question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>We know that gravitational waves are emitted (at least in GR) when the system has a time-varying quadrupole (or higher) moment. My question is</p>
<p><em>Is it possible to easily tell (e.g. just by looking) if a system has such moments?</em></p>
<p>Is there some kind of symmetry to look for that lets you know that the system will emit such radiation?</p> | g11940 | [
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<p>For instance evidence that a highly energetic laser beam attracts objects nearby?</p>
<p>In the framework of Einstein's general relativity all energy curves spacetime and hence exerts an attraction, but my question is whether it is an experimentally verified fact that energy that doesn't come from mass (such as photons) indeed attracts massive objects?</p> | g512 | [
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<p>I would like to know if light is affected by gravity, also, I would like to know what is the correct definition of gravity:</p>
<p>"A force that attracts bodies with mass" or "a force that attracts bodies with energy, such as light"?</p>
<p>Is light massless after all?</p> | g143 | [
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<p>Suppose that a hollow truncated cone is placed in a wind tunnel with a steady wind speed $V$. The cone is placed in such a way that it's base of area $A_1$ faces the wind (rather than the other side of area $A_2$ for which $A_1>A_2$). Here's a contradiction:</p>
<p>Supposing that $V_2$ is the speed for which wind appears from that end of the cone of area $A_2$, using the conservation of mass law, we get $A_1V=A_2V_2$ and hence $V_2>V$. Now using the relation $\sum F=\dot{m}\Delta V$ (which results from the more general relation $\sum F=\frac{\partial}{\partial t}\int_{C.V}V.\rho (dv)+\int_{C.S}V.\rho (VdA)$) we see that a net thrust is generated which pushes the cone forward and against the wind, but this is impossible.</p>
<p>What's wrong with this argument? I've been giving it some thought but I can't figure out a way to solve it.</p> | g11941 | [
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<p>Consider a situation where a wheel is rolling without friction on a level surface. Call the center of the wheel $C$, the point where the wheel contacts the ground $G$, and some arbitrary other point on the rim of the wheel $P$.</p>
<p>The normal force has no torque when $G$ or $C$ is picked as the axis of rotation, but it does if $P$ is chosen for any point (minus the top of the wheel). If a physics problem then says to pick the force that gives the largest torque, how am I meant to choose if the axis of rotation choice changes the answer?</p>
<p>The physics book I have states that $G$ or $C$ are points at which an axis of rotation may be placed because they both have the same angular acceleration around each other. This seems fine to me; I can visualize the concept of the $C$ rotating about $G$. The trouble is that it seems to be the same situation for any $P$.</p>
<p>Working out the math, it does seem that every point on the rim chosen as the axis of rotation is such that the center of mass rotates about the chosen point at the same speed as the chosen point rotates about the center of mass.</p>
<p>What is going on here? How does one 'get a feel' for these problems where it seems that the axis of rotation choice is so critical?</p> | g11942 | [
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<p>I'm wondering is there any way to decompose the deformation of an object into different components? For example, into stretching, bending and twisting part respectively? The decomposition could be applied to any description of deformation, either to deformation gradient tensor, strain tensor or stress tensor.</p>
<p>To my knowledge, there is some literature using the decomposition of deformation gradient tensor into rotation and deformation part. But what I want is to further decompose the deformation, leave away the rigid transformation like translating and rotating.</p>
<p>Thanks!</p> | g11943 | [
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<p>I was informed that in a circuit, the current will stay the same, and this is why the lightbulbs will light up (because in order for the current to stay the same, the drift speed of the electrons need to get faster). However, I do not understand why the current needs to stay the same from point to point.</p>
<p>Why does the current stay the same from point to point in a circuit?</p> | g11944 | [
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<p>If the universe started from Big Bang and everything is expanding outwards and actually accelerating away from each other, than "<strong>How is it possible for two galaxies to collide as they all are moving in the same direction</strong>". To collide they must in opposite direction!</p>
<p>Edit:<strong>How is it possible for two galaxies to collide as those colliding galaxies are moving in the same direction.</strong></p> | g11945 | [
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<p>I use the sign convention:</p>
<ul>
<li>Heat absorbed by the system = $q+$ (positive)</li>
<li>Heat evolved by the system = $q-$ (negative)</li>
<li>Work done on the system = $w +$ (positive)</li>
<li>Work done by the system = $w -$ (negative)</li>
</ul>
<p>Could anyone please tell me, that volume increased in system does positive or negative work?</p> | g11946 | [
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<p>Ok so I understand the PN junction, and how when 2 Semiconductor materials are placed together the Electrons will jump into the Holes near the junction creating a Negatively Ionized Atoms on the P-Side (Near the Junction) and Positively Charged Atoms near the Junction on the N-Side.</p>
<p>Makes sense.</p>
<p>HOWEVER, the Donor Atoms Give out Electrons at room temperature and the Acceptor Atoms move around holes at room temperature.</p>
<p>How come these Ionized Atoms aren't Displacing Electrons to create more holes (In the Ionized P-Side) or Accepting more electrons (In the Positively Ionized Region on the N-Side)?</p>
<p>I understand That the Electric Field is causing some resistance....but Regardless at room temperature why aren't the Electrons getting excited out of the Negatively Ionized Atoms on the P-Side near the Junction....Why are they now "fixed" to the lattice? Like why aren't these Atoms near the Junction allowing Electrons to Get Excited and move at room temperature (Like the Electrons that have filled the holes on the P-Side)?</p>
<p>Every Book/Semiconductor Physics book i've read talks about how the Ionized Atoms are fixed to the lattice (Makes sense)....but it doesn't say why THEY themselves aren't changing due to thermal excitations at room temperature. </p>
<p>edit:
to rephrase:Why arent the acceptor atoms releasing the electrons they obtained from the N-Biased junction at room temp? Because I know That the electric field at the depletion region is caused by electrons filling holes in the P-region and Lack of Electrons in the N-Region.....im asking whats stopping those acceptor atoms near the junction in the P-region from "releasing electrons (that they just gained)" or whats stopping the donor atoms from being filled? (the atoms that are producing an electric field). I understand the electric field opposes more electrons from filling the n-side, but whats stopping the p-side negative ions from being excited again?</p>
<p>I guess im confused how the electric fields are stable...when room temperature is what excited the electrons in the first place.</p> | g11947 | [
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<p>When a sink drains it forms a vortex. Does that vortex speeds drainage. If yes, how does the vortex speed drainage?</p>
<p>The only relevant thing I could find was an <a href="http://www.sciencedirect.com/science/article/pii/S0378437103005946">expensive article</a> and a <a href="http://www.usc.edu/CSSF/History/2010/Projects/J0102.pdf">science fair project</a>. </p> | g11948 | [
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<p>I want to prove the Bethe-Bloch stopping power formula but I don't know where to start. Any one can offer a book or paper?</p>
<p>Related: <a href="http://en.wikipedia.org/wiki/Bethe_formula" rel="nofollow">http://en.wikipedia.org/wiki/Bethe_formula</a></p> | g11949 | [
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<p>I'm currently reading up on quantum computing and it seems like I have found some contradiction about how to represent <a href="http://en.wikipedia.org/wiki/Qubit" rel="nofollow">qubits</a>.</p>
<p>It is often stated that a qubit is represented as $a|0\rangle + b|1\rangle = (a, b)$ with both a and b being complex numbers.</p>
<p>However, it is stated just as often, that there is only one complex number needed, namely b, since to ignore the global phase shift means, that a becomes real while b stays complex. See for example: <a href="http://demonstrations.wolfram.com/QubitsOnThePoincareBlochSphere/" rel="nofollow">this</a> and <a href="http://en.wikipedia.org/wiki/Bloch_sphere" rel="nofollow">this</a>.</p>
<p>What is it now? What don't I get here?</p> | g11950 | [
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<p>The <a href="http://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients" rel="nofollow">Clebsch-Gordan coefficients</a> can only be non-zero if the triangle inequality holds:
$$\vert j_1-j_2 \vert \le j \le j_1+j_2$$
In my syllabus they give the following proof:
$$-j \le m \le j$$
$$-j_1 \le m_ \le j_1$$
and $$
-j_2 \le m_2 \le j_2$$
For maximal values: $m = j$, $m_1 = j_1$ and $m_2 = j_2$ we get:</p>
<p>1) $-j_1 \le j-j_2 \le j_1$ which implies $j_2-j_1 \le j \le j_1+j_2$</p>
<p>2) $-j_2 \le j-j_1 \le j_2$ which implies $j_1-j_2 \le j \le j_1+j_2$</p>
<p>Which should prove the triangle inequality.</p>
<p>This proof looks really simple, but I don't completely understand it though. It seems that I'm missing some essential reasoning, and I can't find where. Why for instance do they take for $m_1$, $m_2$ and $m$ all maximal values? Can't I also take $m$ maximal and $m_1$ minimal? This would give bad results though. So I really don't understand it, and I hope that someone can clarify it. </p> | g11951 | [
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<p>EDIT: I found both answers to my question to be unsatisfactory. But I think this is because the question itself is unsatisfactory, so I reworded it in order to allow a good answer.</p>
<hr>
<p>One take on contextuality is to develop an inequality on measurement outcomes that is satisfied for any ontological noncontextual theory, and see that it is violated by quantum mechanics.</p>
<p>Another take would be to assume an algebraic structure and see that if one restricts the observable algebra to be commutative, the expected values of certain operators are restricted to lie in a given range, whereas if we allow non-commutativity the range is greater.</p>
<p>These approaches coincide? I've seen plenty of works that assume that it does, but without discussing it; in particular there is <a href="http://www.tau.ac.il/~tsirel/download/hadron.html" rel="nofollow">this paper</a> by Tsirelson that states (in the particular case of Bell inequalities) that both approaches are equivalent, but without proving it. Is it too obvious?</p>
<p>At first sight, an ontological noncontextual theory is much more general than some theory embedded in a C*-algebraic framework. Why then can't it generate stronger correlations than theories with commuting algebras of observables?</p>
<p>Can one find a more direct connection between non-commutativity and the violation of a contextual inequality?</p> | g11952 | [
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<p>I hope someone can help me find the page or chapter where Helstrom discusses his famous measurement for distinguishing between two mixtures in the textbook <em>Quantum Detection and Estimation Theory</em>.</p>
<p>Thanks in advance.</p> | g11953 | [
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<p>A pneumatic cylinder is kept vertically straight on a weighing scale, which is set at 0 for the setup.</p>
<p>now a force of 1000 N is applied on the cylinder.</p>
<p>what is the reading of scale.</p>
<p>assume the outlet/ inlet to be blocked hence the mass of air inside the cylinder shall remain constant all the times and cylinder can move in y(vertical) direction by compressing the air inside it on application of external force.</p>
<p>let diameter of bore of cylinder be 60 mm and stroke be 50 mm.</p>
<p>will the reading be less than 1000N or less or more??</p>
<p>more info can be supplied if required.</p> | g11954 | [
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<p>In the first days of July 1997, after a long driving effort, crossing all of Europe to come to a meeting in Peñiscola, Vladimir Gribov fell fatally sick and he passed away one month later. His paper "<em>QCD at large and short distances</em>" was uploaded posthumously to arXiv:hep-ph/9708424 and, in edited version, to <a href="http://es.arxiv.org/abs/hep-ph/9807224" rel="nofollow">arXiv:hep-ph/9807224</a> one year later. Still a remaining write-up, "<em>The theory of quark confinement</em>", was collected, edited and uploaded later to arXiv:hep-ph/9902279.</p>
<p>I guess that I am asking for some general review of these articles, but I am particularly intrigued by the conclusion as it is exposed in the introduction to the first one (bold emphasis is mine). </p>
<blockquote>
<p>"The conditions for axial current conservation of flavour non-singlet
currents (in the limit of zero bare quark masses) require that eight
Goldstone bosons (the pseudo-scalar octet) have to be regarded as
<strong>elementary objects</strong> with couplings defined by Ward identities."</p>
<p>"... the flavour singlet pseudoscalar η′ is a "normal bound state of
qq¯ without a <strong>point-like</strong> structure"</p>
</blockquote>
<p>How serious is this elementary status? For instance, in order to do calculations of electroweak interaction, should the bosons in the octet be considered as point particles, say in a Lagrangian? Does it imply that the QCD string, at low energy at least, is point-like?</p>
<p>And, does it happen the same for the colored state having two quarks? (What I mean here is the following: the color-neutral states have been produced from the decomposition $3 \times \bar 3 = 8 + 1$ of SU(3) flavour, joining a quark and an antiquark. Similarly, we could use QCD to join two quarks, and then SU(3) flavour should decompose as $3 \times 3 = 6 + 3 $) <strong>Is the flavour sextet "pointlike"</strong>? And the triplet then, is it still a "normal bound state"?</p>
<p>I expect the argument does not depend of the number of flavours, so the same mechanism for SU(5) flavour should produce a point-like color-neutral 24 and, if the answer to the previous question is yes, a point-like colored 15. Is it so?</p>
<p>Let me note that most work on diquarks concludes that only the antisymmetric flavour triplet, not the sextet, is bound by a QCD string --e.g., measured as $\sqrt 3/2$ times the meson string here in <a href="http://link.aps.org/doi/10.1103/PhysRevLett.97.222002" rel="nofollow">PRL 97, 222002 (2006)</a>--. </p> | g11955 | [
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<p>If $|0 \rangle$ is the vacuum state in quantum mechanics and $\alpha$ is any complex number, what is $\langle 0 | \alpha | 0 \rangle$? I need to have that $\langle 0 | \alpha | 0 \rangle = \alpha$, but this seems to imply that $\langle 0 | 0 \rangle = 1$. Is this true? If so, why? </p> | g11956 | [
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<p>I have a doubt about a couple of exercises tha asks to find the work done on introducing a dieletric between the plates of a capacitor. Yes, this question is in the general case, how do we procede? I really don't know how to start those questions. I know how to find the new capacitance, the new field between the plates and the new voltage, but I don't know how to find the work required to introduce the dieletric.</p>
<p>So, given a capacitor of capacitance $C$ and charge $Q$ what's the procedure if we want to find the work on introducing a dieletric of constant $k$ inside the plates?</p>
<p>I just want some ideas on how to start those problems.</p>
<p>Thanks very much in advance.</p> | g11957 | [
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<p>I am trying the following problem. A resistor with $295\Omega$ and an inductor are connected in series across an AC source that has voltage amplitude of $550V$. The rate at which electrical energy is dissipated in the resistor is $224W$. </p>
<p>What is the impedance of the circuit. </p>
<p>I tried this: $224W=I^2R$, from which $I=.87A$. Then, we have that $V=IZ$ in an AC circuit, so $550V=.87A(Z)$, and from here I get that $Z=631.17\Omega$. </p>
<p>I was wondering what is wrong here. Am I using the correct formulas?</p> | g11958 | [
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<p>Recently there is renewed interest in the ideas of Vasiliev, Fradkin and others on generalizing gravity theories on deSitter or Anti-deSitter spaces to include higher spin fields (utilizing known loopholes in the Weinberg-Witten theorem by including infinitely many higher spin fields and by working with asymptotic conditions that do not permit S-matrix to exist). There is also a conjecture for a duality for the theory as formulated in asymptotically AdS space with the O(N) vector model in the large N limit.</p>
<p>So in this context I am curious if there are supersymmetric generalizations of the theory, and how much supersymmetry can be shown to be consistent with this set of ideas (given that the usual restriction to 32 supercharges comes from forbidding higher spin fields).</p> | g11959 | [
0.0052412161603569984,
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0.... |
<p>How can parts of a laser beam be made visible while others left invisible using something electronically controllable (for example, another laser beam crossing it, or a magnetic field, or heat, etc).</p> | g11960 | [
0.05821746587753296,
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0.0086... |
<p>I understand that the <a href="https://en.wikipedia.org/wiki/Electromagnetic_tensor" rel="nofollow">Electromagnetic Tensor</a> is given by</p>
<p>$$F^{\mu\nu}\mapsto\begin{pmatrix}0 & -E_{x} & -E_{y} & -E_{z}\\
E_{x} & 0 & -B_{z} & B_{y}\\
E_{y} & B_{z} & 0 & -B_{x}\\
E_{z} & -B_{y} & B_{x} & 0
\end{pmatrix}$$</p>
<p>where $\mu$, $\nu$ can take the values {0,1,2,3} or {$t,x,y,z$}.</p>
<p>So, for example
$$F^{01}=F^{tx}=-E_x$$</p>
<p>My question is, what would the following expression be?</p>
<p>$$F^{t\rho}=?$$
or
$$F^{z\rho}=?$$</p>
<p>where $\rho=\sqrt{x^{2}+y^{2}}$ is the radial coordinate in <a href="http://en.wikipedia.org/wiki/Cylindrical_coordinate_system" rel="nofollow">cylindrical coordinates</a>?</p>
<p>And <strong>more generally</strong>, how can we construct the Electromagnetic Tensor in cylindrical coordinates? Where $\mu$, $\nu$ now take the values {$t,\rho,\varphi,z$}.</p> | g11961 | [
0.01514458004385233,
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<blockquote>
<p><em>Consider the product of vectors coordinated relative to a given coordinate frame, defined by</em>
$$\vec{a}\square\vec{b}=((a_{1},b_{1})\square(a_{2},b_{2})):=(a_{1}b_{1},a_{2}b_{2})$$
<em>Explain why that in the context of vectors this is no good.</em></p>
</blockquote>
<p>My work:</p>
<p>I think that it is no good because if you change the coordinate system, you may change the vector. (Like a vector in Cartesian coordinates would be a different vector in polar coordinates [Not a 100% sure about that, but seems to make sense]).</p>
<p>If anyone could expand as to why this is true, it would be greatly appreciated. Also please note, that I am fairly new to vectors, so if the advanced physics jargon could be kept to a minimum it would be appreciated as well. </p> | g11962 | [
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<p>I asked a version of this question over on <a href="http://math.stackexchange.com/questions/667027/naming-and-meaning-of-exponential-power-functions">Math.SX</a>, and never received a response… perhaps it will be more appropriate here.</p>
<p>I'm looking at spectroscopic data (specifically a $T_2$ coherence decay curve of some NMR data). Normally, this data is fit to a single or multi-exponential decay to account for multiple components. However, I have a data set that fits best to a function with a power in the exponent near 1.4 (in between a Gaussian and single exponential decay). </p>
<p>Is there any physical meaning for <a href="http://en.wikipedia.org/wiki/Generalized_normal_distribution" rel="nofollow">generalized normal distribution functions</a>? To elaborate on what I mean by "physical meaning", when working with spectroscopic absorptions, an an exponential decay (n=1) indicates a system with homogeneous broadening of lifetimes, while a Gaussian decay indicates inhomogenous broadening of lifetimes. What does a power between these two values indicate? Is there a precedent for using this sort of peak shape (or decay function in this case) in spectroscopic analysis?</p>
<h3>--EDIT--</h3>
<p>To demonstrate the phenomenon, here are a couple of sample curves with some data. The depressed points at the start <strong>may</strong> be an experimental artifact, but I'd still be curious to know if there is any physical precedent for the exponential power between 1 and 2.</p>
<p>$e^{-t/T_2}$</p>
<p><img src="http://i.stack.imgur.com/XFvIb.png" alt="Exponential decay ($e^{-t/T_2}$"></p>
<p>$e^{-(t/T_2)^{1.6}}$</p>
<p><img src="http://i.stack.imgur.com/hPjhK.png" alt="Modified exponential decay ($e^{-(t/T_2)^{1.6}}$)"></p> | g11963 | [
-0.006681883707642555,
-0.04776474088430405,
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0.014255753718316555,
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<p>What is the difference between <a href="http://en.wikipedia.org/wiki/Isospin" rel="nofollow">isospin</a> and <a href="http://en.wikipedia.org/wiki/Weak_isospin" rel="nofollow">weak Isospin</a>? What is the difference between <a href="http://en.wikipedia.org/wiki/Hypercharge" rel="nofollow">hypercharge</a> and <a href="http://en.wikipedia.org/wiki/Weak_hypercharge" rel="nofollow">weak hypercharge</a>?</p> | g11964 | [
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0.03481939062476158,
0.03... |
<p>As we all know temperature of space is near to absolute zero.Then why super conductors aren't used there?</p> | g11965 | [
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<p>Here is a question that a friend asked me. He had to an experiment in school and do some calculations afterwards. Those calculations require maximal current that the DC source can produce. He has measured the maximal currents for two separate sources but forgot to measure it for both connected in series.</p>
<p>If maximal current of one battery is $a$ and maximal current of other battery is $b$, what will be the maximal current if one connects these batteries in series?</p>
<p>I could imagine the equation system:
$$I=\frac{\varepsilon_1 + \varepsilon_2}{r_1+r_2}$$
$$I_1=\frac{\varepsilon_1}{r_1}$$
$$I_2=\frac{\varepsilon_1}{r_1}$$
where $I$ is for current, $\varepsilon$ for electromotive force and $r$ for inner resistance.</p>
<p>But it seems to have too many unknowns. And I'm not even sure if it's correct to describe the system in this way.</p> | g11966 | [
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... |
<p>If molecules at the surface of a liquid have higher energy and want to minimise the surface area, then why is a mensicus formed which of course increases the surface area?</p> | g11967 | [
0.03590645268559456,
0.015572557225823402,
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<p>I'm looking for unique and illustrative ways to explain the phenomenon of interference to a tour group consisting of all types of people, from elementary school kids to adults. I run into this problem from time to time at the <a href="http://www.ligo-la.caltech.edu/" rel="nofollow">LIGO Livingston Observatory</a>. I often use my hands to illustrate two waves adding up constructively or destructively, but I don't think it gets across to people who aren't already familiar with the idea. </p>
<p>I have the possibility to use small gadgets or home-made devices, but they can't be too complex or bulky. </p> | g11968 | [
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0.0336679108440876,
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0.... |
<p>The wikipedia page "<a href="http://en.wikipedia.org/wiki/Force_carrier">Force Carrier</a>" says:</p>
<blockquote>
<p><em>The electromagnetic force can be described by the exchange of virtual photons.</em></p>
</blockquote>
<p>The virtual photon thing baffles me a little. I get that <a href="https://en.wikipedia.org/wiki/Virtual_particle">virtual particles</a> are supposed to be short lived, but as photons live for zero units of proper time I can't see how their lifetime can be used to distinguish between virtual and non-virtual.</p>
<p>Another idea I had was that virtual photons are only those associated with the electromagnetic field, non-virtual ones are not. But in this case, I could not see what was wrong with this: If I have a photon detecting instrument it is just detecting the force carrying particles of the electromagnetic interactions between it and the thing I am using it to observe? (even if that thing is a long way away)</p>
<p>Are virtual photons just photons that you don't observe? Or, is there some kind of photon that is not connected with the electromagnetic field? Or something else? Or perhaps there is no concrete distinction to be made?</p> | g808 | [
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<p>I apologize if this question is naive. I am wondering about what would happen with the following experiment.</p>
<p>Start with a standard Bell's Theorem setup: We have two quibits entangled in a particular way and sent in opposite directions, where they are measured by independent observers. The distribution of joint measurements is, Bell says, inconsistent with any theory of local variables.</p>
<p>But now, before we send the quibits out, a single central person measures both quibits. That person does not communicate with either observer.</p>
<p>My question is, <strong>does the distribution of measurements of the observers change?</strong></p>
<p>This seems like a paradox to me for the following reason. The central person actually knows what the outcomes will be of the observers' measurements. Therefore, the central person can set or calculate "local variables" that always explain what measurements will occur. Yet, to the observers, this experiment seems indistinguishable from the standard Bell's Theorem experiment (they can't even tell whether the central person is there or not!). So they should see the same distribution, which no local variable theory can explain.</p>
<p>...</p>
<p>One possibility that I thought of is that the answer might depend on whether the light cones of the central person and the observers overlap, in some way, i.e. on whether the information can be transmitted at conventional speeds or not. However, we are assuming that the central person does not communicate with them in any way...(is this assumption even well-defined?).</p>
<p>But my guess is that the observers should see the same distribution of measurements. The resolution of the paradox would be that, from the observers' perspectives, the central person and her local variables are in a superposition, just like Schrodinger's cat. Could this be right?</p> | g11969 | [
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<p>Lightning strike is categorized as DC because of its electrostatic nature. The negative flash/stroke is found to have 200KA of current with a voltage close to 300KV (cloud to ground). But why is it referred to as a High frequency source, since it does not have a frequency component? In an electric circuit diagram will lightning be represented as a voltage source or current source?</p> | g11970 | [
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<p>My wife made Rose-hip syrup and the final part was boiling it in a saucepan. While still hot she placed it in a glass bottle. To keep it sterile she plugged it with a wine-saver top and sucked out some of the air - so the (inch or so) space in the bottle is at lower than atmospheric pressure. Large bubbles are spontaneously appearing in the bottle and quickly rising to the top. This has been happening for half an hour. The bottle is still quite warm . It <em>looks</em> like it is on a slow boil: is it?</p> | g11971 | [
0.04155975207686424,
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0.03767923638224602,
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-0.... |
<p>This is probably a stupid and simple question, but does the heisenberg uncertainty principle set this upper bound? That knowledge of the momentum is limited, so it can't reach a very low value and thus have a very large (visible) debroglie wavelength? I am figuring if you wanted to test this on a macroscopic particle you would need it frozen to near-absolute zero, but I assume QM comes in and makes it impossible to see visible wavelengths with the naked eye. Thanks!</p> | g379 | [
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0.006814217660576105,
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-... |
<p>I'm not sure if this is a duplicate.</p>
<p>Whenever physics buffs talk about Einstein's relativity (I forget which kind) at high speeds, they always talk about "length contraction", or shortening of the object due to the high speeds. This happens even at the relatively low speeds we travel at every day, but there is so little contraction we don't notice it. However, these physics buffs only talk about <strong>length</strong> contraction, implying a single dimension. Why do they never talk about contraction in more than 1 dimension? Is it because the contraction happens in the direction the object is going, which is usually only a single direction? If so, are there <em>any</em> cases which would involve 2- or 3-dimensional contraction?</p> | g11972 | [
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0.010072698... |
<p>A bug eats through an apple and forms a vertical, infinitesimally thin canal parallel to the vertical diameter at a distance $\frac{R}{2}$ from the center. The apple rotates at angular velocity around that center equal to $\sqrt{\frac{g}{R}}$. As the bug attains the other side of the apple it slips and falls through that canal, whose coefficient of friction is $\mu$, and I am asked to find its velocity as it passes through the bottom.</p>
<p>Now, the length of the canal is obviously $R\sqrt{3}$. The location of the bug may be written as: $(\frac{R}{2},y)$ wrt to the center of the apple. Coriolis would have an effect in the negative $x$ direction whereas the centrifugal force, unless I am mistaken, should have an effect in both $x$ and $y$ directions.
Hence,
$$N = m \omega^2 \frac{R}{2} - 2m \omega \left(\frac{\mathrm{d}y}{\mathrm{d}t}\right)$$
and
$$-mg + \mu N + m \omega^2 y=m\left(\frac{\mathrm{d}^2y}{\mathrm{d}t^2}\right)$$</p>
<p>Is this how this problem ought to be approached?</p> | g11973 | [
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0.013211570680141449,
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0.008184061385691166,
-0.02299... |
<p>The mathematical formula for <a href="http://en.wikipedia.org/wiki/Work_%28physics%29" rel="nofollow">work</a> says that work is force into displacement, but what is the philosophy behind it? I mean what does the quantity suggest?</p> | g380 | [
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0.006755204871296883,
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0.06019063666462898,
-0.024... |
<p>It seems that popular textbooks on electrodynamics do not discuss how to solve the <a href="http://www.google.com/search?as_q=Laplace+equation+ellipsoidal+coordinates" rel="nofollow">Laplace equation</a> in <a href="http://en.wikipedia.org/wiki/Ellipsoidal_coordinates" rel="nofollow">ellipsoidal coordinates</a>. I could not find any reference, but there must be references about this. Could anyone give a reference?</p>
<p>As an example, the question can be how to calculate the charge distribution on an ellipsoid by solving the Laplace equation. (I know there is a way to solve this particular problem without solving the Laplace equation, but I want to know how the ellipsoidal coordinates works.)</p> | g11974 | [
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0.03572217375040054,
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0.009725312702357769,
0.07069764286279678,
0.017854... |
<p>According to Darcy's Law, the volumetric flow rate Q of a fluid occuring due to a pressure difference $\Delta p$ over a distance L and through a cross-sectional area A of a porous medium (volume V) is given by:</p>
<p>$$Q = \frac{k\cdot A}{\mu}\cdot \frac{\Delta p}{L}\tag{1}$$</p>
<p>When calculating the pressure increase caused by that inflow of Q over a time $\Delta t$, it is typically considered for porous media that only a fraction of its total volume can actually be filled by the fluid, where the fraction of "free space" is characterized by the porosity $n = V_{free}/V_{total}$:</p>
<p>$$\Delta p = K\cdot Q\cdot \frac{\Delta t}{n\cdot V_{real}}\tag{2}$$</p>
<p>My question now is:
Why is the porosity considered in the last equation, but not in the cross-sectional area of the first equation? By the very same logic I could say, that only a fraction of the cross-sectional area is "open" for fluid to flow into, couldn't I? Especially since (1) is often used for the determination of material permeabilities, but always the total cross-sectional area is used for the calculation.</p>
<p>This is just something that seems odd to me and maybe one of you guys has some insight on that and tell me where I'm thinking wrong.</p> | g11975 | [
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<p>A friend asked me if it would be possible to make soap bubbles out of a gas like hydrogen and if you did, would they float higher, faster. Due to the lower mass of light gases (compared to the air) I know they will float up faster (buoyancy). I wonder how stable they would be though.</p>
<p><strong>My question is, will bubbles filled with a light gas like helium or hydrogen be stable for similar time periods to bubbles filled with air?</strong> I suspect there are complicated effects between the gas and the surface tension of the soap. Will the smaller molecules of the light gases be able to breach the soap bubble faster?</p>
<p>I <a href="http://www.youtube.com/watch?v=7x8KgONMAjs" rel="nofollow">found a video that shows</a> bubbles filled with air having helium added to them. They seem stable but I wonder if they'd be stable if they didn't have the air mixed in (pure helium).</p> | g11976 | [
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... |
<p>If I have two pieces of steel that I would like to weld with a laser (say $d$ in diameter). If I wanted to melt the two pieces to a depth of $d$ along the edge and then combine them together, how much power for the laser would I need?</p>
<p>Is this simply $ P = A*\sigma * T_{\text{melting}}^4$?</p>
<p>Also how fast can the laser stay on such that it wont over heat? How would you calculate upperbound on the max distance the laser can cut per second?</p>
<p>How do you calculate whether or not molten steel will drip? Depends on viscosity and surface area right? Any help is appreciated</p> | g11977 | [
0.03475214168429375,
0.002331735100597143,
0.0006987325032241642,
-0.012152189388871193,
-0.018308671191334724,
-0.05219186469912529,
-0.045527659356594086,
0.039254482835531235,
-0.06627052277326584,
0.008752898313105106,
-0.015405015088617802,
0.049052800983190536,
0.03312272951006889,
-... |
<p>[This is a version of the question that I've revised based on helpful comments from Dan.]</p>
<p>I haven't studied inflation at a technical level. My picture of the process is that we have an inflaton field $\phi$ which is a scalar and has a potential $V(\phi)$. Before inflation, the field starts at some $\phi_o$ that doesn't equal the value $\phi_m$ that minimizes $V$. It then rolls downhill to the minimum.</p>
<p>Assuming I have this right, what I don't understand is (1) why $\phi$ initially has a <em>single value</em> $\phi_o$ everywhere, and (2) what sets $\phi_o$. Before the onset of inflation, the universe's temperature was much higher than any scale set by $V$. When the age of the universe was on the order of the Planck time, presumably its temperature was on the Planck scale. If the temperature was that high, wouldn't thermal fluctuations cause the field to sample a wide range of values of $\phi$, contradicting #1? And if it could sample all those values, I would expect that thermodynamically, it would consist overwhelmingly of values of $\phi$ close to $\phi_m$, not some other value $\phi_o$.</p> | g11978 | [
0.030615899711847305,
0.025564968585968018,
0.0023430073633790016,
0.010390388779342175,
0.034011129289865494,
0.051580723375082016,
0.004452962428331375,
0.021626506000757217,
-0.0422404482960701,
-0.0596790574491024,
-0.05828581377863884,
0.038324348628520966,
0.013829500414431095,
0.019... |
<p>Poiseuille's Law relies on the fact that velocity is not constant throughout a cross-section of the pipe (it is zero at the boundary due to the no-slip condition and maximum in the center). By Bernoulli's Law, this means that pressure is maximum at the boundary and minimum at the center. But in the book I have it is assumed that the pressure gradient is independent of radius (distance from the center of the pipe), and the pressure gradient is thus extricated from a radius-integral. Can anyone justify this?</p> | g11979 | [
0.015862395986914635,
0.019616181030869484,
0.0005240527680143714,
-0.019961323589086533,
-0.00008757148316362873,
0.01726742833852768,
0.029998404905200005,
0.05286933109164238,
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0.06807220727205276,
-0.10048537701368332,
-0.05222160369157791,
-0.028851766139268875,
-... |
<p>I am trying to understand how is it possible for electric force to behave like this (path independence)?</p>
<p>I am repeatedly failing to get an intuitive meaning behind its (electric field) nature of doing the work.</p>
<p>Does it have to do with the radial direction of electric force ? or Its inverse-square law nature?</p> | g11980 | [
0.014270629733800888,
0.04777528718113899,
-0.01680118776857853,
0.029439019039273262,
0.07122016698122025,
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0.03907979279756546,
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-0... |
<p>I am writing an article and the central results are summarized in a graph so I want it to be very beautiful and physically intuitive. It has 3 regions in which a certain quantity is conserved, partially conserved or not conserved so I want them to be respectively green, yellow/orange and red. The problem is that I can't find a good combination of colors... Maybe someone has done something of similar before and can give some suggestion.. I post here my figure:</p>
<p><img src="http://i.stack.imgur.com/gdLfq.png" alt="enter image description here"></p>
<p>Maybe it is not the right place where ask this question but I can not find a more appropriate Stack Exchange site to post it...</p> | g11981 | [
0.06360026448965073,
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0.004488697741180658,
0.037887778133153915,
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0.03823942691087723,
-0.0... |
<p>Many quantum-gravity theories are strongly interacting. It is not clear
if they produce the gravity as we know it at low energies. So I wonder, is there
any quantum-gravity theory that</p>
<p>a) is a well defined quantum theory at non-perturbative level (ie can be put in a computer to simulate it, at least in principle). </p>
<p>b) produces nearly flat space-time.</p>
<p>c) contains gravitons as the ONLY low energy excitations. (ie the helicity $\pm 2$ modes are the ONLY low energy excitations.)</p>
<p>We may replace c) by</p>
<p>c') contains gravitons and photons as the ONLY low energy excitations. (ie the helicity $\pm 2$ and $\pm 1$ modes are the ONLY low energy excitations.
This is the situation in our universe.)</p> | g11982 | [
0.03511319309473038,
0.05046357586979866,
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0.04693973809480667,
-0.02849089726805687,
0.0058520096354186535,
0.0... |
<p>I am very puzzled by the motivation for Mohr's circle in Wikipedia <a href="http://en.wikipedia.org/wiki/Mohr%27s_circle" rel="nofollow">here</a>. Please, explain why we need something called <em>"Mohr's circle"</em>. Use as little words as possible and be precise.</p>
<p><strong>Helper questions</strong></p>
<blockquote>
<ul>
<li>To illustrate normal stresses and shear stresses? </li>
<li>Why is it used? When is it really used? </li>
<li>Some example to show why it may have some usage scenarios?</li>
<li>Is it just a tool to show two-dimensional stresses on a two-dimensional plane?</li>
</ul>
</blockquote> | g11983 | [
0.037785854190588,
0.036941636353731155,
-0.014926465228199959,
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0.0572841502726078,
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0.00549467746168375,
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0.045460641384124756,
0.0... |
<p><img src="http://i.stack.imgur.com/SIL3d.jpg" alt="enter image description here"></p>
<ol>
<li><p>What is $V_{\alpha\beta}$? </p></li>
<li><p>And what is a symmetric, <a href="http://en.wikipedia.org/wiki/Positive-definite_matrix" rel="nofollow">positive definite</a> potential energy matrix? </p></li>
<li><p>And why is there a linearized equation like this?</p></li>
</ol> | g395 | [
0.05724634975194931,
-0.03628925234079361,
-0.04766717180609703,
-0.01048891618847847,
0.04598798602819443,
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0.006385469809174538,
0.04184231907129288,
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-0.022039147093892097,
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0.0305766761302948,
0.00394488126039505,
-0.004768... |
<p>Suppose I can compute interaction energy of two rigid bodies as a function of their coordinates of centers of masses and Euler rotation angles (total 6 + 6 degrees of freedom). Now I can numerically compute force acting on the center of mass of the body by calculating numerical derivatives e.g. $F_x = (E(x + dx) - E(x - dx)) / (2 * dx)$.
But if you do the same for Euler angles this doesn't give you torques. So how do I convert numerical derivatives of energy by Euler angles to the resulting torque on a body?</p> | g11984 | [
0.07062066346406937,
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0.020049385726451874,
0.0031614787876605988,
0.014300982467830181,
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0.0008834847249090672,
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0.03386889025568962,
-0.0... |
<p>My friend keeps telling me that according to physics...</p>
<p><em>"The sun attracts a grain of sand on the earth with the same force that the grain of sand attracts the sun"</em></p>
<p>or</p>
<p><em>"A grain of sand on the earth attracts the sun"</em></p>
<p>Is that true? Does in theory a grain of sand really attract the sun?</p> | g11985 | [
0.05242009088397026,
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0.005316832568496466,
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0.04211527109146118,
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-0.034292664378881454,
0.05055342614650726,
-0.014501960016787052,
0.009795727208256721,
-0.0... |
<p>Gentlemen I have a similar yet very practical problem that might provide further insight.
I'm trying to model a moving plunger in a syringe (something like a piston in a cylinder).
At time zero the plunger is at rest, the pressure (behind the plunger) is atmosphere and the volume zero. Then I open (hydrogen) gas which flows at a certain flow rate (which varies in time) and the pressure to move the plunger also varies in time. So my idea is to model using:</p>
<p>$$\frac{\mathrm{d}}{\mathrm{d}t}(PV)=\frac{\mathrm{d}}{\mathrm{d}t}RT≡P\frac{\mathrm{d}V}{\mathrm{d}t}+V\frac{\mathrm{d}P}{\mathrm{d}t}=R\frac{\mathrm{d}T}{\mathrm{d} t}$$</p>
<p>If I assume constant temperature $P\frac{\mathrm{d}V}{\mathrm{d}t}+V\frac{\mathrm{d}P}{\mathrm{d} t}=RT$ </p>
<p>Is this right? </p>
<p>How do I go about solving this if I know the change in flow rate and pressure versus time? </p>
<p>Note also that as the volume of gas increases so does m (the mass)....I'm puzzled...has anyone every modeled a syringe in detail? </p> | g11986 | [
0.031448300927877426,
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0.00412194337695837,
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0.02764931507408619,
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0.026776308193802834,
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0.020950721576809883,
0.03256195783615112,
0.050... |
<p>Why does Quantum Field Theory use usually Lagrangians rather than Hamiltonains?</p>
<p>I heard many reasons, but I'm not sure which is true. </p>
<p>Some say it's just a matter of beauty, so Lagrangians are more beautiful because they don't break/separate the space-time variables (so space-time is a single variable, like in the Klein-Gordon Lagrangian and Hamiltonian).</p>
<p>Some say that Hamiltonians are not always Lorentz invariant.</p>
<p>Could someone explain in a little bit more details?</p>
<p>Thanks.</p> | g381 | [
0.07741089165210724,
0.00005736197635997087,
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0.03137366846203804,
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0.013665821403265,
0.027987999841570854,
0.04613467678427696,
-0.006656799465417862,
0.086... |
<p>From my understanding of relativity, gravity is not a force, but a result of the curvature of spacetime. If Object1 moves past Object2, even though it's moving in a straight line, its direction may change due to the distortion caused by Object2's mass.</p>
<p>However, what about the situation where Object1 is not moving? How can there be an attraction between two objects that are at rest relative to each other? i.e. what makes them move towards each other?</p> | g11987 | [
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0.023559702560305595,
0.04340210556983948,
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0.033383797854185104,
-0.023449478670954704,
0.023310478776693344,
-0.... |
<p>Is there any generalized Schwarzschild solution for an arbitrary number of dimensions? Is it necessary to calculate each individually, or is there a relationship between them?</p> | g11988 | [
0.0000679584700264968,
0.05410945415496826,
0.006561886984854937,
0.03690745308995247,
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0.02322724089026451,
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-0.00988138746470213,
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0.020528752356767654,
0.023333745077252388,
0.0701... |
<p>Let's say you have a point charge inside a conducting shell with an inner radius of 5cm and an outer radius of $7cm$. The point charge has a chard of $-4C$ and the shell a charge of $6C$. This means that the $-4C$ point charge attracts $4C$ worth of charge from the shell to the shell's inner surface. This leaves $2C$ of charge on the shell's outer surface. If you use the Gaussian-surface method at a radius of $6cm$, the Gaussian surface encloses both the $-4C$ point charge and the shell's $4C$ inner surface, so the net enclosed charge is $0C$, and therefore there is no electric field inside the shell (between the inner surface and outer surface).</p>
<p>But is there a potential there? My first intuition was "no", but then I was thinking that if you put a positive point charge there, the positive charge would join the other positive charges on the shell's outer surface, which makes it seem there'd have to be some potential energy being converted to kinetic energy somehow...</p> | g11989 | [
0.04399726912379265,
-0.01838686130940914,
0.00724258366972208,
-0.02529975213110447,
0.04600221663713455,
0.05963088572025299,
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0.001597108319401741,
-0.05764104053378105,
0.04185979440808296,
0.015825403854250908,
-0.00494... |
<p>The <strong>E.M.F</strong> of a cell is the work done in moving a unit positive charge in a loop or from the terminal to the same terminal. The force it experiences is a <strong><em>conservative force</em></strong>. Therefore, the work-done in a loop should be zero which means the <strong>E.M.F</strong> of any cell is zero, which is not correct...What happens there?</p> | g11990 | [
0.031009668484330177,
-0.00611791480332613,
0.011503062210977077,
0.014138494618237019,
0.12186722457408905,
-0.0035537658259272575,
0.01913560926914215,
0.03573264181613922,
-0.057702772319316864,
-0.04252144321799278,
-0.03061412274837494,
-0.005494831595569849,
0.03428959473967552,
-0.0... |
<p>How can you use the relaxation method to model negative dielectrics?</p>
<p>The relaxation method is usually used to model electrostatics problems but negative dielectrics are only see in dynamic systems.</p>
<p><strong>EDIT:</strong> To my knowledge at frequency, $f=0$, no materials act like they have a negative dielectric properties.</p>
<p>The university I attend offers a numerical electrodynamics course, every year as part of a homework they ask for a a negative dielectric be put into the relaxation method simulation that the students have programmed through the course. A negative dielectric slab in a parallel plate would be an example. I assume even though all of the voltages are static in time domain, that a f!=0 system is being simulated.</p>
<p>What I am interested in is what systems can be modelled in this fashion? How do I correlate the results of the simulation to a physical system. Or a example of a physical system that can be simulated in the above fashion.</p> | g11991 | [
0.044364720582962036,
0.038237545639276505,
0.016126178205013275,
0.02171221561729908,
0.018795795738697052,
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-0.014681229367852211,
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-0.0038357197772711515,
-0.017791638150811195,
0.0012897249544039369,
0.006271249148994684,
... |
<p>When an object is in free fall, we have:</p>
<p>$a(t) = g - \frac{c}{m}v(t)^2$</p>
<p>where $g$ is acceleration due to gravity, $m$ is the mass of the object, and $c$ is the coefficient of air resistance.</p>
<p>How does one get the distance traveled after t seconds? I tried integrating it, giving</p>
<p>$v(t) = gt - \frac{c}{3m}s(t)^3$</p>
<p>$s(t) = \sqrt[3]{\frac{3m}{c}(gt - v(t))}$</p>
<p>Which is a function defined in terms of its derivative. How would I find a better definition of s(t)?</p> | g11992 | [
0.05398668348789215,
0.024880198761820793,
-0.038566283881664276,
-0.007470916491001844,
0.027867062017321587,
0.06127792224287987,
0.07803523540496826,
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-0.02711956575512886,
-0.0912318229675293,
-0.0034106275998055935,
0.06507991999387741,
-0.03... |
<p>I am trying to understand this, and want to be very very clear. This is a homework question but I <strong>already attempted to answer it</strong>, so please don't put this question on hold.</p>
<p>The question </p>
<blockquote>
<p>What atomic terms are possible for the electronic configuration ns1nd1? Which term is likely to lie in the lowest energy?</p>
</blockquote>
<p>Here is my attempt at answering this question.</p>
<p>Some of the things I understand like calculating Multiplicity, you do that by the following relationship:</p>
<blockquote>
<p>$$S = s_1 + s_2, s_1 + s_2 - 1, \ldots , |s_1 - s_2|.$$</p>
</blockquote>
<p>Then apply it to the multiplicity rule:</p>
<blockquote>
<p>$$ 2S + 1$$</p>
</blockquote>
<p>I got the values 1, and 3 for the multiplicity and understand that the maximum multiplicity is the one that lies in the lowest energy.</p>
<p>I also understand that the maximum $L$ value corresponds to the lowest energy, and since $L = 2$ therefore the term Symbol will be D, and the supercript for S will be either 1, or 3.</p>
<p>What I don't get is how to calculate the $J$ values, the $J$ values the solutions manual has are 3, 2, 1 but it didn't explain how they derived those values. Do you use the Clebsch-Gordan relationship for the $J$ values as well, as such?</p>
<blockquote>
<p>$$J = L + S, L + S -1, \ldots |L - S|$$</p>
</blockquote>
<p>Really having trouble. Can someone please explain this to me?</p>
<p><strong>Here is my attempt:</strong></p>
<p><img src="http://i.stack.imgur.com/WYEsS.png" alt="enter image description here"></p>
<p>I don't understand how they obtained the $J$ values</p> | g11993 | [
0.031931035220623016,
0.06542256474494934,
-0.0031858880538493395,
0.0024117412976920605,
0.05827755853533745,
-0.06997670978307724,
-0.05150657892227173,
0.04178232699632645,
0.018862586468458176,
-0.0008669429225847125,
-0.06527293473482132,
0.02052425593137741,
-0.0055096992291510105,
-... |
<p>so the question is:</p>
<blockquote>
<p>I whirl a mass m attached to a wire with length L and diameter d
around my head in the horizontal plane. The mass takes t seconds to
move around a circle. How far do the atoms in the wire move apart,
compared to their spacing at rest? Young's modulus is given as Y.</p>
</blockquote>
<p>I know the value of Young's Modulus(Y).</p>
<p>So:
Y = Stress/Strain</p>
<p>For me to find the Strain I need to find the Stress first, which requires force(F)
Stress = Force/A , A = cross-sectional area = pi*(d/2)^2</p>
<p>=> Y = (F/A)/strain = (F/(pi*(d/2)^2))/strain</p>
<p>So, to find the strain, I need to find the Force and from the answer I can find how far the atoms move. </p>
<p>My question is how to I go about to find the force?</p>
<p>Thanks</p> | g11994 | [
-0.004526452627032995,
0.05351481959223747,
-0.016336772590875626,
-0.05886392295360565,
-0.029885774478316307,
-0.02835853397846222,
0.02878027968108654,
-0.03936324641108513,
-0.03468535095453262,
0.012719286605715752,
-0.05219697207212448,
-0.006738999392837286,
-0.060930702835321426,
-... |
<p>All discussions of Pauli exclusion principle I read usually talked about antisymmetric wavefunctions, from which the princinple appears. But I would like to see a Hamiltonian for multiple fermions, which would have Pauli exclusion principle already incorporated into its eigenstates. I've looked into <a href="http://en.wikipedia.org/wiki/Pauli_equation" rel="nofollow">Pauli equation</a>, but it seems to only describe one fermion. The same would hold for the more complete <a href="http://en.wikipedia.org/wiki/Dirac_equation" rel="nofollow">Dirac equation</a>.</p>
<p>So, my question is: what equation describes <em>multiple</em> (more than two) fermions <em>with spin</em> in non-relativistic regime, so that its eigenstates would automatically obey Pauli exclusion principle? Do I need the full machinery of QFT for this?</p> | g11995 | [
0.038008108735084534,
0.05830180644989014,
-0.02546820417046547,
-0.04276599362492561,
0.011529701761901379,
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0.01850287988781929,
0.050706662237644196,
0.014037510380148888,
0.009627182967960835,
-0.05238601565361023,
-0.04805506393313408,
0.01351474691182375,
0.0598... |
<p>I have the basic question that why so many superconducting materials are s-wave and d-wave pairing, but the p-wave superconductors are so rare in nature? An equivalent question may be that why topological materials are so rare in nature, but the answer to the this question may be more complicated then my first question. </p> | g11996 | [
0.04638337343931198,
0.12233459204435349,
0.010343166999518871,
0.05755302309989929,
0.07763244956731796,
0.023881589993834496,
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0.018052462488412857,
0.03165396675467491,
-0.06502555310726166,
-0.041671011596918106,
-0.017238793894648552,
-0.01925327628850937,
0.0288... |
<p>I am learning dynamics in <strong>special relativity</strong> and come across the <a href="http://en.wikipedia.org/wiki/Stress-energy_tensor" rel="nofollow">stress-energy tensor</a>. I have real trouble understanding it. I would love answers on </p>
<ol>
<li>How to motivate the definition of this tensor. </li>
<li>How to deduce the equation of motion, i.e. the divergence of the stress-energy tensor is 0.</li>
</ol>
<p>A toy model would be best for a demonstration. </p>
<p>(You may use the language of Riemannian Geometry freely.)</p> | g11997 | [
0.048076122999191284,
0.12533223628997803,
-0.028238801285624504,
0.026797950267791748,
0.011933501809835434,
-0.014797649346292019,
0.04717090353369713,
0.020883632823824883,
-0.006424096878618002,
-0.04612152650952339,
-0.07793870568275452,
-0.022485435009002686,
0.07532123476266861,
-0.... |
<p>Some sources suggest that the <a href="http://en.wikipedia.org/wiki/Andromeda_Galaxy">Andromeda Galaxy</a> is likely to collide with our own in approximately 3 to 5 billion years.</p>
<p>We can estimate the distance to the Andromeda Galaxy using various techniques, including measuring the apparent brightness of <a href="http://en.wikipedia.org/wiki/Cepheid">Cepheid variable stars</a>; its distance is currently estimated to be about 2.5 million light-years.</p>
<p>We can measure its radial velocity (i.e., the rate at which it's either approaching or receding from us) using Doppler shift. <a href="http://en.wikipedia.org/wiki/Andromeda_Galaxy">One source</a>, the same Wikipedia article I linked to above, indicates that its radial velocity with respect to the Sun is about 300 km/s in our direction; <a href="http://en.wikipedia.org/wiki/Andromeda%E2%80%93Milky_Way_collision">another article</a> says the radial velocity relative to our galaxy is about 120 km/sec, also in our direction. (Presumably the difference is due to the Sun's orbital motion around the core of the Milky Way.)</p>
<p>But that's just the radial component of the velocity. Taking the 120 km/sec figure, it could be moving directly toward the Milky Way (more precisely, its core could be moving directly toward the core of the Milky Way) at 120 km/sec, or it could be moving at a 45° angle at about 170 km/sec, or any of a number of other possibilities.</p>
<p>Without an estimate of the lateral component of the velocity, there's no way to be sure whether the collision will occur or not. I'm reasonably sure we can't measure the lateral velocity directly; 120 km/sec over a century would cause Andromeda to move only about 0.04 light-year (if my calculations are correct).</p>
<p>And yet <a href="http://en.wikipedia.org/wiki/Andromeda%E2%80%93Milky_Way_collision">this Wikipedia article</a> says:</p>
<blockquote>
<p>The best indirect estimates of the transverse velocity indicate that it is less than 100 km/s.</p>
</blockquote>
<p>with a reference to "Abraham Loeb, Mark J. Reid, Andreas Brunthaler and Heino Falcke The Astrophysical Journal, 633:894–898, 10 November 2005", but the link is invalid.</p>
<p>So how can a galaxy's lateral velocity be measured, or at least estimated? How accurate can such an estimate be with current technology? Can we expect improvements in the near future?</p> | g11998 | [
0.017898136749863625,
0.008430837653577328,
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-0.00704861618578434,
0.08684306591749191,
0.06079697608947754,
0.044177599251270294,
0.00391... |
<p>Whenever I did calculations in high school physics involving gravity, it was either "a ball falling to the earth" type scenario, or a basic measurement of the gravitational attraction between two planetoids. </p>
<p>I think I read somewhere recently that gravitational changes "aren't reflected instantly across the universe but instead propagate at the speed of light" somewhat like the ripples in a pond expanding. </p>
<p>Is this true? Is there experimental evidence to confirm or deny this? What is the theoretical basis for it?</p> | g4 | [
0.03439176082611084,
0.06653197854757309,
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0.03111562319099903,
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0.03500209003686905,
0.007037660107016563,
0.09289480000734329,
0.0297... |
<p>Why is it such a good idea to plot the logarithm of the form factor vs $Q^2$ in Guinier plots. It seems arbitrary to me.</p>
<p>Thanks</p> | g382 | [
-0.003867075778543949,
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0.06823153793811798,
-0... |
<p>We know that the theory of heat engines is that, if you accept the second law of thermodynamics,
$\Delta S > 0$
then you can define temperature using
$\frac{1}{T} = \frac{\partial S}{\partial E}$
And you would arrive at the conclusion that heat can only go from higher temperature to lower temperature reservoirs. And the best efficiency we can get is to use a reversible engine.</p>
<p>Now my question is "What's so special about energy?"
If we replace energy with any conservative, for example, one component of angular momentum $L$. Then is it possible to define a "temperature" as
$\frac{1}{T_L} = \frac{\partial S}{\partial L}$
And we would conclude that "in order to get useful angular momentum out of a reservoir, there is a maximum efficiency achieved by a reversible angular momentum engine" ?</p> | g11999 | [
0.08448635041713715,
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0.06614331156015396,
-0.0485... |
<p>sorry for reposting.</p>
<p>I dont get why it is such a good idea to plot the logarithm of the form factor vs $Q^2$ in Guinier plots. It seems arbitrary to me.</p> | g382 | [
-0.00637045269832015,
0.030316362157464027,
0.0034066501539200544,
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0.0654008612036705,
-... |
<ul>
<li><p>Einstein has suggested that light can behave as a wave as well as like a particle i.e, it has dual character. In 1924, de-Broglie suggested that just as light exhibits wave and particle properties, all microscopic material particles such as electrons, protons , atoms, molecules, etc. also have dual character. They behave as a particle as well as a wave. This means that an electron which has been regarded as a particle also behaves like a wave. Thus, according to de-Broglie, </p>
<blockquote>
<p><em>all the material particles in motion possess wave characteristics.</em> </p>
</blockquote>
<p>According to de-Broglie, the wavelength associated with a particle of mass m, moving with velocity v is given by the relation,<br>
<strong>$$\lambda=\frac{h}{mv}=\frac{h}{p}$$</strong><br>
where h is Planck's constant, v is the velocity and p(=mv) is momentum of the particles. The waves associated with material pariticles are called de Broglie waves. </p></li>
<li><p>My book says that: </p>
<blockquote>
<p>"Although the dual nature of matter is applicable to all material objects but it is significant for microscopic bodies only. For large bodies, the wavelengths of the associated waves are very small and cannot be measured by any of the available methods. Therefore, practically these bodies are said to have no wavelengths. Thus, any material body in motion can have wavelength but it is measurable or significant only for microscopic bodies such as electron, proton, atom or molecule. This may be illustrated as follows:<br>
The wavelength of an electron with mass $9.11*10^{-31}$kg and moving with the velocity of $10^6$ m/s is $7.28$ m as shown below:<br>
$$\lambda=\frac{h}{mv}=\frac{6.63*10^{-34}kg m^2 s^{-1}}{(9.11*10^{-31}kg)(10^6m/s)}=7.28*10^{-10}m$$<br>
This wavelength associated with the moving electron is of the same order of magnitude as of $X$-rays which can be easily measured." </p>
</blockquote></li>
<li><p>I made an attempt to check the wavelength associated with a car of mass $10^{6}$ kg and moving with velocity of $9.11*10^{-31}$ m/s, and I got the wavelength associated with it as shown below:<br>
$$\lambda=\frac{h}{mv}=\frac{6.63*10^{-34}kg m^2 s^{-1}}{(10^6kg)(9.11*10^{-31}m/s)}=7.28*10^{-10}m$$<br>
This shows that a car or any material object with mass $10^{6}$kg and moving with velocity $9.11*10^{-31}$m/s (almost at rest) has the wavelength same as that of an electron, but this result in contradiction with the statement of my book. And even I thought that it is practically impossible to see any wavelength associated with such mass of $10^{6}$kg. </p></li>
</ul>
<p>I have heard about rest and relativistic mass, and theory of relativity, but I have naive idea about it. If I have made mistake there, correct me. Or else "<em>is it that macroscopic body can have same wavelength as that associated with an electron?</em>" Please explain.</p> | g379 | [
0.024968888610601425,
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0.013453121297061443,
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0.09003680944442749,
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0.04935993626713753,
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0... |
<p>I was reading a thread about <a href="http://astronomy.stackexchange.com/questions/1182/if-the-earth-didnt-rotate-how-would-a-foucault-pendulum-work/1183#1183">how a pendulum would be affected if the Earth did not rotate</a> and Larian's answer made me wonder if all planets rotate necessarily due to physics.</p>
<p>So that's the question: is it possible for there to exist a planet* that doesn't rotate at all and why?</p>
<p><em>* In any solar system or galaxy.</em></p> | g12000 | [
0.016845639795064926,
0.036293283104896545,
0.017898857593536377,
-0.04679355025291443,
0.10330431163311005,
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0.029284389689564705,
-0.08647886663675308,
0.022587956860661507,
-0.00551346642896533,
0.004945551976561546,
-0.0... |
<p>Does anyone know any way of estimating the net baryon density in collision experiments, e.g. in LHC, RHIC, or the upcoming ones at GSI-FAIR?</p>
<p>I have comes across many hand-waving arguments, sample - </p>
<ol>
<li><p>Electron-positron colliders start with $\rho_B = 0$, and since conservation laws have to respected, matter and anti-matter must be produced in equal amounts. Hence, barring inhomogeneities, LHC is essentially in the $\rho_B \approx 0$ regime.</p></li>
<li><p>Antikaon-proton interaction is known to be attractive, through various model-dependent calculations, so if we have a ${\bar K}-p$ collision experiment, it shall involve the formation of quasi-matter having a larger density than usual, and hence, via these kind of reactions, GSI-FAIR plans to study QCD matter at high densities (especially in the <a href="http://www.fair-center.eu/for-users/experiments/cbm.html" rel="nofollow">Compressed Baryonic Matter experiment</a>), while it remains inaccessible at LHC.</p></li>
</ol>
<p>(Please correct me if the hand waving is inappropriate.) I am wondering, if there is any way of making this a little more calculation oriented, though I understand that a fully rigorous calculation would be very difficult. (I don't want that, too.)</p>
<p>Also, is it possible to have any model-independent answers, since model-dependent answers can be found with a bit of googling, e.g. <a href="https://journals.aps.org/prc/abstract/10.1103/PhysRevC.72.034613" rel="nofollow">Phys. Rev. C 72, 034613 (2005)</a>, which even has the evolution of these densities in lead-lead collisions. Though these calculations are the order of the day, model-independent calculations, if possible, teach you much more.</p> | g12001 | [
0.040999505668878555,
0.03948128595948219,
0.0116750942543149,
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0.1014714390039444,
0.011996709741652012,
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0.0030931737273931503,
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-0.009553994052112103,
0.047966405749320984,
0.01851654052734375,
-0.000158930808538571,
0.034... |
<p>Consider a string stretched between a D0-brane and an anti-D0-brane. In this case as the stretching energy is greater than the quantum zero point energy the string will have a positive mass. But, as the D0-brane and the anti-D0-brane come closer to annihilate the string becomes a tachyon as now the major is from quantum zero point energy as the string is no longer stretched.</p>
<p>But will the sudden "coming closer" of the brane and anti-brane give the string extra vibrations? </p>
<p>If so,is it that the energy due to these vibrations is not enough to overcome that of zero point energy finally resulting in a tachyon?</p> | g12002 | [
0.03802827373147011,
0.028829926624894142,
0.03946541249752045,
-0.02947385609149933,
-0.002442015102133155,
0.04238535091280937,
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0.0653376504778862,
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-0.013558939099311829,
-0.013434101827442646,
-0.01619272492825985,
-0.030914733186364174,
-0.0... |
<p>A string which doesn't have any kind of vibrations will have mass whose square is negative due to quantum zero point energy. But why does it contribute negative rather than positive mass to strings? </p> | g12003 | [
0.03656599670648575,
0.018814750015735626,
0.03356018662452698,
-0.018684063106775284,
0.043222326785326004,
0.04434393346309662,
-0.01594068668782711,
0.02862289547920227,
-0.001698059611953795,
-0.028886092826724052,
-0.005996720865368843,
-0.029752124100923538,
-0.012333676218986511,
0.... |
<p>I was reading Wikipedia about the <a href="http://en.wikipedia.org/wiki/St._Francis_Dam" rel="nofollow">St. Francis Dam</a> and came across this sentence.</p>
<blockquote>
<p>Water that collected in the drainage pipes under the dam to relieve
the hydrostatic uplift pressure was carried off in this manner as
well.</p>
</blockquote>
<p>What is hydrostatic uplift pressure? The word "uplift" in particular confuses me.</p> | g12004 | [
0.05837799608707428,
0.05819902941584587,
-0.010210631415247917,
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0.027072520926594734,
0.031457144767045975,
0.037693172693252563,
0.01817367598414421,
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-0.01493495237082243,
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0.013377235271036625,
0.04104667529463768,
-0.0... |
<p>So I noticed for a few years ago while I'm riding on the bus and as we stop at a corner i tend to just look at the road while I'm listening to music, I noticed that as the bus driver had stopped i would see the ground shift forwards as if the bus is going backwards, but we are stopped and not in reverse. Also I have never been in an earthquake and I didnt feel any vibrations so that's excluded. So could my eyes are playing tricks on me or am I actually seeing some sort of movement. Also the shift isn't big; it stops after a second or two and it shifts at an angle rotating CCW.</p> | g12005 | [
-0.025029029697179794,
0.021763181313872337,
0.036603596061468124,
0.03270579129457474,
0.05237282067537308,
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0.04333654046058655,
0.05093307048082352,
0.023175761103630066,
-0.022413138300180435,
0.03406769037246704,
-0.05070105195045471,
-0.06365279853343964,
0.009865... |
<p>I'm trying to learn more about momentum and I'm a little confused. Based on my understanding, in an isolated system, total momentum is conserved in a collision. Today in class the professor went over an example of a car on a ferry driving from one end to the other, in the opposite direction of the ferry. According to him, the total momentum for the system was zero in this case. I understand why total momentum is zero in a collision: because the objects come at rest. But in the example both the car and the ferry are moving (the goal is to find the ferry's new velocity as the car takes off).</p>
<p>So my question is: Is total momentum always zero if two objects are in touch with each other and are applying the same amount of force (but in the opposite direction) to each other? Also, the water applies the same amount of force to the ferry (again in the opposite direction) but how come it's not considered in our "system"?</p> | g12006 | [
0.050999805331230164,
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0.02287667989730835,
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0.06937989592552185,
0.020752253010869026,
0.033133476972579956,
0.048246219754219055,
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-0.03201115503907204,
0.015479526482522488,
-0.05439817160367966,
-0.005580209661275148,
0.0110... |
<p>As per newton's first law, only an external force can bring any change in the acceleration of a body, internal forces cannot. So, when we apply brakes to an accelerating car, aren't those brakes(opposing force) part of internal forces? How can they put the car to a halt?</p> | g12007 | [
0.02694966457784176,
0.04111660271883011,
0.019266553223133087,
0.034720733761787415,
0.032171159982681274,
0.048531364649534225,
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0.027116483077406883,
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-0.042679451406002045,
-0.009589200839400291,
-0.053096141666173935,
-0.03375227004289627,
-0... |
<p>What really <em>is</em> the <a href="http://en.wikipedia.org/wiki/Maxwell_stress_tensor" rel="nofollow">Maxwell Stress Tensor</a>? I understand that it's derived from $$\mathbf {F} = \int _V ( \mathbf E + \mathbf v \times \mathbf B )\rho \ d \tau$$</p>
<p>Griffiths describes this as "total EM force on the charges in the volume $\mathcal V$". </p>
<p>$$T_{i j} = \epsilon_0 \left(E_i E_j - \frac{1}{2} \delta_{ij} E^2\right) + \frac{1}{\mu_0} \left(B_i B_j - \frac{1}{2} \delta_{ij} B^2\right)$$</p>
<p>This leads us the the stress tensor, but there's something that I don't understand. The description given is </p>
<blockquote>
<p>Physically, $T$ is the force per unit area acting on the surface.</p>
</blockquote>
<p>What surface are we speaking about here? An arbitrary surface? In the case of example 8.2 (net force on a uniformly charge sphere's upper hemisphere), the surface in question is clearly the boundary of the upper hemisphere and it's "disk" separating the two hemispheres. In other cases, such as problem 8.4, where we have two point charges separated by a distance, we must integrate over a particular surface. For such a problem, we must "integrate the stress tensor over the plane equidistant from the two charges", but <em>why</em>? How would summing up the force on the plane separating the two point charges equal the force on each charge? </p>
<p>How could there be "force per unit area" across an empty plane? </p> | g12008 | [
0.04548748582601547,
0.04372352361679077,
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0.042105600237846375,
0.049720827490091324,
0.09525073319673538,
0.00021429875050671399,
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-0.024619678035378456,
-0.016200413927435875,
-0.007813827134668827,
0.022225821390748024,
-0... |
<p>I am looking for an estimate on the relationship between the rate of increase of power usage as the frequency of the processor is increased.</p>
<p>Any references to findings on this would be helpful.</p> | g12009 | [
0.039633557200431824,
0.08084098249673843,
0.010029044933617115,
0.008073749020695686,
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0.015205117873847485,
0.022745734080672264,
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0.0073417904786765575,
-0.0007157720974646509,
0.04335896670818329,
0.029107965528964996,
0... |
<p>I recently bought a new phone (Samsung Galaxy 3) and when the battery is fully loaded, it says like "Battery fully loaded, pull out the chord".
Is this a typo from Samsung, or would there theoretically be any reason (for battery saving purposes) to always have it going from the battery, and not from the chord.</p>
<p><em>(Ftr my phone is set to Swedish language)</em></p> | g12010 | [
0.06308301538228989,
-0.029081126675009727,
0.01362050324678421,
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0.04547150433063507,
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0.032456979155540466,
-0.... |
<p>I read some posts on this forum and some articles which repeatedly state that it is not impossible to build q-comps but to make it successful, physics needs a great breakthrough.
I tried finding but most of the material talks about how it works and what are current limitations, but how physics is going to help solving it?</p>
<p>Can somebody please explain precisely 'what is that breakthrough?'.</p> | g12011 | [
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0.02196580357849598,
-0.0... |
<p>Perhaps this is a very basic question.</p>
<p>In chapter 14 of Srednicki's QFT textbook (2007), $O(g^2)$ loop corrections to the propagator of $\phi^3$ theory is discussed. However, I don't know how to derive the Eq. 14.34 on page 103 (I can't present the full context as it would be too long).
From
\begin{equation}
\Pi(k^2)=\frac{1}{2}\alpha\Gamma(-1+\epsilon/2)\int_0^1\,dxD(4\pi\mu^2/D)^{\epsilon/2}-Ak^2-Bm^2+O(\alpha^2), (14.32)
\end{equation}
and take the $\epsilon \rightarrow 0$ limit using
\begin{equation}
A^{\epsilon/2}=1+\frac{\epsilon}{2}ln(A)+O(\epsilon^2)
\end{equation}
and the following property of Gamma functions
\begin{equation}
\Gamma(-n+x)=\frac{(-1)^n}{n!}\left[\frac{1}{x}-\gamma+\sum_{k=1}^nk^{-1}+O(x)\right],
\end{equation}
he got
\begin{equation}
\Pi(k^2)=-\frac{1}{2}\alpha\left[\left(\frac{2}{\epsilon}+1\right)\left(\frac{1}{6}k^2+m^2\right)+\int_0^1\,dxDln\left(\frac{4\pi\mu^2}{e^\gamma D}\right)\right]-Ak^2-Bm^2+O(\alpha^2), \qquad (14.34)
\end{equation}
where $\alpha\equiv\frac{g^2}{(4\pi)^3}$.</p>
<p>I don't know how to do the integral correctly (although it seems elementary). Can anyone familiar with this part help me out? </p> | g12012 | [
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0.05200422927737236,
0.0048547713086009026,
... |
<p>I remember reading this passage in the "Feynman Lectures", where Dr. Feynman describes an experiment in which a theoretical metal rod of length equal to the distance between Mars and Earth is arranged between mars and earth. Then the "rod handler" on earth gives the rod a push upwards. So the question posed is, will the rod instantaneously move backwards on Mars? He then proceeds to say that actually the movement will be felt roughly after the time it would take for sound to propagate from Earth to Mars i.e. at the speed of sound. This is because the atoms in the rod actually propagate their position at the speed of sound. See also <a href="http://physics.stackexchange.com/q/2175/2451">this</a> Phys.SE post and links therein. <strong>My question is:</strong> If this were true, how is supersonic travel possible? Won't there be a scenario where the atoms in the components of the aircraft won't "catch up" because the propagation of the new positions is slower than the actual speed? Won't the aircraft disintegrate? </p> | g4 | [
0.02030077949166298,
0.0805669054389,
0.0075712124817073345,
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0.01346906740218401,
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0.01731174625456333,
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0.005855... |
<p>Suppose I have a pot with diameter $D$ containing a volume of water $V$, being heated by a flame under it. If the ambient air temperature is $T$ and relative humidity is $R$, how can I calculate the expected rate of loss due to evaporation over a period of time, $t$? Assume the period of time begins once the water begins boiling.</p>
<p><strong>Edit:</strong> For simplicity's sake, also assume the flame is just hot enough to get the water boiling.</p> | g12013 | [
0.03805255517363548,
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0... |
<p>It is known that <a href="http://physics.stackexchange.com/questions/65893/why-we-call-the-ground-state-of-kitaev-model-a-spin-liquid">the Kitaev Hamiltonian and its spin-liquid ground state both break the $SU(2)$ spin-rotation symmetry</a>. So what's the spin-rotation-symmetry group for the Kitaev model?</p>
<p>It's obvious that the Kitaev Hamiltonian is invariant under $\pi$ rotation about the three spin axes, and in some recent papers, the authors give the "group"(see the <strong>Comments</strong> in the end) $G=\left \{1,e^{i\pi S_x}, e^{i\pi S_y},e^{i\pi S_z} \right \}$, where $(e^{i\pi S_x}, e^{i\pi S_y},e^{i\pi S_z})=(i\sigma_x,i\sigma_y,i\sigma_z )$, with $\mathbf{S}=\frac{1}{2}\mathbf{\sigma}$ and $\mathbf{\sigma}$ being the Pauli matrices. </p>
<p>But how about the quaternion group $Q_8=\left \{1,-1,e^{i\pi S_x}, e^{-i\pi S_x},e^{i\pi S_y},e^{-i\pi S_y},e^{i\pi S_z}, e^{-i\pi S_z}\right \}$, with $-1$ representing the $2\pi$ spin-rotation operator. On the other hand, consider the dihedral group $D_2=\left \{ \begin{pmatrix}1 & 0 &0 \\ 0& 1 & 0\\ 0&0 &1 \end{pmatrix},\begin{pmatrix}1 & 0 &0 \\ 0& -1 & 0\\ 0&0 &-1 \end{pmatrix},\begin{pmatrix}-1 & 0 &0 \\ 0& 1 & 0\\ 0&0 &-1 \end{pmatrix},\begin{pmatrix}-1 & 0 &0 \\ 0& -1 & 0\\ 0&0 &1 \end{pmatrix} \right \}$, and these $SO(3)$ matrices can also implement the $\pi$ spin rotation.</p>
<p>So, which one you choose, $G,Q_8$, or $D_2$ ? Notice that $Q_8$ is a subgroup of $SU(2)$, while $D_2$ is a subgroup of $SO(3)$. Furthermore, $D_2\cong Q_8/Z_2$, just like $SO(3)\cong SU(2)/Z_2$, where $Z_2=\left \{ \begin{pmatrix}1 & 0 \\ 0 &1\end{pmatrix} ,\begin{pmatrix}-1 & 0 \\ 0 &-1 \end{pmatrix} \right \}$.</p>
<p><strong>Comments:</strong> The $G$ defined above is <strong>even not a group</strong>, since, e.g., $(e^{i\pi S_z})^2=-1\notin G$.</p>
<p><strong>Remarks:</strong> Notice here that $D_2$ can <em>not</em> be viewed as a <em>subgroup</em> of $Q_8$, just like $SO(3)$ can <em>not</em> be viewed as a <em>subgroup</em> of $SU(2)$.</p>
<p><strong>Supplementary:</strong>
As an example, consider a two spin-1/2 system. We want to gain some insights that what kinds of wavefunctions preserves the $Q_8$ spin-rotation symmetry from this simplest model. For convenience, let $R_\alpha =e^{\pm i\pi S_\alpha}=-4S_1^\alpha S_2^\alpha$ represent the $\pi$ spin-rotation operators around spin axes $\alpha=x,y,z$, where $S_\alpha=S_1^\alpha+ S_2^\alpha$. Therefore, by saying a wavefunction $\psi$ has $Q_8$ spin-rotation symmetry, we mean $R_\alpha\psi=\lambda_ \alpha \psi$, with $\left |\lambda_ \alpha \right |^2=1$. </p>
<p>After a simple calculation, we find that a $Q_8$ spin-rotation symmetric wavefunction $\psi$ could <strong>only</strong> take <strong>one</strong> of the following 4 possible forms:</p>
<p>$(1) \left | \uparrow \downarrow \right \rangle-\left | \downarrow \uparrow \right \rangle$, with $(\lambda_x,\lambda_y,\lambda_z)=(1,1,1)$ (Singlet state with <em>full</em> $SU(2)$ spin-rotation symmetry), which is annihilated by $S_x,S_y,$ and $S_z$,</p>
<p>$(2) \left | \uparrow \downarrow \right \rangle+\left | \downarrow \uparrow \right \rangle$, with $(\lambda_x,\lambda_y,\lambda_z)=(-1,-1,1)$, which is annihilated by $S_z$,</p>
<p>$(3) \left | \uparrow \uparrow \right \rangle-\left | \downarrow \downarrow \right \rangle$, with $(\lambda_x,\lambda_y,\lambda_z)=(1,-1,-1)$, which is annihilated by $S_x$,</p>
<p>$(4) \left | \uparrow \uparrow \right \rangle+\left | \downarrow \downarrow \right \rangle$, with $(\lambda_x,\lambda_y,\lambda_z)=(-1,1,-1)$, which is annihilated by $S_y$.</p>
<p>Note that <em>any</em> kind of superposition of the above states would <em>no longer be</em> an eigenfunction of $R_\alpha$ and hence would break the $Q_8$ spin-rotation symmetry.</p> | g12014 | [
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0.04731999710202217,
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0.0024353875778615475,
0.0004174952337052673,
-0.009017613716423512,
-0.013540525920689106,
... |
<p>I'm told that if the total energy of an object near the Sun is negative, then it comes from the Solar System; if positive, it is extrasolar.</p>
<p>I don't understand why. Can someone please explain this?</p> | g12015 | [
0.04842310771346092,
0.030024947598576546,
0.009827026166021824,
0.02825796976685524,
0.00487864064052701,
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0.047227516770362854,
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<p>I am having a hard time picturing waves, the image that comes to mind is a bobbing device submerged in still water which generates pulses in all directions (similarly in air). Then how can a wave be two dimensional? The classic image of an electromagnetic wave is a 3D wave function, x-y represent the electrical component, z-x represents the magnetic component. But this is a wave function, so its just a plot, and that is not how I should picture it (or is it?). So in real life, if I have a source of EMR in space, I can imagine concentric spheres of Electrical fields, but what about the magnetic fields? How will they be perpendicular to a sphere of electric fields? Can someone help me picture EMR? Thanks! (apologies in advance for the noobish language, I am an absolute beginner to physics)</p> | g12016 | [
-0.008541214279830456,
0.024722421541810036,
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0.003523708088323474,
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0.049050070345401764,
0.038... |
<p>When you flip a coin, you hear a ringing sound. I know that the source of the sound is the thumbnail hitting the coin, but it seems to be filtered by the spinning of the coin. Specifically, the faster the coin spins, the smoother the tone and it seems the spectrum becomes more uniform.</p>
<p>So my question is, physically, what is the exact phenomenon that is causing the filtering? It seems to be some form of frequency modulation (or amplitude modulation? I suspect it's the former but I could be wrong).</p>
<p>my other question is, what are the exact characteristics of this filter? I know that the filter will be a function of the angular frequency of the coin, which I'll call $\omega_m$, but other than that I don't know where to start on how to characterize it.</p> | g12017 | [
-0.014528568834066391,
0.017214788123965263,
0.00932969432324171,
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0.0044527314603328705,
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0.07423005998134613,
-0.0... |
<p>let's say I want to model a star of radius $R$ at a distance $r$ from the Earth. I need to show that the apparent luminosity for frequency $\nu$ is equal to</p>
<p>$$\ell(\nu)=\frac{2\pi h}{c^2}\left( \frac{R}{r}\right)^2\frac{\nu^3}{\exp\displaystyle\left(\frac{h\nu}{kT}\right)-1} $$</p>
<p>Which is Planck's law multiplied by $$\pi\left(\frac{R}{r}\right)^2$$</p>
<p>Given the nature of the factor (adimensional function of $R,r$) I would say that the result follows from geometrical considerations, however I fail to see which ones.</p>
<p>Thanks.</p> | g12018 | [
-0.03570982813835144,
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0.011011697351932526,
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-0.... |
<p>In the famous paper by Polchinski where he shows that D-branes are sourcing RR fields, he says (before we known the result) that RR sources must be objects with tension going like $1/g_s$ (page two of the paper). How do we know that? I understand that it must be non-perturbative in $g_s$ (essentially because strings aren't charged under RR fields), but why it has to be precisely $1/g_s$ ?</p>
<p>Thanks.</p> | g12019 | [
0.007595023140311241,
0.04444986954331398,
-0.023704104125499725,
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0.05521722882986069,
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<p>I remember being taught in elementary physics that while it makes
sense to add volumes, masses, or heat, it makes no sense to add
temperatures.</p>
<p>As I wanted to use that to illustate some other issue, I checked it on
wikipedia, and discovered the concept of intensive and extensive
properties of materials and systems, which is apparently a century
old, though I do not remember it being taught to me (it was not as old
then :-).</p>
<p>The concept seems to be particularly useful in material and systems
thermodynamics. But I was wondering how far it extends, and I was
keeping in mind my original problem of determining when adding values in
a given unit (not necessarily a physical one) made sense or did not.</p>
<p>I noticed the fact that the ratio of two extensive variables is
intensive. So I started looking, a bit ramdomly I confess, at ratios,
and the first that came to mind was speed. And I wondered whether
adding speeds made sense.</p>
<p>We do that all the time, so it should. But then, my initial problem
was not about adding two quantities, but a long list of them (it was a
database question). While adding a few speeds (or velocities) makes sense
when I move in the bus, or analyse the motion of the Moon in the solar
system, I cannot imagine it would ever make sense to add a list of a
hundred or a thousand speeds (though computing the average would make
sense, as it would for temperature). But I makes perfect sense to sum
the masses of a thousand objects.</p>
<p>So there is apparently something special, not quite right, about
adding speeds. Of course, I know that slightly older results state
that adding speeds is not done with simple addition, but I feel that my
problem is elsewhere (though there may possibly be a connection).</p>
<p>I am aware that temperature in some materials is related to speed of
motions inside it, so I am not too surprised. But speed in general
seems to go beyond that (sorry for the vagueness). Also speed is not
listed by Wikipedia as an intensive property.</p>
<p>So, my question is : why does it seem improper to add many speeds (or velocities)?</p>
<p>I guess this must also be true of other physical quantities, and I am
wondering what is the right way to look at this, and understand it. Is
there a more general notion than intensive and extensive?</p> | g12020 | [
0.04425123333930969,
0.0487852469086647,
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0.006132637150585651,
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0.0024309498257935047,
0.06050943210721016,
-0.03161470592021942,
0.04379481449723244,
0.0399... |
<p>I'm reading the book Gödel, Escher, Bach: an Eternal Golden Braid and on Chapter V, Hofstadter talks about different examples of recursive structures and processes. By page 142 of the 20th anniversary edition, he starts talking about recursion at the lowest level of matter, that is, according to him, related to the structure of elementary particles.</p>
<p>To explain his point, he draws a little example I'm unable to understand due to, most likely, my poor knowledge of physics in general. He starts by limiting himself to two kinds of particles: electrons and photons: "Imagine first a dull world where a bare electron wishes to propagate from point A to point B. A physicist would draw a picture like this:"</p>
<p><img src="http://i.stack.imgur.com/4FmjZ.png" alt="Initial diagram"></p>
<p>Based on this, my initial set of questions are:</p>
<ul>
<li>He says in such a world there is an easy mathematical expression to represent this line, does anybody know which expression is that?</li>
<li>And how exactly is an electron simply traveling from point A to B?</li>
</ul>
<p>Next, in a world where electrons and photons interact, the electron is now capable of emitting and then reabsorbing "virtual photons - photons which flicker in and out of existence before they can be seen.":</p>
<p>Electron and photon interaction: <img src="http://i.stack.imgur.com/HqEQ9.png" alt="enter image description here"></p>
<p>"Now as our electron propagates, it may emit and reabsorb one photon after another, or it may even nest them, as shown below:"</p>
<p><img src="http://i.stack.imgur.com/NHzTF.png" alt="Nested interactions"></p>
<p>Also here he says that "the mathematical expressions corresponding to these diagrams - called Feynman diagrams - are easy to write down." So my last set of questions are:</p>
<ul>
<li>How do these diagrams relate to Feynman ones?</li>
<li>I'm not quite sure I actually understand them, could someone help me with a gentle introduction to the topic?</li>
<li>More importantly to the book reading at hand, where is the recursion in all this? I fail to see it.</li>
</ul>
<p>For those interested, I found all of this part of chapter V <a href="http://www.cs.virginia.edu/cs150-fall2005/readings/ch5.pdf" rel="nofollow">online</a>.</p>
<p>Edit: I accepted the answer given by Gugg below. For completion, follow the interesting discussion we had <a href="http://chat.stackexchange.com/rooms/7084/discussion-between-jokerbrb-and-gugg">on chat</a> as well.</p> | g12021 | [
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0.06906788051128387,
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0.07948321104049683,
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0.017... |
<p>I know only that it states some variations of the Sun's magnetic fields. What is the <a href="http://www.google.com/search?q=rosenberg+coleman+effect" rel="nofollow">Rosenberg-Coleman effect</a> specifically?</p> | g12022 | [
0.016442405059933662,
0.02736900933086872,
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0.04285849258303642,
0.02837218903005123,
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-0.02696746028959751,
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0.01893242821097374,
0.02624479867517948,
-0.01... |
<p>Can anybody explain how Rutherford bombarded a 0.0004 cm thick gold foil? How did he put it in a photographic sheet? Wasn't the foil too thin to be held? How did he know that the atoms were deflected at various angles? Did he calculate every alpha particle's angle of deflection?</p> | g12023 | [
0.06695715337991714,
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0.011923415586352348,
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0.06499497592449188,
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0.010246762074530125,
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-0.... |
<p>Suppose one knows in full detail the phase and intensity of monochromatic light in a plane. This is basically what a hologram records, at least for some section of a plane. By using this as the boundary condition for the wave equation, you should in principle be able to solve for the phase and intensity of light at every point in space (up to some global phase factor that changes in time). Now, how do you translate this into an image? Say, if the hologram is given by a complex field $\phi(x,y)$ on the $XY$ plane, the light has wavelength $k$ and I have a pinhole camera located at position $\vec{p}$ pointing in direction $\vec{r}$, is there a simple formula to translate this field into an image intensity?</p>
<p>In more detail: think of the light at each point in space as being given by a complex number, where the intensity is the magnitude squared and the phase is, well, the phase. I'm leaving out the $z$ coordinate of the field because it shouldn't matter for this problem. The Green's function for the wave equation (basically, the field emitted by a point source located at $\vec{s}$) is given by </p>
<p>$G(\vec{x},\vec{s},t) \sim e^{i(k||\vec{x}-\vec{s}|| - \omega t)}$</p>
<p>where $\omega$ is the frequency of the light, and I've dropped a constant term that doesn't really affect the answer. Also, the $\omega t$ term in the solution shouldn't matter either, since it will be the same globally and doesn't change the magnitude of the field. We can solve for the field $\psi(\vec{s},t)$ at any point in space by taking the integral</p>
<p>$\int \int dx dy \phi(x,y)G(\vec{s},(x,y,0)^T,t)$</p>
<p>but how do we go from this field to an image? Basically, how is the light transformed on passing through the pinhole?</p> | g12024 | [
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0.003631127532571554,
0.007413994520902634,
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0.0006726119900122285,
-0.03... |
<p>I'm taking a particle physics course and we're using Perkins Introduction to High Energy Physics as the text. I am looking at problem 1.7. It asks whether $$\pi^0\rightarrow e^- + e^+$$ is allowed or forbidden by the Standard Model based off of conservation laws. I feel it doesn't violate any of them. Energy and momentum can clearly be conserved, charge is conserved, lepton number is conserved, etc. However, I know Dalitz decay is a very similar process, but that the pion decays into $$\pi^0 \rightarrow e^- + e^+ + \gamma$$ so feel as though I must have overlooked something. I would be greatly appreciative if someone could point me in the right direction.</p> | g12025 | [
0.02026994712650776,
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0.019413448870182037,
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0.05172031372785568,
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0.010639914311468601,
0.011643953621387482,
0.03598899766802788,
0.0... |
<p>I have to find the uncertainty of a quantity $Q$ doing two mean values. For example for a set of parameters I measure ten times $Q$, I obtain a mean value $Q_1$ and variance ${\rm Var}(Q_1)$. Then for a different set of parameters I measure ten times $Q$ and obtain $Q_2$ and ${\rm Var}(Q_2)$ etc. At the end I compute the mean value which is the sum of $Q_i$ but these 10 from one set of parameter to the other are correlated so I don't know how to compute the variance.</p>
<p>Put differently, I don't know how to compute the variance if I have two averages.</p> | g12026 | [
-0.0026634365785866976,
0.012539183720946312,
-0.004086395259946585,
0.0035798160824924707,
0.03215780854225159,
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-0.04633903503417969,
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-0.00026015323237515986,
-0.01674321852624416... |
<p>In quantum field theory or condensed matter physics, the fermionic one-loop diagram gives rise to the polarization tensor</p>
<p>$$ Π^{µν} = Tr[ γ^µ G γ^ν G ] $$</p>
<p>If we couple the electrons to an electromagnetic field, we can integrate out the electrons again and obtain an effective action for the electromagnetic field $A^µ$ as</p>
<p>$$ S \propto \frac14 F^{µν}F_{µν} + A_µ Π^{µν} A_ν + \dots $$</p>
<p>where the dots indicate corrections of higher order in $A$. (Apologies for my prefactors, they are probably all wrong.)</p>
<p>Of course, the effective action for the e.m. field has to be be gauge invariant, which poses certain restrictions on the polarization tensor $Π^{µν}$.</p>
<blockquote>
<p>What is the most general form of the polarization tensor $Π^{µν}$, i.e. the form dictated by gauge invariance alone?</p>
</blockquote>
<p>According to my calculations, gauge invariance imposes the restriction $Π^{µν}q_µ = 0$, but I'm not entirely sure whether this is correct.</p>
<p>Also, I have heard that one possible form is
$$ Π_{ij} = \tilde Π(q)(\delta_{ij} - \frac{q_iq_j}{q^2}) $$
at least for the spatial components $i,j$, but I don't think that this is the most general form.</p>
<blockquote>
<p>What is the general form of the polarization tensor in a condensed matter context? Are there other restrictions aside from gauge invariance?</p>
</blockquote> | g12027 | [
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0.021231679245829582,
0.0000761346600484103,
0.02830754593014717,
0.014273772947490215,
-0.0... |
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