question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>For small thicknesses of wire, it's pretty obvious why resistance affects thickness. (The electronics squeeze to get through). But after a certain thickness shouldn't the thickness become irrelevant?</p>
<p>For example if your trying to pour a bucket of water through a straw, the thickness of the straw is obviously gonna be a bottle neck- the bigger the straw, the easier it is for water to get through.</p>
<p>But if you try to pour a bucket of water through a tunnel - the size of the tunnel doesn't really matter, because the tunnel is already big.</p>
<p>So after a certain thickness shouldn't the thickness stop mattering?</p> | g11479 | [
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<p>A picture in my text book shows a three dimensional wave packet dispersing, "resulting from the fact that the phase velocity of the individual waves making up the packet depends on the wavelength of the waves."
Does this mean a particle moving through space has a gradually diminishing probability of being in it's location? Also, why does the wavelength of the the wave change the speed for a probability wave? I thought the dispersion was characteristic of the medium, and I thought for things like vacuums&light, air&sound, and also probability waves and space, that they wouldn't disperse.</p> | g11480 | [
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<p>I have a measurement method for which I want to study the measurement error by an error budget. Therefore, I listed all possible errors (error sources) (lets say $x_1, x_2, x_3,\ldots$). For each error $x_i$, I have derived an analytical expression from which I can calculate the resulting measurement error $\epsilon_i$. To calculate the total measurement error epsilon, I specified an interval for the possible values of each error value $x_i$ and performed an Monte-Carlo simulation calculating the measurement error $\epsilon_i$ 100.000 times for each error $x_i$. This means that I have 100.000 error values $\epsilon_i$ for each $x_i$. From this data I can calculate the standard deviation $\sigma_i$ of each measurement error $\epsilon_i$. However, I am interested in the total measurement error epsilon, not in the independent measurement errors $\epsilon_i$. How can I combine each measurement error $\epsilon_i$ to come to the total measurement error $\epsilon$? Suppose the errors $x_i$ are independent.</p> | g11481 | [
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<p>Let $\mathcal N^{A_1\rightarrow B_1}_1,..,\mathcal N^{A_1\rightarrow B_1}_k$ be a set of valid quantum evolutions with equal input and output dimensions. And let the effect of a channel on a system $\rho_{A_1A_2}$ be: </p>
<p>$$\mathcal N^{A_1A_2\rightarrow B_0B_1}(\rho_{A_1A_2})=\int dB_0|b_0\rangle\langle b_0|\otimes\sum_ip_i\mathcal N^{A_1\rightarrow B_1}_i(\rho_{A_2})$$</p>
<p>where $B_0$ is a random basis which is given as output and $p_i=tr(B_0^i\rho_{A_1})$ is the probability of obtaining outcome $i$ after measuring the system $A_1$ in the $B_0$ basis. </p>
<p>If the maps $\mathcal N^{A_1\rightarrow B_1}_1,..,\mathcal N^{A_1\rightarrow B_1}_k$ are random unitaries, I have seen without proof that the optimal input for the coherent information, is a product state between $A_1$ and $A_2$, does anyone know how to prove it? Is that also true for general channels, i.e. non random unitaries?</p> | g11482 | [
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<p>Okay, my buddy tells me this:</p>
<p>Let there be a starship, ovoid, and me and my buddy stand each at the extremities of the ship, him below the roof, me on the floor.</p>
<p>We start a journey and the ship accelerates at a constant rate, let's say $1g$, in the direction of the axis of the ship.</p>
<p><em>My buddy says</em>: since the ship is accelerating, when he strobe (on off on off) a light from the room, back to me, at a frequency $F$, I'll see a shifted frequency $F' = F + \delta f$.</p>
<p>If he switches the light at $1Hz$, I'll see $1.01Hz$ for instance.</p>
<p><em>My take on the thing</em> tells me that in this case, there's no shift: we're both immobile in our referential, and the light will travel at $c$ in this referential. </p>
<p>Who's wrong?</p> | g11483 | [
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<p>Since neither the object nor its field could exist without the other, it would seem strange not to include the field energy as part of the object. But how exactly does the accounting go? How is the mass of the system divided between the rest mass and the field mass?</p>
<p>For a Schwarzschild black hole, the mass appears to be shifted completely to the field.</p>
<p>According to Lynden-Bell and Katz, <a href="http://adsabs.harvard.edu/full/1985MNRAS.213P..21L" rel="nofollow">http://adsabs.harvard.edu/full/1985MNRAS.213P..21L</a>, the total energy distributed in the gravitational field of a Schwarzschild black hole is mc^2. In other words, <em>all</em> the mass of the black hole resides outside the event horizon. </p> | g11484 | [
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<p>If you strip the valence electrons apart with a very short intense electromagnetic field the remaining core explodes in a so called coulomb explosion.</p>
<p>But experiments have shown that under certain cases fusion does occur in a manner, that the ions are accelerated and you get a non maxwellian velocity distribution. Can you explain the process a little bit more and show how it is possible to overcome the nuclear repulsion for fusion?</p>
<p>The wikipedia page to this topic is a little bit missleading, so I give you a paper <a href="http://pra.aps.org/abstract/PRA/v80/i5/e051201" rel="nofollow">Efficient fusion neutron generation from heteronuclear clusters in intense femtosecond laser fields</a> that this kind of fusion is indeed possible and experimentally proven.</p> | g11485 | [
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<p>How much charge is on each plate of a 4.00-F capacitor
when it is connected to a 12.0-V battery?</p>
<p>I said 2.4 x 10^-5 C because there are two plates of a parallel plate capacitor. But the key said only 4.8 x 10^-5 C</p>
<p>Why?</p> | g11486 | [
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<p>This is a school exercise.</p>
<p>We tend to think that the action of a constant force produces a constant movement speed as well. How can you explain this situation in accordance with Newton's second law?</p>
<p>Because as the force will end up in a certain time that means there will not be a movement of constant speed; I'm correct?</p> | g11487 | [
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<p>In the derivation of drift velocity I have seen two variations and want to know which one's correct.</p>
<ul>
<li><p>$s=ut+\frac{at^2}{2}$<br>
Assume that the drift velocity of any electron in any conductor is :
$$\vec{v_d}=\frac{\vec{l}}{t}$$
Due to the electric field the acceleration of electrons in any conductor is:
$$a=\frac{-e\vec{E}}{m}$$
Now the distance travelled by an electron after a long time (initial thermal velocity = 0)
$$l=\frac{at^2}{2}\implies \frac{-e\vec{E}t^2}{2m}$$
the time between the collisions is $\tau$ $\therefore$ $$l=\frac{-e\vec{E}\tau^2}{2m}$$
thus the velocity is $$\vec{v_d}=\frac{-e\vec{E}\tau}{2m}$$</p></li>
<li><p>In another proof I saw the author using $v=u+at \implies v_d=\frac{-e\vec{E}\tau}{m}$</p></li>
</ul>
<p>My question is which of the the two equations of motion can be used in the proof? Can they be used at all.</p> | g11488 | [
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<p>When I see a new accelerator in real life or on a picture, I always find it interesting to see how many thing I can recognize. In that way, I can also get a small first idea of how the accelerator is working.
Here is a picture, I have taken of LEIR at CERN<img src="http://i.stack.imgur.com/d8t7B.jpg" alt="LEIR"></p>
<p>Help me to be able to recognize even more stuff, than I can now(I will post a few answers myself)</p>
<p>Suggested answer form:</p>
<ul>
<li><p><strong>Title</strong></p></li>
<li><p><strong>Images</strong></p></li>
<li><p><strong>One line description</strong></p></li>
<li><p><strong>Link</strong></p></li>
</ul> | g11489 | [
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<p>I'm suppose to write out reactions where atoms send out alpha radiation and decay. The book uses the 4-2 H, 4 as nucleon number and 2 as proton number, but isn't that wrong? The mass of helium is greater than the alpha particle due to two electrons? Shouldn't they use a different notation for the alpha-particle other than that for helium? </p> | g11490 | [
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<p>The binding of quarks in mesons baffles me. It's an Occam's Razor thing.</p>
<p>Since a meson is a colorless, the simplest way to bind its two quarks together is to use a $U(1)$ Cartan subalgebra of $SU(3)$. That is, the two quarks would bind by exchanging only gluons whose color and anticolor components cancel out.</p>
<p>But if those were the only types of gluon exchanges occurring in a meson, then the color and anticolor of the two quarks in the meson would remain unchanged and persistent over time. That in turn would imply the existence of three orthogonal "varieties" or polarizations of meson, e.g. $r\overline{r}$, $g\overline{g}$, $b\overline{b}$ and their compositions. There are more elegant ways to say that in group theory, but if you picture all the possible ways of orienting a symmetric stick in 3D space you've already captured the idea quite nicely.</p>
<p>By Occam's Razor, nothing beyond Cartan subalgebra binding is needed to explain the existence of mesons. And if the time slice is small enough, I do not easily see how at least some degree of transient color polarization in mesons can be avoided, e.g. while they are "exchanging" a gluon.</p>
<p>So, by Occam's razor there must exist experimental evidence in particle physics proving that mesons are not color polarized, or at least that they change their color polarization very quickly indeed.</p>
<p>So, three questions:</p>
<ol>
<li><p>Does anyone know references or keywords for finding theoretical and experimental articles on meson color polarization, or why it does not exist? </p></li>
<li><p>If meson color polarization does exist, what studies have been done on the duration of color polarization in mesons?</p></li>
<li><p>If meson color polarization does exist, how are meson-to-meson interactions affected when mesons with similar or diverse color polarizations encounter each other?</p></li>
</ol>
<hr>
<p>Relevant past questions:</p>
<blockquote>
<p><a href="http://physics.stackexchange.com/q/66891/7670">What is the role of the color-anticolor gluons?</a></p>
<p><a href="http://physics.stackexchange.com/q/39666/7670">Does the color of a quark matter in a meson?</a></p>
</blockquote> | g11491 | [
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<p>I realize that the permittivity $\epsilon$ of a substance is easily calculated based on diffraction angles, but I am not satisfied with merely measuring it experimentally. I wish to understand its origin within the laws and equations of physics. I realize that it is a vector as demonstrated by the anisotropy of birefringence and $\epsilon$ also depends on wavelength. I did some reading in Griffiths' <em>Intro to Electrodynamics</em> p. 400-404:</p>
<blockquote>
<p><em>The dampened harmonic motion of electrons can account or the frequency dependance of the index of refraction, and it expains why $n$ is ordinarily a slowly increasing function of $\omega$, with occasional anomalous regions where it precipitously drops.</em></p>
</blockquote>
<p>Where $n$ is the index of refraction and $n=\frac{c k}{\omega}$. </p>
<p>I found some vague references to this phenomena as it relates to negative refraction. </p> | g11492 | [
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<p>My textbook and the following extract from feynman's lectures present the same idea regarding wavetrains and uncertainty in their wavelengths. Why is it that a wavetrain confined to some space has an uncertainty in its wavelength or the wave number? Is not a confined wave-train equivalent to a burst of successive pulses which can have a definite wavelength according to their origin or nature of origin. <img src="http://i.stack.imgur.com/goJ1e.png" alt="Extract"></p>
<p>Next, i understand that the De Broglie relation relates the uncertainty in wavelength to the uncertainty in momentum but what links the finiteness of the wave-train to the uncertainty in position?</p> | g575 | [
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<p>When magmas begin to crystallise, a first step is the formation of a crystal nucleus around an impurity (nucleation centre), whereby a few of the right atoms get together to form a speck of a crystal. I know that impurities are not always necessary for crystallisation to occur but I'm curious to know what these impurities are?</p> | g11493 | [
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<p>Electrostatic force between two charged particles depends on the magnitude of the charges and the distance between them. If the charges have mass $m$ and $m'$ then, what will be the total force including gravitational and electrostatics forces? Distance between them is $d$.</p> | g11494 | [
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<p>Can we treat any charge configuration as small point charges by using superimposition principle to derive electric fields, forces and other things ?</p>
<p>For example suppose we have a symmetrically charged cylinder, from the distance outside the cylinder, we can treat it like a line charge along the axis of the cylinder. We know that in the original charge distribution the charges do not sit together at 0 distance from one another, but when we consider it as a line charge we do not think about the quantisation therein; We treat the line charge as one continous thread of point charges placed at 0 distance from one another.</p>
<p>Back to my question, since this line charge is just an assumption, can we extend our assumption and treat it like individual point charges sitting next to each other, is there any limitation to this assumption ? </p> | g11495 | [
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<p>What is the "momentum" referred to in the energy momentum tensor from GR?</p>
<p>Is it $m\dot{x}$ or is it the canonical momentum $\frac{d}{dt} \left(\frac{\partial L}{\partial \dot{x}}\right)$</p>
<p>Also, I find it very difficult to think of the density and flow of momentum. Momentum is, to me, not an object that moves and has mass, but rather something which characterizes the mass and movement of objects. It is in the same category as things like velocity. So, if someone can explain the intuition behind attributing physical meaning to "momentum density" and "momentum flow," I appreciate it.</p> | g11496 | [
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<p>It's said that potential energy is "energy of position." If an object is sitting on a shelf five feet above the floor, its potential energy can be thought of as equal to the amount of energy that would be involved in it falling off the shelf and onto the floor.</p>
<p>Conservation says that energy is neither created nor destroyed, only transformed. Therefore, the potential energy of an object has to be absolute, a constant in some sense. But that makes me wonder. If a meteor is drifting through space, and it ends up caught in Earth's gravitational field (and is coming in at the right angle, etc,) it will fall to the surface of the Earth, converting potential energy into <a href="http://en.wikipedia.org/wiki/Tunguska_event" rel="nofollow">possibly a few megatons of kinetic energy.</a></p>
<p>On the other hand, if that exact same meteor were to meet the exact same fate, except the planet in question was Jupiter, which has much stronger gravity, the impact would therefore be much more intense. So how does that work? If the potential energy of the meteor in space is constant, how can it be determined?</p> | g11497 | [
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<p>I have read in a few books that all Brillouin zones have the same volume, and I can vaguely see how it works, but have not been able to think up a formal proof.</p>
<p>Help?</p> | g11498 | [
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<p>The more I learn about General Relativity, the more it seems like it isn't fully understood. It seems that before it's full consequences were exhaustively understood, not 10 years after its discovery, QM came on the scene and stole the limelight. Now it seems like a "boring" field without much funding, even though all but the most trivial and artificial types of solutions to the field equations are known. <a href="http://physics.stackexchange.com/a/35518/1247">Here</a>, for example, @Ron Maimon describes how classically a type of black hole allows solutions in which a particle can cross the event horizon, and then exit the event horizon at an earlier time, seemingly leading to causal paradoxes. It sounds like this is an issue that was never fully resolved. It seems the sort of very messy thing that, once properly understood, could lead to some very odd physical behavior.</p>
<p>Is it possible that all particles are just extremal black holes, and that Quantum Mechanics is just an emergent property of the solution to Einstein's field equations for the interactions between extremal black holes going backwards and forwards and time? Does something like Bell's inequality rule out this sort of idea?</p>
<p><strong>EDIT</strong>:</p>
<p>There are some papers purporting to do this. Mitchel Porter pointed out these:
<a href="http://iopscience.iop.org/1402-4896/40/6/004/pdf/1402-4896_40_6_004.pdf" rel="nofollow">McCorkle</a>,
<a href="http://arxiv.org/abs/gr-qc/0703150" rel="nofollow">Hadley</a></p>
<p>I also found:
<a href="http://arxiv.org/pdf/hep-th/9612045v3.pdf" rel="nofollow">McCorkle</a></p>
<p>And then there is Mendel Sachs who has written a number of books purporting to derive QM from GR.</p> | g11499 | [
0.02655981481075287,
0.04270614683628082,
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0.02086525969207287,
0.04284466803073883,
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0.031028790399432182,
0.024655885994434357,
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-0.0184599868953228,
0.016827382147312164,
0.0012405331945046782,
0.031146163120865822,
-0.005... |
<p>I am trying to produce graphene with few layers(<10) on a TEM-Grid. Until now I've been trying this with the scotch-tape-method with slight modifications. Unfortunately it requires a lot of time und there are often TEM-Grids without any flakes of the required thinness.</p>
<p>Is there a more efficient way to place graphene flakes having a size above $$ 150 \mu m * 150 \mu m $$
on a TEM-Grids? Is there a better quality of graphite blocks on the market than the SPI-1 quality?</p> | g11500 | [
0.044530075043439865,
0.08125050365924835,
0.0076094078831374645,
-0.06766802072525024,
-0.025603652000427246,
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0.0013970057480037212,
0.03386031463742256,
-0.02132716402411461,
0.028179356828331947,
0.... |
<p>Currently i am studing about quantum confinement in semiconductors and came across effective mass approximation.but i am unable to understand this concept. what is the use of effective mass approximation in semiconductours.i am not a physicist so if possible please use less equations.</p>
<p>Advance thanks</p> | g11501 | [
-0.05160694196820259,
-0.0012488147476688027,
0.019755488261580467,
-0.005581738892942667,
0.0010804820340126753,
0.03820706531405449,
0.026812050491571426,
0.010901408270001411,
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0.05372907966375351,
-0.01249639131128788,
-0.008030122146010399,
-0.015954740345478058,
... |
<p>My question is more about climate sciences, but I hope that it is still related to physics.</p>
<p>What would be possible atmospheric conditions for planet with some kind of "fire" ocean?
I had some thoughts about Venus and Titan (and about gas planet from BBC movie with iron rains and incredible winds), but nothing specific.</p>
<p>How would this kind of atmosphere look like? How would fire ocean (and sky above it) look like? What are possible specifics?</p>
<p><strong>Update</strong>: I am talking about magmatic fire or some kind of fission like in Oklo's natural fission reactor.</p> | g11502 | [
-0.00038670003414154053,
0.0021971315145492554,
-0.008207754231989384,
0.022582469508051872,
0.023710202425718307,
0.03206317499279976,
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0.0014329785481095314,
0.018757371231913567,
-0.03795000538229942,
0.04256533086299896,
0.04821860045194626,
0.05286117270588875,
0.... |
<p>Suppose an event is observed in 3 inertial frames K, K' and K''. The coordinates in K are $(x,t)$ in K' are $(x',t')$ in K'' are $(x'',t'')$. The K' and K'' coordinates are then Lorentz-transformed to K-coordinates: $(x',t') \rightarrow (x_1, t_1)$ and $(x'',t'') \rightarrow (x_2, t_2)$. Now there are 2 sets of coordinates in K for the same event and they are proably different. </p>
<p>$x_1 = \gamma_1(x' + v_1t') \neq \gamma_2(x'' + v_2t'') = x_2$?</p>
<p>What is the correct interpretation?</p>
<p>Note that it is not allowed to assume that e.g. $x'$ and $x''$ are transformations of $x, t$.</p> | g11503 | [
0.02135581709444523,
-0.018597528338432312,
0.0005253119161352515,
-0.021145058795809746,
0.05656181648373604,
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0.0220929104834795,
0.024346468970179558,
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0.007079190108925104,
0.009591418318450451,
0.01235279906541109,
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-0.03... |
<p>The data from the Planck probe's observations are in, and <a href="http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=51559" rel="nofollow">according to the European Space Agency</a> they show a "hemispheric asymmetry in the cosmic microwave background (CMB)". Quote:</p>
<blockquote>
<p>an asymmetry in the average temperatures on opposite hemispheres of
the sky [...] with slightly higher average temperatures in the
southern ecliptic hemisphere and slightly lower average temperatures
in the northern ecliptic hemisphere. This runs counter to the
prediction made by the standard model that the Universe should be
broadly similar in any direction we look.</p>
</blockquote>
<p>How unexpected is this variance from the Standard Model and can it be quantified? </p>
<p>How certain is it that the data are accurate? For the recent discovery of the Higgs boson at the LHC, a five sigma result was considered sufficient to make the announcement. What is the sigma for the reported hemispherical asymmetry?</p>
<p>Yet the report of <a href="https://en.wikipedia.org/wiki/Faster-than-light_neutrino_anomaly" rel="nofollow">faster-than-light neutrinos</a>, subsequently withdrawn due to equipment failures, was based on six sigma evidence. And in <a href="https://en.wikipedia.org/wiki/Copernican_principle#Ecliptic_alignment_of_cosmic_microwave_background_anisotropy" rel="nofollow">one of the backwaters of Wikipedia</a>, we learn that:</p>
<blockquote>
<p>Some anomalies in the background radiation have been reported which
are aligned with the plane of the solar system, which contradicts the
Copernican principle by suggesting that the solar system's alignment
is special.[10] Land and Magueijo dubbed this alignment the "axis of
evil" owing to the implications for current models of the cosmos,[11]
although several later studies have shown systematic errors in the
collection of that data and the way it is processed.[12][13][14]
Various studies of the CMB anisotropy data either confirm the
Copernican principle,[15] model the alignments in a non-homogeneous
universe still consistent with the principle,[16] or attempt to
explain them as local phenomena.[17] Some of these alternate
explanations were discussed by Copi, et. al., who looked at data from
the Planck satellite to resolve whether the preferred direction and
alignments were spurious.[18][19]</p>
</blockquote>
<p>(Wikipedia's <a href="https://en.wikipedia.org/wiki/Planck_probe" rel="nofollow">main Planck probe article</a> makes no mention of the hemispherical asymmetry.) </p>
<p>When can we expect this controversy to be resolved, and are more outcomes possible than (1) the Planck probe data are found to be in error or (2) the Standard Model must undergo major revision?</p> | g11504 | [
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0.006639489904046059,
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0.005544715560972691,
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0.... |
<p>Does normalization of wave function mean that we are getting our state vector to unit length? If that's the case what does it mean physically? Also is the underlying vector space finite dimensional? If yes, then what is the dimension and how do I find the basis vectors? </p> | g11505 | [
0.018233446404337883,
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0.03894410654902458,
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-0.042536064982414246,
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0.... |
<p>In Classical Mechanics there's this notion of <a href="http://en.wikipedia.org/wiki/Configuration_space" rel="nofollow">configuration manifold</a>. Although I've heard about that a lot and although I often use that concept, I'm not sure I really understand them well because I've found no book talking about that, except Spivak's Physics for Mathematicians.</p>
<p>So my understanding is the following: the configuration manifold of a system in Classical Mechanics is basically one smooth manifold $M$ whose points are possible states of the system. In that case, for one particle in three dimensions, each state can be considered the point in space the particle is and so $M=\mathbb{R}^3$ is the configuration manifold.</p>
<p>Now, reading about that on Spivak's book it seems he only talks about configuration manifolds when talking about constraints. So what is the relationship between configuration manifolds and constraints? The configuration manifold <em>must</em> already include the constraints in some way? </p>
<p>I thought before reading this that the configuration manifold would be simply a manifold we choose whose points label states and that a constraint would be to restrict the allowed states to a submanifold of the first one.</p>
<p>What really is the precise definition of configuration manifold and how it relates to constraints?</p> | g11506 | [
0.01685161143541336,
0.05306973308324814,
-0.012372330762445927,
-0.01781739480793476,
0.029368406161665916,
0.02651793882250786,
0.04447126388549805,
-0.013255284167826176,
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0.005105332471430302,
0.021320708096027374,
-0.055018067359924316,
-0.01000912208110094,
-0.007... |
<p>Is this a correct formula for calculating the induced EMF of a wire after the current stabilizes/ or while it stabilizes in the beginning of a DC circuit? </p>
<p><img src="http://i.stack.imgur.com/8JKcE.png" alt="enter image description here"></p>
<p>What is the difference between the above and this:</p>
<p><img src="http://i.stack.imgur.com/uHB48.png" alt="enter image description here"></p> | g11507 | [
0.030243385583162308,
-0.026570742949843407,
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0.07339968532323837,
0.018108520656824112,
0.06105974316596985,
0.014277542009949684,
-0.052051842212677,
-0.017438974231481552,
-0.10035905987024307,
0.056618258357048035,
-0.041895993053913116,
0.0... |
<p>I have task to compare eignevalues gained by exact calculation on electron in Coulomb attractive field (hydrogen) and gained by WKB method..
As far as I get, eigenvalues gained with exact method are E=13.6 / (n^2)
and for WKB method all i find is exact same answer E=13.6 / (n+l+1)^2 exept there is l.
I Don't understand what does it means exactlly...</p> | g11508 | [
0.003138517728075385,
-0.03281742334365845,
0.010915230959653854,
0.008798319846391678,
0.08124687522649765,
0.0076858652755618095,
0.024152204394340515,
0.02695317007601261,
-0.045729860663414,
0.043551430106163025,
-0.04750687628984451,
0.015080125071108341,
0.033017802983522415,
0.07658... |
<p>This question is similar to previously asked questions, but the responses to them are confusing and I think it may be better covered by listing out all the potential answers for clarity.</p>
<p>It's a simple and common question: why does light seem to travel more slowly in media which is transparent to its wavelength than it does in vacuum? I have seen responses all over the web from PhD professors at major universities whose answers are <em>completely different</em>. Here are all of the general categories of answers I have seen professional physicists put forth:</p>
<ol>
<li><p>Light actually does move slower through transparent media. We don't really know why.</p></li>
<li><p>Light actually does move slower through transparent media. The reason is that light's EM effects induce nearby charged particles (electrons and nuclei) to alter the EM field with a harmonic vibration that "cancels out" some of the velocity of the light wave.</p></li>
<li><p>Light does not move slower. We don't know why it seems to.</p></li>
<li><p>Light does not move slower. It bounces around in the media which causes it to progress more slowly.</p></li>
<li><p>Light does not move slower. It is absorbed and emitted by electrons in the media which causes it to progress more slowly.</p></li>
</ol>
<p>My thoughts on each of these:</p>
<ol>
<li><p>If light actually moves slower but we haven't figured out why, I would expect it to behave relativistically in a manner similar to bradyons (particles with invariant mass which cannot reach the speed of light); but this is inconsistent with a form of energy which does not experience time. I don't see how any explanation for "slowed" light, other than 2, can be consistent.</p></li>
<li><p>I am currently leaning toward this answer, even though it is the rarest one I have seen. However, I don't understand the mechanics of how a light wave can be cancelled out or slowed by EM induction. My strong suspicion is that quantum effects are necessary: that is, light wouldn't be slowed at all were the environment always entangled with it (if you're one of those Copenhagen oddballs, this means if the wavefunction were continuously collapsed such that the light behaves as individual photons).</p></li>
<li><p>This seems pretty likely. I don't expect physicists to talk out their asses, but I have a hard time understanding why so many qualified physicists have completely different explanations for this basic principle.</p></li>
<li><p>This seems very unlikely to me, despite being the second-most common explanation I have found. If light were scattered, it wouldn't progress in the same direction through the media: it would disperse (to slow appreciably it would need to ricochet off of billions of atoms along the way). But we can see a beam of light refract through transparent media, and it doesn't diffuse much at all.</p></li>
<li><p>This is the most common explanation, yet I find it to be the least convincing! Not only do the issues from 4 apply here, but also we are talking about material which is almost completely transparent to the wavelength of light being refracted. <strong><em>EDIT</strong>: I previously asserted here that the slowing effect does not depend upon the frequency of light, which is incorrect. See below.</em></p></li>
</ol>
<p>Is anybody who actually does physics for a living <em>certain</em> you understand this phenomenon? Or are we all spitting blind in the dark? It's very frustrating to see physicists giving incompatible explanations (with an air of certainty!) for a phenomenon known since antiquity, but I suppose it may be possible that more than one explanation is true...</p>
<hr>
<p><strong>EDIT</strong>: I believe I have the answer! I have answered my own question below.</p> | g11509 | [
0.06544657051563263,
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0.013819287531077862,
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-0.03232324495911598,
0.028396066278219223,
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0.03811709210276604,
0.02586... |
<p>Correct me if i'm wrong here, but if you consider the analogy of inflating balloon when explaining the universe expansion, then the center of the universe lies within the center of the inflating balloon and outside our space and time, so our own 3d universe is analog to the surface of the expanding balloon. Does that mean the black holes push the space towards the center? Mass lying on the surface of the balloon is bending the space (surface), in our case as it tries to return to its previous state at the t=0, much like the ball that is picked up and dropped to fall back down on the ground. It resists the expansion of the universe as it pushes inwards (has "weight") towards the center of the "expanding balloon" that we call universe, so the expansion of the universe is a sort of measurement from t=0 to today since anything that is about to happen still hasn't, and the mass hinders the expansion and causes things to fall down and slows time (and thus the expansion). In the case of black holes it is said the time stops completely, thus expansion stops because the black holes infinitely curve the space around them. Than it would mean it bends the surface all the way back to ground zero, or the center, where t=0, or maybe they just stop the expansion and there is no way to use them to "travel back in time"? Hopefully someone can explain if it works this way or not.</p> | g11510 | [
0.03394850715994835,
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0.07113045454025269,
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0.04654723405838013,
0.004740557633340359,
-0.029495565220713615,
0.02242252044379711,
-0.015619496814906597,
-0.0053673600777983665,
-0.... |
<p>Yesterday I read that we can affect the path and the 'form' (particle or wave) of a photon after the fact (<a href="http://en.wikipedia.org/wiki/Wheeler%27s_delayed_choice_experiment" rel="nofollow">Wheeler's delayed choice experiment</a>). Part of what is puzzling me is the beam-splitter. Are the individual photons actually being split into two new photons of lesser energy?</p>
<p>This <a href="http://physics.stackexchange.com/questions/13851/can-you-split-a-photon">question</a> implies that you <i>cannot</i> split a photon but it seems that beam splitters do exactly that.</p> | g11511 | [
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-0.012163005769252777,
-0.05036845803260803,
-0.06613890081644058,
-0.03... |
<p>Is there a scientific approach that can explain the <a href="http://en.wikipedia.org/wiki/Street_light_interference_phenomenon" rel="nofollow">street light interference phenomenon</a>? Everytime I walk past a Streetlight it turns off.</p> | g11512 | [
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0.03753192350268364,
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0.04210932180285454,
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0.024894554167985916,
0.029... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/24324/spacetime-expansion-and-universe-expansion">spacetime expansion and universe expansion?</a> </p>
</blockquote>
<p>So I've heard that space is expanding very quickly and that the redshift we see when we look at other galaxies is evidence of this. But why doesn't this expansion affect orbits of the planets in our solar system, for instance? I would think that the expansion of space is uniform through the universe...why doesn't it tear our bodies apart?</p> | g56 | [
0.028479743748903275,
0.08468624949455261,
0.026949606835842133,
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-0.07975861430168152,
0.10831727832555771,
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0.011547492817044258,
-0.007... |
<p>Fundamentally i want to know: <strong>How do holograms work?</strong></p>
<p>The problem with that question is that normally you will end up with pages and pages talking about:</p>
<ul>
<li>a laser</li>
<li>a beam splitter</li>
<li>a diffuser</li>
<li>the object being imaged</li>
<li>object beam</li>
<li>reference beam</li>
<li>mirror</li>
<li>holographic emulsion</li>
</ul>
<p>Even Wikipedia is heavy on <a href="http://en.wikipedia.org/wiki/Holography" rel="nofollow"><em>how to make a hologram</em></a>, rather than <strong>how does a hologram work</strong>.</p>
<hr>
<p>Other people have mentioned stereoscopic vision; how having two eyes gives the illusion of a 3d object. That is also irrelavent, since someone with one eye (or, in my case, one eye closed) can still experience a hologram.</p>
<p>What i am trying to figure out is <em>how does a hologram work?</em>. More to the point, how is it that rotating a <strong>flat</strong> holographic sticker allows the virtual object to change orientation - allowing me to see content that was not there a moment ago?</p>
<hr>
<p>Wikipedia has an image that mentions <em>reconstructing a virtual 3d object</em>:</p>
<p><img src="http://i.stack.imgur.com/tEyZM.png" alt="enter image description here"></p>
<p>Some problems that that image, though, is that my credit card:</p>
<ul>
<li>has no <em>reference beam</em></li>
<li>is not being viewed at a 45 degree angle (meaning no interference can happen)</li>
</ul>
<p>Assuming i have a holographic image of a simple cube. If i am looking at the holographic plate straight on, i will only see a square (i.e. the face of the cube closest to me):</p>
<p><img src="http://i.stack.imgur.com/BHgQO.png" alt="enter image description here"></p>
<p>If i rotate the holographic plate, so the right side of the plate is further away, the virtual cube will rotate, and i will actually be able to see the <strong><em>left</em></strong> face of the cube:</p>
<p><img src="http://i.stack.imgur.com/1XT9U.png" alt="enter image description here"></p>
<p>What is happening in the <strong>flat, 2-dimensional, holographic sticker</strong> that it can display <em>continuously</em> different information as i rotate it?</p>
<p>What is the mechanics of this holographic <em>"paper"</em> that it can present my eye different images?</p> | g11513 | [
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0.01650899648666382,
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-0.013026321306824684,
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0.011010539717972279,
-... |
<p>Potential wells, such as infinite and finite potential well, have been the standard examples in quantum mechanics textbooks for tens of years. They started being only theoretical toy models but as time progresses scientists succeeded in fabricated them which resulted in the nanotechnology revolution.</p>
<p>1-Is the fabrication process too technical to be explained to the undergraduate students who are taking a course in quantum mechanics?</p>
<p>2-How such potential wells are fabricated in practice ?</p>
<p>3-Why engineering potentials of certain shapes became only possible recently, what changed in science that made it possible (since obviously on the theoretical level quantum mechanics did not change) ?</p> | g11514 | [
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0... |
<p><img src="http://i.stack.imgur.com/wMjhh.jpg" alt="enter image description here"></p>
<blockquote>
<p>My text book says: "Magnetic quantum number describes the behavior of electron in a magnetic field. We know that the movement of electrical charge is always associated with magnetic field. Since the revolving electron possesses angular momentum, it will give rise to a very small magnetic field which interact with the external magnetic field of the earth. Under the influence of external magnetic field, the electrons in a given subshell orient themselves in certain preferred regions of space around the nucleus. These are called orbitals". </p>
</blockquote>
<p>I got a question here. If external magnetic field of the earth is the reason for the electrons in a given subshell orient themselves in certain preferred regions of space, then </p>
<ul>
<li><p>would there be no particular orientations of electrons when there is no earths magnetic field? If this is the case, won't geometry of the compounds change (because of varied angle between the orbitals) without earth's magnetic field? </p></li>
<li><p>And won't it also cause crashing of orbitals in the absence of particular orientation? But this never happens, I hope. Then what could be the possible explanation that can be given for the above cases.</p></li>
</ul>
<p>Even I am not convinced with my text book explanation regarding orientation of electron in the subshell. How could the $p$ orbitals be oriented exactly perpendicular to each other, only because of the earth's magnetic field? We can even consider other orbitals too. Is there any other factor which is responsible for the orientations? </p>
<p>I don't know whether I have misunderstood anywhere, if so please explain and pardon me.</p> | g11515 | [
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-0.02889391966164112,
0.005024328362196684,
0.041396364569664,
0.06507786363363266,
0.006298729... |
<p>Today I was wondering about this situation. Let's imagine I have a circle of wire with a homogeneous section. I connect the wire with 2 terminals from ohmmeter. What minimum and maximum resistance can be measured? What resistance should I measure when terminals enclose an angle α with the center circle?</p> | g11516 | [
0.010356541723012924,
-0.020404396578669548,
-0.01771203614771366,
-0.04447321966290474,
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0.01802688278257847,
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0.009557174518704414,
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0.... |
<p>I do not understand how is $r^2 = x^2+y^2+z^2$ in spherical coordinate system. Can anybody give a simple derivation? I need to understand this in order to understand the lorentz transformation.</p> | g11517 | [
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0.01756621152162552,
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-0.01828174851834774,
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0.06963413208723068,
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<p>Bell-diagonal states are 2-qubit states that are diagonal in the <a href="http://www.quantiki.org/wiki/Bell_basis" title="bell basis">Bell basis</a>. Since those states lie in $\mathbb{C}^{2} \otimes \mathbb{C}^{2}$, the <a href="http://en.wikipedia.org/wiki/Peres%E2%80%93Horodecki_criterion">Peres-Horodecki criterion</a> is a sufficient condition to show separability and it's also pretty easy to check: $\rho = \sum_{i \in [0,3]}\lambda_i|\psi_{i}\rangle\langle\psi_{i}| $ is PPT (or separable) if and only if $Tr(\rho) \geq 2\lambda_i \geq 0$ for every $i$.
(Here {$|\psi_{i}\rangle$} are the Bell states)</p>
<p>In my research I am dealing with a generalization of those states. In particular, my question is about states in $\mathbb{C}^{2^d} \otimes \mathbb{C}^{2^d}$ that are diagonal in the basis given by the $d$-fold tensor product of Bell states.</p>
<p>For example, for $d=2$, the states I am considering are diagonal in the basis:
$$
|\psi_{0}\rangle\otimes|\psi_{0}\rangle,|\psi_{0}\rangle\otimes|\psi_{1}\rangle, \ldots,|\psi_{3}\rangle\otimes|\psi_{3}\rangle.
$$</p>
<p>I am wondering the following:</p>
<blockquote>
<p>are there some nice criteria already known to check when these states are PPT
or separable?</p>
</blockquote>
<p>Notice that those states are in general different from the states diagonal in what is called the generalized Bell basis in literature.</p> | g11518 | [
-0.01713555119931698,
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0.0001603258278919384,
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-0.017150966450572014,
-... |
<p>How do I solve the speed of light in gravitational field?</p>
<p>Should I just add gravitational acceleration in speed of light?</p>
<p>$c'=c_0+g(r)t$?</p> | g11519 | [
0.05365424603223801,
0.07370389997959137,
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0.07636060565710068,
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0.00965... |
<p>As we know from coulomb's law that:
$$\vec{E} = \frac{q}{4\pi\epsilon R^2} \hat{R}$$</p>
<p>using the above equation, how can I verify that:
$$\vec{\nabla}\cdot \vec{E}=\frac{q}{\epsilon}$$</p>
<p>I have tried to do it a home, but couldn't figure it out. Explicitly showing all steps would be very much appreciated.</p> | g327 | [
0.022171668708324432,
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0.031051509082317352,
0.0... |
<p>I am trying to choose the best approach to digitally analyse a signal, which is a mix of an unknown number (but less than 16) fundamental signals at specific frequencies (e.g., sines). </p>
<p>The goal is to determine which of the fundamental signals are present in the signal. </p>
<p>Some of the fundamental signals might be distorted, so they are actually more like square waves than sine waves. </p>
<p>I can decide what the fundamental signals are going to be, including their frequencies, waveforms and amplitudes, since I am going to generate them digitally. </p>
<p>However, I have no control over the distortion process, which can increase the amplitude of the fundamental signals by some unknown amount, resulting in distortion of some or all of the fundamental signals.</p>
<p>The analysis approach should be robust, such that it can still figure out which signals are present even if all the fundamental signals have been distorted. </p>
<p>The fundamental signals all have limited bandwidth, obviously, and the total bandwidth in which to fit the fundamental signals is also limited. </p>
<p>One idea I've already had is to increase the amplitude of the fundamental signals over a short window of time, such that for a brief moment in the window, they will get through without being distorted, making the job of detecting using an FFT easier. </p>
<p>But perhaps there is a much better way to deal with this? I haven't explored other techniques like wavelets, Kalman filters, etc. and to be honest my signal processing knowledge is a bit limited.</p> | g11520 | [
0.04498817399144173,
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0.03975437954068184,
0.04... |
<p>I'm wondering if the Clebsch-Gordan series generalize to any orthonormal set of basis functions? If so, how would one go about deriving an expression for an arbitrary set of basis functions (perhaps an example derivation of the well known expression of spherical harmonics would be helpful)?</p>
<p>I know it has something to do with being able to compute the multiplicities of the tensor product of the irreducible representations, but I don't know how one would do that.</p> | g11521 | [
0.018681135028600693,
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<p>Let $\rho_{ABCD}$ be a sparse matrix of 4 systems each in a $d$-dimensional Hilbert space. </p>
<p>For $d<7$ in a reasonable time (few seconds) I able to perform the partial trace $\rho_{AD}$ using the code proposed in <a href="http://www3.imperial.ac.uk/people/m.tame/research">http://www3.imperial.ac.uk/people/m.tame/research</a>. I would need an efficient algorithm for calculating $\rho_{AD}$ where $d\geq7$. The algorithm of the site above does not exploit any properties of the matrix and it requires a lot of permutations and rearrangements.</p>
<p>Do you know an efficient algorithm for calculating the partial trace of qudit which uses the fact that the matrix is sparse? It would also be interesting if the algorithm can take advantage of parallel computation.</p>
<p>Thank you very much in advance for your answers.</p>
<p>Regards,</p>
<p>Silvio</p> | g11522 | [
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0.025447260588407516,
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<p>Consider a problem in classical electrodynamics, when a monochromatic beam experiences total internal refraction when traveling from a medium with $n>1$ to a medium with refractive index $1$ - <a href="http://i.stack.imgur.com/2vXIy.png" rel="nofollow">see schematic below</a>. Using Fresnel equations one gets the penetration depth
$$d = \frac{1}{\sqrt{k_x^2+k_y^2-(\tfrac{2\pi}{\lambda})^2}},$$
where $k_x$ and $k_y$ are the perpendicular components of the wave vector, and $\lambda$ is the wavelength (in the vacuum).</p>
<p>At least in theory, it is possible to have an evanescent wave of an arbitrary penetration depth $d$. However, in such case one needs to use a plane wave, thus a wave of unbounded spatial size. For a beam with a finite variance $\langle x^2\rangle$ (and $k_y=0$ to reduce the problem to two dimensions) there <strong>seems</strong> to be a relation that $\langle
d\rangle/\sqrt{\langle x^2\rangle}$ is lesser than a constant. </p>
<p>The main questions: is there any strict bound in the form of
$$\text{a measure of penetration depth}\leq f(\text{transversal beam size},n)$$
(perhaps in the style of Heisenberg uncertainty principle, or using other moments of $x$, $y$ and $d$)?</p>
<p><img src="http://i.stack.imgur.com/2vXIy.png" alt="Schematic of an evanescent wave size"></p> | g11523 | [
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0.0072077373042702675,
0.04465871304273605,
0.021406028419733047,
-0.0628761500120163,
0.0226730... |
<p>I've just now rated David Bar Moshe's post (<a href="http://theoreticalphysics.stackexchange.com/questions/551/how-does-one-geometrically-quantize-the-bloch-equations/553#553">below</a>) as an "answer", for which appreciation and thanks are given. </p>
<p>Nonetheless there's more to be said, and in hopes of stimulating further posts, I've added additional background material. In particular, it turns out that a 2003 article by Bloch, Golse, Paul and Uribe “<a href="http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.dmj/1085598341" rel="nofollow">Dispersionless Toda and Toeplitz operators</a>” includes constructions that illustrate some (but not all) of the quantization techniques asked-for, per the added discussion below. </p>
<hr>
<p>The question asked is:</p>
<blockquote>
<p>How does one geometrically quantize the Bloch equations?</p>
</blockquote>
<h2>Background</h2>
<p>From a geometric point-of-view, the Bloch sphere is the simplest (classical) symplectic manifold and the Bloch equations for dipole-coupled spins specifies the simplest (classical) nontrivial Hamiltonian dynamics.</p>
<p>In learning modern methods of geometric quantization — as abstractly described on Wikipedia's <a href="http://en.wikipedia.org/wiki/Geometric_quantization" rel="nofollow"><em>Geometric Quantization</em></a> article for example — it would be very helpful (for a non-expert like me) to see the quantum Hamiltonian equations for interacting spins derived from the classical Hamiltonian equations. </p>
<p>To date, keyword searches on the Arxiv server and on Google Books have found no such exposition. Does mean that there's an obstruction to geometrically quantizing the Bloch equations? If so, what is it? Alternatively, can anyone point to a tutorial reference?</p>
<p>The more details given, and the more elementary the exposition, the better! :) </p>
<hr>
<h2>Some engineering motivations</h2>
<p>It is natural in quantum systems engineering to pullback quantum Hamiltonian dynamics onto tensor network state-spaces of lower-and-lower dimension (technically, these state-spaces are <a href="http://faculty.washington.edu/sidles/FRIAS_2011/index.html#burningArrow" rel="nofollow">a stratification of secant varieties of Segre varieties</a>). </p>
<p>It should be appreciated too that in this context “quantum Hamiltonian dynamics” includes stochastic unravellings of Lindbladian measurement-and-control processes (per these <a href="http://info.phys.unm.edu/~caves/reports/lindblad.pdf" rel="nofollow">on-line notes by Carlton Caves</a>). Presenting the unravelled trajectories in Stratonivich form allows the open quantum dynamics of general Lindblad processes to be pulled-back with the same geometric naturality as closed quantum dynamics of Hamiltonian potentials and symplectic forms. This Lindbladian pullback idiom is absent from mathematical discussions of geometric quantization, e.g. the above-mentioned article <a href="http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.dmj/1085598341" rel="nofollow">Bloch et al.</a>. In essence we engineers are using these pullback techniques with good success, without having a complete or even geometrically natural understanding of them.</p>
<p>Pulling back through successive state-spaces of smaller-and-smaller dimensionality, we arrive (unsurprisingly) at an innermost state-space that is a tensor product of Bloch spheres that inherits its (classical) symplectic structure from the starting Hilbert space. Moreover, the Lindblad processes pull back (also unsurprisingly) to classical noise and backaction that respects the standard quantum limit.</p>
<p>For <a href="http://faculty.washington.edu/sidles/FRIAS_2011/index.html#ST" rel="nofollow">multiple systems engineering reasons</a>, we would like to understanding this stratification backwards and forwards, in the following geometrically literal sense: on any state-space of this stratification, we wish the dual option of either pulling-back the dynamics onto a more classical state-space, or pushing-forward the dynamics onto a more quantum state-space.</p>
<p>Insofar as possible, the hoped-for description of geometric (de/re)quantization will illuminate this duality in <em>both</em> directions. Needless to say, the simpler and more geometrically/informatically natural the description of this duality, the better (recognizing that this naturality is a lot to hope for). :)</p> | g11524 | [
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0.016... |
<p>How can we prove the following <a href="http://en.wikipedia.org/wiki/Cluster_decomposition_theorem" rel="nofollow">cluster decomposition formula</a></p>
<p>$$\langle \phi_1 \phi_2 \rangle ~=~ \langle \phi_1 \rangle \langle \phi_2 \rangle,$$</p>
<p>where brackets denote <a href="https://en.wikipedia.org/wiki/VEV" rel="nofollow">vacuum expectation value</a> (VEV) on some vacuum state, and $\phi_i$ are constant fields in some quantum field theory?</p>
<p>The only justification for this I'm aware of comes from Weinberg (QFT 2, p. 166).</p> | g11525 | [
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0... |
<p>I'm currently studying an article by <a href="http://arxiv.org/abs/cond-mat/0506035">Maslov</a>, in particular the first section about higher corrections to Fermi-liquid behavior of interacting electron systems. Unfortunately, I've hit a snag when trying to understand an argument concerning the (retarded) self-energy $\Sigma^R(ε,k)$.</p>
<p>Maslov states that in a Fermi liquid, the real part and the imaginary part of the self-energy $\Sigma^R(ε,k)$ are given by</p>
<p>$$ \mathop{\text{Re}}\Sigma^R(ε,k) = -Aε + B\xi_k + \dots $$
$$ -\mathop{\text{Im}}\Sigma^R(ε,k) = C(ε^2 + \pi^2T^2) + \dots $$</p>
<p>(equations 2.4a and 2.4b). These equations seem reasonable: when plugged into the fermion propagator,</p>
<p>$$ G^R(ε,k) = \frac1{ε + i\delta - \xi_k - \Sigma^R(ε,k)} $$</p>
<p>the real part slightly modifies the dispersion relation $ε = \xi_k$ slightly and the imaginary part slightly broadens the peak. That's what I'd call a Fermi liquid: the bare electron peaks are smeared out a bit, but everything else stays as usual.</p>
<p>Now, Maslov goes on to derive higher-order corrections to the imaginary part of the self-energy, for instance of the form</p>
<p>$$ \mathop{\text{Im}}\Sigma^R(ε) = Cε^2 + D|ε|^3 + \dots .$$</p>
<p>First, I do not quite understand how to interpret this expansion.</p>
<blockquote>
<p>How am I to understand the expansions in orders of $ε$? I suppose that $ε$ is small, but in relation to what? The Fermi level seems to be given by $ε=0$.</p>
</blockquote>
<p>Second, he states that this expansion is to be understood "on the mass-shell".</p>
<blockquote>
<p>I take it that "on the mass shell" means to set $\xi_k=ε$? But what does the expansion mean, then? Maybe I am supposed to expand in orders of $(ε-\xi_k)$?</p>
</blockquote>
<p>Now the question that is the most important to me. Maslov argues that the real part of the self-energy can be obtained via the Kramers-Kronig relation from the imaginary part of self-energy. My problem is that the corresponding integrals diverge.</p>
<blockquote>
<p>How can
$$ \mathop{\text{Re}}\Sigma^R(ε,k) = \mathcal{P}\frac1{\pi}\int_{-\infty}^{\infty} d\omega \frac{\mathop{\text{Im}}\Sigma^R(\omega,k)}{\omega-ε} $$
be understood for non-integrable functions like $\mathop{\text{Im}}\Sigma^R(ε,k) = ε^2$?</p>
</blockquote>
<p>It probably has to do with $ε$ being small, but I don't really understand what is going on.</p>
<hr>
<p>I should probably mention my motivation for these questions: I have calculated the imaginary part of the self-energy for the one-dimensional Luttinger liquid $\xi_k=|k|$ as</p>
<p>$$ \mathop{\text{Im}}\Sigma^R(ε,k) = (|ε|-|k|)θ(|ε|-|k|)\mathop{\text{sgn}}(ε) $$</p>
<p>and would like to make the connection to Maslov's interpretation and results. In particular, I want to calculate the imaginary part of the self-energy with the Kramers-Kronig relations.</p> | g11526 | [
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0.04193631559610367,
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0.045835673809051514,
0.024824807420372963,
0.08... |
<p>The law that</p>
<p>$$\frac{d\vec{L}}{dt}= \vec{T}$$</p>
<p>where $\vec{T}$ is torque about a frame's origin $o$ and $\vec{L}$ is the angular momentum about that origin $o$. </p>
<p>Can this law be ultimately (always?) traced backed to Newton's Second Law ?</p> | g11527 | [
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0.010112748481333256,
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-0.024530768394470215,
0.04734154790639877,
-0.051... |
<p>The definition of a classical black hole is when even electromagnetic radiation can not escape from it. Why then can <a href="http://en.wikipedia.org/wiki/Hawking_radiation" rel="nofollow">Hawking radiation</a> be emitted from semi-classical black holes?</p>
<p>What is difference between Hawking radiation and electromagnetic radiation?</p> | g367 | [
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0.01586288772523403,
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0.015891926363110542,
0.06570159643888474,
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0.... |
<p>I'm trying to understand this image of a particle tracing experiment (which can be found all over the net if you <a href="https://www.google.com/search?hl=en&site=imghp&tbm=isch&source=hp&biw=1194&bih=960&q=particle+collision&oq=particle+collision&gs_l=img.3..0l10.2086.6479.0.6774.18.13.0.5.5.0.132.1159.11j2.13.0...0.0...1ac.1.9.img.p_fh-c_z2NA#hl=en&site=imghp&tbs=ic%3agray%2Cisz%3Al&tbm=isch&sa=1&q=bubble+chamber&oq=bubble+chamber&gs_l=img.3..0l10.10731.12545.0.12777.14.11.0.3.3.0.153.1340.1j10.11.0...0.0...1c.1.9.img.YP8io5uLEkY&bav=on.2,or.r_qf.&fp=909a10acbf62f3be&biw=1194&bih=960" rel="nofollow">google for "bubble chamber"</a>):</p>
<p>(<img src="http://i.stack.imgur.com/ZdKcl.jpg" alt="Bubble chamber experiment"></p>
<p>There are two things that I can't figure out:</p>
<ol>
<li><p>The background has some kind of pattern made up of irregularly sized, semi-rectangular patches. Where does that come from?</p></li>
<li><p>There is a vertical line of 4 circles in the middle of the image, each marked with an X. These seem to be part of the setup, but what is their function? Also, the pattern in the background in these circles is not continuous w.r.t. to the outside pattern, although the traces are. Why?</p></li>
</ol>
<p>In addition, if anyone has the original source or more information about that particular experiment then that would be very welcome, too.</p>
<p><strong>EDIT:</strong> It seems that the image stems from a <a href="http://vms-db-srv.fnal.gov/fmi/xsl/VMS_Site_2/000Return/photography/r_online_mrdetail.xsl?-db=VMS_Frames&-lay=WWWBrowse&-recid=127102&-find=" rel="nofollow">1980 Fermilab experiment</a>.</p> | g11528 | [
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0.0577668622136116,
0.009833630174398422,
0... |
<p>If I have, for example a particle with $s = 3/2$ and $\ell = 2$, what are the allowed values of $j$?
I'm slightly confused because I know that $j = \ell + s$, so surely there is only one allowed value?</p> | g11529 | [
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0.06792193651199341,
0.04444358870387077,
0.029... |
<p>When doing electron diffraction on graphite (a popular experiment for students at universities) always diffraction at these two planes with distances $d_1$ and $d_2$ are observed:</p>
<p><img src="http://i.stack.imgur.com/dhKLG.png" alt="enter image description here"></p>
<p>But a plane parallel to the ones with distance $d_2$ can also be formed with a distance of the atom spacing $s$. When looking through crystal diffraction databases there's also no data about diffraction on these "$s$" planes.</p>
<p><strong>Why is it not possible that electrons or X-Rays scatter at the planes with distance $s$ or some multiple of it?</strong></p> | g11530 | [
0.03149078041315079,
0.07054183632135391,
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-0.0... |
<p>I am referring to <a href="http://arxiv.org/abs/1306.5242" rel="nofollow">this paper</a>. </p>
<p>I guess that in this paper one is trying to relate the massless spin $s$ gauge fields in $AdS_4$ to conformal spin $s$ theory on $S^3$. </p>
<ul>
<li><p>So am I right that the operator $K$ that has been defined here in $2.8$ is something in the boundary? How does one derive the explicit expression for $K$ as given in $2.12$? </p>
<p>Is it solely through this particular choice of $K$ in section $2.12$ that one is implementing in section $3$ the fact that the spin-$s$ theory on the boundary is conformal? </p></li>
<li><p>In section $3$ they seem to be solely focussed on symmetric traceless rank $s$ tensors (to represent spin-$s$ on the boundary $S^3$). But why is this enough? I would think that the spin-s fields to be considered are the fields on $S^3$ which lie in those representation of $SO(4)$ which when restricted to $S0(3)$ become its highest weight $s$ representation and these are not just symmetric and traceless but also have to be transverse and also satisfy some harmonic wave equation. What about these two conditions? (This was the definition of spin-$s$ as was discussed <a href="http://physics.stackexchange.com/q/75452/">here</a>.)</p>
<p>But when considering spin-$s$ fields on the bulk $AdS$ in equation $5.1$ the condition of transversality and the wave-equation condition seem to be back! </p>
<p>I basically don't understand equations $3.1$ and $3.6$.
It would be great if someone could help explain these two. </p></li>
<li><p>Is there a value of $m^2$ (in equation 5.1) at which this spin-s field on $AdS$ will be conformally coupled? (...in this paper they are focussed at the massless case ($m^2 =0$) which I would think is not necessarily conformal..) </p></li>
<li><p>With reference to the discussion below equation 5.6,</p>
<p>When the bulk spin-$s$ field is massless, there are two possible dimensions of the boundary spin-$s$ current, $J_{(s)}$ - at the UV fixed point it has dimensions, $\Delta_{-} = 2-s $ and at the IR fixed point it has dimensions, $\Delta_{+} = s+d-2$</p>
<p>Here two things are not being very clear to me, </p>
<p>(1) How does one see the claim that at the IR fixed point the value of $\Delta_{+}$ somehow implies that now $J_{(s)}$ is a conserved current and hence the spin-s field in the boundary is now a gauge field? </p>
<p>(2) Is it also being claimed that at the UV fixed point the value of $\Delta_{-}$ is precisely the same as the dimension of a spin-$s$ gauge field? What theory is this? How do we understand this? I can't wrap my head around the fact that this $J_{s}$ which I thought of as the conserved current spin-s current till now happens to have the same dimension as a gauge field!? </p></li>
</ul> | g11531 | [
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<p>More precisely, how small is the potency a listener hears, compared to the potency of the emitter.</p>
<p>I'd like to present a simple and yet reasonable approximation, to a high school audience (I am a teacher)</p>
<p>Intuitively, it should decrease with a square (of distance; because of the expansion of the area the wave covers) and exponentially (because of accumulation losses in the way) .Here, they mention both decreases: <a href="http://www.sfu.ca/sonic-studio/handbook/Sound_Propagation.html" rel="nofollow">http://www.sfu.ca/sonic-studio/handbook/Sound_Propagation.html</a> . The air absorption component is linear in dB (which, as far as I know, means exponential on energy)</p>
<p>I am just not sure of how to put them together, and if there are other ideas that a first approximation should cover.</p> | g11532 | [
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<p>AFAIK Glass is insulator, it doesn't have free electron. It's said metal is a good conductor of heat because it has free electron, glass doesn't have free electron, why it is a good conductor of heat?</p> | g11533 | [
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<p>Let's say I have a ceramic slab on a conveyor belt that is initially at $450\,^{\circ}\mathrm{C}$ and there is air being blown over it at a speed of $35 \frac{m}{s}$ with an ambient temperature of $18\,^{\circ}\mathrm{C}$ until the slab reaches a temperature of $35\,^{\circ}\mathrm{C}$.</p>
<p>I understand the overall procedure of the problem. I have to find the <a href="http://en.wikipedia.org/wiki/Reynolds_number" rel="nofollow">Reynolds number</a>, the <a href="http://en.wikipedia.org/wiki/Nusselt_number" rel="nofollow">Nusselt number</a>, etc. But here is where I am confused. </p>
<p>The properties that can be found in the back of the book rely on the mean fluid temperature which is $T_{f}=\frac{T_{s}+T_{\infty}}{2}$ where $T_{s}$ is the surface temperature and $T_{\infty}$ is the free stream temperature. Once that temperature is found, the properties can be determined from the tables in the back. </p>
<p>But this problem involves a surface temperature that is constantly changing which means that the mean fluid temperature is constantly changing. This causes the Reynolds and Nusselt numbers to constantly change. I could easily do this problem if it weren't for transient convection, so is there a way to solve the problem that I am having here?</p> | g11534 | [
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<p>Long storage times for qubits will be integral in the construction of a scalable quantum computer. This leads me to ask the current state of affairs in our ability to store qubits. Namely, what is the <strong>record</strong> storage time for a qubit at <strong>any</strong> temperature? </p>
<p>Upon searching for the record storage time I found the following result at <strong>room</strong> temperature: <a href="https://www.sciencemag.org/content/342/6160/830" rel="nofollow">https://www.sciencemag.org/content/342/6160/830</a></p>
<p>I'd be quite surprised if cooling the system didn't provide an increase in storage time. However, the costs of cooling might outweigh the gain in storage time. Thus, I am interested in how the storage time depends upon temperature. </p> | g11535 | [
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<p>Does a large thick wire that has over 1000 amperes of current flowing
through it generate powerful magnetic fields? </p>
<p>What formula is best here to predict $B$?</p> | g368 | [
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<p>I am not doing a physics degree but an engineering degree but i am planning using my free time to self study all the math in preparing myself to self study subjects in theoretical physics. (I've always wanted to do theoretical physics but there are no scholarships offered in my country for the subject and my family is not rich so I had no choice but to self study) </p>
<p>By "self studying" I mean buying books and reading online materials on my own and try to understand everything I can.
So far this is my plan, </p>
<p>Analytic geometry -> Single Variable Calculus -> Advanced Calculus (basic Linear algebra + multivariable and vector calculus) -> Linear Algebra -> ODEs -> but here I am stuck as to where do I go from here? </p>
<p>Well first of all is this plan okay?<br>
If it is : how do I continue? Should I continue to real and complex analysis and do more things from pure math? Or should I just stick to the more computational part of math and learn more advanced techniques in solving differential equations or learn more algebraic techniques? How about geometry? Topology? Group theory and more things from pure Math? </p>
<p>If its not : what is the better way of doing it? Should I learn all the basic math first before reading Goldstein's classical mechanics ? Or should I just start with the physics and just pick up the math along the way? </p>
<p>And I also have the time issues to worry about how I wish I can just do a physics degree but unfortunately things don't always go your way. Due to imminent time constriants (engineering has lots of projects im sure) i would like my self study and learning to be as efficient as possible. Hence good advice from all experienced physicists would be very much helpful. Thanks in advance.</p> | g108 | [
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<p>My 'government-issued' book literally says:</p>
<blockquote>
<p>Energy is the capacity to do work and work is the product of net force and the 1-dimensional distance it made a body travel while constantly affecting it.</p>
</blockquote>
<p>I didn't want to say it, but what!?</p>
<p>Seriously though; why does <a href="http://en.wikipedia.org/wiki/Work_%28physics%29">work</a> equal $F \cdot d$ ?</p>
<p>Where did the distance part come from?</p>
<p>I always thought of time as the one thing we can only measure (not affect) so it justifies why we may measure other things in relation to time. But we have a much greater control over distance (since it's just a term for a physical dimension we can more or less influence as opposed to time).</p>
<p>How does distance translate to this here?</p>
<p><em>Level:</em> <a href="http://en.wikipedia.org/wiki/Tenth_grade#North_America">US tenth grade</a> equivalent.</p> | g11536 | [
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<p>The most recent discussion of what axioms one might drop from the Wightman axioms to allow the construction of realistic models that I'm aware of is <a href="http://dx.doi.org/10.1088/0034-4885/38/7/001">Streater, Rep. Prog. Phys. 1975 <strong>38</strong> 771-846, "Outline of axiomatic relativistic quantum field theory"</a>. I'm looking for any more recent review that seriously discusses the axioms.</p>
<p>A critique of the Haag-Kastler axioms would also be welcome, but I would prefer to stay close enough to Lagrangian QFT to allow relatively immediate characterization of the difference between models of the reduced axiomatic system and the standard models that are relatively empirically successful.</p>
<p>I'm specially interested in any reviews that include a discussion of what models are possible if one relinquishes the existence of a lowest energy vacuum state (we know that, at least, this weakening allows the construction of thermal sectors of the free field, and that such a sector contains a thermal state that is thermodynamically stable even though it is not minimum energy, and that a Poincaré invariant "extra quantum fluctuations" sector is also possible—I'd like to know what is the full gamut of such models?).</p>
<p>[Added: This question was partly inspired by <a href="http://blogs.discovermagazine.com/cosmicvariance/2012/02/07/how-to-think-about-quantum-field-theory/">a Cosmic Variance post</a> on the subject of QFT, particularly <a href="http://www.pitt.edu/~pittcntr/Being_here/last_donut/donut_2011-12/10-14-11_qft.html">the link to John Norton</a>, obviously with my research interests added.]</p> | g11537 | [
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<p>I would like to understand the mathematical language which is relevant to instanton moduli space with a surface operator.</p>
<p>Alday and Tachikawa stated in 1005.4469 that the following moduli spaces are isomorphic.</p>
<ol>
<li>the moduli space of ASD connections on $\mathbb{R}^4$ which are smooth away from $z_2=0$ and with the behavior $A\sim (\alpha_1,\cdots,\alpha_N)id\theta$ close to $r\sim 0$ where the $\alpha_i$ are all distinct and $z_2=r\exp(i\theta)$. (Instanton moduli space with a full surface operator)</li>
<li>the moduli space of stable rank-$N$ locally-free sheaves on $\mathbb{P}^1\times \mathbb{P}^1$
with a parabolic structure $P\subset G$ at $\{z_2=0\}$ and with a framing at infinities, $\{z_1=\infty\}\cup\{z_2=\infty\}$. (Affine Laumon space)</li>
</ol>
<p>I thought the moduli space ${\rm Bun}_{G,P}({\bf S}, {\bf D}_\infty)$ in [B] also corresponds to the instanton moduli space with a surface operator. Note that ${\rm Bun}_{G,P}({\bf S}, {\bf D}_\infty)$ is the moduli space of principal $G$-bundle on ${\bf S}=\mathbb{P}^2$ of second Chern class $-d$ endowed with a trivialization on ${\bf D}_\infty$ and a parabolic structure $P$ on the horizontal line ${\bf C}\subset{\bf S}$.</p>
<p>[B] <a href="http://arxiv.org/abs/math/0401409" rel="nofollow">http://arxiv.org/abs/math/0401409</a></p>
<p>However, [B] considers the moduli space of parabolic sheaves on $\mathbb{P}^2$ instead of $\mathbb{P}^1\times \mathbb{P}^1$. What in physics does ${\rm Bun}_{G,P}({\bf S}, {\bf D}_\infty)$ correspond to? Is it different from the affine Laumon space?</p>
<p>In addition, I would like to know the relation between [B] and [FFNR]. </p>
<p>[FFNR] <a href="http://arxiv.org/abs/0812.4656" rel="nofollow">http://arxiv.org/abs/0812.4656</a></p>
<p>Do \mathfrak{Q}<em>{\underline d} and $\mathcal{Q}_{\underline d}$ in [FFNR] correspond to $\mathcal{M}_{G,P}$ and $\mathcal{QM}_{G,P}$ in the section 1.4 of [B]? (Sorry, this does not show \mathfrak properly. \mathfrak{Q}</em>{\underline d} is the one which appears the first line of the section 1.1 in [FFNR].)</p> | g11538 | [
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<p>I'm especially interested in elegant illuminating proofs which don't involve a lot of straightforward technical computations</p>
<p>Also, does a non-perturbative proof exist?</p> | g11539 | [
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<p>By now, there has been enough grasp on quantum chaos for systems with a small number of degrees of freedom. The major tool used is periodic orbit theory to approximate the spectral distribution. Is there any suitable generalization to a quantum field theory with one spatial dimension whose classical analog exhibits spatiotemporal chaos? Periodic orbit theory breaks down because we can always combine prime cycles at spatially adjacent regions to form another prime cycle with an order far greater than any of the original prime cycles. The prime cycles become too dense with a combinatorial explosion.</p>
<p>On a related note, what is the qualitative distribution of a one dimensional quantum cellular automata which is Turing complete?</p> | g11540 | [
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<p>In terms of gravity and electric fields, I'm not sure what the difference is between field strength and potential is and how they are related? Both using maths and not.</p> | g11541 | [
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<p>Where can I find a way to construct the hamiltonian of a water molecule bounded to a surface? More generally,how can one write the hamiltonian of an atom bounded to a surface?</p> | g11542 | [
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<p>When you hear about <a href="http://en.wikipedia.org/wiki/Atomic_clock" rel="nofollow">atomic clocks</a>, it's accuracy is described by saying something like, " it neither gains or loses $x/y$th of a second in $z$ years." How is this error calculated? Does an error imply that we have a more regular physical phenomena with which to compare the atomic clock? Or does this error simply mean there are quantum phenomena that occur extremely rarely in the clock that might throw off its regularity every once and a while? </p> | g11543 | [
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<p>I was reading about <a href="http://en.wikipedia.org/wiki/No-cloning_theorem">no cloning theorem</a> and it arose a thought experiment, if there were a way of compare quantum states (for being equal) then you could build a pseudocloning machine that searches for quantum states till it finds an equal state, so I think there could be something like a No-Comparison theorem. </p>
<p>Does exist something like that? </p> | g11544 | [
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<p>Given a closed chain with a total length of 1.2m rotating at 1'800 rpm and a total mass of 0.4kg, what is the drag force pulling on one chain link?</p>
<p>I originally thought that since no link size was given I need to assume the link sizes to be infinitely small. Thanks to the answers below I now know this won't work. Yet I am still baffled as to how I could calculate the drag force without it, sure I could give a function of the drag force that is dependent on the link size, but looking at the parameters given I think I should be able to calculate the actual force.</p>
<p>Here is a video of a very similar experiment as we conducted and are asked to describe now: <a href="http://www.univie.ac.at/elearnphysik/video/PhysikI/rotKette_648x480.flv" rel="nofollow">http://www.univie.ac.at/elearnphysik/video/PhysikI/rotKette_648x480.flv</a></p>
<p>I am glad for any hints and explanations.</p>
<p><strong>Edit:</strong> Rewrote question to match exactly the problem description</p> | g11545 | [
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<p>I've seen several video which claims that is <a href="http://en.wikipedia.org/wiki/Anti-gravity" rel="nofollow">anti-gravity</a>. I am sure at least one of them, use a kind of electricity to lift an object! (triangle lifter), I would guess electricity lift that object by air. But what is the equation?, I have no idea.</p> | g11546 | [
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<blockquote>
<p><strong>Question</strong>: How to <strong>classify/characterize the phase structure of (quantum) gauge theory</strong>?</p>
</blockquote>
<p>Gauge Theory (say with a gauge group $G_g$) is a powerful quantum field theoretic(QFT) tool to describe many-body quantum nature (because QFT naturally serves for understanding many-body quantum problem with (quasi-)particle creation/annihilation). </p>
<p><strong>Classification of gauge theory</strong> shall be something profound, in a sense that gauge fields (p-form $A_\mu$, $B_{\mu\nu}$, or connections of $G_g$-bundle etc) are just mediators propagating the interactions between matter fields (fermion $\psi$, boson $\phi$). Thus, effectively, we may "integrate out" or "smooth over" the matter fields, to obtain an effective gauge theory described purely by gauge fields ($A_\mu$, $B_{\mu\nu}$, etc).</p>
<p><strong>Characterization of gauge theory</strong> should NOT simply rely on its gauge group $G_g$, due to <a href="http://physics.stackexchange.com/questions/13870/gauge-symmetry-is-not-a-symmetry">"Gauge symmetry is not a symmetry"</a>. We should not classify (its distinct or the same phases) or characterize (its properties) ONLY by the gauge group $G_g$. What I have been taught is that some familiar terms to describe the phase structure of (quantum) gauge theories, are:</p>
<p>(1) confined or deconfined </p>
<p>(2) gapped or gapless</p>
<p>(3) Higgs phase</p>
<p>(4) Coulomb phase </p>
<p>(5) topological or not.</p>
<p>(6) weakly-coupling or strongly-coupling</p>
<blockquote>
<p><strong>sub-Question A.</strong>:
Is this list above (1)-(6) somehow enough to address the phase structure of gauge theory? What are other important properties people look for to classify/characterize the phase structure of gauge theory? Like entanglement? How?</p>
</blockquote>
<p>(for example, in <strong>2+1D gapped deconfined weak-coupling topological gauge theory</strong> with finite ground state degeneracy on the $\mathbb{T}^2$ torus describes anyons can be classified/characterized by braiding statistics $S$ matrix (mutual statistics) and $T$ (topological spin) matrix.)</p>
<blockquote>
<p><strong>sub-Question B.</strong>:
Are these properties (1)-(6) somehow related instead of independent to each other?</p>
</blockquote>
<p>It seems to me that <strong>confined</strong> of gauge fields implies that the matter fields are <strong>gapped</strong>? Such as 3+1D Non-Abelian Yang-Mills at IR low energy has <strong>confinement</strong>, then we have the <a href="http://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap">Millennium prize's Yang–Mills(YM) existence and mass gap</a> induced <strong>gapped</strong> mass $\Delta>0$ for the least massive particle, both(?) for the matter field or the gauge fields (glueball?). So <strong>confinement</strong> and <strong>gapped</strong> mass $\Delta>0$ are related for 3+1D YM theory. Intuitively, I thought <strong>confinement $\leftrightarrow$ gapped</strong>, <strong>deconfinement $\leftrightarrow$ gapless</strong>.</p>
<p>However, in 2+1D, condensed matter people study $Z_2$, U(1) spin-liquids, certain kind of 2+1D gauge theory, one may need to ask whether it is (1) confined or deconfined, (2) gapped or gapless, separate issues. So in 2+1D case, <strong>the deconfined can be gapped</strong>? <strong>the confined can be gapless?</strong> Why is that? Should one uses Renormalization group(RG) argument by Polyakov? how 2+1D/3+1D RG flow differently affect this (1) confined or deconfined, (2) gapped or gapless, separate issues?</p>
<blockquote>
<p><strong>sub-Question C.</strong>: are there <strong>known mathematical objects to classify gauge theory</strong>? </p>
</blockquote>
<p>perhaps, say <strong>other than/beyond the recently-more-familiar group cohomology</strong>: either topological group cohomology $H^{d+1}(BG_g,U(1))$ using classifying space $BG_g$ of $G_g$, or Borel group cohomology $\mathcal{H}^{d+1}(G_g,U(1))$ recently studied in <a href="http://arxiv.org/abs/1106.4772">SPT and topological gauge theory</a> and <a href="http://adsabs.harvard.edu/abs/1990CMaPh.129..393D">Dijkgraaf-Witten</a>?</p> | g11547 | [
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-0.0139... |
<p>I am trying to understand the <a href="http://www.google.com/search?q=landauer+approach" rel="nofollow">Landauer approach</a>. Consider the setup: (left contact)-(conductor)-(right contact). For simplicity, the conductor is a 1d wire (the transverse part is not relevant for this question). The eigenstates of the conductor are </p>
<p>$$\psi_n(x)=\sin(k_nx), \qquad k_n=\frac{n\pi}{L}$$ </p>
<p>($L$ length of conductor). I also ignore disorder. In the Landauer approach you assume the left (right) contact populates the right(left)-going states $e^{ik_n x}$ where $k_n=\frac{2\pi}{L}$ with $n>0$ ($n<0$). Then you assume these "scattering states" are populated with a Fermi distribution and you compute the conductance.</p>
<p>I would like to understand why you should think in terms of these scattering states because they do not satisfy the boundary condition $\psi(0)=\psi(L)=0$.</p> | g11548 | [
0.008952455595135689,
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0.00622179452329874,
0.022099167108535767,
-0.03418790176510811,
0.06200... |
<p>I want to consider a thought experiment. Lets ignore technical problems of actually performing such an experiment.
Consider two photons having the same wavelength. We send 1 photon to a distant galaxy (millions of light years away). The photon would hit a mirror there and return to Earth. On Earth (I assume) a cosmological redshift would be detected. At the same time we keep the second photon on Earth in small container with perfect mirrors where it bounces back and forth. Would the photon in the container exhibit the same cosmological redshift as the photon that traveled to the distant galaxy and back? If so, (now back to technical problems) could the redshift be ever measured in the lab or is the effect many orders of magnitude too small to be ever measured in a lab on Earth, not to mention the problem of constructing a perfect mirror to keep the photon?</p> | g11549 | [
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0.0059874760918319225,
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0.01991509459912777,
0.04880199953913689,
0.00890155415982008,
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<p>Since $\text{force = mass}\times\text{acceleration}$,</p>
<ol>
<li><p>is it right to say that an object traveling at a high
constant velocity (zero acceleration), exerts zero
force upon impact with a stationary object?</p></li>
<li><p>I understand that upon impact, the projectile
decelerates rapidly from initial velocity down to zero.
Could force then be computed using integrals and differential equations?</p></li>
</ol> | g11550 | [
0.06613080948591232,
0.037784408777952194,
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0.007475793827325106,
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-0.017600489780306816,
-0.05362137407064438,
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0.02914164774119854,
-0.038... |
<p>If you were to upload our bodies onto a computer. Exactly how much storage would we take up?</p> | g11551 | [
-0.000704313802998513,
0.08532603085041046,
0.0002105382300214842,
-0.018722528591752052,
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0.022815726697444916,
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0.0... |
<p>Somewhere in a two dimensional convex bulk of particles (pic related) on a random position a reaction takes place and a particle is sent out in a random direction with a constant velocity $v$. </p>
<p>What is the average distance such a particle travels until it leaves the bulk?</p>
<p><img src="http://i.imgur.com/PxTWz.gif" alt="enter image description here"></p>
<p>Might be codable if one puts a grid over the planes and weightens with a yes/no function if the stating position is within the bulk. Then I'd cut that object with n corners (8 in the pic) into pizza slices and do some geometry to compute the distances in all directions and integrate over all of these and all staring point. I really wonder if there is a good way to do this on a piece of paper, the problem being how to parametrize the points which are inside and not counting these outside.</p>
<p>Monte-Carlo computations for regular polygons would be an interesting semi-solution too.</p>
<p>Edit: Not that it matters much, but the question is motivated by the question <a href="http://physics.stackexchange.com/questions/32358/mean-free-path-of-uv-photon">Mean free path of UV photon</a> and is part of me wondering about the escape route for particle entering a bunch of mass, and there specifically on the the dependence on the two length characteristica cloud dimensions and mean free path derived by the clouds constitution. Given that the direction of a particle after a collision is random and so it will probably have to make a detour through the cloud, what is the relation between the average cloud radius to the mean free patch such that the particle is able to leave after only one reaction. Because a collision is almost a reset, I have the suspicion that the escape time only falls slowly with the number of collisions a particles had to endure. The simulation of this might be a more standard question, i.e. starting at a random position and choosing a random direction after the mean free path traveled, how manny mean free paths does it take for a particle to escape a random polygon with characteristic measure being some multiple of the mean free path.</p> | g11552 | [
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0.02346227318048477,
0.06210379675030708,
... |
<p>Let us assume that a person moves at the speed of light say towards a planet -say Neptune. Neglecting the relativistic mass effects of the person, what would be his perception?
In Vsauce- a YouTube channel, in "travel inside a black hole " video, he describes that the field of view would be enormous since he can perceive all the light that surrounds him . This increase in the field of view creates an illusion of the planet moving away relatively but eventually converging on the planet.
This is convincing but I require more opinions and ideas on this...</p> | g11553 | [
-0.018337108194828033,
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-0.03399863839149475,
0.03092266246676445,
0.04273819923400879,
0.05947526544332504,
0.0001347... |
<p>I have some questions about the excluded volume parameter :
1. What is the definition of the excluded volume parameter , or how could I describe the excluded volume of a polymer system？
2. What is the excluded volume parameter of homopolymer without solvents? Is it the same as the case in athermal solvents?
Thank you !</p> | g11554 | [
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-0... |
<p>Can the collapse of a quantum mechanical state in general into one the eigenstates of an observable whenever its measurement is made written mathematically? If yes, how?</p> | g11555 | [
-0.03449989855289459,
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0.023904725909233093,
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0... |
<p>In one of the two main theoretical approaches used in describing ultracold Fermi gases and the BEC-BCS crossover, the so-called BCS-Leggett approach, the starting point is the BCS trial wavefunction:</p>
<p>$$ \mid BCS \rangle \equiv \prod_{\mathbf{k}} \left( u_{\mathbf{k}} + v_{\mathbf{k}} P^\dagger_{\mathbf{k}} \right) \mid 0 \rangle $$</p>
<p>where the $P^\dagger_{\mathbf{k}}$ operator creates a Cooper pair. It is often asserted that this wavefunction, which may seem tailored for a BCS-like problem, has far greater validity and can also be successfully exploited in describing the BEC-BCS crossover (see for instance: <a href="http://arxiv.org/abs/cond-mat/0404274">http://arxiv.org/abs/cond-mat/0404274</a>).</p>
<p>Even looking at the original articles by Leggett and Eagles (cited in the reference above) I cannot see why $\mid BCS \rangle$ should be valid in the BEC regime: I am looking for a review article (or even a textbook) addressing this issue.</p> | g11556 | [
0.0032339051831513643,
0.007898434065282345,
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0.04765100032091141,
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0.01614297926425934,
-0.0... |
<p>I have been thinking about something thing... </p>
<p>I want to attach four or any number of magnets with arms to an axle..</p>
<p><img src="http://i.stack.imgur.com/VLEnx.png" alt="enter image description here"> </p>
<p>Blue dots be magnets.</p>
<p>Its is not a wheel configuration, all arms can move independently, lets say i move first arm and it rotates and approaches the magnet on second arm with some momentum,
and repels the other magnetic, and then the second arm swings in motion, and son on an so forth, creating a chain reaction which is simulating rotation of magnets around axis.. </p>
<p>Now this is an impossibility because what i have stated above is an ideal system, there is always friction at work which will highly damp this process... wheel-axle-friction, air resistance, weight of magnets & arm etc etc.. </p>
<p>I was thinking about how close can we push this to being an ideal system.</p>
<p>I am going to provide some torque by electric motors to arms to compensate for damping... </p>
<p>lets say if there is no magnetic repulsion then the whole rotation is powered by electric motors but after introducing method of magnetic repulsive hammering to What Percentage the
electric power required could be dropped.. </p> | g11557 | [
-0.009868340566754341,
0.07856161892414093,
0.0028167981654405594,
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0.06269466876983643,
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0.05146324262022972,
0.02880815789103508,
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-0.005602302495390177,
0.004460644442588091,
0.0007511794101446867,
0.011810076422989368,
-0... |
<p>My friends and I are designing a bench press spotter. Essentially, when the user needs help lifting the barbell due to muscle fatigue, an arm on each side of the user raises to provide assistance. These arms are essentially cantilever beams. We determined that a rectangular beam would experience the least amount of stress when the bar provides a force equal to half its weight on each arm but we need to maximize the aspect ratio of the height and the width of the rectangle. </p>
<p>Our professor said to use fore-aft forces when doing this. Basically he means that if the user ends up tipping the bar and one end of the bar hits one of the arms at an angle without touching the other then the bar provides a force on the corner of the rectangular arm and this force is greater than if it touches each arm at the same time. Is there a way using forces to analyze the best dimensions for this?</p> | g11558 | [
0.03659456968307495,
0.026515215635299683,
0.001489266287535429,
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0.002675996394827962,
0.054431963711977005,
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... |
<p>Consider an experiment that produces photons in an entangled state such as $1/\sqrt{2}(|{H,H}\rangle+|{V,V}\rangle)$. The photons are in a superposition of horizontal and vertical polarization, and the way we analyze this is to say that the photons are in <strong>both</strong> states at the same time. Though this is odd, I can eventually reconcile it. However, the photons can also be in an entangled state such as $\sqrt{0.2}|H,H\rangle+\sqrt{0.8}|V,V\rangle$. Again, the photons are in <strong>both</strong> states at the same time, but do we say that they is somehow more in one state than the other? How can we think of this unevenly weighted superposition of states?</p> | g11559 | [
-0.03430125117301941,
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0.04862204194068909,
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0.01491326093673706,
0.04074160009622574,
0.012877016328275204,
0.030331401154398918,
-0.03330932930111885,
-0.024069685488939285,
-0.010716267861425877,
-0.... |
<p>Below is an excerpt from a physics textbook:</p>
<blockquote>
<p>One common way to charge a capacitor is to connect these two wires to opposite terminals of a battery. Once the charges $Q$ <strong>and</strong> $-Q$ are established on the conductors, the battery is disconnected. This gives a fixed potential difference $V_{ab}$ between the conductors (that is, the potential of the positively charged conductor $a$ with respect to the negatively charged conductor $b$) that is just equal to the voltage of the battery.</p>
</blockquote>
<p>Why does the potential difference between the conductors equal the voltage of the battery when the battery is disconnected? Could someone please provide a detailed explanation? Thanks in advance.</p> | g11560 | [
0.05924273282289505,
0.019759006798267365,
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0.04296676069498062,
0.07114210724830627,
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0.01290799118578434,
-0.06558512896299362,
-0.0012849505292251706,
-0.002905417699366808,
0.01... |
<p>Some cubic thermodynamical equations of state predict <a href="http://en.wikipedia.org/wiki/Pressure#Negative_pressures" rel="nofollow">negative pressures</a>, have negative pressures any physical meaning? Could they be related to <a href="http://en.wikipedia.org/wiki/Negative_mass" rel="nofollow">negative mass</a>?</p> | g11561 | [
0.04351304471492767,
0.008689775131642818,
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0.003922898788005114,
0.06834867596626282,
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0.035808220505714417,
-0.... |
<p><img src="http://i.stack.imgur.com/s2KzU.png" alt="enter image description here"></p>
<p>The picture is just for example. I don't know why $i$ and $i_1$ have different directions and $i+i_1=0$ according to KCL. Also, the value of voltage at each element. I mean in why the $V$ of the end of $R_1$ is negative but the start of $R_2$ is positive. Is the sign is just to indicate the direction of current, where the voltage is higher than the other at each element but not tell its value is positive or negative. Moreover, does the $V$ value of each element is define by its difference in $V$ which mean $\Delta V$.</p> | g11562 | [
-0.025488145649433136,
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-0.03438152000308037,
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0.07678988575935364,
0.01812034472823143,
0... |
<p>"If a wire loop is completely in magnetic field no current is induced as voltage induced is balanced by an equal and opposite voltage. "</p>
<p>My guess for this statement is that the loop wire must be stationary and that voltage is zero if its equal on both sides of the wire
my question is if current will stil be induced if the wire loop is moving but is still completely in the magnetic field.
(I know how as it enters and leaves induced current moves either clockwise or anti so what wil happen if its moving but not entering or leaving)</p> | g11563 | [
0.02335016429424286,
-0.01636705920100212,
0.012069088406860828,
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0.008589250035583973,
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0.013613831251859665,
-0.09603019803762436,
0.01281... |
<p>My question has an inclined plane of mass $M$ and simple block kept on it, of mass $m$ (Both on a table). All surfaces are friction-less. Both of the objects would move, block down the incline and inclined plane parallel to the table, somewhat opposite to the block. Can the two equations I make be from the Free Body Diagram (FBD) of incline, in GROUND frame, and FBD of block in the INCLINED-PLANE frame?
Or do I need to solve in a single frame(either GROUND or INCLINED-PLANE)?</p> | g11564 | [
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0.05147499963641167,
0.01129131019115448,
0.0285464059561491,
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0.002541189081966877,
0.01376570388674736,
-0.0043881... |
<p>In the definition of the electrical field we use the concept of a test charge because we state that the point charge is required for the direct application of the Coloumb's Law and its infinitesimal small magnitude ensure that it does not distort the actual field that we intend to measure. But once the electrical field is defined we directly apply F=qE even if the considered point charge is of a finite magnitude. Why don't we consider the effect of the distortion of the original field here ?</p> | g11565 | [
0.05780893936753273,
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0.06346543878316879,
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-0.04753507301211357,
0.... |
<p><em>NOTE: Because this was a long question I have split it up in two different questions!</em></p>
<p>For a course on quantum integrability I am reading <a href="https://people.sissa.it/~ffranchi/BAnotes.pdf" rel="nofollow">these</a> notes.
(Franchini: Notes on Bethe Ansatz Techniques. Lecture notes (2011))</p>
<p>Some questions have arisen to me, concerning the Heisenberg XXZ model. The general idea is that we will solve several versions of this model in class, using the Bethe Ansatz Approach. However, the basics are not yet clear to me.
Consider the Hamiltonian:
\begin{equation}
\hat{H} = - J \sum_{i=1}^N \left(S^x_jS^x_{j+1} + S^y_jS^y_{j+1} + \Delta S^z_jS^z_{j+1}\right) - 2h\sum_{i=1}^NS^z_j,
\end{equation}
where we have periodic boundary conditions: $S^{\alpha}_{j+N} = S^{\alpha}_j$. In the following I will set $h=0$.</p>
<ol>
<li><p>For $\Delta = 1$ we recover the Heisenberg XXX model. At first I thought that a ground state would be all spins making an angle of 45 degrees with the z-axis and the projected part an angle of 45 degrees with both the y and the x axis. Equivalent ground states would then follow by performing rotations of 90 degrees around the z-axis. However, it occurred to me that the model is solved by introducing the spin flip operators: $S^{\pm}_n := S^x_n \pm iS^y_n$. I think this effectively means that you are quantizing along the z-direction, yielding a ground state $|0> = |\uparrow\uparrow\uparrow\dots\uparrow>$, with all spins in the z-direction. Is this reasoning correct? Of course I have done spin in my quantum mechanics course, but I fail to make the connection with this case and have lost my handiness with it.</p></li>
<li><p>$\Delta=0$: the XX or XY model. Apparently <em>"the model can be exactly mapped into free lattice fermions"</em>. I have no clue what this means and how it works. References?</p></li>
</ol> | g11566 | [
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-0.03574664518237114,
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0.01192953996360302,
0.03483829274773598,
0.0... |
<p>We all know the explanation videos and other material using the water waves analogy to illustrate the propagation of electrons or photons and the interference patterns measured in the the single-slit and double-slits experiments.</p>
<p>Being just an analogy it misses for sure many attributes by which light/electron waves differ from water waves.</p>
<p>BUT: If limited only to use water-waves analogy would it be possible to simulate the impact of the observer/detector in the experiments by means of water waves (yes, i'm smiling my self at this a little ;) </p>
<p>What would be the properties of such a detector-by-means-of-waves needed to simulate the collapse of the interference pattern, for example?</p>
<p>In other words is it possible to rebuild the double-slit experiment with such a water-waves setup and with same known results?</p>
<p>How about in theory? What ("strange") requirements are there?</p>
<p>For starters maybe let's drop the switching the slit-result and let's assume when the observer is turned on the water wave shows to be originating always from the same slit...</p>
<p>At what earliest point does this "model" break? How?</p>
<p>Thanks!</p> | g11567 | [
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0.0517... |
<p>In QED and the basic Higgs mechanism, there is a local gauge transformation where a scalar field $\phi$ is transformed as:</p>
<p>$e^{i\theta\eta(x)} \phi$ </p>
<p>The partial derivative of this however makes the above not
invariant, and so a covariant derivative is introduced in this way:</p>
<p>$D_\mu e^{i\theta\eta(x)} \phi$=$(\partial_\mu- i \theta A_\mu)$$e^{i\theta\eta(x)} \phi$ </p>
<p>So, the derivative remains invariant. However, what if the scalar field is transformed by TWO U(1) symmetries like this:</p>
<p>$e^{i\lambda_1\eta_1(x)} e^{i\lambda_2\eta_2(x)} \phi$ </p>
<p>This may be a strange symmetry transformation, but I wonder how would one make the derivative of this invariant like this:</p>
<p>$e^{i\lambda_1\eta_1(x)} e^{i\lambda_2\eta_2(x)} D_\mu \phi$ </p>
<p>For the derivative is now of three different functions which differentiate by the product rule like this:</p>
<p>$f'(x)g(x)h(x)$+$g'(x)f(x)h(x)$+$h'(x)f(x)g(x)$ </p>
<p>Thus, the derivative of the function would be:</p>
<p>$i \lambda_1 \eta_1' (x)e^{i\lambda_1\eta_1(x)} e^{i\lambda_2\eta_2(x)} \phi$ +$i \lambda_2 \eta_2' (x)e^{i\lambda_2\eta_2(x)} e^{i\lambda_1\eta_1(x)} \phi$+$(\partial_\mu \phi) e^{i\lambda_1\eta_1(x)} e^{i\lambda_2\eta_2(x)}$ </p>
<p>So, how would the local gauge invariance derivative be applied in this situation? Would another gauge field be introduced such as $B_\mu$ along with $A_\mu$ ?</p> | g11568 | [
0.039577119052410126,
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<p>Say I am measuring a quantity $x$ in physical system whose true value is approximately sinusoidal in time. I have an instrument to sample this quantity, for which the manufacturer gives an accuracy spec. Can I use this accuracy spec $(\Delta x?)$ to compute the uncertainty of the sample mean $\bar{x}$ of the quantity based on a finite amount of samples, $N$?</p>
<p>My guess is that the naive calculation would be</p>
<p>$$
\Delta{\bar{x}} = \frac{\Delta{x}}{\sqrt{N}},
$$</p>
<p>but this would assume the samples are all statistically independent. Can I use this assumption, or should $N$ be based on the number of periods sampled, or something else?</p> | g11569 | [
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<p>Wolf's paper <a href="http://nzaier.com/nzaierbb/system/upload_files/Physica1985_wolf_LyapunovExpo.pdf" rel="nofollow">Determining Lyapunov Exponents from a Time Series</a> states that:</p>
<blockquote>
<p>Experimental data typically consist of discrete measurements of a
single observable. The well-known technique of phase space
reconstruction with delay coordinates [2, 33, 34] makes it possible to
obtain from such a time series an attractor whose Lyapunov spectrum is
identical to that of the original attractor.</p>
</blockquote>
<p>One of the cited papers, <a href="http://tuvalu.santafe.edu/~jdf/papers/geometrytimeseries.pdf" rel="nofollow">Geometry from a Time Series</a>, elaborates:</p>
<blockquote>
<p>The heuristic idea behind the reconstruction method is that to specify
the state of a three-dimensional system at any given time, the
measurement of <em>any</em> three independent quantities should be sufficient
[...]. The three quantities typically used are the values of each
state-space coordinate, $x(t)$, $y(t)$, and $z(t)$. We have found
that [...] one can obtain a variety of three independent quantities
which appear to yield a faithful phase-space representation of the
dynamics of the original $x$, $y$, $z$ space. One possible set of
three such quantities is the value of the coordinate with its values
at two previous times, e.g. $x(t)$, $x(t - \tau)$, and $x(t - 2\tau)$.</p>
</blockquote>
<p>Finally, Rosenstein's paper <a href="http://www.physionet.org/physiotools/lyapunov/RosensteinM93.pdf" rel="nofollow">A practical method for calculating largest Lyapunov exponents from small data sets</a> states that:</p>
<blockquote>
<p>The first step of our approach involves reconstructing the attractor
dynamics from a single time series. We use the method of delays [27,
37] since one goal of our work is to develop a fast and easily
implemented algorithm. The reconstructed trajectory, X, can be
expressed as a matrix where each row is a phase-space vector. That is,
$$ X = [X_1\;X_2\; ...\,X_M]^T$$
where $X_i$ is the state of the system at discrete time $i$.</p>
</blockquote>
<p>All three papers seem to implicitly assume that the system under study has a multi-dimensional phase space, but that only one dimension can be measured experimentally, and therefore that the full phase space data must be reconstructed from a one-dimensional time series. </p>
<p>However, what if the time series is multi-dimensional, indeed of the same dimension as the phase space, to begin with? For instance, consider the problem of showing experimentally that a simple pendulum is not chaotic. The phase space is 4-dimensional ($r$, $\dot r$, $\phi$, $\dot \phi$) and it is straight-forward to design an experiment which generates a 4-dimensional time series of the values of these variables at each time step. </p>
<p>Is it possible to skip the reconstruction in this case, and use $X = [r\; \dot r\; \phi\; \dot \phi]^T$ in place of the reconstructed trajectory in Rosenstein's paper, with no additional modifications? Is there a simpler way to calculate Lyapunov exponents when the full phase-space state of the system is known?</p> | g11570 | [
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-0.047450724989175797,
0.0003183552180416882,
-0.001991308992728591,
0.027454908937215805,
... |
<p>In Weinberg's book <em>The Quantum Theory of Fields, Volume 1</em> on p.388 (Chapter 9), the following identity is used (with f being any "reasonable" function):</p>
<p>$$f(+\infty) + f(-\infty) = \lim_{\epsilon \rightarrow 0^+} \epsilon \int_{-\infty}^{+\infty} d\tau f(\tau) e^{-\epsilon |\tau|}.\tag{9.2.15} $$</p>
<p>I don't understand the identity in a qualitative / heuristic way.</p> | g11571 | [
-0.016813352704048157,
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0... |
<p>Some phenomena in physics defy intuition. Others have very intuitive explanations which you could explain easily to a layman. Sometimes, these intuitive explanations are simply wrong.</p>
<p>What phenomena in physics have intuitive, but totally wrong, explanations? An explanation you could use to easily convince your non-physicist spouse: something that would make them <em>think</em> they understand what's happening while being incorrect?</p>
<p>I'll present one (somewhat contrived) example: </p>
<blockquote>
<p>Bernoulli's principle is often used to explain how airplanes fly.
After explaining Bernoulli's principle, the layman might ask "okay, so
why does the air on top of the wing move faster than the air below
it?" A seemingly intuitive explanation is that because the wing is
curved, the top surface has a longer length from leading edge to
trailing edge than the bottom surface. Therefore, if two air particles
hit the leading edge simultaneously, and one travels above the wing
while the other travels below it, the one traveling above must move
faster in order to arrive at the trailing edge at the same time as its
under-wing counterpart. This explanation is totally wrong because
there is no rule of physics that states the two particles have to
arrive at the same time. (And a non-curved "barn door" wing is quite
capable of producing lift.) So the phenomenon here is genuine -- a
wing does generate lift, Bernoulli's principle is involved, and the
air above the wing is moving faster and has lower pressure than the
air below it. But the "two particles racing each other, ending in a
tie" explanation is simply wrong.</p>
</blockquote> | g11572 | [
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0.006467668805271387,
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-0.04330615699291229,
-0.02119993418455124,
0.0... |
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