question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>I need something like a summary of existing results, including the treatment of BCS Hamiltonian and Hubbard model. Auerbach's book is a good one but I still hope to get more comprehensive review. My purpose is to compare the methods and give an outline of the mathematical framework behind this. Currently I am working on a small problem, where I am asked to obtain some effective action from variational method. To really understand what I am doing, I need to understand other applications of the variational methods and hopefully to draw some analogies.</p> | g10464 | [
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<p>Take a look at this diagram: <a href="http://www.chegg.com/homework-help/questions-and-answers/7-pipe-assembly-supports-vertical-loads-shown-determine-components-reaction-ball-socket-jo-q2260091" rel="nofollow">http://www.chegg.com/homework-help/questions-and-answers/7-pipe-assembly-supports-vertical-loads-shown-determine-components-reaction-ball-socket-jo-q2260091</a></p>
<p>If you calculate moment around point B, you can ignore the forces of the tension and only the forces at the ball and socket and the weights come into play. Therefore for moment at B to be zero, the Y and X components of the ball and socket have to be zero. </p>
<p>However, if the x and y components at the ball and socket are at 0, theres nothing to cancel out the X and Y components of the tension forces, meaning the forces are at unbalanced.</p>
<p>What am I missing?</p>
<p><strong>Please answer MY question not the question at the link</strong></p> | g10465 | [
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<p>How would the non-interacting electron orbitals from a perfect <a href="http://en.wikipedia.org/wiki/Density_functional_theory" rel="nofollow">DFT</a> solution for a given potential shape differ from the 'true' electron wavefunctions? Or can you only really talk about the total wavefunction? Would they be less localised as they do not include interaction effects?</p>
<p>Since Hohenberg-Kohn showed that a functional of the wavefunction could be transformed into a functional of the density, any 'measurements' on the total density would have to yield the same results as measurements on the total wavefunction, I think.</p>
<p>Intuitively, if we imagine a 3-electron system, the ground state consists of spin-up and -down electrons in the lowest state, and a singlet electron in the next state. Since there is correlation and exchange, the total wavefunction would be a superposition of the various possible combinations of these. </p> | g10466 | [
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<p>I am interested in the vibrations of a thin, flexible rod that would only be clamped at one point, properly I'd like to calculate its eigenvalue. But the way I learned it in wave mechanics doesn't seem to apply here. The equation is: </p>
<p>$$ \frac{1}{c^2}\frac{\partial^2 u}{\partial t^2} = \frac{\partial^2 u}{\partial x^2}$$ </p>
<p>with $u = u(x,t)$ defined has the micro-displacement in one transverse direction, $x$ the longitudinal direction of the string, $c$ the speed of sound. Or applying </p>
<p>$$u (0,t) = \partial_x u(x,t)|_{x=0}=0$$ </p>
<p>has no non trivial solutions, and so no spectrum. My real interest is to calculate the vibrational spectrum of a cantilever clamped at one of it extremities, which also obeys a second degree wave equation. (and I know that software can calculate these spectra, with the same boundary conditions, using the same equations)</p> | g10467 | [
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<p>I have some questions about Nanotechnologies. I'm not physicist and my knowledges about the topic are limited by the "Engines of Creation" book by Eric Drexler. So I think that my questions are related mostely to popular science.</p>
<ol>
<li><p>As far as I know the molecular mechanisms like nanoassemblers and nanofactories exist in nature(I mean alive cells). Why have they not been created artificially by now?</p></li>
<li><p>In case that they have been artificially created yet, do they have any limitations in developing of macro objects?</p>
<p>For instance, macromechanisms which exist in nature like animals are grow very slowly(months and years) and the initial program(i.e. DNA encryption) doesn't allow to make accurate copies. I mean that the twins who are growing from the same genetic material have a significant difference in adulthood(i.e. different phenotypes). Is this phenomena the result of some fundamental low of nature like Heisenberg uncertainty principle or any other that can't be resolved by modern technological methods?</p></li>
<li><p>What are the top well known laboratories and organisations in the world which are engaged to resolve such kind of problems?</p></li>
</ol>
<p>Thanks in advance.</p> | g10468 | [
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<p>Let $O$ be an observable on a Hilbert space $\mathcal{H}$, and let $B$ be a subset of the spins composing $\mathcal{H}$, and let $\bar{B}$ be its complement. Now define</p>
<p>$\displaystyle O_B = \frac{1}{\operatorname{Tr}_{\bar{B}}\mathbf{1}_{\bar{B}}} \operatorname{Tr}_{\bar{B}}(O) \otimes \mathbf{1}_{\bar{B}}$.</p>
<p>Is this quantity equal to</p>
<p>$\displaystyle \int d\mu(U) U O U^\dagger$?</p>
<p>The integral is taken over the set of unitary operators acting on $\bar{B}$ and $\mu$ is the Haar measure of $U$. If so, why is this the case?</p>
<p>What physics course/book/reference introduces these sorts of integrals? </p>
<p>Note: this question came up from trying to understand the following paper: <a href="http://arxiv.org/abs/quant-ph/0603121" rel="nofollow">http://arxiv.org/abs/quant-ph/0603121</a></p> | g10469 | [
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<p>From <a href="http://en.wikipedia.org/wiki/Kelvin">Wikipedia</a>:</p>
<blockquote>
<p><em>The kelvin is defined as the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water.</em> </p>
</blockquote>
<p>That presupposes that we can take a fraction of temperature.</p>
<p>Now, taking a fraction of mass, distance, or duration is well defined. Is taking a fraction of temperature well defined? Doesn't this depend on operational definitions of temperature - such as change in length?</p>
<p>This is similar to the objection many physicists had with measuring human perceived loudness: What does it mean to say that humans perceive loudness as proportional to log of pressure? We can order perceived loudness, but how do you add two perceptions of loudness, so that any type of proportionality makes sense?</p>
<p>Related question: If $K$ cannot be defined in terms of basic units, why do we say $mgs$ and not $mgsK$?</p> | g10470 | [
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<p>At what depth in the water atmospheric pressure is 100 times greater than on the ground?
This question comes from the fact that average pressure in Earth( 1000 mbar) is 100 times greater than in Mars( 7 mbar).</p> | g10471 | [
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<p>Numerical Aperture (NA) (for fiber optics) is usually used to denote the acceptance cone for a multi-mode fiber. </p>
<p><strong>Does NA also describe the expansion of light emitted from the end of a fiber?</strong></p>
<p>I have a 1mm core 0.22 NA PMMA fiber, I would like to collimate the light once it's reached a 1.5" diameter. </p>
<p>$$
n\sin(\theta)=NA \\
\theta = \arcsin(\frac{.22}{1.4914}) \\
\frac{.5 \cdot 38 [mm]}{ \tan(\theta)}=\left \{ \text{focal length} \right \}
$$</p>
<p>So, I should need a ~130 mm focusing lens?</p>
<p><strong>edited in response to answer bellow</strong></p>
<p>is n the index of refraction of the fiber core (1.4914), or free space (1)?</p> | g10472 | [
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<p>Does it make sense to say, "The speed of light varies?" Some may say right off the bat "Yes, it changes as a wave passes through a different medium." However, I'd like to say no, because when I hear someone say the speed of light, I always think of the constant $c$ (unless the medium is specified to not be a vacuum, but then it isn't $c$ anymore), not the speed of a particular wave. To me, it makes more sense to say something like, "The speed of a particular wave varies." What is the correct way to state this in the professional world? And in general, when professional physicists say "the speed of light," are they referring to the constant or the actual speed of the wave?</p> | g1028 | [
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<p>There's this question that has been bugging me most of my life: how is it that wet clothes left hanging to dry, get actually dry?
If I get it right, the clothes are a mesh of fibers (we could assume synthetic fibers to make it simpler) that capture droplets of water in the mesh.
When one hangs the cloth gravity makes some of the droplets fall from the mesh; still if there's a side that's exposed to a heat source it dries faster, so in addition to gravity there's also heat. However, the heat does not boil the droplets.</p>
<p>So...
- what is actually going on there ?
- could the drying be optimized, e.g. maximizing surfaces exposed, etc ?</p> | g10473 | [
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<p>The Yukawa coupling of the top quark is Dirac-natural in a too excellent way, it is within one sigma experimentally, and within 99.5% in absolute value, of being equal to one. Without some symmetry, it seems too much for a quantity that is supposed to come down from GUT/Planck scale via the renormalization group. Is there some explanation for this?</p> | g10474 | [
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<p>While determining the electric field in a Non-Conducting Sphere using Gauss's law,why the positive charges are considered inside the surface,but in determining the electric field in a conducting Sphere,why the positive charges are considered outside the surface? </p>
<p>And,why if any point charge is inside a sphere,the the net electric field is considered zero?</p> | g10475 | [
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<p>Can someone explain nuclear isomers to me, and in particular what the energy involved is? I understand generally that we're talking about moving from a less to more stable configuration of nuclear particles, but that's about as far as my understanding goes.</p> | g10476 | [
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<p><a href="http://en.wikipedia.org/wiki/Mechanical_advantage" rel="nofollow">Mechanical advantage</a> is defined as Force Output/Force Input</p>
<p>For a symmetrical wedge with the length of the slopes being equal and the width being the distance between the end points, </p>
<p>articles quote the Mechanical advantage as length/width</p>
<p><img src="http://www.essential-physics.com/samples/Images/SB/28/LR/WedgeForces.png" alt="forces in a wedge"></p>
<p>I will assume that you are splitting wood using a symmetrical wedge (lengths of the slopes are equal) and driving the wedge into the wood with a hammer vertically starting with the center of the wooden block. Let us say the width is $w$ and the slope length is $l$. The Input vertical force is resulting in two sideward forces on the wood. Each of these sideward forces is causing the separation in the wood. If, based on the above diagram, I assume that each of these output forces is $F_{in} sin \theta$ where $\theta$ is the angle between the vertical direction of $F_{in}$ and the slope, I have</p>
<p>$$\sin \theta = \left(\frac12 w\right)\cdot\frac{1}{l}, $$</p>
<p>Output force,
$$F_{out} = 2 F_{in} \cdot \sin \theta = 2 F_{in} \left(\frac12 w\right)\cdot\frac{1}{l} = F_{in} \cdot \frac{w}{l}$$</p>
<p>or
$$\frac{F_{out}}{F_{in}} = \frac{w}{l}$$</p>
<p>This is the inverse of the expected mechanical advantage.</p>
<p>When I equate work done, I get $F_{in} \times height = Load moved \times distance$. </p>
<p>Assuming Load moved is $2*F_{out}$ and distance moved is the perpendicular from center on the slope (perhaps, this statement is wrong. Each point along the vertical was moved by a different amount), I have</p>
<p>$$2*\frac{F_{out}}{F_{in}} = 2\frac{\rm height }{\rm perpendicular\,from\,center\,on\,the\,slope} = 2\sin \theta = 2\left(\frac12 w\right)\cdot\frac{1}{l}= w/l$$</p>
<p>But the mechanical advantage of a wedge is mentioned as $l/w$. Why?</p> | g10477 | [
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<p>In studying rotational dynamics of a rigid body , I can't seem to understand why you can solve the problem correctly only using certain points in a body and not all ? Means angular momentum and torque leads to correct answer only in some cases</p> | g10478 | [
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<p>How is the boxed step , physically as well as mathematically justified and correct ?</p>
<p>Source:Wiki <a href="http://en.wikipedia.org/wiki/Electric_potential_energy" rel="nofollow">http://en.wikipedia.org/wiki/Electric_potential_energy</a></p>
<p>As work done = $- \Delta U $. for Conservative force and it shouldn't matter whether we take $ds$ or $-dr$ ?</p>
<p>And when $dr$ is just a notation to specify the variable and the real thing behind it , is a limit , why is it that $dr$ is so important here .</p>
<p><img src="http://i.stack.imgur.com/HCWeH.jpg" alt="enter image description here">
Image : <a href="http://www.artofproblemsolving.com/Forum/download/file.php?id=43358&mode=view" rel="nofollow">http://www.artofproblemsolving.com/Forum/download/file.php?id=43358&mode=view</a></p>
<p>What is wrong here ?</p>
<blockquote>
<p>$$\newcommand{\newln}{\\&\quad\quad{}} \begin{align}&\int^{r_b}_{r_a}\mathbf{\vec{F}}\cdot d\mathbf{\vec{r}}=-(U_a-U_b) \newln \Rightarrow \int^{r}_{\infty}\mathbf{\vec{F}}\cdot d\mathbf{\vec{r}}=-(U_r-U_\infty) \newln \Rightarrow \int^{r}_{\infty}\mathbf{\vec{F}}\cdot d\mathbf{\vec{r}} =-U_r ~~~~~~~ [U_\infty = 0], \cos\theta=-1 , \vec{A} \cdot \vec{B}=|A||B|\cos\theta\newln \Rightarrow -\int^{r}_{\infty}k\cdot\frac{q.q_o}{r^2}dr=-U_r ~~~~~~~ [\textrm{Coulomb's Law}]\newln \Rightarrow kq\cdot q_o\int^{r}_{\infty}\frac{1}{r^2}dr=U_r\newln \Rightarrow kq\cdot q_o\left[\frac{-1}{r} \right]^r_\infty=U_r\newln\Rightarrow \frac{-kq.q_o}{r}=U_r\newln \Rightarrow U_r=-\frac{kq.q_o}{r}
\end{align}
$$</p>
</blockquote> | g10479 | [
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<p>This is just a curiosity and you need to bear with me as my math skills were always sub-par and so is my English academic language. My specialty is Electronics but I have always been a programmer.
Years ago I was working on my diploma paper that dealt with locating leaks using auto-correlation.<BR>
Basically you have several sound sensors along a pipe which record the sound wave. If a leak appears then you get a peak in the autocorrelation function. Then you perform a 'triangulation' from two or more sound sensors and you can locate the leak pretty accurately. Anyway, my task was mostly to help a PHD student with transposing her algorithms into Matlab.<BR><BR>
We have succeeded doing this with air but as soon as we switched to water I could not use any kind of windowing and/or transformation to get relevant peaks. At some point I just hunted blindly for some Matlab functions that would give me a relevant peak somewhere that would correlate with the distance to the leak, but failed.<BR><BR>
I cannot to this day understand why we were not able to succeed, though I do assume that is has to do with water's turbulence. The setup was a running tap routed through metal pipes (about 10cm diameter), with about 5 very sensitive sound sensors (going to about 100kHz) placed about 3 meters apart and some taps along the way that simulate leaks. Everything was placed in a phonic-insulated basement, signals were truncated taken to stabilize against footsteps/vibrations so measurements were pretty good.<BR><BR>
The multiple question is: what could have been done to achieve the goal or at least get closer to it? Is it really achievable (probably not in real life where you have trucks running above)?<BR>
Some variables that could influence but for which I lack the knowledge to explain: pipe diameter, water debit rate, tap/leak rate and diameter, choice of liquid, pipe material, sound spectrum and possible frequency filtering.</p> | g10480 | [
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<p>Light is a transverse wave. Therefore, light in the optical range (i.e. visible light) couples to transverse collective excitations of a material when measuring the optical conductivity for instance. Likewise, X-rays are also transverse waves, but somehow couple to longitudinal collective excitations of a material. </p>
<p>I understand that it is because X-ray photons couple to the electron density as detailed in this <a href="http://iopscience.iop.org/0953-8984/13/34/304" rel="nofollow">paper</a>, but what I am looking for is a plausible intuitive explanation with some physical insight as to why this might be so.</p>
<p>(Sorry if you can't view the paper from the publisher without incurring a fee, but I couldn't find it anywhere else. I think the question is clear enough without the link, though.)</p> | g10481 | [
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<p>I am still very new to many physics theories, however while sat in class today, a thought came to mind that I have not been able to answer from simple googling. </p>
<p>What is so specific about our sun that we orbit it? It is by no means the largest star and it's mass is apparently around average for a star. So why, out of all the stars, do we orbit the sun? Is it due to position, pure coincidence or is it something I do not know about with my limited knowledge. Thanks for your help. </p> | g10482 | [
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-0.019806919619441032,
0.06359986960887909,
0.01420265156775713,
0.06416469812393188,
-0.01370... |
<p>I just met with a very basic question.(Might even sound silly!) My textbook kinda says(not exactly), 'Whatever flows is a fluid'. That got me wondering because we are creating a whole category of matter just because they flow! So there must be some significance to 'flowing'. That further led me to ask why in the first place should we say liquids and gases "flow" and not "move"?! It seems to tell me that there should be a major difference between the physics of flow and movement. What is it?</p>
<p>PS:- I don't want the difference in meaning from a dictionary but a scientific difference. Please don't get too mathematical. I haven't acquired good mathematical skills YET.</p>
<p>Edit:- Okay. Since a comment below says "Movement is actually seldom defined very rigorously", I suppose I must refine my question here. Consider someone is saying that a box moves on a table as you applied a force on it. Now why is that person saying it 'moved' rather than it 'flowed', here? What is the difference between flow and movement in this case and how can we generalize the idea?</p> | g10483 | [
0.02347751148045063,
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0.0009866415057331324,
0.03186413645744324,
0.060917191207408905,
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0.018017904832959175,
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-0.0984368696808815,
0.04119762033224106,
0.013744911178946495,
0.05795085057616234,
0.01098... |
<p>I know this question is probably not adequate to this SE either, but let me explain my situation: I'm civil engineering's college, so, there isn't a SE for civil engineering, and my doubts about integration in engineering are pratically pure physics. So, as I said, I'm graduating, but I'm from Brazil, education here is the same thing as nothing (belive me, it really sucks, I see people come out of physics's college without knowing who Maxwell was..), and I read my calculus books and see they all use Riemann integrals (of course, they don't say that..); but, in my searchs, I see a lot of <a href="http://en.wikipedia.org/wiki/Lebesgue_integration" rel="nofollow">Lebesgue integration</a>, especially concerning problems of calculating the center of mass of an object, in continuum mechanics, etc. So, here's my question:</p>
<ol>
<li><p>Lebesgue integration isn't the most easy thing in the world, I don't have a lot time, and education here sucks, should I spent my time studying Lebesgue integration instead of Riemann's? </p></li>
<li><p>Which one do you guys use more in physics with applications in engineering?; of course, the last one it's a little trouble, because engineering just "borrow" from physics. But, in general, which compensates more? </p></li>
</ol> | g10484 | [
0.04939114674925804,
0.06113400310277939,
0.018251659348607063,
0.0005945333978161216,
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0.04048779979348183,
0.04265568032860756,
0.00950054544955492,
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-0.0003878776333294809,
-0.01959962584078312,
0.001187264104373753,
0.031407542526721954,
-0.01... |
<p>So I am studying the laws of Newton and I'm wondering, are there any deficiencies related to the laws? I mean, somewhere where I can't use them or anything?</p> | g10485 | [
-0.02987786941230297,
0.018148191273212433,
0.02167494036257267,
0.03519381955265999,
0.04549705237150192,
0.038729630410671234,
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0.00876534916460514,
0.02403087541460991,
0.0006572023266926408,
-0.020198728889226913,
-0.04378846660256386,
-0.033745575696229935,
0.0127... |
<p>Feynman suggested that there is an infinity of trajectories for a single electron travelling from the source to the phosphorescent screen. He said that one electron goes through both holes (Fig 4.10, page 110, The Elegant Universe, Brian Greene).</p>
<p>Is it possible that there is a simpler explanation? </p>
<p>The double slits bear a parallel resemblance to the characteristics of a simple slot antenna equal to a simple dipole antenna. Can the incident electrons induce a charge into the area surrounding the slot and cause an electric field to be created between the slot edges. This would serve to convert the electron from a transverse particle wave to a longitudinal magnetic wave which is then radiated forward. The interference pattern is created as the output of each slot interferers with each other producing the interference pattern on the phosphorus screen. It would also explain why, when a sensor is introduced to monitor what is happening in the slit, it causes the magnetic wave to change back to a particle wave, because it has disturbed the field in the slots.</p> | g10486 | [
-0.012924361042678356,
0.06133703142404556,
-0.021554110571742058,
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0.08893665671348572,
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0.062463823705911636,
0.028182778507471085,
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-0.011058022268116474,
0.007946259342133999,
0.07462666183710098,
0.029503939673304558,
-0.0... |
<p>The following decay is possible according to the PDG and according to my notes it is a strong decay:</p>
<p>$$\omega(1420) \to \rho^0 + \pi^0$$ </p>
<p>The JPC values are:</p>
<p>$\omega(1420)$ 1-- </p>
<p>$\rho$ 1--</p>
<p>$\pi$ 0-+</p>
<p>So, all three particles have, for themselves, a parity of -1.</p>
<p>The combined parity on the right side should then be (-1)*(-1)=1. But the left side has a parity of -1. This violates parity, but parity should not be violated in a strong decay.</p>
<p>1) What's going on and where is the error in my argument? </p>
<p>2) How can I calculate the orbital angular momentum the two decay products have in relation to each other?</p> | g10487 | [
0.013722083531320095,
-0.016289373859763145,
-0.008914527483284473,
0.015851790085434914,
0.10214221477508545,
0.024057704955339432,
0.005058574955910444,
0.05065910145640373,
0.01050557754933834,
-0.0461055152118206,
-0.018338171765208244,
0.014918048866093159,
-0.011390931904315948,
-0.0... |
<p>I'm a physics graduate now working with computers. I study GR in my spare time to keep the material fresh. In the Wikipedia article about <a href="http://en.wikipedia.org/wiki/Mathematics_of_general_relativity" rel="nofollow">the mathematics of GR</a>, one can read the following:</p>
<blockquote>
<p>The term 'general covariance' was used in the early formulation of general relativity,
but is now referred to by many as diffeomorphism covariance. Although diffeomorphism
covariance is not the defining feature of general relativity, and <em>controversies remain
regarding its present status in GR</em>, the invariance property of physical laws implied in
the principle coupled with the fact that the theory is essentially geometrical in
character (making use of geometries which are not Euclidean) suggested that general
relativity be formulated using the language of tensors. [My italics.]</p>
</blockquote>
<p>Do anyone know what kind of controversy the author(s) may be aiming at? Isn't general covariance, ehrm ... diffeomorphism covariance, a founding principle of GR?</p>
<p><strong>UPDATE:</strong>
Evidently there is no "right" answer to a question like this (unless you happen to be the author of said article and thus could share with the world what you where aminig at). Anyway, it seems as there isn't a widely known, heavily debated controversy regarding general covariance. <del>Even so, I've chosen to accept Ron's answer.</del></p>
<p><strong>UPDATE 2:</strong>
I've retracted the acceptance due to the linked article by prof. Norton. I think that, for all practical purposes, Ron's answer still stands, yet I want to review said article first. However, nobody should hold their breath waiting for me to figure this out. :)</p> | g10488 | [
0.01651189476251602,
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0.024909531697630882,
0.07934015244245529,
-0.03496875986456871,
0.025924168527126312,
-0.... |
<p>I am curious. If you were to put a solar panel up in high altitude or on the surface of the moon, both of which have much less atmosphere to reflect/refract light, would that solar panel produce more energy?</p>
<p>I am curious because an article comments discussion got me thinking about setting up a low Earth orbit solar collection platform as a power plant for a city or nation. Then I got thinking about how to bring it down to the surface (the energy that is). Which had me thinking about using really long cables stretched from the satellite to a high-altitude dirigible platform that would then allow it to more easily bring the energy to our planets surface.</p>
<p>From there I started wondering if the high altitude dirigible platform would instead be up high enough to garner any added energy collection benefits. It would certainly help with space saving on the ground and could be rather quickly moved into a disaster area for emergency power purposes. Being a dirigible it would also be relatively easy to keep it aloft. With it far above the clouds it should be able to avoid many weather issues as well (as far as I am aware).</p>
<p>So does anyone know if there would be any added benefits from solar collection in a thinner atmosphere environment from a power generation perspective? What pitfalls can you think of? The biggest one I can think of is the efficient transport of the energy.</p> | g10489 | [
0.046227533370256424,
0.0224785003811121,
0.022381961345672607,
0.06294035166501999,
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0.0870169922709465,
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-0.031900882720947266,
0.02688463404774666,
0.006831945385783911,
0.007958860136568546,
-0.0300... |
<p>After finding the eigenfunctions $u_p(x)=Ce^{ipx/\hbar}$ of the <a href="https://en.wikipedia.org/wiki/Momentum_operator" rel="nofollow">momentum operator</a> just like in <a href="http://quantummechanics.ucsd.edu/ph130a/130_notes/node138.html" rel="nofollow">this UCSD lecture notes</a>, one seeks to normalize them, so one first tries:
$$\int\limits_{-\infty}^{\infty} dx \, |C|^2 e^{-ipx/\hbar} e^{ipx/\hbar} = \int\limits_{-\infty}^{\infty} dx \, |C|^2 \rightarrow \infty $$
which diverges unless $C =0$. </p>
<p>Then it is shown that $u_p(x)=\frac{1}{\sqrt{2\pi \hbar}}e^{ipx/\hbar}$ satisfies the normalization condition $\langle p'|p\rangle=\delta(p-p')$</p>
<p>Why does the UCSD page say that the first solutions (the divergent ones) "are not normalizable to one particle"? How does the development that follows relate to many particles?</p>
<p>Does this have something to do with $\int\limits_{-\infty}^{\infty}dp \delta(p-p') =1$? Then all the $p'$ are the other particles?</p>
<p>I have no source to show for this, but how would $\frac{1}{2\pi \hbar}$ particles per unit of length and unit of momentum relate? Is it correct to say that $2\pi \hbar$ is the expected number of times one repeats the measurement of the momentum? Then where would the 'per unit of length' part come from?</p> | g10490 | [
0.03148747980594635,
0.057195745408535004,
-0.0330238938331604,
-0.04927339777350426,
0.09749671816825867,
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-0.0235967468470335,
-0.05551449581980705,
-0.036693353205919266,
-0.01447200682014227,
0.01761751... |
<p>How would you read the following particles' names in a conversation in English? I am looking for some "proper" way of doing it. Say, imagine you are reading a technical description in a semi-formal occasion that you would like to avoid being lousy or overly simplistic.</p>
<p>$$\Delta(1750)^0 P_{31}$$
$$\bar\Delta(1910)^0 P_{31}$$
$$\Delta(1910)^- P_{31}$$</p>
<p>[EDIT]
One additional question, would you write $\Delta^0(1750) P_{31}$ or $\Delta(1750)^0 P_{31}$ ?</p> | g10491 | [
0.01667390577495098,
0.00942259095609188,
0.00208149547688663,
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0.0703098326921463,
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0.029698016121983528,
0.061774980276823044,
0.0005784531240351498,
0.02915218099951744,
-0.01420... |
<p>I am having trouble in understanding the following concepts :</p>
<p>Pg 231 Appendix B of the link <a href="http://books.google.ca/books?id=lEu7CTGjdDkC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q=entropy&f=false" rel="nofollow">http://books.google.ca/books?id=lEu7CTGjdDkC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q=entropy&f=false</a> which is of the book Chaos and the Evolving Universe by Sally J. Goerner mentions that Entropy $S$:
$$ S = \ln V $$
where $V$ is the phase space volume. According to the book, this equation is from the concept of Boltzmann's entropy. </p>
<p>(Q1) How is This equation coming? How can we say that entropy = log of phase space volume? References and explanation would be appreciated. According to the book, the Bolzmann's constant, $k_B$, is taken to be $1$. But actually there is a value to the constant. Can I take the Boltzmann constant to be equal to $1$?</p>
<p>Also, if the entropy increases, does this mean that the volume decreases?</p>
<p>(Q2) Secondly, can Kolmogorov entropy, from Information theory be stated as logarithm of phase space volume that is equivalent to entropy from statistical mechanics? I am unsure if I can replace Boltzman with Kolmogorov Sinai (KS) entropy. </p>
<p>(Q3) What is the difference between Gibb's entropy and Shannon's entropy since the formula <a href="http://en.wikipedia.org/wiki/Entropy_%28statistical_views%29" rel="nofollow">http://en.wikipedia.org/wiki/Entropy_%28statistical_views%29</a> is the same.</p> | g917 | [
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0.003044458571821451,
0.020517276600003242,
0.00707476818934083,
-0.004626757465302944,
0.042110610753297806,
-0.023874253034591675,
0.03958119451999664,
-0.009606522507965565,
0.01735413447022438,
0.030417723581194878,
0... |
<p>Take a bucket of hot water and the other bucket of cold water. Why does the bucket full of cold water weigh more than bucket full of hot water?</p> | g10492 | [
0.07223650068044662,
0.0063525899313390255,
0.014378119260072708,
-0.015001611784100533,
0.03936316445469856,
0.0496537908911705,
0.018604211509227753,
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-0.02596455067396164,
-0.035845737904310226,
-0.05499185621738434,
-0.005353440996259451,
0.... |
<p>It seems there are a lot of respected physicists appearing on pop-sci programs (discovery channel, science channel, etc.) these days spreading the gospel of <a href="http://en.wikipedia.org/wiki/Ignoramus_et_ignorabimus#Hilbert.27s_reaction">"we can know, we must know."</a></p>
<p>Three examples, quickly: 1) Many programs feature Michio Kaku saying that he is on a quest to find an equation, "perhaps just one inch long," which will "describe the whole universe." 2) Max Tegmark has come out with <a href="http://www.goodreads.com/book/show/17797249">a new book</a> in which he expresses the gut feeling that "nothing is off-limits" to science. The subtitle of this book is <em>My Quest for the Ultimate Nature of Reality</em>. 3) In the series <a href="http://en.wikipedia.org/wiki/Through_the_Wormhole"><em>Through the Wormhole</em></a> there is talk about a search for the "God equation."</p>
<p>(A good counter-example would be Feynman, but his self-described "non-axiomatic" or "Babylonian" approach does not seem popular with physicists today.)</p>
<p>Is there any sense among physicists that it might be impossible to articulate the "ultimate nature of reality" in equations and formal logic? It seems to me that physicists are following in the footsteps of the 19th century mathematicians (led by Hilbert) who were on a similar quest which was put to rest by Gödel's incompleteness theorems in 1931. Is there any appreciation for how the Incompleteness Theorems might apply to physics?</p>
<p>Has any progress been made on <a href="http://mathworld.wolfram.com/HilbertsProblems.html">Hilbert's 6th problem</a> for the 20th century? Shouldn't this be addressed before getting all worked up about a "God equation?"</p> | g10493 | [
-0.05243426188826561,
0.06818300485610962,
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0.025688540190458298,
0.017483020201325417,
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-0.04130319878458977,
0.056664030998945236,
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0.042059801518917084,
0... |
<p><a href="http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=Cu&ascii=html&isotype=some" rel="nofollow">This URL</a> lists the mass of Copper-63 as 62.9295975(6) and <a href="http://physics.nist.gov/PhysRefData/Handbook/Tables/coppertable1.htm" rel="nofollow">this other URL</a> lists the mass as 62.939598. These values differ by almost exactly 0.01 which seems hard to explain by experimental error. Why is it that these values differ in a significant digit but have the same less-significant digits? Is one of them a typo of the other? What is the correct value? What is the origin of both of these values?</p>
<p>This discrepancy was noted by commentators in <a href="http://www.theoildrum.com/node/7942" rel="nofollow">this article about a supposed cold-fusion reactor</a>. According to those commentators, this value is relevant to the cold-fusion debate because it makes all the difference as to whether or not the supposed reaction is energetically feasible. The linked article concerns the same cold-fusion claim discussed in <a href="http://physics.stackexchange.com/questions/3799/why-is-cold-fusion-considered-bogus">this previous physics.SE question</a>.</p>
<p>EDIT: user9325, voix, and user3673 have indicated that the correct answer is 62.929... I have started a bounty on the <em>origin</em> of both the correct and incorrect values.</p> | g10494 | [
0.034948185086250305,
0.004309765994548798,
0.0015682309167459607,
0.026832779869437218,
0.055075038224458694,
0.007347026839852333,
0.010117405094206333,
0.0775931179523468,
-0.04544949531555176,
-0.011792059987783432,
0.0009799276012927294,
-0.008063441142439842,
0.033690258860588074,
-0... |
<p>So as far as I know, nuclear fission uses high weight atomic elements to manufacture power. If the risk of runaway reactions are a major reason for not expanding this technology, why don't we use elements with lower atomic weight (eg. less energy) or lower amounts of fuel (eg. less total mass)?</p> | g10495 | [
0.03359099477529526,
0.08613370358943939,
0.02510114200413227,
0.05754614621400833,
-0.0053263320587575436,
0.013378246687352657,
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0.025042640045285225,
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-0.076541967689991,
0.016281776130199432,
0.007994280196726322,
-0.005910222884267569,
-0.01... |
<p>I have a question about the gravity probe B experiment.</p>
<p>According to this site:</p>
<p><a href="http://science.nasa.gov/science-news/science-at-nasa/2011/04may_epic/" rel="nofollow">http://science.nasa.gov/science-news/science-at-nasa/2011/04may_epic/</a></p>
<p>The measurements they made confirm Einsteins theory. What I'm wondering is:</p>
<ol>
<li>Did they use a control in the experiment? That is did they put gyroscopes in some place where space time was not supposed to be twisted and get a measurement that was not deflected?</li>
<li>If they didn't measure a negative result too, how does this the experiment prove the theory correct?</li>
</ol> | g10496 | [
0.023413177579641342,
0.007272074930369854,
0.01197135541588068,
-0.0002508058096282184,
0.04817330837249756,
0.03362582251429558,
0.03100786916911602,
0.004531544167548418,
-0.019417565315961838,
0.01256035827100277,
0.051028721034526825,
-0.002438387367874384,
0.016959596425294876,
0.024... |
<p>First, a quick remark: I'm a mathematician, now working on some problems coming from physics (in particular Ising models on quasiperiodic chains). A few things I find rather mysterious. I would appreciate your help.</p>
<p>For the purpose of generality, let's consider the following Ising model on a chain of $N$ nodes. </p>
<p>$$H_N = - \sum_{i = 1}^N J_i\sigma_i^{(x)}\sigma_{i+1}^{(x)} - \sum_{i = 1}^N\sigma_i^{(z)},$$</p>
<p>with $J_i$ depending on the node $i$ (we assume no particular order for generality), and $\sigma_i^{(x),(z)}$ the Pauli matrices. By Jordan-Wigner, we can consider the corresponding Fermionic operator given by</p>
<p>$$\widehat{H}_N = \sum_{i,j}\left[c_i^{\dagger}A_{ij}c_j + \frac{1}{2}\left(c_i^{\dagger}B_{ij}c_j^{\dagger}+ H.c.\right)\right],$$</p>
<p>where $c_i$, $1\leq i \leq N$ are anticommuting Fermionic operators and $\left\{A_{ij}\right\},\left\{B_{ij}\right\}$, $1\leq i, j \leq N$ are the elements of appropriately chosen matrices $A, B$, which depend on $\left\{J_i\right\}_{1\leq i \leq N}$.</p>
<p>We use periodic boundary conditions. Now we can extend $\widehat{H}_N$ to a lattice of infinite size, by gluing the unit cell of size $N$ infinitely many times. Let us call this new extension $\tilde{H}_N$. Now the questions:</p>
<p>1) What is $H.c.$? </p>
<p>2) I am interested in the thermodynamic limit $N\rightarrow\infty$. Is it obvious whether the sequence of operators $\left\{\tilde{H}_N\right\}$ converges, say in strong operator topology, to some well-defined operator $\tilde{H}$ as $N\rightarrow\infty$? </p>
<p>Let me motivate the second question: For a certain sequence $\left\{J_i\right\}$, constructed deterministically with certain properties (so-called <em>quasi-periodic sequence</em>), I believe I can say something about what Physicists call the "energy-spectrum in the thermodynamic limit". I'm interested to know whether this energy spectrum is the spectrum (in the usual functional-analytic sense) of some operator $\tilde{H}$. </p>
<p>Thanks for any help!</p> | g10497 | [
-0.02377370186150074,
0.023682469502091408,
-0.005623768083751202,
-0.006899503991007805,
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0.004099518992006779,
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0.0021628316026180983,
-0.07515914738178253,
0.04594660922884941,
-0.012354890815913677,
... |
<p>Is it impossible for a universe that only contains particles/fields with no rest mass to develop life/intelligence? Assume there is no mechanism to generate a rest mass (Higgs, symmetry breaking, etc.)</p>
<p>It seems ridiculous, but I can't think of a good reason why it can't happen since the life/intelligence may not resemble us. Maybe there is an argument using entropy, information theory, etc. that would be persuasive.</p> | g10498 | [
0.023112643510103226,
0.018457777798175812,
0.010432458482682705,
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0.05580036714673042,
0.06140480935573578,
0.008204673416912556,
0.004338500555604696,
0.019120750948786736,
-0.10645799338817596,
-0.009158765897154808,
-0.049163129180669785,
-0.01637686975300312,
-0.... |
<p>I'm not sure if someone's already asked this before, but I was wondering, in field theory, </p>
<ol>
<li><p>when we say that a certain field is gauge invariant but not gauge covariant, what does this mean? In particular, in <a href="http://en.wikipedia.org/wiki/Pauli%E2%80%93Villars_regularization">Wikipedia</a>, the regulator of Pauli-Villars is said to be as such. </p></li>
<li><p>Moreover, as a consequence of not being gauge covariant, the Wikipedia article says that this regulator can't be used in QCD. How to see the link between not being gauge covariant and QCD here? And, why can one use it in QED then? </p></li>
</ol> | g10499 | [
0.02802421897649765,
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0.0841127261519432,
0.035497501492500305,
0.028690025210380554,
0.04543476924300194,
-0.003084248397499323,
0.02187761478126049,
-0.03973805531859398,
0.02519412338733673,
-0.0035285362973809242,
-0.0135... |
<p>While travelling by train (travelling West to East), it seems the moon is moving in opposite direction when seen from the window, but then it reverses its direction, after a certain amount of time and moves along the train, but then flips back again. And it kept oscillating, as the train kept moving. Can anyone point out the reason?</p> | g10500 | [
-0.013298964127898216,
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0.057694531977176666,
0.02390... |
<p>Why there is always cold at high altitudes. e.g. at peak of mountains. Also as we go high from see level, temperature starts decreasing, so why is it.</p> | g10501 | [
0.08862196654081345,
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0.015199711546301842,
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0.0552818588912487,
0.015296060591936111,
0.050828218... |
<p>How can astronomers find the difference between a parabolic and a hyperbolic comet ? What are the criteria that helps them distinguish these ? Can a parabolic comet switch over to become a hyperbolic one and the vice-versa ?</p> | g10502 | [
0.026309402659535408,
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-0... |
<p>Does the Hilbert space of the universe have to be infinite dimensional to make sense of quantum mechanics? Otherwise, decoherence can never become exact. Does interpreting quantum mechanics require exact decoherence and perfect observers of the sort which can only arise from exact superposition sectors in the asymptotic future limit?</p> | g10503 | [
-0.037889447063207626,
0.01648591458797455,
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0.... |
<p>I really got to thinking about this. The speed of sound is measured at 761.2 MPH <strong>at sea level</strong>. But how does this number change as air density decreases? The lack of air density is what allowed his terminal velocity to much lower than say a jump at 5k feet high. I am not disputing his maximum velocity (800+ MPH), <strong>but did Felix Baumgartner actually produce a sonic boom in the process</strong>? I mean, I beleive most people subconsioulsy associate "sonic boom" and "faster than the speed of sound".</p> | g10504 | [
0.03177715837955475,
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0.07589... |
<p>How are the comet-hunters able to precisely locate/know about the required comets ? How can they distinguish between comets from such a far distance ? How are they able to estimate the exact time period of these comets like Hale-Bopp's and Halley's comets have orbital time periods 2520-2533 yrs and 75.3 yrs respectively ? Do they have to follow the comet throughout its whole orbital path to deduce that or are there any other procedures ?
I've heard of using computer generated programs that help in here. Please notify me some of these.</p> | g10505 | [
-0.024366464465856552,
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0.0654609352350235,
... |
<p>Given a stream of moving charged particles that encounter a uniform magnetic field such that they are trapped in a circular orbit, what effect do these particles have on the net magnetic field over time? Would the magnetic field get stronger or weaker as the number of trapped particles increase?</p> | g10506 | [
-0.013617446646094322,
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... |
<p>My original question was in an effort to understand the electrical analogy to Markov chains, which is explained in Snell's article. There are some neat parallels that involve taking a Markov chain and considering the edge weights to be wire conductances. Unfortunately, after reading the article, I realize that they specifically say that their analogy is unrealistic. </p>
<p>So, how is electrical energy transmitted?</p> | g10507 | [
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<p>I would like to ask a stupid question here.</p>
<p>If a body 'b' moving downward with a velocity v in a rotating frame of reference with angular velocity w, and w and v not being parallel and anti parallel. We all know that the body 'b' experiences a Coriolis force.</p>
<p>If it gets deflected in its trajectory then according to newtons third law shouldn't it push some body with equal force?</p>
<p>what if the fame of reference was moon where there is no atmosphere? will the body be deflected?</p> | g10508 | [
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0.002938104560598731,
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<p>I recently learnt that a suit called <a href="http://en.wikipedia.org/wiki/Pressure_suit" rel="nofollow">pressure suit</a> is worn by fighter plane pilots to prevent red-outs and black-outs. And it seems to be work by -</p>
<blockquote>
<p>"..applying pressure to selective portions of the body."</p>
</blockquote>
<p>How do these suits work; i.e. by what means, selective portions of the body are pressurised? </p>
<p>Do astronauts wear these while takeoffs, and also F1 drivers?</p> | g10509 | [
-0.02770203910768032,
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-0.016980601474642754,
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0.05039563030004501,
0.00... |
<p>If I have an over-damped mechanical system that is excited with a sinusoidal motion. That sinusoidal motion starts with a determined frequency then increases frequency over time.
Of course, it is known that there will be a phase shift between the driving force and the motion of the hanging mass.</p>
<p>My question is, how to figure out phase lag of mass motion in relation to driving force?</p> | g10510 | [
0.056623075157403946,
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0.016429878771305084,
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... |
<p>If I throw a ball straight up, it deflects slightly to the west due to Coriolis forces. If instead I watch a bubble float up in water, is the bubble deflected west, east, or neither?</p>
<p>I think the bubble also moves west, but am not sure. My reasoning is that the air in the bubble must feel a Coriolis force to the west because it is rising. Further, as the bubble rises, the water around it moves, and the net motion of the water is down. Water moving down experiences a Coriolis deflection to the east. Bubbles move the opposite direction of water, so if the water is moving east, then the bubble should move west.</p>
<p><strike>I don't have any reasonable-sounding counter-arguments, but I'm not completely convinced by my argument, either.</strike></p>
<p><b>Edit</b>: One reason I'm a unsure about this problem is that a bubble does not get thrown outward by a centrifugal force. Imagine a plastic ball filled with water and spinning fast. A bubble is sitting in the water in the equatorial place, half way to the edge of the ball. There's centrifugal force out towards the wall, but the bubble does not move that way. The bubble moves up the pressure gradient. The water gets thrown to the wall, and thus there is higher pressure at the wall than at the center. The bubble moves towards the center. If a bubble moves counter to the centrifugal force, I should be careful before claiming it moves with the Coriolis force.</p> | g10511 | [
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0.04355711489915848,
0.004054526798427105,
-0.0067651... |
<p>When a heavy quark hadronizes it has some probability of forming a meson vs forming a baryon. I suspect there is a well known branching ratio for each type of hadron. Does anyone know what the probability is or, even better, a reference that discusses this? An ideal answer (though not necessary) would further give a crude approximation of this probability (though I don't know if this is even possible).</p> | g10512 | [
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0.019956082105636597,
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0.00... |
<p>I would to know if there is a correlation between isospin and energy. Consider for example the $\eta$ meson ($I =0$) and the pions($I=1$). The $\eta$ turns out to be much heavier then the pions ($m_\pi \approx 150 \mbox{MeV}$,$m_\eta\approx 550\mbox{MeV}$). </p>
<p>A counterexample is the $\Lambda_b$ ($I=0$) and the $\Sigma_b$ ($I=1$) baryons. Here the $\Sigma_b$, the higher isospin state, has a larger mass. </p>
<p>Are there any known trends between isospin and energy?</p> | g10513 | [
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0... |
<p>I assume the twin paradox from special relativity is well known. I wish to focus on the apparent symmetry of the problem: both observer seems to move away from each other, and then come back. Yet, the outcome is asymmetrical.
That paradox is resolved because the travelling twin has to turn around at some point. Then he has to change inertial frames, or accelerate, and this means that the situation is not symmetric anymore.</p>
<p>What now if the "turn around" is not caused by an acceleration, but a "gravitational slingshot". Say, the traveling twin's trajectory passes by the graviational field of a couple of stars, freely falling, such that the twins just happen to end up in the same place after a while again.
According to general relativity, both twins then remain in an inertial frame. Both see the other initially disappear with slowly ticking clocks, and later reappear from some other direction. All the while, they stayed at rest in their own reference frame. So the other twin must have aged less than themselves. The situation seems completely symmetric again. Of course, since they meet in the same point again, they cannot consider the other one younger from both perspectives.</p>
<p>What is the resolution?</p>
<p>I found this other thread which seems related: <a href="http://physics.stackexchange.com/questions/361/symmetrical-twin-paradox">Symmetrical twin paradox</a>
This refers to a paper that claims that this is due to the fact that the topology of the space induces some preferred reference frame. I don't pretend to understand that paper, but I think it refers to a similar paradox obtained by assuming that the large-scale structure of the universe is spherical/cylindrical, or something like that, allowing one twin to travel "around". Surely it is possible to set up my above scenario with only a few local stars. So it seems strange to me that a local paradox should be solved by relying on a global topologically prefered frame.</p> | g10514 | [
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0.08797279745340347,
... |
<p>So i read this in some article on the net</p>
<blockquote>
<p>Consider a boy is standing at distance of 10 metres from the wall. Boy
holds a rubber ball and cloth ball in his hands. Firstly, the boy
throws rubber ball with force 2N (Newton) on the wall. The rubber ball
after striking the wall rebounds to 10 metres. Thus, action and
reaction are equal in this case. Secondly, the boy throws cloth ball
with an equal 2N force on the wall. The cloth ball rebounds to five
metres. Thus action and reaction are not equal.</p>
</blockquote>
<p>Is this really right? o.O</p>
<p>P.S: i dont have any background in physics and hence this question</p> | g10515 | [
0.06737001240253448,
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0.0007660166011191905,
0.011099078692495823,
-0.02... |
<p>I've had a question about this topic previously, but the material was inelastic.</p>
<p><a href="http://physics.stackexchange.com/questions/92089/forces-in-a-balloon-popping">Forces in a balloon popping?</a></p>
<p>What happens when a material is non-hookian? </p>
<p>Say rubber,</p>
<p>I've found this pdf on the web:
<a href="http://www.researchgate.net/publication/245382031_Inflating_a_Rubber_Balloon" rel="nofollow">http://www.researchgate.net/publication/245382031_Inflating_a_Rubber_Balloon</a></p> | g10516 | [
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0.01127516571432352,
0.01540288794785738,
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-0... |
<p>Let $r_{P/Q}$ be the position vector of $\overrightarrow P$ relative to vector $\overrightarrow Q$ and $v_{P/Q}$ the velocity vector of $\overrightarrow P$ relative to $\overrightarrow Q$. </p>
<p>Suppose $|v_Q| > |v_P|$ and you want to set the direction of $v_P$ such that $|r_{P/Q}|$ becomes minimal at some point in time. According to the text I have, doing so requires that $v_P \cdot v_{P/Q} = 0$ </p>
<p><img src="http://i.stack.imgur.com/g45Jd.png" alt="enter image description here"></p>
<p>Sorry for the horrendous image but I hope the idea is clear. $v_P$ could be any direction and the blue circle represents all possible directions of $v_p$</p>
<p>Anyway, my problem lies in that I do not understand why this is the necessary condition for the closest approach. </p>
<p>Could someone enlighten me? </p>
<p>If you know of a resource containing information relevant to this question, that would also be great. </p>
<p>Edit: I would add more detail but unfortunately there isn't much more that I know. Of course there are two angles where this works and I guess you choose the one depending on the initial positions of the two objects. </p>
<p>Edit: I'm really sorry but I didn't label the image properly which resulted in the post being confusing</p> | g10517 | [
0.06263992190361023,
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0.026345156133174896,
0.028379514813423157,
0.01... |
<p>Is it energy?</p>
<p>Is it energy per unit volume?</p>
<p>Is it energy per unit time i.e power?</p>
<p>What is it?</p> | g10518 | [
0.028737302869558334,
0.05389342084527016,
-0.03323342278599739,
0.022315792739391327,
-0.013002247549593449,
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0.03957768902182579,
-0.02318711206316948,
-0.025949029251933098,
-0.02... |
<p>So I keep reading all these articles on the <a href="http://en.wikipedia.org/wiki/EPR_paradox" rel="nofollow">EPR paradox</a>, and I follow them pretty easily right up until it gets to the most important matter.</p>
<p>Assuming you are trying to measure x and y spin,</p>
<p>Wikipedia and others say that when you measure x-spin on the first particle, it suddenly becomes impossible to measure the y-spin on the other particle.</p>
<p>But no one really goes on to say what this means in a physical sense.</p>
<p>Let's say you have 2 actual detectors. When the first particle hits the x-detector, now x-spin is measured for both particles. When the second particle hits the y-detector, now y-spin is measured for both particles. But all these articles say the second detector is unable to measure y-spin. So what happened? Did the detector just explode or something?!</p> | g10519 | [
0.027782458811998367,
0.03890015929937363,
-0.029959969222545624,
-0.008438758552074432,
0.10704334825277328,
0.012690259143710136,
0.00756568368524313,
0.015869664028286934,
0.0024759818334132433,
-0.036266524344682693,
-0.06099637970328331,
0.011303001083433628,
0.041595932096242905,
-0.... |
<p>This is a quote from Dirac's Principles of Quantum Mechanics:</p>
<blockquote>
<p>"(...) if an atomic system has its equilibrium disturbed in any way
and is then left alone, it will be set in oscillation and the
oscillations will get impressed on the surrounding electromagnetic
field, so that their frequencies may be observed with a spectroscope.
Now whatever the laws of force governing the equilibrium, one would
expect to be able to include the various frequencies in a scheme
comprising certain fundamental frequencies and their harmonics. This
is not observed to be the case. Instead, there is observed a new and
unexpected connexion between the frequencies, called Ritz's
Combination Law of Spectroscopy, according to which all the
frequencies can be expressed as differences between certain terms, the
number of terms being much less than the number of frequencies. This
law is quite unitelligible from the classical standpoint."</p>
</blockquote>
<p>I'm having trouble understanding this paragraph. Assuming that the atom is a system in equilibrium that emits e-m waves when perturbed and these e-m waves are product of the oscillations of the atom about its equilibrium configuration that result from the perturbation, does it follow that the Ritz's law is in contradiction with classical mechanics? Why? Thanks.</p> | g10520 | [
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0.04632433131337166,
0.008881175890564919,
0.0028782158624380827,
0.06004201993346214,
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0.018447209149599075,
0.0027121766470372677,
0.0022920749615877867,
0.01030336506664753,
-0.04728410020470619,
0... |
<p>This question has come to me from my friend in fact: he noted that the heating in the pub is painted black. I replied that it's better for heat emission.</p>
<p>I don't know where did I know that from. And he disagreed, asking me: "Why would black emit more heat than white?" I didn't know. We could, however, agree on fact, that black <em>absorbs</em> more heat than white.</p>
<p>I quickly created a thought experiment to proof by contradiction that the black must emit more light than white:</p>
<blockquote>
<p>Assume that white and black both emit the same amount of light. Put a black and white object in an area. Assume that any light (or heat) emitted by the objects can only be absorbed by them. Imagine that the white object emits light and heat. The black one will absorb considerable amount of it. When the black object emits the light the light one will reflect a great portion of it - which can be then absorbed back by the black one.</p>
</blockquote>
<p>Written like this, it seems that second law of thermodynamics is being broken by this concept. However, my friend has also thought something to oppose me:</p>
<blockquote>
<p>If black objects emits more heat than the white one, why the black objects are hotter when put in the sun? Shouldn't they emit the extra light they absorbed?</p>
</blockquote>
<p>I understand that it's not all that simple. There's <a href="http://www.schoolphysics.co.uk/age11-14/Heat%20energy/Transfer%20of%20heat%20energy/text/Heat_radiation/index.html" rel="nofollow">an article that says I'm right</a> but it doesn't really satisfy me.</p>
<p>For start, infrared is no color at all - how could it have to do anything with black, white or any other color? Shouldn't an <em>"infrared</em>" painted stuff reflect most heat?</p>
<p>I ask for an answer that sufficiently explains why the black and white things absorb/emit heat as they do. And, if questions post by both mine and my friend's arguments are asked, I will be very happy.</p> | g10521 | [
0.03281885012984276,
0.000862560176756233,
0.021098265424370766,
-0.00901850312948227,
0.08149895071983337,
-0.002728839172050357,
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0.0824260413646698,
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-0.010245158337056637,
0.05490235611796379,
0.07151949405670166,
0.04217562824487686,
0.03227... |
<p>Suppose we have a quantum state, well described by its time-independent wave function Psi. And we have a well-defined Hermitian (self-adjoint) operator $A$. We successfully evaluate the expectation value of the operator $A$. Next we derive the general formula for the higher moments of $A$ (i.e. the expectation value of $A^n$ for $n=2,3,4\ldots $).</p>
<p>In this situation, is it permitted to regard each of the $A^n$ for $n=1,2,3,\ldots$ as a proper operator by itself? </p>
<p>For example, should every $A^n$ have a positive variance and other statistical properties (as long as we restrict ourselves to the state $\Psi$)? </p>
<p>Can one make linear combinations of different powers to construct a new operator, e.g. $B = A + A^2$?</p>
<p>Is it allowed to construct new operators acting on $\Psi$, that are defined in terms of their series expansion in $A^n$? For example, $D = \exp(CA)$ where $C$ is a constant?</p> | g10522 | [
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0.00752214202657342,
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0.05823546275496483,
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... |
<p><a href="http://www.nature.com/news/simulations-back-up-theory-that-universe-is-a-hologram-1.14328" rel="nofollow">http://www.nature.com/news/simulations-back-up-theory-that-universe-is-a-hologram-1.14328</a></p>
<p><a href="http://guardianlv.com/2013/12/compelling-evidence-says-our-universe-is-a-hologram/" rel="nofollow">http://guardianlv.com/2013/12/compelling-evidence-says-our-universe-is-a-hologram/</a></p>
<p>I thought the holographic Principle was just a sexy way of referring to the fact that a black hole's maximum entropy is bounded by its surface rather than its volume, and since the surface is a Schwarzschild radius, and that can be said to be 2D, then that's where they got the notion of calling the principle, holographic, since holograms are thought to be 2 dimensional(even though they are not 2 dimensional).</p>
<p>But the notion that the holographic principle applies to all the Universe, not just black holes, and that it shows the universe is a holographic illusion, won't go away, as shown by the two links above.</p>
<p>So, is there a real possibility that the Universe is a hologram, and that we live in the matrix, and that what we think is real, which is the 3D, material world, is just an illusion?</p> | g10523 | [
0.03396297246217728,
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<p>Earth's atmosphere is a chaotic system. In such systems arbitrarily small changes the conditions can give rise to very large effects.</p>
<p>There are many rumors about the physical and large scale environmental impacts that global warming will cause in the future. (for example, <a href="https://en.wikipedia.org/wiki/Physical_impacts_of_climate_change" rel="nofollow">here</a>)</p>
<p>After a remark made by one of the users <a href="http://physics.stackexchange.com/questions/95131/why-global-warming/95136#comment194702_95136">here</a>, I thought to ask this question:</p>
<p><strong>Can a small change in Earth's temperature (that can't be <em>felt</em>) give rise to large-scale climate changes?</strong></p> | g10524 | [
0.045271601527929306,
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0.0198... |
<p>I have a particle and a potential $V(x)=\frac{\hbar^2}{2m}k\delta(x)$.</p>
<p>Where $\delta (x)$ is the Delta function, and I am interested in the solutions of the <strong>stationary</strong> Schroedinger equation.</p>
<p>If $\psi_1$ is the solution for $x<0$ and $\psi_2$ for $x>0$, must be that $\psi_1'(0) \neq \psi_2'(0)$, because of the delta function.</p>
<p>Now I read that the condition is $$\psi_2'(0) -\psi_1'(0) = -k\psi_2(0).$$</p>
<p>My question is: why? How do I get at this conclusion?</p> | g10525 | [
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0.0... |
<p>Imagine we have a diffraction grating consisting of N slits (being N very large) with a separation of "d" from slit to slit. Now, we could regard this grating as a diffraction grating constructed by a repeated double slit, in which case the periodicity would be 2d. </p>
<p>I realize this can't be legitimate since the theoretical positions of the maximums would change and this can't be (since the grating is doesn't change no matter how we regard it). Nonetheless, dealing with examples of defectuous grating exercises I have seen examples that regard gratings as repetitions of double slits or triple slits. </p>
<p>So, my question is the following, why is it possible in some cases and not in others? I mean, why can't we regard the typical grating mentioned above as a repetition of double slits (or triples or whatever)? </p>
<p>(my guess is that maybe we always have to choose the $\textit{minimum}$ periodicity but I am not sure)</p> | g10526 | [
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... |
<p>If it is established that the Earth does have a dark matter disk as this recent discovery suggests.</p>
<p><a href="http://www.newscientist.com/article/mg22129503.100-gps-satellites-suggest-earth-is-heavy-with-dark-matter.html" rel="nofollow">http://www.newscientist.com/article/mg22129503.100-gps-satellites-suggest-earth-is-heavy-with-dark-matter.html</a></p>
<p>Then could the Earth have a dark matter core as well as a disk? </p> | g10527 | [
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<p>I know there exists surfaces that only reflect light (mirrors), but are there surfaces that only refract light? If so, how does that happen?</p> | g10528 | [
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<p>Our professor hasn't explained what <a href="http://en.wikipedia.org/wiki/Bound_state" rel="nofollow">bound states</a> are. Could you give me an idea of what they mean and their importance in quantum-mechanics problems with potential (e.g. a potential described by a delta function)?</p>
<p>And why, when a stable bound state exists, the energies of the related stationary wavefunctions are negative?</p>
<p>I mean, I figure it out, mathematically, in the case of a potential described by a Delta function, but which is the physics sense of that?</p> | g10529 | [
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<p>We all know that (visible for human) light essentially is an electromagnetic wave with a frequency around 1/((any value between 380 and 760)*pow(10,9)) Hertz. </p>
<p>So, if we will build (hypothetically) an electromagnet and feed it with such a frequency, would we observe a light beam coming out of it?</p> | g334 | [
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<p>I am studying for my Bachelor thesis (in Mathematics). I and my advisor agreed on the <a href="http://en.wikipedia.org/wiki/Penrose%E2%80%93Hawking_singularity_theorems" rel="nofollow">Penrose-Hawking singularity theorems</a>.</p>
<p>My question is: </p>
<p>1) Which mathematical background should I focus on mastering in order to be able to approach the singularity theorems? </p>
<p>2) Is it the Lorentzian (Pseudo-Riemannian) manifolds which is flat (and there isn't very much to say about it) or the Einstein (Riemannian) manifolds (which for what I know now is in a important way different form the nature of space-time? Or both? Perhaps am I missing something important?</p>
<p>3) What is the role of Schwarzschild metric in this? How is it related to the manifolds above?</p>
<p>4) Is the next statement correct?</p>
<blockquote>
<p><em>Schwarzschild metric is a particular solution of Einstein field equations (under which hypothesis?) in the sense that it models the space time of a portion of universe as a manifold with that particular metric. In this setting the singularity theorems can be proved.</em></p>
</blockquote>
<p>5) Can anyone give me a complete statement of the singularity theorems so that I can see what mathematical objects are involved? </p>
<p>I still haven't looked for them because I taught that studying the math before even reading them could save me some time. But I have been studying Manifolds for two weeks now and I am getting more and more confused and I fear I am wasting time.</p> | g10530 | [
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<p>Suppose there are two slopes. Imagine its just small slope and can be placed on your floor. One slope is made of a very smooth material and another which provides a lot of friction for example made of rubber. Now you place a cubical metal block on each of the slopes. Both the blocks are exactly identical. The metal block on the smooth surface will slide down due to the action of gravity but the one place on the rubber slope will not. Where did the rubber slope get energy from to work against the action of gravity and holding the block in its position?</p> | g10531 | [
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<p>My professor said that a law was stated and announced as a law because it happens in our everyday life. He gave us an example of Newton's 3 laws. He said that walking possess 3 laws of Newton's. Is it true that all laws really happen in our daily motion?</p> | g10532 | [
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<p>I'm trying to analyze the motion of the particles which exert the gravitational force each other. Let $M_1$, $M_2$ be the masses of the particles, and the equation of motion of particle $M_1$</p>
<p>$$
F=G\frac{M_1M_2}{r^2}=M_1\ddot{r} \\
\ddot{r}r^2-GM_2=0
$$</p>
<p>I find it doubtful that the simple motion has difficult equation of motion.</p>
<p>Should I just use some form of successive approximation?</p> | g10533 | [
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<p>I want to know if the following has been done experimentally; after the spin (or any other characteristic with a probability of 50%) of 2 entangled particles has been measured, we change the spin of one and we see the spin of the other changing instantaneously at a distance. </p>
<p>For example, entangled particle A is spinning up and entangled particle B is spinning down, we make A spin down and see B start spinning up at the same time.</p>
<p>I know entanglement has been proven experimentally but it always seems to imply this "spooky action at a distance" and I wonder if THAT has actually been proven experimentally. Maybe my question should have been has anyone seen spooky action at a distance...</p> | g10534 | [
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<p>While playing racquetball, I frequently hear a very prominent "boing" sound (or more formally, a <a href="http://en.wikipedia.org/wiki/Chirp">chirp</a>). For example, you can hear it in <a href="https://www.youtube.com/watch?v=mfWllzz-6YI">this video</a> when the ball hits the front wall.</p>
<p>Does anyone know what the origin of this sound is, and why the pitch rises? </p>
<p>Here is the spectrogram from the above video:</p>
<p><img src="http://i.stack.imgur.com/G2tdWm.png" alt="enter image description here"></p>
<p>A careful examination shows that there are at least four linear chirps, which I've highlighted below. If you really listen carefully, all four of these are audible. (However I can only distinguish between the two high frequency chirps when the audio is played at half speed.)</p>
<p><img src="http://i.stack.imgur.com/lzyGMm.png" alt="enter image description here"></p> | g10535 | [
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0.040964096784591675,
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<p>How do I find the values of $x$ for a given wave function $\Psi(x)$ such that it's probability density function $|\Psi(x)|^2$ will be maximized? </p>
<p>My guess is to to constrain the derivative by the conditions $\frac{d\Psi}{dx} = 0$, and then plug those values into $|\Psi(x)|^2$. Is this the right approach?</p> | g10536 | [
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0.015... |
<p>When it comes to questions of existence of bounds for PDE's and such, one must often make some assumptions regarding the topology of the space-time to use well known theorems. </p>
<p>My question is two-pronged:</p>
<p>i) I've often read, on Wikipedia (<a href="http://en.wikipedia.org/wiki/Spacetime" rel="nofollow">http://en.wikipedia.org/wiki/Spacetime</a>) for example, that space-time is paracompact. I am aware of the mathematical definition and this seems counter-intuitive to me. Since the form of the stress-energy tensor entering Einstein's equations need only satisfy the conservation of energy $\nabla_{\mu} T^{\mu \nu} = 0$ condition from the Bianchi identities, how does one show this result? Can someone give me a reference for a proof?</p>
<p>ii) In (electro)-vacuum, what other topologies are permitted globally? I have seen some papers finding solutions that resemble black holes (in the sense they have singularities, event horizons...) but are topologically not 2-spheres at their cross section (seemingly in violation of Hawking's theorem, see e.g, <a href="http://arxiv.org/abs/hep-th/9808032" rel="nofollow">http://arxiv.org/abs/hep-th/9808032</a>, but perhaps the fact the space-time is asymptotically anti de-Sitter is why there is no violation). What space-times are compact? The spheres $S^{n}$ are all compact, but presumably even the Schwarzschild space-time is not globally? I think one can only have a compact space-time if its Euler characteristic $\chi = 0$, can this be translated into a demand on $T^{\mu \nu}$?</p>
<p>I am particularly interested in compact space-times, for one can then apply the Yamabe problem.</p>
<p>Thanks!</p> | g10537 | [
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0.0490... |
<p>Given potential $V(x) = Asec(x)$ for $x > 0$. I want to calculate the ground-state energy $E_0$ via the Schrödinger equation. </p>
<p>I'm completely stuck on this one. I've set up the time-independent Schrödinger equation, but it can't be solved without using special functions. I don't see how I can calculate the energy without solving the schrodinger equation. Any hints?</p> | g10538 | [
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0... |
<p>Why is the topological phase in a <a href="http://en.wikipedia.org/wiki/Gaussian_beam#Laguerre-Gaussian_modes" rel="nofollow">Laguerre-Gaussian transverse mode</a> is the sum of orbital angular momenta per photon, and why is it quantized? </p> | g10539 | [
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0.05937696248292923,
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<p>A yoyo on a horizontal table is being pulled by a string to the right, the table is not frictionless. If we only know that the object doesn't slip, how do we know if the string is winding up or unwinding? My reasoning is initially the friction is not ever effect so the force pulling the yoyo to the right will act a torque to the object such that the string is unwinding. But someone else said it should be winding up. I don't know why.</p> | g10540 | [
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0.022564... |
<p>I am a biochemistry and molecular biology major. If photons can be absorbed by electrons, wouldn't that mean light has a charge? Electrons only attract positive charges. Isn't it?</p> | g335 | [
0.02533370442688465,
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0.01... |
<p>Like the title say, does quark color matter in counting contributions in a early universe plasma (QGP), as when adding up the total plasma energy density, or is it just spin? The book I have (Pathria) only does one example and doesn't really firmly say one way or the other. I kind of thought it was to account for all degeneracy but the table in the book only has "spin degeneracy".</p>
<p>E.g.: $u_{total}(T) = X\,u_{\gamma}(T) = \left(2 + 8 + 7/2 \right)\,\frac{u_{\gamma}(T)}{2}$ where the terms are for, photons, gluons, and charm/strange quarks. (I know these together do not make sense, but it is just an example).</p> | g10541 | [
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<p>I was reading about the planet <a href="http://www.ras.org.uk/news-and-press/217-news2011/2000-alien-world-is-blacker-than-coal" rel="nofollow">TrES-2b</a> which is less reflective than charcoal. What could possibly be its composition?</p> | g10542 | [
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0.0021... |
<p>If we currently can look into some of the furthest stars, actually seeing the past<br>
Isn't it conceivable that given enough distance we should be able to see <br>
Parts of the Big Bang? If the Universe is endless, it means we should be able to see into its beginning. <br>
Has this theory ever been presented ? Is there anyone looking in to this possibility ?</p> | g10543 | [
-0.011156061664223671,
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0.016819816082715988,
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-0.07817242294549942,
0.08890193700790405,
0.03704347833991051,
0.044184211641550064,
0.00... |
<p>So tonight's Quatrantids shower got me thinking. Why does the debris from comets and former comets hang around so long? Each year the earth sweeps through the region of space that the comet went through. However, the comet doesn't come by each year, so the earth must be going through the same cloud numerous times. And each time we get a meteor shower as a result.</p>
<p>I suspect an answer, but I'd rather hear from professionals.</p> | g10544 | [
0.05997338891029358,
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0.011757263913750648,
-0.07745913416147232,
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-0.06488633900880814,
0.02467942424118519,
0.0073698232881724834,
0.06542922556400299,
-0.01099... |
<p>I'm a little confused as to when to use <a href="http://en.wikipedia.org/wiki/Significant_figures" rel="nofollow">significant figures</a> for my physics class. For example, I'm asked to find the average speed of a race car that travels around a circular track with a radius of $500~\mathrm{m}$ in $50~\mathrm{s}$.</p>
<p>Would I need to apply the rules of significant figures to this step of the problem?
$$ C = 2\pi (1000~\mathrm{m}) = 6283.19 $$</p>
<p>Or do I just need to apply significant figures at this step?
$$ \text{Average speed} = \frac{6283.19~\mathrm{m}}{50~\mathrm{s}} = 125.664~\mathrm{m}/\mathrm{s} $$</p>
<p>Should I round $125.664~\mathrm{m}/\mathrm{s}$ to $130~\mathrm{m}/\mathrm{s}$ since the number with the least amount of significant figures is two?</p> | g941 | [
-0.001440049265511334,
0.0756000429391861,
-0.012134013697504997,
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0.03768691420555115,
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0.007224411703646183,
-0.02061041258275509,
0.05292618274688721,
0.010949440... |
<p>Suppose we have a spherical surface with a surface charge density varying as $cos(\theta)$. Apparently one can find the electric field both outside and inside such a spherical surface by superposing the fields of two slightly offset charged spheres with uniform volume charge density.</p>
<p>Tips regarding how one goes about doing such a thing would be greatly appreciated. </p> | g10545 | [
0.0715847760438919,
0.0348244234919548,
-0.017362022772431374,
-0.0013599025551229715,
0.060124337673187256,
0.026640726253390312,
0.009720316156744957,
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0.007836570963263512,
-0.030823485925793648,
-0.040069255977869034,
0.024448033422231674,
0.0... |
<p>The observable universe is approximately 13.7 billion years old. But yet it is 80 billion light years across. Isn't this a contradiction?</p> | g10 | [
0.02042851224541664,
0.04068112373352051,
0.013019407168030739,
-0.051318999379873276,
-0.01605830155313015,
0.07714265584945679,
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-0.008381839841604233,
0.04976917430758476,
-0.0353856161236763,
0.013849572278559208,
0.04642... |
<p>Let's say I have a spinning steel ball that I have somehow managed to be completely free in all axes of movement. If I fire a BB at it with enough force on a north-south (to the ball) angle, what will happen. Will it start to wobble by a certain amount? Will it change it's orientation and then stay there? I welcome complex answers, but please summarize them in laymen's terms as well.</p>
<p>When I say north-south, I'm referring to the earth so that means it would be fired along a plane of the axis of the spin at about 45 degrees (or whatever) to the axis if that makes any sense. In other words, not with or opposing the spin, just perpendicular to it at an angle.</p> | g10546 | [
0.033646631985902786,
0.013492991216480732,
0.009775606915354729,
0.027107195928692818,
0.05253492668271065,
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0.055243853479623795,
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0.005113403312861919,
-0.05789913609623909,
0.06351462751626968,
0.04707920178771019,
-0.070... |
<p>If time stops inside a black hole, due to gravitational time dilation, how can it's life end after a very long time? If time doesn't pass inside a black hole, then an event to occur inside a black hole needs infinite time relative to the outside. Thus, it will never age.</p>
<p>Please keep it simple..</p> | g10547 | [
0.04323139414191246,
0.006218602880835533,
0.0356057733297348,
-0.0012830281630158424,
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0... |
<p>I have seen someone putting a sandstone in water. With only about 10% of the stone sitting in the water. One could see the stone getting soaked with water. So there must be a force, which lets the water climb up through the stone against gravity.</p>
<p>What is that force? Or is there some other effect present?</p> | g10548 | [
0.04094300419092178,
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0.0181... |
<p>If $A$ is the vector potential, the London equations imply that:</p>
<p>$$(\nabla^{2}-\mu^{2})A=0$$</p>
<p>if there is no external current. This can be interpreted as an effective photon mass and
so, light cannot propagate indefinitely within a superconductor. Let $\lambda = 1/\mu$ be the
London penetration depth. As a thought experiment, assume we had a thin (< $\lambda$) slab
of superconducting material and shined high frequency light on it. Some of the energy would
be lost as heat (photons hitting atoms, etc.). The rest would ``decay" exponentially but manage to
get to other side of the slab. My thoughts and chain of questions:</p>
<p>How would the light emerge? Would the exiting light have lower frequency but proportionally higher intensity?
Would it have the same frequency and just be the surviving
fraction of photons? Then, what did the photons which didn't survive decay into?
Or, does the decay just mean absorption of the photons e.g. heat generation?</p>
<p>The $U(1)$ gauge symmetry of quantum electrodynamics is broken/hidden. How do the Feynman
diagrams look inside a superconductor?</p> | g10549 | [
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0.... |
<p>I have <a href="http://astronomy.stackexchange.com/questions/3649/is-the-expansion-accelerating-or-decelerating">already asked this on Astronomy.SE</a> but I couldn't understand the answer there.</p>
<blockquote>
<p>According to Hubble's Law, the farther a galaxy is, the farther it is moving away. But do we take into account the fact that we are actually looking in the past?</p>
<p>For example, there are two galaxies A and B at distance of 5 and 10 billion light years respectively. Now, when we observe A we are looking at how it was moving 5 billion years ago. The same applies for B. So, now we conclude that 5 billion years ago space was expanding at a slower rate while it was expanding comparatively faster 10 billion years ago. What's wrong with this conclusion?</p>
</blockquote> | g336 | [
0.06587070971727371,
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0.0174084883... |
<p>Here we have a wire. At both ends there is an equal and opposite field caused by a chemical reaction. So, if we decrease or increase the distance between the two points, the strength of the field increases/decreases with the square of distance. Why then is resistance linearly proportional to distance then?</p> | g10550 | [
0.04678403213620186,
-0.00256648613139987,
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0.047658521682024,
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-0.0... |
<p>I have a question about the mechanism of Cooper instability. I know the naive picture with two interacting electrons and noninteracting fermi sea wchich leads to the bound state formation. However, if you take all electrons into acount and introduce these effective attractive interaction coming from phonon exchange the Cooper pair will also form. </p>
<p>My question is the following: do the Cooper pairs form only in the vicinity of the Fermi level (magic $2\hbar\omega_{D}$ interval) or is the whole Fermi sea composed of Cooper pairs like the BCS ground state? Which situtation is the correct one? </p>
<p>Is the BCS ground state just an approximation?</p> | g10551 | [
-0.0038223154842853546,
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0.04470069706439972,
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-0.012116755358874798,
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0.014269674196839333,
-0.046671126037836075,
... |
<p>Recently, I was studying about Thomson's experiment with cathode rays. My textbook shows it like this. <img src="http://i.stack.imgur.com/GrPY3.jpg" alt="enter image description here"></p>
<p>It says:</p>
<blockquote>
<p>When only electric field is applied, the
electrons deviate from their path and hit the
cathode ray tube at point A. Similarly when
only magnetic field is applied, electron strikes
the cathode ray tube at point C.</p>
</blockquote>
<p>But if we apply Fleming's Right Hand Rule, then we get the direction of force in the upward direction, so the rays should deviate towards A but they deviate towards C. I think it is because Fleming's Left Hand Rule is defined for conventional current(flow of positive charges) and what we are dealing with are negative charges. Is that correct?</p> | g10552 | [
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0.08471985906362534,
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0.049714189022779465,
0.009383323602378368,
... |
<p>I'm trying to write with a ball-point ink pen on a plastic<sup>[1]</sup> sandwich bag. When I try to write on some parts of the bag, no ink transfers to the bag: I can continue trying for quite a while in vain. I move to another part of the bag, and the ink transfers just fine. Then in other parts of the bag again, the ink will not transfer, and in yet others it will.</p>
<p>Why?</p>
<hr>
<p><sup>[1]</sup> I don't know what kind of plastic it is. The box only says "Ingredients: Plastic and Dye. SCJ Formula # 35*12700". (SCJ is S.C. Johnson & Son, Inc., the manufacturer.)</p> | g10553 | [
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0.009236952289938927,
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0.003608959261327982,
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<p>In many artistic impressions or movies there are pictures or scenes where the sky is filled with an enormous moon (as seen from a planet) or vice versa.
I wonder if there is an upper limit to the apparent size when viewed with the naked eye (no tele lens). Since the Roche Limit forbids celestial bodies coming too close to each other, there certainly is a limit to the apparent size.</p>
<p><img src="http://i.stack.imgur.com/B3mEm.jpg" alt="Artistic image of a large planet seen from a moon"></p> | g10554 | [
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0.04474503919482231,
0.... |
<p>Just as circumference of circle will remain $\pi$ for unit diameter, no matter what standard unit we take, are the speeds of light and sound irrational or rational in nature ? </p>
<p>I'm talking about theoretical speeds and not empirical, which of course are rational numbers.</p> | g10555 | [
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0.024063920602202415,
0.021... |
<p>I know that there are several questions about the naturalness (or hierarchy or fine-tunning) problem of scalars masses in physics.stackexcange.com, but I have not found answers to any of the following questions. Suppose that we add to the SM Lagrangian the following piece:</p>
<p>$(\partial b)^2-M^2 \, b^2-g\, b^2 \, h^2+ \, ....$</p>
<p>where $b$ is a real scalar field (that is not contained in the SM) and $h$ is the Higgs real field. Then the physical mass $m_P$ of the Higgs is given by the pole of its propagator (I am omitting numerical factors):</p>
<p>$m^2_P=m^2_R (\mu)+I_{SM}(\mu)-g\, M^2\, ln(M/\mu)$</p>
<p>where $m_R(\mu)$ is the renormalized Higgs mass, $I_{SM}(\mu)$ (which also depends on the SM couplings and masses) is the radiative contribution of the SM fields (with the Higgs included) to the two point function of the Higgs fields (note that is cut-off independent because we have subtracted an unphysical "divergent" part) and the last term is the one-loop contribution of the new field $b$ (where we have also subtracted the divergent part). </p>
<p>I have two independent questions:</p>
<ol>
<li><p>The contribution of the $b$ particle (the last term) is cut-off independent (as it has to be) so the correction to Higgs mass is independent of the limit of validity of the theory, contrary to what is usually claimed. However, it does depend on the mass of the new particle. Therefore, if there were no new particles with masses much higher than the Higgs mass, the naturalness problem would not arise. It could be new physics at higher energies (let's say beyond 126 GeV) as long as the new particles were not much heavier than the Higgs (note that I'm not discussing the plausibility of this scenario). Since this is not what people usually claim, I must be wrong. Can you tell me why?</p></li>
<li><p>Let's set aside the previous point. The naturalness problem is usually stated as the fine-tunning required to have a Higgs mass much lighter than the highest energy scale of the theory $\Lambda$, which is often taken as GUT scale or the Planck scale. And people write formulas like this: $\delta m^2 \sim \Lambda^2$ that I would write like that: $m^2_P=m^2 (\Lambda) + g\, \Lambda^2$. People think it is a problem to have to fine-tune $m^2 (\Lambda)$ with $\Lambda^2$ in order to get a value for $m^2_P$ much lower than $\Lambda^2$. And I would also think that it is a problem if $m^2 (\Lambda)$ were an observable quantity. But it is not, the observable quantity is $m^2_P$ (the pole of the propagator). I think that the misunderstanding can come from the fact that "interacting couplings" (coefficients of interacting terms instead of quadratic terms) are observables at different energies, but this is not the case, in my opinion, of masses. For example, one talks about the value of the fine structure constant at different energies, but the mass of the electron is energy independent. In other words, the renormalized mass is only observable at the energy at which it coincides with the physical mass (the specific value of the energy depends on the renormalization procedure but it is usually of the order of the very physical mass), while one can measure (i.e. observe) interacting couplings at different energies and thus many different renormalized couplings (one for every energy) are observables. Do you agree?</p></li>
</ol>
<p>*(Footnote: since free quarks cannot be observed the definition of their masses is different and one has to give the value of their renormalized mass at some energy and renormalization scheme.)</p>
<p>Thank you in advance.</p> | g10556 | [
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