question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>This question arose while reading Peskin and Schroeder, specifically, it arose in regards to the sum of diagrams above their Eq. (10.20) on pg. 326.</p>
<p>The context is $\phi ^4$ theory and they are using a vertex renormalization condition to compute the counterterm $\delta _\lambda$ corresponding to the coupling constant $\lambda$. To do this, they calculate the $4$-point amplitude up to one-loop order in perturbation theory. In the process of doing this, however, they do not seem to include any one-loop diagrams involving the counterterms. Indeed, they only seem to include counterterm diagrams up to tree level.</p>
<p>Why is this? It seems, at least naively, that if one is doing a one-loop computation, one should compute all one-loop diagrams, and not discriminate between those Feynman rules in the 'original' theory and those that only arise during renormalization.</p> | g12587 | [
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<p>I am having trouble reconciling two facts I am aware of: the fact that the charge conjugate of a spinor tranforms in the same representation as the original spinor, and the fact that (in certain, dimensions, in particular, in $D=4$), the charge conjugate of a left-handed spinor is right-handed, and vice versa.</p>
<p>To be clear, I introduce the relevant notation and terminology. Let $\gamma _\mu$ satisfy the Clifford algebra:
$$
\{ \gamma _\mu ,\gamma _\nu \} =2\eta _{\mu \nu},
$$
let $C$ be the <em>charge conjugation matrix</em>, a unitary operator defined by
$$
C\gamma _\mu C^{-1}=-(\gamma _\mu )^T.
$$
One can show that (see, e.g. West's <em>Introduction to Strings and Branes</em>, Section 5.2) that $C^T=-\epsilon C$ for
$$
\epsilon =\begin{cases}1 & \text{if }D\equiv 2,4\, (\mathrm{mod}\; 8) \\ -1 & \text{if }D\equiv 0,6\, (\mathrm{mod}\; 8)\end{cases}.
$$
Define $B:=-\epsilon \mathrm{i}\, C\gamma _0$. Then, the <em>charge conjugate</em> of a spinor $\psi$ and an operator $M$ on spinor space are defined by
$$
\psi ^c:=B^{-1}\overline{\psi}\text{ and }M^c:=B^{-1}\overline{M}B,
$$
where the bar denotes simply complex conjugation. We define
$$
\gamma :=\mathrm{i}^{-\left( D(D-1)/2+1\right)}\, \gamma _0\cdots \gamma _{D-1},
$$
and
$$
P_L:=\frac{1}{2}(1+\gamma )\text{ and }P_R:=\frac{1}{2}(1-\gamma ).
$$
We then say that $\psi$ is <em>left-handed</em> if $P_L\psi =\psi$ (similarly for right-handed). Finally, the transformation law for a spinor $\psi$ is given by
$$
\delta \psi =-\frac{1}{4}\lambda ^{\mu \nu}\gamma _{\mu \nu}\psi.\qquad\qquad(1)
$$</p>
<p>Now that that's out of the way, I believe I am able to show two things:
$$
\delta \psi ^c=-\frac{1}{4}\lambda ^{\mu \nu}\gamma _{\mu \nu}\psi ^c \qquad\qquad(2)
$$
and
$$
(P_L\psi )^c=P_R\psi ^c\text{ (for }D\equiv 0,4\, (\mathrm{mod}\; 8)\text{)}.\qquad\qquad(3)
$$
The first of these says that $\psi ^c$ transforms in the same way as $\psi$ and the second implies that, if $\psi$ is left-handed, then $\psi ^c$ is right-handed (in these appropriate dimensions).</p>
<p>I'm having trouble reconciling these two facts. I was under the impression that when say say a Fermion is left-handed, we mean that it transforms under the (1/2,0) representation of $SL(2,\mathbb{C})$ (obviously, I am now just restricting to $D=4$). It's charge-conjugate, being right-handed, would then transform under the $(0,1/2)$ representation, contradicting the first fact. The only way I seem to be able to come to terms with this is that the two notions of handedness, while related, are not the same. That is, given a Fermion that transforms under $(1/2,0)$ and satisfies $P_L\psi =\psi$, then $\psi ^c$ will transform as $(1/2,0)$ and satisfy $P_R\psi =\psi$. That is, the handedness determined in the sense of $P_L$ and $P_R$ is independent of the handedness determined by what representation the Weyl Fermion lives in.</p>
<p>Could someone please elucidate this for me?</p> | g12588 | [
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<p>In the weakly-coupled BCS regime two-dimensional chiral (p+ip) spinless superconductors and superfluids posses a chiral gapless fermionic Majorana state localized near the boundary. This gapless edge mode is a direct manifestation of the topological quantum phase transition present in this system. Indeed the boundary is the line which separates two topologically different phases, it is localized in the region where the gap closes. My question is what happens to the edge states if we tune fine-tune the bulk value of the chemical potential to the critical one, i.e. approach quantum criticality in the bulk. The gapless fermions should penetrate into the bulk, right? What happens to their chiral and Majorana property? </p> | g12589 | [
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<p>The question is</p>
<blockquote>
<p>In a combat exercise, a mortar at M is required to hit a target at O, which is taking cover 25 m behind a structure of negligible width 10 m tall. This mortar can only fire at an angle of 45 degrees to the horizontal, but can fire shells of any velocity. Find the minimum initial velocity required to hit the target.
<img src="http://i.imgur.com/yoTXyv8.png" alt="diagram"></p>
</blockquote>
<p>I solved it as follows.</p>
<p>Forming a parabola with $ r_v $ against $ r_h $:</p>
<p>$ r_v = u_vt + \frac{1}{2}a_vt^{2} $ (1) </p>
<p>$ r_h = u_ht + \frac{1}{2}a_ht^{2} $</p>
<p>but $ a_h = 0 $</p>
<p>so $ r_h = u_ht $</p>
<p>$ t = \frac{r_h}{u_h} $ (2)</p>
<p>Substituting (2) into (1):</p>
<p>$ r_v = u_v\frac{r_h}{u_h} + \frac{1}{2}a_v\frac{r_h^{2}}{u_h^{2}} $ (3) </p>
<p>and because the angle of inclination is 45°</p>
<p>$ u_v = u_h = \frac{u}{\sqrt{2}} $ (4)</p>
<p>From (4) and (3):</p>
<p>$ r_v = r_h^{2}\frac{a}{u^{2}} + r_h $ (5) </p>
<p>Let the distance between the mortar and the building be $ d $.</p>
<p>Then when $ r_h = d + 25 $, $ r_v = 0 $. (6)</p>
<p>From (5) and (6):</p>
<p>$ 0 = (d + 25)\frac{a}{u^{2}} + 1 $ </p>
<p>so $ u^2 = -a(d + 25) $ (7)</p>
<p>Substituting (7) into (5):</p>
<p>$ r_v = -r_h^{2}\frac{1}{(d + 25)} + r_h $ (8) </p>
<p>We also know that to clear the building, when $ r_h = d $, $ r_v > 10 $. (9)</p>
<p>From (9) and (8):</p>
<p>$ 10 < -d^{2} \frac{1}{(d + 25)} + d $</p>
<p>After simplifying... ($ d + 25 $ is positive)</p>
<p>$ d > \frac{50}{3} $ (10)</p>
<p>Rearranging (7):</p>
<p>$ d = -\frac{u^{2}}{a} - 25 $ (11)</p>
<p>And then from (10) and (11) and with $ a = -9.8 $:</p>
<p>$ \frac{50}{3} < \frac{u^{2}}{9.8} - 25 $</p>
<p>Simplifying, and with the knowledge that $ u > 0 $:</p>
<p>$ u > 20.2073... $</p>
<p>So the minimum initial velocity required to hit the target is <strong>20 m/s</strong> (2 s. f.).</p>
<p>Huzzah!</p>
<p>My question is: <strong>is there a faster way to solve the problem?</strong></p> | g12590 | [
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<p>Fish achieve neutral buoyancy (so they don't have to swim constantly to stay in place) via a swim bladder. A swim bladder is a little internal sack that they can inflate/deflate with air, which changes their volume but not their total mass. To see how this allows them to change their buoyancy, let's consider the situation of a fish floating at rest in the ocean at some arbitrary depth. It inflates its swim bladder and increases its volume to 1.1 times its original volume without losing any mass. It therefore should begin to accelerate upwards automatically without having to swim. What is its acceleration in $m/s^2$?</p> | g12591 | [
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<p>I have a few related questions about static electricity and conductors.
1. when we say static electric field inside a conductor is zero, let us take an example of two concentric conductors, outer one positively charged and inner negative charged -- inside inner sphere field will be zero, but there will be field directed from outer sphere towards inner sphere -- why is not that field zero?</p>
<ol>
<li><p>Inside it is zero, but outside it is present and that too only tangential?</p></li>
<li><p>When we are talking about time varying fields, electric field is present inside a conductor only at inner surface or inside whole conductor? What will we answer when asked about the electric field inside a conductor in such case?</p></li>
</ol> | g12592 | [
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<p>The problem provided by my professor goes as follows:
"Now consider a situation in which all charges are equal to q and they simultaneously become "unglued". What speed will each charge have when a hexagonal configuration has doubled in size (each side has a length).
The work done was found to be $$U=\frac{kq^2}a\left(\frac{5}2+\frac{2}{\sqrt2}\right)$$</p>
<p>So far I have done:</p>
<p>$$\Delta K=-\Delta U$$</p>
<p>$$K_f=U_i-U_f$$</p>
<p>$$6\cdot\left(\frac{1}2mv^2\right)= k\frac{q^2}a\left(\frac{5}2+\frac{2}{\sqrt3}\right)-\frac{kq^2}{2a}\left(\frac{5}2+\frac{2}{\sqrt3}\right)$$</p>
<p>However, the solution is:</p>
<p>$$6\cdot\left(\frac12mv^2\right)=k\frac{q^2}a\left(\frac{15}2+\frac{6}{\sqrt2}\right)-\frac{kq^2}{2a}\left(\frac{15}2+\frac{6}{\sqrt3}\right)$$</p>
<p>Can anyone explain why?</p> | g12593 | [
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<p>In a classic demonstration of inducing a charge on a dielectric, the latter is exposed to an external field. There is a resulting charge separation in the dielectric. What is the velocity of propagation of this charge separation? Is it the velocity of electromagnetic waves in the dielectric i.e. "the speed of light"?</p> | g12594 | [
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<p>So is it possbile to build a system from lenses and mirrors that can make faint gas nebulas brighter or can be used as nightvision? </p>
<p>If you increase the size of the aperture of a telescope it will collect more light, but the exit pupil will be also bigger, so not all light will enter the eye.</p>
<p>In order to direct all light into the eye you'll need to shrink the exit pupil and you'll need a stronger eyepiece. But this will increase the magnification too and the collected light will spread on a larger image so the surface brightness will remain the same.</p>
<p>Is it possible to work this limitation around?</p> | g12595 | [
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<p>In section 134 of Vol. 3 (Quantum Mechanics), Landau and Lifshitz make the energy complex in order to describe a particle that can decay:</p>
<p>$E = E_0 - \frac{1}{2}i \Gamma$</p>
<p>The propagator $U(t) = \exp(-i H t)$ then makes the wavefunction die exponentially with time. But also, $H$ is non-Hermitian.</p>
<p>My question: Do we have to modify the basic postulates of quantum mechanics (as described by Shankar, say, or the earlier sections of Landau & Lifshitz) to describe unstable particles?</p> | g12596 | [
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<p>An hourglass H weighs h. When it's placed on a scale with all the sand rested in the lower portion, the scale reads weight x where x = h.</p>
<p>Now, if you turn the hourglass upside down to let the sand start to flow down, what does the scale read?</p>
<p>I imagine initially, when the sand starts to fall but before the first batch of grains touch the bottom of the hourglass, these grains of sand effectively are in a state of free fall, so their weight would not register onto the scale. The weight at this point has to be less than h. However, what about the steady state when there is always some sand falling and some sand hitting the bottom of the hourglass? In the steady state, although we are having some sands in the free fall state and thus decrease the weight of H, there are also sands that are hitting (decelerating) the bottom of the hourglass. This deceleration should translate increase the reading on the scale more than the actual weight of those impacting sands. To illustrate the last point, imagine a ball weighing 500g rested on a scale. If you drop this ball from a mile high onto the same scale, on impact, the scale would read higher than 500g. in the same way, in our hourglass question, will the decreasing effect of weight due to free-fall cancel out exactly the increasing effect of weight due to sand impacting? does it depend on the diameter of the opening? does it depend on the height of the free-fall? Does it depend on the air pressure inside the hourglass?</p> | g12597 | [
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<p>Suppose there is a slanted capillary tube and a fluid rises in it. Why does the fluid rise to the same vertical height as when the tube is perfectly vertical?</p>
<p>If I'm right surface tension force balances the weight of the lifted fluid. But in the case of a slanted tube, more fluid will be lifted and thus weight also increases. So why will fluid rise to same height?</p> | g12598 | [
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<p>Can solar furnace achieve higher temperature than sun surface?</p>
<p>I guess not, but I'm not sure about that. Can you check my reasoning:</p>
<p>-------- My reasoning -----------</p>
<p>Consider Sun as a black body and (almost) Lambertian radiator. If there would be an optical system which can focus <strong><em>all</em></strong> radiation from one black body to an other body in such way, that you achieve higher temperature, it would be possible to make a Maxwell daemon, because you can than produce useful work by using one body as heater and the second body as cooler in an heat engine.</p>
<p>I think there is some theorem in optics which say that you cannot increase radiance by any focusing without loss of power.
<a href="http://en.wikipedia.org/wiki/Spectral_radiance">http://en.wikipedia.org/wiki/Spectral_radiance</a></p>
<p>However, I'm not quite sure how this theorem is called, and what is a background. As well I'm not able to make rigorous reasoning, how this limit the temperature of solar furnace.</p>
<p>Only what I can say that two black bodies of different size in elliptical cavity does not create Maxwell daemon, because of this radiance limit (You actually does not focus all the light from the bigger body to the smaller one ).</p>
<p>But <strong>what if I don't have to use all the light power</strong> from sun? For example you can limit the aperture by diaphragm. In this case you can increase radiance without braking second law of thermodynamics nor the radiance invariant. I'm not sure if in this case (if you sacrifice some power) you can get higher temperature?</p>
<p>If so, is it possible to formulate equation which connect power efficiency and temperature difference for this "<strong>optical heat pump</strong>"</p> | g398 | [
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<p>I'll a appreciate a layman's explanation, if there exists one, to this question that arose when reading an popular-science level article on Einstein and the $E=MC^2$ equation.</p>
<p>What I mean is that, why is the product of the reaction <strong>not</strong> an electrically neutral doublet of mass $2M_e$ (= 1.022 MeV) and which the opposite charges keep the two particles attracted to each-other?</p> | g12599 | [
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<p>Jupiter has many <a href="http://en.wikipedia.org/wiki/Jupiter_Trojan" rel="nofollow">Trojan asteroids</a> located at Lagrangian points L4 and L5 and <a href="http://en.wikipedia.org/wiki/Hilda_family" rel="nofollow">Hilda asteroids</a> dispersed between points L3, L4, and L5.</p>
<p>Does the Earth have similar asteroids? If so, how many?</p> | g12600 | [
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<p>This is a two part question about the technology described here:</p>
<p><a href="http://www.engadget.com/2011/06/22/light-field-camera-captures-unprecedented-images-lets-you-cho/" rel="nofollow">Lytro's light field camera lets you choose focus later</a></p>
<ol>
<li>I'd love to get an explanation of the technology.</li>
<li>What is the possibility/feasibility of creating a display that would output those images, allowing the viewer to focus on whatever piece of the image s/he chooses? Essentially eliminating the main issue with current 3D technology.</li>
</ol> | g12601 | [
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<p>This article is certainly an interesting alternative perspective, but is it factual or does it contain fallacies?</p>
<p><a href="http://www.circlon-theory.com/HTML/EmcFallacies.html" rel="nofollow">http://www.circlon-theory.com/HTML/EmcFallacies.html</a></p>
<p>Are mass and energy not convertible after all? Do photons really have kinetic mass?</p>
<p>Is it really fair to classify the energy stored in the nuclear strong force as "rotational kinetic energy"?</p> | g12602 | [
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<p>the question is: </p>
<p>A ball is thrown directly downward with an initial speed of 8.00m/s from a height of 30.0m. After what time interval does it strike the ground.</p>
<p>so i went through the problem and got the answer 1.79 sec.
but after reviewing some notes from my teacher, I got the idea that in equations where an object is dropped down, the height has to be counted as negative.
so I went through the problem again using -30m, but now my answer doesn't check out when plugged back in to x - x0 = V0 (t) + 1/2 at^2</p>
<p>Is there something I'm missing about this idea that height or distance is negative in drop-down questions? </p> | g12603 | [
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0.0386364683508873,
0.024258363991975784,
-0.0... |
<p>I've been racking my brain over this, and I can't find any clues in my textbook as to how to approach it.</p>
<p>I have the following circuit:</p>
<p><img src="http://i.stack.imgur.com/SaOrc.png" alt="enter image description here"></p>
<p>My goal is to find R such that, <strong>right after the switch is unplugged</strong>, the voltage between A and B is <strong>no more than 80V</strong></p>
<p>I can easily apply Kirchoff's rules to find the currents after the switch has been closed a long time:</p>
<p>$$
I_1- I_2 - I_3 = 0
$$</p>
<p>$$
12 - RI_3 = 0
$$</p>
<p>$$
10 + 7.5I_2 - RI_3 = 0
$$</p>
<p>The result is:</p>
<p>$$
I_3 = \frac{12}{R}
$$</p>
<p>$$
I_2 = \frac{4}{15}
$$</p>
<p>$$
I_1 = \frac{4R + 180}{15R}
$$</p>
<p>Now, the switch is thrown open. The new circuit is described by a single loop. The thing I don't understand is the fact that $I_2$ is different than $I_3$, and yet the single loop must have a single constant current when the switch is thrown open. I don't know how to go about finding this new current. Furthermore, I would have to write down Kirchoff's loop rule for the new circuit, and that would require knowing the emf generated by the inductor, which would require $\frac{dI}{dt}$, which I also wouldn't quite know how to determine at the first instant.</p>
<p>Any guidance on this problem would be MUCH appreciated, I would really like to understand it and my textbook doesn't provide much to go on =\</p>
<p>Thanks!</p> | g12604 | [
0.011380989104509354,
-0.005930271930992603,
-0.026305921375751495,
-0.047781046479940414,
-0.020822111517190933,
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0.01860615611076355,
0.0561051145195961,
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0.021349072456359863,
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0... |
<p>I'm trying to model the behaviour of aerosols in response to blast waves. (This is for visual effects.)</p>
<p>Intuitively, if a flare left a smoke trail above a field and then a bomb detonated elsewhere in the field, one would expect the smoke to be dispersed, to a degree varying with the bomb's energy (among other things.)</p>
<p>Studying blast waves, it has come to my attention that the associated overpressures have both a static pressure and a dynamic pressure component, as seen in this graph:</p>
<p><img src="http://i.stack.imgur.com/kEVI0.png" alt="Source: D. R. Richmond"></p>
<p>If I understand correctly, <em>static pressure</em> is due to thermodynamic motion while <em>dynamic pressure</em> is due to net motion of the medium.</p>
<p>The dynamic pressure component is fairly easy to understand: it's basically a wind, and figuring out how something moves in response to it should be straightforward.</p>
<p>The static pressure part is more confusing. I'm assuming this is ordinary longitudinal wave propagation without mass transport, similar to sound. Kind of like shoving one person in a lineup and only the 'shove' itself is transmitted.</p>
<p>One thing I find confusing is that static pressure is a directionless (scalar) quantity, so how does a pressurized region transmit energy only in the direction of propagation? Why doesn't the 'shove' just scatter? (I almost asked this as a separate question.)</p>
<p>Rather than worry about it, my first question is, would the static pressure component of a blast wave even effect any bulk transport of an aerosol?</p> | g12605 | [
0.02449401095509529,
0.01565629057586193,
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0.0829651951789856,
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-0.036499135196208954,
0.006199579685926437,
-0.029377032071352005,
0.05125417187809944,
-0.03441... |
<p>A star is probably visible/detected by it's radiation. But that star may or may not belong to our own galaxy ... yet news reports speak of detecting a star/nova in a distant galaxy. </p>
<p>How does one determine whether the star she/he views belongs to Milky Way, or some other galaxy ... or is galactic orphan? Is it merely a matter of the distance to that star?</p> | g12606 | [
-0.008531041443347931,
-0.018566565588116646,
0.002496145898476243,
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0.017905661836266518,
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0.02105298638343811,
0.029525764286518097,
-0.06441383808851242,
-0.004102594684809446,
0.07497904449701309,
0.08101988583803177,
0.01... |
<p>What is the phase difference of the oscillation of a tuning fork? </p> | g399 | [
0.013917394913733006,
0.0444110669195652,
0.0037814397364854813,
0.01155526377260685,
0.06153804808855057,
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0.013776814565062523,
0.0031637295614928007,
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0.05254888907074928,
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-0.... |
<p>I have two questions regarding (possibly counter intuitive results) Schrodinger equation and its application to two (strictly hypothetical) scenarios.</p>
<ol>
<li><p>Consider the 1D potential $V(x) = - \frac{\alpha}{|x|}$, which is an attractive one. As it is attractive, after a sufficiently large amount of time I'd expect the probability density of finding the particle at $x=0$ (center) to be higher than that anywhere else. I hope it is reasonable to expect such a thing.</p>
<p>But the solution according to Schrodinger equation is (as given in this <a href="http://physics.stackexchange.com/a/69923/540">answer</a>) is $$u_n(x,t) \sim \lvert x\rvert e^{-\lvert x\rvert/na} ~L_{n -1}^1\biggl(\frac{2\lvert x\rvert }{na}\biggr) e^{-E_nt/\hbar}$$ Consider the amplitude at $x=0$ $$\lvert u_n(0,t)\rvert = 0$$ which I think is contradictory to our reasonable expectations based on intuition. I'd appreciate some comments on why it is counter intuitive.</p></li>
<li><p>Consider the particle in box problem and according to Schrodinger's equation, in almost all energy states the probability of finding the particle close to the boundaries is zero.
Now instead of intuition (which is not predicting anything) I'd give a practical example where it is quite contradictory. (Pardon me if this example is not suitable, I am learning and I'd love to know why it isn't intuitively not suitable). Consider a metal conductor, I guess its an example for particle in a box as the potential inside is zero and we know that the charge is usually accumulated at the edges of the conductor.</p></li>
</ol>
<p><strong>EDIT</strong> </p>
<p>An interesting thing to add. The probability density vanishing at center does not seem to arise in 3-D hydrogen atom. Check the wave function of 1s orbital of Hydrogen atom, it of the form $\psi_{1s}(r) = a e^{-kr}$, where $k$ and $a$ are some constants and $r$ is the radial distance from nucleus.</p> | g12607 | [
0.027741067111492157,
0.030248740687966347,
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0.039528314024209976,
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0.010260739363729954,
0.023194754496216774,
0.01883184351027012,
0.049376316368579865,
... |
<p>I have a question concerning the Faddeev-Popov ghost boundary conditions in the path integral quantization of bosonic strings. My ghost action is:</p>
<p>$S_g= - \frac{i}{2\pi} \int d^2 \xi \sqrt{-h} \; b_{ab} \nabla^a c^b$</p>
<p>I can derive the equations of motion, but I cannot see the boundary conditions of the ghost and anti-ghost fields. They should be: </p>
<p>$c^+ = c^-$ </p>
<p>and</p>
<p>$b_{++}=b_{--} $</p>
<p>for $\sigma = 0 , l$.<br>
It always says, that those conditions arise from the boundary terms, when deriving the equations of motion. My boundary terms of the integration by parts are:</p>
<p>$ -\int \left. d\tau c^+ b_{++} \right|_{\sigma_i}^{\sigma_f} + \int \left.d\tau c^- b_{--} \right|_{\sigma_i}^{\sigma_f} + \int d\sigma \left. c^+ b_{++} \right|_{\tau_i}^{\tau_f} + \int \left. d\sigma c^- b_{--} \right|_{\tau_i}^{\tau_f}=0$ </p>
<p>and </p>
<p>$\int \left. d\tau c^- \delta b_{--} -c^+ \delta b_{++}\right|_{\sigma_i}^{\sigma_f}=0$</p>
<p>Thank you very much for any help</p> | g12608 | [
0.0691639706492424,
0.008284416049718857,
0.023302236571907997,
0.012560647912323475,
0.052449338138103485,
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0.04035606235265732,
0.023853849619627,
0.007472558878362179,
0.00027020758716389537,
-0.04963347688317299,
0.020078515633940697,
-0.09565544128417969,
0.01757... |
<p>How to calculate work when a block is moving with constant velocity?
As we know $f=ma$, and for constant velocity $a=0$, so $f=0$ and $w=fs=0$? Can anybody make it clear?</p> | g12609 | [
0.035303883254528046,
0.01056880597025156,
0.020128080621361732,
0.049248065799474716,
0.008375205099582672,
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0.05265166237950325,
0.04273640364408493,
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-0.011697056703269482,
-0.059393420815467834,
0.030884668231010437,
0.02383105643093586,
0.0132... |
<p>I am trying to understand net force intuitively and this is what I think.</p>
<blockquote>
<p>If a net force is towards the positive $x$ direction, which of the following is true ?</p>
<p><strong>a)</strong> It can be moving in the negative $x$ direction</p>
<p><strong>b)</strong> It can be speeding up</p>
<p><strong>c)</strong> It can be slowing down</p>
<p><strong>d)</strong> It can be moving in the positive $y$ direction</p>
</blockquote>
<p><strong>a)</strong> No, because if an object is moving towards the left, $x_f-x_i$ is negative, so the velocity is negative as well as the acceleration. So, impossible.</p>
<p><strong>b)</strong> Yes. as a matter of fact it has to because positive acceleration means speeding up.</p>
<p><strong>c)</strong> No. Same reason as <strong>b</strong>.</p>
<p><strong>d)</strong> No, because the y-direction is perpendicular to the x. </p>
<p>I got this problem wrong and I don't think I am really understanding acceleration. Can someone help me out ?</p> | g12610 | [
0.043873440474271774,
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0.027137111872434616,
0.010725692845880985,
0.023438328877091408,
-0.0041... |
<p>Assume that we have some non-constant electric field $E(x,t)$ and a point-dipole at a position $q$ with a constant dipole moment $\vec{p}$. How would you describe the time evolution, i.e. the motion of such a dipole?</p> | g12611 | [
-0.020754538476467133,
0.05598555505275726,
-0.018293995410203934,
0.002411948051303625,
0.07533778995275497,
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0.02431940846145153,
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0.004489094018936157,
0.03814800828695297,
-0.07552020996809006,
-0.002701766090467572,
0.004973593167960644,
-0... |
<p>I need to implement a random force in my code according to the fluctuation dissipation theorem. I have a Gaussian distribution function ready width average 0 and distribution 1 and I know I need to multiply it by something but I'm not sure what. The fluctuation dissipation theorem gives (in one dimension):</p>
<p>$\left \langle A (t_1) A (t_2) \right \rangle = 2 m \gamma k_B T \delta (t_1 - t_2 )$</p>
<p>I can't convince my self if I should multiply my Gaussian with my $\sqrt{dt}$ or divide by it. I can find justification for both direction:</p>
<ol>
<li>The force should act like delta function (no correlation between times) hence, I should divide by it. </li>
<li>The units are ok when multiplying by $\sqrt{dt}$.</li>
<li>The larger the time step, the more collision happened hence the force should be larger.</li>
</ol>
<p>I remember that in some place I read or heared I should divide by the $\sqrt{dt}$ but I couldn't find where. </p>
<p>I should note that I tried both approach, when I divide I suspect the forces to be too large (I only see noise) and when I multiply, I almost can't see any random effect.</p> | g12612 | [
-0.005878100637346506,
-0.022173164412379265,
0.005080614238977432,
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0.011166555806994438,
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0.028287602588534355,
0.03585820272564888,
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-0.04992036521434784,
0.011311927810311317,
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0.011123862117528915,
... |
<p>I conducted an experiment , i put a silver foil on a a CRT TV , then i open the TV, charging the foil (acting like a capacitor plate), if i approach a grounded rod to it , it will discharge with a spark of about 1.8 cm length , which is equivalent to about 18 kV.
What i am really interested in is once that spark goes in the rod and becomes current, i wanted to know the voltage of that current, so i asked a question on SE and the answer that it will be 18 kV, but when i connected a LED 3V in the wire connecting the rod to the ground , it worked. Another thing, will the current be simply the charge on the plate , or a normal relation between V and R?</p> | g12613 | [
0.061545222997665405,
0.0009947186335921288,
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0.0899914801120758,
-0.06271232664585114,
... |
<p>Do electrons move randomly, with no preference of directions?
And why electrons don't fall into the nucleus? About this question, I read the article on Chemistry wiki, which says that when electron falls towards nucleus, its kinetic energy becomes extremely large so there is a battle between electrons and nucleus, and no one is gonna win the battle, there is a compromise state instead. My question is why can't we say that electrons with great kinetic energy are moving towards the nucleus? Why should it escape？</p> | g132 | [
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0.05748125910758972,
0.002628565998747945,
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0.07084183394908905,
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0.031942836940288544,
0.021650658920407295,
0.018624717369675636,
-0... |
<p>For a very long time now, I've been thinking about the <a href="http://en.wikipedia.org/wiki/Drude_model" rel="nofollow">Drude Model</a> derivation of Ohm's Law. I know that a rigorous derivation requires a Quantum Mechanical approach. However, the mere fact that the Drude Model churns out the right equation seems to suggest to me that it is at least partially sound from a qualitative viewpoint. A particular assumption strikes me. Electrons are assumed to collide with protons. However, a direct collision doesn't seem possible to me (the kind you think of when you typically think of collisions). And in these electron-proton collisions, the momentum of electrons is assumed to be reset, and protons are assumed to be fixed. The only way I can think of this is that certain electrostatic interactions take place that cause protons to gain all the momentum, and electrons lose it all (for conservation of momentum to hold). And in such a scenario, protons will move very slowly, thus having a negligible effect. Over time, as the momentum on proton builds up, the rate of collisions, and increases. This seems to explain the temperature-resistance relationship at least qualitatively. However, something else that strikes me is how energy is released during the "collisions". I've heard that accelerating charges produce EM waves, and therefore find reason to believe that this is how energy is released.</p>
<p>This also makes Kirchhoff's Loop Rule appear reasonable. I could not accept it at first because it seemed to suggest that a non-conservative "collision" force opposed the work done by the electric force, and I could not think of what would cause such a force at the microscopic level. But, if EM waves are released, this alternate picture of energy loss seems much more reasonable; the work done by the electric force is released as heat. I guess this is "friction" on the macroscopic scale.</p>
<p>I just want to know, does this mechanism seem reasonable, and can I accept it till such time I learn Quantum Mechanics, and learn the true story? Or is the Drude Model simply too flawed to accept?</p>
<p>Also, I want to know if momentum is actually transferred to the proton.</p> | g12614 | [
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0.025429870933294296,
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0.045943036675453186,
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0.01876583695411682,
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0.02297235280275345,
0.032... |
<p>I am studying classical Maxwell fields and I am stuck on this differentiating part. How can I derive the result given below ?</p>
<p>$$\dfrac{\partial}{\partial(\partial A_{\mu}/\partial x_{\nu})} \left(2\dfrac{\partial A_{\sigma}}{\partial x_{\lambda}}\dfrac{\partial A_{\sigma}}{\partial x_{\lambda}}-2\dfrac{\partial A_{\sigma}}{\partial x_{\lambda}}\dfrac{\partial A_{\lambda}}{\partial x_{\sigma}}\right)$$</p>
<p>The answer is</p>
<p>$$4\dfrac{\partial A_{\mu}}{\partial x_{\nu}}-4\dfrac{\partial A_{\nu}}{\partial x_{\mu}}$$</p>
<p>where $A$ is vector potential and $x$ is four-vector.</p> | g12615 | [
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0.04382089897990227,
-0.06198238953948021,
-0.05... |
<p>Let me set up the notation I am using. $(abc,de)$ denotes the standard Young tableau where the first row is $abc$ and the second row is $de$. Each young tableau corresponds to the young symmetriser, and I use the convention that given the Young tableau $\lambda$ young symmetriser is given by,</p>
<p>$P_{\lambda} = Na.b$ where $a = \sum_{\sigma \in Rowgroup} \sigma$, and $b = \sum_{\sigma \in Column-group} (sgn \,\sigma) \sigma$. N stands for normaliser such that $P_{\lambda}$ is idempotent ($P_{\lambda}^2 = P_{\lambda}$).</p>
<p>The action of the symmetric group on an abstract tensor is by means of shuffling the indices. I know that the following identity is true.</p>
<p>$\mathbb{1} = \sum_iP_{\lambda_i}$
Here $\lambda_i$ are all the Standard young tableau of a given number of boxes.
Applying this identity to any abstract tensor should give the same tensor back. And if this abstract tensor is completely arbitrary, i.e does not have any symmetries in its indices this decomposition yields components living in each irreps. OK. My question is when we have tensor products, then we use Littlewood-Richardson rule to find a one of the basis tensors representing each irreducible space. However I am interested in not just treating the tensor product as a vector space and finding the disjoint union of irreducible vector spaces, that each young tableau corresponds to and acting with the Young symmetriser yields one of the basis tensors. </p>
<p>I would like to find out the given tensor in each irreducible space. Let me give an example. Suppose I have a rank 3 tensor that is antisymmetric in the first 2 indices. I can treat this as a tensor product of $(a,b) \otimes c$(Here ab is a column as per my notation.) Applying LRH I get, $(ac,b),(a,b,c)$. Using the young symmetriser I defined above, I act with this normalised young symmetriser on the tensor $T^{ab|c}$ (here the bar is used to group anti-symmetric indices). I get,</p>
<p>$T_1^{abc}= P_{ac,b} T^{ab|c} = \frac{2}{3}(T^{ab|c} + T^{cb|a})$ (1)</p>
<p>$T_2^{abc}=P_{a,b,c} T^{ab|c} = \frac{1}{3}(T^{ab|c} + T^{bc|a} + T^{ca|b})$ (2)</p>
<p>Now $T_1 + T_2 \neq T$ as is clear. However when I project each component using the young symmetrisers associated with the factors of the tensor product, in this case it is $P_{a,b}$ I get T back. That is </p>
<p>$T = P_{a,b}(T_1 + T_2) $
Explicitly,
$P_{a,b} T_1^{abc} = \frac{2}{3} T^{ab|c} + \frac{1}{3}(T^{cb|a} - T^{ca|b})$, </p>
<p>Therefore,
$P_{a,b}(T_1^{abc} + T_2^{abc}) = \frac{2}{3} T^{ab|c} + \frac{1}{3}(T^{cb|a} - T^{ca|b})+ \frac{1}{3}(T^{ab|c} + T^{bc|a} + T^{ca|b}) = T^{ab|c}$. </p>
<p>Is this relationship true in general i,e suppose I have a tensor product which I write as $T^{\lambda_1|\lambda_2}$ where $\lambda_1,\lambda_2$ denote the factors belonging to irreps corresponding to the Standard tableaux. Then is the following relationship TRUE, and how do I prove this?</p>
<p>$T^{\lambda_1|\lambda_2} = P_{\lambda_1}P_{\lambda_2}\times$(irreducible components we get by using young symmetrisers generated by LRR and acting on $T^{\lambda_1|\lambda_2}$). In short I want to know if the component of this tensor product living in the irreducible rep characterised by the tableau $\nu$ generated by LRR is,</p>
<p>$\mathbf{P_{\lambda_1}P_{\lambda_2} T_{\nu}}?$</p> | g12616 | [
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0.0014315495500341058,
-0.016126150265336037,
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-0.028299415484070778,
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-0.0083028525114059... |
<p>Prompted by <a href="http://math.stackexchange.com/questions/96331/in-russian-roulette-is-it-best-to-go-first">this discussion on the math exchange</a></p>
<p>My thought was that the added mass of a bullet in an otherwise empty revolver would bias the chamber spin such that the bullet would remain in one of the lower chambers.</p>
<p>Obviously not something I'm going to try in practice (+: </p>
<p>Anyway I find myself wondering whether my thought carries any weight. (pun not intended)</p> | g12617 | [
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0.022657182067632675,
-0.... |
<p>I am not seeing the "big picture" here. If I have two conducting spheres separated by a long conducting wire, why would the spheres share the same electric potential?</p>
<p>I think of the spheres as point charges, what does the conducting wire do? The $E$ field inside the conducting wire is 0, so what is it really doing?</p> | g12618 | [
0.027933303266763687,
0.008326128125190735,
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0.08127321302890778,
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0.030411867424845695,
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0.013899830169975758,
0.004523386713117361,
0.0... |
<p>In "introductory Quantum Optics", by Gerry and Knight, the Jeynes model is considered. In this model of electron-EM field interaction the electron is approximated by a two state system ($\lvert g\rangle$ and $\lvert e\rangle$), and the form of the dipole operator $\hat{d}$ is said to be constrained by parity consideration not to have on-diagonal terms:</p>
<blockquote>
<p>Only the off-diagonal elements of the dipole operator are
nonzero, since by parity consideration $\langle e\rvert\hat{d}\lvert e\rangle=0=\langle g\rvert\hat{d}\lvert g\rangle$.</p>
</blockquote>
<p>Why? What does parity have to do with it?</p> | g12619 | [
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-... |
<p>i) Do people use axial gauge with a $\xi$ term? When $\xi\neq 0$, ghosts do not decouple, but maybe it's still useful?</p>
<p>ii) Is it proved that the term $\frac 1 {2\xi}(n.A)^2$ in the Lagrangian does not renormalize, for $\xi=0$ and $\xi\neq 0$?</p> | g12620 | [
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<p>I keep on hearing that magnetism is just another form of electricity and vice versa. If that's the case why can't we use magnets as batteries, and why aren't my batteries magnetic?</p> | g12621 | [
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0.03331... |
<p>The displacement current is due to changing electric field. Since, after the capacitor gets fully charged there is no changing electric field there is no displacement current.(capacitor connected to a DC voltage input) This is my understanding. Please correct me if I'm wrong.</p> | g12622 | [
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<p>Why is the <a href="http://en.wikipedia.org/wiki/Gravitational_constant" rel="nofollow">Gravitational constant</a> about $10^{23}$ times of the <a href="http://en.wikipedia.org/wiki/Planck_constant" rel="nofollow">Planck constant</a> in SI-units? Is there any relation between them?
I mean Planck constant is about $6.6\times 10^{-34}$ $Js$ and Gravitational constant is about $6.6×10^{−11} \frac{N·m^2}{kg^2}$. </p> | g12623 | [
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0.020894378423690796,
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<p>Ref. 1, page 15, equation (23) defines the $U(1)_V$ and $U(1)_A$ actions as $$e^{i\alpha F_V}: \Phi(x,\theta^{\pm},\bar{\theta}^{\pm}) \rightarrow e^{i\alpha q_V}: \Phi(x,e^{-i\alpha }\theta^{\pm},e^{i\alpha }\bar{\theta}^{\pm}) $$
The superfield can be written as $$\Phi(x,\theta^{\pm},\bar{\theta}^{\pm}) =x+\theta^+ \psi_+ +\theta^- \psi_- + \bar{\theta}^+ \bar{\psi}_+ + \bar{\theta}^- \bar{\psi}_- \ldots $$</p>
<p>The question is how to judge the $U(1)_V$ charge of $\psi_+$, $\psi_-$, $\bar{\psi}_+$ and $\bar{\psi}_-$ like table 2 in page 17. that the $U(1)_V$ charge of $\psi_\pm$ is -1 and the $U(1)_V$ charge of $\bar{\psi}_\pm$ is +1.</p>
<p>References:</p>
<ol>
<li>A. Klemm, <em>Introduction to topological string theory on Calabi-Yau manifolds,</em> lecture notes, 2005. The pdf file is available <a href="http://www.math.ist.utl.pt/~strings/AGTS/klemm.html" rel="nofollow">here</a>.</li>
</ol> | g12624 | [
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0.01578250154852867,
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0.028... |
<p>Quarks have the unusual characteristic of having a fractional electric charge.
here there is a new model that suggests maybe an up Quark has no electric charge and infact down Quark has electric charge of (+1,-1), through weak interaction between Up Quark and W$^{\pm}$</p>
<p>$$u^{0}+W^{+}\to d^{+},$$
$$u^{0}+W^{-}\to d^{-},$$</p>
<p>sounds like this idea consisted with neutron decay.
$$n^{0}\to p^{+}+W^{-},$$
$$u^{0}d^{-}d^{+}\to u^{0}u^{0}d^{+}+W^{-}.$$</p>
<p>Reference: <a href="http://meetings.aps.org/Meeting/OSS13/Event/195666" rel="nofollow">http://meetings.aps.org/Meeting/OSS13/Event/195666</a></p> | g400 | [
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<p><strong>Question:</strong> Which of the following affect the frequency of a tuning fork?</p>
<ul>
<li>Tine stiffness</li>
<li>Tine length</li>
<li>The force with which it's struck</li>
<li>Density of the surrounding air</li>
<li>Temperature of the surrounding air</li>
</ul>
<p><strong>Answer Attempt:</strong> Based on the formula for the frequency, I know that tine stiffness (or density) affects it, and so does the tine length. I believe the temperature and density of air can have a slight affect as well. What about the force with which it's struck?</p> | g12625 | [
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<p>If an object is designed to cope with large forces such as tension, would removing these forces risk damaging the object?</p>
<p>For example: The neck of a guitar is built to handle the tension of steel strings (~800 Newtons),
if you removed/reduced the tension (removed the strings) for a long period of time would this risk damaging the guitar neck?</p> | g12626 | [
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<p>In this question I am talking about the following situation:</p>
<p><img src="http://i.stack.imgur.com/Q4brH.gif" alt="enter image description here"></p>
<p>Now, I know that the max kinetic energy of the electrons emitted is</p>
<p>$KE_{max} = h\nu - e\phi_{em}$</p>
<p>where $\phi_{em}$ is the work function of the emitter electrode (on the left in the diagram). And my lecturer agrees with that, but he tells us that the stopping potential $V_0$ can be found using</p>
<p>$eV_0 = h\nu - e\phi_{col}$</p>
<p>where $\phi_{col}$ is the work function of the collector electrode (on the right in the diagram). The emitter and collector electrodes are made from different metals.</p>
<p>What I don't understand is why the stopping potential doesn't depend on the kinetic energy of the emitted electrons.</p>
<p><strong>EDIT</strong></p>
<p>I have attached the slide from the lecture course</p>
<p><img src="http://i.stack.imgur.com/vJ2aF.png" alt="Lecture slide"></p> | g12627 | [
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0.038275450468063354,
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0.026175741106271744,
0.01590024121105671,
0.029724... |
<p>The title really says it all. One follow-up question is: How could one falsify this?</p> | g12628 | [
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0.0015105924103409052,
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... |
<p>Due to increase in forward bias voltage, the intensity of light increases but after a particular value the intensity decreases. Why?</p> | g12629 | [
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<p>In an extrinsic semiconductor the electric potential is:
$$\phi = \frac{1}{q}(E_{\mathrm{F}} - E_{\mathrm{Fi}})$$
where $E_{\mathrm{F}}$ is the Fermi energy, $E_{\mathrm{Fi}}$ is the intrinsic Fermi energy, $q$ is the electron charge and $\phi$ is the electric potential. I am not sure where this equation comes from. I understand why a potential will be created qualitatively, but where does this equation come from quantitatively?</p>
<p>From what I understand , the expected value of the electron energy is the Fermi energy.
You take $E_{\mathrm{Fi}}$ as the reference for the electron potential. This is the equilibrium condition of an intrinsic semiconductor. If you dope the semiconductor, you introduce an imbalance and that causes the generation of an electric field, hence the new expected value $E_{\mathrm{F}} - E_{\mathrm{Fi}}$. Is that correct?</p> | g12630 | [
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0.004... |
<p>I am sure all of us have played with rubbing things and producing static electricity and when I was charging my comb by rubbing it on my hair and watching it attracting a small piece of paper, I heard a very feeble noise just like an electric buzz sound. I could feel the electron "cloud" all around the comb and the paper it I could find no reason as to why a sound should be produced. From where is that sound coming from?</p> | g12631 | [
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<p>for example, i have a vague notion that the actual answer is that the permittivity and permisivity are different in each different material, so all waves refract at every boundary, but we only call it that if it makes it out with any real magnitude left which depends on the skin depth or something like that, but is there a simple off the cuff way to estimate based on the ratio of the wavelength and that of the object?</p>
<p>for example, will a radio wave refract through a tree?</p> | g12632 | [
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0.0... |
<p>If we ignore 5GHz WiFi, then both microwaves and WiFi create photons at ~2.4GHz but one of them will boil water in a few seconds but the other doesn't have any effect. So what's the difference?</p>
<p>Is it simply the number of photons created? Is that what the wattage of a microwave measures? If so, what would be the wattage of a wireless router?</p>
<p>Does the enclosed space have anything to do with it?</p>
<p>
If it all has to do with power output could I put enough WiFi routers together in a room to cook a turkey (from microwaves and not waste heat)?
</p> | g230 | [
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0.011401901952922344,
0.028681648895144463,
-0.046038806438446045,
... |
<p>Imagine a following thought experiment.</p>
<p>Suppose we have a large amount of entangled particle pairs, several million or billion.
Now suppose there are two observers, each carrying one member of particle pair - a slower-then-light spaceship and mission control on Earth, for example.</p>
<p>Before departure, both spaceship crew and Earth crew agreed to order their entangled pairs by into sets of 100 (or 1000,10000, ...), ordered by the time of particle pair creation or any other way, as long as the order is the same on both Earth and spaceship.</p>
<p>Now, spaceship departs Earth with v << c, so relativistic effects are negligible and the clocks on the ship and Earth are more-or-less in sync for the foreseeable future. Each day mission control on Earth is using the their particles in the pre-determined pair set to construct a quantum computer (can entangled particle in a pair be used as qubit? used for quantum gate?) and runs a specific quantum algorithm that should give some defined answer (Shor's, or Grover's). </p>
<p>Afterwards results are measured, breaking the entanglement and then compared against the expected one. Each day next set of particle is used and discarded. The spaceship crew does nothing, except noting which particle set has been used up by Earth team.</p>
<p>Now, suppose after many hundreds years of flight spaceship is several light-years away from Earth, but there are still entangled particle sets available for both crew and Earth team and both team know which sets have been used and what set is going to be the next one for the next day.</p>
<p>Now, imagine our spaceship encounter hostile aliens. On that day and all the subsequent ones as long as the spaceship crew survives, they <em>observe</em> all remaining particle pair sets, breaking the entanglement with the matching ones on Earth. Earth team is not aware of the encounter and they still attempt to construct quantum computer from their matching half of the particle pair sets every day. </p>
<p>But each day as they try to run the quantum algorithm on their half of particle pair set, their computation FAILS as their particles are no longer in a quantum superposition state and can no longer be used for quantum computation. So, after a few days, Earth team learns that spaceship crew sent them a 1-bit distress signal, even though a ship is several light-years away, receiving this information faster then light. </p>
<p>Now question: where is the mistake in my chain of thought?</p> | g12633 | [
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0... |
<p>In an electron multiplier (discrete dynode detector), one electron triggers the release of more electrons in a cascade.</p>
<p>Is it possible that a "large" number of electrons hitting the detector can temporarily (course of hours) reduce the number of electrons available to amplify future incident electrons? (E.g. is there a cumulative recharge time?)</p>
<p>Or is it possible for the anode to have temporarily reduced sensitivity if the electrons are not flushed quickly enough?</p>
<p>(Assume real-world, non-ideal physics. This is an actual mass spec we're talking about. Something is causing reduced sensitivity over the course of hours of usage, aside from reduced transmission and ionization due to dirt.)</p> | g12634 | [
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0.033799465745687485,
0.010... |
<p>I'm trying to understand the basics of <a href="http://en.wikipedia.org/wiki/Anyon" rel="nofollow">anyons</a> physics. I understand there is neither a Fock space they live in (because Fock is just the space of (anti-)symmetrized tensor product state, see <em>e.g.</em> <a href="http://en.wikipedia.org/wiki/Fock_space" rel="nofollow">Wikipedia</a>), nor a (pseudo / fictitious) commutation relation for them, as discussed at <a href="http://physics.stackexchange.com/q/43125/">this</a> Phys.SE post. But still I've a few questions regarding their statistics: </p>
<ul>
<li><p>Can we associate a creation / destruction operator to an anyon mode ? Does it make sense to talk about <em>mode</em> of anyons?</p></li>
<li><p>Is there a general occupation function like Fermi-Dirac or Bose-Einstein for fermions or bosons ? Is it model dependent, <em>i.e.</em> does it depend on the type of anyon ? Does it make sense to discuss <em>number</em> of anyons?</p></li>
<li><p>What is the ground state of anyons, like a Fermi sea or a Bose-Einstein condensate for fermions or bosons ? Does it make sense to talk about a <em>ground state</em> of a gas of anyons?</p></li>
</ul>
<p>I believe this bunch of questions can all be contracted to </p>
<ul>
<li><strong>Does it make sense to talk of the anyons as particles ?</strong></li>
</ul>
<p>Because in principle a particle exists independently of the Fock space construction, isn't it ? We could still construct a space of the tensor product of non (anti-)symmetrised states.</p>
<p>I realised that a perhaps better approach on the question would be:</p>
<ul>
<li><strong>To which extend is the anyon statistic a (quantum) statistic ?</strong></li>
</ul>
<p>provided the two other quantum statistics I know (Bose and Fermi) provide a ground state, an occupation number, and some second-quantised version of operators.</p>
<p><em>Post-scriptum :</em> <a href="http://physics.stackexchange.com/q/61915/">This</a> Phys.SE question is partially related to mine.</p> | g12635 | [
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<p>I'm trying understand how to rotate Dirac fields to absorb complex phases in masses. I have a few related questions:</p>
<ol>
<li><p>With Weyl spinors, I understand, $$ \mathcal{L} = \text{kinetic} +
|M|e^{i\theta}\xi\chi + \textrm{h.c.} $$ The phase removed by separate
left- and right-handed rotations, e.g. $\xi \to e^{-i\theta/2}\xi$
and $\chi \to e^{-i\theta/2}\chi$. These phases cancel in the
kinetic terms.</p>
<p>Is it correct that with Dirac spinors, $$ \mathcal{L} = \bar\psi
|M|e^{i\theta\gamma_5} \psi = \text{Re}(M)\bar\psi\psi
+i\text{Im}(M)\bar\psi\gamma_5\psi $$ and the phase is removed by $\psi \to e^{-i\theta\gamma_5/2}\psi$? The appearance of the
$\gamma_5$ in the phase troubles me a little - I suppose this is
telling us that Weyl spinors are a more suitable basis than Dirac
spinors?</p></li>
<li><p>If the field is Majorana, $\xi = \chi$, and the field can still
absorb a phase? I think I must be making a trivial mistake. </p>
<p>For example, Majorana neutrino fields cannot absorb phases, leading to extra CP violation.</p>
<p>And in SUSY, the gaugino Majorana soft-breaking
masses are e.g. $M_1e^{i\theta}$. Can their phases be re-absorbed via a field redefinition? I don't think they can. So I must have a mistake.</p></li>
</ol> | g12636 | [
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-0.0... |
<p>How is <a href="http://en.wikipedia.org/wiki/Fermat%27s_principle" rel="nofollow">Fermat's least time principle</a> proven? Or it is what usually is observed and is basis for the theories?</p> | g12637 | [
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... |
<p>Is the particle entanglement a boolean property? That is, when we consider two given particles, is the answer to the question "are they entangled" always either "yes" or "no" (or, of course, "we are not sure if it's yes or no")? Is there such thing as partial entanglement?</p> | g12638 | [
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0.022108133882284164,
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0.00015971041284501553,
-0.030713113024830818,... |
<p>Let's have Schrodinger equation or Dirac equation in Schrodinger form:
$$
i \partial_{0}\Psi = \hat {H}\Psi .
$$
Sometimes we can introduce some operators $\hat {A}, \hat {B}$ (the second is not always Hermitian conjugate to the first) for which
$$
\hat {H} = \hat {B}\hat {A} + \varepsilon ,
$$
which is look like rewriting $\hat {H}$ through destruction and creation operators.</p>
<p>Right commutation or anticommutation laws $[\hat {B}, \hat {A}] = 1, \quad [\hat {B}, \hat {A}]_{+} = 1$ are not necessarily too.</p>
<p>I heard that it helps to simplify the way of solution of equation. But I don't know what physical sense of $\hat {A}, \hat {B}$, so I don't understand how to use these operators fo finding energy spectra and functions for corresponding state. </p>
<p>What do you know about this?</p>
<p>An example.</p>
<p>For electron in Hydrogen atom Schrodinger equation can be rewritten in form
$$
\partial^{2}_{\rho}\kappa + \frac{2m\alpha}{r}\kappa - \frac{l(l + 1)}{\rho^{2}}\kappa = -E\kappa ,
$$
where $\kappa$ is $R(\rho)\rho$ and $R(\rho )$ is the radial part of Schrodinger equation.</p>
<p>So $\hat {H}\kappa = E \kappa$, and we may construct some $\hat {A}, \hat {B}$ operators, for which
$$
\hat {A} = \partial_{\rho} + \omega , \quad \hat {B} = -\partial_{\rho} + \omega, \quad \omega = \gamma + \frac{\beta}{\rho },
$$
and
$$
\hat {H} = \hat {B}\hat {A} + \epsilon = -\partial^{2}_{\rho} - \frac{2m\alpha}{r} + \frac{l(l + 1)}{\rho^{2}},
$$
from which it is possible to find $\gamma , \beta$.</p>
<p>I heard that this representation also can help to find the spectra and state functions, but I don't know why, because physical sense of introduced operators is incomprehensible for me.</p> | g12639 | [
-0.03143426403403282,
-0.09543833881616592,
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0.011646797880530357,
0.09973260015249252,
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-0.02653028443455696,
-0.0368746779859066,
-0.006039480213075876,
0.021372489631175995,
0.026... |
<p>Is there a general systematic procedure or approach to obtain the analytic functions $c_{ijk}$
as well as the corresponding operators $$A_i(z)$$ that appear in the operator product expansion (OPE)</p>
<p>$$
A_i(z)A_j(w) = \sum\limits_k c_{ijk}(z-w)A_k(w)
$$</p>
<p>for any given two operators $A_i(z)$ and $A_i(z)$? </p>
<p>I have followd (a limited number of) examples of OPE calculations that involved things like expanding until some correlators for which the expression is known appear and power series expansions of derivatives of operators, but from this I was not able to discern the general way to go. </p> | g12640 | [
0.0067855678498744965,
0.026024438440799713,
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0.0374312587082386,
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0.043386682868003845,
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0.003193735610693693,
0.044274814426898956,
0.... |
<p>If the sun is the hottest known thing to humans is it possible to have a temperature greater than the sun?</p> | g12641 | [
0.07573430985212326,
0.011892449110746384,
0.03026379831135273,
0.035398971289396286,
0.001668148091994226,
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0.010430860333144665,
0.005145098082721233,
0.0005441962275654078,
0.03777093440294266,
0.01... |
<p>As a condensed matter physicist, I take it for granted that a Fermi surface is <em>stable</em>.</p>
<p>But it is stable with respect to what? </p>
<p>For instance, Cooper pairing is known as an instability of the Fermi surface.</p>
<p>I'm simply wondering what makes the Fermi surface stable? </p>
<p>Possible way of thinking: Is it a topological property of the Fermi gas (only of the free one ?, only robust against disorder?)? What is the modern, mathematical definition of the Fermi surface (shame on me, I don't even know this, and all my old textbooks are really sloppy about that, I feel)? What can destroy the Fermi surface, and what does <em>destroy</em> mean? </p>
<p>Any idea / reference / suggestion to improve the question is welcome.</p>
<p><em>Addenda / Other possible way to discuss the problem:</em> After writing this question, I noted <a href="http://physics.stackexchange.com/a/5742/16689">this answer by wsc</a>, where (s)he presents a paper by M. Oshikawa (2000), <em>Topological Approach to Luttinger’s Theorem and the Fermi Surface of a Kondo Lattice</em> <a href="http://dx.doi.org/10.1103/PhysRevLett.84.3370" rel="nofollow">PRL <strong>84</strong>, 3370–3373 (2000)</a> (available freely on <a href="http://arxiv.org/abs/cond-mat/0002392" rel="nofollow">arXiv</a>), and a paper by J. Luttinger & J. Ward <em>Ground-State Energy of a Many-Fermion System. II.</em> <a href="http://dx.doi.org/10.1103/PhysRev.118.1417" rel="nofollow">Phys. Rev. <strong>118</strong>, 1417–1427 (1960)</a>. An other interesting reference to start with is a paper by J. Luttinger, <em>Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions</em>, <a href="http://dx.doi.org/10.1103/PhysRev.119.1153" rel="nofollow">Phys. Rev. <strong>119</strong>, 1153–1163 (1960)</a>, where he shows (eq.33) that the volume of the Fermi surface is conserved under interaction, using analytic properties of the Green function including the self-energy as long as the total number of particles is conserved. I'm not sure if it's sufficient to proof the <em>stability</em> of the Fermi surface (but what does <em>stability</em> means exactly, I'm now confused :-p ) Is there absolutely no modern (topological ?) version of this proof ?</p> | g12642 | [
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-0.04186895862221718,
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0.012218618765473366,
0.02286270260810852,
0... |
<p>In "String theory and M-theory" (K. Becker, M. Becker and H.Schwarz) page 81, they said that among the background fields, the fields associated with massless bosonic fields are especially significant. My question is, why is that? What's the most general form for the action in bosonic string theory with background theory if all fields are included?</p>
<p>Thank you!</p> | g12643 | [
0.07043614983558655,
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0.04748614877462387,
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0.0262... |
<p>In history class in elementary school I remember learning that the Greeks would build their stone columns hollow because they thought this provided more support. Is it true that a hollow column is stronger? Thanks!</p> | g12644 | [
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0.015117461793124676,
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0.010418047197163105,
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<p>What I know so far:
- Charges (electrons) inside a conductor will repel (Coulomb's law).
- The charges will experience repulsion which results in maximum separation distances between the charges.
- The charges will then redistribute along the surface of the conductor in order to achieve electrostatic equilibrium (ie. net force of zero on each charge)
- Thus, no electric field exists inside the conductor.</p>
<p>Please feel free to correct me if I am wrong in any of the above statements.</p>
<p>Appreciate the help. Thanks.</p> | g12645 | [
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0.009277451783418655,
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-0.03... |
<p>Consider the ray model of light. Let's say an object such as a pencil is illuminated, and consider one point on that pencil. Since there could be many rays of light bouncing off the same point on the pencil, one ray could hit the left side of your eye and another ray from the same point could hit the right side of that same eye. Why don't you see that point in 2 different places then? Thanks!</p> | g12646 | [
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0.07648614794015884,
-0.016... |
<p>The drag force on a spherical body according to <a href="http://en.wikipedia.org/wiki/Stokes%27_law" rel="nofollow">Stokes' law</a> is given by</p>
<p>$$F = 6π\mu rv$$
Where $\mu$ is the dynamic viscosity of the fluid, $r$ is the radius of the spherical object, and $v$ is its velocity.</p>
<p>At low speeds, the drag force is directly proportional to the speed of the object. While at high speeds, the <a href="https://en.wikipedia.org/wiki/Drag_%28physics%29" rel="nofollow">drag force</a> is proportional to the square of the speed of the spherical object:</p>
<p>$$F = \frac{1}{2}\rho v^2C_dA$$</p>
<p>Why does this happen?</p> | g401 | [
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0.008358710445463657,
0.042810115963220596,
0.00... |
<p>The correlation function g1 is pretty easy to understand and the relation to young's double slit experiment is also clear to me. </p>
<p>In every quantum optics book I read so far correlation functions $g^n(x_1, ... , x_{2n})$ of an order greater than 1 are defined, but not related to an experiment or explained any further.</p>
<p>What is an example for an experiment that requires a correlation function of a higher order?</p>
<p>In my understanding $g^1(x_1,x_2)$ gives the similarities between two functions for different $\tau$. How is this possible for more than one function, if $g^n(x_1,...,x_{2n})$ is still scalar?</p>
<p>The definitions I used can be found in any book an quantum optics or here <a href="http://www.matthiaspospiech.de/files/studium/skripte/QOscript.pdf" rel="nofollow">http://www.matthiaspospiech.de/files/studium/skripte/QOscript.pdf</a> (p 64)</p> | g12647 | [
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0.04168272390961647,
0.038773223757743835,
... |
<p>For example, consider the $\phi^3$ theory in $d=8$, with Lagrangian: </p>
<p>$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}-\frac{1}{3!}\lambda_{3}\phi^{3}$.</p>
<p>In 8 dimensions, the box diagram now diverges. We would need to add a $\lambda_{4}\phi^{4}$ coupling to our Lagrangian. Then, this box divergence is thought of as the one-loop correction to our 4-point vertex.</p>
<p>Now, what if the $\phi^4$ term was not allowed in our Lagrangian due to some symmetry constraints? Can we argue that we wouldn't see the box divergence in the first place? That the same symmetry forbids the divergence?</p>
<p>This is not terribly realistic, but if you look at 't Hooft and Veltman's 1-loop Gravity paper, we see that we can't write down a counterterm due to Gauss-Bonnet. Could we stop there and immediately say that there will be no 1-loop graviton divergence without even calculating?</p>
<p>Punchline: No allowed counterterm $\Rightarrow$ No relevant divergence?</p>
<p>Edit: Here's a more relevant example: <a href="http://www.conferences.itp.phys.ethz.ch/lib/exe/fetch.php?media=qg11:ld.ethz.qg.pdf" rel="nofollow">http://www.conferences.itp.phys.ethz.ch/lib/exe/fetch.php?media=qg11:ld.ethz.qg.pdf</a>. Check out slides 6 and 7. It argues that in SUGRA at two loops in 4 dimensions, the only possible counterterm, $R^3$, "cannot be supersymmetrized." He implies that it follows that no divergence is allowed at two loops; however, at three loops, since we can write down a $R^4$ counterterm, a divergence is allowed but not necessarily present.</p>
<p>Edit 2: Signs seem to be pointing me to the BPHZ Theorem. Weinberg (Vol. 1, Chapter 12) says, "...the cancellation of ultraviolet divergences does not really depend on renormalizability; as long as we include every one of the infinite number of interactions allowed by symmetries, the so-called non-renormalizable theories are actually just as renormalizable as renormalizable theories." The disconnect may be coming when I try to relate the BPHZ subtractions method to the counterterm method, which appears to be explained in <a href="http://prd.aps.org/abstract/PRD/v25/i2/p392_1" rel="nofollow">http://prd.aps.org/abstract/PRD/v25/i2/p392_1</a>.</p> | g12648 | [
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0.... |
<p>There is a question regarding basic physical understanding. Assume you have a mass point (or just a ball if you like) that is constrained on a line. You know that at $t=0$ its position is $0$, i.e., $x(t=0)=0$, same for its velocity, i.e., $\dot{x}(t=0)=0$, its acceleration, $\ddot{x}(t=0)=0$, its rate of change of acceleration, $\dddot{x}(t=0)=0$, and so on. Mathematically, for the trajectory of the mass point one has</p>
<p>\begin{equation}
\left. \frac{d^{n}x}{dt^n}\right|_{t=0} = 0 \textrm{ for } n \in \mathbb{N}_0\mbox{.}
\end{equation}</p>
<p>My physical intuition is that the mass point is not going to move because at the initial time it had no velocity, acceleration, rate of change of acceleration, and so on. But the mass point not moving means that $x(t) \equiv 0$ since its initial position is also zero. However, it could be that the trajectory of the mass point is given by $x(t) = \exp(-1/t^2)$. This function, together with all its derivatives, is $0$ at $t=0$ but is not equivalent to zero. I know that this function is just not analytical at $t=0$. My question is about the physical understanding: How could it be that at a certain moment of time the mass point has neither velocity, nor acceleration, nor rate of change of acceleration, nor anything else but still moves?</p> | g12649 | [
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-0.010239939205348492,
0.08220356702804565,
-0.016... |
<p>I can't really understand why two higgs doublets are required in SUSY. </p>
<p>From the literature, I have found opaque explanations that say something along the lines of: the superpotential W must be a holomorphic function of the chiral supermutiplets and thus we need to introduce another chiral supermutiplet.</p>
<p>I also know that this is somehow related to an anomaly cancellation. Can somebody help to make this a bit more clear?</p> | g12650 | [
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0.06507734954357147,
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-0.0005364372627809644,
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0.003705272451043129,
0... |
<p>If gravity can be thought of as both a wave (the gravitational wave, as predicted to exist by Albert Einstein and certain calculations) and a particle (the graviton), would it make sense to apply quantum mechanics (which I understand only applies to mass/energy) and therefore wavefunction collapse to gravity? In other words, does gravity exhibit wave-particle duality as light does, and thus is it susceptible to wavefunction collapse? If so, what would the implications of the wavefunction collapse of a gravitational wave be?</p>
<p>To better sum up my question: could a gravitational wave be described as a wavefunction?</p>
<p>I would appreciate it if anyone could help me understand if this is a valid concept, or if there are any other theories and concepts that would help me understand gravity and quantum mechanics combined (quantum field theory?).</p> | g12651 | [
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0.03127053380012512,
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0.0603138767182827,
0.05... |
<ol>
<li><p>What is <a href="http://en.wikipedia.org/wiki/Background_independence" rel="nofollow">background independence</a> and how important is it?</p></li>
<li><p>In order to be a theory of everything, will the final string-theory/m-theory have to be background independent? </p></li>
<li><p>Does the current lack of background independence show string theory is currently <em>NOT</em> a theory of everything? </p></li>
</ol>
<p>My understanding from Wikipedia is that the ADS/CFT shows hopeful hints. Are there any recent papers that have made progress in this direction?</p>
<p>I've tried google but get haven't been able to get a definitive answer to this question.</p>
<p>I found <a href="http://motls.blogspot.com/2005/07/background-independence.html" rel="nofollow">this</a> interesting post by Lubos Motl, but it is from 2005.</p> | g12652 | [
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0.01789562590420246,
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<p>Can all of the predictions made in <a href="http://en.wikipedia.org/wiki/Special_relativity" rel="nofollow">Special Relativity</a> (SR) also be made in <a href="http://en.wikipedia.org/wiki/General_relativity" rel="nofollow">General Relativity</a> (GR)?</p> | g12653 | [
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0.0362163744866848,
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<p>One of the major reasons SUSY was adopted in particle physics is to Naturally have a Higgs boson (a fundamental scalar) at the weak scale. </p>
<p>If we abandon this argument, what other motivation for low-scale ($\mathcal{O(1)}$ TeV) SUSY exists? </p> | g12654 | [
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-0.06151833385229111,
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0.011588022112846375,
0.03769312798976898,
0.08737... |
<p>I understand (supposedly) the mathematics concerning the relativity of simultaneity in Special Relativity, but I have a nagging question regarding the original example given by Einstein supporting it (I'm only disagreeing with this specific example, not the concept).</p>
<p>It is normally given as a person on an embankment and a person on a train. There is a relative speed between them (usually presented as the train passing the embankment). Now, when both people are at the same x-position (x=0), there is a flash of light at x = +dx and x = -dx. The argument as I keep seeing it is that the person on the embankment will say that both flashes reach him at the same time, whereas the person in the train will say that the flash in front of him reaches him before the other because he was moving toward it, and thus the observers will disagree on the simultaneity of the flashes.</p>
<p>But given that the flashes occurred at the same distance from each of them, the speed of light is constant in both frames, and either one can claim to be at rest, then won't they, according to SR, necessarily see the flashes as simultaneous (both flashes have to travel the same distance in both frames since at the time of emission, the sources of both flashes were equidistant from both observers). I agree that the person on the embankment will say that the person on the train shouldn't see them as simultaneous (and vice versa) since either observer will see the other moving relative to the sources, but in each of there own frames, they must see the flashes as being simultaneous shouldn't they? Am I just misunderstanding the example?</p>
<p>Thanks.</p> | g12655 | [
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<p>I'm now studying Quantum Mechanics, and I took a course on Vibration and Waves last year.
I have been trying to make an analogy between classical and the quantum waves.
Is it true that both the modes of a quantum and classical wave can not be excited individually?</p>
<p>Whenever you pluck a classical string, its motion can be described as a superposition of many different modes , n=1,2,3... you can never excite a single mode.</p>
<p>In analogy, can we say that whenever you try to measure the wave function, the
measured value will be a composition of different eigenvalues?</p>
<p>Any ideas or contributions much appreciated.</p> | g12656 | [
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<p>In non-relativistic QM, does it make a difference if an energy shift is applied to the systems's Lagrangian or Hamiltonian?</p> | g402 | [
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-0.0212517362087965,
0.0... |
<p>I've seen many applications of topology in Quantum Mechanics (topological insulators, quantum Hall effects, TQFT, etc.) Does any of these phenomena have anything in common?</p>
<p>Is there any intuitive explanation of why topology is so important? </p>
<p>Is there a similar application of topology in Classical Mechanics?</p> | g12657 | [
0.035004571080207825,
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0.04839088022708893,
0.0189... |
<p>After working in air fed suits,operatives are required to give samples from their nasal passages by blowing their nose into a tissue,which is then counted in a noseblow counter. How does this work?</p> | g12658 | [
0.00014804763486608863,
0.0022014868445694447,
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0.013854427263140678,
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0.018246768042445183,
-0.049722325056791306,
0.002214775187894702,
-0.0016043708892539144,
0.03163808956742287,... |
<p>When matter is condensed the mass stays the same and we also know that only the volume and density are the only other two effected variables. But is there a point in which the matter cannot condense anymore? Or a point in which the volume cannot decrease anymore?</p> | g12659 | [
0.02056107670068741,
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0.002788188634440303,
0.014593309722840786,
0.03316742926836014,
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0.005759924650192261,
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0.... |
<p>Let's imagine that there is a lamp on the floor. There is a dice on that same floor casting a shadow from our light source, the lamp. Why is it that there are different shades of the shadow phasing from darkest to dullest (darkest being closest to dice and dullest being farthest)?</p> | g12660 | [
-0.012332978658378124,
0.007358618546277285,
0.005567430984228849,
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0.0439426563680172,
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0.0525... |
<p>Let's say I have two planets that are one hundred thousand lightyears away from each other. I and my immortal friend on the other planet want to communicate, with a strong laser and a tachyon communication device.</p>
<p>I record a message on the tachyon communication device and release the message at exactly the same time as I activate the laser, both of which are directed to the other planet which is one hundred thousand lightyears away. Say it is the year 0 for both of us at the time I did this.</p>
<p>If tachyons existed, then the message would arrive to my friend before the photons in the laser. It would arrive, say, a thousand years earlier. From my vantage point, that message will arrive to her at year 99,999; the same would be true for my friend's vantage point. However, she will only see the laser at year 100,000.</p>
<p>So since she got the message at year 99,999, she immediately sends me a reply back going through the same procedure as I did. She records a message and releases it at the same time as the laser. The tachyons will arrive 1,000 years earlier than the laser, so for me, I will receive the message at year 199,998. I will receive the laser, however, at year 199,999.</p>
<p>It seems to me that communication this way does not violate causality. I will still have received the message after I had sent it. </p>
<p>If tachyons truly violated causality, though, I realize it should arrive at year -1 for her, and so she can reply to me at year -2, which would mess me up by year 0 as I will ask her how she knew I was planning on sending her a message before I sent it. I could send her a different message, which she would end up receiving at year -1, and will end up confusing her as she would have received one message asking her out, and the other asking her how did she know I was asking her out. She then decides I am crazy and sends me a message at year -2 that she does not want to date me, and so she will have both turned me down and entertained me before I have even asked her out.</p>
<p>On the other hand, let's go back to year 0 and add a third device to our list: an Alcubierre drive. After I send out the message and the laser, I get impatient and do not feel like waiting 99,999 years, so I get on my Alcubierre drive spaceship and arrive on her planet at the same year 0. My friend is not in her office, so I leave a note to her also immortal secretary saying I dropped by and that she should expect a message for her in year 99,999.</p>
<p>I then get back on my Alcubierre drive and land back on my planet, still on year 0. Meanwhile, the tachyons and photons I sent out are still racing to arrive to her. By year 99,999, she receives the message just as I Alcubierre drive back to her, and I pick her up for dinner.</p>
<p>But the point of my question is, it seems to me that just going faster than light, if that alone was what you had, would not violate causality. It must be something else. I understand time dilation and that things with mass cannot travel at the speed of light, but using the Alcubierre drive, hypothetically speaking, I was still able to outpace the photons while also having mass. It still did not produce causality problems. Alcubierre drives are also valid solutions to GR.</p>
<p>It seems circular to me to say that what makes traveling faster than light violate causality is because it violates causality (if faster than light communication was divorced from causality problems, then the causality problem would cause itself -- thereby violating causality and, hence, we would scrap it and conclude that there is no causality problem after all).</p>
<p>What is it that I am missing? If someone could help me out, that would be excellent. I've been itching to ask my friend out for a few millenia now. :)</p> | g12661 | [
0.053320176899433136,
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0.02127... |
<p>Is it theoretically possible to create some system such that the energy distribution creates a gravitational potential offset from its center of mass (or energy?) so that the body continually 'falls' into its own potential (i.e., as the body moves, the center of the potential moves with it such that it constantly falls forward)? I get the feeling that this doesn't make sense in the context of GR so I'd like to know why (I'm trying to understand the frame dependance of gravitational effects).</p> | g12662 | [
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0.005184017587453127,
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0.020283205434679985,
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<p>The wiki article states that <a href="http://en.wikipedia.org/wiki/D%27Alembert%27s_principle" rel="nofollow">D'Alembert's Principle</a> cannot derived from Newton's Laws alone and must stated as a postulate. Can someone explain why this is? It seems to me a rather obvious principle.</p> | g12663 | [
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<p>First let me clarify what I mean by vacuum.</p>
<p>Suppose we are concerned with a theory of fields $\phi ^i$ defined on a stationary globally hyperbolic spacetime $M$ (I want the spacetime to be stationary so that I have a canonical choice of time-derivative and I want the spacetime to have a Cauchy surface so that I can speak of the Lagrangian) by an action functional $S(\phi ^i)$. For $\phi ^i$ stationary (i.e. $\dot{\phi}^i=0$), we define the potential by $V(\phi ^i):=-L(\phi ^i)|_{\dot{\phi}^i=0}$, where $L$ is the Lagrangian of $S$.</p>
<p>A <em>classical vacuum</em> (the definition of quantum vacuum is a part of the question) of this theory is a solution $\phi _0^i$ to the equations of motion $\tfrac{\delta S}{\delta \phi ^i}=0$ such that (1) $\phi _0^i$ is stationary and (2) $\phi _0^i$ is a local minimum of $V(\phi ^i)$ (by this, I mean to implicitly assume that $V(\phi ^i)<\infty$).</p>
<p>In what way do these vacuum solutions of the classical equations of motion correspond to quantum vacuums? For that matter, <a href="http://physics.stackexchange.com/questions/75834/the-vacuum-in-quantum-field-theories-what-is-it">what is a quantum vacuum</a>? In particular, I am interested in theories with interesting space of vacua, for example, how $SU(3)$ instantons relate to the <a href="http://en.wikipedia.org/wiki/QCD_vacuum" rel="nofollow">QCD vacuum</a>.</p> | g12664 | [
0.0466582328081131,
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0.0645... |
<p>What equations to use on this system to form a matrix $A$ with dimensions $[n,n]$ and load vector $q$ with dimension $[n]$ ? I am trying to get vertical displacement $w$.</p>
<p>$$w = A^{-1}\times q$$</p>
<p>Boundary conditions are as follows:
$$w(o) = 0 $$
$$w(L) = 0 $$
$$\phi(o) = 0$$
$$\phi(L) = 0$$
It is becouse in any point of beam I can't make equation: $$d^2y/dx^2*E*I=M=0$$ so I can't get the exact values of displacement. The problem is that everywhere I look for solution it is done on a beam with continous load over entire beam or with at least one joint and I have only half of the beam covered with continous load and no joints.</p>
<p>From $d^4y/dx^4*E*I=q=0$ again I have too many unknown values.</p>
<p><img src="http://imgur.com/YkIdCAI.jpg" alt="Scheme"></p> | g12665 | [
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0.007369298487901688,
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-... |
<p>What are the ways electrostatic charged objects leak charge in humid conditions?</p>
<p>Can airborne particles pick up charge by contact, then be repelled hence removing charge? If so would it be a significant factor?</p> | g12666 | [
0.055089496076107025,
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<p>Lets say I have two cars.<br>
They are identical in every way, except that Car A has a normal breaking system, where most of the breaking power is inflicted on the front wheels, and some on the back, and Car B has a breaking system where all of the power is inflicted on the front wheels and none on the back. </p>
<p>In the long run, in which car will the tires on the back wheels experience more wearing?<br>
(For the sake of comparison, let's say we measure wear by the weight lost from the tires.)</p> | g12667 | [
0.055674873292446136,
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0.026545213535428047,
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<p>Imagine $N$ oscillators with only two possible energies, $\epsilon_0$ and $ \epsilon_1$, with $\epsilon_1 > \epsilon_0$. Taking $\epsilon_0 = 0$ for now</p>
<p>I showed $\Omega(q\epsilon_1) = \frac{N!}{(N-q)!q!}$ and then</p>
<p>$$\frac{\partial S}{\partial q} = k \log(N/q - 1) $$</p>
<p>How can I use the above equation to show that</p>
<p>$$U = N\epsilon_1\frac{e^{-\epsilon_1/(kT)}}{1+e^{-\epsilon_1/(kT)}} $$</p>
<p>I tried moving the $\partial q$ over to the right, and then have $dS = dU/T$, but i wasn't getting anything meaningful.</p> | g12668 | [
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0.04924224689602852,
0.04680657014250755,
0.0... |
<p>Why is the light speed a limit? Why can't anything go faster than light? Not even a single atom?</p> | g109 | [
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0.0195... |
<p>Is there a fast and convenient way of calculating the neutron stopping power of materials, consisting of multiple elements (e.g. doped crystals) without the need for Monte Carlo Simulation, that is more exact than simple cross-section additivity?</p> | g12669 | [
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... |
<p>In the Shockley diode equation, why the exponential $\exp$ and the ideality factor $n$ are there? What do they represent & what is their significance?</p>
<p>I have to work on Solar Photovoltaics, and I need to understand the <a href="http://en.wikipedia.org/wiki/Diode#Shockley_diode_equation" rel="nofollow">Shockley diode equation</a> clearly. </p> | g12670 | [
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0.07700669020414352,
0.05304... |
<p>I've been attempting to calculate how much torque a motor needs to produce in order to start a stationary object on wheels moving. (The torque is being applied to the rear 2 wheels, the front 2 are on bearings.)</p>
<p>I keep seeing Torque = Force * Radius (of the torqued wheel). I can't figure out how to calculate the Force in this equation though, so that I may find the Torque.</p>
<p>The radius of the wheel is 3cm.</p>
<p>The weight of the entire object (including wheels and everything else) is 5kg.</p>
<p>I don't need an incredibly accurate result, so I haven't even been trying to factor in friction from the non-powered front wheels' bearings. </p>
<p>I tried something with a friction coefficient and gravity, but the more I read the less I believe that my calculation was correct.</p>
<p>Can anyone point me in the right direction?</p> | g267 | [
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0.020049892365932465,
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0.01829129457473755,
0.0... |
<p>Plenty of research activity in physics have been vigorously opposed by their opponents as pseudoscience or fringe science, while other research are mainstream. It is possible some topic is pseudoscience if the experts claim it is so, but they could potentially be biased. For the nonexperts out there, short of appealing to authority, what objective criteria can be used to distinguish between valid science, fringe science and pseudoscience, i.e. topics which are a waste of time compared to topics worth pursuing.</p> | g12671 | [
0.03156888857483864,
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0.0125515... |
<p>I'm having some trouble understand what the difference is between these two.
It seems as though there are kind of the same, but that spin-orbit coupling reduces to LS coupling under certain circumstances.</p>
<p>But, I can't seem to make sense of it. So I was hoping anyone could explain the difference briefly, and maybe explain when you use one of them, instead of the other.</p>
<p>Thanks in advance.</p> | g12672 | [
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0.024863053113222122,
0.04360406845808029,
... |
<p>In my math course we're taught to solve PDE (partial derivative equations) like transport equation:
$$
c\frac{\partial u}{\partial x} +\frac{\partial u}{\partial t}~=~0.
$$</p>
<p>If $u(x,t)$ is the quantity transported and $c$ has speed dimension (according to my book), $\frac{\partial u}{\partial t}$ must be speed too. What does $\frac{\partial u}{\partial x}$ represent? Does anybody have a good physical example to help me understand?</p> | g12673 | [
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<p>When I was in school, I learned (from Democritus) that an atom was
similar to a solar system, with the nucleus being the sun, and the
electrons being the planets. Of course, there are some differences: </p>
<ul>
<li><p>The "sun" isn't a single entity, but a collection of protons and nuetrons. </p></li>
<li><p>Two planets can share an orbit (which might be possible in a solar
system too, but it doesn't happen in our solar system). </p></li>
</ul>
<p>Is this model still valid? Here are my problems with it: </p>
<ul>
<li><p>In "Surely You're Joking, Mr Feynman", Richard Feynman implies
that electrons are more a theoretical concept than real objects. </p></li>
<li><p>I have trouble understanding atomic bonds (ionic and covalent) in
this model. </p></li>
<li><p>I also have trouble understanding electron "orbit jumping" in this
model, as well as several other things. </p></li>
</ul>
<p>Is there a better model for someone learning this for the first time? </p> | g12674 | [
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0.00826507993042469,
-0.028591353446245193,
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0.09009125083684921,
-0.0306929... |
<p>first my actual problem. then my try on improving the current way of solving this with the wish for feedback or even a solution :)</p>
<p>gpx file with lat/long, elevation and time. wanna calculate speed... easy! when visualizing the speed on a chart you would figure it needs a little smoothing. done you have a pretty accurate speed, average-speed, max-speed...</p>
<p>...but i want more ;)</p>
<p>1) the coordinates are from an object that is adjusting there direction in a more or less smooth/curved fashion (aka. car, bike,...). thus smoothing the path would/could be nice. right? maybe something like a Bézier curve? but the path should still follow thru the actual measured points. any ideas?</p>
<p>2) smoother path would be generated by creating more points...right? so how do i split the time to the newly create points along the path in a similar way (so the new points along the path are timed like the measured ones)?</p>
<p>3) as long as the resulting data isn't less accurate i'm happy with it. still, feedback about how much or little improvement those calculations might bring are highly appreciated.</p>
<p>thx.</p> | g12675 | [
0.013950511813163757,
-0.02895205095410347,
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0.001261030207388103,
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-0.001986967632547021,
0.04085339605808258,
0.018779346719384193,
0.0974358543753624,
0.01357... |
<p>Is it just a historical choice that both magnetic field and the Lorentz force equation include the speed of light?
I figure that whoever wrote up the equations (in cgs!) could have put both factors of $c$ in either the force equation, or have define the magnetic field as being smaller by a factor of c- but they didn't.
Any ideas why? </p> | g12676 | [
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0.0202321894466877,
0.009... |
<p>We’re told that ‘all forces are gauge forces’. The process seems to start with the Lagrangian corresponding to a particle-type, then the application of a local gauge symmetry leading to the emergence of the force bosons via the associated symmetry group.</p>
<p>But where did <em>exactly four forces</em> come from? Could new, perhaps supersymmetric particles hint at new fundamental forces? Is there a deeper theory which predicts what final set of forces we’ll eventually end up with?</p>
<p>Finally, is the concept of force in unified physics really that fundamental at all?</p> | g12677 | [
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-0.017153387889266014,
-0.023751119151711464,
0.027449721470475197,
-0... |
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