = \pm (1 - \omega^2 r^2)^{1/2}$ from my worldline to that of the mirror's so a photon emitted by myself towards the mirror will come back to me in the same radial direction. Will not then the gyroscope remain fixed in the radial direction? But this does not constitute Fermi-Walker transport as the polar axes of the local frame fixed to the disk rotate relative to the momentarily comoving local inertial frame due to Thomas precession. So where in the above is my incorrect application of Pirani's "bouncing photon" method?</p>
<p>(2) Let $(M,g_{\mu\nu})$ be a static axisymmetric space-time having a time-like and hypersurface orthogonal Killing field $\xi^{\mu}$ and an axial Killing field $\psi^{\mu}$; it is easy to see that $M$ being static is equivalent to $\psi_{\mu}\xi^{\mu} = 0$. Now consider a congruence of circular orbits in the rest space of $\xi^{\mu}$ given covariantly by the time-like Killing field $\eta^{\mu} = \xi^{\mu} + \omega \psi^{\mu}$ where $\nabla_{\mu}\omega = 0$ with $\omega$ being the angular velocity relative to spatial infinity. Then, given the above conditions, it can be shown that $\eta_{[\alpha}\nabla_{\beta}\eta_{\gamma]} = 0$ for <em>all</em> permissible values of $\omega$ on a time-like integral 2-manifold of $\eta^{\mu}$ if and only if the null vector field $k^{\mu} = \xi^{\mu} + \Omega \psi^{\mu}$ is a geodesic on this 2-manifold, where $\Omega^2 = -\xi_{\mu}\xi^{\mu}/\psi_{\nu}\psi^{\nu}$. This is a generalization of the situation at the photon radius in Schwarzschild space-time due to $\eta_{[\alpha}\nabla_{\beta}\eta_{\gamma]} = 0$ being equivalent to Fermi-Walker transport. </p>
<p>However intuitively I do not understand why the space-time must be static as opposed to just stationary. Consider a freely falling circular photon orbit in some stationary (but not static) axisymmetric space-time. If an observer were to be in circular orbit at this photon radius then why couldn't he just use Pirani's "bouncing photon" procedure from above to conclude that Fermi-Walker transport of a comoving gyroscope implies that its axis remains tangent to the circle? Intuitively speaking, under what circumstances would this fail in a stationary but non-static space-time, and why? Thanks in advance!</p> | 5,005 | [
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<p>Would a rotating sphere of magnetic monopole charge have electric moment ? </p>
<p>In a duality transformation E->B.c etc. how is the magnetic moment translated m = I.S -> ?
Mel = d/dt(-Qmag/c).S ? </p>
<p>A more general question would a sphere charged with monopoles have other moments that the monopole in the multipole expansion ? Like electron is predicted to have electric dipole moment also.</p> | 5,006 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/17741/how-does-electricity-propagate-in-a-conductor">how does electricity propagate in a conductor?</a> </p>
</blockquote>
<p>I have read that in an electrical wire electrons movement is very slow while the energy or charge is very fast.
What's the difference anyway?</p> | 174 | [
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] |
<ol>
<li><p>Why non integer spins obey Fermi statistics?</p></li>
<li><p>Why is fractional statistics and non-Abelian common for fractional charges?</p></li>
</ol> | 5,007 | [
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<p>I came across a contraction which is not giving the desired result. This is a toy problem in how to get a supergravity theory in low energy limit of a superstring theory using the vanishing of beta function in the $\sigma$ model, however there is no use of this context.</p>
<p>What I want to ask is contracting d and m in the following expression where T is torsion two-form and R is the curvature two-form.</p>
<p>The expression is $T^{[c}_{[pq}\delta^{d]}_{m]} +2a\partial_{[p}R^{cd}_{{qm}]}=0$</p>
<p>There is one extra condition $R^{mc}_{mq}=0$.
It is clear that second term would look like $\frac{2a}{3}\partial_m R^{mc}_{pq}$, apart from some sign probably.
The first term however after writting out explicitly gives $\frac{1}{6}T^c_{pq}$ ( one can eliminate terms like $T^c_{cm}$ which can shown to be cancel ), which gives something like </p>
<p>$T^c_{pq}+4a\partial_m R^{mc}_{pq}$=0 ( May be there is a minus sign before $4a\partial_m R^{mc}_{pq}$ but that is not the problem). The problem however is that the result should be following one</p>
<p>$T^c_{pq}+\frac{4a}{9}\partial_m R^{mc}_{pq}$=0 and I don't know how he is getting the factor of 9 there. For reference one can look at Castellani ' Supergravity and superstrings: a geometric perspective vol. 3' around page 1850.</p> | 5,008 | [
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<p>Suppose we have a simple harmonic oscillator, let's consider the ground state, $|0\rangle$ and the first excited state $|1\rangle$.</p>
<p>$\langle 0|\hat p|0 \rangle$ is zero right? Since the particle can either be travelling to the left or right, where $\hat p$ is the momentum operator.</p>
<p>Similarly, I think $\langle 1|\hat p|1 \rangle = 0$</p>
<p>But, $\langle 0 | \hat p | 1 \rangle$ is non-zero, right? Since they are different states. Also, since $\hat p$ is Hermitian, $\langle 0 | \hat p | 1 \rangle = \langle 1 | \hat p | 0 \rangle $, right?</p> | 5,009 | [
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<p>When studying from the book by Wise and Manohar, <em>Heavy Quark Physics</em> (pg 102), I came across a seemingly simple identity that I am not able to prove. It's likely an easy problem but I can't for the life of me figure out why. </p>
<p>First they define the transverse covariant derivative,</p>
<p>$$D_\perp \equiv D^\mu - D \cdot v v ^\mu$$</p>
<p>where $v^\mu$ is some four-vector that squares to 1 and then they write down the identity,</p>
<p>$$ \require{cancel} \cancel{D_{\perp}}\cancel{D_{\perp}} = D_\perp^2 +\frac{1}{2}[\gamma_\mu,\gamma_\nu] D_\perp^\mu D_\perp^\nu$$</p>
<p>I would have naively thought that we would still have the usual, $D_\perp^2= \cancel{D_{\perp}}\cancel{D_{\perp}} $. Why is this not the case?</p> | 5,010 | [
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<p>So, the way I understand this is as follows :</p>
<p>The alveoli (pretend they're bubbles) have diameters of the order of microns implying a massive pressure required to inflate them by the Young-Laplace equation.</p>
<p>$p_{in}-p_{out}=\frac{2\gamma}{r}$</p>
<p>However, the presence of pulmonary surfactant molecules (lets just pretend they're like detergents molecules in washing liquid) can effectively reduce the surface tension at the unexpanded alveoli and hence allow easy inflation.</p>
<p>Now this bit I don't understand :</p>
<p>As the alveoli expand the <strong>distance between the individual surfactant molecules on the alveoli increases and hence the surface tension rises again</strong> therefore decreasing the rate of expansion.</p>
<p>What is the mathematical connection between surface tension and separation between surfactant molecules ? How can I rationalise the statement in bold ?</p> | 5,011 | [
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] |
<p>How to calculate electric field between two electrodes - square and circular?</p> | 5,012 | [
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<p>The question is the same as the one I put in the title but here it is in more words.</p>
<p>I was wondering if there were any substances that allowed sound to travel more efficiently. For example water is obviously a much worse way to transport sound then air. </p> | 5,013 | [
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<p>I'm reading <a href="http://www.sciencedirect.com/science/article/pii/0040609082905909" rel="nofollow">this paper</a> which is essentially about connecting the complex permittivity $\epsilon$ with the microstructure of a thin film. They talk about how you can place limits on the possible values of $\epsilon$ depending on how much information you have on the microstructure, and say:</p>
<blockquote>
<p>We use the fact that all bounds are circular arcs in the complex $\epsilon$ plane to give...</p>
</blockquote>
<p>Why is this the case? My intuition tells me it has something to do with the Kramers-Kronig relations or energy conservation, but I don't know why.</p> | 5,014 | [
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<p>In <a href="http://de.wikipedia.org/wiki/Stefan-Boltzmann-Gesetz#Beispiel" rel="nofollow">a German Wikipedia page</a>, the following calculation for the temperature on the surface of the Sun is made:</p>
<p>$\sigma=5.67*10^{-8}\frac{W}{m^2K^4}$ (Stefan-Boltzmann-constant)</p>
<p>$S = 1367\frac{W}{m^2}$ (solar constant)</p>
<p>$D = 1.496*10^{11} m$ average distance earth-sun</p>
<p>$R = 6.963*10^8 m$ (radius of ths sun)</p>
<p>$T = (\frac{P}{\sigma A})^\frac{1}{4} = (\frac{S4 \pi D^2}{\sigma 4\pi R^2})^\frac{1}{4}=(\frac{SD^2}{\sigma R^2})^\frac{1}{4} = 5775,8$</p>
<p>(Wikipedia gives 5777K because the radius was rounded to $6.96*10^8m$)</p>
<p>This calculation is perfectly clear.</p>
<p>But in Gerthsen Kneser Vogel there is an exercise where Sherlock Holmes estimated the
temperature of the sun only knowing the root of the fraction of D and R.
Lets say, he estimated this fraction to 225, so the square root is about
15, how does he come to 6000 K ? The value $(\frac{S}{\sigma})^\frac{1}{4}$
has about the value 400. It cannot be the approximate average temperature
on earth, which is about 300K. What do I miss ?</p> | 5,015 | [
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<p>If we can think about the universe as a wave function then many particles should be entangled with many other particles in the universe. The obvious question arises why we don't see those entanglements in everyday circumstances. One standard explanation given is those entanglements average out and cancel so we can ignore those. However, hardly any mathematical justification is given for them to cancel. My question is how much trust one should have on that particular assertion? Is there any mathematical arguments already put forward by anyone?</p> | 5,016 | [
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<p>What velocity would a small body moving towards a large body reach under gravity alone?
More importantly, is there a 'terminal velocity' for the small body due to the increasing energy required to accelerate the body as its velocity increases?</p>
<p>Assumptions: No other forces, gravity acts over infinite distances.</p>
<p>Parameters: Large mass=$10^{24}$kg Small mass=$100$kg, Distance between them=$10^{12}$m.</p> | 5,017 | [
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<p>Seiberg traced the nonrenormalization of supersymmetric theories to holomorphy of the superpotential in chiral superspace. However, this overlooks the fact that with a different number of supersymmetric generators, supersymmetry can be real or symplectic, instead of complex. But yet, even for those cases, we still have nonrenormalization. If holomorphy isn't the reason, what is?</p>
<p>If the reason for nonrenormalizability is totally different for different dimensions and number of supersymmetry generators and choice of superfields, is it then <em>ad hoc</em> that nonrenormalizability always holds in each case?</p> | 5,018 | [
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<p>My question refers to an overview of the biggest stars we know: <a href="http://farm5.static.flickr.com/4138/4820647230_faba1c9f3b_o.jpg" rel="nofollow">http://farm5.static.flickr.com/4138/4820647230_faba1c9f3b_o.jpg</a></p>
<p>Why are some of those blue?</p> | 5,019 | [
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<p>What does it mean that the Higgs has a nonzero vacuum expectation value? Are there any other important field with nonzero VEV? How is this related to the 100-orders magnitude wrong prediction?</p> | 5,020 | [
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<p>For one of my experimental setup I need to place a mirror perfectly parallel to a wall. It can be placed at any distance from the wall. I would like to use any method other than direct measurement. I am free to use the following:</p>
<p>a webcam</p>
<p>a secondry mirror</p>
<p>Edit: It's not necessary to use all or either of them.</p> | 5,021 | [
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<p>This has always puzzled me. Yesterday (in London) it started hailing despite it being about $20^oC$. A couple of years ago I experienced hail in Sicily when it was about $35^oC$ in the shade!. How is this possible?</p> | 5,022 | [
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<p>I have a question regarding the <a href="http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence" rel="nofollow">energy-mass</a> conversion. Well, when a particle starts moving with a speed comparable to that of light, its (relativistic) mass increases that means some matter is created and that too of the same particle...energy being converted to mass is ok but how does energy perceive what atoms it has to form? Say I take a stone to a high speed, then constituents of stone is formed. And if I perform same thing with another substance, its constituents are formed..How? Energy can be converted to mass but a mass of what? Does that mean we can create matter of any desirable substance?</p> | 5,023 | [
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<p>I know this is essentially a mathematic question, but I received no answer on math SE. Moreover it has a direct application in physics, so I thought to ask this here too.</p>
<p>The momentum operator in one dimension in quantum mechanics is $P=-i\frac{d}{dx}$ (with $\hbar=1$). Consider it as an operator on $L_2(0,2\pi)$, the space of square-integrable functions on $(0,2\pi)$. It isn't continuous in fact if I consider the sequence
$$
g_n(x)=\frac{e^{inx}}{\sqrt{2\pi n}}
$$
it's a Cauchy sequence but $\{Pg_n\}_n$ does not converge.</p>
<p>I am searching a domain where $P$ is a continuous functional. My professor gave me the example
$$D_P=\{\varphi \in L_2(0,2\pi):\varphi(0)=\varphi(2\pi) \}$$
but I'm not convinced because if I consider the function $\psi$</p>
<p>\begin{equation}
\begin{cases}
-\frac{x}{\sqrt{\pi}}+\sqrt{\pi},\hspace{0.5cm} 0\leq x<\pi\\\sqrt{x-\pi},\hspace{0.5cm} \pi\leq x \leq 2\pi
\end{cases}
\end{equation}
it belongs to $D_P$, but if I apply $P$ on it I obtain</p>
<p>\begin{equation}
\begin{cases}
\frac{i}{\sqrt{\pi}},\hspace{0.5cm} 0\leq x<\pi\\ -\frac{i}{2\sqrt{x-\pi}},\hspace{0.5cm} \pi\leq x \leq 2\pi
\end{cases}
\end{equation}
that is not square-integrable on $(0,2\pi)$.</p>
<p><img src="http://i.stack.imgur.com/Mv1d7.png" alt=""></p>
<p>Am I wrong? If not, which is a correct continuity domain for $P$?</p> | 5,024 | [
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<p>I want to describe the interaction between a target and a probe and know that this is described by some unitary operator that acts on both systems.</p>
<p>My operator needs to implement a $\pi/q$ rotation in the equatorial plane. I need to perform a Von Neumann measurement on the probe which is described by a projection onto one of the probe states.</p>
<p>In my case this is the spin either up or down at and angle $\phi$ to the x-axis.</p>
<p>I have a formula for the unitary operator that acts in the tensor product space which is $$U=\sum{u_{nk,n\prime k\prime}|n>|S_{k}><n\prime|<S_{k\prime}|}$$
where {|n>} are the probe states, $|S_{k}>$ are a set of basis states for the target, and $u_{nk,n\prime k\prime}$</p>
<p>are the matrix elements
of U</p>
<p>Could somebody give an example explicitly of finding such a unitary matrix for a combined system or some hints for my problem.</p> | 5,025 | [
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<p>In addition, to get light to other side of the wall, could it be converted to radio waves and then back to light waves?</p>
<p>Edit: My idea was if there was a special material that was painted on both sides of a wall that converted radio waves to light waves and light waves to radio waves would the wall appear invisible? (My thought being that the electromagnetic radiation would travel through the wall since radio waves can travel through walls) </p>
<p>Also, thanks for all the responses!</p> | 5,026 | [
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<p>To give context to this question, I am currently looking into non-locality / hidden variables / Bell's Theorem, EPR / etc.</p>
<p>I've noticed the assertion that the values / state of something when measured aren't what the values / state would be if the measurement were not made.</p>
<p>How is this known? Or is it an assumption?</p>
<p>I have no science background so please explain in layman's terms, if possible.</p> | 5,027 | [
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<p>How important are proofs in physics? If something is mathematically proven to follow from something we know is true, does it still require experimental verification? Are there examples of things that have been mathematically proven to some reasonable degree of rigor (eg satisfy a mathematician) that turned out to be false based on experiment? </p> | 5,028 | [
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<p>Say you have two planes flying next to each other at the same speed and one decides to pick up speed by burning a tank of rocket fuel.</p>
<p>If someone on the ground wanted to know that plane's new speed after burning the fuel and knew the plane's mass, initial speed, and energy stored in the fuel, he could calculate it using conservation of energy.</p>
<p>If the pilot of the other plane wanted to calculate the same thing but didn't know his own speed, he could calculate the speed of the first plane relative to himself using conservation of energy--the initial relative speed is 0 and all the work done by the rocket fuel is converted into the plane's new kinetic energy.</p>
<p>He could then relay this relative speed to someone on the ground who knew his plane's speed, but adding the speed of the second plane to the calculated speed of the first relative to the second would give a different value for the first plane's speed than the first guy on the ground would have calculated.</p>
<p>I see why this doesn't work mathematically (a^2+b^2 isn't (a+b)^2), but why can't the second pilot calculate the new speed of the first plane relative to himself by converting the stored fuel energy into kinetic energy? Why when on the ground do we not consider our motion relative to, say, the moon when calculating the first plane's speed relative to us, but the second pilot must consider his speed relative to the ground before calculating the first plane's speed relative to himself? Or maybe to put it better, why is having no movement relative to the Earth instead of relative to the plane's initial speed (the second plane) or anything else the correct way to approach this problem?</p> | 5,029 | [
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<p>We know, that one-particle states can be earned from relativistic fields, which can be interpreted as functions determined on Minkowski space-time. Field must satisfy some conditions, by which we classify them as massive/massless, spin/helicity, etc. Electron can be represented as one-particle state of bispinor field, which satisfy Dirac equation. But what is the electron field? Does it exist? Or it is only convenient method for describing, for example, scattering processes?</p> | 5,030 | [
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<p>I'm trying the following:</p>
<p>The filament inside a 100 W lightbulb has an absorption coefficient of 0.25, and while operating, it is at a temperature of 2,573 K. What's the size of the surface of the filament? (done with Stefan-Boltzmann) At what wavelength does it emit the highest intensity? (done with Wien displacement law). Relative to all emitted radiation, how much power is emitted as visible light (400 nm - 800 nm)?</p>
<p>The last one is causing me trouble. I have been trying to integrate Planck's radiation law for quite some time now, but I can't manage to do it(and neither can Mathematica). Is there another way of doing this?</p> | 5,031 | [
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<p>The notes state that $N=mg$. However, if I have a $4\text{kg}$ box on a table, taking upward as positive
$$N=-mg=-4*-9.81$$
Is this correct? If it is correct, why do the notes state that $N=mg$. Should I only use the magnitude of gravity?</p> | 5,032 | [
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<p>I have a problem with this exercise because I really don't know how to proceed. It's related with the "S-matrix".</p>
<p>In class we saw this example:</p>
<p>Consider the spherically symmetric potential:</p>
<p>$$V(r)=\begin{cases}
-V_{0}, & 0\leq r\leq a\\
0, & r>a
\end{cases} $$</p>
<p>We know that for $r>a$ and $l=0$ we have</p>
<p>$$U_>''(r)+k^{2}U_>(r)=0 \qquad (1)$$</p>
<p>where $U(r):=rR(r)$, and $R(r)$ satisfies the radial part of the Schrödinger equation in spherical coordinates (for $l=0$):</p>
<p>$$-\frac{\hbar^{2}}{2m}\frac{1}{r^{2}}\frac{d}{dr}\left(r^{2}\frac{dR}{dr}\right)+\left[V(r)+\frac{\hbar^{2}l(l+1)}{2mr^{2}}\right]R=ER$$</p>
<p>In this case ($l=0$), from (1) we have the solution (for $r>a$)</p>
<p>$$U_>(r)=A e^{ikr}+Be^{-ikr} \qquad (2)$$</p>
<p>Or</p>
<p>$$U_{>}(r)=\frac{i}{2}\left[e^{-ikr}-S(k)e^{ikr}\right] \qquad (3)$$</p>
<p>Since we saw this really quick in class, I have 3 <strong>questions</strong>:</p>
<p><strong>1</strong> How do I manipulate (2) in order to obtain (3)?</p>
<p>After writing this, my teacher said the classical "it can be shown that:"</p>
<p>$$S(k)=\frac{-ik\sin qa-q\cos qa}{ik\sin qa-q\cos qa}e^{-2ika} \qquad (4)$$</p>
<p>then, my second question is: </p>
<p><strong>2</strong> How do I obtain (4)? I've been searching for this topic in my books (Griffiths, Schaum's Outlines) but I don't find anything related. Our reacher said that the function $S(k)$ is related with the "S-Matrix".</p>
<p><strong>3</strong> Could you suggest me a book where I can study this, please?</p> | 5,033 | [
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<p>Accelerating away from a mass mitigates gravity's pull on the accelerating object. Would the same be true for an object accelerating towards the center of the mass?</p> | 5,034 | [
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<p>can anyone help me to determine the heat flux (Kw/m2) on a focal point of a parabolic dish having a diameter of 1.5 meter and a focal length 60 cm ???
please awaiting your soonest reply for my senior project :(
Regards</p> | 175 | [
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<p>Why is it that currents don't flow at the speed of light, but rather significant ratios of the speed of light.
I don't have any formal reasoning as to why they would flow at the speed of light-I just feel as if it would make sense.
That being said, the fact that they do move at near the speed of light is also peculiar to me.
Lastly, if you have current and area determined, can you figure out the velocity of the charges? I suppose you would also need to know how big the charges are.
I just have no intuition as to how to go about analyzing the speed of current in some given wire.</p> | 5,035 | [
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<p>When one travels in a bus, if he's sitting at any window, he will feel that the air is coming inside. If someone is standing at the open door of the bus, he'll also feel that the air is coming inside.
If so much air is coming inside, why doesn't the bus blow due to internal pressure?</p> | 858 | [
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<p>Why is it that we can use the Poynting Vector to find the power dissipated in a Coaxial Cable? Unlike the situation with light, where the c makes sense, inside the coaxial cable I see no reason why there should be a factor of c considered, and while we have both electric and magnetic fields, it's just not light!
Any help with the reasoning/intuition?</p>
<p>My problem may be that I saw the 'derivation' via the example of a light wave, and not pulling from Poynting's Theorem. I'm trying to understand how electromagnetic fields can be viewed as light, and it may be that I'm just looking at it backwards. Although I still feel that a static E&M field should have some analog to a light wave that should be readily understandable. </p> | 5,036 | [
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<p>When receiving servers (while playing tennis), I've noticed that the tennis ball seems to bounce up higher on me when the server uses a topspin serve than when the server hits a flat serve. Why is that?</p>
<p>Is it because of something about how the spin affects the bounce of the ball (i.e., the effect of the spin during the time when the tennis ball is in contact with the court)? Is it because of how the spin affects the flight of the ball while it is in the air? Perhaps it's because topspin serves tend to be hit with a higher, "loopier" trajectory, and this changes the angle of incidence when the ball hits the court during the bounce? Or maybe it's something else entirely? What would you expect the effect of the topspin to be on the trajectory of the ball, based upon physical principles?</p>
<hr>
<p>Background on tennis: When serving, the server has to hit the tennis ball over the net and then into the service box; the ball is required to bounce within the service box. The receiver stands back a bit, and after it bounces up, the receiver hits it back.</p>
<p>A flat serve is a serve where the ball has no spin. A topspin serve is a serve with topspin: the top of the tennis ball is rotating forward (in the direction of the ball's travel) and the bottom of the ball is moving backward (opposite the direction of the ball's travel). Topspin causes the tennis ball to "curve downwards", due to <a href="https://en.wikipedia.org/wiki/Magnus_effect" rel="nofollow">the Magnus effect</a>.</p>
<p>From the server's perspective, topspin is useful, because it means the server can hit the ball higher over the net and the serve will still go in. That allows a topspin serve to be more reliable: the server has more margin for error. In contrast, with a flat serve, the serve has to be aimed very precisely: aim too high, and the ball will "go long" and bounce outside of the service box; aim too low, and the ball will hit the net. A flat serve will usually look like a "line drive" (the path of the ball is close to a straight line), while a top spin serve will look more "loopy" (the ball goes higher over the net, then swerves down).</p>
<p>Flat serves usually travel faster. With a topspin serves, the ball usually doesn't have quite as much velocity (I imagine some of the energy of the server is spent on imparting spin, rather than propelling the ball forward). Nonetheless, from my personal experience, it feels like when I am receiving a topspin serve, the ball bounces up higher and often gets out of my comfort zone: the flat serve might bounce up to waist level, where it's comfortable to hit the ball, but the topspin serve might bounce up to shoulder level, where it's less comfortable. Why does this happen? Or, is it an illusion?</p> | 5,037 | [
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<p>I'm attempting to approach this using the identity
$$F/A = I/c$$
I can solve for Area easily enough
$$A = F(c/I)$$
and I know the distance $d$ is
$$d=1/2(at^2)$$</p>
<p>But I'm having difficulty trying to relate this to the time it would take to reach mars.</p>
<p>Any ideas where to go from here?</p> | 5,038 | [
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<p>I came across the use of the unit barn and inverse barn while reading about the operation of LHC. What is an inverse femtobarn ? What does it tell about the experiment being described ? </p> | 5,039 | [
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<p>I've heard it said many times that you're more likely to burn food on an electric stove than a gas one, but I can't tell a difference. This seems to me to be a fallacy perpetuated by the natural gas industry, and I would expect the issue to just be people are not sure how to accurately adjust the system they're not used to. Once the heat energy gets into the cooking vessel, say a cast iron skillet that will quickly disperse the heat, I can't even identify a physical (physics) reason why there would be a difference.</p>
<p>So my question is, is there something I'm missing; is there a physical reason why cooking on a gas vs stovetop would be different?</p> | 5,040 | [
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<p>Quite often I go out in the morning and I'm in Milton Keynes, so I would expect the moon to rise in the east and set in the west. Sometimes at about 2, 3, 4 o’clock in the morning the moon is low in the east. I was just wondering how that worked out?</p> | 5,041 | [
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<p>Fluorescent lights are already efficient when they’re running but I’ve heard that it takes a lot of energy to turn a fluorescent light tube on. So is it more efficient to turn off a fluorescent tube immediately when you’ve finished using it or is it better to leave it on and then wait until you’re more likely to not use it again for a while?</p> | 5,042 | [
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<p>On every ductless mini-split air conditioner I've ever seen, both the high and low pressure lines are insulated between the compressor and the building. </p>
<p>It seems like the liquid refrigerant coming out of the condensing coil can never be cooler than the outdoor ambient air temperature because the outdoor air is what is cooling it in the condenser coil. </p>
<p>It can, however, be warmer than the outdoor ambient temp. Therefore, it seems like leaving that high pressure line coming out of the compressor uninsulated would at worst save costs for some insulation, and at best give the high pressure refrigerant some additional cooling before it gets back to the indoor unit.</p>
<p>What am I missing here? </p>
<p>NOTE: I can think of some reasons why you'd want to insulate that line on the inside of the building where the high pressure liquid refrigerant would be warmer than the ambient indoor air temp. </p> | 5,043 | [
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<p>So I have a question about what i should do with my path to learning quantum physics. I just have no idea where to start or to continue from where I left off. I have been studying quantum mechanics for a good year now. I dont know what level my knowledge of QM is but I finished Griffiths qm and i have gone through many chapters in Shankar. But where do i go from here? Do I go to QFT or QED? I have a good knowledge of E&M and Maxwell's equations but I just don't know what path do go on.</p> | 5,044 | [
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] |
<p>Angular momentum causes the <a href="http://en.wikipedia.org/wiki/Event_horizon" rel="nofollow">event horizon of a black hole</a> to recede. At maximum angular momentum, $J=GM^2/c$, the <a href="http://en.wikipedia.org/wiki/Schwarzschild_radius" rel="nofollow">Schwarzschild radius</a> is half of what it would be if the black hole wasn't spinning. </p>
<p>Can someone explain why angular momentum reduces the Schwarzschild radius?</p> | 5,045 | [
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<p>I am confused about Newton's 3rd Law. If a person jumps off the ground a force is applied both to the person and to the ground. However, as $F=ma$ acceleration experienced by the Earth is much less than that experienced by the person.</p>
<p>But: I press with gravitation force on the ground so it should press with the same force on me, so if my mass is less than earth mass my acceleration should be greater as well but I am not moving (flying)?</p>
<p>Second: If small rocket(with small mass) pressure against bigger rock with greater mass the rocket should have greater acceleration towards direction opposite to its flying path so how the rocket can actually move the rock(towards left at picture where rock acceleration is small) and not the opposite(rocket acceleration at picture towards right is bigger)?<br>
<em>Edited</em><br>
If a rocket with mass $m_{rocket}$ pushes against a rock with mass $m_{rock}$ with force $F_{thrust}$ the rock will push back with equal force (Newton's 3rd Law). The rocket will experience an acceleration $a_{rocket}$ in the opposite direction of $F_{thrust}$ and the rock will experience $a_{rock}$ in the <em>same</em> direction as the thrust. However, in this example $m_{rocket} < m_{rock} \therefore a_{rocket} < a_{rock}$<br>
Why doesn't the rocket move in the opposite direction of $F_{thrust}$ since the rock has a greater mass?</p>
<p><img src="http://i.stack.imgur.com/9kKKg.jpg" alt="enter image description here"></p>
<p>Not sure if it helps but added picture to second question</p>
<p>Edit:To put second question simple how a small(low mass) object can push big(great mass) object if according to newton 3rd law a big mass object causes greater acceleration on small mass object</p> | 5,046 | [
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<p>When an atom bomb goes off some matter is converted to energy according to $E = m c^2$.</p>
<p>I'd like to know exactly what matter in the original atom bomb is converted to energy. Is it protons, neutrons, electrons? Is it a collection of atoms? What goes?</p> | 5,047 | [
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<p>Related: <a href="http://physics.stackexchange.com/questions/79212/which-green-spectral-lines-are-emitted-in-a-thomson-tube">Which green spectral line(s) are emitted in a Thomson tube?</a></p>
<p>After reading Lisa Lee’s OP on an electron deflection tube, although she had some misunderstandings on its operation, I still believe that her question is still relevant. If one looks at the Thomson e/m tube filled with helium gas (made by <a href="http://www.pasco.com/prodCatalog/SE/SE-9646_e-m-tube/#overviewTab">Pasco</a>), the tracer light is created by de-excited electrons, not by an electron beam interacting with a phosphor as in Lisa Lee's OP. That is, the accelerated electrons scatters off of a low pressure helium gas and emit a tracer line to follow the electrons path, as shown below. </p>
<p><img src="http://i.stack.imgur.com/HJMxO.jpg" alt="enter image description here"></p>
<p>Now if you look at the bright line spectrum of helium, </p>
<p><img src="http://i.stack.imgur.com/Yvmrp.jpg" alt="enter image description here"></p>
<p>One can clearly see that there are two “cyan” color lines around 500 nm. Following in Lisa Lee’s footsteps, there is a series of question one can ask: (1) which line is emitted by the Helium gas atoms? Or are both lines emitted? (2) How can a variable accelerating voltage for the electrons always produce the same tracer line color? In theory, I assume that if I decreased the energy of the electron beam, I could produce red (around 670 nm) or yellow (around 590 nm) tracer lines, but that doesn’t happen. Somehow, it appears to me that the e/m tube is “tuned” just right so that the emitted light is always this “cyan” color. Why? </p> | 5,048 | [
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<p>Why is it that solids on compression [As in striking a hammer etc.] heat up,
but liquids and gases on compression [Pressurizing liquids causes them to freeze or gases to liquify] cool down?
Can someone explain this please?</p> | 5,049 | [
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<p>I am very sorry for posting these problems in this forum, but i don't know where to post otherwise... I have a weird special relativity problem where i get a relative speed $u$ which is larger that $c$. I dont need an solution but rather some guidance towards my understanding of the special relativity...</p>
<blockquote>
<p>Two sticks (both with the proper length $1m$) travel one toward
another along their lengths. In the proper system of one stick they
measure time $12.5ns$ between two events: </p>
<ol>
<li>right ends are aligned,</li>
<li>left ends are aligned.</li>
</ol>
<p>What is the relative speed $u$ between the sticks?</p>
</blockquote>
<p>I first draw the picture:</p>
<p><img src="http://i.stack.imgur.com/mjSP0.png" alt="enter image description here"></p>
<p>If i use the Lorentz transformation and try to calculate the relative speed $u$ i get speed that is supposed to be greater than the speed of light:</p>
<p>Here is what i did:
\begin{aligned}
\Delta x' &= \gamma (\Delta x - u \Delta t) \xleftarrow{\text{Is this ok? I don't think my system is in the standard configuration}}\\
\frac{1}{\gamma}\Delta x &= \gamma (\Delta x - u \Delta t)\xleftarrow{\text{$\Delta x$ is equal to the proper length (in $xy$ the botom stick is standing still)}}\\
\tfrac{1}{\gamma^2}\Delta x &= \Delta x - u \Delta t\\
\left( 1 - \tfrac{u^2}{c^2}\right)\Delta x &= \Delta x - u \Delta t\\
\Delta x - \tfrac{u^2}{c^2}\Delta x &= \Delta x - u \Delta t\\
\tfrac{u^2}{c^2}\Delta x &= u \Delta t\\
\tfrac{u}{c^2}\Delta x &= \Delta t\\
u &= \tfrac{\Delta t}{\Delta x} c^2\\
u &= \tfrac{12.5\cdot 10^{-9}s}{1m} 2.99\cdot 10^{8}\tfrac{m}{s} c\\
u &= 3.74 c
\end{aligned}</p>
<p>In the solutions it says i should get $u=0.5 c$, but i get $u=3.74c$. I used the Lorentz transformation found on <a href="https://en.wikipedia.org/wiki/Lorentz_transformation#Lorentz_transformation_for_frames_in_standard_configuration" rel="nofollow">Wikipedia</a>. These are for the standard configuration, but in my case is it the standard configuration? </p> | 5,050 | [
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<p>One way Wikipedia <a href="http://en.wikipedia.org/wiki/Ohm_%28unit%29" rel="nofollow">defines Ohm</a> is (this is also teached in school):
$$1\Omega =1{\dfrac {{\mbox{V}}}{{\mbox{A}}}}$$
They describe this definition in words, too:</p>
<blockquote>
<p>The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1.0 volt, applied to these points, produces in the conductor a current of 1.0 ampere, the conductor not being the seat of any electromotive force.</p>
</blockquote>
<p>The definition of Ohm in SI basic units is:
$$1\Omega = 1{\dfrac {{\mbox{kg}}\cdot {\mbox{m}}^{2}}{{\mbox{s}}^{3}\cdot {\mbox{A}}^{2}}}$$
It's really hard for me to get that this definition is correct. It's clear that mathematical calculations confirm this definition. But how do you describe the definition of the SI in words like that paragraph on wikipedia?</p>
<p>Edit:
How <em>would</em> you describe it? Although it is not common to do it that way, I think describing it that way, could be very interesting. </p> | 5,051 | [
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<p>I got really confused about real gases volume and ideal gas volume. Ideal gas molecules take up no space, if we put gas into a 2.4L water bottle, we know that all the gas will expand all over the bottle and we say at this moment the gas has volume of 2.4L. So what is this volume? </p> | 5,052 | [
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<p>I'm wondering how can one formally justify the electromagnetic response of a system which does not verify local U(1) gauge invariance.</p>
<p>A good example of what I would like to consider is given by the two-body interaction term discussed in relation with superconductivity as I'll elaborate below, but many examples can be found and the question is rather general.</p>
<p>Most of the people starts with a BCS Hamiltonian having generically the following form<br>
$$H_{\text{BCS}}=\sum_{k,k'}\hat{c}_{k\alpha}^{\dagger}\left(\mathbf{i}\sigma_{y}\right)_{\alpha\beta}^{\dagger}\hat{c}_{-k\beta}^{\dagger}U\left(k,k'\right)\hat{c}_{k'\alpha}\left(\mathbf{i}\sigma_{y}\right)_{\alpha\beta}\hat{c}_{-k'\beta}$$</p>
<p><em>i.e.</em> describing singlet Cooper pairing of electron with fermionic operators $\hat{c}_{k}$ in mode $k$, the greek indices being the spin ones. I think this Hamiltonian is manifestly not U$(1)$ local gauge invariant, due to the $k$ and $k'$ on different operators. </p>
<p><strong>I'm wondering</strong> whether it makes sense to talk about the electrodynamic response of a superconductor when one starts with a non gauge invariant Hamiltonian. More generally, <strong>does it makes sense to discuss non-gauge invariant Hamiltonian in the context of condensed matter ?</strong> How should we understand such non-gauge-invariant Hamiltonians, $H_{\text{BCS}}$ being a simple example ?</p>
<p>More details:</p>
<ul>
<li>The original BCS Hamiltonian has $k=k'$ and $U\left(k,k'\right) \rightarrow -g$ a constant, and so the $s$-wave interaction <em>is</em> both local and global U(1) invariant. $H_{\text{BCS}}$ is only U(1) symmetry global invariant, as far as I can see.</li>
<li>The Hamiltonian $H_{\text{BCS}}$ given above is particularly useful to describe some non-conventional effects ($d$-wave pairing for instance) and can be further generalise. I have not doubt about the validity of the results obtained using this Hamiltonian (some of them are even justified experimentally).</li>
<li><em>I'm wondering about the possibility to formally define an electromagnetic response in a non-U(1) gauge invariant theory.</em> It is for instance clear that one can add some gauge invariant part of the above Hamiltonian, such that the constitutive Maxwell equations are preserved (no magnetic monopole and Faraday's law). But it seems also clear for me that one intrinsically imposes from the beginning some different matter-field interaction, isn't it ? Or at least that the covariant substitution is no more a correct prescription... </li>
</ul> | 5,053 | [
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<p>If I place a solenoid connected to a bulb inside a bigger solenoid which is connected to a power source, will the bulb glow?</p> | 5,054 | [
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<p>I am reading 't Hooft's noted on Black holes, where he quotes the Kerr metric for a black hole rotating about the z-axis as follows:
<img src="http://i.stack.imgur.com/rW8v0.png" alt="enter image description here"></p>
<p>He later says:
"The parameter a can be identified with the angular momentum i.e. $$J=aM$$"</p>
<p><strong>How can I prove this statement?</strong> How is the angular momentum tensor defined for an arbitrary metric satisfying Einstein's equations? Do, I have to find all the components of $T_{\mu \nu}$ by first calculating the curvature tensor or is there an easier way?</p> | 5,055 | [
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<p>I am studying for an exam, and this is part of a problem in my book.</p>
<p>A projectile is launch from level ground and is intended to hit a target 100m away. Instead, it explodes into two fragments of equal mass, one of which lands 100m beyond the target. If the fragments don't take the same amount of time to land, must the second one land 100m short of the target?</p>
<p>The back of the book tells me that this isn't true, but I'm having a hard time figuring out why.</p>
<p>I know that the trajectory of the center of mass for the system is going to follow the trajectory of the projectile before it exploded. Thus, the CM of the system is at a distance of 100m from the origin. However, the equation for the center of mass would be $100 = mx_{cm} = \frac{1}{2}mx_1 + \frac{1}{2}mx_2$. Now $x_1 = 200$ by the conditions of the problem, so $ \implies x_2 = 0$. So clearly there must be some reason why this doesn't hold, but I can't figure it out.</p>
<p>Could anyone explain to me why this won't work?</p> | 5,056 | [
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<p>Can substances other than H2O have a triple point, where the three usual phases of matter (solid/liquid/gas) can exist?</p> | 5,057 | [
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<p>Is the electric field between two positively charged parallel infinite plates one with a charge density twice the other effect the electric field on the outside of the plates? I am thinking no, because the field lines cannot cross in the field between the plates since they have positive charges. What does the electric field in the middle look like? How would I draw electric field lines to geometrically interpret this situation? If I have a Gaussian cylinder between the plates will the field go out the walls of the cylinder like in the case of two positive point charges within a Gaussian cylinder? </p> | 5,058 | [
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<p>How to easily, using standard <a href="http://en.wikipedia.org/wiki/DIY">DIY</a> equipment measure the strength of magnetic field generated by a permanent magnet?</p>
<p>Narrowing down the "loose language" of the above:</p>
<p>strength of magnetic field: either flux density <strong>B</strong> at given point relative to the magnet or magnetic flux Φ<sub>B</sub> over area enclosed by a loop made of wire - whichever will be easier to measure, either of those is fine.</p>
<p>standard DIY equipment: commonly found household items, rudimentary tinkering tools. Soldering tools, multimeter, simple electronic parts, or maybe an easy to make spring-based dynamometer - anything of this class of complexity.</p>
<p>The distance of measurement is such that the field is easily noticeable through simplest methods e.g. another magnet held in hand exerts perceptible force - distance of maybe 5cm away at most.</p>
<p>The measurement doesn't need to be very accurate - error of order of 50% is quite acceptable. Simplicity is preferred over accuracy.</p>
<p>Rationale: trying to estimate what coil I need to generate sufficient amount of power to light a LED with a frictionless generator based on that magnet (knowing speed of movement of the magnet and location of the coil relative to the path of the magnet). If you know other simple methods of doing that (without need for measuring the field), they are most welcome them too.</p> | 5,059 | [
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<p>I'm sorry for this question but, I just don't get it. According to the electromagnetic field theory, electrons repel each other by exchanging photons. How do protons attract electrons, by photon exchange?</p> | 5,060 | [
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<p>We are conscious to live in a 3 dimension universe. Maybe it has more than 3 spatial dimensions (like the 10 mentioned in the string/M-theory) but that is not my concern here. My question is the following.</p>
<p>Is this number of (at least) 3 related with our cognitive process? I mean: in a cognitive process, there are 3 terms: </p>
<ol>
<li><p>observing subject; </p></li>
<li><p>observed object; </p></li>
<li><p>link. </p></li>
</ol>
<p>Implies that to observe the universe we necessarily build a link. This link must have numerous degrees of freedom and this is not possible in a 2-D universe.</p> | 5,061 | [
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<p>Suppose an object is thrown parallel to the ground. The gravity acts downward (ie. perpendicular to the direction of motion of the object). The work done by gravity on that object will be given by : </p>
<p>$\text{Work}, W = F \cdot S = FS\times\cos \theta$</p>
<p>$\implies W=FS \cos 90$ ($\because$ direction of gravity $\perp$ direction velocity of the object)</p>
<p>$\implies W= FS \times 0$ ($\because \cos 90 = 0$)</p>
<p>$\implies W = 0$</p>
<p>From the calculation above, gravity will not do any work on the object. So why does it follows a parabolic path and eventually falls down.</p> | 5,062 | [
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<p>According to the Wikipedia page on the Standard Model, the Higgs field interact with fermions through a Yukawa interaction coupling only left to right chiralities. What is the reason for that? Is that the case with all Yukawa couplings?</p> | 5,063 | [
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<p>What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories? I'd think that these hypotheses lead to physically "nice" theories in some way, but I've never, even from a computational perspective. really given these assumptions much thought.</p> | 5,064 | [
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<p>In a textbook about semicoductor physics, I came across a passage about deriving the carrier concentration at thermal equilibrium in semiconductors I didn't quite grasp:</p>
<blockquote>
<p>The recombination $R(T,n,p)$ rate depends on the ionization energy, temperature $T$, and carrier concentrations $n$, $p$. As the recombination rate must be zero if one of the carrier concentrations $n$, $p$ is zero, it follows for the first non-vanishing term of a Taylor expansion: $$R(T,n,p) = r(T)np$$ </p>
</blockquote>
<p>The Taylor expansion, as I know it from the mathematics class, is defined only for functions of one variable. Besides that, there is always a point involved about which the expansion is carried out. Strictly speaking, $R$ is a function of three variables. And no point is given. I guess this is the kind of inaccuracy practiced among physicists in order not to bloat their argumentation, and generally understood -- among physicists.</p>
<p>So, how does an expansion of a function of three variables work and which point should I assume here?</p> | 5,065 | [
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<p>What is the name for a particle with zero mass, zero charge, no strong force, no weak force and has no energy?</p> | 5,066 | [
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<p>Plant X has a radius of 5000 km and is composed of two layers. </p>
<p>The first inner layer ranges from the centre to 2000 km from centre, it's density is 8 kg / dm^3. </p>
<p>The second layer ranges from 2000 km to 5000 km from the centre, it's density is 4 kg/ dm^3. </p>
<p>What is the gravitational acceleration inside the planet at 4000 km from it's centre?</p> | 5,067 | [
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<p>After reading about light polarization I understood, that if light is polarized:</p>
<ul>
<li>circularly left then the spin of each photon is parallel to the velocity</li>
<li>circularly right then the spin of each photon is antiparallel to the velocity</li>
<li>elliptically - then there's more one photons, then the others</li>
<li>linearly - then there's exactly the same number of both spins.</li>
</ul>
<p>But now my question is - if my above understanding is correct, then how can be linearly polarized light different, than not polarized at all? Both have the same amount of photons having spin parallel and antiparallel to the velocity.</p>
<p>In other words - what is the relation between spin of each photon (or distribution of spins of all photons) and polarization plane?</p>
<p>The problem can be rephrased as follows: when you consider a single photon, where does it "know" from whether it can go through a polarizer or no? Is there some vector property of a single photon, that must be aligned with the polarization plane of the filter? What is this property?</p> | 5,068 | [
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<p>I'm trying to design a quasi-simple vertical axis wind turbine, and a coworker came up with <a href="https://docs.google.com/drawings/d/1B-NzCTWUyBIhNcv9b46hKvyk6R-l4NXiVzGHsb01fTI/edit?hl=en&authkey=CNeWgdwL" rel="nofollow">this design</a> to focus the wind as it reaches the turbine in a wind tunnel. He says that there's going to be turbulence caused by some of the design factors, but I'm not quite sure why and he doesn't know why, either. Why, and where, would this design cause turbulence, and what improvements could be made to improve it?</p> | 5,069 | [
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<p>Given I have two identical balloons on earth, how will the buoyancy compare between the one filled with helium and another filled with hydrogen?</p>
<p>How can I calculate the ratio of buoyancy given two different substances and identical balloons?</p>
<p>I am also interested in the equations relating to this problem. </p> | 5,070 | [
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<p>I have recently come across some cosmological assertions (based on empirical data) about the universe being self contained in the sense that it is entirely capable of coming into existence from a zero-energy initial state . This is based on the observation that at grand scale the positive and negative gravity/energy etc. cancel out each other.</p>
<p>What do the terms positive and negative actually mean in this context ?</p> | 5,071 | [
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<p>Title says it all - recently I encountered a strange homework exercise on de Broglie dual theory with an electron wavelength of few millimeters - which implies the velocity lower than 1 m/s. I personally considered the problem very artificial and unrealistic, but it made me wonder - what is the smallest electron velocity recorded in experiments? What does the theory on the other hand say?</p> | 5,072 | [
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<p>Just need a clarification here, how the current is produced due to the movement of electrons, in an external circuit,having a very slow drift speed.</p>
<p>Normally in a battery there is high potential terminal and low potential. Using these two terminals the external circuit is closed. Now within the battery the direction of the current flow and the electron flow is opposite to that of the external circuit. If I consider that positive current is flowing from the positive terminal to the negative terminal of the battery through the external circuit then we can say that positive terminal is at higher potential then the negative terminal of the battery. </p>
<p>Now when we are closing the switch of an external circuit, in that case the electrons are moving from negative terminal to positive terminal of the battery, through the external circuit. But we also know that the drift speed is very slow, of the electron. But when we
switch on some of the electrical devices, within a fraction of second the device starts working. If drift sped of electron is low, so how the device is working so fast ,(near about the speed of light,I guess), as we know that current flows due to the flow of the electrons.So how it is possible, in spite of electrons are having such a low drift speed ?</p>
<p>Please help me guys !!!!! </p> | 5,073 | [
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<p>How did Kepler arrive at his <a href="http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion">laws</a>? If one already knows the distances to the planets (and the eccentricity of the orbits etc.) it is understandable how one might proceed to establish the second and the third Kepler's laws. However how did Kepler do this <em>without</em> knowing the distances? His third law seems a true revolution since it establishes the distances between the Sun and the planets (in astronomical units at least); it just seems such a huge and daring step ahead. What he was basing this on?</p> | 5,074 | [
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<p>We have some discussions in Phys.SE. about the <a href="http://physics.stackexchange.com/questions/90257/braiding-statistics-of-anyons-from-a-non-abelian-chern-simon-theory">braiding statistics of anyons from a Non-Abelian Chern-Simon theory, or non-Abelian anyons</a> in general. </p>
<p>May I ask: <strong>under what (physical or mathematical) conditions, when we exchange non-Abelian anyons</strong> in 2+1D, or full winding a non-Abelian anyon to another sets of non-Abelian anyons of a system, <strong>the full wave function of the system only obtain a complex phase, i.e. only $\exp[i\theta]$ gained</strong> (instead of a braiding matrix)? </p>
<p>Your answer on the conditions can be freely formulated in either physical or mathematical statements. This may be a pretty silly question, but I wonder whether this conditions have any significant meaning... Could this have anyon-basis dependence or anyon-basis independence. Or is there a <strong>subset</strong> or <strong>subgroup</strong> or <strong>sub-category</strong> concept inside the full sets of anyons implied by the conditions.</p> | 5,075 | [
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<p>An object sits on an inclined plane. The weight of the object will have a normal and parallel component. I always thought that the reaction of the plane was simply the negative of the normal component of the weight.</p>
<p>Similarly, an object swings on a pendulum. The weight of the object can be decomposed into a radial and tangential component. I assumed that the reaction (tension) of the string must be the negative of the radial component.</p>
<p>But several examples have made me doubt my assumptions. One exercice in my textbook involves determining the reaction on a mass as it slides down a parabolic surface, as a function of $\theta$, the angle the vertical makes with the surface at any given point. Under my assumptions about reaction force, the answer is so trivial as to make the exerice pointless (since they give you $\theta$), but instead the exerice launches into a lot of complicated reasoning involving the Frenet-Serret base and comes out with a very different answer to just $-mg\ sin(\theta)$.</p>
<p>Also, consider the second example I gave. If the object is swinging in a circle (to make it even simpler, say it has uniform circular motion), then it must have radial acceleration (centripetal, specifically). But that's impossible if the reaction is exactly the negative of the radial weight.</p>
<p>But then... how can I determine a reaction force? In the absence of the simple rule I gave in the first paragraph, what else is there? Can it be done without making assumptions about the motion (eg. if you suppose the motion of an object is uniform circular, you have a formula all ready for the centripetal force and may thus be able to deduce the reaction force).</p> | 5,076 | [
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<blockquote>
<p>[I]f you want a universe with certain very generic properties, you seem forced to <em>one</em> of three choices: (1) determinism, (2) classical probabilities, or (3) quantum mechanics. [My emphasis.]</p>
</blockquote>
<p><sup>Scott Aaronson, <a href="http://www.cambridge.org/9780521199568" rel="nofollow"><em>Quantum Computing since Democritus</em></a></sup></p>
<p>Aaronson then proceeds by arguing that there are only two theories that are "like" probability theory: probability theory itself and quantum mechanics. Probability theory is based on the $1$-norm, whereas quantum mechanics is based on the $2$-norm.</p>
<blockquote>
<p>Call $\{v_1,\ldots,v_N\}$ a <em>unit vector in the $p$-norm</em> if $|v_1|^{\ p}+\cdots+|v_N|^{\ p}=1.$</p>
</blockquote>
<p>The slide below is from a presentation of his.</p>
<blockquote>
<p><a href="http://www.scottaaronson.com/talks/latke-aaronson.ppt" rel="nofollow"><img src="http://i.stack.imgur.com/NeOio.png" alt="[]"></a></p>
</blockquote>
<p>Now, <a href="http://math.stackexchange.com/q/378751/56801">it seems</a> that there is yet another candidate out there: the $0$-norm. For <em>this</em> purpose one would have to define $0^0=0$, and, if one does, one has a theory "like" probability theory that <em>is</em> determinism. <br>($0^0$ is <a href="http://en.wikipedia.org/wiki/Indeterminate_form#The_form_00" rel="nofollow">indeterminate</a>, which, I understand, means that you can do as you please, as long as you do it consistently.)</p>
<p>It was <a href="http://math.stackexchange.com/a/378788/56801">remarked</a> that the $0$-norm can be seen as a special case of both the $1$ and $2$-norms, in fact, that it can even be defined as the intersection between the two.</p>
<p>From there on I'm sort of questioning the original trilemma posed by Aaronson. It seems one can choose one of three possible realities; <em>not</em> the three that were mentioned, but rather options 1, 2 and 3:</p>
<p>$$\begin{array}{|l|c|c|c|}
\hline
&\text{Determinism}&\text{Classical probabilities}&\text{Quantum mechanics}\\
\hline
\text{Option 1}&\color{green}{\text{True}}&\color{green}{\text{True}}&\color{green}{\text{True}}\\
\hline
\text{Option 2}&\color{red}{\text{False}}&\color{green}{\text{True}}&\color{red}{\text{False}}\\
\hline
\text{Option 3}&\color{red}{\text{False}}&\color{red}{\text{False}}&\color{green}{\text{True}}\\
\hline
\end{array}$$</p>
<p>Scientific evidence favours quantum mechanics. That seems to rule out Option 2 (by, e.g., <a href="http://en.wikipedia.org/wiki/Bell%27s_theorem" rel="nofollow">Bell's theorem</a>), but, mathematically, doesn't seem to point to Option 3 <em>only</em> (meaning, of course, that <em>I</em> don't see it ruling out Option 1). (Bell's theorem <a href="http://en.wikipedia.org/wiki/Counterfactual_definiteness" rel="nofollow">is sort of empty</a> under determinism.)</p>
<p>How does one rule out that reality can be described by Option 1, notwithstanding the fact that it's certainly <em>easier</em> (and more practical) to describe it by Option 3? In what sense is Option 3 the scientific one, if it is <em>indeed</em> the scientific one? (Some might say that quantum mechanics <em>is</em> deterministic, but <em>then</em>, according to the table, it is <em>also</em> classically probabilistic.)</p>
<p>Taking it possibly further then necessary: <em>If</em>, on scientific grounds, we can't make a distinction between Option 1 and Option 3, isn't the whole thing (i.e., the statuses of determinism and classical probability) just exclusively philosophical?</p> | 5,077 | [
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<p>my question concerns the interaction of light and matter in a semi-classical approach.
(Quantized Atoms, Classical Fields)</p>
<p>In the Coulomb gauge (div A = 0 , $\phi$=0) we have $E = -\frac{1}{c}\partial_{t}A$ and
$B = rot(A)$. </p>
<p>Let's now consider a system of N charged particles (all denoted by an index k). </p>
<p>Let $H_{0}$ be the unperturbed time-independent Hamiltonian and suppose that the eigenvalue problem corresponding to this Hamiltoninan is solved. </p>
<p>Let $H_{1}=-\sum\limits_{k=0}^{N} \frac{e_{k}}{m_{k} c} A(x_{k},t) \cdot p_{k} + \sum\limits_{k=0}^{N} \frac{e_{k}^2}{2 m_{k} c^2} A(x_{k},t)^{2}$ be the time-dependent pertubation. </p>
<p>The atom is now placed at the origin.
The wavelength of the considered light is large compared to the diameter of the atom.
Hence we have approximately $A_(x_{k},t)\psi(x_{1},...,x_{n}) \approx A_(0,t)\psi(x_{1},...,x_{n})$. (Note that the atom is placed at the origin). </p>
<p>Now the second term in the perturbed Hamiltonian $H_{1}(t)$ (proportional to A^{2})
is of the form $\lambda \cdot f(t)$ for some real number $\lambda$ and some scalar time-dependent function f(t) using this approximation. </p>
<p>Nowit is said that this term only causes a phase factor in the wave function $\phi_{I}(t)$
viewed in the interaaction picture. I don't really understand why that is the case.
A time -depnedent Hamiltonian does not trigger in genereal a propagator of the form exp( i*...) . </p>
<p>Can someone help me with this question??</p>
<p>Thanks in advance for the responses. </p> | 5,078 | [
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<p>For a missile travelling from (0,0) at angle $\theta$ (to the horizontal) and initial velocity $u$, the y (vertical) position at time t is given by</p>
<p>$s_{y} = u\sin (\theta) t - 0.5gt^{2}$</p>
<p>and the x position id</p>
<p>$s_{x} = u\cos(\theta)t$,</p>
<p>but I am struggling to calculate the angle $\theta_{t}$ at time $t$ to the horizontal. For example when the missile reaches its apex the angle is zero, after which it will be negative and hopefully on arrival it will be $-\theta$.</p>
<p>So my thinking is to differentiate $s_{y}$ w.r.t. $t$ I will in effect get the gradient and hence I can arctan this to get the angle $\theta_{t}$.</p>
<p>$s'_{y} = u\sin (\theta) - gt$</p>
<p>So</p>
<p>$\theta_{t} = \arctan(u\sin (\theta) - gt)$</p>
<p>Is this line of thinking correct? If not, lease explain how to figure this out. Thanks in advance.</p>
<p>EDIT
I should admit that I am sure what I have done is not correct as it doesn't even work for $t=0$, but I am at a loss as to how to figure this (seemingly easy) problem out.</p>
<p>EDIT 2
Another idea is to simply do</p>
<p>$gradient = s_{y}(t)/S_{x}(t)$ at time $t$
and then $\theta_{t} = \arctan(\frac{u\sin (\theta) t - 0.5gt^{2}}{u\cos(\theta)t})$ which works much better.</p> | 5,079 | [
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<p>I have read many descriptions of electron double slit experiment but I could not find the description from the first principles of quantum mechanics. Most of the descriptions makes comparison with light waves or water waves and after some arguments from optics explain why the interference happens. Light waves and water wave description are not fundamental, they are phenomenological models. Could somebody explain the electron double slit interference only from the first principles of quantum mechanics? I know the answer from the Feynman path integral approach but I would like to understand it from the pre-Feynman Integral approach. </p> | 5,080 | [
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<p>Quantum dots are quantum systems that are confined by definition on the nano scale. Why didn't people study similar systems on a much smaller scale, something as small as the dimension of the nucleus? Is it practically difficult? or useless?</p>
<p>R.</p> | 5,081 | [
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<p>Can anyone explain why $T_{\mu \nu} = \frac{2}{\sqrt{-g}} \frac{\delta \mathcal{L}_M}{\delta g^{\mu \nu}} $, other than justifying it from the Einstein field equations?</p> | 5,082 | [
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<p>$\newcommand{\ket}[1]{\left| {#1} \right> }$
I have no academic background in physics, but I'm attempting to study quantum computation.</p>
<p>I have read that a quantum system of two qubits is represented by normalized combinations of the basis $\left\{ \ket{00},\ket{01},\ket{10},\ket{11} \right\} $.
A measurement was defined only for a single qubit of the two - that is, a state represented by $\ket{0}\otimes(a\ket{0}+b\ket{1})+\ket{1}\otimes(c\ket{0}+d\ket{1})$ can have its first qubit measured and collapse to either $\ket{0}\otimes(a\ket{0}+b\ket{1})$ or $\ket{1}\otimes(c\ket{0}+d\ket{1})$ with the appropriate probabilities, and a similar thing can be done to the second qubit.</p>
<p>The paper did say that the are other kinds of measurement, such as comparing the two qubits, but they are all equivalent to performing this type of measurement after a unitary transformation. From this I infer that the general representation of measurement is taken by splitting a basis $\mathcal{B}$ into two new bases $\mathcal{B}_1, \mathcal{B}_2$ of equal sizes, and then the state collapses to its projection to either $\mathcal{B}_1$ or $\mathcal{B}_2$ with appropriate probabilities.</p>
<p>What I don't understand is why do $\mathcal{B}_1$ and $\mathcal{B}_2$ have to be of equal sizes - for example, would it be possible for me to measure a system $a\ket{00}+b\ket{01}+c\ket{10}+d\ket{11}$ with the bases $\left\{\ket{00}\right\},\left\{\ket{01},\ket{10},\ket{11}\right\}$, so that it will collapse to $\ket{00}$ with probability $|a|^2$ and to $b\ket{01}+c\ket{10}+d\ket{11}$ with probability $|b|^2+|c|^2+|d|^2$?</p>
<p>If not, is there an explanation (for a non-physicist) as to why this is?</p>
<p>Thanks in advance.</p> | 5,083 | [
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<p>My understanding from my QFT class (and books such as <a href="http://rads.stackoverflow.com/amzn/click/0521469465" rel="nofollow">Brown</a>), is that many-particle QM is equivalent to field quantization. If this is true, why is it not an extremely surprising coincidence? The interpretation of particles being quanta of a field is -- at least superficially -- completely different from the quantum mechanical description of N point particles.</p> | 5,084 | [
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<p>Quantum search enables square-sped up search for marked element. When there are multiple maked element, grover search provides only superposition of them. If I want to find all the marked elements, not superposition, I could try this:</p>
<p>1) Do Grover search, get superposition of t marked ele, </p>
<p>2) observe ele space, get one marked ele,</p>
<p>3) remove that ele,</p>
<p>4) goto 1)</p>
<p>This takes time step $O(\sqrt{\frac{N}{t}}+\sqrt{\frac{N-1}{t-1}}+\dots+\sqrt{\frac{N-t+1}{1}})$.</p>
<p>My question is, is this optimal?</p> | 5,085 | [
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<p><a href="http://en.wikipedia.org/wiki/navier-stokes_equations">Navier-Stokes equation</a> is non-relativistic, what is relativistic Navier-Stokes equation through Einstein notation?</p> | 5,086 | [
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<p>I have a general question concerning a given interacting Lagrangian:</p>
<p>$$\mathfrak{L}_I = \frac{g}{\Lambda^2} \bar{\chi} \ \gamma^\mu \gamma_5 \ \chi \ \partial^\nu F_{\mu\nu}$$</p>
<p>where $F_{\mu\nu}$ is the electromagnetic field strength tensor. $g$ is a coupling constant and $\Lambda$ a cutoff-scale.</p>
<p>My question is pretty simple: What do the coupling constant and cutoff scale actually describe? Why is it necessary to introduce them?</p> | 5,087 | [
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<p>I am trying to determine the boltzmann constant by using a bipolar junction transistor.</p>
<p>In my circuit (apparently I don't have enough point to join a image sorry), the Ebers and Moll model gives the relation
$ i_c = I_s\exp\left(\frac{V_{BE}}{V_T}\right)$</p>
<p>where</p>
<p>$ V_T= \frac{k_b\cdot T}{q}$
and $V_{BE}$ is the difference of potential between the emiter and the base. </p>
<p>I'm plotting the $\log(i_c)$ as a function of $V_{BE}$ and use the slope of the line ($\alpha$) to deduce boltzmann constant. So</p>
<p>$ log(i_c)= \alpha\cdot V_{BE} + b $</p>
<p>from which I deduce</p>
<p>$k_b = \frac{q}{\alpha\cdot T\cdot \ln(10)}$</p>
<p>I have done that for 4 different temperatures.
I average the different values of $k_b$ to find $k_b = 1.57\cdot 10^{-23}$</p>
<p>How can I calculate the error margin for each of the $\alpha$ coefficient and how do I calculate the error for the mean coefficient $\bar\alpha$?</p> | 5,088 | [
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<p>Could a particular Standard Quantum Mechanics representation be a constrained 2 + 1 space-time theory (membrane theory) ?</p>
<p>(i) This question is motivated by a possible (approximative) analogy with Matrix theory for M-Theory (see this <a href="http://hep1.c.u-tokyo.ac.jp/workshop/komaba99/taylor.ps" rel="nofollow">reference</a> and these blogs articles <a href="http://motls.blogspot.fr/2012/05/matrix-theory-novel-alternative-to.html?m=1" rel="nofollow">1</a> and <a href="http://motls.blogspot.fr/2012/06/why-matrix-theory-contains-membranes.html?m=1" rel="nofollow">2</a> )</p>
<p>(ii) More precisely, standard quantum mechanics is a (infinite) matrix theory (or operator theory), which basics degrees of freedom as represented as $O_{lm}(t)$, where $O$ is some operator. An observable $O(t)$ is an hermitian operator. We could so consider $lm$ as a (maybe non-trivial) discretization of some compact 2-dimensions. So it is expected that there exists a correspondance between $O_{lm}(t)$ and some function $O(\sigma_1, \sigma_2, t)$ defined on a 2D manifold (like a plan, a sphere, a torus, or maybe a Klein Bottle)</p>
<p>(iii) If we restrict the infinite operators of Quantum mechanics to a $N*N$ matrix, we will find for observables, $N*N$ hermitian matrix, so living in the adjoint representation of $SU(n)$. So we could expect, as $N$ goes to infinity, that this is representing some diffeomorphism for the 2D manifold.</p>
<p>(iv) It will be interesting to see, if it is only the topology of the 2D manifold which is important, or/and the shape and size (the geometry).</p>
<p>(v) Here, we don't want at all to say that Quantum mechanics is replaced by a non-sense classical mechanics, it's only, if it is possible, a different representation of Quantum Mechanics. In particular, it will be very interesting to see how quantum constraints (Heinsenberg inequalities) are expressed in this representation</p> | 5,089 | [
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<p>I would particularly like to know why this process is considered the main search mode for Tevatron but useless for search at LHC.</p> | 5,090 | [
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<p>I just started learning about vector components and relative motion. I don't understand what relative to something means. I looked online but none of the explanations are helpful. </p>
<p>If someone could give me a very simple explanation, it would be appreciated.</p> | 5,091 | [
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<p>Introduction:</p>
<p>When toying with gravitational and electromagnetic equations in my undergrad days I stumbled upon this interesting relationship. </p>
<p>With the very childish hopes of unifying gravitation and electromagnetism all by myself;) I thought to equate the classical gravitational field to the classical electric field... My motivation for doing this had much to do with the expectation that the energy densities would eventually match at some radial limit (If we are working with simple spherical fields). </p>
<p>\begin{equation}
F_{G}\equiv F_{E}
\end{equation}</p>
<p>\begin{equation}
\frac{-GMm}{r^{2}}\mathbf{\hat{r}}=\frac{-kQq}{r^{2}}\mathbf{\hat{r}}
\end{equation}</p>
<p>Assuming that there is a constant charge to mass ratio for all mass-energy (I admit at first seems absurd but my reasons for doing this is much deeper than I can explain at this time. A previous question of mine regarding a Machian mechanism for inertial emergence dives deeper into this concept and it somewhat served as a motivation for the previous formula)</p>
<p>\begin{equation}
\frac{Q}{M}=\frac{q}{m}=\sqrt{4\pi \varepsilon _{0}G}
\end{equation}</p>
<p>\begin{equation}
U_{E}=\frac{\varepsilon _{0}}{2}\int \left | \mathbf{\vec{E}} \right |^{2}dV
\end{equation}</p>
<p>\begin{equation}
U_{E}=\frac{\varepsilon _{0}}{2}\int_{R}^{\infty }\frac{Q^{2}}{\left ( 4\pi \varepsilon _{0}r^{2} \right )^{2}}\left ( 4\pi r^{2} \right )dr
\end{equation}</p>
<p>\begin{equation}
U_{E}=\frac{Q^{2}}{8\pi \varepsilon _{0}R}\rightarrow Q=Q_{G}
\end{equation}</p>
<p>Here is where things get interesting. When you plug the Schwarzschild radius into the formula you get a very interesting result. This seemed the ideal choice for a value of $R$ since this is the limit where gravitational energy reaches a maximum.</p>
<p>\begin{equation}
U_{E}=\frac{Q_{G}^{2}}{8\pi \varepsilon _{0}R}\rightarrow R=\frac{2GM}{c^{2}}
\end{equation}</p>
<p>\begin{equation}
U_{E}=\frac{1}{4}Mc^{2}
\end{equation}</p>
<p>These days I have a greater respect for the general relativistic theory on gravitation, however since GR reproduces classical laws at the v << c limit I couldn't help but remain intrigued by this result. </p>
<p>Conclusions:</p>
<p>It is as if mass-energy is not stored IN the object itself but the gravitational field surrounding it. This should not be too surprising since mass energy equates to space-time curvature by virtue of EFE. </p>
<p>What matters here to me is that even though this approach is unfortunately classical, the order of magnitude for the energy requirements are the same.</p>
<p>Questions:</p>
<ol>
<li><p>Has anyone ever come across this before? If so, what is the publication?</p></li>
<li><p>Is this result an artifact of mathematical manipulation or does it genuinely admit new information? If it is an artifact can someone explain to me why it is? </p></li>
<li><p>Is there any suggestions for incorporating the magnetic field energy in this formula?</p></li>
</ol> | 5,092 | [
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<p>A distance on a straight line from point $a$ to $b$ is $2 km$. A student walks from this line with a speed of 4km/h and another student walks with a speed of 6km/hour. what is the average velocity and average speed of student?</p> | 5,093 | [
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<p>We all know that subatomic particles exhibit <a href="http://en.wikipedia.org/wiki/Introduction_to_quantum_mechanics#Copenhagen_interpretation" rel="nofollow">quantum behavior</a>. I was wondering if there's a cutoff in size where we stop exhibiting such behavior.</p>
<p>From what I have read, it seems to me that we still see quantum effects up to the nanometer level.</p> | 5,094 | [
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<p>One explanation I read:</p>
<p>Because of the wing's geometry, the "upper" side of the wing is longer, so the air has to travel faster:</p>
<p><img src="http://i.stack.imgur.com/HDgVA.jpg" alt="enter image description here"></p>
<p><strong>My wondering</strong>: Who said (and what was his/her explanation) that air must travel the distance above and under the wing in the <em>same</em> time?</p>
<p>I'll try to be clearer. Considering the below image, does <strong>m1</strong> and <strong>m2</strong> meets at the same point exactly at the same time on point <strong>T</strong>?</p>
<p><img src="http://i.stack.imgur.com/j7Icc.png" alt="enter image description here"></p> | 17 | [
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<p>In a continuous medium the Lorentz force density is known to be written in the form:</p>
<p>$f_\alpha = F_{\alpha \beta} J^\beta$,</p>
<p>where $F_{\alpha \beta}$ is an electromagnetic field tensor, and $J^\beta$ is a charge-current density.</p>
<p>Whould it be correct saying that the action of this force on charge-current density reads as follows:</p>
<p>$\frac{dJ^\alpha}{dt} = f^\alpha = F^{\alpha \beta}J_\beta$ ?</p>
<p>It seems reasonable because in this case the charge-current density 4-vector undergoes Lorentz transformation, i.e. it is "accelerated" along direction of $\vec{E}$ proportionally to the magnitude of $\vec{E}$, and "rotated" around direction of $\vec{B}$ to the angle proportional to the magnitude of $\vec{B}$.</p> | 5,095 | [
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<p>What is the motivation for assuming "Page" scrambling for Hawking radiation?</p>
<p>Obviously, at the semiclassical level, we want the outgoing Hawking radiation to look thermal and mixed. However, surely there are possible pure states which are scrambled enough that it looks effectively thermal when not nearly all of them are taken into account, but yet not satisfy the "Page" property. Only Susskind calls it Page, but whatever...</p>
<p>That if you take less than half the Hawking radiation, it's maximally entangled with the rest. Is this assumption far stronger than necessary?</p>
<p>It leads to bizarre conclusions like Presskill-Hayden and AMPS.</p> | 5,096 | [
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