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<p>I am trying to represent the result of a dimensional analysis calculation and I can't find an official document that lists the order that unit symbols should appear.</p>
<p>For example, when I google $5\text{ m}\times 2\text{ kg}$ or $2\text{ kg}\times 5\text{ m}$ the result is always meters first, or $10\text{ m kg}$. But when I plug both of those calculations into Wolfram Alpha the result has kilograms first, or $10\text{ kg m}$. </p>
<p>I would assume that Wolfram Alpha would take more care in displaying a mathematical results than Google but I would like an <strong>official reference (at least for SI)</strong> explaining the order unit symbols should appear and if possible other formatting rules. </p>
<p>EDIT: I (as a human) will not be doing the rearranging of the symbols so I am looking for a spec that will produce the same output every time.</p> | 4,369 | [
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<p>Kane and Fu proposed a few geometries how to create Majorana zero modes using a s-wave superconductor in proximity to a 3D topological insulator (TI).</p>
<p>-> <a href="http://www.physics.upenn.edu/~kane/pubs/p56.pdf" rel="nofollow">http://www.physics.upenn.edu/~kane/pubs/p56.pdf</a></p>
<p>I understand that we need the superconductor to induce the particle-hole symmetry and we need
the topological insulator to get a protected edge state at zero energy. But overall I must admit that I have no intuitive description for this process. Especially the importance of the Berry phase, the vortex or the magnetic flux quantum is not clear to me. Especially in the so called Antidot-experiment, where there's a hole in a s-wave superconductor on top of a TI and a magnetic flux quantum through this hole creates a Majorana zero mode.</p>
<p>It seems like a big question, but maybe someone can give a simple intuitive answer why we need all these ingredients and end up with a Majorana zero mode.</p> | 4,370 | [
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<p>I often read about s-wave and p-wave superconductors. In particular a $p_x + i p_y$
superconductor - often mentioned in combination with topological superconductors.</p>
<p>I understand that the overall Cooper pair wavefunction may have orbital momentum = 0 (s-wave)
or orbital momentum = 1 (p-wave) where the first one is spherically symmetric.</p>
<p>Now what does the splitting in a real ($p_x$) and imaginary ($p_y$) part mean? Why
is it written in this form and why is that important (e.g. for zero Majorana modes) ?</p> | 4,371 | [
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<p>This is a homework question, so please don't give me the answer outright. I just need help conceptually.</p>
<p>"A cylindrical shell of length 190 m and radius 4 cm carries a uniform surface charge density of σ = 12 nC/m2.</p>
<p>(a) What is the total charge on the shell? </p>
<p>Find the electric field at the ends of the following radial distances from the long axis of the cylinder.</p>
<p>(b) r = 2 cm"</p>
<p>To part (a) I answered 573nC</p>
<p>circumference*length*(charge density)=(2pi*.04)*190*12E-9=573E-9</p>
<p>Part b is obviously very difficult to calculate absolutely correctly, since there is no obvious gaussian surface perfectly orthogonal to the electric field at every point. However, it seems to me that a short cylinder with its axis aligned with the charged cylindrical surface would make a good approximation, and I believe that is what is expected of me in solving this problem.</p>
<p>So I'll do it with a cylinder of length 1m for simplicity's sake. Since (to a good approximation) the field will be orthogonal to the cylinder's curved surface at all points, and the flux through the ends will be 0, the flux through the curved survace will equal the field strength times the surface area of this surface, which will also equal the charge enclosed over epsilon naught (natural permittivity of space, I'll write this e0).</p>
<p>E*A=Q/e0</p>
<p>E=Q/(e0*A)</p>
<p>So the charge enclosed will simply be the charge in a 1m section of the charged cylinder.</p>
<p>Q=(2pi*.04)*12E-9</p>
<p>The surface area of my Gaussian surface is...</p>
<p>A=(2pi*.02)</p>
<p>(ends not included because the flux through the ends of the cylinder is 0)</p>
<p>E=.04*12E-9/(en*.02)=2710.581760219553</p>
<p>When I put this answer into Webassign (online homework, graded immediately) it is marked as wrong. My answer to part (a) is, however, correct. What is my problem?</p> | 4,372 | [
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<p>In a laboratory course we had to perform an experiment with a pendulum (just an iron weight on a wire) and play around for some time with its wire's length and so on. </p>
<p>This was quite boring and we decided to make something more interesting:</p>
<p>We took two magnets (like <a href="http://www.artec-educational.com/images/8078-Ferrite-Ring-Magnet-%2810-piece-set%29---L.jpg" rel="nofollow">this</a> one) an tied one on the previously mentioned wire (which is made of plastic), and placed the other one on the surface of the table (I've tried to create <a href="http://s9.postimg.org/f7epljikt/Schematic.png" rel="nofollow">a schematic</a>).</p>
<p>We tried to create a regular damped oscillator but the lab's staff told us it's not a good approximation, the problem is that we've only had one semester of mechanics and we've just began electricity.</p>
<p>So my question is what what be a good relatively easy to understand theory which we actually apply to our measurements (we've measured the amplitude , the angle the time we've just video taped the whole motion).</p> | 4,373 | [
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<p>How can a light passed though a single slit produce a similar interference pattern to the double-slit experiment? How does the diffracted wave produce the points of cancellation and reinforcement, if there is only one wave?</p> | 689 | [
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<p>Thomas Young used a single slit between the light source and the double slits. I can't understand why did he used the single slit, since the light from only one source is coherent already or isn't it? Does the narrow single slit make incoherent source coherent? </p> | 4,374 | [
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] |
<p>From Wikipedia:</p>
<blockquote>
<p><a href="https://en.wikipedia.org/wiki/Bremsstrahlung" rel="nofollow">Bremsstrahlung</a> is electromagnetic radiation produced by the
deceleration of a charged particle when deflected by another charged
particle, typically an electron by an atomic nucleus. The moving
particle loses kinetic energy, which is converted into a photon
because energy is conserved.</p>
</blockquote>
<p>Isn't energy conserved for the moving particle in an electrostatic potential, $E_{kinetic} + E_{potential} = \frac{mv^2}{2}+\frac{kqQ}{r}$? If so, where does the extra energy for photons come from?</p>
<p>Why don't electrons in atoms radiate away their energy?</p> | 4,375 | [
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<p>In classical mechanics the motion of a particle is bounded if it is trapped in a potential well. In quantum mechanics this is no longer the case and there is a non zero probability of the particle to escape the potential through a process call quantum tunneling. </p>
<p>This seems extraordinary from the point of classical mechanics because it implies the particle must cross a zone where it has imaginary momentum. I understand that from the point of view of quantum mechanics there is a non zero probability for the particle to be in such zones. </p>
<p>What is it know about the behaviour of the particle in this zone? </p>
<p>Links to research experiments or papers would be appreciated. </p> | 4,376 | [
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] |
<p>My <a href="http://en.wikipedia.org/wiki/Incandescent_light_bulb" rel="nofollow">light bulb</a> cast a clear light toward adjacent wall and I can clearly see, that <a href="http://en.wikipedia.org/wiki/Incandescent_light_bulb#Filament" rel="nofollow">wire filament</a> inside bulb shakes, though lamp itself does not moves even an inch</p>
<p>What is causing this? Is it a permanent effect, happening all the time? Or is it a syndrome of near end of life of this current light bulb?</p> | 4,377 | [
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<p>It is known fact, that boiling point of water decreases by decreasing of pressure. So there is a pressure at which water boils at room temperature.
Would it be possible to cook e.g. pasta at room temperature in vacuum chamber with low enough pressure?</p>
<p>Or "magic" of cooking pasta is not in boiling and we would be able to cook pasta at 100°C without boiling water (at high pressure)?</p> | 4,378 | [
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<p>In expanding the classical Klein-Gordon field in Fourier space to write it in terms of $\phi(\mathbf{p})$ instead of $\phi(\mathbf{x})$, I reached the following result.
$$\int \mathrm{d}^3p\exp({i\mathbf{p}\cdot\mathbf{x}})\left[\frac{\partial^2}{\partial \mathrm{t}^2}+|\mathbf{p}|^2 + m^2\right]\phi(\mathbf{p},t) =0$$</p>
<p>Now, how is it concluded that
$$\left[\frac{\partial^2}{\partial \mathrm{t}^2}+|\mathbf{p}|^2 + m^2\right]\phi(\mathbf{p},t) =0.$$</p>
<p>I suspect there is a physical rather than mathematical reasoning for this, since, at least apparently, the integrand could have the whole complex plane as its range. (Or is the assumption that $\phi(\mathbf{x})$ is real, and therefore $\phi ^*(\mathbf{p})=\phi(\mathbf{-p})$, relevant?)</p> | 4,379 | [
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<p>If I understand this correctly, accelerating charges lose energy in the form of EM waves because they change the electric and magnetic fields, which "costs" energy. Does that mean that accelerating masses lose energy too, because they change the gravitational field (i.e. curve spacetime)?</p> | 4,380 | [
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<p>Measuring temperature in joules instead in the artificial units of Kelvin would render entropy as a dimensionless quantity. This is quite appealing since entropy has always been quite a misterious quantity: it is used a measure of the disorder in a system but its units are J/K, which makes it really hard to interpret. The reason why entropy and temperature were defined this way is because they were studied before the athomical composition of matter was completeley accepted. You can read more about this in these posts:</p>
<p><a href="http://physics.stackexchange.com/questions/60830/why-isnt-temperature-measured-in-joules">Why isn't temperature measured in Joules?</a>
<a href="http://physics.stackexchange.com/questions/78137/should-entropy-have-units-and-temperature-in-terms-of-energy?lq=1">Should entropy have units and temperature in terms of energy?</a></p>
<p>Arieh-Ben Naim, a chemistry from Israel, has really good books in this topic such "Entropy demystified". He is one the main defenders that entropy should be a unitless quantity.</p>
<p>I have always like to understand the gist of things, and the first step to understand a magnitud like entropy is understanding how it can be measured. For instance, I think I know what a speed is because I can reason in terms of space and time. But in entropy, as the way is normally defined, this is hard and tricky, and all the explanations I have heard so far seem to me like quite far-fetched.
So here it goes my question. Let's accept for the sake of argument that we are considering entropy a dimensionless quantity. Now we heat a gas, and we calculate the entropy associate to this process. The result would be a number, whatever. Let us say that number is going to be 100. <strong>How to interpret this number? What would it be measuring?</strong> And finally, <strong>do you agree with this vision of temperature units?</strong></p> | 4,381 | [
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<p>I was working out the minimum tangential velocity required for a swing to complete a full revolution and assumed the centripetal force is equal to the centrifugal force, so that I could set the weight force equal to the formula for centripetal (i.e. net force 0 at the top so swing won't fall). I'm pretty sure the answer is correct but doubt my reasoning.</p> | 4,382 | [
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<p>I have a couple of different LED flashlights. One of them has three different "modes" of brightness, and the way it controls it is via pulse width modulation (PWM). Here is a picture that illustrates how it works: </p>
<p><img src="http://i.stack.imgur.com/GF3LQ.gif" alt="enter image description here"></p>
<p>I know that this particular flashlight's PWM circuit operates at about 120Hz. What this means is that when you move something very quickly under it, when running a low duty cycle, it produces a strobe-light effect, where you'll see many "copies" of the moving object. It reminds me of the way video-games are rendered, and it actually creates a really neat effect because you only "see" very small time-slices. Watching running water this way is absolutely fascinating. </p>
<p>From empirical observation I determine that on the lowest setting it seems to be on about a 2-5% duty cycle. The ghost-images produced are remarkably sharp. On Medium, I reckon it's about 25 to 30%. </p>
<p>Something I've noticed very recently is that when I use this flashlight under dark-adjusted conditions, the brightness that is perceived definitely doesn't seem to scale linearly. I have no scientific light intensity equipment to perform measurements with, but I am more or less convinced that a 1000 lumen light on a 2% square-wave duty cycle appears brighter than a 20 lumen light, all else being equal (which would include incident light energy). </p>
<p>I think there may be some biological explanation for this. Is this an effect that has been observed by others? </p> | 4,383 | [
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<p>Terminal Velocity depends on two things- surface area and speed. These are inversely proportionate.</p>
<p>If both these variables affect terminal velocity, why do parachutes slow you down? Initially you had a small surface area but a fast speed- with the parachute you have a larger surface area but lower speed. You have increased one variable but decreased the other. Therefore why do parachutes decrease speed?</p> | 4,384 | [
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<p>As it is.</p>
<p>As I study through classical mechanics and quantum mechanics, I began to wonder whether there is a relationship between classical electromagnetic wave frequency and quantum wave function and de broglie frequency).</p>
<p>I think this is somehow related to quantum electrodynamics...but anyway.</p> | 4,385 | [
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<p>Some explanations of the device base it on a simple echo of light: "The camera transmits invisible near-infrared light and measures its “time of flight” after it reflects off the objects. Time-of-flight works like sonar: If you know how long the light takes to return, you know how far away an object is." (<a href="http://www.wired.com/gadgetlab/2010/11/tonights-release-xbox-kinect-how-does-it-work/">wired.com</a>). Is it so easy? On other hand, the developers, Primesense, speak about "a sophisticated parallel computational algorithm to decipher the received light coding". And they claim to avoid noise from ambiance light and to be able to obtain a resolution of 1cm at 2 meters.</p>
<p>A motivation to ask this here in physics is that some other questions were asking for measurement of light speed with household devices.</p> | 4,386 | [
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<p>Consider a spherical body of uniform density $\rho$ and initial radius R. You can imagine this body containing another sphere of radius R/2 which touches the center and the periphery of the larger sphere. The smaller sphere has 8 times less mass, since the mass goes as the radius cubed.</p>
<p>If you let the big sphere collapse gravitationally along with the smaller one, keeping the density uniform, the whole thing just shrinks proportionally. The Schwarzschild radius is proportional to the mass, so $R_S= 2GM/c^2$ for the larger mass, and for the smaller sphere $r_S= 2GM/8c^2$, one eigth as big. So when the large mass collapses, the smaller one hasn’t.</p>
<p>It follows that the smaller sphere can still communicate with things outside, but the larger sphere should prevent it from doing so. The outgoing world lines at P due to the smaller sphere must be trapped by the spacetime effects of the residual portion ie, the portion represented by the larger sphere minus the smaller one.It seems that the remaining larger irregular shaped mass has a greater attractive power than the regular shape of greater mass at specific points like P.Is it really so?</p>
<p>For a sphere of a larger fraction of the size, say 3/5R, which touches the boundary of the larger sphere at some point and includes the center [of the larger sphere, the smaller Schwarzschild radius is about .2 of the larger Schwarzschild radius.</p>
<p>When the larger sphere collapses the smaller one has not collapsed---it has world lines in the outward direction.The smaller sphere is not supposed to have a singularity on its own.But it contains the singularity of the bigger mass , though not at its center.Is the singularity, [of the larger sphere], produced by the effect of the residual portion?</p>
<p>Related question: Can we conclude solely on the basis of these “Experiments’ that different parts of the body can exchange signals after it has collapsed?
[QM effects are not being considered in this problem]</p> | 4,387 | [
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<p>My book says a capacitor is two conducts being connected by an insulator. Now let's take a parallel plate capacitor to simplify the problem I have.</p>
<p>Suppose I got two parallel plate capacitor in series and I hook the circuit up with a battery. </p>
<p><img src="http://i.stack.imgur.com/YWnG8.jpg" alt="enter image description here"></p>
<p>As soon as I hook it up, electrons flow (forget conventional current for now) into on the right plate and builds up on that capacitor (and spreads on the surface of conducting plate) and remains stuck there because there is an insulator that blocks the electrons from going anywhere. </p>
<p>Now here is my confusion, how does the left plate of $\ C_1$ even build the positive charges and how do the current even run through the circuit if there an insulator blocking the electrons from moving? Is there even current through the circuit?</p> | 4,388 | [
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<p>I'm just struggling a little with this question:</p>
<p>A uniform sphere, of radius $R$, contains a spherical cavity of radius $R/4$, whose centre is $3R/8$ from the surface. The diameter passing through the centres of the sphere and cavity meets the surface at points $X$ and $Y$. Find the ratio of the gravitational field at $X$ and $Y$.</p>
<p>My attempt at the solution goes something like this:</p>
<p>Using the superposition principle, the gravitation field due to the whole mass is equal to the sum of the gravitational fields due to the remaining mass and the removed mass.</p>
<p>The gravitational field due to a uniform solid sphere is zero at its centre. Therefore, the gravitational field due to the removed mass is zero at its centre.</p>
<p>The gravitational field due to the solid sphere is equal to the gravitational field due to the remaining mass. Now we know g acts towards the centre of the sphere. As such, both the gravitational field of the combination of the sphere and removed mass and the gravitational field of the sphere only act in the same direction, so we can use the scalar form of the equation.</p>
<p>Therefore the gravitational field is given by $g=GMr/R^2$.</p>
<p>Then insert $r=-R$ and $R$ for the gravitational field at $X$ and $Y$.</p>
<p>But this doesn't seem to be correct as it is just the same as if the removed mass wasn't there..... have I gone wrong in my logic somewhere?</p> | 4,389 | [
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<p>Assuming a solid rectangular plate, hinged along one edge. How does one calculate the mass of the plate if the force necessary to lift the opposite edge is known?</p> | 4,390 | [
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<p>Can an Electric Field with field lines Like So Exist:</p>
<p><img src="http://puu.sh/tWkJ" alt=""></p>
<p>One Of my friends said it couldn't as the field lines here are not conservative ; so it cannot exist ; Is he right?</p>
<p>Or can it be made to exist</p> | 4,391 | [
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<p><a href="http://en.wikipedia.org/wiki/Bell_test_experiments#Conduct_of_optical_Bell_test_experiments" rel="nofollow">Wiki</a> tells us that <em>In practice most actual experiments have used light, assumed to be emitted in the form of particle-like photons (produced by atomic cascade or spontaneous parametric down conversion), rather than the atoms that Bell originally had in mind. The property of interest is, in the best known experiments, the polarisation direction</em></p>
<p>What device can actually be used for that source which creates a photon pair with entangled polarisations?</p> | 4,392 | [
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<p><img src="http://i.stack.imgur.com/zubVb.jpg" alt="enter image description here"></p>
<p>I have seen in <a href="http://books.google.fr/books/about/Molecular_theory_of_capillarity.html?id=_ydSF_XUVeEC&redir_esc=y" rel="nofollow">http://books.google.fr/books/about/Molecular_theory_of_capillarity.html?id=_ydSF_XUVeEC&redir_esc=y</a> that there is a formula for the contact angle with a solid wall of a liquid-gas interface. The formula is</p>
<p>$$ \cos \theta=\frac{ \sigma_{liquid-solid}-\sigma_{gas-solid}}{\sigma_{gas-liquid}}$$
where $\sigma_{AB}$ are the surface tensions between $A$ and $B$. </p>
<blockquote>
<p>Does this formula work also in the case where instead of gas we have another liquid?</p>
</blockquote> | 4,393 | [
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<p>It is known that electromagnetic (EM) fields action on particles is limited to the Lorentz force action. In terms of spinors and currents, the EM field:</p>
<p>(i) rotates the Dirac current around the direction of the field $B$ to the angle proportional to the magnitude of $B$, and</p>
<p>(ii) "accelerates" the Dirac current in the direction of $E$ to the extent proportional to the magnitude of $E$.</p>
<p>Action of Lorentz force exhausts all possible rotations and boosts.</p>
<p>In fact, nothing else could "happen" to the Dirac current (which is a Minkowski space 4-vector) except (a) rotation and boost described above, and (b) change in magnitude of the Dirac current vector prohibited by conservation of charge and/or mass.</p>
<p>Unless the action of weak and strong forces is always limited to change of mass/charge of the particle, is it possible to consider the effect of these forces on particles as a kind of "special" electromagnetic action?</p> | 4,394 | [
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<p>Is the universe finite, both in the sense of being a closed spacetime manifold, as viewed from the macro level, but also in the sense of being fully discrete and finite in all of its intricate quantum level construction?</p>
<p>The most popular current research, i.e. string theory, builds a machinery on top of a continous notion of spacetime. Would a more accurate model of the physical world have to build on top of a finite, discrete, network like, relational spacetime model? </p> | 4,395 | [
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<p>In this experiment, a number of coins are put into a cup <em>full</em> of water, without spilling it.</p>
<p><a href="http://www.youtube.com/watch?v=N2mKpZHnEzw" rel="nofollow">http://www.youtube.com/watch?v=N2mKpZHnEzw</a></p>
<p>Firstly, let me clarify one thing. </p>
<blockquote>
<p>If you fill up a cup of water to the brim, in such a way that even another <em>drop</em> of water will cause it to overflow, <strong><em>can this cup take a coin, instead of a water-drop</em></strong>?<br>
- If no, then it doesn't matter and there's no point to this question.<br>
- If yes, then my question is this: <em>why another coin</em> and not another water-drop?</p>
</blockquote>
<p><strong>---This part exists only if the answer to the question above is yes---</strong> </p>
<p>They say it's because of surface tension, but I still don't get how that explains it. If the surface tension can hold together <em>another coin</em>, then why not <strong><em>another drop</em></strong> (which actually has less volume than a coin)?</p>
<p>The only reason I can think of is that the adhesion between the water and the coin is high, which sorta pulls the water molecules towards the coin, increasing the density of water immediately around the coin - thereby making up for the extra space the coin takes.<br>
<em>(But thinking about that, that doesn't seem to make much sense either. The coin is at the bottom, and I don't know if adhesive forces can produce such increases in density.)</em></p>
<p>So: what <em>is</em> the reason for this? Why a coin and not another water-drop?</p> | 4,396 | [
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<p>Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I think "inverting" may have been the word the author used.)</p>
<p>The paper was in one of the endorsed groups (not General Physics), and seemed quite authoritative. But I've never seen this property mentioned elsewhere, and wanted to know:</p>
<ol>
<li><p>A reference, as stupidly I didn't note the paper's ArXiv code at the time (The reference needn't be to that or another ArXiv paper of course - Quite likely this is better explained in some other source such as a textbook.)</p></li>
<li><p>Whether this is considered just a curiosity with no known use or, like the Lorentz transforms, which are another well-known Maxwell Equations invariant, does it have any practical application?</p></li>
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<p>While reading Stanislaw Lem's essays on advanced civilizations, I had a question: When did the earliest generation of <a href="http://en.wikipedia.org/wiki/Population_1_star#Population_I_stars" rel="nofollow">population 1 star</a> systems <a href="http://en.wikipedia.org/wiki/Star_formation" rel="nofollow">form</a>? How much older could they reasonably be than our star system?</p> | 4,398 | [
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<p>Let's say we are building Nd:YAG laser.
It is optically pumped by some linear xenon flash lamps, it absorbs light around 750nm and 800nm, and emitted light is at 1064nm.</p>
<p>The question is why doesn't 1064nm emission from the flash lamps interfere with laser operation?</p>
<p>Why doesn't 1064nm photons emitted in the Nd:YAG at 'wrong' directions (not coaxially to the resonator path) and reflected back and forth from the cylindrical/oval reflector (for the flashlights) interfere with the laser emission?</p>
<p>As far as I see it, both these factors should consume precious atoms in excited state, and probably require some 1064nm filter around the Nd:YAG rod...</p> | 4,399 | [
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<p>I wish to study supersymmetry in field theory(sometime in december). However, I am quite not sure what is needed for its study. In supersymmetry, I just want to get the mathematical idea, such as its algebra. I will finish a course in QM this semester. I have studied some lie algebra (Cahn, Georgi). I also have some knowledge about classical field theory such as E-L equations, yang-mills theory, gauge invariance, symmetry breaking, higgs mechanism which I acquired through the study of solitons. I DONT HAVE ANY KNOWLEDGE OF QUANTUM FIELD THEORY. Is this knowledge enough to study supersymmetry? What exactly in supersymmetry can I hope to learn in addition to the mathematics? WOuld it be possible for me to apply it to the standard model?</p>
<p>Hope this will not be closed as too specific. I am looking for brief information on what exactly can one study in supersymmetry and its prerequisites. </p> | 4,400 | [
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<p>I want to know from the smallest possible originating structures how the light I see generated from heat is made by atoms themselves.</p> | 4,401 | [
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<p>I know a family that grows fruit such as blueberries in a climate that frosts on occasion. When this happens, they turn on sprinklers which covers the buds and fruit with a layer of water which turns to ice.</p>
<p>Why would this layer of ice prevent damage to the plants/fruit? Perhaps it insulates them, keeping temperature at 0 degrees but now below it?</p> | 4,402 | [
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<p>At CMB recombination (z=1090), what is the radial extent of the last scattering "shell"?
a) Delta(z) = ....
b) Delta(comoving angular distance)= ....Mpc</p>
<p>The WMAP first-year parameters give
Delta(z) = 195. Is this still correct?</p> | 4,403 | [
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<p>The models/depictions I've seen of warp bubbles show space compressed ahead of the bubble and expanded behind, so that the space inside the bubble moves with respect to the space outside. If that is so, then what is happening at the sides? It would seem that there is some sort of shear taking place between the space inside and outside. Is that correct, or is that based on a misinterpretation of the model?</p> | 4,404 | [
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<p>I am currently finishing my undegraduate degree in physics and would like to do PhD in Theory of Condensed Matter field. Could you give advice on which are good groups/supervisors in the field. Please, justify by adding citations to important research papers they have produced, any awards received etc.</p> | 4,405 | [
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<p>Is there any way in which a bound state could consist only of massless particles? If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy cause it to travel on a time-like trajectory?</p> | 4,406 | [
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<p>If water is flowing through big pipe is branched into 4 branches of small pipe. Lets say the flow is around 4 m/sec. </p>
<p>I have the following questions:<br/></p>
<ol>
<li><p>What will be the flow rate in each of the pipes? I would be knowing diameter, height of the pipes. Considering all pipes are rigid.<br/></p></li>
<li><p>What will be the flow rate in each of the pipes, if I close one pipe of the 4 branches? Will water flow speed increase in other 3 pipes? If yes, how we can calculate the gain of speed of flow?<br/></p></li>
<li><p>What if the pipes are non-rigid, will that have any effect?</p></li>
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<p>In my research, I found that the speed of light is not fixed. IS it true?</p>
<p>Namely, We know that light refracts when the medium it travels through changes. Actually, light travels in the same medium without refraction . This is a relative motion in two dimension. </p>
<p>However, in the medium light up to ‘’(△v)t ’’ is behind of observer. The wavelength of the light entering the medium, shortened according to the wavelength in vacuum ( such as a compressed spring). Observed by the observer's motion a relative movement. According to v > v2. (v2 =c ). In water do not refracted light only according to the observer, up to (△v)t been remains behind in time. So, speed of the observer is greater than speed of light in the medium. Electromagnetic waves loses speed while passing inside medium.</p>
<p>I tested it several times, it is possible to explain with equations of relative motion in two dimension.</p>
<p>This mean is that; speed of our universe is ''c'' and same direction spherical wave and this speed creates time. ( All masses are moving in the same direction with speed of ''c'', this way we can not observe this speed)</p>
<p>I also observed this; the light coming from upright to x and y coordinates ( Normal) do not refract, but shorter (We observe an object a higher position than initial position in water) . Is this right?</p>
<p>We can explain this with the equations of relative motion in two dimention. How can we, assuming the Fermat and snell says true? How can I explain it with the equations of relative motion in two dimensions? If I am wrong, could you please explain me why.</p> | 4,408 | [
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<p>I guess this is more of a chemistry question, but whatever. I think it's interesting.</p>
<p>Suppose you had two bare atomic nuclei. For concreteness, lets assume the nuclei are the same with atomic number $Z$. Lets bring in a single electron and focus on the ground states of the nuclei.</p>
<p>When the nuclei are far apart, the ground states are degenerate. When we bring the nuclei together, the ground state splits into the bonding and anti-bonding orbitals. Let $\Delta E$ represent some measure of the energy difference between the bonding and anti-bonding orbitals.</p>
<p>From intuition, I would expect $\Delta E$ to increase with decreasing internuclear distance $R$. What happens as $R$ shrinks to zero?</p>
<p>I expect the bonding orbital to become the ground state of an "atom" with charge $2Z$. Is that correct? More importantly, what happens to the anti-bonding orbital?</p>
<p>This isn't an exercise in the Born-Oppenheimer Approximation. I magically hold the nuclei at a distance $R$, so their repulsion doesn't matter. Also, electron-electron repulsion doesn't matter because I only introduce one electron.</p> | 4,409 | [
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] |
<p>What experiments could provide observable "stringy" effects.</p>
<p>All valid experiments are acceptable (also theoretical experiments).</p> | 4,410 | [
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<p>I am wondering if it makes sense to state that the upper limit is roughly 10<sup>12</sup> eV (up to know the physics probed by the LHC seems to be pretty consistent with the SM) and the lower one is ... the upper bound for the photon mass (somewhere between 10<sup>-14</sup> and 10<sup>-26</sup> eV according to <a href="http://arxiv.org/pdf/hep-ph/0306245v2.pdf" rel="nofollow">http://arxiv.org/pdf/hep-ph/0306245v2.pdf</a>).<br>
If I understand well the argument in this article, one could say the larger value 10<sup>-14</sup> eV comes from the Standard Model of particles (the photon would acquire mass by the Higgs mechanism, its large-scale behavior beeing effectively Maxwellian) while the smaller value 10<sup>-26</sup> eV would come from the standard model of cosmology (the value of the galactic field today leading to this value from the hypothesis of a "Proca regime for all scales" ??).</p>
<p>Edit 06/12/13: I removed the expression : "domain of validity" that sounds too much like a mathematical closed interval. It is not adapted to the Standard Model because it is not a theory. I have chosen the formulation "phenomenological spectrum" to insist on the fact that this spectrum can be enriched with new particles whose masses are in the same energy range as the old ones. </p> | 4,411 | [
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<p>What methods could be used to determine (<em>or</em> estimate within a <em>reasonable</em> margin of error) the mass of a living human's limbs, short of cutting them off? And more interestingly, how can this be done without any high tech equipment, just with the means commonly found in households?</p>
<p>A scale for example is allowed. An MRI isn't ;)</p> | 4,412 | [
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<p>Leonard Suskind gives the following formulation of the energy-momentum tensor in his Stanford lectures on GR (#10, I believe):</p>
<p>$$T_{\mu \nu}=\partial_{\mu}\phi \partial_{\nu}\phi-\frac{1}{2}g_{\mu \nu}\partial_{\sigma}\phi \partial^{\sigma}\phi$$</p>
<p>In an intro to GR book I find this formulation of the same:</p>
<p>$$T^{\mu \nu}=[\rho+\frac{P}{c^2}]u^{\mu}u^{\nu}+g^{\mu \nu}P$$</p>
<p>I'm having trouble seeing how they are describing the same thing. Is $\partial_{\sigma}\phi \partial^{\sigma}\phi$ equal to $P$? In the book equation, $u^{\nu}$ and $u^{\mu}$ are four velocities differentiated w.r.t. time. Where do these appear in Suskind's equation? What happens to the factor of $\frac{1}{2}$? If I understand the lectures correctly, $\rho$ is essentially the $T^{00}$ component of the tensor in the Newtonian limit. I don't see how the second equation reduces to $\rho$ in that limit (slow and flat).</p>
<p>I appreciate your help.</p> | 4,413 | [
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<p>A properly oriented calcite crystal will separate an unpolarized beam into two beams, one vertically polarized and one horizontally polarized. Other polarizers pass just one polarization and absorb the perpendicular one.<br>
Is there a device that splits an unpolarized light beam into a right circulaly polarized one and a left circularly polarized one, instead of just absorbing one or the other?<br>
(If so, please tell me where I can buy one.)<br>
If not, is this theoretically impossible?</p> | 4,414 | [
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<p>Approaching the following question:</p>
<blockquote>
<p>Consider two experiments in which 2 moles of a monatomic ideal gas are
heated from temperature $T$ to temperature $T + \Delta T$: in the
first experiment the volume $V$ is kept constant, in the second
experiment the pressure $p$ is kept constant. How much more heat is
needed in the second experiment than in the first experiment to raise
the temperature by the given amount $\Delta T$?</p>
</blockquote>
<p>The answer is $2 R \Delta T$.</p>
<p>The origin of the problem may be found <a href="http://online.physics.uiuc.edu/cgi/courses/shell/phys213/practice.pl?exam1/su11" rel="nofollow">here</a> under <em>Question 14</em>.</p>
<p>I am confused as to home to come to this conclusion. I believe I am able to utilize $pV = N k_B T$ and $VT^\alpha = const$, $pV^\gamma = const$ but I am unsure of how the two constants apply to this.</p>
<p>Do both constant apply to each of the experiments? How do I manipulate these equations to achieve my desired result?</p> | 4,415 | [
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<p>I'm looking around the net to find good resources on how to compute total radiation flux from a given star at a given orbiting distance.</p>
<p>Ideally I'd like to get not just the $W/m^2$ of the star, but also the expected high-energy particles, EM, thermal, solar wind pressure.. well, the works.</p>
<p>Everywhere I looked they seem to compute these values for our Sun and at 1AU, then I'm left to wonder how this relates to stellar mass, composition type, luminosity, distances, etc. </p>
<p>In the end, I'm trying to quantify a sort of habitability range around a given star. Much in the way of saying: well, given this blue-hypergiant you could get close to about $40$ $AU$ before you get toasted in your puny spacecraft. Or, habitable planets could exist between $100$ AU and $120$ AU.etc..</p>
<p>I would have thought this would have been more common around sf projects, but radiation seems to go unnoticed in most sf themes.</p> | 4,416 | [
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<p>In cosmology, we have two quantities and I want to understand the physical relation between these two :</p>
<p>$\chi = \int_{t_e}^{t_0}c\frac{dt'}{a(t')}$ : the comoving distance with $t_e$ the time at emission and $t_0$ the current cosmic time</p>
<p>$\eta_0 = \int_{0}^{t_0}\frac{dt'}{a(t')}$ : the conformal time with $0$ the time at Big-Bang and $t_0$ the current cosmic time</p>
<p>My question are :</p>
<p>1) Is it possible to know the conformal time of a galaxy only knowing its comoving distance from us</p>
<p>2) What are the physical meaning difference between $\eta$ and $\frac{\chi}{c}$ ?</p>
<p>3) What are the physical meaning difference between $\chi$ and $c \eta$ ?</p>
<p>Than you very much !</p> | 4,417 | [
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<p>Picture yourself standing on a ball that is expanding at such a rate that it makes you stick to the ball.
Everything in the universe is expanding at this same rate.
To escape the earths gravitational pull we would need to jet upward faster than the expansion of the earth.
Each object expands at a different rate on its surface according to its size.
Thus different gravity affects for different size planets.</p>
<p>When in space we are subject to being affected by the most distant body if we stand in its way.</p>
<p>I just can not explain the reaction of our tides with our moon.</p>
<p>Have any scientists seriously considered an idea like this?</p>
<p>Follow up July 23</p>
<p>I am no scientist, but I think someone with more knowledge might explore this idea a little further.</p>
<p>At the very lease the idea that every thing in the total universe is expanding, including all parts of the atom can be used as a simple way to see formulas and the same results to the effects of gravity of anything on the surface of a sphere planet or a donut shaped planet.</p>
<p>The area of mass will grow but the density will remain the same.</p>
<p>The idea can be cross referenced by light shifting etc, to see if it falls in line with the known action of planet gravity and the known expansion affect of the whole universe.</p>
<p>Maybe the gravity affect of a planet on its surface dweller is a completely different force than is the force that maintains the orbits of planets. keplers law I believe.</p>
<p>What happens when we have an eclipse of the moon?, does the earths orbit around the sun change for time of this eclipse?</p>
<p>My summary is that if all scientists can not explain gravity totally, then maybe the common thought for all these years is not completely a correct one.</p> | 4,418 | [
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<p>In Fick's first law, the diffusion coefficient is velocity, but I do not understand the two-dimensional concept of this velocity. Imagine that solutes are diffusing from one side of a tube to another (this would be the same as persons running from one side of a street) to unify the concentration across the tube.</p>
<p>Here we have a one-dimensional flow in x direction. The diffusion coefficient should define the velocity of solutes or persons across the tube or street direction. How the two-dimensional velocity does this? I wish to understand the concept to imagine the actual meaning of the diffusion coefficient.</p> | 4,419 | [
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<p>While hammering a nail (before it is in the wall) it is pretty evident that the tip of the nail is going to be applying a force directed along th axis of the nail, then why is it said that pressure is always non directional ?</p> | 138 | [
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<p>In our quantum mechanics script, it states that $[L^2, X^2] = 0$ and $[L^2, P^2] = 0$, therefore for the following Hamiltonan</p>
<p>$$H = \frac{P^2}{2m} + V(X^2)$$</p>
<p>it is that $[H, L^2] = 0$ therefore $H$ and $L^2$ have the same eigenvectors, and then it continues to calculate orbitals of the hydrogen atom.</p>
<p>My question is: Is there a nice and simple proof of $[L^2, X^2] = 0$ and $[L^2, P^2] = 0$?</p> | 4,420 | [
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<blockquote>
<p>Due to application of force tow blocks of mass 1Kg and 0.5Kg move together. Each block exerts a force of 6N on each other. What is the acceleration by which both the blocks move?</p>
</blockquote> | 4,421 | [
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<p>It seems that a common statistical model for the count numbers of a photomultiplier is a Poisson distribution whose parameter $\lambda$ equals to the square-root of the number of counts.(e.g. <a href="http://www.sciencedirect.com/science/article/pii/S1350448711005750" rel="nofollow">http://www.sciencedirect.com/science/article/pii/S1350448711005750</a>).</p>
<p>This in particular, implies that the variance of the resulting statistic </p>
<ol>
<li>increases with the number of photons to detect,</li>
<li>is not directly dependent from the duration of the counting process.</li>
</ol>
<p>I did not manage to find the basis of this modeling choice. If somebody has some intuitive idea or a good reference I will apreciate. (I am not physicist and maybe I make a bad interpretation of the modeling applied to PM)</p> | 4,422 | [
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<p>Consider the Hamiltonian $H = -J_\text{F}S^{(1)}_zS^{(2)}_z + J_{AF}S^{(1)}_zS^{(2)}_z$, describing the graph</p>
<p><img src="http://i.stack.imgur.com/3lg1R.png" alt="enter image description here"></p>
<p>Here, F means ferromagnetic and AF means antiferromagnetic interactions. I am having problem with the value of $S^{(1)}_zS^{(2)}_z$.Someone suggested to me that
$$S^{(1)}_z=\frac{1}{2}\begin{pmatrix}
-1 & 0 &0 &0 \\
0&-1 &0 &0 \\
0 &0 &1 &0 \\
0 &0 &0 &1
\end{pmatrix},\quad S^{(2)}_z=\frac{1}{2}\begin{pmatrix}
-1 & 0 &0 &0 \\
0&1 &0 &0 \\
0 &0 &-1 &0 \\
0 &0 &0 &1
\end{pmatrix},$$ and therefore $$S^{(1)}_z\cdot S^{(1)}_z=\frac{1}{4}\begin{pmatrix}
1 & 0 &0 &0 \\
0&-1 &0 &0 \\
0 &0 &-1 &0 \\
0 &0 &0 &1
\end{pmatrix}.$$</p>
<p>On the other hand, from page 7 of <a href="http://web.uconn.edu/~ch351vc/pdfs/spin1.pdf" rel="nofollow">these notes on Pauli spin matrices</a>, I know that for two spin systems $$\Sigma_z = \begin{pmatrix}
2 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & -2 \\
\end{pmatrix}.$$ I asked the person but never got a reply. I don't see what is the difference between $S^{(1)}_z\cdot S^{(1)}_z$ and $\Sigma_z$; when I should use what?</p> | 4,423 | [
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<p>Object A can move at 50km/h, wants to intercept object B (currently $15^{\circ}$, east of north from A) moving at 26km/h, $40^{\circ}$ east of north. What angle should A take to intercept B? AB is 20km apart</p>
<p><img src="http://i.stack.imgur.com/Kcm8I.png" alt="enter image description here"></p>
<p>The provided answer looks like: </p>
<hr>
<p>Choose x axis along 20km distance. </p>
<p>$26t \sin{(40-15)} = 50t \sin{\theta}$</p>
<p>$\theta = \sin^{-1}{\frac{11}{50}} = 12.7$</p>
<p>$15 + 12.7 = 27.7$</p>
<hr>
<p>I took a different approach and used $\cos$ and got a different answer ... why is that? </p>
<p>$26t \cos{(40-15)} = 50t \cos{\theta}$</p> | 4,424 | [
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<p>A ball rocks around an arc. In the following illustration, the ball reaches the end of the arc (its velocity magnitude is zero at that particular moment).</p>
<p><img src="http://i45.tinypic.com/16ixldw.png" alt="Illustration"></p>
<p>Now, I want to know which forces are acting on that ball at that particular moment. We have the tension force $\vec T_2$ acting on the ball, which is the centripetal force. We also have the gravity which consists of two Cartesian components: radial $mg \cos\alpha$ and tangent $mg \sin \alpha$. In the radial axis our net force ($\vec T_2 - mg \cos \alpha = mv^2 / R $) is zero because $v = 0$. However, in the tangent axis our net force is not zero - $mg \sin \alpha$. My question is - how it could be if the ball at that particular moment is not moving because he reaches the edge of his trajectory? If it doesn't move then there should be some opposite force acting on it. My intuition says that that tangent force $mg \sin \alpha$ is forcing the body to slow down in that direction, so it slowly "cancels" the force which caused the body to move initially. But how can I describe it with formulas and/or illustrate it from the point of view of inertial system (i.e., Earth)?</p> | 4,425 | [
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<p>By Carnot Theorem, the efficiency of Carnot cycle is$$\eta=1-\frac{T_C}{T_H}$$</p>
<p>where $T_C$,$T_H$ are the absolute temperature of the cold reservoir and hot reservoir respectively. Since $T_C > 0$, that means $\eta < 1$, so it concludes the Kelvin statement:
"no process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work"</p>
<p>However, I think in that period they don't know the <a href="http://en.wikipedia.org/wiki/Negative_temperature" rel="nofollow">negative temperature</a>, if we let $T_C=300K$ and $T_H=-300K$, it is easy to get $\eta=2$. That seems a counterexample of the second law of thermodynamics.</p> | 4,426 | [
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<p>I am calculating the buoyancy flux ($B$) for a stratified fluid as follows:
$$
B=\frac{g\alpha S}{C_{pw}\rho_0}
$$</p>
<p>where $g = 9.81$ $m/s$; $\alpha = 1.6 t\times10^{-5} + 9.6\times10^{-6} \times (20 \text{ degC})$; $S = 100\text{ }Wm^{-2}$, $\rho_0 = 1000$ $kg/m^3$, and $C_{pw}$ is the specific heat of water.</p>
<p>The question I have is: Is $C{pw} = 4200$ or $4.2$ I've seen it used both ways, and I am unsure which I would use with the units of the other terms in the equation. </p> | 4,427 | [
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<p>So I was recently wondering what happens to the excess charge when it is placed on an insulator or conductor e.g. rubbing two objects together. I know in the conductor the electrons are free to move whereas in the insulator they in general are not very mobile so the charge stays in a small region. But why does this happen? I know about the differences in insulator and conductor band structure, how is this related? Do the excess electrons become part of the band structure?</p>
<p>Thanks! </p> | 4,428 | [
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<p>When introducing the 't Hooft diagrams from Feynman diagrams on a torus has there been a classification in terms of knots and <a href="http://en.wikipedia.org/wiki/Seifert_surface" rel="nofollow">Seifert surfaces</a>?</p> | 4,429 | [
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<p>I read in various places <a href="http://en.wikipedia.org/wiki/Geon_%28physics%29">geons</a> are "generally considered unstable." Why? How solid is this reasoning? </p>
<p>Is the reason geons are not studied much anymore because we can't make more progress without better GR solutions or a better theory of quantum gravity, or is it because it really is a failed theory with fundamental problems (other than the unproven stability question)?</p> | 4,430 | [
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<p>I've wondered how far would be able to send a concentrated beam of electrons in space. The reason is would we be able to launch a magnetic ring with an electron absorbing material on one side and just fire electrons through the ring to create a push? </p> | 4,431 | [
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<p>If I lift a book of mass $m$ from the ground and put it at height $h$,then initial and final energies with respect to ground are 0 and $mgh$ respectively. </p>
<p>So how energy is conserved here?</p> | 4,432 | [
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<p>One of the main sources of subtlety in the AdS/CFT correspondence is the role played by boundary terms in the action. For example, for a scalar field in AdS there is range of masses just above the Breitenlohner-Freedman bound where there are two possible quantizations and which one you get depends on what boundary terms you add to the action. Boundary terms are also essential in the treatment of first-order Lagrangians for fermions and self-dual tensor fields. These all involve the "UV" boundary as $z \rightarrow 0$ in Poincare coordinates. Then there are dual models of QCD like the hard-wall model where one imposes an IR cutoff and imposes boundary conditions at the IR boundary and/or adds IR boundary terms to the action. My question is a bit vague, but basically I would like references to reviews, books or papers that give a good general treatment of the variational principle when one has to be careful about boundary terms. It would help if they clearly distinguish the requirements that follow from mathematical consistency from those that are imposed because of a desire to model the physics in a certain way.</p> | 4,433 | [
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<p>i was reading a specific book on quantum mechanics, partiicularly on the tunnel effect section. I am trying to understand how the probability of an eletron passing a barrier of energy V0 is calculated for both $E>V0$ and $E<V0$, i.e., the electron having more energy and less energy, respectively.</p>
<p>For simplification, the book assumes that, for x>0, there is a potential barrier of intensity V0. Applying Shroedinger EDP, it is concluded that:</p>
<p>$f_1(x)=Ae^{ikx}+Be^{-ikx}, x<=0$ and $f_2(x)=Ce^{\gamma x}+De^{-\gamma x}, x>0$, where $\gamma=\sqrt{2m(V_0-E)}/h$, where the functions represent the electron wavefunctions in space.</p>
<p>After applying boundary conditions on x=0 and x=+infinity, it is concluded that $f_2(x)=De^{-\gamma x}, x>0, V0>E, \gamma \in R$. Then assuming a barrier of length $a$, the book concludes that the probability of the electron going through the barrier is $e^{-2\gamma a}$. Question 1: could someone explain me exactly how to get this value? How are the wavefunctions normalized in this case? Question 2: what is the probability when $E>V0$?</p> | 4,434 | [
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<p>Is it correct to say that 9.0 is one order of magnitude smaller than 10.0? </p>
<p>Has anyone a link/source about confronting order of magnitudes, apart from wikipedia?</p> | 4,435 | [
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<p>Perhaps I am completely wrong, but as I understand it our observation of a system can affect the outcome. The example I remember is the double slit experiment where electrons behave as a wave at first, but when observing it behaves as a particle. The conclusion, as I remember hearing, is that <strong>observing</strong> the system is what caused the different outcomes.</p>
<p>Why is this that case? Couldn't it have been the camera (or whatever is used to detect/observe/etc.) that causes the difference? It just seems like there are a few potential explanations that get skipped over here.</p>
<p>Excuse me while I most likely butcher this experiment with an example. Say I turn on the sink and water goes from the faucet to the drain. Now when I hold a cup under the water, it no longer hits the drain, instead it is captured in the cup. My explanation, having my hand there causes the behavior.</p>
<p>This has bugged me since I first heard it, and I have yet to find an explanation that I can accept. Given, that may be due to my inability to comprehend some of the more complex explanations, but I would still like to figure it out.</p> | 139 | [
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<p>I don't know how to explain the issues at hand in a way that nonphysicists are certain to understand. Can anyone point me to some resource (book, video, it doesn't really matter) that will help me?</p> | 140 | [
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<p>Sound can be a destructive force. However, could it be used to separate say the Hydrogen atom from the Oxygen atoms?</p> | 4,436 | [
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<p>How can one go from the 3D compressible <a href="http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations" rel="nofollow">Navier-Stokes equations</a> to the simpler <a href="http://en.wikipedia.org/wiki/Euler_equations_%28fluid_dynamics%29" rel="nofollow">Euler equations</a>, <a href="http://en.wikipedia.org/wiki/Bernoulli%27s_principle" rel="nofollow">Bernoulli's equation</a> and other fluid dynamic equations?</p> | 4,437 | [
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] |
<p>There have been several Phys.SE questions on the topic of <a href="http://en.wikipedia.org/wiki/Zero_mode">zero modes</a>. Such as, e.g., </p>
<ul>
<li><p><strong>zero-modes</strong> (<a href="http://physics.stackexchange.com/q/2951/">What are zero modes?</a>, <a href="http://physics.stackexchange.com/q/68706/">Can massive fermions have zero modes?</a>), </p></li>
<li><p><strong>majorana-zero-modes</strong> (<a href="http://physics.stackexchange.com/q/29314/">Majorana zero mode in quantum field theory</a>),</p></li>
<li><p><strong>path-integral-with-zero-energy-modes</strong> (<a href="http://physics.stackexchange.com/q/47571">Path integral with zero energy modes</a>), etc.</p></li>
</ul>
<p>Here I would like to understand further <strong>whether "Zero Modes" may have physically different interpretations</strong> and <strong>what their consequences are</strong>, or <strong>how these issues really are the same, related or different.</strong> There at least 3 relevant issues I can come up with:</p>
<h2>(1) <strong>Zero eigenvalue modes</strong></h2>
<p>By definition, <a href="http://en.wikipedia.org/wiki/Zero_modes"><strong>Zero Modes</strong></a> means zero eigenvalue modes, which are modes $\Psi_j$ with zero eigenvalue for some operator $O$. Say, </p>
<p>$$O \Psi_j = \lambda_j \Psi_j,$$ with some $\lambda_a=0$ for some $a$.</p>
<p>This can be Dirac operator of some fermion fields, such as $$(i\gamma^\mu D^\mu(A,\phi)-m)\Psi_j = \lambda_j \Psi_j$$ here there may be nontrivial gauge profile $A$ and soliton profile $\phi$ in spacetime. If zero mode exists then with $\lambda_a=0$ for some $a$. <strong>In this case, however, as far as I understand, the energy of the zero modes may not be zero.</strong> This zero mode contributes nontrivially to the path integral as
$$\int [D\Psi][D\bar{\Psi}] e^{iS[\Psi]}=\int [D\Psi][D\bar{\Psi}] e^{i\bar{\Psi}(i\gamma^\mu D^\mu(A,\phi)-m)\Psi } =\det(i\gamma^\mu D^\mu(A,\phi)-m)=\prod_j \lambda_j$$
In this case, if there exists $\lambda_a=0$, then we need to be very careful about the possible long range correlation of $\Psi_a$, seen from the path integral partition function (<strong>any comments at this point?</strong>).</p>
<h2>(2) <strong>Zero energy modes</strong></h2>
<p>If said the operator $O$ is precisely the hamiltonian $H$, i.e. the $\lambda_j$ become energy eigenvalues, then the zero modes becomes zero energy modes:
$$
H \Psi_j= \lambda_j \Psi_j
$$
if there exists some $\lambda_a=0$.</p>
<h2>(3) <strong>Zero modes $\phi_0$ and conjugate momentum winding modes $P_{\phi}$</strong></h2>
<p>In the chiral boson theory or <a href="http://physics.stackexchange.com/questions/65092">heterotic string theory</a>, the bosonic field $\Phi(x)$
$$
\Phi(x) ={\phi_{0}}+ P_{\phi} \frac{2\pi}{L}x+i \sum_{n\neq 0} \frac{1}{n} \alpha_{n} e^{-in x \frac{2\pi}{L}}
$$
contains zero mode $\phi_0$.</p>
<hr>
<p>Thus: <strong>Are the issues (1),(2) and (3) the same, related or different physical issues?</strong> If they are the same, why there are the same? If they're different, how they are different? </p>
<p>I also like to know when people consider various context, which issues they are really dealing with: such as
the <a href="http://dx.doi.org/10.1103/PhysRevD.13.3398"><strong>Jackiw-Rebbi</strong></a> model,
the <a href="http://dx.doi.org/10.1016/0550-3213%2881%2990044-4"><strong>Jackiw-Rossi</strong></a>
model and <a href="http://dx.doi.org/0.1103/PhysRevLett.47.986"><strong>Goldstone-Wilczek</strong></a> current computing induced quantum number under soliton profile,
<a href="http://physics.stackexchange.com/questions/29314/majorana-zero-mode-in-quantum-field-theory"><strong>Majorana zero energy modes</strong></a>,
such as the <a href="http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1103%2FPhysRevLett%252E100%252E096407&v=a4efcc27">Fu-Kane model</a> (<a href="http://arxiv.org/abs/0707.1692">arXiv:0707.1692</a>),
<a href="http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1103%2FPhysRevLett%252E86%252E268&v=478a24b8">Ivanov half-quantum vortices in p-wave superconductors</a> (<a href="http://arxiv.org/abs/cond-mat/0005069">arXiv:cond-mat/0005069</a>),
or the issue with <strong>fermion zero modes under QCD instanton</strong> as discussed in Sidney Coleman's book ``Aspects of symmetry''.</p>
<p>ps. since this question may be a bit too broad, it is totally welcomed that anyone attempts to firstly answer the question partly and add more thoughts later.</p> | 4,438 | [
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<p>Suppose there is an entangled state of two electrons, the spin part is
$$| \downarrow \uparrow \rangle - | \uparrow \downarrow \rangle \tag{1} $$.
If I add the spatial part of the wavefunction as two Gaussians, it should be something like
$$ ( e^{- (r_1-R_a)^2- (r_2-R_b)^2} + e^{- (r_1-R_b)^2- (r_2-R_a)^2})( | \downarrow \uparrow \rangle - | \uparrow \downarrow \rangle ) \tag{2} $$.</p>
<p>Now I measure the spin of the electron at position $R_a$, and I get down result. The wavefunction should be
$$ e^{- (r_1-R_a)^2- (r_2-R_b)^2} | \downarrow \uparrow \rangle - e^{- (r_1-R_b)^2- (r_2-R_a)^2} | \uparrow \downarrow \rangle \tag{3} $$
, which is still indistinguishable and antisymmetric. ( I cannot get just $ e^{- (r_1-R_a)^2- (r_2-R_b)^2} | \downarrow \uparrow \rangle $, which breaks the antisymmetry)</p>
<p>Since the entanglement is defined by anything more than simple product, both wavefunctions (2) and (3) are entangled. However, is wavefunction (3) too trivial to be called entangled? It looks antisymmetrization itself will automatically produce entanglement. </p> | 4,439 | [
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<p>As postulated by Stuart Hameroff in his article "quantum consciousness",that it is one of the reasons for reduction of quantum superposition.
Roger Penrose suggested that consciousness is not necessary for reduction but a system can undergo self reduction or objective reduction due to intrinsic feature of spacetime.
But he too added that consciousness is also responsible for decoherence.
Their ideas were intensively criticized. So i want to know why consciousness should not be a reason?</p> | 4,440 | [
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<p>In the book <em>physical foundations of cosmology</em>, it saids that Hubble law is unique and a problem seems to be a hint of proving that.</p>
<blockquote>
<p>In order for a general expansion law,<strong>v</strong>=f(<strong>r</strong>,t), to be the same for all observers, the function f must satisfy the relation
$$f(\bf{r_{CA}}−\bf{r_{BA}}, t) = f(\bf{r_{CA}},t)−f(\bf{r_{BA}},t),$$
where ABC are three points in space. Show that the only solution of this equation is given by the Hubble law.</p>
</blockquote>
<p>With a little help of Taylor approximation, I can convince myself $f$ should be linear and then a linear function without constant. But it seems to me that's not good enough for a proof...So how can one prove it in a more mathy way?
Thanks !</p> | 4,441 | [
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<p>In "String Theory and M-Theory" by K. Becker, M. Becker and J.H. Schwarz, page 222, they give a brief introduction about the (space-filling) Orientifold Plane $O9$ as an object needs to be add in the theory to make the it consistence (or at least, that what I thought). However, I still don't really get their arguments. </p>
<ol>
<li><p>What are the physical properties of the Orientifold Plane $Op$ in String Theory? </p></li>
<li><p>How are they described in the context of targer space? How do they couple with objects in String theory (string + brane)? </p></li>
<li><p>Is there any low-effective description for it? What're the theoretical evidences of their existence in String theory?</p></li>
<li><p>Moreover, they also say that (on the same page) the presence of $\bar{Dp}$ branes breaks all the SUSY. How can I see that? </p></li>
</ol> | 4,442 | [
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<p>Negative probabilities are naturally found in the Wigner function (both the original one and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the Klein-Gordon equation.</p>
<p>The question is if there is a general treatment of quasi-probability distributions, besides naively using 'legit' probabilistic formulas? For example, is there a theory saying which measurements are allowed, so to screen negative probabilities?</p>
<p><em>Additionally</em>, is there an intuition behind negative probabilities? (Providing other examples than ones mentioned in the question can illuminate the issue.)</p> | 4,443 | [
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<p>I am covering the classic literature on predictions of Cabibbo angle or other relationships in the mass matrix. As you may remember, this research was a rage in the late seventies, after noticing that $\tan^2 \theta_c \approx m_d/m_s$. A typical paper of that age was Wilczek and Zee <a href="http://dx.doi.org/10.1016/0370-2693%2877%2990403-8" rel="nofollow">Phys Lett 70B, p 418-420.</a></p>
<p>The technique was to use a $SU(2)_L \times SU(2)_R \times \dots $ model and set some discrete symmetry in the Right multiplets. Most papers got to predict the $\theta_c$ and some models with three generations or more (remember the third generation was a new insight in the mid-late seventies) were able to producte additional phases in relationship with the masses.</p>
<p>Now, what I am interested is on papers and models including also some prediction of mass relationships, alone, or cases where $\theta_c$ is fixed by the model and then some mass relationship follows.</p>
<p>A typical case here is <a href="http://dx.doi.org/10.1016/0370-2693%2878%2990485-9" rel="nofollow">Harari-Haut-Weyers</a> (<a href="http://slac.stanford.edu/spires/find/hep/www?j=PHLTA,B78,459" rel="nofollow">spires</a>) It puts a symmetry structure such that the masses or up, down and strange are fixed to:</p>
<p>$m_u=0, {m_d\over m_s} = {2- \sqrt 3 \over 2 + \sqrt 3} $</p>
<p>Of course in such case $\theta_c$ is fixed to 15 degrees. But also $m_u=0$, which is an extra prediction even if the fixing of Cabibbo angle were ad-hoc.</p>
<p>Ok, so my question is, are there other models in this theme containing predictions for quark masses? Or was Harari et al. an exception until the arrival of Koide models?</p> | 4,444 | [
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<p>I'm interested in the pure gauge (no matter fields) case on Minkowski spacetime with simple gauge groups.
It would be nice if someone can find a review article discussing all such solutions</p>
<p>EDIT: I think these are relevant to the physics of corresponding QFTs in the high energy / small scale regime. This is because the path integral for a pure gauge Yang-Mills theory is of the form</p>
<p>$$\int \exp\left(\frac{iS[A]}{ \hbar}\right) \, \mathcal{D}A$$</p>
<p>In high energies we have the renormalization group behavior $g \to 0$ (asymptotic freedom) which can be equivalently described by fixing $g$ and letting $\hbar \to 0$.</p>
<p>EDIT: For the purpose of this question, an "exact" solution is a solution in closed form modulo single variable functions defined by certain ODEs and initial / boundary conditions.</p> | 4,445 | [
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<p>Say we have a two star system with both stars of equal mass $M$. The center of mass of this system is by definition in the center of the two stars. </p>
<p>There is a small asteroid with mass m in orbit around the center of mass of the two stars. (What is known as a halo orbit apparently)
The orbital distance is x. </p>
<p>The question is why the gravitational force on the asteroid cannot be calculated using the center of mass. ie $F=Gm(2M)/x^2$? </p>
<p>I can only get the force on the asteroid if I resolve the centripetal component of force on the asteroid due to each star individually and sum them. </p>
<p><a href="https://www.dropbox.com/s/ft5ipvknczqsr0a/Photo%2029-12-13%207%2028%2013%20pm.jpg" rel="nofollow">https://www.dropbox.com/s/ft5ipvknczqsr0a/Photo%2029-12-13%207%2028%2013%20pm.jpg</a></p> | 4,446 | [
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<p>Point charges q1=− 5.00nC and q2=+ 5.00nC are separated by a distance of 3.50mm , forming an electric dipole. The torque exerted on the dipole has a magnitude of 7.60*10^-9 N*m at an angle of 37∘ with the horizontal.
Using this information, I calculated that the magnitude of the electric dipole moment would be 1.75 * 10^-11 C*m. From here, I attempted to calculate the magnitude of the field by using the formula T = p * E sinθ, getting a result of 674.8 N/C, but this is not correct. Is the error with the formula I am using or one of my calculations?</p> | 4,447 | [
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] |
<p>There are several online services that let you control a large
telescope (eg, lightbuckets.com and slooh.com), even some that are
free (eg, telescope.org). </p>
<p>Unfortunately, the pay services are expensive, and you get very little
reserved time on the scopes. The free services are painfully slow: I
had to wait several months for a picture of Jupiter I wanted. </p>
<p>Has anyone set up automated (ideally free) remote access to a smaller
telescope? I'd much rather play with a 10" telescope in real-time than
a larger one in limited/delayed time. </p>
<p>In fact, even a CCD or camera would be nice for wide-angle shots. </p> | 4,448 | [
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<p>If I put my feet into a pool of water that contains a live wire, why do i get shocked? For electrons to flow through my body, there has to be a E-field/wave that passes through my body along a certain path, that motivates the electrons to flow through me. Now given that the live-wire is in the water and on the ground, aren't both my feet at the same potential:
1. Lets say i hop into the pool (with both feet hitting the water surface at the same time.
2. Let's say i place one foot in and keep the other out and on dry land.</p>
<p>Both my feet are in contact with the earth.. so why does electricity have to flow through my upper body, or beyond my knee?</p>
<p>At the most, I should loose a few toes but why? There's no incentive for a cable lying on the ground to send its current through me when it's already on the ground. Am i not like a bird standing on a transmission line - both feet on the transmission line?</p>
<p>Agreed that's not an ideal 'earth-ground' representation - you'd need salt and a proper copper plate for that.. even so..</p> | 4,449 | [
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<p>I have read somewhere that the best/easiest way to watch meteor showers is to lie on the ground or other horizontal surface with your feet oriented towards the "apparent point of origin" (what was that called again?) of the shower and just relax while having eyes open to the heavens.</p>
<p>Last November I actually tried this method to watch the Leonids and I did see some nice meteors where I have not really consciously seen any before. (Which was probably because I had not watched a meteor shower before purposefully, I guess.)</p>
<p>Is this really the best way for amateurs to watch a meteor shower with the naked eye? What might be other/better ways? How about when you use binoculars? Or would that just limit your field of vision, making you be better of to just use eyes alone?</p> | 4,450 | [
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<p>If a particle is totally localized at $x=0$, its wave function $\Psi(x,t)$ should be a Dirac delta function $\delta(x)$. Accordingly, its Fourier transform $\Phi(p,t)$ would be a constant for all $p$, thus the particle's momentum is totally uncertain. I guess this is what the Uncertainty Principle told us.</p>
<p>But in another hand, since the particle is totally localized at $x=0$, it is not moving and therefore static. Its velocity should be 0, so is its momentum, which contradicts the conclusion above.</p>
<p>So, what's wrong with my thinking?</p>
<p>Is it that there shouldn't be a TOTALLY STATIC particle, or it's in a non-normalizable state, so the uncertainty principle is not applicable?</p> | 4,451 | [
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<p><br/>
This is <a href="http://en.wikipedia.org/wiki/Logistic_map" rel="nofollow">the logistic map</a>:<br/>.
<img src="http://i.stack.imgur.com/ooYe8.png" alt="Image of bifurcation diagram of the logistic map"><br/>
It is a fractal, as some might know here.<br/>
It has a <a href="http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension" rel="nofollow">Hausdorff fractal dimension of 0.538</a>.<br/>
Is it possible to calculate/measure its fractal dimension using the <a href="http://en.wikipedia.org/wiki/Box_counting" rel="nofollow">box counting</a> method?<br/>
A "hand waving calculation" is good enough.<br/>
<br/></p>
<p><strong>Update:</strong> I understand there is another way to calculate the logistic map using the <a href="http://mathworld.wolfram.com/Kaplan-YorkeConjecture.html" rel="nofollow">Kaplan-Yorke Conjecture</a>. Can anyone explain that and how it can help calculating the fractal dimension of the logistic map?</p>
<p><strong>Update2:</strong> Seems like the way to go around this is not Kaplan-Yorke Conjecture (which is a unproven Conjecture still), but use the <a href="http://en.wikipedia.org/wiki/Correlation_dimension" rel="nofollow">correlation dimension</a>. There is a <a href="http://www.sciencedirect.com/science/article/pii/0167278983902981" rel="nofollow">paper with the solution here</a>, hope I'll know more as I read it.</p> | 4,452 | [
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<p>I am struggling with a derivation that calculates the cross sections for Mie scattering and since the incident light is considered to be a x-polarized plane wave I thought that we would have $$I_i = \frac{1}{2} \sqrt{\frac{\epsilon}{\mu}} \vert E_0 \vert^2$$, but I do not understand this derivation then, since a factor $2 \pi $ seems to be missing. </p>
<p>It starts with an expression for the scattered field, explains how they got this expression by using some orthogonality properties and then - in my opinion argue - that this $Re(g_n)=1$. But then I do not understand what they take as the incident intensity in order to get the expression $C_{sca}$. Does anybody have an idea?</p>
<blockquote>
<p>$$
W_s=\frac{\pi|E_0|^2}{k\omega\mu}\sum_{n=1}^\infty(2n+1)\mathcal{Re}\{g_n\}(|a_n|^2+|b_n|^2),
$$ where we have used (4.24) and the relation $$
\int_0^\pi(\pi_n\pi_m+\tau_n\tau_m)\sin{\theta}\text{
}d\theta=\delta_{n\text{ }m}\frac{2n^2(n+1)^2}{2n+1}, $$ which follows
from (4.27). The quantity $g_n$, is defined as - $i\xi_n^*\xi_n^{'}$,
may be written in form $$
g_n=(\chi_n^*\psi_n^{'}-\psi_n^*\chi_n^{'})-i(\psi_n^*\psi_n^{'}+\chi_n^*\chi_n^{'}),
$$ where the Riccati-Bessel function $\chi_n$ is - $\rho y_n(\rho)$
and, therefore, $\xi_n=\psi_n-i\chi_n$. The functions $\psi_n$ and
$\chi_n$ are real for real argument; therefore, if we use the
Wronskian(Antosiewicz, 1964) $$
\chi_n\psi_n^{'}-\psi_n\chi_n^{'}=1,\tag{4.60} $$ it follows that the
scattering cross section is $$
C_{sca}=\frac{W_s}{I_i}=\frac{2\pi}{k^2}\sum_{n=1}^\infty(2n+1)(|a_n|^2+|b_n|^2).\tag{4.61}
$$</p>
</blockquote> | 4,453 | [
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<p>Hypothetical brain teaser here, no real kittens involved! - </p>
<p>For some bizarre reason I have a sack of kittens, I need to find the total weight of the kittens and the sack but I'm only allowed to use a spring scale and I'm only allowed use my arms to hold the scale. My arms are unsteady and the kittens are constantly moving around in the sack, causing the weight display on the scale to dance around wildly.The kittens all weigh different weights and they are in constant motion. I am wondering if it is possible to very accurately get a reading from the scale, perhaps by incorporating some kind of accelerometer? This has been puzzling me for some time!</p>
<p>Looking forward to hearing your input.</p> | 4,454 | [
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<p>IS there any quantum analogy where a three state (or three body) system shows chaotic dynamics as three body problem in classical mechanics?</p> | 4,455 | [
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<p>Can classical mechanics be derived from quantum mechanics as the same way thermodynamics derived from statistical mechanics?</p> | 141 | [
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<p>As far as I understand it, the first principle of thermodynamics is a mere definition of the quantity “Heat”: $$\text d Q: = \text d L + \text d U.$$
This is somewhat the point of view taken in Fermi's introductory book "Thermodynamics": </p>
<blockquote>
<p>[...] $$\Delta U + L=0$$If the system is not thermally isolated, the first member of [eqn.] will be generally not equal to zero [...]
Substitute the [eqn.] with the more general: $$\Delta U + L = Q.$$
[...] Now we will call $Q$, by definition, the quantity of heat received by the system during the transformation.</p>
</blockquote>
<p>(if you want to read the full text you might want to google “Fermi Thermodynamics"... pag. 17).</p>
<p>I think that this point is logically sound and I have a quite good understanding of some of the above structure starting from here (e.g. the second principle). On the other hand I feel as I'm missing something. </p>
<p>To give an example, from mechanics, this is how I understand Newton's equation:</p>
<blockquote>
<p>It is a matter of fact that the positions and the velocities of a
mechanical system fully determine the accelerations of the system. Hence, the dynamic of each system follows second order differential equations: $$\ddot x = F(x,\dot x, t).$$</p>
</blockquote>
<p>An other example might be the second law of thermodynamics, that (in Clausius' form) is simply the statement of the fact that heat doesn't flow spontaneously from a cold body to an hotter one.</p>
<p>Since I find strange that something that is called a “principle” is a mere definition (after all, there's no assumption involved in making a definition), I ask: what are the experimental facts behind the first principle of thermodynamics?</p>
<p>Note: I understand that this is really about my personal understanding, however I think that this question can be useful to others. Furthermore, if something isn't clear and if I can improve my question, let me know.</p> | 4,456 | [
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<p>In n-body simulation you need to know the positions of the particles in order to calculate the force between them. The new velocity of each particle can then be calculated given a simulation timestep dt.</p>
<p>If the gravitational interaction propagates at the speed of light, do we need to specify the force between particles given their retarded positions (not instantaneous positions)? If not, why not?</p>
<p>Note that I am interested in special relativity only (not GR), I am more concerned with what happens when bodies move quickly or are separated by distances larger than the distance light travels in one timestep.</p>
<p>I am also interested in whether or not the electric force between charges is any different in this respect.</p>
<p>Thanks.</p> | 4,457 | [
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<p>I was wondering if anyone knew the formula to calculate how much force is required to lift a tire or any object by the edge. </p>
<p>For example if a tire weighs 500 lbs (or has a mass of 226.8 kg). I would just like to know the formula how to calculate how much of that 500 lbs we are actually lifting since it is only from the edge. </p> | 4,458 | [
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<p>Recent results from the BICEP2 experiment have produced a lot of talk about the primordial gravitational waves produced during the inflationary period.</p>
<p>I would like to have some explanation about how inflationary models predict the generation of these gravitational waves. Have these gravitational waves been described as metric perturbations around a de Sitter spacetime? Are they predicted using a semiclassical gravity formalism so as to take into account the quantization of a scalar field (the inflaton) in such "perturbed" spacetime?</p> | 4,459 | [
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<p>I got one more stupid question in Polchinski's string theory book. In p. 44, it is said</p>
<blockquote>
<p><em>The currents</em>
$$j(z)=i v(z) T(z), \tilde{j}(\bar{z}) = i v(z)^* \tilde{T}(\bar{z}) \tag{2.4.5}$$
<em>are conserved for any holomorphic $v(z)$.</em></p>
</blockquote>
<p>Did he mean
$$\partial_z j(z)=0, \qquad \partial_{\bar{z}} \tilde{j}({\bar{z}})=0? $$
How to show that? The previous page states $\bar{\partial} T_{zz} = \partial T_{\bar{z} \bar{z}} =0 $. It seems these relations are insufficient to derive Eq. (2.4.5).</p> | 4,460 | [
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<p>I am wondering about a specific question regarding the speed at which an electrical current traverses through salt-water / saline. </p>
<p>By this I do <em>not</em> mean the electron drift speed - I mean, at what speed would a current travelling from an anode to a cathode immersed in salt water be? </p>
<p>A ball park figure will do. Thank you.</p> | 4,461 | [
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<p>If the sinusoidal electric component of a light wave were off-set to one side of the magnetic component and then the smaller "lobe" were to cancel out with much of the larger side, then where would the energy go? Would it not form a closed loop much like a mass-bearing string? Could the electrical energy not be converted into a gravitational field to bend space-time over the length of the wave to form a 1-D "string" along the junction of the perpendicular E and B fields? This would be much like folding a sheet of paper in half so that one edge protrudes past the other. The protruding edge being the electric component and the rest being electrical energy converted into mass/gravity (comparable to a mass-bearing string). The magnetic component could then arise from Lorentz symmetry <a href="http://physics.stackexchange.com/questions/3618/can-maxwells-equations-be-derived-from-coulombs-law-and-special-relativity">as described by Lubos</a>: </p>
<blockquote>
<p>If you only start with the $E_z$ electric field, the component $F_{03}$ is nonzero. However, when you boost the system in the $x$-direction, you mix the time coordinate $0$ with the spatial $x$-coordinate $1$. Consequently, a part of the $F_{03}$ field is transformed into the component $F_{13}$ which is interpreted as the magnetic field $B_y$, up to a sign.</p>
</blockquote>
<p><strong>Is the described "string wave" model possible?</strong></p>
<p>I realize that I haven't provided a mechanism to explain the proposed model. However "I do not reject food because I do not understand digestion." -Oliver Heavenside</p>
<p>From here on the rest of this post is merely a compilation of the "evidence" that circumstantially supports the proposed idea. Please do not feel required to address these topics. They are here because I think electromagnetic mass is real. I realize this borders on "promoting unaccepted theories," but it is merely my way of assessing the possibility. I promise not to bring this up again on SE if it is refuted. </p>
<p><strong>The concept seems compatible with the standard model:</strong> </p>
<p>a.) an origin of charge has been proposed. </p>
<p>b.) eliminating one lobe has reduced the "spin" or magnetic field by 1/2 relative to a light wave. </p>
<p>c.) Lepton number 1 applies due to the "strong interaction" of the remaining electric component </p>
<p>d.) a mechanism of mass has been proposed.</p>
<p><strong>Maxwells equations seem to fit:</strong> </p>
<p>The Laws of Electromagnetism have geometric relations incorporated into them that naturally arise from the proposed electron-as-an-EM-wave model: the dot product and the cross product specifically. </p>
<p>Ampere's Law </p>
<p>Ampere’s Law describes the magnetic field produced by the flow of electrons along a wire. The negative components of electrons flowing along the wire should repel each other, which would mean that the negative components should protrude from the wire like the dorsal fins of sharks swimming parallel and breaking the surface. Since the electrons are travelling in the same direction along the wire the magnetic components (in the direction of the side fins of the shark analogy) should be tangent to the surface of the wire, which results in a circular magnetic field around the wire just as Ampere’s Law and the Biot-Savart Law predict. </p>
<p>Faraday's Law</p>
<p>Faraday’s Law describes the electric voltage produced in a coil of wire as a magnetic field through it changes. The voltage is proportional to the number of loops of wire, which is counter-intuitive/non-conservative. Why should the voltage depend on the number of loops? An explanation naturally arises from the proposed model. Electrons inherently have velocity in the form of a "Poynting-like" vector. When the loop of wire encounters a changing magnetic field the "poyinting vectors" align and under the right orientations they align with the wire loops and thereby form electric current. </p>
<p><img src="http://i.stack.imgur.com/eyCkq.jpg" alt="enter image description here"></p>
<p>In the bottom orientation the magnet produces no EMF along the wire. In the top orientation the EMF is along the wire as seen in generators.</p>
<p>Schrodinger's statistical model won because Maxwells equations had already divorced physics from first causes. Saying that the surface covered area of a loop was the cause of EMF instead of the poynting vectors of electrons adding over the distance of the circumference.</p>
<p>Gauss's Laws</p>
<p>Gauss’ laws of electricity and magnetism are easily integrated with the proposed model as the net magnetic flux is zero and the net charge is unchanged. However Coulombs Law does not hold true at the subatomic level. The force between two charged electrons is modified by the presence of other electrons if electrons are not point charges, but electric components of an EM-wave. </p>
<p>Coulomb's law</p>
<p>Coulomb's law for point charges:</p>
<p>$$F=k\frac{q_1 q_2}{r^2}=\frac{1}{4\pi\epsilon_0}\frac{qq_0}{r^2}\hat{u}$$</p>
<p>Does not hold at the subatomic level for all directions if a blip of negative charge sticks off one side of a mass-bearing electromagnetic wave. This naturally provides a classical explanation for "quantum tunnelling:" certain orientations of subatomic particles behave unlike point charges. </p>
<p><strong>Atomic Orbitals</strong></p>
<p>Take one electron and one proton and place them near each-other. The proposed model suggests an intrinsic and intuative reason why electrons don’t fall into the nucleus, which current theories lack. The velocity of an imbalanced EM wave is perpendicular to both the electric and magnetic components, which means that the radial acceleration of attraction towards the nucleus experienced by the electric component of an electron is always perpendicular to its velocity or the “Poynting vector” of an electron. All that is left for the electron to do is to set up the lowest energy standing wave possible. This also suggests that the proton rotates with the electron's orbit so that the "fins" constantly point toward eachother. Spherical harmonics should arise naturally from this arrangement and approximate to the schrodinger equation. </p>
<p><strong>Relativistic Explanation of the Lorentz Force</strong></p>
<p>Using relativistic tensors: "If you only start with the $E_z$ electric field, the component $F_{03}$ is nonzero. However, when you boost the system in the $x$-direction, you mix the time coordinate $0$ with the spatial $x$-coordinate $1$. Consequently, a part of the $F_{03}$ field is transformed into the component $F_{13}$ which is interpreted as the magnetic field $B_y$, up to a sign\cite{Lubos}."</p>
<p>If the electron is an E-M wave as proposed and the magnetic components align with the extern magnetic field, then performing the reverse of the above transformation should convert the external magnetic field into an electric component in the $E_z$ direction so that the electron feels the equivalent to a charge perpendicular to its direction of motion, which explains the Lorentz force. </p>
<p><strong>Numerous Other Explanations</strong></p>
<p>There are many other phenomena that seem to fit with the proposed model. I'm just running out of steam!</p>
<p><strong>A Little History</strong></p>
<p>Electrons were viewed as "matter waves" in DeBrogli's model. "Matter waves" is a polite way of saying: something is waving but we don't know what. Heisenberg came along and said that despite not knowing what is waving we can assume that the wave doesn't have any undiscovered properties that would allow for knowing both position and momentum (an arrogant assertion!). Schrodinger then came along and noticed that tweaking spherical harmonics provided a reasonable model of atomic orbitals (statistically). That all led to the Copenhagen interpretation, which Einstein called the "Born-Heisenberg tranquilizing philosophy, or religion." Electrons have continued to be treated as point charges or matter waves as is convenient for interpreting experimental results ever since.</p>
<p>QED and QCD have introduced "virtual photons" in explaining the interactions of "point charges" and light, etc. Surely "virtual photons" would be unnecessary if the point charges were instead modelled as EM waves themselves. </p>
<p>Particle physicists have invented a "higgs field" which they propose vibrates to create mass. The higgs field seems like adding epicycles: sorta unnecessary when there is a simpler and better alternative (that I have not really understood yet!). It has been obvious for decades that physics has stalled while trying to model hadrons as point charges. String theory has been a lonely success story waiting to happen. Electromagnetic string-waves are the future! (unless someone refutes me :-). </p> | 4,462 | [
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<p>If a conductor - a long rod - moves at constant speed across the "lines" of a uniform magnetic field, is there an EMF within this conductor? Or, if a conducting rod rotates at uniform rate, pivoted in the middle or at one of its ends in a uniform magnetic field perpendicular to the plane of rotation, is there an EMF generated within the conductor?</p> | 142 | [
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