question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>What happens when a neutrino and an anti-neutrino interacts together? For example, what does a muon neutrino and anti-muon neutrino produce? it says in my book that it creates "muons and antimuons". But, how? Don't the particle and the antiparticle annihilate when they interact with each other? </p> | g14544 | [
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<p>So if you have a light bulb in a room, and you had a tool to measure the amount of light that's in the room, then let's assume the amount of light only caused by the bulb is "1"</p>
<p>If you place a mirror next to the bulb, does the amount of light in the room in crease to "2"?</p>
<p>Can you keep going so that the light in the room in creases to 3..etc with more mirrors?</p>
<p>How far can you take this? Also, is it actually adding light to the room, or is it simply causing the same photons to move faster (reflecting from one mirror to the next) making it seem like there is more light in the room, but there really isn't?</p>
<p>Made me think, so I thought I ask here :)</p> | g14545 | [
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<p>Are the 8 Maxwell's equations enough to derive the formula for the electromagnetic field created by a stationary point charge, which is the same as the law of Coulomb? </p>
<p>If I am not mistaken, due to the fact that Maxwell's equations are differential equations, their general solution must contain arbitrary constants. Aren't some boundary conditions and initial conditions needed to have a unique solution. How is it possible to say without these conditions, that a stationary point charge does not generate magnetic field, and the electric scalar potential is equal to</p>
<p>$$\Phi(\mathbf{r})=\frac{e}{r}.$$ </p>
<p>If the conditions are needed, what kind of conditions are they for the situation described above (the field of stationary point charge)?</p> | g14546 | [
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<p>I would like to know which fields in physics have seen growth or benefited by applying <a href="http://en.wikipedia.org/wiki/Quantum_field_theory" rel="nofollow">QFT</a>? I know that approaches to quantum gravity such as string theory use QFT, HEP and also some branches of condensed matter physics. Where is it applied in condensed matter physics exactly? And in what other areas of theoretical physics, has QFT been applied?</p> | g14547 | [
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<p>How can increasing the radius of earth may cause an impact on the solar system ? Like, would earth may start making a bigger orbit (due to increase in size and wait) or vice versa ? or else ?</p>
<p>PS: The base of my question arises from the point of view of "Growing Population", and managing it by "artificially increasing the size of earth" (Instead of say, finding possibilities to live on other planets like Mars). So, if the radius increases, naturally the circumference of the sphere, and hence surface to live on will increase.</p>
<p>I understand however that probably exploring newer planets might be more feasible solution. But just for curiosity I shared my query. :)</p> | g14548 | [
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<p>Some time ago I was talking to a professor in college about some of the fundamental aspects and origin of General Relativity. I was surprised to learn, in fact, that a pretty good approximation to GR can be achieved simply by using Special Relativity and applying a series of (infinitesimal?) Lorentz boosts to simulate acceleration/a gravitational field. In fact, I believe this is precisely the approach used by GPS system for accurate triangulation/location, as mathematically and computationally it is a somewhat simpler process than applying the Einstein field equations.</p>
<p>So my question is: has anyone else heard of this? An explanation of how exactly this approximation works, and where/why it fails in comparison to true GR (perhaps the strong gravitational field case?) would be much appreciated.</p> | g14549 | [
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<p>I was going through some of the theory behind <a href="http://en.wikipedia.org/wiki/Zener_diode" rel="nofollow">Zener diodes</a>. I know what they're used to work at constant voltage, but I don't know how they work. Actually, I kind of get that too, I know that voltage is constant until breakdown occurs (avalanche breakdown), but I don't get why a minimum current is needed to maintain a constant voltage, which is what the textbooks say. Why is there a <em>minimum</em>? I thought any current below the breakdown voltage was constant. I don't see why the voltage would vary through the diodes if it's below a set amount of current, yet remain constant between voltages x-y? </p>
<p>Any help would be greatly appreciated, I can't wrap my head round exactly what's going on inside the little buggers.</p>
<p>P.S, is there more of an appropriate question for the electronics section? As I know electronics is a natural part of physics, and I heard this kinda stuff gets studied quite a lot in physics exams.</p> | g14550 | [
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<p>Recently I've heard that there exist alternative interpretations of quantum mechanics which, while not as widespread as the Copenhagen intepretation (or so it would seem), are equally valid in the sense that they describe all the observable effects. <a href="http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics" rel="nofollow">Wikipedia</a> mentions a few ones, the more popular of which seems to be the many worlds interpretation.</p>
<p>What are some books, suitable for someone with an undergraduate level knowledge of QM, that describe these alternatives? Something not too mathematical might be best for an introduction to the subject, but I'm not looking for a popular book either, of course.</p> | g14551 | [
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<p>Consider a charged particle in a static electromagnetic field. Suppose that the domain is simply connected so that the second law of Newton's dynamics reads:
$$
m\frac{\mathrm{d}^2\vec{x}}{\mathrm{d}t^2}=-e\left(\vec{\nabla}\Phi+\frac{\mathrm{d}\vec{x}}{\mathrm{d}t}\times(\vec{\nabla}\times\vec{A})\right)
$$
where:</p>
<ul>
<li>$m$ is the mass of the particle,</li>
<li>$\vec{x}$ is position vector,</li>
<li>$\Phi$ the (scalar) electric potential,</li>
<li>$\vec{A}$ the (vector) magnetic potential.</li>
</ul>
<p>My question is how to derive the Hamiltonian formulation from here. The Hamiltonian is:
$$
H(\vec{x},\vec{p})=\frac{1}{2m}\left\|\vec{p}-e\vec{A}\right\|+e\Phi(\vec{x})
$$
and the Hamilton equations look like:
$$
\begin{cases}
\frac{\mathrm{d}x_i}{\mathrm{d}t}=\frac{1}{m}(p_i-eA_i)\\
\frac{\mathrm{d}p_i}{\mathrm{d}t}=\frac{e}{m}\sum_{j=1}^3(p_j-eA_j)\frac{\partial A_j}{\partial x^i}-e\frac{\partial\Phi}{\partial x^i}
\end{cases}
$$
Another question related to this one is why the magnetic potential is "included" in the "generalized" moment $\vec{p}-e\vec{A}$. I undertand why from the Lagrangian of the system but perhaps there is a physical explanation.</p>
<p><strong>EDIT:</strong></p>
<p>Consider a single particle in a conservative force field $F=-\vec{\nabla}V$. Then the Newton's equations are:
$$
m\frac{\mathrm{d}^2\vec{x}}{\mathrm{d}t^2}=-\vec{\nabla}V
$$
This is a second order differential equation, which we can transform into a system of first order differential equations, by adding a new variable which is usually the speed $v$ in mathematics but here we will take the momentum $p=mv$. The system I am talking about is:
$$
\begin{cases}
\frac{\mathrm{d}\vec{x}}{\mathrm{d}t}=\frac{\vec{p}}{m}\\
\frac{\mathrm{d}\vec{p}}{\mathrm{d}t}=-\vec{\nabla}V(x)
\end{cases}
$$
which is just the hamiltonian form of the Newton's equations. Can we do the same kind of trick in the case of the system above?</p> | g14552 | [
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<p>Normal mode and wavenumber integration methods allow the evaluation of an integral transform solution.</p>
<p>The text book that I am reading states that the normal mode method evaluates the field as a sum of residues for the poles enclosed by the integration contour. On the other hand, wavenumber integration uses direct numerical quadrature to evaluate the integral. Normal mode methods are only applicable to problems dominated by the pole contributions.</p>
<p>My question is why the Normal mode models are considered to be only an approximation, and only applicable when pole contributions dominate. Shouldn't the integral expressed as a sum of residues be exact?</p> | g14553 | [
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<p>I've seen many versions of the figure shown below -- the famous <em>Swordy plot</em>. They tend to explicitly point out two features in the CR spectrum, the <strong>knee</strong> and the <strong>ankle</strong>. I know that the source of UHECR's above the <em>ankle</em> is currently a mystery. But I'm having a devilish time sussing out the cause of this feature at the knee.</p>
<p>Is it known why the slope changes?</p>
<p><img src="http://i.stack.imgur.com/kSBuo.png" alt="enter image description here"></p> | g14554 | [
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<p>I am still getting used to the braket notation. Is this manipulation correct?
$$
\frac{-\hbar^2}{2m}\int_{-\infty}^{\infty}\frac{\partial^2\phi_n^*}{\partial z^2}
\phi\,dz = \int_{-\infty}^{\infty}\phi\left(\frac{-\hbar^2}{2m}
\frac{\partial^2}{\partial z^2}\right)\phi_n^*\,dz = \int_{-\infty}^{\infty}
\phi \hat{K}\phi_n^*\,dz = \left( \int_{-\infty}^{\infty}
\phi^* \hat{K}\phi_n\,dz \right)^{*} = \langle\phi|\hat{K}|\phi_n\rangle^{*}
$$</p> | g14555 | [
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<p>Does this paragraph make sense?</p>
<p>"The vector potential emitted by a current carrying wire is a packet of
coherent virtual photons, all with the same momentum traveling in
the same direction. They cannot annihilate each other, for this would
violate conservation of momentum. They travel to infinity. Momentum
must always be conserved."</p> | g14556 | [
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<p>How do we determine how much the surface of the Earth deflects due to <a href="http://en.wikipedia.org/wiki/Tidal_forces" rel="nofollow">tidal forces</a> from the Moon (and Sun)?</p> | g14557 | [
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<p>I have heard that communication using mobile phones begins to degrade when used on a vehicle moving at speeds above 200 km/hr due to <a href="http://en.wikipedia.org/wiki/Doppler_effect" rel="nofollow">doppler effect</a> as described <a href="http://ptgmedia.pearsoncmg.com/images/art_sklar6_mitigating/elementLinks/art_sklar6_mitigating.pdf" rel="nofollow">here</a> (p-22). How is this limitation overcome in airplanes. What is the specific technology used to overcome this limitation.</p> | g14558 | [
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<p>In standard (non-Wilsonian) renormalization we split the bare Lagrangian $\mathcal{L}_0$ into </p>
<ul>
<li>a physical Lagrangian $\mathcal{L}_p$ with measurable couplings and masses </li>
<li>counterterms $\mathcal{L}_{ct}$ with divergent couplings</li>
</ul>
<p>We then calculate with the bare Lagrangian perturbatively to a cutoff $\Lambda$ adjusting the counterterms so that it's valid to take the continuum limit.</p>
<p>In the Wilsonian theory we start with a Lagrangian $\mathcal{L}_w$ and a scale $\Lambda$. We suppose $\mathcal{L}_w$ is a small perturbation to some fixed point of the renormalization group flow. Using the renormalization group we deduce an effective Lagrangian $\mathcal{L}_{eff}$ at some scale $\mu<\Lambda$. We then take the limit $\Lambda \to \infty$. </p>
<p>What do we calculate with in the Wilsonian theory? Is it the case that $\mathcal{L}_{eff} = \mathcal{L}_0$ from the standard renormalization theory? If so, why?</p>
<p><strong>Example:</strong></p>
<p>In $\phi^4$ theory we have </p>
<ul>
<li><p>$\mathcal{L}_0 = \frac{1}{2}Z_0(\partial_\mu
\phi)^2-\frac{1}{2}Z_0m_0^2\phi^2+ \frac{\lambda_0Z_0^2}{4!}\phi^4$</p></li>
<li><p>$\mathcal{L}_p = \frac{1}{2}(\partial_\mu\phi)^2-\frac{1}{2}m^2 \phi^2+\frac{\lambda}{4!}\phi^4$</p></li>
<li><p>$\mathcal{L}_{ct} = \frac{1}{2}\delta_Z(\partial_\mu\phi)^2-\frac{1}{2}\delta_Z\delta_{m^2}\phi^2+ \frac{\delta_\lambda\delta_Z^2}{4!}\phi^4$</p></li>
</ul>
<p>I have no idea what $\mathcal{L}_w$ and $\mathcal{L}_{eff}$ are though? And no book (Peskin and Schroeder, Deligne and Witten etc.) seems to explain it. My guess is as follows</p>
<p>$\mathcal{L}_w = \frac{1}{2}(\partial_\mu\phi)^2-\frac{1}{2}m_\Lambda^2 \phi^2+\textrm{all interactions}$</p>
<p>and that at fixed $\mu$ we have $\mathcal{L}_{eff}\to\mathcal{L}_0$ as $\Lambda\to\infty$. I have no real reason to think this though, and still less idea how to prove it!</p> | g14559 | [
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<p>If I press on something, it presses me back with the same force. if I press a pillow with my fist, l do not feel pain but if I press a rock with my fist with the same force, I do feel the pain. why?</p>
<p>Regardless of the fact that my force gets distributed over the pillow surface, I should still get a reaction on my fist that should equal the force I applied.</p>
<p>To be able to compare the two well, please assume that my force on the rock is also over a similar area to the pillow and not concentrated on narrow points that do not cover the whole fist area.</p> | g14560 | [
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<p>People often talk about <a href="http://www.google.com/search?q=%22particle+hole+symmetry%22" rel="nofollow">particle-hole symmetry</a> in solid state physics. What are the exact definition and physics picture of particle-hole symmetry? How to define the density of particles and holes?</p> | g14561 | [
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<p>From <a href="http://en.wikipedia.org/wiki/Energy_Catalyzer" rel="nofollow">Wikipedia</a>:</p>
<blockquote>
<p>The Energy Catalyzer is an apparatus built by [...] Andrea Rossi, [and] Sergio Focardi. The 2009 patent application claims "a method and apparatus for carrying out nickel and hydrogen exothermal reactions," with production of copper. Although the patent cites previous works on cold fusion, one statement by Rossi asserted that it is not cold fusion, but rather LENR, Low-Energy Nuclear Reaction.</p>
<p>[...]</p>
<p>According to Focardi, "the hydrogen is heated at a given temperature with a simple resistor. When the ignition temperature is reached, the energy production process starts: the hydrogen atoms penetrate into the nickel and transform it into copper.”</p>
</blockquote>
<p>Are these claims true?</p> | g14562 | [
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<p>Dark energy physically can be interpreted as either a fluid with <em>positive</em> mass but pressure the negative of its density (pressure has units of energy/volume, and energy is mass), or a property of space. If it's a fluid, it should add to the mass of black holes like any form of energy (no hair), and the black hole should grow? However, if dark energy is a property of space, then this won't happen. Is my reasoning correct that we can differentiate (in theory) by looking at black hole's growth rate?</p>
<p>Edit: There are many ways to define growth quantitativly. For example, we can put test particles in orbit and look at decreases in their proper time to orbit the hole.</p> | g14563 | [
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<p>To an an external observer it appears that time has stopped for photon. But this relation is reflexive, so for an observer travelling with the photon it appears the universe has stopped everywhere.</p>
<p>Is this right?</p>
<p>Space also gets distorted parallel to the direction of motion, but not perpendicular to it. </p>
<p>Does this mean that for an observer travelling with a photon sees spacetime as a flat plane?</p>
<p>NOTE: I'm using language <em>vividly</em> not <em>literally</em> when I say a photon experiences space and time. Not that I'm against idealist or panpyschist interpretations of matter or energy come to that.</p> | g361 | [
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<p>This is kind of a continuation of <a href="http://physics.stackexchange.com/questions/60566/dimensional-regularization-and-ir-divergences-and-scale-invariance">this</a> and <a href="http://physics.stackexchange.com/questions/53768/defining-a-cft-using-beta-functions">this</a> previous questions. </p>
<ul>
<li><p>Say one has a free "classical" field theory which is scale invariant and one develops a perturbative classical solution for an interacting version of that. Then what can be the constraining effects on the perturbation theory from the fact that the free theory was scale invariant? (for an example like this see <a href="http://arxiv.org/pdf/1301.7182.pdf" rel="nofollow">this</a> recent paper) </p></li>
<li><p>Can one give a QFT example where this can happen that a non-marginal coupling flows to a non-zero fixed point and the anomalous dimension of the corresponding operator adjusts so that the coupling becomes marginal at that point? (..for the fixed point of the RG flow to be interpreted as a point of scale invariance this adjustment has to happen!..) </p></li>
</ul> | g14564 | [
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0.015233777463436127,
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0... |
<p>If you wanted to at least semi-realistically model the key components of Human running, what are the factors that determine the top running speed of an individual? The primary things to consider would be the 'thrust' provided by the legs, with significant components in the vertical and horizontal, and also wind resistance and energy dissipated by muscles and bones during the 'landing' half of each step, before the thrust part kicks in.</p>
<p>If a human was running in a vacuum (somehow...) would they be able to run much quicker, or is the wind resistance part negligible compared with the losses involved in the running action itself?</p>
<p>If anyone has references great, but I'd be happy with a well reasoned back of the envelope calculation.</p> | g14565 | [
0.002380595775321126,
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0.01433922816067934,
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0.031725186854600906,
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0.035740... |
<p>My son's science project involves liquifying air. I found the Linde process which is the way it was done first. We are trying and not getting very far so I am looking for advice.</p>
<p>I have an air compressor good to 150psi. We are slowly ramping up the pressure in the system. We are currently testing at 80psi. We pressurize 20 feet of copper tube bent in a coil running through an ice bath. The tube exits and goes into the bottom of a thermos.
The end of the tube is capped, and we allow a small leak so that pressure drops from 80psi to 1atm.</p>
<p>We insulated the few inches between the ice bath and the thermos. We do not yet have a double walled tube, but we taped the thermos so all the air coming out is exiting through the insulation.</p>
<p>When we run, the thermos drops from room temperature (about 68F in the basement) to our best of 45F. I'm quoting in Fahrenheit right now because the boys are very obnoxious about not wanting to use a temperature system they aren't comfortable with, and I just haven't been able to convince them that they are being unreasonable.</p>
<p>The point is, we are not even achieving the temperature of the ice bath. Incidentally, as measured with my multimeter, the ice bath is always 3C. I'm curious about that too, but that will be a separate question. Needless to say, we are not achieving any refrigeration.</p>
<p>The next step we will increase the leak so that the flow through the system is much higher. And we will start trying to use a Peltier cooler so we can have an intermediate stage that is 20C or so cooler than the ice bath.</p>
<p>Obviously we can up the pressure, but I would think we should see something more than we are getting. Any suggestions? Should I take a picture of our setup?</p> | g14566 | [
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0.0009026077459566295,
0.057157233357429504,
-0.03564712405204773,
... |
<p>tl;dr: Hohmann Transfer appears to be the optimal way to achieve a circular-to-circular orbit, but is it possible to lower the periapsis in order to achieve a more elliptical orbit with apoapsis at the same distance, using less delta-v than a Hohmann transfer?</p>
<p>I've been playing an awesome game called Kerbal Space Program, which models to quite an accurate degree the spacecraft mechanics that you may encounter within a solar system. </p>
<p>I was reading about how the Oberth effect dictates that rocket burns are much more efficient when orbital velocity is higher. </p>
<p>I want to minimize fuel consumption, which is a noble and practical endeavor. The situation is this. A stable circular (or nearly circular) orbit has been established around a planet. The goal is to travel to a target location in orbit around the same planet that is in a much larger orbit. Being already in a circular low orbit makes it easy to adjust the inclination to match that of the target body, so I'm currently most interested in the case where I am already in a near-circular orbit in the same plane as that of my target body. </p>
<p>It is the next step that I'm confused about. I see two approaches. </p>
<ol>
<li><p>Fire engines in prograde direction at periapsis to gain enough energy to reach the vicinity of target body. </p></li>
<li><p>Fire engines in retrograde direction at apoapsis to lower the periapsis to the lowest point possible before entering atmosphere. (this step is "undoing" some of the work done in entering the original circular orbit; If the planet we're orbiting is the one we launched from, it is possible to angle the launch to match target inclination and produce this elliptical orbit from the beginning. But let's not assume this is possible for now.) At the new lowered periapsis, the prograde engine burn is more efficient. </p></li>
</ol>
<p>I am ignoring the fact that these will have us arriving at the target at different times; going back around a few times should eventually produce a capture opportunity. </p>
<p>So I believe what this means is that approach #2 may be preferable if it can be established that the same target distance can be reached by #2 using less total engine delta-v than with approach #1. </p>
<p>I started out by thinking that perhaps the most mathematically simple way to attack this is by observing the rate of orbital energy change introduced by these burns. How much delta-v does it take to lower periapsis to half its current location from a circular orbit? This must be balanced with the amount of extra energy rate gained by engine burn at periapsis, but does halving the periapsis mean that the delta-v here produces 4 times as much energy because orbital speed is 4 times as high? Or is it 16 times? </p>
<p>But then I realized that a circular orbit of radius N has a lot more orbital specific energy than a highly elliptical orbit with apoapsis N. I'm not sure I understand the proof, but the Hohmann transfer (e.g. approach #1 forms the first half of a Hohmann transfer) is apparently the most efficient way to gain a larger circular orbit. However I'm not interested in the second burn. The second burn is going to be for establishing an orbit around the target body and that should hopefully be negligible. It would not be predictable anyway. </p>
<p>I can't really even make up my mind as to whether it's always, sometimes, or never worth it to do this!</p>
<p><strong>Update:</strong> I thought about it a little more, and it is possible that a Hohmann transfer is more or less necessary because having very low orbital speed at apoapsis for target body encounter is not conducive to establishing an orbit around it: the speed must be a close match in order to achieve gravitational capture. In this case the answer to my question would be "Probably, but your assumptions are flawed". It is possible that if we are in an orbit that is actually retrograde to your target body that this sort of high-eccentricity attack would reduce the backwards transverse motion upon arrival at apoapsis, so that's one thing I've learned (stumbled upon) today. </p>
<p>The original question still stands, can we get our orbit to swing out farther by intentionally reducing periapsis? </p> | g14567 | [
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<p><a href="http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf#page=51" rel="nofollow">On page 51 Srednicki states</a>, "Note that the operators are in time order...we can insert $T$ without changing anything". This I agree with. But then on the next paragraph he states "The time order operator $T$, moves all...where they annihilate...". How correct is this paragraph? <strong>Is equation (5.14) always valid? Is equation (5.14) the reason why the time-ordering symbol $T$ appears all over the place in QFT?</strong></p>
<p>The equations I'm referring to are (braket package available?): </p>
<p>$$\langle f|i\rangle = \langle0|~a_{1'}(+\infty)a_{2'}(+\infty)a_{1}^\dagger(-\infty)a_{2}^\dagger(-\infty)~|0\rangle$$</p>
<p>and since time goes from right to left inside the braket we put the $T$-symbol</p>
<p>$$\langle f|i\rangle = \langle 0|T ~a_{1'}(+\infty)a_{2'}(+\infty)a_{1}^\dagger(-\infty)a_{2}^\dagger(-\infty)~|0\rangle$$ without changing anything. </p>
<p>After this, the $T$-symbol appears everywhere!</p> | g14568 | [
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0.06797947734594345,
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<p>I've always learned that a mixture of ice and water should reach equilibrium at approximately 0C. I've actually tried to create that a number of times in different contexts and always fail.</p>
<p>First, an ice bath in a plastic container. I get 3C, occasionally as low as 2C with a multimeter thermocouple. Granted those are inaccurate, so I've tried a digital thermometer from Vernier with claimed accuracy of 0.5C. I confirmed with an IR thermometer. Same story.</p>
<p>Thinking that perhaps it is due to warming from the outside, I have put the ice bath in a thermos and chilled it a while. Same story. I am not using distilled water, so there are some minerals in the water, but if anything I thought that would lower the temperature of the ice bath.</p> | g14569 | [
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0.028... |
<p>Looking for a way of calculating the maximum weight (W) to the rod with the given length (L) where the rod did not break and that only bend for (b) mm.</p>
<p><img src="http://i.stack.imgur.com/o5lps.jpg" alt="enter image description here"></p>
<p>Need only approximative solution (read: simple as possible :), nothing with finite-elements or integrals or so.</p>
<p>The practical background: What rod i should to use for suspension of 100kg with L=1.5m and max bending approx. b=1cm? For what <em>constants</em> should I looking for in the published "properties" for the different materials and different profiles? E.g. steel rod vs bamboo? :)</p>
<p>Some URL's to helpful practical solutions (read: easy math) is very welcomed - my googling failed.</p> | g14570 | [
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0.03412256017327309,
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0.... |
<p>A <a href="https://en.wikipedia.org/wiki/Y-%CE%94_transform" rel="nofollow">$Y-\Delta$ transformation</a> can be applied to circuits in order to make an equivalent circuit (but simpler to put in terms of series/parallel devices). Wikipedia and other books show how to deduce the relation between resistances in a network. You can use <a href="http://spruce.flint.umich.edu/~jalarie/jaa_un.htm" rel="nofollow">this tool</a> (as pointed by @Alfred_Centauri) to calculate the relation between capacitances in a capacitors network. But, How exactly is derived that relation from basic principles?</p> | g14571 | [
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<p>I am undecided about the field I want to do my PhD in, in graduate school. I am asking because the applications that I am filling ask me to write the intended field of study. </p>
<p>I found the people who do theoretical high energy physics are the best one able to describe physics and explain it at all levels, otherwise my choices are neutral. Since I am just a student and do not know the big picture of this field and other fields in physics, I want to ask what are the advantages and disadvantages of doing a PhD in theoretical high energy physics?</p> | g14572 | [
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<p>what growth conditions should the potential inside the Hamiltonian $ H=p^{2}+ V(x) $ has in order to get ALWAYS a discrete spectrum ??</p>
<p>for example how can we know for teh cases $ |x|^{a} $ , $ exp(b|x|) $ and so on with real parameters a,b and c </p>
<p>how can we prove that for theses potentials we will have only a discrete set of eigenvalues ??</p>
<p>another question is it possible to find a potential which have the eigenvalues $ E_{n}=n^{c} $ for some positive real number 'c' , i have heard that no potential in QM could have eigenvalues bigger than $ E_{n}=n^{2} $</p> | g14573 | [
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<p>The motivation for my question is understanding how electricity gets through your skin as opposed to running along it, and how the presence of things like water on the skin affect the relative deadliness of electricity, or ability of it to permeate the skin. </p>
<p>I don't understand how to view the body as a resistor, as the skin, and all the components of the body have different resistances and thicknesses. How do I know what parts of the body carry significant current? And how much current in total?</p> | g14574 | [
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0.02... |
<p>The paper I am trying to understand is here:
<a href="http://pra.aps.org/abstract/PRA/v49/i2/p1473_1" rel="nofollow">http://pra.aps.org/abstract/PRA/v49/i2/p1473_1</a></p>
<p>The paper describes the quantum teleportation protocol in a general case with continuous dynamical variables (position and momenta) in contrast to what is always discussed here, the discrete case.</p>
<p>I am very confused as to <strong>what is being teleported</strong> in this this scheme. I understand that in the discrete case, its its polarization state of a photon or the spin of an electron.</p>
<p>What I understand is that you start out with an entangled pair of particles in position and momentum in the original EPR State:
<a href="http://prola.aps.org/abstract/PR/v47/i10/p777_1" rel="nofollow">http://prola.aps.org/abstract/PR/v47/i10/p777_1</a></p>
<p>So if you are to try to teleport the position and momenta information of a particle, what is this exactly? Don't we need an origin point? </p>
<p>Going on with the teleportation procedure, you interact the input particle with one of the entangled pairs, now somehow an analogous bell measurement is made on the position and momentum of the combined pair?? Now you communicate that result to the other entangled particle and you do appropriate "shifts" so that the particle is now the input particle in terms of position and momentum.</p>
<p>Does this mean that the position and momentum distribution of one particle is teleported to another? What happens if the input particle was moving? Does this mean that after teleportation, the other particle keeps on moving too? This is extremely confusing.</p> | g14575 | [
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<p>While I've covered a basic course in Quantum Mechanics, I'm self-studying Landau & Lifshitz's book to help me understand what's going on.</p>
<p>Unfortunately, I'm stuck on the very first equation in the book.</p>
<p>Landau & Lifshitz write:</p>
<blockquote>
<p>The basis of the mathematical formalism of quantum mechanics lies in the proposition that the state of a system can be described by a definite (in general complex) function $\Psi(q)$ of the coordines</p>
</blockquote>
<p>so far so good...</p>
<blockquote>
<p>The square of the modulus of this function determines the probability that a measurement performed on the system will find the values of the coordinates to be in the element $dq$ of configuration space. The function $\Psi$ is called the <strong>wave function</strong> of the system</p>
</blockquote>
<p>again, fine...</p>
<blockquote>
<p>A knowledge of the wave function allows us, in principle, to calculate the probability of the various results of any measurement (not necessarily of the coordinates) also. All these probabilities are determined by expressions bilinear in $\Psi$ and $\Psi^*$. The most general form of such an expression is </p>
<p>$\int \int \Psi(q)\Psi^*(q')\phi(q,q')dq dq'$</p>
<p>where the function $\phi(q,q')$ depends on the nature and the result of the measurement, and the integration is extended over all configuration space. The probability $\Psi\Psi^*$ of various values of the coordinates is itself an expression of this type.</p>
</blockquote>
<p>OK, there's a lot here I don't understand. I can accept most of the statements on faith, but what I don't understand is what the hell $q'$ is for. Why can't the equation just use q throughout?</p> | g14576 | [
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<p>How can I apply <strong>C.O.E</strong> to a system that applies magnetic & electric fields at the same time to do work, and convert energy from one form to another? </p>
<p>Let assume we have a conductor that moves within a magnetic field(electric motor) how can <strong>C.O.E</strong> be applied so that input $E$ = output $E$ ?</p>
<p>Or in general a wire that has current flowing, and the work done to do that. And the work done by the magnetic forces to move it.
And in many other applications... Is there a general way to calculate it?</p>
<p>It seems a bit difficult.</p> | g14577 | [
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<p>Forgive me for the silly question, but I just don't get it.</p>
<p>I just completed an elementary course in mechanics, and I am curious to know what I am about to ask.</p>
<p>We have, all year, dealt with many forces like gravity, friction, normal forces, tensions etc. </p>
<p>But only one of them is listed as a fundamental force, that is, gravity.</p>
<p>I know that the only forces that exist in nature are the four fundamental force, and all of these are, apparently, non-contact forces.</p>
<p>But then how do you account for, for example, <a href="http://en.wikipedia.org/wiki/Friction" rel="nofollow">friction</a>? We know that $F_\text{frictional}=\mu N$, But how do we arrive at that? Is this experimental?</p>
<p>I cannot see how contact forces like friction can exist, when none of the fundamental force is a contact force.</p>
<p>Again, forgive me for my ignorance.</p> | g14578 | [
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<p>What are the actual factors that play a role in the accretion of matter into galaxies? I read about Accretion Disks but I don't quite understand how they work yet. </p> | g14579 | [
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<p>How can you prove the uncertainty for position is:</p>
<p>$$\Delta{x} =\sqrt{\langle x^2\rangle-\langle x\rangle^2}$$</p>
<p>$\Delta{x}$, taken to be the root mean square of x.</p>
<p>$$\Delta{x} =\sqrt{\langle \left(x-\langle x\rangle\right)^2\rangle} $$</p>
<p>$$\Delta{x} =\sqrt{\langle \left(x-\langle x\rangle\right) \left(x-\langle{x}\rangle\right)\rangle}$$</p>
<p>$$\Delta{x} =\sqrt{\langle x^2-2x\langle x\rangle +\langle x \rangle^2\rangle}$$</p>
<p>This is the bit which I am not sure about and why I can do it (taking the outer braket and acting it on the inner x values:</p>
<p>$$\Delta{x} =\sqrt{\langle x^2\rangle -2\langle x \rangle \langle x\rangle +\langle x \rangle^2}$$</p>
<p>$$\Delta{x} =\sqrt{\langle x^2\rangle -2\langle x\rangle^2 +\langle x \rangle^2}$$</p>
<p>$$\Delta{x} =\sqrt{\langle x^2\rangle - \langle x \rangle^2}$$</p> | g14580 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/4704/black-hole-analog-experiment">Black hole analog experiment?</a> </p>
</blockquote>
<p>I will explain my situation a little bit:</p>
<p>My teacher assign a experimental project that must be including the diary product: egg and milk to finish a black hole analogous experiment project, so what is some clues that could help me to finish this motivating project?</p> | g448 | [
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0.008895720355212688,
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0.03730413317680359,... |
<p>To my understanding, matter and energy are one and the same. Shifting from $E$ to $M$ in Einstein's famous equation requires only a large negative acceleration. If $M$ really is $E/c^2$, does that make matter the solid state of energy? I've read a lot about positron-electron collisions at high energies creating larger particles, and there is obvious matter conversion in fusion and fission reactions, but I can't find anything describing the physics of the conversion from energy to matter, rather than the interactions of what is already matter.</p>
<p>Specifically, the thing I'm getting hung up on is the reason energy would take on a solid state in the first place. If energy is represented by waves, how does it become particles? If gravity is determined by mass, and mass is nothing more than static energy, does that make gravity a static-electromagnetic force?</p> | g46 | [
0.0647335797548294,
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<p>Ordinary matter and antimatter have the same physical properties when it comes to, for example, spectroscopy. Hydrogen and antihydrogen atoms produce the same spectroscopy when excited, and adsorb the same frequencies. The charge does not make a difference in the potential (regardless if it's generated by a proton or an antiproton) nor in how the positron behaves in this potential (being its mass equal to the mass of an electron)</p>
<p>How can astronomy evaluate if a far galaxy is made of matter or antimatter, given that from the spectroscopy point of view, they behave in the same way? In other words, how do we know that an asymmetry exists between matter and antimatter in the universe? </p> | g321 | [
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<p>say you had a large quantity of a heavy element such as uranium... AND you put a massive amount of energy into it, so that it began to undergo nuclear fission and transformed to a significantly smaller element(s). Would it be possible to use this energy to now begin a process of fusion, to output energy? And then once it's fused beyond a certain size, back to fission? Basically the idea is to extract back and forth as much energy as possible from the original sample.</p> | g14581 | [
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<p>I am interested in modeling water flow including boundary flow (with friction) against other objects in the path of the water flow.</p>
<p>I'm not a physicist but I am interested to learn the relevant physics (and the corresponding mathematical model) required to begin modeling a generic simulation engine. </p>
<p>I've searched this forum using "model water flow surface friction" search string, and I've read <a href="http://physics.stackexchange.com/questions/8352/water-flow-in-a-sink">water flow in a sink</a>, and <a href="http://physics.stackexchange.com/questions/20482/what-is-the-velocity-area-method-for-estimating-the-flow-of-water">What is the velocity area method for estimating the flow of water?</a>. </p>
<p>Please suggest topics and other search strings, and advise if this is off-topic for this Physics forum. Thanks in advance.</p>
<p>Clarification: I'm looking at </p>
<ul>
<li>no-slip condition (i.e. solid walls)</li>
<li>with turbulence</li>
</ul>
<p>and </p>
<ul>
<li>introduction of another body (with mass) into model for calculating the displaced
water flow around the body.</li>
</ul> | g14582 | [
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<p>Is it (the output, i.e, spherical, flat, hyperbolic) describing the physical shape of the universe and its curvature at any given instance of time <em>or</em> is it describing the shape of the expansion function applied to the universe? (i.e, the evolution of the universe spatially over time)</p>
<p>So a cone shaped universe could have a "flat" solution applied to it and this just means it keeps expanding forever. Or a "positive" solution applied which means expansion will eventually halt and reverse, ending in a Big Crunch. The original arbitrary shape (conical) not being affected at all?</p> | g14583 | [
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<p>In particle physics experiments, pileup occurs when two particles hit the same detector (say a calorimeter) at roughly the same time, resulting in what looks like a single event with higher energy than either one. Naturally, this can be a pain when analyzing data, and I've heard bits and pieces about methods for subtracting off the pileup events in the final analysis. Presumably this entails identifying events that seem to have a two-peak structure and either dropping the event from the analysis (eek, systematic error) or finding a way to separate them into the two events they are. All the analysis comes after the experiment, in which pileup can be reduced by segmentation of detectors (identify separate events because they are recorded on different parts of the detector) and faster data-taking (making it easier to identify that double-peak structure).</p>
<p>But I can't seem to find any accessible information on pileup (the only article Google seems to turn up is a fairly advanced one from the LHC, which I can't quite follow) or its reduction, and would really appreciate a brief summary of pileup subtraction techniques or a pointer to the right place to look. </p> | g14584 | [
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<p>It seems to me that the notion of an "S-matrix" refers to several different objects</p>
<p>One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in the asymptotic past and future. This means the incoming and outgoing states belong to the free theory and the S-matrix is an operator on the free theory state space (Fock space). It is the ratio between the time evolution operators of the interacting (but adiabatically "turned off") and the free theory over an infinite time span</p>
<p>This construction already yields potentially several objects since there can be several free field limits. For example if the model admits something like S-duality then both the g -> 0 and the 1/g -> 0 limits are free. It is then possible to consider 2 kinds of S-matrices: in one we adiabatically set g -> 0, in the other 1/g -> 0</p>
<p>But it seems that there also should be something like a "fully interacting" S-matrix. This S-matrix should be an operator on the space $Fock(H_{discrete})$ where $H_{discrete}$ is the subspace of the full state space corresponding to the discrete part of mass spectrum</p>
<p>Is it indeed the case there are several different S-matrices? If so, why is it "carefully hidden" in the literature? Is it possible to compute the "fully interacting" S-matrix in perturbation theory using the Bethe-Salpeter equation to extract the bound state spectrum?</p> | g14585 | [
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<p>In q. 22 in page 141, I am asked to show that if $U^{\alpha}\nabla_{\alpha} V^{\beta} = W^{\beta}$, then $U^{\alpha}\nabla_{\alpha}V_{\beta}=W_{\beta}$.</p>
<p>Here's what I have done:
$V_{\beta}=g_{\beta \gamma} V^{\gamma}$
so, $U^{\alpha} \nabla_{\alpha} (g_{\beta \gamma} V^{\gamma})=U^{\alpha}(\nabla_{\alpha} g_{\beta \gamma}) V^{\gamma} + g_{\beta \gamma} (U^{\alpha} \nabla_{\alpha} V^{\gamma})$.</p>
<p>Now, I understand that the second term is $W_{\beta}$, but how come the first term vanishes?</p> | g14586 | [
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0.0319... |
<p>I think I've come across a paradox while studying general relativity. Wikipedia states that the deflection angle of light by a point mass is $4GM/(c^2b)$.</p>
<p><a href="http://en.wikipedia.org/wiki/Gravitational_lensing_formalism" rel="nofollow">http://en.wikipedia.org/wiki/Gravitational_lensing_formalism</a></p>
<p>Where b is the impact parameter, the limit of the perpendicular distance of the light ray from the point mass as the light gets far away. By shining a light that gets pulled close to the photon sphere of a black hole I can make a photon orbit the black hole an arbitrary number of times before escaping, leading to a deflection angle much greater than 2*pi. However, to make this angle go to infinity (at the photon sphere) according to the equation, I need to make b go to zero. However, if I shine a light very close to to center, it passes the event horizon and will go into the black hole without orbiting forever. What am I missing in this analysis?</p> | g14587 | [
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<p>This is a student inquiry sparked by sheer curiosity.</p>
<p>Wikipedia states the <a href="http://en.wikipedia.org/wiki/Drag_%28physics%29" rel="nofollow">drag equation</a>, $F = 1/2v^2pC_dA_c$.</p>
<p>(p = mass density of fluid/gas, v = velocity, c_d = drag coefficient, a_c = cross sectional area perpendicular to velocity.)</p>
<p>Wikipedia claims that this equation is only accurate under certain conditions:</p>
<blockquote>
<p><em>The objects must have a blunt form factor and the fluid must have a large enough Reynolds number to produce turbulence behind the object.</em></p>
</blockquote>
<p><strong>Does there exist a more general equation that can accurately measure the drag of all objects, at all speeds/Reynolds numbers and considering all physical properties affecting the drag?</strong></p> | g14588 | [
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<p>I was wondering about hydrostatic equilibrium (the balance of radially inward and outward forces) in large (i.e. above the Chandrasekhar limit) stars. It is often said that when the gravitational force exceeds any outward forces or pressures, mainly the electron degeneracy pressure I'm thinking, the star collapses into a black hole. But how can this happen without the Pauli exclusion principle being violated?</p>
<p>A similar question: <a href="http://physics.stackexchange.com/questions/93988/does-black-hole-formation-contradict-the-pauli-exclusion-principle">Does black hole formation contradict the Pauli exclusion principle?</a></p>
<p>The answer by @Siva in that question makes some sense to me, but I don't understand at what point we start our counting of states from the object being a star to a black hole. What happens in the middle? Is there a sharp change?</p> | g14589 | [
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<p>I've been trying to get familiar with string field theory (SFT) and I've stumbled upon the statement that the Ramond-Ramond (RR) sector of Nathan's SFT has not been constructed yet. Why is that? </p> | g14590 | [
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<p>Examining cosmic ray neutron radiation near ground by neutron monitors for example (<a href="http://www.nmdb.eu" rel="nofollow">http://www.nmdb.eu</a>), different stations show similar dynamics in the signal.</p>
<p>At one station, I like to "substract" the incoming radiation in order to obtain information about local effects. Can I take the incoming signal from another station? But signals of two stations differ:</p>
<ol>
<li><strike>sometimes lags up to 10 days between similar peaks</strike></li>
<li>peaks differ in amplitude</li>
<li>efficiencies differ between the detectors</li>
</ol>
<p>How to correct for such effects analytically? (like the known corrections for pressure, latitude, altitude, etc.) Or are there appropriate techniques for statistical decomposition?</p> | g14591 | [
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<p>The question comes from Ryder's Quantum Field Theory, 2nd edition. The author was looking for relativistic spin operator. It was concluded that it cannot be $J^2:=\mathrm{J} \cdot \mathrm{J}$, where $J_i$ is the generator for rotation in Lorentz group.</p>
<p>p.56:</p>
<blockquote>
<p><em>$\ldots \Sigma$ is, of course, the matrix representative of $\mathrm{J}$, so we conclude that the relativistic spin operator is not $\frac{1}{2} \mathrm{J}$. This is confirmed by the fact that $\mathrm{J} \cdot \mathrm{J}=J^2 $(c.f.(2.167)) does not commute with all the generators of the Lorentz group. For example, $\ldots$, $[J^2,K_1] \neq 0 $.</em></p>
</blockquote>
<p>Later Ryder found the square of the Pauli-Lubanski operator is the Casimir, but still not the relativistic spin operator. (It was refered to literature)</p>
<p>I have a question about the logic here. Why the spin operator needs to commute with all the generators in the Lorentz group. If the spin operator commutes with the Hamiltonian, it is a conserved quantity. We can use the eigenvalue to label states (good quantum number). That is precisely $[H,J_i]=0$. Is that still insufficient, because it may be frame-dependent? </p> | g14592 | [
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... |
<p>Actually I can't expand much as the question pretty much explains the query. I would be interested in the method of estimating an answer as well as a potential way to measure it experimentally. Thanks.</p>
<p>P.s. I'm not sure what tags to include for this one - for those that can, feel free to edit them as you see fit.</p> | g14593 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/7838/on-causality-and-the-big-bang-theory">on causality and The Big Bang Theory</a> </p>
</blockquote>
<p>Asking here in layman's terms..</p>
<p>When theoretical physicsists discuss the origin of our Universe, the wider consensus appears to be that it originates from a singularity; a position that rests on observations about the apparent expansion of our Universe. </p>
<p>However, the question why singularity itself came into being, still remains.</p>
<p>But this question takes a different angle: Does the Universe as a whole need a cause to exist at all? </p>
<p>If the law of conservation of energy is universally valid, then questions about a beginning become irrelevant since there can't be any by definition and everything boils down to dynamics of interaction. Thoughts?$$\mbox{ }$$</p> | g51 | [
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<p>I was reading about this asteroid (apparently, it has a moon, isn't that awesome?) and I started thinking about if I was on this asteroid, and I jumped, would I fall off?</p>
<p>It's been a while since I did something like this, so I went to Wikipedia to get some formulas. There I found</p>
<p>$$v_e = \sqrt{\frac{2GM}{r}}$$</p>
<p>Where</p>
<ul>
<li>$G$ is the gravitational constant ($6.673 × 10^{-11}\ \mathrm{m}^3\mathrm{kg}^{-1}\mathrm{s}^{-2}$)</li>
<li>$M$ is mass of the body (found to be $4.2 × 10^{16}\ \mathrm{kg}$)</li>
<li>$r$ distance from center of mass (found to be $53.6\ \mathrm{km}$)</li>
</ul>
<p>$$v_e = \sqrt{\frac{2(6.673\times 10^{-11})(4.2\times 10^{16})}{53600}} = \sqrt{104} = 10.22\,\frac{\mathrm{m}}{\mathrm{s}}$$</p>
<p>I'm a fairly fit guy, about 73kg and .6m vertical leap here on earth.</p>
<p>I found a formula for the speed of a free falling object to be</p>
<p>$$v = \sqrt{2gd}$$</p>
<p>If I assume that my speed when I hit the ground is the same as when I jump up, that means my jump speed is about 3.4 m/s, which is significantly less than the required 10.4 m/s.</p>
<p>So it would seem I would not be able to jump off of this asteroid.</p>
<p>Are my formulas, assumptions, and calculations correct here?</p>
<p>Also, how would I use this information to determine how high I would jump (would it be enough to freak me out? Well I'd be jumping off an asteroid, so it would freak me out anyway... although I imagine I would be going slow enough for (my ship?) to pick me back up.)</p> | g14594 | [
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<p><a href="http://physics.stackexchange.com/q/2230/">This Phys.SE question</a> asks why and how the speed of light is constant. I would like to ask a related, almost converse question: <strong>Given that the speed of light is constant,</strong> how could I explain to a young-earth-creationist who is still a proponent of the disgraced Barry Setterfield <a href="http://en.wikipedia.org/wiki/Creationist_cosmologies" rel="nofollow">$c$-decay theory</a> that the $c$-decay theory contradicts observed physical reality, as described and understood by all scientists, including those in the Physics and Astronomy fields?</p>
<p>Surely a variable speed of light would throw a monkey wrench into all sorts of fundamental laws or systems in physics? Surely it would be measurable on instruments today, if there was even a <strong>miniscule change</strong> in the speed of light relative to a continuous cold caesium fountain atomic clock? The fact that there is no observable change in any recent trustworthy data, is the beginning, middle, and end of the scientific argument. Am I correct?</p>
<p>My physics education ended at Grade 12. So I'm asking for a high-school level explanation.</p>
<p>I also wonder if $c$-decay theorists are contradicting themselves, or have sawn off the branch upon which they themselves sit; For example, I wonder this; Would we have to modify our expectations of what the doppler effect (red shift) would look like, as light comes towards us from distant stars, if the speed of light is variable? Would we not have to throw all our doppler data out, and all the distances themselves, if the speed of light is variable in some undefined way, and thus unknown and unknowable? The $c$-decay theory was spawned because redshift data indicates that the stars are too far away for their light to have reached us in the mere 6000 years the universe has existed. In short, if $c$-decay theory exists to explain distant stars to young earth creationists and help them breathe a sigh of relief, wouldn't it be slightly-less-scientifically-bogus, to just dispute the doppler effect and the distance of those stars?</p> | g14595 | [
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<p>Doing a Google search i found a paper called <a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TJ4-4M21SWY-4&_user=10&_coverDate=06%2F30%2F2007&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1716211562&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=25e00e3ba9bac4c17fe64b8a9de5bc6c&searchtype=a" rel="nofollow">The maximum number of elementary particles in a super symmetric extension of the standard model</a>.</p>
<p>It claims in the abstract that the upper bound is 84 (i don't have access to the article)</p>
<p>My question is: Is there a max number of types of elementary particles predicted in advanced physics theories such as string theory? What are the reasons for this?Are the arguments purely mathematical?</p> | g14596 | [
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0.0324622243642807,
... |
<p>I read on Wiki that <a href="http://en.wikipedia.org/wiki/Earnshaw%27s_theorem" rel="nofollow">Earnshaw's theorem</a> has been proven for extended conducting bodies.
If we consider the case of a positive charge at the centre of a symmetric metal cavity-
the positive charge and the induced negative charge constitute a system which violates Earnshaw's law.</p>
<p>Where am I wrong in thinking this way?</p> | g14597 | [
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<p>Context: The recent paper <em>The quantum state cannot be interpreted statistically</em> by Pusey, Barrett and Rudolph (now On the reality of the quantum state, <a href="http://dx.doi.org/10.1038/nphys2309"><em>Nature Physics</em> <strong>8</strong>, 475–478 (2012)</a>, <a href="http://arxiv.org/abs/1111.3328">arXiv:1111.3328</a>) shows under suitable assumptions that the quantum state cannot be interpreted as a probability distribution over hidden variables (go read it now).</p>
<p>In the abstract they claim: "This result holds even in the presence of small amounts of experimental noise, and is therefore amenable to experimental test using present or near-future technology." </p>
<p>The claim is supported on page 3 starting with: "In a real experiment, it will be possible to establish with high condence that the probability for each measurement outcome is within $\epsilon$ of the predicted quantum probability for some small $\epsilon> 0$."</p>
<p>Something felt like it was missing so I tried to fill in the details. Here is my attempt:</p>
<p>First, without even considering experimental noise, any reasonable measure of error (e.g. <a href="http://dx.doi.org/10.1214/aos/1176344613">standard squared error</a>) on the estimation of the probabilities is going to have worst case bounded by
$$
\epsilon\geq\frac{2^n}{N},
$$
(tight for the maximum likelihood estimator, in this case) where $n$ is the number of copies of the system required for the proof and $N$ is the number of measurements (we are trying to estimate a multinomial distribution with $2^n$ outcomes).</p>
<p>Now, they show that some distance measure on epistemic states (I'm not sure if it matters what it is) satisfies
$$
D \ge 1 - 2\epsilon^{1/n}.
$$
The point is we want $D=1$. So if we can tolerate an error in this metric of $\delta=1-D$ (what is the operational interpretation of this?), then the number of measurements we must make is
$$
N \ge \left(\frac4\delta\right)^n.
$$
This looks bad. But how many copies do we really need? Note that the proof requires two non-orthogonal qubit states with overlap $|\langle \phi_0 |\phi_1\rangle|^2 = \cos^2\theta$. The number of copies required is implicitly given by
$$
2\arctan(2^{1/n}-1)\leq \theta.
$$
Some back-of-the-Mathematica calculations seems to show that $n$ scales at least quadratically with the overlap of the state.</p>
<p>Is this right? Does it require (sub?)exponentially many measurements in the system size (not suprising, I suppose) <em>and</em> the error tolerance (bad, right?).</p> | g14598 | [
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0.... |
<p>How is the violation of the usual CHSH inequality by a quantum state related to the entanglement of that quantum state?</p>
<p>Say we know that exist Hermitian and unitary operators $A_{0}$, $A_{1}$, $B_{0}$ and $B_{1}$ such that
$$\mathrm{tr} ( \rho ( A_{0}\otimes B_{0} + A_{0} \otimes B_{1} + A_{1}\otimes B_{0} - A_{1} \otimes B_{1} )) = 2+ c > 2,$$
then we know that the state $\rho$ must be entangled. But what else do we know? If we know the form of the operators $A_{j}$ and $B_{j}$, then there is certainly more to be said (see e.g. <a href="http://prl.aps.org/abstract/PRL/v87/i23/e230402">http://prl.aps.org/abstract/PRL/v87/i23/e230402</a> ). However, what if I do not want to assume anything about the measurements performed?</p>
<p>Can the value of $c$ be used to give a rigourous lower bound on any of the familar entanglement measures, such as log-negativity or relative entropy of entanglement?</p>
<p>Clearly, one could argue in a slightly circular fashion and define an entanglement measure as the maximal possible CHSH violation over all possible measurements. But is there anything else one can say?</p> | g14599 | [
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0... |
<p>I'm just curious. I figure atoms fuse occasionally just by chance, like quantum tunneling or <a href="https://en.wikipedia.org/wiki/Rogue_wave">rogue waves</a>. Is this true? If so, any idea how often?</p> | g14600 | [
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<p>I am hoping to discuss some details of electronic structure calculations. I am not an expert on this topic, so please forgive any abuse of terminology. It is my understanding that first principles electronic structure calculations are based on perfect translational symmetry of a crystalline lattice. Further, that the first round of calculations traditionally treat the atomic nuclei as fixed points due to the large disparity in nuclei and electron velocities, and after the initial electronic structure is solved, one can then turn on the nuclear motions and understand the interaction between the nuclear and electronic motions. The heart of my question is: is it possible to investigate local distortions of structures using existing techniques? By a local distortion, I mean a distortion which does not disrupt the long range crystalline periodicity, but results in a very different local atomic environment? </p> | g14601 | [
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<p>Now we always talk about the so-called <a href="http://www.sciencedirect.com/science/article/pii/S0003491605002381" rel="nofollow">Kitaev spin liquid</a>. One important property of spin liquid is <strong>global spin rotation symmetry</strong>. Let $\Psi$ represents a spin ground state, if $\Psi$ has global spin rotation symmetry, then it's easy to show this simple identity $< \Psi \mid S_i^xS_j^x\mid \Psi >=< \Psi \mid S_i^yS_j^y\mid \Psi >=< \Psi \mid S_i^zS_j^z\mid \Psi > $. But <a href="http://prl.aps.org/abstract/PRL/v98/i24/e247201" rel="nofollow">Baskaran's exact calculation of spin dynamics</a> in Kitaev model shows that <em>only the components of spin-spin correlations(nearest neighbour sites) matching the bond type are nonzero</em>, which violates the above identity, further means that the ground state of Kitaev model <strong>does not</strong> have global spin rotation symmetry.</p>
<p>So why we still call the ground state of Kitaev model a <em>Spin Liquid</em> ?</p> | g14602 | [
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<p>I have to simulate the electric field within a gas filled discharge gap generated by a radio frequency voltage generator. The circuit, provided to me by the experimenters somewhat far away, is given in the second picture below. </p>
<p>Now the program I use expects me to feed it the time depended voltage curve and three values do describe the circuit: <strong>R, L, C</strong>. </p>
<blockquote>
<p>How to match the more complicated real circuit to the model? In any case, I'll have to plug in some values for the three parameters R, L, C eventually. </p>
</blockquote>
<p>(Numerical values: $C1 = 22\ nF=2.2\cdot 10^{-9}, R1 = 2\ Om, L1+L2 = 8\ \mu H=8.0\cdot 10^{-6}, C2 = 3.4n\ F=3.4\cdot 10^{-9}$ [transformer parasitic capacitance]$, R2 = 100\ MOm=10^8\ Ohm, R3 = 1\ Om, L3 = 100\ nH=10^{-7}\ H.$ Moreover, it's running at 1MHz, sinusoidal, about $10kV$.)</p>
<hr>
<p><strong>Edit.:</strong></p>
<p>So computing the resistence of the "real" model, setting $R_2=\infty$, I get </p>
<p>$$Z_\text{tot}=Z_{C_1,L_1,R_1,L_2}+\frac{1}{\frac{1}{Z_{C_2}}+\frac{1}{Z_{R_3,L_3,R_\text{Gap}}}}$$</p>
<p>$$=\left(R_1+i\ \omega\ (L_1+L_2)-i\frac{1}{\omega\ C_1}\right)+\frac{1}{\frac{1}{-i\frac{1}{\omega\ C_2}}+\frac{1}{R_3+R_{Gap}+i\ \omega\ L_3}}$$</p>
<p>$$=\left(R_1+i\ \omega\ (L_1+L_2)-i\frac{1}{\omega\ C_1}\right)+\left(R_3+R_{Gap}+i\ \omega\ L_3\right)\frac{1}{1+(i \omega\ C_2)\left(R_3+R_{Gap}+i\ \omega\ L_3\right)}$$</p>
<p>with </p>
<p>$\omega\ C_2\approx 2\cdot 10^{-2}F\ Hz,$</p>
<p>$\omega\ L_3\approx 6.8\cdot 10^{-1}H\ Hz,$</p>
<p>$R_3=1\Omega$</p>
<p><img src="http://i.imgur.com/4vQHuRv.png" alt="enter image description here"></p>
<p>I tried to ask this on the electrical engineering page, but with no responses.</p>
<hr>
<p>I have no idea if it's of relevance, but I can post the text of the manual of the generator, which I also have, but which isn't really written in my language. I have no idea how the picture even corresponds to the question above. The letter symbols seem a little off. So if the following doesn't make any sense, then ignore it and just take the question above this at face value.</p>
<p><img src="http://i.imgur.com/HvQPuZL.png" alt="enter image description here"></p>
<p><em>"This generator simplified block diagram is presented on Fig. 5</em>*' (the third picture). <em>Clock signal generator, protect and control circuits are realized by using programmable logic device(PLD) Xilinx XCR32256XL. This chip configuration(and generation parameters) could be changed in-system by special JTAG (Joint Test Action Group)-programmer. Control signal are boosted by gate drivers and gone to the power switch gates. The converter is designed as half-bridge circuit using MOSFET(Metal-Oxide-Semiconductor Field Effect Transistor) switches and fed by voltage up to 400 VDC. Power oscillatory circuit, included elements C1 and high voltage step-up transformer having loss inductance L and parasitic capacitance C2, forms output voltage. In fire mode this circuit part can be simulated as two coupled oscillators; one of them consists of L and C2 and has resonance frequency about 1 MHz. As a result, output voltage will increase fast, have sinusoidal-like shape and reach breakdown level of load. After discharge gap breakdown, in limit mode, capacitance C2 is shunted by small plasma impedance and we can ignore its influence on power oscillation. Resonance of power oscillatory circuit in this mode will be defined by elements L and C1 and resonance frequency value will be less significantly than clock signal frequency(~1MHz). Output voltage will decrease a lot, its shape is changed to near triangle and power supply passes to limit mode.
Powerful 1.3 kW capacitor charging module is used to feed RF converter circuit. It has galvanic isolation from mains and adjustable output voltage. Control circuits and gate drivers are fed by auxiliary AC/DC and DC/DC supplies.
External synch signal is transferred by digital isolator, it has standard 50 Ohms impedance, active level is “HIGH”(+5 Vampl). Control signal is inactive if input connector is not jointed."</em></p>
<p>I also don't actually know where the voltage they measure (which is supposed to be 10kV) is taken from in the circuit. Maybe the pictures plainly say it, but I can't read it.</p>
<hr>
<p>Lastly, I want to post this, because I find it pretty amusing:</p>
<p><em>"High output voltage (up to 25 kV) and high level of electromagnetic interferences require highly experienced personnel to operate with generator. Careless use may be cause of electrical shock, health hazard, malfunction or even damage of nearby equipment."</em></p> | g14603 | [
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<p>I was considering the S-dual of the Type I' String theory (the solitonic Type I string theory).</p>
<p>That is the same as the S-dual of the T-Dual of Type I String theory. Then, that means both length scales and coupling constant are inverted. So, since inverting the length scale of the theory before inverting the coupling constant is the same as inverting the coupling constant before the length scale, I think the S-dual of the T-dual of the Type I String theory is the same as the T-dual of the S-dual of the Type I String theory. The S-dual of the Type I string theory is the Type HO String theory. The T-dual of the Type HO string theory is the Type HE String theory.</p>
<p>Therefore, the S-dual of the Type I' String theory is the Type HE String theory. But the Type HE String theory is S-dual to M-theory compactified on a line segment.</p>
<p><em><strong>So does this mean that the Type I' String theory is M-theory compactified on a line segment?</em></strong></p>
<p>Thanks!</p> | g14604 | [
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0.008008870296180248,
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-0... |
<p>A Stirling engine evidently functions by heating and cooling air, thus making the piston move up and down. What if the heated side of the cylinder were shaped as a sort of cone with a gentle slope, cut off before a point forms (I guess it would look like a trapezoid from the direct side), so that the surface that must be heated is reduced in size, lets say by half? Would that still permit the engine to run as well as it did with a large top surface?</p> | g14605 | [
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0.... |
<p>How fast does the water travel down river when the discharge gates of a large dam are opened? Can the discharge-wave travel downstream faster than the water? Is this likely to occur for a real river and an actual sudden discharge from a large reservoir?</p> | g14606 | [
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<p>As is usually said, measurement of an observable $q$ leads to collapse of wavefunction to an eigenstate of the corresponding operator $\hat q$. That is, now the wavefunction in $q$ representation is $\psi(q)=\delta(q-q_0)$ where $q_0$ is result of measurement.</p>
<p>Now, in reality measurements are never exact, so the wavefunction should not have that sharp peak. Instead it should be broadened depending on precision of measurement. In this case, can we still introduce an operator, an eigenstate of which would the new wavefunction appear? Is it useful in any way? Or does the new wavefunction depend too much on the way it was measured so that each instrument would have its own operator? How would such opeartor look e.g. for a single-slit experiment?</p> | g14607 | [
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0.... |
<p>In my curriculum, the <a href="http://en.wikipedia.org/wiki/Decay_constant" rel="nofollow">decay constant</a> is "the probability of decay per unit time"</p>
<p>To me, this seems non-sensical, as the decay constant can be greater than one, which would imply that a particle has a probability of decaying in a time span that is greater than 1.</p>
<p>Can someone explain this?</p> | g14608 | [
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0.0300431... |
<p>is it possible to either demonstrate the principle or make a SEM ( electron microscope ) at home or lab as an enthusiast??
and how can i start?</p> | g14609 | [
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<p>I hope this isn't a stupid question for you guys but here we go.
As you travel close to the speed of light, it is to my understanding you gain mass.. does this also apply when the brain sends electrical signals to the muscles? Do the signals (that are traveling at the speed of light) cause the body to weight more? Plz help this question has been bugging me </p> | g14610 | [
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0.014... |
<p>I understand that in the limit that h_bar goes to zero, the Feynman path integral is dominated by the classical path, and then using the stationary phase approximation we can derive an approximation for the propagator which is a function of the classical trajectory (see <a href="http://www.blau.itp.unibe.ch/lecturesPI.pdf" rel="nofollow">http://www.blau.itp.unibe.ch/lecturesPI.pdf</a> pg 46).</p>
<p>I am under the impression that this further implies that the particle follows the classical trajectory but I don't understand how the above mentioned fact implies this.</p>
<p>The propagator describes the time-evolution of the wavefunction, so I would think that this classical limit form of the propagator should give a time-evolution in which the wavefunction follows the classical trajectory, but I have not been able to find such work. Moreover, even this statement itself is problematic since the wavefunction describes a probability distribution and not a single trajectory.</p>
<p>$\textbf{New Edit:}$ In section 7 of Feynman's paper introducing the path integral (see <a href="http://imotiro.org/repositorio/howto/artigoshistoricosordemcronologica/1948c%20-FEYNMAN%201948C%20Invention%20of%20the%20path%20integral%20formalism%20for%20quantum%20mechanics.pdf" rel="nofollow">http://imotiro.org/repositorio/howto/artigoshistoricosordemcronologica/1948c%20-FEYNMAN%201948C%20Invention%20of%20the%20path%20integral%20formalism%20for%20quantum%20mechanics.pdf</a>) he discusses the classical limit. It appears that the key to understanding why the fact that the classical path dominates the path integral further implies that the particle follows the classical trajectory may be found in Feynman's remark on pg 21: "Now we ask, as $\hbar → 0$ what values of the intermediate coordinates $x_i$ contribute most strongly to the integral? These will be the values most likely to be found by experiment and therefore will determine, in the limit, the classical path." However, I don't understand why "These will be the values most likely to be found by experiment" ?</p> | g141 | [
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0.0168237... |
<p>As far as I know, quantum hall effect and quantum spin hall effect has chiral edge state. Chiral edge state is usually closely related with delocalization, since back scattering is forbidden. However, some topological nontrivial state does not have chiral state, such as majorana bound state in topological superconductor.</p>
<p>I am quite interested whether the existance of chiral edge state is determined by bulk topological properity?</p>
<p>Thanks in advance</p> | g14611 | [
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<p>I'm wondering if there are any good indicators on how even the heat is distributed on an object (for simplicity, a flat object maybe)? What are the possibly reasonable ways to maximize the evenness if varying the shape of the object is allowed. </p> | g14612 | [
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<p>I learned in my undergraduate physics class that atoms have magnetic fields produced by the orbit of electrons and the spin of electrons. I understand how an orbit can induce a magnetic field because a charge moving in a circle is the same as a loop of current. </p>
<p>What I do not understand is how a spinning ball of charge can produce a magnetic field. Can someone explain how spin works, preferably in a way I can understand?</p> | g14613 | [
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<p>I'd like to know what are the differences in timbre - or the acoustic properties of a sound - that allow us to differentiate between a sound which is quiet (but close-by) and one which is far away.</p>
<p>For example, you can tell when someone near to you is playing an instrument quietly even without looking to see where they are - they don't sound 'far away'.</p>
<p>Hearing a loud gig or a car stereo playing from the next street doesn't sound like it's quiet - it sounds loud, but far away.</p>
<p>But other times we can't differentiate - I sometimes hear a siren on TV and think it's on the street!</p>
<p>I thought only the amplitude (i.e. volume) of a sound wave diminished with distance - does the shape/frequency alter too?
Is this ability just to do with having two ears to locate the source - surely someone who is deaf in one ear can still tell an orchestra is playing a <em>diminuendo</em> and not gradually getting further away?!</p> | g14614 | [
0.023568840697407722,
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0.0012560025788843632,
0.05028216913342476,
0.004... |
<p>I know that:<p>
$G=6.67300 × 10^{-11}\dfrac{Nm^2}{kg^2}$(Gravitational constant)<p>
$K_e=9×10^9\dfrac{Nm^2}{C^2}$(Electric constant or Coloumb's constant)<p>
$k_m=1×10^{-7}\dfrac{Ns^2}{C^2}$(Magnetic constant)<p></p>
<hr>
<p>But what are the meaning of this values? Would the universe be much different with a little change on this values? What if we hadn't known them?</p> | g14615 | [
-0.01563561148941517,
0.028627680614590645,
-0.03515981510281563,
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0.01954065077006817,
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0.062456049025058746,
... |
<p>I have a question about entangled state. Suppose I consider the entangled state $\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$. I saw an argument for how measurement of the first bit is affected by whether or not the second bit is measured because this is an entangled state in an article I am reading. The argument is clear to me and I describe it below, so please keep reading:</p>
<p>If I measure the first bit without first measuring the 2nd bit, then the probability that I get $|0\rangle$ is 1/2. This is clear to me. If I measure the 1st bit after measuring the 2nd bit, the probability that it is $|0\rangle$ is 0 or 1 depending on whether the measured value of the 2nd bit was $|0\rangle$ or $|1\rangle$. This is clear to me too. But what I am confused about is this: </p>
<p>If I measure the first bit after the second bit, this is what I would calculate the probability of measuring the first bit being $|0\rangle$ to be: $\frac{1}{2}\times 1 + \frac{1}{2}\times 0 = \frac{1}{2}$. The first term is the prob. of measuring the second bit as $|0\rangle$ and then the 1st bit as 0 and the 2nd term is the prob of measuring the 2nd bit as 1 and then measuring the 1st bit as zero. If the probability of measuring the first bit as 0 is to same regardless of whether the 2nd bit was measured or not is unchanged, what is the effect of the entangled state? Or am I missing something?</p> | g14616 | [
-0.012893089093267918,
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0.008... |
<p>In consistent histories, for gauge theories, can the projection operators used in the chains be not gauge invariant?</p>
<p>In quantum gravity, for a projection operator to be gauge invariant means it has to be diffeomorphism invariant. There are no localized diffeomorphism invariant operators, not even localized in time. No localized observables.</p>
<p>So, what are the permissible chains in quantum gravity? Do they have to be delocalized, or localized on the boundaries of spacetime?</p>
<p>Are space and time illusions, as Andrew Strominger <a href="http://fqxi.org/community/articles/display/176" rel="nofollow">claimed</a>? A Cosmic Hologram projecting out the illusion that is spacetime from the future boundary of time?</p> | g14617 | [
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<p>Here is the question from my textbook:</p>
<p>"In an insulated vessel, 250g of ice at $0^{\circ}$C is added to 600g of water at $18^{\circ}$C. What is the final temperature of the system?" </p>
<p>The solution says that it takes more heat to melt ice than to cool water, so some ice will remain. It says the final temperature should be $0^{\circ}$C, but no equation is given to explain that conclusion. Can the final temperature of this system be determined by reasoning alone?</p> | g14618 | [
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<p>This is based upon an question I had, since in Jupiter there is no oxygen a simple fire cannot be started let alone even happen due to its temperature. Anyway that being said, If I somehow used a space-shuttle to take a atomic weapon size of Tsar Bomba and successfully detonated the mass-destruction weapon would the entire planet simply be destroyed or what would happen? </p>
<p>That in mind do be aware hydrogen (major component of its atmosphere) is flammable so what would happen?</p> | g449 | [
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-0.0101... |
<p>I was reading <a href="http://www.messagetoeagle.com/speedoglightnotfixed.php">this article</a> recently, which summarizes a couple of new studies into the speed of light.</p>
<blockquote>
<p>In one paper, Marcel Urban from the University of Paris-Sud, located in Orsay, France and his colleagues identified a quantum level mechanism for interpreting vacuum as being filled with pairs of virtual particles with fluctuating energy values.</p>
<p>As a result, the inherent characteristics of vacuum, like the speed of light, may not be a constant after all, but fluctuate.</p>
<p>Meanwhile, in another study, Gerd Leuchs and Luis L. Sánchez-Soto, from the Max Planck Institute for the Physics of Light in Erlangen, Germany, suggest that physical constants, such as the speed of light and the so-called impedance of free space, are indications of the total number of elementary particles in nature.</p>
</blockquote>
<p>Now, my knowledge and understanding of electromagnetic waves is a bit rusty, but I guess I don't follow: <strong>how does fluctuating energy values affect the speed of light?</strong> </p> | g14619 | [
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<p>Assuming one were in a capsule of some kind, with no window or instruments, and you swung into the gravitational field of a massive object (planet). Assuming no atmosphere to provide friction, could you tell you were curving...there wouldn't be like centrifugal force, would there? Would you even feel gravity until you slammed into the planet's surface? </p>
<p>Addendum: Is gravitational lensing proof of space time curvature?</p> | g14620 | [
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<p>I am posting this question again because, Willie Wong asked me to do it. So it is a continuing post of the <a href="http://physics.stackexchange.com/questions/52590/interaction-potential-in-standard-phi4-theory/52642?noredirect=1#comment122497_52642">Interaction potential in standard ϕ4 theory</a>.</p>
<p>I have been studying about solitions so I had to deal with scalar field theory. The problem I faced in Lagrangian of Scalar field is interacting potential. </p>
<p>According to Scalar field theory we can write:
$$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$
The potential can be written separately $$ V(\phi)= \frac{m^2}{2}\phi^2 +\frac{\lambda}{24}\phi^4 \tag {2}$$
I found on Srednicki (Quantum Field Theory, page 188) that, the author wrote the potential as,
$$ V(\phi)= \frac{1}{24} \lambda (\phi^2- v^2 )^2-\frac{\lambda}{24} v^4 \tag {3}$$
After that the author excluded the term $-\frac{\lambda}{24} v^4 $. </p>
<p><strong>why is that?</strong></p>
<p>In another paper an author wrote the potential as $$V(\phi)= \frac{1}{8} \phi^2 (\phi -2)^2 \tag{4}$$<br>
<strong>I don't see coupling constant $\lambda$ in the equation (4).</strong></p>
<p><strong>What I'm trying to find is to get the potential in equation (4) from the equation (2)</strong></p> | g14621 | [
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<p>There are 51 stars within 17 light years of the Earth (<a href="http://en.wikipedia.org/wiki/List_of_nearest_stars">source</a>). If one of these stars was to become a supernova, how would they effect the Earth?</p>
<p>I have read the Wikipedia article <em><a href="http://en.wikipedia.org/wiki/Near-Earth_supernova">Near-Earth supernova</a></em>, but what would the explanation be in more layman's terms? What would happen if one of the 51 stars above became a supernova?</p> | g14622 | [
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<p>I know the relationship between normal and correlated two-particle Green Functions for fermions:
$$G_c(1,2,3,4)=\Gamma(1,2,3,4)=G(1,2,3,4)+G(1,3)G(2,4)-G(1,4)G(2,3)$$
Also known as irreducible n-particle Green function or n-particle vertex (there are many definitions so I'm confused).</p>
<p>Definitions for G also vary, I use this one: $G(1..2n) = (-1)^{n}\langle T\ c_1\dots c_n c_{n+1}^\dagger\dots c_{2n}^\dagger \rangle$</p>
<p>I need a similar relationship for three-particle functions.</p>
<p>Now I have this formula:
$$
\Gamma(1,2,3,4,5,6) =
G(1, 2, 3, 4, 5, 6)
-2 G(1, 4) G(2, 5) G(3, 6)
+2 G(1, 4) G(2, 6) G(3, 5)
-2 G(1, 5) G(2, 6) G(3, 4)
+2 G(1, 5) G(2, 4) G(3, 6)
-2 G(1, 6) G(2, 4) G(3, 5)
+2 G(1, 6) G(2, 5) G(3, 4)
-G(1, 4) G(2, 3, 5, 6)
+G(1, 5) G(2, 3, 4, 6)
-G(1, 6) G(2, 3, 4, 5)
+G(2, 4) G(1, 3, 5, 6)
-G(2, 5) G(1, 3, 4, 6)
+G(2, 6) G(1, 3, 4, 5)
-G(3, 4) G(1, 2, 5, 6)
+G(3, 5) G(1, 2, 4, 6)
-G(3, 6) G(1, 2, 4, 5)$$
But it doesn't always satisfy Wick's theorem for the Hamiltonian I'm working with. Is this formula correct?</p>
<p>Also it would be great to get an explanation of how these formulas appear in many-body theory, from logarithm of time-ordered exponential. </p> | g14623 | [
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<p>I just watched <a href="http://www.youtube.com/watch?v=MP3jAg1C_hA" rel="nofollow">this SpaceRip video on YouTube</a> which shows pictures taken by Hubble while looking into the disk of the Andromeda galaxy to study a certain type of variable star. It occurred to me that if we can study individual stars in Andromeda, we must be able to use most of our methods of exoplanet detection on them. </p>
<p>Is this true? If so, why not look for exoplanets <em>in another galaxy</em>? My logic tells me that since it's difficult to look through the disk of our own galaxy (since we're inside it), we're limited to a relatively local region for detecting exoplanets. But if we turned our sights to Andromeda, couldn't we study the differences in planet formation between different regions of a galaxy?</p>
<p>I also suspect that the reason we're not doing this is because we would need <em>much</em> more sensitive instruments for this, and because we already have one planet finding telescope in space (so it'd be tough to justify sending up another one).</p>
<p>Am I mostly right in this reasoning? Are we capable of searching for exoplanets in Andromeda? Would there be a benefit to doing it (besides the obvious cool factor)? Is cost pretty much the only limiting factor?</p> | g14624 | [
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<p>Physics is a hobby interest of mine, so I may be asking a senseless question, but there is something I cannot get my head around when it comes to relative frames, the <strong>constant</strong> speed of light (as a top-limit for any speed) and the following situation:</p>
<p>Imagine two spaceships, capable of reaching speed close to $c$, flying in opposite directions and passing each other by. According to the special relativity, we will calculate the speeds this way:
$$ V_{\rm total} = \frac{u+v}{1+\frac{uv}{c^2}} $$
where ${u}$ and $v$ would be the speeds of each spaceship, both close to $c$.</p>
<p>According to this, I perfectly understand that each ship will "see" the other moving with near the speed of light, not faster. An observer in a separate reference frame will see each ship moving with a speed near that of the light too, and it is OK. </p>
<p>Now, let's assume the ships crash. Would the effect of the crash be the same as if only one of them was moving, as opposed to both speeding against each other?
I am thinking there would not be much difference, as if the first ship is stationary, it will still experience the other crashing at him with the speed near that of the light. The external observer would also confirm this.</p>
<p>If this is so, would there be any reason to accelerate particles near the speed of light in opposite directions as it is being done in CERN? I assume (may be wrongly) that the above observation for the spaceships can be applied to particles also. So, would it be enough if the particles are just accelerated in one direction to "bomb" a stationary object, in order for them to get scattered? Am I missing something that would apply to particles but not to larger objects (like ships) or even something more-fundamental?</p> | g14625 | [
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<p>Considering that there's a lot of debris in space and that impacts fling out rocks into space all the time, why do we only have one large natural satellite - the Moon? Shouldn't there be all kinds of rocks in all shapes and sizes orbiting the Earth?</p> | g14626 | [
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<p>I can't think of any better title. Here is the content that I got question
<a href="http://cnx.org/content/m10247/2.31/" rel="nofollow">http://cnx.org/content/m10247/2.31/</a></p>
<p>As it state the nature of DTFT's spectrum is periodic as it show in figure 1
<img src="http://i.stack.imgur.com/RHr9S.png" alt="enter image description here">
<img src="http://i.stack.imgur.com/892ct.png" alt="enter image description here"></p>
<p>However, in figure 3, spectrum is non-periodic
<img src="http://i.stack.imgur.com/lO3dP.png" alt="enter image description here"></p>
<p>So, the spectrum of DTFT is periodic or not or it is dependent on each case of $s(t)$</p> | g14627 | [
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<p>Where can I find pictures of the shadow of any of the <a href="http://en.wikipedia.org/wiki/Moons_of_Jupiter" rel="nofollow">Jovian moons</a> partially covering the <a href="http://en.wikipedia.org/wiki/Atmosphere_of_Jupiter#Great_Red_Spot" rel="nofollow">Great Red Spot</a>?</p>
<p>A series of such pictures over time would even be better. The idea is to learn more about the structure of the storm by observing how the shadow behaves as it is passing over the boundaries and body of the Great Red Spot storm.</p> | g14628 | [
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0.0021831959020346403,
0.03962043672800064,
-0.0006149101536720991,
0.05752108618617058,
0.008003... |
<p>Jupiter has many <a href="http://en.wikipedia.org/wiki/Jupiter_Trojan">Trojan asteroids</a> located at Lagrangian points L4 and L5 and <a href="http://en.wikipedia.org/wiki/Hilda_family">Hilda asteroids</a> dispersed between points L3, L4, and L5.</p>
<p>Does the Earth have similar satellites? If so, how many?</p> | g14629 | [
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-0.0... |
<p>This question is if the von Neumann–Wigner interpretation, aka "consciousness cause collapse" (see e.g. John von Neumann's 1932 book The Mathematical Foundations of Quantum Mechanics) is compatible with the quantum Zeno effect (see Sudarshan, E. C. G.; Misra, B. (1977) "The Zeno's paradox in quantum theory", Journal of Mathematical Physics 18 (4): 756–763) respectively its empirical observation (such as by Wineland 1989 or by Raizen 2002). Or if the Quantum Zeno effect falsies or created the possibility to empirically verify the von Neumann-Wigner interpretation.</p>
<p>Assume measuring the state of a system every second causes a zeno effect and measuring every three seconds causes an anti-zeno effect.</p>
<p>Now let's assume the state is measured every second and recorded. A proponent of the "consciousness causes collapse" interpretation would argue that the wave function only collapses when a conscious observer actually looks at the measurement results. </p>
<p>But what if the conscious observer first looks at only every third result and decides only afterwards on whether to look at the other results too. Will she observe the zeno effect depending on her future decision?</p>
<p>Wouldn't such an experiment show that either (1) the consciousness of the observer has no impact and there is a zeno effect even if two out of three measurement results are destroyed before a conscious observer looks at them or that (2) the observer has no free will and whenever she observes a zeno effect looking at every third measurement she can't help but looking at the other results too, and conversely if the first set of results she looks at shows an anti-zeno effect she has an irresistible urge to destroy the other results?</p>
<p>Well the first option looks more plausible to me, but it seems like something that could be experimentally tested.</p> | g14630 | [
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<p>So I've read a question on here about <a href="http://physics.stackexchange.com/questions/88824/capillary-action-in-a-slanted-tube">Capillary action in a slanted tube</a>, but my question goes a little further. Firstly though, could someone explain to me what is meant by the only answer to that question. The answer states that the lift force isn't dependant on the weight of the fluid whereas the capillary lift hight equation is a combination of the forces from gravity and capillary action. When I have tried to balance these equation for both a upright tube and a slanted tube I get different lift heights and masses of fluid lifted. I'll explain some more at the bottom of the question.</p>
<p>If we have a slanted tube that slants 15 degree to the right for 10mm and then 15 degree to the left (from normal - not going back to upright)for 10mm would this tube have the same lift height as a tube that slanted 15 degrees for 20mm? (Assuming the tube radius is constant in and equal). Essentially is there any issue with the fluid going around the bend?</p>
<p>As promised more explanation of what I've done thus far.</p>
<p>A tube filled to a given height has the same volume irrespective of the angle the tub is at (see <a href="http://math.stackexchange.com/questions/431236/volume-of-a-slanted-cylinder">Volume of a slanted tube</a>). So with this in mind and knowing that the side length of the cylinder up to the water level is longer than the height of the water (if the cylinder is slanted), we can comfortably say that to lift the same mass of water the height will be the same, but the length up the pipe will be lower.</p>
<p>However the lifting force from capillary action is based on the circumference of the pipe (2*pi*r), but <strong>this</strong> changes dependant on angle since a slanted pipe will have a cross section that is a ellipse. So I expect the lifting force to be greater, allowing for a greater amount of fluid to be lifted, thereby increasing the height that the fluid is lifted to.</p> | g14631 | [
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<p>Two distinguishable gases are in separate volumes $xV$ and $(1-x)V$ $(x\in [0,1])$ respectively, and the number of particles on each side is $xN$ and $(1-x)N$ respectively. The volumes are separated by some tap or something at first. If we then open the tap, the gases will mix, the ideal mixing entropy is given by
$\Delta S=-Nk_B(x\ln x + (1-x)\ln(1-x))$.</p>
<p>I'm trying to get this result using Gibbs' entropy formula $S=-k_B\sum_i P_i\ln P_i$.
My first way is considering the case of 1 particle, such that we only have 2 states with probabilities $x$ and $1-x$, so then $S=-k_B(x\ln x + (1-x)\ln(1-x))$. Then using that entropy is extensive we get the answer. Correct?</p>
<p>Now I'm trying to derive the entropy by using the binomial distribution: the chance of $n$ particles being in the volume $Vx$ is $P(n)=\binom{N}{n}x^n(1-x)^{N-n}$. Inserting this in Gibbs' formula yields:</p>
<p>$S=-k_B\sum_nP(n)\ln\left(\binom{N}{n}x^n(1-x)^{N-n}\right)$, then expanding the log gives
$S=-k_B\sum_nP(n)\left(\ln\left(\binom{N}{n}\right)+n\ln x +(N-n)\ln(1-x)\right)$, then using that $<n>=xN$ we get
$S=-Nk_B(x\ln x + (1-x)\ln(1-x))-k_B\sum_nP(n)\ln\left(\binom{N}{n}\right)$.</p>
<p>How do I get rid of this last term? Or is the problem that I calculated $S$ rather than $\Delta S$? </p> | g14632 | [
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<p>Can anyone please explain me on this matter along with day to day examples?</p> | g14633 | [
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<p>Consider the following parallel plate capacitor made of two plates with equal area $A$ and equal surface charge density $\sigma$:</p>
<p><img src="http://i.stack.imgur.com/E3Mkn.png" alt="enter image description here"></p>
<p>The electric field due to the positive plate is </p>
<p>$$\frac{\sigma}{\epsilon_0}$$</p>
<p>And the magnitude of the electric field due to the negative plate is the same. These fields will add in between the capacitor giving a net field of:</p>
<p>$$2\frac{\sigma}{\epsilon_0}$$</p>
<p>If we try getting the resultant field using Gauss's Law, enclosing the plate in a Gaussian surface as shown, there is flux only through the face parallel to the positive plate and outside it (since the other face is in the conductor and the electric field skims all other faces). </p>
<p>$$\Phi = \oint \vec{E}\cdot\vec{dA} = EA$$</p>
<p>where $E$ is the electric field between the capacitor plates. From Gauss's Law this is equal to the charge $Q$ on the plates divided by $\epsilon_0$</p>
<p>$$\frac{Q}{\epsilon_0}\implies E = \frac{Q}{A\epsilon_0} = \frac{\sigma}{\epsilon_0}$$</p>
<p>I know there is something fundamentally incorrect in my assumptions or understanding, because I frequently get conflicting results when calculating electric fields using Gauss's Law. I am, however, unsuccessful in identifying this. </p>
<p><strong>Edit:</strong> Also, another problem I noticed was that even if we remove the negative plate from the capacitor and then apply Gauss's Law in the same manner, the field still comes out to be $\sigma/\epsilon_0$ which is clearly wrong since the negative plate contributes to the field. So, maybe the problem is in the application of Gauss's Law. </p> | g14634 | [
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<p>Suppose we have the following experimental values for $\eta' \rightarrow \eta \pi \pi$ decay width:</p>
<p>$\Gamma_{\eta' \rightarrow \eta \pi^+ \pi^-} = 0.086 \pm 0.004$</p>
<p>$\Gamma_{\eta' \rightarrow \eta \pi^0 \pi^0} = 0.0430 \pm 0.0022$</p>
<p>We are investigating this decay in the isospin invariant limit and want to compare our results with experimental rates. So we should average over these 2 values to find the experimental decay width in this limit.
It is written in one paper that we should average</p>
<p>$\Gamma_{\eta' \rightarrow \eta \pi^+ \pi^-} = 0.086 \pm 0.004$</p>
<p><strong>2$\Gamma_{\eta' \rightarrow \eta \pi^0 \pi^0} = 0.0860 \pm 0.0044$</strong></p>
<p>in a specific way (which is not my question).
I don't know why we should <strong>twice</strong> the second value and then average? </p> | g14635 | [
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<p>In Landau's Fluid Mechanics p. 8 (2nd edition) he writes for the thermal expansion coefficient $\beta = (1/V) (\partial V/\partial T)_P$:</p>
<blockquote>
<p>For a column of gas in equilibrium which can be taken as a thermodynamically
perfect gas, $\beta T = 1$ [...]</p>
</blockquote>
<p>This is not not obvious to me. Can somebody provide me with a derivation or an argument under which circumstances I can approximate this expression like that?</p>
<p>Or is it as easy as taking Clapeyron's equation for $V$, i.e. $PV = NT \implies V = NT/P$, so that we get
$$
\beta T = \frac{TN}{VP} = 1
$$</p>
<p>This leaves me somehow unsatisfied; is there maybe a more physical argument for this?</p> | g14636 | [
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