question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>I have a vacuum chamber with a pressure 10<sup>-8</sup> Torr.
Then I open an Oxygen valve with a set flow of 2 sccm from a tank with a pressure of 2 bars. The pressure in the chamber decreases to 10<sup>-2</sup> Torr. What is the partial pressure of the Oxygen in the chamber?</p>
<p>Is it 10<sup>-6</sup> Torr or 10<sup>-2</sup> Torr?</p> | g11573 | [
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<p>NASA is providing very brief updates on the <a href="http://www.nasa.gov/mission_pages/uars/index.html" rel="nofollow">reentry of the UARS satellite</a>. They also published an extensive study of the <a href="http://www.nasa.gov/pdf/585584main_UARS_Status.pdf" rel="nofollow">Re-entry and risk assessment for the NASA Upper Atmosphere Research Satellite (UARS)</a></p>
<p>The Planetary Society Blog has some nice coverage and a graph of altitude over time: <a href="http://planetary.org/blog/article/00003192/" rel="nofollow">Keeping track of UARS' reentry</a></p>
<p>The well-known satellite tracking site Heavens Above site provides <a href="http://www.heavens-above.com/PassSummary.aspx?satid=21701&Session=kebgfdhakmplnnekcikpjceo" rel="nofollow">UARS - Visible Passes</a> data which seems relatively up-to-date, but without information on the uncertainty.</p>
<p>What I want is actual tabular historical data, e.g. the changes in the <a href="http://en.wikipedia.org/wiki/Orbital_elements" rel="nofollow">Orbital elements</a> over the last months, weeks or days of its flight, and a characterization of how those elements other than altitude change over time.</p>
<p><em><strong>Update:</em></strong> The Center for Orbital and Reentry Debris Studies has a prediction and map for <a href="http://reentrynews.aero.org/1991063b.html" rel="nofollow">UARS</a> orbits.</p>
<p><em><strong>Update 2:</em></strong> One authoritative source is <a href="https://www.space-track.org/perl/login.pl" rel="nofollow">Space-Track</a>, run by United States Strategic Command (USSTRATCOM), but you need to be an "approved registered user"....</p> | g11574 | [
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<p>I am doing photometric calibration of a telescope and am trying to work out the errors on the flux that I measure. I have attempted to work out the errors due to the process of removing bias, dark frames, etc. using Poisson statistics, but this gives a fractional error of about 0.7, which is poor. I may try this analysis again using Gaussian stats, but I also want a measure of the error on the raw flux in the image (ignoring processing). </p>
<p>I have tried to do this by taking many observations of one star to look at the variation of flux; it roughly looks like a Gaussian, but I can't get a fit to it without altering the data.</p>
<p>Is there a good way to find a flux variation from data I have taken?</p> | g11575 | [
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<p>Could a neutron star be a bit like our Sun or any other star?</p>
<p>Just to have a different scale: </p>
<p>A neutron star fusioning not hydrogen and other elements but neutrons and quarks in its core at a stable, constant speed, would release energy, and the neutron star would therefore be larger than just packed neutrons would be. </p>
<p>It would shine with very high frequency electromagnetic waves like gamma rays and far beyond. Finally it would be burning all its "material" into someting weird and collapse. Would it be possible for the neutron star to explode as a supernova or <a href="http://en.wikipedia.org/wiki/Gamma-ray_burst">gamma-ray burst</a>?</p> | g11576 | [
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<p>I'm working on a 2d physics simulation. It's a continuous time simulation, that is, it uses swept shapes over the time-frame and geometrical/vector 'analysis' to determine most immediate time of contact. The world is then stepped forward to that point and collisions are resolved before proceeding to step the world forward to the next time of collision.</p>
<p>I do not use relaxation techniques or any kind of intersection resolution. The objects are moved to contact states and contact events are resolved as collisions.</p>
<p>I have tried a CONTACT_RANGE of 0.001f down to 0.00001f. This value determines whether objects are in contact. Lowering this value leads to less overlap states, but presumably at some point, lowering the value further will lead to the simulation missing contact events because inaccuracies will lead to the systems of bodies being stepped into the discrete or overlap state.</p>
<p>Now, to the problem, the simulation seems to compute the outcome of collisions between 2 bodies (circles in the case I'm looking at), correctly. But I have not correctly dealt with 3 or more bodies being in contact. </p>
<p>In the past, I did not deal with momentum / KE correctly, but I did constrain velocities such that multi-body systems would not intersect in the next sub-frame. But now that I have a correct solution to 2 body collision, I want to do it properly for more bodies.</p>
<p>I'm not sure how to proceed. I have read an interesting suggestion, that in reality, no collisions are simultaneous, and they can be dealt with one after the other. Is this true ?</p>
<p>Could I simply compute the resultant velocity of a body from one contact, then do the same with the next contact etc?</p>
<p>And would that lead to the same solution as though I computed velocity in one step, from all contacts simultaneously?</p>
<p>Or do I need a single function for solving the velocity from multiple contacts?</p>
<p>Any guidance is appreciated.</p>
<p>Gavin</p> | g11577 | [
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<p>If for some reason, an Astrophysics graduate decides to shift to Finance will he/she be in a better position (given his/her overspecialization) to make a transition compared to his/her counterparts who've been doing Analytical/Observational Astrophysics?</p> | g11578 | [
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<p>Are there any resources online for astronomy experiments that I can perform myself?</p>
<p>I am looking if anyone knows any measurements to take while looking for various objects during the evening particularly using a telescope/binoculars.</p>
<p>A couple of examples would be determining the orbits of the moons of Jupiter through an evenings observations or trying to measure a stars parallax from measurements throughout the year.</p>
<p>I can think of a handful of other ones but was wondering if there were any other resources to provide some more ideas.</p> | g11579 | [
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<p>I have this question: $q_1$ is a Uniformly Charged long Wire(inf in z axis) with $\lambda$ (charge per unit length).<br>
In (0,0,0) I have A very long conducting cylinder of radius a (also inf in z axis). <strong>NOT GROUNDED!!!</strong><br>
I want to find the electric potential everywhere. Where do i start? thanks!</p>
<p>PICTURE:
<img src="http://i.stack.imgur.com/s1ZJ1.png" alt="http://i.stack.imgur.com/H2WI7.png"></p> | g11580 | [
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<p><strong>"Masses $M_1$ and $M_2$ are connected to a system of strings and pulleys as shown. The strings are massless and inextensible, and the pulleys are massless and frictionless. Find the acceleration of M1.
(Clue if $M_2 = M_1$, A(acceleration)=g/5.)”</strong>
(The problem is from “An Introduction to Mechanics” – Kleppner & Kolenkow)
<img src="http://i.stack.imgur.com/BpZr4.png" alt="enter image description here"></p>
<p>My try:
Let T be the tension of the rope connected to $M_2$. So the tension of the rope connected to $M_1$ will be 2T.
The acceleration of both the masses is A.
<img src="http://i.stack.imgur.com/b8rnb.png" alt="enter image description here"></p>
<p>Now,
$M_2g – T = M_2A$ … (i)</p>
<p>$2T – M_1g = M_1A$ … (ii)</p>
<p>From (i) and (ii) ,</p>
<p>$$A=\frac{g(2M_2-M_1)}{(2M_2+M_1)}$$
Now if $M_2 = M_1$,
I get,
A = g/3.</p>
<p>But the answer is A=g/5.</p>
<p>Where am I wrong?
Will the accelerations of $M_1$ and $M_2$ not be the same? or, are there anything about the tensions ?</p> | g11581 | [
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<p>I'm not sure if this is the right place to ask this question. I realise that this maybe a borderline philosophical question at this point in time, therefore feel free to close this question if you think that this is a duplicate or inappropriate for this forum. Anyway, I'm an electrical engineer and I have some basic knowledge of quantum mechanics. I know that Schrödinger's equation is deterministic. However, quantum mechanics is much deeper than that and I would like to learn more. If this question is not clearly answerable at this point than can anyone point out some recognized sources that try to answer this question. I would appreciate it if the source is scientific and more specifically, is related to quantum theory.</p> | g634 | [
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<p>As I understand it, the renormalization group is only a semi-group because the coarse graining part of a renormalization step consisting of </p>
<ol>
<li><p>Summing / integrating over the small scales (coarse graining)</p></li>
<li><p>Calculating the new effective Hamiltonian or Lagrangian</p></li>
<li><p>Rescaling of coupling constants, fields, etc. </p></li>
</ol>
<p>is generally irreversible. </p>
<p>So when doing a renormalization flow analysis one usually starts from an initial action valid at an initial renormalization time $t_0$ (or scale $l_0$)</p>
<p>$$
t = \ln(\frac{l}{l_0}) = -\ln(\frac{\Lambda}{\Lambda_0})
$$</p>
<p>and integrates the renormalization group equations</p>
<p>$$
\dot{S} = -\Lambda\frac{\partial S}{\partial \Lambda} \doteq \frac{\partial S}{\partial t}
$$</p>
<p>forward in renormalization time towards the IR regime.</p>
<p>Under what conditions (if any) are the renormalization group transformations invertible such that the renormalization group equations are reversible in renormalization time and can be integrated "backwards" towards negative renormalization times and smaller scales (the UV regime)? </p>
<p>As an example where it obviously can be done, the calculation of coupling constant unification comes to my mind.</p> | g11582 | [
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<p><img src="http://i.stack.imgur.com/nKuqh.jpg" alt="enter image description here"></p>
<p>That is what my crystal structure looks like. The blue atoms sit on every lattice point (basis vector of $\{0,0\}$) and the red atoms have basis vector of $\left\{{2\over3},{1\over3}\right\}$. The lattice vectors are:</p>
<p>$$a~=~\left\{-{1\over2}, -{\sqrt3\over2}\right\},$$$$b~=~\{1, 0\}.$$</p>
<p>I used these two lattice vectors and found their reciprocal ones, and plotted them:</p>
<p><img src="http://i.stack.imgur.com/TSC0j.jpg" alt="enter image description here"></p>
<p>I know that the blue atoms are correct because I know from previous experience that the reciprocal lattice of the hexagonal structure just looks like the direct lattice but rotated $45^\circ$. The problem is the location of the red atoms. To plot the above I took the basis vectors and displaced them by the reciprocal vectors. I don't know if that's correct.</p>
<p>The other alternative is to find the reciprocals of the basis vectors too and then plot them. Which is here:
<img src="http://i.stack.imgur.com/h2Nsb.jpg" alt="enter image description here"></p>
<p>So do I have to find the reciprocals of the basis vectors or not? The literature only specifies finding the reciprocals of the lattice vectors, but no mention of what to do when there's an atomic basis.</p> | g11583 | [
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<p>I read on the website of European Space Agency that the altitude of Galileo satellites, which is 29600 Km from the center of the Earth, is chosen to avoid gravitational resonances so that station keeping manoeuvres are not needed during the lifetime of a satellite. </p>
<p>Note: I read before that GPS satellites' manoeuvres are controlled from the ground. GPS satellites are at an altitude of 26561 Km.</p>
<p>Note 2: Galieo and GPS satellites are orbiting on circular orbits.</p>
<ol>
<li>What is gravitational resonance? </li>
<li>How it is calculated?</li>
</ol> | g11584 | [
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<p>In my book they don't really derive the equation of the magnetic field inside of a finite solenoid. They just give me equation 1 and image and the end result, equation 2.</p>
<p>$$dB=\frac{\mu_0Ndlr^2I}{2ly^3}\tag{1}$$
<strong>Equation 1: contribution of $dl$ for $dB$ in point P</strong></p>
<p><img src="http://i.stack.imgur.com/o8AfB.jpg" alt="Sketch"></p>
<p><strong>Image 1: This image is shown next to the equation</strong></p>
<p>$$B=\mu_0NI/2l\int\sin( \theta) d\theta\tag{2}$$
<strong>Equation 2: Total magnetic field inside a finite solenoid. The intervals of the integral are $a=\theta_1$ and $b=\theta_2$.</strong></p>
<p>So my question was, where does equation 1 come from and how do they get from equation 1 to 2?</p> | g11585 | [
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<p>Aluminum foil is said to be <em>not</em> absorbing light at all.
It reflects light. So, does it mean that a more shiny aluminum foil will reflect more light and thus make the room more cooler as compared to less shiny foil?</p>
<p>If yes, then where does unreflected light go in case of less shiny aluminum foil?</p>
<p>Does less shiny and more shiny actually make a difference? Why?</p>
<p><em><strong>In order to keep whole room cool will it help if I stick the foil to the outside of wooden door (exposed to the sunlight) too?</em></strong></p> | g11586 | [
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<p>If a baryon wavefunction is $\Psi = \psi_{spatial} \psi_{colour} \psi_{flavour} \psi_{spin}$,
and we consider the ground state (L=0) only.
We know that the whole thing has to be antisymmetric under the interchange of two quarks. We know that colour is antisymmetric (always colourless) and spatial is symmetric. Therefore, the combination of flavour and spin has to be symmetric. </p>
<p>That's fine, I understand that. However, I'm very uncertain about what the 'interchange of two quarks' actually means. Interchange how? </p>
<p>For the 'easy' example of |uuu>. How is the flavour symmetric?</p>
<p>Basically, what does it mean to be symmetric in the quark model?</p> | g11587 | [
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<p>I know that there are some metals that just "like" to be on a surface, so if I make an alloy of such metal and some other metal, the first one will be on the surface after solidification of initially liquid alloy. This happens due to reduction of free surface energy, and I think that Gibbs' equation would be helpful here.</p>
<p>I'm especially interested in gold alloys</p>
<p>Howewer:</p>
<ol>
<li>I'm not sure if I'm right about Gibbs</li>
<li>I don't know where should I search for coefficients needed in this equation</li>
<li>I don't know how to solve and interpret it (Library at my Alma Mater is poor, and the Internet isn't sufficient)</li>
</ol> | g11588 | [
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<p>I am currently working my way through John S. Townsend book "A Fundamental Approach to Modern Physics" (ISBN: 978-1-891389-62-7). Exercise 3.12 (p.111) is about the 1D infinite square well. The box has the potential barriers at $x=0$ and $x=L$.
$$
V\left(x\right) = \begin{cases} \infty & x < 0 \\ 0 & 0 \leq x \leq L \\ \infty & x > L \end{cases}
$$</p>
<p>The text states the following:</p>
<blockquote>
<p>A particle of mass $m$ is in the lowest energy (ground) state of the infinite potential energy well. At time $t=0$ the wall located at $x=L$ is suddenly pulled back to a position at $x=2L$. This change occurs so rapidly that instantaneously the wave function does not change. ($a$) Calculate the probability that a measurement of the energy will yield the ground-state energy of the new well.</p>
</blockquote>
<p>The answer to this question involves re-solving the T.I.S.E., applying new boundary conditions, and re-normalizing the wave function. Then we project the new wave-function onto the old one, and calculate the overlap of the two wave-functions (initial and final wave-function). </p>
<p>I cannot find any discussion about this particular problem that would make me able to reason my way to calculate an overlap between the initial and final wave-function. No way. Unless I have a background in linear algebra, and would be able to foresee the need to project the one onto the other, and sort of find my way logically to the answer, I see no way any student without any experience with quantum physics would be able to solve this on their own. I had to use Google until I found the solution to a similar problem.</p>
<p>Or, maybe QM just does not come naturally to me. A lot of problem-solving is required in these types of courses to for us to build up some "intuition" about what to expect as results, what to do, etc. I still do not fully understand the logic behind the solution to the problem. </p>
<p>Phenomenologically, there is a particle inside the box. Then, suddenly, the box widens to twice its size. However, the wave-function does not change. Even though the particle has a bigger box in which to move around, the initial wave-function does not take this extra room into account, and would equal zero when $x>L$. Hence, I would not expect for the particle to venture out to the new region much, if we used only the initial wave-function. Or, is the problem that the particle will indeed venture out there (since $V(x)=0$, and it is physically allowed to), but we have not considered this in our normalizing of the function? Hence, it makes no sense to calculate any property of the particle with the "initial" wave-function, since this is simply the incorrect wave-function for the new well?</p>
<p><strong>New ideas and thoughts</strong></p>
<p>Okay, so I have to evaluate the integral</p>
<p>$$
c_1 = \int\limits_{- \infty}^{\infty} \psi_1 (x) \Psi (x) dx
$$</p>
<p>where $\psi_1$ is the theoretical wave-function for a particle in the entire box, that is from $0$ to $2L$, and $\Psi$ is the wave-function for the actual particle, that is from $0$ to $L$.</p>
<p>Now, I can split this integral into two parts:</p>
<p>$$
c_1 = \int\limits_{- \infty}^{\infty} \psi_1 (x) \Psi (x) dx = \int\limits_{0}^{L} \psi_1 (x) \Psi (x) dx + \int\limits_{L}^{2L} \psi_1 (x) \Psi (x) dx
$$</p>
<p>We see that since the actual particle's wave-function is not defined when $x>L$, the second term will be zero - that is, the wave-functino is normalized for $0<x<L$, and the boundary conditions ensures that $\Psi \rightarrow 0$ when $ x=0$ and $x=L$. Thus, the the integral over is reduced to</p>
<p>\begin{align*}
c_1 &= \int\limits_{0}^{L} \psi_1 (x) \Psi (x) dx \\
&= \int\limits_{0}^{L} \sqrt{\frac{1}{L}} \sin \left( \frac{\pi x}{2L} \right) \sqrt{\frac{2}{L}} \sin \left( \frac{\pi x}{L} \right) dx \\
&= \frac{\sqrt{2}}{L} \int\limits_{0}^{L} \sin \left( \frac{\pi x}{2L} \right) \sin \left( \frac{\pi x}{L} \right) dx \\
&= \frac{4 \sqrt{2}}{3 \pi} \\
\Rightarrow c_1^2 &= \frac{32}{9 \pi ^2} \\
c_1^2 & \approx 0.36
\end{align*}</p>
<p>I think maybe my difficulty with "visualzing" the problem is that I do not fully understand the expression for $c_n^2$, and how this gives the probability for measuring the energy level $n$.</p>
<p>I know this seems like I am rambling, and maybe I am, but I hope you understand my confusion. I appreciate any help!</p> | g11589 | [
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0... |
<p>Is more of the thermal radiation due to acceleration of electrons or acceleration of the nuclei? Do electrons and nuclei carry the same fractions of thermal energy in a hot body? </p> | g11590 | [
0.07274136692285538,
0.04425380378961563,
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0.02188... |
<p>From <a href="http://en.wikipedia.org/wiki/Coherent_states" rel="nofollow">Wikipedia</a>:</p>
<blockquote>
<p><em>[...]Off-diagonal long-range order (ODLRO) [...] exists whenever there is a macroscopically large factored component (eigenvalue) in a reduced density matrix of any order.</em></p>
</blockquote>
<p>How to understand the ODLRO in superfluidity? </p> | g11591 | [
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0.0... |
<p>According to the kinetic molecular theory obeying Maxwell-Boltzmann distribution of speeds, the rate of effusion through a pinhole of area $A$ is<br>
$$R=\frac{PA}{\sqrt{2\pi M R T}}$$ where $M$ is the molecular weight, $R$ is the gas constant and $T$ the absolute temperature. </p>
<p>To derive this, I consider the collision frequency on any small area ($A$):-<br>
using $$v_{avg}=\sqrt{\frac{8RT}{\pi M}}$$
I get the result, that the atoms in volume $v_{avg}A$ can hit the area. The number of particles in this volume is $nv_{avg}A$ ($n$=number density). But the derivation includes a factor of $\frac14$ before this term to find the actual number of atoms in this volume hitting the wall. I want to know how that factor of $\frac14$ came into picture to make the collision frequency per unit area as $\frac14nv_{avg}=\frac{P}{\sqrt{2\pi M R T}}$. </p>
<p>I know the origins of a factor of $\frac12$ before the pressure term while calculating it, considering change in momentum of a molecule on collision with the wall, which is to account for the fact that $<v_x^2>$ includes both the $v_x$ terms, going towards and going away from the wall(positive and negative directions) but the ones colliding are just the half of these $\frac12<v_x^2>$(going in any one direction).</p> | g11592 | [
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0.... |
<p>Suppose your have any magnetic object and no external force acts upon it, and the object comes near a metal which causes an impulse (think that will happen). However, the magnetic force is internal to the object, and momentum should be conserved, so where have I gotten it wrong?</p> | g11593 | [
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<p>What are the Physics/Astrophysics blogs you regularly read? I'm looking to beef up my RSS feeds to catch up with during my long commutes. I'd like to discover lesser-known gems (e.g. not well known blogs such as Cosmic Variance), possibly that are updated regularly and recently.</p>
<p>Since this is a list, give one entry per answer please. Feel free to post more than one answer.</p> | g11594 | [
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<p>I've been reading about fusion fuels for a while now, and I understand that in Lithium-Deuterium fuel, the neutrons from the fission reaction bombard the Lithium to produce Tritium and the D-T reaction occurs and we get the energy.</p>
<p>So what about Deuterium-Deuterium fusion ? Is it possible without the presence of Tritium at all ?
If so, then does it release more or less energy than D-T fusion ? </p> | g11595 | [
-0.01069138664752245,
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-... |
<p>I'm a big fan of the podcast Astronomy Cast and a while back I was listening to a Q&A episode they did. A listener sent in a question that I found fascinating and have been wondering about ever since. </p>
<p>From the show <a href="http://www.astronomycast.com/listeners/questions-shows/questions-show-decelerating-black-holes-earth-sun-tidal-lock-and-the-crushing-gravity-of-dark-matter/">transcript</a>: </p>
<blockquote>
<p><em>Arunus Gidgowdusk from Lithuania asks: "If you took a one kilogram mass and accelerated it close to the speed of light would it form into a black hole? Would it stay a black hole if you then decreased the speed?"</em></p>
</blockquote>
<p>Dr. Gay, an astrophysicist and one of the hosts, explained that she'd asked a number of her colleagues and that none of them could provide a satisfactory answer. I asked her more recently on Facebook if anyone had come forward with one and she said they had not. So I thought maybe this would be a good place to ask.</p> | g112 | [
0.02311084046959877,
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<p>All big rockets are burning either gas or fluid to create thrust. While this is so, I have filled up a plastic bottle with air at high pressure, and it can go long distances by blowing the pressurised air at reverse direction. If my bottle can do this without using any fire, why don't rockets just use air? How is the effect of combustion in thrust?</p> | g11596 | [
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-0.019... |
<p>Something I have read multiple times that I've never intuitively understood is that "heavier" particles are harder to detect than "lighter" ones... For example, I quote from Stephen Hawking's "The Grand Design" in relation to supersymmetry:</p>
<blockquote>
<p>But various calculations that physicists have performed indicate that the partner particles corresponding to the particles we observe ought to be a thousand times as massive as a proton, if not even heavier. That is too heavy for such particles to have been seen in any experiments to date, but there is hope that such particles will eventually be created in the Large Hadron Collider in Geneva.</p>
</blockquote>
<p>Could someone please explain, in simple terms, why heavy particles are harder to detect? Intuitively (to me, a non-physicist) it would seem that it should be the other way around, because a particle with more mass should interact more strongly with other matter.</p> | g11597 | [
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0.... |
<p>Say you have two charged capacitors in series. Zoom in on one capacitor. For this specific capacitor, the charge on the two plates will be the same in magnitude, according to my textbook.</p>
<p>My teacher said that the charge on the two plates won't be the same if the gap between the the plates is large. In fact, the charge on each plate in a capacitor is <em>never</em> the same. They're only approximated to be the same if the gap is small.</p>
<p>Why is the charge not the same on both plates on a capacitor in series if the gap is large?</p>
<p><img src="http://i.stack.imgur.com/u9x6F.png" alt="enter image description here"></p> | g11598 | [
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0.07358667254447937,
0.0012146364897489548,
-0.0... |
<p>If the earth's gravity exerts a net downward gravitational force on all air molecules, how come the molecules don't eventually lose their momentum and all settle down? How is the atmosphere is still miles thick after billions of years?</p> | g11599 | [
0.08233422785997391,
0.017106037586927414,
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0.04050074890255928,
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0.004... |
<p>Suppose we have a block A and is moving on a rough horizontal surface with a velocity 60 m/s and another block B of same mass moving with velocity 5 m/s on same horizontal surface and suppose they move same distance . The block A due to friction gets more tear on its bottom surface than block B so can we conclude that friction is varying with velocity? If not then why it happens ? does it happens or not ?? I know friction depends on normal reaction in solids.</p> | g11600 | [
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0.006... |
<p>We've previously discussed why it is that spinning tops do not fall over, see: <a href="http://physics.stackexchange.com/questions/271/why-dont-spinning-tops-fall-over">Why don't spinning tops fall over?</a></p>
<p>However, as the highest rated answer notes, the angular momentum of the spinning top is "quite high". On the other hand, I know that if the angular momentum of the top is zero it will, in fact, fall over. This suggests that increasing the angular momentum cannot stop the top from falling over, but instead can only increase the time (but this turns out not to be the case).</p>
<p>So suppose a top with mass concentrated in a spherical body M of radius S with center situated a distance R to a point a horizontal table at an angle $\theta$ while rotating at angular speed $\omega$. How long does it take for the top to fall over?</p>
<p>Some simplifying assumptions: (1) Assume the point of the top is fixed on the table. (2) Assume that the time at which the top falls over is when $\theta = 0$.</p>
<p><img src="http://i.stack.imgur.com/Ch8dP.jpg" alt="Drawing"></p> | g11601 | [
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<p>As I read in <a href="http://rads.stackoverflow.com/amzn/click/0679454438" rel="nofollow">The Road to Reality</a> by <a href="http://en.wikipedia.org/wiki/Roger_Penrose" rel="nofollow">Roger Penrose</a>, the <a href="http://en.wikipedia.org/wiki/Joukowsky_transform" rel="nofollow">Joukowsky transform</a> $$w(z) = \frac12\left( z + \frac1z \right)$$
after <a href="http://en.wikipedia.org/wiki/Nikolai_Zhukovsky" rel="nofollow">Nikolai Zhukovsky</a> (transcribed in several versions from <a href="http://ru.wikipedia.org/wiki/%D0%96%D1%83%D0%BA%D0%BE%D0%B2%D1%81%D0%BA%D0%B8%D0%B9,_%D0%9D%D0%B8%D0%BA%D0%BE%D0%BB%D0%B0%D0%B9_%D0%95%D0%B3%D0%BE%D1%80%D0%BE%D0%B2%D0%B8%D1%87" rel="nofollow">Никола́й Его́рович Жуко́вский</a>) can be used to <strong>calculate the flow</strong> of a non-viscious, incompressible and irrotational flow <strong>around an airfoil</strong>.</p>
<p>This can be done since the solution of a <a href="http://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder" rel="nofollow">potential flow around a cylinder</a> is known in full analyticity and the given transform <a href="http://en.wikipedia.org/wiki/Conformal_map" rel="nofollow">conformally maps</a> a circle on an airfoil-like geometry. I don't understand this argumentation, so:</p>
<blockquote>
<h3>How is the Joukowsky Transform used to calculate the Flow of an Airfoil?</h3>
</blockquote>
<p>An <strong>example</strong> of such a transformation is given in the mentioned Wikipedia article:</p>
<p><img src="http://upload.wikimedia.org/wikipedia/commons/d/d5/Jouktrans.png" alt="RotatingDisc"></p>
<p>Thank you in advance.</p> | g11602 | [
-0.016228867694735527,
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<p>I am aware about different interpretations of quantum mechanics out there but would mostly like to see an answer from the perspective of Copenhagen interpretation (or relative quantum mechanics if you wish).</p>
<p>Let an observer being a man with brain consisting of molecules and atoms. According the basic principles of quantum mechanics each of these particles has a wave function. </p>
<p>The question is: is there a combined wave function of all those particles which constitute the observer? Can such wavefunction be (in theory) determined by the observer himself?</p>
<p>Since the observer cannot isolate himself from his own brain, this would mean that the wave function, at least the part which determines his thoughts is permanently collapsed (i.e. the measurement happens instantly once the state changes). Does this "permanently collapsed" wave function imply special physical properties of the observer's own brain?</p>
<p>Does knowing his own thoughts constitute a measurement? Which moment should be counted as the moment of the collapse of wave function when making measurements on own brain?</p>
<p>Pretend an observer tries to measure the wave function of his own brain by a means of an X-ray apparatus or other machinery and read his own thoughts. Would not his own knowledge of that measurement or its results invalidate the results thus making the whole measurement impossible? </p>
<p>Does the behavior of particles which constitute the observer's brain differ statistically (acoording his measurements) from the behavior of particles which constitute the brains of other people?</p>
<p>Is there a connection with quantum immortality here?</p> | g11603 | [
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0... |
<p>I looked at the wikipedia entry and it doesn't give a very detailed or thorough description of the principles of operation of Barkhausen-Kurz oscillator triodes. But I do wonder if it is physically possible to design such a self-oscillating thermionic valve(DC input) that can oscillate in the audio frequency range(20Hz - 20 KHz).</p> | g11604 | [
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<p>While riding a bike at a higher velocity, I go over the speed breakers (Hump)
I get jumped over the bike for a certain height. How do I calculate this height of jump with respect to the seat of the bike?</p> | g11605 | [
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0.012292... |
<p>This should hopefully be a quick one.</p>
<p>Is there any difference between the <a href="http://www.google.com/search?as_q=&as_epq=big+bang" rel="nofollow">Big Bang Theory</a> and the <a href="http://www.google.com/search?as_q=&as_epq=hot+big+bang" rel="nofollow">Hot Big Bang Theory</a>?</p>
<p>Around Cambridge I hear everyone using "Hot Big Bang Theory", for example ther first line <a href="http://www.ctc.cam.ac.uk/outreach/origins/big_bang_one.php" rel="nofollow">here</a> of the pages of the Centre for Theoretical Cosmology.</p>
<p>In my undergraduate university it was referred to as the "Big Bang Theory".</p>
<p>I have tried searching online, and there does not seem to be much more mention of a "Hot Big Bang Theory" theory anywhere else on the internet. For example, <a href="http://en.wikipedia.org/w/index.php?search=hot+big+bang&title=Special%3ASearch&go=Go" rel="nofollow">wikipedia</a> returns no results for the term.</p>
<p>I am almost certain that they are one and the same theory, and that this is simply a case of nomenclature, with Cambridge trying to be different as usual, but I just want to make sure. It's terribely unnecessiarly confusing!</p>
<p>So can someone confirm that there is no difference between these two theories for me please?</p> | g11606 | [
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<p>For some experimental and practical reason, I have created a new coordinate system in the form</p>
<p>$$x^\prime_i=T_{ij}x_j$$</p>
<p>where $T_{ij}$ <strong>isn't</strong> a square matrix. $x_i$ is standard Cartesian coordinates, and $x^\prime_j$ is a point in the new system. I have to mention that the new system's axes <strong>are not linearly independent</strong>. So the last relation can be written as</p>
<p>$$\left(\matrix{x_0^\prime\\x_1^\prime\\x_2^\prime\\x_3^\prime}\right)=\left( \matrix{T_{11} & T_{12} & T_{13} \\ T_{21} & T_{22} & T_{23} \\ T_{31} & T_{32} & T_{33} \\ T_{41} & T_{42} & T_{43} } \right)\cdot \left(\matrix{x\\y\\z}\right)$$</p>
<p>The matrix $T_{ij}$ is well defined.</p>
<p>What I need is a rotation operator that will transform a point in the primed system, as the standard rotation operator does. So say I have the standard rotation matrix in Cartesian coordinates around the z-axis:</p>
<p>$$R_{ij}= \left( \matrix{\cos{\theta}&-\sin{\theta}&0\\ \sin{\theta}&\cos{\theta}&0\\0&0&1} \right)$$</p>
<p>So to rotate a point in Cartesian coordinates, we use the standard operator formula:</p>
<p>$$P^\prime_i=R_{ij}P_j$$</p>
<p>where $P_j$ is the point before rotation, and $P^\prime_i$ is the point after rotation.</p>
<p>How can I write this rotation formula for a point in the new coordinates system that uses 4 points? How will the rotation matrix look like? I expect a rotation matrix that is $4\times4$, but I don't know how to derive it. Please help in that.</p> | g11607 | [
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<p>If you take a look at <a href="http://www.youtube.com/watch?v=izy4a5erom8" rel="nofollow">this video</a> you will see what kind of a coupled pendulum I'm talking about.</p>
<p>So I made a similar one in my high school's physics lab, using light metal bobs(much lighter than the Easter eggs he's used in the video) and thin copper wire. </p>
<p><strong>Some Data About My Experiment:</strong></p>
<p>My pendulum did work the same way, i.e. one would stop as the other would swing with max amplitude, which continues periodically without much damping. But the frequency of the combined periodic motion in my case was much slower than that in the video. His pendulum stops after a few oscillations while mine took 10-15 oscillations to completely transfer the energy(I think this is because I used a lighter weight)</p>
<p><strong>My Question:</strong></p>
<blockquote>
<p>In the video the person swings one of the pendulums <em>perpendicular</em> to the wire. I tried swinging it <em>parallel</em> to the wire and nothing happened. The pendulum I initially provided energy to kept swinging with the same amplitude for a long time.<br>
<strong>Why doesn't energy transfer take place when I swing the one of the pendulums <em>parallel</em> to the above wire?</strong> It should because the energy is being transferred by waves through the string. This motion should also produce waves.</p>
</blockquote>
<p><strong>Possible Reasons:</strong> </p>
<ul>
<li>Maybe the energy transfer takes a lot of time, hours perhaps? I hardly observed it for ten minutes.</li>
<li>There's too much damping, although in which case the first pendulum should stop quickly too.</li>
<li>The energy transfer is happening in a way not compatible with the direction the bob is swinging in.</li>
</ul>
<p>I really can't seem to explain any of the above reasons. Maybe it's an entirely different reason altogether. Any help would be appreciated!</p> | g11608 | [
0.1001131683588028,
0.01425428967922926,
0.011625204235315323,
-0.03336958959698677,
0.030465060845017433,
0.051873642951250076,
0.053492672741413116,
0.021434320136904716,
0.008079322054982185,
-0.025994693860411644,
-0.021295828744769096,
0.031179454177618027,
-0.052241068333387375,
0.02... |
<p>$$
\DeclareMathOperator{\dif}{d \!}
\newcommand{\ramuno}{\mathrm{i}}
\newcommand{\exponent}{\mathrm{e}}
\newcommand{\ket}[1]{|{#1}\rangle}
\newcommand{\bra}[1]{\langle{#1}|}
\newcommand{\braket}[2]{\langle{#1}|{#2}\rangle}
\newcommand{\bracket}[3]{\langle{#1}|{#2}|{#3}\rangle}
\newcommand{\linop}[1]{\hat{#1}}
\newcommand{\dpd}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\dod}[2]{\frac{\dif{#1}}{\dif{#2}}}
$$</p>
<p>Using the Schrödinger equation and the definition of the expectation value it can be shown that the time dependence of the expectation value of an observable $A$ for a system in arbitrary state $\ket{\Psi(t)}$ is given by
$$
\dod{\langle A \rangle}{t} = \frac{\ramuno}{\hbar} \langle [\linop{H}, \linop{A}] \rangle + \big\langle \dpd{\linop{A}}{t} \big\rangle \, , \tag{1}
$$
and this equation shows that, in general, if an operator $\linop{A}$ commutes with the Hamiltonian operator $\linop{H}$ and does not have an explicit time dependence, then the expectation value of the corresponding observable $A$ is time independent.</p>
<p>For stationary states $\ket{\Psi(t)} = \exponent^{-\ramuno E_{k} t / \hbar} \ket{E_{k}}$
the first term in the expression for the time dependence of the expectation value of an observable vanishes
$$
\langle [\linop{H}, \linop{A}] \rangle =
\bracket{ \Psi(t) }{ \linop{H} \linop{A} }{ \Psi(t) } - \bracket{ \Psi(t) }{ \linop{A} \linop{H} }{ \Psi(t) } =
\bracket{ E_{k} }{ \linop{H} \linop{A} }{ E_{k} } - \bracket{ E_{k} }{ \linop{A} \linop{H} }{ E_{k} } =
E_{k} \bracket{ E_{k} }{ \linop{A} }{ E_{k} } - E_{k} \bracket{ E_{k} }{ \linop{A} }{ E_{k} } = 0 \, ,
$$
and so the time dependence of the expectation value is simply given by
$$
\dod{\langle A \rangle}{t} = \big\langle \dpd{\linop{A}}{t} \big\rangle \, . \tag{2}
$$</p>
<p>Nevertheless, the statement like the following one </p>
<blockquote>
<p>A stationary state is called stationary because the system remains in the same state as time elapses, in every observable way. <a href="http://en.wikipedia.org/wiki/Stationary_state" rel="nofollow">Wikipedia</a></p>
</blockquote>
<p>is found in many books.</p>
<p>The thing that troubled me is the word <em>every</em>, since from (2) it appears that if an operator $\linop{A}$ carries some explicit time dependence, then the expectation value of the corresponding observable $A$ changes in time.
So stationary states are, in fact, not so stationary. </p>
<p>I have the feeling that I am missing something.
And our discussion with Bubble helped clarify what's bothering me.</p>
<p>As far as I know operators in the Schrödinger picture <em>usually</em> do not carry an explicit time dependence. Again, <em>usually</em>, but not always.
In many books (see, for instance, Griffiths, D.J., Introduction to quantum mechanics, 2nd ed.) one can find that</p>
<blockquote>
<p>Operators that depend explicitly on $t$ are quite rare, so <em>almost always</em> $\dpd{Q}{t} = 0$. </p>
</blockquote>
<p>And, yet the author claims that</p>
<blockquote>
<p>Every expectation value is constant in time.</p>
</blockquote>
<p><strong>I feel like there is a gap between operators being <em>almost always</em> explicitly independent of time and <em>every</em> expectation value being constant.</strong></p> | g11609 | [
-0.013813064433634281,
-0.004539863206446171,
0.0051193637773394585,
-0.008530951105058193,
-0.01087386254221201,
0.04768574982881546,
0.04396149888634682,
0.012531700544059277,
0.01585657149553299,
0.02241482026875019,
-0.018296614289283752,
0.029648859053850174,
-0.04763109236955643,
0.0... |
<p>I have taken only QM I, which is the 1st half of Griffiths including the chapter on identical particles, will that be enough to understand Kittel's solid state? </p>
<p>Should one have also taken a course in statistical mechanics before studying kittel?</p>
<p>I have seen in some universities in the states that the prerequisite of an introductory course in solid state physics sometimes are QM I, II, SM, and other times are QM I only (or with SM and QM II are corequisite)</p> | g11610 | [
0.03968459740281105,
0.016659926623106003,
0.02073190174996853,
-0.018242429941892624,
0.014628042466938496,
0.052321795374155045,
-0.013746568001806736,
0.010961289517581463,
0.010614222846925259,
-0.03968683257699013,
-0.010220657102763653,
-0.034934282302856445,
0.05206883326172829,
0.0... |
<p>When a wire that has current $I$ flowing within it and its in a magnetic field, the wire experience the Lorentz force, and that force moved the wire over a certain distance $x$(no matter how small), can we state that work is done by the Lorentz force on the wire? </p>
<p>If so...</p>
<p>What kind of energy is transferred here?
And, what potential energy was converted for this wire to move?
What is the source of energy?</p> | g11611 | [
0.019256914034485817,
0.03266160935163498,
-0.01091449148952961,
-0.02072995901107788,
-0.01422365102916956,
0.004827185533940792,
0.008644135668873787,
0.013327092863619328,
-0.06323127448558807,
0.013563502579927444,
-0.0389273464679718,
0.0302121601998806,
-0.06433147937059402,
-0.02912... |
<p>$\alpha_L = \frac{1}{a}\frac{da}{dT}$</p>
<p>I know error in $a$, i.e., $da$</p>
<p>I need to find out $d\alpha$ from data of $da$.</p>
<p>$d\alpha_L = -\frac{1}{a^2}\frac{da}{dT}da$</p>
<p>Is this correct?</p>
<p>Note: </p>
<p>$\alpha_L$ = Linear thermal expansivity</p>
<p>$a$ = Lattice constant</p> | g11612 | [
0.03339624032378197,
0.005411284510046244,
-0.04368698596954346,
-0.04488429054617882,
-0.003016556380316615,
-0.025812892243266106,
0.038153424859046936,
0.03675345331430435,
-0.07531620562076569,
-0.007457796484231949,
-0.0005691586411558092,
0.05785652995109558,
0.03059816174209118,
0.0... |
<p>In many theoretical setups it is implicitly assumed that the underlying manifold (i.e. spacetime) is orientable. Then our analysis depends on this implicit assumption. For example, Stokes' theorem assumes orientability of the chain on which we integrate. However, we accept that time "always" points forwardly.</p>
<p>My question is: doesn't a 1-directional arrow of time provides a hint that spacetime should be modeled, afterall, by a non-orientable manifold?</p> | g11613 | [
-0.012312318198382854,
0.014465621672570705,
-0.00682048499584198,
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0.010621084831655025,
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0.07404910027980804,
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0.05168740078806877,
0.06132162734866142,
0.007966752164065838,
0.04321403428912163,
0.037... |
<blockquote>
<p>A wind-powered generator converts wind energy into electrical energy.
Assume that the generator converts a fixed fraction of the wind energy
intercepted by its blades into electrical energy. For wind speed $v$,
show that the electrical power output will be proportional to $v^3$.</p>
</blockquote>
<p>I tried hard but I get power output is proportional to $v^2$.</p> | g11614 | [
0.0868140459060669,
0.057265058159828186,
-0.005127322394400835,
-0.022192759439349174,
0.011517714709043503,
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0.027516594156622887,
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0.026834024116396904,
0.035779375582933426,
0.017688937485218048,
-0.030359378084540367,
-0... |
<p>Is it possible to make a metallic object move in a circular contained tube around and around in which a magnetic field is setup to cause the metallic object to move through the electric field within the tube through magnetic forces alone? If not, what other forces must be present to make the object move around and around in the circular tube?</p> | g11615 | [
-0.022532518953084946,
0.04923011362552643,
-0.01180022582411766,
-0.02599792182445526,
0.09305451810359955,
0.037604086101055145,
0.017678644508123398,
-0.017114154994487762,
-0.06967609375715256,
-0.023828960955142975,
-0.033447735011577606,
0.03972642496228218,
-0.010445991531014442,
-0... |
<p><a href="http://uqu.edu.sa/files2/tiny_mce/plugins/filemanager/files/4190016/Quantum_Mechanics_1/ch4-virtual-book.pdf" rel="nofollow">http://uqu.edu.sa/files2/tiny_mce/plugins/filemanager/files/4190016/Quantum_Mechanics_1/ch4-virtual-book.pdf</a></p>
<p>On page 2 of the above pdf they describe how they select their wavefunctions. Finding the general solution is easy but they then go on to say that D= 0 because 'this is not physically meaningful' leaving $\psi=Ce^{ik_2x}$.</p>
<p>Fine, I can see that if the wave is transmitted through the barrier it is best represented by such a travelling wave moving in the +x direction.</p>
<p>Now, my lecturer also supports and uses the above explanation.</p>
<p>However, there are a few university websites and a textbook (Introduction to Quantum Mechanics by Bransden) that state that the wavefunction for the section $V(x) = V_0$ cannot be represented by $\psi=Ce^{ik_2x}$ as this tends to infinity at x= infinity. Also, by the postulates of QM the wavefunction must have a real quantifiable integral which such a function is in violation of.</p>
<p>What do I follow ? Who is right ?</p> | g11616 | [
-0.008833285421133041,
-0.036679092794656754,
-0.022395240142941475,
-0.051367178559303284,
0.06636932492256165,
0.01010408066213131,
0.029354151338338852,
0.034024063497781754,
-0.02789812535047531,
-0.006522016599774361,
0.0012286071432754397,
-0.015920164063572884,
0.00016953196609392762,... |
<p>My professor told me recently that Area is a vector. A <a href="http://www.google.co.in/#sclient=psy&hl=en&source=hp&q=what%20is%20a%20vector&pbx=1&oq=what%20is%20a%20ve&aq=1&aqi=g5&aql=&gs_sm=sc&gs_upl=1666l6221l0l7939l12l9l0l2l2l0l541l3051l2-3.1.2.2l8l0&bav=on.2,or.r_gc.r_pw.&fp=5b60a6a8a4733e57&biw=1024&bih=629&pf=p&pdl=300">Google search</a> gave me the following definition for a vector:</p>
<blockquote>
<p>Noun: A quantity having direction as well as magnitude, esp. as
determining the position of one point in space relative to another.</p>
</blockquote>
<p>My question is - what is the direction of area? I can relate to the fact that velocity is a vector. The velocity of a moving motorbike for example, has a definite direction as well as a definite magnitude assuming that the bike is moving in a straight line & not accelerating.</p>
<p>My friend gave me this explanation for the direction of Area vector. Consider a rectangular plane in space. He argued that the <em>orientation</em> of the plane in space can only be described by considering area as a vector & not a scalar. </p>
<p>I still wasn't convinced. Suppose the plane was placed such that its faces were perpendicular to the directions, North & South for example. Now the orientation of the plane is the same <em>irrespective</em> whether the so called vector points to north or to the south. Further what is the direction of a sphere's area?</p>
<p>Does considering area as a vector have any real significance? Please explain.</p>
<p>Thanks in advance.</p> | g11617 | [
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0.030095959082245827,
-0.03775022178888321,
-0.04721098020672798,
0.05279194936156273,
0.01701091229915619,
0.07861863821744919,
0.02... |
<p>Equation 1.2 of <a href="http://www.staff.science.uu.nl/~hooft101/lectures/genrel_2010.pdf" rel="nofollow">'t Hooft's Introduction to General Relativity</a> gives the <em>Lorentz transformations</em>:</p>
<p>$$
(x^\mu)' = \sum\limits_{\nu = 1}^4 {L^\mu}_\nu x^\nu
$$</p>
<p>Is this the sum of four square matrices each one multiplied by a column vector? Or is this a single square matrix multiplied by a single column vector?</p> | g11618 | [
-0.032839518040418625,
0.015695955604314804,
-0.01723933406174183,
-0.025778571143746376,
0.014721089042723179,
0.004116825293749571,
0.034585099667310715,
0.001656027277931571,
-0.013406750746071339,
0.012762944214046001,
-0.030644550919532776,
0.011636708863079548,
0.00025505057419650257,
... |
<p>I've read that the angle for viewing a Primary Rainbow is between 40-42 degrees. How would I go about showing this? How would I calculate that angle from scratch? I figured that Snell's Law and the Law of Reflection would be used for light bouncing off and through a (spherical) water droplet. But I only have a vague idea of how to begin.</p>
<p>I would imagine that once you know how to calculate the Primary Rainbow angle, calculating the Secondary Rainbow angle would be very similar if not identical process. Is this right?</p> | g11619 | [
0.0013291118666529655,
0.02492436394095421,
0.0026518062222748995,
-0.06191685423254967,
-0.035136349499225616,
0.015364408493041992,
0.07203955203294754,
-0.01228842232376337,
0.018173057585954666,
0.0019327024929225445,
-0.01609082706272602,
0.0651523768901825,
0.049055248498916626,
-0.0... |
<p>The internal potential energy of an $N$ particle system is a general function of the coordinates of the particles: $U(r_1,...,r_N)$. In some approximations and expansions - e.g. <a href="http://www.soft-matter.uni-tuebingen.de/teaching/Tutorial_Virial_Expansion.pdf">virial expansion</a> - it is assumed that the potential energy is a sum of pairwise interactions:</p>
<p>$$U(r_1,...,r_N) = \sum_{ij}u(r_{ij})$$</p>
<p>with $r_{ij} = |r_i - r_j|$. But most of the interactions between particles I am aware of are pairwise <em>per se</em>. The only three-particle interaction I know of is a chemical reaction which needs a catalyst.</p>
<blockquote>
<p>Which other specific examples of three- or $n$-particle interactions
are there?</p>
</blockquote>
<p><strong>Addendum</strong>: I found this in the Wikipedia article on <a href="http://en.wikipedia.org/wiki/Reaction_mechanism#Molecularity">reaction mechanisms</a>: </p>
<blockquote>
<p><em>In general, reaction steps involving more than three molecular
entities do not occur.</em></p>
</blockquote> | g11620 | [
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0.046729348599910736,
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0.04183937981724739,
0.026873940601944923,
-0.022925319150090218,
-0.018444016575813293,
-0... |
<p>I am interested in Quantum Information and Cryptography in particular. I have gone through Neilson's text and Preskill's notes . Can someone suggest me some good text for Quantum Cryptography ? I thank you for your time.</p> | g11621 | [
0.019257640466094017,
0.07570108026266098,
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0.03229370713233948,
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0.0065184226259589195,
-0.04179304838180542,
0.04190585017204285,
0.030780591070652008,
-0.045... |
<p>When sliding a magnet over a ferromagnetic surface there is no magnetic force at all, however,there is a magnetic force only at the edge, when the magnet is being pulled of I assume the magnetic field is trying to resist.
However, a fact it noticeable, the sliding/lateral magnetic force at the edge is a lot less, by a factor of half - ten times less.</p>
<p>What could be the reasons that detains the magnitude of the lateral force?
Pelase do explain in detail.</p>
<p>Thank you.</p> | g11622 | [
0.05667251721024513,
0.0737961009144783,
0.011667799204587936,
0.007229470182210207,
0.007464059628546238,
0.03814728185534477,
0.043936751782894135,
0.07993891090154648,
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-0.027262428775429726,
-0.036584191024303436,
-0.02876301482319832,
0.023426929488778114,
-0.000... |
<p>This answer gives a great explanation of why the field inside a wire connected to a battery must be equal at all points: <a href="http://physics.stackexchange.com/questions/102930/why-doesnt-the-electric-field-inside-a-wire-in-a-circuit-fall-off-with-distance/102936#102936">Why doesn't the electric field inside a wire in a circuit fall off with distance from the battery?</a></p>
<p>The answer uses the concept of surface charge buildup to show why the field has to be equal at all points and why it must be perpendicular to the wire.</p>
<p>However, there are a lot of ways a field could exist in a wire that is not perpendicular to the wire, but would not cause surface charge buildup:</p>
<p>For example these fields:</p>
<p><img src="http://i.stack.imgur.com/Or4yG.png" alt="enter image description here"></p>
<p>could exist instead of:</p>
<p><img src="http://i.stack.imgur.com/iQuaO.png" alt="enter image description here"></p>
<p>and there would still be no surface charge build up.</p>
<p>So my questions are:</p>
<p>1) Can these "exotic" fields exist"?</p>
<p>2) If not, why not?</p>
<p>3) If these exotic field exist, how would current be defined in the wire? Since the electrons are not flowing perpendicular to the wire, would current be defined as the component of the movement of the electrons perpendicular to the wire or just the entire movement of the electrons?</p>
<p>4) The image below is a resistor. The "lines" represent the current direction and density ("the current density streamlines") . The "gray objects" represent wires through which a voltage difference is applied. If the electric field is <em>always</em> parallel to the surface how can the current lines be at an angle in the first resistor? </p>
<p><img src="http://i.stack.imgur.com/SKO6R.png" alt="enter image description here"></p>
<p>**</p>
<h2><strong>Please address all my questions separately. Thank you.</strong></h2>
<p>**</p> | g11623 | [
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0.011685095727443695,
0.07883802056312561,
0.07595212012529373,
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0.010197464376688004,
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0.017789632081985474,
-0.027327440679073334,
0.03509651869535446,
-0.023606404662132263,
0.00... |
<p>The Hadamard Operator on one qubit is:</p>
<p>\begin{align*}
H = \tfrac{1}{\sqrt{2}}\left[\,\left(\color{darkgreen}{|0\rangle + |1\rangle}\right)\color{darkblue}{\langle 0|}+\left(\color{darkgreen}{|0\rangle - |1\rangle}\right)\color{darkblue}{\langle 1|}\,\right]
\end{align*}</p>
<p>Show that:
\begin{align*}
H^{\otimes n} = \frac{1}{\sqrt{2^n}}\sum_{x,y}(-1)^{x \cdot y}\,\left|x\rangle \langle y\right|
\end{align*}</p>
<p>I can evaluate things like $H \otimes H$ in practice, but I don't know how to get a general formula for $H^{\otimes n}$. Are there any tricks I could use?</p> | g11624 | [
-0.02695537731051445,
0.03618047758936882,
-0.014487110078334808,
-0.07553263008594513,
0.043064184486866,
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0.0018710752483457327,
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-0.03406219929456711,
0.05686162784695625,
0.001195228542201221,
0.06177197024226189,
-0.023727871477603912,
0.0725... |
<p>I read the section <em>closed forms and cycles</em> in Arnold's <em>Mathematical Methods of Classical Mechanics</em> (page 196-200), but the problems in this section is too difficult to solve in the way following the hints. What's more, There seems no other materials teach closed forms and cycles in the same way as this book. So, this post is meant to ask for solutions(in the way following the hints) and recommended materials. The problems are following:</p>
<blockquote>
<ol>
<li><p>Let $X$ be a vector field on $M$ and $\omega$ a differential $k$-form. We define a $(k-1)$-form $i_X\omega$ (the interior derivative of $\omega$ by $X$) by the relation
$$
(i_X \omega)(\xi_1,\ldots,\xi_{k-1}) = \omega(X,\xi_1,\ldots,\xi_{k-1}).
$$
Prove the <a href="http://en.wikipedia.org/wiki/Lie_derivative#The_Lie_derivative_of_differential_forms" rel="nofollow">homotopy formula</a>
$$
i_X d + di_X=L_X.
$$</p></li>
<li><p>Prove the formula for differentiating a vector product on three dimensional Euclidean space (or on a Riemannian manifold) :
$$
\mathrm{curl}[a,b] = \{a,b\} + a~\mathrm{div}[b] - b~\mathrm{div}[a],
$$
where $\{a,b\} = L_ab$ is the Poisson bracket of the vector field. </p></li>
</ol>
</blockquote> | g11625 | [
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-0.0002672878617886454,
0.014561926946043968,
-0.012386697344481945,
0.03923420608043671,
-0.07479682564735413,
-0.00840314757078886,
0.010714001022279263,
-0.049008533358573914,
0.006605241913348436,
-0.006596094463020563,
... |
<p>There is a <a href="https://www.youtube.com/watch?v=7ne0GArfeMs" rel="nofollow">lecture</a> on how facts about the cosmos can be derived form rather simple observation. Is there an analogy for the small scale? Is there a technically simple observation that would imply, say, atoms? Anything smaller?</p> | g11626 | [
0.037594154477119446,
0.04630226269364357,
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0.007258857134729624,
0.018167568370699883,
0.00031738445977680385,
0.01048084907233715,
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-0.09600289911031723,
0.02559966966509819,
-0.009269787929952145,
0.07178761810064316,
0.0... |
<p>As far as I know a collisions of matter and antimatter leads to the complete annihilation of both, whereby 100% of the rest mass of the particles is converted into gamma rays. Could this mechanism be responsible for the Gamma Ray bursts seen by satellites? Could therefore Gamma Ray Bursts tell us something about where all the antimatter is in the universe?</p> | g11627 | [
0.049174390733242035,
0.032568030059337616,
0.013659712858498096,
0.00556973135098815,
0.03832424804568291,
0.06143907830119133,
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-0.008115218952298164,
0.056618478149175644,
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0.08019312471151352,
-0.002352... |
<p>We all know that in <a href="http://en.wikipedia.org/wiki/Rayleigh%E2%80%93Jeans_law" rel="nofollow">Rayleigh-Jeans law</a>, </p>
<p>$$N(f)df ~=~ 8\pi f^2 df/c^3.$$ </p>
<p>How do you derive $N(\lambda)d\lambda$?</p>
<p>I am sort of confused...</p> | g11628 | [
0.018892256543040276,
0.007551736198365688,
-0.01157850120216608,
-0.04642200097441673,
0.04835362732410431,
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-0.0625930055975914,
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0.0... |
<p>Given current accuracy of the techniques, is it possible to identify a real, existing tunnel (stright I think) to make the direct comparison of the speed of light and of neutrinos?
The hypotetical tunnel from CERN to OPERA would-be too long. If we were able to increase accuracies by two decades, then would a 7.3 Km tunnel suffice ? The 60ns difference would
become around 600ps.
Suppose there is such a tunnel, suppose it can be availabe to physicists. Apart from all the logistics problems of generating and detecting light and neutrinos at the two ends of such tunnel, are there other difficulties?</p> | g11629 | [
-0.01947096176445484,
0.04337918758392334,
0.007464668247848749,
0.06197153404355049,
-0.0062921298667788506,
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0.03903475031256676,
0.035944823175668716,
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0.03914131596684456,
0.00... |
<p>It has been claimed by some people that Schrödinger's picture is more misleading compared to the Heisenberg principle or path integrals, and that we would be better off abandoning the Schrödinger picture in favor of either the Heisenberg picture or path integrals. However, when it comes to open quantum systems in a constant interaction with the environment, which isn't fully modeled, it is not at all clear how to apply the Heisenberg picture or path integrals. The Heisenberg picture requires the operators of the system to evolve in such a way in time what it becomes extremely mixed up with the environmental degrees of freedom, and the only way this can be done is to fully model the environment as a whole, or at least all of the part of the environment which ever has a chance of interacting with the system in question. Similarly, how do you even go about adapting path integrals to open systems without including the entire environment, or at least all of those parts which can ever interact with the system?</p>
<p>Might it be the case that the Heisenberg picture and path integrals can only be strictly applied to the universe as a whole, or at the very least, causal diamonds?</p> | g11630 | [
0.011460737325251102,
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0.015070325694978237,
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0.04865718632936478,
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0.0... |
<p>In sports it is commonplace to distinguish</p>
<ul>
<li><p>a "<i>team</i>" (as characterized by the players who took part in a match, playing together against another team), from </p></li>
<li><p>the "<i>score</i>" (such as the final score of two teams having played a match against each other), and from </p></li>
<li><p>the "<i>ranking</i>" (e.g. the ranking of teams within a league at the end of a season). </p></li>
</ul>
<p>Similarly, considering a clock it is possible to distinguish </p>
<ul>
<li><p>its "<i>instants</i>" (or "<i>indications</i>", as characterized for instance by the pointing of clock hands to certain elements of the clock face), along with</p>
<p>the fact (or idea) that a clock "<i>progresses</i>" (considering some or all of its indications as a set in a particular order), from </p></li>
<li><p>the "<i>duration</i>" of the clock between any two of its indications, along with </p>
<p>comparisons of durations (in particular determining, durations between which pairs of indications are equal to each other), from</p></li>
<li><p>parametrizations of the indications of a clock by real numbers (often called $t$).</p></li>
</ul>
<p>Use and comprehension of this entire terminology then allows for instance certain parametrizations $t$ to be qualified as monotonous wrt. the progress of a given clock (while others are not);<br>
and among those, certain parametrizations as "<i>good</i>" (or proportional, or affine) wrt. the duration ratios between indications of the given clock (while other monotonous parametrizations are not).</p>
<p>My question:<br>
Is there a didactical disadvantage in projecting much if not all of the described clock-related terminology into one and the same word: "<i>time</i>" ?</p> | g11631 | [
0.032445214688777924,
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0.06674481928348541,
-0.013917768374085426,
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0.029127592220902443,
0.01... |
<p>My physics textbook says that friction mainly arises due to intermolecular attraction between atoms of the objects in contact and clashes between peaks are only significant for rough surfaces. I was wondering, if friction arises due to intermolecular attraction, why doesn't it oppose lifting a body as well(considering that the atoms are attracted to each other). Why doesn't it oppose rolling? (even when there is no slippage, if atoms of the contact patch are attracted to the atoms in the ground, there should be a force opposing movement) </p>
<p>Another related question: Is there an intuitive reason why(for most pairs of surfaces) kinetic friction is lower than static friction?</p> | g11632 | [
0.05091657117009163,
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-0.03570827469229698,
0.0264128390699625,
-0.018353374674916267,
-0.04161220043897629,
-0.007... |
<p>When differential equation like Schrodinger is separable in some coordinate system? What needs to satisfy the potential ?</p> | g11633 | [
0.0006633958546444774,
0.05544460564851761,
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0.016488077118992805,
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0.0034544963855296373,
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-0.022566692903637886,
0.006133404094725847,
-... |
<p>Are there some toy model QFTs where the <a href="http://en.wikipedia.org/wiki/Asymptotic_safety" rel="nofollow">asymptotic safety</a> scenario is realized? </p> | g11634 | [
-0.021700719371438026,
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-0.01261958759278059,
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-0.0481560155749321,
0.03949269279837608,
-0.0... |
<ol>
<li><p>Since the concept of the singularity in a <a href="http://en.wikipedia.org/wiki/Black_hole">black hole</a> leads to infinite densities, I wonder if it is really certain that black holes exist? </p></li>
<li><p>Is there a possibility that massive objects (which are believed to be black holes) are in reality dense stars not emitting light (dark neutron stars)?</p></li>
<li><p>Is there a possibility to explain the observed facts without the use of black holes?</p></li>
<li><p>One more question: According to the mainstream, are <a href="http://en.wikipedia.org/wiki/Neutron_star">neutron stars</a> believed to
eventually collapse to a black hole, or are they stable objects?</p></li>
</ol> | g11635 | [
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-0.017499258741736412,
0.01535240188241005,
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0.03083886206150055,
-0.0... |
<p>I am trying to determine why electric field may be confined to a certain region if there is a large difference in the permitivity for example if electric field flows through water and then reaches a water air boundary. </p>
<p>I have also been reading about EM waves, is it possible to model electric field as a wave because if so then the transmission T and reflection R coefficients given below in terms of n which is $\propto \epsilon_{r}^{1/2} $ and so if $\epsilon_{1}>>\epsilon_{2}$ then $n_{1}>>n_{2}$ ;</p>
<p>$\displaystyle R$ $\textstyle =$ $\displaystyle \left(\frac{n_1-n_2}{n_1+n_2}\right)^2, \rightarrow 1$</p>
<p>$\displaystyle T$ $\textstyle =$ $\displaystyle \frac{n_2}{n_1}\left(\frac{2 n_1}{n_1+n_2}\right)^2 \rightarrow 0.$</p>
<p>and so it is clear that the wave is reflected at the boundary, is this approach valid ?</p>
<p><a href="http://farside.ph.utexas.edu/teaching/em/lectures/node103.html" rel="nofollow">http://farside.ph.utexas.edu/teaching/em/lectures/node103.html</a></p> | g11636 | [
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0.06432580202817917,
0.038149647414684296,
0.07591522485017776,
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-0.013299636542797089,
0.005784941371530294,
0.05501982942223549,
0.03150072321295738,
0.0317... |
<p>If we take a hydrogen atom as qubit, let</p>
<p>$\lvert0\rangle$ = unexcited state<br>
$\lvert1\rangle$ = excited state</p>
<p>then what is the meaning of measuring the qubit value in the sign basis? If the atom may only be in excited or unexcited state, but $\lvert+\rangle$ and $\lvert-\rangle$ are superpositions of those states — then what would the outcome of the measurement be — also a superposition of $\lvert+\rangle$ and $\lvert-\rangle$? Can anyone please help to understand the idea behind the sign basis?</p> | g11637 | [
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0.02108466625213623,
-0.05558203533291817,
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0.02101418748497963,
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-0.0... |
<p>I am building a 3d model of the solar system and need to figure out the position of the pole stars of each planet in order to tilt the planets in the correct direction the correct amount. I've already found the information of the pole star locations, the problem is that these are in earth relative coordinates. For instance the pole star of Mars is Gamma Cygni at RA 20h 22m 13.70184s, Dec +40° 15' 24.0450".</p>
<p>Right Ascension (RA) is hours east from the prime meridian. Declination (Dec) is degrees north (+) or south (-) from the equator. These together define a position on an imaginary celestial sphere on the surface of which one can imagine all the stars.</p>
<p>So how do I go from those coordinates to a vector that defines the position of the star somewhere far far away on the celestial sphere?</p>
<p>I am using ThreeJS. <a href="http://stackoverflow.com/questions/10431632/showing-coordinate-lines-of-a-3d-earth">This</a> question points to a partial solution in terms of defining an origin for a sphere, or at least its texture.</p>
<p>I've posted the same question to <a href="http://stackoverflow.com/questions/12125124/coordinate-transformation-from-earth-to-solar#comment16214194_12125124">Stack Overflow here</a> in case some programmer wizard has the answer.</p> | g11638 | [
-0.006637373939156532,
-0.013659517280757427,
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0.016970720142126083,
0.028991099447011948,
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0.023381095379590988,
-0.02922940067946911,
-0.006153010297566652,
-0.00613995548337698,
0.010143500752747059,
0.08748596161603928,
... |
<p>Has quantum mechanics been studied on highly singular and/or discrete spaces? The particular space that I have in mind is (usual) <a href="http://en.wikipedia.org/wiki/Cantor_set">Cantor set</a>. What is the right way to formulate QM of a particle on a Cantor set? </p>
<p>I can only guess that:</p>
<p>i) There will be no momentum operator. </p>
<p>ii) Hilbert space will be spanned by position vectors corresponding to points of Cantor set. </p>
<p>iii) Corresponding to any two points $x$ and $y$ in Cantor set there will be a unitary operator $P_{xy}$ (analog of the exponential of momentum operator) such that $P_{xy}|x>=|y>$; $P_{xy}=P_{yx}^{-1}$; and $P_{yz}P_{xy}=P_{xz}$ for all $x,y,z$.</p>
<p>But I am not able to see what would be correct notion of free particle, and what would be corresponding Hamiltonian.</p> | g11639 | [
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0.030650554224848747,
0.0008780431817285717,
... |
<p>In solid state physics emergent particles are very common. </p>
<ol>
<li><p>How one determines if they are gap-less excitations? </p></li>
<li><p>Do the defects in spin ice called magnetic monopoles have mass? </p></li>
<li><p>What is the mass of emergent particles in the fractional quantum hall effect (FQHE)? </p></li>
</ol>
<p>I am not looking for a deep theory, just the general picture.</p> | g11640 | [
0.025785675272345543,
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-0.03895556181669235,
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0.0013756578555330634,
0.01657726615667343,
0.017304... |
<p>Given two environments that are identical, except for air density (e.g. Cape Canaveral, but at Mount Everest's height), would launching a rocket require more or less fuel at the lower air density?</p> | g11641 | [
0.015162920579314232,
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0.08263096958398819,
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0.012299052439630032,
0.01679500751197338,
-0.03996318206191063,
0.017099658027291298,
0.03... |
<p>We restrict ourselves to ground states of translationally invariant 1d quantum systems.</p>
<p>I understand that there is the scale invariant MERA(multiscale entanglement renormalization ansatz) which describes quantum critical points in which the tensors ("isometries" and "disentaglers") are the same across different levels. I also understand that away from a quantum critical point, these tensors must vary across different levels (and are same within a level due to translational invariance). Is there a way to obtain an RG flow equation based on the details of how these tensors must vary across adjacent layers. Also, is it possible to go backwards: i.e., to obtain conditions for these tensors across adjacent levels from the correct flow equation.
More generally, what are the techniques used to obtain these tensors?</p>
<p>A commentary about where I can find answers to these question in the literature will be very helpful. Thank you.</p> | g11642 | [
-0.030755069106817245,
0.026658492162823677,
-0.030463609844446182,
0.013725530356168747,
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0.024832168594002724,
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0.01746809110045433,
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0.05472846329212189,
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-0.0020675589330494404,
0.029905950650572777,
... |
<p>When a magnetic north(N) pole is placed close to an coil with out energy source, the coil behaves like an magnet and we find a North pole which opposes the magnet bar which was approximating onto the coil.</p>
<blockquote>
<p>My question is, what conditions and mathematcal treatment assure us
about the creation of the pole on the coil.</p>
</blockquote>
<p>Please write if you have any confusion to get the question.</p> | g11643 | [
0.013834844343364239,
0.02046245150268078,
0.01802353747189045,
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0.017822111025452614,
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0.062083929777145386,
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0.04537723585963249,
-0.03666422888636589,
0.0400... |
<p>On page 24 of these lecture notes <a href="http://arxiv.org/abs/hep-th/0309149" rel="nofollow">http://arxiv.org/abs/hep-th/0309149</a> it is stated that products of chiral superfields do not suffer from short distance singularities. In other words, if I want to calculate the dimension of a composite operator built out of chiral superfields, I may just add the dimensions of the individual field operators that form the product (in other words, it is sufficient to just renormalize the individual operators). This is definitely not the case in ordinary QFT. Can someone please explain why this is the case? Is the same true for products of vector superfields (the wording in the notes seems ambiguous)?</p> | g11644 | [
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-... |
<p>A friend offered me a brain teaser to which the solution involves a $195$ pound man juggling two $3$-pound balls to traverse a bridge having a maximum capacity of only $200$ pounds. He explained that since the man only ever holds one $3$-pound object at a time, the maximum combined weight at any given moment is only $195 + 3=198$ pounds, and the bridge would hold.</p>
<p>I corrected him by explaining that the acts of throwing up and catching the ball temporarily make you 'heavier' (an additional force is exerted by the ball to me and by me onto the bridge due to the change in momentum when throwing up or catching the ball), but admitted that gentle tosses/catches (less acceleration) might offer a situation in which the force on the bridge never reaches the combined weight of the man and both balls.</p>
<p>Can the bridge withstand the man and his balls?</p> | g957 | [
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-0.02... |
<p>According to the Wikipedia article on <a href="https://en.wikipedia.org/wiki/GNSS_positioning_calculation" rel="nofollow">GNSS positioning calculation</a>, GNSS-based positioning needs $t_\text{satellite}−t_\text{receiver}$ for a series of satellites, along with the satellite positions. This is an element of <a href="https://en.wikipedia.org/wiki/Trilateration" rel="nofollow">trilateration</a>. However, the clock in a GNSS-receiver is not atomic, and not nearly accurate enough to determine $t_\text{receiver}$ with sufficient accuracy for trilateration. Therefore, it needs a 4th source to determine the time, such as indicated by <a href="http://www.maptoaster.com/maptoaster-topo-nz/articles/how-gps-works/how-gps-works.html" rel="nofollow">maptoaster.com</a> or <a href="http://answers.yahoo.com/question/index?qid=20110420155214AAFE398" rel="nofollow">this Yahoo Answers post</a>. That makes sense: it simulatenously determines time, latitude, longitude, and elevation, and therefore it needs four satellites.</p>
<p>Why, then, do we still consider this positioning trilateration rather than multilateration? In my understanding, <em>A GNSS receiver does not need a clock at all</em> — after all, the clock that it has, is not nearly good enough. Isn't the implication that it's using the <em>difference</em> between the distances to the satellites for positioning — the principle of <a href="https://en.wikipedia.org/wiki/Multilateration" rel="nofollow">multilateration</a>? Yet the latter Wikipedia article states that:</p>
<blockquote>
<p>Multilateration should not be confused with trilateration, which uses distances or absolute measurements of time-of-flight from three or more sites, or with triangulation, which uses the measurement of absolute angles. Both of these systems are also commonly used with radio navigation systems; trilateration is the basis of GPS.</p>
</blockquote>
<p>Is GNSS-based positioning considered trilateration or multilateration? Why?</p> | g11645 | [
0.004981380887329578,
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-0.007619188167154789,
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0.03472784161567688,
-0.... |
<p>Given that the plane $y=0$ separates the vacuum ($y>0$) from the optical medium ($y<0$), I would like to calculate the trajectory of a light ray starting at the point $(x_1,y_1)$ and ending in $(x_2,y_2)$ where $x_2>x_1$ and $y_1>0>y_2$. Specifically, I would like to find the point $(x,0)$ at which the light enters the medium. However, using Snell's law, I obtain an equation of fourth degree in $x$. Is there a smarter way of doing this?</p> | g11646 | [
0.0019541671499609947,
0.0018032740335911512,
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0.013026795350015163,
0.036314018070697784,
... |
<p>I have a telescope with focal length 1200mm. My camera has 5184x3456 pixels with size 4.3um. This combination should give me a resolution of 0.74"/pixel and thus a field of view of 1.06° x 0.71°.</p>
<p>Given this FOV and some specified center coordinates for RA and DEC, what equations will give me the max/min right ascension and declination within this area?</p>
<p>My first thought was just to add/subtract 1/2 the FOV from each side of the center coordinates, but that doesn't solve the problem at ±90 DEC where the full range of RA should be found in this FOV.</p> | g11647 | [
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-0... |
<p>My professor told us that the fringes formed by interference will always be countable or finite. But I am just wondering, if, it is possible to have infinite fringes? Is there such a case? I am thinking that if the slit is placed too far from the screen, an infinite number of bright fringes will form. Or, in two-slit interference, suppose the screen is placed very far from the slits, will there be an infinite number of bright fringes formed on the screen? Your take on this?</p> | g11648 | [
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0.00... |
<p><img src="http://i.stack.imgur.com/8dRQE.png" alt="enter image description here"></p>
<p>Now normally (if it was a block not rotating) all you would have to do is use $w^2 = k/m$ and $E= \frac12k(A\cos(2wt+\theta))^2 + \frac12m(Aw\sin(wt+\theta))^2$ or in other words the translational kinetic and spring potential. </p>
<p>But here I don't even know how to start. </p>
<p>Please could someone set up what I have to do? </p> | g11649 | [
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0.001... |
<p>I have found a document refering to the following two equations </p>
<p>\begin{align*}
&\frac{\partial^2 a\left(x,t\right)}{\partial t^2}+2u\left(x,t\right)\frac{\partial^2 a\left(x,t\right)}{\partial x \partial t}+\left[u^2\left(x,t\right)-a^2\left(x,t\right)\right]\frac{\partial^2 a\left(x,t\right)}{\partial x^2}=0\\
&\frac{\partial^2 u\left(x,t\right)}{\partial t^2}+2u\left(x,t\right)\frac{\partial^2 u\left(x,t\right)}{\partial x \partial t}+\left[u^2\left(x,t\right)-a^2\left(x,t\right)\right]\frac{\partial^2 u\left(x,t\right)}{\partial x^2}=0
\end{align*}</p>
<p>Which can be obtained by combining the mass and momentum conservation equations (As stated in the reference).</p>
<p>I kept looking for such <a href="http://www.google.com/search?as_q=doppler+alembert" rel="nofollow">Doppler -D'Alembert laws</a> on the internet, but could not find any reference.</p>
<p>Does anyone have an idea?</p> | g11650 | [
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<p>I wonder how to determine the directions, in which the collision debris is launched when 2 asteroids collide.
I am aware of: m1*v1 + m2*v2 = m*v = m3*v3 + m4*v4 + m5*v5 + ...
and this works just fine for the masses and valocity, however I find it difficult to determine the boundaries of the directions and under what circumstances shatter be produced or the asteroids will just "merge". </p>
<p>All info is appreciated :)</p> | g11651 | [
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<p>If we take the double slit experiment as a way of demonstrating the wave-particle duality, which types of particles would show an interference pattern?</p>
<p>For example, I know that electrons show such a pattern. But do protons, too? What about atoms? Where is the boundary between "wavey particles" and "classical particles"?</p> | g11652 | [
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<p>I'm trying to write down the equations of motion for a <a href="http://en.wikipedia.org/wiki/Tetherball" rel="nofollow">tetherball</a> moving around a pole while the string is getting shorter. </p>
<p><strong>--- MAJOR EDIT ---</strong></p>
<p>I started with Lagrange:</p>
<p>$$
x(t)=l(t) \sin (\theta) \cos (\phi)\\
y(t)=l(t) \sin (\theta) \sin (\phi)\\
z(t)=h(t)+l(t) \cos(\theta)\\ \\
T = \frac{1}{2}m(\dot x^2 +\dot y^2+\dot z^2)\\
U=m g l(t)(1-\cos(\theta)) + mg(S-(h(t)+l(t)))
$$
where $l(t)$ is the length of the string. Here only I am assuming the radius of the pole is really small compared to $l$. The polar angle is $\theta(t)$. $h(t)$ is the change in height due to the string wrapping on the pole. $S$ is the length of string when unwrapped.</p>
<p>The change in length is given by:
$$
\dot l(t) = -\frac{r\dot\phi}{ \sin(\theta)}
$$
where $r$ is the radius of the pole. And the sliding pivot point is given by:
$$
\dot h(t) = \frac{r\dot\phi}{ \tan(\theta)}
$$</p>
<p>After plugging those in $T$ I apply the Lagrange derivative to $L = T-U$ and solve for $\ddot \theta$ and $\ddot \phi$</p>
<p>Now when I simulate the results I get a linear velocity that is some how increasing which is not supposed to happen for a tetherball because no new energy has been introduced to the system and the angular momentum is not conserved.</p> | g11653 | [
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<p>I have a question about Landau's theory of quantum phase transition. In his model, the free energy is assumed to be </p>
<p>\begin{equation}
F = f_0 + \alpha (T-T_c) \Delta^2 + \beta \Delta^4
\end{equation}</p>
<p>The ground state of the system depends strongly on the sign of $T-T_c$. In this way, we find that the scaling exponent near the critical point is $1/2$, which may be somewhat different from that in experiments -- as a results, we need renormalization group method to understand the discrepancy. This is a theory that has been accepted by this community. </p>
<p>OK, now my question is why in the second term the coefficient is $\alpha (T-T_c)$, instead of $\alpha (T-T_c)^\gamma$, where $\gamma$ is a constant, e.g., $\gamma = 3/5$ or $1/3$. This is perhaps a trivial problem, but has never been discussed explicitly in standard textbooks. The answer to this problem is not so straightforward for most of us. </p>
<p>A related question maybe like that: how to prove this point in experiments. Thanks very in advance. </p> | g11654 | [
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<p>Is there an accepted analogy / conceptual aid for the Higgs field?</p>
<p>In Physics there are many accepted conceptual aids such as<br>
* Schrödinger's cat<br>
* Maxwell's Demon<br>
* I'm sure I'm missing many, but you get the idea </p>
<p>Is there an accepted/standard aid for the Higgs?<br>
I saw a popular treatment of the Higgs boson with Peter Higgs.<br>
He talked about pearls being dragged through <a href="http://en.wikipedia.org/wiki/Treacle" rel="nofollow">treacle</a>.<br>
But the analogy wasn't fully fleshed out, just a two second video clip</p>
<p>If there is not an accepted standard aid, what do the various professionals here use to aid explicating to non professionals? </p> | g183 | [
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<p>With present day materials and technology what is the physical size of a one milli Tesla magnet? How much "power" it has to attract pieces of iron? Please compare it with the objects we have around. What difference in size and "power" it gets each order of magnitude that I go up? What is a weak magnet what is a powerful magnet in this scale?</p> | g11655 | [
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<p>I am stuck with understanding the following construction. I am breaking it up into segments which I think can be separately answered. </p>
<p>This is related to an <a href="http://physics.stackexchange.com/questions/6084/dimensional-reduction-from-31-to-21-for-caln-2-vector-superfield">earlier question of mine</a>. Note that this previous question was edited a lot after the initial comments came in. </p>
<ul>
<li>Firstly I would like to know how the following field multiplet is determined, </li>
</ul>
<p>The gauge multiplet of $\cal{N}=3$ in $2+1$ dimensions is apparently , </p>
<p>$A_\mu$, a massive vector field of spin $1$</p>
<p>$\lambda_a$, $3$ Majorana fermions of spin $\frac{1}{2}$</p>
<p>$C_a$, $3$ neutral scalar bosons</p>
<p>$\chi$, a Majorana fermion of spin $\frac{1}{2}$</p>
<p>(I guess there should be another scalar field $D_a$ not mentioned in the above list)</p>
<ul>
<li><p>Its not clear to me as to what are the superfields one has in mind with the above multiplet structure that helps construct the lagrangians below. </p></li>
<li><p>Like in the linked earlier question above one had to "know" what exactly is the meaning of doing the dimensional reduction on a given set of supersymmetric transformations, here its not clear to me as to what are the corresponding starting points. (I wonder if I can start from the $\cal{N}=2$ SYM in $3+1$ lagrangian that is given in say equation $27.9.3$ in Weinberg's QFT book) </p></li>
</ul>
<p>Then dimensional reduction of $\cal{N}=2$ SYM in $3+1$ apparently gives the following $\cal{N}=3$ SYM in $2+1$, </p>
<p>$L_{\cal{N}=3,2+1,SYM} = \frac{1}{g^2}Tr\left [ -\frac{1}{2}F_{\mu \nu} ^2 + (D_\mu C_a)^2 + (D_a)^2 + i \bar{\lambda_a}\gamma^\mu D_\mu \lambda_a + i \bar{\chi}\gamma^\mu D_\mu \chi
+ i\epsilon_{abc}\bar{\lambda_a}[\lambda_b,C_c] -2i\bar{\lambda_a}[\chi,C_a] - \frac{1}{2}[C_a,C_b][C_b,C_a] \right ]$</p>
<p>where the notation is, $D_\mu = \partial_\mu -iA_\mu$, $ab,c=1,2,3$. The gauge group generators in the fundamental representation satisfy $[T^m,T^n]=if^{lmn}T^l$ with normalization as $Tr{T^mT^n}=\frac{1}{2}\delta ^{mn}$ and $f^{kmn}f^{lmn}=c_v\delta^{kl}$. ($c_v$ being the quadratic Casimir) The fields belong to the adjoint representation and $A_\mu = A_\mu^mT^m$. The metric is given by $\eta_{\mu \nu} = diag(1,-1,-1)$. The purely imaginary gamma matrices satisfy, $\gamma^\mu \gamma ^\nu = \eta^{\mu \nu}-i\epsilon^{\mu \nu \rho}\gamma_\rho$. </p>
<ul>
<li><p>It is not clear to me as to how does one argue that the above has $\cal{N}=3$ supersymmetry. </p></li>
<li><p>The dimensional reduction of the $\cal{N}=2$ supersymmetry somehow implies that the theory has the not-so-obvious $\cal{N}=4$ supersymmetry. </p></li>
</ul>
<hr>
<p>One also notes that supersymmetrizing the Chern-Simon's terms one is supposed to get the Chern-Simon's lagrangian as, </p>
<p>$L_{\cal{N}=3,2+1,SCS} = kTr\left [ \epsilon^{\mu \nu \rho}(A_\mu \partial_\nu A_\rho - \frac{2}{3}iA_\mu A_\nu A_\rho) - \bar{\lambda_a}\lambda_a + \bar{\chi}\chi
+ 2C_aD_a + \frac{i}{3}\epsilon_{abc}C_a[C_b,C_c] \right ]$ </p>
<ul>
<li>In all these lagrangians apparently the corresponding $\cal{N}=2$ theories can be obtained by setting $C_1=C_2=D_1=D_2=\lambda_3 = \chi = 0$ and the $\cal{N}=1$ theories can be obtained from the $\cal{N}=2$ theories by further setting $C_3=\lambda_2=0$. </li>
</ul>
<p>(I am unable to get the equations to wrap around properly!) </p> | g11656 | [
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0.0000... |
<p>Consider a rectangular slab of permanently magnetized material. The slab's dimensions are $L_x$, $L_y$, and $L_z$, and the slab is uniformly magnetized in the $\hat{x}$-direction. The slab is not accelerating or spinning. Does the slab generate an electric field?</p>
<p>In a frame where the magnet is stationary, we know $\mathbf{E}$ is zero everywhere. In a frame where the magnet is moving, there are at least two ways to attack the problem:</p>
<ol>
<li>Drop $d\mathbf{M}/d t$ into Maxwell's equations, solve for $\mathbf{E}$ and $\mathbf{B}$ </li>
<li>Solve for $\mathbf{B}$ in the slab's rest frame, and use a relativistic boost to transform $\mathbf{B}$ in the slab's frame to $\mathbf{E}$ and $\mathbf{B}$ in the frame where the magnet is moving.</li>
</ol>
<p>Both these methods give the result that $\mathbf{E}$ is nonzero in a frame where the magnet is moving.</p>
<p>Now let's consider a long, thin slab ($L_x, L_y \ll L_z$). In a frame where the slab is moving in the $\hat{z}$-direction, is there an electric field (external to the slab) near the 'center' of the magnet? Both the $d\mathbf{M}/d t$ argument and the Lorentz-boost argument seem unchanged. The magnetic field external to the slab does not vanish near the center of the slab, suggesting there is a nonzero electric field.</p>
<p>With the backstory laid out, here's my real question: In a frame where the slab is moving in the z-direction, is there still an electric field in the case where $L_z \rightarrow \infty$?</p>
<p>The Lorentz-boost argument seems unchanged, and suggests that there is. However, in the $L_z \rightarrow \infty$ case, $d\mathbf{M}/d t = 0$, suggesting no electric field. Can this case be calculated without Lorentz boosts? How do Maxwell's equations account for moving permanent magnets in the case where $d\mathbf{M}/d t = 0$?</p>
<p>EDIT:
Followup questions:</p>
<p><a href="http://physics.stackexchange.com/questions/6479/whats-a-good-reference-for-the-electrodynamics-of-moving-media">What's a good reference for the electrodynamics of moving media?</a></p>
<p><a href="http://physics.stackexchange.com/questions/6581/what-is-the-electric-field-generated-by-a-spinning-magnet">What is the electric field generated by a spinning magnet?</a></p> | g11657 | [
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<p>I am a bio-chemist by profession and recently written an essay for a book which is related to the subject of cosmology. This is not my area of expertise. Is there a cosmologist out there who will be kind enough to review this 8 page essay for me to check it for accuracy, or perhaps give me criticism or even suggestions? I am a member of the APS and its division of Biological Physics. Thanks Paul</p> | g11658 | [
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<p>Needles to say I am a visitor here. I do not belong to the science world;)</p>
<p>But I have read both of these things before:</p>
<ol>
<li>Apple falls to the ground because curved spacetime pushes it there (same force as keeps moon in orbit)</li>
<li>Apple 'falls' to ground because the ground is rushing up to meet the apple (which is actually suspended in space) because of Earth's acceleration through space.</li>
</ol>
<p>I don't think these can both be true. I'd appreciate any clarification - thank you.</p> | g11659 | [
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0.... |
<p>Most of us have seen microwave ovens with metal racks or shelves, which challenges the common notion that you can't (safely) put metal in a microwave oven. What's going on here? Is it a matter of these shelves being made of a specific metal (if so what are the properties that allow it to be used in a microwave oven?) or of being placed in just the right place in relation to the waves that will be emitted, or something else entirely?</p>
<p>If it is a matter of using just the right metal (or alloy), then which metals are okay to use in a microwave oven?</p> | g369 | [
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<p>I've been trying to compute the moment of inertia of a uniform hollow sphere (thin walled) wrt the centre, but I'm not quite sure what was wrong with my initial attempt (I've come to the correct answer now with a different method). Ok, here was my first method:</p>
<p>Consider a uniform hollow sphere of radius $R$ and mass $M$. On the hollow sphere, consider a concentric ring of radius $r$ and thickness $\text{d}x$. The mass of the ring is therefore $\text{d}m = \frac{M}{4\pi R^2}\cdot 2\pi r\cdot\text{d}x$. Now, use $r^2 = R^2 - x^2:$
$$\text{d}m = \frac{M}{4\pi R^2}\cdot 2\pi \left(R^2 - x^2 \right)^{1/2}\text{d}x$$
and the moment of inertia of a ring wrt the centre is $I = MR^2$, therefore:
$$\text{d}I = \text{d}m\cdot r^2 = \frac{M}{4\pi R^2}\cdot 2\pi\left(R^2 - x^2\right)^{3/2}\text{d}x $$
Integrating to get the total moment of inertia:
$$I = \int_{-R}^{R} \frac{M}{4\pi R^2} \cdot 2\pi\cdot \left(R^2 - x^2\right)^{3/2}\ \text{d}x = \frac{3MR^2 \pi}{16}$$</p>
<p>which obviously isn't correct as the real moment of inertia wrt the centre is $\frac{2MR^2}{3}$. </p>
<p>What was wrong with this method? Was it how I constructed the element? Any help would be appreciated, thanks very much. </p> | g11660 | [
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... |
<p>How did Fresnel explained the phenomenon of rectilinear propagation of light using concept of half period zones?</p> | g11661 | [
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0.06074235960841179,
0.082... |
<blockquote>
<p>Consider an unormalized wavefunction of a rotor at $t = 0$, a combination of $n=0$ and $n=2$ states:</p>
<p>$$\psi(\phi) = 3 - 2 \cos (2\phi).$$</p>
<p>Find the probability distribution in angle.</p>
</blockquote>
<p>The book simply takes probability as</p>
<p>$$\lvert\psi(\phi)\rvert^2 = \lvert 3 - 2\cos(2\phi)\rvert^2 = 9 + 4\cos^2(2\phi) - 12\cos(2\phi).$$</p>
<p>I have found the normalized wavefunction to be:</p>
<p>$$\psi(\phi) = \frac{3}{\sqrt {11}}\lvert 0\rangle - \frac{2}{\sqrt {22}}\lvert 2\rangle.$$</p>
<p>Do I use probability as $\left\lvert\frac{3}{\sqrt {11}} - \frac{2}{\sqrt {22}}\cos(2\phi)\right\rvert^2$ ? or the one in the book?</p> | g11662 | [
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-0.014800... |
<p>Let foo be some unit of distance and bar be some unit of time which have been chosen so that the speed of light c = 1 foo/bar. Position several observers along a line each separated by one foo, and place light sources some distance apart amongst the observers, initially off. All observers and light sources are stationary with respect to one another.</p>
<p><img src="http://i.stack.imgur.com/3GK3n.gif" alt="diagram"></p>
<p>So in my diagram the tick marks are the observers, and the scale is one foo. For the example, the light sources are ten foo apart at points L and R.</p>
<p>Now at time 0 bars, ignite both light sources.</p>
<p>In the diagram, at time 4 bars, A has observed source L but not R, C has observed R but not L, and B has not yet observed either light source. At time 5 bars, B observes both light sources, and at time 6 bars all three labeled observers have observed both light sources. At time 7 bar, a total of five observes (A, B, C, and two unlabeled) have observed both sources.</p>
<p>Let r be the length of the line segment containing all observers that have observed both light sources. In other words, r is the length of the intersection of the event horizons on the two ignition events (I think I am using that term right, if not, please let me know). It seems that dr/dt = 2 foo/bar; for instance, in the 1 bar interval from 6 to 7, the change in r was 2 foo. As c = 1 foo/ bar, r is growing at twice the speed of light.</p>
<p>Since r is not a particle and cannot be used to transmit information amongst the observers, is there any contradiction here? Have I made any logical falicies?</p> | g11663 | [
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0.00... |
<p>Are there any quantum properties that would enable isotope fractionation?</p>
<p>For example, atoms with odd versus even numbers of neutrons are fermions and bosons, respectively. Has any work been done using the distinct properties of fermions and bosons to isolate isotopes?</p> | g11664 | [
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<p>As I understand it, the value of a 4-vector $x$ in another reference frame ($x'$) with the same orientation can be derived using the Lorentz boost matrix $\bf{\lambda}$ by $x'=\lambda x$. More explicitly,
$$\begin{bmatrix}
x'_0\\
x'_1\\
x'_2\\
x'_3\\
\end{bmatrix}
=
\begin{bmatrix}
\lambda_{00}&\lambda_{01}&\lambda_{02}&\lambda_{03}\\
\lambda_{10}&\lambda_{11}&\lambda_{12}&\lambda_{13}\\
\lambda_{20}&\lambda_{21}&\lambda_{22}&\lambda_{23}\\
\lambda_{30}&\lambda_{31}&\lambda_{32}&\lambda_{33}\\
\end{bmatrix}
\begin{bmatrix}
x_0\\
x_1\\
x_2\\
x_3\\
\end{bmatrix}
$$
I have seen examples of these components written in terms of $\beta$ and $\gamma$, which are defined as
$$\beta=\frac{v}{c}$$
$$\gamma=\frac{1}{\sqrt{1-\beta\cdot\beta}}$$
where $v$ is the 3-velocity and $c$ is the speed of light. My question is this: How can the components of $\lambda$ be written in terms of the 4-velocity $U$ alone?</p>
<p>I know that $U_0=\gamma c$ and $U_i=\gamma v_i=\gamma c\beta_i$ for $i\in\{1,2,3\}$, but I'm having trouble deriving the components for $\lambda$ using the matrices based on $\beta$ and $\gamma$. An example of one of these matrices <a href="http://en.wikipedia.org/wiki/Lorentz_transformation#Matrix_forms" rel="nofollow">can be found at Wikipedia</a>. How can I rewrite this matrix in terms of $U$ alone?</p> | g11665 | [
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0.0086... |
<p>I want to move to Sprite Kit framework offered by apple which has physics integrated right into it. The back bone of the physics engine is famous Box2D. Sprite Kit has made it pretty easy by wrapping C++ inside Objective-C but unfortunately some features lack in Sprite Kit. One them is GetReactionForce function, that returns the impulse applied on the body B of a joint. Just disregard the software related terms if you find it difficult to understand. Basically what I need is to create my own function that will calculate impulse. Here are the ingredients I have:
Mass, gravity, delta time. </p>
<p>P.S. Sorry for the tags, I couldn't find anything more suitable and I have no right to create new ones</p> | g11666 | [
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-0... |
<p>Suppose we built a enormous torus shaped space station that encompasses and leaves about 330 kilometers between it and the earth. So it's radius is about 6,371 kilometers . Obviously, this structure will have to spin very quickly to not collapse. So let's say it's going 28,000 kilometers per hour so people in the spaceship will feel weightless.</p>
<p>If we now were to build a rail inside this spaceship with a rocket car on it, that holds on to the rail much like a roller coaster holds on to its rail and have the rocket car go in the opposite reaction the space station is spinning. Would it start to exert downwards force on the space station since it moving more slowly relative to the earth? And reach almost 1g when the car is going 28,000 kilometers per hour?</p>
<p>The boarder question I guess is, how is the absolute rotation of something determined. What's the reference frame you should use? Is there an absolute reference frame for rotation or should you maybe use the local curvature of spacetime as a reference? </p> | g11667 | [
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0.031059816479682922,
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0.07257618010044098,
-0.011... |
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