question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
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<p>I came across this paper recently called <a href="http://arxiv.org/abs/1009.1136v1" rel="nofollow">The Small Scale Structure of Spacetime</a> and the following idea occured to me:</p>
<p>To uninformed humans the universe appears Euclidean but we know from GR that on a larger scale it behaves like a Riemannian manifold. Now the paper claims that on a smaller scale, things are 2-dimensional. However, the underlying space is still the same, i.e. that of a manifold.</p>
<p>I have two questions:</p>
<ol>
<li><p>Why do we always deal with manifolds. Perhaps there is a better topological space that explains what happens on all scales. Does anyone know of any competing theory to GR say that does not use manifolds? Are there any theories that make use of the idea of a topologically stratified space?</p></li>
<li><p>Have their been attempts at a unified theory where the geometry of the universe varies at different scales, thus affecting the physics of things at different scales? For example, think of a toy universe that is a sphere. However, this sphere is not made of a smooth material but rather out of a fine mesh of wire. There are thus three scales here: on a larger scale, the universe is curved; on a medium scale, the universe looks flat and 2D; and on a smaller scale, the universe looks 1D almost everywhere.</p></li>
</ol> | g12118 | [
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<p>Can Einstein's equations in vacuum $R_{ab} - \frac{1}{2}Rg_{ab} + \Lambda g_{ab}= 0$ be treated as a Dirichlet problem?</p>
<p>I am thinking of something along those lines:
Consider a compact manifold $M$ with boundary $\partial M$. For a given metric $g_{ab}$ on $\partial M$, does a unique (up to diffeomorphisms) solution to Einstein's equations on $M$ exist? Are there any constraints on the metric on the boundary?</p>
<p>Einstein's equation can be recovered by looking for critical points in the Einstein-Hilbert action, but I don't know enough about variational problems to deduce anything about existence or uniqueness. The fact that general relativity is generally covariant also seems to complicate things, since this leads to a huge coordinate freedom.</p>
<p>Does this depend on the dimension of the manifold or can a general statement be made? I am mostly interested in the three and four dimensional cases.</p>
<p>Note that I am <em>not</em> interested in the initial value formulation usually considered.</p> | g12119 | [
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<p><strong>The given state</strong>:<br/>
Let $\psi$ be a wave that passes from medium $a$ to medium $b$.<br/>
Let $A$ be the amplitude of $\psi$.<br/>
Let $R$ be the amplitude ratio of the reflected wave $\psi_r$ and the original one, and $T$ the amplitude ratio of the transmitted wave $\psi_t$ and the original one.<br/>
<br/>
<strong>The question</strong>: What is the intensity of the transmitted wave?<br/>
<br/>
<strong>An attempt</strong>:<br/>
The condition at the boundary of the two media demands that $1+R=T$.<br/>
The intensity of a wave is $I_\psi=|\psi|^2$.<br/>
<br/>
On one hand we have $I_t\propto T^2=1+2R+R^2$.<br/>
But on the other hand, assuming that the intensity is preserved and that intensity is additive, we also have $I_t=I_\psi - I_r \propto T^2=1-R^2$.<br/>
<br/>
Assuming that $R\neq 0$ there is a contradiction between the 2 answers.<br/>
Which one is the right answer?<br/><br/>
Thanks.</p> | g12120 | [
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<p>In an episode of Discovery's Curiosity with host Stephen Hawking, he claims the Big Bang event can be explained from physics alone, and does not require the intervention of a creator. </p>
<p>1) His argument is based on that, in the beginning, the universe is an equivalent of a black hole behaving as a quantum mechanical particle that can simply "appear" like a Helium particle in alpha radiation. For a large gravitational field like the black hole in question, time did not exist, and therefore there could not exist a being to create the Big-Bang, since time did not exist. </p>
<p>2) During the Big-Bang, positive energy appeared and negative energy was stored in space, and the net energy created is zero and therefore nothing was created.</p>
<p>I am curious on the foundations of Hawking´s claims in the episode. </p>
<p>Is the Big-Bang black hole really modeled as a quantum mechanical particle? Was there really a black-hole at all? What is the resulting entropy change of this black-hole during an event such as the Big-Bang? Are his claims of negative energy stored in space sound or well accepted? </p> | g12121 | [
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<p>I am not into all the tech details of communication via RF with implant chips (tracking chips) and so would like to ask how the known atmospheric pertubations of shortwave radio affect the distances over which one can closely and continuously track an animal with an implanted chip (e.g. a chip transmitting physiological information). </p>
<p>Thanks in advance !</p>
<p>J</p> | g12122 | [
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<p>More specifically, how does a wave-particle duality differ from a quasiparticle/collective excitation?</p>
<p>What makes a photon a gauge boson and a phonon a Nambu–Goldstone boson?</p> | g12123 | [
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<p>Power is known to be equal to the force x velocity (P=FV).</p>
<p>Im solving a question that states the following :</p>
<p>Car with engine working at 32 kW, mass of 1 tonne, travels at a constant speed of 40m/s along a level road.</p>
<p><strong>Given that the resistance to motion is directly proportional to the speed at which the car is travelling</strong>, find the resistance experienced when the car is travelling at 30m/s</p>
<p>How is the text in <strong>Bold</strong> correct ?? P=FV .. Which means F=P/V, Velocity(speed) of car is indirectly proportional to the Force !! Can someone please explain this ?</p> | g12124 | [
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<p>A 50.0 g Super Ball traveling at 25.0 m/s bounces off a brick wall and rebounds at 22.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the magnitude of the average acceleration of the ball during this time interval?</p>
<p>I am using the equation Aavg = (Vf-Vi)/(Tf-Ti) where Vf = 22, Vi=25, Tf = .0035 and Ti = 0</p>
<p>So, (25 - 22)/.00035ms = -857.14m/s? But that doesn't seem right. </p>
<p>I think I am getting confused because it is in milliseconds and am forgetting a conversion or something. Could anyone lend a hand? thanks</p> | g12125 | [
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<p>1) What does the <a href="http://en.wikipedia.org/wiki/Electric_potential" rel="nofollow">electric potential</a> at a point <em>exactly</em> mean? My teacher tells me that current flows from higher potential to lower potential but when I ask him the reason, he fails to give me a convincing answer. </p>
<p>2) And can anyone explain how electric potential is related to <a href="http://en.wikipedia.org/wiki/Potential_energy" rel="nofollow">potential energy</a> & <a href="http://en.wikipedia.org/wiki/Work_%28physics%29" rel="nofollow">work</a> done?</p>
<p>3) Further, when I referred a Physics textbook it said that since Coulomb's force & Gravitational force are mathematically similar, electric potential is a charge's equivalent of a the potential energy of mass. Hence I related Electric potential to the potential energy of a ball for example. A ball falls from a height to the ground because of Potential energy- so similarly, current flows from higher to lower potential. Is this analogy correct?</p>
<p>Even if the above analogy is correct, I still cannot understand why current flows between two electrodes of an electrochemical cell. The only explanation my teacher offers is that there is a potential difference & thus current flows from higher to lower potential. This explanation is not of any help since I don't understand what potential is in the first place!</p>
<p>4) If the analogy is valid, then how do the electrons in the Electrochemical cell move without an electric field to impart the electric potential energy? (as in gravitational energy where the potential energy is present only if gravitational force is present? In space, no object of any mass has weight)</p> | g12126 | [
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<p>We live in a dark world, and the light is results of big bang.
The world is really made mostly of <a href="http://en.wikipedia.org/wiki/Dark_matter" rel="nofollow">dark matter</a> and <a href="http://en.wikipedia.org/wiki/Dark_energy" rel="nofollow">dark energy</a>?
Why the world is so deep and dark?</p>
<p><img src="http://upload.wikimedia.org/wikipedia/commons/a/a5/080998_Universe_Content_240.jpg" alt="Dark world"></p> | g12127 | [
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<p><img src="http://i.stack.imgur.com/neYV0.jpg" alt="enter image description here"><br>
I'm doing independent studies on electron-positron scattering, specifically the annihilation diagram contribution to the M matrix in Bhabha scattering, and this is the equation I recovered with the following initial conditions: An electron, associated with external momentum p_1, and a positron, associated with p_2, annihilate to produce a virtual photon, associated with internal momentum q, that produces a positron-electron pair (p_4 and p_3, respectively). I'm just going to assume you have a running understanding of the Feynman Rules.</p>
<p>These are the associated spinors for the particles involved in the interaction.</p>
<p>$$u\to e^- enters\\\overline u\to e^- exits \\ v \to e^+ exits\\ \overline v \to e^+ enter$$</p>
<p>This is the term added when a vertex is reached, it is a 4 x 4 matrix for fermions.
$$-ig_e\gamma^\mu$$</p>
<p>The recovered equation:</p>
<p>$$ (2\pi)^4\int{[\overline u ^{(S3)} (p_3)(-ig_e\gamma^\mu)v^{(S4)}(p_4)}](\frac{-ig_{\mu \nu}}{q^2})[u ^{(S1)} (p_1)(-ig_e\gamma^\nu) \overline v^{(S2)}(p_2)]\ \delta^4(q-p_3 -p_4) \\ \times \delta^4(p_1+p_2 -q)\ d^4q
$$</p>
<p>where $g_e$ is the quantum-electrodynamic coupling constant.</p>
<p>How do I reduce this down (I see that I can contract the index on $\gamma^\nu$) and integrate the derivatives of the Dirac delta function with arguments $q, p_1,p_2,p_3,$ and $p_4$? I've never come across having to integrate derivatives of the delta function. </p>
<p>Is it possible to use Eq. (17) on <a href="http://mathworld.wolfram.com/DeltaFunction.html" rel="nofollow">http://mathworld.wolfram.com/DeltaFunction.html</a> ? </p>
<p>Any help is appreciated.</p> | g12128 | [
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<p>For example there are anti-particles to every particle we know, <p>
Similary in some sense, is there a possibility that we can charge photons..if not what are the reasons and has there been any attempt to do this experiment ? If it is possible to bend it than why not charge ?</p> | g12129 | [
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<p>I'm working in Taylor and Wheeler's "Exploring Black Holes" and on p.2-14 they use two honorary constants: Newton's constant divided by the speed of light squared e.g. $G/c^2$ as a term to convert mass measured in $kg$ to distance. </p>
<p>Without doing the arithmetic here, the "length" of the Earth is 0.444 cm; and of the sun is 1.477 km. To what do these distances correspond? What is their physical significance, generally? </p> | g12130 | [
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<p>I have a 2D flow velocity field $\bar{V} = y^2\hat{i} + 2\hat{j}$. I'd like to find the equations for the streamlines and pathlines. Since $\bar{V}$ has 0 time derivative, the flow is steady, and so the equations for the streamlines should be identica, right?</p>
<p>Streamlines:
$$\left. \frac{dy}{dx} \right)_{streamline} = \frac{v}{u} = \frac{2}{y^2}$$
$$ \therefore y^2 dy = 2 dx \Rightarrow \int_{y_0}^y y^2 \, dy = \int_{x_0}^x 2 \, dx $$
$$ \therefore \tfrac{1}{3}y^3 - \tfrac{1}{3}y_0^3 = 2(x - x_0) \Rightarrow y^3 - 6x = y_0^3 - 6x_0$$</p>
<p>Pathlines ($x_p$ and $y_p$ the particle coordinates):</p>
<p>$$ \frac{dx_p}{dt} = y^2 \Rightarrow x_p = y^2(t-t_0) + x_{p,0} $$
$$ \frac{dy_p}{dt} = 2 \Rightarrow y_p = 2(t - t_0) + y_{p,0} $$
Now eliminating $(t-t_0)$:
$$x_p = y^2 \left( \frac{y_p - y_{p,0}}{2} \right) + x_{p,0}$$
Without expanding this final equation for the pathline, it is obviously different from the equation of the streamlines; but it shouldn't be, as the flow is steady? Normally this might suggest I've been fast and loose with the math, but I just can't see where I'm wrong here...</p> | g12131 | [
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<p>Does polarized light interfere?</p> | g12132 | [
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<p>Is it possible that if you have 2 ultraviolet lasers, that are invisible to the human eye, and if you aim their beams to intersect at some point, that the place of intersection will show a lower visible wavelength of light, caused by interference of the light freqency? Can any other form of heat or energy be generated at the intersection?</p>
<p>If so, can someone provide a link to the explanation? I am curious about this.</p>
<p>EDIT: I should add that the 2 lasers would have different light frequencies while they are both invisible to the human eye. So, I am wondering about interference between light freqencies.</p> | g12133 | [
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<p>Let us take the standard QED ($e^-, e^+, \gamma$) as a model of QFT and ask what is its "short-distance" physics? </p>
<p>They say the UV infinities appear because we do not know the real physics of short distances and initially we introduce it wrong. OK, but after renormalizations, what physics does remain? Do we replace the unknown/wrong physics with certain/right one? Can anybody describe it without appealing to unphysical bare particles? Have we an idea about the real electron from QED? If so, why we cannot use it as the input to construct a reasonable theory from the very beginning?</p>
<p>P.S. Moderators, please do not close my questions before they are answered, let people answer.</p> | g12134 | [
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<p>When a droplet is deposited on a surface with some surface roughness and subsequently tilted it can stick due to pinning (think of droplets on a window after rain).</p>
<p>What I am interested in is how/whether I can show that all the potential energy from tilting the droplet is converted in surface energy needed for the deformation of the droplet. In other words, is there any energy dissipated in tilting the droplet, when I do it slow 'enough'? (ignoring the motor used for tilting)</p>
<p>Intuitively I would expect zero dissipation, because if I tilt the droplet a bit and then back to the initial position it will have exactly the same shape tilting forward as tilting back to horizontal. Thus if I would draw a force-displacement (of the center of mass) curve I would have a single line indicating, in analogy with elastic behaviour, no hysteresis, thus no energy dissipation. Is this reasoning correct? If so, how can I rigorously make this claim?</p> | g12135 | [
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<p>Given is a mechanical multiple degree of freedom system described by the following matrices and equation:</p>
<ul>
<li><p>mass matrix ${\bf{m}} = \left[\begin{matrix} m & 0 & 0 \\ 0 & m & 0 \\ 0 & 0 & m/2 \end{matrix}\right]$,</p></li>
<li><p>stiffness matrix ${\bf{k}} = \left[\begin{matrix} 2k & -k & 0 \\ -k & 2k & -k \\ 0 & -k & k \end{matrix}\right]$,</p></li>
<li><p>displacements ${\bf{u}} = \left[\begin{matrix}u_1(t) \\ u_2(t) \\ u_3(t)\end{matrix}\right]$,</p></li>
<li><p>external force ${\bf{p}} = \left[\begin{matrix}0\\0\\p_0\sin(\omega t)\end{matrix}\right]$, and</p></li>
<li><p>equation of motion ${\bf{m\ddot{u}}}+{\bf{ku}} = \bf{p}$.</p></li>
</ul>
<p>The natural frequencies $\omega_i$ have been derived from the eigenvalue problem $\det({\bf{k}}-\omega_i^2{\bf{m}})=0$ which led to:</p>
<p>$\omega_1^2=(2-\sqrt{3})\frac{k}{m}\,,\,\omega_2^2=2\frac{k}{m}\,,\,\omega_3^2=(2+\sqrt{3})\frac{k}{m}$.</p>
<p>I know that the steady-state solution for $\bf{u}$ is</p>
<p>${\bf{u}}=\frac{1}{\det({\bf{k}}-\omega^2{\bf{m}})}\rm{adj}({\bf{k}}-\omega^2{\bf{m}})\,\bf{p}$,</p>
<p>so I have to calculate the determinant and adjugate. I actually have no problem doing that, but the textbook solution looks much more elegant than mine and I don't know how to get there.</p>
<p>My solution:</p>
<p>$\det({\bf{k}}-\omega^2{\bf{m}}) = \frac{1}{2}(2k-\omega^2m)^3-3k^3$,</p>
<p>${\rm{adj}}({\bf{k}}-\omega^2{\bf{m}}) = \left[\begin{matrix}
\dots & \dots & k^2 \\
\dots & \dots & k(2k-\omega^2m) \\
\dots & \dots & (2k-\omega^2m)^2-k^2
\end{matrix}\right]$ (only the third column is relevant to the solution)</p>
<p>Textbook solution:</p>
<p>$\det({\bf{k}}-\omega^2{\bf{m}}) = \frac{1}{2}m^3(\omega_1^2-\omega^2)(\omega_2^2-\omega^2)(\omega_3^2-\omega^2)=k^3(1-\frac{\omega^2}{\omega_1^2})(1-\frac{\omega^2}{\omega_2^2})(1-\frac{\omega^2}{\omega_3^2})$,</p>
<p>${\rm{adj}}({\bf{k}}-\omega^2{\bf{m}}) = \left[\begin{matrix}
\dots & \dots & 1 \\
\dots & \dots & 2(1-\omega^2/\omega_2^2) \\
\dots & \dots & 4(1-\omega^2/\omega_2^2)^2-1
\end{matrix}\right]k^2$</p>
<p>My question is: How can I get the textbook solution which is written in terms of the natural frequencies? It seems to me like there is some way to express ${\bf{k}}-\omega^2{\bf{m}}$ mostly in terms of the natural frequencies and then I could go from there, but I don't know how I should do that.</p> | g12136 | [
0.010957208462059498,
0.008942488580942154,
0.0013456837041303515,
-0.06979666650295258,
0.02565693110227585,
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0.0014783693477511406,
0.015247374773025513,
... |
<p>I assume that all mass-objects curve time-space but the curvature is only measurable with celestial bodies large enough to be significant gravity-wells.
What you call "curvature" seems to me to be only a graphic representation-- a map-- of the varying thickness of time-space, a curve which being continuous can be rendered by Calculus. What is being diagrammed is the continuous function of varying thickness within a more ultimate field.</p>
<p>My question is: Do we have any idea how the thickness varies inside the Schwarzschild radius? Does the curvature go to infinity (graphed by an orthogonal vertical line) at the singularity? Or does the curvature go to infinity at the Schwarzschild radius?
Can a form of Calculus be profitably applied to a mass-object of infinite thickness?</p> | g12137 | [
0.026960814371705055,
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0.011808089911937714,
0.013786998577415943,
0.0048040286637842655,
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0.0013088886626064777,
0.09669153392314911,... |
<p>I wrote a simple android app that shows the magnetic field(using the magnetic field sensor in the phone) in the current location. </p>
<p>When I place a two inch steel screw on the top of the phone (which is running the app), there is a change in magnetic field for a while. I'm guessing that it's due to the induced voltage in the screw due to the EM radiation, flowing in my room. However, after a few seconds, the magnetic field stops to change and stabilizes to a value. I am not sure why. </p>
<p>My doubt is, since EM is generally alternating radio waves, shouldn't it induce an alternating voltage in the screw and result in the magnetic field changing continuously? </p>
<p>If the induced voltage is too small, then why did the magnetic field reading change for a while?</p> | g12138 | [
0.07250731438398361,
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0.0... |
<p>This is a sample test question I've encountered twice in some practice chemistry finals. I'm a little bit confused about what it's asking. </p>
<blockquote>
<p>You are conducting an experiment on the photoelectric effect, and
observe that, at a certain frequency and intensity of light, no current flows. According to classical physics, what should you do to make current flow between the electrodes?</p>
</blockquote>
<p>According to the Planck equation, $E=h\nu$, says that if I want electrons to escape from one electrode to the other, I need to hit it with a specific frequency. Is that correct? And is that the classical interpretation of the photoelectric effect? How would you phrase the answer to the question, in 3 sentences or fewer? Thanks!</p> | g12139 | [
0.002083571394905448,
0.027037929743528366,
0.003970680292695761,
0.05192674696445465,
0.06982260197401047,
0.021671853959560394,
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0.004738259594887495,
0.002846467774361372,
0.042702566832304,
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<p>I am considering a Lagrangian that is of the following form:
$$\mathcal{L}=-{1\over 2}\partial_\mu\phi\partial^\mu\phi+2\mu^2\phi^2+2\sqrt{6}{\mu^3\over \lambda}\phi + {9\mu^4\over 2\lambda} + \text{interactions}$$
Now, I am unsure what to do with a the term that is proportional to $\phi$: I think I heard at some point that terms like these can be absorbed in $\phi$ by a suitable redefinition, but I can't really see how that could happen here. Does anyone know what exactly to do with the term? Any help would be much appreciated</p>
<p>EDIT: Lagrangian fully written out is the following: There are $N-1$ fields labeled as $\chi_a$ and one field labeled as $\sigma$.
\begin{align*}
\mathcal{L}&=-{1\over 2} \sum_{a=1}^{N-1} \Biggl(\partial_\mu\chi_a\partial^\mu\chi_a+\partial_\mu\sigma\partial^\mu\sigma\Biggr)
+\mu^2\Biggl(\sum_{a=1}^{N-1}\chi_a^2+2\sigma^2\Biggr)+2\mu^3\sqrt{{6\over \lambda}}\sigma+{9\mu^4\over 2\lambda}\\
&\quad\
-{\lambda\over 12}\Biggl({1\over 2}\sum_{a=1}^{N-1}\chi_a^4
+\sum_{a=1}^{N-1}\sum_{b\neq a}\chi_a^2\chi_b^2
+{1\over 2}\sigma^4 +\sum_{a=1}^{N-1}\chi_a^2\sigma^2\Biggr)
-\mu\sqrt{{\lambda\over 6}}\Biggl(\sum_{a=1}^{N-1}\chi_a^2\sigma+\sigma^3\Biggr)
\end{align*}</p> | g12140 | [
0.07439817488193512,
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0.004849297925829887,
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0.07768147438764572,
0.04236610233783722,
0.031... |
<p>I read somewhere that the earth has to be smaller than 1 cm to become a black hole, according to Schwarzschild. Since big bang came from a singularity, I am wondering, is there any minimum volume for anything? </p> | g12141 | [
0.05492747202515602,
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0.025194... |
<p>Suppose that there is a quantity in Heisenberg picture as the following:</p>
<p>$A=u_1\Sigma_1 + u_2\Sigma_2 +u_3\Sigma_3$</p>
<p>I am not sure why $u_1,u_2,u_3$ is normalized to be ${u_1}^2 + {u_2}^2 + {u_3}^2 =1$. (The matrices $\Sigma$ are the Pauli matrices.) </p> | g12142 | [
0.005496908910572529,
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0.074... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/37571/formulas-for-compressibility-of-solids">Formulas for compressibility of solids</a> </p>
</blockquote>
<p>I have a question which is technically a physics question, but since I have yet to find a good physics forum which accepts Latex, I am posting this question here. I hope that's OK. </p>
<p>I am taking a course in mechanics this semester, as well as a course in reservoir physics. Both courses have sections devoted to pressure/compressibility of solids, but the formulas look slightly different, so I wondered if they really mean the same or not.</p>
<p>In my mechanics class I am told that:</p>
<p>$$\Delta P = B \left(\frac{- \Delta V}{V_0}\right)$$</p>
<p>Where $B$ is a constant known as the <strong>bulk modulus</strong> of a given material.</p>
<p>In my reservoir physics class I am presented with the formula:</p>
<p>$$c = -\frac{1}{V} \left(\frac{\partial V}{\partial p}\right)_{T}$$</p>
<p>Where $c$ is referred to as <strong>isothermal compressibility</strong>.</p>
<p>So my question is - are these formulas basically the same, where $c = \frac{1}{B}$? And if they are not the same, can someone please explain the difference to me? I would really appreciate if someone could help me with this!</p> | g387 | [
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0.0008047944284044206,
-0.036876380443573,
-0.004433721769601107,
0.027632953599095345,
-0.... |
<p>My apologies for such a basic question--I am a musician, not a physicist. But I cannot anywhere find the word, if one exists, that describes that elegant pause of an object such as a ball, thrown straight up, as it reaches the apex of its trajectory's power and before it obeys the power of gravity commanding it to earth.</p> | g12143 | [
0.04285884276032448,
0.08596335351467133,
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0.05727585777640343,
-0.... |
<p>I am not sure if anyone has ever researched this but I am curious about underground reservoirs of natural gas and plate tectonics. Specifically, as the Earth's crust gets pulled down to the mantle do pockets of natural gas get ignited and explode? Or do these pockets of gas get pushed to the surface or further back along the crust as the pressure increases?</p>
<p>Given that we have such large underground reservoirs of natural gas that we have discovered I would think that some exist in or near subduction zones. I guess the same question could be asked of reservoirs of oil. But I would think that the natural gas deposits would be a bit more volatile.</p> | g12144 | [
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0.04185224696993828,
-0.030... |
<p>I know this conclusion in topological order for a while: "the topological degeneracy on torus is equal to the number of quasiparticles types."</p>
<p>But can anyone give a physical argument that supports this conclusion?
Especially in Non-Abelian case.</p> | g12145 | [
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0.03770854324102402,
0.005919956136494875,
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0.028234777972102165,
0.025550... |
<p>A solid right cylinder of rock core is surrounded by four rods made of mild steel (all-thread rods). The rods are placed equidistantly around the core in a square formation. The tops and bottoms of the four rods are fixed to the top and bottom rigid plates, but the rock is just fitted snugly between the top and bottom plates. The rock is wrapped in an impermeable jacket. The whole system is submerged into a pressure vessel holding water and the water pressure is increased. When the water in the pressure vessel is increased to a certain amount, the fluid in the pore space of the rock is increased (pore pressure) accordingly to give the rock pressure support resulting in an effective stress on the rock. After reaching final pressures the temperature of the pressure vessel and all its contents is then increased.</p>
<p>Determine the following quantities: (a) the resulting load $P_s$ in the rock cylinder and $P_r$ in the steel rods; (b) the corresponding axial stresses $\sigma_s$, $\sigma_r$; and (c) the axial deformation $\delta$ of the assembly and (d) the principle stresses on the core.</p>
<p><img src="http://i.stack.imgur.com/ELknN.jpg" alt="fixture"></p>
<p>Below is my initial attempt at this problem. I assumed that lateral strain is insignificant but I don't know if that is true. If it is not true then I suppose this problem would have to be solved with iterations? I am hoping someone can tell me if the methodology is correct or how to correctly solve this problem. I've included some values to solve with, but I would ultimately like to have the equations/methodology to solve for any values of the system. Thanks.</p>
<p>When trying to solve this problem I assumed the deformation of the rods are uniform throughout their volume, the rods are prismatic, the compressive load acts at the center of the rods, rods are homogeneous, isotropic, and behave linearly elastically. I made the same assumptions about the rock aswell.</p>
<p>The bottom rigid plate is a circle with a diameter $d_p=15$ in., each rod has a diameter $d_r=0.4$ in., and the core has diameter $d_s=7$ in. The rods have a Young's modulus $E_r=30,000$ ksi and the rock has a modulus of elasticity of $E_s=1,450$ ksi. The starting length of both the rods and the core is $L= 20$ in.</p>
<p>Before temperature is introduced to the system the entire fixture is subjected to the overburden water pressure $\sigma_{ob}=25,000$ psi and internal pore pressure $\sigma_{Pp}=20,000$ psi. Therefore the resulting load on the core and rods imposed by the plate is</p>
<p>$$P = \sigma_{ob} \cdot A_{plate} + \sigma_{Pp} \cdot A_s=\sigma_{ob} \cdot \left(A_{plate}^{bottom}-A_{plate}^{top}\right) + \sigma_{Pp} \cdot A_s $$</p>
<p>$$=\sigma_{ob} \cdot \left(A_s+4A_r\right) + \sigma_{Pp} \cdot A_s $$</p>
<p>$$ = (-25\, \text{ksi}) \left(\frac{\pi}{4} \cdot (7 \, \text{in.})^2 + \pi \cdot (0.4 \, \text{in.})^2 \right) + (20\, \text{ksi}) \left(\frac{\pi}{4} \cdot (7 \, \text{in.})^2 \right) \approx -205 \, \text{k}$$</p>
<p>The plate is subjected to the force $P$ and the the unkown compressive forces $P_s$ and $P_r$; thus the equation of equilibrium is:</p>
<p>$$\Sigma F_{vert} = 0$$ and $$4P_r + P_s - P = 0$$ </p>
<p>This equation, which is the only nontrivial equilibrium equation available, contains two unkowns. Therefore, we conclude that the structure is statically indeterminate.</p>
<p>Because the end plates are rigid, the rock cylinder and steel rods must shorten by the same amount. Denoting the shortenings of the rock and steel parts by $\delta_s$ and $\delta_r$, respectively, we obtain the following equation of compatibility:</p>
<p>$$\delta_s = \delta_r$$ </p>
<p>The changes in lengths of the cylinder and rods can be obtained from the general equation $\delta = PL/EA$. Therefore, in this problem the force-displacement relations are:</p>
<p>$$\delta_s = \frac{P_sL}{E_sA_s}$$ and $$\delta_r= \frac{P_rL}{E_rA_r}$$</p>
<p>We can now solve simultaneously the three stes of equations to obtain the axial forces in the rock cylinder and steel rods:</p>
<p>$$\frac{P_sL}{E_sA_s}=\frac{P_rL}{E_rA_r} \rightarrow P_r=P_s \frac{E_rA_r}{E_sA_s} \rightarrow 4P_s \frac{E_rA_r}{E_sA_s}+P_s-P=0$$</p>
<p>Solving for $P_s$ we have $$P_s=P \left(\frac{E_sA_s}{4E_rA_r+E_sA_s}\right)$$</p>
<p>Likewise, solving for $P_r$ we have $$P_r=P \left(\frac{E_rA_r}{4E_rA_r+E_sA_s}\right)$$</p>
<p>Substituting our values we can solve for the resulting loads:</p>
<p>$$P_r=(-205 \, \text{k}) \left(\frac{(30000 \, \text{ksi})(\frac{\pi}{4}(0.4 \, \text{in.})^2)}{4(30000 \, \text{ksi})(\frac{\pi}{4}(0.4 \, \text{in.})^2)+(1450 \, \text{ksi})(\frac{\pi}{4}(7 \, \text{in.})^2)}\right) \approx -11 \, \text{k}$$</p>
<p>Similarily, plugging values in for $P_s$ we get: $$P_s \approx -161 \, \text{k}$$</p>
<p>The change in length of the core and rods due to the pressure increase will be: $$\delta_r=\delta_s=\frac{PL}{4E_rA_r+E_sA_s}=\frac{(-205 \, \text{k})(20 \, \text{in.})}{4(30000 \, \text{ksi})(\frac{\pi}{4}(0.4 \, \text{in.})^2)+(1450 \, \text{ksi})(\frac{\pi}{4}(7 \, \text{in.})^2)} \approx -0.057 \, \text{in.}$$</p>
<p>At this point the temperature is increased to $400\,^{\circ}\mathrm{F}$. The thermal strain relation $\epsilon_T$ induced on a body is $$\epsilon_T = \alpha (\Delta T)$$ where $\alpha$ is the coefficient of thermal expansion and $\Delta T$ is the change in temperature. We assumed $\alpha_r = 6.5 \times 10^{-6} \,^{\circ}\mathrm{F}^{-1}$ and $\alpha_s = 3 \times 10^{-6} \,^{\circ}\mathrm{F}^{-1}$. </p>
<p>The equivalent stress induced due to thermal expansion is: $$\sigma_{eq} = E\alpha(\Delta T)$$</p>
<p>And the equivalent load can be calculated as: $$P_{T} = \sigma_{eq} \cdot A$$ </p>
<p>Substituting values we can solve for the equivalent loads due to temperature increase in the rods and rock: $$P_T^s = (1450 \, \text{ksi})(3 \times 10^{-6} \,^{\circ}\mathrm{F}^{-1})(400\,^{\circ}\mathrm{F})(\frac{\pi}{4}(7 \, \text{in.})^2) \approx 67 \, \text{k}$$</p>
<p>$$P_T^r = (30000 \, \text{ksi})(6.5 \times 10^{-6} \,^{\circ}\mathrm{F}^{-1})(400\,^{\circ}\mathrm{F})(\frac{\pi}{4}(0.4 \, \text{in.})^2) \approx 9.8 \, \text{k}$$</p>
<p>We then add these loads to the loads due to compression to get the final loads:</p>
<p>$$P_r + P_T^r = -11 \, \text{k} + 9.8 \, \text{k} \approx -1.1 \, \text{k (compression)}$$ $$P_s + P_T^s = -161 \, \text{k} + 67 \, \text{k} \approx -94.4 \, \text{k (compression)}$$</p>
<p>With these values we can calculate the axial stresses: $$\sigma_s = \frac{P_s}{A_s} = \frac{-94.4 \, \text{k}}{\frac{\pi}{4}(7 \, \text{in.})^2} \approx -2.45 \, \text{ksi}$$</p>
<p>$$\sigma_r = \frac{P_r}{A_r} = \frac{-1.1 \, \text{k}}{\frac{\pi}{4}(0.4 \, \text{in.})^2} \approx -8.76 \, \text{ksi}$$</p>
<p>We now solve for the resulting length change in the rods and core do to the temperature increase:</p>
<p>$$\delta_r=\delta_{r}^i+\alpha_r(\Delta T)L'= -0.057 \, \text{in.} + (6.5 \times 10^{-6} \,^{\circ}\mathrm{F}^{-1})(400\,^{\circ}\mathrm{F})(20 \, \text{in.} - 0.057 \, \text{in.}) \approx -0.006 \, \text{in.}$$</p>
<p>$$\delta_s=\delta_{s}^i+\alpha_s(\Delta T)L'= -0.057 \, \text{in.} + (3 \times 10^{-6} \,^{\circ}\mathrm{F}^{-1})(400\,^{\circ}\mathrm{F})(20 \, \text{in.} - 0.057 \, \text{in.}) \approx -0.034 \, \text{in.}$$</p>
<p>From this result we can conclude that the expansion in length of the rods due to the temperature increase causes a seperation between the bottom core face and the bottom fixture plate. This result may have came about due to incorrect assumptions on the values for the young's modulus and/or coefficient of thermal expansion. This separation will cause a fluid connection between overburden pressure and pore pressure which is not acceptable. If the resulting axial stress on the rock is to be a 1000 psi less than the resulting rock lateral stress, what would be the required material properties for the rock and rods?</p> | g12146 | [
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<p>This problem is about color science and it is short but tricky: Where do you get $I_p=\frac{P}{4 \pi r^2} sin \alpha$, where $I_p$ is radiant intensity(color science: radiometric quantities). Look at the link( exercise 2 a)): <a href="http://cs.joensuu.fi/~ot14/vo/IMG.jpg" rel="nofollow">http://cs.joensuu.fi/~ot14/vo/IMG.jpg</a>
I know that radiant intensity is $I=\frac{\Phi}{\Omega} = \frac{\Phi}{4\pi}$ if source radiates uniformly to all directions as they are according to problem.</p>
<p>The right solution is: $I=\frac{\Phi}{\Omega} = \frac{\Phi}{4\pi}$ as stated previously( radiant intensity), because source(s) radiate uniformly to all directions. Then you use that $E=\frac{I}{d^2} \cos \theta$. So for source 1( lefthand side),
$\Omega=P = 100 W$, $I=\frac{\Omega}{4 \pi}=\frac{100}{4 \pi}= 7,96 W/sr$, $d=\sqrt{1,5^2+1,5^2}= 2,12 m$, $\alpha = 45^{\circ}$, $\theta = 45^{\circ}$ and $E_p = \frac{I}{d^2}cos \theta = 1,25 W/m^2$ </p>
<p>And for source 2( righthand side),
$\Omega=P = 40 W$, $I=\frac{\Omega}{4 \pi}=\frac{40}{4 \pi}= 3,18 W/sr$, $d=\sqrt{2,5^2+1,5^2}= 2,92 m$, $\alpha = 30,96^{\circ}$, $\theta = 59,04^{\circ}$ and $E_p = \frac{I}{d^2}cos \theta = 0,19 W/m^2$</p>
<p>So answer to the problem 2 a) is: Irradiance at point a is $E_1 + E_2 = 1,25 + 0,19 = 1,44 W/m^2$.</p> | g12147 | [
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... |
<p>Is there any way to survive solarwinter like in Sunshine - movie?
Solar winter is where for some reason sun looses its capasity to produce radiation( heat etc.). It doesn't loose everything but some of its radiation energy( say 50 %) That causes earth to cool down causing next "ice age"</p> | g12148 | [
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<p>Having only really known two designs for paper airplanes since my days as a child, one which flies about eight feet and another which flies about ten feet, I have always wondered how people manage to come up with designs that are able to fly much, much further than that. Clearly, these have no propulsion after their initial burst of energy (from being thrown); after that it's all about gliding.</p>
<p>So what design considerations should I make in order to create a plane that has the maximum flight time and distance? What are general best practices in this endeavor, and what are the physical bases for these choices?</p>
<p>I'm not looking for specific designs necessarily, but what qualities makes up a good paper airplane that can fly for a very long distance?</p> | g12149 | [
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<p>Can there be a charge configuration in space such that at any instant of time I can change the electric field at one and only one point?</p> | g12150 | [
0.029338838532567024,
0.005316834896802902,
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0.002868319395929575,
0.08084297180175781,
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0.013856676407158375,
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... |
<p>I have been trying for hours and cannot figure it out. I am not asking anyone to do it for me, but to understand how to proceed. </p>
<p>We have the relations
$$[L_i,p_j] ~=~ i\hbar\; \epsilon_{ijk}p_k,$$
$$[L_i,r_j] ~=~ i\hbar\; \epsilon_{ijk}r_k,$$
$$[L_i,L_j] ~=~ i\hbar\; \epsilon_{ijk}L_k.$$</p>
<p>Now I am trying to calculate </p>
<p>$$[L_i,(p\times L)_j].$$ </p>
<p>I do not know how to reduce it. When I try I am left with too many dummy indices that I don't know what to do. For example, using </p>
<p>$$[AB,C] = A[B,C]+[A,C]B,$$ </p>
<p>and expanding the cross product in terms of Levi-Civita symbols </p>
<p>$$[L_i,\epsilon_{jmn}p_m L_n],$$</p>
<p>but I don't know how to proceed correctly from here. For example, I tried, </p>
<p>$$ =~ \epsilon_{jmn}(\;p_m[L_i,L_n]+[L_i,p_m]L_n ).$$ </p>
<p>Is this correct? If so, in the next step I used the known commutation relations</p>
<p>$$ =~i\hbar\; \epsilon_{jmn}(\; \epsilon_{ink}p_mL_k+\epsilon_{imk}p_kL_n).$$ </p>
<p>Once again, I am stuck and do not know how to evaluate this further. Could someone tell me what I am doing wrong, or if not, how to proceed? </p> | g12151 | [
-0.007119023706763983,
0.07567431777715683,
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0... |
<p>Browsing Quora, I saw the following <a href="http://www.quora.com/Particle-Physics/Is-a-hard-drive-heavier-by-an-incredibly-tiny-amount-when-its-full-What-about-flash-memory">question</a> with contradicting answers.</p>
<p>For the <a href="http://www.quora.com/Particle-Physics/Is-a-hard-drive-heavier-by-an-incredibly-tiny-amount-when-its-full-What-about-flash-memory/answer/Alon-Amit">highest voted answer</a>:</p>
<blockquote>
<p>The bits are represented by certain orientations of magnetic fields
which shouldn't have any effect on gravitational mass.</p>
</blockquote>
<p>But, <a href="http://www.quora.com/Particle-Physics/Is-a-hard-drive-heavier-by-an-incredibly-tiny-amount-when-its-full-What-about-flash-memory/answer/Brandon-Benton">another answer</a> contradicts that one:</p>
<blockquote>
<p>Most importantly, higher information content correlates with a more
energetic configuration and this is true regardless of the particular
type of storage... Now, as per Einstein's most famous formula, energy
is equivalent to mass.</p>
</blockquote>
<p>Which answer is correct?</p> | g442 | [
0.08943050354719162,
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<p>A light modifier that is commonly used in studio photography is a honeycomb grid. </p>
<p>It narrows the beam of light to a circle with soft edges, as it can be seen <a href="http://www.honeycombgrids.com/info/grid-diffusion-patterns" rel="nofollow">here</a>:</p>
<p>My question is: how is this happening? </p>
<p>A small reporter flash has a rectangular shape, if you place a rectangular shaped grid on it, it produces a "soft" circle of light. How is the light travel modified by the structure of the grid?</p> | g12152 | [
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0.02170591428875923,
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<p>Given a certain running pace uphill, I want to be able to determine an equivalent pace running with no elevation change. Assumptions: similar effort in both cases (say for example running at 90% max heart rate), ignore wind, slope is constant for simplicity, ignore physiological and bio-mechanical factors, weight of the runner is 135 lbs if that matters. </p>
<p>Example: Elevation change +236 feet, distance traveled 1 mile, elapsed time 6 minutes 55 seconds. What could I theoretically run for 1 mile with no elevation change given the same effort?</p> | g12153 | [
0.023983141407370567,
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... |
<p>I was discussing the reason why we see beating from a Michelson interferometer, and one of my friend said it 's because the light have different frequencies, therefore, they would be out of phase.</p>
<p>But my argument is, Because two frequencies travel at the same speed, their phase difference remain the same. But when you keep adjusting the movable mirror of Michelson interferometer, you can shift their phase difference more quickly, and that's why you get beating phenomena.</p>
<p>What is the actual source of beating?</p> | g12154 | [
0.07462624460458755,
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0.00002722238059504889,
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0.... |
<p>The statement of the time-reversal invariance of Maxwell's electromagnetism, as I understand it, is the following.</p>
<p>Given $\mathbf{E}(\mathbf{r},t)$ and $\mathbf{B}(\mathbf{r},t)$ that satisfy all Maxwell's equations (with $\mathbf{J}(\mathbf{r},t)$ and $\rho(\mathbf{r},t)$) and the boundary conditions, then the fields defined by
$$\mathbf{E'}(\mathbf{r},t) \equiv \mathbf{E}(\mathbf{r},-t), $$
$$\mathbf{B'}(\mathbf{r},t) \equiv \mathbf{B}(\mathbf{r},-t), $$
satisfy Maxwell's equations, with
$$\mathbf{J'}(\mathbf{r},t) \equiv \mathbf{J}(\mathbf{r},-t), $$
$$\rho'(\mathbf{r},t) \equiv \rho(\mathbf{r},-t). $$</p>
<p>(It would be nice for me to find out that I understand time-reversal incorrectly.)</p>
<p>Just two of Maxwell's equations (div equations) were fine with me. For example, a problem arises with the following equation:
$$\nabla\times\mathbf{E}(\mathbf{r},t)=-\frac{\partial \mathbf{B}(\mathbf{r},t)}{\partial t},$$
when replacing $t\rightarrow-t$:
$$\nabla\times\mathbf{E}(\mathbf{r},-t)=+\frac{\partial \mathbf{B
}(\mathbf{r},-t)}{\partial t},$$
using our definitions:
$$\nabla\times\mathbf{E'}(\mathbf{r},t)=+\frac{\partial \mathbf{B'}(\mathbf{r},t)}{\partial t}.$$</p> | g12155 | [
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0.054211851209402084,
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0.043573394417762756,
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-0.0... |
<p>Consider the well known demonstration of diffraction by a narrowing slit.
(See for example the demonstration at the 30 minute mark of <a href="http://ocw.mit.edu/high-school/physics/physical-optics/interference-diffraction/" rel="nofollow">this lecture</a> at MIT by Walter Lewin)</p>
<p>It is my (possibly mistaken) understanding that the light emerging after the slit becomes substantially slimmer than one wavelength is polarized.<br>
This would seem to imply that light of perpendicular polarization would not be transmitted, thus implying a fairly substantial and dramatic difference in the results of the experiment with parallel and perpendicularly polarized light. That is, instead of spreading out, the light polarized in the wrong direction would essentially just shut down as the slit narrows below one wavelength. Is this true? </p> | g12156 | [
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0.01805087924003601,
0.024439500644803047,
0.011... |
<p>A while ago, <a href="http://arxiv.org/abs/0802.2041v1" rel="nofollow">there was some conspicuous evidence that supermassive black holes didn't seem to be eating dark matter at the expected rate of 70%-30%, in fact, only 10% of the black hole mass increase could in principle be attributed to non-baryonic mass</a>.</p>
<p>Was there some follow-up evidence for or against this observation? because it is 2012 and every astrophysicist that is out there seems to be happy and dandy about dark matter, despite this huge clue (together with MOND, and the negative results from CoGENT) that dark matter doesn't actually exist</p> | g12157 | [
0.05267782509326935,
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0.015730753540992737,
-0.0120... |
<p>I have been told (not sure if it is true), that mirror (and glass) do not allow to pass the electromagnetic signals of mobile signals. </p>
<p>but for a standard mirror what type of wave can pass through it? </p>
<p>thanks</p> | g12158 | [
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0.049075618386268616,
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-0.00... |
<p>I'm trying to make a program that simulates shadows in a 2D environment and I need some help in determining how things should look.</p>
<p>For example, if my light source is red and the illuminated object is blue (only radiates light in the blue frequency), how should it look when I shine red light on it?</p>
<p>How about the other way around? Since blue light has higher frequency/energy than red light, will the result be different if the light is blue and the object is red?</p>
<p>If these things depend on a lot of factors (like the properties of the material), I would rather not go into that, the simulation does not need to be that realistic. I would just want an approximate idea of what should happen.</p> | g12159 | [
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0.... |
<p>I am curious what the electric and magnetic field's of light look like when time is stopped. A "photograph" or illustration/description of these fields at a moment in time is what I desire. </p>
<p>Also, does the picture change at various points in the wave?</p>
<p>I assume that <a href="http://physics.stackexchange.com/questions/4071/popular-depictions-of-electromagnetic-wave-is-there-an-error">this</a> is like a "time exposure" of a light wave.</p> | g12160 | [
-0.009073580615222454,
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0.023437323048710823,
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0.05... |
<p>I heard on a podcast recently that the <a href="http://en.wikipedia.org/wiki/Supermassive_black_hole" rel="nofollow">supermassive black holes</a> at the centre of some galaxies could have densities less than water, so in theory, they could float on the substance they were gobbling up... can someone explain how something with such mass could float?</p>
<p>Please see the below link for the podcast in question:</p>
<p><a href="http://www.universetoday.com/83204/podcast-supermassive-black-holes/" rel="nofollow">http://www.universetoday.com/83204/podcast-supermassive-black-holes/</a></p> | g12161 | [
0.028393693268299103,
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0.0829642042517662,
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0.06793928146362305,
... |
<p>Does gravity effect the "sphericalness" of the Coulomb force?</p>
<p>For example, is the field 1 meter above a charge weaker than the field 1 meter below the charge?</p>
<p>Could a 0.014% difference in the field be detected?</p>
<p>Have there been any such experiments run?</p>
<p><strong>Edit:</strong></p>
<p>In answer to firtree's question below, I am working on the admittedly heretical idea that the "curvature of space" is actually the flow of space into a massive body and as such space is flowing into Earth at 11km/s at its surface (its escape velocity).</p>
<p>At the moment, I'm trying to develop a model for length contraction. Using the notions of perturbation theory and $r=ct$ one could perhaps reformulate Coulomb's Law:
$$F(r)=\frac{q_1q_2}{\epsilon_0}\frac{1}{4\pi r^2}$$
as:
$$F(t)=\frac{q_1q_2}{\epsilon_0}\frac{1}{4\pi c^2t^2}$$
Time moving against the flow:
$$t_u=\frac{d}{c-v}$$
and with the flow:
$$t_d=\frac{d}{c+v}$$
The 0.014% comes from comparing the force for the two times plugging in $d=1$ and $v\approx11,000$ m/s</p>
<p>However, as the calculation of length contraction illustrates, the actual effect is dependent on the two way speed of light. And aside from that, if things actually worked this way it would seem to violate Newton's 3rd law. But, I just wanted to get a sanity check and see if there were any experimental (or theoretical) results related to this.</p> | g12162 | [
0.040028881281614304,
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0.0030951849184930325,
0.017279546707868576,
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0.02551392652094364,
0.0316869... |
<p>In the electron double slit experiment, why is it not, in principle, possible to know which slit the electron went through by the electron's effect on the surrounding EM field? As the electron travels, it would disturb the field, and presumably this disturbance measured at a point far from the experiment would be slightly different depending on whether it went through one slit or the other. So couldn't you (in principle) measure the disturbance in the field at a far enough distance such that the electron hits the detector before the disturbance is measured?'</p> | g12163 | [
-0.0058653103187680244,
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0.0032495474442839622,
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0.04904298111796379,
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0.023194361478090286,
0.06634114682674408,
0.041292302310466766,
-0.... |
<p>I'm very new to the topic of surface plasmons and I have been reading about different methods of exciting them. There is one method in which a prism is set up to allow phase matching of an incident light ray to the required wave vector for exciting a surface plasmon. The light goes through total internal reflection in the prism and then either tunnels through the metal (on which we want to excite the surface plasmon), or a lower indexed dielectric to excite the surface plasmon.</p>
<p>This might be a lack of understanding of attenuated total internal reflection, but apparently this field harbors no energy and 100% of the incident light is reflected. My question is how is energy conserved (how can it excite surface plasmons)? Is it because the energy of the attenuated field only time averages to 0? But then how can all the light be reflected?</p> | g12164 | [
0.052213456481695175,
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0.03741685673594475,
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-0.0... |
<p>This question has been bugging me for a while now. I am not sure this is the correct forum to ask, please close if it is not the right forum.</p>
<p>Lets say a bus is traveling at $60\: \mathrm{km/h}$ and there is a mosquito flying inside the bus. Since the mosquito's speed is considerably less than that of the bus why it wouldn't end up hitting the back side of the bus?</p> | g12165 | [
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0.04980862885713577,
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0.0139316... |
<p>I've got to teach the concepts of "Electric Potential" & "Potential Energy" to 10th grade students. I don't understand how to express these things and make them understand.</p>
<blockquote>
<p>“If you can't explain it simply, you don't understand it well enough” ~ Albert Einstein</p>
</blockquote>
<p>Probably I didn't understand well enough.</p> | g12166 | [
0.01036098413169384,
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0.008484715595841408,
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0.05080008506774902,
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0.0132113853469491,
0.01600428856909275,
0.03636958822607994,
-0.002630762755870819,
0.03016287... |
<p>If the space of universe is expanding at fast rates..(even faster than light)</p>
<p>Why we do not see the trace of the stars?</p>
<p>A possible answer could be that the stars are only moving away but mantaining in geodesic respect earth and each other, that is strange, in a 2D model of an inflating balloon with dots as analogy, one can suspect that, but I can't imagine how that structure should be in 3D.</p>
<p>Any other explanation or possible idea or analogy to explain why we don't see those traces are welcome (or perhaps the information that they are already seen)</p>
<p>Thanks</p> | g12167 | [
0.030337097123265266,
0.0576128326356411,
0.007077554240822792,
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0.019627636298537254,
0.08440711349248886,
0.02126... |
<p>What are the real dates that are represented in the figure 10, page 17, in the <a href="http://static.arxiv.org/pdf/1109.4897.pdf" rel="nofollow">OpERA paper</a> </p>
<p>Imo the X axis labels are inconclusive, or absent. </p>
<p>(in the investigation of a crime it is relevant the place and the time of the event). </p> | g12168 | [
0.05277129262685776,
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0.024823203682899475,
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0.04031698405742645,
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<p>On damnlol.com, I came across this picture:</p>
<p><img src="http://i.stack.imgur.com/Bwxxl.jpg" alt="enter image description here"></p>
<p><a href="http://www.damnlol.com/hello-god-i-have-a-fault-to-report-7549.html" rel="nofollow">http://www.damnlol.com/hello-god-i-have-a-fault-to-report-7549.html</a></p>
<p>My question is: Is this possible without glue? If not are there similar situations in which something like this is possible ?</p> | g12169 | [
0.02794879674911499,
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0.009085196070373058,
0... |
<p>I know the basics, that by measuring how much x-ray signal reaches each 'pixel' on the receiver we can measure how much has been absorbed. But this gives only a single channel of information, e.g a greyscale image.
However I'm sure I've seen images where there are opaque white parts (bones) and opaque black parts (metal)... this seems to imply color and opaqueness are two separate channels and I cannot see how that works.</p>
<p>Can anyone go beyond the basics to describe the <em>real</em> way a fluoro scan ends up as a picture I can look at? Better references than wikipedia would also be welcome.</p> | g12170 | [
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0.05113895609974861,
0.01358888577669859,
0.07510454952716827,
-0.014... |
<ol>
<li><p>What are <a href="http://en.wikipedia.org/wiki/Lagrangian_point" rel="nofollow">Lagrange points</a> in gravitation fields? </p></li>
<li><p>Additionally, what are their properties? For example, if a satellite or asteroid rested at a Lagrange-point.</p></li>
</ol> | g12171 | [
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0.017477547749876976,
-0.02963261865079403,
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0.0617312416434288,
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-0.03182770311832428,
-0.0017880150116980076,
0.046212173998355865,
0.05045757815241814,
-0.025... |
<blockquote>
<p>There are m*n identical cells of emf E and internal resistance r connected in parallel rows. This combination of cells is connected across an external resistance R. For what arrangement of the cells will the current through R be maximum?</p>
</blockquote>
<p>I don't understand when the current will be maximum, ie, there when the number of resistors in each row is same or if the number of resistors in each row is different or if there is any other specific arrangement.
. </p> | g12172 | [
0.02255943976342678,
0.014822743833065033,
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0.019820747897028923,
0.0959397703409195,
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0.043275441974401474,
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0.01651134341955185,
-0.04389425739645958,
0.018791886046528816,
-0.04869263246655464,
-0.0009... |
<p>In an alternating current, how are frequency, voltage, amperage, and watts related?</p>
<p>For instance, imagining the power as a sine wave, what is amperage if voltage is the amplitude? Is there a better analogy than a sine wave?</p>
<p>EDIT: One of the things I specifically wanted to know is whether frequency and voltage are related? A 60 Hz power signal seems to only be transmitted at 120 or 240 volts - does it have to be a multiple?</p> | g12173 | [
0.03198350965976715,
0.006611572112888098,
-0.017558608204126358,
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0.010371233336627483,
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0.02151920460164547,
0.009211370721459389,
... |
<p>Lets deal with wave propagation in a cylindrical duct. </p>
<p>We ask the question: "what is the general form of a pressure wave which can propagate through the duct?" In answering this, we assume that the pressure wave in question has harmonic time dependence, i.e. $\exp(i\omega t)$ dependence.</p>
<p>The critical thing about solutions of the wave equation is that they must obey the boundary conditions of the duct. Without going into detail, for an infinite length duct of radius $a$ the solution is:</p>
<p>$p(r,\theta,x,t) = \exp(i(\omega t-n\theta) J_n(z_{mn}r/a) \left( A_{mn}\exp(-ik_{mn}x) + B_{mn}\exp(ik_{mn}x) \right)$ </p>
<p>Where $J$ is the bessel function with corresponding zeros $z_{mn}$. Mathematically the significance of $m,n$ is simply that we can assign any positive integer value to these as a feasible solution. <strong>This determines the mode mathematically.</strong> As an aside it should be pointed out that for a particular value of $\omega = \omega_c$ only certain modes with low enough $\max(m.n)$ can actually propagate- any "higher order" modes will decay rapidly along $x$. $\omega_c$ is therefore known as the cut-off frequency.</p>
<p>My question now is <strong>how are modes created in the first place by an acoustic source?</strong> Does the source select a particular mode or are many present at the same time? Please explain.</p>
<p>To start with an answer I thought of a vibrating disc or membrane in the duct which vibrates with velocity $v = \hat{V}\exp(i\omega t)$ in the $x$ (axial) direction. Assuming linearity, the pressure wave form should have same harmonic time dependence. Now it is important for the sake of this argument that $v$ is exactly sinusoidal, i.e. I am not assuming there would be any higher order coefficients in the Fourier decomposition of $v$. So what mode or modes would <strong>initially</strong> (even if they are cut-off) be set up by this scenario? </p> | g12174 | [
0.019089341163635254,
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0.06422913074493408,
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0.010291674174368382,
... |
<blockquote>
<p>Water, dripping at a constant rate from a faucet, falls to the ground. At any instant there are
many drops in the air between the faucet and the ground. Where does the center of mass of
the drops lie relative to the halfway point between the faucet and the ground? (a) Above it
(b) Below it (c) Exactly at the halfway point</p>
</blockquote>
<p>When I looked at this, I thought the answer is (b) below it since if the water drop and the ground are in a system, then the center of mass will be nearer to the heavier object, which is the ground. But when I looked up the answer it was (a) above it. Could you please explain why? Thank you!</p> | g12175 | [
0.052188940346241,
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0.011882935650646687,
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0.003527263645082712,
0.0755373015999794,
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-0.02254463918507099,
-0.03430840000510216,
0.03618582710623741,
-0.00750525901094079,
0.0507761463... |
<p>Can anyone explain how photogenerated current in the base gets amplified in a <a href="http://www.google.com/search?as_q=phototransistor" rel="nofollow">phototransistor</a>.
If you use band energy diagram, then I would understand more quickly and clearly.</p>
<p><img src="http://i.stack.imgur.com/Bljdo.png" alt="enter image description here"></p> | g12176 | [
0.02246660552918911,
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0.04044872149825096,
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0.03301885724067688,
-0.011143451556563377,
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0.057993147522211075,
0.01062899362295866,
-0.... |
<p>If a wave packet is given by: </p>
<p><img src="http://i.stack.imgur.com/AItyP.jpg" alt="enter image description here"></p>
<p>My question is basically how do we choose the write $A(k)$ to fit the particle we are looking at, or does it not matter (as my matter as my textbook seems to imply) which seems counterintuitive? </p> | g12177 | [
0.046855613589286804,
0.023683641105890274,
0.003906880505383015,
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0.07714812457561493,
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-0.026019984856247902,
0.046711623668670654,
0.028735745698213577,
0.06399355083703995,
0.04... |
<p>How exactly is the <a href="http://en.wikipedia.org/wiki/Weyl_tensor" rel="nofollow">Weyl tensor</a> is connected with information about <a href="http://en.wikipedia.org/wiki/Gravitational_wave" rel="nofollow">gravitational waves</a>? And what are physical reasons for that?</p> | g12178 | [
0.01247072871774435,
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0.09401717036962509,
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-0.05896647274494171,
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0.08308246731758118,
0.013807... |
<p>I am trying to follow a book (Introduction to Ligand Field Theory by Ballhausen in 1962 on pg 15), but it isn't clear how they make a particular leap.</p>
<p><strong>Background</strong>
I want to find the wave function for the term $^1 D$. We know that $\psi(L,M_L,S,M_S) = \psi (2,2,0,0)$ is made up of three micro states: $(2^+,0^-)$, $(2^-,0^+)$, $(1^+,1^-)$. Thus, a linear combination must be taken of these micro states. Now in the book they say they must be orthogonal to $\psi(3,2,1,0)$ and $\psi(4,2,0,0)$. Presumably these are picked because we just determined those via lowering operators in the previous section. I don't take it that there is another reason those two wave functions are mentioned.</p>
<p>$(2^+,0^−)$ means that electron 1 has $m_s=+1/2$ and $m_l=2$ and that electron 2 has $m_s=−1/2$ and $m_l=0$. We write that $\Psi=|(\psi^+_1)(\psi^−_2)|$ where we have written the short form of the determinantal antisymmetrized normalized wave function, which comes from the diagonal element in the Slater determinant AND separated the orbital- and spin-dependent parts of the wave function (spin is denoted by super plus or minus sign).</p>
<p><strong>Problem</strong>
Anyway, I understand that $\psi(2,2,0,0) = a (2^+,0^-) + b (2^-,0^+) + c(1^+,1^-)$.
Then they write "and we get $a \sqrt{3} - b \sqrt{3} + c \sqrt{8} = 0$ and $a + b = 0$." I'm totally lost how they made this leap and why these must be equal to zero. Does this have to do with the orthogonal wave functions just mentioned? Where did the numbers in the sqrt come from? And the minus sign! Greatly appreciated.</p> | g12179 | [
0.016195934265851974,
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0.015982061624526978,
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-0.05395185947418213,
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0.05583121255040169,
-0.06... |
<p>This question was prompted by <a href="http://physics.stackexchange.com/questions/79054/can-matter-really-fall-through-an-event-horizon">Can matter really fall through an event horizon?</a>. Notoriously, if you calculate the Schwarzschild coordinate time for anything, matter or light, to reach the event horizon the result is infinite. This implies that the universe ages by an infinite time before someone falling into the black hole reaches the event horizon, so could that person see the universe age by an infinite time?</p>
<p>To be more precise, suppose the observer starts falling from rest at time $t = 0$ and some initial distance $r > r_s$. If we wait for some time $T$ then shine a light ray at the falling observer. Will the light ray always reach the falling observer before they cross the event horizon? If not, what is the formula for the longest time $T$ that we can wait and still be sure the ray will catch the observer? If $T$ is not bounded it implies that observer could indeed see the end of the universe.</p>
<p>I can think of a qualitative argument for an upper limit on $T$, but I'm not sure how sound my argument is. The proper time for the observer to fall to the event horizon is finite - call this $\tau$. The proper time for the light ray to release the horizon is zero, therefore the light ray will reach the observer before they cross the event horizon only if $T < \tau$. Hence $T$ is bounded and the observer won't see the end of the universe.</p>
<p>I think a more rigorous approach would be to determine the equations of motion (in the Schwarzschild coordinates) for the falling observer and the light ray, and then find the condition for the light to reach the falling observer at some distance $\epsilon$ from the event horizon. Then take the limit as $\epsilon \rightarrow 0$. In principle this seems straightforward, but in practice the algebra rapidly defeated me. Even for a light ray the radial distance:time equation isn't closed form (Wolfram claims it needs the $W$ function) and for the falling observer the calculation is even harder.</p> | g12180 | [
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0.009808647446334362,
0.02346074767410755,
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0.007969154976308346,
0... |
<p>This is a question I've had a while about quantum theory.</p>
<p>Many times when I look at books and equations about this subject matter I see that the use many concepts in probability. (Correct me if Im wrong) Like how the movement of atom can be modeled using probability distributions. So I was wondering when physics takes this approach to this subject matter is it saying that the movement of an atom is actually random or that the details of explaining may be to cumbersome and be approximated with great accuracy just by using these distributions? </p> | g12181 | [
0.01671941764652729,
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0.014119913801550865,
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0.040273964405059814,
0.0057... |
<p>I would like to do a calculation of an expanding balloon represented by a triangular spring-damper mesh system. Also the behavior of the balloon when it is put in a container, where its shape conform to the shape of the container while expanding. Can anybody point me to any studies being done?</p> | g12182 | [
0.059681087732315063,
0.01880544237792492,
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0.0024094581604003906,
0.018813561648130417,
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0.0029542658012360334,
0.009900916367769241,
0.0655367448925972,
-0.00... |
<p>The common perception regarding what happens when two objects of equal sizes but unequal mass are allowed to fall freely towards the ground is that - both the objects make contact with the ground at the same instant.</p>
<p>This is attributed to the fact that the acceleration of both the objects towards the earth are the same for a given height.
This was the reason for <a href="http://en.wikipedia.org/wiki/Galileo%27s_Leaning_Tower_of_Pisa_experiment" rel="nofollow">Galileo's expirement</a>.</p>
<p>But the above fact ignores the fact that each of the three objects are attracting each other. In particular, the heavier object also attracts the lighter object, thus decreasing the distance between the lighter object and earth. </p>
<p>Note : I am ignoring the fact that the lighter object would also attract the heavier object (but to a lesser extent) and since the earth moves approximately in the same direction as a result of the attraction from the other two spheres, that is also ignored. Otherwise the earth can be said to move diagonally towards the heavier object (again to a small extent).</p>
<hr>
<p>I have included an illustration showing the movement of the lighter object towards the heavier one.
<img src="http://i.stack.imgur.com/SuIwb.png" alt="Gravity Free Fall - Scenario 1"></p>
<hr>
<p><strong>As such the lighter object should fall first is it not?</strong></p>
<p>Note : Generally, the two objects are placed close to each other (the distance-d between the objects is lesser than the height-h from the ground - 'd < h' ).</p>
<p>Continuing with the same logic, I have the following understanding :</p>
<p>When two spheres of equal size but unequal masses are allowed to fall freely towards the ground -</p>
<p>1.) From a height greater than the distance between the two spheres, the lighter sphere makes contact with the ground first.</p>
<p>2.) From same height as the distance between the two spheres, both the spheres make contact with the ground at the same time.</p>
<p>3.) From a height lesser than the distance between the two spheres, the heavier sphere makes contact with the ground first.</p>
<p>Note : </p>
<p>a.) The ground is also a sphere.</p>
<p>b.) The distance between the spheres are measured from their centers.</p>
<p><strong>Is my understanding correct?</strong></p>
<p>I also found <a href="http://physics.stackexchange.com/q/3534/">this</a> Phys.SE post. Which speaks of a scenario where in only two objects are involved. My question is similar to it.</p>
<p>PS: I have blogged about it before as well, saying it is so and also elaborated on two other cases ($d=h$ and $d>h$).</p> | g12183 | [
0.06799205392599106,
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0.038870587944984436,
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0.0553605817258358,
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-0.02942347712814808,
0.0036507192999124527,
-0.0294808316975832,
0.02694706991314888,
0.021687... |
<p><a href="http://en.wikipedia.org/wiki/Quantum_electrodynamics" rel="nofollow">Quantum electrodynamics</a> (QED) is the relativistic quantum field theory of electrodynamics that is the first theory where full agreement between quantum mechanics, special relativity and electrodynamics is achieved.</p>
<ul>
<li>What is the 'quantum-developed' equation of the classical <a href="http://en.wikipedia.org/wiki/Coulomb%27s_law" rel="nofollow">electrostatic force</a>?</li>
</ul>
<p>$$F=\frac {q^2}{4\pi \epsilon_o r^2}$$</p>
<ul>
<li>What is, it's 'relativistic-developed' equation?</li>
</ul> | g12184 | [
0.03400467336177826,
-0.008588028140366077,
-0.04028593748807907,
-0.007096956484019756,
0.11736814677715302,
0.04703585058450699,
0.0409717820584774,
0.010980193503201008,
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0.03465034440159798,
-0.01... |
<p>In the following lecture, starting at minute 29:00 and going further, the professor resolves the Twin Paradox using Lorentz velocity addition. I have a question about this:</p>
<p>Isn't the figure given below (taken from a slide in the lecture, at time 37:50) referring to the case where there is an independent object moving relative to the inertial frames S and S'? In the example of the twins that he discusses, there is no object independent of the frames of reference. We simply have the twins, each attached to her respective reference frame. Why, then, does he use the formula for Lorentz velocity addition? What object is he referring to?</p>
<p>Link for the lecture: <a href="http://www.youtube.com/watch?v=4A5EQaXhCTw" rel="nofollow">http://www.youtube.com/watch?v=4A5EQaXhCTw</a></p>
<p><img src="http://i.stack.imgur.com/qxbMm.jpg" alt="enter image description here"></p> | g12185 | [
0.039760589599609375,
0.049930389970541,
0.0075168912298977375,
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-0.02805699035525322,
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0.027902234345674515,
0.03991810232400894,
0.001... |
<p>What exactly is a lepton number of a particle? With the charge (eg proton is just 1, not the exact charge), I can understand because it's a physical property, put a particle with charge + next to another particle with charge + and they will repel.
What is the lepton number in similar terms? Or is it just a convention that worked in the observable particle interactions (that it is conserved, like charge)</p> | g12186 | [
0.04203573986887932,
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0.08991312980651855,
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0.028022846207022667,
0.029626093804836273,
0.0... |
<p>The rate of change of magnetic flux through a surface (open) is related with the line integral over the closed loop binding the selected surface by one of the Maxwell's equation. But that means even if a changing magnetic flux is present anywhere on the surface such that the electric and magnetic field at the chosen surface's loop is zero. For example, for a perfect toroidal solenoid, all the magnetic field and hence flux is confined within the windings. Therefore, for a wire making a loop surrounding the toroid and passing through the centre, the fields (electric and magnetic) at the wire is zero yet the changing flux produces an emf and a current in the loop-wire! </p>
<p>Is this not spookier than the conventional "action at a distance". <strong>So what induces the EMF in this wire?</strong></p> | g12187 | [
0.03882195055484772,
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0.033208008855581284,
0.05314576253294945,
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0.03031616285443306,
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-0.00760276522487402,
-0.07087334990501404,
0.007740041706711054,
0.014860441908240318,
0.014140... |
<p>I have some questions about renormalization. To my understanding, in order to deal with infinities that appear in loop integrals, one introduces some kind of regulator (eg, high momentum cutoff, taking $d\to d+\epsilon$, etc.) so that we get a finite answer, which blows up as we remove the regulator. Then we renormalize various coefficients in the Lagrangian in a regulator-dependent way so that, in scattering amplitudes, a finite piece remains as we remove the cutoff. The regulator seems to always require introducing some arbitrary scale (eg, the momentum cutoff or $\mu^\epsilon$ for dim-reg), although I'm not sure why this must be the case.</p>
<p>Now, this finite piece is completely arbitrary, and depends on what scheme we want to use (eg, on-shell, minimal subtraction, etc). The beta function is then, roughly speaking, the rate of change of this finite piece under changes in the scale in the regulator. My question is, what exactly is the invariant information in the beta function? Under changing renormalization scheme, it obviously changes, but it seems that this roughly corresponds to a diffeomorphism on the space of couplings (is this always true? for example, in on-shell renormalization, if we set the mass to the physical mass and the coupling to the corresponding exact vertex function at zero momentum, these seem to be independent of scale - do the beta functions vanish here?). Also, it seems to depend on exactly what regulator we are using, and how the dimensionful scale enters into it. There are certain quantities, such as the anomalous dimension of a field at a fixed point, which must be independent of all these choices, but I don't understand why this is the case.</p>
<p>Finally, and this is more of a philosophical question, what exactly do the infinities in the loop integrals mean in the first place? Why is it that we can remove them by any of these various regulators and expect to get the same answer? I've read something about Haag's theorem, that interacting theories live in a different Hilbert space than the free-field Fock space, and that this is somehow related, but I'm not sure why. Thank you.</p> | g12188 | [
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0.017015736550092697,
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0.0003678705252241343,
0.051125284284353256,
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0.009536005556583405,
-0.12799666821956635,
0.01661319099366665,
-0.018218979239463806,
... |
<p>In many countries, solar panels are heavily subsidized because they replace fossil fuels that apparently cause global warming. A mirror of the same size would - through a completely different effect - also reduce some global warming by reducing the solar energy reaching the earth. Considering that mirrors are much cheaper than solar panels, wouldn't they be more cost-effective in mitigating global warming?</p> | g12189 | [
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0.03440766781568527,
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0.051185984164476395,
0.028... |
<p>Are there any interesting, important or (for the non physicist) astonishing examples where the recoil principle (as special case of conservation of linear momentum) is applied beside rockets and guns?</p>
<p>I am teaching physics in high school and was just wondering if there are any more interesting examples than the two textbook standard examples above. </p>
<p>I am not interested in examples which are not in the domain of macroscopic, classical physics like Mößbauer-effect or something like that.</p> | g12190 | [
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0.02358887903392315,
-0.00129412... |
<p>Every morning, when I ride my bicycle, there is a very loud squeak coming from the brakes. I have an aluminum rim (I think that they are of the sprint type) and rubber pad brakes. A couple of brake events afterward end that and after that the breaks are silent. I suspect it has something to do with the morning plumpness but yet:</p>
<ol>
<li>Why would a damp rim give a noise under friction?</li>
<li>Why is it so loud? There is no amplification mechanism I can think of in the braking system.</li>
</ol>
<p>Some photos:</p>
<p>A <a href="http://en.wikipedia.org/wiki/File%3aBicycle_rim_diagrams_04_.png" rel="nofollow">sketch</a> of what I believe is my rim is.<br>
A <a href="http://upload.wikimedia.org/wikipedia/commons/7/78/Roller_Cam_Bicycle_Brake_Front_crop.JPG" rel="nofollow">braking mechanism</a>, Not mine but quite similar. The rim also looks similar.<br>
A closeup on a <a href="https://store.nexternal.com/reparto/images/c-br-pad.jpg" rel="nofollow">brake pad</a></p>
<p><em>Photos 1 and 2 are taken from wikipedia, photo 3 is taken from a reparto corse</em></p> | g12191 | [
0.06965797394514084,
0.024780087172985077,
0.004405677318572998,
0.039776090532541275,
0.05672600865364075,
0.030761871486902237,
0.031647805124521255,
0.025186866521835327,
0.02066645398736,
-0.016057239845395088,
0.004253490827977657,
-0.04864494502544403,
0.04331589862704277,
0.04353755... |
<p>I have a little trouble with the <a href="http://en.wikipedia.org/wiki/Stimulated_emission" rel="nofollow">simulated emission</a>. I know of the <a href="http://en.wikipedia.org/wiki/No-cloning_theorem" rel="nofollow">no-cloning theorem</a> which states that it is not possible to duplicate any state.</p>
<p>One the other hand, I know about the stimulated emission which out of a photon produce exactly the same (wavelength, polarisation, etc...). Maybe the fact is that the excited atom do a measure. (Let's say it can stimulate emission with only one direction of polarisation.)</p>
<p>But now if I have a statiscal number of atoms with random "polarisation" direction, I should be able to copy any incident photon. I've made a cloning machine.</p>
<p>This cannot be true because of the no-cloning theorem. But I can't figure why.</p> | g12192 | [
-0.051547273993492126,
0.018326861783862114,
-0.0033020314294844866,
-0.027876082807779312,
0.0024333572946488857,
0.005083519499748945,
0.009627307765185833,
0.032361481338739395,
0.04286057874560356,
-0.03954030200839043,
-0.004994486458599567,
0.05171370878815651,
0.01142542902380228,
-... |
<p>Parametric resonance is a situation where the driving frequency is a multiple of the eigenfrequency. Various people say that using a swing and propelling it oneself is such a case, with the driving frequency being the double of the eigenfrequency. But when I use a swing, as I did today, my own motion has the same frequency as that of the swing, not twice the frequency.</p>
<p>An example description is <a href="http://www.hk-phy.org/articles/swing/swing_e.html" rel="nofollow">http://www.hk-phy.org/articles/swing/swing_e.html</a> which claims that self-propelled swinging is normal resonance.</p>
<p>The opposite is said here: <a href="http://en.wikipedia.org/wiki/Parametric_oscillator" rel="nofollow">Wikipedia entry</a></p>
<p>What is the correct view: is self-propelled swinging normal resonance or is it parametric resonance?</p> | g12193 | [
0.016055099666118622,
0.07961774617433548,
-0.017269274219870567,
0.004863480571657419,
0.016464781016111374,
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0.04645299166440964,
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0.005037777591496706,
-0.005064490716904402,
-0.05179421603679657,
-0.01801237277686596,
0.01... |
<p>What is the simplest derivation of the following two well-known formulas that work for crystal lattice [1]:
$$
F[f(\mathbf{x})] \equiv \tilde f(\mathbf{G})
= {1\over\Omega_\mathrm{cell}} \int_{\Omega_\mathrm{cell}} f(\mathbf{x})
e^{-i\mathbf{G} \cdot \mathbf{x}}\,d^3 x
$$
$$
F^{-1}[\tilde f(\mathbf{G})] = f(\mathbf{x}) = \sum_{\mathbf{G}}
\tilde f(\mathbf{G}) e^{+i\mathbf{G} \cdot \mathbf{x}}
$$
See the question <a href="http://physics.stackexchange.com/q/88017/6396">How to derive inverse Fourier transform for periodic functions (in crystal lattice)?</a> for context. The difference from that question is that here we allow any derivation.</p>
<p>[1] Martin, R. M. (2004). Electronic Structure -- Basic Theory and Practical Methods (p. 642). Cambridge University Press.</p> | g12194 | [
-0.019644727930426598,
0.018337925896048546,
-0.006648785900324583,
-0.021298155188560486,
0.019216399639844894,
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0.029683399945497513,
0.008778689429163933,
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-0.00006311442120932043,
-0.055052224546670914,
0.08393439650535583,
0.028786439448595047,... |
<p>Any metal conductor such as aluminium or copper is a conductor because of the free electrons in such metals. </p>
<p>Plasma also has free electrons so I would like to know if you can repel plasma the same way as aluminium is repelled when near an AC electro magnet?</p>
<p>If so how come when I spin a magnet near my plasma globe there is no noticeable reaction compared to an aluminium can?</p> | g12195 | [
0.05514960363507271,
0.012832703068852425,
0.0022841328755021095,
-0.05928740277886391,
0.04868124797940254,
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0.01965203508734703,
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0.06150953844189644,
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-0.0... |
<p>What is a good, single, "periodic table" of all the particles of the <a href="http://en.wikipedia.org/wiki/Standard_Model" rel="nofollow">Standard Model</a>?</p>
<p>I thought <a href="http://pdg.lbl.gov/" rel="nofollow">Particle Data Group</a> would have a single-page PDF of this, but I couldn't find a single table listing all the particles.</p> | g12196 | [
0.004303081426769495,
0.021974612027406693,
-0.012100880965590477,
-0.08887219429016113,
0.04414216801524162,
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0.02181747555732727,
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0.014956029132008553,
0.012810634449124336,
0.021166518330574036,
0.054977305233478546,
-0... |
<p>As the title suggests I was wondering why the International Bureau of Weights and Measures
decided a mole to be a standard <a href="http://en.wikipedia.org/wiki/SI_units">(SI-)unit</a>. After some research I found I was not alone with this problem.</p>
<p>The core of my question is: </p>
<ol>
<li>How is the unit “mole” necessary as a standard unit?</li>
<li>If mole is the standard unit, why wouldn't I have a give all numbers in mole?</li>
</ol>
<p>Of course a mole is a convenient unit but I can't see how it is as fundamental as i.e. a meter, as it is clearly based on the concept of counting the atoms.</p>
<p>EDIT:
Due to the first answer I got I realized my question is probably misleading: by fundamental I do not mean dictated by nature but considered a base unit. The need of units is obvious in the case of meters and seconds: no matter how you want to measure time or length, you will necessarily have to compare it to some standard (in this case meter and seconds, independently of how they are defined). In the case of "number of particles" this is not needed, instead one could say they are compared to "1". This is normally not considered a unit. Is this difference only a personal opinion?</p> | g12197 | [
0.014793448150157928,
0.022613689303398132,
-0.002016168087720871,
-0.01783522218465805,
0.034807201474905014,
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0.0032913186587393284,
0.04178304225206375,
-0.030752811580896378,
-0.020203815773129463,
-0.017606128007173538,
0.020935993641614914,
0.02573612704873085,
... |
<p>Does anyone take the <a href="http://en.wikipedia.org/wiki/Wightman_axioms" rel="nofollow">Wightman axioms</a> seriously? Mainly with respect to quantum gravity or gauge theores, abelian or non-abelian?
Anyone doing any research on axiomatization of QFTs in some way?</p> | g12198 | [
0.005965287797152996,
0.04797206073999405,
-0.01971520483493805,
-0.06424985826015472,
0.05381667613983154,
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0.06219892576336861,
-0.017702100798487663,
0.01267228089272976,
0.013478328473865986,
0.00017071017646230757,
0.0064434572122991085,
-0.023138735443353653,
0.... |
<p>In Lagrangian Mechanics we choose the path of least action. </p>
<p>Given a uniform gravitational field, and a particle of finite mass; and fixing two points the start & end-point we consider all paths connecting the two points and minimise the action. This turns out to be a Brachistone, as first shown by Bernouilli.</p>
<p>When we fix the end-point vertically below; the Brachistone is in fact astraight-line.</p>
<p>But is there a principle in Lagrangian Mechanics that allows me to choose the point vertically below?</p>
<p>Of course, we know from Newtons Mechanics that this must be the case. But how do we determine that end-point entirely within Lagrangian Mechanics?</p> | g12199 | [
0.11380435526371002,
0.008584472350776196,
-0.008892571553587914,
-0.028980199247598648,
0.05920512601733208,
0.0174710750579834,
0.0632510855793953,
0.0003357542445883155,
-0.0575399175286293,
-0.0026953546330332756,
-0.046131305396556854,
-0.013452568091452122,
-0.004556340165436268,
-0.... |
<p>I'm currently trying to solve a problem that involves estimating the minimum energy of a particle in the potential:</p>
<p>$$
V(x) = \frac{-V_0a}{|{x}|}
$$</p>
<p>I'm quite confused about how to handle the absolute value in the potential. So far I know that the total energy of the particle will be </p>
<p>$$
E = \frac{p^2}{2m} - \frac{V_0a}{|{x}|}
$$</p>
<p>The expectation value of the energy is therefore</p>
<p>$$
\langle E\rangle = \frac{\langle p^2\rangle}{2m} - \frac{V_0a}{\langle|{x}|\rangle}
$$</p>
<p>Now, can I use the fact that $$\frac{1}{|x|}=\frac{1}{\sqrt{x^2}}$$ and then $\langle|x|\rangle = \sqrt{\langle x^2\rangle} = \Delta x$? Then from the uncertainty principle we know that $\Delta p = \hbar/2\Delta x$ and $\Delta p^2 = \langle p^2\rangle$ ($\langle p\rangle = 0$ and $\langle x\rangle$ = 0 in a minimum energy state) </p>
<p>Plugging this back into the energy equation gives
$$
\langle E\rangle = \frac{\hbar^2}{8m\Delta x^2} - \frac{V_0a}{\Delta x}
$$</p>
<p>When minimising this I get</p>
<p>$$
E_{min} = \frac{-2mV_0^2a^2}{\hbar^2}
$$</p>
<p>Now this doesn't look wildly wrong but I'm not sure if I've used the right approach with $\langle|x|\rangle = \sqrt{\langle x^2\rangle} = \Delta x$.</p> | g12200 | [
0.0418330654501915,
-0.025432979688048363,
0.0010122214443981647,
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0.017133669927716255,
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0.04537317901849747,
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0.014116935431957245,
0.044142551720142365,
0.005708620883524418,
-0.006312748417258263,
-... |
<p>I'm looking for the <a href="https://en.wikipedia.org/wiki/Critical_mass" rel="nofollow">critical mass</a> of <a href="https://en.wikipedia.org/wiki/Polonium" rel="nofollow">Polonium</a>; is there a formula? E.g.:$$\text{Neutrons / Protons}\cdot\text{ Constant = X kg}$$</p>
<p>There is a little table in the Wikipedia. E.g.:</p>
<p>$\begin{array}{ccccr}
\text{Name}&\text{Symbol}&\text{Neutrons}&\text{Protons}&\text{Crit. mass}
\\\hline
\text{Uranium-233}&{}^{233}\text{U}&141&92&15\:\mathrm{kg}
\\\text{Plutonium-238}&{}^{238}\text{Pu}&144&94&9\text{–}10\:\mathrm{kg}
\\\text{Plutonium-240}&{}^{240}\text{Pu}&146&94&40\:\mathrm{kg}
\end{array}$</p>
<p>I'm wondering, is there any dependence? What about with a neutron reflector?</p>
<hr>
<p>What is the critical mass of Polonium?</p> | g12201 | [
-0.02988319657742977,
-0.013153363019227982,
-0.017214644700288773,
-0.030278541147708893,
0.05612187832593918,
-0.0054516540840268135,
0.03157367929816246,
0.043373461812734604,
-0.0626433938741684,
-0.00894930399954319,
-0.009573428891599178,
-0.013120854273438454,
0.03464746102690697,
-... |
<p>I have a question about the pressure placed on a plate of material X, how the force is distributed and what would be the material property that would determine its failure. </p>
<p>To simplify things "suppose" I wanted to build a vacuum chamber with a viewing window made of material X, that could handle a external pressure of 0.990Bar, and has a dimension of 500mm x 500mm x thickness. How could I calculate a for safety reasons the minimum thickness needed for the window so that it doesn't implode, ignoring safety factors for now. Also could this calculation be then used on a box of some arbitrary dimensions to calculate the minimum thickness of the material?</p>
<p>Thanks.</p> | g12202 | [
0.0734541118144989,
-0.009158671833574772,
0.007134728599339724,
0.02472045086324215,
0.002689685672521591,
0.05576043576002121,
-0.003312093438580632,
-0.008991326205432415,
-0.07582094520330429,
-0.024892907589673996,
-0.0037566479295492172,
0.05378870666027069,
-0.02087029069662094,
0.0... |
<p>Well I'm not sure how many people remember the crazy ball - a small ball made of rubber which bounced like crazy. What I noticed is that the ball seemed to bounce higher than the point from which it was actually dropped. How is this possible? Doesn't this violate the law of energy conservation?</p> | g12203 | [
0.0700974091887474,
0.00620686449110508,
0.007227175869047642,
0.058271098881959915,
-0.004254537634551525,
0.05604621395468712,
0.033440981060266495,
0.033884692937135696,
-0.01263686828315258,
-0.03882911056280136,
-0.049727991223335266,
-0.00907406397163868,
0.0893382728099823,
-0.01742... |
<p>I had a <a href="http://math.stackexchange.com/questions/431126/laplace-beltrami-operator-on-sphere">question</a> at MSE which gave a rise to another question.</p>
<p><a href="https://en.wikipedia.org/wiki/Maxwell%27s_equations#Alternative_formulations" rel="nofollow">Maxwell equations</a> can be written in form $$d\star F = J$$</p>
<p>Then by Stokes theorem we have</p>
<p>$$ \int_U J = \int_U d \star F = \int_{\partial U} \star F.$$</p>
<p>If $U$(universe) is closed then $\partial U=\emptyset$ is empty. So $\int_U J=0$.</p>
<p>What does says about space time. Is it possible that $\int_U J=0$? Or is it proof that universe cannot be closed?</p> | g12204 | [
0.0205228254199028,
-0.031664036214351654,
-0.01997353881597519,
-0.04630732536315918,
-0.026296032592654228,
0.03450688347220421,
0.04089006409049034,
-0.047489993274211884,
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-0.016364365816116333,
0.008983057923614979,
0.03318316116929054,
0.00489087775349617,
0.057... |
<p>I know Einstein was great and all. Why is it that exactly at the speed of light is where infinite energy is required to accelerate any object with mass? Is it simply because the math of relativity checks out and explains most of everything? Are there any physicists who disagree with Einstein's theory? </p> | g122 | [
0.04491554573178291,
0.041078150272369385,
0.020704222843050957,
0.03470279276371002,
0.006203265395015478,
0.03235173970460892,
0.009002377279102802,
0.054333530366420746,
-0.0829765647649765,
-0.01364459004253149,
0.05620122328400612,
-0.05613883584737778,
-0.008241740055382252,
-0.01783... |
<p>Very often when people state a relaxation time $\tau_\text{kin-kin}, \tau_\text{rot-kin}$,, etc. they think of a context where the energy relaxation goes as $\propto\text e^{-t/\tau}$. Related is an approach to compute it via
$$\tau=E(0)/\left(\tfrac{\text d E}{\text d t}\right)_{E=0}.$$</p>
<p>Both are justified from considering dynamics for which</p>
<p>$$\frac{\text d E}{\text d t}=-\frac{1}{\tau}(E-E(0)).$$</p>
<p>My question is: What fundamentally leads to this relation? </p>
<p>I conjecture it relates to a Master equation, which mirrors the form "$\dot x=Ax+b$". But I'm not sure how the degrees of freedom in the Master equation translate to the time dependence of the macroscopic energy value. There will also be a derivation from the Boltzmann equation somehow, for some conditions, but what is the general argument and where does it work?</p> | g12205 | [
0.021554989740252495,
0.027039479464292526,
-0.008822767063975334,
-0.005559869110584259,
0.0214748103171587,
-0.027501076459884644,
0.04613083600997925,
0.03152088075876236,
-0.03918161615729332,
-0.0016612476902082562,
-0.04211033880710602,
0.03236466646194458,
0.05716467276215553,
0.007... |
<p>OK, lets formulate it differently and say water works as a blue passing / red restricting filter.</p>
<p>It is actually observable. Just do a dive in a swimming pool with white light (maybe even at night) and a pool with a metal casing or white tiles. The further you look, the more blue it is.</p>
<p>So why is this so? Why is water not transparent?</p>
<p>And how does it happen on a molecular, subatomar or electron shell level?</p>
<p>Do 'red' waves become absorbed and retransmitted as 'blue' light waves or do only the 'red' waves get absorbed and the 'blue' can pass?</p>
<p>Can Maxwell help? </p> | g12206 | [
0.012861708179116249,
0.03567688539624214,
0.005239631049335003,
0.018077360466122627,
0.11407167464494705,
0.1001514196395874,
0.029571963474154472,
0.018932495266199112,
0.0016169024165719748,
-0.031211957335472107,
0.015565063804388046,
0.046367254108190536,
0.038896020501852036,
0.0612... |
<p>I understand that evaporative cooling takes place thanks to small pores contained in the pot and that allow some water to go through and evaporate. However I couldn't understand clearly whether water inside the pot stays at its original temperature or would it cool further?
If it will become cooler then how?</p> | g12207 | [
0.041733164340257645,
-0.0037430196534842253,
0.016038957983255386,
0.035592760890722275,
0.004097523633390665,
0.02412411756813526,
0.04019753634929657,
0.007398085668683052,
-0.041670385748147964,
-0.07119621336460114,
-0.05479571223258972,
0.03505367413163185,
0.05832447484135628,
-0.00... |
<p>In an article from the <a href="http://fisica.ciencias.uchile.cl/~gonzalo/cursos/termo_II-05/seminarios/AJP_Callen-relativistic-thermo71.pdf" rel="nofollow">reference</a> there are following words (page 2):
"...pressure P is a Lorentz invariant... the result follows from standart properties of the relativistic stress-energy tensor...". </p>
<p>What properties are used by the authors of an article? </p>
<p>For example, I used the expression for stress-energy tensor of an isotropic body:
$$
T_{\alpha \beta} = (\varepsilon + p)\frac{v_{\alpha }v_{\beta}}{c^{2}} - g_{\alpha \beta }p.
$$
If pressure is determined as a 3-trace of this tensor, it's obviously that it isn't Lorentz invariant.</p> | g12208 | [
0.0536389984190464,
-0.003256319323554635,
-0.007791388779878616,
0.04037246108055115,
0.05762692540884018,
0.05429088696837425,
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0.029796311631798744,
-0.06607495993375778,
0.040457095950841904,
-0.049280475825071335,
0.01418849267065525,
-0.03748450428247452,
-0.076... |
<p>Is it possible to consider <a href="http://en.wikipedia.org/wiki/Gravitational_constant" rel="nofollow">Newton's universal gravitational constant</a>, $G$, as inverse of vacuum permittivity of mass?</p>
<p>$$\epsilon_m=\frac {1}{4\pi G}$$</p>
<p>if so, then vacuum permeability of mass will be:</p>
<p>$$\mu_m=\frac {1}{\epsilon_m c^2}$$</p>
<p>then Gravitational force will be:</p>
<p>$$F_G=\frac {1}{4\pi \epsilon_m}\frac {m.M}{r^2}$$</p> | g12209 | [
-0.021096471697092056,
0.009536364115774632,
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0.006056889891624451,
0.014987297356128693,
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0.04961507022380829,
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0.018037883564829826,
0.024901458993554115,
0.022979365661740303,
0.01924828439950943,
-0.0... |
<p>I remember reading about the groundbreaking experiment by <a href="http://arxiv.org/abs/hep-ph/0502081" rel="nofollow">Nesvizhevsky (et al. 2001)</a> some 12 years ago using ultra-cold neutrons which showed the first experimental evidence of quantum gravity. It is my understanding that these experiments has been repeated since then in labs around the world and similar results observed(neutrons bouncing off the reflector in a discrete set of quantized energy states rather than varying continuously)and more recently by Kobakhizde(2010), who was testing Erik Verlinde's "entropy theory of gravity". Am I correct about the reproducibility of Nesvizhevsky's results? If so, these experiments seem to suggest that gravity is indeed an actual force after all and not simply an emergent property as posited by GR. But do any of the results of these experiments conflict with the weak/strong equivalence principles? Someone on Yahoo! answers with the handle OzoneGuy claimed that the observations were explainable simply by diffraction. But this could be tested by positioning the diffraction grating to be parallel to the neutron reflector.So it is simply diffraction? Or is there actual evidence of quantum gravity?</p> | g12210 | [
0.022092681378126144,
0.04740854725241661,
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0.019514374434947968,
0.027960121631622314,
0.03236160799860954,
0.03097536414861679,
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-0.034867554903030396,
0.007894095964729786,
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0.006060466170310974,
-0.... |
<p>What (if any) is the relationship between the conserved (non-topological) noetherian charges and <a href="http://en.wikipedia.org/wiki/Topological_quantum_number" rel="nofollow">topological charges</a>? Namely, is there any "generalization" of the <a href="http://en.wikipedia.org/wiki/Noether%27s_theorem" rel="nofollow">Noether's first theorem</a> that includes topological charges as subcase and it provides some relationship between these two classes of charge?</p> | g12211 | [
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... |
<p>How can Hawking radiation with a finite (greather than zero) temperature come from the event horizon of a black hole? A redshifted thermal radiation still has Planck spectrum but with the lower temperature (remember CMB with temperature redshifted by expansion of the universe). Now, redshift at the event horizon is infinite (time is frozen for a distant observer) so the temperature of the radiation would be zero for him/her, that is no radiation is detected</p> | g12212 | [
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0.01... |
<p>A sinusoidal oscillator has :</p>
<p>$$x=x_{max} \cos(\omega t - \varphi )$$</p>
<p>Period is 2, initial displacement is 100mm
initial velocity is 200mm/s</p>
<p>What is the phase angle assuming $-\pi < \varphi < \pi$</p>
<p>How do I go about solving this?</p>
<p>Is the phase $(\omega t - \varphi)$? But I do not know what $x_{max}$ is, how am I supposed to solve for the angle?</p> | g12213 | [
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<p>One example of a <a href="http://en.wikipedia.org/wiki/Nonholonomic_system" rel="nofollow">nonholonomic</a> constraint is a disk rolling around in the cartesian plane that is constrained to not be slipping.</p>
<p>These leads to the constraint $dx - a \sin\theta d\phi = 0$ and $dy - a\cos\theta d\phi = 0$ Where $\phi$ is the angle of how far the disk has rotated, $-\theta$ is angle that velocity makes with respect to $x$.</p>
<p>We know that these aren't exact differentials because to put it in form $Mdx + Ndy = 0$, we don't have $\partial M/\partial y = \partial N / \partial x$. But that doesn't mean we can't find some integrating factor to multiply it by and make it an exact differential? So I don't see how we know that is it nonintegrable?</p>
<p>If I take $f(x,\phi)[ dx - a \sin\theta d\phi] = 0$ and try to manipulate it to get something analogous to $\partial M/\partial y = \partial N / \partial x$, then I get a tricky PDE, which I don't know how to solve.</p> | g12214 | [
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0.0... |
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