question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>Say that a closed system has $n$ dimensions and is in the shape of a $n$-ball with a radius of 1, it's volume will be</p>
<p>$$\frac{\pi^\frac{n}{2}}{\Gamma(\frac{n}{2}+1)}$$</p>
<p>which tends to 0 yet is not empty as n tends to infinity.</p>
<p>My question might not make any sense, and my understanding of entropy might make things even worse, but if it's sensible, what will become of the entropy of such a system?</p>
<p>If my first exposé really makes no sense, I would reformulate as follows: let's say that an unfathomable force compresses a closed system such that it's volume decreases towards zero, what will become of the entropy of such a system? (I realise it might not be the same problem/question)</p> | g12215 | [
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<p>I have a problem with understanding of these sentences:</p>
<blockquote>
<p>We have indicated in the opening paragraph of the Introduction that surface plasmon polaritons are solutions
of Maxwell’s equations in which the effects of retardation—the finiteness of the speed of light—are
taken into account. An important subclass of surface plasmon polaritons are surface plasmons. These can
be viewed as the limiting case of surface plasmon polaritons when the speed of light is allowed to become
infinitely large.</p>
<p>Nano-optics of surface plasmon polaritons (1.1.2) - Anatoly Zayats et.al.</p>
</blockquote>
<p>How can we allow c be infinite? Why is it correct in case of surface plasmons?</p>
<p>The article is available online, easy to find with Google Scholar</p> | g12216 | [
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<p>I understand that one can measure a single photon being absorbed using a photomultiplier tube or CCD.</p>
<p>Can one measure a single photon being <em>emitted</em> by monitoring the current through an LED or the recoil of an emitting ion?</p>
<p>Is it therefore possible to detect the same photon both being emitted and later being absorbed?</p>
<p>After the photon's emission has been detected, but before its absorption has been registered, is it real or virtual?</p>
<p>I assume a QED calculation would proceed on the assumption that the photon is virtual but if its emission has been measured then surely it should be treated as real?</p>
<p>Is there a paradox here?</p> | g12217 | [
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<p>Can <a href="http://en.wikipedia.org/w/index.php?title=Template%3aTheories_of_gravitation&oldid=558771017" rel="nofollow">this template at Wikipedia</a> be true? It seems to suggest that <a href="http://en.wikipedia.org/wiki/Einstein%E2%80%93Cartan_theory" rel="nofollow">Einstein-Cartan theory</a>, <a href="http://en.wikipedia.org/wiki/Gauge_theory_gravity" rel="nofollow">Gauge theory gravity</a>, <a href="http://en.wikipedia.org/wiki/Teleparallelism" rel="nofollow">Teleparalleism</a> and <a href="http://en.wikipedia.org/wiki/Euclidean_quantum_gravity" rel="nofollow">Euclidean Quantum Gravity</a> are fully compatible with observation! </p>
<p>It also suggests that <a href="http://en.wikipedia.org/wiki/Loop_quantum_gravity" rel="nofollow">Loop Quantum Gravity</a> and <a href="http://en.wikipedia.org/wiki/Superfluid_vacuum_theory" rel="nofollow">BEC Vacuum Theory</a> among others, are experimentally constrained whereas <a href="http://en.wikipedia.org/wiki/Superstring_theory" rel="nofollow">string theory</a>/<a href="http://en.wikipedia.org/wiki/M-theory" rel="nofollow">M theory</a> are disputed!</p>
<p>What I understand by "Fully compatible with observation" is that all its predictions are confirmed by experiments and it has been found to be more accurate than General Relativity. Has such evidence really been found? Or am I misinterpreting "Fully compatible with observation"? Maybe it means it has been tested only when it reduces to General Relativity? But if that where the case, shouldn't M theory/String theory also be listed under "Fully Compatible" since their predictions also go down to Classical General Relativity at the low-energy, classical limit, if all other forces (other than gravity?) are gotten rid off?</p>
<p>What I understand by "Experimentally constrained" is that it is true given certain modifications. However, as far as I know, Loop Quantum Gravity violates Lorentz symmetry and has thus been experimentally "excluded" while BEC Vacuum theory isn't even mainstream?</p>
<p>What I understand by "Developmental/Disputed" is that it is still undergoing development OR it has <strong>almost</strong> been experimentally proven wrong but it is still not settled in mainstream physics. If LQG doesn't go to the excluded section, it should at least come here? Since the violation of Lorentz symmetry has been disproven according to <a href="http://motls.blogspot.in/2004/10/objections-to-loop-quantum-gravity.html#Clash_with_special_relativity" rel="nofollow">this</a>.</p>
<p>So my question is "Is this template really reliable?".</p> | g12218 | [
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<p>Q: When does the wavefunction collapse? A: When a measurement is made. But when exactly is this? I have a question about the time at which a measurement can be considered to have occurred: what exactly constitutes a measurement?</p>
<p>Consider the following experiment: A beam of spin $½$ particles of well defined momentum,p, and pure spin state $\lvert+z\rangle$ enter a Stern gerlach loop like those in Feynman’s lectures lec5 vol3. The loop is oriented to select $\lvert+x\rangle$ and $\lvert-x\rangle$ states depending on which channel of the loop is blocked, if neither is blocked the loop passes the $\lvert+z\rangle$ unchanged. Suppose we block the $\lvert-x\rangle$ channel and measure the spin of the emerging particle; with certainty it is |+x>. We say that the wavefunction $\lvert+z\rangle$= $\lvert+x\rangle$ + $\lvert-x\rangle$ has been collapsed to $\lvert+x\rangle$ by interaction with the filter. Now remove the detector far from the loop, distance D, so that most of the flight time of a particle of mass m, to the detector $(=\frac{Dm}p)$ , occurs after passing the filter. ( we could make D so large that a light signal could not go from the filter to the detector in the time between unblocking a channel and detecting the particle spin).</p>
<p>Can we say there is a time after which the particle has passed the filter and is thus definitely in the $\lvert+x\rangle$ state but has yet to be detected?</p>
<p>What if at the last moment, just before detection, the blocked channel of the filter was opened so that when the detection takes place both channels were open? Has the wavefunction now been instantly ‘uncollapsed’ ? If so we detect $\lvert+z\rangle$ with certainty rather than $\lvert+x\rangle$. If so we cannot assign a time at which the particle interacted with the original filter apparatus because in a sense the interaction has not finished until the particle is detected and removed from further interaction. </p>
<p>Is the state of the whole apparatus which the particle may have passed through only considered at the moment at which the particle is detected and irreversibly removed from play? This seems very odd. In a sense this means the particle has no history. Only the state of the whole apparatus at the time of detection becomes important.</p>
<p>Do we in fact detect $\lvert+z\rangle$ with certainty in this experimental situation? Have I missunderstood something here?</p>
<p>Is a measurement necessarily irreversible? So if the particle just passes through the filter butis not detected then that is not a measurement?</p> | g12219 | [
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<p>"Even if a magnet is broken into atoms, each atom shall be a complete magnet. If the atom is further broken into electrons, protons, neutrons, etc. even then each particle shall behave like a complete magnet." </p> | g12220 | [
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<p>Gravitational force is mediated by graviton exchange. If I am standing outside a black hole, I can of course feel the attracting force towards the black hole. This should correspond to gravitons mediated between the matter inside the horizon and myself; but then these gravitons should cross the horizon from the inside to the outside.</p>
<p>My question is: how is this paradox precisely solved?</p>
<p>I guess a starting point for an answer is that these gravitons are off-shell, much like in QED where photons exchanged between electrons that feel each other are virtual. But still, this confuses me a bit - is there some references explaining this in detail?</p> | g215 | [
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<p>We all know that gravity decreases as we go upward, we also know that gravity decreases as we go inside the earth? I don't know why gravity decreases as we go downward or inside the Earth? Please explain? </p> | g50 | [
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<p>Your goal is to complete your 10,000-m run in less than 30.0 min. Apparently you've started too slowly because at 27.0 min, you still have 1100 m to go!
Part A You can accelerate at 0.20 m/s2. For how many seconds should you accelerate (and after this have constant velocity) in order to complete the run on time? </p> | g12221 | [
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<p>We all know that sound sensation is produced only when sound waves reach upto us. We all know that sound waves are disturbances propagating in air, Vibration is necessary for the generation of sound, but it always forces me to ponder that how was it known or deduced that vibration is necessary for any form of sound wave? Hope someone explains me this.</p> | g12222 | [
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<p>In a paper, I ran into the following definition of the zero point fluctuation of our favorite toy, the harmonic oscillator:
$$x_{ZPF} = \sqrt{\frac{\hbar}{2m\Omega}} $$
where m is its mass and $\Omega$ its natural frequency.
However, when I try to derive it with simple arguments, I think of the equality:
$$E = \frac12 \hbar\Omega=\frac12 m \Omega^2 x_{ZPF}^²$$
(using the energy eigenvalue of the $n=0$ state)
giving me:</p>
<p>$$x_{ZPF} = \sqrt{\frac{\hbar}{m\Omega}} $$
differing from the previous one by a factor $\sqrt2$. I am just puzzled, is it a matter of conventions or is there a fundamental misconception in my (too?) naive derivation? </p> | g12223 | [
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<p>We know the escape velocity from the Earth is 11.2km/s. Isn't it the velocity required to escape from earth if we go normal to the surface of earth? i.e while we derive the formula for the escape velocity from earth we never consider the slanted motion of the object. So when we launch a rocket we need to use very less value of velocity compare to escape velocity to escape from earth because rocket follows a slanted path so curvature of earth has an effect?</p>
<p>If what I said above is right, then how we can say escape velocity is 11.2 km/s?</p> | g12224 | [
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<p>I want to learn how to construct spaces of quantum states of systems.</p>
<p>As an exercize, I tried to build the space of states and to find hamiltonian spectrum of the quantum system whose Hamiltonian is the Hamiltonian of the harmonic oscillator with the quadratic term: $\hat{H}=\hat{H}_{0}+\hat{H}_{1}$, where</p>
<p>$\hat{H}_{0}=\hbar\omega\left(\hat{a}^{\dagger}\hat{a}+1/2\right)$, $\hat{H}_{1}=\dot{\imath}\gamma\left(\hat{a}^{\dagger}\right)^{2}-\dot{\imath}\gamma\left(\hat{a}\right)^{2}$; $\hat{a}$, $\hat{a}^{\dagger}$-ladder operators, $\gamma$-real parameter</p>
<p><em>For this purpose, we should define a complete set of commuting observables (CSCO)</em>.</p>
<p>As for the harmonic oscillator, we can define a "number" operator $N=\hat{a}^{\dagger}\hat{a}$.</p>
<p><em>We can prove the following statement:</em></p>
<p>Let be $a$ and $a^{\dagger}$ Hermitian conjugated operators and $\left[a,a^{\dagger}\right]=1$. Define operator $N=aa^{\dagger}$. Then we can prove that $\left[N,a^{p}\right]=-pa^{p}, \left[N,a^{\dagger p}\right]=pa^{\dagger p}$ and that <strong>the only algebraic functions of $a$ and $a^{\dagger}$, which commute with $N$, are the functions of $N$</strong>. (For example, see Messiah, Quantum Mechanics, exercises after chapter $12$)</p>
<p>Using this statement, we conclude(am i right?) that <strong>operator $N$ forms a CSCO</strong>. So, sequence of eigenvectors of operator $N$ forms the basis of the space of states. So, I've come to the conclusion that <em>the space of states of the described system is the same as the space of states of harmonic oscillator</em>.</p>
<p><strong>But</strong> operators $a$, $a^{\dagger}$ can always be determined (as i think), so this arguments will be valid, so I've come to the conclusion, that <strong>spaces of states of all systems will be the same</strong>. <strong>After that I realized that I am mistaken</strong>.</p>
<p>Would you be so kind to explain where is a mistake in the arguments above?
And can you give some references/articles/books where i can read some additional information about constructing spaces of states for different systems?</p> | g12225 | [
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<p>For a report I'm writing on Quantum Computing, I'm interested in understanding a little about this famous equation. I'm an undergraduate student of math, so I can bear some formalism in the explanation. However I'm not so stupid to think I can understand this landmark without some years of physics. I'll just be happy to be able to <em>read</em> the equation and recognize it in its various forms.</p>
<p>To be more precise, here are my questions.</p>
<p>Hyperphysics tell me that Shrodinger's equation <em>"is a wave equation in terms of the wavefunction"</em>.</p>
<ol>
<li><p>Where is the wave equation in the most general form of the equation?</p>
<p>$$\mathrm{i}\hbar\frac{\partial}{\partial t}\Psi=H\Psi$$</p>
<p>I thought wave equation should be of the type</p>
<p>$$\frac{\partial^2}{\partial^2t}u=c^2\nabla^2u$$</p>
<p>It's the difference in order of of derivation that is bugging me.</p>
<p>From Wikipedia </p>
<blockquote>
<p><em>"The equation is derived by partially differentiating the standard wave equation and substituting the relation between the momentum of the particle and the wavelength of the wave associated with the particle in De Broglie's hypothesis."</em></p>
</blockquote></li>
<li><p>Can somebody show me the passages in a simple (or better general) case?</p></li>
<li><p>I think this questions is the most difficult to answer to a newbie. What is the Hamiltonian of a state? How much, generally speaking, does the Hamiltonian have to do do with the energy of a state?</p></li>
<li><p>What assumptions did Schrödinger make about the wave function of a state, to be able to write the equation? Or what are the important things I should note in a wave function that are basilar to proof the equation? With both questions I mean, what are the passages between de Broglie (yes there are these waves) and Schrödinger (the wave function is characterized by)?</p></li>
<li><p>It's often said <em>"The equation helps finds the form of the wave function"</em> as often as <em>"The equation helps us predict the evolution of a wave function"</em> Which of the two? When one, when the other?</p></li>
</ol> | g12226 | [
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<p>I've heard an explanation for this, and my professor wasn't really able to clarify my questions, so I was hoping someone could help:</p>
<p>Suppose there is an electrostatic field $\vec{E_{net}}\ne\vec{0}$, then the electrons on/in the conductor would be free to move, and then $\vec{E}_{net}$ wouldn't be an electrostatic field. Contradiction.</p>
<p><strong>Question</strong>: It seems like we are considering the electrons as both the source and test charges, because electrostatic field means that the source charges are stationary (and the contradiction is that the electrons are moving), but this supposed $\vec{E_{net}}$ is also moving the electrons. How is this different from just having a collection of source charges? If you have a collection of stationary charges, and you're trying to find the electrostatic field, then by the argument above, any supposed electrostatic field would cause these charges to move, and so this would contradict the field being electrostatic.</p> | g12227 | [
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<p>What is the difference of work $W$ and thermal energy $Q$ in thermodynamic <a href="http://en.wikipedia.org/wiki/Stirling_cycle" rel="nofollow">Stirling-process</a> (in simple form) for ideal gas?</p>
<p>I think that you need work to preserve this process and you bring thermal energy so that temperature $T$ rises in the process.</p> | g12228 | [
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<p>Why laundry dry up also in cold/frost? When you have frost, water in the clothes should freeze, but if clothes are dry, then it should be possible that steam in the clothes does not have time to freeze.</p> | g12229 | [
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<p>I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom.</p>
<p>Taking into account Newton equations for the electron and the proton and Maxwell equations for the electromagnetic field produced by these charges one obtains a higly non-linear set of coupled equations.
In such a nonlinear system could some feedback effects between proton and electron take place so to make possible a stable dynamics (or at least a dynamics unstable on such long time scales longer that we can consider hydrogen to be stable)? In this way the system's stability already obtained through quantum mechanics could be reproduced by a full classical approach!</p>
<p>P.s.: Please, as I know of the great successes that quantum theory has had since its birth, try not to answer the question telling how quantum mechanics wonderfully solves the problem.</p>
<p>P.p.s.: I'm also aware of the fact that electron should lose energy and that this should cause it to fall on the proton in a very short time, so please try to avoid also this argument.
I asked this question to understand if the oversymplifing hypothesis', which are fundamental in solving this problem (neglect proton's motion and, as a consequence, magnetic effects) and are quiet ubiquitous in physics, wouldn't mask the potential richness that could arise from mathematical complexity.</p> | g626 | [
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<p>With the approaching <a href="https://en.wikipedia.org/wiki/Hurricane_Sandy" rel="nofollow">hurricane</a>, I am curious about what would happen if I go outside, in particular whether the wind gusts might be fast enough to blow me away. How fast would the wind have to be to blow away a person?</p> | g12230 | [
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<p><img src="http://hyperphysics.phy-astr.gsu.edu/hbase/particles/imgpar/pidec1.gif" alt="Pion Plus Decay"></p>
<p>Since the charged pions decay into two particles, a muon and a muon neutrino, seems quarks disappeared!,</p>
<p>The decay proceeds by the weak interaction $W^{+}$ and can be visualized in terms of Feynman diagrams.</p>
<p>Isn't it why Quarks are not directly
observed!?</p>
<p>I read somewhere:</p>
<blockquote>
<p>If you are consistent thinker you can go even further and question existence of quarks themselfs then you will not have a problem with fractional charge</p>
</blockquote> | g12231 | [
0.0799882635474205,
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0.026636268943548203,
0.047600265592336655,
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0.037... |
<p>I am trying to work out the steps of the proof of the expression: $$\sum_n (\mathcal{E_n}-\mathcal{E_s})|\langle n|e^{i\mathbf{q}\cdot\mathbf{r}}|s \rangle|^2 = \frac{\hbar^2q^2}{2m}$$ from Eq. (5.48) in the book <em>Principles of the Theory of Solids</em> by Ziman. In the book it is mentioned that this can be shown by expanding out: $$[[\mathcal{H},e^{i\mathbf{q}\cdot\mathbf{r}}],e^{-i\mathbf{q}\cdot\mathbf{r}}]$$ where $$\mathcal{H} = -\frac{\hbar^2}{2m}\nabla^2+\mathcal{V}(\mathbf{r})$$ with $\mathcal{V}(\mathbf{r})$ being periodic. What I did is a simple expansion: $$[[\mathcal{H},e^{i\mathbf{q}\cdot\mathbf{r}}],e^{-i\mathbf{q}\cdot\mathbf{r}}] = 2\mathcal{H}-e^{i\mathbf{q}\cdot\mathbf{r}}\mathcal{H}e^{-i\mathbf{q}\cdot\mathbf{r}}-e^{-i\mathbf{q}\cdot\mathbf{r}}\mathcal{H}e^{i\mathbf{q}\cdot\mathbf{r}}$$ Then I took the inner product with the eigenstates of the Hamiltonian $\mathcal{H}|s\rangle = E_s |s\rangle$ to get $$\langle s|[[\mathcal{H},e^{i\mathbf{q}\cdot\mathbf{r}}],e^{-i\mathbf{q}\cdot\mathbf{r}}]|s\rangle = 2E_s - \langle s|e^{i\mathbf{q}\cdot\mathbf{r}}\mathcal{H}e^{-i\mathbf{q}\cdot\mathbf{r}}|s\rangle - \langle s|e^{-i\mathbf{q}\cdot\mathbf{r}}\mathcal{H}e^{i\mathbf{q}\cdot\mathbf{r}}|s\rangle$$ Now, what's obstructing my calculation is the fact that I cannot justify the last two terms in the above expression being equal. I really need them to be equal to show the top identity (also known as the Bethe sum rule). The main obstacle is the fact that $e^{i\mathbf{q}\cdot\mathbf{r}}$ is non-Hermitian.</p>
<p>I have found this identity in many books and journal articles. But I cannot find a satisfactory proof anywhere. One such example is this article:</p>
<blockquote>
<p>Sanwu Wang. Generalization of the Thomas-Reiche-Kuhn and the Bethe sum rules. <a href="http://dx.doi.org/10.1103/PhysRevA.60.262" rel="nofollow"><em>Phys. Rev. A</em> <strong>60</strong> no. 1, pp. 262–266 (1999)</a>.</p>
</blockquote>
<p>Th result is stated in Eq. (3) and proof is given in section III. A. At the end of the proof they set $F = e^{i.\mathbf{q}.\mathbf{r}}$ to recover Eq. (3). The fact that they did not assume any form for $F$ means it must hold for <em>any</em> function. There is, however, one step that I cannot justify. In Eq. (9) how can they write: $$\langle 0|F(x)|l \rangle = \langle l|F(x)|0 \rangle$$ If I can even justify the above equality (for my case) then I'm set.</p> | g12232 | [
0.014883613213896751,
0.04757902771234512,
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0.02057277224957943,
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0.01900397427380085,
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0... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/937/how-does-gravity-escape-a-black-hole">How does gravity escape a black hole?</a> </p>
</blockquote>
<p>If nothing in the universe can travel faster than light, how come light can't escape a black hole? I mean, Einstein's relativity says nothing can travel faster than light, but yet, light can't escape a black hole. Does this mean that light really <em>isn't</em> the fastest thing? That the pull of the black hole is really <em>faster</em> than light? That Einstein was wrong, even though it's been backed up by scientific evidence? I'm very confused. If anyone would be able to answer my question, I would appreciate it: Why can't light escape a black hole if nothing can travel faster than light?</p> | g215 | [
-0.017107797786593437,
0.05799010768532753,
0.03266232833266258,
0.06712542474269867,
0.03497045114636421,
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-0.024111386388540268,
0.0324532575905323,
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0.0389365628361702,
-0.02171... |
<p>If a stone is launched upward, of which is subject to gravity and air resistance, which of the following will have a greater kinetic energy? The stone at a point on its way up, or the stone at the same point on its way down?</p>
<p>I know $KE=1/2mv^2$, and $PE=mgy$.</p>
<p>If I had to guess I would say the kinetic energy is equal up and down, but I'm not sure. Could someone explain this concept to me?</p> | g12233 | [
0.04688724875450134,
0.019862866029143333,
-0.0008927439339458942,
0.024164853617548943,
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0.04122046008706093,
0.009587668813765049,
0.016501815989613533,
0.044562146067619324,
-0.015... |
<p>{..everything that follows is in the domain of relativistic kinematics..}</p>
<p>Say a particle A collides with a particle B at rest and produces particles C and D. </p>
<p>What exactly is the definition of "threshold energy" for a reaction ? </p>
<p>Is it the energy that A should have so that so that the heavier of C and D is produced at rest? </p>
<p>Given the masses of all the particles, how does one calculate the threshold energy that A must have to cause this reaction ? </p>
<p>I intuitively feel that a threshold energy scenario would mean that C and D are moving along the same direction in which A was coming in. I think it is an unnecessary "waste" of energy for C and D to develop momentum in the two transverse directions of A's motion. But I can't prove this in general. </p>
<p>I would like to know how this situation is analyzed. </p> | g12234 | [
0.04626864194869995,
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-0.010025626048445702,
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0.01644229330122471,
-0.03222... |
<p>Are there any references that present the explicit variation of the Hilbert-Einstein action plus the Hawking-Gibbons-York boundary term, and demonstrate the cancellation of the normal derivatives of metric variations? I have tried to read the original papers by York and Gibbons&Hawking, but they are not that pedagogical to me...
Thanks to anyone who can help me!</p> | g12235 | [
0.03650316596031189,
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0.03842393308877945,
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0.023681264370679855,
0.03534746542572975,
0.009336460381746292,
0.03289397805929184,
0.022... |
<p>Is it possible to formulate classical electrodynamics (in the sense of deriving Maxwell's equations) from a least-action principle, without the use of potentials? That is, is there a lagrangian which depends only on the electric and magnetic fields and which will have Maxwell's equations as its Euler-Lagrange equations?</p> | g12236 | [
0.05529271811246872,
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0.06643442064523697,
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0.01477019488811493,
0.007035121321678162,
-0.007177622523158789,
... |
<p>As far as I see from wiki, 'consumer'-grade(non-cryogenic) thermal imaging cameras use microbolometer sensors to get integrated IR intensity over some 5-12um range. But I had an impression, that having just integrated IR intensity you can't get surface temperature precisely, especially with 0.1C precision we see on consumer cameras.</p>
<p>IR thermometers (pyrometers) for example use 2-band IR measurement, but I don't see this principle being used in thermal imaging. </p>
<p>Or there is some sort of 'know-how' matrix of IR band filters in front of the sensor?</p> | g12237 | [
0.007816431112587452,
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0.0027826556470245123,
0.0630224272608757,
0.0192963145673275,
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-0.02204255387187004,
-0.037195682525634766,
0.051937032490968704,
0.018810084089636803,
0.0... |
<p>Does electric field caused by time varying magnetic field form closed loops(electric field starts from a positive charge and ends at a negative charge)? and are they conservative or non-conservative fields?</p> | g12238 | [
0.05947224795818329,
-0.019231420010328293,
0.0014754346339032054,
0.01939224824309349,
0.06629230827093124,
0.055602896958589554,
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0.005107382778078318,
0.003351381979882717,
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0.008571282960474491,
-0.01970657706260681,
0.... |
<p>I was going to buy this add on, as I almost exclusively use my sunglasses for driving. I'm just stacking them over my normal ones now... but it's quite annoying that I almost paid the extra $$$ for this feature. Found out at the last second, luckily.</p> | g12239 | [
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0.032433394342660904,
0.026772039011120796,
0.027870886027812958,
-0.04664035886526108,
-0.0870603397488594,
... |
<p>I am trying to derive the equation for buoyancy frequency in a stratified fluid and am struggling with some of the equations. I have a limited background in fluid dynamics so I basically just need someone to break down the continuity equation for me, in terms that are easily understood.</p>
<p>From the set of notes I am looking at:</p>
<p><img src="http://i.stack.imgur.com/x3SJV.png" alt="enter image description here"></p>
<p>This is the first step of the method for deriving the equation, can anyone explain this in simplistic terms?</p> | g12240 | [
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0.014175992459058762,
-0.009073291905224323,
0... |
<p>Two concentric rings dielectrics and uniformly charged are suspended on the same floor.</p>
<p>The outer ring has a radius R and mass M,
while the other has radius r << R and mass M.</p>
<p>The outer ring that has overall charge Q,
is made to rotate around the axis passing through the center and perpendicular to the plane of the ring itself, with angular acceleration α. </p>
<p>Calculate the angular acceleration α' of thr inner ring.</p>
<hr>
<p>My solution is the following:</p>
<p>The outer ring produce a variation of magnetic flux on the inner ring equal to </p>
<pre><code>(μ * Q * π^2 * r^2 ) / ( α * R ) (*)
</code></pre>
<p>The inner ring produce a self-induced variation of magnetic flux for the law of Faraday-Lenz equal to</p>
<pre><code>(μ * Q * π^2 * r' ) / α' (**)
</code></pre>
<p>Comparing the ( * ) and ( ** ), I obtain </p>
<pre><code>α' = α * R / r
</code></pre>
<p>Is it my solution right? </p> | g12241 | [
0.057800520211458206,
0.04136405512690544,
0.010125280357897282,
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0.040879327803850174,
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0.025757940486073494,
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0.035626694560050964,
-0.03029128536581993,
0.0... |
<p>It is known that molecules at the surface are strongly attached to each other (more attraction less repulsion) than those within the bulk attraction and repulsion are balanced). This is the molecular description of the surface tension and its net direction i.e., parallel to the water surface. Briefly, considering energy (total energy cost) - the cost of excluding a surface molecule is less, than to break a molecule from bulk and evaporate it from the surface! Now, considering evaporation - the question is - why evaporation occurs towards molecules of the surface (the stronger attachment than those of the bulk) and not through molecules from the bulk (like assumed in boiling)? </p> | g12242 | [
0.025399336591362953,
-0.00012557073205243796,
0.0011106613092124462,
-0.007741284091025591,
0.013078798539936543,
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-0.05099181830883026,
0.0037748152390122414,
-0.041387856006622314,
0.020876329392194748,
... |
<p><strong>Q1:</strong> As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ dimensional general coordinates space described by the Lagrangian $L(q,\dot{q})$, where $q=(q_1,...,q_n)$ and $\dot{q}=(\dot{q_1},...,\dot{q_n})$ are general coordinates and general velocities, respectively. If the system has $SO(n)$ spatial rotation-symmetry, e.g.$\forall A\in SO(n),L(Aq^T,A\dot{q}^T)=L(q,\dot{q})$, then we can get $\frac{n(n-1)}{2}$(number of the generators of group $SO(n)$) conserved angular momentum.</p>
<p><strong>My question is as follows</strong>, now note that our spatial dimension is $n$, when $n=3\rightarrow $ number of angular momentum$(\frac{n(n-1)}{2})$$=$spatial dimension$(n)$$=$3, otherwise, number of angular momentum$\neq $spatial dimension, so why spatial dimension 3 is so special? Is there any deep reason for number 3 or it's just an accidental event? Or even does this phenomena have something to do with the fact that we "live" in a 3D world? </p>
<p><strong>Q2:</strong> In quantum mechanics(QM), a Hermitian operator $J=(J_x,J_y,J_z)$ is called an angular momentum iff $[J_x,J_y]=iJ_z,[J_y,J_z]=iJ_x,[J_z,J_x]=iJ_y$. </p>
<p><strong>And my question is as follows</strong>, in QM, we can have 1-component momentum operator $\hat{p}$ , or 2-component momentum operator$(\hat{p_x},\hat{p_y})$, and so on. But Why we have never encountered a angular momentum with only two components $J=(J_x,J_y)$? Can we define a 2-component angular momentum? Like in the <strong>CM</strong> case, again the <strong>number 3</strong> is special in <strong>QM</strong> case, why?</p>
<p>Thanks in advance.</p>
<p><strong>By the way:</strong> More questions concerning the <strong>definition of rotation groups</strong> for angular momentum can be found <a href="http://math.stackexchange.com/questions/380588/do-these-two-sets-of-matrices-form-groups">here</a> , who are interested in may have a look, thanks.</p> | g12243 | [
0.03601858764886856,
-0.014181254431605339,
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0.024781761690974236,
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0.0493791326880455,
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-0.003051368985325098,
0.010691925883293152,
0.01823366992175579,
-0.008164791390299797,
... |
<p>Suppose there are two wheels linked by some kind of apparatus with a transmission, in a vacuum. Wheel A is spinning, wheel B is not. Is it empirically possible for the transmission to transfer the energy from wheel A to wheel B such that wheel A stops spinning and wheel B spins at a speed very close to that which wheel A was originally spinning? If so, how would such a transmission look?</p>
<p>If I understand correctly, this should be a question of gear ratios and how close the gear ratio can come to infinity. Please help me understand this better. Thanks!</p> | g12244 | [
0.009583109058439732,
0.010739373974502087,
0.01701486110687256,
0.022568784654140472,
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0.04434311017394066,
-0.01956794410943985,
-0.009439361281692982,
0.008602826856076717,
-0.02... |
<p>In boiling soapy water, globs of soap coalesce as the temperature increases to boiling. Does this mean that temperature increases the gravitational pull of bodies?</p> | g12245 | [
0.006091981660574675,
0.06362704187631607,
0.003237346885725856,
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-0.038287654519081116,
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-0.003023450495675206,
0.0971420630812645,
0.... |
<p>The difference between <a href="http://physics.stackexchange.com/q/1957">a white object and a mirror</a> is mainly scattering versus reflection. If we neglect this difference and define the reflectivity by input energy minus transmitted energy minus absorbed energy, what is the material with the highest reflectivity? With material, I mean something like <a href="http://www.optocity.com/mirror-metal.htm" rel="nofollow">a single element mirror</a>, any <a href="http://en.wikipedia.org/wiki/Dielectric_mirror" rel="nofollow">multi-layer mix in a dielectric mirror</a> or any sort of white-colored surface.</p>
<p>As the reflectivity depends on the wavelength, let's assume, our input energy is distributed according to the sun's spectrum (on the earth's ground). Let's further assume, there is no polarization. With these definitions, it should be possible to define a reflection coefficient as a scalar.</p>
<p>I am interested in theoretical aspects of the problem, laboratory results/examples and home-made solutions (alumium foil, wall color, etc)</p> | g12246 | [
0.00724059296771884,
0.015781160444021225,
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0.0007812288822606206,
0.047363098710775375,
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0.0025070635601878166,
0.03609193488955498,
-0.007672368083149195,
0.004143148194998503,
0.02370932698249817,
0.06613167375326157,
0.05001959204673767,
-0.... |
<p>I have been more or less struggeling to understand an equation that is apparently used in almost all books covering crystals in any way.
Basically every book that I have found explains the following:</p>
<p>In a system with a one-component vapour at the phase boundary vapour-solid, the difference in chemical potential between the two phases is given by:</p>
<p>$\Delta\mu = \Delta\mu_v - \Delta\mu_c,$</p>
<p>where $\Delta\mu_v$ and $\Delta\mu_s$ are the deviaitions of the chemical potentials of the vapor and solid states from their equilibrium positions, both being functions of pressure only (T is being kept constant).
If those deviations are small then we can write the $\Delta$s as partial derivatives which are integrated from $P_0$ (equilibrium pressure) to $P$ (actual pressure). By treating the vapor as an ideal gas, they finally arrive at:</p>
<p>$\Delta\mu = kT\ln(\frac{P}{P_0}),$</p>
<p>which explains how the change in chemical potential leading to nucleation is affected by the deviation of the pressure from the equilibrium point.</p>
<p>This all is quite easy to understand and fine with me, but now every book says the following: In case of solution crystallization the equation may be rewritten to give:</p>
<p>$\Delta\mu = kT\ln(\frac{C}{C_0}),$</p>
<p>where $C$ and $C_0$ are the actual and equilibrium (saturated) concentrations of the solute, however, no book that I have found (and I searched through a lot) actually derives or even explains why the pressures can be swapped by concentrations in case of solutions.</p>
<p>My explanation would be that thinking of pressure being linearly dependent on the amount of particles crossing unit area in unit time in the vapor and comparing that to the concentration which gives a linear dependence on the amount of particles crossing unit area in unit time in the solution, the two equations could be the same. However, I don't know if that is correct, nor have I read this explanation anywhere but I need some proper source that can be quoted for the last equation or a derivation for the latter from first principals.
Could somebody please help me with that?</p> | g12247 | [
0.01553246658295393,
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0.023237459361553192,
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0.00648701936006546,
-0.... |
<p><img src="http://i.stack.imgur.com/jLunv.gif" alt="enter image description here"></p>
<p>Assuming $T_1$ is the force that acts on box $1$ and $T_2$ is the force that acts on box $2$.</p>
<p>Exactly what causes the Tension? Why does $T_1 = T_2$?</p>
<p>The problem is we are told to memorize that $T_1 = T_2$ for mass less ropes, but I do not understand why, especially in an Atwoods machine.</p>
<p>When I think about it, I know it has something to do with the force $m_2g$ which causes the box with mass $m_1$ to rise, and vice versa. But I cannot apply physics terminology to this, or really understand whats going on.</p> | g12248 | [
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0.04732045903801918,
-0... |
<p>I was reading my Engineering Mechanics book, and it derived some strange looking integrals I'll have to apply. I could memorize them, but I'd rather understand them - then I won't have to memorize. </p>
<p>A few words mentioning Leibniz notion, and viola - we have these relationships:</p>
<p>$$\int_{v_0}^vdv=\int_0^ta_cdt$$
$$\int_{s_0}^sds=\int_0^t(v_0+a_ct)dt$$
$$\int_{v_0}^vvdv=\int_{s_0}^sa_cds$$</p>
<p>I can manipulate them given appropriate data, but they don't really <em>mean</em> much to me. (I <em>do</em> easily understand things like $a=\frac{dv}{dt}$,however).</p>
<p>I anyone could point me to website that discuss or even just show me how to derive these, I would really appreciate it - I find it easier to understand geometric interpretations, but I would appreciate any knowledge you would be willing to share.</p> | g12249 | [
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-0.0261525921523571,
0.021420586854219437,
-0.0027791967149823904,
0.019498080015182495,
-0.00717800110578537,
-0.07940387725830078,
-0.016466651111841202,
0.03472760319709778,
-0.... |
<p>Through the photoelectric effect among many others we learn that light is actually comprised of discreet quanta of energy. That's because of the energy of the emitted electrons as well as the minimum frequency of incident light that is able to start the process. A photon of frequency (energy) less than the threshold frequency is not able to free the electron from the surface. However if the required energy to free the electron was greater than this frequency by an integral value why couldn't the electron simply absorb two photons or three photons (or any required number of photons) so as to be released? In this case even with frequencies lesser than the threshold frequency there would be photoelectric effect.</p> | g388 | [
0.004471585154533386,
0.06506571918725967,
0.004798307549208403,
0.03842126578092575,
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0.01879768632352352,
0.03379454463720322,
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-0.004815667401999235,
-0.01881268434226513,
-0.0049387384206056595,
0.04740322381258011,
0.00... |
<blockquote>
<p>The distance to the galaxy NGC3198 is found to be $15.9 MPc$ and recession velocity is $680km s^{-1}$. What value of Hubble Constant is implied? If $H_0$ is in fact $72 km s^{-1} Mpc^{-1}$, what does this imply?</p>
</blockquote>
<p><strong>Attempt</strong></p>
<p>Using $v = H_0D$, I found $H_0 = 49 km s^{-1} MPc^{-1}$.</p>
<p>Using the value of $H_0' = 72 m s^{-1} Mpc^{-1}$, $v = 1001 km s^{-1}$.</p>
<p>The solution then writes that this implies that the galaxy is moving towards us at $1001-680 = 321 km/s$.</p>
<p>How can this be? I'm confused with the application of Hubble's Law here: Galaxy moving away from us -> gives value of hubble constant, simple as that.</p>
<p>What's the deal with the expansion and all?</p> | g389 | [
0.020009208470582962,
-0.01250531617552042,
-0.003311300650238991,
0.0009546195506118238,
0.04983152076601982,
0.03736523538827896,
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0.03868062421679497,
0.004965971689671278,
-0.061537571251392365,
0.03526388108730316,
0.011903997510671616,
0.07991740852594376,
-0.01... |
<p>Energy is defined more in the mathematical sense, and tends to show true with observations in the physical world.</p>
<p>But why is energy conserved aside from "<a href="http://en.wikipedia.org/wiki/Noether%27s_theorem" rel="nofollow">Noether's theorem</a>"?</p>
<p>In a closed system that has an energy $E$, we know that system will always have this much energy, but why? </p>
<p>In the cosmological scale I heard that energy is not conserved, why? </p>
<p>Is the universe creating more energy? </p>
<p>OR</p>
<p>Is the expansion of the universe due to the energy at the beginning that caused it's creation?</p>
<p>Could anyone explain their point in layman terms? Without using difficult Mathematics, I'm not as "qualified" to understand such rigorous equations yet.</p> | g12250 | [
0.06168753281235695,
0.02499637007713318,
-0.008705404587090015,
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0.028543345630168915,
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0.05072673782706261,
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-0.03283625468611717,
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0.005846381653100252,
0... |
<p>Suppose I have a Gold Leaf Electroscope and the leaves are observed to diverge by a certain amount. Now if I send a beam of X-rays and allow it to fall upon the electroscope for a very short period of time, what exactly will happen?</p> | g12251 | [
0.08829697966575623,
0.03318864107131958,
0.01405244879424572,
-0.02226310223340988,
0.055509790778160095,
0.07379961013793945,
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0.03633103147149086,
-0.01728304848074913,
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0.05732231214642525,
0.021241653710603714,
-0.02364... |
<p>I was reviewing some analytical chemistry and stumbled upon a section that explained the imperfection of using a salt bridge. </p>
<p>It said that the using dissimilar ions is a problem because in, for example, the case of KCl the $K^+$ and $Cl^-$ have different mobility and so you get regions that are rich in $K^+$ and others rich in $Cl^-$. This means that some specific parts of solution (even though it's small) to be not electrically neutral i.e. electrically charged. So I imagine in theory at least it must be possible to somehow extract these charge-rich areas and put them into a beaker. So what is all this I've been learning about solutions having to be electrically neutral? Physics people?</p> | g12252 | [
0.0047094388864934444,
0.018679296597838402,
-0.009814542718231678,
0.02492174506187439,
0.06254135072231293,
0.004322590306401253,
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0.033547528088092804,
0.03988698497414589,
-0.006477345246821642,
0.014977259561419487,
0.05699911713600159,
-0.005891855806112289,
0.00... |
<p>I understand the concept of why the signal speed is higher than the electron drift velocity, but I can't understand the concept of joule heating. If electrons move slow then how do they produce a lot of heat when they hit the nucleus. Besides my friend once told me that the drift velocity is the net movement and electrons move fast in all directions, if that is the case why do they move like that?</p> | g12253 | [
-0.0057815685868263245,
0.052764397114515305,
-0.0017740909243002534,
0.04470966383814812,
0.10026679188013077,
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0.00018626134260557592,
0.0744977593421936,
-0.044810015708208084,
-0.03485887125134468,
0.003323064651340246,
0.04148169606924057,
0.05970066040754318,
0.... |
<p>How do you explain point 44 of the attached pdf document on surface tension? Here's the <a href="http://www.sakshieducation.com/EAMCET/QR/Physics/Jr%20Phy/12Surface%20tension%20_198-208_.pdf" rel="nofollow">link</a>.</p>
<p>How is the direction of surface tension found out?
(I know it tangential but in which direction along the tangent?)</p>
<p>Also why is surface tension for solid-air surface considered when balancing the forces on liquid? Any help will be appreciated.</p> | g12254 | [
0.07647110521793365,
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0.06558125466108322,
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... |
<p>In <a href="http://www.sciencemag.org/content/318/5851/766.abstract" rel="nofollow">"Quantum Spin Hall Insulator State in HgTe Quantum Wells"</a>, researchers observed a 2D topological insulator by sandwiching HgTe between CdTe. Is the CdTe really necessary? Would Vacuum/HgTe/Vacuum itself be a topological insulator?</p> | g12255 | [
-0.03181672841310501,
-0.00800244603306055,
0.019595598801970482,
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-0.01098442543298006,
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0.00990070030093193,
-0.01208... |
<p>Is it possible to design a physical experiment that shows that a time limited signal, such as a rectangular pulse is composed of infinite continuous sine/cosine waves?</p> | g12256 | [
0.022133024409413338,
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<p>I've seen multiple times now in MotoGP that motorcycles were leaving a curve, and because of the acceleration the front wheel is slightly leaving the ground. But at the same time they were still leaning to the inside of the curve, just following the curve to the end and then going straight again.</p>
<p>Now I understand why the can lift the front wheel. But what I don't get is why they can still finish the curve on one wheel, instead of just going straight and leaving the track. I thought the front wheel is supposed to use its traction on the surface of the ground to lead the motorcycle around the curve, but they keep going around the curve while the front wheel is in the air.</p>
<p>Which force makes the motorcycle do a curve while the front wheel is not touching the ground?</p>
<p>I'm not sure if my explanation was understandable, here are some pictures of what I mean. They still lean into the curve and follow the curve while already lifting the front wheel:</p>
<p><a href="http://50to70.com/wp-content/uploads/2012/07/jorge-lorenzo-motogp-2012-mugello-test.jpg">http://50to70.com/wp-content/uploads/2012/07/jorge-lorenzo-motogp-2012-mugello-test.jpg</a>
<a href="http://farm3.static.flickr.com/2224/2331275819_ccbe52129f.jpg">http://farm3.static.flickr.com/2224/2331275819_ccbe52129f.jpg</a></p> | g12257 | [
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0.0681070014834404,
0.03628716245293617,
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-0.05382094159722328,
0.006173285190016031,
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-0.0009702227544039488,
0.0502... |
<p>I'm just starting to come across <a href="http://en.wikipedia.org/wiki/Path_integral_formulation" rel="nofollow">path integrals</a> in quantum field theory, and want to get the right intuition for the them from the start. The amplitude for propagation from $x_a$ to $x_b$ is typically written </p>
<p>$$U(x_a,x_b)=\int\mathcal{D}x(t) e^{\frac{i}{\hbar}S[x(t)]}$$</p>
<p>where $S$ is the classical action functional. Some books I read seem to treat $\int \mathcal{D}x(t)$ as a formal sum over all paths connecting $x_a$ and $x_b$. Is this the right way to think about it?</p>
<p>I come from quite a pure maths background so I've been trying to imagine this as some kind of measure on the space of smooth curves $x(t)$. I'm having trouble visualising this though. Does anyone have an intuitive argument as to how to picture this perspective?</p>
<p>Finally, how does one go about evaluating a general path integral in practice? I know that one can get an approximation by breaking the path up into piecewise linear segments. Is this a method that's used? Presumably also one can do the formal sum, and I assume this is the origin of many infinities.</p>
<p>I'd be happy to be told that there is no 'general' method for solution, or 'right' intuition. I'd just be interested to hear a range of ideas on the subject! Many thanks in advance!</p> | g12258 | [
0.023006027564406395,
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0.018461935222148895,
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0.0025669028982520103,
0... |
<p>I hope that I am using appropriate terminology. My confusion about quantum theory (beyond my obvious unfamiliarity with its terminology) is basically twofold: </p>
<ol>
<li>I lack an adequate understanding of how the <em>mathematics</em> of quantum theory is supposed to correspond to phenomena in the physical world</li>
<li>I still have an incomplete picture in my mind of how cause and effect relationships occur at the quantum level of reality. </li>
</ol>
<p>This is why phenomena such as "entanglement" make absolutely no sense to me. So, in an attempt to come to some understanding of all of this, I would like to know that if what we conceptualize as a "field" is merely an interaction among particles (bosons and fermions in the case of quantum fields), and particles (themselves) are actually fluctuations in "fields", then which comes first in the hierarchy of cause and effect relationships, particles or "fields"? </p> | g12259 | [
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0.08061347901821136,
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0.026799039915204048,
0.025048131123185158,
0.0... |
<p>if I stretch two wires parallel to each over and in a little distance and I let through them slow moving electrons, do I measure a current in the wires? Of course the electrons don't hit the wire. Some sources where such experiments described? </p> | g12260 | [
0.04693913087248802,
0.02243194356560707,
0.010870388709008694,
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0.025187643244862556,
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-0.00026993127539753914,
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0.018311824649572372,
-0.09488159418106079,
... |
<p>In single slit diffraction, why (according to the equation for $\theta$) do successive dark spots exist at whole number intervals ($n=1,2,3, \ldots$) and not half? The correct path difference for destructive interference is $1/2$ a wavelength, so why in $\theta = n(\lambda)/(\mbox{slit width})$ do we use $n = 1,2,3,\ldots$?</p> | g12261 | [
0.02808033861219883,
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0.03216766193509102,
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-0.07783927023410797,
0.022035058587789536,
0.06271347403526306,
-0.0349760465323925,
-0.00502... |
<p>Is there a substance that doesn't reflect or absorb visible light but may reflect light from another spectrum? Is there a theoretical substance that would have these properties?</p>
<p><strong>EDIT</strong>:<br>
Sorry I wasn't quite clear with my original question. I've updated it to express more what I was thinking. Would a substance be "invisible" if it didn't reflect or absorb light? Does a real or theoretical substance like that exist? I assume we can see glass and so on because it refracts light and to a certain extent reflects it.</p> | g12262 | [
-0.006240671966224909,
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-0.016671886667609215,
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-0.028071874752640724,
0.020994916558265686,
0.053936075419187546,
0.07277173548936844,
-0.... |
<p>Can someone show me a formula in order to convert an angle from [V] to degree or rad? (i use aPotentiometer measuring steering angle)</p>
<p>Edit: Well let me exlpain it. I photo of my experiment is shown below. I apply a force to my material and measure the torsion angle with a potentiometer. For example for P=1,18 bar , θ=1,67 V. I want to convert V into degrees or rad. My only clue is that at the full extent of the piston the angle indication in V is 5,33 V –</p>
<p><img src="http://i.stack.imgur.com/tAaxq.png" alt="enter image description here"></p> | g12263 | [
0.056224726140499115,
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0.04919007793068886,
0.004854683298617601,
0.019241034984588623,
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0.003173169447109103,
0.07223513722419739,
0.009526539593935013,
0.03699449822306633,
-0.0326407253742218,
-0.067... |
<p>I am fascinated by the gyroscope, like everyboy who was so lucky as to get such a toy as a kid. But probably also grown-ups are not immune to its charm.
I am not asking for a theoretical explanation. My question is more practical:</p>
<p><strong>I am looking for a clear and simple way to determine quantitatively the reaction</strong> to a tilt to the spinning axle of a gyro.</p>
<p><a href="https://www.youtube.com/watch?v=UZlW1a63KZs" rel="nofollow">Here</a> at 0:50 we can see a concrete example.
We can guess the girl weighs G= 44/45 Kg, the wheel W = 1 Kg and the platform P_0 = 0.5 kg, her arms are (presumably) R= 40 cm long and the radius of the wheel r = 25 cm. and it is spinning roughly at 4/5 rps. If you have better extimates, please plug in your figures.</p>
<p>Can you you explain how you derive/ predict the angular velocity of the system G+P+W = P = 46 Kg when she at 0:56 tilts the wheel by 90° and then at 180° $ L_w = 1*.25^2* 4 = 0.25 $, right?</p> | g12264 | [
0.054983075708150864,
0.05318651720881462,
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0.0017653900431469083,
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0.11116687953472137,
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0.02849903330206871,
-0.01188657432794571,
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0.0016187694855034351,
0.08283617347478867,
-0.... |
<p>What is the significance of the <a href="http://www.google.com/search?as_epq=magnetic+translation+operator" rel="nofollow">magnetic translation operator</a> used in describing the <a href="http://en.wikipedia.org/wiki/Fractional_quantum_Hall_effect" rel="nofollow">Fractional Quantum hall effect</a>? I was following Anthony Leggett's lecture video in which he defines these operators and describes their commutation relation in order to find the degeneracy of the ground state. Does it have any physical importance as such or is it just a mathematical construct in order to prove a result about the degeneracy of the ground state ?</p> | g12265 | [
0.006603825371712446,
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0.060639768838882446,
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0.003958866465836763,
0.0... |
<p>My General relativity skills suck. I need a good paper that</p>
<ul>
<li>does not start with equivalence principle and pages of elevator experiments</li>
<li>derives principles mathematically, not by physical intuition</li>
<li>explicitly shows how to compute things, again not via Penrose diagrams, in fact<br>
just for completion no modern dualities or any such. Just dirty old GR</li>
<li>does not make outlandish statements without proper(mathematical) justification</li>
<li>Uses understandable English</li>
<li>Is short ( 15>pages>35 ) and concise</li>
</ul>
<p>:::::::::::::::::::</p>
<p>It should probably be an older paper with language closer to that of the intrinsic geometry school, may be closer to Tullio-Levi's absolute differential calculus, but with a slight modern improvement in the language.
It should have the spirit of Dirac, by this his sweet way of keeping it short and relevant, as in his General Relativity book, but not using his exact style.</p> | g390 | [
0.005903614219278097,
0.025436684489250183,
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0.023839637637138367,
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0.017196059226989746,
0.05207149311900139,
-0.021914219483733177,
0.06638291478157043,
-0.02... |
<p>I may be badly mixing things up here. If I am, please kindly correct me.</p>
<p>As I understand it, if the universe was too dense at the start of the big bang, it would have collapsed back in on itself. Too sparse, and it would have expanded violently leaving no galaxies. I also read that the ratio of the actual density to the critical density (Omega) leaves little room for error, if you want to have a universe that lasts. The value seems to not be able to vary more than one part in 10^62.</p>
<p>Now I've also read that a recent estimate says there are about 10^23 stars (300 sextillion). I noticed that the number of stars is far fewer than the amount of variance allowed for in Omega.</p>
<p>So my question is: If you took away one solar mass worth of matter from the early universe, would that have thrown off the balance of the expansion of the universe? Would the universe have not been here if one star was missing?</p>
<hr>
<p><strong>The TL;DR:</strong> The Acccepted Answer is "Yes, one star would make a difference. It would take even less to throw off Omega."</p>
<p>(For the benefit of others coming across this question)</p> | g12266 | [
0.03107825107872486,
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0.04959721118211746,
0.035335589200258255,
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-0.06222733110189438,
0.00551209831610322,
-0.042034223675727844,
0.01681789755821228,
0.021571... |
<p>Does any branch of physics, study the passing off of information/knowledge from one body to another ( body would obviously be living beings here, as they only can do so ). And resultant changes in the physical state of the universe because of that information. </p>
<p>For example, whatever physical state, a living being or nature exists, largely depends upon, how information has flowed to that particular point of time. Based on that information only, humans and other living beings act and behave. They react accordingly, resulting into chain of other events that ultimately decide state of non-living things in the nature.</p>
<p>A small example can be like two states of universe possible, when :</p>
<p>1) A person A tells ( informs ) B, there is a path-hole ahead. ( Thus B is careful, and does not fall)</p>
<p>2) A person A does not tell B , about the path hole. ( B falls into the path-hole).</p> | g12267 | [
0.01604846492409706,
0.0182616226375103,
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0.007208012510091066,
0.015340945683419704,
0.05718791484832764,
0.016704849898815155,
-0.01860804669559002,
0.02598421648144722,
-0.0767269879579544,
0.08499164134263992,
-0.03393588215112686,
0.024085581302642822,
0.01227702... |
<ol>
<li><p>From <a href="http://en.wikipedia.org/wiki/CPU_power_dissipation#cite_note-0" rel="nofollow">Wikipedia</a></p>
<blockquote>
<p>The power consumed by a CPU, is approximately proportional to CPU
frequency, and to the square of the CPU voltage: $$
P = C V^2 f $$ (where C is capacitance, f is frequency and V is voltage).</p>
</blockquote>
<p>I wonder how that is derived from basic circuit theory? </p>
<p>How is a CPU modeled as a circuit? Why is it modeled as a
capacitance, how about a mixture of resistance, capacitance, and
inductance?</p>
<p>Is the above formula for $P$ related to that the energy/work of a
capacitance is $$ W = \frac{C V^2}{2}? $$</p>
<p>Do we have to distinguish between AC and DC circuits here?</p></li>
<li><p>From <a href="http://easycalculation.com/physics/electromagnetism/cpu-power-consumption.php" rel="nofollow">another source</a>, the temperature of a CPU is estimated as a
constant factor $$ \text{Processor Temperature} = ( \text{C/W Value} \times \text{Overclocked
Wattage}) + \text{Case Temperature} $$ where, if I understand correctly,
$\text{Overclocked Wattage}$ is the $P$ in my first formula, and $\text{C/W
Value}$ is the constant factor multiplied to $P$.</p>
<p>I wonder why we can model the temperature as a linear function of
$P$? Specifically, why is there a <em>constant</em> factor $\text{C/W Value}$?</p></li>
<li><p>In practice, I have encountered two cases.</p>
<p>When I scale down the CPU frequency, the CPU temperature decreases. If the CPU frequency is $f$ in my first part (is it?), then the first formula explains this case well.</p>
<p>But there is another case that I cannot find explanation from the
above parts. When I am running a heavy program, if I use another program called <code>cpulimit</code> in Linux to limit the
percentage of CPU usage to for example $50\%$ for the program's
process (originally there is no limitation, i.e. CPU usage
percentage can be 100% for the program), the CPU temperature can
also go down. How will you explain this?</p>
<p>I posted my questions on <a href="http://superuser.com/questions/432377/whats-more-harmful-to-a-cpu-high-load-or-high-temperature">http://superuser.com/questions/432377/whats-more-harmful-to-a-cpu-high-load-or-high-temperature</a>, but replies (especially the one by Dennis) there don't seem convincing.</p></li>
</ol>
<p>Thanks and regards!
?</p> | g12268 | [
0.06356822699308395,
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0.01320275291800499,
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0.02508796937763691,
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-0.008396001532673836,
-0.04539749398827553,
0.050827689468860626,
0.05282997712492943,
0.0397... |
<p>How would quantum mechanics explain doppler effect?</p>
<p>And just for curiosity, is there any effect similar to doppler effect occuring at quantum level?</p> | g12269 | [
0.034024517983198166,
0.04194924235343933,
0.008835087530314922,
0.017197832465171814,
0.06977809220552444,
0.03890351951122284,
0.010485020466148853,
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-0.0025098267942667007,
-0.03185310214757919,
-0.021623466163873672,
0.016412949189543724,
0.0... |
<p>Is there an example where model building that is motivated only by Naturalness, has led to experimentally verified observations?</p>
<p>If the question is unclear, or if the reader wants more elaboration, then continue reading.</p>
<p>Naturalness is defined by 't Hooft as: "A theory with a parameter $m$ is natural if the limit where $m \rightarrow 0$ results in an enhancement of the symmetry of the theory."</p>
<p>For example, take fermions in the Standard Model, if you set their masses to zero then you restore chiral symmetry. And the log-divergent radiative corrections will vanish.</p>
<p>Now, take the Higgs boson (a scalar), if you calculate the loop correction the Higgs squared mass parameter, you'll get quadratic divergence. If you set the mass to zero, this won't help as you still have quadratic divergence. And no symmetry is restored.</p>
<p>If the scale of new physics is at the <a href="http://en.wikipedia.org/wiki/Planck_scale" rel="nofollow">Planck scale</a> or GUT scale, then you'll have to tune the mass of the Higgs by something like $10^{30}$.</p>
<p>If Supersymmetry exists, then the quadratic divergence cancels out. Also, the limit where the Higgs mass goes to zero will result in restoring SUSY. So, SUSY will give you a "natural" model. </p>
<p>However, I came across this article: <a href="http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-11911.pdf" rel="nofollow">"Is Naturalness Unnatural?"</a> by Nobel laureate Prof. Burton Richter. It addresses three things: Naturalness (which what I'm concerned about), the cosmological anthropic principle, and the landscape in string theory.</p>
<p>Concerning Naturalness, in his view, in balancing between having a natural theory with extra parameters, and having a theory with huge fine-tuning (or as he says: somethings are simply initial conditions) but fewer parameter, the latter is more important, while the former can be misleading. </p>
<p>Hence, I'm tempted to ask, are there examples in the past where naturalness considerations led to experimentally verified results?</p> | g12270 | [
0.0308328066021204,
0.026783611625432968,
0.05057322606444359,
-0.005196413490921259,
0.04676418378949165,
0.01526219118386507,
0.0032172848004847765,
0.027285298332571983,
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0.01585020311176777,
0.008598050102591515,
-0.006896494887769222,
0.026905497536063194,
0.0457... |
<p>i heard that fission activation energy of (235)U is less than of neutron separation energy of (236)U <strong>so this must the reason that (235)U is fission able</strong></p>
<p>$$E_s+(236)U\to (235)U+n$$
in this interaction $E_s$ is neutron separation energy ( energy required to separate neutron )</p>
<p><img src="http://www.files.chem.vt.edu/RVGS/ACT/notes/activation-energy.gif" alt="activation-energy"></p>
<ol>
<li><p>how to measure activation energy of fission?</p></li>
<li><p>is there any relation or equation?</p></li>
</ol> | g12271 | [
-0.04059150442481041,
0.056566014885902405,
-0.004757005721330643,
-0.022309789434075356,
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0.07069322466850281,
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-0.03256676346063614,
-0.060733597725629807,
0.0028492107521742582,
-0.004009464755654335,
... |
<p>Basically I need to get an initial vertical velocity to make the ball reach a specific height, but also I need to get a horizontal verlocity so that the ball will travel the distance. For an example lets say the distance is 100m and the max height is 50m starting at 0m. Any help is welcome appreciated.</p>
<p>Also correct me if I have the wrong tag or am in the wrong part of stack overflow...</p> | g12272 | [
0.07920347899198532,
0.044007956981658936,
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0.027669986709952354,
0.041862603276968,
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0.008779766038060188,
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0.02814558520913124,
0.06894946843385696,
-0.017... |
<p>I don't have a clear picture of what is "by definition" the multiverse appearing in the models of eternal inflation. A long time ago I heard that it is a quantum state, but in the cosmology books I have looked into (all treating the subject superficially, may I suspect it's because the object is still not clearly defined?) they define a non spatially homogeneous scalar field on it, entering in the slow-roll inflation regime in some areas, and creating a nucleation this way... So it must also be a manifold, so we can define a coordinate chart on it. Then how many dimensions is it? Because they is also this picture where it solves the landscape problem of string theory and each bubbles becomes a particular vacua of ST (but I am not sure about that neither as I have not read enough of string theory so far). Well to summarize I have a really blurry picture of this mysterious multiverse, so if someone could share his clear definition of it (assuming it exists) I would be really thankful.</p>
<p>ps: is it even a physical object? in the sense obeying itself to some physical laws (which ones?) not like Newton's universe for example? is it dynamical? </p> | g12273 | [
-0.02663821540772915,
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0.04009746015071869,
-0.016... |
<p>How can I interpret the parameter <em>temperature</em> $T$, if I'm not given the description of the system in terms of the equation of state, $E(S,V\ )$ or $S(E,V\ )$ and so on.</p>
<p>In many systems it makes sense to think of it as an "energy" itself, e.g. when the entropy is such, that $T$ basically represents the mean kinetic energy of particles. The general definition goes like
$$\frac 1 T=\small{\left(\frac{\partial S(E,V\ )}{\partial E}\right)_V}.$$</p>
<p>However, very often, especially when I'm reading about phase transitions, examples for systems with critical exponents and so on, they usually talk about the parameter $T$ and an associated critical $T_c$ without taking any specific system into accound. There is usually some abstract free energy $F$, which pops out abstract quantities. Or in the Boltzman distribution and derived quantities, often something gets activated when the value of $kT$ catches up with some system specific energy value $E_0$. And it gets more complicated when it takes QFT like form. </p>
<p>What <em>is</em> the temperature in a general setting. </p>
<p>How do I read this kind of things and what should I have in mind when reading these kinds of texts? </p> | g12274 | [
0.03380953520536423,
-0.024959467351436615,
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0.026990335434675217,
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0.0032022257801145315,
0.046087685972452164,
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0.02886880189180374,
0.018946846947073936,
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0.07790717482566833,
-... |
<p>Imagine that one could theoretically trap a single electron in a small box, with walls that somehow prevent the electron from passing through and out of the box. Now, the box begins to move in on itself, gradually cornering and trapping the electron. The box continues trapping the electron until it perfectly encases it, disallowing the electron to move anywhere. I know that this scenario is seemingly impossible, but intriguing to think about. It has raised two questions in my mind:</p>
<ol>
<li><p>Would we then be able to know with exact certainty the electrons velocity and location, thereby negating the Uncertainty Principle?</p></li>
<li><p>What would happen if the box kept on caving in even after perfectly encasing the electron? Could you actually crush an electron?</p></li>
</ol> | g12275 | [
0.014293179847300053,
0.07218707352876663,
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0.02557893842458725,
0.04073966667056084,
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0.028615320101380348,
0.006000623572617769,
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<p>If we consider a charged black hole in AdS spacetime, we can either do thermodynamics in the grand canonical or the canonical ensemble. In the former, we fix the electrostatic potential $\Phi=A_t(r=\infty)$ at the boundary of the bulk such that $\left<Q\right>=-\frac{1}{\beta}\left(\frac{\partial S}{\partial\beta}\right)_{\beta}$, where $S$ is the Euclidean action. In the latter, we fix the charge $Q$ of the black hole and we do not consider $\Phi$ at all. The phase diagram of the black hole is highly dependent on the choice of ensemble, see for example <a href="http://arxiv.org/abs/hep-th/9902170" rel="nofollow">this paper by Chamblin, Emparan, Johnson and Myers</a>. One could therefore expect that this choice also has an influence on the CFT side.</p>
<p>In the AdS/CFT dictionary, the charged black hole gives a global $U(1)$ symmetry on the CFT side. Here $\Phi$ in the bulk corresponds to a chemical potential $\mu$ on the CFT, so that we usually consider the grand canonical ensemble when using the correspondence.</p>
<p>My questions are as follows:</p>
<ul>
<li>Do we ever consider the <em>canonical</em> ensemble in AdS/CFT? </li>
<li>If so, what would $Q$ determine on the CFT side (in the same way $\Phi$ determines $\mu$)? </li>
<li>If we work in the grand canonical ensemble, does $\left<Q\right>$ play any role on the CFT side, or do we only need $\Phi$?</li>
</ul>
<p>EDIT: For my last question: I just looked into holographic superconductors and it seems that from $\Phi$ one can derive both the chemical potential and the charge density of the CFT. The charge density seems to coincide with $\left<Q\right>$ in this case (up to some constant factors), but we don't need $Q$ to calculate it as we can derive it from an asymptotic expansion of $\Phi$. Specifically see page 8 of <a href="http://arxiv.org/pdf/1002.1722v2.pdf" rel="nofollow">this paper by Horowitz</a>. I don't think this answers my first 2 questions though.</p> | g12276 | [
0.00788327306509018,
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0.06663869321346283,
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0.010016589425504208,
0.021781565621495247,
0.05247391015291214,
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0.01... |
<blockquote>
<p>"..." First, we will familiarize us with a collision between a homogeneous beam of length,
$L$, mass $M$ attached with a frictionless hinge in point $O$ at one of the endpoints of
the beam. The moment of inertia of the beam for rotations around the point $O$ in the
direction given by the hinge is $I$. The beam is macroscopic and affected by gravity.
The acceleration of gravity is $g$ in the negative $y$-direction. Initially, the beam hangs
straight down in the negative $y$-direction, as illustrated in figure 0.12. A small bullet
of mass $m$ is fired along the $x$-axis, hitting the beam at the bottom. The bullet has
an initial velocity $v_0$ and remains lodged in the beam after the collision.</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/o9P7V.png" alt="enter image description here"></p>
<p><strong>One of the exercises is:</strong> Show that the linear momentum of the system is generally not conserved during the collision. In what special case would the linear momentum of the system be conserved?</p>
<p>As $\vec{G}$ is the only external force acting on the system, and it is perpendicular to both the linear velocity $v$ and the angular velocity $\omega$ during the collision, $\vec{G}$ surely does no work.</p>
<p>I'm able to show that $p_o \neq p_1$:
$$ m v_0 = (M + m) \omega r$$
$r = \frac{(1/2M+m)L}{M + m}$ , $\omega = \frac{mv_0 - constant*(1-\cos{\theta_2})}{(1/3M+m)L}$ found in earlier exercises
$$ \Rightarrow m v_0 \neq \frac{2}{3}m v_0$$</p> | g12277 | [
0.08755216747522354,
-0.0017971587367355824,
0.020003683865070343,
0.03697714954614639,
0.02101277932524681,
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0.017684727907180786,
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0.00527168158441782,
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-0.003309916704893112,
-0.0346616767346859,
-0.0... |
<p>On studying quantum states of the hydrogen atom, I came with a question: what is the precise definition of a <a href="http://en.wikipedia.org/wiki/Quantum_state" rel="nofollow">quantum state</a>? Particularly, when solving the Schroedinger eq for the H using separation of variables, the quantum numbers and wavefunctions for the states are clear. However, mathematically speaking, any combination (linear) of wavefuntions is still a solution for the H atom; is this solution a state? Moreover, what are the quantum numbeers of this solution? It blows my mind, since this solution has 6 quantum numbers, instead of 3.</p>
<p>More generally, my question is: is there a precise definition of state of system?</p> | g12278 | [
-0.017595048993825912,
0.018857121467590332,
-0.013718941248953342,
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0.01023145206272602,
0.041833922266960144,
0.026684686541557312,
-0.036525823175907135,
-0.028844118118286133,
-0.03347551077604294,
-0.0032386898528784513,
... |
<p>I have tried to understand paragraph 10.7 (Kallen-Lehmann Representation) in Weinberg's Quantum theory of fields (vol.1). He calculated matrix element </p>
<p>$$\langle0|\Phi(0)|p\rangle =(2\pi)^{-3/2}\left(2\sqrt{p^{2}+m^{2}}\right)^{-1/2}N.\tag{formula 10.7.19}$$</p>
<p>$N$ is constant. I can't understand how it was obtained. I don't even undestand why it depends on $p$. If we consider the Lorenz invariance of vacuum and operator $\Phi(0)$: </p>
<p>$$U_{\Lambda}|0\rangle=|0\rangle\ \ \text{ and } \ \ U_{\Lambda}\Phi(0)U_{\Lambda}^{-1}=\Phi(0)$$ </p>
<p>then we have:</p>
<p>$$\langle0|\Phi(0)|p\rangle=\langle0|U_{\Lambda}^{\dagger}\Phi(0)|p\rangle=\langle0|U_{\Lambda}^{-1}\Phi(0)|p\rangle=\langle0|\Phi(0)U_{\Lambda}^{-1}|p\rangle=\langle0|\Phi(0)|U_{\Lambda}^{-1}p\rangle,$$</p>
<p>so </p>
<p>$$\langle0|\Phi(0)(p)=\langle0|\Phi(0)(U_{\Lambda}^{-1}p).$$ </p>
<p>So my first guess was that this matrix element does not depend on $p$ and equals to constant. </p>
<p>Can you help me?</p> | g12279 | [
0.005321567878127098,
-0.007153474260121584,
-0.014349366538226604,
0.025563903152942657,
0.04293118044734001,
0.01880914717912674,
0.03168144449591637,
0.03130044788122177,
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0.023282548412680626,
-0.08427637815475464,
0.0440935418009758,
-0.0614452101290226,
0.03110... |
<p>For ordinary spontaneously broken symmetries, you can demonstrate relations between S-matrix elements with a soft <a href="http://en.wikipedia.org/wiki/Goldstone_boson" rel="nofollow">goldstone</a> emission and another S-matrix element without the emission. </p>
<p>If I break SUSY I get <a href="http://en.wikipedia.org/wiki/Goldstone_boson#Nambu.E2.80.93Goldstone_fermions" rel="nofollow">Nambu-Goldstone fermions</a>. Does there exist a relation between matrix elements with a soft goldstino emission and a matrix element without the emission? Basically, what is the complication because the soft particle is a fermion? References are also useful.</p> | g12280 | [
-0.0013502903748303652,
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0.024860166013240814,
-0.030845969915390015,
-0.051823776215314865,
0.03279069811105728,
-0.01107262633740902,
0... |
<p>I came upon this while studying S.H.M.</p>
<p>Well,is there a difference between writing</p>
<p>$$a=\frac{dv}{dt}\;$$</p>
<p>and $$a=v\frac{dv}{dx}\;$$
do they differ on the basis of one being a vector and the other being a scalar equation?Please explain.</p> | g12281 | [
0.05134442076086998,
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0.040272057056427,
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0.04311266168951988,
0.0069063142873346806,
-0.05328533425927162,
-0.04747956618666649,
-0.0216886717826128,
0.025206636637449265,
0.042131926864385605,
0.0052589... |
<p>are sub-atomic particles really particles or mere concepts in our minds? do they exist independently of human thought?</p>
<blockquote>
<p>In the tenth century, Ibn al-Haytham initiated the view that light
proceeds from a source, enters the eye, and is perceived. This picture
is incorrect but is still what most people think occurs, including,
unless pressed, most physicists. To come to terms with the Universe,
we must abandon such views. The world is quantum mechanical: we must
learn to perceive it as such. One benefit of switching humanity to a
correct perception of the world is the resulting joy of discovering
the mental nature of the Universe. We have no idea what this mental
nature implies, but — the great thing is — it is true. Beyond the
acquisition of this perception, physics can no longer help. You may
descend into solipsism, expand to deism, or something else if you can
justify it — just don’t ask physics for help. There is another benefit
of seeing the world as quantum mechanical: someone who has learned to
accept that nothing exists but observations is far ahead of peers who
stumble through physics hoping to find out ‘what things are’. If we
can ‘pull a Galileo,’ and get people believing the truth, they will
find physics a breeze. The Universe is immaterial — mental and
spiritual. Live, and enjoy.</p>
</blockquote>
<p>■ Richard Conn Henry is a Professor in the Henry A. Rowland Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA</p> | g12282 | [
0.007252088747918606,
0.054111383855342865,
0.013860471546649933,
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0.038005486130714417,
0.03783330321311951,
0.04171450436115265,
-0.03316449373960495,
0.038255974650382996,
-0.01544165052473545,
0.08149796724319458,
0.04216674715280533,
0.0090516097843647,
-0.0211032... |
<p>So I'm hoping I can get some help. I have a 2d image and need to get the 1d power spectrum. I know the basic steps: take fft, take fft^2 to get power, then take average power in radial bins to get 1d power- but it's in the details that I'm unsure.</p>
<p>The image has been smoothed/convolved with a Gaussian beam. I have also applied a taper in the image plane that serves the purpose of keeping the noise constant across the image and makes it so that the edges fall to zero. </p>
<p>So my issues/concerns are:</p>
<p>1) correcting for the beam smoothing. I know I need to correct for this and that can be done by dividing P_image by P_beam, but do I do the division with the 2d power spectras or the 1d? And should there be any kind of normalization?? Like sum(P_beam)=1 or something?? Just doing the division does not conserve the amplitude of P_image and in not sure if that's ok or if I should do something like P_corrected/sum(P_corrected)*sum(P_image) ??</p>
<p>2) correcting for the taper. I'm not sure how to do this as the taper was applied as multiplication in the image plane which is convolution in Fourier, so how would I deconvolve from the power? Or do I need to? </p>
<p>And once all corrections are done (or even if none were needed) do people apply any normalizations to the power spectrum, as I am interested not just in the shape of the curve but the amplitude as well?</p> | g12283 | [
0.03368539363145828,
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-0.004179489798843861,
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0.006067069713026285,
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0.03445950150489807,
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-0.02910170890390873,
0.03922789916396141,
0.061899635940790176,
0.04161405190825462,
0.08755... |
<p>What is your opinion of the hawking radiation mechanism, does that actually lower the entropy of the black hole?</p> | g12284 | [
-0.006004155147820711,
0.016767801716923714,
0.029394539073109627,
-0.01679561845958233,
0.030653182417154312,
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0.0220048688352108,
0.036259401589632034,
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0.0021616036538034678,
0.06315365433692932,
0.003585523460060358,
-0.00814764853566885,
0.008... |
<p>I have derived the <a href="http://en.wikipedia.org/wiki/Larmor_formula" rel="nofollow">Larmor equation</a> as $$P = \frac{q^2}{6\pi \epsilon_0 c^3} |\ddot{r}|^2.$$ </p>
<p>How do I make this relativistic?
Apparently, I have to consider the acceleration parallel and perpendicular to the velocity of the accelerating charge like: $$P = \frac{q^2}{6\pi \epsilon_0 c^3} (|\ddot{r}'_{\perp}|^2 + |\ddot{r}'_{\parallel}|^2).$$</p>
<p>But how does this lead to the answer: $$P = \frac{q^2}{6\pi \epsilon_0 c^3} \gamma^4(\gamma^2|\ddot{r}_{\perp}|^2 + |\ddot{r}_{\parallel}|^2).$$</p>
<p>I understand that parallel to the velocity, the will be relativistic effects, so where does this extra $\gamma^4$ come from?</p> | g12285 | [
0.06972867995500565,
0.035054873675107956,
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0.08460092544555664,
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0.01194709911942482,
0.018162569031119347,
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-0.00014430815645027906,
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0.06948962807655334,
0.039089400321245193,
0.036... |
<p>Imagine we have a frictionless semicircular skateboard ramp and we release a cart filled with sand from one edge of the ramp. The cart has a hole and it loses sand at a constant rate. My question is will the cart reach the other extreme edge of the ramp or will it stop midway and slide back down?</p>
<p>I am confused because I am not too sure whether the potential energy will constantly decrease because of decrease of mass and so it should not reach the other end</p> | g12286 | [
0.06908220797777176,
0.01254044659435749,
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0.015151157975196838,
0.03888450562953949,
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0.015566186979413033,
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0.019579... |
<p>We have several definitions of distances in cosmology. Take angular diameter distance. $$d_A = a(t)\int \frac{dt}{a(t)}\;.$$ If an object has proper length $L$ then the angle $\theta$ it is seen at is</p>
<p>$$\theta = \frac{L}{d_A}$$
This is similar to the way an angle $\theta$ and arc length $s$ are related in a circle with radius $r$
$$ \theta = \frac{s}{r}$$
On cosmological scales distances are so vast that the arc length $s$ is indistinguishable from the proper length $L$ of the star or galaxy observed. All this is fine. But when it comes to the cosmic microwave background, we look at temperature correlations between two directions $\vec{n_1}$ and $\vec{n_2}$ with an angle $\theta$ between them on the sky today.
$$ C(\theta) = C(\vec{n_1}\cdot\vec{n_2})$$ </p>
<p>These angles are not small necessarily. For the quadrupole there is $90$ degrees between the two directions. Subsequent Higher multipoles have smaller angles. With such wide angles we should no longer use
$$\theta = \frac{L}{d_A}$$
but instead use
$$tan(\theta) = \frac{L}{d_A}$$
Where am I going wrong with this line of thought?</p> | g12287 | [
0.053197454661130905,
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-0.002273459453135729,
-0.08568913489580154,
0.005672023165971041,
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0.0701909139752388,
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0.009837664663791656,
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0.05941860377788544,
0.... |
<p>My question: Is it possible to manufacture a lens whose focal point doesn't shift in any direction during the day when the sun shines from different angles? It is understood that the focused energy will reach a maximum only if the lens is in the ideal angle to the sun, but I need to build a system that always collects the rays in one point, even if the angle is not perfect. I can cope with a lower energy as long as at least some light is focused constantly at the same spot. I do NOT want to move the lens or the setup in any way.</p>
<p>If it is possible:</p>
<p>Can you please let me know what kind of lens would be needed for this?</p>
<p><img src="http://i.stack.imgur.com/xDdH4.jpg" alt="enter image description here"></p> | g12288 | [
0.012711046263575554,
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0.04866573587059975,
0.03204682096838951,
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0.012746362946927547,
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-0... |
<p><a href="http://en.wikipedia.org/wiki/Gamma_matrices" rel="nofollow">This Wikipedia page</a> explains that for each of the four main gamma matrices $\gamma^{\mu}$, you can find the covariant matrices $\gamma_{\mu}$ with the equation $\gamma_{\mu} = \eta_{\mu\nu}\gamma^{\mu}$. But that formula doesn't make any sense for $\gamma^5$ because $\eta_{\mu\nu}$ does not have that many indices. So what is $\gamma_5$?</p> | g12289 | [
-0.021375887095928192,
-0.0013465560041368008,
-0.021785754710435867,
-0.07399548590183258,
0.058990512043237686,
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0.06474309414625168,
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0.0023432991001755,
-0.027156887575984,
0.009266884997487068,
0.01758858934044838,
0.0046... |
<p>How does one use the concept of microstate evolution and definition of macrostate in a consistent manner. As my understanding goes the thermodynamic concepts are defined in equilibrium. How does one apply these concepts in situations out of equilibrium.</p>
<p>I am looking for a simple example involving thermodynamics out of equilibrium. Such as 2 system previously in equilibrium with Temperatures T1 and T2, are coupled. Given the details microscopic coupling, initial statistical distribution of micro-states, what can one say about the evolution and definition Temperature in such a system.</p>
<p>I know this is a rather broad subject, and any pointers to the existing body of knowledge will be much appreciated. It would be lovely if an example is discussed for illustration purposes.</p> | g12290 | [
0.031028615310788155,
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0.006332421209663153,
0.0056724222376942635,
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0.005912699270993471,
0.007072536274790764,
-0.0067997886799275875,
-0.023496918380260468,
-0.025818239897489548,
0.03865599259734154,... |
<p>Special relativity says that anything moving (almost) at the speed of light will look like its internal clock has (almost) stopped from the perspective of a stationary observer. How do we see light as alternating electric and magnetic fields? Also does light never age? </p> | g361 | [
0.025171536952257156,
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0.024784481152892113,
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0.03976953774690628,
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0.00672235619276762,
0.0184... |
<p>I know that thought experiment about trains when a flash of light in the middle reaches the both end simultaneously for a passenger but different times for the bystander.</p>
<p>So were there (non-thought) experiments that directly checked this?</p> | g12291 | [
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0.... |
<p>I see the similarity between the Lattice Gauge and Spin Network .
(For example , the both theories depict the node part as quantum (the latter is explained as spin))
Are there any other mathematical,Physical similarity between the two theories ?</p> | g12292 | [
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0.04316665604710579,
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0.040497586131095886,
... |
<p>When reading some literatures on topological insulators, I've seen authors taking Brillouin zone(BZ) to be a sphere sometimes, especially when it comes to strong topological insulators. Also I've seen the usage of spherical BZ in these answers(<a href="http://physics.stackexchange.com/questions/104258/topological-insulators-why-k-theory-classification-rather-than-homotopy-classif%22">1</a>,<a href="http://physics.stackexchange.com/questions/70057/topological-band-structure-difference-between-a-sphere-and-a-donut/70074#70074">2</a>) by SE user <a href="http://physics.stackexchange.com/users/1469/heidar">Heidar</a>. I can think of two possibilities:</p>
<p>(1)Some physical system has a spherical BZ. This is hard to imagine, since it seems to me that all lattice systems with translational symmetries will have a torodal BZ, by the periodicity of Bloch wavefunctions. The closest scenario I can imagine is a continuous system having $\mathbf{R}^n$ as BZ, and somehow(in a way I cannot think of) acquires an one-point compactification.</p>
<p>(2)A trick that makes certain questions easier to deal with, while the true BZ is still a torus.</p>
<p>Can someone elaborate the idea behind a spherical BZ for me?</p>
<p><strong>Update</strong>: I recently came across <a href="http://socrates.berkeley.edu/~jemoore/Moore_group,_UC_Berkeley/Welcome_to_the_Moore_group,_Department_of_Physics,_UC_Berkeley_files/mitcourse.pdf">these notes(pdf)</a> by J.Moore. In the beginning of
page 9 he mentioned </p>
<blockquote>
<p>We need to use one somewhat deep fact: under some assumptions, if $π_1(M)
= 0$ for some target space $M$, then maps from the torus $T^
2\to M$ are contractible to maps from the sphere $S^2
\to M$</p>
</blockquote>
<p>I think this is a special case of the general math theorem I want to know, but unfortunately Moore did not give any reference so I'm not sure where to look.</p>
<p><strong>EDIT</strong>: The above math theorem is intuitively acceptable to me although I'm not able to prove it. I can take this theorem as a working hypothesis for now, what I'm more interested in is, granted such theorem, what makes a $\pi_1(M)=0$ physical system candidate for strong topological insulators(robust under local perturbations), and why in $\pi_1(M)\neq 0$ case we can only have weak topological insulators.</p>
<p>Crossposted: <a href="http://www.physicsoverflow.org//16620/when-can-we-take-the-brillouin-zone-to-be-a-sphere">When can we take the Brillouin zone to be a sphere?</a></p> | g12293 | [
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0.013411333784461021,
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0.014011027291417122,
0.016314921900629997,
-0.0031748793553560972,
0.02904321439564228,
0.017747031524777412,
0.034808751195669174,
-... |
<p>If we obtain something like a single isolated hydrogen atom I.e. $H^+$ is it possible by keeping it in a system of charged rings to contain and stop it at the centre of the system?</p>
<p>Any positively charged ring would have electric field pointing towards its centre, if the ion tries to move then it will be pushed towards center! Clearly this would violate the uncertainity principle because we would know that the atom is at the Centre of the ring and is stopped, I think therefore it must have atleast some difficulty but I can't figure out why it may not be possible!</p>
<p>The question is that if it is possible, what does it say about the uncertainty priniciple and if it is not possible then why not?</p> | g12294 | [
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-0.... |
<p>I have a length of string and I want to know the maximum tension the string can support. I tie one end of the string to the ceiling and the other end to a glass of mass 100 g. The glass is cylindrical, with a cross-sectional radius of 4 cm and a height of 15 cm. I fill the glass with water (density of 1 g/cm3) and discover that the string breaks when the glass is 2/3 full. What is the maximum tension in N the string can support?</p> | g12295 | [
0.04736637696623802,
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0.014957597479224205,
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0.0009613216971047223,
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0.038218628615140915,
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-0.005162313114851713,
-0.06853848695755005,
... |
<p>Grocery stores often have spring scales in their produce department to weigh fruits and vegetables. </p>
<p>The pan of one particular scale has a mass of 0.5 kg, and when you place a 0.5 kg sack of potatoes on the scale the pan lowers by 6 cm. </p>
<p>As we reach for the potatoes to toss in the cart, we accidentally knock the pan, making the pan and potatoes oscillate up and down. </p>
<p>What is the frequency of their oscillation in Hz?</p>
<pre><code>we may treat the spring as an ideal spring.
The acceleration due to gravity is −9.8 m/s2.
</code></pre> | g12296 | [
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0.014484387822449207,
0.03057859092950821,
0.0581383... |
<p>This is in continuation to my <a href="http://physics.stackexchange.com/questions/8303/does-the-hup-alone-ensure-the-randomness-in-qt">previous question</a>. It is not a duplicate of the previous one. This question arises because of the answers and discussions in that question.</p>
<p>Can we call a theory, quantum theory, if it is consistent with HUP? For example, suppose there is a finite and self consistent theory of gravity which incorporates the uncertainty principle. Can we at once call this theory a quantum theory of gravity or does it have to satisfy other conditions too?</p>
<p>This question may be too basic but it is intriguing my mind.</p> | g12297 | [
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0.005232448223978281,
0.053061094135046005,
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0... |
<p>Researchers at Michigan State University recently invented the <a href="http://www.physorg.com/news/2011-03-msu-prototype-video.html/" rel="nofollow">Wave Disk Generator</a> that is supposed to get 60% fuel efficiency. What allows it to be so much more efficient than a traditional Internal Combustion Engine?</p>
<p>I am aware that there is better mixing of fuel and air, but surely this alone does not produce the extreme efficiency. </p> | g12298 | [
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0.05860966444015503,
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0.04672965034842491,
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<p>If we look at the atomic positions in a single crystal sample with a diamond like lattice, there exist directions along which there are long hexagonal "tubes" (I'm not sure if these have a proper term). </p>
<p><img src="http://i.stack.imgur.com/a4Y2v.jpg" alt="hexagonal tubes in diamond like lattice"></p>
<p>This happens in silicon for example. Now if a hydrogen atom was inserted in the material, it would be too large and just get trapped in the 'matrix' of the silicon and present a defect in the material.</p>
<p>If instead I took a proton and muon in a bound "muonic hydrogen" state, the bohr radius which goes like 1/m would be ~ 200x's smaller. Due to being neutral, small, and tightly bound (a binding energy > 2.5 keV), I am tempted to view it almost like a large neutron.</p>
<p>My question is:<br>
Due to its much smaller size, could such a 'large neutron' pass freely through a crystal along one of these tubes?<br>
Could one eliminate trapped hydrogen in a crystal by making it "mobile" in this fashion by putting the sample in a muon beam of low enough energy that it won't damage the crystal structure but still create 'muonic hydrogen'?</p> | g12299 | [
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0.05932771414518356,
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-0.02578677423298359,
0.020753540098667145,
0.07132324576377869,
-0.04571089893579483,
-0.... |
<p>What is a <a href="http://en.wikipedia.org/wiki/Virtual_ground" rel="nofollow">virtual ground</a>? I would like to know what it is.</p> | g12300 | [
0.016018280759453773,
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0.03304... |
<p>The field equations (e.g. Schrödinger’s/Maxwell’s) describe the four-dimensional universe as the time evolution of a three-dimensional system. This implies that the universe contains only three dimensions of information: the fourth is derivable deterministically (albeit not practically) from the other three via these formulas.</p>
<p>My understanding is that this is exactly what the holographic principle posits: that the universe contains only three dimensions of information (commonly presented as two spatial, one temporal). Yet the holographic principle remains unproven. Where is my misunderstanding?</p> | g12301 | [
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<p>One of the active research areas in present is Strong interacting, Strong Coupling, Strong Correlated regime of the phases of matters.</p>
<p>It seems to me that some physicists in the fields often mix the usages of these twos: <strong>Strong Coupling, Strong Correlated</strong>.</p>
<p>However, in my viewpoint, they are NOT the exactly same, I regard that </p>
<blockquote>
<p>$\bullet$ <strong>Strong Coupling</strong>: implies the large coupling of interactions comparing to the free part of theory. Say, suppose there is a Lagrangian description, then the action $S$
$$
S=S_{free} +g S_{interact}
$$
the <strong>Strong Coupling</strong> means $g >>1$. So this can be the confined phases of QCD, where coupling $g$ of quarks and gluons runs large.</p>
</blockquote>
<p>--</p>
<blockquote>
<p>$\bullet$ <strong>Strong Correlated</strong>: in my view, usually implies the <strong>fractionalization of the elementary particles into fractional quantum numbers</strong>. For example, this happens at 1+1D Luttinger liquids, where spin and charge can separated their degree of freedom from the elementary constituents(electrons), but the system needs NOT to be <strong>Strong Coupling</strong>. i.e.
this example is <strong>Strong Correlated</strong> but NOT <strong>Strong Coupling</strong>. This is about the fields of <a href="http://arxiv.org/list/cond-mat.str-el/recent" rel="nofollow"><strong>Strong Correlated Electron</strong> on arXiv</a>.</p>
</blockquote>
<p>--</p>
<p><strong>My question</strong>, so what are other <strong>examples of systems</strong> that are:</p>
<blockquote>
<p><strong>1. YES Strong Coupling and YES Strong Correlated</strong></p>
<p><strong>2. YES Strong Coupling but NOT Strong Correlated</strong></p>
<p><strong>3. NOT Strong Coupling but YES Strong Correlated</strong></p>
</blockquote>
<p>See also <a href="http://physics.stackexchange.com/questions/117196/">this relevant post</a>.</p> | g12302 | [
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0.011543503031134605,
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<p>Suppose a large mass $M$ travelling at $v$ impacts a small stationary mass $m$, then following through the elastic collisions from high school, we get that the smaller mass can exit the collision FASTER than $v$.</p>
<p>In the limit of huge $M$, we can change reference frame and make $M$ basically stationary, and $m$ simply bounces off, thereby having a velocity change of $2v$.</p>
<p>How can I visualise this from a microscopic level? If the normal force between objects only exists while they are in contact, the moment contact was lost between two objects they no longer act on each other. So as soon as the target balls speed reaches the tiniest amount above the impact ball speed, the balls should separate and no longer interact. This would lead to all collisions being "sticky" and completely inelastic.</p>
<p>So why are not all collisions sticky? How do collisions work that apparently allow acceleration past the point where contact is lost? And if this is something to do with Coulomb interaction, is there any historical commentary on how Newton and peers felt about this prior to the understanding of electrodynamics?</p> | g12303 | [
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<p>I want to understand clearly why $ P \gamma^{\mu} P = \gamma^{\mu} $, where $ P $ is the parity operator. </p>
<p>This result follow for example from pag. 66 of Peskin-Schroeder.
The parity operator acts on Dirac fields in this way: $ P \psi (t, \textbf{x}) P = \gamma^0 \psi (t, -\textbf{x}) $, assuming no other phase factors.
On the Dirac bilinear $ \bar{\psi} \gamma^{\mu} \psi (t, \textbf{x}) $, using the fact that $ P^2=1 $, you have $P \bar{\psi} \gamma^{\mu} \psi (t, \textbf{x})P = P \bar{\psi} P P \gamma^{\mu} P P \psi (t, \textbf{x}) P = \bar{\psi}\gamma^0 P \gamma^{\mu} P \gamma^0 \psi (t,- \textbf{x}) = \bar{\psi}\gamma^0 \gamma^{\mu} \gamma^0 \psi (t,- \textbf{x}) = (-1)^{\mu}\bar{\psi} \gamma^{\mu} \psi (t, -\textbf{x}) $</p>
<p>With $(-1)^{\mu} =1 $ if $ \mu=0 $ and $(-1)^{\mu} =-1 $ if $ \mu=1,2,3 $.
So $ P \gamma^{\mu} P = \gamma^{\mu} $ follows because $ P$ and $\gamma^{\mu} $ act on different spaces? Or there are other explanations? (Please, do all the steps in the answer)</p>
<p>To be clear: I use $ \gamma^0= \bigl(\begin{smallmatrix}
0&1\\ 1&0
\end{smallmatrix} \bigr)$ and $ \gamma^{i}= \bigl(\begin{smallmatrix}
0&\sigma^i\\ -\sigma^i&0
\end{smallmatrix} \bigr)$. </p> | g12304 | [
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<p>I started a little bit of Googling around the topic, and found very few information. There are mainly upper limits. I found lower limits only to the rest mass differences of the different neutrino flavors.</p>
<p>Thus, what are the actually current known lower mass limits to the <a href="http://en.wikipedia.org/wiki/Neutrino" rel="nofollow">neutrino</a> flavors?</p> | g12305 | [
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0.009422751143574715,
-0.0151033541187644,
0.006770588457584381,
-0.051737070083618164,
-0.06715629994869232,
0.0032219879794865847,
0.019679531455039978,
-0.023078378289937973,
... |
<p>For determining the drift velocity of a flow of charge we need to find the <strong>average relaxation time</strong> for that flow at that specific temperature.</p>
<p>My question is, how does one find that? Is there some experimental way to find that? Or it is derived by some Mathematical derivations and statistical calculations? </p> | g12306 | [
0.028701579198241234,
0.0004312258097343147,
-0.01352249551564455,
0.020508047193288803,
0.0681867003440857,
-0.03165475279092789,
0.025763841345906258,
-0.010140984319150448,
-0.03367617726325989,
0.015310889109969139,
-0.032269444316625595,
0.011601664125919342,
0.029157165437936783,
0.0... |
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