question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>How much force (Newtons) is required to compress normal air in a chamber to 2 atm?
For example, if I had a sealed piston pump, how much force would need to be exerted in order for the air to be compressed to 2 atm?</p>
<p>Also, a side note, if I were to compress air from 1 atm to 2 atm, would this have the total volume? </p> | g11113 | [
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<p>I have been going back over this problem with a friend for the better part of a day:</p>
<p>A potential is glued to a cube-shaped insulator so that outside of the insulator the field is the same as a point particle. How can we calculate the surface charge distribution and the volume charge distribution?</p> | g11114 | [
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<p>Suppose there are two light beams. One is red while the other is violet. The energy of both is the same.</p>
<p>Which one of these beams has a larger number of photons, or is the number of photons relevant?</p> | g11115 | [
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<p>I'm reading a paper on 2D hydrodynamics, specifically on the drag of a rod in a 2D fluid. It is a low-Reynolds number regime, therefore linear hydrodynamics and the velocity of the rod can be expressed via:</p>
<p>$$v_i^{rod} = \mu_{ij}F_j$$</p>
<p>then it says: By in-plane rotational symmetry combined with the $\hat{n} → -\hat{n}$ symmetry of the rod, the mobility tensor must take the form:</p>
<p>$$\mu_{ij} =\mu_\parallel\hat{n}_i\hat{n}_j + \mu_\perp(\delta_{ij}-\hat{n_i}\hat{n_j})$$</p>
<p>Here, $\mu_\parallel$ and $\mu_\perp$ are the mobilities for motion parallel and perpendicular to the rod's long axis, respectively.</p>
<p>I'm having a hard time connecting the dots with this logic, can anyone show me how this follows?</p> | g11116 | [
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<p>A rear-wheel driven large sedan, weighing $4 ,120$ lbs, with a $10¼$-foot wheel base, traveled up an inclined ramp of $11$ degrees. The vehicle left the ramp at $22$ mph, traveled through the air for $26$ feet, tumbled forward (flipped) about $60$ degrees, and landed on its windshield upside down in a ditch $7$ feet lower than the ramp with the nose of the car pointed back toward the end of the ramp. Tire marks were found on the ramp for $45$ feet from start to finish.</p>
<p>Which makes more sense: the tire marks were due to locked brakes on all four wheels (deceleration)? Or the tire marks were due to “laying rubber” (acceleration)? The vehicle could attain an acceleration of $13.3$ ft./sec.2</p> | g11117 | [
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<p>paraxial plane wave = $\exp{(-jkz)}$ for waves propagating to the right</p>
<p>I can't figure out why it's not $\exp{(+jkz)}$. Any help would be greatly appreciated, thank you.</p> | g11118 | [
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<p>When we have Hubble constant and it's inverse Hubble Time (1/H) what units are they measured in? I know Hubble constant is in "km/s per Mpc" but is there any other units which are popular used with it, and if so is there any conversion between the two?
And would Hubble Time unit still be in billion years, seeing it is just displaying a time? </p> | g11119 | [
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<p>I am confused about the set of quantum states.</p>
<p>I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.)</p>
<p>In quantum physics, the set of all states is not a simplex. Does this have anything to do with the superposition principle? If we didn't have the superposition principle in quantum mechanics, would the set of states be a simplex, like in the classical case?</p>
<p>Thanks for your help!</p> | g11120 | [
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<p>In my general relativity textbook (Carroll), he says that "the geodesic equation (together with metric compatibility) implies that the quantity</p>
<p>$\epsilon =-g_{\mu\nu}\frac{dx^\mu}{d\lambda}\frac{dx^\nu}{d\lambda}$</p>
<p>is constant along the path. For any trajectory we can choose the parameter $\lambda$ such that $\epsilon$ is a constant; we are simply noting that this is compatible with affine parameterization along a geodesic."</p>
<p>Maybe I'm missing something really obvious, but where does the conservation of this quantity come from?</p> | g11121 | [
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<p>The second answer to this <a href="http://physics.stackexchange.com/questions/54323/collision-of-two-photons">question</a> describes how this process might occur, and I'm curious for more details about it:</p>
<ol>
<li>What is the probability distribution of the interaction producing electron-positron pairs (and what's the general process for calculating it)?</li>
<li>Is it possible to produce beams of positrons and/or electrons, through this process? </li>
</ol>
<p>I would love some references that describe this kind of interaction in depth.</p> | g11122 | [
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<p>Lawrence Krauss and James Dent <a href="http://prl.aps.org/abstract/PRL/v111/i6/e061802" rel="nofollow">recently proposed a mechanism</a> for producing the observed scale of dark energy. This proposal was inspired by the <a href="http://en.wikipedia.org/wiki/Seesaw_mechanism" rel="nofollow">see-saw mechanism</a> that produces light yet non-zero neutrino masses. </p>
<p>I can't help but notice there are <a href="http://arxiv.org/abs/hep-ph/0410140" rel="nofollow">many reasons to doubt the see-saw mechanism package</a> since it suffers from the the flavor, CP, and gravitino problems and several alternatives have been proposed. </p>
<p>Would it be feasible to come up with a mechanism based on the alternatives to the seesaw and hence extend Krauss' and Dent's proposal?</p> | g11123 | [
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<p>I am having trouble understanding how Eq (2.6) in <a href="http://arxiv.org/abs/0706.3384" rel="nofollow">this</a> paper <a href="http://arxiv.org/pdf/0706.3384v2.pdf" rel="nofollow">(PDF)</a>
$$Z[\mathcal{L},\mathcal{M}_{n}]\propto\langle\Phi(u,0)\tilde{\Phi}(v,0)\rangle_{\mathcal{L}^{(n)},\mathbb{R}^{2}}$$</p>
<p>generalizes to Eqn (2.7)
$$\langle\mathcal{O}(x,y;\mbox{ sheet i })...\rangle_{\mathcal{L},\mathcal{M}_{n}}=\frac{\langle\Phi(u,0)\tilde{\Phi}(v,0)\mathcal{O}_{i}(x,y)...\rangle_{\mathcal{L}^{(n)},\mathbb{R}^{2}}}{\langle\Phi(u,0)\tilde{\Phi}(v,0)\rangle_{\mathcal{L}^{(n)},\mathbb{R}^{2}}}$$</p>
<p>It's quite possible that some of you with more experience in CFTs will be able to immediately answer this for me without the context, but here it is anyway: we want to evaluate the partition function on the Riemann manifold $\mathcal{M}_{n}$ which consists of $n$ flat 2D sheets joined together at the branch cut between $u$ and $v$ in the manner shown in Fig 1 in the paper. We do this by modeling the manifold as $n$ disconnected flat sheets with twist fields inserted at the branch points. It turns out that the original partition function is proportional to the correlation function of two twist fields as in Eq. 2.6.</p>
<p>Later on, the paper makes use of the correlation function with insertions of the stress-energy tensor, so that generalization (with the equality sign) is crucial. Your help is appreciated!</p>
<p>In particular, how does this NOT mean that the partition function in Eq 2.6 is not actually proportional to the two-point function but is simply equal to one? (I am replacing the $\mathcal{O}$'s in (2.7) with one to make this claim)</p> | g11124 | [
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<p>I understand that <a href="http://en.wikipedia.org/wiki/Quantum_field_theory" rel="nofollow">QFT</a> is the theoretical framework for combining <a href="http://en.wikipedia.org/wiki/Quantum_mechanics" rel="nofollow">QM</a> and <a href="http://en.wikipedia.org/wiki/Special_relativity" rel="nofollow">Special Relativity</a>, but as I understand it, though even without proof or experimental confirmations; has QFT managed to "behind all the rigor" design a mathematical construct that fully explains and logically computes there conflicts? Or does it continue to struggle for a formulary solution? </p> | g11125 | [
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<p>The formula of time dilation at constant speed v is known.
The formula $T_0'= T /\gamma$ where gamma is the Lorentz factor. </p>
<p>I would be interested, as Einstein's original formula was. </p>
<p>I've checked in "Zur Elektrodynamik bewegter Körper".
Something was on page 904 (original page number of Einstein). </p>
<p>There is indicated $\tau=t*\sqrt{1-v^2/V^2} = t-(1-\sqrt{(v^2/V^2)})*t$</p>
<p>$V$ is the speed of light.</p>
<p>Is that the original formula? </p> | g11126 | [
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<p>In relativity, an event A can occur before another event B in one frame while A may occur after
event B in another. In quantum mechanics, we may measure the spin of two entangled electrons: If you measure spin of an electron to be +1/2 then the other would have opposite spin, so when you measure the spin of one electron the wave function for both electron collapses. But, if a person measures the spin of electron A before another person measures spin of electron B in one frame while in other frame the spin of electron B is measured first, then when does wave function collapse?</p> | g11127 | [
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<p>I've been having a go at programming an orbital simulator from scratch (without using any existing libraries) using the formula below to find the acceleration first for particle A and then for particle B towards each other.</p>
<p>$$F = \frac{m_Am_BG}{r^2}$$</p>
<p>$$a_{AB} = \frac{m_BG}{r^2}$$
$$a_{BA} = \frac{m_AG}{r^2}$$ </p>
<p>The particles have masses: $m_A = 300\times10^{23}, m_B = 10\times10^{23}$</p>
<p>This produces what looks to be almost a correct orbit with the lighter particle B orbiting around particle A however particle A does not move in an ellipse rather a half ellipse before continuing upwards with another half ellipse and so on. This can be seen in the image below:</p>
<p><img src="http://i.stack.imgur.com/YDYOT.png" alt="Orbits issue image"></p>
<p>The time step does not seem to be an issue as I've adjusted that and it made no difference, it is currently set to $0.000001\mathrm{s}$. I'm not sure as to what might cause this.</p> | g11128 | [
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<p>I wonder how I can solve the <a href="http://mathworld.wolfram.com/BrachistochroneProblem.html" rel="nofollow">Brachistochrone problem</a> for 3 points?
The matter starts from point A that is the highest point and it must pass from B and must finish with point C. (No any friction in the system)
I wonder what the shortest time path for that problem?</p>
<p>Is it enough to use <a href="http://en.wikipedia.org/wiki/Brachistochrone_curve" rel="nofollow">Johann Bernoulli's solution</a> from A to B and then Use the solution from B to C? </p>
<p>Or do I need to follow a different way to solve the shortest time path problem for 3 points?</p> | g11129 | [
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<p>The <a href="http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation" rel="nofollow">cosmic microwave background</a> (CMB) has a modern temperature of about 2.7 K. At the time of the origin of the CMB, about 13.6 billion years ago, it had a temperature of about 3000 K.</p>
<p>There is a well-known problem that the Sun should have been too faint at the time the Earth formed, about 4.6 billion years ago, to allow the Earth to avoid becoming a permanent <a href="http://en.wikipedia.org/wiki/Snowball_Earth" rel="nofollow">Snowball Earth</a>. This problem is called the <a href="http://en.wikipedia.org/wiki/Faint_young_Sun_paradox" rel="nofollow">faint young Sun paradox</a>.</p>
<p>I was thinking about that, and it occurred to me that those two things may not be completely unrelated.</p>
<p>What was the temperature of the CMB at the time the Earth formed, and what effect would that temperature have on the equilibrium temperature of the Earth?</p>
<p>It seems to me that there should be two effects in play.</p>
<ol>
<li><p>The equations describing the equilibrium temperature of the Sun then needs to be adjusted for the fact that rather than being a blackbody radiating to a near zero background, it would be radiating to a background with a significant temperature of its own. I would think that would raise the required temperature for the Sun to achieve radiative equilibrium there-by making the Sun brighter.</p></li>
<li><p>The equilibrium temperature of the Earth should also be boosted by the increased temperature of the CMB for similar reasons of having a less efficient heat 'sink'.</p></li>
</ol>
<p>Could those two effects together have shifted the equilibrium temperature of the Earth enough to solve the faint young Sun paradox?</p>
<p>Edit: Having done some more googling on it, the CMB would only have been about a degree or so warmer than it is now because 4.6 billion years only corresponds to a Z of about 0.4. This isn't anywhere near enough to solve the faint young Sun paradox. I'm going to leave this question in place just so if someone else has the same idea this will explain why it can't solve the paradox.</p> | g11130 | [
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<p>For elastic collisions of n particles, we know that momentum in the three orthogonal directions are independently conserved:$$ \frac{d}{dt}\sum\limits_i^n m_iv_{ij} =0,\quad j=1,2,3$$</p>
<p>From this, it follows there's also a corresponding scalar quantity conserved:$$\frac{d}{dt}\sum\limits_i^n m_i(v^2_{i1} + v^2_{i2} + v^2_{i3}) = \frac{d}{dt}\sum\limits_i^n m_iv^2_i =0,\quad j=1,2,3$$</p>
<p>So why is there a need to put 1/2 in front of this conserved scalar quantity, kinetic energy?</p> | g501 | [
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<p>Since GR assumes that gravity waves travel at speed c, we expect we would be able to some day detect an aberration effect similar the that of light. Of course, gravity waves are so tiny in magnitude, we haven't yet unambiguously detected them, so aberration measurements aren't yet possible.
However, planetary orbits appear to behave as if gravity waves have "infinite" speeds, since they aren't seemingly affected by the finite time between where a planet is currently located and the time lapse from Sun's force.</p>
<p>Can someone explain why planetary orbits behave as if gravity waves have Newtonian-like "infinite" velocities? I'd appreciate a response that doesn't resort to tensor notation.</p> | g11131 | [
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<p>The Dieke diagrams like this:</p>
<p><img src="http://i.stack.imgur.com/2CVSU.jpg" alt="Dieke diagram"></p>
<p>could be easily found in internet.</p>
<p>But it is impossible to determine from where they get values initially, everyone is making cross-links. I'm especially interested in $\rm Tb^{3+}$ ion. </p>
<p>Please help me to find original works from the past, I think from very old times, so I will take from them experimental values to compare with my experimental data.</p> | g11132 | [
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<p>National Geographics TV has a series called "None of the above". In one episode the presenter shows that by stacking 4 bricks (here shown as 'xxxxxxxx') you can have one of the bricks completely hang free of the edge:</p>
<pre><code> xxxxxxxx
xxxxxxxx
xxxxxxxx
xxxxxxxx
[edgeedge]
[edgeedge]
</code></pre>
<p>It barely hangs free, but it does work if you are careful. I have found a more efficient way also using only 4 bricks:</p>
<pre><code> xxxxxxxx
xxxxxxxx xxxxxxxx
xxxxxxxx
[edgeedge]
[edgeedge]
</code></pre>
<p>This will let the brick be much further out. This gets me to think: Is there an even more efficient method - either using fewer bricks or a different way of stacking to shift the brick even further out? How do I compute the optimal shift lengths of each brick?</p>
<p>Edit:</p>
<p>After a few more experimentations it seems the optimal is symmetrical:</p>
<pre><code> xxxxxxxx
xxxxxxxx xxxxxxxx
xxxxxxxx
[edgeedge]
[edgeedge]
</code></pre>
<p>The lower brick will be at 50% over the edge. The two middle bricks will be pulled as far out as they can before they drop. So the hard part seems to be computing how far it can be pulled out. Experimentally it is around 1/3.</p> | g11133 | [
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-0.01718880608677864,
-0.018406562507152557,
-0.05180191993713379,
0.03484555333852768,
0.01007168274372816,
-0.04519060254096985,
0.009050775319337845,
-0.010263725183904171,
0.030806848779320717,
-0.020227013155817986,
-0.021... |
<p>When we calculate the spin-orbit interaction in a Hydrogen atom we just work in the electron's frame of reference: the proton is moving and produces a magnetic field which the electron's spin interacts with.</p>
<p>We can show <a href="http://en.wikipedia.org/wiki/Spin%E2%80%93orbit_interaction" rel="nofollow">here</a> that the answer is $$ \Delta H = \frac{2\mu_B}{\hbar m_e e c^2}\frac{1}{r}\frac{\partial U(r)}{\partial r} \mathbf{L} \cdot\mathbf{S}$$ where $U(r)$ is the potential energy = $eV(r)$ with $V(r) = \frac{1}{4\pi\epsilon_0}\frac{e}{r}$ for a proton.</p>
<p>NOW: I want to get the <strong><em>same</em></strong> answer from the <strong>reference frame of the proton</strong>, where the proton is stationary and the electron is moving.
Since Physics must be the same in all frames of reference, we should get the same answer.</p>
<p>I guess that the only this can happen is if the electron's magnetic field (due to its motion, i.e. charged particle moving around) interacts with the electron's own spin.</p>
<p>We can calculate the current density $\mathbf{j}$ of the electron in Hydrogen, and it is given by:
$$
j_\phi=-e\frac{\hbar m}{\mu r\sin\theta}\left|\psi_{nlm}\left(r,\theta,\phi\right)\right|^2
$$
(<a href="http://www.phys.spbu.ru/content/File/Library/studentlectures/schlippe/qm07-05.pdf" rel="nofollow">derivation found here</a> on page 6)</p>
<p>I could use the Biot-Savart law to calculate the magnetic field due to this current density:
$$\textbf{B} = \frac{\mu_0}{4\pi} \frac{1}{r^2} \int \textbf{J}d^3\textbf{r}$$
where the integration should be (at least classicaly) the along the current loop.</p>
<p>Here, I get stuck.</p>
<p>Does anyone know how to get the $\textbf{L}\cdot\textbf{S}$ factor from this approach?</p> | g11134 | [
0.035292401909828186,
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0.023012246936559677,
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0.04100159555673599,
0.009862575680017471,
-... |
<p>Physicists define the trace of an operator $\rho$ as the follows,</p>
<blockquote>
<p>$Tr(\rho)=\sum\limits_{|s\rangle \in B} \langle s| \rho |s\rangle$ </p>
</blockquote>
<p>where B is some orthonormal basis, and this quantity is basis independent. </p>
<p>If we swapped B with a non-orthogonal basis,C , which, if any, of the properties of the trace will be preserved? In particular, </p>
<ul>
<li>
1) Is it now basis dependent? (The intuitive answer seems to be YES, but can we do better?) </li>
<li> 2) Under what conditions (on C and $\rho$) will this value exceed the value of the actual trace? I will settle for an answer assuming $\rho$ is a density operator . </li> </ul>
<p>Thanks!</p> | g11135 | [
0.03140532970428467,
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0.029216652736067772,
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0.015835363417863846,
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0.03654719144105911,
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... |
<p>I'm asked to establish the following relations:</p>
<p>$\left( \frac{\partial C_V}{\partial V} \right)_{T,N} = \frac{T}{N} \left( \frac{\partial^2 P}{\partial T^2} \right)_{V,N} $</p>
<p>$\left( \frac{\partial (\beta F)}{\partial \beta} \right)_{V,N} = U $ where $\beta = \frac{1}{k_B T}$</p>
<p>I'm a bit puzzled by the first one since I can't seem to find a relation between the heat capacity $C_V$ and the other term in the equation, though I do know that $C_V = (\frac{\partial E}{\partial T})_V$</p>
<p>Note that F and U are the Helmholtz free energy and internal energy, respectively.</p>
<p>Also how does the fact that certain quantity are maintained constant throughout the differentiation should be accounted for when expanding say the left hand sides? </p>
<p>Any help would be appreciated.</p> | g11136 | [
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<p>I'm trying to model isotropic linear elastic deformation in two dimensions. In one dimension, I know that a linear elastic material can be thought of as a spring which obeys Hooke's law $F=-k\Delta x$. In two dimensions, I want to describe a material that obeys Hooke's law in both directions (for simplicity, let's say the x and y directions). I want to say that the deformation in one direction does not influence the deformation in the other directions (i.e. it is isotropic). </p>
<p>Because it is in two dimensions, I don't think the 'spring' analogy applies. Is there an analogous object similar to a spring but which obeys Hooke's law in a two dimensional isotropic sense? Also, since it is two dimensional, can I write Hooke's law as $\vec{F}=k\Delta \vec{x}$? Is there another way to describe hooke's law in higher dimensions?</p> | g11137 | [
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<p>So I'm reading <a href="http://rads.stackoverflow.com/amzn/click/1563475189" rel="nofollow">this book</a>, where after the preface and before the models there is a section called <em>General Notions and Essential Quantities</em>, which introduce some things I don't understand. They regard different temperatures of one system, especially in a non- or near equilibrium state. </p>
<hr>
<p>At first I give a direct quote (pages 17, 18, section "VI Particle Distribution over Velocities and Energy: Temperatures of Different Degrees of Freedom": </p>
<ul>
<li>"The Maxwellian distribution over translational energy $\epsilon$ of particle motion is represented by
$$f(\epsilon)=\ ...$$
The Boltzmann distribution for population $N_i$ of the $i$th energy level relative to the population $N_0$ of the ground energy level $E_0$ is
$$\tfrac{N_i}{N_0}=\tfrac{g_i}{g_0}e^\left({-\tfrac{E_i-E_0}{k T}}\right)$$
and relative to the total particle number $N$ of the given species is
$$\tfrac{N_i}{N}=\tfrac{g_ie^\left({-\tfrac{E_i}{k T}}\right)}{Q},\ \ \ \ Q=\sum g_ie^\left({-\tfrac{E_i}{k T}}\right).$$
Maxwellian and Boltzmann distributions determine the temperature of the considered system. In the equilibrium system the temperatures of different degrees of freedom (translational, rotational, vibrational, electronic) are equal. In the nonequilibrium system involving the subsystems of the indicated degrees of freedom the single temperature is absent. If in any subsystem the velocity distribution or the energy distribution may be approximate by Maxwellian or Boltzmann functions, these function determine the temperatures of the appropriate degrees of freedom. </li>
<li><ul>
<li><em>Translational temperature</em> (gas temperature, or temperature of translational degrees of freedom): This is the parameter of Gibbs canonical distribution of particles over velocities and energy of the translational motion of particles. It is represented by the qunatity $T$ in the Maxwellian distribution as previously described.</li>
</ul></li>
<li><ul>
<li><em>Rotational temperature</em> (temperature of rotational degrees of freedom): This is the parameter of Gibbs canonical distribution of molecues over rotational energy. It is represented by the quantity $T_r\equiv T_R$ in the Boltzmann distribution for a population $N^r_i$ of the $i$th rotational level:
$$\tfrac{N_i^r}{N_0^r}=\tfrac{g_i^r}{g_0^r}e^\left({-\frac{E_i^r}{k T_r}}\right)\tfrac{N^r_i}{N^r} = \tfrac{g_i^r e^\left({-\frac{E_i^r}{k T_r}}\right)}{Q(T_r)}.$$</li>
</ul></li>
<li><ul>
<li><em>Vibrational temperature</em>: ..."</li>
</ul></li>
</ul>
<p>This is then also followed by several partition functions $Q_i$, with $i=t,r,v,e$ and the formulas
$$\epsilon=\sum\epsilon_k,\ \ \ \ Q=\prod Q_k.$$</p>
<p>Wikipedia knows such quanities (<a href="http://en.wikipedia.org/wiki/Translational_partition_function" rel="nofollow">$Q_t$</a>,<a href="http://en.wikipedia.org/wiki/Vibrational_partition_function" rel="nofollow">$Q_v$</a>,<a href="http://en.wikipedia.org/wiki/Rotational_partition_function" rel="nofollow">$Q_r$</a>,<a href="http://en.wikipedia.org/wiki/Vibrational_temperature" rel="nofollow">$T_v$</a>,<a href="http://en.wikipedia.org/wiki/Rotational_temperature" rel="nofollow">$T_r$</a>)
but doesn't explain much about them.</p>
<hr>
<p>Now of course I could just give the name <em>temperature</em> to every composition of quantities, which happen to have energy as a unit, but I have a problem with the possibility of defining something like a new temperature (and the unique partition function), given that they are supposed to coincide in total equilibrium. </p>
<p>Viewed especially from the microcanonical ensamble, one defines temperature
$$\frac{1}{T}=\frac{\partial S(E,V )}{\partial E},$$
which as a variable is fixed by a single number - the curse of non-equilibrium thermodynamics. Say I break my system into parts like suggested above and it actually turns out that these aspects of the problem are describable by the distribution of an equilibrium system (Maxwell, Boltzmann, Gibbs). What is the temperature of the subsystem and how do I get to it? Is the plan to define objects which generate the variables $T_k$, like $T$ is canonical to $E$ in the sense of the entropy formula stated above? The counting of possible configurations (like over vibrational degrees of freedom) and therefore the associated entropy function should heavily depend on the type of degree of freedom. And then it wouldn't feel the functional dependences of the rest of the model. Why would the values for different $T_k$ overlap for the perfect equilibrium limit? Especially regarding translational degrees in the Boltzmann theory, when you consider spatially varying temperatures $\theta(\vec x)$. What would they have in common with a temperature derived from a counting of vibrational degrees of freedom? Is there a concept of a derivative with respect to just an aspect of the energy (translational/kintec, rotational, vibrational,...). The partition function seem to depend on these seperated energies after all. The computed expressions on wikipedia look very distinct. I also don't see how in this limit the factors $\frac{1}{Q(T_k)}$ would suddently join to one big partition function? How does this partitioning of the system work anyway?</p>
<p>I also have a problem with how to get the different temperatures from the partition function. In practice, I can solve an (empirical) equation of state like $pV=NkT$ for the temperature if I know $p,V$ and $N$. But how can I compute the different temperatures for the associated <a href="http://en.wikipedia.org/wiki/Grand_canonical_ensemble#Thermodynamic_quantities" rel="nofollow">more general</a> expression in statistical mechanics, when their knowledge implies a functional dependence of the temperature of a bath? </p> | g11138 | [
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0.024317290633916855,
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0.024701034650206566,
0.015051630325615406,
0.... |
<p>Is the detection of <a href="http://en.wikipedia.org/wiki/Gravitational_wave" rel="nofollow">gravitational waves</a> a reality with nowadays technology?
Are there recent news?</p> | g357 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/7819/why-does-venus-rotate-the-opposite-direction-as-other-planets">Why does Venus rotate the opposite direction as other planets?</a><br>
<a href="http://physics.stackexchange.com/questions/12140/why-does-every-thing-spin">Why does every thing spin?</a> </p>
</blockquote>
<p>As far as I can imagine, almost each celestial body, star, planet, solar-systems, galaxies do rotate on their center.
Where this come from ?
Is it the normal work of gravity?
And why Venus has a retrograde rotation? (Or, why all the solar systems rotate in the same way - except Venus?)</p> | g231 | [
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0.030476918444037437,
0.03993450850248337,
-0.011... |
<p>I have two pipes divided from main pipe. If I add one more pipe, what would be the amount of velocity in each pipes. I know the velocity of main pipe, then diameter and radius of each pipe.</p>
<p>Edit:</p>
<p>1) Viscosity - The liquid is Ethanol, viscosity would be 1.07 * 10^-3 Pa.s<br/>
2) Flow profile - can be either laminar or turbulent. It can be like, In one pipe it would be laminar and another pipe it would be turbulent.<br/>
3) Pressure would be 90mmHg<br/>
4) Main pipe length 50cm, diameter 6cm, velocity 21.22*10^-3 m/s<br/></p>
<ol>
<li>Branch 1 - length 9144cm, diameter 2cm.<br/></li>
<li>Branch 2 - length 1524cm, diameter 3cm.<br/></li>
<li>New Branch, Branch 3 - 500cm, diameter 1cm <br/></li>
</ol> | g11139 | [
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0.0... |
<p>Most of you will be familiar with the phenomenon: you have bought a new towel and you first have to wash it or use it a couple of times before it starts to work properly, i.e. dry your body after taking a shower instead of smearing out the water .</p>
<p>My simple question is: why is this the case? Why do new towels dry better after a few uses?</p>
<p>Do the pores in the towel somehow have to be 'opened' after the production process which reduces capillary action in the first couple of uses? Or is it perhaps because of some coating the new towels have to protect them while kept in stores, which causes lower wettability? Or is it perhaps related to the way in which the towel dries after it has been wet?</p> | g11140 | [
0.003700071480125189,
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0.00624858308583498,
0.0009443180169910192,
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-0.03224610537290573,
0.0013061064528301358,
0.009654074907302856,
0.07581768929958344,
0.011617... |
<p>In Wikipedia article <a href="http://en.wikipedia.org/wiki/EPR_paradox#Description_of_the_paradox" rel="nofollow">EPR paradox</a>,</p>
<blockquote>
<p>The original paper purports to describe what must happen to "two systems I and II, which we permit to interact ...", and, after some time, "we suppose that there is no longer any interaction between the two parts." In the words of Kumar (2009), the EPR description involves "two particles, A and B, [which] interact briefly and then move off in opposite directions."[9] According to Heisenberg's uncertainty principle, it is impossible to measure both the momentum and the position of particle B exactly. However, according to Kumar, it is possible to measure the exact position of particle A. By calculation, therefore, with the exact position of particle A known, the exact position of particle B can be known. Also, the exact momentum of particle B can be measured, so the exact momentum of particle A can be worked out. Kumar writes: "EPR argued that they had proved that ... [particle] B can have simultaneously exact values of position and momentum. ... Particle B has a position that is real and a momentum that is real."</p>
</blockquote>
<p>But isn't measurement in quantum mechanics not related to Heisenberg <a href="http://en.wikipedia.org/wiki/Uncertainty_principle" rel="nofollow">uncertainty principle</a>? According to my knowledge, measurement collapses wavefunction into one basis state, and has nothing to do with uncertainty principle..</p>
<p>I am bit confused of the paper. </p> | g11141 | [
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-0.03395926207304001,
-0.04514539986848831,
-0.030464349314570427,
0.0... |
<p>Can anyone explain the path of light to me, using a wave model, that show the angled path in different reference frames?</p> | g11142 | [
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0.03359... |
<p>Does the <a href="http://en.wikipedia.org/wiki/Special_relativity" rel="nofollow">Special Theory of Relativity</a> "form" the foundation of Modern Physics?</p>
<p>My question is in reference to Geoff Brumfiel's Scientific American article "<a href="http://www.scientificamerican.com/article.cfm?id=particles-found-to-travel&print=true" rel="nofollow">Particles Found to Travel Faster than Speed of Light</a>", about which I have two questions. </p>
<p>I have become engaged in discussions about this news that include some confusion about Mr. Brumfiel's wording. Mr. Brumfiel's sub-heading & a portion of the article state: </p>
<ul>
<li>"Neutrino results challenge a cornerstone of Albert Einstein's
special theory of relativity, which itself forms the foundation of
modern physics." </li>
<li>"The idea that nothing can travel faster than light in a vacuum is
the cornerstone of Albert Einstein's special theory of relativity,
which itself forms the foundation of modern physics."</li>
</ul>
<p>Please help me with answers to the following:</p>
<ol>
<li>Is it appropriate to say that Special Theory of Relativity
"<strong><em>forms</em></strong>" [serves as the framework to] the foundation of Modern Physics? </li>
<li>Is it appropriate to say the idea that "<strong><em>nothing</em></strong> can travel faster than light in a
vacuum" <strong><em>is the cornerstone</em></strong> of the Special Theory of
Relativity?</li>
</ol>
<p>I have added highlights to my question help specify where in Mr. Brumfiel's wording the confusion rests. </p>
<p>(the confusion question 1 asks about is the phrase "[Special Theory of Relativity] <strong><em>forms</em></strong> the foundation", not is the foundation... If I reword the question, I may ask, "Is it appropriate to say Special Theory of Relativity serves as the framework to the foundation of Modern Physics?")</p> | g11143 | [
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0.00994... |
<p>Below is a picture of a typical transmission line(about 200 kV). Is there a simple physics experiment which can be performed safely near the line, to determine the power flow direction. Or in other words: where is the generator and where a consumer. </p>
<p><img src="http://i.stack.imgur.com/JByCq.jpg" alt="enter image description here"></p> | g11144 | [
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0.03752407059073448,
0.0016842593904584646,
0.01625451073050499,
0.0... |
<p>Since the Earth is moving around the Sun, which is moving around Milky Way, etc... What reference frame is used for the complete motion of the begin/end points (which are non-inertial right?)?</p> | g11145 | [
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0.004215380176901817,
... |
<p>Using the electron bombardment method, if I wanted to ionize, for example, Xenon gas electrons with an electron gun, under what conditions is it possible to do so? (Heat, pressure?)</p> | g11146 | [
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<p>As a programming (technology), physics and math project in school, I'm considering programming my own 3D physics engine as a learning exercise. The physics engine should then be able to be used in a simple game.</p>
<p>Is this a viable project to do over a year? I want a prototype up pretty quick (even if it can be a bit unaccurate and maybe support a limited range of shapes and other physical properties).</p>
<p>If it is viable, where do you think I should start the research that is necessary to write one? When thinking about it myself, what I believe that it involves is, among others:</p>
<ul>
<li>Linear algebra (which I know quite a bit of)</li>
<li>Rigid body dynamics (I know a little of it)</li>
<li>Collision detection (I haven't looked into this yet, but I can imagine it involves linear algebra)</li>
<li>Numerical methods (of integration) for accuracy</li>
<li>Performance concerns (spatial hashing, anyone?)</li>
</ul>
<p>I'm sure there is more. Feel free to fill me in and recommend some resources where I can begin to read about stuff.</p> | g11147 | [
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<p>What's the relationship between <a href="http://en.wikipedia.org/wiki/Uncertainty_principle" rel="nofollow">uncertainty principle</a> and <a href="http://en.wikipedia.org/wiki/Symplectic_group" rel="nofollow">symplectic groups</a>? Does the symplectic groups mathematically capture anything fundamental about uncertainty principle?</p> | g11148 | [
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0.... |
<p>This question has been asked many times all over the Internet and answers can be found on places such as yahoo and ask.com, but I'm not satisfied with those answers and I don't trust the validity of those places. This seems like a more appropriate place to ask. So, here's my train of thought and I would like to ask you if you think I'm right or wrong.</p>
<p>Even though most of the answers point to the fact that the ball does not achieve equilibrium because the force of gravity is constantly acting upon it, thus causing an acceleration, I still think there's a moment of equilibrium and here's why:</p>
<p>When the ball is traveling up, it's accelerating towards the ground and eventually reaches a point at which its speed reaches 0. At this moment, isn't the reason the speed is 0 is due to the fact that net force is 0? The force that made the ball travel in the upward direction was canceled out by the gravitational force. So, the sum of forces at that brief moment is equal to 0, otherwise the ball would be moving. I don't think gravity is the only force acting on the ball at that moment, since the throwing force was acting on it as well, until both canceled each other out for that brief moment.</p>
<p>Am I right or wrong?</p> | g11149 | [
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0.0143... |
<p>When discussing the quantum mechanical harmonic oscillator we are talking about energy eigenstates. How would one actually measure in which state an harmonic oscillator is in? Could you weigh it and use Einstein's relation $E=mc^2$ to derive the energy?</p> | g11150 | [
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<p>This may seem like a simple question, but I cant seem to make any headway. </p>
<p>Consider the following; I have two beams of light, a reference beam $(A=\cos(wt))$ and phase shifted beam $(B=\cos(wt+\phi))$.</p>
<p>What is the normal way (say in a lab) that $\phi$ is detected & measured with respect to the reference beam?</p>
<p>I believe an interferometer is used, but I dont understand how this yields a measurement.</p>
<p>Thanks for any insight.</p>
<p>EDIT: I don't know if I've explained this very well. I think better in pictures, so here is a VERY crude diagram of my thought experiment.</p>
<p><img src="http://i.stack.imgur.com/EAeQi.png" alt="enter image description here"></p> | g11151 | [
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<p>In quantum mechanics, when hamiltonian $H$ is constrained ($H = \sqrt{m^2 - \hbar^2 \nabla^2} $) so that it would produce simple "relativistic" model of quantum mechanics, we can show that it results in non-locality (Reference: <a href="http://physics.stackexchange.com/questions/39415/nabla-and-non-locality-in-simple-relativistic-model-of-quantum-mechanics">$\nabla$ and non-locality in simple relativistic model of quantum mechanics</a> )</p>
<p>The question is would Taylor-expanding every constraint equation on some quantity/operator, such as Hamiltonian, show that it will result in non-locality? Or in some case, should we check other expansions/methods?</p> | g11152 | [
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<p><strong>Easy</strong></p>
<p>Consider the following figure</p>
<p><img src="http://i.stack.imgur.com/brY4S.jpg" alt="enter image description here"></p>
<p>Each red point is a particle of a known mass that carries charge Q/2 and connected to a the box by a thread of known length. This problem can be solved easily to find Q</p>
<p><strong>Crazy</strong></p>
<p>How would one handle the situation, had the two branches been leaves of an electroscope of equal known masses instead of point particles? (now every leaf is charged continuously)
Is this problem solvable?</p>
<p>[In this new situation the left branch is carrying same total charge as the right one by symmetry. But to analyse the problem for static equilibrium for the left branch say, I tried to identify the forces on the left branch: </p>
<ul>
<li>there will be the weight of the branch acting at the center of mass
(at a distance 35 cm) points down.</li>
<li>an electrostatic force (which is not uniform?) acting on the whole branch because of the<br>
electric field (which is not uniform?) due to the right branch </li>
<li>the force on the leave at the connection point with the red box (how to find it?)]</li>
</ul>
<p>Is it possible to find the total charge/charge density on every branch?</p> | g11153 | [
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<p>Inside a single proton for example, what is the force(s) that keeps the quarks together? Why don't they leave the proton? If they do, how does that even happen?</p>
<p>And maybe an additional sub question: Is it always three quarks inside the protons/neutrons? Why?</p> | g11154 | [
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<p>is well known that composition of point reflections generate <a href="http://en.wikipedia.org/wiki/Point_symmetry#Point_reflection_group" rel="nofollow">pure displacements</a>. This implies that the commutator of two point reflections will be a pure displacement. Are there similar elemental transformation operations which can generate pure displacements from their <strong>anticommutators</strong>?</p> | g11155 | [
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<p><a href="http://www.quantumdiaries.org/2011/03/25/an-idiosyncratic-introduction-to-the-higgs/" rel="nofollow">Quantum Diaries</a> has an interesting introduction to the higgs. It makes it seem like the way that the higgs field gives mass to particles is via all of the interactions with virtual higgs particles.</p>
<p>My question is, how can interaction with the field give rise to mass? It seems almost like Flip Tanedo is saying that, due to the interaction with the higgs field, the particle (electron, say) is experiencing a large number of changes in direction, and thus it takes a path much longer than the one that you measured.</p>
<p>It seems to imply that, when going from A to B, the electron 'bounces' off of a number of virtual higgs particles and takes a much longer path than the straight line from A to B, travelling at light speed all the while.</p>
<p>Is this a good way to look at the creation of 'mass' (i.e. a particle appears to move slower than light speed because it takes a path longer than the shortest one)? Or is there some other way to understand how the higgs mechanism imparts mass?</p> | g11156 | [
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<p>Why are "Laue Spots" spots instead of rings? Or is there an effective way to estimate the number of Laue spots? I can't find any formulas or theory concerning this issue. Thanks for your attention! </p> | g11157 | [
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0.03999... |
<p>I'm trying to understand the mechanics which determine if a car making a turn will skid.</p>
<p>Are the following correct or incorrect:</p>
<ol>
<li><p>A vehicle making a turn will skid unless the centripetal force is adequate to produce the centripetal acceleration. In a simple turn, where $r$ is constant, the force needed is $mr\omega^2$.</p></li>
<li><p>If the road is flat, this force can only come from friction created by turning the wheel. The maximum force is $\text{weight}\times\mu_\text{static}$. All of this force will be directed centripetally, and will therefore be available to prevent the skid.</p></li>
<li><p>If the road is banked by $\phi$, the friction force will be lessened by $\cos\phi$, but there will also be a centripetal component of the normal force, equal to $\sin\phi\cos\phi$.</p></li>
</ol>
<p>Are these all correct? I believe they are but my results using them don't seem to work.</p>
<p><strong>UPDATE:</strong> I believe my mistake was in the direction friction will be in. Determining the direction of friction in this case is tricky, because it has to both counteract the sliding due to normal force of the banked road, and also accelerate in the centripetal direction. It requires 3 dimensions. How do I determine the direction of friction, with respect to $r$ and $\theta$ vectors?</p> | g11158 | [
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<p>Why must an <a href="http://www.labsphere.com/products/spheres-and-components/general-purpose-spheres/default.aspx">integrating sphere</a> be a sphere? Why can't it be an integrating cube? What is the difference? Could I use a cube to measure total illuminance like an integrating sphere does?</p>
<p><img src="http://i.stack.imgur.com/kf0Rz.gif" alt="enter image description here"></p> | g11159 | [
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<p>Everyone has seen cartoons of bombs being dropped, accompanied by a whistling sound as they drop. This sound gets lower in frequency as the bomb nears the ground.</p>
<p>I've been lucky enough to not be near falling bombs, but I assume this sound is based on reality.</p>
<p>Why does the frequency drop? Or does it only drop when it is fallling at an oblique angle away from you, and is produced by doppler shift?</p>
<p>I would have thought that most bombs would fall pretty much straight down (after decelerating horizontally), and therefore they would always be coming slightly closer to me (if I'm on the ground), and thus the frequency should <em>increase</em>..</p> | g11160 | [
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<p>It seems common for an ordered phase to have some amount of disorder present. For example, the average moment of a ferromagnet is less than maximum except at T=0 due to the presence of fluctuations. Also, a liquid is typically only in equilibrium if a portion of it is vapor at the right vapor pressure. Is there an analogue for the solid-liquid transition? In other words, for, say, an elemental solid below the melting point, should we expect a portion of its surface to be liquid at any given time, with this portion increasing steadily until the melting point when the whole thing becomes liquid?</p> | g11161 | [
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<p>I am currently working on my bachelor's thesis on the anapole / toroidal moment and it seems that I am stuck with a tensor decomposition problem.</p>
<p>I have actually never had a course about tensors, so I am a complete newbie.</p>
<p>I need to expand a localized current density, which is done by expressing the current via delta distribution and expanding the latter:</p>
<p>$$\vec{j}(\vec{r},t) = \int\vec{j}(\vec{\xi},t) \delta(\vec{\xi}-\vec{r}) d^3\xi$$
$$\delta(\vec{\xi}-\vec{r}) = \sum_{l=0}^{\infty} \frac{(-1)^l}{l!} \xi_i ...\xi_k \nabla_i ... \nabla_k \delta(\vec{r}) $$</p>
<p>So I get some result containing the following tensor:</p>
<p>$$B_{ij...k}^{(l)}(t) := \frac{(-1)^{l-1}}{(l-1)!} \int j_i \xi_j ... \xi_k d^3\xi$$</p>
<p>So far, I have understood the math. But now comes the tricky part. In the paper, it says that "we can decompose the tensors $B_{ij...k}^{(l)}$ into irreducible tensors, separating the various multipole moments and radii." and further "...of third rank, $B_{ijk}^{(3)}$ can obviously reduced according to the scheme $1 \times (2+0) = (3+1)+2+1$. It can be seen that the representation of weight $l=1$ is extracted twice from $B_{ijk}^{(3)}$." And then follows what seems like the decomposition and I am hopelessly lost.</p>
<p>$$j_i\xi_j\xi_k = \frac{1}{3} \left[ j_i\xi_j\xi_k + j_k\xi_i\xi_j + j_j\xi_k\xi_i - \frac{1}{5} \left( \delta_{ij}\theta_k + \delta_{ik}\theta_j + \delta_{jk}\theta_i \right) \right] - \frac{1}{3} \left( \epsilon_{ijl} \mu_{kl} + \epsilon_{ikl}\mu_{jl}\right)$$
$$+ \frac{1}{6} \left( \delta_{ij}\lambda_k + \delta_{ik}\lambda_j - 2 \delta_{jk}\lambda_i \right) + \frac{1}{5} \left( \delta_{ij}\theta_k + \delta_{ik}\theta_j + \delta_{jk}\theta_i \right)$$</p>
<p>with</p>
<p>$$\mu_{ik} = \mu_i\xi_k + \mu_k\xi_i \ , \ \mu_i=\frac{1}{2} \epsilon_{ijk}\xi_j j_k$$
$$\theta_i=2\xi_i \vec{\xi}\cdot \vec{j} + \xi^2 j_i$$
$$\lambda_i=\xi_i\vec{\xi}\cdot \vec{j} - \xi^2 j_i$$</p>
<p>This decomposition obviously contains many quantities that later on appear also in the multipole expansion, e.g. the magnetic quadrupole moment $\mu_{ik}$. So on the physics side of things, this makes sense to me.</p>
<p>But not on the mathematical side. On this board I found some questions regarding tensor decomposition and in the answers I learned something about symmetric and antisymmetric tensors and that every tensor can be decomposed in several irreducible ones, which better represent physical properties of the system and symmetries.</p>
<p>But I still, some questions are still there...
1.) What do the numbers $\frac{1}{3}$, $\frac{1}{5}$, etc. mean? Is this some kind of normalization?
2.) How exactly does one decompose the tensor? How can I reconstruct what exactly has been done, which steps one has to follow to decompose it like this?</p> | g11162 | [
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<p>This question is more a philosophical question than a physics one.
When we appreciate particle physics we study that in order to explain some experimental results we have to introduce a new particle (for instance thinking about neutrinos). This is obviously true but I just want to ask you: is there a wave interpretation of this results? I mean, consider for example the so-called sea quarks, which coming up as a mixture of different quarks, if I describe this processes in a wave model can I see this as an interference of wave function? I am not sure that this question is clear. generalizing, why do not we study subnuclear physics both in particle and wave model, as quantum mechanics suggest?</p> | g11163 | [
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<p>I was watching Nima's very popular <a href="http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Hamed_4-3.html" rel="nofollow">talk (download if you're using chrome)</a> (also mirrored at youtube <a href="http://www.youtube.com/embed/q4Dj8fq30sk" rel="nofollow">here</a>) about the "Amplituhedron", which has suddenly become very popular recently. </p>
<p>He talks all about how the amplituhedron computes the same result for the scattering amplitudes as ordinary peturbation theory in a simple and elegant way, but I fail to understand how one actually computes the amplituhedron for a certain scattering process anyway? </p>
<p>As per the recent TRF <a href="http://motls.blogspot.in/2013/09/diaperhedron-cant-match-amplituhedron.html" rel="nofollow">pos</a><a href="http://motls.blogspot.in/2013/09/amplituhedron-wonderful-pr-on-new.html" rel="nofollow">ts</a> about amplituhedron and why they don't wear diapers, I can understand that one may calculate the scattering amplitudes by simply taking the volume of the amplituhedrons (ignoring constants, I guess), but how does one actually calculate the amplituhedron? </p>
<p>I'm especially stunned by the image (looks like a sort of a concrete example, don't know how they constructed the amplituhedron): </p>
<p><img src="http://i.stack.imgur.com/cxuzg.jpg" alt="enter image description here"></p>
<p>To summarise my question, how does one actually figure out, or construct, the amplituhedron based on the specific scattzering process? </p> | g11164 | [
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<p>I'm confused: Big Bang nucleosynthesis is adamant about the 1 neutron to 7 proton ratio which yields 75% hydrogen to 25% helium (with a nominal amount of partially-reacted deuterium and heavier lithium). But everything I read about the interstellar medium gives a helium figure closer to 10%, so what happened to the missing 60% of the helium in the Universe?</p>
<p>Of the gas in the ISM, 89% of atoms are hydrogen and 9% are helium, with 2% of atoms being elements heavier than hydrogen or helium, which are called "metals" in astronomical parlance. </p> | g11165 | [
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<p>I would like to understand basic concepts of the general relativity in 2+1 spacetime. As far as I know, GR predicts that such a spacetime is flat everywhere except for the point masses which create angular deficit proportional to their mass. Flatland with one point mass is like surface of cone. I imagine that when one adds other point masses the Flatland can be folded to a (convex) polyhedron (then there is the constraint on total masses, since total angular deficit is 720 degrees) (see note #1). I assume that a 2d Flatlander would not (at least locally) notice crossing the edges when moving from one face of polyhedron to another.</p>
<p>The problem I have with this model is that when one heavy body which defines the Flatland is set to motion, its mass must change and - more surprisingly from a local point of view - also masses of the neighboring bodies to keep the total of 720 degrees. The image shows cube with a vertex moving along edge to its middle with corresponding angular deficits.</p>
<p>On the other hand, I know that 2+1 gravity and motion of point masses have been considered seriously by Gott (in his two strings time machine), Caroll, Guth, t' Hooft and others. Where is error in my naive model?</p>
<p><strong>Edited</strong>: Given the first answer and comments I should maybe be more precise:</p>
<p><em>Is a motion which requires change of angular deficit (and hence mass) of the surrounding point masses possible, or is possible only motion when all angular deficits are kept constant? Anyway, for a Flatender living on the polyhedron surface the situation looks like there is an interaction between the point masses, despite the fact the spacetime is flate in between them. Or is such a configuration (initial condition) simply impossible?</em></p>
<p><strong>Edited</strong>: I have overlooked the fact that a point mass cannot be just "set to motion" by a miracle - <em>total momentum must be conserved</em>. I will think it over and prepare a better example.</p>
<p><strong>Edited</strong>: This papers by 't Hooft may contain answer:</p>
<p><a href="http://www.staff.science.uu.nl/~hooft101/gthpub/evolution_2plus1_dim.pdf">The evolution of gravitating point particles in 2+1 dimensions</a> (pdf)</p>
<p><a href="http://www.staff.science.uu.nl/~hooft101/gthpub/Deser_Jack_tH_ThreeD_Grav_1984.pdf">Three-dimensional Einstein gravity: dynamics of flat space</a> (pdf)</p>
<p><img src="http://i.stack.imgur.com/Xf3xC.png" alt="enter image description here"></p>
<p><strong>Notes</strong> (added in later edits):</p>
<p>1) Gott & Alpert: <em>General Relativity in a (2+1)-Dimensional Space-Time</em> (Gen. Relat. Gravit. 16:243-247, 1984):</p>
<p>"Consider a convex polyhedron with a finite number of faces. The faces and
edges have no intrinsic curvature and represent solutions to the vacuum field
equations. The vertices each have an angle deficit (like the vertex of a cone) and
represent point masses. For example, a universe shaped like the surface of a cube
represents a vacuum with 8 point masses of $M = \pi/2$ each (three squares meet at
each vertex giving each an angle deficit of $\pi/2$). The Einstein static universe of
equation (6) may be approximated by a polyhedron of many faces containing
many vertices each with small angle deficits. The total mass in such a closed
universe is always $M_u = 4\pi$."</p>
<p>In my opinion, there are also some <em>nonconvex</em> polyhedra which work well.</p> | g11166 | [
0.021122166886925697,
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0.06078094244003296,
0.01483493484556675,
0.05904380604624748,
-0.005... |
<p>In David Chandler's 'intro to statistical mechanics' he states that for an ideal gas at high-temperature</p>
<p>$$
\langle n_j\rangle=\langle N\rangle\frac{e^{-\beta \epsilon_j}}{\sum e^{-\beta \epsilon_j}}
$$</p>
<p>Which I can believe from intuition, but he losses me on the derivation. </p>
<p>Starting with the general form for the occupancy of a boson or Fermion gas:</p>
<p>$$
\langle n_j \rangle=[e^{\beta (\epsilon_j-\mu)} \pm 1]^{-1}
$$</p>
<p>Then at high-temperature, $\beta \rightarrow 0$, <em>[ page 101 (b) ]</em></p>
<p>$$
e^{\beta(\epsilon_j-\mu)}>>1
$$</p>
<p>So the assumption can be made that </p>
<p>$$
\langle n_j \rangle=e^{-\beta (\epsilon_j-\mu)}
$$</p>
<p>Which would make sense if $e^{\beta(\epsilon_j-\mu)}>>1$, but it sure seems like that $ e^{\beta(\epsilon_j-\mu)}\approx 1$ in that case. Is there another assumption that's made here?<br>
He does say:</p>
<blockquote>
<p>Note that if this eqn is true for all $\epsilon_j$, then $-\beta \mu >>1 $</p>
</blockquote>
<p>so, $\mu \rightarrow -\infty$ at high-temperature? That doesn't strike me as something that's obvious. </p>
<p><strong>The rest of the derivation:</strong></p>
<p>$$
\langle N \rangle = \sum \langle n_j \rangle =\sum e^{-\beta(\epsilon_j-\mu)}=e^{\beta \mu} \sum e^{-\beta \epsilon_j} \\
e^{\beta \mu} = \frac{\langle N \rangle}{\sum e^{-\beta \epsilon_j}}
$$</p>
<p>using $\langle n_j \rangle = e^{-\beta(\epsilon_j - \mu)}$</p>
<p>$$
\langle n_j\rangle=\langle N\rangle\frac{e^{-\beta \epsilon_j}}{\sum e^{-\beta \epsilon_j}}
$$</p> | g11167 | [
0.01136406697332859,
0.014793667942285538,
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0.06328082829713821,
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0.030893072485923767,
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0.018562916666269302,
0.018288135528564453,
0.026... |
<p>I want the basic reason. I want the description of answer graphically also.</p> | g358 | [
0.04890334606170654,
0.09837398678064346,
0.021735908463597298,
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0.004977890755981207,
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0.02642097696661949,
0.02148609794676304,
0.04686518386006355,
0.067679... |
<p><img src="http://i.stack.imgur.com/lm41R.jpg" alt="Wheatstone bridge Capacitor,Dead Capacitor"></p>
<p>I want to know that if in a Wheatstone Bridge ,that is made of capacitors only
we have this condition $c_1c_3=c_2c_4$. </p>
<p>The $c_5$ capacitor would be dead and it's voltage would be zero? Actually I am looking for a mathematical proof. </p> | g11168 | [
0.05438544973731041,
-0.0010506348917260766,
0.0008262823102995753,
-0.006271976046264172,
0.03310815989971161,
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0.00949687510728836,
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-0.024524416774511337,
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0.05761777609586716,
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-0.... |
<p>I was reading on up <a href="http://en.wikipedia.org/wiki/Lagrangian_point" rel="nofollow">Lagrangian points</a> and the restricted three-body problem.</p>
<p>From what I was able to tell, the Lagrangian points are 5 points in a two-body system such that a third body would be relatively at rest. The first three are unstable, and the last two are stable.</p>
<p>How is this possible? Because we know from Kepler's laws that the orbits are in the shape of ellipses with the sun at a focus, and we also know the planes sweep out equal areas in equal time and so the speed varies. And so, how can the third body have a constant distance when there is an ever-changing speed gap between the orbital speeds.</p>
<p>And could anyone provide (visually) an explanation for the Lagrangian points, how to deduce them, and what assumptions were made in order to deduce them?</p>
<p>LE: So, in the three body problem, the orbits more closely resemble circles than ellipses? And if so, is the speed relatively constant so that the difference in distance between the third and second body is negligible?</p> | g11169 | [
0.057689134031534195,
0.08271873742341995,
0.018456973135471344,
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0.05019555613398552,
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0.019595902413129807,
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0.02473059482872486,
0.03138842433691025,
0.024891111999750137,
0.059936970472335815,
-0.0131... |
<p>In recent publications there is a frequent mentioning of the so-called "Higgs transition" in connection with magnetic monoples. Can anybody please describe the phenomenon in simple terms?</p>
<p>For example, it seems that <a href="http://www.sciencedaily.com/releases/2012/08/120807113243.htm" rel="nofollow">here</a> it is claimed that found a material that exhibits magnetic monople superconductivity and can sustain magnetic current. </p>
<p>Does in mean that a cable of such material will have circular electric field around it?</p> | g11170 | [
0.0102565111592412,
0.05587724596261978,
0.00632713595405221,
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0.08097197115421295,
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0.00885669607669115,
0.004775857087224722,
-0.09671004861593246,
0.013999776914715767,
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-0.01707653... |
<p>I actually want to know whether space-time supersymmetry is important for string theory consistency? I see that NS and GS supersymmetric strings have worldsheet supersymmetry, but the first one does not have a manifest space-time SUSY while the second one has it manifest. I want to know if this space-time SUSY is really having an impact on string theory. </p>
<p>I know the answer is Yes, but in which way it effects the consistency of string theory? (compactification?)</p>
<p>Edit- I would like to add that the only way I think this space-time SUSY adds to string theory is the notion of a constant covariant spinor, which gives the Calabi-Yau manifold for compactification. Is this the necessity of space-time SUSY?
And what else can we say about it in connection to string theory.</p> | g11171 | [
-0.01681569218635559,
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0.032804038375616074,
0.027707481756806374,
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0.014262774027884007,
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0.02132168971002102,
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0.... |
<p>I started learning a bit ahead from an old physics book, and they were discussing the photoelectric effect and after that Planck's hypotheses and energy quantas.</p>
<p>The book said that the mass of a microscopic oscillator (what is that?) is not continuous, but discrete and the difference between states is an energy quanta:</p>
<p>$ \varepsilon = h\nu = E_k - E_i $</p>
<p>And since
$ E = mc^2 $ then the (relativistic) mass of the photon is</p>
<p>$ m = \frac{h\nu}{c^2} $</p>
<p>How did they deduce that?</p> | g11172 | [
0.04654276743531227,
-0.007403066381812096,
-0.019369054585695267,
0.011845303699374199,
0.036222442984580994,
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0.016386277973651886,
0.015241652727127075,
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-0.01786738634109497,
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-0.04862537980079651,
0.03246753662824631,
... |
<p>I'm porting <a href="http://en.wikipedia.org/wiki/Maxwell%27s_equations_in_curved_spacetime" rel="nofollow">Maxwell's equations to curved spacetime</a> and am having trouble reconciling the tensor and forms treatments. I think the problem boils down to a misunderstanding on my part concerning the exterior covariant derivative rather than just the exterior derivative, but that's only a guess. So in Minkowski spacetime we have</p>
<p>$$
F_{\mu \nu} = A_{\nu,\mu}-A_{\mu,\nu}\text{, }F_{[\mu \nu , \kappa]}=0
$$</p>
<p>and</p>
<p>$$
F=\text{d}A\text{, }\text{d}F=0,
$$</p>
<p>the equivalence of which is easy to show. However, suppose we're working in curved spacetime. We get</p>
<p>$$
F_{\mu \nu} = A_{\nu;\mu}-A_{\mu;\nu}\text{, }F_{[\mu \nu ; \kappa]}=0.
$$</p>
<p>However, the connection coefficients in the covariant derivatives neatly cancel out, so both tensor expressions are equivalent to each other. However, suppose we attempt to bring the flat space forms expression into curved spacetime, by turning the exterior derivative into an exterior covariant derivative. We start with </p>
<p>$$F = \text{d}_DA$$</p>
<p>and then (naively?) find</p>
<p>$$
\text{d}_DF =\text{d}_D \text{d}_D A = \Omega \wedge A \neq 0
$$</p>
<p>where $\Omega$ is the curvature 2-form. So suddenly the tensor and forms methods seem to give differing versions of Maxwell's laws. Is one not obligated to employ the covariant exterior derivative in this situation? Maybe I am seriously missing something but it seems like the exterior covariant derivative gets much less mention than it should in relativity, if it is required to deploy forms at all on curved manifolds! The Hodge star of course contains information about the metric, but it seems here like we arrive at an inconsistency before needing to invoke it to find the other two Maxwell's equations.</p>
<p>Thanks for any insight.</p> | g11173 | [
-0.0032880855724215508,
-0.050769004970788956,
-0.001782812993042171,
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0.045343417674303055,
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0.059300173074007034,
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-0.0020895751658827066,
0.026344502344727516,
-0.013120385818183422,
0.058010004460811615... |
<p>When we can say that two particle are momentum entangled ? I just read an article where it's said that two momentum entangled particles share the same momentum value in opposite directions no matter how far they are when it's provided a measurament
...It's a correct description?</p> | g11174 | [
0.040863264352083206,
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0.0055824583396315575,
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0.005362765397876501,
-0.015512465499341488,
... |
<p>I understand that the maximum free charge carrier density for aluminum has been measured using the Hall effect (in the case of electric current). However, I'm not clear how to determine the maximum surface charge density to which aluminum (or any conductor) can be charged, assuming the neighboring medium does not breakdown. </p>
<p>Say for instance we had a parallel plate capacitor with an idealized dielectric that could withstand infinite potential across it. What is the max surface charge density that the plates could be charged to? I assume that at some point all of the surface atoms are ionized. </p>
<p>Is this simply the volumetric free carrier density multiplied by the atomic diameter?</p> | g11175 | [
0.06695476174354553,
0.0566142201423645,
0.010795238427817822,
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0.019434142857789993,
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0.019112873822450638,
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0.026594458147883415,
-0.010222259908914566,
0.03958772495388985,
0.032145943492650986,
-0.0... |
<p>Why is gravitational potential energy negative? How is it different from other forms of energy? I recently saw a video by Dr. Michio Kaku, he said that the total energy content of the universe is zero, since gravitational potential energy is negative, thus balancing all the positive energy. Can anyone help me out here?</p> | g27 | [
0.06639467179775238,
0.09152928739786148,
0.0029631340876221657,
0.05242369696497917,
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0.03451789170503616,
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-0.022269196808338165,
0.05099362134933472,
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0.010687213391065598,
0.01888... |
<p>Generally, to let my bolognese thicken, I leave the lid off in order to "let water vapor escape." I am however distracted from enjoying the taste because I'm having doubts that my physical reasoning is sound.</p>
<p>Given a constant power output from my stove, it seems a given that having the lid on to make the contents of my pot come to a boil makes good sense: Less hot air is released to the surroundings thus more energy is left in the pot to heat the food faster. But does the same argument not apply to reducing my sauce? There's no tight seal, so I can't assume there will be an increased pressure. Where else would the energy go but with steam escaping from cracks around the lid?</p>
<p><strong>Edit:</strong>
To clarify: Will my sauce reduce faster with or without the lid? Why?</p> | g11176 | [
0.030408071354031563,
0.016293752938508987,
0.033993154764175415,
0.037917155772447586,
-0.015345418825745583,
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0.044987838715314865,
0.050342172384262085,
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0.03815679997205734,
-0.01958552375435829,
-0.02043207734823227,
0.0... |
<p>I am looking for a resource that clearly exposes the concepts of a particle source and a particle detector in the context of Quantum Field theory. I want to understand <a href="http://en.wikipedia.org/wiki/Irreversible_process" rel="nofollow">Irreversibility</a> in this context. </p> | g11177 | [
0.05791649967432022,
0.04307958483695984,
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0.04887412115931511,
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0.015956347808241844,
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0.0732211321592331,
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0.00718... |
<p>Discussion about Landau's "Theoretical Minimum" has already been posted <a href="http://physics.stackexchange.com/questions/13861/lev-landaus-theoretical-minimum">here</a>. Unfortunately I couldn't find much about some examples of questions he gave to students. There are three questions in the post I linked and also in the linked arXiv <a href="http://arxiv.org/abs/hep-ph/0204295v1" rel="nofollow">article</a>.</p>
<p>What I am mostly interested in are math exercises.</p>
<p>There is a history of Alexei Abrikosov who after presenting himself as a 3rd year student to Landau was asked if he had a pen and then was given an integral to solve. He managed to solve it and Landau was very happy :). </p>
<p>There are many other such anecdotes but they all lack exercise formulation. Maybe you know what this integral could be or at least of what type it was?</p> | g11178 | [
0.0000399921991629526,
0.03761827573180199,
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0.03148286044597626,
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0.009539568796753883,
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-0.006289253477007151,
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0.03096623905003071,
-0.011287149041891098,
0.0... |
<p>I am unable to find the solution to the following equation:<br></p>
<p>Tr$_{2}[U(|\psi\rangle \langle\psi|\otimes \rho)U^{\dagger}]=\rho$</p>
<p>Here $\psi$ is state vector representing a qubit and $\rho$ state of second qubit(the partial trace is over its subspace).<br></p>
<p>Also $U$ is a unitary operator given by $\sum |x \vee y\rangle |y\rangle \langle x| \langle y|$ where $x,y \in \{0,1\}$<br><br>
$\vee$ stands for bit XOR and $\otimes$ for tensor product and $U$ operates on joint space of both the qubits.</p>
<p><br></p> | g11179 | [
0.015370066277682781,
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0.004762933123856783,
0.016288848593831062,
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0.0179673470556736,
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0.015987711027264595,
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0.04754040762782097,
-0.060336459428071976,
-0.... |
<ol>
<li><p>I'd like to learn how much energy I need to lift a 200 kilograms weight on normal earth conditions? </p></li>
<li><p>For example how much electric power do we need?</p></li>
</ol>
<p>I'm not a physicist and not a student and this is not my hw:) I just wondering. </p> | g11180 | [
0.008578957058489323,
0.06571535766124725,
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0.04317546263337135,
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0.004907782655209303,
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-0.04360954463481903,
-0.020024407655000687,
... |
<p>Hamiltonian is defined by $H_I = \hbar \omega (\hat{a}^+ \hat{a} + 1/2)$</p>
<p>What is the expectation value of the energy on the number state </p>
<p>$$\vert \psi \rangle = \frac{1}{\sqrt{2}} ( \vert 1 \rangle + \vert 2 \rangle )$$</p>
<p>So I think that its</p>
<p>$$\langle E \rangle = \langle \psi \vert H_I \vert \psi \rangle$$</p>
<p>$$ = \hbar \omega (\langle \psi \vert \hat{a}^+ \hat{a} \vert \psi \rangle + 1/2) $$</p>
<p>$$ = \hbar \omega ((\langle 2 \vert + \langle 1 \vert) \hat{a}^+ \hat{a} (\vert 1 \rangle + \vert 2 \rangle) + 1/2) $$</p>
<p>Now we use that $\hat{n} = \hat{a}^+ \hat{a}$, and then I get confused...does the last expresion become </p>
<p>$$ = \hbar \omega (\langle 1 \vert \hat n \vert 1 \rangle + \langle 2 \vert \hat n \vert 2 \rangle + 1/2) $$</p>
<p>or </p>
<p>$$ = \hbar \omega (\langle 1 \vert \hat n \vert 1 \rangle +\langle 2 \vert \hat n \vert 2 \rangle +\langle 1 \vert \hat n \vert 2 \rangle + \langle 2 \vert \hat n \vert 1 \rangle + 1/2) $$</p>
<p>any advice?</p>
<hr>
<p>EDIT I think I have the answer </p>
<p>E = $$ = \hbar \omega (\langle 1 \vert \hat n \vert 1 \rangle +\langle 2 \vert \hat n \vert 2 \rangle +\langle 1 \vert \hat n \vert 2 \rangle + \langle 2 \vert \hat n \vert 1 \rangle + 1/2) $$</p>
<p>Where </p>
<p>$$\langle i \vert \hat n \vert j \rangle = j \langle i \vert j \rangle = j \delta_{ij}$$</p>
<p>So $\langle E \rangle = \hbar \omega (3 + 1/2) = \frac{7 \hbar \omega}{2}$</p> | g11181 | [
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0.052789244800806046,
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0.018125411123037338,
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... |
<p>Why is that when I'm standing in a moving double deck bus, my body doesn't move a lot; whereas, in a moving single deck bus, my body moves quite a bit? It seems like I swing a lot in single deck buses, much more than in double-decked buses. Why is this?</p> | g11182 | [
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0.0476... |
<p>I am interested in computing the integral of this function:
\begin{align}
\int_0^\infty\frac{2du(u^2+1)}{(1-e^{2\pi u})},
\end{align}
which of course at first sight, does not converge. But in QFT it's usually possible to regulate such a function. Thus, the question is, does anyone know how to regulate this function?</p> | g11183 | [
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0.03823787719011307,
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0.010727438144385815,
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0.039135683327913284,
0.017708079889416695,
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-0.02665502019226551,
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0.05337994918227196,
0.021498875692486763,
0.01... |
<p>Let's consider a 0-dimensional $N \times N$ Hermitean one matrix model.
It is defined by a potential V(M). Its partition function
is
$Z = \int_{H_{N}} dM e^{-\frac{1}{g}V(M)}$
where $H_{N}$ is the space of $N \times N$ Hermitean matrices
and g is the coupling constant. I usually think at such a matrix model as
a 0+0 dimensional QFT : the matrix M is a field over a space-time reduced to a
point.</p>
<p>Let's consider the large N limit of this matrix model : $N \longrightarrow \infty$,
$g \longrightarrow 0$, $\lambda = gN$ fixed. In this limit, the free energy $F= log(Z)$
has an expansion $F = \sum_{g=0}^{\infty} F_{g} \lambda^{2g-2}$.
In this limit, the repartition of eigenvalues of $M$ converges to a deterministic measure
with density $y(x)$ function of the eigenvalue x. The graph of this function is a real curve in the x-y plane called the (real) spectral curve.
(In the simplest case where the potential V is quadratic, this curve is a half-circle, it is the well known Wigner's semicircle law).</p>
<p>In general, the real spectral curve is defined by an algebraic equation in x,y.
In particular, it is possible to consider this equation with x,y complex to obtain
a non-compact Riemann surface that I call the complex spectral curve.
So in the large $N$ limit, we have emergence of some geometry via the real or complex
spectral curves.</p>
<p>My question is :</p>
<p>Is there a precise holographic description of this emergence of geometry ?</p>
<p>In usual holography, we have a duality between a 1+(d-1) QFT and a 1+d quantum gravity theory with emergence of one space-like direction.
If I look at the matrix model as a 0+0 QFT then in particular I have no time and it is not clear for me what an holographic description should be. If there is some kind of emergence of the spectral curve, is it of the real or of the complex one?</p>
<p>Things related but which does not answer the question:</p>
<p>The existence of a relation between matrix models and quantum gravity can be guessed from the similarity between the large N expansion of the free energy F and the genus expansion of the free energy of a string theory (the perturbative expansion of the matrix models can be written in terms of ribbon graphs, it is the same argument as the 't Hooft one on the possibility of a relation between gauge theory in the large color limit and string theory).</p>
<p>Dijkgraak, Vafa and all have shown that starting from the complex spectral curve, it is possible to construct a non-compact Calabi-Yau 3-fold whose B-model topological string has for genus expansion the large N expansion of the matrix model.</p>
<p>There is a long story of relations between matrix models and 2d quantum gravity, which
I don't know very well (essentially, the combinatorics problems of triangulations of surfaces have a matrix model interpretation because of the ribbon graph form of the large N expansion of the matrix model). An additional question would be : </p>
<p>Is the relation between matrix models and 2d quantum gravity an example of holography ?</p>
<p>(Intuitively it should be but detailed formulation is not clear to me: for example, it seems we pass from 0 to 2 dimensions...) </p> | g11184 | [
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<p>From basic principals, how does one prove that energy is conserved? Or a little more specifically - Why does this hold:</p>
<p>$$\Delta \mbox{ PotentialEnergy} + \Delta \mbox{ KineticEnergy} = 0 $$</p>
<p>Or, for extra credit, why does this hold:</p>
<p>$$\Delta \mbox{ PotentialEnergy } + \Delta \mbox{ KineticEnergy} + \Delta \mbox{ ThermalEnergy } = 0 $$</p> | g307 | [
0.08207524567842484,
0.022288085892796516,
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0.0... |
<p>It seems that the limitation to subluminal travel can be practically circumvented (so to speak...not breaking any physical laws here) if we consider the viewpoint of the traveler, not some outside observer:</p>
<ul>
<li>As your ship approaches $c$ (as measured from some inertial observer) the proper time of the trip decreases. Hence, if you measured the distance to your location as 10 light years, you would reach your destination having aged less than 10 years, given that you travel at a sufficient fraction of $c$. Thus, to you, you traversed the distance faster than light.</li>
</ul>
<p>Is this a valid interpretation, or will something intervene to prevent this apparent superluminal travel?</p> | g11185 | [
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<p>I need a part or material for a planned experiment (the experiment is similar to those described in my articles <a href="http://arxiv.org/abs/1208.0066" rel="nofollow">http://arxiv.org/abs/1208.0066</a> and <a href="http://arxiv.org/abs/1109.1626" rel="nofollow">http://arxiv.org/abs/1109.1626</a> ). The problem is that the required resistivity (about 0.3 Ohm-cm or of the same order of magnitude) is much higher than that of metals and much lower than that of dielectrics. Eventually, I need a long cylindrical part, about 1.5 mm diameter and about 1 m length. So far I have considered semiconductors, conducting polymers, and absorbing materials of <a href="http://www.eccosorb.com/Collateral/Documents/English-US/Electrical%20Parameters/ls%20parameters.pdf" rel="nofollow">http://www.eccosorb.com/Collateral/Documents/English-US/Electrical%20Parameters/ls%20parameters.pdf</a> . The latter materials seem good, but they are essentially foams, and the required part cannot be machined from them. As for semiconductors and conductive polymers, I don't have a clear idea how to get (to order) a material with the required resistivity and how to make (to order) the required part. I need the above resistivity at a frequency of about 25 GHz, so, in principle, I could use a nonconductive, but absorbing (at the required frequency) material, but I would prefer a material that is conducting for direct current as well, to be able to measure the absorbed power. I would prefer a material with decent mechanical properties, so that I could, e.g., strain (tighten) the cylindrical part.</p>
<p>Any advice?</p>
<p>EDIT (02/02/2014): I have finally obtained the required parts. They are made of doped polysilicon. I am grateful for the answers. </p> | g11186 | [
0.057528406381607056,
0.00017336734163109213,
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0.03125782683491707,
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0.05478498339653015,
-0.05298137664794922,
... |
<p>Ring cavity lasers usually has a intracavity element like a optical diode to forbid standing wave pattern and, consequently, spacial hole burning and related instabilities. So, my question is: why to beams exist (before install the optical diode-like element) inside the cavity, since (as far as I know) stimulated emission radiation "follows" the direction of the pump beam? The beam propagating in the opposite direction is the amplification of the spontaneously emitted radiation amplified by the resonator?</p>
<p><img src="http://i.stack.imgur.com/7LVu5.gif" alt="Laser"></p> | g11187 | [
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0.0280591007322073,
0.00817... |
<p>If I understand correctly, Einstein's theory of General Relativity predicted the expansion of space itself, and Hubble confirmed this prediction by observing the red shift of receding galaxies.</p>
<p>I have always wondered how physicists know that this red shift indicates that space itself is expanding, as opposed to simply indicating that these galaxies are moving through space and away from Earth. I can accept that Einstein's theory predicts the expansion of space itself, but as far as confirming this prediction by observation, if space was static (neither expanding nor contracting), but the observed galaxies were moving through space at a high velocity away from Earth, wouldn't that also produce a red shift when observed from Earth?</p> | g359 | [
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0.032679... |
<p>Is it same as the direction?Then , why another term "sense"is used ,instead of direction?
Can anyone illustrate it?</p> | g11188 | [
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0.0229862779378891,
... |
<p>I have been reading lately about <a href="http://en.wikipedia.org/wiki/Lie_group">Lie groups</a>, and although all books keep listing the groups, and talk about Lie algebras and all that, one thing I still don't know how is it made, and I guess it's the most important question as much as my understanding goes, but most textbooks keep ignoring.</p>
<p>My question is, <strong>Now if I have a <a href="http://en.wikipedia.org/wiki/Symmetry">symmetry</a>, and I could put it into equation</strong> (symmetry of sea waves - simplified for example, or symmetry of planetary motion), <strong>how to use Lie groups to express this symmetry?</strong> How to identify which Lie group responsible for that?</p>
<p>I am still at the very beginning but for some reason whatever I research I cannot find an answer to this question. I hope I would find help here!</p> | g11189 | [
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0.0315... |
<p>so I had my first approximation to the gravity equation</p>
<p>\begin{equation}
F=GmM/r^2
\end{equation}
and some questions arose that my teacher couldnt respond:<br>
if r approximates to 0 with mM being constant, then the force should tend to infinity, right? so that being true, then if we would travel to the center of the earth, we would be crushed by gravity? if so, how can there be anything right in the center of the earth? wouldnt anything there be compressed and destroyed by the infinite force?
having that in mind, my next question is as gravity force is measured from the center of an object, any part of the same object which is not at the center would be affected by the same object's gravity? if so, how can we differentiate between two objects that are not in a vacuum? my question originated thinking in us standing on the earth, in contact with it, are we, in a gravitational sense, one object? this lead to the last question, if gravity is a property of matter, then how applying the same logic as before, how does it work between two neutrons?(chose neutrons because i assumed it would be more difficult obtaining gravitational force if there was electrostatic forces from charges inbetween) do two newtrons in contact count as 1 gravitational object? and how thats its own gravity affect the newtron from center and out?</p>
<p>sorry for the big text.</p> | g11190 | [
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<p>I'm a PhD student in maths, and attended my last physics class some 15 years ago, so you can imagine my competences in the field.
My supervisor (also not a mechanist) cant tell me how to proceed either, and after having spent already way too much time on wikipedia to try to understand the elementary concepts, I am turning to you, here is my problem:</p>
<p>Given is a discrete curve in $\mathbb{R}^3$, i.e. an ordered set of points $x_1,...,x_n$ all in $\mathbb{R}^3$, representing the branch of a (botanical) tree. $x_1$ denotes the point where the branch in question branches off from the trunk, $x_n$ is the branches ending point.
This discrete curve may be curved and twisted arbitrarily. At each point $x_i$, there is a mass $M_i$ concentrated. Moreover all the branch radii, $r_i$, at point $x_i$ are known (which - I think I at least got this right - is relevant to calculate the "second moment of area").
(If it helps, I would also have a continuous version of the problem, i.e. a continuous curve $s\to g(s)$ instead of the points etc...)</p>
<p>The discrete curve $[x_1,...,x_n]$ describes the branch without gravity being taken into account and the task is to find the new curve $[x_1'(=x_1),x_2'...,x_n']$ resulting from the original curve when taking gravity into account. (By the way the trunk itself is considered to be unaffected by the branches growth and weight, thus remains vertical).</p>
<p>Apparently the problem is trivial if the curve is not twisted, in the way that all $x_i$ lie in one and the same plane perpendicular to the ground (discussed on the second half of page 2 of "<a href="http://rd.springer.com/article/10.1007/s00468-001-0139-1" rel="nofollow">Bending of apricot tree branches under the weight of axillary growth</a>" by Alméras et al., in: Trees. Structure and Function, 2002.).
However, I have unsuccessfully searched for a generalization for twisted branches.</p>
<p>Could you point me in the right direction? Or, if applicable, tell me that the problem is much more complicated than I think.
Thanks a lot in advance.</p>
<p>PS: If, as it seems to me in the article mentioned, there exists a very easy way to approximate the real solution to some extend, making possibly questionable assumptions (the "small deflection assumption" seems to be of that sort), that's fine by me. I do not require an exact solution, any (halfway justified) rough approximation works perfectly for me.</p> | g11191 | [
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... |
<p>I have often heared, that Leyden jars are used because they have a high breakdown voltage. For that reason the are used for example in Whimshurst machines. </p>
<p>But what is the physical reason that they have a high breakdown voltage? And what means "high" in this context? Compared to what? How does it compare for example to a parallel plate capacitor with glass as dielectric between the plates? Why are parallel plate capacitors not used for Whimshurst machines?</p> | g11192 | [
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0.... |
<p>If I have a wavefunction $\psi = \sum_{n=0}^{\infty} a_n e^{i \phi_n} | n \rangle$ and $(|n \rangle)$ is a set of orthonormal functions. Is it correct that the probability to be in a state $|k\rangle $ is given by $|a_k|^2$?-So is it really true, that the probability to be in this state is independent of the phase factors $e^{i \phi_n}$ that is DIFFERENT for every $n$?</p> | g11193 | [
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-0.003509270492941141,
... |
<p>I'm new to this forum. This is half a question, half a challenge. And it's more engineering then physics but I thought I might get good insights from a physics forum.</p>
<p>I would like to cure a UV activated resin using a collimated 390 to 420nm light source. The area I need to cure is 3" (7.5cm) by 3". ( althoug the light beam can be bigger then this area and of any shape) so long as it's colimated and as efficient and low cost as possible. I want to get at least 3 watts of light power over that area and it has to have light everywhere and ideally as evenly distributed as possible. Ouff!</p>
<p>I'll have to build some sort of DIY apparatus to collimate light coming from 390 to 420nm LED's.</p>
<p>There are different types of LEDs on the market.
Single point high power ones (1-3W) with viewing angles 40 to 160 degrees ( the angle at which the light cone expands out) or some even higher power arrays of diodes : 5w +</p>
<p>Or low power 5mm diameter ones with witch I could build a large array of evenly spaced LEDs. ( but not necessarily) these have viewing angles of 25 to 160 degrees.</p>
<p>In all cases, the actual light emmiting part is generally square and very small, then it is encapsulated in another package.</p>
<p>I don't know much about optics and I have been pondering about this problem for a while now.</p>
<p>How would you go about doing this? From lenses to mirrors, to what type of led tp use, there's pretty much an infinite different ways to approach this and I needed to get the idea out there, so others could share their insight.</p>
<p>Feel free to throw any ideas but try to remain as technically and scientifically correct as possible.</p>
<p>Also, although the problem makes sense to me maybe I failed to share it with you appropriately, feel free to ask questions or clarifications!</p>
<p>EDIT
I intend to pass the light through an LCD screen before hitting the resin. Which brings me to another question. At these wavelength, will diffraction come I to play if the LCD "holes " the light is passing through are 100 microns large?</p>
<p>Edit wavelength can be between 390 and 420 blow that will damage the LCD. Above will not cure the resin.</p> | g11194 | [
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0.0471220389008522,
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0.00... |
<p>Say you have two objects colliding, and there is some elasticity between them. Some of the kinetic energy of the objects will change into elastic potential energy when they collide, but when they bounce off each other again, the energy does not return to being kinetic. What happens with it? Does it stay stored as elastic potential energy, or does it change to thermal energy? Or does it perhaps do something entirely else?</p> | g11195 | [
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... |
<p><img src="http://i.stack.imgur.com/oc8js.png" alt="enter image description here"></p>
<p>Normally, when a distributed force is acting on a bar, if it's 'rectengular' we multiply the length with q, but I have no idea what I'm supposed to do at this situation.</p>
<p>I first need to calculate to forces acting on C so that I can find the displacement of it by using Hooke's Law, one of the forces is 25kN and the other one comes from the distributed one, but since I can't calculate it, I'm stuck. What do I do? </p> | g11196 | [
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<ol>
<li><p>Is there any other solar system far away from ours in the universe?</p></li>
<li><p>Why don't we expect another solar system based on another star similar to sun in the universe? </p></li>
<li><p>If so, Why probably there wouldn't be some life based on those atmospheric conditions?</p></li>
</ol> | g11197 | [
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0.01070... |
<p>Question is inspired by a recent burst of <a href="http://en.wikipedia.org/wiki/Perpetual_motion" rel="nofollow">perpetuum mobile</a>-type questions. It would be nice if one could simply discard them all by an argument that shows it's impossible to create a perfect vacuum. Intuitively, I have some hope that there will be a thermodynamics/statistical mechanics argument that we can never even eliminate air friction <em>completely</em>, thereby eliminating all these elaborate constructions requiring specific arguments from the get-go. My question is therefore twofold:</p>
<ol>
<li>Does it take infinite energy to create a perfect vacuum (in a macroscopic box)?</li>
<li>If yes, can you include a derivation? If no, can you give an explicit construction with a finite amount of work being done?</li>
</ol> | g11198 | [
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<p>A $(d,\lambda)$-quantum expander is a distribution $\nu$ over the unitary group $\mathcal{U}(d)$ with the property that: a) $|\mathrm{supp} \ \nu| =d$, b) $\Vert \mathbb{E}_{U \sim \nu} U \otimes U^{\dagger} - \mathbb{E}_{U \sim \mu_H} U \otimes U^{\dagger}\Vert_{\infty} \leq \lambda$, where $\mu_H$ is the Haar measure. If instead of distributions over unitaries we consider distributions over permutation matrices, it's not difficult to see that we recover the usual definition of a $d$-regular expander graph. For more background, see e.g.: <a href="http://arxiv.org/abs/0811.2597">Efficient Quantum Tensor Product Expanders and k-designs</a> by Harrow and Low.</p>
<p>My question is - do quantum expanders admit any kind of geometric interpretation similar to classical expanders (where spectral gap $\sim$ isoperimetry/expansion of the underlying graph)? I don't define "geometric realization" formally, but conceptually, one could hope that purely spectral criterion can be translated to some geometric picture (which, in the classical case, is the source of mathematical richness enjoyed by expanders; mathematical structure of quantum expanders seem to be much more limited).</p> | g11199 | [
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<p>By the "No Hair Theorem", three quantities "define" a black hole; Mass, Angular Momentum, and Charge. The first is easy enough to determine, look at the radius of the event horizon and you can use the Schwarzschild formula to compute the mass. Angular Momentum can be found using the cool little ergosphere Penrose "discovered". However, I don't know how to determine the charge of the black hole. </p>
<p>How can an electromagnetic field escape the event horizon of a Reissner-Nordström black hole? Is there any experiment we could theoretically do to a black hole to determine its charge?</p> | g709 | [
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<p>I am confused about a method used in the following problem. There is an arrangement as shown below. The surface is smooth, and the pulleys are light. We have to find the acceleration $a_0$ of $m_1$.</p>
<p><img src="http://i.stack.imgur.com/X1esM.png" alt="Problem"></p>
<p>The method I used to solve it was to consider the pulley B and masses $m_2$ and $m_3$ as a single system that goes down with the same acceleration as that of $m_1$. If this acceleration be $a_0$, then the equations of motion give $$a_0=\frac {m_2+m_3}{m_1+m_2+m_3}g$$</p>
<p>However, the textbook solution treats motions of all objects individually, where $m_1$ has an acceleration $a_0$, $m_2$ has an acceleration $a_0-a$ and $m_3$ has an acceleration $a_0+a$, all from the lab frame(inertial). The answer calculated thus does not match with mine. The texbook gives $$a_0=\frac {g}{1+ \frac {m_1(m_2+m_3)}{4m_2m_3}}$$</p>
<p>The question is, what is the problem with considering the pulley B and the masses $m_2$ and $m_3$ as a single system of mass $(m_2+m_3)$? Or do we have to take some precautions, when the system is accelerated? (The textbook solution is perfectly alright and I understood it too, but what is the problem with mine?)</p> | g11200 | [
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<p>In his first lesson (transcripted in "Tips on Physics"), Feynman talks about math for physicists in a very cool and practical way. And at the end of the section he talks something like "so the first thing to do is to learn to learn derivative, integral and algebra" (I don't know how much precise I'm being because I've read it in Portuguese).
I would to know if there is some book that deals with math as Feynman did it in this lesson (respecting formalities, but teaching how to use the practical rules)? Also, someone have any recommendations for algebra book (college level)? </p> | g98 | [
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<p>So a coil is rotating in a magnetic field, and at $\theta=0$ the coil is perpendicular to the field lines. At $\theta=90$ the coil is parallel to the field lines.</p>
<p>The the angle, theta, is the angle between the normal to the coil and the direction of the magnetic field lines.</p>
<p>This implies that the magnetic flux induced in the coil will be at a maximum when $\theta=0$ and 0 when $\theta=90$. </p>
<p>The question I was asked was to sketch a graph of induced emf, $\epsilon$, against $\theta$. Since $\epsilon=\dfrac{\Delta\phi}{\Delta t}$, where $\phi$ is the magnetic flux linkage, the induced emf should be at a maximum when the magnetic flux is a maximum. So at $\theta=0$, $\epsilon$=maximum and at $\theta=90$, $\epsilon=0$. </p>
<p>This means that the curve sketched should look like a cosine graph, starting at the maximum value for emf induced. </p>
<p>However, in the mark scheme for this exam question the correct answer was a sine graph. It says that at $\theta=0$, the emf induced is zero. How can this make sense? Is my logic wrong?</p> | g11201 | [
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<p>I know how to detect when resistors are arranged in parallel or series arrangement and<br>
I can also find their equivalent resistance in simple circuits or when resistances are connected in form of<br>
triangle but what happens when the arrangement is complex like this :<br>
<img src="http://i.stack.imgur.com/MM06V.png" alt="Resistors"></p>
<p>Which resistors are parallel and which are in series ? How can I find the equivalent resistance in such cases ? Is there rule or method for figuring this out ?</p> | g11202 | [
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<p>I have been viewing this video :<BR><a href="http://www.youtube.com/watch?v=Ehlw-9PJkIE" rel="nofollow">Masaru Emoto's Rice Experiment</a> <BR>
Anybody has any physical explanation of this phenomena? </p> | g11203 | [
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