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<p>Since <a href="http://en.wikipedia.org/wiki/Quantum_electrodynamics" rel="nofollow">QED</a> treats photons as individual units (quanta) how does it treat the concept of the "wavelength" associated with the photon?</p>
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<p>I understand that the Moon's phases are determined by its position in orbit relative to the Sun. (See: <em><a href="http://www.extremescience.com/zoom/index.php/space/35-space-science/77-about-the-moon">Full Story on the Moon</a></em>). The "shadow" is not cast by the Earth (a common misconception - this is actually...
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<p>I asked this Phys.SE question <a href="http://physics.stackexchange.com/q/96408/">Does car lose kinetic energy when turning?</a></p> <p>Assume a car turning without losing its speed by holding to a point by a rope.</p> <p>IMO, while the car is turning, its kinetic energy is constant $E=(1/2)mv^2$, but it has addit...
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<p>I understand only a little of general relativity, but that's why I'm here! :)</p> <p>Consider the hypothetical situation of some extra-terrestrial intelligence pushing all the mass in the universe, every last subatomic particle, into a giant black hole. What is the surface area of such an object? For the sake of ar...
g18121
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<p>Does anyones know which materials (or type of steel) are used to make rocket engines nozzles &amp; combustion chambers?</p> <p>What are the tricks to reduce temperature of the engine except trying to cool it with fuel/oxidant?</p> <p>Are there any good books around on rocket engines design?</p>
g18122
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<p>Is it possible to create periodic potentials that instead of creating a well for an atom to be trapped in, repulsed by that specific location?</p> <p>If yes, can we use this as a means to make artificial objects that we can feel, with let's say our hands, by putting lots of these repulsive points together?</p> <p>...
g18123
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<p>I've heard that a spacecraft could never exceed the speed of light because it's (relativistic) mass quickly approaches infinity and therefore there could never create a big enough rocket to propel it faster and faster. </p> <p>I'm 99% sure this is a stupid question, but I'll ask it anyway :). Theoretically if a spa...
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<p>In preparation for an exam, I'm revisiting old exam questions. This one seems neat, but also quite complicated:</p> <blockquote> <p>A soccer ball with Radius $R=11cm$ is inflated at a pressure of $P =9 \times 10^4 Pa$, then dropped from a height of $0.1m$ (distance floor to lowest part of ball) onto a hard floor ...
g18125
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<p>I know that rotational kinetic energy is $\frac{1}{2}I\omega^2$. Therefore, the rotational kinetic energy will depend on the moment of inertia.</p> <p>I came to the conclusion that since both have the same mass, both should have the same moment of inertia as<br> $$I = \sum_\text{over all mass} m r^2$$</p> <p>But ...
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<p>Usually, the sound speakers have this metal grid.</p> <p><img src="http://i.stack.imgur.com/6PKMc.png" alt="enter image description here"></p> <p>However, not all of them have this.</p> <p>Is there any purpose, maybe related to the sound quality, that justifies this? Or is it only for physically protect the speak...
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<p>What is the typical half life of material released from <a href="http://en.wikipedia.org/wiki/Nuclear_fission" rel="nofollow">nuclear fission</a>? This is a question I received for yr 12 physics and I can't find a proper answer telling me what the material released is and what the <a href="http://en.wikipedia.org/wi...
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<p>Um .. naive question perhaps but if somebody wanted to store heat, how would they go about it? Can heat be stored? </p> <p>I'm told that decomposing kitchen waste in a closed vessel results in a rise in temperature on the body of the vessel. I'm just wondering whether it could be stored for later use. </p>
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<p>So I've just learned <a href="http://en.wikipedia.org/wiki/Gauss%27s_law" rel="nofollow">Gauss' Law</a> a few days ago. I also worked out some applications of Gauss' Law. But I have a little confusion. In a couple of books that I referred, I found a statement that I don't quite understand. It says "Gauss' law works ...
g18130
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<p>What is the law of spatial dispersion of a photon in an optical fiber?</p> <p>Say I have a femto second photon ($\lambda$ around $700\,\text{nm}$) with gaussian shape ($\sigma = c\cdot 1\,\text{fs}\approx 3\cdot 10^{-7}\,\text m$). How will it look at the end when I send it through a 50 km long optical fiber?</p> ...
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<p>How can one adjust the properties of a sound wave to use it to spin an arbitrary object of shape S in a medium comprised of the same material. My intuition tells me that it would be much more difficult (if not impossible) to do this with spherical objects, so for now we can assume the object is assymetric if that ma...
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<p>If I am given the dipole moment of very short dipole antenna as $P = P_0 sin (\omega t)$, what will be the magnetic field and polarization of far field radiation?</p> <p>Do I need to consider the time variation when calculating near and far fields, as in how many half or full cycles will exists along the dipole ?<...
g18133
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<p><img src="http://imgs.xkcd.com/comics/neutrinos.png" alt="XKCD"></p> <p>I was quite surprised to read this all over the news today:</p> <blockquote> <p>Elusive, nearly massive subatomic particles called neutrinos appear to travel just faster than light, a team of physicists in Europe reports. If so, the observat...
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<p>Does the density equation for air on Earth change in the outer atmospheres? I am generating a model for the Red Bull Stratos jump and am trying calculate a precise air density function.</p>
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<p>After a star lives and dies, I assume virtually all of it's mass would be photons. If enough stars have already lived and died, couldn't there be enough photon energy out there to account for all the "missing mass" (=dark matter) in the universe?</p> <p>And if there were enough photons to account for all the missin...
g18135
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<p>I'm having trouble understanding the simple "planetary" model of the atom that I'm being taught in my basic chemistry course. </p> <p>In particular, </p> <ol> <li>I can't see how a negatively charged electron can stay in "orbit" around a positively charged nucleus. Even if the electron actually orbits the nucleus,...
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<p>Can polarization produce heat? If so will this energy oppose dipoles aligning in the field direction?</p>
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<p>I am attempting to derive the following equation of motion for a simple pendulum:</p> <p>$$\theta''(t) = - \frac{g}{l} \sin(\theta).$$</p> <p>For background, see <a href="http://en.wikipedia.org/wiki/Pendulum_%28mathematics%29#Simple_gravity_pendulum" rel="nofollow">this Wikipedia article</a>. I understand this p...
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<p>Apparently <a href="http://www.edge.org/responses/what-is-your-favorite-deep-elegant-or-beautiful-explanation#descshort_2957" rel="nofollow">Boscovich's argument</a> shows that force must act at a distance:</p> <blockquote> <p>But how did the velocity of the faster body come to be reduced from 12 to 9, and that...
g18138
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<p>Computing the angular diameter distance $D_{A}$ is a well known academic exercise in an homogeneous Universe. But now suppose that we are in an inhomogeneous Universe and that I am interested in computing the angular diameter distance of a source $S$ viewed by an observer $O$. Consider furthermore that I know :</p> ...
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<p>Consider a metal rod parallel to $x$-axis moving with velocity $\vec v =(0,v,0)$ perpendicular to magnetic field $\vec B=(0,0,B)$.</p> <p><img src="http://i.stack.imgur.com/jZeu5.jpg" alt=""></p> <p>Lorentz force will give rise to the electric field $\vec E = - \vec v \times \vec B$, so the rod becomes polarized.<...
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<p>In a quasi-crystal, there is no translational invariance. This means there is no delta-function in the Fourier transform. But to get a sharp scattering spot, we need a delta function. </p> <p>Physically, in a crystal, we get sharp scattering spots because it is possible to get all the scattering waves from each ce...
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<p>If we take an imaginary planet which consists entirely of water (i.e. a big ball of water in space), what would be the pressure at the center of it?</p> <p>My friend argued that it would be zero, since the forces coming from every direction would cancel out, furthermore, at the center gravity is zero. I find this v...
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<p>I tried to check the statement that Dirac free Hamiltonian commutes with inversion operator. For $$ \hat {P}\Psi(\mathbf r , t) = i\hat {\gamma}_{0}\Psi (-\mathbf r , t), \quad \hat {H} = (\hat {\alpha} \cdot \hat {\mathbf p}) + \hat {\gamma}_{0}m $$ I got</p> <h1>$$ [\hat {H}, \hat {P}]\Psi (\mathbf r, t) = i\hat ...
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<p>For quite some time now, physicists have been able to estimate the <a href="http://en.wikipedia.org/wiki/Observable_universe" rel="nofollow">mass of the observable universe</a>.</p> <p>Reportedly it's around $10^{50} \:\mathrm{kg}$.</p> <p>There is also general relativity, which states that $E=mc^2$.</p> <p><stro...
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<p>I would like to find the helmholtz free energy of a system</p> <p>$F=-T ln(Tr[e^{\frac{-H}{T}}])$</p> <p>namely a bcs superconductor (using Annett's notation)</p> <p>$H=\sum E_k (b_{k\uparrow}^\dagger b_{k\uparrow}+b_{-k\downarrow}^\dagger b_{-k\downarrow})$</p> <p>I've managed to get my expression for F down t...
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<p>I have two equations on my equation sheet:</p> <p>$$y=v_o t \sin \theta - \frac{1}{2} g t^2.$$</p> <p>And then another:</p> <p>$$y_{\max} = \frac{v_o^2 \sin 2 \theta }{2g}.$$</p> <p>I understand that the first one is an equation for the height of the projectile (as a function of time $t$) but what is the second ...
g18145
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<p>I have a question about Polchinski's string theory book, volume I, p 108. When we write the Polyakov action in curved spacetime, it is said</p> <blockquote> <p>$$ S_{\sigma} = \frac{1}{4\pi\alpha'} \int_M d^2 \sigma g^{1/2} g^{ab} G_{\mu\nu}(X) \partial_a X^{\mu} \partial_b X^{\nu} \tag{3.7.2} $$ <em>[...] A c...
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<p>I've noticed a motionless kingfisher over a lake looking for prey and wondered what amount of energy does a bird, weighing 0.15kg, require to hover for 15s?</p>
g18147
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<p>The Basal Metabolic Rate is intuitively expressed as "the amount of energy you consume just sitting around." In some places it seems to be equated with the amount of heat that you give off.</p> <p>Is this true? It seems to me that energy could be used to repair cells etc. which would not necessarily all convert to...
g18148
[ 0.059081170707941055, 0.007816515862941742, 0.024105899035930634, 0.032838255167007446, -0.012722059153020382, -0.06063144654035568, 0.021435150876641273, 0.10176905244588852, -0.026592010632157326, -0.05844363570213318, 0.05211970955133438, 0.006520305294543505, -0.011119059287011623, 0.0...
<p>We know that the ground state degeneracy of Toric Code model is 4. An easy way of seeing this is the following: </p> <p>Consider a 2D spin model where all the spins live on the links. The Hamiltonian is $H=-\sum_v{A_v}-\sum_p{B_p}$, where $A_v=\sigma_{v1}^z\sigma_{v2}^z\sigma_{v3}^z\sigma_{v4}^z$ is the product of ...
g18149
[ -0.012287535704672337, 0.007538794539868832, -0.014438505284488201, -0.02106441929936409, 0.05025050416588783, 0.027129175141453743, 0.10921955853700638, 0.014181782491505146, -0.03836948424577713, 0.030890611931681633, -0.057093799114227295, -0.01102086715400219, -0.02848939411342144, 0.0...
<p>Let's consider simple two-level system with frequency gap of $\omega_0$ between ground and excited state. Now, when we turn on external electromagnetic field with frequency $\omega &lt; \omega_0$, there is non-zero probability that starting from ground state system will become excited.</p> <p>Energy of exicted stat...
g18150
[ 0.012596740387380123, 0.03074093535542488, -0.014671890996396542, 0.020058264955878258, 0.05966292321681976, 0.05140553414821625, 0.04629328474402428, 0.08906309306621552, -0.004534873180091381, -0.06881976872682571, -0.00021758885122835636, -0.007508537266403437, -0.0066292062401771545, 0...
<p>Some searching gives that above 6,000 meter altitude the air density is less than half of that at sea level. Speed of sound is about 15-20% slower and "acoustic impedance" seems to change too.</p> <p>Do humans notice these differences in sound? Does the pitch of tones change noticeable?</p>
g18151
[ 0.038121212273836136, -0.011821554973721504, -0.00003638570706243627, 0.027433710172772408, 0.002078987192362547, 0.04464656114578247, 0.014363227412104607, -0.01126472745090723, -0.005306647624820471, 0.013530613854527473, -0.02029183693230152, -0.028313621878623962, -0.007583264261484146, ...
<p>The <a href="http://en.wikipedia.org/wiki/Hubble_volume" rel="nofollow">Hubble volume</a> is the volume that corresponds to objects so far from the Earth that the space between us and them is expanding faster than the speed of light. (I.e. objects outside this volume could never again be visible to us, even in princ...
g18152
[ 0.05187921226024628, 0.04712102562189102, 0.014708276838064194, 0.0010250189807265997, -0.0508800633251667, 0.026820942759513855, 0.014377803541719913, 0.024290461093187332, -0.03411521390080452, -0.06069958582520485, 0.07507739961147308, -0.03251604735851288, 0.07255278527736664, 0.060481...
<p>I've been involved in a Internet debate:</p> <p><strong>Is it possible to have a special cosmic configuration consisted of multiple bodies such that a planet's surface can be lit up by light focused by gravitational lens effect caused by some giant mass bodies inside the system?</strong></p> <p>Somebody say it is...
g18153
[ -0.023272842168807983, 0.0743180513381958, 0.010516898706555367, 0.0009560308535583317, 0.05066702142357826, 0.04730582982301712, -0.041300218552351, -0.013471398502588272, -0.018403809517621994, -0.04373345524072647, 0.03874727338552475, 0.02427714690566063, 0.037766534835100174, -0.00881...
<p>Suppose we have two particles with initial separation of $|x_2^\text{init}-x_1^\text{init}|=d$. At time $t=0$ they start accelerating with proper acceleration of $w$. Then position of the $i$th particle in laboratory frame will be:</p> <p>$$x_i(t)=\frac{c^2}w\left(\sqrt{1+\frac{w^2t^2}{c^2}}-1\right)+x_i^\text{init...
g18154
[ 0.02909926138818264, -0.005591459572315216, 0.0015285562258213758, 0.006597781553864479, 0.05113527551293373, 0.01646595261991024, 0.027703268453478813, 0.02907976694405079, -0.03214729204773903, 0.014029065147042274, -0.015053444541990757, 0.039125557988882065, 0.007348625920712948, -0.03...
<p>Are there any compelling models that include a past eternal singularity that ultimately gave rise to our universe? Does the "no-boundry" hypothesis that utilizes imaginary time have past eternal imaginary time and real time being created at the big bang? What are the underlying aspects of physics that allow or disal...
g18155
[ -0.013211152516305447, 0.019416216760873795, 0.016294194385409355, -0.024738818407058716, -0.02904563583433628, 0.03002917394042015, 0.02420993708074093, 0.004611981566995382, -0.010156990960240364, 0.008798599243164062, 0.012970148585736752, -0.06496155261993408, 0.05798286199569702, 0.05...
<p>There's a voltage difference of 1000 Volts between two points 2 meters apart. An electron starts at the point of lower potential and is left to travel alone in a straight line until it reaches the other point. <strong>Question</strong>: What speed does the electron have when it reaches the second point?</p> <p>My c...
g18156
[ 0.05776956304907799, -0.01247295830398798, 0.006789203733205795, 0.05488146096467972, 0.0903659388422966, -0.00749098090454936, 0.01651410199701786, 0.03610707074403763, -0.03541243076324463, 0.05353256314992905, -0.01340868417173624, 0.09924104809761047, -0.0249544195830822, 0.02705927565...
<p>I am sorry to ask a question that obviously is a sum of separate questions about a process: Should the decay rate of Z0 be related to the decay of the "higgs" composite field it is eating? And, should this composite field, being a pseudoscalar, decay at the same rate of the neutral pion? But I hope that people will ...
g18157
[ 0.028813956305384636, 0.068882517516613, 0.002852331381291151, -0.022518251091241837, 0.07892096787691116, -0.0007581901736557484, 0.03359026089310646, 0.05242837220430374, 0.039071615785360336, -0.06305650621652603, 0.0010233699576929212, 0.007944378070533276, 0.011750573292374611, 0.0602...
<p>The question is, "A $45.5~kg$ girl is standing on a $140~kg$ plank. Both originally at rest on a frozen lake that constitutes a friction-less, flat surface. The girl begins to walk along the plank at a constant velocity of $1.47~m/s$ relative to the plank."</p> <p>(a) What is the velocity of the plank relative to t...
g18158
[ 0.08613384515047073, 0.06550762802362442, -0.0003963826166000217, -0.008965426124632359, 0.04244602471590042, 0.03184801712632179, 0.10411018133163452, 0.01284582819789648, -0.06041642278432846, -0.015511622652411461, -0.06867112964391708, -0.013901634141802788, 0.010149357840418816, 0.029...
<p>These news are in Finnish: <a href="http://www.hs.fi/ulkomaat/Kaukaisin+havaittu+galaksi+et%C3%A4%C3%A4ntyy+maasta+valoa+nopeammin/a1305618680897" rel="nofollow">http://www.hs.fi/ulkomaat/Kaukaisin+havaittu+galaksi+et%C3%A4%C3%A4ntyy+maasta+valoa+nopeammin/a1305618680897</a></p> <p>The main excerpt is: "Distant gal...
g18159
[ -0.0002815013867802918, 0.06952842324972153, -0.006534479092806578, 0.022882869467139244, 0.015433095395565033, 0.01403382420539856, -0.03571324050426483, 0.015705473721027374, -0.040219515562057495, -0.022393357008695602, 0.032923802733421326, 0.053824104368686676, 0.05754849687218666, -0...
<p>if all magnets have to have two poles(one north one south), is it possible to construct a hollow sphere where the inside face of the sphere was one pole, and the outside face another pole?</p> <p>is it also possible to make a magnetic sphere (not hollow) where the outside face is one pole?</p> <p>If both of these ...
g18160
[ -0.012721069157123566, 0.0010828771628439426, 0.019144756719470024, 0.002236150437965989, 0.023126892745494843, 0.04009049013257027, -0.033302273601293564, -0.009411747567355633, -0.016041764989495277, -0.015944521874189377, -0.06984931230545044, 0.004801617469638586, 0.030341971665620804, ...
<p>The suggestion that quantum mechanics implies that instantaneous action at a distance occurs is normally based on the contention that this follows from the entanglement of particles that share a common origin. My question is: does quantum mechanics predict that this happens even when there is no entanglement? In par...
g18161
[ 0.045644260942935944, -0.0003620877687353641, 0.03272033855319023, -0.02635762467980385, 0.05564640089869499, 0.06882915645837784, -0.01360035315155983, 0.03643137216567993, -0.027613593265414238, 0.004705504048615694, -0.001127780182287097, -0.009948437102138996, -0.025974215939641, 0.007...
<p>I've never liked discontinuous quantities in classical physics, so I find the discontinuity in heat capacity weird. </p> <p>My question is, do first order <a href="http://en.wikipedia.org/wiki/Phase_transition#Classifications" rel="nofollow">phase transitions</a> ever really exist? Or are our discontinuous experime...
g18162
[ 0.010133571922779083, 0.022704003378748894, 0.011640314012765884, -0.00004712261215900071, 0.07141955941915512, -0.06166297569870949, -0.02869105152785778, 0.05340971797704697, 0.0002731319982558489, 0.00615993095561862, -0.03347364068031311, 0.02230885811150074, -0.013718507252633572, 0.0...
<p>I am stuck on a QM homework problem. The setup is this:</p> <p><img src="http://i.stack.imgur.com/uRIu3.png" alt="enter image description here"></p> <p>(To be clear, the potential in the left and rightmost regions is $0$ while the potential in the center region is $V_0$, and the wavefunction vanishes when $|x|&gt...
g18163
[ -0.011129028163850307, 0.012742656283080578, -0.017423005774617195, -0.06098754703998566, 0.04865754768252373, -0.004980086348950863, 0.016213983297348022, 0.05472228303551674, 0.000532977981492877, -0.01997159980237484, 0.004907211754471064, -0.0017678498988971114, -0.032030098140239716, ...
<p>There is a chapter on general relativity in the book <em>Spacetime Physics Introduction To Special Relativity</em> by Taylor and Wheeler, which qualitatively explains how attractive gravitational force can be understood in terms of space(time) curvature. They give (chapter 9.5, pp. 281-283 in 2nd edition) an example...
g18164
[ -0.005551328416913748, 0.010629725642502308, -0.015372274443507195, 0.022715499624609947, 0.02542009763419628, 0.11646249145269394, 0.04755115509033203, -0.009508956223726273, -0.06940840184688568, -0.023040374740958214, 0.0483839176595211, -0.008123410865664482, 0.06674952805042267, 0.012...
<p>I was always intrigued by the phenomena that govern the returning back of a boomerang to the thrower.</p> <p>Even if it is dependent on various factors such as velocity, aerodynamics, wind resistance and so on I was wondering, there must be some concise explanation to it?</p>
g18165
[ 0.07320410013198853, 0.07630414515733719, -0.015164255164563656, 0.001982443267479539, 0.044572290033102036, 0.05229059234261513, 0.05931531637907028, -0.0018974409904330969, -0.029309937730431557, -0.06451456993818283, -0.01769469864666462, 0.03465214744210243, 0.020150551572442055, 0.047...
<p>In <a href="http://www.youtube.com/watch?v=Iuv6hY6zsd0">this Veritasium video</a>, a home experiment is presented which appears to produce a very good double-slit interference pattern with normal sunlight.</p> <p>The experiment is an empty cardboard box with a visor and a placeholder for a microscope slide with two...
g18166
[ -0.0023703023325651884, 0.01785675436258316, 0.010438211262226105, 0.00273911259137094, -0.008521167561411858, -0.004696075338870287, 0.016928983852267265, 0.002856498584151268, 0.015679124742746353, -0.0003229368303436786, 0.06958500295877457, 0.030050287023186684, 0.03257627412676811, 0....
<p>What are the reasons that $SU(3)$ is used for <a href="http://en.wikipedia.org/wiki/Quantum_chromodynamics" rel="nofollow">QCD</a>?</p> <p>Why wouldn't the simpler &amp; smaller group $SO(4)$ make a better candidate?</p>
g18167
[ 0.04880991950631142, -0.0014424683758988976, -0.02333846315741539, -0.026694083586335182, -0.016421837732195854, 0.037124283611774445, 0.019816093146800995, 0.01802477426826954, -0.023902270942926407, -0.04809640347957611, 0.06489034742116928, 0.003633292391896248, 0.007773496676236391, 0....
<p>So instead of assuming that the velocity $c$ is a maximal velocity, proving that while assuming $E=mc^2$.</p>
g18168
[ 0.08688220381736755, 0.01902543194591999, -0.010932994075119495, 0.028606414794921875, 0.012338305823504925, -0.04311520606279373, 0.031699590384960175, 0.03619655966758728, -0.0048026759177446365, -0.00407985458150506, -0.06147784739732742, -0.018990596756339073, 0.012449188157916069, 0.0...
<p>Why does gravitational force of the Earth decrease as we move towards the centre of the Earth? Where as inverse square rule says that distance is less than gravitational force is more. </p>
g50
[ 0.05237533524632454, 0.062095534056425095, -0.01155965868383646, -0.012337418273091316, 0.05177140608429909, 0.05588901415467262, 0.012899262830615044, 0.02043445222079754, -0.0532570444047451, -0.06620659679174423, 0.004587363451719284, 0.003473952878266573, 0.04612121358513832, -0.002119...
<p>I am stuck at the beginning of a problem where I am given an interaction term that modifies the regular QED Lagrangian. It involves the interaction between a photon field and a massive vector boson: $\mathcal{L}_{int_1} = \frac{1}{4}g_1G_{\mu \nu}F^{\mu \nu}$. Here, $F^{\mu \nu}$ is the electromagnetic field tensor....
g18169
[ 0.027391616255044937, 0.018620524555444717, -0.008715236559510231, -0.04632535204291344, 0.019860705360770226, -0.007443415001034737, 0.08676493167877197, 0.019824519753456116, -0.006925150286406279, 0.004753736779093742, -0.012616528198122978, 0.039927829056978226, -0.02735162526369095, -...
<p>Recently I had a quiz in my physics class and I feel like the professor made a mistake on the solution for it. Yes, I already have the answer to this question. I am not trying to get people's answers for homework or anything. But I would like to hear people responses to this. The question was:</p> <p>Which of the f...
g18170
[ 0.012322152964770794, -0.011508210562169552, 0.01877269148826599, -0.0004995380295440555, 0.059855081140995026, 0.059797536581754684, 0.06537270545959473, 0.004921260755509138, -0.01767357811331749, -0.05182702839374542, 0.030777061358094215, 0.004671668633818626, -0.049554817378520966, 0....
<p>An electron is in a region where there is an uniform magnetic field created by a large disc-shaped magnet. As is well known, if the electron is moving with velocity $\vec v$ parallel to the flat surface of the magnet (ie, perpendicular to the magnetic field) experiment the Lorentz force, $\vec F=q(\vec v\times\vec B...
g18171
[ 0.02799193561077118, 0.04333414137363434, -0.007477441802620888, -0.008658144623041153, 0.06790243089199066, -0.0013699096161872149, 0.0252345222979784, 0.03319071978330612, -0.019210271537303925, -0.022453147917985916, -0.05084768310189247, 0.04201112687587738, 0.010465775616466999, -0.01...
<p>What is the rational/reason for neglecting masses at asymptotic non-exceptional space-like momenta. I have come across this as a first fix for being able to extract information from the Callan-symanzik and Gell-Mann-Low methods. Is it purely physical, or is it both physical and mathematically sound reason?</p> <p>A...
g18172
[ 0.045695751905441284, 0.03248465806245804, 0.013881893828511238, 0.013096910901367664, 0.015746986493468285, 0.023359838873147964, 0.024647671729326248, 0.03213103488087654, -0.012571956031024456, -0.03598892316222191, 0.01196901686489582, -0.04786128178238869, 0.04199104756116867, 0.08201...
<p>Let's have two forms of Majorana equation.</p> <p>First form (standart or spinor representations of gamma-matrices). </p> <p>$$ i\gamma^{\mu} \partial_{\mu}\Psi - m\Psi = 0, \quad \Psi = \Psi_{c} = \hat {C} \bar {\Psi}^{T} = \begin{pmatrix} \Psi_{a} \\ \bar {\Psi}^{\dot {a}}\end{pmatrix}, \quad \hat {C} = diag (\v...
g18173
[ 0.04148471727967262, -0.081366628408432, -0.0008334888843819499, -0.05242477357387543, 0.07676699757575989, -0.03801683709025383, 0.06041941046714783, 0.015902044251561165, -0.0015803923597559333, -0.039582833647727966, -0.04271451011300087, -0.014871037565171719, 0.017735345289111137, -0....
<p>From <a href="http://physics.stackexchange.com/questions/54975/quantum-entanglement-whats-the-big-deal/54977#54977">this question</a> and answer from joshphysics, I didn't understand one thing, even after reading the comments:</p> <p>Why should assume that entangled electrons will only "decide" their state after ob...
g18174
[ -0.020343612879514694, 0.04678719863295555, 0.017030084505677223, 0.007953288964927197, 0.07012939453125, -0.004190907813608646, 0.06191156432032585, 0.08660640567541122, 0.012634246610105038, -0.020329978317022324, 0.008303646929562092, 0.013637864030897617, 0.016852954402565956, -0.04101...
<p>Assume you have a rigid body falling into the ocean at terminal velocity. Also assume that the rigid body does not break on impact. How could you figure out how much kinetic energy would be lost in the resulting splash? I promise this isn't a homework question, but an engineering thought experiment. I began to reaso...
g18175
[ 0.06686786562204361, 0.010191895999014378, 0.0038341726176440716, -0.011509375646710396, 0.006812669336795807, 0.025506552308797836, -0.004977213218808174, 0.032135918736457825, -0.046184033155441284, -0.04136228561401367, -0.03428784757852554, 0.021812552586197853, 0.03922967240214348, 0....
<p>According to conservation of linear momentum and angular momentum, one can derive that <a href="http://en.wikipedia.org/wiki/Cauchy_stress_tensor" rel="nofollow">Cauchy stress tensor</a> is symmetric and hence has only 6 independent components. Is it possible that, when breaking one or both of conditions, Cauchy str...
g18176
[ -0.0050242287106812, 0.025245774537324905, -0.018074708059430122, 0.006620170548558235, 0.02296193689107895, -0.012609959580004215, 0.012816185131669044, -0.014881247654557228, -0.013881112448871136, -0.0027469941414892673, -0.04194195196032524, -0.03519614040851593, 0.0028860189486294985, ...
<p>This may be a simple question. I can show this is the case mathematically but cannot explain why it happens. It was only when asked why this happens when I realised I couldn't explain it intuitively/physically. </p> <p>So I suppose there must be some way in which the Klein-Gordan equation can be recovered from the ...
g18177
[ 0.05965723842382431, 0.014917971566319466, 0.011399774812161922, 0.007074941881000996, 0.07117576897144318, -0.049589138478040695, 0.05490351840853691, 0.04493183270096779, 0.01114689651876688, -0.053881626576185226, -0.027871252968907356, -0.06330540031194687, 0.04473702237010002, -0.0220...
<p>I am reading the book "Basic Concepts of String Theory" by Blumenhagen, Lust and Theisen and in page 290 they say:</p> <p>"It follows that the $E8\times E8$ and the $SO(32)$ heterotic string theories have the same number of states at every mass level which are however differently organized under the internal gauge ...
g18178
[ 0.0388215109705925, -0.038004081696271896, 0.020603640004992485, -0.039624013006687164, 0.048196788877248764, 0.0397275947034359, 0.03816625848412514, -0.01484007015824318, 0.014024467207491398, -0.001999535597860813, -0.04086348041892052, -0.012123220600187778, 0.06499750912189484, 0.0404...
<p>I'm doing a course on QM and this concept is entirely new to me:</p> <p>"The eigenvalue $m\hbar$ of $L_z$ can be understood as the result from the rotational motion of probability fluid around the z-axis. " </p> <p>Then I thought, suppose we have a volume element $dV$ at some point $r$ away, and I'm trying to find...
g18179
[ 0.030845368281006813, 0.0004024486115667969, -0.012212897650897503, -0.03025061823427677, 0.028497226536273956, -0.001717739156447351, 0.08612272888422012, 0.02069704234600067, -0.005630644969642162, -0.04984044283628464, 0.013611589558422565, 0.003139273263514042, 0.012214014306664467, 0....
<p>How many parameters are required to specify the density matrix of a $n$-qubit system, and how many parameters are required to specify a quantum operation (completely positive maps between states) on an $n$-qubit system?</p> <p>For example, when $n=1$, there are 3 parameters required to specify the density matrix an...
g18180
[ -0.07107996195554733, 0.061316560953855515, -0.003779658814892173, -0.009588325396180153, 0.00003741274485946633, -0.00949312187731266, -0.02953564003109932, -0.047374095767736435, -0.014285298995673656, 0.06067154183983803, -0.04238850250840187, -0.04235126078128815, 0.005306130740791559, ...
<p>I am having a problem in understanding how in a multiconductor system the Capacitance Matrix influences the measure of voltage between two electrodes.</p> <p>In the case that interest me we have 4 electrodes, 2 emitting ones and 2 receiving ones. We transmit a known sinusoidal current into the the emitting electrod...
g18181
[ -0.017335660755634308, -0.020061513409018517, -0.0011196695268154144, 0.004790670704096556, -0.024171866476535797, -0.037184938788414, 0.03269592672586441, 0.02280724048614502, 0.006482595112174749, -0.021700331941246986, -0.06330029666423798, -0.0020230947993695736, -0.0028648909647017717, ...
<p>How does the field expansion method (by this I mean expanding your fields about a chosen VEV and plugging into a given potential so that the masses of the fields are given by the coefficients in front) corrolate with the vacuum you choose. In SU(3), choosing v = (0,0,v) gives 5 NGB, while v = (v,0,0) gives 6 NGB (us...
g18182
[ 0.057272568345069885, 0.036150164902210236, 0.031421955674886703, 0.02424713596701622, 0.07282494008541107, 0.04272057116031647, 0.012037655338644981, 0.012937862426042557, 0.006789838895201683, 0.016689153388142586, -0.009017756208777428, -0.039202842861413956, 0.025240596383810043, 0.021...
<p>There have been some <a href="http://physics.stackexchange.com/questions/5075/is-anyone-studying-how-the-topology-of-space-arises-from-more-fundamental-notions">very</a> <a href="http://physics.stackexchange.com/questions/6980/what-are-the-reasons-to-expect-that-gravity-should-be-quantized">nice</a> <a href="http://...
g18183
[ 0.054747942835092545, 0.010335205122828484, -0.008969906717538834, 0.009078036062419415, 0.013216854073107243, -0.0009218489867635071, 0.04284396767616272, 0.015832195058465004, -0.004044451285153627, 0.019238505512475967, 0.030500119552016258, 0.007767688017338514, 0.045812107622623444, 0...
<p>What are the equations that describe the flow of a fluid in a porous medium? Is there a variation of the Navier-Stokes equations?</p> <p>I would like to model the flow of air through a sponge-like structure. Instead of modelling the structure of the sponge, I would like to treat it like a homogenous area, where I s...
g18184
[ 0.0008567763725295663, -0.010331685654819012, -0.01903165504336357, -0.03287643939256668, 0.03445610776543617, 0.017572706565260887, 0.016080720350146294, 0.01300783734768629, -0.014717564918100834, -0.042353175580501556, 0.03430761769413948, -0.05673877149820328, 0.014789886772632599, 0.0...
<blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://physics.stackexchange.com/questions/4243/what-does-it-mean-to-say-gravity-is-the-weakest-of-the-forces">What does it mean to say &ldquo;Gravity is the weakest of the forces&rdquo;?</a> </p> </blockquote> <p>It is said nuclear force is the ...
g875
[ 0.03451600670814514, 0.041394464671611786, 0.02178356982767582, -0.004768507555127144, 0.0610891692340374, 0.016593826934695244, -0.03013104945421219, -0.027194764465093613, -0.04574092477560043, -0.02829299308359623, 0.04170365631580353, 0.03214472159743309, -0.037396516650915146, -0.0115...
<p>I would like some help in understanding the derivation of the formula for escape velocity. Why does $t$ approach infinity? And why is $v(t)$ approaching zero? I know that $r(t)$ is infinite because the gravitational field is infinite. But I don't understand why $t$ (time) and velocity would be zero. </p> <p>I don'...
g18185
[ 0.009100372903048992, 0.04473641514778137, -0.0015082786558195949, 0.00447307713329792, 0.018940532580018044, -0.03764145448803902, 0.045614272356033325, 0.058402031660079956, -0.07345835864543915, 0.013226987794041634, -0.07384687662124634, -0.0030067884363234043, 0.0020039898809045553, -...
<p>P. Dirac was worried with the infinities and their discarding in QED. He wanted us to reformulate the theory in order to eliminate infinities and renormalizations from the very beginning. Is there anybody who works professionally on this subject? I mean, who earns his salary for that. I know several amateurs but no ...
g18186
[ -0.006759621202945709, 0.0038003891240805387, -0.006005255505442619, -0.020797664299607277, 0.01620941422879696, -0.045083921402692795, 0.012821652926504612, 0.0738682895898819, -0.016381312161684036, 0.020265284925699234, -0.061022717505693436, 0.003410156350582838, -0.011833705939352512, ...
<p>My question basically is, is Kronecker delta $\delta_{ij}$ or $\delta^{i}_{j}$. Many tensor calculus books (including the one which I use) state it to be the latter, whereas I have also read many instances where they use the former. They cannot be the same as the don't have the same transformation laws. What I think...
g18187
[ -0.0006793724023737013, 0.006442084908485413, 0.00781292375177145, 0.020036347210407257, 0.019856737926602364, 0.009460566565394402, 0.03669166937470436, -0.015532968565821648, -0.01813146099448204, -0.006365348119288683, -0.046525802463293076, 0.017565755173563957, 0.045489467680454254, -...
<p>Given that baryons are not point particles but are composed of three quarks, are there quantized vibrational and rotational states analogous to those of molecules? </p> <p>If not why not, and if so are there spectroscopically observable transitions between such states?</p>
g18188
[ 0.014420464634895325, -0.02316443808376789, 0.006345923990011215, -0.03580552339553833, 0.048537477850914, -0.010739916004240513, -0.06929200142621994, -0.007377633359283209, 0.008705716580152512, -0.03800226375460625, 0.04204186424612999, -0.025980480015277863, -0.03582558408379555, -0.03...
<p>Is it possible to have $Q=0$, $\Delta E=0$ and $W=0$, but $\Delta T\neq 0$?</p> <p>In particular, if there is no change in internal energy, doesn't that imply it is an isothermal process, and therefore that $\Delta T=0$? </p>
g18189
[ 0.030110541731119156, -0.03154491260647774, 0.028269639238715172, 0.017476240172982216, 0.024919642135500908, -0.0012552060652524233, -0.002343491418287158, 0.011805872432887554, -0.040020961314439774, -0.017544088885188103, -0.042260393500328064, 0.007202077656984329, -0.0006384547450579703...
<p>If I have some arbitrary particle, we will call particle 1 and another particle 2 that have the same momentum, yet particle 1 has half the mass of particle 2, how does the kinetic energy compare between the two particles?</p> <p>I guess I am looking for a ratio K2/K1. I can't seem to think it through.</p>
g18190
[ 0.06501632928848267, -0.031414374709129333, 0.013565538451075554, -0.008318029344081879, 0.023621711879968643, -0.039240334182977676, -0.03581705689430237, 0.025422247126698494, -0.05610610544681549, 0.01873686909675598, 0.03096822276711464, -0.006223443895578384, -0.00908579770475626, 0.0...
<p>Consider a conducting wire bent in a circle (alternatively, a perfectly smooth metal ring) with a positive (or negative) electric charge on it. Technically, this shape constitutes a torus. Assume that the radius of the wire is much smaller than the radius of the circle.</p> <p><strong>Find the tension in the wire...
g18191
[ 0.08102410286664963, -0.014683054760098457, -0.009989876300096512, -0.01758546568453312, 0.05431217700242996, 0.04546201229095459, 0.012755844742059708, -0.008306964300572872, -0.06390804797410965, 0.052614737302064896, -0.018385138362646103, 0.022597914561629295, -0.029414137825369835, -0...
<p>Inspired by <a href="http://physics.stackexchange.com/questions/9776/doppler-effect-of-sound-waves/9834#9834">this question</a> on the Doppler shift, suppose there is buoy somewhere on the surface of the ocean emitting a pure frequency.</p> <p>You get to place some boats wherever you want on the surface of the ocea...
g18192
[ -0.026371963322162628, 0.0017143691657111049, 0.00580366887152195, -0.007491447497159243, 0.07746126502752304, -0.02225542441010475, 0.02998362109065056, -0.012242178432643414, -0.03120497427880764, -0.08920475840568542, -0.0055481246672570705, 0.01293484028428793, 0.04655621573328972, 0.0...
<p>This problem is part of one of the free response questions on the 2011 AP Physics C Mechanics exam [<a href="http://apcentral.collegeboard.com/apc/public/repository/ap11_frq_physics_cm.pdf" rel="nofollow">PDF of free-response questions</a>] that was administered last week.</p> <p>(Sorry the problem statement is so ...
g18193
[ 0.06361545622348785, 0.027741938829421997, 0.010669009760022163, -0.018046189099550247, 0.047233037650585175, -0.02851305529475212, 0.03543407842516899, -0.021538129076361656, -0.06626633554697037, -0.03272298350930214, -0.0220013614743948, 0.0029394810553640127, -0.005448170937597752, 0.0...
<p>Does anyone have any references that discuss gravity in three-dimensions? I'm trying to make my way through <a href="http://adsabs.harvard.edu/abs/1988NuPhB.311...46W" rel="nofollow">some</a> <a href="http://arxiv.org/abs/0706.3359" rel="nofollow">papers</a> by Witten relating $SL(2,\mathbb{C})$ Chern-Simons theory ...
g18194
[ 0.047429461032152176, 0.05676073580980301, -0.0014246307546272874, -0.017504652962088585, -0.00031648908043280244, 0.05636269971728325, 0.009564504958689213, -0.029913393780589104, -0.11817282438278198, 0.005929958540946245, -0.012224506586790085, -0.023310834541916847, 0.03708920255303383, ...
<p>I have found the complex Fourier series for my desired force. I now need to find the steady-state forced vibration of my oscillator as a Fourier Series. (The particular solution to the inhomogeneous differential equation) How can I go about finding this.</p>
g18195
[ 0.021960021927952766, -0.0023220540024340153, -0.008583416230976582, -0.048865508288145065, 0.016940532252192497, -0.0370463989675045, 0.015204939059913158, -0.014371837489306927, -0.044015441089868546, -0.04922765865921974, -0.016787610948085785, 0.0022217435762286186, -0.032932206988334656...
<p>A perpendicular plane to an electric field's lines of force has more electric flux than a plane that is in parallel with the lines of force, right?</p> <p>Does this mean that a <strong><em>charged</em></strong> plate would experience less <strong><em>acceleration</em></strong> if parallel to rather than perpendicul...
g18196
[ 0.08377799391746521, 0.08584772050380707, -0.00573144992813468, -0.01667371578514576, 0.0820019394159317, 0.06295990198850632, -0.014467306435108185, 0.004067461006343365, -0.02704458311200142, -0.038875773549079895, 0.006932091433554888, 0.03414270654320717, -0.011298972181975842, 0.00884...
<p>I apologize in advance for what might be a very naive question, and for its science-fictionesque flavor. It's still, I think, a real physics question.</p> <p>Suppose I have a (quantum) particle, whose state is represented by some element $x$ of some Hilbert space $H$. Given an observable $O$, I can express $x$ as...
g18197
[ 0.03438066691160202, 0.05534787476062775, 0.032677773386240005, -0.06056961417198181, 0.04571674019098282, 0.040813274681568146, 0.017447402700781822, 0.0476355217397213, -0.01246760506182909, -0.016148174181580544, 0.007294184993952513, -0.010014456696808338, -0.00012997450539842248, 0.02...
<p>A man is carrying a bucket with water. If a object is kept in it which floats in water, man will feel</p> <p>1) heavier</p> <p>2) lighter</p> <p>3) none</p> <p>I think when the body floats its weight is balanced by upthrust so no further be felt. Is it right or wrong?</p>
g18198
[ 0.03777776658535004, 0.005913661792874336, -0.017568295821547508, -0.0645943209528923, 0.03549248352646828, 0.12718316912651062, 0.07098356634378433, -0.021493665874004364, -0.046494897454977036, -0.06100056320428848, -0.02366219460964203, -0.02813669480383396, -0.04010798782110214, 0.0546...
<p>The Standard Model (SM) predicts an "aspherical" electron due to its possesing a non-zero electron electric dipole moment (EEDM). An experiment by Hinds (2011) placed an upper bound on the asphericity of the electron without absolutely being able to say the EEDM was zero. Most sources I've read somewhat authoritat...
g18199
[ -0.027643464505672455, 0.0072069671005010605, 0.002144749742001295, -0.012537064962089062, 0.037996552884578705, 0.03232012689113617, 0.03619072586297989, 0.018080903217196465, -0.0027954066172242165, -0.04340158775448799, 0.02300363965332508, 0.029353102669119835, 0.08796826004981995, 0.0...
<p>Consider a computer CPU consuming electrical energy to perform calculations and consequently emitting heat.</p> <p><strong>Assumption:</strong> That a CPU consuming <em>x</em> Watts of power, emits the same amount of heat as an incandescent heating element which consumes the same amount of power.</p> <p>The rest o...
g929
[ 0.019341610372066498, 0.09702347218990326, 0.01844402588903904, 0.003918031696230173, -0.029335182160139084, -0.06186496466398239, 0.04500030726194382, 0.01641092449426651, -0.05677289888262749, -0.0047503868117928505, -0.006865749601274729, 0.07071831822395325, 0.009876755066215992, 0.055...
<p>A star emits perfectly (100%) linearly polarized light at an arbitrary angle.<br> How many photons must you detect to measure this angle to a precision of n binary digits? (with greater than 50% probability of being correct.)</p> <p>What is the best strategy for performing this measurement?</p>
g18200
[ -0.041801001876592636, -0.02725689485669136, 0.002435835776850581, -0.020893771201372147, 0.00029413800803013146, -0.05053400248289108, 0.007120002061128616, 0.015342221595346928, 0.017243854701519012, 0.016596421599388123, 0.001705853850580752, 0.03566857427358627, 0.012625073082745075, -...
<p>Hubeny's 1998 paper got a lot of people interested in determining whether cosmic censorship can be violated by dropping too much charge onto a black hole. It suggested that you might be able to get a naked singularity from generic initial conditions rather than requiring infinitely fine-tuned initial conditions as i...
g18201
[ 0.03828972205519676, 0.023080825805664062, -0.006521962117403746, -0.017441799864172935, 0.018791135400533676, 0.011143996380269527, 0.05067369341850281, -0.002340516075491905, -0.06015559658408165, 0.050111182034015656, 0.022843435406684875, 0.027037087827920914, 0.00719837099313736, 0.04...
<p>What are some important approximations, especially those that are state-of-the-art, used to approximate the many-body dynamics of atoms and molecules in the <a href="http://en.wikipedia.org/wiki/Semiclassical_physics" rel="nofollow">semiclassical</a> regime? To be clear, I'm not really looking for semiclassical appr...
g18202
[ -0.05444999411702156, 0.03179480880498886, -0.0023939134553074837, -0.01619536243379116, -0.017890745773911476, -0.027047419920563698, -0.037319160997867584, 0.0359601266682148, 0.03155354782938957, 0.03341415897011757, 0.034064363688230515, -0.025283508002758026, 0.020861433818936348, 0.0...
<p>In the image below (source at bottom), it seems to be suggesting that</p> <p>\begin{equation} a = a_{1} + a_{2}, \hspace{8cm}(1) \end{equation} where $a_{1}$ and $a_{2}$ are the semi-major axis of the two orbits, and $a$ is the semi-major axis of the trajectory for the equivalent reduced-mass star in the one-bo...
g18203
[ -0.01764380745589733, 0.007022046484053135, -0.0013912789290770888, 0.01350113283842802, 0.07444372028112411, 0.013692251406610012, 0.051492225378751755, 0.005605969112366438, 0.021079596132040024, 0.004142004530876875, -0.0406719371676445, 0.04447341710329056, 0.011583523824810982, 0.0273...
<p><img src="http://i.stack.imgur.com/Ec4jC.png" alt="enter image description here"></p> <p>When light reaches a boundary between materials below the critical angle, some of it refracts and some of it reflects. For example, glass acts as a partial mirror with a dark background.</p> <p>Assuming no light is lost in the...
g18204
[ 0.07116681337356567, -0.035316962748765945, 0.00891463365405798, 0.015157646499574184, 0.035112008452415466, -0.01825348660349846, 0.0496206134557724, 0.01380724273622036, 0.011603803373873234, -0.010708806104958057, 0.027939707040786743, 0.0565212145447731, 0.04160985350608826, -0.0184435...
<p>What are the general spectral properties of <a href="http://en.wikipedia.org/wiki/Conformal_field_theory" rel="nofollow">CFT</a>? I mean what is the "spectrum"/eigenvalues of CFT in 2d and d>2 spacetime dimensions? I understand the "spectrum" and "Fock space" realization of Dirac equations, Klein-Gordon equations or...
g18205
[ -0.0020889139268547297, -0.04266626387834549, -0.01686827465891838, -0.030024264007806778, 0.02892770990729332, 0.05702914670109749, 0.06544078141450882, 0.00714386161416769, -0.05443965271115303, -0.051587410271167755, 0.009412557817995548, -0.020268825814127922, 0.029848981648683548, 0.0...
<p>In <a href="http://en.wikipedia.org/wiki/Quantum_graph" rel="nofollow">quantum graph</a> theory, what are the properties of a given graph to own complex conjugated complex eigenvalues, either finite or infinite? <a href="http://en.wikipedia.org/wiki/Spectral_graph_theory" rel="nofollow">Spectral graph theory</a> is ...
g18206
[ -0.019844215363264084, 0.0016641318798065186, -0.009418158791959286, -0.06064332276582718, -0.0037194436881691217, -0.03064008802175522, -0.015583943575620651, 0.057462386786937714, 0.04490872099995613, -0.029981225728988647, 0.0094241788610816, -0.019126396626234055, 0.034159544855356216, ...
<p>I was trying to think but cannot figure it out. For instance, if the interaction is small, for instance limited to a windows, the observers in each universe will see that the other goes in reverse. But what if they can start a more meaningful interaction? (for instance, if one observer crosses the window and moves t...
g18207
[ -0.01145943347364664, 0.0436440110206604, 0.009434791281819344, 0.04530094936490059, 0.02909800596535206, -0.006739355623722076, 0.028574522584676743, 0.02540913037955761, -0.016784055158495903, -0.028815073892474174, 0.02595491148531437, 0.057974155992269516, -0.009342171251773834, 0.0159...
<p>In what sense is a quantum field an infinite set of harmonic oscillators, one at each space-time point?<br> When is it useful to think of a quantum field this way?</p> <p>The book I'm reading now, QFT by Klauber, claims its not true, which is it?</p> <p>I would like to understand this analogy a little better.</p>
g18208
[ 0.015239386819303036, 0.0481521338224411, -0.027374273166060448, -0.042509134858846664, 0.05152910575270653, -0.02932589128613472, 0.006891085300594568, 0.02827923186123371, -0.021903928369283676, -0.012116514146327972, -0.03796951100230217, -0.010306751355528831, -0.0394158810377121, 0.03...
<p>We went to a planetarium last night last night and watched "Black Holes" narrated by Liam Neeson. If I recall correctly, he said that scientists believe that they have identified a number of Black Holes, and that they think there are White Holes at the bottom of Black Holes and instead of drawing matter/light in, th...
g18209
[ -0.02135712094604969, 0.0626387745141983, 0.0252175722271204, -0.0758051797747612, 0.07378923892974854, 0.024400321766734123, -0.023103462532162666, -0.02631506323814392, 0.001622054143808782, 0.03309172764420509, 0.05820388346910477, -0.0046263025142252445, 0.050405535846948624, 0.0085099...
<p>I am trying to understand the equation of the radiance, but there is one thing i don't understand: $L_r = \frac{d^2\Phi}{d\omega \space dA\cos{\theta}}$</p> <p>Why is that second exponent there in the numerator?</p> <p>Thanks ahead!</p>
g18210
[ 0.02961130253970623, 0.005508909001946449, -0.028691159561276436, -0.04927932471036911, 0.04495296627283096, 0.028209364041686058, 0.05179871618747711, 0.043812096118927, 0.004269254859536886, -0.049722492694854736, -0.03820168226957321, 0.07307776808738708, -0.0011758259497582912, 0.00245...
<p>Further to <a href="http://astronomy.stackexchange.com/questions/1211/how-long-does-it-take-to-travel-36-light-years-with-tolerable-acceleration-and-de">this</a> question I asked recently, <a href="http://astronomy.stackexchange.com/users/188/lgritz">lgritz</a> makes a very astute observation about the massive fuel ...
g18211
[ 0.011559095233678818, 0.07484026998281479, -0.002885925816372037, 0.009801063686609268, -0.06399549543857574, -0.000025118522898992524, -0.05808559060096741, 0.005753764882683754, -0.06660019606351852, -0.039940450340509415, 0.03746214136481285, 0.0022197726648300886, -0.0010943136876448989,...