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<p>Suppose Bruce Banner goes back in time, convinced that the Hulk is a stupid menace. Let's say he also borrows Quicksilver's speed abilities (maybe the Flash is more appropriate, but based on the recent X-Men movie Quicksilver is plenty fast enough).</p>
<p>Anyway he decides to run away from the burst of gamma rays that turns him into the Hulk (assuming this would actually do the trick). Now obviously, they will still travel at the speed of light. But, due to frequency shifts, shouldn't he eventually look behind and "see" the burst of gamma rays as really just color, starting with violet? If he kept running, would he not see a rainbow cycle of colors? </p>
<p>Would this mean that the flash could see the whole spectrum in terms of the visible spectrum (that is, he wouldn't see new colors, but new sources of colors), depending of course on his speed?</p>
<p>I guess this is all just a red-shift blue-shift (one shift two shift) problem, so I think it is a valid hypothesis. Am I right, or is Banner doomed to become invincible and mean? </p>
| 1,781 |
<p>I'm trying to understand a concept spin in QM. I've read some explainations, and it seems that the idea is <em>very</em> easy and straighforward, however I didn't find these exact wordings in my books.<br>
My question: is the following explaination <strong>fully correct and strict</strong>, or I'm missing something?</p>
<p>The explaination:</p>
<p>under an inifinitesimal rotation $\vec{\delta\varphi}$ the position vector $\vec{r}$ transforms to</p>
<p>$$\vec{r}' = \vec{r} + \delta\vec{r} = \vec{r}+\vec{\delta\varphi}\times\vec{r} = \left(1+\vec{\delta\varphi}\cdot\hat{\textbf{R}}\right)\vec{r}$$</p>
<p>$\hat{\textbf{R}}$ are three $3\times 3$ matrices of rotation. Thus for any function $f(\vec{r})$</p>
<p>$$f(\vec{r}') = f( \vec{r} ) + \delta \vec{r}\cdot\nabla f(\vec{r}) = \left(1+\vec{\delta\varphi}\cdot[\vec{r}\times\nabla]\right) f(\vec{r}) \equiv\left(1+i\vec{\delta\varphi} \cdot\hat{\textbf{L}}\right) f(\vec{r}) $$</p>
<p>$\hat{\textbf{L}}$ is the angular momentum operator.</p>
<p>However, the state vector $\Psi$ can be of any "geometrical" origin itself (scalar, $1/2$-spinor, vector, ...) and undergoes the transformation as well - there is an addition $\delta\Psi$ similar to $\delta\vec{r}$:</p>
<p>$$\Psi'(\vec{r}') = \Psi(\vec{r}') + \delta\Psi(\vec{r}') \equiv \left(1+i\vec{\delta\varphi}\cdot\hat{\textbf{S}}\right) \Psi(\vec{r}') $$</p>
<p>$\hat{\textbf{S}}$ is the operator of spin. Note that the argument $\vec{r}'$ is the same on both sides. Since $\Psi$ is not necessarily a vector, each of three $\hat{\textbf{S}}$ is not necessarily a matrix of rotation.</p>
<p>Full transformation is the combination of two:</p>
<p>$$\Psi(\vec{r}') = \left(1+i\vec{\delta\varphi} \cdot\hat{\textbf{L}}\right) \left(1+i\vec{\delta\varphi}\cdot\hat{\textbf{S}}\right)\Psi(\vec{r}) = \left(1+i\vec{\delta\varphi} \cdot(\hat{\textbf{L}}+\hat{\textbf{S}})\right)\Psi(\vec{r}) $$</p>
<p>$\hat{\textbf{J}}\equiv\hat{\textbf{L}}+\hat{\textbf{S}}$ is the "total" angular momentum.</p>
<p>There are $0$, $1/2$, $1$, $3/2$. ... representations of the group of rotations. For "angular" part we have a restriction that position vector is an observable so after $360 ^\circ$-rotation it must return to its original value. This is why only integer eigenvalues of $\hat{\textbf{L}}$ are allowed. Since state vector $\Psi$ does not directly correspond to an observable, there are no such restrictions on $\hat{\textbf{S}}$ .</p>
| 1,782 |
<p>From basic airfoil theory the following free body diagram can be determined for a two dimensional asymmetric airfoil: </p>
<p><img src="http://i.stack.imgur.com/MlDJx.png" alt="enter image description here"></p>
<p>Here the direction of the resultant force is governed by the geometry of the airfoil section.</p>
<p>However, I'm unsure on how the direction of the resultant force is affected when instead of an airfoil a two dimensional flat plate is considered.<br>
Do the resultant force $R$ and normal force $N$ just overlay each other as shown below (my suspicion)? </p>
<p><img src="http://i.stack.imgur.com/wZ1wC.png" alt="enter image description here"></p>
| 1,783 |
<p>Is information propagated in any other way than waves? Please distinguish "propagation across a medium" from information "storage within stable states of matter", which might difuse or interact chemically.</p>
<p>Information might be stored in stable configurations of matter, which might diffuse, or interact chemically (odor,DNA), but these might be orders of magnitude weaker, in range and dissipation. Is there a domain in physics comparing wave vs non-wave propagation. The two most known are sensory: sound and electromagnetic propagation. I think gravity probes are still searching for waves in this medium.</p>
<p>Why does nature prefer waves for long distance calls? Perhaps because it involves a minimum dissipation of energy?</p>
| 1,784 |
<p>The <a href="https://en.wikipedia.org/wiki/Drude_model" rel="nofollow">Drude model</a> of electric conduction in solids deals with independent free electrons subject to <em>random</em> collisions with the crystal lattice (the direction where the electrons are scattered after a collision is random). </p>
<p>A simplified model is the Lorentz gas, where the collision are deterministic. If I understand correctly, it was shown by Sinai that this model is ergodic.</p>
<p>What about the original Drude model: is it ergodic? (Are there references on that?) A side question is whether this would have a physical significance?</p>
| 1,785 |
<p>Perhaps more of an engineering question, but with the subject recently in the news about hyperspeed maglev tunnels I'll chance it here. Say you set up a network of line of sight underground tunnels for your maglev transportation system operating roughly 50' above sea level through the American continent. These tunnels would not contour to the curvature of the earth, rather be more akin to a knitting needle piercing the tangent of an orange, shortening travel distance by transecting the arc. My question is, given real world conditions, material strengths and costs, geothermal, fault and groundwater issues, what is the maximum depth a reinforced tunnel could exist under earth's gravity? Since both ends of the tunnel segment are at equal elevations (disregarding surface features) the effect would be a gravitational "rope swing". Couple that with evacuating the tube of air to vacuum or near vacuum levels and you have a very energy efficient delivery system. How a vacuum would increase stress loads on the tube I'm not really sure. Some very crude calculations of my own put a surface distance of 180 miles requiring a center tunnel depth of about 1.1 miles, which would be a very workable distance between stations. </p>
| 1,786 |
<p>Is there a fundamental difference between the statistical methods of science, comparing medicine/biology with small sample sizes(n < 10^2 or 10^3) to the statistics applied in Quantum Mechanics (h: order 10^34) or statistical mechanics (N: order 10^23)</p>
| 1,787 |
<p>It's folklore dating back to von Neumann and Wigner that <a href="http://en.wikipedia.org/wiki/Avoided_crossing" rel="nofollow">time-dependent Hamiltonian systems tend not to have level crossings of their energy eigenvalues</a>. However, we can of course consider smoothly varying Hamiltonians which have been engineered to have level crossings. These don't even have to be complicated: for instance, any Hamiltonian of the form
$$ H = -\sum_{(i,j)} \sigma^{(z)}_i \sigma^{(z)}_j + \epsilon P t $$
on a 1D spin chain, for $0 < \epsilon \ll 1$ and any Hermitian operator $P$, is an example: the all-up state and the all-down are ground-states for $t = 0$, though for $t \ne 0$ such symmetry is typically broken, so that for $|t| \ll 1$ we expect to have eigenstates close to the all-up and all-down states but with distinct eigenvalues.</p>
<p>After some investigation, I've come to suspect the following:</p>
<blockquote>
<p><strong>Conjecture.</strong> If $H$ has a level crossing between energy levels $E_0, E_1$ at some time $T$, and $\Pi$ is the projection onto the span of the $E_0$- and $E_1$-eigenstates then there are well-defined (continuously varying) eigenvectors through the level crossing only if $\Pi [H(T), \dot H(T)] = 0$ — that is, if the change in the Hamiltonian at the level crossing is only a change in the values of the two crossing eigenvalues, for a common pair of eigenvectors. Specifically: if this equality does not hold, then any (unitary) time-dependent change-of-basis operator from the standard basis to the energy eigenbasis of $H$ at time $t$ which is continuous for some neighborhood $t \in (T,T+\epsilon]$ will oscillate infinitely rapidly as $t \to T$.</p>
</blockquote>
<ul>
<li><p>Is this true generally? (If not, can you point to a counterexample?)</p></li>
<li><p>Is this a known result, and is there a reference that I can refer to where this question is treated clearly, and more-or-less formally for bounded operators (e.g. on finite-dimensional systems)?</p></li>
</ul>
| 1,788 |
<p>Does a person get electrified when his feet are on the floor, his right hand is holding $220~V$ and his left hand holding a piece of wood or any other insulator?</p>
| 1,789 |
<p>Like in title, how small can diffraction grating be? And, of course be "fully operational".
I mean, littles diffraction grating possible that still works as full-sized one.</p>
| 1,790 |
<p>Suppose that two spheres, $S1$ and $S2$, with radii $R1$ and $R2$ resp. have the same charge uniform charge $Q$ and $R1 > R2$. After they are forced to come in contact, why does $S1$ gain more charge? Why don't they both continue to have equal charges?</p>
| 1,791 |
<p><strong>Background:</strong><br>
This reminds situation reminds be of an episode from the <em>The Big Bang Theory</em>, although it is quite different from it. My roommate and I have similar temperature preferences and also share the objective of saving money on electricity. The optimal solution towards this objective is what we have differing opinions about.</p>
<p><strong>The problem:</strong><br>
In my opinion, during the daytime when no-one's around, the temperature setting should be at least 4 °F more than the normal setting (given an ongoing summer 90+ °F). I would go far as to argue that during the daytime the cooling should be completely switched off. My roommate's counter-argument is that assuming a PID controlled model, the overshoot caused by the cooling in the evening, in an effort to get the temperature down from the day's high, will more than nullify the electricity saved during the day thereby resulting in higher costs. The controller is a programmable digital thermostat with 4 separate settings for <code>sleep</code>, <code>wake</code>, <code>leave</code> and <code>return</code> for two regimens namely <code>weekday</code> and <code>weekend</code>.</p>
<p><strong>Specifically:</strong><br>
Instead of hand-waving I was looking for a mathematical model to simulate the heating-cooling of a typical apartment. A quick Google search yielded no useful models (most I could get my hands on are macro-models related to multiple commercial units).</p>
<p>I am looking for a model — with elements like the <code>heat exchange</code> (i.e. the ac), the <code>heat sink</code> (i.e. the apartment) and the <code>environment</code> — a general model which can be used for a <em>first-order</em> approximation. Assume that the cost of electricity is constant throughout the period under consideration (even if it isn't, a cost vs time graph can be easily incorporated in the model).</p>
| 1,792 |
<p>If we could build a neutrino telescope capable of viewing relic neutrinos that decoupled after the big bang, with a similar angular and spectral resolution that is possible now for the CMB, what would we see? (And I know this will be technically incredibly difficult.)</p>
<p>How would the C$\nu$B differ because of the finite neutrino mass and earlier decoupling? Would there be additional diagnostics and insights that are unavailable from the CMB? How big would the fluctuations in neutrino temperature be compared with the CMB? Would these fluctuations give us the neutrino mass or tell us more about inflation?</p>
<p>NB: related questions are
<a href="http://physics.stackexchange.com/questions/109103/why-are-we-blind-for-the-era-before-the-recombination">Why are we blind for the era before the recombination?</a>
,
<a href="http://physics.stackexchange.com/questions/129604/seeing-beyond-the-cmbr-with-neutrinos?lq=1">Seeing beyond the CMBR with neutrinos?</a>
and
<a href="http://physics.stackexchange.com/questions/26546/is-it-possible-to-look-into-the-beginning-of-the-universe?lq=1">Is it possible to look into the beginning of the Universe?</a>
but none these ask specifically, or have answers, about what could be seen or probed by the C$\nu$B if we could examine it in detail.</p>
| 1,793 |
<p>Consider the following situation. A block of mass $M$ is resting on a rough horizontal ground, and a frame is moving towards the right horizontally with an acceleration $a$. Suppose the coefficient of static friction on the ground on which the block is standing is $ \mu > a/g$.</p>
<p>Clearly the block is moving towards the left w.r.t. the frame with acceleration $a$. Suppose we try to explain this from the non-inertial frame. Then we add a pseudoforce $Ma$, towards the left, on the block. But observe that $Ma < \mu Mg$ as $\mu g > a$. So the block shouldn't move, due to static friction. </p>
<p>How is this possible?</p>
| 1,794 |
<p>The light would take 93 billion years to reach the edge of universe but nothing can travel faster than the speed of light not even the big bang?</p>
| 10 |
<blockquote>
<p>a short linear object of length b lies along the axis of a concave mirror of focal length f at a distance u from the mirror.what is the size of the image?</p>
</blockquote>
<p>what i have done so far:</p>
<p>since the object is of length b, consider the point of the object closest to the mirror A and the point farthest from the mirror B.</p>
<p>for the image of point A, 1/vA + 1/(-u)=1/(-f)</p>
<p>for the image of point B, 1/vB +1/(-(u+b))=1/(-f)</p>
<p>therefore vA=fu/(f-u)</p>
<p>and vB=f(u+b)/(f-(u+b))</p>
<p>so size of image is vA-vB = b[(f^2)/(f-u-b)(f-u)]</p>
<p>my question:</p>
<p>can this be approximated to b[(f^2)/(f-u)(f-u)] or will that be wrong?</p>
| 1,795 |
<p>I know how transform an integral below, </p>
<p>$$
\iint f(\mathbf v_{1})f(\mathbf v_{2})d^3\mathbf v_{1}d^3\mathbf v_{2},
$$ </p>
<p>using relative speed coordinates: we just use
$$
m_{1} \mathbf v_{1} + m_{2}\mathbf v_{2} = M\mathbf V, \quad \mathbf v = \mathbf v_{1} - \mathbf v_{2} ,
$$</p>
<p>and then we may use spherical coordinates.</p>
<p>But if I have an integral like</p>
<p>$$
\iint f(\mathbf r_{1})f(\mathbf r_{2})d^3\mathbf r_{1}d^3\mathbf r_{2},
$$ </p>
<p>I don't know how to transform it by using a spherical coordinates of center of masses. In Pathria's book called "Statistical Mechanics" I saw a transform that I need, but I don't understand how it was made. Can you help me?</p>
<p><img src="http://i.stack.imgur.com/EyLh8.jpg" alt=""> .</p>
<p>And it's not a homework!</p>
| 1,796 |
<p>I asked a similar question but the wrong way <a href="http://physics.stackexchange.com/questions/24835/scale-invariance-and-self-organized-criticality">here</a>. Because my intention was to ask about non thermodynamic system, i will be more specific:</p>
<ul>
<li>What is the relation between critical behaviour and the scale invariance in these two model (sandpile, forest fire)?</li>
</ul>
<p>What i can't figure out is the meaning of "infinity correlation length" in these two model.</p>
| 1,797 |
<p>In particle Physics it's usual to write the physical content of a Theory in adjoint representations of the Gauge group. For example:</p>
<p>$24\rightarrow (8,1)_0\oplus (1,3)_0\oplus (1,1)_0\oplus (3,2)_{-\frac{5}{6}}\oplus (\bar{3},2)_{\frac{5}{6}}$
(Source: <a href="http://en.wikipedia.org/wiki/Georgi-Glashow_model" rel="nofollow">SU(5) GUT Wikipedia article</a>)</p>
<p>While I do understand the Basics in representation theory from a mathematical viewpoint, as well as Gauge Theory (up to this point), I've been looking High and Low for some good article on how to understand what the above formula means physically? </p>
<p>Specifically I don't understand the following:</p>
<ul>
<li><p>I'm having a bit of a problem with the notation. $(1,1)$ denotes the tensor product of a <strong>1</strong> and <strong>1</strong> of $SU(3) \times SU(2)$ in this case, does the subscript $()_0$ belong to the $U(1)$ part? Or did I completely misunderstand something?</p></li>
<li><p>How to arrive at the above transformation? How to choose the right hand side of the <strong>24</strong> transformation, it seems random to me</p></li>
<li><p>The physical content. $(8,1)_0$ looks to me like gluons, because of the 8, $(1,3)_0$ like W and Z bosons and $(1,1)_0$ like the photon. But these are all guesses I made according to the numbers I see and the fact that the SM should arise from $SU(5)$ breaking. How would one know this? And what are the other 2 components?</p></li>
</ul>
<p>Any reference is also greatly appreciated, especially one that focuses on precisely this.</p>
| 1,798 |
<p>The inverse square law for an electric field is:
<br>
$$
E = \frac{Q}{4\pi\varepsilon_{0}r^2}
$$
Here: $$\frac{Q}{\varepsilon_{0}}$$
is the source strength of the charge. It is the point charge divided by the vacuum permittivity or electric constant, I would like very much to know what is meant by source strength as I can't find it anywhere on the internet. Coming to the point an electric field is also described as:
$$Ed = \frac{Fd}{Q} = \Delta V$$
This would mean that an electric field can act only over a certain distance. But according to the Inverse Square Law, the denominator is the surface area of a sphere and we can extend this radius to infinity and still have a value for the electric field. Does this mean that any electric field extends to infinity but its intensity diminishes with increasing length? If that is so, then an electric field is capable of applying infinite energy on any charged particle since from the above mentioned equation, if the distance over which the electric field acts is infinite, then the work done on any charged particle by the field is infinite, therefore the energy supplied by an electric field is infinite. This clashes directly with energy-mass conservation laws. Maybe I don't understand this concept properly, I was hoping someone would help me understand this better. </p>
| 1,799 |
<p>First off, I swear this is not homework. I'm doing some practice problems because I got an exam coming up. I'm stuck on this one:
<img src="http://i.stack.imgur.com/w7KMz.png" alt="alt text"></p>
<p>I figured I would use energy conservation for this problem. So since the thing is not moving initially, I tried doing</p>
<p>$mgh=1/2 I\omega^2+1/2 mv^2$, but that doesnt give me the right answer. Any ideas?</p>
| 1,800 |
<p>In an ideal gas, the Boltzmann distribution predicts a distribution of particle energies $E_i$ proportional to $ge^{-E_i/k_bT}$.</p>
<p>But, doesn't entropy dictate that the system will always progress towards a state of maximum disorder? In other words the system evolves towards a macro-state which contains the maximum possible number of indistinguishable micro-states. This happens when all particles have the same energy, which seems to contradict the Boltzmann distribution.</p>
<p>I'm pretty sure I've misinterpreted entropy here, but I'd be please if someone could explain how!</p>
| 1,801 |
<p>In the current accelerated expansion universe model will the Hubble constant reach zero asymptotically in the far future?</p>
| 1,802 |
<p>If a particle of mass $M$ is given an electric charge $Q$, will its mass change?</p>
| 1,803 |
<p>Say I have a series of tubes (not the internet) looking like this, where <code>w</code> represents water:</p>
<pre><code>| | | |
| | | |
|wwww| |w|
|wwww| |w|
|wwww+------+w|
|wwwwwwwwwwwww|
+-------------+
</code></pre>
<p>Why is it that if I put some water in either side, the water level changes on the other side until they equalize? Why does this work even if I put water on the thinner side? And why is it that when you tilt the whole contraption, the water level is still even, although slanted?</p>
| 1,804 |
<p>I really hope someone will take a quick look at the following, I would just love to better understand it...</p>
<p>This exercise is from Arnold's "Mathematical Methods of Classical Mechanics", p. 97 in the chapter on d'Alemberts principle:</p>
<p>A rod of weight P, tilted at an angle of 60° to the plane of a table, begins to fall with initial velocity zero. Find the constraint force of the table at the initial moment, considering the table as</p>
<p>(a) absolutely smooth</p>
<p>(b) absolutely rough</p>
<p>(In the first case, the holonomic constraint holds the end of the rod on the plane of the table, and in the second case, at a given point.)"</p>
<p><img src="http://i.stack.imgur.com/Mq3d0.jpg" alt=""></p>
<hr>
<p>I must admit, I am pretty unsure on how to do calculations using this "fancy" mathematical kind of physics.</p>
<p>First off, I'm lost with (a). But I'll have a go at (b):
As far as I understood, d'Alemberts principle states, that if $M$ is a constraining manifold, $x(q)$ is a curve in $M$ and $\xi$ is a vector perpendicular to $T_xM$, then $x$ satisfies Lagrange's equations</p>
<p>$\frac{d}{dt} \frac{\partial L}{\partial \dot q} = \frac{\partial L}{\partial q} \qquad L = \frac{{\dot x}^2}{2} - U(x)$
</p>
<p>iff for the following inner product, we have</p>
<p>$\left(m \ddot x + \frac{\partial U}{\partial x}, \xi \right) = 0$
</p>
<p>I guess that's about right so far? The constraint would in this case essentially be $\mathbb S^1$, since the rod moves on a circe around the point in contact with the table. Can we assume that all the rod's mass is at the center of mass?</p>
<p>Would we then have $U(x) = -gx_2$ in this case (where $x_2$ is the vertical component of $x$)?</p>
<p>If yes, then $\partial U / \partial x = -ge_2$. Where $e_1, e_2$ are the horizontal and vertical unit vectors, respectively.</p>
<p>At the inital moment, we have $x = \cos(60°) e_1 + \sin(60°) e_2$, so by d'Alembert's principle we must have</p>
<p>$\left(m \ddot x + \frac{\partial U}{\partial x}, \cos(60°) e_1 + \sin(60°) e_2 \right) = 0$
</p>
<p>or written differently</p>
<p>$m \ddot {x_1} \cos(60°) + m \ddot{x_2} \sin(60°) - \sin(60°)g = 0$
</p>
<hr>
<p>So: Is this correct so far? Or am I way off? Is (a) handled any differently up to this point?</p>
<p>Thanks for reading (and hopefully thanks for your helpful reply)!</p>
<p>If anyone could recommend a good problem book (with solutions), in which this kind of mathematical approach is used (I don't know if this is how physicists would actually compute stuff??), I would greatly appreciate it.</p>
<p>Kind regards,</p>
<p>Sam</p>
| 1,805 |
<p>I just came across a line in a paper:</p>
<p>"Assume the probability that a Lagrangian parameter lies between $a$ and $a + da$ is $dP(a) = $ [...]."</p>
<p>This reminded me again of my single biggest qualm I have with the "Bayesian school" - that they assign <em>probabilities</em> to facts of nature, say $P(m_\mathrm{Higgs} = 126\,\mathrm{GeV}$). I understand that you can assign a probability to the outcome of an experiment when you perform it many times. I would also say that you don't actually have to do the experiments, since you can reason about ensembles. You can consider the probability that there is an earthquake tomorrow without really having multiple earths. I would not say however that you can assign a probability to a fact of nature, like a natural constant. It is either such, or such, and there is no dynamics changing it.</p>
<p>Bayesians think of probability as "degree of belief", and in that case of course you can assign probabilities to arbitrary hypotheses. $P (\mathrm{SUSY\;exists})\approx 60\%$ and the such.</p>
<p>I myself like to keep the two cases distinct. I say "probability" when I'm talking about dice, or quantum mechanical decays and the such, and "plausibility" when I'm talking about degrees of belief. The probability that SUSY exists is either 1 or 0. The plausibility is a very sociological thing and depends on who you ask, and what experimental and theoretical inputs you consider. The nice thing is that the maths for plausibility is basically the same as for probability, so no new formulas to learn ;-).</p>
<p>I've been using that distinction in conversations for a while, and nobody seemed to find it strange, so I think this concept is pretty widespread. However, I can't find any literature on it (beyond the usual frequentist/Bayesian debate). My question is, are there any references / essays / lectures on the two different kinds of "$P\,$"? What's the degree-of-belief-$P$ (my "plausibility") usually called? What are the implications of keeping the two distinct?</p>
| 1,806 |
<p>Please explain why static friction is greater than kinetic friction logically.
Speak about it microscopically and tell what does happen on surfaces of objects by considering electromagnetic force between atoms on surface.</p>
| 30 |
<p>I have the equation $$F = (NI)^2\mu_0\frac{\text{Area}}{2g^2}$$
Which calculates the force of an electromagnet. I was wondering if anyone knew what plane Area is taken from? I have heard it is the cross sectional area of electromagnet(which doesn't make sense to me because it already uses the number of turns, N and the current, I), I have heard is is the cross-sectional area of plane <strong>b</strong>, and I have heard it as the cross sectional area of plane <strong>a</strong>. I have also heard it as plain "Area".</p>
<p>A ferromagnetic cylinder being acted on by an electromagnet.(Assume this cylinder is being drawn into a solenoid circle-side first)</p>
<p><img src="http://i.stack.imgur.com/0HY5G.png" alt="enter image description here"></p>
<p>Personally, I think it uses the cross sectional area of plane <strong>b</strong>.</p>
<p>Being a physics problem, can anyone confirm whether or not I should be using the area from plane <strong>b</strong>?</p>
| 1,807 |
<p>I had been thinking about the way an air conditioning system moves heat from one place to another. The unit runs and drops the temp. in the building and raises the temp. outside. Also there is mechanical energy that converts to heat (the compressor and fan motors) and is also put outside. If this is the case, is there an effect caused by A/C systems running on the outside temp.? </p>
<p>Can the total amount of heat being moved from inside to outside contribute to global warming? Consider how many systems there.
As more and more A/C systems are installed and more and more buildings built, can't this lead to (if it hasn't started already) a higher temp outside?</p>
<p>I am not a scientist; if this question is wrong, I would like to know why.</p>
| 1,808 |
<p>Suppose we use the metric $(+,-,-,-)$ thus the momentum squared is </p>
<p>$p^2 = p_0^2-\vec{p}^2 = m^2>0$</p>
<p>Defining $p_E:=\mathrm{i}\cdot p_0$ and $\bar{p}:=(\,p_E,\vec{p})$ with Euclidean norm $\bar{p}^2 = p_E^2+\vec{p}^2$. </p>
<p>Here's my question: </p>
<p>If we plug in </p>
<p>$\mathrm{i}\,p_0$ </p>
<p>instead of $p_E$ we see that $\bar{p}^2 = -p^2 = -m^2$? </p>
<p>So $\bar{p}^2$ is negative? </p>
<p>Also if $\bar{p}^2 = -p^2 = -m^2$ is true...is it always so? Since $p^2$
is a Lorentz invariant, but how do we interpret $\bar{p}^2$ if it's equal to $-m^2$</p>
<p>What I want to get to is the following: </p>
<p>Let </p>
<p>$\mathcal{L}_{int} = \frac{1}{2}g\phi_1^2\phi_3+\frac{1}{2}h\phi_2^2\phi_1$</p>
<p>with:
$p_3 = p_1+p_2$ and</p>
<p>$M>2m$</p>
<p>Suppose we have a triangle loop with incoming momentum $p_3$ of mass $M>2m$ and two outgoing identical particles $\phi_2$ and $\phi_2$ momenta $p_1$ and $p_2$ each of mass $m$ (sorry bad notation but $\phi_1$ is not related to $p_1$). The incoming particle $\phi_3$ splits into two light ones (two $\phi_1$'s) of mass $\eta$ each and each of these connects to two $\phi_2$'s. </p>
<p>Thus we have the following momenta flowing inside the loop: </p>
<p>$k$, $ k-p_2$ and $k+p_1$. </p>
<p>After a Wick rotation we get the following integral: </p>
<p>\begin{equation}
\int{\,\frac{\mathrm{d}^4\bar{k}}{(2\pi)^4} \frac{1}{\bar{k}^2+m^2}\frac{1}{\left(\bar{k}-\bar{p}_2\right)^2+\eta^2}\frac{1}{\left(\bar{k}+\bar{p}_1\right)^2+\eta^2}}
\end{equation}
Now to evaluate these let's use Schwingers trick: </p>
<p>\begin{equation}
\frac{1}{\bar{k}^2+m^2} = \int_0^\infty{\mathrm{d}s\,\mathrm{e}^{-s(\bar{k}^2+m^2)}},
\end{equation}
but for this to be OK we need to have $\mathrm{Re}(\bar{k}^2+m^2)>0$ and similarly for the other propagators, and this is where I get confused. </p>
<p>It seems they don't satisfy this condition depending on how we interpret $\bar{k}^2$ and $\bar{p}^2$ and so on...</p>
<p>On the other hand if all the squares in the denominator of the integrand are taken as positive then the convergence condition is trivially satisfied. </p>
<p>So please help me understand what I'm doing wrong and if you guys can show how to satisfy the positivity condition.
Thanks in advance. </p>
| 1,809 |
<p>Operationally, we can only know about the results of experiments and observations. From them, we can conclude our world is one which is complex enough to allow for computers. After all, we're using computers right now. Our universe has the property of Turing completeness, meaning we can embed any possible computer program on it subject to space, time and energy requirements. Unfortunately, any theory which is Turing complete can always be emulated on any other theory which is also Turing complete. What consequence does this have upon our ability to deduce the 'ultimate' theory of everything?</p>
| 1,810 |
<p>I am trying to get to grips with Altarelli-Parisi-type equations. In chapter 17 of Peskin/Schroeder, they first develop the equations for a similar problem in QED. Equation $(17.123)$ introduces the sum rule
$$
\int_0^1 dx ( f_e(x,Q) - f_\bar{e}(x,Q)
) = 1
$$
where $f_e$ and $f_\bar{e}$ are the distribution functions of electrons and antielectrons 'inside' an electron. <strong>I'm trying to prove that this is independent of $Q$.</strong></p>
<p>The evolution equations are ($(17.120)$ in Peskin/Schroeder)
$$
\frac{d}{d\log Q} f_e(x,Q)= \frac{\alpha}{\pi}\int_x^1 \frac{dz}{z} \left( P_{e\leftarrow e}(z) f_e(\frac{x}{z},Q) + P_{e\leftarrow\gamma}(z)f_\gamma(\frac{x}{z},Q)\right)
$$
$$
\frac{d}{d\log Q} f_\bar{e}(x,Q)= \frac{\alpha}{\pi}\int_x^1 \frac{dz}{z} \left( P_{e\leftarrow e}(z) f_\bar{e}(\frac{x}{z},Q) + P_{e\leftarrow\gamma}(z)f_\gamma(\frac{x}{z},Q)\right)
$$
where the relevant splitting functions is given by (equation $(17.121)$ in Peskin/Schroeder)
$$
P_{e\leftarrow e}(z) = \frac{1+z^2}{(1-z)_+}+\frac{3}{2}\delta(1-z)
$$
Using $\frac{d}{d\log Q}$ on $(17.123)$ gives (the part involving $P_{e\leftarrow\gamma}(z)$ cancels):
$$
\frac{\alpha}{\pi}\int_0^1 dx \int_x^1 \frac{dz}{z} P_{e\leftarrow e}(z) \left( f_{e}(\frac{x}{z},Q) - f_\bar{e}(\frac{x}{z},Q) \right)
$$
Insterting $(17.121)$ and using that
$$
\int_0^1 dx \frac{f(x)}{(1-x)_+} = \int_0^1 dx \frac{f(x)-f(1)}{(1-x)}
$$
I get
$$
\frac{\alpha}{\pi}\int_0^1 dx \int_x^1 \frac{dz}{z}
\left(\frac{1+z^2}{(1-z)_+}+\frac{3}{2}\delta(1-z) \right)
\left( f_{e}(\frac{x}{z},Q) - f_\bar{e}(\frac{x}{z},Q) \right)
$$
$$
=
\frac{\alpha}{\pi}\int_0^1 dx
\left(
\int_x^1 dz \left( \frac{1+z^2}{(z-z^2)}\Delta(\frac{x}{z},Q) -\frac{2}{1-z} \Delta(x,Q) \right)
+ \frac{3}{2} \Delta(x,Q) \right)
$$
This expression is singular and it seems that the singularities in the first two terms should cancle. However, I'm at a loss what to do here. My idea was to extract the singularity in the first term, but that seems like i'm doing it backwards (and I haven't figured out how to do it). Any hint would be appreciated, I'm not looking for full solutions.</p>
| 1,811 |
<p>Basically, I can't stop wondering why light (the photon) is so special, compared to all the other particles known (and unknown) to modern day physics.</p>
<p>Could it be that there exists an upper limit on speed that is instead a property of another "entity" (particle / wave), other than the photon?</p>
<p>A question obviously inspired by the recent <em>very slightly possible</em> superluminal neutrino findings</p>
| 1,812 |
<p>How complicated is it to calculate a surface normal on the spherical approximation of the earths surface pointing towards the sun at a given point in time?</p>
<p>What I try do is to highlight a small area on a world map where the radiation from the sun tangential hits a imaginary sphere around the earth.</p>
<p>This is just to get an idea where this area was at the given time, so this information has not to be very accurate. As a mater of fact I will just incorporated this information in the map if it is easy enough to calculate.</p>
| 1,813 |
<p>Does adding heat to a material, thereby increasing electrical resistance in the material increase or decrease entropy? </p>
<p>Follow up questions:<br>
Is there a situation were <a href="http://en.wikipedia.org/wiki/Heat_flux" rel="nofollow">Heat flux</a> ie. thermal flux, will change entropy?<br>
Does increasing resistance to em transfer prevent work from being done?</p>
| 1,814 |
<p>Is there a way to calculate, or a reference table I can to look up which provides the average distance a photon travels before it encounters an electron and is absorbed or re-emitted in a fiber optics cable? I asked a fiber manufacturer but all they could come up with is the index of refraction. I'm just looking for an approximation.</p>
| 1,815 |
<p>I'm working through Mattuck's "A Guide to Feynman Diagrams in the Many-Body Problem", but I'm stuck on a bit which I feel should be trivial.</p>
<p>In section 3.2 (p 43 in the Dover edition) he gives a Hydrogen atom as an example of a system which can be considered to have a p-dependent potential term.</p>
<p>In his words,</p>
<p>"the Hamiltonian of the center of mass motion of a Hydrogen atom is $H = p^2 / (m + m_e)$ where $m$ = proton mass and $m_e$ = electron mass.</p>
<p>(First question: shouldn't there be a factor 2 in the denominator here?)</p>
<p>This may be broken up into</p>
<p>$$H = \frac{p^2}{2m} - \frac{m_e}{(m_e+m)m}p^2$$</p>
<p>and the second term treated as if it were a perturbating potential."</p>
<p>Second question: I can't for the life of me figure out how he breaks it up like that, whether I include the aforementioned factor 2 or not..</p>
<p>Both multiplying by $\frac{m - m_e}{m - m_e}$ and ignoring terms quadratic in $m_e$, and deriving the first order taylor expansion around $m$ (in both cases inclluding the factor 2 which I believe should be there) give</p>
<p>$$\frac{p^2}{2m} - \frac{p^2m_e}{2m^2}$$</p>
<p>which looks kind of close, but not quite it.</p>
<p>Of course this is not a hugely significant part of the text but it's really bugging me so a bit of help would be greatly appreciated...</p>
| 1,816 |
<p>What has the reaction been towards the <a href="http://arxiv.org/abs/1309.4095" rel="nofollow">recent paper</a> claiming to have a proof that scale invariance plus unitarity implies conformal invariance in 4d?</p>
| 1,817 |
<p>I've been reading through FLP Vol. II, and he has proven that as the flux through a closed surface is: $\ \int_{surface} \mathbf{F} \space \mathrm{d}\mathbf{a} $, according to the divergence theorem, the flux through a surface can be defined as: $\ \int_{volume} \nabla \cdot \mathbf{F} \space \mathrm{d}V $, where $\ \mathbf{F} $ is any vector field, and the volume is that which is enclosed by the surface.</p>
<p>Previously he had stated as a word equation that: $\ \text{Flux of } \mathbf{B} \text{ through any closed surface}=0. $ I would therefore assume that $\ \int_{volume} \nabla \cdot \mathbf{B} \space \mathrm{d}V = 0$, however Gauss' law for magnetism states that: $\ \nabla \cdot \mathbf{B} = 0$. Does that mean that $\ \nabla \cdot \mathbf{B} = 0$ and $\ \int_{volume} \nabla \cdot \mathbf{B} \space \mathrm{d}V = 0$ are equivalent statements, or am I making a fundamental error somewhere?</p>
| 1,818 |
<p>Is it true that the mass of air in normal atmospheric pressure over 1$m^2$ is 10326 $kg$?
I calculated it from pressure formula </p>
<p>$p=\frac{F}{A}$. </p>
<p>Let $m=?, A=1 m^2 and p=101300 Pa$. </p>
<p>$p=\frac{F}{A} \Leftrightarrow ...\Leftrightarrow
m= \frac{pA}{g}=\frac{101300 \cdot 1 }{9,81} = 10326 kg $.
So why we don't feel that weight, because if $A=160 cm^2 = 160 \cdot 10^{-4} m^2$( the area of normal man
s feet), then
$m=\frac{pA}{g}=\frac{101300 \cdot 160 \cdot 10^{-4} }{9,81} =165 kg$.</p>
<p>Am I missing something? Why we don't feel that weight?</p>
| 1,819 |
<p>What happens if we lift a box of ideal gas? Work is done to the box but no heat is getting into it. So does it's internal energy increase by the amount of work done? Or is it that lifting is not counted as work done to the system?</p>
<p>Or is it the case that work turns into heat in a box which quickly flows out to the surrounding, thereby resulting in no net internal energy change?</p>
| 1,820 |
<p>If a box of ideal gas and another box of diatomic gas are in thermal equilibrium, </p>
<ol>
<li><p>does it mean that the average translational energy of ideal gas particle (A) is the same as that of diatomic gas particle (B)? </p></li>
<li><p>or does it mean that A is equal to the sum of the average translational energy (B) + average vibrational energy (C) + average rotational energy (D) of diatomic gas particle?</p></li>
<li><p>Equilibrium is achieved when A = B = C = D? </p></li>
<li><p>or is it A = B + C + D?</p></li>
</ol>
| 1,821 |
<p>I am trying to make sense of statements about unitarity in <a href="https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/" rel="nofollow">this popular science article</a> about Nima and Jaroslav's new idea.</p>
<p>My first query is that it is claimed that unitarity is a pillar of quantum field theory:</p>
<blockquote>
<p><em>Locality and unitarity are the central pillars of quantum field theory</em></p>
</blockquote>
<p>In second quantization, however, I recall nothing of unitarity, and one can construct quantum field theories that are not unitary e.g., in the Standard Model without a Higgs boson, the $WW\to WW$ elastic scattering matrix element is greater than unity for $\sqrt{s}\gtrsim1 \textrm{TeV}$. Is it correct that unitarity is a pillar of quantum field theory?</p>
<p>My second query regards a described experiment for measuring unitarity. It is suggested that one repeatedly measures the final state of a scattering process: </p>
<blockquote>
<p><em>To prove [unitarity], one would have to observe the same interaction over and
over and count the frequencies of the different outcomes. Doing this
to perfect accuracy would require an infinite number of observations
using an infinitely large measuring apparatus, but the latter would
again cause gravitational collapse into a black hole.</em></p>
</blockquote>
<p>Take, e.g., a simplified experiment in which one repeatedly measures the state
$$
\psi = a \phi +b\chi.
$$</p>
<p>What would the results for repeated measurements of the state be for $|a|^2+|b|^2>1$? and $|a|^2+|b|^2<1$?</p>
<p>Upon measurement, I would be entangled with the state. I could only see one outcome per measurement. Maybe an omniscient god could see that states were destroyed for $|a|^2+|b|^2<1$ and created for $|a|^2+|b|^2>1$, if he saw all worlds in a many worlds interpretation. But I would see nothing odd? So how is this experiment supposed to work?</p>
| 1,822 |
<p>As we all know, the stars we see in the night sky might already be dead. I was wondering though, when was this fact or conclusion commonly established? Today, most people (let's assume with an above average education) would probably be aware of this fact.</p>
<p>When is the earliest time when the same could be said? I am particularly interested if the same could be said for the time period revolving around the period 1850 - 1900.</p>
<p>I know that the speed of light was approximated fairly accurately in the 17th century. Knowing this (finite) speed, it's not hard for me to draw the conclusion that the source of the light I see may not be there anymore. Would this be an easy conclusion to draw a hundred years ago however? Maybe they thought stars don't die?</p>
| 1,823 |
<p>Beyond one-loop, the beta function of a QFT is scheme dependent. I would like to understand better this ambiguity. </p>
<p>The easiest thing to say is that you haven't calculated something physical, so of course it does not need to be scheme independent. However, the anomalous dimension of operators is I think an observable quantity since we may measure critical exponents in the lab, and the anomalous dimension results from the same sort of calculation.</p>
<p>Moreover, I can relate the beta functions to the trace anomaly. Schematically, $\langle \partial_\mu j_{dilation}^\mu \rangle=\langle T^\mu_\mu \rangle \approx \beta$ (See Peskin 19.5 for the case of QED). If i couple some field to the trace of $T$ I think I should be able to turn this anomaly into a cross-section for some process which would be measurable (think of ABJ anomaly and $\pi^0 \to \gamma \gamma$ for instance). </p>
<p>So the questions is: </p>
<p>1) Is it known how the terms in the beta function may differ between regularization schemes? If I try to calculate the couplings at the fixed point using different schemes, will I get the same answer (I am aware the location of the fixed point is not physical, but if I use the same field variables I could imagine this being scheme independent)? How may I see that although the beta function and location of the fixed point are ambiguous, the anomalous dimensions are not?</p>
<p>2) How would this ambiguity cancel out if I have a theory where I can turn the trace anomaly into a prediction of a scattering amplitude? Or can this simply not be done?</p>
<p>Any clarification or suggestion for references is appreciated.</p>
| 1,824 |
<p>I need some <a href="http://en.wikipedia.org/wiki/Albert_Einstein" rel="nofollow">Einstein</a>'s papers translated into English. There is one complete collection of his papers but only a few of them have been translated in English. The rest are in their original language -- German, which, unfortunately, I can't read. Have you seen anywhere all of his paper translated in English?</p>
| 1,825 |
<p>In classical mechanics coordinates are something a bit secondary. Having a configuration space $Q$ (manifold), coordinates enter as a mapping to $\mathbb R^n$, $q_i : Q \to \mathbb R$. The primary thing is the manifold itself and its points.</p>
<p>On the contrary, quantum mechanics for classical coordinates has operators $\hat q_i$. And I never encountered some sort of "manifold abstraction" for the space operator. Is there a coordinate-free approach to the space operator in a non-relativistic quantum mechanics?</p>
| 1,826 |
<p>I'm attempting a problem from Zwiebach: A First Course in String Theory and am completely stuck. Could anyone give me a hint? The problem is as follows.</p>
<p>Consider $S$, $S'$ two Lorentz frames with $S'$ boosted along the $+x$ axis. In frame $S$ we have a cubic box with sides of length $L$ at rest. The box is filled by a material, also at rest, of uniform charge density $\rho$. In $S$ we assume that the charge density $\underline{j}=0$. Use the Lorentz invariance of charge to calculate the charge density $\rho'$ and current density $\underline{j}'$ in $S'$. Verify that $(c\rho,\underline{j})$ a 4-vector.</p>
<p>The charge density is easy. Indeed $L^3\rho = Q = Q' = L'^3\rho'=\frac{L^3}{\gamma}\rho'$ so $\rho' = \gamma \rho$. I know I'm right here because this agrees with what we'd expect from a 4-vector under Lorentz boost.</p>
<p>To do the current density I tried to use $0=\frac{\textrm{d}Q}{\textrm{d}t}=\frac{\textrm{d}Q'}{\textrm{d}t'}=\int_S\underline{j}'.\textrm{d}\underline{a}=j'_xL^2$ so $\underline{j}'=0$ since $j'_y=j'_z=0$ clearly must be zero.</p>
<p>I know this is wrong though, because it doesn't agree with what I'd expect from a 4-vector! What am I doing wrong? And is this the right way to go about this question?</p>
<p>Many thanks in advance!</p>
| 1,827 |
<p>I am just curious as a non-US person:</p>
<p>how does undergraduate physics course progress in U.S. colleges?</p>
<p>Do they go right into classical mechanics books, or do they teach introductory courses first, then specialize on classical mechanics, electrodynamics etc. in the second year?</p>
<p>First-year, second-year, third-year distinction would be much appreciated.</p>
| 1,828 |
<p><a href="http://www.cchem.berkeley.edu/gsac/grad_info/prelims/binders/dimensionless_numbers.pdf" rel="nofollow">Most dimensionless numbers</a> (at least the ones easily found) used for dimensional analysis are about fluid dynamics, or transport phenomena, convection and heat transfer - arguably also sort of fluid mechanics.</p>
<p>My understanding of dimensional analysis is the following: Derive dimensionless numbers from the description of a system, find the ones physically meaningful, and use them to compare different situations or to scale experiments.</p>
<p>Is this possible in other fields, like classical mechanics, and their engineering applications?
Example: describe a horizontal beam by:</p>
<p>$$
X=\frac
{\text{forces acting on the beam}}
{\text{forces beam can withstand without plastic deformation}}
$$</p>
<p>Both parts of the ratio being functions of shape, density, gravity, material constants etc. </p>
<p>My assumption is yes, it's possible, but most fields outside the sort-of fluid mechanics described above are easy enough to calculate without dimensional analysis. </p>
| 1,829 |
<p>We have known for a long time that graphene has in-plane thermal conductivity ranging between 2000 and 4000 $W m^{-1} K^{-1}$. But in order to model heat transport on a sheet of graphene, we need more than the conductivity: we also need specific heat in order to obtain the thermal diffusivity that is used in the equation.</p>
<p>I couldn't find any measurement results online for this quantity. I've only seen some crude estimates based on phonon transport, but even so, no specific figures.</p>
| 1,830 |
<p>The electric energy stored in a system of two point charges $Q_1$ and $Q_2$ is simply $$W = \frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{a}$$ where $a$ is the distance between them.</p>
<p>However, the total energy can also be calculated through the volume integral of magnitude squared of the electric over all space: $$W = \frac{\epsilon_0}{2}\int_{\mathbb{R}^3} E^2\,dV$$</p>
<p>Suppose that $Q_1$ sits on the origin and $Q_2$ a distance $a$ away on the $z$-axis. Then the electric field is $$\vec{E}(x,y,z) = \frac{1}{4\pi\epsilon_0}\left[\left(\frac{Q_1}{r^3} + \frac{Q_2}{d^3}\right)x\hat{x} +\left(\frac{Q_1}{r^3} + \frac{Q_2}{d^3}\right)y\hat{y} + \left(\frac{Q_1z}{r^3} + \frac{Q_2\left(z-a\right)}{d^3}\right)\hat{z}\right]$$
where
\begin{align}
r &= \sqrt{x^2+y^2+z^2} \\
d&= \sqrt{x^2+y^2+\left(z-a\right)^2}
\end{align}</p>
<p>Calculating $W$ through $\int_{\mathbb{R}^3} E^2\,dV$ seems extremely difficult; Mathematica, for example, appears stumped. Yet its result should simply be $\frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{a}$, correct? The integral formula still applies to point charges, correct?</p>
| 1,831 |
<p>Bernoulli's principle makes sense when you apply it to fluids. If you decrease the diameter of a pipe then the velocity of the fluid increases because it needs to keep the same rate of fluid moving through the pipe. </p>
<p>So my question is:</p>
<p>If Voltage == Diameter of the pipe</p>
<p>and</p>
<p>Current == Rate of which the fluid is moving</p>
<p>Why do resistors work?
Shouldn't the resistor only actually work within itself but then return the current to it's actual rate once you have passed it?</p>
<p>Or have I taken the analogy of wires being like pipes of water to far?</p>
| 1,832 |
<p><img src="http://i.stack.imgur.com/w04j8.jpg" alt="heat exchanger diagram"></p>
<p>I want to design a heat exchanger in a chimney in order to utilize heat from chimney. I have done several experiments, but I could not determine the exact length of tube (carrying water), such that its inlet temp is ambient temperature and outlet temperature is expected to be 100 degree Celsius. I would be very thankful if some one would help me determine the length of the tube. tube diameter is 10mm (almunium), chimney diameter is(120 mm). </p>
<p>Can anyone help me with formulas involved in calculating the heat transfer and length of the tube...</p>
<p>I already calculated the lenght experimentally but I could not do it mathematically.</p>
| 1,833 |
<p>A glass mirror (with metal backing layer) will reverse the polarisation of circularly polarised light upon reflection.</p>
<p>A polished piece of metal will also reverse the polarisation of circularly polarised light upon reflection. (I have tested and confirmed this for myself).</p>
<p>wikipedia states the reason a mirror will reverse the polarisation of circularly polarised light is:</p>
<blockquote>
<p>...[A]s a result of the interaction of the electromagnetic field with the conducting surface of the mirror, both orthogonal components are effectively shifted by one half of a wavelength.</p>
</blockquote>
<p>However, my understanding of mirrors is that only a polished piece of metal will phase shift a wavelength by half a wavelength, whereas a glass mirror (with metal backing layer) will not produce a phase shift. For example wikipedia which states:</p>
<blockquote>
<p>According to Fresnel equations there is only a phase shift if n2 > n1 (n = refractive index). This is the case in the transition of air to reflector, but not from glass to reflector</p>
</blockquote>
| 1,834 |
<p>So I have been trying to learn about entanglement and quantum teleportation and from what I've been able to gather so far, the <strong>teleportation</strong> part seems to be misleading.</p>
<p>At first I thought that the two particles were of a uniform undetermined state which would collapse probabilistically upon observation.</p>
<p>But the more I read into it, it began to seem like the following unimpressive scenario as it relates to the Schrödinger's cat analogy:</p>
<p>It seems as though a dead cat and a live one are put into two boxes that can only be observed once. When one person gets the live cat, they know the other got the dead cat. They can infer this knowledge instantly, but who cares because it took UPS two days to ship the thing.</p>
<p>If this is the case, why do they call it <em>quantum teleportation</em> and if it isn't the case could someone explain it to me better?</p>
| 1,835 |
<p>What is Dalitz decay?</p>
<p>I know there are Dalitz $\pi^0 \to e^+ + e^- + \gamma$ <a href="http://www.nikhef.nl/pub/experiments/zeus/theses/wouter_verkerke/latex2html/node60.html" rel="nofollow">decay</a>, $w \to \pi^0 + e^+ + e^-$ decay, may be more. But is there a rule to say which decay is Dalitz and which is not?</p>
<p>Is there a rule to say which particle can decay by Dalitz decay and which does not?</p>
| 1,836 |
<p>In Pockels electro-optic effect, change in Electric field produces change in refractive index/ birefringence. Moreover this effect becomes electric field squared in the case of Kerr effect. If we increase the electric field more for example 3 ,4 , 5 times . we will observe the same phenomenon of Kerr effect or is it something else ?</p>
| 1,837 |
<p>I want to determine the potential energy of two equally charged spherical charges by using the equation: $V_{pot}= \int_V \frac{1}{2} \epsilon_0 E^2 dV$ and therefore I was wondering what I has to take as $E$? The sum of the electric fields of both charges? Notice, that I want to use this equation on purpose since it enables me to determine the potential energy in a particular volume.</p>
| 1,838 |
<p>Imagine we live on cylinder(we are 2d creature), put a rope around that cylinder and start pulling both ends of the rope against each another. Will the space get deformed? I guess it will, I have to put some energy to the rope and energy deforms the space. Is it possible to calculate shape of the space based on the force I put in the rope? </p>
<p>In order to calculate this I guess you have to make 3d analogy and use laws of general relativity. </p>
| 1,839 |
<p>I am trying to calculate B mixing in the Standard Model (in preparation to go beyond the SM). I have no trouble doing the gamma matrix algebra etc. but the loop integral keeps tripping me up. In my calculation I have
$$ \int \frac{d^4 k}{(2\pi)^4} \frac{k^2}{(k^2-m_1^2) (k^2 - m_2^2) (k^2- M_W^2)^2} $$
I know about Feynman parametrization etc. but the result I get does not comply with what I find in the Literature. Unfortunately basically all calculations simply say "we calculate by standard methods" and have a function
$$S(x_t) = \frac{4x_t - 11 x_t^2 + x_t^3}{4(1-x_t)^2} - \frac{3x_t^3 \ln x_t}{2(1-x_t)^3} $$
with $x_t = m_t^2 / M_W^2$ if $m_1 = m_2 = m_t$. This is not directly the result of evaluating the above integral though, since I have at least a factor of $1/M_W^2$ that is in the integral, but not included in S.</p>
<p>Where can I find a full calculation of the box diagram and what is the exact relation of the loop integrals to the functions $S$?</p>
<p>I do know about the general 1, 2, 3 and 4 point functions, generally called $A_0, B_0, B_1, \dots$. The $S$ is different from $D(0, 0, 0, m_1, m_2, M_W, M_W)$ though!</p>
| 1,840 |
<p>I've been told that a vacuum isn't actually empty space, rather that it consists of antiparticle pairs spontaneously materialising then quickly annihilating, which leads me to a few questions.</p>
<p>Firstly, is this true? And secondly, if so, where do these particles come from?... (do the particles even have to come from anywhere?)</p>
| 1,841 |
<p>I have a setup where a motor is spinning at a constant (known) RPM, under no load. I know the power going into the motor (voltage * current), and I can find out the rotational kinetic energy of the rotor. </p>
<p>My question is, how do I calculate the efficiency of the motor from this? Is it even possible? I understand that the motor is not doing any "useful work", but it is still overcoming frictional forces to keep spinning, and there are definitely energy losses there.</p>
| 1,842 |
<p>Consider the image below. It shows a double slit experiment but with a single photon at a time. <strong>My question is as follows</strong>:</p>
<p>Why is it that the photons always take a different path when shot at the same target? Where does the uncertainty lie? If we shoot it in exactly the middle of the two slits, why does it have a 50-50 chance of going into either slit? And why is the amount of diffraction for a single photon always different?</p>
<p>I know that people will say that the photon enters both the slits at the same time and things like that. But does anyone have an intuitive explanation as to why this happens? Why does a photon, shot with the same frequency and exactly in the same direction, still have the probability of entering either slit. Why is it that the diffraction of a single photon is different for the same wavelength?</p>
<p>So in brief, why does a single photon which is shot in an exactly the same why as the previous one, end up being in a different place. I am looking forward to an answer with the least possible math (if any). Or is it that a photon cannot be shot in the exact same way as the previous one?</p>
<p><img src="http://i.stack.imgur.com/pshsu.gif" alt="enter image description here"></p>
<p>Image source: <a href="http://abyss.uoregon.edu/~js/images/photon_double_slit2.gif" rel="nofollow">http://abyss.uoregon.edu/~js/images/photon_double_slit2.gif</a></p>
| 1,843 |
<p>The macroscopic Maxwell's equations can be put in terms of differential forms as
$$\mathrm{d}\mathrm{F}=0,\quad\delta \mathrm{D}=j\implies \delta j=0,\quad \mathrm{D}=\mathrm{F}+\mathrm{P}.$$
$\mathrm{F}$, $\mathrm{D}$, and $\mathrm{P}$ are 2-forms; $j$ is a 1-form. $\mathrm{F}$ is the $electromagnetic\ field$, which has 3-vector components $E_i,B_i$, usually called the $electric\ field$ and the $magnetic\ field$; $\mathrm{D}$ is a generalized electromagnetic field, generalized in the sense that $\mathrm{dD}\not=0$, which has 3-vector components $D_i,H_i$, called, amongst other names, the $electric\ displacement\ field$ and the $magnetizing\ field$; $j$ is a conserved 4-current; and $\mathrm{P}$ is the electromagnetic polarization/magnetization, which has 3-vector components $P_i,M_i$, usually called, up to a factor $\pm 1$, the $polarization$ and the $magnetization$, which in the macroscopic form of Maxwell's equations model the internal degrees of freedom, whereas in the microscopic form of Maxwell's equations we have $\mathrm{P}=0$. The <a href="http://en.wikipedia.org/wiki/Maxwell%27s_equations" rel="nofollow">Maxwell's equation Wiki page</a>, together with its many links, does a reasonable job of summarizing all this.</p>
<p>In QED, there are internal degrees of freedom associated with the Dirac field, so should we be working with $\mathrm{D}$ when we quantize? Classically, given a differentiable bivector field such as $\mathrm{D}$, there is inevitably a conserved 4-current $\delta \mathrm{D}$, unless the equations of motion are such that this quantity is identically zero. [Edit, to reflect Cristi Stoica's comment] Given an arbitrary 2-form such as $\mathrm{D}$, <em>if</em> Hodge decomposition could be applied, we could decompose $\mathrm{D}$ uniquely as $$\mathrm{D}=\mathrm{dA}+(\mathrm{D}-\mathrm{dA}).$$
For Minkowski space, such decompositions are possible but are <em>not</em> unique because there is no positive-definite bilinear form on the function space; for the forward light-cone component $\mathrm{D}^+$ the decomposition can be restricted by minimizing the positive semi-definite integral $$\int [\widetilde{\delta(\mathrm{D}-dA)}]_\mu(k)[\widetilde{\delta(\mathrm{D}-dA)}]^\mu(k)\theta(k^2)\theta(k_0)\frac{\mathrm{d}^4k}{(2\pi)^4},$$
and similarly for the backward light-cone, but no such restriction is available for space-like components.
Looked at this way, the electromagnetic field $\mathrm{F}$ is just a component of the real object of interest, $\mathrm{D}$, that can be expressed as $\mathrm{F}=\mathrm{dA}$, for which, inevitably, $\mathrm{dF}=0$. The nonunique component $\mathrm{D}-\mathrm{dA}=\mathrm{P}$ of $\mathrm{D}$ cannot be expressed in terms of a single potential. [End of edit -- constructed somewhat in the moment so it may have to be modified.]</p>
<p>If $\mathrm{D}$ is taken to be the real object of interest, with $\delta\mathrm{D}=j$ an independent degree of freedom, then does that mean that we should look for second-order differential equations for $\mathrm{D}$ in the first instance, probably in association with additional degrees of freedom, in view of the additional degrees of freedom that are present in the Standard Model?</p>
<p>I should point out that, for the purposes of this question, I take the Dirac wave function not to be observable in the classical Maxwell-Dirac theory, with $\overline{\psi(x)}\psi(x)$, $(\delta\mathrm{D})^\mu=j^\mu=\overline{\psi(x)}\gamma^\mu\psi(x)$, $\overline{\psi(x)}\gamma^{[\mu}\gamma^{\nu]}\psi(x)$, $\overline{\psi(x)}\gamma^{[\mu}\gamma^\nu\gamma^{\rho]}\psi(x)$, and $\overline{\psi(x)}\gamma^5\psi(x)$ being (non-independent) 0-, 1-, 2-, 3-, and 4-form observables, respectively.</p>
<p>This is almost not a question, for which apologies, however I am interested in any critique of details or of whatever minimally elaborated plan there might seem to be to be here, or in any reference that seems pertinent. The ideas lie somewhat in the same territory as an earlier question of mine, <a href="http://physics.stackexchange.com/questions/26945/gauge-invariance-for-electromagnetic-potential-observables-in-test-function-form">Gauge invariance for electromagnetic potential observables in test function form</a>, in that I prefer to disavow unobservable fields unless there are absolutely clear reasons why they are unavoidable.</p>
| 1,844 |
<p>Explained at the level of a 5$^{\text {th}}$ semester physics student (i.e. pre QFT, but far beyond the level of a news article for non-physicists, which avoids all details and only deals in analogies) ...</p>
<ul>
<li>What has been measured at CERN some days ago?</li>
<li>What are the essential ingredients of the theory necessary to interpret said measurement? And so how do we deduce from the results that there is a new field/particle observed?</li>
<li>How to read the most relevant graphs in the presentation of the results?</li>
</ul>
| 1,845 |
<p>Why do we need neutrino to explain neutron <a href="http://en.wikipedia.org/wiki/Beta_decay" rel="nofollow">decay</a>?
Is there any evidence regarding existence neutrinos in the context of
$n\to p + e + \bar{\nu}_e$?</p>
| 1,846 |
<p>What is the maximum voltage that can be put on a metal sphere before electrons fly off it or the metal itself explodes due to electrostatic forces?</p>
| 31 |
<p>We have the the five <a href="http://en.wikipedia.org/wiki/Lagrangian_point" rel="nofollow">Lagrange points</a> (let consider Earth and Sun):</p>
<ul>
<li>$L_1$ - lie between Sun and Earth;</li>
<li>$L_2$ - beyond the Earth;</li>
<li>$L_3$ - beyond the Sun;</li>
</ul>
<p>And what's the difference between $L_4$ and $L_5$? Does they defined with the respect to rotation of Earth around the Sun?</p>
| 1,847 |
<p>Why does the nature always prefer low energy and maximum entropy?</p>
<p>I've just learned electrostatics and I still have no idea why like charges repel each other.
<a href="http://in.answers.yahoo.com/question/index?qid=20061106060503AAkbIfa">http://in.answers.yahoo.com/question/index?qid=20061106060503AAkbIfa</a>
I don't quite understand why U has to be minimum. Can someone explain?</p>
| 1,848 |
<p>I'm a student and I had to give a talk on seminar about <a href="http://en.wikipedia.org/wiki/Quantum_Zeno_effect">Quantum Zeno effect</a> and Anti-Zeno effect to my colleagues (all listeners have had a course in quantum physics, but not a heavy one with all the bra and ket stuff).</p>
<p>My first idea to give a simple explanation of Zeno's effect was this:
Let's take a look at exponential decay where the chance for particle or state to survive some time $t$ is $P_S=e^{-t/\tau}$. If I measure it after time $\tau$ I have chance $P_S=1/e$ that it will still be intact.</p>
<p>If I instead allow it to do it's things only for time $\tau/N$ and then measure it, the survival chance will be $P_S=e^{-1/N}$ which approaches $1$ as $N$ increases. To achieve the same total time, I have to repeat this procedure $N$ times and the total survival probability is... $P_S=(e^{-1/N})^N=1/e$.</p>
<p>So it obviously doesn't work, I get no Zeno's effect in this way.</p>
<p>It's interesting that after I gave the talk professor rose and said "Well, this can be easily understood if we look at the exponential decay". Then he started drawing exponent and another exponent that's repeatedly interrupted and reset to initial state after small intervals. Later we agreed that this won't actually work, but the question is - why? </p>
<p>Why doesn't this intuitively obvious way doesn't work and what would be the correct law out of which one could see the Zeno's effect? Is there any elegant way to explain this effect without heavy math and angles of state vectors?</p>
<p>ADDITIONAL QUESTION (related):
Is it correct to use name "Quantum Zeno Effect" for turning of polarization by series of inclined polarizers or the thing that is done in <a href="http://research.physics.illinois.edu/QI/Photonics/papers/kwiat-sciam-1996-nov.pdf">this</a> article?</p>
| 1,849 |
<p>How can we compute the integral $\int_{-\infty}^\infty t^n e^{-t^2/2} dt$ when $n=-1$ or $-2$? It is a problem (1.11) in Prof James Nearing's course <em>Mathematical Tools for Physics.</em> Can a situation arise in physics where this type of integral with negative power can be used?</p>
| 1,850 |
<p>By my understanding, if everything doubled in size, such as the Sun and the Earth, and because the space in between them (which is nothing) can't expand, would the gravities greatly change and the Earth be pulled into the Sun? </p>
| 454 |
<p>Suppose we have a system of bosons represented by their occupation numbers
$$\tag{1} | n_1, n_2, ..., n_\alpha, ... \rangle$$
Then we can define creation and annihilation operators
$$\tag{2} a_\alpha^\dagger| n_1, n_2, ..., n_\alpha, ... \rangle = \sqrt{n_\alpha+1} | n_1, n_2, ..., n_\alpha+1, ... \rangle$$
$$\tag{3} a_\alpha| n_1, n_2, ..., n_\alpha, ... \rangle = \sqrt{n_\alpha} | n_1, n_2, ..., n_\alpha-1, ... \rangle$$
This is nice because the number operator is just $a_\alpha^\dagger a_\alpha$. However, would it be sensible to define an alternate set of operators to work with?
$$\tag{4} b_\alpha| n_1, n_2, ..., n_\alpha, ... \rangle = | n_1, n_2, ..., n_\alpha+1, ... \rangle$$
$$\tag{5} c_\alpha| n_1, n_2, ..., n_\alpha, ... \rangle =
\begin{cases}
| n_1, n_2, ..., n_\alpha-1, ... \rangle & n_\alpha>0 \\
0 & n_\alpha=0
\end{cases}$$
$$\tag{6} N_\alpha| n_1, n_2, ..., n_\alpha, ... \rangle = n_\alpha| n_1, n_2, ..., n_\alpha, ... \rangle
$$
Why don't we work with these operators? The bosonic creation and annihilation operators $a_\alpha^\dagger$ and $a_\alpha$ were defined to mimic the harmonic oscillator's raising and lowering operators ($x \pm i p$), but is there any compelling reason to keep the $\sqrt{n_\alpha+1}$ and $\sqrt{n_\alpha}$ factors?</p>
<p>I suppose $a_\alpha^\dagger$ and $a_\alpha$ obey nice properties such as $[a_\alpha,a_\alpha^\dagger]=1$ and the fact that they are Hermitian adjoints of each other. What are the analogous relationships that $b_\alpha$ and $c_\alpha$ would obey?</p>
| 1,851 |
<p>I would like to construct a 2-local Hamiltonian that acts on a 1D spin chain where each spin transforms as the 3D irrep of $A_4$ which is a subgroup of $SO(3)$. I know that an $SO(3)$ invariant Hamiltonian can be constructed using the Casimir operator like $H = \sum_i \vec{S_i} . \vec{S_{i+1}}$. Is there a similar thing for finite groups (i.e equivalent of a Casimir)? I would explicitly like the on site symmetry to be only $A_4$ and nothing bigger. (eg: I cannot just use $H = \sum_i \vec{S_i} . \vec{S_{i+1}}$). I also need parity and translation invariance but I know how to impose those.</p>
| 1,852 |
<p>Is there some optimal layout of items, or types of items (characterized by size, shape, density, solid/liquid, etc) that will allow a common household refrigerator to function with optimal energy efficiency?</p>
<p>I know this is a very broad and any answer will have to make several assumptions, not the least of which include how often the refrigerator is opened and for how long. I'd be perfectly happy with a "steady-state" answer that assumes, e.g. the refrigerator is never opened. But more is always better. If nothing else, I'm curious about what considerations might go into conducting a more thorough analysis.</p>
| 1,853 |
<p>I thought that modern 3d glasses work by having one lens filter horizontally polarized light, and the other filter vertically polarized light.</p>
<p>However, I found this pair of 3d glasses at my parents' house, and looked at the reflection from the floor at different angles:</p>
<p><img src="http://i.stack.imgur.com/GqauM.jpg" alt=""></p>
<p><img src="http://i.stack.imgur.com/hA3oB.jpg" alt=""></p>
<p>What's confusing me is that turning the glasses 90 degreed changed the color of the light from yellow to blue, but it did that on both lenses simultaneously. I expected one to be yellow while the other is blue, and vice versa, since they should be polarized at a 90 degrees difference.</p>
<p>Can someone explain this? </p>
| 1,854 |
<p>In the lecture, the professor said something along the lines of:</p>
<p>"After a suitable gauge transformation, the standard model higgs field can be expanded as</p>
<p>$$\phi =\left(\begin{array}{c}
0 \\
v+H(x)
\end{array}\right)$$
".</p>
<p>Now, the argument I have been able to scramble from different sources goes along these lines:</p>
<ol>
<li><p>We can write small higgs field excitations as $$\tilde\phi =\left(\begin{array}{c}
i \theta_1(x) + \theta_2(x) \\
v+H(x) - i \theta_3(x)
\end{array}\right)$$</p></li>
<li><p>An appropriately chosen local $SU(2)_L$ transformation transforms this into the above form where all $\theta=0$.</p></li>
<li><p>Thus, by applying an appropriate local $SU(2)_L$ transformation to all elements of the Lagrangian, we can use this form without loss of generality.</p></li>
</ol>
<p>I have the following two issues with this argumentation:</p>
<p>First, how do I know that the first statement is true?</p>
<p>Secondly and most importantly, wouldn't any symmetriy transformation that corrects the higgs weak spinor into the above from , given a random but fixed excitation of the higgs field, also mess up the spinors of the left handed leptons?
In other words, how is it possible to find a local gauge transformation on the Lagrangian that corrects any $\tilde \theta$ into $\theta$, but does not change the form of $ \bar L =\left(\begin{array}{c}
\bar\nu \\
\bar e
\end{array}\right)$ ?? </p>
| 1,855 |
<p>This is a bit quirky: For a very long time I've found Stephen Hawking's evaporating small black holes a lot more reasonable and intuitive than large black holes.</p>
<p>The main reason is that gravity is relative only if your gravity vectors are all parallel. When that is true, you can simply accelerate along with the field and have a perfectly relativistic frame going for you.</p>
<p>Not so if your gravity vectors angle in towards each other, as is particularly true for very small black holes. In that case the energy inherent in the space around the hole becomes quite real and quite hot, and that's regardless of whether you have matter in the mix or not. (Hopefully that's fairly intuitive to everyone in this group?)</p>
<p>So, how can the space immediately surrounding a tiny black hole <em>not</em> be incredibly hot? By its very geometry it must be absolutely bursting with energy due to the non-parallel intersection of extremely intense gravity vectors. So, the idea of that energy evidencing itself in the creation of quite real particles <em>outside</em> of the event horizon seem almost like a necessity, a direct consequence of the energetic structure of space itself.</p>
<p>So, that's really the basis for my question: Isn't the <em>curvature</em> of space a better way to understand its entropy adding up the surface area of a black hole?</p>
<p>By focusing on curvature, <em>all</em> space has entropy, not just the peculiar variety of space found on event horizons. Flat space maximizes entropy, while the insanely curved space near a microscopic black hole maximizes it. I also like this because if you get right down to it, entropy is really all about smoothness, in multiple forms.</p>
<p>So: Is the inverse of space curvature considered an entropy metric? If not, why not? What am I missing?</p>
| 1,856 |
<p>I'm puzzled about how to derive the equations of motion for certain classical systems where some entity is controlling some of the DOFs.</p>
<p>For example, consider a double-pendulum, with lengths $l_1$ and $l_2$, masses $m_1$ and $m_2$, and which deviate from the vertical by $\theta_1$ and $\theta_2$. Let's say that at the joint between the two pendulums (pendula?), there is a little device controlling the angle $\theta_1+\pi-\theta_2$, and forces it to be some function of time: $\theta_1(t)+\pi-\theta_2(t)=g(t)$. If I understand correctly, this is a holonomic constraint, since it is simply a functional relationship between the DOFs and t. Obviously the position and velocities of the masses can then be expressed just in terms of $\theta_1(t)$, $g(t)$, and their derivatives.
My question is: can we then determine the equation of motion for $\theta_1$ with the Euler-Lagrange equations in the "usual" way? The reason I have doubts here is that it seems like the Euler-Lagrange equations come from D'Alembert's principle, where the constraints do no "virtual work" on the system; and I'm not sure the constraint in this case satisfies this.</p>
| 1,857 |
<p>From Lagrangian I got two primary constraint $\phi_i$ and $\phi$. And my Hamiltonian in presence of the constraints becomes- $$H_p=p\dot q-L+\lambda_i\phi_i+\lambda\phi$$ here the $\lambda_i$ and $\lambda$ are Lagrange undetermined multiplier. Now from $\dot \phi_i=[\phi_i,H_p]$ I got secondary constraint $\Sigma_k$ and from $\dot \phi=[\phi,H_p]$ I got another secondary constraint $\Sigma$ . To satisfy the consistency condition I calculated the $\dot \Sigma_k=[\Sigma_k,H_p]$ and $\dot\Sigma=[\Sigma,H_p]$.
$$$$ From the relation I have $\dot \Sigma\approx0$. But the $\dot \Sigma_k$ gives the value of of $\lambda_i$. Now can anyone help me how can I further analyze the constraints in this case? Do I have to put the value of $\lambda_i$ in the equation of $H_p$ and calculate the commutation again? An example would be lovely.</p>
| 1,858 |
<p>I am trying to find the following:</p>
<p><strong>How many pieces of toast would you need to make a black hole?</strong></p>
<p>From what I've learnt so far I need to find an equation for the compression force the massive amount of the intergalactic pile of pieces of toast would exert on itself to be able to compress it to within a Schwarzschild radius. As you can tell, this is not an easy or normal question.</p>
<p>Any help is appreciated.</p>
| 1,859 |
<p>I know this question sounds silly, as if there was a potential difference a current would be created when the terminals are connected together and this would mean energy has come from somewhere.</p>
<p>The reason I ask this though is that from my understanding of the depletion region and built in potential of a diode it seems like if you connected a voltmeter across the whole diode it would show the value of the built in potential.</p>
<p>This is explained in the image below:</p>
<p><img src="http://i.stack.imgur.com/SaSH6.jpg" alt="pn junction under equilibrium bias"></p>
<p>At first, electrons flow from the n type to the p type because there are a higher concentration in the n type, and holes do vise versa. This is called the diffusion current. The first electrons and holes to cross the pn boundary are the ones which are closest to it; these carriers recombine when they meet each other and are then no longer a carrier. This means there is a depletion region of no carriers near the pn boundary. because electrons have left the n type material, and holes have left the p type material, there is a surplus of positive and negative charge on the n and p side of the pn boundary respectively. This causes an electric field that opposes the diffusion current, and so no more electrons or holes cross the boundary and combine. In short, only the electrons and holes near the boundary combine, because after they have done that an electric field is formed that prevents any more carriers from crossing. The current due to this electric field is called drift current, and when in equilibrium this will equal the diffusion current. Because there is an electric field at the boundary (pointing from the positive charge to the negative charge) there is an associated voltage. This is called the built in potential.</p>
<p>If you sample the electric field at each point along the diode from left to right, you would start with 0 in the p region because there are an equal number of protons and electrons. As you approach the depletion region you would see a small electric field pointing back towards the p region, caused by acceptor impurities which now have an extra electron (due to recombination) and therefore now have a net negative charge. This electric field would increase in strength as you get closer to the boundary, and then die away as you get further away.</p>
<p>This electric field means there is a voltage, as shown in graph (d). The p side is at an arbitrary potential, and the n side is at a potential higher than this because there is an electric field between them. This means there is a potential difference across the depletion region; this is known as the built-in potential.</p>
<p>But why when I connect a volt-meter across the whole diode will I not see this built in potential?</p>
<p><strong>Edit:</strong></p>
<p>I've also asked this question on another <a href="http://electronics.stackexchange.com/questions/106496/why-isnt-there-a-potential-difference-across-a-disconnected-diode">SE site</a> And they say that the reason is because the net potential difference across the diode once it has been connected to a wire or volt meter is zero, because a metal-semiconductor junction has an electric field between it, and the overall effect of the electric fields at the junctions of the m-p-n-m materials results in zero potential difference.</p>
<p>Regardless of the fact that voltage does not equal electrostatic potential difference, can you please confirm that there is also no net electrostatic potential difference across a diode connected to a wire or volt meter because of the m-s junctions? I'd like to get a physicists answer on this, to see if this is the truth or just a simplified explanation to make it easier to accept.</p>
| 1,860 |
<p>For example, a harmonic oscillator can have an algebraic solution, and hydrogen potential can<br>
also have an algebraic solution. Here the algebraic method of solution means that we can use the similar methods like $a$ and $a^\dagger$ to solve QM problem. So in general what kind of problem in QM can have an algebraic solution. For example, can infinite potential well have a algebraic solution, and so on.</p>
| 1,861 |
<p>Can anyone please explain why: $$a_1=a_2\tan\alpha $$
<img src="http://i.stack.imgur.com/9IPBy.jpg" alt="enter image description here"></p>
<p>We have 2 <strong>same</strong> cubes placed on a platform, between them there is a wedge which is pushing the cubes in opposite directions. The hard part of the question is to find the ratio between the cubes<br>
accelarion and the wedge acceleration, which is given above, and I cant understand why.</p>
<p>I can't understand the physical idea behind this. </p>
| 1,862 |
<p>In open-closed string duality, we can reinterpret the one-loop open string diagram (an annulus or cylinder) as a propagating closed string, depending on the direction in which we take time to be. This duality is reflected in the amplitudes we attach to these two different interpretations of the cylinder diagram. My question concerns the interpretation in a target space with Lorentzian signature: surely whether we treat the string worldsheet as a loop of open string or a propagating closed string depends on the reference frame? It could for example be that in one reference frame, surfaces of target space simultaneity intersect the cylinder as (two virtual) open strings, but when we boost to another reference frame, the surfaces of simultaneity intersect the cylinder as a closed string. Is this possible and, if so, what would it mean, if anything?</p>
| 1,863 |
<p>I am trying to understand the electronic structure of the negatively charged <a href="http://en.wikipedia.org/wiki/Nitrogen-vacancy_center" rel="nofollow">NV centre in diamond</a>, where there is a so-called <a href="http://en.wikipedia.org/wiki/Zero-phonon_line_and_phonon_sideband" rel="nofollow">Zero-Phonon Line</a> (ZPL) in the spectrum. Can anybody explain what a ZPL is? </p>
| 1,864 |
<p>The hotter something is glowing the more white/blue it appears. A dying medium sized star expands, cools and becomes a red giant for a while, but eventually it is going to gravitationally collapse (once enough Iron (Fe) is accumulated in the core). Then it blows the outer layers away and what is left collapses into a white dwarf.</p>
<p>What makes the dwarf shine? and why is it white? </p>
<p>Does the luminosity decreases as the object cools down, or is there some other reaction that keeps it glowing for a long time? </p>
<p>Can a white dwarf turn brown or black never to be seen again?</p>
<p>Do all white dwarfs turn into Neutron stars eventually?</p>
| 1,865 |
<p>We distinguish between the states of matter: gas, liquid and solid. Possibly we could add the plasma state and/or the superconductive state as new states of matter. Phase transistions at certain temperature perhaps with some other conditions should have to exist. What do you think, does it make sense?</p>
| 1,866 |
<p>I'm just going over a few past exams for tomorrow, and I've come across a question that I'm having quite a bit of difficulty with.</p>
<blockquote>
<p>Let $\left|0\right\rangle$ denote the Fock vacuum state so that $b_j \left|0\right\rangle = 0$, for all $j$. For any positive integer $N$, show that the state $(b_1^{\dagger})^N \left|0\right\rangle$ is a maximal weight state of $gl(3)$ formed by $a_{jk} = b_j^{\dagger} b_k$</p>
</blockquote>
<p>Conceptually, I'm just kinda unsure what I'm meant to be doing. Any help would be awesome. :)</p>
| 1,867 |
<p>In <a href="http://en.wikipedia.org/wiki/Quantum_entanglement" rel="nofollow">Wikipedia</a> it is mentioned that position and momentum can be entangled as well as spin and polarization etc. I assume etc. is charge etc.
I understand how if you measure spin up on one of a pair you get spin down on the second of the pair.</p>
<p>What happens to the other particle in an entangled pair if I measure the momentum, position or charge of one of the particles?</p>
<p>Is there a momentum up and down or charge up and down analog?</p>
<p><a href="http://en.wikipedia.org/wiki/Quantum_entanglement" rel="nofollow">http://en.wikipedia.org/wiki/Quantum_entanglement</a></p>
| 1,868 |
<p>I may be totally off with this quite abstract (?) question(s).</p>
<p>But still, here are some closely related sub-questions:</p>
<ul>
<li>Is there a list of currently "known" intrinsic properties of nature?</li>
<li>How exactly is an intrinsic property of nature defined? Is it defined as "<em>it is so, because it is so</em>" or "<em>it is so, because it cannot be otherwise (in our Universe)</em>"?</li>
</ul>
<p>For example, <a href="http://en.wikipedia.org/wiki/Intrinsic_and_extrinsic_properties" rel="nofollow">Wikipedia</a> about mass as intrinsic property:</p>
<blockquote>
<p><em>An intrinsic property is a property that an object or a thing has of
itself, independently of other things, including its context. An
extrinsic (or relational) property is a property that depends on a
thing's relationship with other things. For example, <strong>mass is an
intrinsic property of any physical object</strong>.</em></p>
</blockquote>
<p>Is this a correct explanation of an intrinsic property? </p>
| 1,869 |
<p>If we designate the origin (the reference point from which all displacement vectors are measured) $\vec{0}$, and If we consider a sphere $\mathbb{B}\left(\vec{0},\mathcal{R}\right)$ of radius $\mathcal{R}$ and centered at $\vec{0}$, and say that outside this sphere the charge density $\rho$ and current density $\vec{J}$ are zero at all points and all instants, then it can easily be shown pretty directly using <a href="http://en.wikipedia.org/wiki/Jefimenko%27s_equations">Jefimenko's Equations</a> that for points where $r \gg \mathcal{R}$, if we define:
$$
\vec{\mathcal{Q}}\left(\hat{r}, t\right)
= \iiint_{\mathbb{B}\left(\vec{0},\mathcal{R}\right)} \frac {\partial} {\partial t} \vec{J} \left(\vec{s}, t+\frac {\vec{s}\cdot\hat{r}} c\right)\space dV\left(\vec{s}\right)
$$
Then we have
$$
\vec{E}\left(\vec{r},t\right) \approx \frac {\mu_0}{4\pi r}\left(\vec{\mathcal{Q}}\left(\hat{r}, t-\frac{r}{c}\right)\times\hat{r}\right)\times\hat{r}
$$
$$
\vec{B}\left(\vec{r},t\right) \approx \frac {\mu_0}{4\pi rc}\left(\vec{\mathcal{Q}}\left(\hat{r}, t-\frac{r}{c}\right)\times\hat{r}\right)
$$
$$
\vec{S}\left(\vec{r},t\right) \approx \frac {\mu_0}{16\pi^2 r^2c}\left|\vec{\mathcal{Q}}\left(\hat{r}, t-\frac{r}{c}\right)\times\hat{r}\right|^2 \hat{r}
$$
Now we can apply the <a href="http://en.wikipedia.org/wiki/Hairy_ball_theorem">Hairy Ball Theorem</a> to deduce that the vector $\vec{\mathcal{Q}}\left(\hat{r}, t-\frac{r}{c}\right)\times\hat{r}$ must be zero for at least one value or $\hat{r}$, which as we know rules out the isotropic antenna.</p>
<p>Now my question is, since it is allowable to have exactly one direction $\hat{r}$ in which this vector (and consequently, the radiated power) is zero, <strong>is there any such antenna</strong>--one that exhibits a <strong>non-zero radiated power in all directions</strong> $\left(\theta,\phi\right)$ <strong>except one</strong>? Somewhat like the pattern exhibited by a <a href="http://en.wikipedia.org/wiki/Cardioid_microphone#Cardioid">Cardioid microphone</a> -- a cardioid revolved around its axis? </p>
| 1,870 |
<p>I am to solve the following:</p>
<blockquote>
<p>A jet engine of mass $m$ is fastened to the fuselage of a passenger jet by a bolt. During flight, the plane encounters turbulence, which suddenly imparts an upward vertical acceleration of $2.60\mathrm{~m/s^2}$ to the plane. Calculate the force on the bolt.</p>
</blockquote>
<p>Since the jet engine weighs $9.81m\mathrm{~N}$ and the engine has a net force of $2.60m\mathrm{~N}$, the force on the bolt is either $(9.81+2.60)m\mathrm{~N}$ or $(9.81-2.60)m\mathrm{~N}$, but I do not understand which.</p>
<p>I would like to draw a free-body diagram to help me understand the problem, but I am not sure how to in this case.</p>
<p><strong>UPDATE:</strong></p>
<p>Here is what I have. Suppose the mass of the fuselage is $M$ and the mass of the bolt is negligible. Then the free-body diagram is:</p>
<p><img src="http://i.stack.imgur.com/hHaBi.png" alt="free-body-diagram"></p>
<p>where</p>
<ul>
<li>$F_{FA}=2.60M$ is the force on the fuselage by the air</li>
<li>$F_{AF}=Mg$ is the force on the air by the fuselage</li>
<li>$F_{BE}$ is the force on bolt by the engine</li>
<li>$F_{EA}=2.60m$ is the force on the engine by the air</li>
<li>$F_{AE}=mg$ is the force on the air by the engine</li>
</ul>
<p>However, I am not sure if this is correct.</p>
| 1,871 |
<p><img src="http://i.stack.imgur.com/eHV8x.png" alt="BICEP2 B-mode Signal"></p>
<p>The first image of <a href="http://bicepkeck.org/visuals.html">BICEP2 visuals</a> shows the "BICEP2 B-mode Signal", described as follows:</p>
<blockquote>
<p>Gravitational waves from inflation generate a faint but distinctive
twisting pattern in the polarization of the CMB, known as a "curl" or
B-mode pattern. For the density fluctuations that generate most of the
polarization of the CMB, this part of the primordial pattern is
exactly zero. Shown here is the actual B-mode pattern observed with
the BICEP2 telescope, with the line segments showing the polarization
from different spots on the sky. The red and blue shading shows the
degree of clockwise and anti-clockwise twisting of this B-mode
pattern.</p>
</blockquote>
<p>I think I understand the red and blue, but I don't get what the line segments mean.
<a href="http://wwwphy.princeton.edu/cosmology/capmap/polscience.html">Another web page</a> explains a similar visual as follows:</p>
<blockquote>
<p>Summing over all incident waves [at a given point], the E-fields are
roughly equal in all directions, but not quite. There will be one
direction that has a slightly greater magnitude of E than the other
directions (see figure to the left).</p>
<p>We can represent polarization as a line with length proportional to
the excess magnitude in that direction and at an angle such that it is
aligned with the direction of largest E.</p>
</blockquote>
<p>Aside from the fact that the latter description refers to E-mode, seemingly treating it as isomorphic to B-mode polarization (I'm talking through my hat a bit here)...
I would expect from my understanding of this description that the length of a line segment should correlate to (the "absolute value" of) the intensity of red or blue at that point. But in the first visual referred to above, the correlation doesn't really seem to hold.</p>
<p>(BTW, I'm assuming that each line segment represents information about the point at the <em>center</em> of the line segment, not about a point at one end, unlike a vector field visualization would. That's because these are not vectors, since they don't really have direction in a 360-degree sense, but rather they have 180-degree rotational symmetry. This is consistent with the fact that each line segment's <em>center</em> seems to be on a grid point. Pardon me if I'm belaboring the obvious, but it took me a while to realize this.)</p>
<p>So... what am I misunderstanding here? What aspect of the polarization do the line segments actually show?</p>
<p>To summarize the question a different way: what is the difference between what the length of the line segments represents, and what the intensity of the red/blue color represents?</p>
| 1,872 |
<p>The observed Higgs boson mass is at an interesting place in parameter space, placing the standard model electroweak vacuum right at the edge of metastability. Among the proposed explanations of this value is the existence of a <a href="http://arxiv.org/abs/1204.2551">"shift symmetry" in the Higgs sector</a>. </p>
<p>Today we have the possible detection of gravitational waves produced during inflation, of an amplitude suggesting that the inflationary potential was flat right up to near the Planck scale. Various expert commentaries (<a href="http://motls.blogspot.com/2014/03/bicep2-primordial-gravitational-waves.html">McAllister</a>, <a href="http://users.physics.harvard.edu/~mreece/inflation.pdf">Reece</a>) say that one would expect interactions between the inflaton and the ultraheavy degrees of freedom to appear, and their absence might, once again, imply the existence of a shift symmetry. </p>
<p>One of the many many approaches to inflation is "Higgs inflation": the Higgs field also serves as the inflaton field, the source of inflation. In discussions of Higgs inflation, <a href="http://www.physicsforums.com/showthread.php?t=680506#12">I've been told</a> that it's an unlikely model for exactly the same reason as mentioned above - effective field theory ought to break down near the Planck scale, the flatness of the potential should be disturbed by ultraheavy interactions, Higgs inflation would require finetuning. </p>
<p>But now we may have evidence of such finetuning in inflation! Or perhaps, evidence of a protective symmetry. So my question is, <strong>Could the same symmetry be finetuning both the Higgs mass and the inflaton's interactions?</strong> Could the same shift symmetry make the Higgs mass critical <em>and</em> protect the inflaton from ultraheavy interactions? </p>
<p>These questions might be asked first in the context of basic Higgs inflation - only one fundamental scalar - and later in the context of a multi-scalar theory, in which the Higgs is part of a larger scalar sector with a single big potential.</p>
<p><strong>edit</strong>: I have found a discussion of <a href="http://arxiv.org/abs/1009.2276">shift symmetry in the context of Higgs inflation</a>, but it was written prior to the measurement of the Higgs mass. </p>
| 1,873 |
<p>When light refracts from a medium to a second one, its frequency stays the same, and its wavelength changes. If this is true, why we see the refracted light ray's colour is the same as the incident light ray in the second medium? The colors should not be the same. If the wavelength changes, colour should change too.</p>
| 32 |
<p>Not sure where to ask this question - thought you guys would probably have the best idea!</p>
<p>Today a single key on my keychain in my pocket heated up so that it was too hot to handle and scalded my leg. Any ideas what could possibly have done this?</p>
<p>I always keep a prison guard style set of keys attached to my trousers and in my pocket - one of these keys is very large and thick (longer and thicker than my finger) - this is the key that heated up somehow.</p>
<p>In my pocket was my phone (an htc desire hd).</p>
<p>I was sitting at my desk as I do all the working day - when I felt my pocket getting hotter rather alarmingly quickly. I stood up and pulled everything out of my pocket - and I can't work out how it happened. The phone was not hot at all and worked fine.</p>
<p>My best guess is that there was some form of induction going on. Does anybody have any idea what might have happened? I don't think it was friction or bending of the keys as it's never happened before and I was sitting still all morning.</p>
<p>Thanks for any ideas! I'm more curious than anything else.</p>
| 1,874 |
<p>I am studying a field theory where the field is a matrix. The problem is that I have to calculate some functional derivative. How could we define functional derivative when the field is a matrix ?</p>
| 1,875 |
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