question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>I found this related question: <a href="http://physics.stackexchange.com/questions/51511/what-happens-to-5-electrons-on-a-sphere">What happens to 5 electrons on a sphere?</a></p>
<p>But this question describes the case when there can only be 5 electrons on that sphere at all times. The answer linked to the <a href="http://en.wikipedia.org/wiki/Thomson_problem" rel="nofollow">Thomson Problem</a>, which gives a solution for the stable configuration of $N$ charges placed on a sphere. </p>
<blockquote>
<ul>
<li>So my question is that, will it not repel the extra electrons inside the metal to produce a state of non-uniformly distributed + and - charges?</li>
</ul>
</blockquote>
<p>If not, it would mean that there is a net non-zero field inside the <em>bulk</em> of the sphere, so that configuration cannot be a steady state, i.e. It will cause the sea of electrons to flow and achieve another steady state, which can be said from the <a href="http://en.wikipedia.org/wiki/Faraday_cage" rel="nofollow">Electrostatic Shielding Effect</a>.</p>
<blockquote>
<ul>
<li><p>So, what steady state will be achieved?</p></li>
<li><p>What if it is a solid sphere and not a hollow one? Will the extra electron still be on the surface of the sphere?</p></li>
</ul>
</blockquote>
<p>Any help is appreciated!</p>
<p>P.S. You can leave the last question for me to attempt, if its easily deducible from the answer for the first two!</p> | g10654 | [
0.05548962205648422,
0.039185427129268646,
0.0019619385711848736,
-0.08649113774299622,
0.06991120427846909,
0.040422115474939346,
0.03188987821340561,
-0.03412122651934624,
0.004212571308016777,
-0.03351057693362236,
-0.04192380607128143,
0.017645031213760376,
-0.023704707622528076,
0.009... |
<p>In operator formalism, for example a 2-point time-ordered Green's function is defined as</p>
<p>$\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{op}=\theta(x_1-x_2)\phi(x_1)\phi(x_2)+\theta(x_2-x_1)\phi(x_2)\phi(x_1),$</p>
<p>where the subscript "op" refers to operator formalism. Now if one is to take a time derivative of it, the result will be $\frac{\partial}{\partial x_1^0}\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{op}=\langle\mathcal{T}{\frac{\partial \phi(x_1)}{\partial x_1^0}}\phi(x_2)\rangle_{op}+\delta(x_1^0-x_2^0)[\phi(x_1),\phi(x_2)]$, the delta function comes from differentiating the theta functions. This means time derivative does not commute with time ordering.</p>
<p>If we consider path integral formalism, the time-ordered Green's function is defined as </p>
<p>$\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{pi}=\int\mathcal{D}\phi\phi(x_1)\phi(x_2)e^{iS(\phi)}$. </p>
<p>Of course $\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{op}=\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{pi},$ as is proved in any QFT textbook. However in path integral case time derivative commutes with time ordering, because we don't have anything like a theta function thus $\frac{\partial}{\partial x_1^0}\int\mathcal{D}\phi\phi(x_1)\phi(x_2)e^{iS(\phi)}=\int\mathcal{D}\phi\frac{\partial}{\partial x_1^0}\phi(x_1)\phi(x_2)e^{iS(\phi)}$. I did a bit googling and found out that for the path integral case the time-ordered product is called "$\mathcal{T^*}$ product" and operator case just "$\mathcal{T}$ product".</p>
<p>I am not that interested in what is causing the difference(still explanations on this are welcomed), because I can already vaguely see it's due to some sort of ambiguity in defining the product of fields at equal time. The question that interests me is, which is the right one to use when calculating Feynman diagrams?</p>
<p>I did find a case where both give the same result, i.e. scalar QED(c.f. Itzykson & Zuber, section 6-1-4), but is it always the case? If these two formulations are not effectively equivalent, then it seems every time we write down something like $\langle\partial_0\phi\cdots\rangle$, we have to specify whether it's in the sense of the path integral definition or operator definition.</p>
<p><strong>EDIT:</strong> As much as I enjoy user1504's answer, after thinking and reading a bit more I don't think analytic continuation is all the mystery. In Peskin&Schroeder chap 9.6 they manage to use path integral to get a result equivalent to operator approach, without any reference to analytic continuation. It goes like this : Consider a T-product for free KG field $\langle T\{\phi(x)\phi(x_1)\}\rangle=\int\mathcal{D}\phi\phi(x)\phi(x_1)e^{iS(\phi)}$. Apply Dyson-Schwinger equation, we get $\int\mathcal{D}\phi(\partial^2+m^2)\phi(x)\phi(x_1)e^{iS}=-i\delta^4(x-x_1)$, then they just assume the $\partial^2$ commute with path integration(which is already weird according to our discussion) and they conclude </p>
<p>$(\partial^2+m^2)\int\mathcal{D}\phi\phi(x)\phi(x_1)e^{iS}=(\partial^2+m^2)\langle T\{\phi(x)\phi(x_1)\}\rangle=-i\delta^4(x-x_1)$. </p>
<p>This is just the right result given by operator approach, in which $\delta(x^0-x_1^0)$ comes from $\theta$ function. Given my limited knowledge on the issue, this consistency looks almost a miracle to me. What is so wicked behind these maths?</p>
<p><strong>Response to @drake</strong>:If $a$ is a positive infinitesimal, then $\int \dot A(t) B(t) \,e^{iS}\equiv\int D\phi\, {A(t+a)-A(t)\over a}B(t)\,e^{iS}=\frac{1}{a}\langle T\{A(t+a)B(t)\}\rangle-\frac{1}{a}\langle A(t)B(t)\rangle$, notice the second term has an ordering ambiguity from path integral(say $A=\dot{\phi},B=\phi$), and we can make it in any order we want by choosing an appropriate time discretization, c.f. Ron Maimon's post cited by drake. Keeping this in mind we proceed:</p>
<p>$\frac{1}{a}\langle T\{A(t+a)B(t)\}\rangle-\frac{1}{a}\langle A(t)B(t)\rangle\\=\frac{1}{a}\theta(a)\langle A(t+a)B(t)\rangle+\frac{1}{a}\theta(-a)\langle B(t)A(t+a)\rangle-\frac{1}{a}\langle A(t)B(t)\rangle\\=\frac{1}{a}\theta(a)\langle A(t+a)B(t)\rangle+\frac{1}{a}[1-\theta(a)]\langle B(t)A(t+a)\rangle-\frac{1}{a}\langle A(t)B(t)\rangle\\=\frac{\theta(a)}{a}\langle [A(t+a),B(t)]\rangle+\frac{1}{a}[\langle B(t)A(t+a)\rangle-\langle A(t)B(t)\rangle]$</p>
<p>Now taking advantage of ordering ambiguity of the last term to make it $\langle B(t)A(t)\rangle$(this amounts to defining A using backward discretization, say $A=\dot{\phi}(t)=\frac{\phi(t+\epsilon^-)-\phi(t)}{\epsilon^-}$), then the finally:</p>
<p>$\frac{\theta(a)}{a}\langle [A(t+a),B(t)]\rangle+\frac{1}{a}\langle B(t)[A(t+a)-A(t)\rangle]\to \frac{1}{2a}\langle [A(t),B(t)]\rangle+\langle B(t)\dot{A}(t)\rangle$.(Here again a very dubious step, to get $\frac{1}{2a}$ we need to assume $\theta(a\to 0^+)=\theta(0)=\frac{1}{2}$, but this is really not true because $\theta$ is discontinuous)</p>
<p>However on the other hand, since $a$ was defined to be a postive infinitesimal, at the very beginning we could've written $\frac{1}{a}\langle T\{A(t+a)B(t)\}\rangle-\frac{1}{a}\langle A(t)B(t)\rangle=\frac{1}{a}\langle A(t+a)B(t)\rangle-\frac{1}{a}\langle A(t)B(t)\rangle$, then all the above derivation doesn't work. I'm sure there are more paradoxes if we keep doing these manipulations.</p> | g10655 | [
0.02167312614619732,
0.006730081979185343,
0.0020043200347572565,
0.018896855413913727,
0.05690539628267288,
-0.04415383189916611,
0.043595898896455765,
-0.003726807190105319,
-0.03599100187420845,
0.020724909380078316,
0.011913406662642956,
-0.022179095074534416,
0.013195546343922615,
-0.... |
<p>My interest is purely in $\text{SO}(n)$ tensors and how one works out their irrep decomposition. For instance, for rank 2 tensors we simply split into an antisymmetric part, a traceless symmetric part and the trace. Is there a more general, recursive procedure for higher rank tensors? Even if not, what is the usual method when trying to do it for say rank 3 or 4? Any pointers to the literature would be more than helpful. </p> | g10656 | [
0.009417172521352768,
0.030654266476631165,
-0.019491927698254585,
0.015491833910346031,
0.013782874681055546,
-0.05685441568493843,
0.03745736554265022,
0.05448349565267563,
0.017836356535553932,
0.036005061119794846,
-0.03731391206383705,
-0.006130403373390436,
0.03952336683869362,
-0.01... |
<p>Would different observers agree on the age? Or is this question nonsensical? e.g. what's north of the north pole?</p>
<p>There are ways of estimating the ages of stellar bodies using various methods but is there a method for black holes? </p>
<p>My main stumbling block is the slowing down and 'stoppage' of time of objects near the event horizon as far as faraway observers are concerned. Theoretically one should be able to 'see' everything that 'fell' into the black hole since the time it (the EH) was formed. Obviously the older stuff should be more red-shifted than newer stuff but the entire spectrum should be seen: from slightly shifted to slightly less than infinitely shifted.</p> | g10657 | [
-0.017811553552746773,
-0.010613642632961273,
0.01862415485084057,
-0.07120536267757416,
0.008295790292322636,
0.03271574154496193,
0.011099630035459995,
0.029152249917387962,
-0.009611422196030617,
-0.018513623625040054,
0.062201403081417084,
-0.016073916107416153,
0.06373856216669083,
0.... |
<p>Sorry if this is a dumb question, but I'm only starting to get to grips with this quantum malarkey. Anyway...</p>
<p>Suppose I have two friends, Alice and Bob, both of whom have a random number generator. Alice's number generator will produce a number between 1 and 4, giving a probability density of:</p>
<p>A=[0.25 0.25 0.25 0.25] for each number possibility</p>
<p>Bob has the same generator, but his is faulty and will only give a number between 2 and 4, producing this probability density:</p>
<p>B=[0 0.33 0.33 0.33]</p>
<p>If Alice and Bob randomly select one of their generators and tell me what the number produced is, then it is a trivial matter using classical probability to calculate an odds/likelihood ratio as to which machine was used. But how does this situation work with quantum math?</p>
<p>Quantizing this problem (as far as I gather) produces two kets:</p>
<p>$|A\rangle = \left[\sqrt{\frac{1}{4}} \sqrt{\frac{1}{4}} \sqrt{\frac{1}{4}} \sqrt{\frac{1}{4}}\right]$ = [0.5 0.5 0.5 0.5]</p>
<p>$|B\rangle = \left[\sqrt{0} \sqrt{\frac{1}{3}} \sqrt{\frac{1}{3}} \sqrt{\frac{1}{3}}\right]$ = [0 0.58 0.58 0.58] </p>
<p>Presumably this can then be expressed as a superposition:</p>
<p>$$|\Psi\rangle = \frac{1}{\sqrt{2}} (|A\rangle \otimes |B\rangle)$$</p>
<p>But then, so what? Where does this get me in terms of producing a quantum version of the standard likelihood ratio?</p>
<p>Or am I barking up the wrong tree?</p>
<p>All help appreciated :) Thanks!</p> | g10658 | [
-0.006594473496079445,
-0.030107729136943817,
-0.006508400198072195,
-0.08795741200447083,
-0.0245041623711586,
0.022942135110497475,
-0.019022947177290916,
0.03021175041794777,
-0.038333117961883545,
0.010922019369900227,
-0.00554580707103014,
0.020550142973661423,
0.029031164944171906,
0... |
<p>This is pressure in Newtonian mechanics: </p>
<p>$$P=\frac {dF}{dA}.$$
What does this mean?
(Doesn't it mean that force is a function of area?)
What type of function is force?</p> | g10659 | [
0.03436889499425888,
0.01569853536784649,
-0.02474300190806389,
-0.050017230212688446,
0.034200310707092285,
0.032935980707407,
0.07087331265211105,
-0.017386790364980698,
-0.020453866571187973,
-0.05567772686481476,
-0.012346283532679081,
0.0043822699226439,
0.030996249988675117,
-0.06606... |
<p>Two separate suitably short but intense <a href="http://en.wikipedia.org/wiki/Charged_particle_beam#bunch_structure" rel="nofollow">bunches</a> of <a href="http://en.wikipedia.org/wiki/Muon" rel="nofollow">muons</a>, "A" and "B", are both supposed to be constantly accelerating (in an otherwise sufficiently flat region) with constant proper acceleration vectors $\bf a$ and $\bf b$ (as measured by any system of participants who are mutually at rest) in the same direction and co-linearly (let's say "A leading in front", and "B trailing behind"), but not necessarily equally accelerated (therefore acceleration vectors $\bf a$ and $\bf b$ don't necessarily have equal magnitudes).</p>
<p>Meanwhile the muons of both bunches decay, with equal and constant proper <a href="http://en.wikipedia.org/wiki/Mean_lifetime#Mean_lifetime" rel="nofollow">mean lifetime</a> $\tau_{\text muon}$, and correspondingly with equal proper "half-life duration Log[ 2 ] $\tau_{\text muon}$".</p>
<p>Also, the two bunches are separated such that they always "remain in sight" of each other; such that </p>
<ul>
<li><p>B (or some suitable accompanying instrumentation) always finds that it takes 1 half-life from "stating a ping" until "observing A's reflection", while </p></li>
<li><p>A always finds that it takes 2 half-lives from "stating a ping" until "observing B's reflection".</p></li>
</ul>
<p>Question:<br>
What's the magnitude $| \bf b | $ ?<br>
Can it be calculated at all, in terms of "mean lifetime $\tau_{\text muon}$" and "speed of light $c$", based on the described setup conditions?</p>
<p>(Surely the described setup conditions are consistent with bunches A and B being called "rigid to each other", or having been "ends of a rigid rod", in the sense of <a href="http://physics.stackexchange.com/questions/67037/is-it-possible-to-have-uniform-proper-acceleration-along-a-large-object-without">this question</a> and <a href="http://physics.stackexchange.com/questions/48392/extended-rigid-bodies-in-special-relativity">that question</a> and the various comments there.</p>
<p>My question is intended to obtain illustrations of different approaches to the "rigid rod" problem which were indicated in those comments; even if they obtain the same answer value.) </p> | g10660 | [
0.010630420409142971,
0.009410711005330086,
-0.002285453723743558,
-0.009899575263261795,
0.0679711252450943,
-0.01573498733341694,
0.0470564067363739,
0.026863330975174904,
-0.03025449812412262,
-0.0057005807757377625,
0.028878692537546158,
0.04553163796663284,
-0.049662258476018906,
0.00... |
<p>What's the physical interpretation of constants in <a href="http://en.wikipedia.org/wiki/wave%27s_equation" rel="nofollow">wave equation</a> and <a href="http://en.wikipedia.org/wiki/Diffusion_equation" rel="nofollow">diffusion equation</a>?</p>
<p>$$u_{tt}=c^2u_{xx},$$</p>
<p>$$u_{t}=ku_{xx}.$$</p>
<p>Please introduce some reference about mathematical modeling of physical phenomenons such as wave, shocks and diffusion equation. </p> | g10661 | [
0.005350662395358086,
0.02634931541979313,
-0.03760373964905739,
-0.001389528508298099,
0.0700339749455452,
0.046672604978084564,
0.06678110361099243,
0.0700717493891716,
-0.029777633026242256,
-0.014718643389642239,
0.0015166349476203322,
0.0010242240969091654,
0.0394524522125721,
-0.0187... |
<p>My textbook gives the following explanation on how excess charges are spread over conductors:</p>
<blockquote>
<p>The excess charge on an isolated conductor moves entirely to the
conductor's surface. However, unless the conductor is spherical, the
charge does not distribute itself uniformly.</p>
</blockquote>
<p>I was studying for a test and there was the following question, regarding the thin-wall conducting cylindrical shell below (which is coaxial to the rod inside it):</p>
<p><img src="http://i.stack.imgur.com/jiLmD.png" alt="enter image description here"> $Q_1 > 0, Q_2 < 0$</p>
<blockquote>
<p>What is the charge on the interior and exterior surface of the
shell?</p>
</blockquote>
<p>At first I thought the excess charge on the interior surface would be zero, since all the excess charge would move to the outer surface of the shell. But according to my textbook, it is as follows:</p>
<blockquote>
<p>We consider a cylindrical Gaussian surface whose radius places it
within the shell itself. The electric field is zero at all points on
the surface since any field within a conducting material would lead to
current flow (and thus to a situation other than the electrostatic
ones being considered here), so the total electric flux through the
Gaussian surface is zero and the net charge within it is zero (by
Gauss's law). Since the central rod has charge $Q_1$, the inner
surface of the shell must have charge $Q_{in} = -Q_1 = -3.40 \times 10^{-12}\: \mathrm{C}$.</p>
<p>Since the shell is known to have total charge $Q_2 = -2.00\: Q_1$ it must
have charge $Q_{out} = Q_2 - Q_{in} = - Q_1 = -3.40 \times 10^{-12}\: \mathrm{C}$ on its
outer surface.</p>
</blockquote>
<p>So there is $-Q_1$ excess charge on the inner surface because said charges are being attracted by the rod? What if there was no rod, how would the excess charge be distributed over the shell's surface? Can I tell how the excess charge will be distributed over the surface of any non-spherical conductor, or only in special cases such as the above?</p> | g10662 | [
0.039270635694265366,
0.000853441481012851,
-0.014835109934210777,
-0.009137841872870922,
0.04815445840358734,
0.06735587865114212,
0.05198117718100548,
-0.03172016888856888,
-0.017384788021445274,
0.00920767243951559,
-0.10504058748483658,
0.04590347409248352,
0.029070835560560226,
0.0242... |
<p>The following was originally given to me as a homework question at
my physics 2 course:</p>
<blockquote>
<p>Consider the following circuit</p>
<p><img src="http://i.stack.imgur.com/KntDu.jpg" alt="enter image description here"></p>
<p>The difference of potentials between the point $V_{1}$and the point
$V_{2}$ is $4.4$ volts, the resistance of all the resistors is the
same $R=1\Omega$.</p>
<p>Find the current between point $A$ and point $B$.</p>
</blockquote>
<p>The answer given is simply $0$ and the argument was just the pair
of words ``using symmetry''.</p>
<p>I don't really understand the answer:</p>
<p>First, it is not completely symmetric: There is a difference of potentials
so the potential at the point $V_{1}$ is not the same as the potential
at the point $V_{2}$.</p>
<p>Secondly: How can I see that the symmetric structure will give me
that the current between $A$ and $B$ is $0$ ?</p>
<p>Also, I would appreciate to see a calculation of this current to get
a better feel for whats going on, I know the rule $V=IR$ (which seems
the most useful here, but I also know other rules that can be used),
but I don't understand how to use this rule to find the current.</p> | g10663 | [
0.015029319562017918,
-0.0365680530667305,
-0.04401449114084244,
-0.011718019843101501,
0.1028296947479248,
-0.05623464286327362,
0.07857605814933777,
0.02357635833323002,
-0.05596816912293434,
0.048908814787864685,
-0.005454382859170437,
0.06635945290327072,
-0.0518665611743927,
-0.011509... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/31254/can-the-lightning-be-captured-and-used-as-power-source">Can the lightning be captured and used as power source?</a> </p>
</blockquote>
<p>Each lightning contains several kilo volts of electricity.<br>
Saving them could be a boon to soaring need of it.<br>
Is there a way?</p> | g338 | [
-0.0014941766858100891,
0.07264943420886993,
0.003557769116014242,
0.002868818351998925,
0.02204207517206669,
-0.03934282809495926,
-0.05146826431155205,
0.012683317065238953,
-0.0319705456495285,
0.03502333164215088,
-0.014484694227576256,
0.025432875379920006,
-0.023704882711172104,
0.04... |
<p><a href="http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence" rel="nofollow">$E=mc^2$</a> is the famous mass-energy equation of Albert Einstein. I know that it tells that mass can be converted to energy and vice versa. I know that $E$ is energy, $m$ is mass of a matter and $c$ is speed of light in vacuum. </p>
<p>What I didn't understood is how we will introduce speed of light?</p>
<p>Atom bomb is made using this principle which converts mass into energy; in that the mass is provided by uranium but where did speed of light comes into play? How can speed of light can be introduced in atom bomb?</p> | g1029 | [
0.029599538072943687,
0.03186255693435669,
0.0031219832599163055,
-0.007256711833178997,
0.041043657809495926,
0.03044412098824978,
0.007846272550523281,
0.05254547670483589,
-0.04045818746089935,
-0.00326288933865726,
-0.028390975669026375,
-0.0013272734358906746,
0.05478094890713692,
0.0... |
<p>Here we have two magnets and they are sticking to each other. What I've learned that could possibly explain it is one magnet holds positive charge and the other one holds negative. But when the eletrons travel from the negative one to the positive one in order to be equilirium (just like static electricity won't stay long between a ballon and the wall), will they become both natural and are not sticky anymore? Maybe one day?</p> | g10664 | [
0.024247601628303528,
0.05610388517379761,
-0.000012820052688766737,
0.013012578710913658,
0.09637315571308136,
0.03287992998957634,
-0.014258154667913914,
0.01780129410326481,
-0.02112768590450287,
0.04118549823760986,
0.000815102772321552,
0.029975179582834244,
-0.013014321215450764,
-0.... |
<p>I have this relative simple-looking question that I haven't been able to solve for hours now, it's one of those questions that just drive you nuts if you don't know how to do it.
This is the scenario:</p>
<p>I have a <a href="http://2.bp.blogspot.com/_P4EHIyposmM/TImv2-brnOI/AAAAAAAAAMw/nK-NO8JUSEU/s1600/1781_PotApp_FlexibleMetal_Spring_Big.jpg" rel="nofollow">spring</a> that is on a flat surface, the springs details are like this:</p>
<p>spring constant = 100N/m</p>
<p>height = 0.1m</p>
<p>mass = 0.5kg</p>
<p>g = 10m/s^2</p>
<p>there is nothing attached to the spring.
The initial force exerted on the surface is 5N.
I compress the spring halfway until the force exerted on the surface is double, now 10N and then let it go.</p>
<p>The (simple) oscillation starts, and at one point the force exerted on the surface will be 0N (weightless).</p>
<p>I need to find out how much time has passed after letting it go, and reaching weightlessness.</p>
<p>as in:
10(N)---time--->0(N)</p>
<p>p.s. not homework, read comments.</p> | g10665 | [
0.09118515998125076,
0.033834464848041534,
0.004397398326545954,
-0.024939585477113724,
0.017863454297184944,
-0.006319214124232531,
0.04918196424841881,
0.019016848877072334,
-0.07728824019432068,
-0.029114464297890663,
-0.07071247696876526,
0.017187194898724556,
-0.0019470995757728815,
0... |
<p>all. I have tried Googling but have had no luck. My question is simple (although, I presume the answer is not): If one knows the chemical structure of, well, a chemical, could its optical properties (such as transparency) be mathematically derived from this information alone? Perhaps I'm naive for thinking so, but I would imagine it's possible, given the electron count and three-dimensional structure of the compound. </p>
<p>I ask this on the Physics Stack Exchange because I feel like it falls into the Optics/Physical-Side-of-Physical-Chemistry realm than into pure Chemistry territory.</p>
<p>If I need to elaborate some more, please feel free to comment and let me know. Likewise, if needed, please pardon any idiocy.</p> | g10666 | [
-0.01597709022462368,
-0.009219730272889137,
0.024393942207098007,
-0.02859080769121647,
0.015387353487312794,
-0.013591405004262924,
-0.0509457103908062,
0.029341885820031166,
0.03889051079750061,
0.01596054993569851,
0.03971046954393387,
-0.00207710824906826,
0.07674972712993622,
-0.0539... |
<p>Is the fact that weak eigenstates are not mass eigenstates completely arbitrary? Or is there a deeper reason for the existence of the PMNS and CKM matrices?</p> | g10667 | [
-0.01790497824549675,
-0.008366435766220093,
0.00812189094722271,
-0.03930162638425827,
0.02415495179593563,
0.010312145575881004,
-0.030486926436424255,
-0.014618388377130032,
0.024909641593694687,
-0.059679076075553894,
-0.02132292091846466,
-0.06379125267267227,
0.026582684367895126,
0.... |
<p>I remember in the high school physics, my teacher told us that the design of the plane wing is because we want the air above the wing flowing faster than the air flowing below so the pressure above and below will be different so the net force is pointing upright. I am thinking if it is possible to explain this by bernoulli equation? But I soon stuck there because I don't know if bernoulli equation applicable to the case of the air flow in the open region? If so, what cross section we should choose?</p> | g17 | [
0.03461453691124916,
0.07343865931034088,
-0.006619180552661419,
0.050291262567043304,
-0.030378218740224838,
0.07226665318012238,
0.017765939235687256,
0.011550174094736576,
-0.06992439180612564,
-0.04900868609547615,
0.04305387660861015,
0.015333260409533978,
0.017467979341745377,
0.0593... |
<p>I have an idea of supersymmetry in quantum mechanics, can you suggest a book on "supersymmetry in quantum field theory", which has sufficient mathematical rigour like "Peskin and Schroeder" </p> | g467 | [
0.03319229558110237,
0.05155213549733162,
-0.003050649305805564,
-0.005476339254528284,
-0.026102222502231598,
0.01609172858297825,
-0.024946529418230057,
0.05137152597308159,
0.03320338949561119,
0.013232631608843803,
0.00806573685258627,
-0.02871016412973404,
0.008987224660813808,
0.0536... |
<p>I've been working my way through L. Baulieu's excellent paper [<em>Perturbative gauge theories</em>,
Physics Reports, Volume 129, Issue 1, December 1985, Pages 1-74]. Towards the end, he goes on to prove that renormalized Yang-Mills theories that are BRST invariant exhibit gauge independence and unitary. At the end of the proof he states: </p>
<blockquote>
<p><em>One should note that we have implicitly assumed in this demonstration the existence of the S-matrix, i.e., the applicability of LSZ reduction formula [...] the proof is only valid when all gauge bosons are massive. Whenever massless gauge bosons are present in theory, all our arguments become formal.</em></p>
</blockquote>
<p>In the case of QCD, the gluons are massless, so does the <a href="http://en.wikipedia.org/wiki/LSZ_reduction_formula" rel="nofollow">LSZ formula</a> not apply to QCD? Is there a formal argument that proves gauge-independence as he suggests? </p> | g10668 | [
0.005798195023089647,
-0.00381569960154593,
0.007361035328358412,
-0.03055555559694767,
-0.017500106245279312,
0.00954432226717472,
0.02586851641535759,
0.09331893175840378,
0.007944762706756592,
-0.01554039865732193,
-0.03229823336005211,
0.050312452018260956,
0.009164012968540192,
0.0629... |
<p>Ok so if we setup a camera before the slit we will find a single photon and will follow through accordingly, likewise by having a camera setup after the slit, we can retroactivly collapse the wave function by observation. Here is my question. If we setup the camera to record like above but NEVER EVER EVER look at the result of what was recorded. Does the wave function still collapse. If so then perhaps its the camera causing it. If not then it is truly based upon the observer.</p> | g10669 | [
-0.003212783019989729,
0.011303303763270378,
0.019348453730344772,
0.007181796710938215,
0.002491886029019952,
0.008077988401055336,
0.059904035180807114,
0.04527482017874718,
-0.03770891949534416,
-0.04729611426591873,
0.002112999092787504,
0.036256249994039536,
0.0157817043364048,
0.0704... |
<p>Just out of curiosity. In the game Mass Effect, devices called mass relays contain two rotating rings, one inside of the other. See <a href="http://www.youtube.com/watch?v=qPxw5QjxhIs" rel="nofollow">http://www.youtube.com/watch?v=qPxw5QjxhIs</a> for an example, best seen around 00:10. </p>
<p>I was wondering: is this a stable motion? Intuitively, I'd say it isn't. Obviously, the outer ring describes normal rotational motion, but when the inner ring is taken into consideration, it seems to me that an additional driving force is required to maintain the entire situation. Am I right? I've been trying to apply some mechanical principles to it, but had no luck so far... Could anyone give a decent mathematical description of this?</p>
<p>Richard Terrett pointed out that this is in fact called a 2-axis gimbal. I wasn't aware of this, thanks!</p> | g10670 | [
0.011597448028624058,
0.058386143296957016,
-0.012832432985305786,
-0.019948812201619148,
0.05301445722579956,
0.0033530574291944504,
0.0036789458245038986,
-0.018661096692085266,
-0.021258363500237465,
0.0319911390542984,
-0.014618625864386559,
0.009171955287456512,
-0.011638420633971691,
... |
<p>Is there a minimal string length (maybe the <a href="http://en.wikipedia.org/wiki/Planck_lengthhttp://en.wikipedia.org/wiki/Planck_length" rel="nofollow">Planck length</a>), and is it quantized?</p>
<p>Do strings have a 0-dimensional (ie point) cross-section? </p> | g10671 | [
0.01613660715520382,
0.017555182799696922,
-0.01305378507822752,
-0.05131746083498001,
0.03169313818216324,
0.02619032934308052,
-0.015462285839021206,
-0.010698409751057625,
-0.04440690204501152,
0.03054806776344776,
0.021190719678997993,
0.011413807980716228,
-0.03268915042281151,
-0.024... |
<p>Just what the title states - </p>
<p>Does reversal of magnetic poles in a planet refer to the point in time when reversal is complete? </p>
<p>OR </p>
<p>Does it refer to the entire drawn out process (assuming the poles flip gradually from 0 through 180 degrees?</p> | g10672 | [
0.03076682798564434,
0.051087431609630585,
-0.0027911956422030926,
-0.005180727690458298,
0.05792608484625816,
0.02525169402360916,
0.02830151468515396,
0.018121348693966866,
-0.01819760911166668,
0.018512221053242683,
-0.04498475417494774,
0.028209220618009567,
0.03297623619437218,
-0.047... |
<p>Continuing from my previous question <a href="http://physics.stackexchange.com/q/30355/5265">Is reversal of magnetic polarity in a planet an instantaneous occurence?</a></p>
<p>A change in magnetic flux is expected to generate an EMF. </p>
<p>In the case where the magnetic poles of a planet flip - What would be the magnitude of the induced voltage/current?</p> | g10673 | [
0.007022291887551546,
0.015658581629395485,
-0.01451418362557888,
-0.03958140313625336,
0.09067638963460922,
0.038695573806762695,
0.004628224764019251,
0.04415367543697357,
-0.019522402435541153,
0.00968370120972395,
-0.03537101298570633,
0.04918142408132553,
0.002262117573991418,
-0.0254... |
<p>Angular momentum of an object is a physical quantity that depends on the chosen point about which to calculate the angular momentum.</p>
<p>It is often said that an object that has been thrown up in the air and is rotating, is physically rotating about the center of mass. I don't think that is what is physically happening. We chose the center of mass as the point of rotation because it is convenient mathematically (it makes the separation of translation and rotational energy easier).
We could choose any other point (inside, outside the object, in motion or at rest relative to the object) and calculate the rotation about that arbitrary point.</p>
<p>It is not a physical fact that the free object rotates about the center of mass.</p>
<p>Even an object that is constrained to rotate about a fixed axis, we could describe the rotation about any point, not necessarily points on the fixed, constrained axis.</p>
<p>So when we see an object rotating, its state of rotation is totally relative, as it happens for many other physical quantities.
Is that correct?</p> | g668 | [
0.05134028568863869,
-0.010258452035486698,
0.026354849338531494,
-0.04968879371881485,
0.03347037360072136,
-0.011546912603080273,
0.0738448053598404,
0.0326552651822567,
-0.01338543463498354,
0.026294218376278877,
0.0159849114716053,
-0.032625116407871246,
0.01883954368531704,
-0.0873014... |
<p>Using a bit of classical reasoning I'm imagining black hole formation to be much like an ice skater pulling in her arms:</p>
<p><img src="http://i.stack.imgur.com/9fiOU.png" alt="skater pulls in her arms to increase angular velocity"></p>
<p>Now, the size difference between a star and its black hole can't even be effectively captured in an image. The black hole for our sun would be much less than a pixel in this image:</p>
<p><img src="http://i.stack.imgur.com/XoKDr.png" alt="size comparison of our sun and planets"></p>
<p>That suggests to me that even a very slowly rotating stars would have much more angular momentum than could be supported by their resulting black holes. I haven't done the calculation because I don't really understand the <a href="http://en.wikipedia.org/wiki/Kerr_metric">Kerr metric</a> but even with a bunch of classical hand-waving I'd think that just about every black hole formed in a stellar-collapse would be spinning maximally.</p>
<p>So my question is, do we expect nearly all black holes to be spinning maximally? If so, (roughly) how much angular momentum is lost because the star had much more than the black hole could support? And, how is all of this extra angular momentum shed during collapse? Is it just in the form of tons of matter being ejected until the the angular momentum is low enough to allow for the formation of a Kerr black hole?</p> | g10674 | [
0.0029314993880689144,
0.0011213613906875253,
-0.0018798448145389557,
0.009886356070637703,
0.018766658380627632,
-0.01878543011844158,
0.020698100328445435,
0.04386209324002266,
0.01486465334892273,
0.0104807885363698,
-0.014828674495220184,
-0.03808898851275444,
0.079135462641716,
-0.021... |
<p>What does exactly means "Small molecules may appear as solid, liquid, and gaseous phases without losing their molecular integrity"?, </p>
<p>I can't image how just a molecule can be a gas, liquid or solid. Or in fact the previous phrase refers to the state of aggregations of those small molecules?</p>
<p>My source is this article:</p>
<p><a href="http://www.sciencedirect.com/science/article/pii/S004060319900252X" rel="nofollow">B Wunderlich, A classification of molecules, phases, and transitions as recognized by thermal analysis, Thermochimica Acta, Volumes 340–341, 14 December 1999, Pages 37-52</a></p>
<p>If you could suggest me a reference that extend the previous one to more modern states of matter like Bose-Einstein condensates, i would really appreciate it.</p> | g10675 | [
-0.029759252443909645,
-0.01670723594725132,
0.0020244966726750135,
-0.0451238639652729,
0.03387359529733658,
-0.007456962950527668,
-0.053860921412706375,
-0.014565939083695412,
-0.023201771080493927,
-0.05676983296871185,
0.01091329287737608,
-0.03061436116695404,
0.012032052502036095,
0... |
<p>What are the differences in the types of problems Ricci/Tensor Calculus and Matrix Calculus can solve? One formulation is generally used by the physics community and the other by statisticians and engineers, but what about each of them makes them desirable for each of their fields despite what at least superficially seems to be a great deal of overlap?</p> | g10676 | [
0.062309954315423965,
0.07115962356328964,
0.007332789245992899,
0.047874774783849716,
-0.0075726015493273735,
-0.044338420033454895,
0.08993632346391678,
-0.05157727748155594,
-0.053323857486248016,
-0.0004632840573322028,
0.015539508312940598,
-0.024310965090990067,
0.011624859645962715,
... |
<p>I'm making a table where columns are labelled with the property and the units it's measured in:</p>
<p>Length (m) |||| Force (N) |||| Safety Factor <strong>(unitless)</strong> ||| etc...</p>
<p>I'd like not to write "unitless" on several columns...and I'm quite surprised I can't seem to find a symbol for it. Any suggestions?</p> | g10677 | [
-0.02053036168217659,
0.029292568564414978,
-0.007977028377354145,
-0.07272907346487045,
0.05766822770237923,
-0.009372705593705177,
-0.001885299221612513,
0.01902836002409458,
-0.021747926250100136,
-0.018879415467381477,
-0.011654308065772057,
0.04803811386227608,
0.005961078219115734,
-... |
<p>Consider a solid spherical object of uniform density that is rotating on an axis A1. Perpendicular to that axis one can draw another line that passes through the sphere. On this axis, on both sides of the sphere one attaches mass-less springs with spring constants F, and then attaches point masses of mass M to both springs.</p>
<p>If the object is now rotated around the axis A1 and simultaneously both springs are pulled and then let go, what will be observed?</p>
<p>My intuition is as follows:</p>
<p>The rate of rotation of the system will undergo wave-like behavior. It will rotate faster as the point masses attached to springs come closer to the center and it will rotate slower as they move away from the center. </p>
<p>Is this correct?</p> | g10678 | [
0.03764459490776062,
-0.0009462851448915899,
0.011895452626049519,
-0.01798909343779087,
0.023644745349884033,
-0.008483902551233768,
0.0648159384727478,
-0.00906483642756939,
-0.021373700350522995,
-0.038827624171972275,
-0.016464056447148323,
0.005033525638282299,
0.060281455516815186,
-... |
<p>A continuous charge distribution flowing as a constant current in a closed loop doesn't radiate. Is it therefore true that as you increase the number of proton bunches in the LHC, while keeping the total charge constant, the synchrotron radiation decreases?</p> | g10679 | [
0.08357934653759003,
-0.016055699437856674,
0.026061251759529114,
-0.015263457782566547,
0.05010659992694855,
0.05309811234474182,
-0.04370297119021416,
0.04419410601258278,
-0.03946366161108017,
0.005688529461622238,
-0.037906911224126816,
0.06312616169452667,
-0.023818079382181168,
0.037... |
<p>What is the correct way to use the resistance and temperature correlation formula from <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html" rel="nofollow">http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html</a>?</p>
<p>In particular, does R have to be the higher resistance and R0 the lower or vice versa? The resulting calculated dT differs depending on this choice of R and R0.</p>
<p>Quick example of what I mean:</p>
<blockquote>
<p>Choose R = 7.97 and R0 = 7.28, copper a ~= .00393</p>
<p>dT = 24.1171</p>
<p>Choose R = 7.28 and R0 = 7.97, copper a ~= .00393</p>
<p>dT = -22.0292</p>
</blockquote>
<p>I believe the answer is to use the former (always choose R and R0 so R > R0) because this more closely correlates with my lab data.</p> | g10680 | [
0.04871111363172531,
-0.0521603524684906,
-0.003015679307281971,
-0.02684025838971138,
0.043235186487436295,
-0.014415516518056393,
0.06960718333721161,
0.018941568210721016,
-0.03374059870839119,
-0.007396480068564415,
-0.0029161968268454075,
0.042006537318229675,
-0.0123821422457695,
0.0... |
<p>At time there are talks about <a href="http://en.wikipedia.org/wiki/Quantum_computers" rel="nofollow">quantum computers</a> and lot of talks and discussion on its exponential speed. But studying in some more details it makes reference to "Heisenberg uncertainty principle", which simply says that either position or momentum can be calculated for any electron. If we already know the limitation, then in which direction this research is going?</p> | g10681 | [
0.013811876997351646,
0.08972451835870743,
-0.011474847793579102,
-0.0039399308152496815,
0.029192790389060974,
0.002111887326464057,
0.05964081361889839,
0.026423534378409386,
-0.02896934188902378,
-0.011293408460915089,
0.042345501482486725,
0.0038135338108986616,
-0.02309146150946617,
0... |
<p>I feel like the answer should be "no" since all superfluids are not strictly BEC since they can undergo a Kosterlitz–Thouless transition in 2D, for example. I believe the ideal gas isn't superfluid, but is there any experimental evidence of a BEC without superfluid properties? I've been searching with no luck.</p> | g10682 | [
0.0027528335340321064,
-0.004976373165845871,
0.03618377447128296,
0.018306860700249672,
0.007804774213582277,
0.03266662359237671,
-0.061474159359931946,
0.037053514271974564,
-0.012922754511237144,
-0.07287884503602982,
-0.001955020474269986,
-0.011844063177704811,
0.000490387377794832,
... |
<p>I came across this question in an introductory physics course awhile back and I never got over it: "A hydrogen atom has an electron in the n=5 orbit, what is the maximum number of photons that might be emitted so that it decays to the ground state (n=1)?" The answer the professor was looking for was 4 since he was picturing the atom going $5 \rightarrow 4 \rightarrow 3 \rightarrow 2\rightarrow 1$. This sort of answer is how we are taught to think of atomic transitions in introductory physics courses, but I can't imagine its the complete picture. As far as I can tell the only constraints on the system are energy and angular momentum conservation and if you produce pairs of photons with opposite angular momentum you can produce infinitely many photon pairs, and thus infinitely many photons so there is no max number. There are obviously 'selection rules' on these sorts of transitions but they always seem to procede by some dominant process when as far as I can tell there can be higher-order processes that allow many more transitions to occur. </p>
<p>In short: given the full machinery of quantum mechanics, is the answer to the professor's question even finite? Is he right? Or is the number potentially infinite? </p>
<p>Note: I acknowledge this is a exam/HW problem, but from a loooonnnnngg time ago, and I'm looking for the 'real' answer, not the fake introductory answer, if there is a difference.</p>
<p>Thanks!</p> | g10683 | [
-0.028058459982275963,
0.04520091414451599,
0.0018789971945807338,
-0.01185443252325058,
0.021812012419104576,
-0.009213101118803024,
-0.005477638449519873,
0.05461060255765915,
-0.008986721746623516,
-0.005689500365406275,
-0.030408699065446854,
0.0032263381872326136,
0.007474288810044527,
... |
<p>The origin of linear birefringence in crystal can be easily explained by the symmetry of the crystal. However, it seems it is hard to be applied in circular birefringence (i.e. optical activity), since there is no macroscopic symmetry in sugar solutions. </p>
<p>So I wonder how we explain the levorotatory and the dextrorotatory in atom level POV?</p> | g10684 | [
0.007480415049940348,
0.044055696576833725,
0.003686925396323204,
0.00889816228300333,
0.057743024080991745,
-0.06927929818630219,
0.03827125206589699,
0.00427594780921936,
0.012044107541441917,
-0.008386506699025631,
-0.02675032429397106,
0.02725529856979847,
0.00990784727036953,
-0.02099... |
<p>If we thermally isolate a region in space, say using a hypothetical material of $0$ conductivity, and measure the region's temperature, will it be 2.7K?</p> | g10685 | [
0.039687592536211014,
0.010459952056407928,
-0.0030242858920246363,
-0.018748702481389046,
-0.04618731141090393,
-0.01792692206799984,
-0.024446045979857445,
0.028372570872306824,
0.006500026676803827,
0.007810086011886597,
-0.04404208064079285,
0.06650904566049576,
0.009687901474535465,
0... |
<p>So when people say: 'I am approaching the speed of light, and to get to 100% light I would need infinite energy' they are essentially saying that this situation is impossible?</p>
<p>I read this in Hawking's book and confused me because I assume when he says 99.9% speed of light, he means 99.9% speed of light in relation to someone outside observing?</p>
<p>I just cannot understand this notion of needing more and more energy to get closer to light as absolute velocity does not exist? (in that it is a purely relative concept). Surely the ability to accelerate further cannot possible be impeded because speed is all relative, there should be no limit to acceleration? If I 'accelerate' a further 50MPH, will I get to the destination exactly 50 miles early?</p>
<p>From what I can gather you 'can' accelerate FTL (sort off) but instead space bends towards you so you will get to your destination 'ftl' but only due to the curvature in space? So in effect, you can go light years in seconds (lets forget the practicals for a second), but from anyone observing, this will ALWAYS take light years.</p>
<p>Also, if for me I am going 'FTL', does outside observers see me as going light speed, or is it 99.999%.. is there a specific number?</p> | g10686 | [
-0.010529719293117523,
0.06431876122951508,
0.010573050938546658,
0.00852007232606411,
-0.007158887572586536,
-0.009229029528796673,
0.04245736449956894,
0.020891599357128143,
-0.05301649495959282,
-0.026330234482884407,
0.013420188799500465,
-0.005235625896602869,
0.03819334879517555,
0.0... |
<p>In class when we talked about the harmonic oscillator in QM we noticed that the eigenfunctions to the annihilation operator are coherent states in the sense that they have minimum uncertainty in momentum and position. My question is: What is the physical meaning behind this? Why are coherent states eigenfunctions to the annihilation operator and: Was this only a lucky punch and a special property of the harmonic oscillator or is this true for more physical problems?</p> | g339 | [
0.027947982773184776,
-0.012724224478006363,
-0.002109498716890812,
0.004666045308113098,
0.03803163394331932,
0.04804418236017227,
0.037210628390312195,
0.05037828907370567,
-0.0037222588434815407,
-0.007810811046510935,
0.01075871754437685,
-0.07915865629911423,
0.03935760259628296,
-0.0... |
<p>For example, take a water bottle. Fill it with water and then turn it upside down.
Instead of flowing steadily downward, it gulps down in parts. Why?</p> | g10687 | [
0.06539630889892578,
0.025179624557495117,
-0.024700911715626717,
0.0069192214868962765,
0.06015697494149208,
0.059245046228170395,
0.01863444410264492,
0.022087212651968002,
-0.0527038499712944,
-0.0481124073266983,
0.03729771450161934,
-0.016069184988737106,
0.06349073350429535,
0.030238... |
<p>Does vacuum or outer space contain any gases? Recently i watched a video on youtube,in which NASA installs a camera on a spacecraft.The footage shows some dust particles or some matter floating over the space craft's surface and as well from the thrust.What exactly is that? If there is nothing in vacuum,how come newton third law works out to make it move in turn?
Here is the link</p>
<p><a href="http://www.youtube.com/watch?v=HSnOTaCeSuk" rel="nofollow">http://www.youtube.com/watch?v=HSnOTaCeSuk</a></p> | g10688 | [
0.04563572257757187,
0.03386608511209488,
-0.01865113154053688,
0.04281742870807648,
0.06878767907619476,
0.08556988835334778,
-0.07435533404350281,
0.005479855928570032,
-0.02661035768687725,
-0.0557226836681366,
0.018631525337696075,
0.04226665571331978,
0.06205937638878822,
0.0008883688... |
<p>Related post <a href="http://physics.stackexchange.com/questions/55687/causality-and-quantum-field-theory">Causality and Quantum Field Theory</a></p>
<p>In Peskin and Schroeder's QFT p28, the authors tried to show causality is preserved in scalar field theory.</p>
<p>Consider commutator
$$ [ \phi(x), \phi(y) ] = D(x-y) - D(y-x) \tag{2.53} $$
where $D(x-y)$ is the two-point correlation function,
$$D(x-y):= \langle 0 | \phi(x) \phi(y) | 0 \rangle = \int \frac{d^3 p}{ (2\pi)^3} \frac{1}{ 2E_{\mathbf{p}}} e^{-ip(x-y)}\tag{2.50}$$</p>
<p>P&S argued that each term in the right-hand-side of (2.53) is Lorentz invariant, since
$$\int \frac{d^3p }{ (2\pi)^3} \frac{1}{2E_{\mathbf{p}}} = \int \frac{ d^4 p }{ (2\pi)^4} (2\pi) \delta(p^2-m^2)|_{p^0>0} \tag{2.40}$$ is Lorentz invariant.</p>
<p>Since there exists a continuous Lorentz transformation in the spacelike interval $(x-y)^2<0 $ such that $(x-y) \rightarrow - (x-y) $ and $D(y-x)=D(x-y)$, (2.53) equals zero in the spacelike interval. In timelike interval, since such continuous Lorentz transformation does not exist, (2.53) is non-zero in general.</p>
<p>My question is, consider a non-continuous Lorentz transmation in the timelike interval, $PT$, namely time reversal times parity transformation. I can also let $(x-y) \rightarrow - (x-y) $. Why (2.53) in the timelike interval is non-zero?</p>
<p>I guess $PT$ will let (2.40) go to $p^0<0$ branch. But I am not sure if it breaks the Lorentz invariant of (2.40) and (2.50). </p> | g10689 | [
0.05089600011706352,
-0.028706369921565056,
-0.009915480390191078,
-0.03013659082353115,
0.05227772891521454,
0.029079614207148552,
0.04469152167439461,
0.039109330624341965,
-0.005157435778528452,
0.014029107987880707,
-0.013286194764077663,
0.03493151068687439,
-0.023954184725880623,
-0.... |
<p>Is it possible to have a VEV (vacuum expectation value) for tensor field? I am mainly concerned about second rank tensors. It seems it can have a VEV which will be proportional to the metric tensor (in flat space-time). Does this make any sense at all? If it does, then what are it's implications?</p> | g10690 | [
-0.005328935105353594,
0.04174291715025902,
-0.008557758294045925,
0.01943625509738922,
0.05072817951440811,
0.03278358653187752,
-0.021322395652532578,
-0.024209734052419662,
-0.05437948554754257,
-0.02433709241449833,
-0.04216385632753372,
0.008145974949002266,
0.0254875048995018,
-0.035... |
<p>In the coordinate representation, in 1D, the wave function depends on space and time, $\Psi(x,t)$, accordingly the time dependent Schrodinger equation is </p>
<p>$$H\Psi(x,t) = i\hbar\frac{\partial}{\partial t}\Psi(x,t)$$</p>
<p>In a representation-free notations we deal instead with the ket $|\Psi\rangle = |\Psi(t)\rangle$. Now how to write Schrodinger equation in this case?
I find some books write</p>
<p>$$H|\Psi\rangle = i\hbar\frac{\partial}{\partial t}|\Psi\rangle$$</p>
<p>and others write</p>
<p>$$H|\Psi\rangle = i\hbar\frac{d}{dt}|\Psi\rangle$$</p>
<p>So which one of the last 2 equations is correct?</p> | g10691 | [
0.013377324678003788,
-0.06816042959690094,
-0.03723550960421562,
-0.037559010088443756,
0.02118559181690216,
0.01016651839017868,
0.018318263813853264,
0.05303299054503441,
-0.04471147060394287,
0.010537250898778439,
0.0484260693192482,
0.009988273493945599,
0.016048798337578773,
0.036479... |
<p>Can the wave function solution to Schrodinger's Equation be interpreted as an oscillation between all possible measurements (obviously with some type of weighting that would describe the shape of the wave) in the limit that the frequency of the oscillation goes to infinity?</p>
<p>I don't see how any experiment could test such a claim, but can this be proved/disproved on theoretical grounds?</p> | g10692 | [
-0.011137026362121105,
0.02504296414554119,
0.007648118771612644,
-0.06575779616832733,
0.08521318435668945,
-0.010441076941788197,
0.022034848108887672,
0.04518505558371544,
-0.008421851322054863,
-0.02502463571727276,
0.0005549811176024377,
-0.03275701403617859,
-0.012006377801299095,
0.... |
<p>Well I had this thought experiment in which a particle observes itself, and something like the following is observed.</p>
<p>Taking in mind the uncertainty principle all particles even stopped at 0K jiggle about, but nothing stops us from going into there frame and observing from there. We do just that, we go in the frame of a particle and keep it at the origin, since we are in the frame of the particle it does not move, its entire universe seems to jiggle as from outside frame we would say the particle is jiggling.</p>
<p>So how the principle seems to have failed here? We most definitely know that our particle is motionless at the origin when we see from its own frame, we do not care about the entire universe jiggling about and we notice that the uncertainty principle becomes invalid! Why is such a thing happening? Am I doing something wrong? Or is this a known loophole to the principle?</p> | g10693 | [
0.027831684798002243,
0.020838435739278793,
0.03274795040488243,
-0.01782669685781002,
0.029076164588332176,
-0.002718724310398102,
0.0197458378970623,
0.09371685981750488,
-0.040612462908029556,
-0.03615383431315422,
-0.011563794687390327,
-0.0077427891083061695,
-0.01024753786623478,
0.0... |
<p>I have two questions.</p>
<p><strong>First</strong>, I understand that in a nuclear reaction
$$Q:=K_{after}-K_{before}\equiv E_{0,before}-E_{0,after} \qquad (1)$$
where $K$ is the total kinetic energy, and $E_0$ is the total rest energy.
My question is, in the reaction $^{9}Be\left(\gamma,n\right)^{8}Be$, where should I put the energy of the $\gamma$-photon?
I mean, conservation of energy says
$$Mc^{2}+h\nu=mc^{2}+M'c^{2}+K_{n}+K' \qquad(2)$$
where $M$=mass of $^{9}Be$, $m$=mass of the neutron, $M'$=mass of $^{8}Be$, and $K_{n}$, $K'$ are the kinetic energies of the neutron and of the $^{8}Be$, respectively. </p>
<p>Then, using (1) (with the rest energies version) I wrote
$$Q=(M-m-M')c^2 \qquad (3)$$
but this is equivalent to: (using (2))</p>
<p>$$Q=K_{n}+K'-h\nu \qquad (4)$$
So, my <strong>1st question</strong> is: is (4) the correct expression for $Q$?</p>
<p><strong>Second</strong>, I want to calculate the kinetic energies $K_n$ and $K'$. In order to do this, I'm thinking to use (4) (if it's correct) with $K_{n}=\frac{1}{2}mv^{2}$ and $K'=\frac{1}{2}M'V^{2}$, and the conservation of linear momentum</p>
<p>$$\frac{h}{\lambda}=mv+M'V \qquad (5)$$</p>
<p>Assuming that the neutron and the $^{8}Be$ continue moving in the direction of the $\gamma$-photon.</p>
<p>So, my <strong>2nd question</strong> is: can I make this last assumption? Or in other words, is (5) a correct expression for the linear momentum conservation?</p> | g10694 | [
0.050504542887210846,
-0.0514889620244503,
0.013267657719552517,
0.0035564766731113195,
0.052933257073163986,
-0.030894652009010315,
0.039488811045885086,
0.03287984058260918,
-0.02374577522277832,
0.004717167932540178,
-0.02817542478442192,
0.020926915109157562,
-0.018676619976758957,
0.0... |
<p>Why is light produced when an underwater bubble is collapsed with a sound wave?</p>
<p>I have come across this fact on a page (<a href="http://www.scientificamerican.com/article.cfm?id=tiny-bubbles-explain-puzz">similar to this</a>) but can't understand "Why". I'm just curious about this interesting fact. And, I want to know what's the currently accepted model for this phenomenon and how good it holds. Any kind of help regarding this topic will be highly appreciated.</p> | g340 | [
0.044825904071331024,
0.05056457594037056,
0.028607847169041634,
-0.020699581131339073,
-0.008060313761234283,
0.08865799754858017,
0.03763085603713989,
0.019851606339216232,
0.022556910291314125,
-0.0672796219587326,
-0.021942080929875374,
0.016728730872273445,
0.03003433719277382,
0.0471... |
<p>I recently found out about sending stuff into space and using the unique zero gravity and cosmic radiation riddled environment to investigate stuff like crystal growth. Since thin film science is a hot topic still, I am wondering what can be done in space?</p>
<p>Things that come to mind, which likely have been covered already, include radiation protection, energy conversion, perhaps even using cosmic radiation to stimulate some desirable chemical reactions that only need some high-energy source to get started.</p>
<p>As an aside, it would be preferable if said experiments could be done on an amateur hobbyist's budget, but it not, it's a fun thought experiment at least to see what could be done.</p> | g10695 | [
0.026129720732569695,
0.051715970039367676,
0.01660286635160446,
0.014452509582042694,
-0.049328260123729706,
0.004668102599680424,
-0.05749869719147682,
0.03021143190562725,
0.017152089625597,
-0.07277925312519073,
0.044182226061820984,
0.056900352239608765,
0.030563214793801308,
-0.00945... |
<p>From my high school physics class I remember that there are some particles which exhibit pure alpha decay (i.e. alpha decay to there stable isotope), like Po-210, Po-211 and Bi-209.</p>
<p>What I also know is that alpha particles, due to their low speed, will be absorbed already within a few cell layers of skin ($\sim 40 \mu$m if I remember correctly). </p>
<p>My question comes from the combination of these two points: if you where able to isolate e.g. Bi-209 in a pure form, would it be harmful to swallow it or will all alpha particles be captured in upper tissue layers, thus leaving you fairly unharmed?!</p>
<p>Note: I am asking in particular about particles with pure alpha decay, because if the decay product is a gamma or beta emitter you will probably be harmed by the decay products anyway.</p> | g10696 | [
0.035568442195653915,
0.002965713618323207,
0.01589537039399147,
0.012645414099097252,
-0.0035814112052321434,
0.011441896669566631,
-0.004979684948921204,
0.04449994117021561,
0.04564885050058365,
-0.060057248920202255,
0.0015308912843465805,
0.03206607699394226,
0.004883271176367998,
-0.... |
<p><a href="http://food.thefuntimesguide.com/2010/07/bamboo_cutting_board.php" rel="nofollow">http://food.thefuntimesguide.com/2010/07/bamboo_cutting_board.php</a></p>
<blockquote>
<p>Some bamboo cutting boards are glued together with adhesives that have formaldehyde in them — <strong><em>which could eventually leak into and contaminate food.</em></strong></p>
</blockquote>
<p>I wanted to understand the logic behind the above claim in italics. </p>
<p>The glue is <strong>between</strong> the sheets of bamboo cutting board. So, if I use only one side of cutting board all the time, will the gravitational force not stop the glue from going upwards and mix in the food?</p> | g10697 | [
0.04432510584592819,
0.0698523223400116,
0.008092883974313736,
0.015703193843364716,
0.000861791952047497,
-0.006700406316667795,
-0.028007350862026215,
0.03028125874698162,
-0.08512753993272781,
-0.048139091581106186,
0.03290918841958046,
-0.0031985261011868715,
-0.08087578415870667,
0.02... |
<p>I was going through a problem in which they had given mass and speed and asked its wavelength. Now its de Broglie wavelength $h/\lambda$ and I had to find out which of them had wave nature which could be observed. I thought objects whose wavelength is greater than wavelength of light would have observable wave nature, with calculations I found out that electrons had wavelength of $0.78Å$ in that case so with my reasoning it should not be observed which turned out to be the wrong answer. Please help me how should we know whether one has observable wave nature or not.</p> | g10698 | [
0.013288868591189384,
-0.02031843364238739,
0.031114084646105766,
-0.04326861351728439,
0.09593837708234787,
0.04936687648296356,
-0.01660805009305477,
-0.01389226969331503,
-0.03469737619161606,
-0.0461970716714859,
0.055901773273944855,
0.03300242871046066,
-0.020043721422553062,
0.08612... |
<p>Bohr said that only certain orbits of definite energy are allowed inside the atom. He said that the electrons in their ground state do not emit radiation and that they will emit radiation when they fall from higher energy levels to lower energy levels. My question is what does orbits with definite energy mean? and why do the electron in their ground state not emit radiation?</p> | g341 | [
0.014587030746042728,
0.026313094422221184,
0.026421496644616127,
-0.019968165084719658,
-0.0007199120591394603,
0.061920806765556335,
-0.018742455169558525,
0.061715658754110336,
-0.031005581840872765,
-0.022419936954975128,
-0.012204181402921677,
0.02586953528225422,
0.01629573479294777,
... |
<p>Like all stars, large ones are stable as long as there is a sufficient amount of hydrogen (or helium) to fuse. This fusion process is what prevents them from collapsing in on themselves. However, once the main elements have been fused up to iron, the star becomes unstable. Eventually, it may supernova and leave a black hole; a singularity that sucks in light and matter that enters the event horizon.</p>
<p>The star prevents collapsing in on itself with fusion. When it goes supernova, it expels a large amount of its mass. If the remaining bit is enough to create a black hole that is so dense that fusion cannot balance the gravitational force, then how did the star exist in the first place and why wasn't it dense enough to form a black hole?</p> | g10699 | [
-0.011063105426728725,
0.036573078483343124,
0.022106116637587547,
-0.03292282298207283,
0.02869495004415512,
0.043468035757541656,
-0.0007303819875232875,
0.090619295835495,
-0.037941284477710724,
-0.06214463710784912,
-0.037904828786849976,
-0.0008558098925277591,
0.03610951825976372,
0.... |
<p>Suppose a particle has energy $E>V(+/-\infty)=0$, then the solutions to the Schrodinger equation outside of the potential will be $\psi(x)=Ae^{i k x}+Be^{-i k x}$.
How can one show or explain that $|B|/|A|$ gives the probability that a particle scattering off the potential is reflected?</p> | g10700 | [
0.016620786860585213,
0.02596624568104744,
-0.030724162235856056,
-0.024987028911709785,
0.04779188707470894,
0.05597517266869545,
-0.02730400860309601,
0.08899962902069092,
-0.013599013909697533,
-0.010358248837292194,
0.010505806654691696,
0.043601226061582565,
0.02587491273880005,
0.010... |
<p>How can one prove that the number of images formed by two plane mirrors at right angles to each other is 3?</p>
<p>Is there a mathematical proof for the same ? </p> | g10701 | [
0.006121198181062937,
0.03378885239362717,
0.01435100007802248,
-0.01803554967045784,
0.03326175734400749,
-0.0016934808809310198,
0.026455150917172432,
0.028227010741829872,
-0.040861744433641434,
0.027327217161655426,
-0.02367347478866577,
-0.006944963242858648,
0.017999744042754173,
0.0... |
<p>Where would you say I can start learning about Hamiltonians, Lagrangians ... Jacobians? and the like?</p>
<p>I was trying to read Ibach and Luth - Solid State Physics, and <a href="http://imgur.com/a/5fc56" rel="nofollow" title="Picture from "Solid State Physics" by Ibach and Luth 1991. Published by Springer-Verlag">suddenly</a></p>
<p>(suddenly a Hamiltonian pops up. and then a wave equation and then $H_{aa}\ and\ H_{ab}$?</p> | g10702 | [
0.0640166625380516,
0.001075858250260353,
0.015775620937347412,
-0.03921274095773697,
0.05949628725647926,
-0.015856031328439713,
0.05031006783246994,
0.056442324072122574,
-0.000859662948641926,
-0.025788728147745132,
0.010402453131973743,
0.05647817999124527,
0.0918586254119873,
0.030109... |
<p>I was wondering if the good old quadratic potential was the only potential with equally spaced eigenvalues. Obviously you can construct others, such as a potential that is infinite in some places and quadratic in others, but that's only trivially different. I am not referring to equally spaced as a limiting behavior either, I mean truly integer spaced.</p>
<p>Any ideas? If not, is there a proof for its uniqueness?</p> | g10703 | [
0.033095069229602814,
0.037874650210142136,
0.036470990628004074,
-0.050366755574941635,
0.031216390430927277,
-0.0005582024459727108,
-0.02094154804944992,
-0.014360631816089153,
0.07664306461811066,
-0.0016441157786175609,
0.05676741153001785,
-0.06217564642429352,
-0.002182130701839924,
... |
<p>So again I have two equations:</p>
<p>$$K= \frac{1}{2} m v^2 + \frac{1}{2} I \omega^2$$</p>
<p>And</p>
<p>$$K_w = \frac{1}{2} I \omega^2 $$</p>
<p>What's the difference between these two? Thanks.</p> | g10704 | [
0.028469128534197807,
-0.04245126247406006,
-0.024456363171339035,
0.0452745296061039,
0.044360172003507614,
-0.02292444184422493,
0.02810320258140564,
-0.03838362172245979,
-0.030107446014881134,
0.05292848125100136,
-0.008926807902753353,
0.06099537014961243,
0.0028622907120734453,
0.032... |
<p>In section 5.8 of Misner, Thorne, and Wheeler's "Gravitation" there is a proof that 4-momentum determined as
$$
\tag 1 p^{\mu} = \int T^{\mu 0}\,\mathrm{d}^{3}\mathbf r , \quad \partial^{\mu}T_{\mu \nu} = 0,
$$
transformed as 4-vector under the Lorentz transformation (case "c"). The authors proposed the next explanation: in case "b" they proved that an integral
$$
\tag 2 p^{\mu} = \int T^{\mu \nu}\,\mathrm{d}S_{\nu}
$$
doesn't depend on choise of the hypersurface, so without loss of generality they choosed one with $t = const$ with $p^{\mu} = \int T^{\mu 0}\,\mathrm{d}^{3}\mathbf r$. After that they considered two integrals $(2)$ with hypersurfaces $t = const, t' = const$, but the first has constant $t$ in one Lorentz frame, while the second has constant $t'$ in another frame. Relate to the first frame the $t'$-line of the second surface only has slope in $t-x$ diagram compare to $t$-line. So they added timelike hypersurfaces on infinity and then they got closed surface
$$
\oint T^{\mu \nu} \,\mathrm{d}S_{\nu}.
$$
By the Stokes theorem it is equal to
$$
\int \partial_{\mu}T^{\mu \nu}\,\mathrm{d}\Omega = 0,
$$
and by another side (I wrote it in the first frame)
$$
\int_{t = const} T_{\mu 0}\,\mathrm{d}^{3}\mathbf r - \int_{t'} T_{\mu \nu}\,\mathrm{d}S^{\nu} = 0.
$$
So
$$
\tag 3 \int_{t = const} T_{\mu 0}\,\mathrm{d}^{3}\mathbf r = \int_{t'} T_{\mu \nu}\,\mathrm{d}S^{\nu}.
$$
I don't understand how exactly they made a consequence that this directly leads to the 4-vector nature of $p^{\mu}$ definition given in $(1)$.</p>
<p>I know that in the second frame I also can rewrite the right side of $(3)$ in a form
$$
\int T_{\mu 0}\,\mathrm{d}^{3}\mathbf r.
$$
So may I write
\begin{split}
\int_{t'} T_{\mu \nu}\,\mathrm{d}S^{\nu}
&= \int_{t' = const}{\Lambda_{\mu}}^{\alpha}T_{\alpha \beta}'{\Lambda^{\beta}}_{\nu}{\Lambda^{\nu}}_{\gamma}\,\mathrm{d}S^{\gamma}{'} \\
&= {\Lambda_{\mu}}^{\alpha} \int_{t' = const} T_{\alpha 0 }'\,\mathrm{d}^{3}\mathbf r{'}\\
&={\Lambda_{\mu}}^{\alpha}\int_{t = const}T_{\alpha 0}'\,\mathrm{d}^{3}\mathbf r{'} \\
\Longrightarrow\quad p^{\mu} &= {\Lambda^{\mu}}_{\alpha}p^{\prime\alpha},
\end{split}
which completes the proof? Or the completion is another?</p> | g10705 | [
0.05453852564096451,
-0.028909960761666298,
-0.019886227324604988,
-0.03536897152662277,
0.024402815848588943,
0.02983701042830944,
0.09803654998540878,
-0.03930247947573662,
-0.04862785339355469,
-0.018561450764536858,
-0.04078886657953262,
-0.03600209206342697,
-0.01800082065165043,
0.01... |
<p>Michio Kaku's explanation of universes in hyperspace in <a href="https://www.youtube.com/watch?v=D6XAkVA7RmY" rel="nofollow">this youtube video</a> gives a metaphor of our universe being the surface of a hyperspace bubble that's currently becoming larger. He also says these bubbles colliding would produce the creation of new universes and the destruction of involved universes.</p>
<p>But this makes me think there's a lot of room in hyperspace for a universe to float for a very long time without encountering another universe.</p>
<ul>
<li><p>Is there anything significant to note about areas of hyperspace that don't currently have a universe? </p></li>
<li><p>Is it highly entropic? </p></li>
<li><p>Does hyperspace change in any way as a universe approaches? </p></li>
<li><p>Is it similar to how a galaxy will warp the space-time around it, in that hyperspace follows the same mechanics, but with more dimensions?</p></li>
</ul> | g10706 | [
-0.017710309475660324,
0.08306107670068741,
0.005681282375007868,
0.004823994357138872,
-0.019023844972252846,
0.03888777270913124,
0.018634870648384094,
0.007608878426253796,
0.030477289110422134,
-0.049758389592170715,
0.029873207211494446,
-0.02763454057276249,
0.03030494414269924,
0.08... |
<p>I know that displacement current is due to time-varying electric field and its not an electric current.</p>
<p>But then, is it charge that is actually being displaced?</p> | g342 | [
0.06553281843662262,
0.01779244653880596,
-0.0015989883104339242,
0.013903768733143806,
0.08673460781574249,
0.08884989470243454,
-0.002338138408958912,
0.04036819934844971,
0.0016877042362466455,
0.021760834380984306,
-0.029188621789216995,
-0.02177506312727928,
-0.03768881782889366,
-0.0... |
<p>If negative mass is rotating around fixed positive mass, then what will be the nature of force and how?</p> | g343 | [
0.018152229487895966,
0.0037110557314008474,
0.0008805834222584963,
0.0280916690826416,
0.04290762171149254,
0.031232036650180817,
0.006193794310092926,
-0.027216650545597076,
-0.02501862682402134,
-0.04583555832505226,
-0.0031351549550890923,
-0.02841983549296856,
-0.028172064572572708,
-... |
<p>Usually when discussing Fermi liquid theory, it is stated that due to the quasiparticles effectively behaving like a free electron gas with effective mass, the specific heat is linear in $T$ at small temperatures.</p>
<p>However, it turns out the Helium-3 has also a dependence of type $T^3 \ln T$. I want to understand where this comes from. Apparently it has something to do with spin fluctuations. I found the relevant paper by Pethick et al ( Pethick, C. J., and G. M. Carneiro. “Specific Heat of a Normal Fermi Liquid. I. Landau-Theory Approach.” Physical Review A 7, no. 1 (January 1, 1973): 304–318. ) however a bit dense to read and not very elucidating. </p>
<p>Since at that time Pethick et al
didn't know about renormalization group and other nice modern techniques, is there today maybe a more accessible treatment of spin fluctuations?</p>
<p>For example, I think I have gleaned from their paper that the contribution somehow arises from a dressing of the two-particle vertex. But on the other hand, RG tells me that the Landau parameters $F$ don't renormalize, so I wouldn't expect such a dressing. </p>
<p>It also seems that their contribution to the specific heat gives a term that depends not only on the angle between two scattered momenta, but also their magnitude. However, in the usual RG approach all deviations from the Fermi surface give rise to irrelevant operators... (In the language of the review paper of Shankar, Shankar, R. “Renormalization-group Approach to Interacting Fermions.” Reviews of Modern Physics 66, no. 1 (1994): 129.)</p>
<p>I probably see this way more complicated than it really is... </p>
<p>Does anyone have a comment or a good source for this problem?</p> | g10707 | [
-0.03068803809583187,
0.038381386548280716,
-0.01972518116235733,
-0.023186691105365753,
0.028365889564156532,
0.062126193195581436,
-0.006674864795058966,
0.05161672085523605,
-0.035125985741615295,
0.02645084448158741,
-0.015145597979426384,
0.04615291953086853,
0.006871408317238092,
0.0... |
<p>This troubles me: We are talking about time and space being equivalent, but still only consider Spin in the $x$, $y$ or $z$-direction. What's Spin in time dimension? Is it distinction between particles and antiparticles?</p> | g10708 | [
0.03197813406586647,
0.009859246201813221,
-0.007226523477584124,
-0.03873418644070625,
0.0056036110036075115,
0.032323405146598816,
0.08226171880960464,
-0.03120393678545952,
-0.0002176167326979339,
-0.0032702283933758736,
0.008266261778771877,
0.027072828263044357,
0.00591124314814806,
0... |
<ul>
<li>How Einstein's SR becomes GR?</li>
</ul>
<p>$$ds^2=dr^2-c^2dt^2,$$</p>
<p>$$ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}.$$</p>
<ul>
<li><p>When the $s$ is constant $ds^2=0$, isn't it true?</p></li>
<li><p>How to connect Einstein's SR with GR?</p></li>
<li><p>What is the GR-differential $ds^2$?</p></li>
</ul> | g10709 | [
-0.004477183800190687,
-0.0017478896770626307,
-0.025629036128520966,
-0.046841610223054886,
0.009688211604952812,
0.039887215942144394,
0.033797167241573334,
0.013252317905426025,
-0.04350242391228676,
-0.0649072602391243,
-0.04657857120037079,
0.04867739602923393,
0.05727095901966095,
-0... |
<p>I am not a phycisist, so please forgive my ignorance. This is related to my <a href="http://physics.stackexchange.com/questions/30894/negative-and-positive-energy-and-hawking">posts</a> and <a href="http://physics.stackexchange.com/questions/30965/naive-question-on-quantum-mechanics-and-uncertainty-principle">this</a>.<br>
I am trying to undertand what is meant by the term <em>"Nothing"</em> in physics or Quantum Mechanics since it seems to me that this term is not used in the way we understand it in everyday language.<br>
So QM seems to suggest (in a nutshell) that "things pop out of <strong>nothing</strong>".<br>
But from <a href="http://en.wikipedia.org/wiki/Quantum_fluctuation" rel="nofollow">wiki</a> I see the following quote: </p>
<blockquote>
<p>"According to quantum theory, the vacuum contains neither matter nor
energy, but it does contain fluctuations, transitions between
something and nothing in which potential existence can be transformed
into real existence by the addition of energy.(Energy and matter are
equivalent, since all matter ultimately consists of packets of
energy.) Thus, the vacuum's totally empty space is actually a seething
turmoil of creation and annihilation, which to the ordinary world
appears calm because the scale of fluctuations in the vacuum is tiny
and the fluctuations tend to cancel each other out.</p>
</blockquote>
<p>So what is "Nothing" in QM? If this quote is correct, I can interpret it only as follows:<br>
The "Nothing" is not in the way used in everyday speech but is <em>composed</em> of "transitions" i.e. something that is "about to become"<br>
Is this correct? If yes, why is this defined as "Nothing"? Something that is "about to become" is not nothing but there is something prerequisite.<br>
In very lame terms: Einstein was born a non-physicist but became a physicist, so if this is a correct analogy, then there </p>
<ol>
<li><em><strong>there is something</strong> underlying</em> that was non-something that became
something</li>
<li>A non-something came into something because something else (not
nothing) <em>permitted it to become</em>. E.g. Einstein's talent (or
Mozart's) would have been lost had he been born in Africa or in a
country with no educational facilities. So he would not become a physicist (but the required talent would be present but not come into reality)</li>
</ol>
<p>Could someone please help me understand this (perhaps trivial to you) concept? </p> | g10710 | [
0.022080224007368088,
-0.0022700924891978502,
-0.005296837072819471,
-0.014366361312568188,
0.025343941524624825,
0.04936042055487633,
-0.017553899437189102,
0.001332281157374382,
0.012966213747859001,
-0.03437285125255585,
-0.006058560684323311,
-0.014424473978579044,
0.0347624346613884,
... |
<p>Recently I have been confused by the fact that: </p>
<p>Joseph Polchinski's name appear in FFP Physics Frontiers Prize 2013 here: <a href="https://fundamentalphysicsprize.org/laureates6" rel="nofollow">https://fundamentalphysicsprize.org/laureates6</a> </p>
<p>``<strong>Joseph Polchinski</strong> for his contributions in many areas of quantum field theory and string theory. His discovery of D-branes has given new insights into the nature of string theory and quantum gravity, with consequences including the AdS/CFT correspondence.''</p>
<p>However, the same award in the next year, FFP Physics Frontiers Prize in 2014 here: <a href="https://fundamentalphysicsprize.org/laureates3" rel="nofollow">https://fundamentalphysicsprize.org/laureates3</a>
which awarded Polchinski again. And for the exactly same news announcement. </p>
<p>I wonder <strong>whether Polchinski won the Physics Frontiers Prize twice, in 2013 and 2014? If so, is there a reason for that?</strong> (especially puzzling, since there are so many great candidates out there, why bother to award the same great person for the same acknowledgment?)</p>
<p>Excuse me this question may not be related to physical effect or phenomena, but it is about the puzzle caused by a physics prize. So, it is a puzzle of physics. I wish the physics puzzle is allowed to be asked here. (I am very puzzled!)</p> | g10711 | [
0.00790275726467371,
0.0545356385409832,
0.026983074843883514,
-0.003221227554604411,
0.0660441517829895,
-0.008215529844164848,
0.011522817425429821,
0.0032088225707411766,
0.006083388812839985,
-0.04951896890997887,
0.0002297527971677482,
-0.03586572781205177,
0.026710346341133118,
-0.01... |
<p>A car is moving at a velocity of $10 \, \text{m}/\text{s}$. After point $A$ no acceleration is provided. By simple measurement, the acceleration is found to be $-1 \, \text{m}/\text{s}^2$.</p>
<p>Using standard equations: $$v = u + at, \; v=0, \; u = 10, $$ we arrive at $t = 10 \text{s}$.</p>
<p>$$S = ut + .5 at^2 = 50 \,\text{m}$$</p>
<p>ie- the car stops at $50\, \text{m}$ from point $A$.</p>
<p>However, by manual calculation, the car travels the following distance before coming to stop: $10 \, \text{m}$ at $t=0$, $9 \, \text{m}$ at $t =1$, etc since $a = -1$, the $v$ reduces by $1 \, \text{m}/\text{s}$, so on, so we get $S = 10 +9+..1 = 55 \, \text{m}$</p>
<p>Where am I going wrong here?</p> | g10712 | [
0.030121931806206703,
0.023107172921299934,
-0.01813642680644989,
0.011741242371499538,
0.03652234748005867,
-0.02962014265358448,
0.08150932937860489,
0.055227406322956085,
-0.07855623215436935,
-0.008806711994111538,
-0.03334483504295349,
0.007119237910956144,
0.010508597828447819,
0.004... |
<p>It's not homework (I'm teacher). I would like to compute sum of forces on this study :</p>
<p><img src="http://i.stack.imgur.com/2bLUJ.png" alt="enter image description here"></p>
<p>The shape is symmetrical like that I'm sure the center of gravity is in the center of the shape. I compute forces on axis X only. No external gravity. Air container are fixed on big container. But air container has very low pressure, I don't want to compute it, consider it like vacuum. </p>
<p>I know force of pressure is like :</p>
<p>$\frac{1}{2}{\rho}h_{\epsilon}^2w^2R^2$ with R the distance to container from center of gravity of container, $h_{\epsilon}^2$ is a small area, true ? </p>
<p>I compute forces on water, depth is d, it's:</p>
<p>$$d\omega^2\rho*((\int_{0}^{h1}(r1^2+y^2)cos(atan(\frac{y}{r1}))dy)-(\int_{0}^{h1}(r2^2+y^2)cos(atan(\frac{y}{r2}))dy)+(\int_{0}^{h2}(r3^2+y^2)cos(atan(\frac{y}{r3}))dy))$$</p>
<p>so, it's:</p>
<p>$$d\omega^2\rho*((\int_{0}^{h1}\sqrt{(r1^2+y^2)}r1dy)-(\int_{0}^{h1}\sqrt{(r2^2+y^2)}r2dy)+(\int_{0}^{h2}\sqrt{(r3^2+y^2)}r3dy))$$</p>
<p>Is it ok ?</p>
<p>Now, if I want to compute forces on rectangle solid, I need to integrate 2 times ? Like that :</p>
<p>$$\frac{1}{2}d\rho\omega^2*(\int_{-h2}^{h2}\int_{0}^{r3}(x^2+y^2)^{0.5}cos(atan(\frac{y}{x}))dxdy-(\int_{-h1}^{h1}\int_{r1}^{r2}(x^2+y^2)^{0.5}cos(atan(\frac{y}{x}))dxdy)$$ </p>
<p>So it's:</p>
<p>$$\frac{1}{2}d\rho\omega^2*(\int_{-h2}^{h2}\int_{0}^{r3}(x^2+y^2)^{0.25}xdxdy-\int_{-h1}^{h1}\int_{r1}^{r2}(x^2+y^2)^{0.25}xdxdy)$$ </p>
<p>How to add mass inside integrales ?</p>
<p>I have a problem, I don't find 0 for the sum of forces.</p>
<hr>
<p>There are 2 additionnal forces Fa that decrease forces from liquid:</p>
<p><img src="http://i.stack.imgur.com/4grKT.png" alt="enter image description here"></p>
<p>But the shape can be like that:</p>
<p><img src="http://i.stack.imgur.com/WvBUj.png" alt="enter image description here"></p>
<p>So in this case forces Fa = 0. In last case, Fa are compensated by what forces ? </p>
<p>If I take a macroscopic model, with compressible balls for understand where F forces are compensated, consider the center of gravity like red point (balls have more density than solid, just enough for compensated):</p>
<p><img src="http://i.stack.imgur.com/gHjyW.png" alt="enter image description here"></p>
<hr>
<p>And there is another force to take in account it's the red force :</p>
<p><img src="http://i.stack.imgur.com/L77Pz.png" alt="enter image description here"></p>
<p>This red force is apply all along the surface of container ?</p> | g10713 | [
-0.01084351260215044,
0.05276148021221161,
-0.012559010647237301,
-0.03637154772877693,
0.030060553923249245,
0.010774262249469757,
0.039420995861291885,
-0.020956238731741905,
-0.05857526883482933,
-0.018396615982055664,
-0.02143693156540394,
0.004218794871121645,
0.03929345682263374,
0.0... |
<p>Is <a href="http://en.wikipedia.org/wiki/Loschmidt%27s_paradox" rel="nofollow">Loschmidt's paradox</a> a paradox even today? </p>
<p>In other words, is the paradox resolved or not?</p> | g344 | [
0.017361009493470192,
0.046180397272109985,
-0.022385787218809128,
0.01684746891260147,
0.0403626523911953,
-0.05055750161409378,
-0.0011235777055844665,
-0.01627085544168949,
0.014302258379757404,
-0.01870320737361908,
-0.0013933044392615557,
0.014306973665952682,
0.0336611233651638,
0.01... |
<p>I have a question that's bugging me. Googling it only made me more confused so I really hope someone can help me clear this.</p>
<p>If a plane is flying up and down; or hovering (Like the x-wing scene from star wars for example, when yoda uses the force) does that result in constant acceleration or varied acceleration? </p>
<p>If the final velocity is 0, because it comes back to the same position, (please correct me if i'm wrong) and the time it takes to go up and come back down is 10 seconds, that would make a constant acceleration of (0/10) which is 0?! </p>
<p>EDIT: I know it sounds like such a weird question but the reason I'm asking this is that I'm doing a project on teaching academic subjects using pop culture (hence the yoda reference) and want to make sure the stated acceleration is theoretically correct.</p>
<p>EDIT: I drafted an image to help illustrate my question, I hope it helps.
<img src="http://i.stack.imgur.com/xWnw2.jpg" alt="are the acceleration values (figuratively) correct?"></p> | g10714 | [
0.0719311311841011,
0.03499559685587883,
0.002993229543790221,
0.013332411646842957,
0.043932054191827774,
0.009114819578826427,
0.022913411259651184,
0.040839388966560364,
-0.06540849804878235,
-0.003896960522979498,
0.011907880194485188,
-0.0014460987877100706,
-0.021827293559908867,
0.0... |
<p>Given the Hamiltonian for the the harmonic oscillator (HO) as
$$
\hat H=\frac{\hat P^2}{2m}+\frac{m}{2}\omega^2\hat x^2\,,
$$
the Schroedinger equation can be reduced to:
$$
\left[
\frac{d^2}{dz^2}-\left(\frac{z^2}{4}+a\right)\right]\Psi=0~,
$$
where $a=-\frac{E}{\hbar\omega}$, $z=\sqrt{\frac{2m\omega}{\hbar}}$.
Now, the two independent solutions to this equation are the Wittaker's functions (Abramowitz section 19.3., or Gradshteyn at the beginning, where he defines the Wittaker's functions) $D_{-a-1/2}(z)$ and $D_{-a-1/2}(-z)$.
Apparently, there is no constraint on the values for $a$. In Abramowitz, especially, there is written "both variable $z$ and $a$ can take on general complex values".</p>
<p>Therefore my first question is:
Let us fix $a=i$ and let us therefore take the Wittaker's function $D_{-i-1/2}(z)$. This functions is solution of the time independent Schroedinger equation, and, therefore, is an eigenfunction of the ho hamiltonian. Since its value for the parameter $a$ is $i$, it follows that its eigenvalue $E$ must be $E=-i\hbar\omega$. However, this result is contradictory, since the hamiltonian must have only real eigenvalues, since it is hermitian. What do I do wrong?</p>
<p>My second question is:
Since the functions $D_n(z)$ form a complete set for $n$ positive integer with zero, I can expand my function $D_{-i-1/2}(z)$ onto the basis set $D_n(z)$.
$$
D_{-i-1/2}(z)=\sum_n C_n D_n(z)~.
$$
But, evidently, if $D_{-i-1/2}(z)$ is itself an eigenfunction with a different eigenvalue with respect to any of the $D_n(z)$, the expansion above does not make sense.
This question is somewhat correlated to the previous one. So, I believe I do something
wrong which is in common to both of them.</p> | g10715 | [
-0.0010351442033424973,
-0.045625120401382446,
0.0056742154993116856,
0.012825306504964828,
0.0572551004588604,
-0.005152255296707153,
0.07723043113946915,
-0.012279972434043884,
0.010020152665674686,
0.017374584451317787,
-0.02057120017707348,
0.019991911947727203,
-0.009005658328533173,
... |
<p>I have read multiple answers on StackExchange about this question, but I wasn't able to find a concrete answer. Like other questions, the reason I ask about the s-orbital is because it has a zero orbital angular momentum. But, the implication of having a zero angular momentum is unclear? Some answers discuss probability distributions, but the question is how can there be multiple places for an electron, if it can't move. I read another answer that says that the electron passes through the nucleus or curve around it as a wave. I would appreciate it if anyone could provide a resolution to this question.</p> | g10716 | [
-0.011087503284215927,
0.07800934463739395,
0.0034830220974981785,
0.017965523526072502,
0.074437715113163,
0.02318445034325123,
0.03977572172880173,
0.067075714468956,
0.013040544465184212,
-0.04213123768568039,
-0.03708255663514137,
-0.024084016680717468,
0.04682796448469162,
-0.05380265... |
<p>Suppose I have 2 fermions in a potential $V(x)$. Both particles are moving in one dimension: the $x$ axis.
Then, neglecting the interaction between the particles, the spatial wave function of the system would be of the form
$$\psi_{n_{1}}(x_{1})\psi_{n_{2}}(x_{2}) $$</p>
<p>Now, if I'm considering particles with spin 1/2, the notation $\alpha(1)$ indicates that the particle 1 has spin up, and $\beta(2)$ denotes the particle 2 having spin down.</p>
<p>Now, I want to write the complete wave function, a function of the form
$$\psi_{n_{1}n_{2}s_{1}s_{2}}(x_{1},x_{2},s_{1},s_{2})=\psi_{n_{1}}(x_{1})\psi_{n_{2}}(x_{2})F(\alpha,\beta)$$
where $F(\alpha,\beta)$ is a function of the spin of the system.</p>
<p>To this end, I have that the only physically possible functions $F(\alpha,\beta)$ are:</p>
<p>Symmetric: $\chi_{\alpha}:=\alpha(1)\alpha(2),\quad\chi_{\beta}:=\beta(1)\beta(2),\quad\chi_{+}:=\frac{1}{\sqrt{2}}\left[\alpha(1)\beta(2)+\alpha(2)\beta(1)\right]$</p>
<p>Antisymmetric: $\chi_{-}:=\frac{1}{\sqrt{2}}\left[\alpha(1)\beta(2)-\alpha(2)\beta(1)\right]$</p>
<p>In order to write down the complete wave function with spin, I understand I have to consider the energy levels. For example the ground state: $\psi_{1}(x_{1})\psi_{1}(x_{2})$.</p>
<p>If $\psi_{1}(x_{1})\psi_{1}(x_{2})$ is symmetric (<em>as I understand it is</em>), then I must multiply this function times the antisymmetric function $\chi_{-}$ (in order to get an antisymmetric wave function, for two fermions).</p>
<p>If $\psi_{1}(x_{1})\psi_{1}(x_{2})$ is antisymmetric (and I understand this is impossible, since the ground state is not degenerate), then I'd have 3 wave functions, obtained by multiplying $\psi_{1}(x_{1})\psi_{1}(x_{2})$ times $\chi_{\alpha}$, $\chi_{\beta}$ and $\chi_{+}$.</p>
<p>Now, for the 1st excited level, say $\psi_{2}(x_{1})\psi_{1}(x_{2})$, <strong>my question is</strong>, what happens when this function is not symmetric neither antisymmetric?</p>
<p>I mean, I could built a symmetric</p>
<p>$$f_S=\frac{1}{\sqrt{2}}\left[\psi_{2}(x_{1})\psi_{1}(x_{2})+\psi_{2}(x_{2})\psi_{1}(x_{1})\right]$$</p>
<p>or an antisymmetric</p>
<p>$$f_A=\frac{1}{\sqrt{2}}\left[\psi_{2}(x_{1})\psi_{1}(x_{2})-\psi_{2}(x_{2})\psi_{1}(x_{1})\right]$$
wave function. But which one of these must I choose?
Or, must I calculate the resultant complete wave functions with both? Then, when I count the states with the 1st excited energy, I'd have 4 instead of 1 or 3.</p> | g10717 | [
0.017868248745799065,
-0.022232040762901306,
-0.03232591226696968,
0.017498964443802834,
0.09678163379430771,
-0.01957816071808338,
0.0455445796251297,
0.03270241245627403,
-0.00661088339984417,
-0.026909973472356796,
-0.0696878582239151,
0.0340600311756134,
-0.02025630883872509,
0.0312896... |
<p>I found the problem described in the attached picture on the internet. In the comment sections there were two opposing solutions. So it made me wonder which of those would be the actual solution.</p>
<p>So basically the question would be the following. Assume we would have two identical beakers, filled with the same amount of the same liquid, lets say water. In the left beaker a ping pong ball would be attached to the bottom of the beaker with a string and above the right beaker a steel ball of the same size (volume) as the ping pong ball would be hung by a string, submerging the steel ball in the water as shown in the picture. If both beakers would be put on to a scale, what side would tip?</p>
<p>According to the internet either of the following answers was believed to be the solution.</p>
<ol>
<li>The left side would tip down, because the ping pong ball and the cord add mass to the left side, since they are actually connected to the system.</li>
<li>The right side would tip down, because of buoyancy of the water on the steel ball pushing the steel ball up and the scale down.</li>
</ol>
<p>Now what would the solution be according to physics?</p>
<p><img src="http://i.stack.imgur.com/Mj3Y0.jpg" alt="enter image description here"></p> | g10718 | [
0.06610675901174545,
0.059004515409469604,
0.02647530473768711,
-0.0454142801463604,
0.0788869634270668,
0.02802257426083088,
-0.008160277269780636,
-0.06120340898633003,
-0.05189075320959091,
-0.018910039216279984,
-0.022190183401107788,
0.029848678037524223,
-0.06175878643989563,
0.03931... |
<p>Intuitively I would expect the thermal and electric conductivity to be positively related, and since electric conductivity increases with salinity, so should thermal. But according to <a href="http://web.mit.edu/seawater/Seawater_Property_Tables.pdf" rel="nofollow">this table</a> (p.10) it decreases. Why is this?</p>
<p>Related: is there such a thing as the Wiedemann-Franz law for liquids like water?</p>
<p>There's a paper that has theoretical derivations about it, but it's nowhere to be found:<br>
<code>Predvoditelev, A. S., "Some invariant Quantities in the Theories of Heat Conductance and the Viscosity of Liquids," Russian Journal of Physical Chemistry, Vol. 22, p. 339 (1948)</code></p> | g10719 | [
0.04493675008416176,
-0.015463707968592644,
-0.0010578102665022016,
0.011885132640600204,
0.02561277151107788,
0.028860580176115036,
-0.02160579524934292,
-0.002048675436526537,
-0.05316776782274246,
0.0193837471306324,
-0.02876918576657772,
0.037380874156951904,
0.03294578567147255,
0.073... |
<p>How many different types of (hypothetical) <a href="http://en.wikipedia.org/wiki/Multiverse" rel="nofollow">multiverse</a> theory exist? For example, the obvious Quantum MWI, eternal inflation, cyclic universe etc</p> | g10720 | [
-0.03186923265457153,
0.04484383016824722,
0.018756968900561333,
-0.016330979764461517,
-0.01370193064212799,
-0.030261745676398277,
-0.04606000706553459,
-0.037173714488744736,
0.02173680067062378,
-0.020676691085100174,
-0.008257921785116196,
-0.0047176494263112545,
0.005514666438102722,
... |
<p>I don't get a grip of what that exactly means. What IS an abstract singlet, doublet,... under $SU(N)$ or other groups?</p> | g345 | [
-0.048237551003694534,
0.026362163946032524,
-0.030014172196388245,
-0.04532938078045845,
0.017856577411293983,
-0.0221977848559618,
-0.011615666560828686,
0.008549666032195091,
0.0025853903498500586,
-0.02614421583712101,
-0.061205554753541946,
0.02019089087843895,
0.03401394560933113,
0.... |
<p>I have three DC circuits in my solar array. I have a three lead + ground (bare copper) tec armoured cable (#6). Why not run one circuit using the bare ground as negative? In fact, why not run three circuits and use the the bare copper as the common negative? </p> | g10721 | [
0.014786242507398129,
-0.004232114180922508,
0.002444793004542589,
0.009740275330841541,
0.052912332117557526,
0.05902767553925514,
0.008467665873467922,
0.004715214017778635,
-0.007193852681666613,
-0.009068020619452,
0.04233909770846367,
0.02862304449081421,
-0.00936915259808302,
0.01637... |
<p>The Big Bang looks like a lower bound to the "size" of the universe in the time dimension. Could it also have an upper bound, some furthest point in time from the Big Bang?</p> | g10722 | [
-0.0010675687808543444,
0.046969156712293625,
0.018934693187475204,
-0.04508785530924797,
-0.07947837561368942,
-0.016690954566001892,
0.0004806174256373197,
-0.03443487733602524,
-0.04875176399946213,
-0.07554258406162262,
0.027714872732758522,
0.048106417059898376,
0.013419017195701599,
... |
<p>Why magnetic field generates around a wire when current flow through it ?</p> | g346 | [
0.04735720530152321,
-0.0024026648607105017,
-0.014104721136391163,
-0.030752338469028473,
0.05381425470113754,
0.06466076523065567,
0.057450007647275925,
0.03235315531492233,
-0.04213015362620354,
-0.007257048040628433,
-0.04626638814806938,
0.033717524260282516,
-0.06056278944015503,
0.0... |
<p>Can you help me to do this: </p>
<p>Two frames of references $S$ and $S'$ have a common origin $O$ and $S'$ rotates with constant angular velocity $\omega$ with respect to $S$.<br>
A square hoop $ABCD$ is made of fine smooth wire and has side length $2a$. The hoop is horizontal and rotating with constant angular speed $\omega$ about a vertical axis through $A$. A small bead which can slide on the wire is initially at rest at the midpoint of the side $BC$. Choose axes relative to the hoop and let $y$ be the distance of the bead from the vertex $B$ on the side $BC$. Write down the position vector of the bead in your rotating frame. Show that<br>
$\ddot y-\omega^2 y=0$ using the expression for the acceleration. Hence find the time which the bead takes to reach a vertex $C$. </p>
<p>I showed that $\frac{d^2\vec r}{dt^2}=(\frac{d^2\vec r}{dt^2})'+2\vec\omega\times(\frac{d\vec r}{dt})'+\vec\omega\times(\vec\omega\times\vec r)$ where $'$ indicates that it's done in rotating frame. $\vec r$ is position vector of a point $P$ measured from the origin. </p>
<p>I got that<br>
$\vec r=r\cos\theta\vec i+y\vec j$<br>
$\vec r'=(\dot rcos\theta-r\dot\theta \sin\theta)\vec i+\dot y\vec j$<br>
$\vec r''=(\ddot rcos\theta-\dot r\dot \theta sin\theta-\dot r\dot\theta\sin\theta-r\ddot\theta\sin\theta-r\dot\theta^2cos\theta)\vec i+\ddot y\vec j$<br>
$\omega\times\vec r'=-\omega\dot y\vec i+(\omega\dot r\cos\theta-\omega r\dot\theta\sin\theta)\vec j$<br>
$\vec\omega\times (\vec\omega\times\vec r)=-\omega^2 r\cos\theta\vec i-\omega^2 y\vec j$ </p>
<p>I suppose I have to write Newton's second law now, but I don't know which forces do I have in this motion.</p> | g10723 | [
0.08816937357187271,
0.037391193211078644,
-0.005080450791865587,
-0.019019419327378273,
0.038689304143190384,
-0.05824653059244156,
0.12597155570983887,
-0.027865951880812645,
-0.024582618847489357,
0.05437234789133072,
-0.049772266298532486,
0.06904781609773636,
-0.03464040160179138,
-0.... |
<p>There is perfect parallelepipedal bar made of transparent crystal with cubic lattice floating in vacuum. Faces of parallelepiped are parallel to lattice axis. There is image, forming checkerboard pattern, each cell alternating between two distinct colors.</p>
<p>This image is projected in perpendicular on the one face of crystal bar, so projection has spatial resolution (e.g. density of outgoing photons) such high, so every single molecule in the first layer of crystal bar gets several photons of different wavelength.</p>
<p>Questions:</p>
<ol>
<li><p>How the output image at the opposite side of crystal bar compares to original image projected?</p></li>
<li><p>Will it correlate to thickness of bar?</p></li>
<li><p>How are multiple photons hitting same molecule handled?</p></li>
<li><p>What is the limit of resolution of incoming image, to perfectly match output image? Is it one-to-one correspondence of incoming photons to molecules in the first layer?</p></li>
<li><p>Will there be scattering of photons on the molecules of the last layer? If any, will interference between scattered photons cancel non-perpendicular directions?</p></li>
</ol> | g10724 | [
0.005480329506099224,
0.08076788485050201,
0.004943926353007555,
0.044886503368616104,
0.041384901851415634,
-0.015075947158038616,
-0.003140231827273965,
0.01122207660228014,
-0.028899352997541428,
0.028913650661706924,
0.03622465208172798,
0.022574637085199356,
-0.00085069501074031,
-0.0... |
<p>I'm asking a question that has bothered me for years and years. First of all, let me give some context. I'm a layman in physics (college educated, math major). I've read Feynman's QED cover to cover, and watched his messenger lectures. My hope is to get an answer at the "Feynman level", ideally in the crystal clear terms that feynman himself uses :)</p>
<p>Okay, so with that out of the way, my question is about transparency. My understanding from Feynman and other materials is that when a photon hits an atom, the photon can either be absorbed, or absorbed and released. </p>
<p>What I don't understand is how transparency could arise from this. If the light were absorbed and then a new photon emitted, it seems incredible that the new photon would have the exact trajectory as the old one. Why wouldn't it go off randomly in a random direction? </p>
<p>Here's some of the homework I've done trying to find out the answer on my own:</p>
<p>1) <a href="http://physics.stackexchange.com/questions/11138/transparency-of-materials">Transparency of materials</a> (one commentor alludes to scattering not being explained here)</p>
<p>2) <a href="http://alemassociates.com/mambo/content/view/33/1/">http://alemassociates.com/mambo/content/view/33/1/</a> (this seems to address it, but I will admit it's mostly over my head)</p>
<p>3) <a href="http://www.av8n.com/physics/white.htm">http://www.av8n.com/physics/white.htm</a> (seems to talk about it, but doesn't explain <em>why</em> the photon would ever come out the same direction as it came in)</p>
<p>4) Discover magazine posted this: "when a packet of light energy, or photon, hits a solid object, three things can happen. Light can disappear: If the photon has the same vibrational frequency as the electrons in the material it strikes, those electrons absorb its energy, changing the photon from light into heat. Light can also be scattered: the surface electrons can grab the photon's energy and then eject a photon of the same wavelength which is how you see pretty much everything that doesn't emit light on its own. But if the photon doesn't have the right vibrational energy for absorption, and if the atoms in the material are arranged in patterns that discourage reflection (such as the random jumble of molecules in glass or air) <strong>then the photon's energy passes from atom to atom, emerging on the other side still bright and shiny.</strong> Then you have transparency."</p>
<p>I'm posting here for help. I realize that this forum is geared for graduate level and beyond physics, but I'm hoping that this transgression will be forgiven. I would really, truly, like to understand why anything is transparent at all. From my understanding, nothing should ever be transparent! At best we might get translucency (a bunch of photons coming out in random directions), but I cannot understand transparency. Why would a photon interacting with an atom come out the exact way it came from? In other words, as per that Discover magazine article, why would the photon be passed from atom to atom always at the exact same vector that it came from?</p>
<p>Thank you!</p>
<p>edit: If possible, I'd like to keep it in terms of photons. What's going on at the photon level, and avoid the wave framework. Let's talk about photons and probability amplitudes a-la Feynman.</p> | g10725 | [
0.029930053278803825,
-0.0015128277009353042,
-0.00785834714770317,
0.008912000805139542,
0.046903930604457855,
0.051198285073041916,
0.08056393265724182,
0.02406899258494377,
-0.00007348597137024626,
-0.01158954855054617,
0.02954951673746109,
0.016250092536211014,
0.0436023585498333,
0.02... |
<p>Why does a larger mass in a pendulum have the same period as a lighter mass? i know it has something to do with gravity and length but how can this be explained in depth? like for example the galileo's experiment where both masses were nearly the same but the lighter mass was slower (air resistance)</p> | g347 | [
0.089556023478508,
0.01679280400276184,
0.014260691590607166,
-0.03462687507271767,
0.004298788961023092,
0.11003079265356064,
0.085321806371212,
-0.03551010414958,
-0.014793485403060913,
-0.006179270334541798,
-0.02243894338607788,
-0.051328763365745544,
0.03561290353536606,
0.02147283777... |
<p>I have watched Walter Lewin's lecture(<a href="http://www.youtube.com/watch?v=6QVbE_tU2sA" rel="nofollow">http://www.youtube.com/watch?v=6QVbE_tU2sA</a>) which was about the rainbows. But there is still a question bothering me. </p>
<p>I understood the first part of the lecture which he talked about axial symmetry that holds in the drop of water because the light beam is coming from a preferred direction. But I cannot understand that why he relates the semicircular shape of the rainbow to axial symmetry.<br>
To make my question clearer, I say an example. Considering the red part of the rainbow for instance, we found that this color of rainbow is seen if we look about 42 degrees above the reference line(from the sun). But I think that for looking at other red parts of the bow, one should rotate his head and other red parts have different angles than 42.I know that all red parts should be at 42 degrees but I am confused and cannot understand it. </p>
<p>I have another problem and that is why we emphasize on $\varphi_{max}$. For example,at the angle of 40 degrees, we have both blue and red color but they always use 40 degrees just for blue but we can have a mixture of red and blue.
I will be thankful if you can help me with these. </p> | g10726 | [
-0.003825617954134941,
0.00901314988732338,
0.01408467162400484,
-0.040372833609580994,
0.044127196073532104,
0.021565232425928116,
0.08448956161737442,
-0.0255629513412714,
0.02179146185517311,
0.011167401447892189,
-0.02096732333302498,
0.03314181789755821,
0.030585667118430138,
0.018299... |
<p>What is meant by a local Lagrangian density? How will a
non-local Lagrangian look like and what is the problem that we do not
consider such Lagrangian densities?</p> | g10727 | [
0.11517489701509476,
0.06770668923854828,
0.002171945059671998,
-0.09089893847703934,
-0.0031890482641756535,
0.004245538264513016,
0.0012349945027381182,
0.017359957098960876,
-0.023055894300341606,
-0.006760589312762022,
0.018153801560401917,
0.04561448469758034,
0.010458988137543201,
0.... |
<p>Is there any frequency at which cars can be charged with using wireless? Surely, wireless transmission can be safely assumed to be a form of energy transfer, and there can be charging of cars without physical electric outlets. Is there a frequency at which cars can be charged? One can see the problem of energy transmission as a form of optimization problem in which the parameter energy (E) is to the transmitted with maximal effect(I could be nebulous here!) Is there such a frequency for wireless car charging? </p> | g10728 | [
0.029316244646906853,
0.02659520134329796,
0.005809988360852003,
0.027727035805583,
0.06457880884408951,
-0.025409378111362457,
-0.08348735421895981,
-0.010333799757063389,
-0.08716261386871338,
0.051897287368774414,
0.0185999795794487,
-0.03475873917341232,
0.00449164304882288,
-0.0021051... |
<p>I am studying the global causality of the spacetime. Here, I come across a problem. </p>
<p>Suppose a point $r\in \partial I^+(p)$. $I^+(p)$ is the chronological future of a different point $p$ in spacetime. Then, it is claimed that $I^+(r)\subset I^+(p)$. But why? </p>
<p>Let me first try to prove this conclusion. I notice there is a theorem:</p>
<p>Let a subset $S\subset M$ ($M$ the spacetime manifold) and set $B=\partial I^+[S]$. Then, if $x\in B-\bar S$, there exists a null geodesic $\eta\subset B$ with future endpoint $x$ and which is either past-endless or has a past endpoint on $\bar S$.</p>
<p>So we can set $S=\{p\}=\bar S$. Since $r\in\partial I^+(p)$ and $r\ne p$, $r\in B-\{p\}$ with $B=\partial I^+(p)$. Therefore, there is a null geodesics $\eta$ lying on $B$ and passing through $p$. Is this correct? </p>
<p>Thank you! </p> | g10729 | [
0.09191777557134628,
0.012846988625824451,
-0.02490696683526039,
-0.047738220542669296,
-0.005752988159656525,
0.021145764738321304,
0.03891931101679802,
0.008465487509965897,
-0.028078829869627953,
-0.04146723821759224,
0.08283942937850952,
0.04676150903105736,
0.024983255192637444,
-0.00... |
<p>One often comes across news articles that claim that an earthquake shifted the earth's axis.</p>
<blockquote>
<p><a href="http://news.google.com/?q=earthquake%20shifted%20OR%20shifts%20earth%27s%20axis">http://news.google.com/?q=earthquake%20shifted%20OR%20shifts%20earth%27s%20axis</a></p>
</blockquote>
<p>If you ignore the influence of other celestial bodies, an internal event like an earthquake surely can't change the direction of the angular momentum of the Earth (unless stuff is ejected out of Earth), since angular momentum has to be conserved in the absence of an external torque. So the axis has to remain fixed.</p>
<p>Am I missing something? Or are geologists trying to say that the resulting movement of tectonic plates causes a change in the point of intersection of the axis (which remains the same) and the plates that include the poles, so that it <em>seems</em> as if the axis has shifted?</p>
<p><strong>EDIT</strong>
Some articles mention the value of the shift in the axis and also the change in the length of the day. If, as Ted Bunn's answer indicates below, the shift in the axis isn't actually real but is because of the movement of tectonic plates with respect to the axis, shouldn't the shift be different at the north and south poles? How are the shifts and the change in day-length calculated?</p> | g10730 | [
0.08899890631437302,
-0.0016876229783520103,
-0.01733468659222126,
0.007925610058009624,
0.03672557324171066,
-0.0035056888591498137,
0.041852496564388275,
0.020802490413188934,
-0.011062078177928925,
-0.028705082833766937,
-0.028710149228572845,
-0.04334080219268799,
0.016674503684043884,
... |
<p>I've read a few other posts, and none seem to give me an answer that satisfies my curiosity. Thus far I've only been studying time independent QM, so I'm not even sure how wave functions evolve over time for microscopic things, let alone macroscopic things. However, what mandates that events that expect to happen actually happen? Why does it make sense that when I put something in a box, that it should remain in the box, rather than tunneling elsewhere? Or why should a pot ever come to a boil? Certainly these questions are being caused from a tragic misunderstanding of quantum theory, can someone clarify for me? At the end of the day, there is a nonzero probability that macroscopic anomalies will occur, right?</p> | g10731 | [
-0.0024361982941627502,
0.06360398232936859,
0.002950890688225627,
0.01844705641269684,
0.05565493926405907,
0.01959783025085926,
0.026314841583371162,
0.04010845348238945,
-0.0251788217574358,
-0.09362226724624634,
-0.05849364027380943,
-0.003221714636310935,
0.0326085202395916,
0.0254907... |
<p>This may be a very simple question but somehow I can't seems to solve it. For the sake of completness, I will use the same original question I am working on.</p>
<p><strong>Question:</strong> The density of ice is $917 kg/m^3 $ and the density of seawater is $1020 kg/m^3$. If a piece of ice with dimensions $ 1m $ x $1m $ x $0.65m $ is left in seawater, what height of the ice will be above sea water?</p>
<p><img src="http://i.stack.imgur.com/rGScS.png" alt="enter image description here"></p>
<p>This is all it was given.</p>
<p><strong>My Attempt:</strong> This is how I understand this problem.</p>
<p>There will be two forces acting on this ice block</p>
<ul>
<li>The upthrust force ( which is equivalent to the weight of the seawater being displaced)</li>
<li>The weight of the ice block itself</li>
</ul>
<p>Since the ice block is floating, I assume that the upthrust is either equal or greater than the weight of the ice block.</p>
<p>This is the simple sketch I come up with </p>
<p><img src="http://i.stack.imgur.com/7bc8z.png" alt="enter image description here"></p>
<p>but now I am confused because according to my sketch:</p>
<p>$ upthrust = \rho_{seawater} vg $ (v being the volume of water being displaced by the ice block)</p>
<p>$ weight\,of\, ice\, block = mg = \rho_{ice} vg$ </p>
<p>If i subtract these two equations, the volumes will cancel out each other so there will be no height information left. I supposed I have to somehow retrieve the <code>height</code> inforation from <code>volume</code> using $v = Ah$ but I am not sure how. How do I find the height of ice block above sea water?</p> | g10732 | [
0.09880752116441727,
0.01582322269678116,
-0.0019997868221253157,
-0.021294668316841125,
-0.012301662936806679,
0.04645524546504021,
0.0022735397797077894,
-0.010275188833475113,
-0.053230170160532,
0.0018952310783788562,
-0.01483807060867548,
0.05134805291891098,
-0.02144031785428524,
-0.... |
<p>The Japanese tsunami, moving at about 700 km/h, affected areas as distant as Chile's coast, 20 hours after the earthquake. How does the Coriolis force affect tsunami? Also, I saw an image of a boat caught within a large whirlpool. Is the whirlpool's rotation due to Coriolis force?</p> | g10733 | [
-0.004144543781876564,
0.041829176247119904,
0.004472497850656509,
-0.006797065958380699,
0.052451375871896744,
0.02822459302842617,
0.05971362069249153,
0.0033759227953851223,
-0.05732385069131851,
-0.05640533193945885,
0.024873580783605576,
0.0005643402691930532,
0.01441816333681345,
-0.... |
<p>Does anyone know a reference or a paper which discusses string theory correction to Friedmann equations?</p> | g10734 | [
0.035871218889951706,
-0.051885634660720825,
0.008383671753108501,
0.025927305221557617,
0.05696726590394974,
-0.04088824987411499,
0.014831144362688065,
0.026574183255434036,
-0.02619991824030876,
0.03625183179974556,
-0.0002394840557826683,
0.023006625473499298,
0.03224434703588486,
0.05... |
<p>In the Debye-Scherrer procedure a sample of crystalline powder is hit by a beam of monochromatic photons. The diffracted photons are measured with a detector. We have constructive interference of the photons if the Bragg conditions are met.
In my lecture notes it says that there are always crystalline planes oriented in a way that the Bragg conditions are fulfilled, thus leading to the typical rings observed with powder diffractometer.</p>
<p><img src="http://i.stack.imgur.com/f4Tes.png" alt="Graphic taken from Wikipedia">
(Graphic taken from Wikipedia)</p>
<p>I have a hard time seeing why there are discrete rings, because from the reason above I would expect that for every angle there is constructive interference and hence we would have a continuous intensity distribution for all angles. </p>
<p><strong>Question</strong>: Why are there discrete rings and not a continuous distribution?</p> | g10735 | [
0.0371243916451931,
-0.008191597647964954,
0.0005560063291341066,
0.004874757956713438,
0.020183155313134193,
-0.004184812307357788,
0.05263485014438629,
0.0676247701048851,
-0.028306275606155396,
-0.036996323615312576,
0.002426530234515667,
-0.019441740587353706,
0.0055486843921244144,
-0... |
<p>Isn't this statement regarding projectile motion wrong?</p>
<blockquote>
<p><em>If a body is thrown at an angle to the horizontal with initial velocity $u$, then displacement of body as a function of time is $\vec{s}=\vec{u}t+\frac12\vec{g}t^2$. (Air drag is neglected)</em></p>
</blockquote>
<p>How can it be correct? Gravity acts in downward direction, so wouldn't the displacement be $\sqrt{x^2+y^2}$?</p> | g10736 | [
0.0786217525601387,
0.025088327005505562,
-0.012026782147586346,
0.0038213832303881645,
0.04542503505945206,
0.0934138298034668,
0.061357297003269196,
-0.02869347669184208,
-0.045192036777734756,
-0.029968854039907455,
-0.02121685817837715,
0.033210862427949905,
0.07345534861087799,
-0.030... |
<p>Given a many body spin system, a collection of N spin-1/2 particles, under the interaction of the twisting Hamiltonian:
$$H_{int} = \sum_{i,j=1}^Na_{i,j}\sigma_{z,i}\sigma_{z,j}= A J_{z}^{2}$$
assume all $a_{i,j}$ are equal and define:
$$\mathbf{J} = \sum_{n=1}^{N} \mathbf{\sigma}_{n}$$
the collective spin operator, $\mathbf{\sigma}_{n}$ is the pauli spin operator for the $n$th spin, and $A$ characterizes the strength. </p>
<p>Which component of the spin system will display reduced variance/will be squeezed? What assumptions does this require regarding the initial state? </p>
<p>The context of the question is the notion of spin squeezed states, as originally put forward by (1) <a href="http://dx.doi.org/10.1103/PhysRevA.46.R6797" rel="nofollow">Wineland et al.</a> and (2) <a href="http://dx.doi.org/10.1103/PhysRevA.47.5138" rel="nofollow">Kitagawa & Ueda</a></p>
<p>EDIT</p>
<p>In particular in figure 2 of (2) the evolution of the coherent spin state $|\pi/2,0\rangle$ (pointing along $\hat{x}$) is described, they show that squeezing occurs along the y- and z-axes. As I see it these variances seem to oscillate out of phase.</p>
<p>What would be helpful is if someone could explain how to visualize this so-called twisting dynamics. So far i thought that, starting with an initial (Q-)distribution in phase space,
the distribution evolves with precession frequency proportional to $J_{z}$. But from there I do not see how the variance along $\hat{z}$ would change...</p>
<p>Also as a side note: to my knowledge these type of quadratic in angular momentum terms are not very common, but also appear in nuclear physics as the <a href="http://arxiv.org/abs/0805.4078" rel="nofollow">Lipkin model</a>.</p> | g10737 | [
-0.04402834177017212,
0.044701702892780304,
-0.046044643968343735,
-0.006753706838935614,
0.017588261514902115,
-0.02833632379770279,
0.10385137796401978,
0.010674430057406425,
0.03468421846628189,
0.008410255424678326,
-0.0176373403519392,
0.022763224318623543,
0.021663818508386612,
-0.02... |
<p>Consider a point mass $A$ with mass $m$ in empty space. The point mass $A$ does not have a velocity and does not rotate.
Since gravity is symmetric for nonmoving objects, the spacetime curvature around $A$ is also symmetric.</p>
<p>So at a distance $d$ from the point mass $A$ how strong is the curvature $C$ ?</p>
<p>$$ C = f(d,m) $$ $$f = ???$$</p> | g10738 | [
-0.005927518010139465,
-0.0047876606695353985,
-0.027027014642953873,
-0.008382346481084824,
0.04114444926381111,
0.017831124365329742,
0.06647849082946777,
-0.010757061652839184,
-0.07598431408405304,
0.023829614743590355,
-0.02650042250752449,
0.009971288032829762,
0.01803039200603962,
-... |
<p>How can we get the mass of an uncharged proton, i.e. how varies the mass of the charged proton if i remove the electric charge?</p>
<p>For the isotopic spin theory neutron and proton have the same mass and it is possible to distinguish that particles only for the different values of the third component of the isotopic spin.</p>
<p>This is an approximated symmetry because the masses are different and the charges too. In a ideal world we can remove the electric charge from the proton and we get a "uncharged" proton. The question is how the mass changes.</p>
<p>You can interpret that question as what it is the contribution to the mass due the charge, not only for proton but for all particles.</p> | g10739 | [
0.0372481606900692,
-0.00350187043659389,
0.0017385127721354365,
-0.002790391445159912,
0.09742970019578934,
0.022786036133766174,
-0.012126880697906017,
0.0743301585316658,
-0.0314166396856308,
0.02446812391281128,
-0.014669185504317284,
-0.010566980578005314,
0.0093870609998703,
0.016400... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.