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<p>I'm a pure mathematician by trade, and have been trying to teach myself A-level mechanics. (This <em>is not</em> homework, it is purely self-study.)</p>
<p>I've been working through the exercises and have come up against a stubborn problem. Here it is:</p>
<p><strong>Question</strong></p>
<p>A train of mass 150 tonnes is moving up a straight track which is inclined to 2$^{\circ}$ to the horizontal. The resistance to the motion of the train from non-gravitational forces has magnitude 6 kN and the train's engine is working at a constant rate of 350 kW.</p>
<p><code>Calculate the maximum speed of the train.</code></p>
<p>The track now becomes horizontal. The engine continues to work at 350 kW and the resistance to motion remains 6 kN</p>
<p><code>Find the initial acceleration of the train.</code></p>
<p><strong>Answers</strong></p>
<p><code>Calculate the maximum speed of the train.</code></p>
<p>This is straightforward. When the train reaches its maximum velocity it will have zero net acceleration, i.e. the force from the engine must neutralise the force from resistance. The gravitational resistance has a magnitude of $150000g\sin 2$ and so the total resistance is $(6 + 150g\sin 2)\times 10^3.$ Using this with the formula $P = Fv$ we get $3.5 \times 10^5 = (6 + 150g\sin 2)v\times 10^3$ and so </p>
<p>$$v = \frac{350}{6 + 150g\sin 2} \approx 6.11 \, \text{m/s} \, .$$</p>
<p><code>Find the initial acceleration of the train.</code></p>
<p>This is where I come unstuck. The question asks for the "initial" velocity straight after telling you that the hill levels out. As such I assume it wants the "initial" acceleration right after reaching the peak of the hill. </p>
<p>Since the train is on level ground, the only resistance is the 6 kN non-gravitational resistance. (No value for $\mu$, the coefficient of friction, is given and I assume there is no friction.) We also know that the engine works at a rate of 350 kW. Using the formula $P = Fv$ we get:</p>
<p>$$ 350000 = F \times \frac{350}{6 + 150g \sin 2} \iff F = 1000(6 + 150g\sin 2) \, . $$</p>
<p>Finally, we use the formula $F = ma$ to give $1000(6+150g\sin 2) = 150000a$, and in turn:</p>
<p>$$ a = \frac{6+150g\sin 2}{150} \approx 0.382 \ \text{m/s}^2 \, . $$</p>
<p>This is not the answer in the book. It is very close, but it is slightly out. I feel that either I am misreading the question or the question is under-determined. For example, the maximum possible climbing speed of the train is around $6.11 \ \text{m/s}$, but there is no mention in the question that the train spends a sufficient amount of time climbing in order to reach that speed.</p>
<p>I would be pleased to see your ideas about how to resolve this problem. My misunderstanding is not mathematical, but conceptual; don't worry about using a lot of maths. But please try to explain the physical phenomena in a lucid fashion. Thanks in advance.</p> | g13039 | [
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<p>I am wondering how to deal with an expression like
$$ \int d^4\theta \frac{1}{T + T^\dagger} \big( \dots \big) $$
If the denominator was of the form $1 + T + T^\dagger$, I could assume that $T \ll 1$ and expand the denominator in a Taylor series.</p>
<p>If more context helps, this expression pops up in $5D$ SuGra abelian gauge theory (<a href="http://arxiv.org/abs/hep-th/0106256" rel="nofollow">http://arxiv.org/abs/hep-th/0106256</a>, eq. (5) on page 2).</p>
<p>The authors of the above mentioned paper assume the modulus to be stable ($<T> \equiv R$) before performing the superspace integration. I do not want to do this and keep the dependence on the modulus.</p> | g13040 | [
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<p>Since all the traditional "continuous" quantities like time, energy, momentum, etc. are taken to be quantized implying that derived quantities will also be quantized, I was wondering if Quantum Physicists agree upon any quantity not being quantized?
I couldn't think of a single thing, until I came across this: <a href="http://physics.stackexchange.com/questions/32665/why-position-is-not-quantized-in-quantum-mechanics">Why position is not quantized in quantum mechanics?</a></p> | g13041 | [
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<blockquote>
<p>A ball of mass $0.37\text{ kg}$ is thrown upward along the vertical with a initial speed of $14\text{ m/s}$, and reaches a maximum height of $8.4\text{ m}$.</p>
<p>a) What is the work done by air resistance on the ball? </p>
</blockquote>
<p>I came up with</p>
<p>$$F \times\text{Distance}(8.4) = .5 \times\text{Weight}(.37)\times(0-14^2)$$</p>
<p>But my answer doesn't match with the book's answer which is $-5.8\text{ J}$.</p>
<p>Not sure if I"m doing this wrong; if there's some special way to calculate air resistance that <em>isn't</em> the formula $W = .5(\text{Mass})(v_f^2-v_i^2)$, with $v_f$ being the final speed and $v_i$ being initial speed.</p>
<p>Part B = Assume that air resistance does about the same work on the downward trip. Estimate the speed of the ball as it returns to its starting point.</p> | g13042 | [
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<p>Can someone tell me what does it 20-30% collision centrality mean in terms of impact parameter b?</p> | g13043 | [
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<p>Distant galaxies are said to be moving away from the Milky Way (and us) at speeds approaching the speed of light. Since Special Relativity tells us that any object moving away from us at a velocity of near the speed of light will increase in mass in our observations, i.e. it will appear to be much more massive than its rest mass, approaching infinity as the speed approaches the speed of light. If we observe very large masses (like galaxies) moving away from us at near light speed, wouldn't their rest masses be tiny? So why do we not think these distant galaxies are actually just specks of matter in terms of their actual rest masses? And if that is the case then are we not just looking at what may be sub-atomic particles moving away from us at near light speed? ...The expanding universe explanation is the standard one. The balloon example is perhaps suggestive but not correct. If you occupied one point on the surface of a balloon, and you had a friend next to you and the balloon expanded, your friend would move away from you at a relative velocity v. Einstein's equations would obviously still apply. I see no easy way to explain why when I look at measurements of relative velocity between distant recessive galaxies, those velocities are somehow not what are measured and quoted but something very different because the universe is expanding. Velocity is defined (for Einstein too) as distance divided by the time to travel that distance. And we are talking about objects with mass; not a reflective beam from a searchlight or something like that. Even if the universe expands, velocity is still what it is. And if it is not what it is, then why do astrophysicists state that distant galaxies are moving away from us at nearly light speed? I guess I would like to see the intuitive argument with equations included which must be there but no one knows how to do it. I suppose it took a while before time dilation could be explained on the back of an envelope too.</p> | g13044 | [
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<p>Please explain as simply as possible what the Hubbard-Holtstein model is and what it is used for.</p> | g13045 | [
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<p>I am going through <a href="http://arxiv.org/pdf/1202.2556v1.pdf" rel="nofollow">CURVATURE OF SPIN NETWORKS</a> by Jonckheere et al. The first line of the abstract mentions XX coupling and Heisenberg coupling. What is the difference between these two couplings?</p> | g13046 | [
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<p>is there any way to make electromagnetic waves reach a cell phone in faraday cage although conductor surround cell phone everywhere , can we pass current through conductor to make charges move as a trick then if electromagnetic field reach the conductor then no charge can prevent electric field as they are mobile not static charges </p> | g13047 | [
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<p>I presume the answer is that it depends on the mass and size of the star and black hole, but I was wondering if somebody could provide some rough bounds (e.g. hours vs thousands of years).</p>
<p>By "eating" I mean the time it takes a star to go through the event horizon of the black hole, although maybe there are other easier-to-detect or more relevant events one can measure?</p> | g13048 | [
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<p>I realize this question is very broad but may be I will still get a helpful answers. References and textbooks for the development of the technical and mathematical aspects of QFT abound. However, I never came across a source dealing with the conceptual issues of QFT. I am interested in stuff like, </p>
<ul>
<li><p>the meaning of Gauge symmetry, </p></li>
<li><p>Spontaneous symmetry breaking, </p></li>
<li><p>interpretation of renormalization group, </p></li>
<li><p>etc. </p></li>
</ul>
<p>Are there any reference that deals with these issues mainly? </p> | g13049 | [
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<p>I was reading a book on the history of Quantum Mechanics and I got intrigued by the <em>gendankenexperiment</em> proposed by Einstein to Bohr at the 6th Solvay conference in 1930.</p>
<p>For context, the thought experiment is a failed attempt by Einstein to disprove Heisenberg's Uncertainty Principle.</p>
<p><img src="http://upload.wikimedia.org/wikipedia/en/6/65/Ebohr4.gif" alt="Einstein's box as drawn by Bohr"></p>
<blockquote>
<p>Einstein considers a box (called Einstein's box; see figure) containing electromagnetic radiation and a clock which controls the opening of a shutter which covers a hole made in one of the walls of the box. The shutter uncovers the hole for a time Δt which can be chosen arbitrarily. During the opening, we are to suppose that a photon, from among those inside the box, escapes through the hole. In this way a wave of limited spatial extension has been created, following the explanation given above. In order to challenge the indeterminacy relation between time and energy, it is necessary to find a way to determine with adequate precision the energy that the photon has brought with it. At this point, Einstein turns to his celebrated relation between mass and energy of special relativity: $E = mc^2$. From this it follows that knowledge of the mass of an object provides a precise indication about its energy.<br>
--<a href="http://en.wikipedia.org/wiki/Bohr%E2%80%93Einstein_debates#Einstein.27s_second_criticism">source</a></p>
</blockquote>
<p>Bohr's response was quite surprising: there was uncertainty in the time because the clock changed position in a gravitational field and thus it's rate could not be measured precisely.</p>
<blockquote>
<p>Bohr showed that [...] the box would have to be suspended on a spring in the middle of a gravitational field. [...] After the release of a photon, weights could be added to the box to restore it to its original position and this would allow us to determine the weight. [...] The inevitable uncertainty of the position of the box translates into an uncertainty in the position of the pointer and of the determination of weight and therefore of energy. On the other hand, since the system is immersed in a gravitational field which varies with the position, according to the principle of equivalence the uncertainty in the position of the clock implies an uncertainty with respect to its measurement of time and therefore of the value of the interval Δt.</p>
</blockquote>
<p><strong>Question:</strong> How can Bohr invoke a General Relativity concept when Quantum Mechanics is notoriously incompatible with it? Shouldn't HUP hold up with only the support of (relativistic) quantum mechanics?</p>
<p>Clarifying a bit what my doubt is/was: I thought that HUP was intrinsic to QM, a derived principle from operator non-commutability. QM shouldn't need GR concepts to be self consistent. In other words - if GR did not exist, relativistic QM would be a perfectly happy theory. I was surprised it's not the case.</p> | g13050 | [
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<p><a href="http://blogs.discovermagazine.com/badastronomy/2011/04/05/astronomers-may-have-witnessed-a-star-torn-apart-by-a-black-hole/">http://blogs.discovermagazine.com/badastronomy/2011/04/05/astronomers-may-have-witnessed-a-star-torn-apart-by-a-black-hole/</a></p>
<p>A lot of the star in the disc, a lot of the star in the jets, precisely how much of the star actually falls into the black hole?</p> | g13051 | [
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<p>In a photon gas, we know that pressure, $P$, and energy density, $u$, are related by:
$$P=\frac{u}{3}$$
We also know from relativity that the momentum of a photon is
$$p=\frac{E}{c}$$</p>
<p>Finally, the pressure can usually be thought of as the flux of momentum through a surface, but that would imply that the flux of energy through that surface is:
$$E_{e}=Pc=\frac{u}{3} c$$</p>
<p>However, the standard formula, from kinetic theory, is:</p>
<p>$$E_{e}=\frac{u}{4} c$$</p>
<p>I guess the assumption which is most probably wrong is identifying this sort of thermodynamic pressure with momentum flux, but I'm not sure how this comes about.</p> | g13052 | [
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<p>Having a <code>2D map</code> filled <code>uniformly by random values</code> (<em>Figure:top-left</em>) to demonstrate a disordered phenomena, the next maps are kernel averaged with a kernel of sizes 3x3, 5x5, ..., 11x11.<br>
<strong>The questions are:</strong><br>
What are the patterns appeared in the kernel averaged maps?<br>
What is the physical explanation of existence of such patterns? </p>
<p>For image please <a href="http://stats.stackexchange.com/questions/16742/what-are-the-patterns-appear-after-kernel-averaging">see this link.</a></p>
<p><strong>Note:</strong><br>
To generate the maps a <a href="http://stats.stackexchange.com/questions/16497/about-kernel-based-estimates">kernel based averaging system</a> type <strong>C</strong> was applied on the original data.</p> | g13053 | [
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<p>The cause of surface tension is said to be asymmetry in the forces experienced by the molecules at the surface due to different interactions with air and liquid, but then the same argument also applies for all other surfaces, where the fluid is in contact with the container then why isn't all strange surface tension phenomenon seen at those surfaces?
And how can surface tension be described as perpendicular forces to an imaginary line at the surface, isn't it supposed to act in all direction??</p>
<p>Regarding capillarity, in deriving the equation $ \gamma= \frac{r h \rho g}{2 \cos \theta_Y}$, we use the relation of excess(over the pressure on convex side) pressure on the concave side which is derived only for spherical bubbles or drops. then how can we assume the meniscus formed will be spherical and not defined by some other function?</p> | g13054 | [
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<p>James Joule established that all forms of energy were basically the same and interchangeable. My question is if thas law is relevant in particle physics. Can a positive charge and a negative charge be interchangeable? Will the force carrying particles allow it?</p> | g13055 | [
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<p>How would you go about finding the natural frequencies of solid materials like wood (e.g., teak, pine), stone (e.g., marble, granite) liquid, etc?</p> | g13056 | [
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<p>Is there a repository where one can find unpolarized nuclear Compton scattering data $\gamma (Z,N)\rightarrow \gamma (Z,N)$ for specific nuclei $(Z,N)$? or even some parametrization of structure functions that loosely follows the data? </p> | g13057 | [
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<p>How is the black hole complementarity version of the holographic principle derived from path integrals and/or string theory? That has never been obvious to me. Can someone show me how to do it step by step? </p>
<p>I know string theorists have shown extremal and near-extremal BPS black holes have stringey entropies which match the holographic bound, but not only does this not apply to black holes in general, there are no signs of complementarity in the derivation. The AdS/CFT correspondence is also conjectural and based upon nontrivial consistency checks, but no derivation?</p>
<p>Thanks a lot.</p> | g13058 | [
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<p>Why are ice and oil slippery? In general, why do certain substances make a surface difficult to walk on? </p> | g13059 | [
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<p>what fundalmentel force does a black hole based on?</p>
<p>It seems people is very unfamilar with black holes.</p>
<p>I will take a guess, is it electromantic force? please explain.</p> | g13060 | [
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-0.007418743334710598,
-0.02847609668970108,
0.05375947058200836,
-0.036569368094205856,
0.013995478861033916,
-0.00... |
<p>With all the sudden discussion related to Nuclear power, safety, fuel, waste, etc, there's one question whose answer has so far eluded me.</p>
<p>How big (height and diameter) is the actual pressure vessel of a conventional BWR or PWR? I've seen, now, about a thousand images depicting the structures of Fukushima, Chernobyl, and TMI, but none of them include units of measurement for the size of what I'm looking at.</p>
<p>Thanks!
Eric B</p> | g13061 | [
-0.030406396836042404,
0.05839989334344864,
0.020801177248358727,
-0.03926723077893257,
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0.002333024749532342,
0.04070373252034187,
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-0.010658100247383118,
0.046013813465833664,
-0.00963034201413393,
0.0009644557721912861,
-0.... |
<p>I know that molecules in ideal gas can move freely, and molecules in crystal are bonded to some specific location. But can I describe this in a more quantitative way? Do gas molecules have more degrees of freedom?</p> | g13062 | [
-0.03736991435289383,
0.025379374623298645,
-0.005395384971052408,
0.05203972011804581,
0.025457028299570084,
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0.0025179502554237843,
-0.014785374514758587,
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-0.014735091477632523,
... |
<p>Imagine a pipe which is bent to form a circular arc and a liquid is force through this pipe. How will you find the net force exerted by the fluid on pipe? Is the only force acting on fluid centripetal force or is there a tangential force too?</p>
<p>No drag forces or viscous forces</p> | g13063 | [
0.07936534285545349,
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0.00485974783077836,
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0.06172000616788864,
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-0.06848161667585373,
0.015575718134641647,
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0.0076... |
<p>I have recently carried out an experiment to verify Faradays law for a falling magnet. My starting point was to keep both the area of the coil and the number of turns constant whilst changing the velocity (the different velocities were obtained by dropping from different heights).What would be good is if a graph of emf induced vs. $dB/dt$ could be plotted so that the gradient of the graph will be equal to the product of the area and number of turns. From $e = -nA(dB/dt)$</p>
<p>In short, is there an equation to change velocity to $dB/dt$?</p> | g13064 | [
0.013007521629333496,
0.014797169715166092,
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-0.04897100105881691,
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-0.02876119688153267,
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0.05949832499027252,
0.06188565120100975,
0.03660... |
<p>I am reading a book on Gas dynamics and there is a small section
on thermodynamics before the conservation laws of mass momentum
and energy are introduced. </p>
<p>The book says</p>
<p>$$ p = R \rho T$$
where $R$ is a constant. When that is the case we can write </p>
<p>$$TdS = de + p d (\frac{1}{\rho}) \\
dS = \frac{de}{T} - d(R \log \rho)$$
It follows that $de/T$ must be a perfect differential and therefore a function of $T$ alone.
How does this last statement follow? </p> | g13065 | [
0.018441859632730484,
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-0.022242126986384392,
0.015202537178993225,
0.057829756289720535,
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-0.009755326434969902,
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0.056475307792425156,
-... |
<p>I'm studying vibrations; so I'm using Beer-Johnston-Cornwell Dynamics book. I am worry about the equation for Underdamped Vibration, which in the book it is: $$x_{(t)}=x_0e^{-\lambda t}\sin(\omega_d+\phi)$$; where $$\omega_d=\sqrt{\omega_n^2+c^2/4m^2}$$.</p>
<p>I think that $x_0$ would be replaced by the result vector of constants $c_1$ and $c_2$ affected by the factor $e^{-\lambda t}$. It means, an $x_m$ or an amplitud, but not the initial position, because it could be 0, with an inicial velocity.</p>
<p>Also the graphic, it depicts the boundary equation with $x_0$. I attached a picture.</p>
<p>Can you help me and comment? How I should interpret $x_0$? Maybe I misunderstood this topic.</p>
<p><img src="http://i.stack.imgur.com/obyol.jpg" alt="damp"></p> | g13066 | [
0.0641554668545723,
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0.09067008644342422,
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0.034194037318229675,
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0.... |
<p>I'm trying to figure out the missing step here, in a problem about X-ray crystallography. I am referring to the attached image:</p>
<p><img src="http://i.stack.imgur.com/EkwDw.png" alt=""></p>
<p>In the image, $A =$ electron density, $Z =$ distance traveled, $\lambda =$ X-ray wavelength, $p$ = electron position. It shows two electrons hit by an X-ray, and then excited in all directions. In this case, only one of those directions, S', is considered. rj= pj - p1.</p>
<p>Working off the basics of the image, suppose now there are $n$ electrons, $e_1,\dots, e_n$ at positions, $p_1, \dots, p_n$. And the X-ray scattering from $e_j$ is:</p>
<p>$$X_j = A_j*\exp\left(\frac{2\pi i p_j S}{\lambda}\right)$$</p>
<p>I have understood that equation, but I do not understand how to use that to derive that the total scattering from all n electrons is:</p>
<p>$$X = F*exp\left(\frac{2\pi i p_1 S}{\lambda}\right)$$,
where $F = \sum_{1<=j<=n} A_j*\exp*\left(\frac{2\pi i r_j S}{\lambda}\right)$ </p> | g13067 | [
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0.0591203011572361,
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0.036069776862859726,
0.03992409631609917,
-0.02... |
<p>I'm a layman, but i watched some intereting videos about big bang on youtube[michio kaku, hawking this kind of things, not some crackpots :)] </p>
<p>I described everything on my picture: </p>
<p><img src="http://i.stack.imgur.com/fqZAC.png" alt="enter image description here"></p>
<p>So is there any possibility to see that inner side, for example, by creating wormhole, or entering new dimension? Or i get something wrong, on the way, and my model is totally wrong?</p>
<p>And another question. I heard that even if you would fly a ship across the universe you would eventually end in the place where you started, because we live in a 3d space that is defined on a surface of big sphere. But why a big sphere? Universe might be a big mobius strip, and the same principle of ending at start will apply. Is it possible?</p>
<p>Thanks in advance, and please don't bash me for silly questions. Im just curious, but i don't have any degree in physics. Im also not an english native speaker.</p> | g13068 | [
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0.04562576487660408,
0.0415... |
<p>I'm arriving at a contradiction.</p>
<p>To calculate the scattering amplitude, one usually follows the prescription given by the Feynman rules that you only consider <strong>fully connected</strong> diagrams with the required number of incoming and outgoing external legs (See Peskin & Schroeder pg 111 where they say: Only fully connected diagrams contribute to the $T$ matrix).</p>
<p>By <strong>fully connected</strong>, one means that you consider only graphs from which you can get from one line to any other line <a href="http://www.damtp.cam.ac.uk/user/cdab3/notes/QFTscalarFrules.pdf">(See page 3 of this document)</a>.</p>
<p>On the other hand, we have the LSZ formula, which says that the scattering amplitude is given by the residue (as the momenta go on-shell) of the corresponding correlation function. For example, in $\phi^4$ theory,
\begin{align}
&\mathcal{M}(p_a,p_b \to k_1, k_2) \delta^{(4)}(p_a + p_b-k_1 -k_2) \sim \nonumber\\
&\lim_{p_a^2,p_b^2,k_1^2,k_2^2 \to m^2} (p_a^2 - m^2)(p_b^2 - m^2)(k_1^2 - m^2)(k_2^2 - m^2)G(p_a,p_b,-k_1,-k_2).
\end{align}</p>
<p>But these two prescriptions seems to give a contradiction. Consider in $\phi^4$ theory, the $\mathcal{M}(4 \to 4)$ scattering. We have this diagram (ok if someone could draw the diagram that'll be great),</p>
<p>\begin{align}
\text{X} \text{X}
\end{align}</p>
<p>which consists of two separate $2 \to 2$ scattering processes.</p>
<p>This diagram is not fully connected, so we should ignore it by the first prescription, yet, it does not evaluate to $0$ under the LSZ formula, so we should include it.</p>
<p>Physically it makes sense that the leading order contribution to a $4 \to 4$ process is given by two separate $2 \to 2$ ones, but the fully connected prescription misses that out.</p>
<p>So, is there a caveat to the fully connected rule of drawing Feynman diagrams, since I believe the LSZ formula is mathematically true and physically reasonable?</p> | g13069 | [
0.012937632389366627,
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0.06444769352674484,
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-0.01461373083293438,
0.005138582084327936,
0.007790823932737112,
0.019462255761027336,
0.... |
<p>In the course of circuits and electronics, I remember there is an experiment to show the polarization of the wave as lissajous figures. I am wondering for polarized laser, is there any way to visualize the polarization in the similar way? I try to use a light splitter to split the (circular) polarized light into two perpendicular beams and used photo detector to receive the beam and send them into oscilloscope in X and Y channel. But the scope doesn't really show the 'lissajous' figure. So I am wondering if this is the right way to visualize the polarized light? Thanks</p> | g13070 | [
-0.046460025012493134,
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0.016040703281760216,
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0.016137614846229553,
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0.022417519241571426,
0.06432560831308365,
0.0... |
<p>I came across K. O. Friedrichs' very old book (1953) "Mathematical Apsects of the Quantum Theory of Fields", and hardly any of it makes sense to me.</p>
<p>One of the strange things that he refers to are "Myriotic" fields. What are these? Is there a modern account of what Friedrichs is talking about?</p> | g13071 | [
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-0.02362203225493431,
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0.01563054881989956,
-... |
<p>How does the Fermi energy of extrinsic semiconductors depend on temperature?</p> | g13072 | [
0.03655831888318062,
0.020052684471011162,
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0.006986983586102724,
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0.022618958726525307,
0.008944203145802021,
... |
<p>It's a well known fact that an observer that accelerates at a constant rate from $-c$ at past infinity to $+c$ at future infinity sees a horizon in flat Minkowski spacetime. This is easy to see from a spacetime diagram once you realize that the union of past light cones on such a trajectory has a boundary that divides the spacetime into two regions - one inaccessible by the accelerating observer.</p>
<p>This leads to the classic result of Unruh radiation when one looks at the quantum field theory for such an observer. The horizon plays a crucial role here.</p>
<p>How does one go about determining whether a horizon is seen by a general class of worldines? In particular, is there any reason to believe that a horizon would exist for an observer that is stationary for all time except for a finite period of acceleration and deceleration?</p>
<p>Is there any other class of worldlines other than an indefinitely accelerating observer for which a horizon is known to exist in flat spacetime?</p> | g13073 | [
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0.03238106146454811,
0.002653922885656357,
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0.015656009316444397,
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0.03512364253401756,
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0.014708460308611393,
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0.014234689995646477,
0.06... |
<p>Someone told me that reading glasses (<em>a priori</em> with a magnifying glass effect only) improve one's eyesight of objects lying in the long range distance. I am really sceptic about it since everything is blurry if I look at objects through those glasses! Is it possible (for this particular person at least)?</p> | g13074 | [
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0.029406258836388588,
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0.029234012588858604,
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-0.004478809889405966,
0.08759228140115738,
0.0012877456611022353,
0.0582239143550396,
-0.0... |
<p>Let $\lambda$ be a linear density of a rope which is moving into a scale at velocity v. The additional force on the scale due to the collision is given as
$\frac{d p}{d t} = v\frac{d m}{d t} = \lambda v^2$.</p>
<p>For an incompressible fluid, the stagnation pressure from stopping a column of water <em>in excess of static pressure</em> is</p>
<p>$$\frac{1}{2}\rho v^2$$</p>
<p>We can easily compare the forms by, for example multiplying by the width of the column to obtain a linear density of the fluid, or consider hitting the scale with a continuum of infinitesimal ropes. It seems the $\frac{1}{2}$ factor would remain different.</p>
<p>So what is the explanation for this relative factor of $\frac{1}{2}$? I have tossed around a few ideas but I'm curious what you may think.</p> | g13075 | [
0.05247732624411583,
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0.045317143201828,
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-0.0069462601095438,
-0.011629821732640266,
-0.020896246656775475,
0.03920162469148636,
-0.036552... |
<p>Does it just mean "AC electric conductivity"? If so, why have a special name for it, and why mention optical specifically?</p>
<p>The <a href="http://en.wikipedia.org/wiki/Optical_conductivity" rel="nofollow">wikipedia page</a> on it is very sparse. <a href="http://physics.unl.edu/tsymbal/teaching/SSP-927/Section%2013_Optical_Properties_of_Solids.pdf" rel="nofollow">This</a> (warning, PDF) document just says:</p>
<blockquote>
<p>The term “optical conductivity” means the electrical conductivity in
the presence of an alternating electric field.</p>
</blockquote>
<p>Which sounds exactly like AC conductivity to me.</p>
<p>Is it different? If not, then why the special name?</p> | g13076 | [
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0.008453048765659332,
0.016772540286183357,
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0.05084187909960747,
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0.0036125334445387125,
0.0286124125123024,
0.05003020912408829,
-0.006088155787438154,
0.035469576716423035,
0.045050811022520065,
-0.0... |
<p>Did he invent surface and line integrals, or did they already exist when he formulated his equations. If they did, already exist, how did they come about in pure math?</p> | g13077 | [
0.04827946424484253,
0.007993584498763084,
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0.00782850943505764,
0.03795865550637245,
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-0.07460273802280426,
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-0.038622964173555374,
0.05575021728873253,
0.0143... |
<p>I basically want to observe the electrostatic force between two charges. I want to know if is there a simulator which could both help me to observe and calculate the force between two charges.</p>
<p>I found <a href="http://dept.sfcollege.edu/natsci/physics/simulations/electric_force_sim.htm" rel="nofollow">this simulator</a> which is pretty good I think. However, that would be great if there is a more comprehensive simulator with greater distances, more parameters etc.</p> | g13078 | [
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0.03090106137096882,
-0.00039658622699789703,
-0.05850783735513687,
0.040947407484054565,
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-0.025656742975115776,
0.031221507117152214,
-0.0005680337781086564,
0.008391223847866058,
... |
<p>The question is from ISSP by Kittel and as follows:</p>
<p>(a)Find a solution of the London equation that has cylindrical symmetry and applies outside a line core. In cylindrical polar coordinates, we want a solution of
$$ B-\lambda \nabla^2 B = 0 $$
that is singular at the origin and for which the total flux is the flux quantum:
$$ 2 \pi \int_0^\infty d\rho\rho B(\rho) = \Phi_0$$
The equation is in fact valid only outside the normal core of radius $\xi$</p>
<p>(b) Show that the solution has the limits
$$ B(\rho) \simeq (\Phi_0/2\pi\lambda^2)\ln(\lambda/\rho) , (\xi \ll \rho \ll \lambda) $$
$$ B(\rho) \simeq (\Phi_0/2\pi\lambda^2)(\pi\lambda/2\rho)^{1/2}\exp(-\rho/\lambda) , (\rho \gg \lambda) $$</p>
<p>I have proceeded to solve the equation with CAS software such as Maple and Mathematica; however, they give two arbitrary constants which are to be determined. Is the problem sufficiently defined to fix these arbitrary constants? The solutions given by these programs are:
$$B(r)\to c_1 J_0\left(\frac{i r}{\lambda }\right)+c_2 Y_0\left(-\frac{i r}{\lambda }\right) $$
Furthermore, how can I describe the effect of core? I found a solution manual but got confused by the method employed there (implementation of Dirac Delta) in order to describe the effect of the core. Here is a screenshot of the page. I appreciate your help and contribution.</p>
<p><img src="http://i.stack.imgur.com/CoStX.jpg" alt="enter image description here"></p>
<p>How can I implement 2-D Dirac delta function in cylindrical coordinates? By the way, I think one of the solutions of the homogenous equation is disregarded.</p> | g13079 | [
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0.030665751546621323,
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0.0025275370571762323,
-0.06317801773548126,
0.05013015493750572,
-0.01605459488928318,
-0.00... |
<p>If two gravitational waves came in contact with each other what would happen? In another question entirely, what happens when a higher gravitational field interacts with a weaker one.</p> | g13080 | [
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-0.024055585265159607,
-0.015649709850549698,
0.01... |
<p>I am reading the statistical mechanics by Pathria in Chap 12. I have a question about the Landau free energy. What is the physical reasoning for that the free energy could be a functional of the order parameter? Normally, the free energy is used when we choose the canonical ensemble and we we know that the free energy is the characteristic function of $N,V,T$ of the system.</p> | g13081 | [
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0.018449755385518074,
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0.029463021084666252,
0.0037459724117070436,
-0.... |
<p>Usually we say that equality of masses of particle and antiparticle follows from CPT-theorem. But do we need it for showing this equality?</p>
<p>The first method to show that is following.</p>
<ol>
<li><p>The equation of free fields of an arbitrary spin $s$: all of them have Klein-Gordon or Dirac form (with some conditions of irreducibility), so the general solution is given in a form
$$
\hat {\Psi}_{A}(x) = \sum_{\sigma}\int \frac{d^{3}\mathbf p}{\sqrt{(2 \pi)^{3}2p_{0}}}\left(u^{\sigma}_{A}(\mathbf p)e^{-ipx}\hat {a}_{\sigma}(\mathbf p) + v^{\sigma}_{A}(\mathbf p)e^{ipx}\hat {b}^{\dagger}_{\sigma}(\mathbf p) \right)_{p_{0} = \sqrt{\mathbf p^{2} + m^{2}}} \qquad (1)
$$</p></li>
<li><p>We must write $\hat {b}^{\dagger}_{\sigma}(\mathbf p)$, not $\hat {a}^{\dagger}_{\sigma}(\mathbf p)$, because of existence of some internal symmetries different from Poincare symmetry. If there exist some symmetry, we have conserving quantity $q$ for field, it means that corresponding operator $\hat {Q}$ commutes with hamiltonian of theory. We construct hamiltonian by having the equation of motion and its physical sense as polynomial of $\hat {\Psi}_{A}(x), \hat {\Psi}^{\dagger}_{B}(x)$ and spinor functions. It leads to the fact that
$$
\hat {Q}\hat {a}^{\dagger}(\mathbf p)| \rangle = q\hat {a}^{\dagger}(\mathbf p)| \rangle, \quad \hat {Q}\hat {b}^{\dagger}(\mathbf p)| \rangle = -q\hat {b}^{\dagger}(\mathbf p)| \rangle .
$$</p></li>
</ol>
<p>The second method is following.</p>
<ol>
<li><p>Suppose we don't have the equations for fields. But we know that S-operator must be Lorentz invariant operator or that our theory must be causal theory. S-operator is constructed from hamiltonian. Hamiltonian is constructed from creation and destruction operators and must be poincare scalar. So we must create invariant combination of fock space operators and some non-operator functions. Corresponding object is called creation/destruction field. By having laws of poincare transformation of creation and destruction operators we build the expression $(1)$ for field with one little difference: the first and second summands corresponds, in general, to the different masses. Then we construct the hamiltonian as polynomial of combinations of field functions and some spinor functions. </p></li>
<li><p>The statement of paragraph 1 leads us to the conclusion that
$$
[\hat {\Psi}_{A}(x), \hat {\Psi}^{\dagger}_{B}(y)]_{\pm} = 0 , \quad (x - y)^{2} < 0.
$$
With a bit of derivations we can get
$$
[\hat {\Psi}_{A}(x), \hat {\Psi}^{\dagger}_{B}(y)]_{\pm} = P_{AB}\left(i\frac{\partial}{\partial x}\right)\left( D^{m_{1}}_{0}(x - y)\pm (-1)^{s}D^{m_{2}}_{0}(y - x)\right), \qquad (2)
$$
where
$$
D^{m_{i}}_{0}(x - y) = \int \frac{d^{3}\mathbf p}{(2 \pi )^{3}2p_{0}}e^{-ip(x - y)}, \quad p^{2} = m_{i}^{2}.
$$</p></li>
<li>We conclude that $(3)$ may be equal to sero for spacelike intervals if and only if $m_{1} = m_{2}$.</li>
</ol>
<p>Are these methods of demonstrating of the identity of particle-antiparticle masses correct?</p> | g13082 | [
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0.026052288711071014,
-0.000430821644840762,
... |
<p>I have some data like: </p>
<p>Wind flow from north direction = “X” Numbers of days. </p>
<p>Wind flow from east direction = “Y” Numbers of days. </p>
<p>Then is there any formula to know numbers of days wind flows from North-East direction?</p> | g13083 | [
0.02457345649600029,
0.005120923276990652,
-0.01226075366139412,
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-0.04714822396636009,
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0.0285... |
<p>If we describe a photons with a wave packet, moving towards a potential barrier and E smaller than V, there is a finite chance that it will tunnel to the other side. In this process it is likely that it will arrive before a photon that does not tunnel, not because it exceeds the the speed of light, but because the front of a wave packet will contribute most to tunneling. I would understand this if it was concerned with PARTICLES as follows: because each of the different waves that make a wave packet has a different momentum, the faster moving, higher energy, waves will move to the front of the wave packet when it disperses. According to the formula for tunneling probability indeed the higher energy parts will tunnel more often.</p>
<p>BUT, why would a photon wave packet also have the higher energy elements more in front of it's wave packet, since all light-frequencies move at the same speed in vacuum right? Or does the described system indeed not work in vacuum.</p>
<p>At page 14 of this link the mechanism I describe is presented:</p>
<p><a href="http://www.physics.umass.edu/sites/physics/files/admupld/Tunneling-UMass-12Feb10.pdf" rel="nofollow">http://www.physics.umass.edu/sites/physics/files/admupld/Tunneling-UMass-12Feb10.pdf</a></p>
<p><img src="http://i.stack.imgur.com/2Q7Px.png" alt="enter image description here"></p> | g13084 | [
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0.024117130786180496,
0.04503249004483223,
0.004438094794750214,
0.04922... |
<p>Preferably one that is researched in a paper, not necessarily in production.</p>
<p>I have found various claims of OPVs with an efficiency of 10%, 8% and 7.3%, the only one I can substantiate is referenced in a paper in Advanced Materials (Volume 22, Issue 34 pp 3839–3856) to Solarmer but the web reference there leads to a news page where the news have been removed.</p> | g13085 | [
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-0.021211707964539528,
0.09242312610149384,
0.021530738100409508,
-0.006225464399904013,
0... |
<p>My first question is fairly basic, but I would like to clarify my understanding. The second question is to turn this into something worth answering.</p>
<p>Consider a relativistic electron, described by a spinor wave function $\psi(\vec x ,\sigma)$ and the Dirac equation. The conventional wisdom is that rotating everything by 360 degrees will map the spinor to its negative $\psi \mapsto -\psi$. However, it appears to me that this statement is "obviously false", because a rotation by 360 is, when viewed as an element of the group $SO(3)$, exactly equal to the identity map and cannot map anything to its negative.</p>
<p>Thus, to make sense of the behavior of spin under "rotation", I have to conclude the following</p>
<blockquote>
<p>The rotation group $SO(3)$ does <em>not</em> act on the configuration (Hilbert) space of electrons. Only its double cover $SU(2)$ acts on the space of electrons.</p>
</blockquote>
<p>Is this interpretation correct?</p>
<p>So, essentially, there is a symmetry group $SU(2)$ which acts on "physics", but its action on the spatial degrees of freedom is just that of $SO(3)$.</p>
<blockquote>
<p>What other groups, even larger than $SU(2)$, are there that (could) act on "physics" and are an extension of $SO(3)$? Is it possible to classify all possibilities, in particular the ones that are not direct products?</p>
</blockquote>
<p>Of course, gauge freedoms will give rise to direct products like $SO(3) \times U(1)$ (acting on space $\times$ electromagnetic potential), but I would consider these to be trivial extensions.</p> | g13086 | [
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0.022795846685767174,
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0.0039120824076235294,
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-... |
<p>What is a proper definition of locality in condensed matter lattice model? I emphasize "condensed matter" because there is no Lorentz symmetry or "speed of light". I think it is quite important because this constraint will rules out most nonlocal lattice Hamiltonians. First, let's say local Hilbert spaces are put both on vertices and edges of lattice, and notion of lattice may not be that regular. It could be a very random lattice. </p> | g13087 | [
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<p>If I keep a compass with bar magnets all around it, all of equal strength and a compass in a center then what will happen? Will the compass start rotating?</p> | g13088 | [
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<p>This post is aimed to stimulate some discussions.</p>
<p>We are familiar with many physical descriptions and theories of the (many-body quantum) system, with both <strong>quasi-particle description</strong> and <strong>Lagrangian description</strong>. For example: </p>
<blockquote>
<p>the Landau Fermi-liquids theory.</p>
</blockquote>
<p>Here <strong>quasi-particle description</strong> are simply a way to find <strong>effective excitations</strong> for the (many-body quantum) system. The <strong>effective excitations</strong> may not be the original elementary constituents or elementary particles/spins of the system. These <strong>effective excitations</strong> contain <strong>quasi-particle</strong>, <strong>quasi-string</strong>, <strong>quasi-brane</strong> excitations, etc.</p>
<p>$\bullet$ My question is that:</p>
<blockquote>
<ol>
<li><p>what are systems with No quasi-particle description but with Yes Lagrangian description.</p></li>
<li><p>what are systems with Yes quasi-particle description but with No Lagrangian description.</p></li>
<li><p>what are systems with No quasi-particle description and with No Lagrangian description.</p></li>
</ol>
</blockquote>
<hr>
<p><strong>NOTE</strong>:
For instance, I suppose that, </p>
<blockquote>
<p>1+1-dimensional <strong>Luttinger liquids</strong> are <strong>examples of 1.</strong> No quasi-particle description
but with Yes Lagrangian description. </p>
</blockquote>
<p>See, e.g. T. Giamarchi, "Quantum Physics in One Dimension" Chap 2. </p>
<p><img src="http://i.stack.imgur.com/A9D2g.png" alt="enter image description here"></p>
<p>Fig. 2.4. <em>The occupation factor $n(k)$ of 1+1D Luttinger liquids. Instead of the usual discontinuity at $k_F$ for a Fermi liquid, it has a power law essential singularity. This is the signaturethat fermionic quasiparticles do not exist in one dimension. Note that the
position of the singularity is still at k_F. This is a consequence of Luttinger's theorem.</em></p>
<p>On the other hand, it is likely that </p>
<blockquote>
<p><strong>examples of 2</strong> or <strong>examples of 3</strong> happens in RR fields or D-branes of string theory, which has Yes/No quasi-particle description, with NO Lagrangian description. </p>
</blockquote>
<p>Eg. see this Ref:<a href="http://arxiv.org/abs/hep-th/0503006" rel="nofollow">Stability of Fermi Surfaces and K-Theory by Horava</a>, see page 1 right column: <em>This implies that the RR fields are also objects in K theory, and not differential forms [9], making the low energy description of string theory on manifold Y in terms of Lagrangian (1) questionable. ... once the p-form $C_p$ are reinterpreted as K-theory objects, it is not clear how to even define Lagrangian (1). This crisis of the Lagrangian formulation of low-energy string theory is further supported by the discovery [10] of apparently non-Lagrangian phases in the partition functions of various string and M-theory vacua. Perhaps this means that the Lagrangian framework currently available is insufficient for RR fields but its suitable generalization awaits to be discovered. (Important steps in this direction have been taken [11].) Alternatively, the theory may require a non-Lagrangian formulation. (This may already be suggested by the presence of a self-dual RR field strength in Type IIB theory). Before we settle on either of these two alternatives, however, we should consider a third possibility. The subtle K-theory features of string theory could be an emergent phenomenon, with D-branes and RR fields emerging as composites of some more elementary degrees of freedom that admit a conventional Lagrangian description.</em></p>
<blockquote>
<p><strong>What else physical systems and theories are examples of 1. 2. 3.?</strong></p>
</blockquote> | g13089 | [
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0.04969215765595436,
0.0061356741935014725,
0.0... |
<p>Hi I want to start learning multi variable calculus specifically for learning electrodynamics. What are some good text books?</p> | g185 | [
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<p>I've tried an alternative solution for finding the partition function of this model. </p>
<p>So is what I've done correct? If it isn't then please prove and explain why not. (I'm pretty sure I made a mistake along the way):$$ $$
Starting with the Energy:
$$
E = -J\sum_{i=1}^{N}S_{i}S_{i+1}-J'\sum_{i=1}^{N}S_{i}S_{i+2}-B\sum_{i=1}^{N}S_i
$$
I've used the same trick used for NN but instead of two terms for the energy contribution from B I now have 3:
$$
E = -J\sum_{i=1}^{N}S_{i}S_{i+1}-J'\sum_{i=1}^{N}S_{i}S_{i+2}-\frac{B}{3}\sum_{i=1}^{N}(S_i+S_{i+1}+S_{i+2})
$$
The point of doing this becomes more obvious when I write out the partition function:
$$
Z=\sum_{\{S_{i}\}}e^{-\beta H}
$$
$$
=\sum_{S_i=\pm1}...\sum_{S_N=\pm1}e^{\beta\sum_{i}[JS_{i}S_{i+1}+J'S_{i}S_{i+2}+\frac{B}{3}(S_i+S_{i+1}+S_{i+2})]}
$$
Having written the energy in a way that I think is analogous to Isings method allows me to write this as the product of two exponentials and define two transfer matrices as follows:
$$
Z=\sum_{S_i=\pm1}...\sum_{S_N=\pm1}e^{\beta\sum_{i}(JS_{i}S_{i+1}+\frac{B}{3}(\frac{S_i}{2}+S_{i+1}))}e^{\beta\sum_{i}(J'S_{i}S_{i+2}+\frac{B}{3}(\frac{S_i}{2}+S_{i+2}))}
$$
And introducing $T_{_{NN}}= \left( \begin{array}{cc}
e^{\beta(J+\frac{B}{2})} & e^{-\beta(J+\frac{B}{6})} \\
e^{\beta(-J+\frac{B}{6})} & e^{\beta(J-\frac{B}{2})} \\
\end{array} \right) $ and $T_{_{NNN}}= \left( \begin{array}{cc}
e^{\beta(J'+\frac{B}{2})} & e^{-\beta(J'+\frac{B}{6})} \\
e^{\beta(-J'+\frac{B}{6})} & e^{\beta(J'-\frac{B}{2})} \\
\end{array} \right)$</p>
<p>Writting out the partition function in terms of these two transfer matrices and rearranging:
$$Z=\sum_{S_1=\pm 1}...\sum_{S_N=\pm 1}\langle S_1| T_{_{NN}}|S_2\rangle\langle S_1| T_{_{NNN}}|S_3\rangle\langle S_2| T_{_{NN}}| S_3\rangle\langle S_2| T_{_{NNN}}|S_4\rangle...\langle S_N| T_{_{NN}}|S_1\rangle\langle S_N| T_{_{NNN}}|S_2\rangle$$ </p>
<p>$$=\sum_{S_1=\pm 1}...\sum_{S_N=\pm 1}\langle S_2| T_{_{NN}}^{\dagger}|S_1\rangle\langle S_1| T_{_{NNN}}|S_3\rangle\langle S_3| T_{_{NN}}^{\dagger}| S_2\rangle\langle S_2| T_{_{NNN}}|S_4\rangle...\langle S_1| T_{_{NN}}^{\dagger}|S_N\rangle\langle S_N| T_{_{NNN}}|S_2\rangle$$
And using completeness :
$$=\sum_{S_2=\pm1}\langle S_2|( T_{_{NN}}^{\dagger}T_{_{NNN}})^N|S_2\rangle$$
$$=Tr( T_{_{NN}}^{\dagger}T_{_{NNN}})^N$$
And voila, I have something I can plug into matlab and calculate U,F,M,$\chi$, heat capacity etc. for arbitrary J,J',B T and N (which I've done). The only problem is that it doesn't give me the same results as the NN 1D ising for J'=0 and it doesn't give me exactly the same results as the 4X4 matrix shown here: <a href="http://arxiv.org/pdf/cond-mat/9703187v1.pdf" rel="nofollow">http://arxiv.org/pdf/cond-mat/9703187v1.pdf</a> (equation 9).
So I must have made some kind of mistake along the way, however, I would like to point out that the 4X4 matrix doesn't seem to reduce to the 1D ising model with NN interaction when J'=0 either.
(I should specify that my matlab numerical computations have so far used values of N ranging from 20 to 500, I've also tried calculating U/N and $\frac{\chi}{N}$using the largest eigenvalues from each transfer matrix for certain parameters and obtained the same results for T>0) </p> | g13090 | [
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0.02528974413871765,
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0.03356919437646866,
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0.046845611184835434,
0.04860800504684448,
0.00384... |
<p>We all know the Winter Solstice comes on December the 20th or 21st, which is (by definition) the shortest day of the year.</p>
<p>The Winter Solstice day is <strong><em>not</em></strong> the day of the year the Sun rises later (that would be one or two weeks later), and also is <strong><em>not</em></strong> the day the Sun sets earlier (that would be one or two weeks earlier)...</p>
<p><hr>
<strong>Why is it like this? Why aren't sunset and sunrise times symmetric?</strong><br>
I.e., why isn't there a "middle of the day" time valid throughout the year?<br>
Does it have something to do with the eccentricity of the Earth around the Sun?<br>
Does it have something to do with the fact the Earth is not a perfect Sphere?</p>
<hr>
<p>I would understand a technical explanation, but I am asking for a widely-understandable, simple one.
<img src="http://i.stack.imgur.com/Px5Zo.jpg" alt="Analema on a globe"><br>
<em>Pictured: an <a href="https://en.wikipedia.org/wiki/Analema">analema</a> on a globe.</em></p> | g13091 | [
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0.026552686467766762,
0.04950646311044693,
0.0... |
<p>I drink from a glass of water with a vertical straw. What's the longest straw I can use and still drink water if the ambient pressure is 1 atm?</p>
<p>Details and assumptions</p>
<ul>
<li>1 atm is 101,325 Pa.</li>
<li>The acceleration of gravity is -9.8m/s^2 .</li>
<li>The density of water is 1g/cm^3.</li>
</ul>
<p>I am relatively new to physics, so I have no idea how to start. I greatly appreciate everyone's assistance. Thanks in advance.</p> | g13092 | [
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<p>I got a rather small Netwon's cradle and when I start it, the effect is not very good since all the balls start to swing where the effect we want is obvious. The balls are small and I wonder if larger balls would make the swing more ideal, like only the outer balls appear to move and the 3 inner balls should be still? I know product recommendations are off-topic, but I'm leaning towards buying a <a href="http://www.amazon.com/gp/product/handle-buy-box/ref=dp_start-bbf_1_glance" rel="nofollow">cradle with larger balls</a> and perhaps you can advice which <a href="http://www.giantnewtonscradle.com/" rel="nofollow">alternative</a> to get that best replicates the original ideal cradle where only the outer balls move and the inner balls appear still?</p> | g13093 | [
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0.020227527245879173,
... |
<p>I know that a clock placed on an aeroplane will have slowed with respect to a clock placed on earth because the more our velocities are, compared to the speed of light, the more the time slows down. But, the earth is moving faster than the aeroplane when viewed from outer space. Then, the clock placed on Earth should be slower than a clock placed on the plane.</p>
<p>But the clocks are the same. How would that be different?</p> | g13094 | [
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-0.061183471232652664,
0.017486687749624252,
-0.0012568734819069505,
0.001367264660075307,
0.040... |
<p>I'm just starting to study quantum mechanics. Please explain the error in this thinking:</p>
<p>You set up decay of two $\pi$ mesons and get $2\mathrm{e}^-$ on Mars and $2\mathrm{e}^+$ on Earth. </p>
<p>On Earth you may or may not measure the spin of those positrons, with 50% probability that they are the same spin. </p>
<p>On Mars, your buddy "immediately afterwards" takes a $\mathrm{He}^{2+}$ ion and adds the electrons. </p>
<p>If you made the measurement, the $\mathrm{He}$ has a 50%+ chance of being in a higher-then-base energy level due to Pauli exclusion. </p>
<p>If you didn't make the measurement, the $\mathrm{He}$ has a much lower chance of being in a higher-than-base energy level. </p>
<p>Your buddy measures the energy state.</p>
<p>Result: You just superluminally transmitted $\approx 0.8$ bits of information.</p> | g13095 | [
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0.00043416614062152803,
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0.0321764200925827,
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-0.04979027435183525,
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0.009890931658446789,
-0.0011521512642502785,
-... |
<p>Example. Two bodies with masses m1 and m2 distance between them one year of light. What happens to the force of attraction between the two bodies when one body suddenly disappears? Is the force disappears at the same time or the force will act on second body for one year?</p> | g4 | [
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-0.... |
<p>I'm studying circular motion and centripetal force in college currently and there is a very simple question but confuses me (our teacher doesn't know how to explain either :/), so I hope we can sort it out here ><
So I draw two pictures to show what I was thinking on it.</p>
<p><img src="http://i.stack.imgur.com/IXKXR.jpg" alt="1"></p>
<p>In pic 1 there is a hand rotating a ball attached to a piece of string in a circular motion, by free body diagram we can easily see that the net force produced by tension and gravity is centripetal force, and it towards to the center of the circle.</p>
<p>But in pic 2 as shown below
<img src="http://i.stack.imgur.com/c5Ocp.jpg" alt="2"></p>
<p>When the hand is below the ball, the net force is actually towards downwards, not to the center of the circle. How would that circular motion happen if this free body diagram doesn't make sense? Or is there any other force acting on it?</p> | g13096 | [
0.06338312476873398,
0.009772039018571377,
0.007659421768039465,
0.006814854685217142,
0.054195355623960495,
0.06103505939245224,
0.035521846264600754,
-0.007775922305881977,
-0.029384426772594452,
-0.03679684177041054,
-0.014683297835290432,
-0.025053154677152634,
0.031463611871004105,
-0... |
<p>It is known that the Coulomb potential can be obtained by Fourier transform of the propagator from E&M. Is this because one of Maxwell's equations have the form $\nabla \cdot \mathbf{E}=\rho$? </p> | g13097 | [
0.015599286183714867,
0.005779743660241365,
-0.0034294610377401114,
0.0020552664063870907,
0.0730004608631134,
0.009050707332789898,
0.02282087318599224,
0.054649703204631805,
-0.018557626754045486,
-0.00425794767215848,
-0.009303800761699677,
0.005262448918074369,
0.009040134958922863,
0.... |
<p>I'm reading the specs of an IC (Cypress 5LP SoC) and it says it's available in 30 k g shock resistance configuration. The fastest acceleration I heard of so far was hitting a golf ball hard, which would be around 1000 g. Does anyone have an example of a mechanical impact of 30 000 g (300 000 m$\cdot$s$^2$), applicable to electronics devices?</p> | g13098 | [
0.10374364256858826,
0.1212780624628067,
0.012977157719433308,
0.016001155599951744,
0.04054801166057587,
-0.015925850719213486,
0.009564671665430069,
-0.05633731186389923,
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0.034124843776226044,
0.009233303368091583,
0.0025686712469905615,
-0.05436651036143303,
-0.036... |
<p>A rod of length L & mass M is rotating in a circle about one end then calculate tension in the rod at a distance 'x' from the support ?</p>
<p>For its solution why should we take mass of L-x portion of rod instead of taking mass upto x distance from support as we have the formula </p>
<p>T = m w2 x
I m in confusion....</p> | g13099 | [
0.03545143082737923,
0.002280493965372443,
0.003495102748274803,
-0.060226958245038986,
0.018980547785758972,
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0.06776738911867142,
-0.022163452580571175,
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0.023013977333903313,
0.0009498594445176423,
0.006072275340557098,
-0.004019016865640879,
-... |
<p>So this seemed pretty straight forward at first, but then I wasnt too sure about gravity forces...</p>
<p>So.</p>
<ul>
<li>centerfuge</li>
<li>2 samples</li>
<li>1 sample is 1gram heavier than the other</li>
<li>centerfuge at top speed is exerting 20000 gravitys of force on the samples</li>
</ul>
<p>What kind of weight / ballast is needed to keep the centerfuge from wobbling off the table?</p>
<p>Id imagine this is a linear equation ... So if i could get the equation that would be TOPS!</p>
<p>Ballast should be placed on 4 corners on the outside of the sample</p> | g13100 | [
0.04289315640926361,
0.023552633821964264,
-0.020860908553004265,
-0.0660380870103836,
0.03195836395025253,
0.007390925195068121,
0.011447874829173088,
0.04243602231144905,
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-0.016300324350595474,
0.021638575941324234,
0.005310320761054754,
-0.04451346397399902,
0.0182... |
<p>I have read this article</p>
<p><a href="http://scitation.aip.org/content/aas/journal/aer/9/1/10.3847/AER2010009">SIBBERNSEN, Kendra. Catching Cosmic Rays with a DSLR. <em>Astronomy Education Review</em>, 2010, 9: 010111.</a></p>
<p>and it talks about estimating the muon cosmic ray flux by means of a DSLR camera.</p>
<p>Is it possible to measure the muon's energy with the same apparatus?</p>
<p>If yes, how can I "calibrate" (?) the camera in order to measure the energy?</p> | g13101 | [
-0.006279515102505684,
-0.012622343376278877,
0.008943557739257812,
0.019394930452108383,
0.003376870648935437,
-0.021607624366879463,
-0.07078848779201508,
0.0610412172973156,
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-0.0030045376624912024,
0.002414549235254526,
0.04430439695715904,
0.06163205951452255,
0.... |
<p>Knowing that:</p>
<ul>
<li><p>The Zone of Avoidance (Looking towards the center of the Milky Way) blocks roughly 20%</p></li>
<li><p>Each Milky Way star has an angular size, depending on proximity, that obscures a certain percentage of our optical view.</p></li>
<li><p>Each Galaxy has an angular size, depending on proximity, that obscures a certain percentage of our optical view.</p></li>
</ul>
<p>And so on through Galaxy Clusters, Superstructures, etc...</p>
<p><strong>What percentage of our universe can we not see at visible wavelengths?</strong></p> | g13102 | [
-0.028322188183665276,
0.011682099662721157,
0.0020705703645944595,
-0.041007112711668015,
-0.02748594991862774,
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0.011623557657003403,
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0.07502633333206177,
-0.01970345340669155,
0.0972425788640976,
0.04302086681127548,
0.03172054514288902,
0.01... |
<p>The operator $\hat{F}$ is defined by $F\psi(x)=\psi(x+a)+\psi(x-a)$</p>
<p>Does this mean $\hat{F}=(x+a)+(x-a)$ and that $\hat{F}$ is operating on $\psi(x)$?</p> | g13103 | [
-0.0193403922021389,
-0.008182356134057045,
-0.00819141510874033,
-0.002589187119156122,
0.05100582540035248,
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0.025713417679071426,
-0.011377165094017982,
-0.02452617511153221,
-0.02772711031138897,
-0.06568314135074615,
0.018293574452400208,
0.015064161270856857,
-0... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/886/swimming-in-spacetime-apparent-conserved-quantity-violation">Swimming in Spacetime - apparent conserved quantity violation</a> </p>
</blockquote>
<p>It is well known that a deformable object can perform a finite rotation in space by performing deformations - without violating the law of conservation of angular momentum since the moment of inertia can be changed by the deformations of the object, see e.g. <a href="http://physics.stackexchange.com/q/10720/2451">this</a> Phys.SE question.</p>
<p>It is also well known that in flat space-time, it is not possible for a deformable object to displace it's center of gravity by performing deformations, see e.g. <a href="http://physics.stackexchange.com/q/45982/2451">this</a> Phys.SE question.</p>
<p>However in curved space-time can a deformable object swim through space by performing deformations?</p> | g412 | [
0.011521280743181705,
-0.037022076547145844,
-0.0022973166778683662,
-0.030192770063877106,
0.034511957317590714,
0.04212447255849838,
0.04104255139827728,
-0.014342829585075378,
0.0019475392764434218,
-0.0056031919084489346,
-0.0004193029017187655,
-0.030311791226267815,
0.02351768873631954... |
<p>I am working on upgrading an electromagnet design program. There are currently two types of wire used for the coil, circular and strip (read as: rectangular).</p>
<p>The current algorithms in this program are empirically derived with lots of undocumented constants and so one of the requirements is to move it more into the realm of accepted physics.</p>
<p>The formula I am using to calculate resistance is:</p>
<p>$$
R = \frac{\rho L}{A}
$$</p>
<p>These are aluminum wires so the value of $\rho$ boils down to $2.82\times10^{-8}$ at 20°C.</p>
<p>For circular wires this works perfectly, giving near enough the same results (enough to put it down to the increased accuracy).</p>
<p>For strip wires this doesn't work quite so well. The problem comes from a difference in the cross-sectional area of the wire.</p>
<p>The original program is doing $h^2$ as the area, where $h$ is the height of the wire. Now is that not wrong? The cross-sectional area should be $wh$ where $w$ is the width of the wire.</p>
<p>For example,
If the strip wire is 8.4mm by 2.8mm, the original program would do:</p>
<p>$$
2.8 ^ 2 = 7.84
$$</p>
<p>but should it not be doing:</p>
<p>$$
8.4\times2.8 = 23.52
$$</p>
<p>The entire original algorithm is:
$$
R = \frac{84.09L}{h^2}
$$</p>
<p>Is there a reason the original engineer may have done $h^2$ as apposed to the correct cross-sectional area?</p>
<p>I don't want to just declare his calculations as wrong as the results from this program have been used for the last 30 years and none of the magnets have gone bust or underperformed. Infact if anything they would have been over performing if this calculation is wrong.</p> | g13104 | [
0.03269538655877113,
-0.05031019449234009,
-0.0026620938442647457,
-0.07169973850250244,
-0.015593613497912884,
0.029071401804685593,
0.07073289901018143,
0.02955028787255287,
-0.08982538431882858,
0.06068024784326553,
0.013797221705317497,
0.03949659317731857,
-0.0022253275383263826,
0.04... |
<p>Suppose I have a wave function $\Psi$ (which is not an eigenfunction) and a time independent Hamiltonian $\hat{\mathcal{H}}$. Now, If I take the classical limit by taking $\hbar \to 0$ what will happen to the expectation value $\langle\Psi |\hat{\mathcal{H}}|\Psi\rangle$? Will it remain the same (as $\hbar = 1.0$) or will it be different as $\hbar\to 0$? According to correspondence principle this should be equal to the classical energy in the classical limit. </p>
<p>What do you think about this? Your answers will be highly appreciated. </p> | g13105 | [
0.0070294602774083614,
0.026873447000980377,
0.003765494329854846,
-0.023017890751361847,
0.007095646113157272,
0.006954136770218611,
-0.009386866353452206,
0.05632026121020317,
-0.03729124739766121,
-0.03207145631313324,
0.0032123601995408535,
0.007068191654980183,
-0.074825718998909,
-0.... |
<p>Can someone explain to me the origin of the exchange interaction between two electrically charged spin 1/2 fermions? Quantitative or qualitative accepted. </p> | g13106 | [
0.0541578009724617,
-0.02825467474758625,
-0.01349650975316763,
-0.013425447046756744,
0.07376499474048615,
0.04001437500119209,
0.008917517028748989,
0.0564853809773922,
0.03643598407506943,
0.029535023495554924,
-0.026596760377287865,
0.028352007269859314,
0.0019695626106113195,
0.007292... |
<p>When accounting for the excluded volume for in the Van der Waals equation, it is assumed that the molecules are hard spheres and are of diameter. If we consider a cube of volume V, then we can say that the side of this cube is of length $V^{1/3}$. Consider the diameter of the molecules to be $\sigma$. Suppose that the number of molecules in this box to be $N$. If we anchor $N-1$ molecules at their positions and look at the excluded volume from the perspective of the $N^{th}$! molecule, we see that the center of this molecule can approach the walls of the cube only upto a distance of $\sigma/2$ and can approach the anchored molecules upto a distance of $\sigma$ from their centers as shown:<img src="http://i.stack.imgur.com/v8JE4.png" alt="excluded1">.</p>
<p>Then the excluded volume for this molecule should be $V_{ex}=(V^{1/3}-\sigma)^{3}-(N-1)(\frac{4}{3}\pi\sigma^{3})$. This follows even if we consider any other molecule and anchor the rest. But, according to <a href="http://en.wikipedia.org/wiki/Van_der_Waals_equation#Conventional_derivation" rel="nofollow">wikipedia</a>, we would be overcounting. I don't see how. The correct expression should be $V_{ex}=(V^{1/3}-\sigma)^{3}-(N/2)(\frac{4}{3}\pi\sigma^{3})$. Can anyone please explain?</p> | g13107 | [
0.03665504232048988,
0.0398058146238327,
-0.016467172652482986,
-0.050219014286994934,
-0.0386187806725502,
0.009238108061254025,
0.03504497930407524,
0.010724149644374847,
-0.00499799894168973,
0.01836308464407921,
-0.03152039274573326,
0.009663921780884266,
-0.029104145243763924,
0.00110... |
<p>There are power law of phase transition in physics and Zipf law in linguistics which are similiar to each other ,and some expert think they are in fact just the same.But the diagrams of them base on the data of physics and data of language are not that same.
What is difference and linkage between power law of phase transition in physics and Zipf law in linguistics?And what is the mechanism behind them and the difference?Any reference?</p> | g13108 | [
0.01613461785018444,
-0.0002601825981400907,
0.013185864314436913,
-0.030246034264564514,
0.07209829241037369,
-0.008497057482600212,
-0.013969339430332184,
0.05629980191588402,
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0.001705426606349647,
0.009704053401947021,
-0.03133269399404526,
-0.004182018805295229,
-... |
<p>NASA has recently <a href="http://science.nasa.gov/science-news/science-at-nasa/2014/02jun_saucer/" rel="nofollow">tested a saucer-shaped spaceship</a>. What's the advantage of this new design over traditional aerodynamic designs?</p>
<p>The test launch was performed from within atmosphere which would offer higher air drag. What's the positive side of this that this big thing has been ignored?</p> | g13109 | [
-0.03294559568166733,
0.07246068865060806,
-0.0070313820615410805,
0.046814825385808945,
-0.018615107983350754,
0.08723194897174835,
0.029625535011291504,
-0.04946457967162132,
-0.022800007835030556,
-0.07722330838441849,
0.08979374170303345,
-0.0004037122707813978,
0.051785267889499664,
0... |
<p>Take the Lagrangian with one fermion:
$$ \mathcal{L} = -\frac{1}{4}F^{\mu\nu}_aF^a_{\mu\nu} + \bar{\psi}(i\gamma^\mu D_\mu - m)\psi$$
where the gauge covariant derivative $D_\mu = \partial_\mu+i\frac{g}{2}t^aW^a_\mu$. The Lagrangian is invariant under a local $SU(2)$ transformation:
$$ \psi(x) \rightarrow \exp \left[-i\theta^a(x)t^a \right]\psi(x) $$
$$W^a_\mu(x) \rightarrow W^a_\mu(x) +\frac{1}{g}\partial_\mu\theta^a(x) + \epsilon^{abc}\theta^b(x)W^c_\mu(x)$$</p>
<p>Often, we say that $W_\mu^a$ transforms according to the adjoint representation of $SU(2)$ but how can we say that based on the previous equation?</p> | g13110 | [
0.026296840980648994,
-0.061357948929071426,
-0.038702696561813354,
-0.09991145133972168,
0.05576729401946068,
0.003622097661718726,
0.04278112202882767,
0.047215890139341354,
-0.06618785113096237,
-0.009275443851947784,
0.012346901930868626,
0.08832594752311707,
0.019029878079891205,
0.06... |
<p>If a current in a wire is flowing perpendicular to a magnetic field, the Hall effect will be observed, which is caused by the forces from magnetic fields 'pushing' the electrons to one side or the wire. So, does it increases the resistance of the wire, as there is now less area for current to flow through due to one side of the wire being occupied by these (assumed)immobile electrons?</p> | g13111 | [
0.027478020638227463,
0.05748026445508003,
0.01855185627937317,
-0.034138500690460205,
0.027597719803452492,
0.0630899965763092,
-0.0017298880266025662,
0.03244652599096298,
0.028935695067048073,
0.011277049779891968,
-0.057687412947416306,
0.033334843814373016,
-0.048017971217632294,
0.05... |
<p>I am an undergraduate student (Bachelors of engineering) about to complete my 1st year in the
field of Information science and engineering or information
technology. I am interested in pure physics especially high energy
physics and some parts of quantum Physics. My question is that, is there any
possibilities i can have my post-graduation study in the field of
Physics(purely theoretical physics like high energy physics) ?</p> | g13112 | [
-0.018365537747740746,
0.06324314326047897,
0.011411230079829693,
0.017780307680368423,
-0.007921440526843071,
0.015732435509562492,
-0.02473895438015461,
0.05887007340788841,
0.01040768064558506,
-0.06145587936043739,
-0.00603906437754631,
0.03783569112420082,
0.01977626606822014,
-0.0549... |
<p>While studying radioactivity I found that even the most radioactive substances i.e substances with the shortest half lives do not completely degenerate. </p>
<p>Suppose there is a 1 mole sample of an element <strong>X</strong> whose half life is <strong>1 day</strong>.
But as the <em>degeneration equation</em> is <em>exponential</em> in nature even after 1 million years some amount of <strong>X</strong> would remain in the sample.</p>
<p>What i want to know is how come certain <strong><em>atoms of an element possess such stability that they do not generate after a million years</em></strong>, <strong><em>while some atoms taken form the same sample degenerate after 1 day.</em></strong></p>
<p>Is it because they have some different particles in their nucleus or something ?</p>
<p>What is the role of <strong>quantum tunnelling</strong> ?</p> | g13113 | [
-0.010186129249632359,
-0.014303650707006454,
-0.0017153887310996652,
0.016448114067316055,
0.06137781962752342,
0.03410044312477112,
-0.025709770619869232,
0.01883283630013466,
0.0066809565760195255,
-0.03302893787622452,
-0.0340157151222229,
0.016393795609474182,
0.015197127126157284,
0.... |
<p>I had never seen rotation free transformations called "boosts" (I think I have it right) before reading some questions here. I'm too old perhaps. I have not found the etymology after some searching, though it sounds like something V.I. Arnold would think up, or jargon from inertial navigation. Anyone know where/how it started or was popularized? (If it is in MTW or Ohanian (old edition) or Weinberg, I promise I'll facepalm)</p> | g13114 | [
-0.006898129358887672,
0.035925667732954025,
-0.0198452640324831,
-0.05184214189648628,
0.003845377592369914,
-0.03539496660232544,
0.06039136275649071,
-0.027055591344833374,
0.07193513214588165,
0.005734208971261978,
-0.06619085371494293,
0.005011929664760828,
0.053464002907276154,
-0.00... |
<p>I've noticed that an airplane appears to have more lift when it's almost touching the ground then it has 100 feet or more in the air. What causes this to occur?</p> | g13115 | [
0.030001865699887276,
0.06081988662481308,
-0.01874738559126854,
0.02432643622159958,
0.011603894643485546,
0.07344149053096771,
0.033597432076931,
0.04649526998400688,
-0.044297926127910614,
-0.011208283714950085,
0.004083423875272274,
-0.035814590752124786,
-0.013217301107943058,
0.06319... |
<p>Let $\dot{z} = A(t)z + b(t)$ with $ z(t) \in \mathbb{R}^n$ and $A(t)$ be a linear map from $\mathbb{R}^n \rightarrow \mathbb{R}^n$. A propagator is also a linear map $P(t,s):$ $\mathbb{R}^n \rightarrow \mathbb{R}^n:$ $z(s) \rightarrow z(t)$ and has the following properties:</p>
<ol>
<li>$P(t,r)P(r,s) = P(t,s)$</li>
<li>$P(s,s) = id$</li>
<li>$\frac{\partial}{\partial t}P(t,s) = A(t)P(t,s)$</li>
</ol>
<p>The Duhamel formula is the following (a general solution to: $z(t) = P(t,s)z(s) + \int_s^t d\tau P(t,\tau)b(\tau)$</p>
<p>I'm trying to prove it by simply deriving it:</p>
<p>$\dot{z} = \frac{\partial}{\partial t}P(t,s)z(s) + \frac{\partial}{\partial t}\int_s^t d\tau P(t,\tau)b(\tau) = A(t)P(t,s)z(s) + P(t,t)b(t) + \int_s^t A(t)P(t,\tau)b(\tau) = A(t)z(t) +b(t) + \int_s^t A(t)P(t,\tau)b(\tau)$ </p>
<p>This is nearly the form that I want (I used equation 2 and 3 and standard properties of the integral and dervative, for those wondering), but I can't see right now how the intgeral equals to zero. </p>
<p>Anyone can tell me?</p>
<p>Cheers!</p> | g13116 | [
-0.003147423965856433,
-0.03946046158671379,
-0.029311129823327065,
0.001469679526053369,
0.044654812663793564,
-0.06260170787572861,
0.08779507875442505,
0.027214670553803444,
-0.007927212864160538,
0.0017937063239514828,
-0.030721519142389297,
0.07906901091337204,
-0.003441010834649205,
... |
<p>I was told that the Galilean relative velocity rule does not apply to the speed of light. No matter how fast two objects are moving, the speed of light will remain same for both of them. </p>
<p>How and why is this possible? </p>
<p>Also, why can't anything travel faster than light?</p> | g348 | [
0.043782610446214676,
0.08160333335399628,
0.006292340345680714,
0.02156936191022396,
0.0823327824473381,
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0.03247157856822014,
0.019329115748405457,
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-0.019382668659090996,
0.013342425227165222,
-0.018050961196422577,
0.05064955726265907,
-0.009... |
<p>I have an UPS with two 6V batteries connected in series. Is it possible to use the same system (UPS) to charge another two pieces of 6 volts battery if all the batteries are connected in parallel to maintain a 12 volts circuit?</p>
<p>Will this affect the charging system of the ups if the connection is made?</p> | g13117 | [
0.0016444515204057097,
0.028134040534496307,
0.005288807209581137,
0.016342971473932266,
0.007764697074890137,
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-0.005923774093389511,
-0.017397593706846237,
0.007075815461575985,
0.05298866704106331,
-0.038239121437072754... |
<p>This may or may not be an incredibly stupid thought experiment, but a short time ago I read that most of the "mass" in the proton was actually energy from the quarks and gluons, as opposed to the actual mass which was coupled to the Higgs field. This made me start thinking about objects on macroscopic scales and the effects of energy and mass in a closed macroscopic system.</p>
<p>I have only a superficial highschool level understanding of relativistic mass, and I have read extremely vigorous debates and arguments about the significance of the mass-energy equivalence, and what it means in terms of the "weight" of an object.</p>
<p>So my question is that if said atomic bomb were to explode inside of a completely impenetrable container of some sort, would the measured weight of the container change, assuming no radiation was able to escape the container itself?</p> | g13118 | [
-0.00415035430341959,
0.04437389597296715,
0.05029211565852165,
-0.01599246636033058,
-0.005988548044115305,
0.07197713106870651,
-0.03656123951077461,
0.06762605160474777,
-0.04788370430469513,
0.009227925911545753,
-0.07313714176416397,
0.008201660588383675,
0.023147061467170715,
-0.0348... |
<p>After closing my refrigerator's door I noticed that it's much harder to reopen it immediately, as if there's an underpressure. Only after a minute or so it opens normally. How can this be explained?</p> | g13119 | [
0.03355300426483154,
0.05031973868608475,
-0.014041545800864697,
0.08425696194171906,
-0.005262129008769989,
-0.020280281081795692,
0.05207405611872673,
0.057031434029340744,
-0.0536140538752079,
-0.011483289301395416,
-0.006779056042432785,
0.026314884424209595,
-0.022590823471546173,
0.0... |
<p>The hyperfine structure of the energy levels of the hydrogen atom refers to the shifts in the evergy levels due to the magnetic moments of the nucleus and of the electron. This is an effect of non-relativistic QM, if I understand correctly.</p>
<p>On the other hand, the Lamb shift in the energy levels is due to completely different reasons: it has nothing to do with the spin of nucleus, and can be explained only by the relativistic theory, i.e. QED.</p>
<p>How to compare these two effects? Which one is stronger? Is there any literature about this?</p>
<p>I do know references to literature about the Lamb shift. It would be helpful to have a reference to a detailed discussion of the hyperfine structure, and to a comparison with the lamb shift.</p> | g13120 | [
0.027276430279016495,
0.01087985560297966,
-0.007113394793123007,
-0.015518424101173878,
0.045376550406217575,
-0.007515834644436836,
-0.062084730714559555,
0.03775649145245552,
-0.04558219760656357,
-0.02352684549987316,
0.010332267731428146,
-0.033345554023981094,
-0.05486207827925682,
0... |
<p>Does anyone know the amount of thermal energy that the Earth's mantle and core possess? I don't mean the maximum limit of electrical power we could generate with geothermal plants, but rather: if you took the Earth and magically cooled it down so that its temperature became homogeneously 0K, what would the change in the Earth's internal energy be? (ignoring the Sun)</p>
<p>If we don't have that data, does anyone have an idea how to perform an order of magnitude estimate?</p> | g13121 | [
0.0630359798669815,
0.028977861627936363,
0.014789517037570477,
-0.04748540371656418,
-0.06989786773920059,
-0.05427788570523262,
-0.05434730648994446,
0.08408932387828827,
-0.03727108985185623,
0.019636861979961395,
0.0008762317011132836,
0.002056046621873975,
0.02939927577972412,
-0.0202... |
<p>One model for confinement in quantum chromodynamics is the <a href="http://scholar.google.com/scholar?hl=en&q=savvidy" rel="nofollow">Savvidy vacuum</a>. This is a spontaneous symmetry breaking of color gauge symmetry by the gauge fields. The vacuum is divided into Savvidy domains. Is this process hidden by confinement?</p>
<p>L.Motl: I erased one "d" from Savvidy - everywhere. Link to Savvidy vacuum added.</p> | g13122 | [
0.016695233061909676,
0.004385792184621096,
-0.012194988317787647,
-0.014651947654783726,
0.01402169931679964,
0.053943317383527756,
0.03281565383076668,
0.024299848824739456,
-0.000930315931327641,
0.012009450234472752,
0.04835162311792374,
0.004470400977879763,
0.015130813233554363,
0.01... |
<p>How would you prove that the simultaneous measurements of position and energy are not subject to interference?
I was thinking in calculate the commutation relation between $x$ and $H$ (Because $\Delta E=\Delta H$), but I realized that $[H,x]\neq0$, so I tried to use a more general expression for the Uncertainty Principle that says that if $H_1$ and $H_2$ are Hermitian operators then $\Delta H_1 \Delta H_2\geq\frac{1}{2}|\langle [H_1,H_2]\rangle|$, but again, $[H,x]\neq0$. Can you suggest me a way to do this? Thanks.</p> | g13123 | [
0.014152919873595238,
-0.004835628438740969,
-0.02037869766354561,
0.03205018863081932,
0.021129462867975235,
0.004022838082164526,
0.05091002956032753,
0.049102578312158585,
-0.05105894058942795,
0.015308293513953686,
-0.03187185525894165,
-0.006719083990901709,
-0.061233729124069214,
-0.... |
<p>If you look at most published articles, or those on the preprint server, you find the vast majority of articles have more than one authors. Are collaborations needed to be productive in physics? In other fields like math, single author articles are the norm.</p> | g13124 | [
-0.0006705454434268177,
0.06558684259653091,
0.003467276692390442,
0.04227777570486069,
0.06601860374212265,
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0.013686677441000938,
0.030756132677197456,
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0.007172835990786552,
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-0... |
<p>I was wondering what subjects a freshman in mathematics ought to choose in the future if s/he wanted to help working on energy and environment-related issues we are currently facing, and will very likely be even more profound in the future. </p>
<p>I am currently day-dreaming about using the skills I will acquire as a mathematician to create more efficient solar cells or wind-mills, but I guess a little understanding of the physics involved wouldn't hurt. </p>
<p>Which subjects should I choose to enhance my knowledge on this subject? Could you perhaps suggest a rough pathway by means of which I could deepen my understanding of the subject matter?</p> | g13125 | [
0.02008349820971489,
0.056153539568185806,
0.017385071143507957,
0.04366150125861168,
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0.008342149667441845,
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0.07603015750646591,
0.04938606545329094,
0.034358806908130646,
-0.00... |
<p>It seems that virtual photons also exist in vacuum. So the precise question is:</p>
<p>What is the additional virtual photon density due to the electric field of a unit charge?</p>
<p>Or: How many virtual photons per volume are found around a unit charge?</p>
<p>The answer will depend on distance, but what are the exact numbers?</p> | g13126 | [
0.04243476316332817,
0.029218439012765884,
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0.0056833834387362,
0.05937797948718071,
0.036759890615940094,
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0.0071622636169195175,
0.019827814772725105,
0.01505746878683567,
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0.00291003892198205,
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0.024... |
<p>According to the <a href="http://en.wikipedia.org/wiki/Induction_cooking#Limitations" rel="nofollow">Wikipedia</a>, one of the limitations of the induction cooker is that the bottom surface of the pot should be flat.</p>
<p>Accordingly, I commented on a question on <a href="http://cooking.stackexchange.com/q/14669/641">Seasoned Advise</a>, but I'd like to know whether this is actually true (My username is BaffledCook there).</p>
<p>For a wok, it seems reasonable to believe the induction cooker will not be effective, but how about a wobbly pan? How wobbly should it be before it really affects efficiency?</p> | g13127 | [
-0.05898943915963173,
0.037214815616607666,
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0.04653205722570419,
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0.0941942036151886,
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0.... |
<p>Or said another way - how much counterweight does the base of a sign need to keep it from tipping over given a specific max wind?</p>
<ul>
<li>Assume the sign does not let wind through</li>
<li>Assume the base of the sign cannot slide on the ground</li>
<li>Assume the sign does not flex in the wind</li>
<li>Assume total weight of the sign + base is 125 lbs (base is 96 lbs)</li>
</ul>
<p>Are there any other parameters needed?</p>
<p>The sign has the design and measurements below:
<img src="http://i73.photobucket.com/albums/i211/joelq/ScreenShot2014-06-20at51636PM_zpsb0ca81dc.png" alt=""></p>
<p>Edit: This would probably be helpful: Width of sign is 8' so the sign is 9' high x 8' wide.</p> | g884 | [
0.02443348988890648,
0.05517596751451492,
-0.012708383612334728,
-0.018595699220895767,
0.016856404021382332,
0.003546159015968442,
0.05809397995471954,
0.03775675594806671,
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-0.022116631269454956,
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0.008757895790040493,
-0.02260163240134716,
0.03... |
<p>I was told long time ago that DC relay had a coil. There was a switch (2 wires, one is stable, the other one is flexible) inside the coil. The switch was parallel to the axial direction of the coil. </p>
<p>Today, I am thinking how AC relay works. I go back to think about DC relay. If what I was told is right, the magnetic field direction is parallel to the switch direction. Then how the magnetic field makes two wires touch?</p>
<p>Also, how does AC relay work? </p> | g13128 | [
0.05926787108182907,
-0.013751650229096413,
-0.009377211332321167,
-0.08307644724845886,
0.05532190203666687,
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-0.040832605212926865,
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0.018002662807703018,
-... |
<p>I noticed when I was boiling pasta the other day that the pasta uniformly spread out and formed a donut like torus. Why does this happen? Does it have to do with the shape of the pot? I tried to take a picture when it was boiling, but steam got all over my lens. So, this is a more 2d version of what the pasta looked like with boiling (while boiling, the pasta strands were uniform and seemed to be repelled out uniformly from the center of the pot.<img src="http://i.stack.imgur.com/B9RD4.jpg" alt="I tried to take a picture when it was boiling, but steam got all over my lens. So, this is a more 2d version of what the pasta looked like with boiling (while boiling, the pasta strands were uniform and seemed to be repelled out uniformly from the center of the pot."></p> | g13129 | [
0.02748514898121357,
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0.009534900076687336,
0.014851821586489677,
0.06337052583694458,
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0.03984785079956055,
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-0.008436938747763634,
-0.024990741163492203,
0.0025754400994628668,
0.08446723222732544,
0.0... |
<p>So I was bored and had some clear Scotch tape nearby. Decided to mess around, and now I have questions. </p>
<ul>
<li><p>What is the physics behind the force of tape adhesive? </p></li>
<li><p>Why does the tape hold so much better if it is pulled parallel to the surface
plane it is on? (Excuse my poor drawing skills) </p></li>
<li>Is there a rating for adhesion? Can I found out how "sticky" the tape is by measuring the
area of tape on a table and the force at which it breaks loose from
the table in a similar situation below?</li>
</ul>
<p><img src="http://i.stack.imgur.com/diduF.png" alt="Pulling on tape"></p>
<p>Is this even an appropriate question? Or should I close it? It's definitely not homework. </p> | g13130 | [
0.027425182983279228,
0.021776579320430756,
0.006644812878221273,
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0.019267579540610313,
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0.01600676402449608,
0.002560440683737397,
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0.... |
<p>I'm currently preparing for an examination of course in introductory (experimental) particle physics. One topic that we covered and that I'm currently revising is the universality in weak interactions. </p>
<p>However I don't really understand the point my professor wants to make here. </p>
<p>Let me show you his exposure to the topic: </p>
<p>We stark by looking at three different weak decays: </p>
<ul>
<li>$\beta$-decay in a nuclei: $^{14}O \rightarrow ^{14}N^{*} + e^{+} + \nu_{e}$ (Lifetime $\tau$=103sec) </li>
<li>$\mu$-decay: $\mu^{+}\rightarrow e^{+} + \nu_{e} + \overline{\nu_{\mu}}$ ($\tau$=2.2$\mu$sec)</li>
<li>$\tau-decay$: $\tau^{+}\rightarrow$ $\mu^{+} + \nu_\mu + \overline{\nu_{\tau}}$ or $\tau^{+}\rightarrow$ $e^{+} + \nu_e + \overline{\nu_{\tau}}$ ($\tau = 2 \cdot 10^{13}$ sec).</li>
</ul>
<p>Now he points out that the lifetimes are indeed quiet different.
Never the less the way the reactions behave is the same? (Why? Okay we always have a lepton decaying into another leptons and neutrinos? But what's the deal?)</p>
<p>Then he writes down Fermi's golden rule given by: $W=\frac{2\pi}{\hbar} |M_{fi}|^{2} \rho(E')$. </p>
<p>Now he says that universality means that the matrix element $|M_{fi}|$ is the same in all interactions. The phase space however is the same (Why? First of all I have often read on the internet that universality means that that certain groups of particles carry the same "weak charge"? And secondly: What do particle physicists mean when they talk about greater phase-space? Three dimensional momentum space? But how do you see or measure that this space is bigger? And bigger in what respect? More momentum states?)</p>
<p>Now he says that the different phase spaces come from the different lifetimes. He calculates
$\rho(E')=\frac{dn}{dE}=\int \frac{d^{3}p_{\nu} d^{3}p_{e}}{dE} = p_{max}^{5} \cdot \int \frac{d^{3}(p_{\nu}/p_{max}) d^{3}(p_{e}/p_{max})}{d(E/p_{max})}$.</p>
<p>Now the last integral is supposed to be identical for all decays.
And $p_{max}$is suppose to be different in all decays . But why?
And what is the definition of $p_{max}$?</p>
<p>Now he has $\tau = \frac{1}{M}$. So he gets $\tau = const \cdot \frac{1}{|M_{fi}|^{2} p_{max}^5}$. Hence he gets in the ln($\tau$)-ln($p_{max}$) diagram a line with slope -5.</p>
<p>Now he claims that this "proofs" that $|M_{fi}|$ is constant in all processes.
Again why? </p>
<p>Can someone please give me some overview and explain to me why he is doing all that stuff? I din't really have much background when it comes to particle physics. So can someone explain it to me in a clear and easy way?</p> | g13131 | [
0.04065047204494476,
0.00435273814946413,
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0.10118003934621811,
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0.032261695712804794,
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-0.05587786063551903,
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0.056730158627033234,
0.00016032761777751148,
0.... |
<p>To explain, with a source of 'normal' photons, as the source becomes more and more distant the luminosity fades until finally the stream of photons is no longer continuous, giving the receiver individual peaks of energy with none in between. As recession continues the gaps between energy peaks (photon impacts) becomes longer.</p>
<p>If the electromagnetic force is carried by virtual photons, and these photons are still bound by the speed of light, then unless an infinite number are created there should be some distance at which the observed electromagnetic force applied should no longer be continuous, but instead would break up into individual force applications.</p>
<p>I doubt we have anything like the level of sensitivity to be able to detect such tiny fluctuation, especially with all the background noise being generated by all sources of electromagnetic force that are much closer, but in theory would the force break up at sufficient distance into discrete instances of force instead of a continuous force?</p> | g13132 | [
0.024550100788474083,
0.0014020197559148073,
-0.011018273420631886,
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0.0374964214861393,
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-0.08541577309370041,
0.018298853188753128,
0.0013550638686865568,
0.006816521752625704,
... |
<p>The orbit of the earth seems to be very predictable. But as it is a many-body problem having sun, earth, moon, jupiter and so on, is it really that stable or will it start making strange movements sooner or later?</p>
<p>Are there asteroids or moons in our solar system with obviously chaotic orbits?</p> | g13133 | [
-0.009680275805294514,
0.09124520421028137,
0.013332121074199677,
0.04517637938261032,
0.00934852659702301,
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-0.0546390563249588,
0.05593854933977127,
0.006584285758435726,
0.08680208027362823,
0.006984... |
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