question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>The EM tensor of the $bc$-CFT is
$$
T(z) = \colon \partial b c \colon - \lambda \partial \colon b c \colon
$$
After expanding in a mode expansion, we find
$$
T(z) = \sum_{m} \frac{1}{z^{m+2}} \sum_n \left( \lambda m - n \right) \colon b_n c_{m-n} \colon \implies L_m = \sum_n \left( \lambda m - n \right) \colon b_n ... | g7968 | [
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<p>How can I find the amount of point force at the end of a cantilever plastic beam that produces e.g. 45deg slop at the end of the beam? Is this the right equation: $$F=\frac{2EI\theta ^2}{L^2 sin(\theta)}$$</p>
<p>I derived this equation by putting $x=\frac{L}{\theta}sin(\theta)$ and $\theta_x=\theta$ in the followi... | g7969 | [
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<p>I understand that faster-than-light communication is impossible when making single measurements, because the outcome of each measurement is random. However, shouldn't measurement on one side collapse the wave function on the other side, such that interference effects would disappear? Making measurements on "bunches"... | g7970 | [
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<p>If you line up the suns rays parallel to a Fresnel lens, the light is concentrated, and the focus directly underneath. However, what happens if the sun is off to the side, making the light hit at an angle (ei. 45 degrees)? Will the only difference be the focal point, of will the light be less concentrated? If so, by... | g7971 | [
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<p>Is that true that the big bang caused the quantum entanglement of all the particles of the universe so every particle is entangled to each other particle of the universe?</p> | g7972 | [
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<p>I have an exam in two days for first year university physics. Often for dynamics problems, I am required to solve algebraic systems of equations by hand, and this can be very daunting. </p>
<p>When I see the solutions, however, the steps that the solver took to seem very clean and almost obvious. Are there some rul... | g7973 | [
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<p>I have a slight difficulty understanding the solution to the following problem:</p>
<p>A light inextensible string with a mass $M$ at one end passes over a pulley at a distance $a$ from a vertically fixed rod. At the other end of the string is a ring of mass $m(M>m)$ which slides smoothly on the vertical rod as ... | g7974 | [
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<p>In string theory, we are told strings can split and merge if the string coupling is nonzero, even while the worldsheet action remains Nambu-Goto or Polyakov plus a topological term. However, a classical solution, in say the light cone gauge, shows that provided the worldsheet time increases with light cone cone time... | g7975 | [
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<p>I read the Popular Science books, <em>The Brief history of time</em> (Hawking), <em>The fabric of the cosmos</em> (Greene), and <em>The Grand Design</em> (Hawking), etc. but did could not manage to understand what <a href="http://en.wikipedia.org/wiki/String_theory" rel="nofollow">string theory</a> is, even a... | g7976 | [
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<p>I have studied <a href="http://en.wikipedia.org/wiki/Chern%E2%80%93Simons_theory">Chern-Simons (CS) theory</a> somewhat and I am puzzled by the question of how diff. and gauge invariance in CS theory are related, e.g. in $SU(2)$ CS theory. In particular, I would like to know about the relation between large gauge tr... | g7977 | [
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<p>I am not from a physics background. I came to know this while studying probability? Is this because the planets are nearer than the stars so we get average behaviour rather than random. Is law of large number used here? Can anyone explain in detail. </p> | g261 | [
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<p>I am currently looking at changes in DOS when sampling recipocal space finely. More precisely, I am looking at the expressions</p>
<p>$$\rho_\text{1D}(E)\text{d}E = \frac{m}{\pi \hbar} \sum_i \text{H}(E-E_i)\text{d}E, \\
\rho_\text{2D}(E)\text{d}E = \frac{1}{\pi}\sqrt{\frac{2m}{\hbar^2}} \sum_i \frac{n_i\text{H}(E... | g7978 | [
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<p>The following is a graph of the intensity of Bremsstrahlung generated by accelerating electrons to hit a target vs. its wavelength.</p>
<p><img src="http://i.stack.imgur.com/EbRI9.png" alt=""></p>
<p>I'm wondering what causes the additional peaks for high energies? I have read in my physics script and on Wikipedia... | g7979 | [
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<p>I'm currently writing a simulation in python with scipy and matplotlib to reproduce an one dimensional driven diffusive system described in this <a href="http://prl.aps.org/abstract/PRL/v74/i2/p208_1" rel="nofollow">paper</a> from M.R. Evans et al.</p>
<p>The system consists of positive, negative and hole particles... | g7980 | [
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<p>Wikipedia has this page on <a href="http://en.wikipedia.org/wiki/Gravity_assist">gravity assists</a> using planets. In some cases this effect was used to accelerate the spacecraft to a higher velocity. This diagram shows this in a very <em>oversimplified</em> manner. <img src="http://i.stack.imgur.com/6O45U.png" alt... | g619 | [
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<p>The equations of motion of a double pendulum are well-known. Usually you'd have the them expressed in the rotations $\theta_1(t)$ and $\theta_2(t)$. There are two degrees of freedom. Now consider the case in which the motion at the bottom is constrained in the $x$-direction:</p>
<p><img src="http://i.stack.imgur.co... | g7981 | [
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<p>Can someone explain to me the concept of symmetric, antisymmetric, and mixed symmetry when talking about the states of identical particles?</p> | g7982 | [
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<p>Time symmetry is often explained by the example of orbiting objects... What I can't find an explanation for is the moment when an object enters into orbit around another object. That clearly breaks time symmetry, since once object is in orbit (and you reverse time), it will never leave of it's own. Does this mean la... | g7983 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/25378/how-vacuous-is-intergalactic-space">How vacuous is intergalactic space?</a> </p>
</blockquote>
<p>The <em>emptiness</em> of space is explained in many articles... But, space does contain some matte... | g262 | [
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<p>This is part of an admission exam problem, found at
<a href="http://www.sissa.it/mp/admission/tests//2008_common.pdf" rel="nofollow">http://www.sissa.it/mp/admission/tests//2008_common.pdf</a></p>
<p>Consider the Hamiltonian of Kepler problem
$$H(\boldsymbol{r},\boldsymbol{p})= \frac{|\boldsymbol{p}^2|}{2\mu} +\fra... | g7984 | [
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<p>The field must have properties such as <code>planar wave</code> and <code>moving in glass</code> so</p>
<p>$$\bar E=E \left( \hat i t + \hat j \sin(kz-wt) + \hat k \cos(kz-wt+\phi) \right)$$</p>
<p>that is also moving in the x-axis and right-hand-circular-polarized so the phase difference $\phi=\pm \pi/2$ (more on... | g7985 | [
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<p>Most of the 5-dimensional Higgs models can be seen, if I understand correctly, as models where the Higgs is a composite. </p>
<p>Now, is this true for <a href="http://en.wikipedia.org/wiki/Noncommutative_standard_model" rel="nofollow">Connes models</a>? It is a model of extra dimensions too, in some sense. And when... | g7986 | [
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<p>Knowing that astronomical twilight (i.e. astronomical dawn) is when the sun is 18 degrees below the horizon, I am calculating the astronomical twilight time this way:</p>
<pre><code>Sunrise of day1 - [ (Sunrise of day1 - Sunset of day0) / 180° ] * 18°
</code></pre>
<p>Is that correct?</p> | g7987 | [
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<p>I guess the Hilbert space of the theory is precisely the space of all gauge invariant operators (mod equations of motion..as pointed out in the answers) </p>
<ul>
<li><p>Is it possible that in a gauge theory the Wilson loops are the only observables? </p>
<p>(...I would vaguely think that if a set of Wilson loops ... | g7988 | [
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<p>I'm having problem understanding how to compute a functional derivative when it's involved more than one integral, such as the coulomb potential energy functional:</p>
<p>$$ J[\rho] = \frac 12\int \frac{\rho(r)\rho(r')}{|r - r'|} drdr' $$</p>
<p>According to the functional derivative formula I should d... | g7989 | [
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<p>Here is the thermal resistance data for three speaker coils disengaged from the speaker cone. Any ideas? I would think it would be a horizontal line.</p>
<p><img src="http://i.stack.imgur.com/kV0Sd.png" alt="http://i.stack.imgur.com/pjKyE.png"></p>
<p><a href="http://en.wikipedia.org/wiki/Thermal_resistance" rel="... | g7990 | [
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<p>I did a lab today in Physics in which we launched ball from a spring loaded cannon directly into a pendulum that captured the ball, held it, and swung upwards with it (representing a totally inelastic collision). One question in particular has confused me:</p>
<blockquote>
<p>If the collision between the project... | g7991 | [
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<p>You can dip your hands into a bowl of non-Newtonian fluid but if you are to punch it, it goes hard all of a sudden and is more like a solid than anything else. </p>
<p>What is it about a non-Newtonian fluid that makes it go hard when having a force suddenly exerted on it?
How does it go from being more like a liqui... | g496 | [
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<p>I was wondering if anyone here has calculated before the partition function for the Jaynes-Cummings Hamiltonian:
$H_{JC}=\omega_0 (a^\dagger a + \sigma^+ \sigma^-)+g (a \sigma^+ +a^\dagger \sigma^-)$
(Here I have assumed resonance and $a,a^\dagger$ are bosonic operators and $\sigma^-,\sigma^+$ are ladder operators f... | g7992 | [
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<p><img src="http://i.stack.imgur.com/o8Kjj.jpg" alt="enter image description here"></p>
<p>Hey, im having a bit of trouble with the problem in the added photo.
So, there is the cylinder which is attached by a massless rope to a massless pulley, to a box (assume it is a pointed object).
Now, Im supposed to find the ac... | g7993 | [
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<p>I have trying to show that the continuum limit of N quantum harmonic oscillators gives rise the the klein-gordon field. However, instead of a usual finite string, I want to do it on a ring. Hence, my Lagrangian is </p>
<p>$$L=\frac{m}{2}(\dot{q_1}^2+\dot{q_2}^2+.... \dot{q_n}^2)-\frac{m \omega^2}{2}[(q_1-q_2)^2+(q_... | g7994 | [
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<p>For our project we have to study an infrared filter. This filter is composed of glass and several layers (nanolayers of titanium oxide, silver and cupper deposited on one side of the glass).<br>
Now we have to determine the reflection coefficient of the coating (i.e. the nanolayers alone) given that of the glass and... | g7995 | [
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<p><em>If you think that this question is likely to get closed then please do not answer and only say that in the comments since this system doesn't let me delete the question once it has answers.</em> </p>
<p>Everytime I am faced with an analysis of the spectral function it looks like a "new" unintuitive set of juggl... | g7996 | [
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<p>please look at the fig first
<img src="http://i.stack.imgur.com/KXMi6.jpg" alt="enter image description here"></p>
<p><br></p>
<p>1) How can you claim that the triangle ABC is same as the triangle PQR?
2) How can you claim that the angle between V1 and V2 is same as the angle between AC and AB?</p>
<p>I think i h... | g7997 | [
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<p>I read in a book the following about <a href="http://en.wikipedia.org/wiki/Pendulum#Compound_pendulum" rel="nofollow">compound pendulum</a> and small displacements: </p>
<ol>
<li><p>There are two points only for which the time period is minimum. </p></li>
<li><p>there are maximum 4 points for which the time perio... | g7998 | [
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<p><strong>Background:</strong> Classical Mechanics is based on the Poincare-Cartan two-form </p>
<p>$$\omega_2=dx\wedge dp$$</p>
<p>where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. By the other hand, the so-called Born-reciprocal relativity is based on the "phase-space"-like metric</p>... | g7999 | [
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<p>We are able to look directly at the sun near sunset and sunrise, which clearly demonstrates the fact that our atmosphere attenuates visible light. Let's imagine it follows the typical attenuation profile.</p>
<p>$$ I = I_0 \, e^{-(\mu/\rho)\rho \ell} $$</p>
<p>Where $(\mu/\rho)$ is the mass-attenuation coefficie... | g8000 | [
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<p>Acceleration is directed towards the center of the circle in a uniform circular motion. Is it same for the non-uniform circular motion?</p> | g8001 | [
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<p>In <em>Peskin & Schroeder</em>, chapter 9 introduces the functional methods.</p>
<p>The idea, to recall, is simply to sum over all the possible paths:</p>
<blockquote>
<p>$U(x_a,x_b;T) = \sum_{\text{all paths}} e^{i . \text{phase}} = \int Dx(t) e^{i . \text{phase}} $</p>
</blockquote>
<p>Then, it happens t... | g8002 | [
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<p>Consider a pair of (possibly rotating) charged black holes with masses m1, m2 and like charges q1, q2. It seems that under certain conditions gravitational attraction should exactly cancel electrostatic repulsion and a stationary spacetime will result. </p>
<blockquote>
<p>What are these conditions?</p>
</blockqu... | g8003 | [
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<p>In the next attachements are:
1. Exercise 0.2.5 which I want help with.</p>
<ol>
<li>Proposition 0.2.1 and its proof.</li>
</ol>
<p>Now, basically a few things are changed in the theorem, I don't think I can use here the definition of s(t) in the proof of prop0.2.1 cause its s(t)=0, I don't think I can use this tr... | g8004 | [
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<p>I am trying to understand the difference between Bessel functions and modified Bessel functions (simply googling is yielding complicated, non-intuitive answers). I was under the impression that one allowed for a complex parameter while the other did not - is this true? </p>
<p>My question stems from trying to under... | g8005 | [
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<p>Is it possible to have a membrane that will not let a liquid through it at normal pressures due to gravity, but pass that liquid when substantially pressurised?</p>
<p>For instance, a few inches of water (say 0.1psi) would be blocked, but 100psi would pass through. </p> | g8006 | [
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<blockquote>
<p>Quantum entanglement occurs when particles such as photons, electrons,
molecules as large as buckyballs, and even small diamonds
interact physically and then become separated; the type of interaction
is such that each resulting member of a pair is properly described by
the same quantum mechani... | g8007 | [
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<p>I am currently reading "Magnetic Monopoles" of Ya. Shnir. My problem is I can not retrieve a result the author provides in the first chapter of the first part. In this chapter, he studies the non-relativistic scattering of an electric charge on a magnetic one. </p>
<p>The author writes [p.5, near eq. (1.13)]:</p>
... | g8008 | [
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<p>My understanding of pseudovectors vs vectors is pretty basic. Both transform in the same way under a rotation, but differently upon reflection. I might even be able to summarize that using an equation, but that's about it.</p>
<p>Similarly, I can follow arguments that pseudovectors behave differently in "mirrors" t... | g8009 | [
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<p>Electromagnetic waves travel mostly in vacuum medium, in outer space, but sometimes in gaseous media, such as in gaseous atmospheres involved in nebulae. If electromagnetic-waves come anywhere in the vicinity of a black-hole, the whole of it enters the black-hole. Can we suppose, that the event-horizon of the black-... | g8010 | [
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<p>Question inspired by a question thread <a href="http://www.reddit.com/r/askscience/comments/ik4jj/during_spiral_galaxy_formation_how_does_gas/" rel="nofollow">here</a>.</p>
<p>So when there's lots of dust in a galaxy, the galaxy tends to collapse into a spiral galaxy (to maintain angular momentum and to minimize gr... | g8011 | [
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<p>Random question that popped into my mind after a 4-hours power outage. Let us assume that I am eating an extra dessert (250 kcal) and that I am using a bike and a generator to power my laptop (it consumes 10W while idle). How much time can I use the laptop?</p>
<p>I computed this as follows:
$$
t = \frac{E}{P} = \f... | g8012 | [
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0.04... |
<p>As the question states, what is our current best machine for translating falling gravitational potential energy, such as a large weight, into launching a smaller projectile vertically? A lever? A trebuchet? What sorts of efficiency levels have been achieved?</p>
<p>What I'm looking for is the best way to translate:... | g8013 | [
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... |
<p>The scenario is the following, I am given 2 loops with the same radius, r, a distance of d, and same current of I. In the left loop the current goes counter clockwise, in the right loop the current is clockwise. The two loops centers lie on the same axis which are perpendicular to the plane of the loops. I am asked... | g8014 | [
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<p>This was an experiment I saw in my son's workbook. It said to mark out the top of your forehead and the bottom of your chin on a mirror using a whiteboard marker. Then slowly move backwards, and investigate what happens to the size of the reflection subjective to the two marks made. It actually got me quite flabberg... | g8015 | [
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0.0175... |
<p>My question started out as finding the maximum speed of a go kart, taking into account only the drag forces as force opposing the motor. </p>
<p>I've done some investigation to find:</p>
<p>$$
F_{drag}=\; \frac{\rho v^{2}\ C_{x} A_{f}}{2}
$$</p>
<p>Where $C$ = drag coefficient, and $\rho$ is the density of air. <... | g8016 | [
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<p>I am puzzled why we always see the same side of the Moon even though it is rotating around its own axis apart from revolving around the earth. Shouldn't this only be possible if the Moon is not rotating?</p> | g263 | [
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<p>The title might be misleading, but my question is in regard to what happens when we reach temperatures close to absolute zero (Kelvin). I've found different quotes as to what happens on the low end of the scale:</p>
<blockquote>
<p>At about 10 micro degrees Kelvin, Rubidium atoms move at about 0.11
mph (0.18 km... | g8017 | [
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<p>First, I apologize for being a mathematician and having no scientific background in physics. The following questions on color came up in a discussion at lunch and I would be very happy to get some answers or corrections of my understanding.</p>
<ul>
<li>The first question is, what a color the human eye can see is i... | g8018 | [
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0.08818984776735306,
0.05... |
<p>I think <a href="http://mathoverflow.net/q/165038/14414">this</a> can revolutionize the quantum world! Any ideas on how to impress physicists to get a full fledged funding for research?</p> | g8019 | [
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0.0021600371692329645,
-... |
<p>As title says, how does a system interact with environment? I realize that this interaction can lead to interference terms and non-diagonal terms in density matrix being reduced (quantum decoherence). But what exactly is this interaction of system and environment? What would be the example of this interaction and wh... | g8020 | [
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0.008546059019863605,
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0.028184661641716957,
0.005... |
<p>A vehicle moves from rest to a certain distance. Would the distance time graph always be curved ? Why cannot it be a straight line ? </p>
<p>For example, a car moving from rest to 100m, with a constant velocity of 10m/s . So, if i draw a distance time graph, the line will start from s=0 and end at s=100 ( with t=0... | g8021 | [
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0.04388672113418579,
-0.... |
<blockquote>
<p>Nonlinear field theories contain a large number of localized solutions.</p>
</blockquote>
<p>I have found this text in a article. What I don't understand is "what is localized?". Is it refer defining position of a particle or a wave?
Can someone give me an elaboration with example?</p> | g8022 | [
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0.00... |
<p>In the book <em>String Theory and M-Theory</em> by K. Becker, M. Becker and J.H. Schwarz:</p>
<ol>
<li><p>Why is the potential for moduli given by eq (10.168):
$$\tag{10.168 }V(T,K) ~=~ \frac1{4\mathcal{V}^3} \Big( \int_{CY_4} F \wedge \star F - \frac16 \chi T_{M2} \Big)?$$<br>
Maybe the answer of this question is... | g8023 | [
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0.032642774283885956,
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0.05549592152237892,
0.03504... |
<p>This is a rather soft question, but I would like to know how physicists would approach a problem which seems to be hard from the mathematical prospective. </p>
<p>The Grimmett percolation model is defined as follows. Consider the $\mathbb{Z}^2$ lattice and randomly assign an orientation for every bond of the lattic... | g8024 | [
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... |
<p>Often times in quantum field theory, you will hear people using the term "vacuum expectation value" when referring to the minimum of the potential $V(\phi )$ in the Lagrangian (I'm pretty sure every source I've seen that explains the Higgs mechanism uses this terminology).</p>
<p>However, a priori, it would seem th... | g8025 | [
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<p>Would you outlive everyone?</p>
<p>I'm coming from the point of view that time would be experienced more slowly (although not from your point of view) the denser the gravity gets.</p> | g8026 | [
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<p>Hans de Vries (who happens to be a no-longer-active physics.SE user) has an online book (referenced below) in which ch. 6 is a presentation of an object he calls the Chern-Simons current, electromagnetic spin density, or Chern-Simons electromagnetic spin:</p>
<p>$ C^a = \frac{\epsilon_0}{2} \epsilon^{abcd} A_b F_{c... | g8027 | [
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<p>I am practicing for an exam in my Physics $2$ course.</p>
<p>One of a previews exam questions described a plate capacitor and asked
to calculate the initial energy $U_{0}$, then a dielectric table
was inserted between the plates and I was asked to calculate the energy,
$U_{1}$, at this state.</p>
<p>I got that the... | g8028 | [
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<p>I have a question in <a href="http://www.damtp.cam.ac.uk/user/tong/string/bq4.pdf" rel="nofollow">David Tong's Example Sheet 4</a>
Problem 5b, how to verify the last equation (*) on p.2? (<a href="http://www.damtp.cam.ac.uk/user/cdab3/teaching/StringSoln3.pdf" rel="nofollow">There is a solution for example sheet 3</... | g8029 | [
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<p>I am posing this question with condensed matter systems in mind. <strong>Is it, in principle, possible to obtain emergence using the renormalization group (RG)?</strong> I read in X.-G. Wen's book (Quantum Field Theory of Many-Body systems) that "<em>we cannot use the renormalization group approach to obtain the em... | g8030 | [
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<p>For helping with judging <a href="http://en.wikipedia.org/wiki/Noctilucent_cloud" rel="nofollow">NLC</a> candidates (are they NLC or not) I have a set of formulas to calculate the minimum altitude (in km) of the candidate given an observed altitude (in degrees) of the candidate (using known stars, like <a href="http... | g8031 | [
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<p>In <em>BRST Symmetry in the Classical and Quantum Theories of Gauge Systems</em>, Henneaux says the Fock representation is not applicable to an odd number of constraints. Then he goes on to say that the Kugo-Ojima quartet requires the constraints to be in pairs. For BRST theories, when are they not in pairs? </p> | g8032 | [
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<p>We all know farady effect is observed in linearly polarized wave when it passes through a dielectric medium and magnetic field is along the direction of propagation. Is this phenomenon observable in circularly polarized waves?
<img src="http://i.stack.imgur.com/q0H18.png" alt="enter image description here"></p>
<p... | g8033 | [
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... |
<p>I've just started reading Feynman and Hibbs path integrals and Quantum mechanics after a decade hiatus from my undergraduate math degree (including a few semesters of physics for engineers). It would be tremendously helpful to see the step by step solutions to some of the first set of problems (p27-28, #2.1 and on)
... | g8034 | [
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0.02153267152607441,
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<p>Just wondering when water undergoes electrolysis why does oxygen goes towards cathode and hydrogen towards anode why not the other way round</p> | g8035 | [
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<p>Consider two parallel-plate capacitors $C_1, C_2$ in series. For the "equivalent" circuit, clearly
$$ Q_{equiv} = C_{equiv}V$$
should hold, where V is the total voltage drop between input and output. It is also obvious that
$$ Q_1 = Q_2 $$
where $Q_1$ and $Q_2$ are the charges (plus and minus on opposite sides) ... | g8036 | [
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<p>So, when wavefunction collapses, there is a spike occuring. Does this mean that there are parts with the continuous probability of 0? (For example, x position from -9 to -3 has probability of 0, while from -3 to 3, the probability of 100% (1) and so on)</p> | g8037 | [
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<p>We make an important distinction between the topological insulators (which are essentially uncorrelated band insulators, "with a twist") and topological order (which covers a variety of exotic properties in certain quantum many-body ground states). The topological insulators are clearly "topological" in the sense of... | g8038 | [
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0.01793498545885086,
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0.053116653114557266,
-... |
<p>In David Tong's QFT lecture notes (<a href="http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf" rel="nofollow"><em>Quantum Field Theory: University of Cambridge Part III Mathematical Tripos,</em> Lecture notes 2007, p.8</a>), he states that</p>
<blockquote>
<p>We can determine the equations of motion by the princip... | g8039 | [
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0.05479026213288307,
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... |
<p>We all know that liquid will take a shape of container in which its filled, but What will be the shape of liquid if there is no gravitational force?</p> | g264 | [
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<p>I am a little confused about the workings of the Hubble Redshift. I do understand the classical Doppler-effect, however in special relativity the velocity of light c is a natural velocity limit. So how does Hubble Redshift come about?</p> | g768 | [
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<p>The <a href="http://en.wikipedia.org/wiki/Metric_signature" rel="nofollow">signature</a> of Minkowski spacetime is 2, as is explained here: <a href="http://physics.stackexchange.com/questions/24495/metric-signature-explanation">metric signature explanation</a>. The signature is related to the form the fundamental eq... | g8040 | [
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<p>As I am talking about 'smallest' can I expect that it should be a quantum system? I understand that we use quantum chaos theory instead of perturbation theory when the perturbation is not small. For example when quantum numbers are very high for an EM field interacting with an atom, we cannot use perturbation theory... | g8041 | [
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<p>This is a question which has been puzzling me quite a while.</p>
<p>There was a news report saying that the farthest galaxy spotted so far is at 13.3 billion light-years away, and it is said that the galaxy can show us how the universe at about 500 million years old was looked like.</p>
<p>It is commonly accepted ... | g10 | [
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<p>When discussing stars, theorists tend to use effective temperature $T_\text{eff}$ and luminosity $L$ (on logarithmic scales). Observers, on the other hand, usually talk about observed colours and magnitudes (e.g. $B$ vs. $B{-}V$). These two sets of parameters are obviously related. Temperature corresponds to colour;... | g8042 | [
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<p>I have been taught that water levels will always equal out. However, now I find that sumps and some other setups allow for water not to become equal. What other arrangements allow for the water levels of two containers not to be equal? Also, and more importantly, why does this occur? I hope someone is able to explai... | g8043 | [
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0.026782790198922157,
0.0522... |
<p>What is Mathematical formulation of <a href="http://en.wikipedia.org/wiki/Holographic_principle">Holographic principle</a> </p>
<blockquote>
<p>The holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a bo... | g8044 | [
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0.... |
<p>This is an engineering question, but it is adressed to physicists who build accelerators. This question: <a href="http://physics.stackexchange.com/questions/35375/an-electromagnetic-space-elevator">An electromagnetic space elevator?</a> notices that a NbSn superconducting ring around the equator will launch itself i... | g8045 | [
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<p>I'm doing a project about Moore's Law, one of the subtopics I've come to is photolithography. The way I understand it is that the MOSFET transistors are currently printed on a silicon wafer by projection printing (mostly with 193nm UV light).</p>
<p>With this technique your minimum feature size (CD) will be:</p>
<... | g8046 | [
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<p>I have some difficulty considering the relative size of each and the meaning behind the shape of Higgs boson. I ask relating to the <em>structures</em> of both the Higgs field and quarks. How is it that the structure of a Higgs boson flows into that of, for instance, a bottom-antibottom quark pair? </p>
<p>Essentia... | g8047 | [
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0.017653128132224083,
0.02981257624924183,
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<p>I was looking at old photographs of the nuclear tests on the <a href="http://io9.com/secret-history/" rel="nofollow">bikini atoll</a>. It dawned on me that you don't want to run film through airport x-rays, as it exposes the film. I've been told that a nuclear explosion emits all energy on the spectrum (IR to Gamm... | g8048 | [
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0.03056444227695465,
0.02901250682771206,
0.0151... |
<p>Say I have two quantum systems $A$ and $B$ I can look at the joint (composite) system $AB$ which is given by $H_{AB} \in H_A \otimes H_B$</p>
<p>Measuring a subsystem with respect to a collection of measurement matrices $\textbf{M} = \{M_i\}_{i \in I} \in Meas_{I}(H_A)$ acts as measuring $AB$ with respect to $\text... | g8049 | [
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-0.0... |
<p>Inpired by <a href="http://music.stackexchange.com/questions/7064/physiological-responses-to-different-rhythms">http://music.stackexchange.com/questions/7064/physiological-responses-to-different-rhythms</a>, I'm wondering if the human body has a strong resonant frequency. I guess the fact that that it's largely a b... | g8050 | [
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0.04414929449558258,
-0... |
<p>I have some problems to demonstrate the non affine geodesic equation from Euler-Lagrange's equations. I start defining the Lagrangian $L=\sqrt f$, but then I'm not able to find the <a href="http://en.wikipedia.org/wiki/Christoffel_symbols" rel="nofollow">Christoffel symbol</a>'s expression. Can anybody help me?</p> | g8051 | [
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<p>The Bloch sphere is an excellent way to visualize the state-space available to a single qubit, both for pure and mixed states. Aside from its connection to physical orientation of spin in a spin-1/2 particle (as given by the Bloch vector), it's also easy to derive from first principles mathematically, using the Paul... | g8052 | [
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<p>I have a problem verifying the following equation (in three dimensions)</p>
<p>$$\epsilon_{abc} e^a\wedge R^{bc}=\sqrt{|g|}Rd^3 x$$</p>
<p>where $R$ is the Ricci scalar and $R^{bc}$ is the Ricci curvature</p>
<p>Attempt at a solution:</p>
<p>$$\epsilon_{abc} e^a\wedge R^{bc}=\epsilon_{abc} e_\mu^ae_\alpha^be_\be... | g8053 | [
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0.0... |
<p>Take the Mach-Zehnder interferometer as an example. A photon passes through a beam splitter, is reflected off mirrors, and interferes with itself at another half-silvered mirror. No measurements or disturbances are made in between. The preferred basis of the photon is given by which path it takes after passing the s... | g8054 | [
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<p>I know how the unit vectors are defined in cylindrical coords. If I have a point P, how do I express it as a combination of the unit vectors u<sub>ρ</sub>, u<sub>φ</sub> and u<sub>z</sub>. In the case of Cartesian coordinates this combination is linear. But what about cylindrical coords? Does such a combination exis... | g8055 | [
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<p>I have seen <a href="https://physics.stackexchange.com/questions/53148/in-qft-why-does-a-vanishing-commutator-ensure-causality">this question</a> and I believe I understand the answer to it. However, AFAIK, only for bosons the causality condition is a vanishing commutator. For fermions we expect the <em>anticommutat... | g8056 | [
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<p>There is another paradox that I need to resolve:</p>
<p>The Berezin integration rules for Grassmann odd variables give the same result as differentiation:</p>
<p>If $f=x+\theta\psi$ is a superfunction, the integral</p>
<p>$$\int d\theta(x+\theta\psi)=\psi$$</p>
<p>gives the same result as differentiation</p>
<p... | g8057 | [
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<p>What does one get if the take the tensor product of a bra and a ket, for instance, $\langle\uparrow \rvert \otimes \lvert \downarrow\rangle$?</p>
<p>What I mean it, what is this object? What does it act on? Or does it get acted on? Is it meaningful, like the tensor product of two kets is, etc?</p> | g8058 | [
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<p>Reading some science history, Werner Heisenberg and Bohr created the Copenhagen interpretation, but what I didn't get is how can we connect this interpretation to Schroedinger's cat and the double slit experience? Are they confirming Heisenberg and Bohr's work?</p> | g8059 | [
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