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<p>I would like to know why dry frictional force does not depend on speed(assuming that the heat generated by friction is small so it does not alter the coefficient of friction). </p>
<p>Let me explain how I think about dry friction. When I slide one object on another than their small irregularities on surfaces are bashing to each another and this causes the friction. If I higher the sliding speed than those irregularities will bash to each other more frequently so it seams to me that the friction should rise. But Coulomb's friction force says that the force does not depend on speed.</p>
<p>So can anybody give me intuitive explanation why is that?</p>
| 2,345 |
<p>Consider a particle in a potential well. Let’s assume it’s a simple harmonic oscillator potential and the particle is in its ground state with energy E<sub>0</sub> = (1/2) ℏω<sub>0</sub>. We <strong>measure</strong> its position (measurement-1) with a high degree of accuracy which localises the particle, corresponding to a superposition of momentum (and therefore energy) states.</p>
<p>Now we <strong>measure</strong> the particle’s energy (measurement-2) and happen to find that it’s E<sub>10</sub> = (21/2) ℏω<sub>0</sub>. Where did the extra energy come from?</p>
<p>In the textbooks it’s claimed that the extra energy comes from the act of observation but I wonder how that could work. Measurement-1 which probed the position of the particle can’t have delivered to it a precise amount of energy, while measurement-2 might just have been passive. No doubt there is entanglement here between the particle state and the measuring device but where, and which measurement?</p>
| 2,346 |
<p>How the notion of <em>weak measurement</em> resolves <a href="http://en.wikipedia.org/wiki/Hardy%27s_paradox" rel="nofollow">Hardy's paradox</a>?</p>
| 2,347 |
<p>In general, the Hamiltonian $H$ has non-zero vacuum expectation value (VEV):
$$ H \left.| \Omega \right> = E_0 \left.|\Omega \right>, $$ where $\left.|\Omega\right>$ is the vacuum state. The zero-point energy of the quantum oscillator is a good example to have non-vanishing VEV.</p>
<p>The problem strikes me is that <strong>how is this vacuum state transformed under Lorentz transformation?</strong> </p>
<p>On one hand, we can think of this vacuum state is the trivial representation of the Poincare group, which is a Lorentz invariant. ( In Wigner's classification, vacuum state is in the $(0,0,0,0)$ class, if I understand correctly.) So $$
U(\Lambda) \left.| \Omega \right> = e^{-i \theta} \left.| \Omega \right>
$$</p>
<p>On the other hand, the vacuum state has non-zero 4-momentum: $p = (E_0, \vec{0})$. So it seems it should transform like other irreps: $$
U(\Lambda) \left.|p, \sigma\right> = \sum_{\sigma'}C_{\sigma'\sigma} \left.| \Lambda p, \sigma' \right>,
$$ Now, the important thing is, $\Lambda p$ could have non-zero 3-momentum. But the vacuum state should have zero 3-momentum. Bang!</p>
<p>In textbooks, a common procedure to reconcile this contradiction is to shift the Hamiltonian $H \to H - E_0$; but, the Poincare algebra would be affected:
$$
[ K^i, P^j ] = \delta^{ij} H \to [ K^i, P^j ] = \delta^{ij} H + \delta^{ij} E_0
$$</p>
<p>Thank you.</p>
| 2,348 |
<p>I'm asked to calculate how much POWER a 1210kg car needs to drive with a 85 km/s speed up a 655 meter long slope of 4.5°. I can find how much energy and work is required to do this, but isn't POWER=WORK over TIME? I don't have any time in my problem.</p>
<p>So I ask: If I have a 1000kg car and I drive 500 meters...Could I go 100 km/h with even 1 horse power as long as I got enough time? Is horse power only an indicator of torque (i.e. work over time)?</p>
| 2,349 |
<p>The <a href="http://en.wikipedia.org/wiki/Feynman_checkerboard" rel="nofollow">Feynman Checkerboard Wikipedia article</a> states: "There has been no consensus on an optimal extension of the Chessboard model to a fully four-dimensional space-time."</p>
<p>Why is it hard to extend it to more than 1+1 dimensions?</p>
| 2,350 |
<p>What is the meaning, mathematical or physical, of the anti-commutator term?
$\langle ( \Delta A )^{2} \rangle \langle ( \Delta B )^{2} \rangle \geq \dfrac{1}{4} \vert \langle [ A,B ] \rangle \vert^{2} + \dfrac{1}{4} \vert \langle \{ \Delta A, \Delta B \} \rangle \vert^{2}$,
where $\Delta A, \Delta B, A$ and $ B$ are operators.
The inequality is still true, and the anti-commutator term "strengthens" the inequality, but why does it appear?</p>
| 2,351 |
<p>In my blog post <em><a href="http://thespectrumofriemannium.wordpress.com/2012/11/07/log050-why-riemannium/" rel="nofollow">Why riemannium?</a></em> , I introduced the following idea. The <a href="http://en.wikipedia.org/wiki/Particle_in_a_box" rel="nofollow">infinite potential well</a> in quantum mechanics, <a href="http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator" rel="nofollow">the harmonic oscillator</a> and <a href="http://en.wikipedia.org/wiki/Laplace%E2%80%93Runge%E2%80%93Lenz_vector" rel="nofollow">the Kepler (hygrogen-like) problem</a> have energy spectra, respectively, equal to </p>
<p>1) $$ E\sim n^2$$
2) $$ E\sim n$$
3) $$ E\sim \dfrac{1}{n^2}$$</p>
<p>Do you know quantum systems with general spectra/eigenvalues given by </p>
<p>$$ E(n;s)\sim n^{-s}$$</p>
<p>and energy splitting </p>
<p>$$ \Delta E(n,m;s)\sim \left( \dfrac{1}{n^s}-\dfrac{1}{m^s}\right)$$</p>
<p>for all $s\neq -2,-1,2$?</p>
| 2,352 |
<p>What are some of the most elegant/complex/sophisticated physics experiments one could perform in his garage, if he has enough spare time and technical/theoretical know-how, but a relatively limited budget? Say, a retired emeritus physics professor?</p>
<p>These could be either novel or reproductions of known experiments, either qualitative or quantitative demonstrations.</p>
| 2,353 |
<p>I have observed that the power lines buzz louder when there is less moisture in the air.</p>
<p>Why is this?</p>
<p>If it will help the lines are located on the foot hills of a nearby mountain.</p>
| 2,354 |
<p>I will probably be laughed out of town for saying this, but why can't the Energy Conservation Law be broken?</p>
<p>Everybody thought electricity to motion was impossible until Faraday made his motor, nobody believed Tesla would make a <a href="http://en.wikipedia.org/wiki/Brushless_DC_electric_motor" rel="nofollow">brushless motor</a>, and now everyone ignores the potential existence of energy creation.</p>
<p>I see that no device has been made yet that destroys the Conservation Laws, but that does not mean it is impossible.</p>
<p>Is there anything in our understanding of physics that would break down if this were the case?</p>
<p><strong>P.S :</strong> In the physics videos I have seen, the professor demonstrates that energy cannot be created. His method was hardly scientific. I agreed with him that his setup would not create energy. In other words, saying a brushless motor is impossible while demonstrating a brushed motor proves nothing.</p>
<p>Please note: I mean no offense... just trying to get to the details</p>
| 2,355 |
<p>Suppose 2 capacitors are connected in series, the plates connected to the battery terminals receive charges $+q$ and $-q$, and the isolated plates in the combination receive equal and opposite charges through induction. Now my question is, why is that the induced opposite charge on the plates isolated (i.e. not connected to the rest of the circuit through wires as in any ordinary series combination of capacitors) from the other two plates equal to the inducing charge on the plates connected to the battery? </p>
| 2,356 |
<p>I have a Sunbeam home espresso machine with a steam wand. The steam roars out straight from the end of the wand. When it's first placed in the cold milk it really screams! Once the milk has a bit of a whirlpool action going it's much quieter, so I guess that the noise is because of fast-moving steam hitting stationary cold milk. Something something fluid dynamics?</p>
| 2,357 |
<p>I understand that when cooling water with <a href="http://en.wikipedia.org/wiki/Liquid_nitrogen" rel="nofollow">LN2</a> directly (through pipes for example), that it can be too effective, freezing the water (and blocking the pipe). </p>
<p>From what I read, regulation of the heat transfer is considered complicated to control. Often employing at least a fixed insulation to regulate the rate of heat transfer.</p>
<p>If I immersed a fixed copper heat sink into LN2, the copper interface would be below $0C$ and still risk freezing the water.</p>
<p>My question is directed at those familiar particularly with Peltier cooling devices. Considering an aparatus, where a Peltier is:</p>
<ul>
<li>A) interfaced directly to a flat interface on a heatsink; or</li>
<li>B) interfaced with a fixed insulation</li>
</ul>
<p>The following sub-questions apply:</p>
<ol>
<li>Does a cooler heatsink on the heated side, improve the max. cooling rate?</li>
<li>If turned off, would the peltier device exhibit any insulating effect?</li>
<li>Would there be a minimum operating temperature, in the case where the Peltier was turned off and cooled toward LN2 temperatures?</li>
</ol>
<p>Given favourable answers to the sub-questions, and any additional comments, the title question would be answered. Some helpful additional comments may relate to industry standard heat-exchanger/regulator apparatus and their performance/cost.</p>
<p><strong>Update</strong></p>
<p>To reiterate the specifics of my theoretical apparatus. The "heatsink" is in the LN2 canister, the Peltier device outside with the hot interface on the "heatsink". When the peltier voltage drive is 0, the peltier would have an insulation effect R1, resulting in a Rate of heat transfer (ROHT) on the coldside of C1, changing the voltage to full on the Peltier changes the insulation effect to a negative value R2, and increases the ROHT to C2. For intermediatary voltages, the insulation effect is between R1 and R2, and the RoHT is between C1 and C2.</p>
<ol>
<li>What is R1 (the insulation effect) of a non-specific Peltier device with no voltage applied?</li>
<li>What would be a guestimate for C1 given an LN2 heatsink?</li>
</ol>
| 2,358 |
<p>I don't understand whether something physical, like velocity for example, has a single correct classification as either a contravariant vector or a covariant vector. I have seen texts indicate that displacements are contravariant vectors and gradients of scalar fields are covariant vectors, but in <i>A Student's Guide to Vectors and Tensors</i> by Fleisch I found this statement:</p>
<blockquote>
<p>[I]t's not the vector itself that is contravariant or covariant, it's
the set of components that you form through its parallel or
perpendicular projections. (p.121)</p>
</blockquote>
<p>If physical concepts can be represented as either type of mathematical object, I don't understand how a displacement could be represented as a covector. Wouldn't its components transform the wrong way if the coordinates were changed?</p>
<p>If covariantness/contravariantness is part of the definition of a physical concept, I don't understand how force is classified. The gradient of a potential would have dimensions of length in the denominator, making it a covariant vector. Mass times acceleration has dimensions of length in the numerator, making it contravariant.</p>
<p><strong>Edit:</strong> I read through the accepted answer to <a href="http://physics.stackexchange.com/q/62505/4208">Forces as One-Forms and Magnetism</a>. One thing I don't understand is whether in relativistic spacetime any vector quantity can also be represented as a 1 form (because there is a metric) or whether its classification as a 1 form or vector depends on how its components change under a coordinate transformation. Doesn't a displacement have to be a vector and not a 1 form?</p>
| 2,359 |
<p>I know that Quantum Hall Effect and Fractional Quantum Hall Effect origin from Landau Level quantization.</p>
<p>In magnetic field, the energy of in-plane(plane perpendicular to magnetic field) degree of motion is quantized, which is $E=(n+1/2)\hbar\omega$, $n$ is integer.</p>
<p>In experiment, both QHE and FQHE are observed in low temperature and strong magnetic field, suggesting that landau level quantization is observable under the condition $k_B T<<\hbar\omega$, where $k_B$ is Boltzman constant.</p>
<p>I am not sure why this condition is important in experiment.</p>
| 2,360 |
<p>I am an engineering student who is interested in orbital mechanics. I am doing some self study before taking some orbital mechanics courses next year. I was learning about various orbit types (elliptical, parabolic, hyperbolic, etc.) and the effects of burning in various directions. I have found a lot of good information about about how to manipulate elliptical orbits (raising/lowering apo/periapsis, changing inclinations, etc.).</p>
<p>However, I haven't found a lot of information on manipulating a hyperbolic trajectory. I have found a lot of good information <a href="http://www.braeunig.us/space/orbmech.htm">like this</a> in calculating various parameters (impact parameter, turning angle, etc.) but little specifics on how to change one. </p>
<p>For example, say you were on a hyperbolic flyby like <a href="http://www.braeunig.us/space/problem.htm#4.26">in this example</a>. However, you wanted to lower your radius at periapsis by a couple hundred km for some reason (take some measurements, increase turning angle etc.). What would be the most efficient direction to burn? I could see doing it 2 different ways but unsure of which would be more efficient. You could burn retrograde lowering your velocity magnitude which would pull you closer to the planet. Or you could burn perpendicular to your current velocity vector in the direction of the planet changing your approach angle? Perhaps some combination of the 2?</p>
<p>Anyone know how to determine what would be the most optimal?</p>
| 2,361 |
<p>Perfectly localized states are not normalized so do not belong to the Fock space (they belong to the rigged version). Suppose we approximate localized states with gaussians, what is the mathematical expression for two "approximately" localized particles at points $x_1$ and $x_2$ that takes into account correlations due to vacuum entanglement? how do you build it from the original creation/annihilation operators eigenstates?</p>
<p>The field is supposed to be a 1D massive scalar one.</p>
<p>Thanks.</p>
| 2,362 |
<p><a href="http://en.wikipedia.org/wiki/Kirchhoff%27s_law_of_thermal_radiation" rel="nofollow">Kirchhoff's law of thermal radiation</a> states that for thermal equilibrium for a particular surface the monochromatic emissivity $\epsilon_{\lambda}$ equals the monochromatic absorptivity $\alpha_{\lambda}$:
$$\alpha_{\lambda} = \epsilon_{\lambda}$$
I wonder how this can be only valid for thermal equilibrium, because $\epsilon_{\lambda}$ and $\alpha_{\lambda}$ seem to depend only on the temperature of the surface under consideration, and it seems to me that they don't depend on the other bodies around the surface. So according to this, it should follow that they are equal always, when they are equal in thermal equilibrium, which isn't correct. So I wonder how the lack of thermal equilibrium can change the values of $\alpha$ and $\epsilon$? </p>
| 2,363 |
<p>I've finally managed to get a grasp on the <a href="http://en.wikipedia.org/wiki/Bell_test_experiments" rel="nofollow">Bell test experiments</a> and all that they imply about our reality. Now I'm curious about the mathematical derivation which allowed Schrodinger to predict the existence of entangled entities.</p>
<p>Can someone please provide an explanation of these equations or direct me towards good sources of information on the subject? Thanks.</p>
| 2,364 |
<p>For the past years I am thinking about relating concepts from physics to concepts from economics. Especially since the financial crisis made obvious the instability of the financial system I ask myself whether this could be explained by physics, e.g. by lack of inertia and dissipation during transactions, conservation of energy as the total amount of money available continuously increases, or whatever.</p>
<p>Unfortunately I am indeed not firm in physics and economics myself. However, I am yet very interested whether these ideas make any sense, or whether there is any actual research in this direction. </p>
| 2,365 |
<p>If the strong nuclear force were just 2% stronger, the neutron would be a stable particle instead of having a half life of about 13 minutes. What difference would that have made to Big Bang nucleosynthesis, to the growth of structure, to the formation of stars, nucleosynthesis in stars?</p>
| 2,366 |
<p>Extending the Gaussian model by introducing a second field and coupling it to the other field, I consider the Hamiltonian</p>
<p>$$\beta H = \frac{1}{(2\pi)^d} \int_0^\Lambda d^d q \frac{t + Kq^2}{2} |m(q)|^2 +
\frac{L}{2} q^4 |\phi|^2 + v q^2 m(q) \phi^*(q)$$</p>
<p>Doing a Renormalization Group treatment, I integrate out the high wave-numbers above $\Lambda/b$ and obtain the following recursion relations for the parameters:
$$\begin{aligned}t' &= b^{-d} z^2 t & K' &= b^{-d-2}z^2 K & L' &= b^{-d-4}y^2 L \\
v' &= b^{-d-2}yz v & h' &= zh
\end{aligned}$$
where $z$ is the scaling of field $m$ and $y$ is the scaling of field $\phi$.</p>
<p>One way to obtain the scaling factors $z$ and $y$ is to demand that $K' = K$ and $L' = L$, i.e., we demand that fluctuations are scale invariant. </p>
<p>But apparently, there is another fixed point if we demand that $t' = t$ and $L' = L$ which gives rise to different scaling behavior, and I wonder</p>
<p>a) why I can apparently choose which parameters should be fixed regardless of their value ($K$ and $L$ in one case, $t$ and $L$ in the other case)</p>
<p>b) what the physical meaning of these two different fixed points is...</p>
<p>(My exposure to field theory/RG is from a statistical physics approach, so if answers could be phrased in that language as opposed to QFT that'd be much appreciated)</p>
| 2,367 |
<p>According to L&L, if we fix the initial position of a particle at a given time and consider the on-shell action as a function of the final coordinates and time, $S(q_1, \ldots, q_n, t)$, then...</p>
<p>$$E = -\frac{\partial S}{\partial t}$$</p>
<p>$$p_i = \frac{\partial S}{\partial q_i}$$</p>
<p>Is there a straightforward generalization of this to field theory? Something that would give the energy and momentum densities by differentiating the on-shell action (with respect to... something)?</p>
| 2,368 |
<p>Today I heard an argument to prove that the Earth-Centered Earth-Fixed (<a href="http://en.wikipedia.org/wiki/ECEF" rel="nofollow">ECEF</a>) reference frame is non-inertial. It seriously doesn't make any sense to me but I also heard that same argument was made by Einstein, so I am asking it here. Please explain how it proves that Earth frame is non-inertial. The argument goes like this:
Suppose the Earth frame is inertial. Now, all the heavenly bodies will have to go around the Earth once a day. But, this implies a very fast speed. Hence, the Earth frame can't be inertial.</p>
| 2,369 |
<p><a href="http://en.wikipedia.org/wiki/Critical_mass">Wikipedia</a> gives the following definition for critical mass.</p>
<blockquote>
<p>A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction.</p>
</blockquote>
<p>No mention is made of a neutron moderator in this definition. If critical mass is defined like this, then that should allow infinite moderator material to be used if doing so would lead to the minimum amount of fissile material.</p>
<p>My question: <strong>What is the universally minimum amount of fissile mass needed to achieve a critical configuration (allowing a neutron moderator and no restriction on the moderator) for something like Uranium-235 and what would its configuration be?</strong></p>
<p>Uranium-235 has a <strong>bare sphere critical mass</strong> (BSCM) of around $52 kg$, which is the mass of a critical sphere containing <em>only</em> the fissile material where no neutrons are reflected back into the sphere after leaving the surface. Wikipedia has a good illustration of a bare sphere versus a sphere surrounded by a moderator.</p>
<p><img src="http://i.stack.imgur.com/O6KKI.gif" alt="BSCM and moderator blanket">
<em>Image: First item is a BSCM illustration, 2nd item is a critical sphere that uses less fissile mass than the BSCM due to the introduction of a neutron moderator blanket</em></p>
<p>This example illustrates how a critical configuration can be made with U-235 that uses less than the BSCM, or $52 kg$. It is possible, although unlikely, that the above sphere surrounded by a moderator could be the configuration that answers my question. Alternatives would include a homogenous mixture of the moderator and the fissile material, a mixture of the two that varies radially, or something I have not thought of.</p>
<p>The hard part is showing that the particular fissile material/moderator mix can not be improved by any small change. It would also be necessary to show that it can not be improved by adding more than 1 type of moderator (I suspect this could be done with a reasonably short argument).</p>
<p><strong>Technical mumbo junbo</strong></p>
<p><em>Everything I write here is just a suggestion, answer however you want to or can</em></p>
<p>Both the moderator and fissile material have a certain density. I would make the simplifying assumption that the density of a homogenous mixture of the fuel and moderator would be a linear combination of their specific volumes, with the understanding that this is not true in real life. Changing the mix changes the macroscopic cross section of both. It might help to note that the BSCM almost exactly determines the macroscopic cross section of the pure fissile material, one over the macroscopic cross section is the path length, which is on the same order of magnitude of the radius. Generally fast and thermal scattering from U-235 is small compared to the fission cross section.</p>
<p>I would use 2 neutron energy groups, and assume either diffusion or immediate absorption after scattering to thermal energies. In fact, I would just assume immediate absorption. At that point, all you would need is the scatter to absorption ratio and microscopic cross section at both thermal and fast energies for the moderator and fissile material, in addition to the densities of course. Even then some type of calculus of variations may be necessary (if you're looking for a radially varying mixture) in addition to the fact that it would be hard to describe the fast group without a fairly complicated form of neutron transport. The BSCM is comparatively simple since it has a constant number density of the fissile material and even <em>that</em> is actually pretty complicated.</p>
| 323 |
<p>In the figure, blocks A and B have weights of 45 N and 23 N, respectively. (a) Determine the minimum weight of block C to keep A from sliding if μs between A and the table is 0.21. (b) Block C suddenly is lifted off A. What is the acceleration of block A if $\mu_k$ between A and the table is 0.14?</p>
<p><img src="http://i.stack.imgur.com/9e0Ks.png" alt="enter image description here"></p>
<p>I found the weight of block C to be $64.5 N$ , and I was told that was correct.</p>
<p>For part b, here is my work.</p>
<blockquote>
<p>$\mu_k = 0.14$</p>
<p>$F_k = \mu_k F_N$ $\text{ }$ $F_k = \text{frictional force due to } \mu_k$</p>
<p>$F_k = 0.14 * 45N = 6.3N$</p>
<p>$F_{net} = F_B - F_k$</p>
<p>$F_{net} = 23N - 6.3N = 16.7N$</p>
<p>$F = ma$</p>
<p>$16.7 = \frac{45N}{9.81 {m\over s^2}}*a$</p>
<p><strong>$a = 3.64 {m\over s^2}$</strong></p>
</blockquote>
<p>However, I am told that this answer is wrong. Did I make a mistake anywhere? Any help would be appreciated!</p>
| 2,370 |
<p>Suppose I have a flow of hot air around a cold and unevenly shaped object with holes and tunnels (think about it as a bed packed with some objects). I would like to know the Reynolds number of this flow and its convective heat transfer coefficient. The definition of the Reynolds number contains a "characteristic length" that is somehow mysterious to me and that I do not have at hand. And I am a bit reluctant to use the formula for the packed bed Reynolds number. Is it possible to measure it? How would I design an experiment for this?</p>
<p>I would like to avoid temperature readings of the object. In <a href="http://www.sciencedirect.com/science/article/pii/096014819190107Z" rel="nofollow">this</a> article I found a relation between the Reynolds number of a packed bed and the heat transfer coefficient, so measuring only the Reynolds number would be a good start, even though I do not have a real packed bed. Could this be done by simple pressure drop readings?</p>
| 2,371 |
<p>The Riemann curvature of a unit sphere is shown in many textbooks to be sine-squared theta where theta is the azimuthal angle of spherical co-ordinates. But what is the significance of the angle and how would a value be assigned to it?</p>
| 2,372 |
<p>Given a quantum state function, we can Fourier expand it in terms of stationary states of the Hamiltonian. So if we want to build that same quantum state approximately all we need to do is to superpose stationary states with proper amplitudes. Assuming that we can prepare such stationary states individually, how is their superposition done experimentally? </p>
<p>As a specific example, how to prepare experimentally, an ensemble described by the quantum state that is a superposition of 4 stationary states of the particle in a box (or the hydrogen atom) that corresponds to n = 1, 2, 3, and 4 say ? </p>
| 2,373 |
<p>A theory of quantum gravity is said to be needed when quantum and gravitational effects are strong at the same time i.e. at black hole singularities and at the big bang. This also makes it difficult to test quantum gravity.</p>
<p>But what about testing <a href="http://en.wikipedia.org/wiki/Macroscopic_quantum_phenomena" rel="nofollow">macroscopic quantum phenomena</a> in different gravity regimes like flying a superconductor or liquid helium into Earth orbit and back again - would you expect gravitational time dilation or high-g accelerations to alter macroscopic quantum behaviour in a way that could test quantum gravity theories ?</p>
| 2,374 |
<p>New physics is expected at high energies and cosmic rays have high energies, so have there been or are there any plans to put <a href="http://en.wikipedia.org/wiki/Particle_detector" rel="nofollow">particle detectors</a> in space to study cosmic rays for new physics ?</p>
| 2,375 |
<p>Since <a href="http://en.wikipedia.org/wiki/Anyon#Non-abelian_anyons" rel="nofollow">non-abelian anyons</a> have become quite fashionable from the point of view of theory. I would like to know, whether there has actually been experimental confirmation of such objects.
If you could cite original literature, that would be great!</p>
| 2,376 |
<p>I made some calculations about flow from the bottle, but problems occured when the experimental data came back. Need to refine calculations, but problems occur when trying to link the angle to the flow, because volume changes constantly, and volume that has left in the bottle is governed by the force sensor. And the force sensor is governed by the algorithm that links volume with weight, and weight and volume change with the change of the flow, which again is a function of the change of the angle.</p>
<p>As the bottle is oppened, angle of the fluid will always be parallel to the ground, because of the free surface and $p_{a}$. But problem here is that not every bottle is the same shape, so the height and the angle will not be the same for every bottle, and pouring process will not start for at the same angle for different bottles. With some bottle necks being convex effects of the surface tension will be much grater, and the poured amount of the liquid will be different than the deisred one. Then also, expansion waves will cause turbulance within the flow, and the flow should at least remain laminar, for easier pouring and calculations, but in real time pouring this is not that easy to get, well offcourse on higher pouring speed, with lower pouring speed this is not that big of a problem, but surface tensions tends to splurge liquid under the bottle.</p>
<p><img src="http://i.stack.imgur.com/zVbTj.jpg" alt="Pouring positions"></p>
<p>So for the diagram, I can put this picture, it's selfexplanatory. As I stated angle should correlate with the flow, and weight should be governed by force sensor, with this the force sensors senses the change of the weight (or volume) in the bottle, and this tells the framework on how much fluid has been poured and how much is remaining. Angles that I got from calculations and experiments differ, some of this I can contribute to surface tension. But the flow and the angle of the bottle to correlate to the change of the weight has proved different in a bigger manner.</p>
<p>For the geometry, different bottle types were used, so there is no specific geometry, but formulations were made for a generic bottle, so there could be some referencing points to the problem at hand.</p>
<p><img src="http://i.stack.imgur.com/hjMR9.png" alt="Bottle dimensions"></p>
<p>Any suggestions on how to model this mathematically and to do it correctly. </p>
| 2,377 |
<p>I have seen Gauss Law being used for a uniformly charged hollow sphere rotating with $\omega$. How is that valid to use Gauss law since it is an electrostatic law and if it is valid, why do we get a net constant electric field outside the sphere inspite of the accelerating charges - does the net time dependence cancel out ? How do I see this cancellation intuitively ? Also, can I see intuitively why the net radiation emitted is zero instead of integrating the Poynting flux ?</p>
| 2,378 |
<p>Cosmology (and astrophysics) talk about the "initial singularity" (IS, became the big bang) and "black hole singularities" (BS, inside black holes), and these appear to be quite different: The IS is described as having <strong>zero volume and infinitely high temperature and density</strong>, whereas the BS is likewise zero volume and infinite density, but with a <strong>temperature close to 0 K</strong>. (Personally, I suspect that both the IS and the BS equations suffer from a division be zero error (density = mass/volume, and in both cases the volume is zero (well so they say...)). My question is:</p>
<p><strong>If there is infinite density, how can there be any room for thermal activity (temperature)</strong>, let alone <strong>infinitely high</strong> temperature? Shouldn't the IS be stone cold, just like the BS? The BS case seems more reasonable, other than the difficulty I have trying to grasp "infinite mass in zero volume".</p>
| 2,379 |
<p>The reduced mass in the two body problem is $\mu= \cfrac{m_1 m_2}{m_1 + m_2}$. Is there any analog to this with interacting charged particles (or at least that is of use somewhere in physics)? I have not seen anything like this anywhere, but was curious if someone else has. I would imagine that this is not possible for the repulsive case.</p>
<p>Edit:
To clarify, I understand that the same equations hold for the attractive force since they are both $\frac{1}{r^2}$ force laws. I was curious if anyone had used this for charges before. </p>
| 2,380 |
<p>I was thinking about a situation were I have a long cylindrical jar with some viscous liquid in it. I also have a spherical ball with me. I drop the ball into the liquid inside the jar with some initial velocity. Just after that(before the ball acquires terminal velocity) I drop the system(the jar with the liquid and ball) from certain height.</p>
<p>(A) What would be the buoyant and viscous force in free fall compared to those that were acting before free fall?</p>
<p>(B) Will the answer change if I drop the ball(with some initial velocity) into the jar and drop the jar simultaneously?</p>
<p>(C)I somehow got the courage to jump along with the jar(without the ball in it). Now, I put the ball inside the cylinder with some initial velocity.Will the answer change now? (Remember that the whole system along with me is in free fall). </p>
<p><strong>I tried to answer my own question like this:</strong> In all these cases I think the buoyant force will be zero. By Archimedes Principle it is equal to weight of the liquid displaced.But, as something in free fall has zero weight there will be no weight for the liquid displaced and hence no buoyant force on the ball.</p>
<p>From Stoke's law we know that the viscous force is directly proportional to the velocity of the ball in the liquid. Consider a frame of reference R to be moving at an acceleration g downwards. Thus, in all these situations the acceleration of the ball and the cylinder due to free fall is zero relative to R. Hence, from R's perspective the viscous force would the same to that when the system was at rest.</p>
<p>I'm able to explain about the viscous force only in this way. What will be the viscous force for a man standing on the ground? I'm not very good at answering my own questions so, please help me with your ideas about the situation. </p>
| 2,381 |
<p>I'm trying to figure out which object would have the largest time of flight when launched from a slingshot. To do this, I need the initial velocity. How can I calculate this if I know the mass and diameter of the object? The slingshot always has the same force. I've seen a number of formulas, but none of them take into account the mass and size, which would matter in this case (a 10kg, 10cm rock will not go as fast or as long as a 1kg, 1cm rock).</p>
| 2,382 |
<p>Organic semiconductors differ from inorganic semiconductors. In organic semiconductors the molecules are held together by weak van der Waals interactions and in inorganic semiconductors by covalent bonds. So the bonds are different. How do you express the main difference between the twos? Is it the electronic structure or rather the electronic configuration, or something else? </p>
| 2,383 |
<p>I have a thought-experiment sort of question and I don't know where to start. Suppose you have an entangled pair, e1 and e2, and you split them. Then BEFORE reading them, you spin control e1 to +, then e2 would be -, correct?</p>
<p>Can you then, AFTER, reapply spin control to e1 and make it -. Would e2 then flip back to + also?</p>
| 2,384 |
<p>Given: </p>
<ul>
<li>The pulley is moving towards the right.</li>
<li>All blocks have different masses. (The pulley and the strings are massless.)</li>
</ul>
<p><img src="http://i.stack.imgur.com/unSZF.png" alt="Pulley">
What I don't understand:</p>
<ul>
<li>Is the tension the same for both A and B?</li>
<li>If the tension is the same, then both blocks should have different accelerations, but this is not true?</li>
</ul>
| 2,385 |
<p>Basically, a simple capacitor will consist of 2 plates and a dielectric material between them, what if i took 2 plates, charged one with a +ve charge and the other with equal -ve charge, then i put them together with a dielectric material between them , then i connect them with a wire so it can discharge , can i consider this system a capacitor and thus using E=1/2 *C *V^2</p>
| 2,386 |
<p>Before I start, I'm aware that this question may be better suited on the Chemistry or Biology site, but it's my belief that physicists are more likely to have a clear understanding on what certain terms mean, so by all means move the question if you feel like it will get a better response elsewhere.</p>
<p>Okay.</p>
<p>In Chemistry we learn about this thing called the Gibbs Free Energy (which I understand is borrowed from Thermodynamics). It's pretty simple. $\Delta G < 0$, and the reaction is spontaneous. $\Delta G > 0$, and the reaction is not spontaneous. </p>
<p>Other terms in the equation for Gibbs Free Energy are the total enthalpy change, which I interpret as the amount of energy that the system either takes in or releases, and also the temperature and total change in entropy.</p>
<p>Observe these graphs of an ambiguous 'Energy' plotted against the progress of the reaction:</p>
<p><a href="http://upload.wikimedia.org/wikibooks/en/a/a6/Gibbs_free_energy.JPG">http://upload.wikimedia.org/wikibooks/en/a/a6/Gibbs_free_energy.JPG</a></p>
<p><a href="http://www.citruscollege.edu/lc/archive/biology/PublishingImages/c05_10.jpg">http://www.citruscollege.edu/lc/archive/biology/PublishingImages/c05_10.jpg</a></p>
<p><a href="http://images.tutorvista.com/cms/images/101/exothermic-and-endothermic-reaction.png">http://images.tutorvista.com/cms/images/101/exothermic-and-endothermic-reaction.png</a></p>
<p>The idea is the same. Some reactions take in 'Energy,' and the curve ends higher than where it began. Some reaction release 'Energy,' and the curve ends lower than it began. All reactions seem to require an 'Activation Energy' which prevents the reaction from occurring spontaneously.</p>
<p>Notice how the Y-axis has different names, such as Gibbs Free Energy, PE of molecules, and PE. Is Gibbs Free Energy the same or different from PE? I'm not sure anymore. Also, in one graph, the change in Energy is portrayed as $\Delta G$, so a decrease implies spontaniety, and increase implies nonspontaniety. Yet both require an activation energy to proceed. </p>
<p>One more thing to notice is the change in terms. In a Biology context, the terms are Endergonic and Exergonic. In Chemistry, it is Endothermic and Exothermic. Why different terms for the same idea?</p>
<p>I would very greatly appreciate an explanation for this, which has been bugging me for a while.</p>
| 2,387 |
<p>and that is the internal motion relative to the center of mass?
could give me some examples?
desire to relate since I need to find out what is the kinetic energy in the center-of-mass of two particles, one moving and one stationary.
Note: they collide</p>
| 2,388 |
<p>Assume you charge a (parallel plate) capacitor. This establishes an electric field (the $\mathbf E$ vector points from one plate to the other) and a circular magnetic field (the $\mathbf B$ vector points tangential to circles centered at the capacitors main axis) while the Poynting vector points inwards.</p>
<p>Would this generate a "visible" electromagnetic wave (assuming we could see all wavelengths)? How about the situation where the capacitor is connected to an AC source?</p>
<p>Bonus question: If the above questions can be answered positively, would it be (theoretically) possible to generate actual visible light, by choosing the right frequency of the AC?</p>
| 2,389 |
<p>I assume that the refrigerator's temperature of 4 degrees has something to do with the fact that water is densest at that temperature. Does that inhibit microbe growth? But what about the freezer, what is special about -18 degrees? Is it a trade off of some type?</p>
| 2,390 |
<p>There is <a href="http://en.wikipedia.org/wiki/Electromagnetic_induction" rel="nofollow">a famous law</a> which says that a potential difference is produced across a conductor when it is exposed to a varying MF. But, how do you measure it to prove? It is quite practical. </p>
<p>Particularly, I had once a problem developing a power supply. When transistor rapidly opened a loop of powerful current, I had very strange effects and discovered that there is a voltage difference across the same wire, without any resistor between the probing points! The longer was the distance between probes, the higher was the voltage. Then I have realized how the real the law is. But, what I could not understand if the voltage were spikes induced in the wire indeed or they were purely fictional, induced right in the oscilloscope probes. I expected that voltage drop must be across the loop-breaking transistor but why was it rather distributed along the resistance-free wire?</p>
<p>Look at <a href="http://www.youtube.com/watch?feature=player_detailpage&v=eqjl-qRy71w#t=234s" rel="nofollow">dr. Levin's voltmeter</a>. What does it measure? I ask this question partially because he tells about non-conservative measurements, which depends on the path, but does not explain how to set up the paths to measure -0.1 v in one case and +0.9 v in the other, between the same points.</p>
<p>How the typical voltmeter works? There should be some known high resistance and small current through it shows how large the voltage is. But here, in addition to the D-A induced voltage, the EMF may be added because the is also induced current flowing through the voltmeter. How much is the effect? </p>
<p>In school I also had a problem with understanding what if the loop is open? You have a wire. The law will induce potential difference at its ends. But how do you measure the difference? Created such voltage in a short wire, we can be sure that closing the ends with voltmeter probes will not create any current in the voltmeter (just because magnetic field supports the difference. If it just created it then why should it let the polarized charges reunite when a parallel wire is connected?). So, no current and the voltmeter will show 0 voltage despite we know that Faraday law says that must be some. Do you understand what I am talking about? The field creates the potential difference that cannot be measured. It is like gravity stretches a spring but we cannot measure the force created because spring contraction force is balanced by gravity and your dynamometer shows 0. This is my concern that I cannot understand. How do you measure voltage difference when Faraday law precludes the polarized charges from the opposite ends of the wire to come together?</p>
| 2,391 |
<p>Consider a stationary solution with stress-energy $T_{ab}$ in the context of linearized gravity. Choose a global inertial coordinate system for the flat metric $\eta_{ab}$ so that the "time direction" $(\frac{\partial }{\partial t})^{a}$ of this coordinate system agrees with the time-like killing vector field $\xi^{a}$ to zeroth order. </p>
<p>(a) Show that the conservation equation, $\partial^{a}T_{ab} = 0$, implies $\int _{\Sigma}T_{i\nu} d^{3}x = 0$ where $i = 1,2,3$, $\nu = 0,1,2,3$, and $\Sigma$ is a $t = \text{constant}$ hypersurface (therefore it has unit future-pointing normal $n^{\mu} = \delta ^{\mu}_{t}$).</p>
<p>(there is also a part b but it is trivial given the result of part a so I don't think there is any need to list it here)</p>
<p>I am very lost as to where to start for this question. Usually for these kinds of problems, you would take the local conservation equation $\partial^{a}T_{ab} = 0$ and use the divergence theorem in some way but that doesn't seem to be of any use here given the form of $\int _{\Sigma}T_{i\nu} d^{3}x = 0$ (it isn't the surface integral of a vector field over the boundary of something nor is it the volume integral of the divergence of a vector field over something - it's just the integral over $\Sigma$ of a scalar field $T_{i\nu}$ for each fixed $i,\nu$). The only thing I've been able to write down that might be of use is that since the linearized field equations are $\partial^{\alpha}\partial_{\alpha}\gamma_{\mu\nu} = -16\pi T_{\mu\nu}$, we have that $\partial^{t}\partial^{\alpha}\partial_{\alpha}\gamma_{\mu\nu} = \partial^{\alpha}\partial_{\alpha}\partial^{t}\gamma_{\mu\nu} = 0 = \partial^{t}T_{\mu\nu}$ where I have used the fact that in this global inertial coordinate system with stationary killing field $\xi^{a} = (\frac{\partial }{\partial t})^{a}$, the perturbation cannot have any time dependence. This then reduces the conservation equation to $\partial^{\mu}T_{\mu\nu} = \partial^{i}T_{i\nu} = 0$ where again $i=1,2,3$. I really haven't been able to make much progress from here though. I would really appreciate any and all help, thanks.</p>
| 2,392 |
<p>I'm trying to figure out an example from a textbook (Demtröder -- Experimentalphysik 2, pg. 198) where the energy transport caused by a current is depicted:</p>
<p>Assume you have a wire (with some resistance $R$) and a current $I$ flowing through the wire. The wire will emit energy in form of heat (with $\dot W = I^2 \cdot R$). It states that since the electric field $\mathbf E$ is parallel to to the wire (i.e. the current), and the magnetic field $\mathbf B$ is tangential to the wire, the Poynting vector $\mathbf S$ must point radially (and orthogonally) <em>into</em> the wire.</p>
<p>The book goes on to argue, that therefore, the energy to replenish the "lost" heat-energy <em>flows radially from the outside into the wire</em>. My question is now, <strong>where does that energy come from?</strong> I would have thought that it comes from the source of the current (e.g. a battery) and travels through the wire to the point where the heat is emitted. However, this is explicitly stated to be wrong. Could you please shed some light on the issue?</p>
| 2,393 |
<p>It's not possible for an electron to emit or absorb a photon without the presence of a third particle such as an atomic nucleus; without the third particle, it's impossible for such a process to conserve energy and momentum.</p>
<p>However, if tachyons exist and couple to matter, then a material particle can emit or absorb tachyons while conserving energy and momentum. According to an interpretation originated by Bilaniuk (1962), inspired by the Feynman-Stueckelberg interpretation of antiparticles, tachyons are always taken to have positive energy, but this implies that an event that one observer sees as an absorption can be seen by another observer as an emission. For instance, it's possible for a moving material particle to spontaneously emit a tachyon, but in the particle's rest frame this would be seen as absorption.</p>
<p>Spontaneous emission is hard to make sense of in a classical theory. In a quantum-mechanical theory, it would be analogous to radioactive decay. This decay would have to occur with some rate. We normally expect a radioactive decay to occur at some fixed rate in the parent's rest frame, and this rate is lowered by the Lorentz factor $\gamma$ in any other frame.</p>
<p>What seems suspect to me about the idea of spontaneous tachyon emission is that there seems to be no way to reconcile it with Lorentz invariance. Let's say it occurs with some mean lifetime $\tau$ in a certain frame, in which the parent particle is moving with some speed and has some value of $\gamma$. Lorentz invariance seems to require that in the particle's rest frame, the lifetime should be $\tau/\gamma$. But in the particle's rest frame, the process is absorption rather than emission, and it can't have some fixed rate. The rate has to be determined by how many tachyons are available in the environment to be absorbed.</p>
<p>My question is whether my interpretation is right, and whether it constitutes a problem for Bilaniuk's claim that his approach eliminates all the paradoxes associated with tachyons. (I'm also pretty suspicious of his claimed resolution of the Tolman antitelephone paradox, but that's a different topic.)</p>
<p>Bilaniuk, Deshpande, and Sudarshan, Am. J. Phys. 30, 718 (1962). For an exposition of the ideas, see Bilaniuk and Sudarshan, Phys. Today 22,43 (1969), available online at <a href="http://wildcard.ph.utexas.edu/~sudarshan/publications.htm" rel="nofollow">http://wildcard.ph.utexas.edu/~sudarshan/publications.htm</a> .</p>
| 2,394 |
<p>I found multiple questions where it is stated that dark energy increases as the universe expands. Assuming a big crunch scenario, will this dark energy "go away" again as the size of the universe decreases again, or will there be more energy (=mass) at the Big Crunch than at the Big Bang?</p>
| 2,395 |
<p>You can have two electrons that experience each other's force by the exchange of photons (i.e. the electromagnetic force). Yet if you compress them really strongly, the electromagnetic interaction will no longer be the main force pushing them apart to balance the force that pushes them towards each other. Instead, you get a a repulsive force as a consequence of the Pauli exclusion principle. As I have read so far, this seems like a "force" that is completely separate from the other well known forces like the strong, electroweak and gravitational interaction (even though the graviton hasn't been observed so far). </p>
<p>So my question is: is Pauli-repulsion a phenomenon that has also not yet been explained in terms of any of the three other forces that we know of?</p>
<p><em>Note: does this apply to degenerate pressure too (which was explained to me as $\Delta p$ increasing because $\Delta x$ became smaller because the particles are confined to a smaller space (Heisenberg u.p.), as is what happens when stars collapse)?</em></p>
| 2,396 |
<p>Assume stably stratified fluid but not in equilibrium, e.g. with non-constant temperature gradient for example. Can convection cells be present? Typical example of convection cells is Rayleigh–Bénard convection. But this is example of unstably stratified fluid. In stably stratified fluid which is not in equilibrium is there some mechanism introducing instability? I'm targeting to low viscosity and very high externally-induced heat flux.</p>
| 2,397 |
<p>...to heat a piece of steel so its glowing yellow (1100 C)? Assuming you had a cloudless day at a latitude of, say, San Francisco...</p>
<p>Basically I'm wondering if it is possible/feasible to be able to do basic metal working without a traditional forge, just using the power of the sun to heat the metal. So the diameter of the heated spot would have to be about 6" in order to heat a large enough area of the metal to work it...</p>
<p>I always thought you would need several huge pieces of equipment to do this, but just thought I'd ask if anyone here knew how to figure out it roughly...</p>
<p>Thanks!</p>
| 2,398 |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/44629/elastic-collision-and-momentum">Elastic Collision And Momentum</a> </p>
</blockquote>
<p>I've already asked this question, <a href="http://physics.stackexchange.com/questions/44629/elastic-collision-and-momentum">Elastic Collision And Momentum</a>, but I didn't find the answer particularly helpful--sorry, I don't mean to be rude.</p>
<p>So, here is my newest attempt for this problem:</p>
<p>Before the collision, $m_1$ possesses kinetic energy, which it gained by having its potential energy convert to it as it fell $h$. On the other hand, $m_2$ has no kinetic energy energy before the collision. After the collision, some of $m_1$'s kinetic energy is transferred into $m_2$, which is why it doesn't return to its original height.</p>
<p>Energy Analysis:</p>
<p>$m_1:$ $KE_i=mgh=244.02~J$; $KE_f=\frac{1}{2}mv^2_{f,1}$</p>
<p>$m_2:$ $KE_i=0~J$; $KE_f\frac{1}{2}mv^2_{f,2}$</p>
<p>Velocity of $m_1$ before collision: $\frac{1}{2}mv^2_{i,1}=mgh~\rightarrow v_{i,1}=9.90~m/s$</p>
<p>Momentum Analysis:</p>
<p>$m_1:$ $\vec{p}=(4.98)(9.90)$; $\vec{p}=4.98\vec{v}_{f,1}$</p>
<p>$m_2:$ $\vec{p}_{i,2}=0$; $\vec{p}_{f,2}=9.40\vec{v}_{f,2}$</p>
<p>This is where I get stuck. I have been working on this problem for quite some time, I'd really appreciate some help.</p>
| 44 |
<p>I think I do not understand well the concept of Deborah number.</p>
<p>It is presented in the sources available to me as the ratio between the relaxation time of a fluid and a characteristic time scale of the flow. In other sources the denominator of the ratio is occupied by the "observation time scale".</p>
<p>Firstly, I struggle in front of the definition of a "relaxation time" for a "real world" fluid, characterised by a continuous spectrum of relaxation times.
But the worst is to come, so let us assume a fluid with a clearly defined relaxation time is at hand.</p>
<p>If an harmonic excitation with, say, frequency $\omega$, is applied to the viscoelastic and the flow observed for a duration of time $t$, how to define Deborah number? The relaxation time is fixed as a material property, but what to use in the denominator? The time scale linked to the frequency applied, or the observational time scale?</p>
| 2,399 |
<p>So I was wondering if Electromagnetic wave has the same property of interference as normal waves. I understand that both the electric and magnetic parts of the wave would have to be in the same position at the same time. To negotiate the fact that only one part of the wave would match up at one time due to the fact that light can't go faster than it's self I had the idea for three waves all intersecting at the same point. All of these waves would be of different wavelengths so that they do not interfering with each other before the main point. If I knew of a good easy way off making a fbd I would but i am rather new to really doing physics Ioutside of a high school classroom. So I was wondering if constructive interference worked on electromagnetic waves and if it does whether or not is decrease's the wavelength (increasing the energy). </p>
| 2,400 |
<p>I have been performing an experiment at school in which I test the force on an iron surface from the magnetic field of an electromagnet. The electromagnet has a rectangular iron core. The theory predicts that the force increases linear with the surface area of the iron plate. This is because the volume between the plate and the magnet contains a certain amount of energy, which is equal to the force exerted on the plate times the distance between the plate and the magnet.</p>
<p>I found that the force does not increase linear with the surface. This is because of the divergence of the magnetic field of a bar magnet, which is what the core of the electromagnet essentially is. Researching the magnetic field of a bar magnet, I discovered that there is a higher density of field lines at the edges of the poles, and thus a stronger force on the plate. There are some images on this website: <a href="http://www.coolmagnetman.com/field01.htm" rel="nofollow">http://www.coolmagnetman.com/field01.htm</a>, such as the one below.</p>
<p><img src="http://i.stack.imgur.com/nDMoQ.gif" alt="enter image description here"></p>
<p>I am curious as to why the field is stronger here. I know that the electric field is stronger at edges and corners because the electrons repel and end up at a higher concentration there, is it the same concept for magnetic fields? </p>
| 2,401 |
<p>If a mass of one kilogram is traveling at one meter per second at 90 degrees, how much energy is required to get it to travel going 180 Degrees?</p>
| 2,402 |
<p>I'm trying to think about special relativity without "spoiling" it by looking up the answer; I hope someone can offer some insight - or at least tell me I'm wrong. </p>
<p>Suppose I have an ordinary clock in front of me and I push it back with my hands. The force applied to the clock causes it to retreat away from me and after the push, it will travel away with uniform velocity. Suppose further, I can always see the clock clearly no matter how far away it is. Since the speed of light is constant, the light coming from the clock must travel a longer distance to reach my eye as it moves away. This would make time appear to slow down? If, on the other hand, the clock is moving towards me, the distance the light must travel to reach my eye becomes shorter and shorter, thus time would appear to speed up?</p>
| 2,403 |
<p>It's said that if a space elevator were made then it would be much more efficient to put objects in orbit. I've always wondered about the durability of a space elevator though. I don't mean the material strength but rather what affect using the elevator has on the elevator.</p>
<p>To put some massive object in orbit requires increasing its potential energy by a lot. Where is this energy coming from? Is the energy 100% from the fuel used to power whatever climbs the elevator? Is energy sapped from the Earth's rotation? Does climbing the elevator move the counterweight at all and does the position of the counterweight have to be adjusted after each climb?</p>
<p>I assume that a space elevator can be used over and over but I'd like to understand what the ultimate source of energy is and what allows for elevator re-use.</p>
| 2,404 |
<p>Say you have energy eigenstates</p>
<p>\begin{align}
\begin{split}
|+\rangle=
\frac{1}{\sqrt{2}}|1{\rangle}+\frac{1}{\sqrt{2}}|2 \rangle
\end{split}
\end{align}</p>
<p>\begin{align}
\begin{split}
|-\rangle=
\frac{1}{\sqrt{2}}|1{\rangle}-\frac{1}{\sqrt{2}}|2 \rangle
\end{split}
\end{align}</p>
<p>with </p>
<p>\begin{align}
\begin{split}
|\psi(0)\rangle=
\alpha{_+}|+{\rangle}+\alpha{_-}|- \rangle
\end{split}
\end{align}</p>
<p>and </p>
<p>\begin{align}
\begin{split}
\alpha{_{+}} = {\langle} + | {\psi{(0)}} {\rangle}
\end{split}
\end{align}</p>
<p>\begin{align}
\begin{split}
\alpha{_{-}} = {\langle} - | {\psi{(0)}} {\rangle}
\end{split}
\end{align}</p>
<p>I know that you can find the coefficients $\alpha_+$ and $\alpha_-$ if you have $|\psi(0)\rangle$ already, but I am struggling conceptually with what this means in relation to the Heisenberg uncertainty principle and problem solving for this type of thing in general. </p>
<p>I am also unsure how you find the eigenstates. Though I know mathematically how to get the eigenvalues and eigenvectors from a matrix.</p>
| 2,405 |
<p>What would be the proof for $\langle q| p \rangle = e^{ipq}$?</p>
<p>Is it derived from canonical commutation relation?</p>
<p>($|q \rangle $ represents the position eigenstate, while $|p \rangle$ represents the momentum eigenstate.)</p>
| 2,406 |
<p>The answers to <a href="http://physics.stackexchange.com/q/134473/58796">Where does the extra kinetic energy come from in a gravitational slingshot?</a> state that in a gravitational slingshot the object being accelerated "steal" speed from the planet (or moon).
Does that mean that an excessive number of g-slingshot could stop a planet?</p>
| 2,407 |
<p>Imagine you have a simple pendulum hanging on the ceiling of a train which has a period called T. How will the period be in the following cases:</p>
<ol>
<li>When the train is in circular motion in a curve of radius R with constant speed (I think it would be lower than T (the initial period), that's my intuition).</li>
<li>The train is going up a constant slope with constant speed (I also think it would be lower than T).</li>
<li>The train moves over a hill of radius R with constant speed. (I feel it would be greater than T because the pendulum just moves in step with the change of the slope. That's why the pendulum oscillates completely just when the train has left the hill).</li>
</ol>
<p>Sorry for my poor explanations. I have just tried to figure it out the best way I could. What do you think? Do you agree with me?</p>
<p>Thanks</p>
| 2,408 |
<p>I don't understand why this formula is relevant to the problem:</p>
<p><img src="http://i.stack.imgur.com/9t26Y.png" alt="enter image description here"></p>
<p>This was the relevant worked solution:</p>
<p><img src="http://i.stack.imgur.com/rnX8F.png" alt="enter image description here"></p>
<p><strong>My problem</strong> is that I do not understand this formula because I don't even understand what the variables stand for. I'm also not sure what this formula does, or is even used for.</p>
<p>Would anyone kindly give me a brief explanation so I am able to understand when to use this formula? What is this formula saying to me?</p>
<p>Much thanks, eagerly awaiting your reply. </p>
| 2,409 |
<p>I was trying to solve this problem:</p>
<p>"A punctiform source of light is standing inside a lake, at a height h of the surface. f is the fraction of the total of energy emitted that escapes directly from the lake, ignoring the light being absorbed in the water. Given n, the refractive index of water, determine f."</p>
<p>I understand that, since the maximum refraction angle is 90°, there is a maximum incident angle. The next image explains the principle:</p>
<p><a href="http://img441.imageshack.us/img441/9573/lake01b.png" rel="nofollow">http://img441.imageshack.us/img441/9573/lake01b.png</a></p>
<p>In it, the yellow incident light rays diverge (since the air is less dense than the water), until, at one point, the refractive angle is 90°. Then, the rays stop refracting.</p>
<p>At this point, I applied Snell Law:</p>
<pre><code>n1 * sin i = n2 * sin r
n * sin i = 1 (it's air) * sin 90
sin i = 1/n
</code></pre>
<p>Now let's analyze the following triangle:</p>
<p><a href="http://img690.imageshack.us/img690/8421/lake02.png" rel="nofollow">http://img690.imageshack.us/img690/8421/lake02.png</a></p>
<p>As you can see, the triangle is formed by: <em>90 - i</em>, <em>90 - i</em> and <em>a</em>.</p>
<pre><code>a + 90 - i + 90 - i = 180
a = 2i
</code></pre>
<p>The fraction of light that made out of the lake is <em>a</em> over the total circle, that is, 360°. So:</p>
<pre><code>f = 2i/360 = i/180
i = arc sin (1/n)
f = (arc sin (1/n))/180
</code></pre>
<p>However, the answer I have for this exercise (and it does seem to be right, because it is from a University*) is $f = \tfrac12 - \tfrac{1}{2n} \sqrt{n^2 - 1}$. And I don't know what I did wrong. It is very important for me to solve this exercise, and I hope someone would have a hint of what I am doing wrong.</p>
<p>*It is a very old test (1969), and there is no resolution anywhere (just the final answer).</p>
<hr>
<p>Second try, using Solid Angles:</p>
<p>At is the total Area of the light sphere of radius h:</p>
<pre><code>At = 4 * pi * rt²
rt = h
At = 4 * pi * h²
</code></pre>
<p>Ap is the partial area of the circle of light that gets out of the water:</p>
<pre><code>rp = h / (tg(90 - i))
tg (90 - i) = sen (90 - i)/ cos (90 - i)
sen (90 - i) = sen 90*cos i - sen i*cos90 = cos i
cos (90 - i) = cos 90*cos i + sen 90*seni = sen i
tg (90 - i) = cos(i)/sen(i) = 1/tg(i)
rp = h*tg(i)
Ap = pi * rp²
</code></pre>
<p>So f must be Ap/At:</p>
<pre><code>Ap/At = (pi * rp²) / (4 * pi * rt²)
f = h² * tg²(i) / (4 * h²)
f = tg²(i)/4
</code></pre>
<p>Still not there.</p>
| 2,410 |
<p>To preface, I am not a scientific mind, but a writer looking for some validity to a possible scene. That being said, please forgive me!</p>
<p>In my scene, huge masses of fire are raining from the sky and crashing into a salt-water ocean. </p>
<p>[Edit]: I would imagine the buring substance as some sort of 'napalm'? I am unfamiliar with how fire would exist in the atmosphere. I guess that's the magic part (;</p>
<p>My question is:</p>
<p>What would happen when fire meets water in such a way? Would it make noise? Would it cause large amounts of steam? How about smoke? If it occurred near land, would the steam or smoke drift away or towards the land?</p>
<p>I realize I am asking about the results of interactions between something magical and the physical world, but please bear with me!</p>
| 2,411 |
<p>I want to check that I am getting the concept right here, and my question is: if the expectation value of a Hamiltonian is the same whether you use the time dependent version or not. I thought I had it right initially -- maybe I did -- but I wanted to make sure I didn't go off the rails somewhere. </p>
<p>We have a wave function: $\psi = \alpha \phi_1 + \beta \phi_2$ and normalized it's $\frac{1}{(\alpha^2 + \beta^2)}(\alpha \phi_1 + \beta \phi_2)$. </p>
<p>The time evolution of that state will be $(\frac{1}{\alpha^2 + \beta^2})(\alpha \phi_1 e^{-i\omega_1 t} + \beta \phi_2 e^{-i\omega_2 t})$</p>
<p>And $\hat H \psi = i\hbar \frac{\partial}{\partial t}\psi(x,t)$ and $\langle \hat H \rangle = \int \psi \hat H \psi dx$</p>
<p>$\frac{\partial \psi}{\partial t} = \frac{1}{\alpha^2 + \beta^2} (-i\omega_1 \alpha \phi_1 e^{-i\omega_1 t}-i\omega_2 \beta e^{-i\omega_2 t}\phi_2)$</p>
<p>So the integral is $$\int \psi \hat H \psi dx = \int (\frac{1}{\alpha^2 + \beta^2})(\alpha \phi_1 e^{-i\omega_1 t} + \beta \phi_2 e^{-i\omega_2 t})i \hbar (-i\omega \alpha \phi_1 e^{-i\omega_1 t}-i\omega_2 \beta e^{-i\omega_2 t}\phi_2)dx$$
$$=-\hbar\frac{1}{\alpha^2 + \beta^2}\int(\alpha \phi_1 e^{-i\omega_1 t} + \beta \phi_2 e^{-i\omega_2 t}) (\alpha \omega_1 \phi_1 e^{-i\omega_1 t}-\beta \omega_2e^{-i\omega_2 t}\phi_2)dx$$
$$=-\hbar\frac{1}{\alpha^2 + \beta^2}\int (\alpha^2 \omega_1 \phi_1^2 e^{-2i\omega_1 t}-\beta^2 \omega_2 \phi_2^2e^{-2i\omega_2 t}\phi_2)dx$$</p>
<p>Using a 0 to L limit (we're doing a particle in a box here), and taking the sinusoidal form of $\phi_n$:
$$=\frac{-2\hbar}{L (\alpha^2 + \beta^2)}\int^L_0 \alpha^2 \omega_1 e^{-2i\omega_1 t}\sin^2({\frac{\pi x}{L})}-\beta^2 \omega_2 e^{-2i\omega_2 t}\sin^2({\frac{2\pi x}{L})}dx$$</p>
<p>applying a trig identity </p>
<p>$$=\frac{-2\hbar}{L (\alpha^2 + \beta^2)}\int^L_0 \alpha^2 \omega_1 e^{-2i\omega_1 t}\left( \frac{1}{2}-\frac{1}{2}\cos({\frac{2\pi x}{L})} \right)-\beta^2 \omega_2 e^{-2i\omega_2 t}\left( \frac{1}{2}-\frac{1}{2}\cos({\frac{4\pi x}{L})} \right)dx$$</p>
<p>and doing the integral </p>
<p>$$\frac{-2\hbar}{L (\alpha^2 + \beta^2)}\left[ \frac{\alpha^2 \omega_1 e^{-2i\omega_1 t}x}{2}-\frac{\alpha^2 \omega_1 e^{-2i\omega_1 t}L}{2\pi}\sin{\frac{2\pi x}{L}}- \frac{\beta^2 \omega_2 e^{-2i\omega_2 t}}{2}-\frac{\beta^2 \omega_2 e^{-2i\omega_2 t}L}{4 \pi} \sin{\frac{4\pi x}{L}} \right]_0^L$$
$$=\frac{-\hbar \alpha^2 \omega_1 e^{-2i\omega_1 t}}{(\alpha^2 + \beta^2)}+ \frac{\hbar \beta^2 \omega_2 e^{-2i\omega_2 t}}{L(\alpha^2 + \beta^2)} $$</p>
<p>THis is all very well, but it still looks like it depends on time, unless it's because of one of a couple of things: 1. The difference between the exponentials is a phase difference, so they might be equivalent, or since these are stationary states we're talking about we can treat them as constants. But I wanted to make sure there wasn't some mathematical point I wasn't missing. I feel like I am almost there but not quite. </p>
<p>I also suspect I didn't need to do the full integration but I am not so expert with Dirac notation. I also kind of wanted to see what was "under the hood" so to speak. </p>
<p>and sorry for the long post. </p>
| 2,412 |
<p>If a conductor carrying current is placed inside a magnetic field, we know that there is the Lorentz force pushing the wire. But what about the attraction force between the wire's field and the magnet/electromagnet's field? So, isn't there really two forces involved? Attraction due to two magnetic field, and Lorentz force?</p>
<p>Even if the pole of the "electromagnet" can attract the conductor.</p>
| 2,413 |
<p>I would like some help with the explicit math steps to go from equation 2 to 3. These equations are presented in a paper that I am reading. I will show where these equations came from and my attempt further below. The paper reads:</p>
<blockquote>
<p>The volumetric isothermal flow rate of nitrogen, which behaves as an
ideal gas, from a storage tank at pressure $P_o$ is:</p>
<p>$$\frac{-V_tP'_o(t)}{P(x,t)}=\frac{-k_lA(1+b/P(x,t))}{\mu}\frac{\partial P(x,t)}{\partial x} \tag{1}$$</p>
<p>The subscript $o$ in these equations refers to conditions just
upstream of the inlet face of the sample.</p>
<p>If Eqn. (1) is integrated with respect to lenth and divided by
$1/2(P_l-P_o)$, it becomes</p>
<p>$$\frac{-2V_t \mu P'_o(t)L}{k_lA(P_o-P_l)}=P_l+P_o+2b \tag{2}$$</p>
<p>Pressures in all equations above have been absolute pressures,
expressed in atmospheres and permeability in darcies. If we now
switch to gauge pressure (psig), and express permeability in
millidarcies, Eqn. (2) becomes (since $P_l=0$ psig):</p>
<p>$$\frac{-V_t P'_o(t)}{P_o(t)}=\frac{k_lA}{2000 \times 14.696 \mu L}(P_o(t)+2P_a+2b) \tag{3}$$</p>
</blockquote>
<p><strong>Note: I will be using the notation $P_L$ not $P_l$ as the author did above</strong></p>
<p>Some background information about these equations. The equations are being used to describe a test flowing gas through a rock. </p>
<p>The test setup consists of a tank and pressure transducer that can be pressurized with nitrogen. A rock-core holder is attached to the tank, separated by a quick opening valve. To perform a run, the tank is charged with nitrogen to an initial pressure. If the valve at the bottom of the tank is opened, nitrogen will flow (axially) through the core (a right-cylindrical rock sample) and the pressure in the tank will decline -- rapidly at first, then more and more slowly. The volumetric rate of nitrogen flow at the inlet face of the core can be derived from the ideal gas law, since the compressibility factor (deviation factor) is unity for nitrogen at low pressure and room temperature.</p>
<p><strong>The Derivation to get to Eqn. (1):</strong></p>
<p>The volumetric isothermal flow rate of nitrogen, which behaves as an ideal gas, from a storage tank at pressure $P_o$ is</p>
<p>$$q_o(t)=\frac{M}{\rho_o(t)}\frac{-dn}{dt} = \frac{-MV_t}{\rho_o(t)RT}\frac{dP_o}{dt} \tag{a}$$</p>
<p>where:</p>
<p>$q_o(t)=$ the volumetric flow rate at the inlet face of the core at time $t$</p>
<p>$M=$ molecular weight, g/mol</p>
<p>$\rho_o(t)=$ gas density at the inlet face of the core at time $t$</p>
<p>$n=$ the number of moles of nitrogen in the reservoir tank</p>
<p>$t=$ time</p>
<p>$V_t=$ the volume of the nitrogen tank, which remains constant</p>
<p>$R=$ universal gas law constant</p>
<p>$T=$ absolute temperature</p>
<p>$P_o=$ the absolute pressure of nitrogen gas in the reservoir tank/inlet core face</p>
<p>Density is given by:</p>
<p>$$\rho_o(t)=\frac{MP_o(t)}{RT} \tag{b}$$</p>
<p>Therefore,</p>
<p>$$q_o(t)=\frac{-V_t}{P_o(t)}\frac{dP_o}{dt} \tag{c}$$</p>
<p>Assume for the moment that at any instant in time the mass velocity throughout the length of the core is constant. (This is not rigorously true.) As the nitrogen flows through the core it expands, such that</p>
<p>$$q(x,t)=\frac{q_o(t)P_o(t)}{P(x,t)}=\frac{-V_t}{P(x,t)}\frac{dP_o}{dt} \tag{d}$$</p>
<p>where,</p>
<p>$x=$ distance in core (=0 at inlet end and L at outlet end)</p>
<p>Klinkenberg's relationship</p>
<p>$$k(x,t)=k_l(1+b/P(x,t)) \tag{e}$$</p>
<p>where,</p>
<p>$k=$ apparent permeability, darcy</p>
<p>$k_l=$ Klinkenberg, or "liquid" permeability, darcy</p>
<p>$b=$ Klinkeberg slip factor, psi</p>
<p>Darcy's equation for one-dimentional flow</p>
<p>$$q=\frac{-kA}{\mu}\frac{dP}{dx} \tag{f}$$</p>
<p>where,</p>
<p>$A=$ cross-sectional area of core (normal to direction of flow)</p>
<p>$\mu =$ nitrogen viscosity (=0.0177 cp at 23 deg C)</p>
<p>Substituting Eqn. (d) and Klinkenberg's relationship, Eqn. (e), into the Darcy equation for one-dimensional flow, Eqn. (f), yields Eqn. (1):</p>
<p>$$\frac{-V_tP'_o(t)}{P(x,t)}=\frac{-k_lA(1+b/P(x,t))}{\mu}\frac{\partial P(x,t)}{\partial x} $$</p>
<p><strong>My attempt to derive Eqn. (3)</strong></p>
<p>Substituting the volumetric flowrate relation and Klinkenberg's relationship into the Darcy equation for one-dimensional flow, Eqn. 16, yields:</p>
<p>\begin{equation} -\frac{V_t}{P_s(x,t)}\left(\frac{dP_{s,o}}{dt}\right)=-\frac{k_lA(1+\frac{b}{P_s(x,t)})}{\mu}\frac{\partial{P_s(x,t)}}{\partial{x}}\end{equation}</p>
<p>where,</p>
<p>$P_{s,o}=$ absolute pressure measured at the inlet face of the core sample</p>
<p>$P_g(x,t)=$ gauge pressure in the core that varies with both distance and time, psig</p>
<p>$P_a=$ atmospheric pressure, psia</p>
<p>Recall differential notation:</p>
<p>$$\frac{dP_{s,o}}{dt}=P'_{s,o}(t)$$</p>
<p>Separate variables and integrate pressure with respect to the length of the core. This will sum all the infintesimal changes in pressure over the length of the core. </p>
<p>\begin{align}
\frac{V_t \mu P'_{s,o}(t)}{k_lA} \int_{o}^{L}dx &=\int_{P_s(o,t)}^{P_s(L,t)}(P_s(x,t)+b) \ dP_s(x,t) \\
\nonumber\\
&=\frac{P_s(x,t)^2}{2}\Biggr|_{P_s(o,t)}^{P_s(L,t)}+bP_s\Biggr|_{P_s(o,t)}^{P_s(L,t)} \end{align}</p>
<p>let $P_s(L,t)=P_{s,L}$ and $P_s(o,t)=P_{s,o}$</p>
<p>\begin{align}
&=\frac{P_{s,L}^2}{2}-\frac{P_{s,o}^2}{2}+P_{s,L}b-P_{s,o}b \\
\nonumber\\
&=\frac{1}{2}(P_{s,L}-P_{s,o})(P_{s,L}+P_{s,o}+2b) \\
\nonumber\\
\frac{V_t \mu P'_{s,o}(t)L}{k_lA}&=\frac{1}{2}(P_{s,L}-P_{s,o})(P_{s,L}+P_{s,o}+2b) \\
\nonumber\\
\frac{-1}{-1} \times \frac{2 V_t \mu P'_{s,o}(t)L}{k_lA(P_{s,L}-P_{s,o})}&=P_{s,L}+P_{s,o}+2b \\
\nonumber\\
\frac{-2 V_t \mu P'_{s,o}(t)L}{k_lA(P_{s,o}-P_{s,L})}&=P_{s,L}+P_{s,o}+2b
\end{align}</p>
<p>Since $P_{s,o}$ is the only pressure changing with respect to time, the equation should be written as:</p>
<p>\begin{equation} \frac{-2 V_t \mu P'_{s,o}(t)L}{k_lA(P_{s,o}(t)-P_{s,L})}=P_{s,L}+P_{s,o}(t)+2b\end{equation}</p>
<p>This is the same equation as Eqn. (2) written by the author.</p>
<p>I'm repeating the paper's verbage here: Pressures in all equations above have been absolute pressures expressed in atmospheres and permeability in darcies. If we now switch to gauge pressure (psig), and express permeability in millidarcies, the equation becomes (since $P_l=0$ psig (I will be using $P_L=0$) and $k \text{[mD]}=\frac{k\text{[D]}}{1000}$):</p>
<p>Recall that absolute pressure, $P_s=P_g+P_a$, where $P_a$ is a constant. Therefore, when integrating absolute pressure plus Klinkenberg's coefficient, $(P_s(x,t)+b)$, we get:</p>
<p>$$\int (P_s(x,t)+b) \ dP_s=\int P_g(x,t) \ dP_g + \int P_a \ dP_s + \int b \ dP_s $$</p>
<p>*Question: how should I notate my bounds of integration? Specifically for the $\int P_g(x,t) \ dP_g$ term?</p>
<p>\begin{align}
\int_{P_o}^{P_L}(P_s+b)&=\frac{P_{g,L}^2}{2}-\frac{P_{g,o}^2}{2}+P_LP_a-P_oP_a+P_Lb-P_ob \\
\nonumber\\
&=\frac{1}{2}(P_{g,L}-P_{g,o})(P_{g,L}+P_{g,o}+2P_a+2b)
\end{align}</p>
<p>Therefore,</p>
<p>\begin{equation} \frac{-2 V_t \mu P'_{s,o}(t)L}{k_lA(P_{g,o}(t)-P_{g,L})}=(P_{g,L}+P_{g,o}(t)+2P_a+2b) \end{equation}</p>
<p>\begin{align}
\frac{-2 V_t \mu P'_{s,o}(t)L}{\left(\frac{k_l}{1000}\right)A(P_{g,o}(t)-0)}&=(0+P_{g,o}(t)+2P_a+2b) \\
\nonumber\\
\frac{-2000 V_t \mu P'_{s,o}(t)L}{k_lA(P_{g,o}(t))}&=P_{g,o}(t)+2P_a+2b \end{align}</p>
<p>*Question:Somehow the paper went from Eqn. (2) to Eqn. (3), using the fact that 1 atm is equal to 14.696 psia. How does dividing atmospheres by absolute pressure give you gauge pressure?:</p>
<p>\begin{equation} \frac{-V_t P'_o(t)}{P_o(t)}=\frac{k_lA}{2000 \times 14.696 \mu L}(P_o(t)+2P_a+2b)\end{equation}</p>
<p>I'm not sure how to notate the $P'_o$ term on the left hand side of the equation with regards to subscripts $s$ or $g$. I know that ultimately it needs to be gauge pressure but in my math steps I haven't done anything to that term. I have the same issue with the $P_o(t)$ terms.</p>
<p>Since it was stated that $P_L=0$ psig (because the pressure of the outlet end of the core is at 1 atmosphere), shouldn't $P_a$ also be equated to zero?</p>
<p>Any help will be much appreciated with these matters.</p>
| 2,414 |
<p>Any object traveling at c is observed as traveling at c in all reference frames. When a photon travels through a vacuum at c, all reference frames observe it traveling at c.</p>
<p>When a photon passes through a medium, it's speed is less than c. The moment that it begins to slow down, there is a reference frame in which the photon is stationary, as all reference frames at a speed of less than c (perceived in another reference frame) are equally possible and valid. </p>
<p>This would imply that if a photon were to change speed at all, in some reference frame, the photon is traveling at c, and then its velocity immediately goes to zero. Is this the case?</p>
| 2,415 |
<p>I'm looking for an online coupled oscillation simulation. The best I have got so far is this ---</p>
<p><a href="https://phet.colorado.edu/sims/normal-modes/normal-modes_en.html" rel="nofollow">https://phet.colorado.edu/sims/normal-modes/normal-modes_en.html</a></p>
<p>But I'm looking for something which has more options like changing the mass of the objects, changing the spring constants, cutting off the springs. </p>
<p>Please suggest if you have come across better simulations.</p>
<p>PS : I apologize if this question does not belong here. I need a coupled oscillation simulator for my work. </p>
| 2,416 |
<p>Let's consider an extended version of the Standard Model (SM) with a new Yukawa operator of the form
$$ \sum_\ell g_\ell\bar{\ell}\ell \phi ,$$
where $\ell$ is any lepton of the SM and $\phi$ is a new real spin-0 particle, which is assumed to be a singlet of $SU(2)_L$. This new term breaks the $SU(2)_L$ symmetry, but I'll not try to justify its existence.</p>
<hr>
<p>Now, my question:</p>
<ul>
<li>I want to compute the loop correction to the vertex $\mu e\phi$, which does not exist in the original theory. One possible contribution for this term is show in the figure below (where I also suppose that neutrinos are massive). Does something guarantee that this loop computation will give a finite result in the framework presented here? </li>
</ul>
<p>$\hspace{6.5cm}$<img src="http://i.stack.imgur.com/rdP80.png" alt="enter image description here">,</p>
<ul>
<li>If this is not the case, what conditions must be imposed to the lagrangian in order to have finite contributions? Is it enough to have a Hamiltonian with dimension $d\leq4$ operators? Or is it essential to have a perfectly defined gauge theory? </li>
</ul>
| 2,417 |
<p>I'm trying to understand how infinite mass corrections are cancelled for a particle that is massless at tree level. In short the problem is that we have infinite diagrams, but we don't have a counterterm for them since they don't exist at tree level. As a simple example consider a theory with three charged Weyl fermions, $ \chi _{ ++ }, \psi _- , \psi _+ $, as well a complex scalar, $ \phi _- $ (The $\psi_+ $ isn't really important, but just there to give a large Dirac mass for $\psi_-$)</p>
<p>Furthermore, assume that charge is approximately broken in another sector such that one of the fermions, $ \psi _- $, gets a small Majorana mass (this is very similar to the situation I'm actually interested in, a R symmetric SUSY model with R breaking through anomaly mediated SUSY breaking, so its not as far fetched as it may sound). The Lagrangian takes the form,
\begin{equation}
{\cal L} = {\cal L} _{ kin} - M ( \psi _- \psi _+ + h.c. ) - g ( \phi _- \chi _{ + + } \psi _- + h.c. ) - V ( \phi ) - \underbrace{ m ( \psi _- \psi _- + h.c. )
}_{\mbox{sym. breaking}}\end{equation} </p>
<p>where $ V ( \phi ) $ is the scalar potential.</p>
<p>Due to the symmetry breaking from $ \psi _- $ we can get a symmetry breaking Majorana mass for the $ \chi _{++} $ under loop corrections. However, we don't have a counterterm for it! For example to first order we have (we use chirality Feynman arrow notation),</p>
<p>$\hspace{2cm}$<img src="http://i.stack.imgur.com/KxP0Q.png" alt="enter image description here"></p>
<p>Usually the $ 1 / \epsilon $ is harmless as we hide it in the counterterm. But in this case since we don't have a tree-level contribution to the Majorana mass for $ \chi _{ + + } $, we also don't have a counterterm for it. How is this issue resolved?</p>
<p><strong>Edit</strong>: </p>
<ol>
<li>I've found a related topic in the context of the weak interaction
discussed in the appendix of <a href="http://arxiv.org/abs/1106.3587" rel="nofollow">arXiv:1106.3587</a>. Here, if I understand
correctly, they use the $Z$ boson to cancel the infinity. However, I
don't understand how that would work here since this is not even a
gauge theory.</li>
<li>Weinbeg also discusses a similar topic in the context of the weak
interaction in <a href="http://journals.aps.org/prd/abstract/10.1103/PhysRevD.7.2887" rel="nofollow">"Perturbative Calculations of Symmetry Breaking"</a>,
Phys Rev D Vol 7 Num 10.</li>
</ol>
| 2,418 |
<p>I've edited my original question into horrible monstrosity (I apologize to all who spent their time on it). Here is rephrased version which hopefully will be clear.</p>
<p>Lets have following model situation concerning Poynting's theorem.</p>
<blockquote>
<p><em>Only one standing charged particle in studied area. Energy of coulombic field is $E_1$ (yes I see the singularity too, lets leave it
be for the moment).</em></p>
<p><em>I send in EM wave, which gets the particle move with some constant speed. Rest of the EM wave and all "junk" radiation from accelerating
that particle propagates away in accordance with P. theorem.</em></p>
<p><em>Now I have moving point charge with constant speed. E field is a bit contracted in the direction of the movement, some B fields circles
around because moving charge represents current. So there is some P.
vector associated with fields of this moving particle. Size of this
overall P. vector seems to me dependent (through E, and B) on the
speed of our particle.</em></p>
<p><em>P. theorem will measure the flux of that P. vector when particle goes through the surface of chosen area.</em></p>
<p><em>Size of that flux is through P. vector dependent on speed of the particle. And by decreasing speed I could take flux as close to zero
as I want.</em></p>
</blockquote>
<p>That's why it seems to me P. theorem doesn't register $E_1$. Have I made a mistake in my thinking?</p>
| 2,419 |
<p>In the flat spacetime, one can perform normal-ordering to set the energy of the vacuum state to zero. I read in some places that this procedure cannot be consistently performed in the curved spacetimes. I have not found any explanation of this fact in the literature.
Why is this a case? </p>
| 2,420 |
<p>I was wondering what would happen to all the components on the surface of the Earth if the Earth suddenly stops rotating but does not stop revolving.</p>
| 45 |
<p>I want to prove the following relation</p>
<blockquote>
<p>\begin{align}
\epsilon_{ijk}\epsilon^{pqk}
=
\delta_{i}^{p}\delta_{j}^{q}-\delta_{i}^{q}\delta_{j}^{p}
\end{align}</p>
</blockquote>
<p>I tried expanding the sum
\begin{align}
\epsilon_{ijk}\epsilon^{pqk}
&=&
\epsilon_{ij1}\epsilon^{pq1}
+
\epsilon_{ij2}\epsilon^{pq2}
+
\epsilon_{ij3}\epsilon^{pq3}
\end{align}
I made the assumption that $\epsilon_{ij1} = \delta_{2i}\delta_{3j} - \delta_{3i}\delta_{2j}$, then I tried to argue the following using cyclical permutations
\begin{align}
\epsilon_{ijk}\epsilon^{pqk}
&=&
(\delta_{2i}\delta_{3j}-\delta_{3i}\delta_{2j})(\delta^{2p}\delta^{3q}-\delta^{3p}\delta^{2q})
\\&+&
(\delta_{3i}\delta_{1j}-\delta_{1i}\delta_{3j})(\delta^{1p}\delta^{3q}-\delta^{1p}\delta^{3q})
\\&+&
(\delta_{1i}\delta_{2j}-\delta_{2i}\delta_{1j})(\delta^{1p}\delta^{2q}-\delta^{2p}\delta^{1q})
\end{align}
and then I realized that this was getting long and messy and I lost my way.</p>
<p>How does one prove the Levi-Civita contraction?</p>
| 2,421 |
<p>The gravitational binding energy of a sphere is: $U=\frac{3GM^2}{5r}$, the mass defect is $\Delta E=\Delta m c^2$. Putting: $M=\frac{4}{3}\rho\pi r^3$, we get:
$$U=\frac{16}{15}G\rho^2\pi^2 r^5$$. Now if we put: $U=\Delta E$, we get for $r$:
$$r=\frac{1}{2}\frac{\sqrt5c}{\sqrt{G\rho\pi}}$$ that means:
$$r\approx\frac{2.3\times10^{13} \, \mathrm{kg}^{1/2\, }\mathrm{m}^{-1/2}}{\sqrt\rho}$$
Assuming $\rho=1$, we can conclude that if we have a spherical mass of radius $r$ given by the last equation and density $1$ this mass 'desappears'. So our universe could be full of big invisible masses because the binding energy is equal to the mass defect. Is it this conclusion correct?</p>
| 2,422 |
<p>I encountered a few times the expression of <a href="http://www.google.com/search?as_q=%22statistical+physics%22&as_epq=height+field" rel="nofollow">'height fields' in statistical physics</a>, without ever reading a proper definition. My textbooks don't seem to talk about that, and googling it hasn't been fruitful yet.</p>
<p>Still I know that they are somewhat related to clusters domain (like cluster on spin up or down in the Ising model) for systems with continuous order parameter (such as the $XY$ model). Would you have any bibliographic references to share on this point?</p>
| 2,423 |
<p>Suppose you have 1 kg of lead, can the whole thing be converted into energy so that no mass remains? Or does the conversion stop at the protons/neutrons?</p>
| 46 |
<p>Is it possible to create a telescope with only one convex lens?</p>
<p>Specifically, is the image I drew below possible?<br>
(This was supposed to be rotated 90 degrees counterclockwise.)</p>
<p><img src="http://i.stack.imgur.com/KUkVl.jpg" alt="Picture of my hypothesis(?)"></p>
<p>In this picture, the object (smaller thing) is supposed to be infinitely far away. The lens focuses the light rays on to the eye (top in picture). Then the eyes "sees" as if it is enlarged to be the bigger image (bigger thing).</p>
<p>Some of my friends argue that humans can only see light rays which are parallel to each other. My counter argument is the picture below:</p>
<p><img src="http://i.stack.imgur.com/DfteP.png" alt="Picture of eye seeing at infinity and nearer than infinity."></p>
<p>So if anybody could explain to me why or why not could I create a telescope out of a single convex lens. Thank you!</p>
| 2,424 |
<p>I learned in elementary school that you could get <code>green</code> by mixing <code>blue</code> with <code>yellow</code>. </p>
<p>However with LEDs, TFTs, etc. you always have RGB (red, green, blue) values?</p>
<p>Why is that? From what you learned in elementary <code>yellow</code> would be the 'natural' choice instead of <code>green</code>. </p>
| 2,425 |
<p>In book <a href="http://rads.stackoverflow.com/amzn/click/0070206503" rel="nofollow">"Quantum Mechanics and Path Integral"</a>, 3-2 Diffraction through the slit:</p>
<p>Under the fig. 3-3, why did Feynman say that we cannot approach the problem by a single application of the free-particle law motion, since the particle is actually constrained by the slit?</p>
<p>And why Feynman use Gaussian slit? </p>
| 2,426 |
<p>Consider the following peculiar Lagrangian with two degrees of freedom $q_1$ and $q_2$</p>
<p>$$ L = \dot q_1 q_2 + q_1\dot q_2 -\frac12(q_1^2 + q_2^2) $$</p>
<p>and the goal is to properly quantize it, following <a href="http://en.wikipedia.org/wiki/Dirac_bracket" rel="nofollow">Dirac's constrained quantization procedure</a>. (This is a toy example related to Luttinger liquids and the fractional quantum Hall effect. The degrees of freedom $q_1$ and $q_2$ correspond to two bosonic modes $a_k$ and $b_k$.)</p>
<p>First, note that the equations of motion are</p>
<p>$$ \dot q_1 = -q_2 ,\quad \dot q_2 = -q_1 ,$$</p>
<p>which shows that this model is not complete nonsense as it carries interesting dynamics.
(EDIT: Many thanks to the answerers for pointing out my silly mistake: these equations are wrong, the correct ones would be $q_1=q_2=0$.)</p>
<p>However, the question is</p>
<blockquote>
<p>How to quantize the above Lagrangian in a <em>systematic</em> fashion?</p>
</blockquote>
<p>(I'm actually trying to quantize a different model, but with similar difficulties, hence the emphasis on "systematic"). The usual procedure of imposing canonical commutation relations does not work because the velocities cannot be expressed in terms of the conjugate momenta. According to Dirac, we have to interpret the equations for the canonical momenta as constraints </p>
<p>$$ \phi_1 = p_1 - \frac{\partial L}{\partial \dot q_1} = p_1 - q_2 \approx 0 $$
$$ \phi_2 = p_2 - \frac{\partial L}{\partial \dot q_2} = p_2 - q_1 \approx 0 $$</p>
<p>The hamiltonian is</p>
<p>$$ H = \frac12 (q_1^2 + q_2^2) $$</p>
<p>Unfortunately, the constraints have poisson brackets $\lbrace\phi_1,\phi_2\rbrace = 0$ and the secondary constraints read</p>
<p>$$ \lbrace \phi_1 , H \rbrace = q_1 \approx 0$$
$$ \lbrace \phi_2 , H \rbrace = q_2 \approx 0$$</p>
<p>Clearly, <em>these</em> weirdo constraints no longer have any dynamics and no useful quantization will come out of them.</p>
<p>Is there a systematic method to quantize this theory, for example BRST quantization? Or did I simply make a mistake while trying to apply Dirac's constrained quantization procedure?</p>
| 2,427 |
<p>I saw a great documentary last night about 'nothing'. It's about vacuums, and how if you have a total vacuum atoms will pop out of nowhere! Pretty crazy stuff. Atoms literally coming out of nowhere, then disappearing quickly.</p>
<p>It got me thinking, before the big bang if there was nothing, then presumably atoms would be popping out of nowhere still. If enough atoms suddenly popped simultaneously into the same space could it create the big bang? The chance of this is 1 in trillions on trillions but if time is infinite then surely the chance of this happening is 1?</p>
<p>Also if time is infinite and atoms really do pop out of nowhere, if you go back in time far enough was there ever a moment when a donkey appeared out of nowhere in a giant vacuum simply as a result of a complex pattern of atoms appearing out of nowhere?</p>
<p>I'm a Physics noob but love thinking about all this stuff, is this something people have thought about before? And what other theories of how the big bang happened in the first place are there?</p>
| 2,428 |
<p>I know that if I integrate probabilitlity $|\psi|^2$ over a whole volume $V$ I am supposed to get 1. This equation describes this.</p>
<p>$$\int \limits^{}_{V} \left|\psi \right|^2 \, \textrm{d} V = 1\\$$</p>
<p>How would we calculate a normalisation factor $\psi_0$ for two simple wave functions like:</p>
<p>$$
\begin{split}
\psi &= \psi_0 \sin(kx-\omega t)\\
\psi &= \psi_0 e^{i(kx-\omega t)}
\end{split}
$$</p>
<p>I know this is quite a basic question, but I have to straighten this out so I can continue reading QM.</p>
| 2,429 |
<p>To any nonmagnet, the whole sphere is a magnet. To another spherical magnet though, there is a rough area on the surface where it is strongly repelled. </p>
<p>Given a spherical magnet, <em>how should the poles be found</em>? </p>
<p>My crude attempts were as follows</p>
<ul>
<li>Grip one sphere in a forceps</li>
<li>Bring another sphere close to the forceps</li>
<li>Rotate/roll the spheres until the most repulsion is sensed</li>
<li>Mark the facing surface of the sphere in the forceps using a permanent marker</li>
</ul>
<p>The trouble with the above approach is that I rely upon tactile memory to determine maximum repulsion. </p>
<p>Is there a better, inexpensive way to do this?</p>
| 2,430 |
<p>I'm working with a megapixel camera and lens that needs to be focused for an OCR application. In order to measure the focus quality during the set-up, I've built a tool that gives the contrast value between two pixels. In very simply words, more the contrast is high more the focus is good...
Due to optical distortions, the focus value in the sides of my field of view, is not the same as in the center.
My question is how could I calculate the distortion between center and sides, in %.
For examples fcenter = 62 ; fleftside = 42.
Is that correct to say Leftdistortion = 1-(42/62)*100 ??</p>
<p>Thanks,</p>
<p>Raphael</p>
| 2,431 |
<p>I always wonder how vectors are used in real life.Vectors and decomposition of vectors,dot and cross products are taught in the early stage in every undergraduate physics course and in every university.My question is how and where are vectors used? <strong>Do physicists really use vectors in every day life? If so where?</strong></p>
<p>I'am Looking for Motivation for learning Vectors.</p>
| 2,432 |
<p>I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page <a href="http://preposterousuniverse.com/grnotes/">here</a>. pdf <a href="http://preposterousuniverse.com/grnotes/grtinypdf.pdf">here</a>), a 24-page overview of the topic, very helpful for beginning study. It all got me over the hump of learning the meaning of various terms associated with GR, most of which I had heard before without understanding. It also outlined the most important examples.</p>
<p>Is there a similar document for quantum field theory, which presents the main equations, briefly describes the main ideas, and summarizes the most important applications and results so that the reader can feel the lay of the land before studying in depth?</p>
| 89 |
<p>Let's say I have:</p>
<p>1: one mole of extremely cold ideal gas<br>
2: unlimited amount of ideal gas at temperature 300 K<br>
3: one ideal heat engine</p>
<p>Can I generate for example 1 MWh of mechanical energy using those three things? </p>
<p>Alternative formulation: When temperature of the cold gas approaches 0 K, what does the amount of generated energy approach?</p>
<p>(there is no other heat sink than one mole of cold ideal gas)</p>
| 2,433 |
<p>If I charge a capacitor ($220\mu{F}$) using a 6V battery, and then measure the time it takes to discharge 90% of the initial energy over a resistor (${100k}\Omega$), and then charge the same capacitor using a 12V battery and measure the time it takes to discharge 90% of its initial energy again (over the same resistor).</p>
<p>Why are both times the same? Especially given that the second time there is 4 times more starting energy that the first time. ($E=\frac{1}{2}CV^2$.)</p>
| 2,434 |
<p>I've come across black holes thermodynamics multiple times recently (both at this site and elsewhere) and some things started bugging me.</p>
<p>For one thing, first law bothers me a little. It is a reflection of the law of conservation of energy. This is fine when the space-time is stationary (as in Kerr solution) and is consistent with system being in a thermal equilibrium (so that thermodynamics apply at all). But what about more general systems of black holes?</p>
<blockquote>
<p>What are the assumptions on the system of black holes for it to be in thermal equilibrium so that laws of BH thermodynamics can apply?</p>
</blockquote>
<p><strong>Note:</strong> the reason I am asking is that I heard that the laws should also be correct for system of multiple BH (so that their total event horizon area is increasing, for example). But I cannot wrap my head about <strong>how</strong> might the system of BH be in thermal equilibrium. I mean, they would be moving around, generating gravitational waves that carry energy away (violating the first law) all the time. Right?</p>
| 2,435 |
<p>If the captured object do not have tangential velocity, it's just the free-fall time. But when it has, it may take longer time to fall in, right ?</p>
<p>The function should be </p>
<p>$\ddot{r} = -GM/r^2 + (v_0r_0/r)^2 / r = -GM/r^2 + v_0^2r_0^2 / r^3$ , </p>
<p>where v_0 is the initial tangential velocity . After one integration, it becomes </p>
<p>$\dot{r}^2/2=GM(1/r-1/r_0)-v_0^2r_0^2(1/r^2-1/r_0^2)/2 $ .</p>
<p>I don't know how to deal with it. But I guess there is a analytic solution. </p>
<p>Anyone knows something about it ?</p>
| 2,436 |
<p>Some time ago I came across a problem which might be of interest to the physics.se, I think. The problem sounds like a homework problem, but I think it is not trivial (i am still thinking about it):</p>
<p>Consider a rail tank wagon filled with liquid, say water.<img src="http://i.stack.imgur.com/nunmv.jpg" alt="wagon"></p>
<p>Suppose that at some moment $t=0$, a nozzle is opened at left side of the tank at the bottom. The water jet from the nozzle is directed <strong>vertically down</strong>. Question: </p>
<p>What is the final velocity of the rail tank wagon after emptying? </p>
<p>Simplifications and assumptions: </p>
<p>Rail tracks lie horizontally, there is no rolling (air) friction, the speed of the water jet from the nozzle is subject to the <a href="http://en.wikipedia.org/wiki/Torricelli%27s_law">Torricelli's law</a>, the horizontal cross-section of the tank is a constant, the water surface inside the tank remains horizontal. </p>
<p>Data given: </p>
<p>$M$ (mass of the wagon without water)<br>
$m$ (initial mass of the water)<br>
$S$ (horizontal cross-section of the tank)<br>
$S\gg s$ (cross sectional area of the nozzle)<br>
$\rho$ (density of the water)<br>
$l$ (horizontal distance from the nozzle to the centre of the mass of the wagon with water)<br>
$g$ (gravitational acceleration) </p>
<p>My thinking at the moment is whether dimensional methods can shed light on a way to the solution. One thing is obvious: If $l=0$ then the wagon will not move at all.</p>
| 800 |
<p>How can I derive the Euler-Lagrange equations valid in the field of special relativity? Specifically, consider a scalar field.</p>
| 2,437 |
<p>I'm reading <em>Nano: The Essentials</em> by T. Pradeep and I came upon this statement in the section explaining the basics of scanning electron microscopy.</p>
<blockquote>
<p><em>However, the equation breaks down when the electron velocity approaches the speed of light as mass increases. At such velocities, one needs to do relativistic correction to the mass so that it becomes[...]</em></p>
</blockquote>
<p>We all know about the famous theory of relativity, but I couldn't quite grasp the "why" of its concepts yet. This might shed new light on what I already know about time slowing down for me if I move faster.</p>
<p>Why does the (relativistic) mass of an object increase when its speed approaches that of light?</p>
| 54 |
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