question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>When a Hamiltonian operator apply to a wavefunction, how could we write the hamiltonian as,
$$H \psi = (E_n-\hbar \omega_0) \psi \ \ ? $$</p>
<blockquote>
<p>Is this because $E_n= H+ \hbar \omega_0$?</p>
</blockquote>
<p>where $\omega_0$ is the angular frequency.</p> | g14905 | [
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<p>I know that after invoking the Born-Oppenheimer approximation, the nuclei will move on the adiabatic potential provided by the electronic energy (also called potential energy surface (PES)). Such nuclear motions, can be described following quantum-mechanical, classical or hybrids methods on a fitted potential energy surface (PES) or when we want to avoid any analytical representation or interpolation of the PES, we can resort in “on the fly” calculation of the potential.</p>
<p>My question is, what are those quantum, classical or hybrid theories/methods that are in connection with an statistical description? and how can i make a general classification o each of them?, at least the most important methods.</p> | g14906 | [
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<p>Does the definition of an atomic explosion require the interaction of two or more atoms, or can a single atom be the source of an explosion?</p>
<p>Another way of phrasing the same question. Can there be an atomic explosion involving a single atom without any other atom involved in the start or chain reaction of the explosion.</p> | g14907 | [
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<p>At the time the Big Bang happened the matter had enormous density. According the GR (I may be wrong here) such density dilates time.</p>
<p>If so, could it be that the time periods just after Big Bang which are usually considered happening in small part of a second (such as the Planck epoch), in reaity took billons of year (or may be, infinity) but due to time dilation appear to us as spanning only microscopic parts of a second? Could it be that the age of the universe is dramatically underestimated?</p> | g700 | [
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<p>Grilling in the park today I started to wonder just how implausible a portable battery-powered grill would be. There are of course a lot of parameters in this question, so let's narrow it down for now: How much energy does it take to cook a steak?</p>
<p>To be a bit more specific let's say a 2.5cm thick steak to a core temperature of 63°C. And since we probably need one more measurement, let's say it's circular with a radius of 5cm.</p>
<p>Everything from numbers for cylindrical steaks in a vacuum to precisely the numbers that are needed to get an actual tasty steak would be interesting.</p> | g14908 | [
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<p>This came from a physics wave book. I have a static, massive wire on the x-axis, with a y-displacement due to a force per unit length $F_y$. I start with the equation $F_y = T_0\frac{\partial^2(\eta)}{\partial(x)^2}$, where $\eta$ is a small displacement in the y direction and $T_0$, with units of force, is the tension supporting the wire. I need to find how twire is shaped, so I need to integrate both sides twice with respect to x.
$$F_y\iint{{dx}^2} = T_0\iint{\frac{\partial^2(\eta)}{\partial(x)^2}{dx^2}}$$</p>
<p>Since these are both indefinite integrals this is rather easy and I get $F_y x^2 = T_o\eta +Cx+D$. But if I were to attempt definite integrals, how exactly would I proceed? If both are definite...
$$F_y\int_{x_1}^{x_2}\int_{x_1}^{x_2}{{dx}^2} = T_0\int_{x_1}^{x_2}\int_{x_1}^{x_2}\frac{\partial^2(\eta)}{\partial(x)^2}{dx^2}$$
Then this is how I think the fundamental theorem of calculus would apply $$F_y(x_2-x_1)\int_{x_1}^{x_2}{dx} = T_0\int_{x_1}^{x_2}\left(\frac{\partial(\eta(x_2))}{\partial(x)}-\frac{\partial(\eta(x_1))}{\partial(x)}\right){dx}$$
But this seems very wrong. Having $\eta$ as a function of only the endpoints seems odd. Intuitively I would indefinite integrate this once, then definite integrate the second time to limit it. How do you apply the F.T.C here? </p>
<p>Also I've seen from other questions that the curve is not in fact parabolic as my first equation suggests, what assumption am I making that threw this off?</p>
<p>Any help is appreciated, I feel this hit's on a key concept I missed in calculus.</p> | g14909 | [
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<p>I'm reading articles about black body radiation and why classical mechanics fails to explain it. My question is:</p>
<p>Why do EM waves have to be standing wave in a cavity?</p> | g14910 | [
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<p>Consider a block of mass $m$ attached to a spring. Let it oscillate at a frequency $f$. Now each part of the spring is in SHM. so this means a wave is propagating through this spring.bCan this wave be reflected at the fixed end of the spring resulting in the formation of standing waves?</p> | g14911 | [
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<p>I am trying to clearly express in one or two sentences how increased evapotranspiration could cool a region. The audience is educated but non-scientific.</p>
<p>Is it accurate to say that the water vapor has removed latent heat? Is there a more clear explanation?</p> | g95 | [
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<p>What are the missing lines in the integration?</p>
<p>$$\frac{\text d \langle {p} \rangle}{ \text{d} t} $$
$$= \frac{\text d}{\text d t} \int\limits_{-\infty}^{\infty} \Psi^* \left( \frac{\hbar}{i}\frac{\partial}{\partial x} \right) \Psi ~\text d x$$
$$= \frac{\hbar}{i}\int\frac{\partial }{\partial t} \left(\Psi^*\frac{\partial\Psi}{\partial x}\right)~\text d x $$
$$= \frac{\hbar}{i}\int \frac{\partial \Psi^*}{\partial t}\frac{\partial \Psi}{\partial x} +\Psi^*\frac{\partial }{\partial x}\frac{\partial \Psi }{ \partial t} ~\text {d} x$$
$$= \frac{\hbar}{i}\int\left( -\frac{i\hbar}{2m}\frac{\partial^2 \Psi^*}{\partial x^2}+\frac{i}{\hbar} V\Psi^*\right)\frac{\partial \Psi}{\partial x}+\Psi^* \frac{\partial}{\partial x} \left(\frac{i\hbar}{2m} \frac{\partial^2 \Psi }{\partial x^2} -\frac{i}{\hbar}V\Psi \right)~\text d x$$
$$=\int\left(V\Psi^*-\frac{\hbar^2}{2m}\frac{\partial^2 \Psi^*}{\partial x^2}\right) \frac{\partial \Psi}{\partial x}+\Psi^*\frac{\partial}{\partial x}\left(\frac{\hbar^2}{2m}\frac{\partial^2 \Psi}{\partial x^2}-V\Psi\right)\text d x$$</p>
<p>$$=\left. \left(V\Psi^*-\frac{\hbar^2}{2m}\frac{\partial^2 \Psi^*}{ \partial x^2} \right) \Psi \right|_{-\infty}^{\infty}-\int\left(\frac{\partial}{\partial x} (V\Psi^*)-\frac{\hbar^2}{2m}\frac{\partial^3 \Psi^*}{ \partial x^3}\right)\Psi \text d x+ \left.\Psi^*\left(\frac{\hbar^2}{2m}\frac{\partial^2 \Psi}{\partial x^2} - V\Psi\right)\right|_{-\infty}^\infty-\int\frac{\partial\Psi^*}{\partial x} \left( \frac{\hbar^2}{2m}\frac{\partial ^2 \Psi}{\partial x^2} - V \Psi \right)\text d x$$</p>
<p>$$=0 + \int\left(\frac{\hbar^2}{2m}\frac{\partial^3 \Psi^*}{ \partial x^3}-\frac{\partial}{\partial x} (V\Psi^*)\right) \Psi \text d x+0+\int\frac{\partial\Psi^*}{\partial x}\left(V\Psi - \frac{\hbar^2}{2m}\frac{\partial^2 \Psi}{\partial x^2}\right) \text d x$$
$$=\int\frac{\hbar^2}{2m} \left(\frac{\partial^3\Psi^*}{\partial x^3}\Psi -\frac{\partial\Psi^*}{\partial x} \frac{\partial^2\Psi}{\partial x^2}\right)+\frac{\partial\Psi^*}{\partial x}(V\Psi )-\frac{\partial}{\partial x}(V\Psi^*)\Psi\text d x $$</p>
<p>$$\vdots$$
$$=\int \frac{\hbar^2}{2m}\left( \Psi^* \frac{\partial^3 \Psi}{\partial x^3} -\frac {\partial^2 \Psi^*}{\partial x^2} \frac{\partial \Psi}{\partial x} \right)+\left( V \Psi^* \frac{\partial \Psi}{\partial x}-\Psi^* \frac{\partial}{\partial x} (V \Psi) \right)~\text d x$$
$$\vdots $$
$$= \int \left( V \Psi^* \frac{\partial \Psi}{\partial x}- \Psi^* \frac{\partial V}{\partial x} \Psi-\Psi^*V \frac{\partial \Psi}{\partial x} \right)~\text d x$$
$$= \int\limits_{-\infty}^{\infty} -\Psi^* \frac{\partial V}{\partial x} \Psi ~\text {d} x$$
$$=\left\langle - \frac{ \partial V }{\partial x} \right\rangle $$</p> | g14912 | [
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<p>Often in engineering physics, different vector spaces are used to visualize the trajectories (evolution) of systems. An example being the 6n dimensional phase space of n particles. It is not very clear to me if this space is Euclidean or has a meaning of distance. I understand the 2-norm when the physical quantities are the same (e.g., only positions or only momenta) but not when a vector has both. However even this seems to be a problem with some other spaces. For example if I consider the vector space of chemical composition of chemical system (mole numbers of all chemical species). I don't understand what "length" of a vector would signify?</p>
<p>Thanks</p> | g14913 | [
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<p>It’s easy, relatively speaking, to develop an intuition for higher spatial dimensions, usually by induction on familiar lower-dimensional spaces. But I’m having difficulty envisioning a universe with multiple dimensions of time. Even if such a thing may not be real or possible, it seems like a good intellectual exercise. Can anyone offer an illustrative example?</p> | g480 | [
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<p>I would like to migrate this <a href="http://math.stackexchange.com/questions/514/conjectures-that-have-been-disproved-with-extremely-large-counterexamples">Math</a> Question into physics. The question is:</p>
<ul>
<li>Are there conjectures in Physics which have been disproved with extremely large counterexamples? If yes, i would like to know some of them.</li>
</ul> | g14914 | [
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<p>Do spacelike singularities really exist in quantum gravity? If the memory of anything which falls into a black hole can't get out, is there any sense in which the interior of the black hole is real? Similarly, if we don't have any direct records of the spacelike singularity in the past, is there any sense in which it is real?</p> | g468 | [
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<p>I've heard that common way to get 354nm laser is to triple 1064nm Nd:YAG one.</p>
<p>But how to make non-linear crystal to do tripling instead of doubling?
What are the best crystals for tripling and what's the efficiency?</p> | g14915 | [
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<p>In the context of GTR spacetime, I'm trying to get the basic idea of a Riemannian manifold clear in my mind. Apologies for the longwindedness.</p>
<p>Question 1. Is this a reasonable, simplified summary of the steps needed to define such a manifold?</p>
<ol>
<li><p>Start with an amorphous collection of points.</p></li>
<li><p>Find the minimum number of parameters needed to locate each point in space. That number will be the dimension of the manifold.</p></li>
<li><p>Construct a coordinate system to locate each point in space. I may need more than one coordinate system to to cover the whole manifold. I need a “good” coordinate system so that each point is uniquely described.</p></li>
<li><p>Decide on a metric that gives the infinitesimal distance between two adjacent point. The metric need not be the same all over the manifold (as $g_{\mu\upsilon}$ isn't in spacetime). In that case I would have a metric tensor field defined over the manifold.</p></li>
<li><p>The manifold has to be continuous and differentiable (not quite sure what this means, but I assume it's the obvious - I have to be able to differentiate it everywhere).</p></li>
<li><p>I can now start constructing scalar fields, covariant and contravariant vectors, tensors etc.</p></li>
</ol>
<p>Question 2. Assuming I do all the above with a flat plane (a table top for example), using Cartesian coordinates. Can I impose any kind of metric to my new “table top” manifold? Could I just make a weird one up:
$$\left(\begin{array}{cc}
x^{2} & \sin xy\\
x+y & 13y
\end{array}\right)$$</p>
<p>for example, instead of the Euclidean
$$\left(\begin{array}{cc}
1 & 0\\
0 & 1
\end{array}\right)$$</p>
<p>Thank you.</p> | g14916 | [
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<p>I am writing simple car simulation.</p>
<p>Assume non friction, then in straight line the car doesn't lose speed. But what if the car is turning, there should be some kinetic energy loses to change the direction of the car, so I should subtract some speed based on changing direction, isn't it right?</p>
<p>Deeper explanation is welcome.</p> | g14917 | [
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<p>Quite a few of the questions given on this site mention a photon in vacuum having a rest frame such as it having a zero mass in its rest frame. I find this contradictory since photons must travel at the p of light in all frames according to special relativity.</p>
<p>Does a photon in vacuum have a rest frame?</p> | g94 | [
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<p>Can a functional derivative be calculated if we have a function of more than one variable? </p>
<p>The functional derivative of, for example, $F[b(x)]=e^{\int_0^{x'} dx a(x,y) b(x)}$ is </p>
<p>\begin{equation}
\frac{\delta F[b(x)]}{\delta b(z)} = a(z,y) e^{\int_0^{x'} dx a(x,y) b(x)}
\end{equation}</p>
<p>But what about if there it's a functional of more than one variable? - $F[b(x,k)]=e^{\int_0^{x'} \int_0^p dx dk a(x,y,k) b(x,k) }$? Can we write the following?</p>
<p>\begin{equation}
\frac{\delta F[b(x,k)]}{\delta b(z,k)} = a(z,y,k)e^{\int_0^{x'} \int_0^p dx dk a(x,y,k) b(x,k )}
\end{equation}</p>
<p><strong>Edit:</strong> I just want to note that I've been told that you <strong>cannot</strong> do this by a lecturer. Therefore, is the answer is yes (or no!), please give some details! (I wasn't convinced that he was correct).</p> | g14918 | [
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<p>I have read how the <a href="http://en.wikipedia.org/wiki/BB84" rel="nofollow">BB84</a> protocol could work. However, I couldn't see a way to implement it in the laboratory, so that I could make a demonstration in the university's quantum optics laboratory. </p>
<p>From what I have read, I think that a way to demonstrate this is to somehow shoot only one photon at a time, each time with a prepared setting for the sender and receiver polarization, but it seems very unpractical. </p> | g14919 | [
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<p>I am aware that the formula for <a href="http://www.google.com/search?as_q=Schiff+Equation" rel="nofollow">Schiff Equation</a> in used to determine frame-dragging is:
$$\boldsymbol{\Omega} = \frac{GI}{c^2r^3}\left( \frac{3(\boldsymbol{\omega}\cdot \boldsymbol{r})\boldsymbol{r}}{r^2}-\boldsymbol{\omega} \right).$$</p>
<p>But why does this reduce to: $$\boldsymbol{\Omega} = \frac{GI\boldsymbol{\omega}}{c^2r^3}\frac{\int_0^{2\pi}(3\cos^2\theta - 1)\text{d}\theta}{\int_0^{2\pi}\text{d}\theta} = \frac{GI\boldsymbol{\omega}}{2c^2r^3}$$ in a polar orbit?</p> | g14920 | [
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0.02... |
<p>The idea of “hadronic supersymmetry” originated in the mid-1960s and derives from the observation that baryons and mesons have similar Regge slopes, as if antiquarks and diquarks are superpartners. This is most efficiently explained by supposing a QCD string model of baryons in which a diquark substitutes for an antiquark at one end of the string, but there are <a href="http://arxiv.org/abs/0901.4508">superstring models in which the baryon-meson relationship is a genuine supersymmetry</a>.</p>
<p>In 2005, Alejandro Rivero <a href="http://arxiv.org/abs/hep-ph/0512065">proposed</a> that mesons are to <em>leptons</em> as diquarks are to quarks. If the top quark is excluded from consideration, as too heavy to hadronize, then one has enough quark-antiquark pairings to match the electromagnetic charges of all the leptons, with a few leftover u,c pairings with charge ±4/3. </p>
<p>The construction is a little complicated, but the possibility that supersymmetry is already right in front of us is so amazing that it just cries out to be investigated. I have an <a href="http://www.physicsforums.com/showthread.php?t=485247">ongoing discussion</a> with Rivero, about whether his correspondence might be realized in a preon model, or a "partially composite" model, or a sophisticated string-theory construction. </p>
<p>Meanwhile, I'd like to know, <strong>is there some reason why this can't be realized?</strong> The closest thing to such a reason that I've seen is found in comment #11 in that thread: "For a SUSY theory, not just the spectrum must be supersymmetric, but also the interactions between the particles." So far, all Rivero has is the observation that some quantum numbers of diquarks/mesons can be correlated with some quantum numbers of fundamental quarks/leptons, just as if they were elements of a single superfield. I suspect (but I'm such a susy newbie that I can't even confirm this) that you could realize the correspondence in a QCD-like supersymmetric theory, if it was first expressed in terms of meson and diquark variables, and then supersymmetry was completely broken (see comments #40 through #44), but that this would somehow be trivial. </p>
<p>Nonetheless, I think the possibility that supersymmetry is already right in front of us would be important enough, that someone should investigate even such a "trivial" realization of Rivero's correspondence, with a view to understanding (i) whether such a "hard" form of susy breaking might realistically occur (ii) how it would affect the various roles and problems associated with supersymmetry in contemporary physical thought (protect the Higgs mass, supply dark matter candidates; technical model-building issues like <a href="http://arxiv.org/abs/hep-th/9810155">"the supersymmetric flavor problem, the gaugino mass problem, the supersymmetric CP problem, and the mu-problem"</a>...). </p> | g14921 | [
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0.08... |
<p>In the second chapter of Peskin and Schroeder, <em>An Introduction to Quantum Field Theory,</em> it is said that the action is invariant if the Lagrangian density changes by a four-divergence.
But if we calculate any change in Lagrangian density we observe that under the conditions of equation of motion being satisfied, it only changes by a four-divergence term.</p>
<p>If ${\cal L}(x) $ changes to $ {\cal L}(x) + \alpha \partial_\mu J^{\mu} (x) $ then action is invariant. But isn't this only in the case of extremization of action to obtain Euler-Lagrange equations. </p>
<p>Comparing this to $ \delta {\cal L}$</p>
<p>$$ \alpha \delta {\cal L} = \frac{\partial {\cal L}}{\partial \phi} (\alpha \delta \phi) + \frac{\partial {\cal L}}{\partial \partial_{\mu}\phi} \partial_{\mu}(\alpha \delta \phi) $$</p>
<p>$$= \alpha \partial_\mu \left(\frac{\partial {\cal L}}{\partial \partial_{\mu}\phi} \delta \phi \right) + \alpha \left[ \frac{\partial {\cal L}}{\partial \phi} - \partial_\mu \left(\frac{\partial {\cal L}}{\partial \partial_{\mu}\phi} \right) \right] \delta \phi. $$ </p>
<p>Getting the second term to zero assuming application of equations of motion. Doesn't this imply that the noether's current itself is zero, rather than its derivative? That is:</p>
<p>$$J^{\mu} (x) = \frac{\partial {\cal L}}{\partial \partial_{\mu}\phi} \delta \phi .$$</p>
<p>I add that my doubt is why changing ${\cal L}$ by a four divergence term lead to invariance of action globally when that idea itself was derived while extremizing the action which I assume is a local extremization and not a global one.</p> | g734 | [
0.09142731875181198,
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0.05617121607065201,
0.02709098719060421,
0.07784821838140488,
0.05509233847260475,
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0.025881418958306313,
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0.02627803385257721,
-0.030528780072927475,
0.04798... |
<p>i'm a high school student and i was reading about electromagnetic waves and how they transport energy and that the electric and magnetic fields sustain each other.</p>
<p>I have also read about longitudinal waves which travel due to contractions and rarefactions and also transport energy by changing the relative positions of the particles of the medium.</p>
<p>So,i was wondering whether there could exist a wave which travels 'through' an atom or sub-atomic particle which would traverse by changing the quantum states of the said particles?</p>
<p>For example, a particle may oscillate between different quantum states and the particles surrounding it may do so too but in such a way that a 'wave' appears to pass through them.</p> | g14922 | [
-0.008291882462799549,
0.03277905657887459,
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0.05644051730632782,
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-0.02392614632844925,
0.01581439934670925,
0.03587089851498604,
0.048331256955862045,
-0.03676... |
<p>When light enters materials it slows down due to its refractive index (due to absorbing and re-emission of photons). </p>
<p>But, is there a way to increase the speed of light itself? Can there be some material which would increase rather than decrease the speed of light? </p> | g14923 | [
0.025388136506080627,
0.019054697826504707,
0.04390517622232437,
0.02112574316561222,
0.03803766891360283,
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0.011079559102654457,
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0.07242095470428467,
0.020244214683771133,
0.022765232250094414,
-0.0... |
<blockquote>
<p>A chain of mass $M$ and length $l$ is suspended vertically with its
lowest end touching a table. The chain is released and falls onto the
table. What is the force exerted by falling part of the chain on the
table?(Neglect the size of individual links)</p>
</blockquote>
<p>Here's what I did.
Momentum of a size $dx$ of chain, which was initially at a height $x$ from the bottom of the chain, when it is just touching the table is given by
$$p = M\sqrt{2gx}\frac{dx}{l}$$</p>
<p>This momentum is lost in time
$$t = \frac{dx}{\sqrt{2gx}}$$</p>
<p>Force exerted by table on chain and chain on table is given by
$$F = \frac{p}{t} = 2Mg\frac{x}{l}$$</p>
<p>As it turns out, this is the <strong>right answer</strong></p>
<p>But, the author asks to solve this using Work-Energy Theorem. Here's what I did:</p>
<p>Work done by table on chain:
$$F.dx$$
Energy of part of chain lost to this work done:
$$Mgx\frac{dx}{l}$$</p>
<p>Equating the above two equations, I get
$$F = Mg\frac{x}{l}$$</p>
<p>This is off by the right answer by a factor of two. <strong>What goes wrong when I use Work-Energy Theorem, although I get the right answer when I use momentum?</strong></p> | g14924 | [
0.060464709997177124,
0.04270336404442787,
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0.027086986228823662,
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0.0029547512531280518,
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0.02382834255695343,
-0.042338818311691284,
0.0108224181458354,
-0.062474265694618225,
0... |
<p>If there are two cylinders (A and B) both with the same volume. B's radius is half of A's, so the length of B must be 4 ($2^2$) times that of A. </p>
<p>The uncertainty for the radius of A is the same as the for the radius of B, and the uncertainty is the same for the lengths. But the uncertainty of the volume isn't necessarily the same as for the radius)</p>
<p>Which cylinder A or B would have the greatest uncertainty for volume?
Or would they be the same because as the percentage uncertainty for radius for B is larger than A but the percentage uncertainty for length B is less that for A?
Do the uncertainties need to be know?</p> | g14925 | [
0.08876964449882507,
-0.039207227528095245,
0.025981087237596512,
0.06619962304830551,
0.008851496502757072,
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0.009020128287374973,
0.003404480405151844,
-0.010645581409335136,
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-0... |
<p>I am wondering to what extent the flammability can be predicted from the statistical properties of an ensemble. Given the partition function of an ensemble, can we in principle predict this property? Is there a chance flammability is a classical property of matter?</p> | g14926 | [
0.006860122084617615,
-0.03789101913571358,
0.00029907774296589196,
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0.026463698595762253,
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-0.013780659064650536,
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0.0668046623468399,
0.029847608879208565,
... |
<p>I am trying to derive a formula to calculate the density of a irregulary shaped object.</p>
<p>I can measure the (<strong>false</strong>) weight of the object in pure air (of known density), and the (<strong>false</strong>) weight of the object in water (of known density).</p>
<p>I cannot measure (directly) the volume of the object, nor its real weight (in vaccum).</p>
<p>I tried this approach:
$$G_{air} = G_{vaccum} - B_{air} $$
$$G_{water} = G_{vaccum} - B_{water} $$
where $B$ is the buoyant force.</p>
<p>Solving both equations for $G_{vaccum}$ gives
$$G_{vaccum} = G_{air} + B_{air}$$
$$G_{vaccum} = G_{water} + B_{water}$$
so
$$G_{air} + B_{air} = G_{water} + B_{water}$$</p>
<p>Because $B_{air} = \rho_{air} V g$ resp. $B_{water} = \rho_{water} V g$ and
$$V = \frac{m_{obj}}{\rho_{obj}}$$ I can write:</p>
<p>$$ G_{air} - G_{water} = B_{water} - B_{air}$$
$$ G_{air} - G_{water} = Vg \left(\rho_{water} - \rho_{air}\right)$$
$$ \frac{G_{air} - G_{water}}{\rho_{water} - \rho_{air}} = \frac{m_{obj}g}{\rho_{obj}} $$</p>
<p>And this is where I am stuck, as I cannot measure the real weight of the object $m_{obj}$. It feels like I am missing something here ...</p>
<p>So, how do I solve this equation to finally get an equation for $\rho_{obj}$?
Tell me if I forgot something I could measure.</p>
<hr>
<p><strong>Edit:</strong> Of course I can assume that the influence of the buoyant force in air is negligible and write:
$$ m_{obj}g \approx G_{air} $$
Then I can also assume that the density of air is much less than the density of water and write:
$$ \rho_{water} - \rho_{air} \approx \rho_{water} $$
Using those two assumpions I could write:
$$ \rho_{obj} = \rho_{water} \frac{G_{air}}{G_{air} - G_{water}} $$</p>
<p>Can I only assume the first simplification and not the second and get a better result?</p>
<p>And still: How do I solve the problem without those simplifications?</p> | g14927 | [
0.008119148202240467,
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-0.049323420971632004,
-0.038772184401750565,
-0.013696443289518356,
0.01011227909475565,... |
<p>Is the higgs field in space around us? </p>
<p>I understand it as that the higgs field has a constant value on every space time point, is that right?</p>
<p>And this value is the vacuum expectation value. This value is responsible for giving mass to the elementary particles, like the fermions, right?</p>
<p>In the Lagrangian for e fermion there is a term $g \phi_0 \bar \psi \psi$. </p>
<p>$g$ is the Yukawa coupling constant and $\phi_0$ is the vacuum expectation value, right?</p> | g14928 | [
0.05527346208691597,
0.019618647173047066,
-0.004368517082184553,
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0.012628561817109585,
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0.02671625092625618,
0.011888970620930195,
0.... |
<p>As discussed by Prof.Wen in the context of the <a href="http://arxiv.org/abs/cond-mat/0107071" rel="nofollow">quantum orders of spin liquids</a>, <strong>PSG</strong> is defined as all the transformations that leave the mean-field ansatz invariant, <strong>IGG</strong> is the so-called <em>invariant gauge group</em> formed by all the gauge-transformations that leave the mean-field ansatz invariant, and <strong>SG</strong> denotes the usual symmetry group (e.g., lattice space symmetry, time-reversal symmetry, etc), and these groups are related as follows <strong>SG</strong>=<strong>PSG/IGG</strong>, where <strong>SG</strong> can be viewed as the <em>quotient group</em>.</p>
<p>However, in math, the name of <a href="http://en.wikipedia.org/wiki/Projective_group_%28disambiguation%29" rel="nofollow"><em>projective group</em></a> is usually referred to the <em>quotient group</em>, like the so-called <em>projective special unitary group</em> $PSU(2)=SU(2)/Z_2$, and here $PSU(2)$ is in fact the group $SO(3)$. </p>
<p>So physically why we call the <strong>PSG</strong> <em>projective</em> rather than the <strong>SG</strong>? Thank you very much.</p> | g14929 | [
-0.0009444979950785637,
0.001977647189050913,
-0.05158441141247749,
-0.023850079625844955,
0.013615981675684452,
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0.0020891509484499693,
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0.01237325370311737,
0.039411235600709915,
-0.01173262670636177,
-0.023960012942552567,
... |
<p>I have this question going in my mind from many days, i.e why brightness of light emitted from any light source around us decreases with distance? The brightness of light from tube light, streetlight, etc or any light from any source around us, decreases with the distance. As my teacher has taught me that light is a form of radiation, I thought this decrease in brightness may be due to absorption of radiation in the medium. I don't know whether it is correct or wrong. If it is wrong, please explain <em>why there will be decrease in brightness of light with increase in distance from the light source?</em><br>
If we assume that decrease in brightness of light is due to absorption of radiation in the medium, then <em>in vaccum (where we can assume no energy dissipation), would there be no decrease in brightness of light with respect to distance from the light source?</em><br>
<img src="http://i.stack.imgur.com/x6nhs.jpg" alt="enter image description here"></p> | g14930 | [
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-0.06849095225334167,
0.029099253937602043,
0.02734271064400673,
0.046874865889549255,
0.0353... |
<p>In other words, does a finite set <a href="http://en.wikipedia.org/wiki/Correlation_function_%28quantum_field_theory%29" rel="nofollow">correlation functions</a> sufficient to determine a theory? Is there a chance correlation functions are more fundamental then the lagrangian?</p> | g14931 | [
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-0.08740732818841934,
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0.016549263149499893,
0.010739502497017384,
0.0... |
<p>We are working on problem 6.12 from Griffiths Electrodynamics. It says that we have an infinitely long cylinder of frozen in magnetization of $M=ks\hat z$. We are trying to find the field. We have found:</p>
<p>$$J_b=\nabla \times M=-k\hat{\phi}$$
$$K_b=M \times \hat n=kR\hat {\phi}$$</p>
<p>Then we are stuck on how to find the field. We know to use an amperian loop, but we are lost on what bounds to integrate and how to get a result.</p> | g14932 | [
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0.03039686381816864,
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0.026012800633907318,
-0.026958897709846497,
-0... |
<p>I have a homework problem that I can't get started on, below is the first bit. I feel like I should just be able to integrate to find $C$ but I get a divergent integral. Can someone give me a hint as to where to go here?</p>
<blockquote>
<p>A particle of mass m is in a one-dimensional infinite square well, with $U = 0$ for $0 < x < a$ and $U = ∞$
otherwise. Its energy eigenstates have energies $E_n = (\hbar πn)^
2/2ma^2$
for positive
integer $n.$
Consider a normalized wavefunction of the particle at time $t = 0$
$$ψ(x,0) = Cx(a − x).$$
Determine the real constant $C$.</p>
</blockquote> | g14933 | [
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0.011564293876290321,
-0.006974032614380121,
-0.10817888379096985,
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0.040269363671541214,
0.03006853722035885,
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0.019063491374254227,
-0.07250871509313583,
0.017436547204852104,
-0.02111109159886837,
0.0... |
<p>This question is related to <a href="http://physics.stackexchange.com/questions/89969/6-independent-einstein-field-equations">my previous one</a> and it was a homework problem and was due two weeks ago.</p>
<p><em>Problem</em>：prove that four of Einsteins' equations
$$
G_{0\nu} = 8\pi T_{0\nu}
$$
have to 2nd order time derivative and thus serve as constraint equations. </p>
<p>I found a nice argument in Carroll's <a href="http://arxiv.org/abs/gr-qc/9712019" rel="nofollow">lecture notes</a>,
$$
\partial_0 G^{0\nu} =-\partial_i G^{i\nu} -\Gamma^{\mu}_{\mu\lambda} G^{\lambda \nu} -\Gamma^{\nu}_{\mu\lambda} G^{\mu \lambda}
$$
since there are at most 2nd order time derivative on the RHS, $G^{0\nu}$ has at most 1st order time derivative. </p>
<p>But $G_{0\nu}$ is not proportional to $G^{0\nu}$ for a general metric. In fact $G_{0\nu} = G^{\mu\lambda}g_{0\mu} g_{\lambda \mu}$ contains ingredients other than $G^{0\mu}$. </p>
<p>Of course we can use $G_{\mu\nu}{}^{;\nu}=0$ to prove that there is not 2nd order $\partial^0$ in $G_{0\nu}$. But now "spatial derivative" here is a mixed derivative, $\partial^i = g^{i\mu} \partial_\mu$. Two such spatial derivative could contain 2nd order time derivative. </p>
<p>I suspect that only the $G^{0\nu}$ version is true. However a talk <a href="http://www.qgf.uni-jena.de/gk_quantenmedia/Texte/rinne090616-p-67.pdf" rel="nofollow">here</a> use $G_{0\nu}$ instead of $G^{0\nu}$ for the constraint equations, where they didn't provide a proof.</p>
<p>Now let me compute it explicitly in the explicit form, while terms containing at most 1st order time derivative will be dropped. So the sign $\sim$ really means both sides have the same term of 2nd order time derivative. </p>
<p>$$R_{0\nu} = R^{\alpha}{}_{0\alpha\nu} \sim \Gamma^{\alpha}{}_{0\nu,\alpha}-\Gamma^{\alpha}{}_{0\alpha,\nu} \sim \Gamma^{0}{}_{0\nu,0} -\Gamma^{\alpha}{}_{0\alpha,\nu}$$</p>
<p>$$R \sim \Gamma^{\alpha\beta}{}_{\alpha,\beta} - \Gamma^{\alpha\beta}{}_{\beta,\alpha} \sim \Gamma^{\alpha 0}{}_{\alpha,0} - \Gamma^{0\alpha}{}_{\alpha,0}$$
$$G_{0\nu} =\Gamma^{0}{}_{0\nu,0} -\Gamma^{\alpha}{}_{0\alpha,\nu} - \frac{1}{2}g_{0\nu}(\Gamma^{\alpha 0}{}_{\alpha,0} - \Gamma^{0\alpha}{}_{\alpha,0}) $$</p>
<p>First evaluate things in the parenthesis, namely the scalar curvature, </p>
<p>$$\Gamma^{\alpha 0}{}_{\alpha 0} = (g^{0\beta} \Gamma^{\alpha}{}_{\beta\alpha})_{,0} = (g^{0\beta} \ln(|g|^{\frac{1}{2}})_{,\beta})_{,0} \sim g^{00} \ln(|g|^{\frac{1}{2}})_{,00} $$</p>
<p>$$\Gamma^{\alpha}{}_{0\alpha} = g^{\alpha\beta} \Gamma^{0}{}_{\alpha\beta}=\frac{1}{2}g^{\alpha\beta} g^{0\mu}(g_{\mu\alpha,\beta} + g_{\mu\beta,\alpha} - g_{\alpha\beta, \mu} ) = -g^{\alpha\beta} g^{0\mu}{}_{,\beta}g_{\mu\alpha} - \frac{1}{2} g^{\alpha\beta} g^{0\mu} g_{\alpha\beta,\mu} = -g^{0\mu}{}_{,\mu} -g^{0\mu}\ln(|g|^{\frac{1}{2}})_{,\mu} \sim -g^{00}_{,0} - g^{00}\ln(|g|^{\frac{1}{2}})_{,0} $$</p>
<p>and thus,
$$R \sim 2g^{00}\ln(|g|^{\frac{1}{2}})_{,00} + g^{00}{}_{,00} $$</p>
<p>Now for Ricci tensor,
$$\Gamma^{0}{}_{0\nu} = \frac{1}{2}g^{0\mu}(g_{\mu 0, \nu} + g_{\mu \nu, 0} - g_{0\nu, \mu} )
\sim - \frac{1}{2}g^{0\mu}{}_{,0}( g_{\mu 0} \delta_{\nu 0} + g_{\mu\nu} ) -\frac{1}{2} g^{00}g_{0\nu,0} $$
$$\Gamma^{\alpha}{}_{0\alpha,\nu} \sim \delta_{0\nu} \ln(|g|^{\frac{1}{2}})_{,00}$$</p>
<p>Hence,
$$R_{0\nu} \sim - \frac{1}{2}g^{0\mu}{}_{,00}( g_{\mu 0} \delta_{\nu 0} + g_{\mu\nu} ) -\frac{1}{2} g^{00}g_{0\nu,00}
- \delta_{0\nu} \ln(|g|^{\frac{1}{2}})_{,00}
$$</p>
<p>Finally the Einstein tensor
$$G_{0\nu} \sim - \frac{1}{2}g^{0\mu}{}_{,00}( g_{\mu 0} \delta_{\nu 0} + g_{\mu\nu} ) -\frac{1}{2} g^{00}g_{0\nu,00}
- \delta_{0\nu} \ln(|g|^{\frac{1}{2}})_{,00} - g_{0\nu} g^{00}\ln(|g|^{\frac{1}{2}})_{,00} -\frac{1}{2}g_{0\nu} g^{00}{}_{,00}$$</p>
<p>Maybe there are some subtle mistakes in the calculation(please point them out), but I can't simply it any further and at along show it $\sim 0$. </p>
<p><strong>My questions</strong></p>
<ol>
<li><p>Is the "$G_{0\nu}$" version of the statement right?</p></li>
<li><p>Is it possible to prove it using the trick that similar to that of Carroll's?</p></li>
<li><p>Any mistake I made in the explicit calculation? Or any magic identity could make it $\sim 0$</p></li>
</ol> | g14934 | [
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0.0006290402379818261,
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0.052283164113759995,
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0.015354780480265617,
0.036378588527441025,
-0.011828601360321045,
... |
<p>I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at Klein-Gordon-Lagrangian) or non-covariant (e.g. KdV) ones. Also some pointers to the literature about general properties of such systems are welcome.
Thanks</p> | g14935 | [
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0.033260904252529144,
... |
<p>When performing an experiment to observe electron spin resonance, we use DPPH molecules as they contain an unpaired electron on one of the N atoms. </p>
<p>My question is, why cant free electrons be used in this experiment? What is wrong with a beam of electrons or a metal?</p>
<p>Any help would be greatly appreciated.</p> | g14936 | [
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0... |
<p>In <a href="http://motls.blogspot.de/2013/04/reframing-string-theory-in-terms-of.html?m=1" rel="nofollow">this</a> article discussing <a href="http://arxiv.org/abs/1304.0448" rel="nofollow">this</a> and related papers, it is explained among other things, how the neighborhood of an observer's worldline can be approximated by a region of Minkowsky spacetime. </p>
<p>If I understand this right (corrections of confused fluff and misunderstandings are highly welcome), a coordinate transformation which depends on the observer's current location $p_0$ in the classical backround spacetime, to a free falling local Lorentz frame is applied. In this reference frame, local coordinates ($\tau$, $\theta$, $\phi$) together with a parameter $\lambda$ (which describes the location on the observer's worldline?) can be used. As $\lambda$ deviates too mach from $\lambda(p_0)$, the local proper acceleration $\sqrt{a_{\mu}a^{\mu}}$ becames large and approaches the string scale (is this because flat Minkowsky space is only locally valid?) and stringy effects kick in.</p>
<p>The authors postulate that at these points (called the gravitational observer horizon) some microscopic degrees of freedom have to exist that give rise to the Beckenstein-Hawking entropy describing the entropy contained in spacetime beyond the gravitational observer horizon (?).</p>
<p>This is quite a long text to introduce my question, which simply is: Can these microstates be described by the <a href="http://www.physics.ohio-state.edu/~mathur/faq2.pdf" rel="nofollow">fuzzball conjecture</a> or what are they assumed to "look" like?</p> | g14937 | [
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<p>I am interested in the link between the <a href="http://en.wikipedia.org/wiki/Black%E2%80%93Scholes#The_Black.E2.80.93Scholes_equation">Black & Scholes equation</a> and quantum mechanics.</p>
<p>I start from the Black & Scholes PDE
$$
\frac{\partial C}{\partial t} = -\frac{1}{2}\sigma^2 S^2 \frac{\partial^2C}{\partial S^2} -rS\frac{\partial C}{\partial S}+rC
$$
with the boundary condition
$$C(T,S(T)) = \left(S(T)-K\right)_+.$$
Performing the change of variables $q=\ln(S)$ this equation rewrites
$$
\frac{\partial C}{\partial t} = H_{BS}C
$$
with the Black & Scholes Hamiltonian given by
$$H_{BS} = -\frac{\sigma^2}{2} \frac{\partial^2}{\partial q^2}+\left(\frac{1}{2}\sigma^2 - r\right)\frac{\partial}{\partial q} +r.$$</p>
<p>Now I compare this equation with the Schrödinger equation for the free particle of mass $m$ :
$$i\hbar \frac{d\psi(t)}{dt} = H_0\psi(t),\quad \psi(0)=\psi$$
with the Hamiltonian (in the coordinate representation) given by
$$H_0 = -\frac{\hbar^2}{2m} \frac{d^2}{dq^2}.$$</p>
<p>My problem comes from the fact that the various references I am reading for the moment explain that the two models are equivalent up to some changes of variables (namely $\hbar=1$, $m=1/\sigma^2$ and the physical time $t$ replaced by the Euclidean time $-it$). However, their justifications for the presence of the terms
$$\left(\frac{1}{2}\sigma^2 - r\right)\frac{\partial}{\partial q} +r$$
in the Hamiltonian seem very suspicious to me. One of them tells that these terms are "a (velocity-dependent) potential". Another one tells this term is not a problem since it can be easily removed is we choose a frame moving with the particle.</p>
<p>I have actually some difficulties to justify why, even with this term, we can say that the Black & Scholes system is equivalent to the one coming from the quantum free particle. I don't like this potential argument, since (for me) a potential should be a function of $q$ (so it would be ok for example for the $+r$ term) but not depending on a derivative.</p>
<p>Could you give me your thoughts on this problem? </p> | g14938 | [
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<p>A book by C. J. Ballhausen led me to believe that a quick way to check that I performed step operators properly was by observing that the "wave function should appear normalized," but I have found some issue applying this in practice and believe it is due to my misunderstanding of the underlying physics; I'm trying to understand what C.J.B. meant by that and if it applies in my case.</p>
<p>In his case he was observing two equivalent electrons. Let's say they are two equivalent $p$ electrons for the sake of example. (He was actually considering $d$ electrons and I can provide the specifics of that if it will help.) There are several unperturbed functions which can be described by symbols such as $(1^+ 0^+)$, in which case the first number means $m_l$ of the 1st 2p electron, the next symbol indicates its spin and so forth.</p>
<p>For the term $ ^1 D : M_L = 2, M_S=0: (1^+ 1^-) $ is an eigenfunction of $p^2$ configuration that is known. Using a step down operator on the angular momentum gives: $M_L=1 : (2)^{(-1/2)} [ (1^+ 0^-) - (1^- 0^+) ]$. Here I get the impression that what we observe appears normalized because squaring the coefficients gives unity. I realize one could in principle perform $\int \psi^* \psi d \tau$, but I do not suspect that is what he means.</p>
<p>Now if we apply the step operator again we get $M_L=0: (6)^{(-1/2)} [ (1^+ -1^-) - (1^- -1^+) + 2(0^+ 0^-) ]$. Here the square of the coefficients is decidedly unity. His examples given in the book also happen to go to unity; is this just coincidence or is it going to always be true? </p>
<p>My specific example is as follows, starting with a $d^3$ configuration: $$\psi(L,M_L,S,M_S)=\psi(5,5,\frac{1}{2},\frac{1}{2})=(2^+,2^-,1^+)$$</p>
<p>Applying the lowering operators gives $\sqrt{10} \psi(5,4,\frac{1}{2},\frac{1}{2}) = -\sqrt{4} (2^+,1^+,1^+) - \sqrt{4} (2^+,1^+,1^-) + \sqrt{6}(2^+,2^-,0^+)$ and the coefficients go to unity as expected. Above you will notice that the ordering in the first and third terms has changed and an odd permutation brings about a change in sign. Also notice the first term must be equal to zero by Pauli Principle. Dividing out we get,</p>
<p>$$\psi(5,4,\frac{1}{2},\frac{1}{2}) = \sqrt{3/5} (2^+,2^-,0^+) - \sqrt{2/5} (2^+,1^+,1^-)$$</p>
<p>You'll notice that the coefficients squared sum up to 1, so all appears normalized and well. Now we apply the lowering operator again to give $\sqrt{(L-M_L+1)(L+M_L)} = \sqrt{(5-4+1)(5+4)} = \sqrt{(2)(9)} = \sqrt{18}$ times the function for $M_L=3$ $^1 H$. </p>
<p>Applying to the RHS using $\sqrt{(l-m_l+1)(l+m_l)}$. We are working with $d$ orbitals, therefore $l=2$. So for the case of $m_l=2$ we get $\sqrt{(2-2+1)(2+2)}=\sqrt{4}$ and for $m_l=1$ we get $\sqrt{(2-1+1)(2+1)} = \sqrt{6}$ and finally for $m_l=0$ we get $\sqrt{(2-0+1)(2+0)}=\sqrt{(3)(2)} = \sqrt{6}$. Applying this gives</p>
<p>$$ \sqrt{18} \psi(5,3) = \sqrt{3/5} [ \sqrt{4} (1^+, 2^-, 0^+) + \sqrt{4} (2^+,1^-,0^+) + \sqrt{6} (2^+, 2^-, -1^+)] $$ <br/>
$ - \sqrt{2/5} [ \sqrt{4} (1^+,1^+,1^-) + \sqrt{6} (2^+,0^+, 1^-) + \sqrt{6} (2^+,1^+,0^-) ]$</p>
<p>Simplification results in:</p>
<p>$$ \sqrt{18} \psi(5,3) = \sqrt{12/5} (1^+, 2^-, 0^+) + \sqrt{12/5} (2^+,1^-,0^+) + \sqrt{18/5} (2^+, 2^-, -1^+)$$ <br/> $ - \sqrt{8/5}(1^+,1^+,1^-) - \sqrt{12/5} (2^+,0^+, 1^-) - \sqrt{12/5}(2^+,1^+,0^-) $ <br/></p>
<p>The fourth term cannot exist by the Pauli Principle, so we have instead,</p>
<p>$$ \sqrt{18} \psi(5,3) = \sqrt{12/5} (1^+, 2^-, 0^+) + \sqrt{12/5} (2^+,1^-,0^+)$$ <br/> $ + \sqrt{18/5} (2^+, 2^-, -1^+) - \sqrt{12/5} (2^+,0^+, 1^-) - \sqrt{12/5}(2^+,1^+,0^-) $ <br/></p>
<p>Now we need to fix the ordering of the first term and the fourth term to give,</p>
<p>$$ \sqrt{18} \psi(5,3) = -\sqrt{12/5} (2^-, 1^
+, 0^+) + \sqrt{12/5} (2^+,1^-,0^+) + \sqrt{18/5} (2^+, 2^-, -1^+)$$ <br/> $ + \sqrt{12/5} (2^+,1^-, 0^+) - \sqrt{12/5}(2^+,1^+,0-) $ <br/></p>
<p>Now we divide thru by $\sqrt{18} $ the like terms yielding,</p>
<p>$$ \psi(5,3) = -\sqrt{12/90} (2^-, 1^
+, 0^+) + \sqrt{12/90} (2^+,1^-,0^+) + \sqrt{18/90} (2^+, 2^-, -1^+)$$ <br/> $+ \sqrt{12/90} (2^+,1^-, 0^+) - \sqrt{12/90}(2^+,1^+,0^-) $ <br/></p>
<p>Our problem is that 12/90 + 12/90 +18/90 + 12/90 +12/90 =11/15, instead of 15/15. I'm sure my mistake is stupid somewhere, can somebody point out where I've gone wrong?</p> | g14939 | [
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<p>This may be a trivial question, but I cannot find a good answer to it.</p>
<p>What would happen if the size of everything in the Universe is multiplied by some constant factor at the same time, let's say everything doubles its size for instance. People double their size, houses double their size, streets, towns, Earth... up to the whole known Universe.</p>
<p>The relative proportions and distance between objects would remain... If we measure our own size with a meter, the reading would be the usual one.</p>
<p>From current theories, it this something that can or cannot happen? that can or cannot be detected?</p>
<p>Would that change our perception of constants like c, gravity, or temperature?</p>
<p>Why? (in very simple terms...)
Is there any reference, any previous study of this problem?</p>
<hr>
<p>(This part has been added/edited to improve the question)</p>
<p>From <a href="http://physics.stackexchange.com/questions/63572/if-everything-in-existence-were-increasing-in-size-at-some-rate-would-we-be-abl?rq=1">this question</a>, I went to <a href="http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Subsection8.2.6" rel="nofollow">this book</a> by <a href="http://www.lightandmatter.com/personal/" rel="nofollow">Benjamin Crowell</a>, following <a href="http://physics.stackexchange.com/users/4552/ben-crowell">Ben Crowell</a> advice. This section describe in better words my idea. Citation:</p>
<blockquote>
<p>8.2.6 Observability of expansion</p>
<p>[...]
To organize our thoughts, let's consider the following hypotheses:</p>
<ul>
<li>The distance between one galaxy and another increases at the rate
given by a(t) (assuming the galaxies are sufficiently distant from one
another that they are not gravitationally bound within the same
galactic cluster, supercluster, etc.). </li>
<li>The wavelength of a photon
increases according to a(t) as it travels cosmological distances.</li>
<li>The size of the solar system increases at this rate as well (i.e.,
gravitationally bound systems get bigger, including the earth and the
Milky Way).</li>
<li>The size of Brooklyn increases at this rate (i.e.,
electromagnetically bound systems get bigger).</li>
<li>The size of a helium
nucleus increases at this rate (i.e., systems bound by the strong
nuclear force get bigger). </li>
</ul>
<p>We can imagine that:</p>
<ul>
<li>All the above hypotheses are true.</li>
<li>[...]</li>
</ul>
</blockquote>
<p>The author then propose to look at the first claim, all hypotheses are true...</p>
<blockquote>
<p>If all five hypotheses were true, the expansion would be undetectable,
because all available meter-sticks would be expanding together.
Likewise if no sizes were increasing, there would be nothing to
detect. These two possibilities are really the same cosmology,
described in two different coordinate systems. But the Ricci and
Einstein tensors were carefully constructed so as to be intrinsic. The
fact that the expansion affects the Einstein tensor shows that it
cannot interpreted as a mere coordinate expansion. Specifically,
suppose someone tells you that the FRW metric can be made into a flat
metric by a change of coordinates. (I have come across this claim on
internet forums.) The linear structure of the tensor transformation
equations guarantees that a nonzero tensor can never be made into a
zero tensor by a change of coordinates. Since the Einstein tensor is
nonzero for an FRW metric, and zero for a flat metric, the claim is
false.</p>
</blockquote>
<p>The author says this claim is impossible, the demonstration is not understandable for me as I'm not an expert in the domain, and don't know what are FRW or Ricci and Einstein tensors.</p> | g14940 | [
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<p>In a <a href="http://en.wikipedia.org/wiki/Tug_of_war">tug-of-war</a> match today, my summer camp students were very concerned about putting the biggest people at the back of the rope. Is there any advantage to this strategy?</p> | g14941 | [
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<p>I learned yesterday that the inverse of square roots is used to calculate the vectors of surface normals in 3d graphics. It seems like such a mind-bogglingly simple idea, and it leads me to wonder if it hasn't found use elsewhere. Is there anywhere in physics where one might need to calculate the reciprocal of a number's square root?</p> | g14942 | [
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-0... |
<p>I'm trying to properly understand the meaning of entropy, and how the universe is moving from an orderly state to a chaotic one.</p>
<p>If a glass of wine (for example) only has meaning to a human, what makes a shattered spilled glass any less orderly than a full whole glass?</p>
<p>Or if a particle is observed, and it's probability wave collapses, isn't this moving from a 'chaotic' (uncertain and in many places), to an 'orderly' (certain, definite position) state?</p>
<p>Also, isn't the formation of stars, planets, galaxies etc... a move from a more chaotic state to a more orderly one? </p>
<p>Just trying to get some perspective into what the true meaning of entropy is and why it's important.</p> | g14943 | [
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0.022... |
<p>Consider an outdoors scenario, with good weather and no sensible air currents at the floor level. How turbulent or laminar is the air surrounding this environment?</p> | g14944 | [
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<p>It is known that for any smooth, orientable, compact manifold $X$ without boundary and $\alpha \in \Omega^{r}(X), \beta \in \Omega^{r-1}(X)$ it holds </p>
<p>\begin{equation}
(d\beta,\alpha)= (\beta, d^{\dagger}\alpha),
\end{equation}</p>
<p>where </p>
<p>\begin{equation}
(d\beta,\alpha) = \int_X d\beta \wedge \star \alpha
\end{equation}</p>
<p>and $d^{\dagger}$ (acting on a $r-$form) such that</p>
<p>\begin{equation}
d^{\dagger} = (-1)^{mr+m+1}\star d \star
\end{equation}</p>
<p>with $m=\dim X$ for $X$ Riemannian and with an additional $(-1)$ for Lorentzian manifolds.</p>
<p>This is actually not so hard to prove and I don't see any further assumptions required. </p>
<p>Now, suppose I have a manifold $X$ with the assumptions above (if possible!) but which admits <a href="http://www.google.com/search?as_epq=torsional+cycles" rel="nofollow">torsional cycles</a>. For instance, to the corresponding torsional cycle one can then consider a globally well-defined $r-$form $\alpha_r$ s.t. $d\alpha_r = k \beta_{r+1}$ with some integer $k$. Is it then still possible to write for example </p>
<p>\begin{equation}
(d\alpha_r, d\alpha_r) = (\alpha_r,d^{\dagger}d\alpha_r)?
\end{equation}</p>
<p>Can the existence of torsional cycles spoil this relation? Is the integration well-defined at all? I mean, I could imagine that one constructs a torus by twisting one end of a cylinder when identifying both ends. Then, intuitively, I would doubt that this surface is orientable and allows integration of forms over this manifold. </p>
<p>Unfortunately, I almost don't know anything about torsional cycles and forms. Hence, I'm sorry if my question is sloppy and not precise. This is also, why I'm asking it here in the physics section: 1. At this level, I probably can't follow a mathematician. 2. This question is related to field theory.</p>
<p>I'd be grateful for any help and hints. Thanks!</p> | g14945 | [
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<p>With my little knowledge of optics I have come across some 'known' designs such as the Double Gauss for example, is there a 'beam compressor'.</p>
<p>My requirements are to reduce an incoming parallel wavefront (source at infinity) to either an outgoing parallel beam (ie afocal), by a factor of around 100 within 10cm or coming to focus at an f-number around 4 or 5.</p>
<p>I have access to Zemax but am currently just searching in the dark worried I might be re-inventing the wheel...</p> | g14946 | [
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0.02185731939971447,
0.04198222979903221,
0.008430843241512775,
0.00... |
<p>Here's how my book explains mass defect:</p>
<blockquote>
<p><em>Particles inside the nucleus interact with each other - they feel attraction. The potential energy $U$ of such attraction is negative, because in absence of these forces we consider the potential energy to be zero. So we can write the total energy as:</em>
$$E=E_{rest}+U$$
<em>Dividing $E$ by $c^2$ we obtain the mass, and because $U<0$ the mass of the nucleus is less than the sum of individual nucleons.</em></p>
</blockquote>
<p>Now, I have problem with the $U$ term. We know that we can choose the zero level for PE arbitrarily. Thus, $E$ can't be defined well (up to constant). However, real measurements "obey" the standard convention of zero PE at infinity. So how can I solve the contradiction? (Obviously, I'm wrong, but I fail to understand why).</p>
<p>This question leads me to a more general question regarding the $E=mc^2$ relation. It follows that $m$ has no certain value when we're dealing with potential energies. Only the <strong>change</strong> in mass matters, because only the change in potential energy has physical meaning (and can be defined precisely). But mass is a quantity which we measure everyday very precisely, and there's no ambiguity in its value, despite the fact that the systems we measure include quite often some potential energy.</p> | g14947 | [
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... |
<p><img src="http://i.stack.imgur.com/xRtob.png" alt="two different spring systems"></p>
<p>Two identical springs with spring constant $k$ are connected to identical masses of mass $M$, as shown in the figures above. The ratio of the period for the springs connected in parallel (Figure 1) to the period for the springs connected in the series (Figure 2) is
$ 1/2 $</p>
<p>What would be the better way to solve this?
I have used this law $$\begin{equation} T = 2 \pi \sqrt{\frac{l}{g}} \end{equation}$$ and assumed, $2l$ for the $2^{nd}$ picture but got wrong answer. </p> | g14948 | [
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0.007212983909994364,
0.008856717497110367,
0.008455758914351463,
-0.037787094712257385,
-0.03389797732234001,
0.033131878823041916,
-0.004785454832017422,
0.02295602671802044,
0.022954672574996948,
0.... |
<p>I have an important doubt about the nature of canonical transformations in hamiltonian mechanics.</p>
<p>Suppose I have a one-degree-of-freedom lagrangian system, whose hamiltonian depends explicitly on time:</p>
<p>$$\frac{\partial{\mathcal{H}(p, q, t)}}{\partial{t}} \neq 0$$</p>
<p>so <em>in principle energy is not a conserved quantity</em>. Then I find a canonical transformation, $Q(q, t), P(p, t)$ such that the new hamiltonian, $\mathcal{H}'$ has no explicit time dependency:</p>
<p>$$\mathcal{H}' = \mathcal{H}'(Q, P)$$</p>
<p>Can I say then that <strong>indeed energy is a conserved quantity</strong>?</p>
<p>If the answer is yes, then it's a bit counter-intuitive for me, specially if it is more or less easy to find such transformations. And if the answer is no, then that makes me think that canonical transformations don't conserve the nature of the system.</p> | g14949 | [
0.04647323116660118,
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0.010752293281257153,
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0.0000791297570685856,
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0.04260656610131264,
0.0037033178377896547,
0.005689583253115416,
-0.0015619882615283132,
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0.... |
<p>I'm sorry for this lexical, probably extremely elementary, question. But what is a pseudo-rotation? I just read this term for the first time, in the beginning of the 4th chapter book of CFT by Di Francesco & al. I would say it may be an hyperbolic rotation or a rotation followed by a parity operation (with determinant equals to -1).
Couldn't find it on google, so it doesn't seem to be a standard terminology, otherwise please forgive my ignorance.</p> | g14950 | [
0.03847586736083031,
0.07203588634729385,
-0.013631110079586506,
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0.04505442827939987,
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0.083828404545784,
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-0.06644625216722488,
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0.02911381609737873,
0.03482283651828766,
-0.059199... |
<p>In 2-d, one ripple would mean the velocity of water particles move out radially forming a circular wavefront. The Navier Stokes equations say the divergence of velocity has to be zero, but this circular radiation pattern has nonzero divergence. What am I missing here, since water ripples clearly exist?</p> | g14951 | [
0.0312618725001812,
0.03235761076211929,
0.001436105347238481,
-0.07850117236375809,
0.05822817608714104,
0.06261609494686127,
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0.026829572394490242,
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0.0371992... |
<p>I have been reading about symmetries of systems' actions, e.g. the Polyakov action, and I have encountered Lorentz transformations of the form: $\Lambda^{\mu}_{\nu} X^{\nu}$. I am moderately familiar with $\Lambda$, the Lorentz matrix. If the indices are in superscript then it is the inverse of $\Lambda_{\mu \nu}$. However, what is $\Lambda^{\mu}_{\nu}$ in terms of the Lorentz matrix?</p>
<p>I have chosen mathematical physics as the tag, as I do not think any discipline of pure mathematics is appropriate based on the context. Please correct me if I am wrong.</p> | g14952 | [
-0.006122004706412554,
0.009697549045085907,
-0.013454128988087177,
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0.02251078560948372,
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0.014222193509340286,
-0.022330118343234062,
-0.07565099745988846,
0.10620247572660446,
0.0007515057804994285,
... |
<p>Consider all of sudden the sun vanishes. What would happen to planetary motion. Will it continue to move in elliptical path or move in a tangential to the orbit immediately after sun vanishes or move in elliptical orbit for some time after the vanishing of sun or any other cases?</p>
<p>If so, please explain...</p> | g4 | [
0.07408048212528229,
0.035162150859832764,
0.029891623184084892,
0.05196745693683624,
0.005841840989887714,
0.047788798809051514,
0.027046525850892067,
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0.0024506670888513327,
-0.007672655396163464,
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0.022549500688910484,
0.04347353056073189,
-0.... |
<p>Here on Earth we are blessed with being able to see some other planets, Mars & Venus etc, with the naked eye on a fairly regular basis thanks to the distance between the planets.</p>
<p>What about from Mars? What planets would be visible to the naked eye on a regular basis from Mars?</p>
<p>Earth would obviously be one of them, as we can see it, but are any other planets close enough to mars at any point to be visible?</p> | g14953 | [
-0.00944958534091711,
0.004205755423754454,
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0.016204718500375748,
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0.10711102187633514,
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0.06648977100849152,
0.027... |
<p>If you take any large nucleus and add protons to it, the electrostatic repulsion between them will make the nucleus more unstable, because the electrostatic force between them is more repulsive at a greater distance than the strong force is attractive</p>
<p>So how come if you add more neutrons, which dont have a charge and so there is no electrostatic force, the nucleus still becomes more unstable?</p>
<p>Also why arent there groups of neutrons bound together, so purely neutron nuclei (because they are neutral, im guessing they couldnt form atoms, because of the electrons needed for an atom)</p> | g14954 | [
0.0009017513948492706,
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0.0... |
<p>Is there an updated version of the cosmological triangle with recent PLANCK results included?</p>
<p><img src="http://i.stack.imgur.com/Q31Pq.png" alt=""></p> | g14955 | [
0.013085982762277126,
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0.032009776681661606,
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-0... |
<p><a href="http://www.msnbc.msn.com/id/42044156/ns/world_news-asia-pacific/" rel="nofollow">The recent news</a> says that</p>
<blockquote>
<p>Japanese authorities confirmed Saturday that radiation had leaked from a quake-hit nuclear plant after an explosion destroyed a building at the site.</p>
</blockquote>
<p>What will be the influence of the nuclear leakage?</p> | g14956 | [
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-0.03200880065560341,
0.014692670665681362,
0.004574075806885958,
0.0008214123663492501,
-0.02... |
<p>How can i derive the dynamic of a relativistic charged particle in a uniform magnetic field $B=(0,0,B)$?</p> | g14957 | [
0.04569999873638153,
0.01023206114768982,
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0.012486273422837257,
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0.04646344855427742,
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-0.007... |
<p>I know that we can calculate the maximum potential of a van de graaff generator by ( radius* electric field in which corona discharge begin to form in the surrounding gas( according to wikipedia 30 kv/cm)).
What if i covered the sphere with Mica with a dielectric strength ( according to wikipedia) 1.18 Mv/cm , will that increase the maximum potential of the sphere?
I know it will be hard to discharge the sphere in this case , but is it possible?</p> | g14958 | [
0.0343310721218586,
0.009291483089327812,
0.013294145464897156,
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0.01868574135005474,
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0.022612493485212326,
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<p>I'm trying to obtain <a href="http://en.wikipedia.org/wiki/Euler_equations_%28fluid_dynamics%29" rel="nofollow">Euler equation</a> for a perfect fluid in laminar or stationary flow. A particle fluid is submitted at volume forces and surface force. The fist, in my case, is giving only by gravity and the second by pressure. By Newton's second law I obtain:</p>
<p>$$\vec{F}_V + \vec{F}_s = m\frac{d\vec{v}}{dt}.$$</p>
<p>An element of volume force is given by
$$d\vec{F}_V = dm\vec{g}=\rho d\omega\vec{g}$$
and an element of surface force is given by
$$d\vec{F}_S = -pd\vec{S}.$$</p>
<p>Integrating I obtain</p>
<p>$$ \int_V \rho \,d\omega\vec{g} - \int_S p\,d\vec{S} = \frac{d\vec{v}}{dt}\int_V \rho\, d\omega$$.</p>
<p>Now Euler equation is written in local form as
$$\rho\vec{g} - \nabla p = \rho \frac{d\vec{v}}{dt}.$$</p>
<p>My question is this: where the gradient of $p$ comes from? I must have the following identity
$$-\int_S pd\vec{S} = -\int_V \nabla p\,d\omega.$$</p>
<p>Why the transformation from a surface integral to a volume integral is given by the gradient and not by the divergence? I'm doing something wrong in the previous calculations?</p> | g14959 | [
0.06409884989261627,
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0.09811832755804062,
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0.06675880402326584,
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-0.012071730569005013,
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0.02289024367928505,
0.023415639996528625,
0.03... |
<p>It is generally assumed that there is no limit on how many bosons are allowed to occupy the same quantum mechanical state. However, almost every boson encountered in every-day physics is not a fundamental particle (with the photon being the most prominent exception). They are instead composed of a number of fermions, which can <em>not</em> occupy the same state.</p>
<p>Is it possible for more than one of these composite bosons to be in the same state even though their constituents are not allowed to be in the same state? If the answer is "yes", how does this not contradict the more fundamental viewpoint considering fermions?</p> | g14960 | [
-0.039942603558301926,
0.053906768560409546,
0.039345722645521164,
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0.04091908410191536,
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-0.000802881782874465,... |
<p>When a wheel is rolling, not skidding, and its axle moves at velocity $\vec{v}$, then a point on the top of its circumference will move at velocity $2\vec{v}$, shown below.</p>
<p><img src="http://i.imgur.com/qLXEZ.gif" alt="Velocity wheel top and wheel axis" title="Can't embed image, sorry. Hosted on imgur."></p>
<p>I really don't understand this. I'm quite familiar with the geometry of a circle, but I don't understand how it's being applied on this case. Also:</p>
<ol>
<li>Why doesn't the relation between the velocities depend on the radius of the wheel? </li>
<li>When is this relation valid? Does it take friction into account or it doesn't matter? If it doesn't matter, why?</li>
<li>A consequence of all this is that the point in the bottom has no velocity. Why? That makes no sense to me.</li>
</ol>
<p>This is a very confusing topic to me. <a href="http://www.animations.physics.unsw.edu.au//jw/rolling.htm" rel="nofollow" title="http://www.animations.physics.unsw.edu.au//jw/rolling.htm">Here</a> is a very nice page full of pictures and animations about the physics of a wheel but I still don't get it.</p> | g14961 | [
0.03976212814450264,
0.03837013989686966,
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0.05216795206069946,
0.05951011925935745,
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0.01727229915559292,
0.03971526771783829,
-0.0032637... |
<p>I found this nice <a href="http://cadcam.eng.sunysb.edu/~purwar/MEC501/report.pdf" rel="nofollow">paper</a> about RB convection. However I am confused by what is going on page 6. In particular why we are suddenly using Helmholtz equation to find spatially periodic solutions. Aren't we working with convection, so why are we looking at it from a wave like point of view? Or maybe I'm just missing the point all together. </p>
<p>Furthermore I would like to run a quick experiment to collect data. I was planning on using a heating place, a small glass tube filled with olive oil and a thermometer. Any tips? Suggestions? </p> | g14962 | [
0.05096917599439621,
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0.017516663298010826,
0.004892248194664717,
0.04435862973332405,
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0.0744035467505455,
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-0.048889514058828354,
0.020062493160367012,
0.0753740593791008,
0.00805506482720375,
0.042302... |
<p>This is a problem (Problem 3.16) from the book Statistical Mechanics 2nd Ed. by Pathria.
In the problem I have to calculate the partition function of an ultra-relativistic 1D gas ($E_i=cp_i$) consisting in $3N$ particles moving in one dimension. I know that the partition function is given by</p>
<p>$$Q_{3N}=\frac{1}{(3N)!h^{3N}} \int e^{-\beta H(q,p)}d\omega,$$</p>
<p>where $d\omega$ denotes a volume element of the phase space. In this case</p>
<p>$$d\omega=dq_1dp_1\cdots dq_{3N}dp_{3N},$$</p>
<p>and</p>
<p>$$H(q,p)=\sum_{i=1}^{3N}cp_i.$$</p>
<p>Then, making the substitution I find that</p>
<p>$$Q_{3N}=\frac{L^{3N}}{(3N)!h^{3N}} \left[\int_{-\infty}^{+\infty} e^{-\beta c p_j}dp_j\right]^{3N}.$$</p>
<p>$L$ being the "length" of the space available. But I'm pretty sure that this integral does not converge.</p>
<p>Where am I wrong?</p> | g14963 | [
0.03890284523367882,
0.03330181911587715,
-0.02382696606218815,
-0.028088988736271858,
0.035965271294116974,
0.07184848934412003,
0.01630564220249653,
0.03112088330090046,
-0.05160905793309212,
0.03145080432295799,
-0.025765540078282356,
0.00222330866381526,
-0.05373777821660042,
0.0072120... |
<p>Currently I am planning to get masters degree. So I am thinking about a subject in which I have to get masters degree. Following are my questions to leading physicists..</p>
<ol>
<li>Which technology is the future of telecommunication? Currently electromagnetic waves only rules the world for telecommunication. But now a days there is very vast amount of research going on in quantum mechanics and particle physics. According my knowledge the quantum entanglement and delocalization is the base for teleportation and future of communication. I want from the experts to suggest for choosing the topic for masters degree. Is the quantum communication is possible in real world one day? Can it replace our way of telecommunication through electromagnetic waves?</li>
</ol>
<p>If i will do masters in electromagnetism, will i stay behind in time?</p> | g14964 | [
0.0123872309923172,
0.04138748720288277,
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0.03775499016046524,
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0.019698522984981537,
0.03149589151144028,
0.007587342523038387,
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<p>First of all, I know almost nothing about physics. I was reading Kontsevich´s paper on <a href="http://arxiv.org/abs/q-alg/9709040" rel="nofollow">Deformation quantization of Poisson manifolds</a>, however I could not figure out what´s the intuition for such operation. </p>
<p>Why there is the word "quantization" and the Planck constant in the <a href="http://en.wikipedia.org/wiki/Moyal_product" rel="nofollow">star product</a>? Where's the physics in such formal deformation of the algebra $\mathscr{A} = \mathscr{C}^{\infty}(M)$ ?</p>
<p>In fact, the unique thing that I can understand is the "deformation" part, since (if I'm not wrong) it looks like a deformation of $\mathscr{A}$ along the 2-cocycle $\{ \cdot, \cdot\}$ of the <a href="http://www.cpt.univ-mrs.fr/~coque/articles_html/grassmann/node7.html" rel="nofollow">Hochschild cochain complex</a>.</p>
<p>Another thing, that I never got: why is the deformation done only in the global sections and not in the whole sheaf $\mathscr{C}^{\infty}$?</p> | g14965 | [
0.026032263413071632,
0.009505139663815498,
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0.019213203340768814,
0.0004219183756504208,
0.07384312152862549,
0.029615607112646103,
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0.03329923003911972,
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-0.01845020242035389,
-0.017109479755163193,
0.... |
<p>I have a vehicle traveling at initial speed $100\:\mathrm{m/s}$.
Expected destination speed is also $100\:\mathrm{m/s}$.
Maximum deceleration is $3$.
Maximum acceleration is $10$.
Distance to the target is $2000\:\mathrm{m}$.
The vehicle should reach the target in 40s.</p>
<p>The vehicle should follow a linear path, decelerate($a_1$) to a certain speed($v_1$) and accelerate back($a_2$) to reach the target precisely on $40\:\mathrm{s}$.</p>
<p>Note: $v_1 > 0$, $a_1 < 3$, $a_2 < 10$.</p>
<p>How do we find $a_1$, $a_2$ and $v_1$ ??</p> | g14966 | [
0.012503064237535,
0.0087125264108181,
-0.012783745303750038,
0.07577922940254211,
0.04852599278092384,
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0.00034417680581100285,
0.033682990819215775,
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-0.01702595129609108,
-0.014572279527783394,
0.008866317570209503,
0.047165531665086746,
-0.021... |
<p>Once a quantum partition function is in path integral form, does it contain any operators?</p>
<p>I.e. The quantum partition function is $Z=tr(e^{-\beta H})$ where H is an operator, the Hamiltonian of the system.</p>
<p>But if I put this into the path integral formalism so that we have something like $Z= \int D(\bar{\gamma},\gamma) e^{-\int_0^\beta d\tau H(\bar{\gamma},\gamma)}$, is the $H(\bar{\gamma},\gamma)$ an operator?</p>
<p>Thanks!</p> | g14967 | [
0.03021017462015152,
0.0015809859614819288,
0.0014504487626254559,
-0.019848685711622238,
0.046441372483968735,
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0.011869783513247967,
0.018762487918138504,
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0.05054957792162895,
-0.04874956235289574,
-0.011034783907234669,
-0.04922894015908241,
-0.0... |
<p>I've read over the decades that a magnetic shield might protect a spacecraft from cosmic radiation. Its a fascinating idea that might only be theory or science fiction at the moment. In regards to that here is an article just in case someone isn't sure what I mean:</p>
<p><a href="http://physicsworld.com/cws/article/news/2008/nov/06/magnetic-shield-could-protect-spacecraft" rel="nofollow">http://physicsworld.com/cws/article/news/2008/nov/06/magnetic-shield-could-protect-spacecraft</a></p>
<p>The article even mentions simulations about midway into the article. Does anyone know if research has continued? </p>
<p>My big question though, is how much electrical power would be required to protect a space vessel in this way? How large would the field be in order to be useful?</p>
<p>Better yet, please use some practical objects that anyone can wrap their head around: What if you were using similar technology to protect the Apollo Command Module? Or the Discovery One from 2001 (140 meters long). </p>
<p><em>In laymans terms, how much electrical power would it take to create a magnetic shield?</em></p> | g14968 | [
0.013366149738430977,
0.09171902388334274,
0.0012851804494857788,
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0.01073580514639616,
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0.013736166059970856,
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-0.017997339367866516,
0.07291518896818161,
0.04865839704871178,
0.018111828714609146,
0.006... |
<p>Suppose a vibrating tuning fork compresses air molecules.And for this it has to do work.As compression occurs,its temperature increases.Does the energy spent by the fork go as the increased internal energy of the molecules?If so,then which energy goes as sound energy?As the process is adiabatic,does this given energy always remain inside the air particles even when it is expanded or is it used to compress another layer to make forward the disturbance-energy to our ear as sound? In a word,the main query is what happens to the energy given out by the vibrating fork:does it become sound or the heat of the compressed layer or both?</p> | g469 | [
0.03811746463179588,
0.04039962589740753,
-0.00276516773737967,
0.0052766394801437855,
0.013655065558850765,
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0.027575092390179634,
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-0.0013110832078382373,
-0.0321817509829998,
0.009224959649145603,
-0.05042433366179466,
-0.0... |
<p>I often see the expression $W = V \Delta P$ for the work of a constant volume compression where there are a fixed number of moles and the compression is caused by heating. Is this the work equation for a constant volume, isothermal process where the pressure is increased by adding moles of a gas?</p> | g14969 | [
0.02174956165254116,
0.013212035410106182,
-0.014018481597304344,
0.029800571501255035,
0.006646905560046434,
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0.012395035475492477,
-0.04722064360976219,
-0.0070543186739087105,
-0.056165240705013275,
-0.011802156455814838,
-0.011809565126895905,... |
<h2>Background</h2>
<p>In <a href="http://physics.stackexchange.com/questions/16638/is-it-only-red-green-and-blue-that-can-make-up-any-color-through-additive-mixtu">this</a> thread, I asked whether it is true that the colors red, green and blue, through additive mixture, can make up <em>any</em> color. Turns out they can't.</p>
<p>However, when reading about the trichromatic theory of color vision (see a quote from a popular textbook in psychology in the linked thread), it is stated that this is the case, and also that it was the motivation for proposing the theory in the first place. For example, this is taken from the Wikipedia entry on trichromacy:</p>
<blockquote>
<p>Trichromatic color vision is the ability of humans and some other
animals to see different colors, mediated by interactions among three
types of color-sensing cone cells. </p>
</blockquote>
<p>This concept is described in the following depiction (taken from the very same Wikipedia article) where the x-axis denotes wavelength of light, the y-axis denotes neural response, and the three curves represent three different types of cones in the eye, each with its own neural response profile to different light.</p>
<p><img src="http://i.stack.imgur.com/GhubI.png" alt="enter image description here"></p>
<p>Now, the article states:</p>
<blockquote>
<p>The trichromatic color theory began
in the 18th century, when Thomas Young proposed that color vision was
a result of three different photoreceptor cells. Hermann von Helmholtz
later expanded on Young's ideas using color-matching experiments which
showed that people with normal vision needed three wavelengths to
create the <em>normal range of colors</em> [My emphasis]. Physiological evidence for
trichromatic theory was later given by Gunnar Svaetichin (1956).</p>
</blockquote>
<p>I don't know if there is some hidden meaning embedded in the phrase "normal range of colors" but supposing that isn't the case (please inform me if so), there seems to be somewhat of a contradiction going on here. Different sources states that the fact that the trichromatic theory of color vision was proposed in the first place was because three colors were found to be able to create any color through additive mixture (if there were other reasons, I haven't heard about them); however, this statement isn't true. WTF?</p>
<h2>TL;DR</h2>
<p>On what grounds was the trichromatic color vision theory proposed in the first place? Was it based on a misconception (red, green and blue can make up any perceivable color through additive mixture) that just happened to lead to the right answer (there being three different type of cones)?</p> | g14970 | [
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0.04991856962442398,
0.02780... |
<p>The equation of motion for the density matrix of a many body isolated quantum system is the von Neumann's equation: $\dot{\rho }(t)=i[\rho (t),H]$. How about the equation of motion for the reduced density matrix of one particle, is there a general procedure to obtain it?</p> | g14971 | [
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0.03506629168987274,
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0.0... |
<p>I came across these swimming goggles with a LCD display integrated right on the goggle itself. </p>
<p><a href="http://www.psfk.com/2011/09/smart-goggles-enable-swimmers-to-track-and-record-swim-pace.html/my_pace_goggles2" rel="nofollow">http://www.psfk.com/2011/09/smart-goggles-enable-swimmers-to-track-and-record-swim-pace.html/my_pace_goggles2</a></p>
<p>Does this look possible as shown in the design? Would I need a lens over the LCD to make it easier to focus on? How thick and/or curved would that lens need to be?</p>
<p>Any advice appreciated!</p> | g14972 | [
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0.06326110661029816,
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0... |
<p>I know I should be able to piece together some basic Newtonian equations for this, but I'm not sure where to start. I want to be able to choose one planet as the center and calculate its distance from another planet over time as they both rotate the sun. </p>
<p>First I need to even find equations for the motion of the planets, then... magic?</p>
<p>Thanks for any guidance!</p> | g14973 | [
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0.03083164617419243,
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0.03125271201133728,
-0.007... |
<p>Discussing with colleagues (mostly condensed matter ones), we were astonished there is no mention about the work by Larkin in the <a href="http://www.nobelprize.org/nobel_prizes/physics/laureates/2013/advanced.html" rel="nofollow">announcement of the Nobel Prize committee</a> this year.</p>
<p>The title of the Larkin's paper -- APPLICATION OF SUPERCONDUCTIVITY THEORY METHODS TO THE PROBLEM OF THE MASSES OF ELEMENTARY PARTICLES -- sounds promising, but I have no idea about its content. It seems to be extremely difficult to find. I'm not even sure it has been translated.</p>
<p>So the question is: can anyone provide me with the original publication, some translation in some west-european language, or some extracts of the original paper by Larkin ? <a href="http://www.osti.gov/scitech/biblio/4007891" rel="nofollow">More details about this paper can be found following this link</a>.</p>
<p><em>This question does not intend to open any polemics regarding the attribution of this year Nobel prize. Larkin died in 2005 by the way.</em></p> | g14974 | [
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0.039431601762771606,
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0.0013134796172380447,
-... |
<p>Since neutrinos</p>
<ol>
<li>have a small mass and</li>
<li>are affected by gravity,</li>
</ol>
<p>wouldn't it be theoretically possible to have such a large quantity of them so close to each other, that they would form a <em>kind</em> of a stellar object, i.e. one that would keep itself from dissolving due to the large gravity.</p>
<p>If such objects were possible, how would they interact with rest of the world? Would they be invisible (dark matter?) because of neutrinos' lack of electromagnetic charge? Would this lack also make ordinary matter pass through them, or would the Pauli exclusion principle prevent this passing through due to the high density of neutrinos?</p> | g14975 | [
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0.04694841057062149,
-0.00599... |
<p>Why does mode hopping occur when the temperature of a diode is changed?</p>
<p>Why is a similar effect seen when we change the electric current?</p> | g14976 | [
0.012321814894676208,
0.008585157804191113,
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0.01152106374502182,
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0.032064296305179596,
0.04054412245750427,
0.0498217... |
<p>Before I take P-Chem I would like to understand how physicists view the same material. What Physics course(s) should I take and/or books should I read to learn the same material from a physicist's perspective? Would thermodynamics be equivalent?</p>
<p>Background: I have done the math: Calculus 1-3 and differential equations and have already taken general physics 1+2 and 2 semesters of modern physics (relativity, QM...). </p> | g14977 | [
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-0... |
<p>Why isn't pressure used as flight?</p>
<p>I've heard that 2L bottles can hold a pressure of up to 90 PSI safely. Since $F = PA$, if the nozzle of a pressure rocket is about 4 inches squared in area, that would be a thrust of 360 pounds!? Is there something wrong with my math, or why don't we just pressurize air and use it for flight?</p> | g14978 | [
0.029683412984013557,
0.02922387234866619,
0.01494040060788393,
0.06887048482894897,
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0.01588011346757412,
-0.02... |
<p>I am calculating the action of the conformal generators on fields, to be more precise on wavefunctions. For now, I'm classical. I will just paste the part of my report on this to show what I am talking about:</p>
<p>Now let us use the fact that $\Phi_a(x) = U_P(-x)\Phi_a(0) = e^{iP_\mu x^\mu}\Phi_a(0)$. We can write the action of the generators as follows:</p>
<p>\begin{align*}
G\Phi_a(x) &= Ge^{iP_\mu x^\mu}\Phi_a(0)
\\ &= e^{iP_\mu x^\mu}e^{-iP_\mu x^\mu}Ge^{iP_\mu x^\mu}\Phi_a(0)
\\ &= e^{iP_\mu x^\mu}\tilde{G}\Phi_a(0)
\end{align*}</p>
<p>where have defined $\tilde{G} = e^{-iP_\mu x^\mu}Ge^{iP_\mu x^\mu}$. We can now calculate the $\tilde{G}$ using the Hausdorff formula:</p>
<p>$e^{-A}Be^{A} = B+[B,A] + \frac{1}{2!}[[B,A],A] + \frac{1}{3!}[[[B,A],A],A] + \dots $</p>
<p>We obtain:</p>
<p>\begin{align*}
\tilde{\J}_{\mu\nu} &= e^{-ix^\rho P_\rho}\J_{\mu\nu}e^{ix^\rho P_\rho} = \J_{\mu\nu} + ix^\rho[\J_{\mu\nu}, P_\rho]
\\ &= \J_{\mu\nu} + x^\rho(\eta_{\rho\mu}P_\nu - \eta_{\rho\nu}P_\mu)
\\ &= \J_{\mu\nu} + x_\mu P_\nu - x_\nu P_\mu
\\ &= \J_{\mu\nu} - i(x_\mu \partial_\nu - x_\nu \partial_\mu)
\\ \\ \tilde{D} &= e^{-ix^\rho P_\rho}De^{ix^\rho P_\rho} = D + ix^\rho[D,P_\rho] = D - x^\rho P_\rho = D + ix^\rho\partial_\rho
\\ \\ \tilde{K}_\mu &= e^{-ix^\rho P_\rho}K_\mu e^{ix^\rho P_\rho} = K_\mu + ix^\rho[K_\mu,P_\rho] - \frac{1}{2}x^\rho x^\nu[[K_\mu,P_\rho], P_\nu]
\\ &= K_\mu - 2x^\rho(\eta_{\mu\rho}D - \mathcal{J}_{\mu\rho}) + x^\rho x^\nu(-\eta_{\mu\rho}P_\nu + (\eta_{\nu\mu}P_\rho - \eta_{\nu\rho}P_\mu))
\\ &= K_\mu - 2x_\mu D + 2x^\rho\mathcal{J}_{\mu\rho} + (2 x_\mu x^\nu P_\nu - x_\rho x^\rho P_\mu)
\\ &= K_\mu - 2x_\mu D + 2x^\rho\mathcal{J}_{\mu\rho} - i(2 x_\mu x^\nu \partial_\nu - x_\rho x^\rho \partial_\mu)
\end{align*}</p>
<p>The action of the generators are therefore given by:</p>
<p>\begin{align*}
{\J}_{\mu\nu}\Phi_a(x) &= e^{iP_\mu x^\mu}(\J_{\mu\nu} - i(x_\mu \partial_\nu - x_\nu \partial_\mu))\Phi_a(0)
\\ &= (\Sigma_{\mu\nu})_a^{\;\;b}\Phi_b(x) + i(x_\mu \partial_\nu - x_\nu \partial_\mu))\Phi_a(x)
\\ D\Phi_a(x) &= e^{iP_\mu x^\mu}(D + ix^\rho\partial_\rho)\Phi_a(0)
\\ &= D_a^{\;\;b}\Phi_b(x) - ix^\rho\partial_\rho\Phi_a(x)
\\ K_\mu &= e^{iP_\mu x^\mu}(K_\mu - 2x_\mu D + 2x^\rho\mathcal{J}_{\mu\rho} - i(2 x_\mu x^\nu \partial_\nu - x_\rho x^\rho \partial_\mu))\Phi_a(0)
\\ &= (K_\mu)_a^{\;\;b}\Phi_b(x) + 2x_\mu D_a^{\;\;b}\Phi_b(x) - 2x^\rho(\mathcal{\Sigma}_{\mu\rho})_a^{\;\;b}\Phi_b(x) - i(2 x_\mu x^\nu \partial_\nu - x_\rho x^\rho \partial_\mu)\Phi_a(x)
\end{align*}</p>
<p>As you can see, every time from the first to the second line there is a minus sign appearing precisely where there is an x. This is what happens in Salam's paper Finite component field representations of the conformal group and it has to happen in my case for it to be consistent with what I wrote before. BUT I don't understand why this change of sign appears. $e^{iP}$ and $P$ commute, so why is this happening.</p>
<p>I have been annoyed by this for a moment now. Please help me!</p> | g14979 | [
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0.008485236205160618,
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0.044357456266880035,
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0.... |
<p>I am talking here about dry friction between solid objects, for example a ruler and a table, not anything lubricated or fluid.</p>
<p>I noticed that with a ruler and a table for example, if you drag the ruler like it was a knife, it is much easier to do it than if still holding the ruler in the same position you drag it sideways (like if you are scrapping something).</p>
<p>Also I noticed that when I am washing dishes, if I leave two metal objects (ie: to flat metal areas) in contact, they don't move much, but the same objects, if I try to find deformations that make the area of contact between them smaller, then they can be easily pushed around from rest, or spun.</p>
<p>This also applies to tyre sizes (ie: for dramatic effect, dragster cars with HUGE rear tyres and tiny front tyres).</p>
<p>Also I did some experiments with a paper, ie: holding it down with a finger make it much easer to slide than if I make sure more of its area is in contact, but doing that also is a downforce on the paper, so I guess I can sum that on the normal force.</p>
<p>My best guess is that it all has to do with the normal force, but I am not sure at all... Can someone quench my curiosity here?</p> | g14980 | [
0.04456329345703125,
0.03258277475833893,
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0.027535051107406616,
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0.04897884652018547,
-0.0302790... |
<p>Since a particle in one dimension can only move in a straight line. Is it possible to have potential energy? And how would the kinetic energy and potential energy differ in higher dimensions?</p> | g14981 | [
0.04222570359706879,
0.042524319142103195,
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0.022758418694138527,
0.022476553916931152,
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-0.0033708231057971716,
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0.019775567576289177,
0.0021403662394732237,
-... |
<p>I have read a lot on Higgs bosons, yet I do not fully comprehend how they are created and how they are "flicked off" the Higgs field. I have also had trouble comprehending why a Higgs boson quickly becomes unstable and decays into more common particles.</p>
<p>How is a Higgs boson created and how and why does it quickly decay?</p> | g14982 | [
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0.03847724571824074,
0.03866179659962654,
0.025899... |
<p>According to <a href="http://en.wikipedia.org/wiki/Noether%27s_theorem" rel="nofollow">Noether's theorem</a>, every continuous symmetry (of the action) yields a conservation law.</p>
<p>In fluid, there is a local particle number conservation law, which is $$\partial{\rho}/\partial{t}+\nabla \cdot \vec{j} ~=~0,$$ where $\rho$ and $\vec{j}$ is the density and current respectively. I just wonder is there any symmetry associated with this conservation law?</p> | g14983 | [
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0.02339724265038967,
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0.025002632290124893,
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0.0... |
<p>A stationary observer very close to the horizon of a black hole is immersed in a thermal bath of temperature that diverges as the horizon is approached. $$T^{-1} = 4\pi \sqrt{2M(r-2M)}$$ The temperature observed by a stationary observer at infinity can then be obtained through the gravitational redshift formula (see <a href="http://en.wikipedia.org/wiki/Hawking_radiation#Emission_process" rel="nofollow">http://en.wikipedia.org/wiki/Hawking_radiation#Emission_process</a>) to be $$T^{-1} = 8 \pi M$$ which is what is often quoted as the temperature of a black hole.</p>
<p>As QGR points out <a href="http://physics.stackexchange.com/questions/3698/flat-space-limit-of-the-schwarzschild-metric-and-hawking-temperature">here</a> in an answer to my related question <a href="http://physics.stackexchange.com/q/3698/520">here</a>, the resulting non-zero stress-energy tensor at infinity is incompatible with the asymptotic flatness of the Schwarzschild spacetime. What exactly is going wrong here?</p> | g14984 | [
0.026337556540966034,
0.013621291145682335,
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0.013270428404211998,
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0.04295087978243828,
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-0.010880859568715096,
0.03717854246497154,
0.023503273725509644,
0.010096460580825806,
0.... |
<p>I need help with the following problem. I think I almost have it . . .</p>
<p>A parachutist bails out and freely falls a distance of $y_1$. Then the parachute opens and thereafter, the parachutist decelerates at a rate of $a_2$. She reaches the ground with a speed of $v_2$. Find her average speed for the fall. (The answer should be $18.5\ \text{m/s}$.)</p>
<p>Note: In the diagram, replace "x" with "y". :)</p>
<p><img src="http://i.stack.imgur.com/5lnSe.png" alt="http://i.imgur.com/OPTZfWI.png"></p>
<p>$
\text{Let upwards be the positive y direction.}\\
\text{Givens:}\\
y_1 = -59.7\ \text{m}\\
v_0 = 0\ \text{m/s}\\
v_2 = -3.41\ \text{m/s}\\
a_1 = -9.8\ \text{m/s$^2$}\\
a_2 = 1.60\ \text{m/s$^2$}\\
\text{Solve for $t_1$:}\\
y_1 - y_0 = \frac{1}{2}a_1t^2+v_0t\qquad\text{for}\ \ y_1 = 0; v_0 = 0; t=t_1.\\
t_1 = \pm\sqrt{\frac{2y_1}{a_1}}\\
t_1 \approx \pm 3.4905\ \text{s}.\\
\text{Plug $t_1$ into the velocity equation for $v_1$ to find $v_1$:}\\
v_1 = a_1t_1 + v_0\\
v_1 \approx -34.207.\\
\text{Plug $v_1$ into the velocity equation for $v_2$ to find $t_2$:}\\
v_2 = a_2t_2 + v_1\\
t_2 = \frac{v_2 - v_1}{a_2}\\
t_2 \approx 19.248\ \text{s}.\\
\text{Plug $t_2$ into the position equation for $y_2$ to find $y_2$.}\\
y_2 = \frac{1}{2}a_2t_2^2+v_1t_2 + x_1\\
y_2 \approx -422\ \text{m}.\\
\text{Now solve for $\lvert\overline{v}\rvert$:}\\
\lvert\overline{v}\rvert = \lvert\frac{x_2 - x_0}{t_2 - t_0}\rvert\\
\lvert\overline{v}\rvert \approx 21.9\ \text{m/s} \neq 18.5\ \text{m/s}.
$</p>
<p>My solution is incorrect. What am I doing wrong?</p> | g14985 | [
0.0471222847700119,
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0.015679629519581795,
0.04334978759288788,
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0.008272478356957436,
0.06369993090629578,
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0.0035662883892655373,
-0.036875687539577484,
-0.03587236627936363,
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0.... |
<p>In a rainbow the colors order is red then orange (made from red and yellow, thus making sense that it appears in between them) the yellow followed by green after which comes blue (again green formed from yellow and blue). The final color is purple, which is next to the blue' but not in any contact with the red.</p>
<p>The question is - is there any actual connection between the colors and there source as known to as (such as orange from yellow and red, the last two being the source) to its appearance in a rainbow? If so, why doesn't the purple follow the same logic? How is the purple seen were it is seen in a rainbow (where there is no red nearby)?</p>
<p>thx</p> | g14986 | [
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-0.0015923550818115473,
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0... |
<p>I am trying to understand the application of the operator product expansion to calculate the radially ordered product in the complex plain of $T_{zz}(z)\partial_w X^{\rho}(w)$ which should result in</p>
<p>$$
\langle R(T_{zz}(z)\partial_w X^{\rho}(w))\rangle = -l_s^2\frac{1}{(z-w)^2}\partial_w X^{\rho}(w) - l_s^2\frac{1}{(z-w)}\partial_z^2 X^{\rho}(z) + \cdots
$$</p>
<p>but embarassingly I encounter a stumbling block right at the beginning. After inserting $T_{zz}(z) \doteq \, :\eta_{\mu\nu}\partial_z X^{\mu}\partial_zX^{\nu}:$ one has </p>
<p>$$
\langle R(T_{zz}(z)\partial_w X^{\rho}(w))\rangle = R(:\eta_{\mu\nu}\partial_z X^{\mu}(z)\partial_zX^{\nu}(z):\partial_w X^{\rho}(w))
$$</p>
<p>which can obviously be further expanded to</p>
<p>$$
... = \eta_{\mu\nu}\langle \partial_z X^{\mu}(z)\partial_w X^{\rho}(w)\rangle \partial_z X^{\nu}(z)
+ \eta_{\mu\nu}\langle \partial_z X^{\nu}(z)\partial_w X^{\rho}(w)\rangle \partial_z X^{\mu}(z)
$$</p>
<p>It is exactly this last step I dont understand. If this initial stumbling block is removed, I can understand the rest of the derivation, so can somebody help me remove it?</p>
<p>To generalize a bit, it seems I do not yet properly understand how such expressions involving normal and radial (time) ordered products are generally evaluated. So if somebody could give me a more general hint about this, I would probably be able to see how the last expression in my particular example is obtained. </p> | g14987 | [
0.02263762056827545,
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-0.02297130785882473,
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0.010113763622939587,
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0.10673128068447113,
0.018995216116309166,
0.0090946601703763,
0.03738357499241829,
-0.037868015468120575,
0.003980863373726606,
-0.03804660215973854,
0.013968... |
<p>A <a href="http://www.universetoday.com/85927/australian-student-uncovers-the-universes-missing-mass/" rel="nofollow">recent article from a popular astronomy website</a> tells of discovery of missing mass (not dark matter) that has puzzled astronomers for some time. Apparently, the discovery involves enhanced electron density in filaments associated with superclusters of galaxies. How were astronomers able to determine that this baryonic mass was missing in the first place, and what percentage of total baryonic mass did it entail?</p> | g14988 | [
0.06131528317928314,
0.016078026965260506,
-0.011211858130991459,
-0.034368280321359634,
0.08911550790071487,
-0.0027840938419103622,
-0.025883642956614494,
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0.008190070278942585,
-0.04128367453813553,
0.009509412571787834,
-0.02730819396674633,
0.05102292075753212,
0.... |
<p>It might be a silly question, but I was never mathematically introduced to the topic. Is there a representation for <a href="http://en.wikipedia.org/wiki/Grassmann_number" rel="nofollow">Grassmann Variables</a> using real field. For example, gamma matrices have a representation, is it not possible for Grassmann Variables? The reason for a representation is, then probably it will be easier to derive some of the properties. </p> | g14989 | [
0.009492168202996254,
-0.010081901215016842,
-0.010798316448926926,
-0.07523807883262634,
0.039146311581134796,
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0.020567169412970543,
0.035276249051094055,
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-0.000685488514136523,
-0.01283788587898016,
-0.006761124357581139,
0.027638902887701988,
... |
<p>A person wants to throw an object from the top of a tower $9,0m$ high towards a target which is $3,5m$ far from the place where the person is launching the object. Suppose that this object is thrown horizontally.</p>
<p>What I want to find out is:</p>
<ol>
<li>What initial speed does the object need to have in order to hit the target?</li>
<li>What is the acceleration of the object one moment before it touches the ground?</li>
</ol>
<p>I suppose that the answer to the second question is simply $9,81m/s^2$, but I am not sure about it because it looks so simple :D</p>
<p>As far as the first question is concerned, I was thinking about using the formula $y_{MAX} = \frac{v_0^2 + sin^2\theta}{2g}$, with $y_{MAX}$ being $3,5m$ and $\theta$ being $45°$, but the result in this case would be extremely unrealistic ^^</p>
<p>Am I going in the right direction (in both questions)?</p> | g14990 | [
0.050465986132621765,
0.06873279809951782,
-0.009306739084422588,
0.008583232760429382,
0.031254708766937256,
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0.038553740829229355,
0.009329034015536308,
-0.0718403160572052,
0.00032325979555025697,
-0.07718639075756073,
0.06552944332361221,
0.02109544537961483,
0.01... |
<p>What observables are indicative of BCS Cooper pair condensation?</p>
<p>"Thought" experiments and "numerical" experiments are allowed.</p>
<p>This question is motivated by the question <a href="http://physics.stackexchange.com/questions/43876/has-bcs-cooper-pair-condensate-been-observed-in-experiment">Has BCS Cooper pair condensate been observed in experiment?</a> ,
and by our recent research on anyon superfluidity where anyons are emergent from a fermion system.</p> | g14991 | [
0.03231222555041313,
-0.007069144397974014,
0.02186037413775921,
-0.048013344407081604,
0.0743665024638176,
-0.04165634512901306,
-0.051242414861917496,
0.06681260466575623,
0.03522472828626633,
-0.074808269739151,
0.023470403626561165,
-0.003089433303102851,
-0.020662132650613785,
0.05017... |
<p>In my quantum mechanics class, my professor explained that the Hamiltonian along with position and momentum operators can be represented by matrices of countable dimension. This is especially usefull in harmonic oscillator problems. My professor explained that the eigenvalues of the Hamiltonian are (of course) the discrete allowed energies of the system, while the eigenvalues of the position operator are all possible positions, a continuum. How can a countable matrix have an uncountable number of eigenvalues? Why do the Hamiltonian and the position operator have the same dimension but different numbers of eigenvalues?</p> | g632 | [
0.05912674963474274,
0.029686875641345978,
-0.012618595734238625,
-0.0471888966858387,
0.0391499400138855,
0.01361677423119545,
0.059094179421663284,
0.024906082078814507,
-0.0004109904693905264,
-0.002636190038174391,
0.004006082657724619,
-0.006962323561310768,
0.012657270766794682,
0.03... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/14968/superluminal-neutrinos">Superluminal neutrinos</a> </p>
</blockquote>
<p>An article in the newspaper a few months ago said that Neutrinos travel faster than Light. Another article then said that this observation was flawed due to faults in the electrical systems. Is this true? And if not, will this lead to redefining the Cosmic Speed Limit (<em>c</em>) as proposed by Einstein?</p> | g83 | [
0.034334439784288406,
0.08797314763069153,
0.020988991484045982,
0.036094292998313904,
0.035301290452480316,
-0.0029171782080084085,
-0.011875887401401997,
0.01109697949141264,
-0.008824490010738373,
-0.03488150238990784,
0.0134322140365839,
0.0064790816977620125,
-0.0002282349596498534,
0... |
<p><strong>My question:</strong> What (physical or mathematical) reasons (not philosophical) do some physicists ('t Hooft, Penrose, Smolin,...) argue/have in order to think that Quantum Mechanics could be substituted by another theory in the future? Namely...Why should it be an effective and non-fundamental (``non-ultimate'') theory? 't Hooft has spent some years trying to "prove" that Quantum Mechanics can arise from a classical theory with information loss through some particular examples (cellular automata, beable theory,...). Penrose advocated long ago that gravity should have a role in the quantum wave function collapse (the so called objective reduction), Smolin wrote a paper titled , I believe, Can Quantum Mechanics be the approximation of another theory?. What I am asking for is WHY, if every observation and experiment is consistent (till now) with Quantum Mechanics/Quantum Field Theory, people are trying to go beyond traditional QM/QFT for mainly "philosophical?" reasons. Is it due to the collapse of wavefunctions? Is it due to the probabilistic interpretation? Maybe is it due to entanglement? The absence of quantum gravity? Giving up philosophical prejudices, I want to UNDERSTAND the reason/s behind those works...</p>
<p><strong>Remark:</strong> Currently, there is no experiment against it! Quite to the contrary, entanglement, uncertainty relationships, QFT calculations and precision measurements and lots of "quantum effects" rest into the correction of Quantum Mechanics. From a pure positivist framework is quite crazy such an opposition! </p> | g14992 | [
0.022932499647140503,
0.005292557645589113,
0.01453361101448536,
-0.005738336592912674,
0.015589233487844467,
0.023710664361715317,
-0.008952593430876732,
0.01272710133343935,
-0.012377769686281681,
-0.018805893138051033,
0.065543532371521,
-0.07395879924297333,
0.012314112856984138,
0.012... |
<p>I want to know if you could theoretically travel from your house to work via a wormhole but stay in the present day...without changing time. Kind of like teleportation but harnessing the energy of a black hole or wormhole. My background is chemistry not physics so I'd prefer a mathematical explanation. Thanks.</p> | g14993 | [
-0.035208944231271744,
0.024436770007014275,
0.014592494815587997,
0.020729364827275276,
-0.00824351143091917,
-0.050784364342689514,
0.009624687023460865,
0.03587457165122032,
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-0.00123648252338171,
-0.006004016380757093,
-0.0032830897253006697,
0.02541813626885414,
... |
<p>I am having a problem with reflection on an acrylic surface, in the IR part of the spectrum. This reflection is interfering with an algorithm that looks at objects, as it makes two show up when only one exists.</p>
<p><strong>Some background:</strong></p>
<p>An IR sensitive (and IR filtered) camera must view an IR backlit stage below at a steep angle, the walls of which are perpendicular to the IR light source, the cameras are at about 30 degrees tilted back with respect to the walls of the stage. </p>
<p>Because the walls of the stage must be translucent to visible light, they are made of acrylic (just about the same optical properties as glass). </p>
<p>A problem arises when an object comes close to the surface of the glass, as a reflection of that object appears from the acrylic. This confuses the software that uses the camera into thinking there are two objects. To get rid of this problem, a matte finish is applied to the inner surface of the wall to blur the reflection enough, and this works. However it doesn't work perfectly, and the inner surface of the wall would ideally be perfectly smooth.</p>
<p><strong>The first question is:
How can I eliminate the reflection due to the internal reflection, in the IR part of the spectrum, of my object?</strong></p>
<p><strong>Specifications:</strong></p>
<ul>
<li><p>A wall of acrylic is reflecting an object at a steep angle in the IR spectrum</p></li>
<li><p>The inner wall must be kept smooth (although could have some filter added, and then a smoothing film added over top, perhaps, if it would still elimiate the reflection)</p></li>
<li><p>The viewing angle is steep and cannot be changed</p></li>
<li><p>Visible light must be able to pass from the outside of the wall to the inside.</p></li>
</ul>
<p><strong>Proposed solution is now:</strong> </p>
<p>Using an IR filter applied to the outside wall to prevent the reflection from coming in and up to the camera as strongly, this leaves the inside smooth. Or applying a matte to the outside of the wall to blur the reflection, which also leaves the inside able to be perfectly smooth.</p>
<p><strong>A second question is: will the proposed solution work?</strong></p> | g14994 | [
0.021567007526755333,
0.009354779496788979,
0.0171193964779377,
0.017733410000801086,
-0.0025791486259549856,
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0.08493403345346451,
0.048818957060575485,
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0.017613565549254417,
0.021203195676207542,
0.08392395824193954,
-0.00359271839261055,
0.022... |
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