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<p>I have read in numerous places <a href="http://physics.stackexchange.com/q/24319/">like here</a> that an object in free fall into a black hole will be travelling the speed of light when it passes the event horizon. How is it possible to go this fast? Does it continue accelerating, faster than light until it is cru...
g557
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<p>W bosons decay into an electron and electron-neutrino or into a muon and muon-neutrino. The W lifetime is about $3 \cdot 10^{-25} s$, that means the decay occurs close to the collision point, not in a detector.</p> <p>The energy of the resulting electron or muon can be measured quite accurately, but for the neutr...
g17932
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<p><a href="http://i.stack.imgur.com/ndLgm.png" rel="nofollow">http://i.stack.imgur.com/ndLgm.png</a></p> <p>I don't see the how the author derived that $\frac { dv }{ dt } \leftrightarrow\overrightarrow { V } j\omega$.</p>
g17933
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<p>I'm currently reading these <a href="http://theory.fi.infn.it/casalbuoni/lezioni99.pdf" rel="nofollow">notes</a> about the Ward identity (pages 259 - 261). I will repeat some of the steps to make the question self-contained.</p> <p>Let us consider a <strong>local</strong> transformation on the field $\phi$: \begin{...
g17934
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<p>I am a little bit confused when thinking of the momentum representation in QM and CM.</p> <p>In QM, momentum is represented as $-i\hbar\vec\nabla$, while in classical, momentum is represented as $m\vec{v}$.</p> <p>At least, where does the mass $m$ in CM gone when meets QM please?</p> <p>Once I saw a sentence like...
g17935
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<p>To calculate the gravitational potential at any point inside a solid sphere, why do we need to separately integrate gravitational field from infinity to radius and then from radius to the point? </p> <p>Why can't we do it like for a point outside or on the surface where we just need to integrate from infinity to th...
g17936
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<p>I'm not entirely sure if this is correct. I have to take the time derivative of the following:</p> <p>$$\frac{d}{dt}mr^{2}\dot{\phi}$$</p> <p>Now, both $r$ and $\dot{\phi}$ depends on the time $t$, so I have to use the product rule to get what I want. Now, what is bothering me is, is it only one of the $r$'s I nee...
g17937
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<p>I know that temperature plays a crucial role in the process of ignition, as most combustible materials will spontaneously start burning in presence of enough oxygen when heated above the kindling point. Anyway, I'm not really clear whether or not heat is just as important to keep a fire alive when a material is alre...
g17938
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<p>fluid-dynamics is not my preferred discipline, yet I have been landed with this problem and just seeking some clarification.</p> <p>I have a nozzle at the end of a tube, with 8 holes in it, and we are going to block 1 hole to change the air flow</p> <p>My though was if we blocked 1 hole, and the net flow remains t...
g17939
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<p>given the 2 loop integral</p> <p>$$ \int dq_{1} \int dq_{2}F(q1,q2) $$ (1)</p> <p>then in dimension D=4 our integral will be a 8-dimensional integral</p> <p>so why can not make a change of variable to 8-dimensional spherical coordinates? can we , the idea is to simplify the integral so we have</p> <p>$$ \iint d\...
g17940
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<p>I am looking into some new physics and had the following question come up:</p> <p>You have a neutral gas of let's say, CO atoms at 1 nanoTorr. An electron(s) comes passing through the gas ionizing only 1% of the gas atoms. How long does it take for the gas to come back to neutrality? In other words, what is the rec...
g17941
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<p>A ball is allowed to fall from rest on a horizontal floor from a height of 10m If there is 20% loss of energy due to impact then after one impact ball will go upto?</p>
g17942
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<p>I'm a biologist with some raw powder XRD data of biominerals, need to quantify different phases, can't access commercial software or databases at the moment.</p> <p>Does anyone have experience with using the cif standards from the AMCSD with MAUD? It seems to display the list of phases fine, but when I pick one it ...
g17943
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<p>It is said that at neutral points in a gravitational field the net force on a moving mass becomes zero, which means the mass should be moving with constant velocity-and not zero! However, certain textbooks make use of this paradox to solve problems. Is it explicable?</p> <p><img src="http://i.stack.imgur.com/Y1MWt....
g17944
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<p>A <a href="http://goo.gl/f4mvz" rel="nofollow">Recent report</a> about a cosmic burst 3.8 billion light years away. It is written as though it is happening now. However, my question is, if the event is 3.8 billion light years away, doesn't that mean we are continuously looking at history, or is it possible to detect...
g17945
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<p><a href="http://www.feynmanlectures.info/docroot/III_08.html#Ch8-S6" rel="nofollow">Feynmann Lectures Vol 3 Ch 8 Sec 6</a> describes how an ammonia molecule can have two definite energy states. If the amplitudes of the base states are</p> <p>$ C_1(t) =\frac{a}{2}\,e^{-(i/\hbar)(E_0-A)t}+\frac{b}{2}\,e^{-(i/\hbar)(...
g17946
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<p>I was talking to Roger Penrose about calculus in the appendix in his book <em>Cycles Of Time</em> and he said I'd need a good understanding of calculus if I wanted to read his book in great depth. He said I even need calculus to understand the movement of a particle in depth.</p> <p>What is the calculus that descri...
g17947
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<p>The Voyager 1 &amp; 2 spacecraft launched in 1977 with Plutonium as their source of electricity. 34 years later they claim these two spacecraft have enough power to last them until <em>at least</em> 2020. That means they'll have had enough power to last them at least 42 years. It obviously offers enough power to lit...
g17948
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<p>I've recently watched a "<a href="http://www.imdb.com/title/tt1513168/" rel="nofollow">Through the Wormhole</a>" episode from 2010 named "<a href="http://www.imdb.com/title/tt1667180/" rel="nofollow">What Happened Before the Beginning?</a>", where cyclic and ekpyrotic cosmological models are explained. In this episo...
g17949
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<p>Hyperloop is a proposed mode of High speed transportation by Elon Musk. Theoretically it's speed is about 760 mph. </p> <p>Can 760 mph speed be achieved with this project ? </p> <p>Hyperloop - Alpha - <a href="http://www.teslamotors.com/sites/default/files/blog_images/hyperloop-alpha.pdf" rel="nofollow">http://ww...
g17950
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<p>I recently read an article in the NY Times called <a href="http://www.nytimes.com/2013/08/13/science/space/a-black-hole-mystery-wrapped-in-a-firewall-paradox.html?pagewanted=all&amp;_r=0" rel="nofollow">A Black Hole Mystery Wrapped in a Firewall Paradox</a>. I really liked the article, but reading one quote immediat...
g17951
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<p>Alastair Rae states that there are 4 postulates of Quantum Mechanics in his text on the subject matter. The first part of his second postulate can be stated as: </p> <blockquote> <p><em>Every dynamical variable may be represented by a Hermitian operator whose eigenvalues represent the result of carrying out a me...
g17952
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<p>Here was my argument against this, the second law of thermodynamics, in effect says that, there is no heat engine that can take all of some energy that was transferred to it by heat and do work on some object. So, if we can not take a 100% the thermal energy of an object, and use it to do work, what about the therma...
g17953
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<blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://physics.stackexchange.com/questions/937/how-does-gravity-escape-a-black-hole">How does gravity escape a black hole?</a> </p> </blockquote> <p>Nothing escapes black holes, gravitons mediate gravity, so why do black holes gravitate?</p> <p>...
g215
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<p>I have seen the scattering matrix defined using initial ("in") and final ("out") eigenstates of the free hamiltonian, with</p> <p>$$\left| \vec{p}_1 \cdots \vec{p}_n \; \text{out} \right\rangle = S^{-1} \left| \vec{p}_1 \cdots \vec{p}_n \; \text{in} \right\rangle$$</p> <p>so that</p> <p>$$\left\langle \vec{p}_1 \...
g17954
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<p>There is this general result that for any metric $ds^2$ that is asymptotically $AdS_{d+1}$, then there is a coordinate system in which $$ ds^2 = \frac{1}{r^2}(dr^2 + g_{ij}(r,x^k)dx^i dx^j) $$ where $g_{ij}(r,x^k)$ admit the following expansion close to the (conformal) boundary of $AdS_{d+1}$: $$ g_{ij}(r,x^k) = g^{...
g17955
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<p>In billions and billions (thanks Carl Sagan) of years I have heard that atoms will lose energy and their temperature will approach absolute zero and thus their entropy will approach a minimum level. If we take this to be true then it logically follows that there will be no way to distinguish one instant of time from...
g17956
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<p>It is often said that substances, objects have color because they selectively absorb all color of sunlight except one. The wavelength that is not absorbed reaches our eyes and we perceive it as "color". This "color" phenomenon is often described as light of a certain wavelength being reflected. I think it is more ap...
g17957
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<p>Do <a href="http://mathworld.wolfram.com/ChristoffelSymbol.html" rel="nofollow">Christoffel symbols</a> commute? For example, does $\Gamma^{e}_{db}\Gamma^{c}_{ea} = \Gamma^{c}_{ea}\Gamma^{e}_{db}$?</p>
g17958
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<p>I hope, this question isn't too broad or vague.</p> <p>In a recent paper, Ognyan Oreshkov et al. worked out a theory of quantum correlations in absence of any causal order, dropping the assumptions of a space-time: <a href="http://www.nature.com/ncomms/journal/v3/n10/full/ncomms2076.html">See their paper here</a>.<...
g17959
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<p>Given the following pair of operators $a$ and $a^{\dagger}$ that satisfy the usual bosonic CCR:<br> $$[a,a]=[a^{\dagger},a^{\dagger}] = 0;\ [a,a^{\dagger}] = 1$$<br> For what values of $\alpha \in\mathbb C$ are the following expressions well defined?<br> $$a^{\alpha} \ \text{and}\ (a^{\dagger})^{\alpha}$$<br> For i...
g17960
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<p>It has been reported that nonlocal Transport in the can be realized in topological insulator. Why non-local transport through edge channels has the potential application for low-power information processing?</p>
g17961
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<p>I have the following equations describing the electron field in a (classic) electromagnetic field:</p> <p>$$ c\left(\alpha _i\right.{\cdot (P - q(A + A_b) + \beta mc) \psi = E \psi } $$</p> <p>where $A_b$ is the background field and $A$ is the one generated by the local Dirac field</p> <p>I presume that the equ...
g17962
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<p>Imagine that I board a spacecraft and head away from the Earth at top speed until I've aged twenty years, then I turn around and come back. How much younger will I be than the unexciting folk who hung around Earth the whole time?</p> <p>I realize that the practical impossibility of doing this could complicate answe...
g17963
[ -0.027510885149240494, 0.07032503187656403, 0.011552657932043076, 0.02242741733789444, -0.06050918251276016, 0.025796322152018547, 0.029039490967988968, 0.02228710614144802, -0.028864460065960884, -0.057345278561115265, 0.011470804922282696, 0.04344920814037323, 0.0019623066764324903, 0.00...
<p>When a firework explodes, the powder in the firework burns rapidly to produce a small volume of gas at high temperature and pressure. Can anyone explain to me why the temperature of the gas falls rapidly? Thank you :)</p>
g17964
[ 0.05229029059410095, 0.03888722136616707, -0.0031754961237311363, 0.010742053389549255, -0.035399314016103745, 0.03974908962845802, 0.024182889610528946, 0.0725717768073082, -0.033814217895269394, -0.05661255866289139, -0.046216774731874466, 0.007191239390522242, 0.0392381027340889, 0.0166...
<p>a heap of chain is lying on a horizontal table a small part of the chain is released through the hole in the table . Calculate the velocity of the chain as a function of length of the vertically hanging portion</p>
g17965
[ 0.08092301338911057, 0.05566348880529404, 0.005486172623932362, -0.08973357081413269, 0.011706153862178326, -0.04304049536585808, 0.03243028372526169, -0.010618345811963081, -0.07683201879262924, 0.005217407364398241, -0.04066315293312073, 0.05882546678185463, -0.017695829272270203, 0.0200...
<p><strong>1. The problem statement</strong></p> <blockquote> <p>Incomming photon gives half of its energy to an electron during scatering. After scattering, photon is headed $\phi=120^\circ$ according to the original direction. What is the $\lambda$ of the incomming photon?</p> </blockquote> <p><strong>2. Re...
g17966
[ 0.014610855840146542, 0.002212273422628641, 0.012628396973013878, 0.001174157951027155, 0.0013929572887718678, -0.025544699281454086, 0.02623009867966175, 0.02145240269601345, 0.005114758852869272, 0.032435886561870575, -0.008793131448328495, 0.06527933478355408, 0.031058838590979576, 0.00...
<p>As hot air in the atmosphere rises it expands and cools at the same time. If the air cools though, shouldn't its density increase?</p>
g17967
[ 0.054377783089876175, 0.014378905296325684, 0.018676212057471275, 0.03832648694515228, 0.03976737707853317, 0.0571896918118, 0.00613396568223834, 0.03767511993646622, -0.014050036668777466, -0.05820309743285179, 0.011362357996404171, -0.007107530254870653, 0.033907290548086166, 0.020535660...
<p>In Einstein's exposition of the foundations of General Relativity (cmp. <a href="http://en.wikisource.org/wiki/The_Foundation_of_the_Generalised_Theory_of_Relativity" rel="nofollow">http://en.wikisource.org/wiki/The_Foundation_of_the_Generalised_Theory_of_Relativity</a> , end of §3) there appears an emphasis on cons...
g17968
[ 0.053726837038993835, 0.04086167737841606, -0.01551963109523058, -0.02707359567284584, 0.026298247277736664, 0.01194784790277481, 0.09865148365497589, 0.0009223620872944593, -0.003677154192700982, 0.021103566512465477, -0.020379576832056046, -0.0010257777757942677, 0.014551143161952496, 0....
<p>What criteria should I consider when determining the non-relativistic limit of a Lagrangian density? For example, how would I take the non-relativistic limit of the following Lagrangian density:</p> <p>$$\mathcal{L}=-\frac{1}{4}F_{\mu \nu }F^{\mu \nu }+\left( D_{\mu }\phi \right) \left( D^{\mu }\phi \right) -U\left...
g17969
[ 0.04671259969472885, 0.05907124653458595, -0.0019751654472202063, -0.05860237032175064, 0.03574580326676369, -0.002075737342238426, 0.04244375601410866, -0.014706863090395927, -0.02968953177332878, 0.0065631503239274025, 0.018163198605179787, -0.012788332998752594, 0.007567534223198891, 0....
<p>I've been searching for this for a while. There is a principle of equivalence in general relativity: <a href="http://en.wikipedia.org/wiki/Equivalence_principle" rel="nofollow">http://en.wikipedia.org/wiki/Equivalence_principle</a></p> <p>But I need the <a href="http://www.google.com/search?as_q=principle+equivalen...
g17970
[ 0.03467637673020363, 0.023706993088126183, 0.017792828381061554, -0.05034121125936508, 0.007543612737208605, -0.0016649272292852402, -0.00965904351323843, 0.014789294451475143, -0.05928000062704086, 0.06399380415678024, 0.01058268453925848, -0.032802190631628036, -0.013409098610281944, -0....
<p>My limited understanding of metrics comes from Cartan. From there, I understand that a metric is something invariant under certain transformations, e.g. Lorentz in special relativity. But with the metric varying from point to point (event-to-event), what is the meaning of the metric?</p>
g17971
[ 0.007159378379583359, 0.04220975935459137, -0.030093945562839508, -0.023150892928242683, 0.053610511124134064, 0.014655462466180325, 0.03425528481602669, 0.04368036612868309, -0.04458728805184364, -0.037603892385959625, -0.015258700586855412, 0.007685563527047634, 0.10172773897647858, -0.0...
<p>See the <a href="http://www.youtube.com/watch?v=bFsZ1NrtIMk" rel="nofollow">YouTube video</a> (click) named "Testing the Magnetic Nature of MagneGas.mp4". A helium balloon is attracted to a metal bar.</p>
g17972
[ 0.007985220290720463, 0.05672817677259445, 0.031064964830875397, -0.03506484255194664, 0.05432673916220665, 0.05387623608112335, -0.012719054706394672, -0.008220835588872433, -0.0341503731906414, -0.028471222147345543, -0.03961847350001335, 0.06645595282316208, -0.06409361213445663, 0.0159...
<p>I have found the tensor of inertia of a rectangle of sides $a$ and $b$ and mass $m$, around its center, to be $$I_{11}=ma^2/12,$$ $$I_{22}=mb^2/12,$$ $$I_{33}=(ma^2 + mb^2)/12.$$ All other elements of that tensor are equal to zero. I would now like to use this result to determine the tensor of inertia of a hollow cu...
g17973
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<p>In <a href="http://what-if.xkcd.com/35/" rel="nofollow">this XKCD What If</a>, an indestructible hairdryer outputs 2 GW of power, turning the earth under it into gas:</p> <blockquote> <p>Periodic explosions of gas beneath the box launch it into the air, and it starts fires and forms a new lava pool where it lands...
g17974
[ 0.020723219960927963, 0.04302358627319336, -0.007813395000994205, 0.0030897511169314384, 0.007673643063753843, 0.05397576466202736, -0.03557823598384857, 0.04399948567152023, -0.060433145612478256, -0.08946279436349869, -0.010676831938326359, 0.041830115020275116, 0.05177217349410057, -0.0...
<p>Is there a way to create an image/projection in the water? Or form the water to project an image, little dot/pixel? Use some type of frequency to modulate the little dot in the fluid?</p>
g17975
[ -0.028462685644626617, -0.007970248349010944, 0.027897484600543976, -0.11452505737543106, -0.0013919634511694312, 0.023011064156889915, -0.035999707877635956, -0.05905080586671829, 0.009785719215869904, -0.053822919726371765, 0.045376382768154144, 0.049212295562028885, 0.1031285747885704, ...
<p>I am a dilettante in physics; I ask for pardon for my confusion-causing (if any) terminology usage, and also for my imprecise choice of question tags.</p> <p>I know that basic particles of any individual stopping vibrating contradicts Heisenberg's uncertainty principle, so the particles must whenever vibrate. Then ...
g17976
[ 0.03549354150891304, 0.0781160220503807, 0.006395078729838133, 0.03294572979211807, 0.005895627662539482, 0.05790058895945549, 0.059866439551115036, -0.0012812713393941522, 0.013946729712188244, -0.003795509459450841, -0.013400974683463573, -0.03155997022986412, -0.02438153326511383, 0.034...
<p>I am currently looking into solutions for Sound Classification, and I came across Ludvigsen's methodology (if anyone wishes to refer to it).</p> <p>The problem is that a sample graph of amplitudes in one of his demos shows only positive amplitudes, while Sound Waves have both negative and positive amplitudes.</p> ...
g17977
[ 0.026757733896374702, -0.02069990709424019, 0.012598411180078983, -0.08206823468208313, 0.005026104860007763, -0.02214573696255684, 0.013863402418792248, -0.017140241339802742, -0.015496949665248394, -0.059131477028131485, -0.02990441769361496, 0.046321626752614975, 0.09118302911520004, 0....
<blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://physics.stackexchange.com/questions/2175/is-it-possible-for-information-to-be-transmitted-faster-than-light-by-using-a-ri">Is it possible for information to be transmitted faster than light by using a rigid pole?</a> </p> </blockquote> <p>...
g4
[ 0.023000091314315796, 0.03568526357412338, 0.014553960412740707, -0.03388084098696709, 0.002940477803349495, -0.027655381709337234, 0.019294580444693565, -0.022062767297029495, -0.0029104710556566715, -0.017030568793416023, 0.04139041155576706, 0.015903431922197342, 0.03707895055413246, -0...
<p><em>[EDITED] by mistake, the subject was regarding 1m^3 instead of 1mm^3. There should be a significant difference between the two...</em></p> <p>A 1x1x1mm pit filled with water is frozen at a slow rate (1K/minute). </p> <p><img src="http://i.stack.imgur.com/DraGI.png" alt="enter image description here"> <img src=...
g17978
[ 0.08234336972236633, 0.03835156559944153, -0.008023704402148724, -0.02584109827876091, 0.04097345471382141, 0.015322440303862095, 0.04109197109937668, 0.011396792717278004, -0.05468302220106125, 0.016613883897662163, 0.006709163077175617, 0.04435236006975174, -0.04685714840888977, -0.03444...
<p>Please note I am not a physicist I just read every article I can on it, I understand a good amount on it though. But no maths. (currently trying to learn the maths)</p> <p>By what means can we as humans entangle two particles? How does (just examples are fine) it happen in nature? And I would guess technically ther...
g17979
[ 0.0016896999441087246, 0.0017080908874049783, 0.019903868436813354, 0.020751947537064552, 0.07745303213596344, 0.05966312810778618, -0.01721368357539177, 0.03569300100207329, 0.014876431785523891, -0.016078166663646698, -0.04169658571481705, 0.023276273161172867, 0.040535785257816315, -0.0...
<p>For an accelerated charge to radiate, must an electromagnetic field be the source of the force?</p> <p>Would it radiate if accelerated by a gravitational field?</p>
g17980
[ 0.05932160094380379, 0.07354024052619934, 0.01594759151339531, 0.01834917813539505, 0.04193873703479767, 0.06649333238601685, -0.032963529229164124, -0.0010320860892534256, -0.049737051129341125, -0.024556677788496017, 0.027216415852308273, 0.05030819773674011, -0.013969394378364086, -0.01...
<p>I am interested in learning more about this interdisciplinary approach. </p> <p>1) What are some of the top questions in particle cosmology (e.g nature of dark matter, inflationary structure, topological defects in the universe)?</p> <p>2) Who are some of the top researchers in this field?</p> <p>3) Recommended r...
g639
[ 0.04640823230147362, 0.04935825616121292, 0.01838286779820919, 0.006457628682255745, 0.013197952881455421, 0.0033633799757808447, -0.027843613177537918, -0.002861650660634041, -0.019946804270148277, 0.018753813579678535, 0.09120433032512665, 0.007083315402269363, 0.07470930367708206, -0.04...
<p>In his excellent treatment of the history of the science of astronomical distances and sizes, Albert van Helden says (<a href="http://books.google.com/books?id=L-yb7GX9mQIC&amp;lpg=PA29&amp;vq=producing%20two%20perigees&amp;pg=PA30#v=snippet&amp;q=producing%20two%20perigees&amp;f=false" rel="nofollow">p.29</a>) that...
g17981
[ 0.027245042845606804, 0.04206818342208862, 0.010787623934447765, -0.03077644295990467, 0.03521104156970978, -0.0010656850645318627, 0.09308253228664398, -0.023094791918992996, -0.02021142467856407, 0.024529915302991867, -0.015789246186614037, 0.02655467763543129, 0.05906789004802704, -0.05...
<p>In the derivation of the geodesic, one starts with the integral of the line element (arclength):</p> <p>$$L(C)=\int_{\tau_1}^{\tau_2}d\tau\sqrt{g_{\mu \nu}\dot{x}^{\mu} \dot{x}^{\nu}}$$</p> <p>The integrand is then substituted into the Euler-Lagrange equation, which simplifies to the geodesic equation.</p> <p>My ...
g17982
[ 0.09572327136993408, -0.005890779197216034, -0.008992969058454037, -0.07013209909200668, -0.0038637309335172176, 0.038834456354379654, 0.014532715082168579, -0.003797877114266157, -0.047543715685606, -0.04373897239565849, 0.0470770001411438, 0.03482222184538841, 0.10641224682331085, 0.0069...
<p>A very basic question here; it's related to <a href="http://physics.stackexchange.com/questions/11686/finding-angular-velocity-and-regular-velocity-when-bouncing-off-a-surface-with-f">this one</a>, but not quite the same.</p> <p>If a rotating rigid body (a sphere for the sake of discussion) with mass $m$, radius $r...
g17983
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<p>Provided that the notion of "$\mbox{spacelike}$"-ness (of an interval) is symmetric: $$\text{spacelike}( \, x - y \, ) \Longleftrightarrow \text{spacelike}( \, y - x \, ),$$ then for any set $X$ (of sufficiently many elements) the set $X^2$ (of all pairs, regardless of order, of not necessarily distinct elements of ...
g17984
[ -0.012264961376786232, 0.035613253712654114, -0.002158144721761346, -0.028663475066423416, -0.0025442438200116158, -0.00791948288679123, -0.015470553189516068, -0.027918756008148193, 0.010110849514603615, -0.008223984390497208, -0.013476871885359287, 0.029578013345599174, 0.02687551453709602...
<p>The problem itself is short, but my concept question is...long. So be prepared. Note that problem 1 and problem 2 are related to my concept questions, so I am not taking advantage of asking two in one.</p> <p><strong>Problem #1</strong></p> <p><img src="http://img815.imageshack.us/img815/7890/problem1.jpg" alt="">...
g17985
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<p>Suppose a classical free field $\phi$ has a dynamic given in Poisson bracket form by $\partial_o\phi=\{H, \phi\}$. If we promote this field to an operator field, the dynamic after canonical quantization is given by $\partial_o\phi=i[H, \phi]$.</p> <p>How do we prove the equivalence of these two equation of motions?...
g17986
[ 0.07883934676647186, 0.0091071967035532, -0.004682304337620735, 0.0029161577112972736, 0.062076348811388016, -0.030900975689291954, 0.0606536865234375, -0.026054272428154945, -0.0004145304556004703, -0.003833682741969824, -0.07503195852041245, 0.04991089180111885, -0.03046850487589836, 0.0...
<p>If you concentrated sunlight to points in the ocean, could you make the water evaporate significantly faster to induce a substantial amount of rain? Assuming you could do that, could you use <a href="http://en.wikipedia.org/wiki/Cloud_seeding" rel="nofollow">silver iodide</a> to bias rain toward certain areas of lan...
g17987
[ 0.03581325709819794, 0.061124760657548904, -0.0035800738260149956, -0.018616104498505592, 0.014157244004309177, 0.0036209297832101583, 0.02439938113093376, -0.029115062206983566, 0.0028891568072140217, 0.006174388807266951, 0.027060426771640778, 0.07402440160512924, 0.08700460195541382, -0...
<p>I know that the title of the question is rather vague, so let me clarify what I mean.</p> <p>For a quantum system, the set of states has infinitely (even continuously) many extreme points, i.e. there are infinitely many pure states. By the set of states, I mean the convex set of <em>density operators</em> $\mathcal...
g17988
[ 0.05206633359193802, 0.017878174781799316, 0.002835079561918974, -0.018033411353826523, -0.010407540947198868, -0.018094738945364952, 0.012178392149508, 0.08139756321907043, 0.029981844127178192, -0.030273744836449623, -0.005655074026435614, -0.021651653572916985, -0.004077817779034376, 0....
<p>I took an optics course a few years back, and am trying to figure out how to build an infinity-corrected microscope from discrete optical components which are listed in references [2] (lenses) and [3] (mounting equipment).</p> <p><img src="http://i.stack.imgur.com/OttSp.jpg" alt="Diagram of Infinity Corrected Objec...
g17989
[ 0.026226336136460304, -0.09759736061096191, 0.004598995205014944, -0.005039324052631855, 0.034183699637651443, -0.019051019102334976, -0.026051649823784828, 0.048044268041849136, -0.004140595905482769, 0.028888171538710594, 0.04221019521355629, -0.0359368734061718, 0.04711221158504486, -0....
<p>In other words, does $\frac{dJ}{dt} =0$ imply $J \times \omega =0$?</p> <p>Counterexamples or proofs would be helpful!</p> <p>EDIT: This question originally asked if $\frac{dJ}{dt} =0 \Leftrightarrow J \times \omega =0$, but clearly the $\Leftarrow$ direction is not true.</p>
g17990
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<p>why momentum is conserved when a bullet hit a block horizontally even when force of bullet is acting on it and net external force is not zero ?</p>
g17991
[ 0.08018150180578232, 0.012542148120701313, 0.010874706320464611, 0.02334936335682869, 0.061027850955724716, 0.056590911000967026, 0.043706465512514114, 0.0089088324457407, -0.05755898356437683, -0.04271377623081207, 0.003404829418286681, -0.04470439255237579, -0.01696852035820484, 0.035225...
<p>To date, what is the most mathematically precise formulation of the AdS/CFT correspondence, and what are the most robust tests of the conjecture?</p>
g17992
[ 0.03892216831445694, -0.024189628660678864, -0.0042972988449037075, 0.036326270550489426, 0.002370132366195321, -0.0271435659378767, 0.03998810052871704, -0.01962578110396862, 0.009856165386736393, -0.024928992614150047, 0.05884816497564316, -0.007996857166290283, 0.030189894139766693, -0....
<p>Interstellar space is pretty empty but there a small number of of atoms (mostly hydrogen?) floating around. How many atoms per light year would a photon encounter while traversing interstellar space?</p>
g17993
[ -0.02907481975853443, 0.0521114356815815, 0.014344099909067154, 0.0028722237329930067, -0.05176547169685364, 0.046422846615314484, -0.017464088276028633, 0.01046251505613327, 0.0040412466041743755, -0.031193599104881287, 0.06823462247848511, 0.008277012035250664, -0.03476386144757271, -0.0...
<p>I was reading about interesting article <a href="http://www.donnee.com/universe-as-computer.htm" rel="nofollow">here</a> which suggests that our universe is a big computer simulation and the proof of it is a Quantum Physics. </p> <p>I know quantum physics tries to provide some explanation about unpredictable behav...
g227
[ 0.004543656017631292, 0.10292007029056549, 0.0028542920481413603, -0.05123152211308479, -0.009758715517818928, 0.04679518938064575, 0.0009109145612455904, -0.026804843917489052, 0.029227368533611298, -0.03522021323442459, 0.02899963967502117, 0.027719790115952492, 0.025663021951913834, 0.0...
<p>The cowbell in question: <a href="http://www.youtube.com/watch?v=OuU0BzXm-qk" rel="nofollow">http://www.youtube.com/watch?v=OuU0BzXm-qk</a></p> <p>In most cowbells, the larger the metal dome, the lower the frequency produced. What would cause a phenomenon where the opposite is true: the larger dome creates a higher...
g17994
[ 0.05250285938382149, 0.07074759900569916, 0.00572796119377017, -0.034018374979496, 0.0762874186038971, 0.029649117961525917, 0.03684549406170845, -0.032992277294397354, 0.010498696938157082, -0.034580837935209274, -0.10456634312868118, 0.04979090392589569, 0.058160450309515, 0.043094940483...
<p>Aren't they basically made up of the same stuffs (quarks) in almost the same configuration? </p>
g17995
[ 0.029240058735013008, -0.016800692304968834, -0.0008948408649303019, -0.043209657073020935, 0.04263699799776077, 0.006084120832383633, -0.025578442960977554, -0.06780408322811127, -0.021056903526186943, -0.03479604795575142, 0.05414418503642082, -0.014632083475589752, -0.033955324441194534, ...
<p>Kohmoto (1985) pointed out in <em>Topological Invariant and the Quantization of the Hall Conductance</em> how TKNN's calcuation of Hall conducance is related to topology, in which topologically nontriviality is said to be equivalent to impossiblility choosing a global phase of Bloch function $u_k (r)$ in Brillouin z...
g17996
[ 0.05009361729025841, -0.008965719491243362, 0.012648990377783775, 0.028525371104478836, 0.062329936772584915, -0.01741832122206688, 0.03409028798341751, 0.01940213330090046, -0.013719601556658745, 0.06511301547288895, -0.046011146157979965, 0.019039304926991463, -0.019827215000987053, 0.04...
<p>I'm a mathematician learning physics to provide some background for my mathematical work (especially pde's!). I have been reading through Jackson's Classical Electrodynamics (3rd edition), and I was puzzled by an assumption he makes. On page 214, he derives the equation $W=\frac12 \int_{V_1} \mathbf{J} \cdot \mathbf...
g17997
[ 0.03665751591324806, -0.024250373244285583, -0.0155354468151927, -0.06429855525493622, 0.01045979280024767, 0.01670626364648342, 0.027244435623288155, 0.011659933254122734, -0.05853550508618355, 0.036563269793987274, -0.003051420906558633, -0.01526997983455658, -0.025602512061595917, 0.021...
<p>The Ancient Greek astronomers had quite an obsession over uniform circular motion; I was wondering if there was a logical reason for this. Did it develop through actual observations of the stars? Do they appear to move uniformly? If so, why?</p> <p>I've read a few things online that attributes this belief mainly to...
g17998
[ -0.0030081814620643854, 0.013672016561031342, -0.009883278049528599, -0.08397244662046432, 0.05475456267595291, -0.012165726162493229, 0.03311888501048088, -0.0048370580188930035, 0.022611064836382866, -0.01961885765194893, -0.00676066754385829, 0.016372404992580414, 0.07501591742038727, 0...
<p>In all astrophysical calculations I'm aware of, the thomson cross-section (for electron scattering) is taken as a constant in time, why is this the case? I have only weak experience in cosmology and GR, but naively I would have guessed that if the wavelength of photons is red-shifted from expansion, then the debrog...
g17999
[ 0.018337152898311615, 0.018676765263080597, 0.015195784159004688, -0.057342007756233215, 0.07305656373500824, 0.056550029665231705, -0.026172732934355736, 0.007233112584799528, -0.032099008560180664, -0.029007138684391975, 0.0701872706413269, -0.0184438768774271, 0.06672396510839462, 0.018...
<p>I have this problem to solve:</p> <p>Two protons are on the x axis at x=-1 and x=0. An alpha particle is placed at x=2, and the proton on the left is released, find its speed at infinity.</p> <p>I know that this involves the change in kinetic and potential energies of the particles, but I dont understand which par...
g18000
[ 0.06650203466415405, 0.022029154002666473, 0.012035558931529522, -0.030985917896032333, 0.08585807681083679, -0.012259607203304768, 0.004562612622976303, 0.09442567080259323, -0.07377408444881439, 0.037628769874572754, -0.0007016993477009237, 0.035473257303237915, -0.029925789684057236, 0....
<p><img src="http://i.stack.imgur.com/d7Ggl.png" alt="enter image description here"></p> <p>What is the total capacitance of this capacitor? Is it analogous to the case of inserting a plate into a capacitor (essentially creating two capacitors in series)?</p>
g18001
[ 0.041077569127082825, 0.062287356704473495, -0.0027297562919557095, -0.04348475858569145, 0.01816866546869278, -0.011914235539734364, 0.033176034688949585, -0.0015742853283882141, -0.024550791829824448, -0.027607722207903862, -0.1098007932305336, 0.030862009152770042, -0.0014276865404099226,...
<p>The action for the Brans-Dicke-Jordan theory of gravity is $$ \\S =\int d^4x\sqrt{-g} \; \left(\frac{\phi R - \omega\frac{\partial_a\phi\partial^a\phi}{\phi}}{16\pi} + \mathcal{L}_\mathrm{M}\right). $$ And the field equations of the gravitation field are $$ G_{ab} = \frac{8\pi}{\phi}T_{ab}+\frac{\omega}{\phi^2} (\...
g18002
[ 0.0034225021954625845, 0.014526796527206898, -0.03183716535568237, -0.012742588296532631, 0.05518967658281326, -0.023467039689421654, 0.08413539826869965, -0.03210322558879852, -0.0007640158873982728, -0.00951483752578497, -0.03453804552555084, 0.005139679182320833, -0.030106455087661743, ...
<p>Yeah, I haven't quite understood, or been told, what happens to, for example an electron and it's wavefunction, when you stop to measure it?</p> <p>I mean, an electron has a wave function describing it's position and so on in the region of space it is confined. When I measure it, I get an output, and the wavefuncti...
g18003
[ 0.00020504290296230465, -0.032243601977825165, 0.0055471849627792835, -0.045060522854328156, 0.011618315242230892, 0.020343275740742683, 0.04764072969555855, 0.021588042378425598, -0.0265565924346447, -0.036298032850027084, -0.05857575684785843, 0.031418800354003906, 0.004059983883053064, ...
<p>I was wondering if on the recieving end of a black hole can you see the photons being sucked in</p>
g18004
[ -0.027199609205126762, 0.022036457434296608, 0.002604932291433215, -0.008607280440628529, -0.0017751922132447362, -0.011779162101447582, -0.06159372255206108, 0.015450062230229378, 0.008925407193601131, 0.03296415135264397, 0.03894325718283653, 0.0656551867723465, -0.02481020614504814, -0....
<p>I'm having trouble differentiating the following when making a change of co-ordinates to determine the Schwarzchild metric.</p> <p>$$r'^{2}=r^{2}C(r)$$</p> <p>Then taking the total derivative of both sides, the answer says;</p> <p>$$dr^{2}=\frac{4r'^{2}dr'^{2}}{2C(r)r+r^{2}C'(r)}$$</p> <p>I cannot seem to get th...
g18005
[ 0.028847916051745415, -0.020439784973859787, -0.05086664482951164, 0.01726951077580452, 0.01387772522866726, -0.03586326539516449, 0.0758788213133812, 0.0040007722564041615, -0.0474175363779068, 0.01942906342446804, -0.01958533190190792, -0.0067922198213636875, 0.035436611622571945, 0.0023...
<p>Assume that astronomers on Earth have been monitoring a distant binary star system for a long time (relative to the orbital periods of the binary system) and then they see one star go supernova.</p> <p>Let $c_g$ = "speed of gravity" and $c$ = speed of light. What differences would we expect between observations in...
g18006
[ -0.0033354575280100107, 0.03868967294692993, -0.005923600401729345, -0.01823495700955391, 0.03539138287305832, 0.004685192368924618, 0.032746266573667526, -0.0029794059228152037, -0.05389127507805824, -0.07221722602844238, 0.015377696603536606, 0.0457935631275177, 0.003586200997233391, 0.0...
<p>I am implementing the <a href="http://www.opticsinfobase.org/josab/abstract.cfm?uri=josab-10-3-524" rel="nofollow">Monte Carlo wave-function approach</a> to dissipation problems. So far, I have simulated the quantum harmonic oscillator coupled to a finite temperature reservoir given in section 5A of the above paper...
g18007
[ -0.013939100317656994, -0.01638161949813366, -0.0012299376539885998, -0.04329926520586014, 0.054565027356147766, -0.04229404777288437, 0.035575833171606064, 0.021781111136078835, -0.027051031589508057, 0.014871306717395782, -0.05819860100746155, 0.03290832042694092, 0.015062994323670864, 0...
<p>For example the eq 2.1 <a href="http://arxiv.org/abs/hep-th/9804085">here</a> with regards to Type IIB. </p> <p>Unless I am terribly missing/misreading something Polchinski doesn't ever seem to derive these low energy supergravity actions.</p> <p>I would like to see a beginner's explanation (maybe together with re...
g18008
[ 0.024600431323051453, 0.03736606985330582, -0.028353117406368256, 0.023652756586670876, 0.05851629748940468, 0.015674103051424026, 0.05972727760672569, 0.019420230761170387, -0.01604546047747135, -0.057888664305210114, -0.044887248426675797, 0.028127750381827354, 0.03798144683241844, -0.01...
<p>The formula given for compton scattering shows that when x-ray of one specific wavelength hits carbon or some materials, emitted x-ray will be of one new specific wavelength.</p> <p>However, according to scattered x-ray intensity (y-axis) vs wavelength (x-axis) graph, it shows that there are multiple wavelengths fo...
g18009
[ 0.020025605335831642, 0.03655235096812248, -0.010283371433615685, 0.017714973539114, 0.03604617342352867, 0.006102800369262695, -0.02569187991321087, -0.001779978396371007, -0.031011637300252914, -0.0026628542691469193, 0.022469762712717056, 0.056760888546705246, 0.040741853415966034, -0.0...
<p>In QFT when one works out the cross section between two colliding electrons one gets a formula which is proportional to $\theta^{-4}$ where $\theta$ is the scattering angle which is due to a nearly on-shell photon with momentum $\approx 0$. See for example Peskin and Schroeder pg 155. This is also seen in ordinary R...
g18010
[ 0.03308212384581566, -0.009833760559558868, 0.001425847876816988, -0.03790833428502083, 0.08211565762758255, 0.03376341238617897, 0.0063572959043085575, 0.06635472923517227, 0.006836815271526575, 0.06850123405456543, 0.02105003036558628, -0.0027164206840097904, -0.008636824786663055, -0.02...
<p>I've done some search with the Nasa Extragalactic Database (NED) and I have a very basic question about the velocity/redshift conversion. For example, for the first object of <a href="http://ned.ipac.caltech.edu/cgi-bin/nph-objsearch?refcode=1988AJ.....95..284D&amp;hconst=73&amp;omegam=0.27&amp;omegav=0.73&amp;corr_...
g18011
[ 0.0825718566775322, 0.041957736015319824, 0.0034995335154235363, -0.0569106787443161, 0.04756521061062813, -0.006444710306823254, 0.058723822236061096, 0.008275756612420082, -0.05204785242676735, -0.026888765394687653, 0.03450227528810501, 0.06569747626781464, 0.012518675066530704, 0.01177...
<p>Analysis of data is integral in bridging the gap between theory and experiment. My question is about the two major methods of approaching the analysis - Bayesian and Frequentist. How much do the results of the analysis depend upon the choice of the method?</p> <p>For instance, consider experiments in Particle Physi...
g18012
[ 0.039557069540023804, -0.007989094592630863, 0.002275844570249319, -0.029822470620274544, 0.015556015074253082, 0.0014387769624590874, 0.059007059782743454, 0.025289414450526237, -0.03326638042926788, -0.03735839203000069, 0.067617267370224, -0.0032868136186152697, 0.038055818527936935, 0....
<p>In several early (pre-1600) astronomical texts I read about "cycles of anomaly" and "cycles of longitude", but it us unclear to me what these terms mean. They were clearly familiar to authors at the time and are undefined in any of the texts I've looked through. </p> <p>How were these terms employed in pre-1600s so...
g18013
[ 0.005094787571579218, -0.004240584094077349, 0.003490178845822811, -0.038959845900535583, 0.046484753489494324, 0.0234091617166996, 0.013254649937152863, -0.038791101425886154, 0.0257407259196043, -0.024025097489356995, -0.012130120769143105, 0.0053497967310249805, 0.07440844923257828, -0....
<p>Are moments relevant to the thicknesses of beams in a structure (ie. the larger the moment the thicker the beam)?</p>
g18014
[ 0.01363831851631403, 0.001656720181927085, -0.0042528146877884865, 0.000762938754633069, 0.018132919445633888, -0.028179379180073738, 0.01945175789296627, 0.02418500743806362, -0.028596866875886917, 0.02034016326069832, -0.023188624531030655, -0.01863504946231842, -0.04140196740627289, 0.0...
<blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://physics.stackexchange.com/questions/13157/what-is-a-field-really">What is a field, really?</a><br> <a href="http://physics.stackexchange.com/questions/30517/what-are-electromagnetic-fields-made-of">What are electromagnetic fields made of?</a...
g558
[ 0.037235960364341736, 0.024520421400666237, -0.03191809728741646, -0.004927719943225384, 0.07207296788692474, 0.036089878529310226, 0.005571634508669376, 0.03140810504555702, 0.049607131630182266, -0.04322047159075737, -0.03901262208819389, 0.008554897271096706, 0.0009079142473638058, -0.0...
<p><a href="http://en.wikipedia.org/wiki/Spin-statistics_theorem">Wikipedia's article on the spin-statistics theorem</a> sums it up thusly:</p> <blockquote> <p>In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin of a particle is its intrinsic...
g18015
[ 0.022570693865418434, -0.015299955382943153, 0.029783282428979874, -0.07046186178922653, 0.02697787433862686, -0.030802391469478607, 0.04278950020670891, 0.02542278543114662, 0.05290038138628006, 0.036515094339847565, -0.04503435641527176, 0.03684812784194946, -0.0015155875589698553, -0.05...
<p>I'm optimizing the geometry of a system composed of several interacting masses (a molecule). The energy of the system depends on the relative position of the masses, and all velocities are zero.</p> <p>In a simple case, the energy is invariant with translation and rotation of the whole system, so I can optimized us...
g18016
[ 0.017103703692555428, 0.014596224762499332, -0.0070921811275184155, -0.011237917467951775, -0.0014258597511798143, -0.040223147720098495, 0.017563845962285995, 0.049883708357810974, -0.07326193153858185, 0.021532533690333366, -0.011361482553184032, -0.06973131000995636, 0.003150098491460085,...
<p>When learning for physics (hydrodynamics and gases) I wanted to know what would be examples of nearly <a href="https://en.wikipedia.org/wiki/Perfect_fluid" rel="nofollow">perfect fluids</a> (no surface effects and no friction) and <a href="https://en.wikipedia.org/wiki/Ideal_gas" rel="nofollow">perfect gases</a> (on...
g18017
[ 0.019130006432533264, -0.01750507764518261, -0.008661745116114616, -0.014770223759114742, 0.055687639862298965, 0.0036935955286026, 0.004929888062179089, 0.003504785941913724, -0.05733717605471611, -0.005333054345101118, 0.031001634895801544, -0.028441932052373886, 0.01971745677292347, -0....
<p>I've read on the Internet that wearing plastic shoes doesn't allow electric charges we collect from our environment (PC, TV, appliances) to be earthed.</p> <p>Is this reasoning correct?</p>
g18018
[ 0.026895642280578613, 0.083948515355587, -0.010894548147916794, 0.05148746073246002, 0.03834906220436096, 0.0779174268245697, -0.004566175863146782, 0.01692494936287403, -0.011236031539738178, 0.009974077343940735, 0.006223450880497694, -0.013349569402635098, -0.023966815322637558, 0.04799...
<p>Intuitively I've been able to understand a Fourier transform a change-of-basis formula - you're basically moving from position to momentum basis or from time to frequency - but what does it mean that these spaces are 'conjugate' to each other? Does this have to do with them being complete bases? </p> <p>A related q...
g18019
[ 0.013950036838650703, 0.0005966896424070001, -0.019825343042612076, -0.04999896138906479, 0.07530283182859421, -0.07259997725486755, 0.056074146181344986, -0.01162807922810316, -0.005778181366622448, -0.004747857805341482, -0.03702815622091293, -0.004458664916455746, 0.018547218292951584, ...
<p>Working in only two dimensions and assuming that the central body is at the origin of the coordinate system, given two points in space and knowing the transit time between those points, as well as the direction of motion, is it possible to calculate a body's orbit?</p> <p>It seems to me that there should be enough ...
g18020
[ -0.008504068478941917, 0.07327144593000412, -0.0005524373264051974, 0.013077673502266407, 0.020996656268835068, 0.0037312391214072704, 0.008796966634690762, 0.009839920327067375, -0.031894661486148834, 0.016588183119893074, 0.009169194847345352, 0.052478134632110596, 0.11987511813640594, -...
<p>Is the Voyager 1 (or any similar exploration spacecraft) equipped with the ability for space to dock with it (attach to it)?</p> <p>Hypothetically, if a voyager or similar spacecraft were in Earth's orbit, could a NASA spacecraft dock with it in a similar fashion as it would the ISS?</p>
g18021
[ -0.05315699055790901, 0.07093619555234909, 0.032234691083431244, -0.00939206127077341, -0.029807118698954582, 0.017483660951256752, -0.003796973964199424, 0.004478613380342722, 0.021375177428126335, -0.0425947941839695, 0.05456528812646866, -0.00786626897752285, 0.04200228303670883, 0.0616...
<blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://physics.stackexchange.com/questions/6997/will-a-machine-or-a-technique-ever-be-possible-that-allows-gravity-in-space">Will a machine or a technique ever be possible that allows gravity in space?</a> </p> </blockquote> <p>I'm wondering how ...
g559
[ 0.03547590225934982, 0.10304384678602219, 0.005879268050193787, 0.023409737274050713, 0.006730907596647739, 0.0970233753323555, 0.005129413213580847, 0.0036001442931592464, -0.05899153649806976, -0.06573624163866043, 0.05929024890065193, -0.0034562034998089075, 0.00864901952445507, -0.0022...
<p>Is there any intuitive reasoning behind why the units of a "Newton" is $kg \frac{m}{s^{2}}$ and how it represents force? I always wanted to understand why objects of different mass fall at the same rate on earth and I found an explanation that uses Newtons Second Law of Motion and it made sense, but I'm confused as ...
g18022
[ 0.05965769290924072, -0.012293336912989616, -0.0022436173167079687, -0.004838586784899235, 0.04508262127637863, 0.05045979842543602, 0.0057192612439394, 0.005976985674351454, -0.030358368530869484, -0.01654239371418953, -0.01362613495439291, -0.01814337633550167, 0.0490916408598423, 0.0104...
<p>Which symbols are usually used to denote an arbitrary operator in quantum mechanics, such as <em>O</em> in the following example?</p> <p>$O \mbox{ is Hermitian} \Leftrightarrow \Im{\left&lt; O \right&gt;} = 0$</p>
g18023
[ 0.0026625520549714565, -0.04013298079371452, 0.0016590041341260076, -0.022375743836164474, 0.049067579209804535, -0.013578223064541817, 0.004283285699784756, 0.008613957092165947, 0.02450583502650261, 0.020533287897706032, 0.0017477782675996423, 0.057945262640714645, 0.013926456682384014, ...
<p>Often in textbooks Noether's theorem is stated with the assumption that the Lagrangian needs to be invariant $\delta L=0$.</p> <p>However, given a lagrangian $L$, we know that the Lagrangians $\alpha L$ (where $\alpha$ is any constant) and $L + \frac{df}{dt}$ (where $f$ is any function) lead to the same equations o...
g18024
[ 0.04839992895722389, -0.04545830562710762, -0.010991583578288555, -0.059126272797584534, -0.0033129106741398573, 0.015489133074879646, 0.02019052393734455, 0.04439804330468178, -0.04835173487663269, -0.01961147040128708, -0.029115408658981323, 0.027617620304226875, -0.00781344436109066, 0....