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<p>A particle starts at the origin and has an initial velocity represented by a 3D vector. The particle experiences gravity and air resistance with quadratic drag (based on velocity^2). What I've been looking for are parametric equations for $x$, $y$, and $z$ position and velocity of the particle at a given time $t$.</p>
<p>To keep answers similar the two constants will be g as gravity and a as the air resistance. Also assume $z$ is positive elevation. $v_x(t)$ will be the velocity for the $x$ component at time $t$. ${v_x}_0$ would represent the initial velocity for the $x$ component.</p>
<p>At the bottom of this <a href="http://en.wikipedia.org/wiki/Trajectory_of_a_projectile#Trajectory_of_a_projectile_with_air_resistance" rel="nofollow">wikipedia article</a> it suggests there's an analytic solution to the 2D problem by a teenager Shouryya Ray. The corresponding <a href="http://math.stackexchange.com/q/150242/">Math.SE</a> and <a href="http://physics.stackexchange.com/q/28931">Phys.SE</a> links have people discussing solving for a constant of friction, but there's no parametric equations given anywhere. I'm not sure how to go from what they're talking about to the actual parametric equations I need.</p>
<p>To cover what I've learned so far. In 3D with gravity and no drag the following parametric equations can be used:</p>
<p>$v_x(t) = {v_x}_0$</p>
<p>$v_y(t) = {v_y}_0$</p>
<p>$v_z(t) = {v_z}_0-gt$</p>
<p>$s_x(t) = {v_x}_0t$</p>
<p>$s_y(t) = {v_y}_0t$</p>
<p>$s_z(t) = {v_z}_0t - \frac{1}{2} g * t^2$</p>
<p>With linear drag per the Wikipedia article we'd used:</p>
<p>$v_x(t) = {v_x}_0e^{-\frac{a}{m}t}$</p>
<p>$v_y(t) = {v_y}_0e^{-\frac{a}{m}t}$</p>
<p>$v_z(t) = -\frac{mg}{a}+({v_z}_0+\frac{mg}{a})e^{-\frac{a}{m}t}$</p>
<p>$s_x(t) = \frac{m}{a}{v_x}_0(1-e^{-\frac{a}{m}t})$</p>
<p>$s_y(t) = \frac{m}{a}{v_y}_0(1-e^{-\frac{a}{m}t})$</p>
<p>$s_z(t) = -\frac{m * g}{a}t + \frac{m}{a}({v_z}_0 + \frac{m*g}{a})(1 - e^{-\frac{a}{m}t})$</p>
<p>With quadratic drag we have the velocity's length so each component's velocity and position over time depends on the other velocity components. Starting with <a href="http://math.stackexchange.com/a/150945">this post</a> I can write the 3D version for the first part:</p>
<p>$v_x' = -av_x*\sqrt{v_x^2 + v_y^2 + v_z^2}$</p>
<p>$v_y' = -av_y*\sqrt{v_x^2 + v_y^2 + v_z^2}$</p>
<p>$v_z' = -av_z*\sqrt{v_x^2 + v_y^2 + v_z^2}-g$</p>
<p>But I lack the mathematical background to continue. It's not even clear to me what the constant of friction they calculate is used for since it's not based on time. I would think any trick that attempts to calculate a constant coefficient would need to know about t. I'm probably thinking of this wrong. Any help would be appreciated as I imagine this is a common problem in physics.</p>
<p>edit: Also my problem case is specifically for a constant gravity vector if that helps for specific solutions so the path must be a parabola of sorts. As far as I can tell there should be a function as there's one y value for every x.</p> | g11668 | [
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<p>In the introduction (page 5) of <em>Supersymmetry and String Theory: Beyond the Standard Model</em> by Michael Dine (<a href="http://rads.stackoverflow.com/amzn/click/0521858410">Amazon</a>, <a href="http://books.google.com.au/books?id=MWcnme8c9NEC">Google</a>), he says</p>
<blockquote>
<p>(Traditionally it was known that)
the interactions of particles typically became stronger as the
energies and momentum transfers grew. This is the case, for example,
in quantum electrodynamics, and a simple quantum mechanical argument,
based on unitarity and relativity, would seem to suggest it is general.</p>
</blockquote>
<p>Of course, he then goes on to talk about Yang-Mills theory and the discovery of negative <a href="http://en.wikipedia.org/wiki/Beta_function_%28physics%29">beta-functions</a> and <a href="http://en.wikipedia.org/wiki/Asymptotic_freedom">asymptotic freedom</a>. But it is the mention of the <em>simple but wrong argument</em> that caught my attention.</p>
<p>So, does anyone know what this simple argument is?
And how is it wrong?</p> | g11669 | [
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<p>Not sure which stack exchange forum to put this in. Moderators feel free to migrate it.</p>
<p>One definition of the <a href="http://en.wikipedia.org/wiki/Tortuosity" rel="nofollow">tortuosity</a> $T$ of a curve is:</p>
<p>$$T=\frac{C}{L}$$ </p>
<p>Where $C$ is the chord length (distance between the ends of the curve) and $L$ is the total length of the curve.</p>
<p>I am trying to calculate the tortuosity of a white noise signal. But it is not clear to me what the unit length should be. Here's what I mean:</p>
<p>The white noise is a time series $X(t)$ of length $N$ of normally distributed random numbers with mean $0$ and standard deviation of $1$.</p>
<p>To calculate the length $L$ of this signal I do the following: </p>
<p>$$dy(t)=\left| X(t+1)-X(t) \right |$$
$$L=\sum_{t=1}^{N-1} \sqrt{dy(t)^2+dx^2}$$</p>
<p>Where $dx$ is the unit interval. The question is how to select a suitable value for $dx$. Should it just be $1$? Or perhaps the mean or minimum value of $dy(t)$?</p>
<p>The chord length $C$ of this signal is $N/dx$, so it also depends upon the selection of $dx$.</p> | g11670 | [
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<p>There have been quite a few plane crashes the past week and this question popped into my head of which I need a good explanation in science about the possibility of survival or not and why. </p>
<p>Assuming I am on a plane that is quickly losing altitude, just before the plane hits the ground I jump off the plane.</p>
<ol>
<li>Is it even possible to jump?</li>
<li>If I can jump, will the gravitational pull be different and thus make me survive? Would this be equal to jumping off the ground? (Assume that I am immune to the plane explosion)</li>
</ol> | g370 | [
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<p>I have figured out that:</p>
<ol>
<li>When photons leak out from a container, the entropy of the photon collection increases, because each photon has a different escape time.</li>
<li>Photons that have leaked out from a container can be collected into a container of the same size, if that container is in a gravity well deep enough.</li>
<li>When photons fall some distance in a gravity field, each photon's energy becomes multiplied by some factor, which does not change the entropy.</li>
<li>After aforementioned container has been winched up from the gravity well, the entropy of the photons inside must be increased compared to the entropy of the photons inside the first leaky container. </li>
</ol>
<p>So I suspect that lifting some radiation increases its entropy. Am I on a right track here? </p>
<p>Addition1:</p>
<p>I have a suggestion how the entropy increases when a cube-shaped mirror walled container of radiation is lifted: A photon moving into just right direction does not touch the floor or the ceiling of the container during the lifting process. The lifting agent does not do any work on that photon. Work done on a photon ranges from zero to X joules, which increases entropy. When gravity does work on photons, every photon's energy increases by K percents, which does not increase entropy.</p>
<p>Clarification to point 2: Observer in the gravity well sees the radiation to leak out rapidly. The short time implies small entropy increase. Observer outside the gravity well sees that radiation slows down when the radiation enters the gravity well. The line of photons contracts when photons at the front are slowing down.</p>
<p>Oh yes, optically dense material has the same effect as gravity well. And also if a photon catcher device moves rapidly towards the photons, then photons go in rapidly and come out slowly, which allows an arbitrarily large photon gas cloud to be caught into a small volume container, in this process temperature of radiation increases without entropy of radiation increasing.</p> | g11671 | [
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-... |
<p>Quantum mechanical observables of a system are represented by self - adjoint operators in a separable complex Hilbert space $\mathcal{H}$. Now I understand a lot of operators employed in quantum mechanics are unbounded operators, in nutshell these operators cannot be defined for all vectors in $\mathcal{H}$. For example according to "Stone - von Neumann", the canonical commutation relation $[P, Q] =-i\hbar I$ has no solution for $P$ and $Q$ bounded ! My basic question is : </p>
<ul>
<li>If the state of our system $\psi$ is for example not in the domain of $P$ (because $P$ is unbounded), i.e., if $P\cdot \psi$ does not, mathematically, make sense, what does this mean ? Does it mean we cannot extract any information about $P$ when the system is in state $\psi$ ?</li>
</ul> | g11672 | [
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<p>Unstable atomic nuclei will spontaneously decompose to form nuclei with a higher stability. What is the algorithm for deciding what sort of it is? (alpha, beta, gamma, etc. Also, given that alpha and beta emission are often accompanied by gamma emission, what is an algorithm for deciding about the distribution of the radiation?</p> | g11673 | [
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... |
<p>What happens to the kinetic energy of matter when it is annihilated? Is it released in the resultant explosion? In that case shouldn't it be $E=(mc^2 + \frac{1}{2} mv^2)$ ?</p> | g11674 | [
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<p>During a relatively non-technical astronomy seminar the other day, the speaker displayed the famous <a href="http://map.gsfc.nasa.gov/media/121238/index.html" rel="nofollow">WMAP full-sky image</a> as an aid to describing what the CMB is, the scale of its fluctuations, etc. This speaker mentioned that there are correlations between the higher-temperature regions on the map and regions of large-scale galaxy structure seen in deep-sky surveys.</p>
<p>I was surprised to hear this. My understanding is that CMB is an image of events currently about 14 billion light years away, while the observed large-scale filaments of galaxies are at approximately half that distance. I wouldn't have expected any density fluctuation 14 billion light years away to share any correlation with a density fluctuation 7 billion light years away.</p>
<p>When I asked, the speaker admitted to being "mostly a star guy" and continued with his excellent talk.</p>
<p>Is there actually a correlation between the warmer, denser regions of the CMB and the distribution of dense galaxy clusters? Is there a causal reason for these distant objects to be correlated with each other? Is there a lensing effect on the CMB temperature? Or is this "correlation" just an enticing-sounding mistake, slowly working its way into common knowledge?</p> | g11675 | [
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0.0268... |
<p>I have read a lot about dark matter and dark energy, the fact that we are spending a small fortune trying to detect their presence, but the only reason they have been postulated it is an effort to protect the standard model. Dark Energy seems to act at a galactic scale, but do we notice it in our solar system? Come on, do we really believe that our solar system is some how special and has no dark energy or dark matter? </p>
<p>What else is wrong - Gravity is still absent from the model, so that is 25% of forces not accounted for (and the only force that actually shapes the universe!). Neutrino mass not accounted for, absence of anti-matter, I could go on.</p>
<p>From my perspective every barrier we come to we make up more and more unbelievable / incredible solutions in order to try and hold on to a model that is clearly flawed. When the standard model was suggested its simplicity was what made it seem so believable. </p>
<p>Do we not need to just get a clean sheet of paper and start again?</p> | g11676 | [
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<p>I'm not sure this is the correct place to ask my question... but maybe someone could still help me.</p>
<p>I'm looking for a way to calculate the residence time/turnover rate.
I have the production and consumption rate (they are different, but stable over time).
And I have the volume (resp. concentration) change over time.</p>
<p>How can I calculate how long a molucule stays in the pool?
Or how long it takes until the whole "population" of molecules is renewed?</p>
<p>I tried several approaches, but it seems I did not yet find the correct direction (?)</p>
<p>1) close the "inflow" and look how long it takes until the pool is emptied. Then open the inflow, close the outflow and calculate how long it takes to reach the start-concentration.
But the problem here is, that it does not take into consideration, that "new" and "old" molecules are mixing and the uptake-change is the same for the new and old molecules. Also it doesn't adress the problem of the changing volume and therefore changing probabilites of the uptake of the "old" molecules.</p>
<p>2) normal residence time. Not usable for me, since I have a different in-outflow and changing volume. I found something from a pulp fabric but this didn't take into consideration, that there is a free mixing of the molecules.</p>
<p>3) next possibility would be in a direction of the "Urn problem". But I do not know how to build it up around the circumstance that there isn't a steady number of balls in there and that I remove "red balls" while put "white ones" into it.</p>
<p>Can someone point me into the correct direction?</p> | g11677 | [
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0... |
<p>That is, the quanta are in bound states where there are least upper bounds and greatest lower bounds to their energy states but there are at least a countably infinite many energy levels they can assume? I'm particularly interested in examples of entangled systems with this property. Any physical examples that can be created in the laboratory?</p> | g11678 | [
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<p>I learned last semester that a Faraday cage shields people (among other things) from getting electrically shock, say, from a tesla coil. This was well demonstrated in lecture so I believe it. </p>
<ol>
<li><p>The person was in a Faraday cage made from chicken wire (i.e. it was full of holes) so why did the Faraday cage "shield" the person?</p></li>
<li><p>Is this always true that a person is always shield under all circumstances? That is, is there a situation where some low frequency discharge (this implies large skin depth) able to penetrate the Faraday cage and shock a person inside the cage?</p></li>
</ol> | g11679 | [
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<p>The sun will last, at its current brightness for 9 billion more years. How long until the sun gets burned down to the point where it cannot sustain life on Earth anymore?</p>
<p><strong>Updated</strong>: I am more concerned with how long until <em>human</em> life cannot be sustained, not how long until the water on Earth vaporizes.</p> | g11680 | [
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<p>Searching the literature for the term "quantum memory" seems to bring up results from two different communities.</p>
<p>On the one hand there are quantum opticians, who see a quantum memory as something used to absorb a photon and store its quantum state before re-emitting it again. The memory in this case could be something as small as a single atom. More details on these are exponded in a review <a href="http://arxiv.org/abs/1003.1107">here</a>.</p>
<p>On the other hand, there are those who see a quantum memory as a many-body system in which quantum information is stored. Possibilities for this include error correcting codes, such as the surface code, or the non-Abelian anyons that can arise as collective excitations in certain condensed matter systems. In this case it is not necessarily assumed that the quantum information existed anywhere before it was in the memory, or that it will be transferred elsewhere after. Instead, the state can be initialized, processed and measured all in the same system. An example of such an approach can be found <a href="http://arxiv.org/abs/quant-ph/0110143">here</a>.</p>
<p>These two concepts of quantum memories seem, to me, to be quite disjoint. The two communities use the same term for different things that store a coherent state, but what they refer to is otherwise pretty unrelated. Is this the case, or are they really the same thing? If so, what exactly are the connexions?</p> | g11681 | [
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<p>I can't find an answer anywhere - I even asked my physics teacher, he hasn't a clue. Is superposition an illusion, or can a particle literally act as [x] particles? </p> | g11682 | [
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<p>Why is electron spin quantized? I've seen the derivation for the Hydrogen atom's energy levels, but my professor jumped to electrons having spin 1/2 or -1/2 as experimental. Why do electrons obey the same quantization rules for angular momentum as the Hydrogen atom does? Why must the two states be one apart?</p> | g11683 | [
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<p>It is known that the Klein Gordon equation does not admit a positive definite conserved probability density. Nonetheless, in Wikipedia (for example), you can read that with the $\textit{appropriate}$ interpretation it can be used to describe a spinless particle (such as the pion I think it says).</p>
<p>My question is the following, which is this appropriate interpretration? and how can we get the wave-function of a particle described with the Klein Gordon equation?</p> | g11684 | [
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<blockquote>
<p>The typical example of the <a href="http://en.wikipedia.org/wiki/Casimir_effect" rel="nofollow">Casimir effect</a> is of two uncharged metallic plates in a vacuum, placed a few micrometers apart.</p>
</blockquote>
<p>Why do the plates need to be metallic? </p> | g11685 | [
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0.0395728... |
<p>Something that's always confused me. How large is a black hole's physical size - not mass?</p>
<p>From descriptions, it would seem that the 'singularity' is a single point, but is it really?</p>
<p>Say for arguments sake, a 110 solar mass black hole. Obviously it's not going to be the same massive size as a 110 solar mass star (such as Cygnus OB2-12 at a physical size of 246 R☉), but would it really be a tiny point smaller than say a pin head?</p> | g11686 | [
-0.02665487490594387,
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0.028558608144521713,
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0.004053487442433834,
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<p>We just had a lesson about elementary mass-spring systems (SHO), and I thought about a horizontal situation with two springs with the test mass oscillating in between. If we are to manually stretch the mass a distance $\Delta x<\Delta_0$ , we obtain opposing restoring forces, which yields the familiar SHO equation. But do thesee conditions change when we stretch it beyond $\Delta_0$(a little beyond, it's still elastic with Hooke's law), in some intervals the restoring forces point in the same direction and in others don't. Does the system retain its "SHO-ness"?</p>
<p><img src="http://i.imgur.com/g0rBIf3.png" alt="System diagrams"></p> | g11687 | [
0.05572944134473801,
0.008135758340358734,
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0.00415431521832943,
-0.... |
<p>what is the difference between constant and changing magnetic and electric fields? How do they occur?
How do they form an electromagnetic wave?</p> | g11688 | [
0.03930875286459923,
-0.015623334795236588,
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0.09005870670080185,
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-0.035439785569906235,
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0.0026042424142360687,
-... |
<p>According to some <a href="http://www.ecm.ub.es/~espriu/teaching/classes/fae/LECT5.pdf" rel="nofollow">lecture notes on propagators (see bottom of page)</a> the Feynman particle/anti-particle hypothesis states:</p>
<blockquote>
<p><em>The emission (absorption) of an antiparticle of 4-momentum $p^\mu$ is physically equivalent to the absorption (emission) of an particle of 4-momentum $-p^\mu$.</em></p>
</blockquote>
<p>The antiparticle of a photon is a photon.</p>
<p>So if an electron emits a photon with 4-momentum $p^\mu$ that is equivalent to it absorbing a photon with 4-momentum $-p^\mu$.</p>
<p>Is that right?</p>
<p>So is this the origin of Newton's 3rd law of action and reaction?</p> | g11689 | [
0.05560598149895668,
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0.01630990020930767,
0.041334155946969986,
0.0399613194167614,
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-0.010962... |
<p>This question is continuation to the <a href="http://physics.stackexchange.com/questions/106102/lie-group-homomorphism-su2-to-so3">previous post</a>. The lie algebra of $ \mathfrak{so(3)} $ is real Lie-algebra and hence, $ L_{\pm} = L_1 \pm i L_2 $ don't belong to $ \mathfrak{so(3)} $. </p>
<p>However, when constructing a representation for $\mathfrak{so(3)} $, one uses these operators and take them to be endomorphisms (operators) defined on some vector space $V$. Let $\left|lm \right> \in V $,then</p>
<p>$$ L_3\left|lm \right> = m \left|lm \right> \;\;\;\;\; L_{\pm}\left|lm \right> = C_{\pm}\left|l(m\pm1) \right> $$</p>
<p>Now, how do we justify these two things ? If $L_{\pm} \notin \mathfrak{so(3)}$, then how is this kind of a construction of the representation possible ?</p>
<p>I belive similar is the case with $\mathfrak{su(n)}$ algebras, where the group is semi simple and algebra is defined over a real LVS.</p> | g11690 | [
0.017446544021368027,
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0.013647116720676422,
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0.02448328398168087,
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<p>If physics is time reversal invariant, there ought to be white hole complimentarity as well. Imagine a white hole so enormous that it is possible for life to evolve entirely within it for billions of years before emerging to tell their story about the interior of the white hole. Meanwhile, an external observer can observe and keep note of everything in the vicinity of the white hole and what comes out of it. Both observers can meet and compare notes. Can the external observer really claim the white hole interior doesn't exist?</p> | g11691 | [
-0.026021309196949005,
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0.043276648968458176,
0.06355631351470947,
-0.015048699453473091,
0.03556426987051964,
0.... |
<p>I'm trying to solve a problem involving parallel capacitor. I can't decide whether to use poisson's formula or laplace's formula.</p>
<p><img src="http://i.stack.imgur.com/hArz0.png" alt="enter image description here"></p>
<p>The question is, is there $\rho_v$ in a piece of dielectric and why?</p> | g11692 | [
0.057684525847435,
0.057650405913591385,
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0.011925332248210907,
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0.004004092887043953,
-0.08310440927743912,
0.07383497059345245,
-0.05125846341252327,
-0.0015... |
<p>Quantities like the chemical potential can be expressed as something like </p>
<p>$$\mu=-T\left(\tfrac{\partial S}{\partial N}\right)_{E,V}.$$</p>
<p>Now the entropy is the log some volume, which depends on the particle number $N$. As in this definition, we sum over natural numbers of particles, is there any good way of actually evaluating the derivative? </p>
<p>What one practically does, i.e. when dealing with an ideal gas, is computing the quantity $\Gamma_N$, which might turn out to be $\frac{\pi^{N/2}}{(n/2)!}$, and then one will get an expression $S(E,N,V)$ which can of course <em>be treated as if</em> it was a function over $\mathbb{R}^3$. Even if that assumes that one has a closed expression which is a function $N$.
In principle I'd be fine with that - if one has a given function (Or at least the bunch of values for all $N$) over a grid and a procedure to introduce more and more grid points to get a finer mash, then there is a notion of convergence to a derivative. But here the N's are clearly always at least 1 value apart - no matter how many N s there are (thermodynamics limit), the mesh doesn't get finer between any two given points. </p>
<p>You might define the derivative as computing the average rate of change between two partcle numbers $n$ and $n+d$ and say $\tfrac{\partial S}{\partial N}$ evaluated at $N'$ gives the same value for all $N'$ in one of the $d$-Intervals, but then you would have to postulate how to come up with $d$ in every new situation. This might be overcome in very specific situations in coming up with a "reasonable" fraction of Avogadros number, but this is not quite mathematical and the values of different finite difference approximation schemes are always different.</p>
<p>In full generality, I feel there is no categorical understanding of what the fractional dimensional space (phase space in this case) has to be and so the procedure of evaluation of the derivative should be explicitly postulate.</p> | g11693 | [
0.0221867598593235,
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0.03... |
<p>Comment: This stuff is new to me so it doesn't entirely make sense (yet). </p>
<p>Question:<br>
As I understand from Peskin and Schroeder chap 10 if you have a theory with interaction terms $\lambda \phi^n$ in the Lagrangian (density) and the dimension of the coupling constant ($\lambda$) is given by $d-n(2-d)/2$. Superficially, if $d\geq0$ the theory is renormalizable.</p>
<p>Secondly, I am aware that the Einstein Hilbert action $S\rightarrow C*\int d^4x \sqrt{-g}R$ is superficially non-renormalizable. (The constant $C$ in the above is of course proportional $G^{-1}$.) The constant $C$ ,itself, has mass dimension 2. Why do these dimensional criteria appear to be reversed for this form of action compared to the $\phi^n$ type terms? To rephrase another way: I understand that the dimension for $G$ itself is negative, but why is it important to look for the dimensionality of $G$ here instead of the dimensionality of what happens to actually be constant in front of the Lagrangian term as was the case in the $\lambda \phi^n$ example? </p> | g11694 | [
0.06308559328317642,
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0.0039863367564976215,
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0.02233738824725151,
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0.011675229296088219,
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0.04601212218403816,
0.026229510083794594,
0.0725670... |
<p>My mom told me to use speed control, which would allow the car to remain at constant speed. I told her that its impossible for a car to maintain constant speed, as slight changes in friction on the road cause differences in the acceleration of the car, and hence the velocity. </p>
<p>But that got me thinking: Even the differences in acceleration caused by differences in the friction due to the road need not be constant. Thus, the car's acceleration is also always changing, implying that it has non-zero "jerk," defined as the change in acceleration over time. </p>
<p>Is this reasoning correct? If so, is there anything keeping the "jerk" constant? How about snap, crackle, and pop (the 4th, 5th and 6th time derivatives of position)? Does it even have to stop there?</p> | g11695 | [
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0.011525075882673264,
0.0... |
<p>I'm taking QFT course in this term. I'm quite curious that in QFT by which part of the mathematical expression can we tell a quantity or a theory is local or non-local?</p> | g11696 | [
0.04611552134156227,
-0.01784834824502468,
-0.0009766146540641785,
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0.03381653130054474,
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0.009238962084054947,
0.03335990756750107,
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0.022567035630345345,
-0.03062356822192669,
0.06415622681379318,
0.008730709552764893,
0.020... |
<p>I always use to wonder how the experimental physicists discover new particles every now and then whose dimensions/properties/mass/charge several order of magnitudes below that of anything that is visible/perceptible. So as engineers do, I guess they also set up a extremely complicated equipment and do some pretty complicated experiments and measure some physical quantity, say (pardon me if my example is poor) an voltage or a magnetic field intensity or could be anything depending on the experimental setup. Now they compare this measured voltage variation with that of what is expected theoretically and then go on to prove the hypothesis. ( This is the hardest thing I could imagine).</p>
<p>Now my request is where can i find a set of data (preferable a continuous variation of a physical parameter with respect to another... may be sampled at sufficient sampling frequency) along with the context of experiment (as minimal as possible but sufficient) so that i can carry out some processing of data in my own way so that i can verify the hypothesis or any such a thing. Simply put i need some really cool real world data ( in the form of signal).</p>
<p>Is any such thing available on the internet or where could I find one?
Please suggest me something which involves signal processing.</p> | g11697 | [
0.04126589000225067,
-0.03680865094065666,
0.012930084019899368,
-0.03931991010904312,
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-0.0332283079624176,
0.03378502279520035,
0.02619129978120327,
0.010184400714933872,
0.011... |
<p>Question goes: "An anvil hanging vertically from a long rope in a barn is pulled to the side and raised like a pendulum 1.6 m above its equilibrium position. It then swings to its lowermost point where the rope is cut by a sharp blade. The anvil then has a horizontal velocity with which it sails across the barn and hits the floor, 10.0 m below. How far horizontally along the floor will the anvil land?"</p>
<p>Now I've been working a while on it and what i got was
$PE \ at \ side = 1.6\times 10 (gravitational\ constant) \times m (mass\ of\ anvil).$</p>
<p>$KE\ at\ lowermost\ point = \frac{1}{2} m v^2 = PE$</p>
<p>$16m = \frac{1}{2} m v^2$</p>
<p>$16 = \frac{1}{2} v^2$</p>
<p>$32 = v^2$</p>
<p>$v = \sqrt{32}$</p>
<p>Now to the free-fall problem, </p>
<p>$10 = \frac{1}{2} g t^2$</p>
<p>$20 = g t^2$</p>
<p>$2 = t ^ 2$</p>
<p>$t = \sqrt{2}$</p>
<p>So the distance traveled horizontally = $\sqrt{2} \times \sqrt{32} = 1.414$ meters.</p>
<p>I checked the model-answers and the answer was 8 meters, would someone please explain this? (The model-answer might be wrong though)</p> | g11698 | [
0.04589047655463219,
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0.04113141819834709,
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0.019041307270526886,
0.01887308806180954,
-0.04334... |
<p>Is there any theory in which every particle can be further subdivided into any number of particles and the total number of particles any where in the space time are infinity in theory and only due to practical constraints that we are capable of observing the known particles in the current World.</p>
<p>Also could you please explain the nature of the two widely accepted theories which explain the small scale and large scale universe which are QP and GR repectively in the current context of the question. </p> | g11699 | [
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0.028718311339616776,
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0.031441155821084976,
0... |
<p>I have to use $\vec{P}+\vec{R_N}+\vec{F_f}=m\vec{a}$ with $\|\vec{F_f}\|=\mu\|\vec{R_N}\|$ to express the acceleration as $$a_{x'}=g\sin\alpha(1-\frac{\mu}{\tan\alpha})$$
The configuration is (sorry about the poor image) :</p>
<p><img src="http://www.beziaud.org/~work/upload/docs/131112083008.schema.jpg" alt="scheme"></p>
<p>I'm totally lost. How could I do that?</p> | g11700 | [
0.04330972954630852,
0.018192710354924202,
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0.0005805417895317078,
0.02726181596517563,
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0.0... |
<p>I'm having a small question regarding $K_{\alpha}$ and $K_{\beta}$ emissions.</p>
<p>If I'm not mistaken this happens when there is a transition from the L shell to the K shell (Depending on the orbital), in which a photon is emitted with a given energy.</p>
<p>My question is: Is there any difference between the energy of the photon that is emitted in $K_{\alpha}$ emission for example, and the binding energy of the electron in the same orbital, or...?</p>
<p>Thanks in advance</p> | g11701 | [
0.010699625127017498,
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0.02148125320672989,
0.02007121965289116,
0.00970542337745428,
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0.03373907133936882,
0.03547651320695877,
0.041420575231313705,
0.031356... |
<p>What is the sense of Green function
$$
\langle | \hat {T}(u_{1}(x_{1})...u_{n}(x_{n})\hat {S})|\rangle , \quad \hat {S} = \hat{T}e^{i\int \hat {L}(x)d^{4}x} ?
$$
How is it connected with scattering processes?</p> | g11702 | [
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0.... |
<p>I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or conformal field theories, and of older approaches such as algebraic QFT, and the classic works of Wightman, Streater, etc. etc . I am more interested in more current approaches, in particular such approaches that incorporate the modern understanding of the subject, based on the renormalization group. I know such approaches exists and have had occasions to hear interesting things about them, I'd be interested in a brief overview of what's out there, and perhaps some references.</p>
<p>Edit: Thanks for all the references and the answers, lots of food for thought! As followup: it seems to me that much of that is concerned with formalizing perturbative QFT, which inherits its structure from the free theory, and looking at various interesting patterns and structures which appear in perturbation theory. All of which is interesting, but in addition I am wondering about attempts to define QFT non-perturbatively, by formalizing the way physicists think about QFT (in which the RNG is the basic object, rather than a technical tool). I appreciate this is a vague question, thanks everyone for the help.</p> | g234 | [
0.018972663208842278,
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0.03351661190390587,
0.0... |
<p>The <a href="http://en.wikipedia.org/wiki/Riemann_curvature_tensor" rel="nofollow">Riemann curvature tensor</a> can be expressed using the Christoffel symbols like this:</p>
<p>$R^m{}_{jkl} = \partial_k\Gamma^m{}_{lj}
- \partial_l\Gamma^m{}_{kj}
+ \Gamma^m{}_{ki}\Gamma^i{}_{lj}
- \Gamma^m{}_{li}\Gamma^i{}_{kj}$</p>
<p>How did they come up with this? What was the idea?</p>
<p>I searched the web but the descriptions I found were too formal, and I was unable to decipher what the author tries to describe. </p>
<p>So I'm looking for some thoughts or an easy paper I can start from and derive this formula myself.</p> | g11703 | [
0.005979258567094803,
0.02044927142560482,
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0.003946058917790651,
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-0.0018888296326622367,
-0.05002230405807495,
0.003977672662585974,
0.08062838017940521,
... |
<p>Hopefully Weinberg is sufficiently popular that this question isn't too localized. I'm reading Volume II (16.1, p. 63) and he refers to the state $\lvert\text{VAC}\rangle$ quite a lot. Does this mean the vacuum of the free theory or of the interacting one? </p>
<p>I think it means the vacuum of the free theory, from how he uses it. But I can't find the page where it's defined (and there's a lot of rather dense pages, so I'd rather not spend my whole afternoon trying to find the right line)! </p> | g11704 | [
0.01354155596345663,
0.0287887342274189,
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-0.014226204715669155,
0.0017702113837003708,
0.02897578291594982,
0.060713328421115875,
0.0024282282683998346,
0.057015612721443176,
-0.03054901957511902,
-0.051423393189907074,
-0.049675025045871735,
0.04962307959794998,
0.0... |
<p>I have a series of daily readings (NOx emissions) measured in parts per million. </p>
<p>I need to aggregate the daily readings into a monthly measure. </p>
<p>Clearly a sum operation will be incorrect (parts per million is a ratio). </p>
<p>Am I correct that aggregating samples in parts per million can be achieved with a simple mean operation?</p>
<p>e.g (if a month had 2 days).</p>
<pre><code>100ppm (day1) + 500ppm (day2) = (100+500)/2 = 300ppm
</code></pre>
<p>What's the correct way to get the NOx in ppm over a whole month?</p> | g11705 | [
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-0.019479801878333092,
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0.0063415043987333775,
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0.05402454361319542,
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0.024801107123494148,
... |
<p>Let's have an interval expression for Friedmann Universe with 3-metric of a sphere,
$$
ds^{2} = c^{2}dt^{2} - c^{2}\frac{ch^{2}(Ht)}{H^{2}}\left( d\rho^{2} + sin^{2}(\rho )(d\theta^{2} + sin^{2}(\theta )d\varphi ^{2})\right),
$$
with metric tensor, which is given by
$$
\hat {\mathbf g} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & -ch^{2}(Ht) & 0 & 0 \\ 0 & 0 & -ch^{2}(Ht) \sin^2 (\rho ) & 0 \\ 0 & 0 & 0 & -ch^{2}(Ht) \sin^2 (\rho ) sin^{2} (\theta ) \\ \end{bmatrix}.
$$
What physical sense has transformation
$$
\hat {\mathbf T}, \quad |\hat {\mathbf T} = 1|, \quad T_{\alpha \beta } = T_{\beta \alpha},
$$
which is given by
$$
\hat {\mathbf T}\hat {\mathbf g} \hat {\mathbf T} = \hat {\mathbf g}?
$$
Maybe, the only space part of transformations determines the motion on the sphere, but what means the time part? It's something like Lorentz transformations, but for non-inertial systems.</p>
<p>The trivial solution for $\hat {\mathbf T}$ is $\hat {\mathbf T} = diag(1, 1, 1, 1)$. But maybe there exist other solutions, don't they?</p> | g11706 | [
-0.029924426227808,
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0.011740532703697681,
0.07867731899023056,
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-0.04100389406085014,
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0.001685295719653368,
0.025227544829249382,
0.0030837... |
<p>Is it possible for small object (small mass, let's say bullet) to hit large object (big mass, let's say rock) and still move forward (or stop) instead of being reflected (let's say objects don't crush and collision takes place in one dimension)?</p> | g11707 | [
0.020155275240540504,
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-0.... |
<p>First off, sorry to throw in another question from someone who hasn't studied the maths.</p>
<p>I'd like to see if I have a correct (if very basic and non-mathematical) understanding of the wave and statistical nature of Quantum Mechanics, and to avoid any complexity I'd like to look at the Double Slit Experiment without the slit.</p>
<p>So we have a macro object (which is itself a very complex Quantum object that for the most part can be modeled with "classical physics") that emits electrons and can be switched to emit one electron at a time. Off to one side of the electron emitter is a flat screen that acts as an electron detector.</p>
<p>When we tell the emitter to produce a single electron what we get is a (spherical in 3-d space?) wave of some specific energy that travels from the emitter at the speed of light. As the wave intersects with objects (other waves, fields, "classical objects") with which it is capable of interacting with there is a percentage chance (that can be modeled through QM maths) that the wave will interact with it. Not each electron emission will interact with the screen, which is expected, and the wave will continue until it reacts with an object that absorbs its energy and becomes part of the Quantum state of another object.</p>
<p>So, is my understanding as presented in the previous paragraph correct?</p> | g11708 | [
-0.02203134447336197,
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-0.06344513595104218,
0.019962742924690247,
0.05392185598611832,
0.05693204700946808,
-0.0108... |
<p>I am modeling a gas flowing through a liquid. How do I calculate the Reynolds number in multiphase flows? And, at what Reynolds number should I consider the flow to be turbulent?</p>
<p>The problem is of a typical drilled wellbore in the oil and gas industry. Fresh cement is poured into an annulus between the steel casing and the drilled formation. Before the cement is set it is vulnerable to formation gas over coming its pore pressure (or hydrostatic head) and flowing through the cement, often times forming channels for more gas to flow through in the future, rendering the cement sheath useless.</p>
<p><strong>EDIT:</strong></p>
<p>I am currently using a <a href="http://en.wikipedia.org/wiki/Bingham_plastic" rel="nofollow" title="Bingham fluid">Bingham fluid</a> to describe the viscosity of the cement slurry. The yield stress will be in the range of 300 to 700 kPa. The plastic viscosity will be in the order of 0.05-0.10 Pa.s.</p>
<p>It is hard for me to estimate gas velocity but in preliminary models I have seen velocities in the range of 5-10 mm/s in preliminary models.</p> | g11709 | [
0.02173561044037342,
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0.024849209934473038,
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-0.006936527788639069,
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0.012739886529743671,
0.009181439876556396,
-... |
<p>Is force the unique possible relation between particles? </p>
<p>It was requested to further specify my question. The followings paragraphs contain some of my thoughts and confusions.</p>
<p><strong>Historical motivation:</strong></p>
<ul>
<li>Since Aristotle the notion of force (dunamis, energeia) was intrinsic to the substance itself. The driving force was that the which caused movement (kinesis). Change from A to B is movement. The cause of this movement is force. However, Aristotle considered motion in a much broader sense than contemporary physics does. For example, he considered the transition between seeing and not-seeing, or sickness and health, as a kind of motion. Since the 17th century the concept of motion was restricted to spatio-temporal movement. Accordingly, the notion of force was changed into that which causes modifications of interrelated moving particles embodied in space-time. So, whereas the notion of force began as something intrinsic to a substance, it became something extrinsic, dependent on the structure of space, relating different particles and their properties.</li>
</ul>
<p><strong>To go back to my original question:</strong> </p>
<ul>
<li><p>The nature of the formula $F_G = G \frac{m_1 m_2}{r^2}$ contains the spatial distance between the two particles, as well some intrinsic properties of the particles (i.e. their mass). The formula of $F_C = k \frac{Q_1 Q_2}{r^2}$ has a similar form, and also captures some intrinsic properties of the two particles (i.e. their charge). But not only does force "captures" spatio-temporal relationships and some properties of particles, it also expresses the reason of their modification. Let's look at the formula: $F=m \cdot a$. Even though this is a mathematical identity, the equation can be interpreted as a physical difference. On the left-hand-side $F$ can be read as a "cause," whereas $m \cdot a$ on the right-hand-side can be read as an "effect." Force is the cause which brings out an effect (i.e. acceleration). I am aware that this notion of "cause" may be be outdated and that Newton's action-at-distance has been replaced by the notion of a field. But the nature of a field is even more ambiguous to me. Is it merely a mathematical construct? Does it have physical meaning?</p></li>
<li><p>When I look carefully at the fundamental formulas of physics, they all seem to express relations between particles and their respective states. Force is in this sense a relational concept. Moreover, whatever a particle (or a system of particles) undergoes (motion, acceleration, etc.): there was a force which caused this change. However, it's not obvious for me how particles are able to <em>inter</em>-act and can in-fluence each other. My first guess was that forces were responsible for establishing this inter-<em>connection</em>. Forces "mediate" "between" particles. Be aware that I don't understand the words "mediate" and "between" here.</p></li>
</ul> | g11710 | [
0.05720432847738266,
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<p>My dad has a HUGE magnet on his workshop.</p>
<p>I love magnets, and when I saw it, I asked him what it was for.</p>
<p>His reply was: "I don't know why, but inox steel bolts don't get attracted to it, so I use it to identify them."</p>
<p>Thus I got curious, why a magnet don't attract <a href="http://en.wikipedia.org/wiki/Stainless_steel" rel="nofollow">inox steel</a> bolts? Steel, even if a inox variation is still mostly iron, no?</p> | g11711 | [
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<p>I have been reading in <a href="http://www.schoolphysics.co.uk/age11-14/Heat%20energy/Transfer%20of%20heat%20energy/text/Heat_radiation/index.html" rel="nofollow">this</a> and found a statement saying : " Glass will not transmit heat radiation.". So now I am confused. If glass won't transmit heat radiation, then why do we feel hot when we sit in front of a glass window in a sunny day ? Also, why do we find the car seats facing the windshield so hot in a sunny day ?</p>
<p>One other thing, let's say a nuclear detonation happened somewhere nearby and I was standing behind a glass window, will this window protect me from thermal or heat radiation effects of the bomb ?</p> | g11712 | [
0.014806486666202545,
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0.008931341581046581,
0.05842698737978935,
0.013718370348215103,
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0.00580... |
<p>The $\pi$-meson is a boson, but consists of quark-antiquark (fermions). It seems to me that at some energy level (equivalently distance) the inner structure (fermionic nature of the quarks) of the particle in question should become important and the bosonic nature less so. </p>
<p>Question:<br>
Can we have a bunch of pions occupying the same quantum state at all temperatures, or is this model bound to fail due to the fermionic nature of its constituents?</p>
<p>I'm thinking for example of the pion-cloud (in some models) surrounding the nuclei. </p>
<p>EDIT: I found <a href="http://physics.stackexchange.com/questions/45644/can-bosons-that-are-composed-of-several-fermions-occupy-the-same-state?rq=1">this question</a> which is very related to the present one. Although I should add that my question (regarding the pion-cloud) is more specific and less general. </p> | g11713 | [
-0.029686005786061287,
0.02956484444439411,
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0.002391217043623328,
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<p>Suppose that I produce an image of a dog using a converging lens. I can draw ray diagrams for the nose of the dog as well as the back leg. These are definitely longitudinal points, not transverse. However, one typically captures a two-dimensional image of the dog using some screen. But isn’t this dog really a three-dimensional image? If so, how would one capture such an image?</p> | g11714 | [
0.04052257910370827,
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0.018446533009409904,
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0.020330531522631645,
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0.05429573357105255,
0.01468604989349842,
0.08840101957321167,
-0.018... |
<p>Meteorilogical stations in my country report relative humidity. I am not sure why as this is actually misleading, as relative humidity will change with temperature. Unless I miss my guess, what is important for human feeling is a dew point.</p>
<p>How can I calculate dew point from relative humidity and temperature?</p>
<p>PS: I have found quite a nice tool: <a href="http://www.dpcalc.org/" rel="nofollow">http://www.dpcalc.org/</a></p> | g11715 | [
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0.005562385078519583,
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0.023432143032550812,
0.07412966340780258,
0.0225... |
<p>The terms <em>fluctuations</em> and <em>perturbations</em> are frequently used in physics with different meanings. But they are confusing. Both terms seems to be same. Is there any one who can explain lucidly these terms and show difference between these two terms?</p> | g11716 | [
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0.016... |
<p>What is the exact difference between wavenumber and propagation constant in an electromagnetic wave propagating in a medium such as a transmission line, cause i am a bit confused. Does it have to do with loss in the medium?</p> | g11717 | [
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<p>In Young's Double Slit experiment, why is it that two waves vibrating perpendicular to each other doesn't show interference?</p>
<p>I know that for interference to happen, the waves must be coherent ( i.e., they maintain a constant phase w.r.t each other) and if the waves meet at same point in the screen it results in constructive interference and destructive if there is a phase change of lambda/2 and so on. </p>
<p>Any help regarding the query would be nice. </p> | g11718 | [
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<p>I know that the distance that a free falling body has traverse through time is given by $d=0.5*g*t^2$. I would like to know how to get to this equation to study a bit more how it was obtained. I have been searching around with any luck. Could anybody give any tip?</p> | g11719 | [
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0.1193232536315918,
-0.022516... |
<p>Is there a type of glass, mirror or lens that allows only lights of amplitude equal to or greater than a fixed value to pass/reflect through them?</p> | g11720 | [
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<p>It might be just a simple definition problem but I learned in class that a central force does not necessarily need to be conservative and the German Wikipedia says so too. However, the <a href="http://en.wikipedia.org/wiki/Central_force">English Wikipedia</a> states different on their articles for example:</p>
<blockquote>
<p>A central force is a conservative field, that is, it can always be
expressed as the negative gradient of a potential</p>
</blockquote>
<p>They use the argument that each central force can be expressed as a gradient of a (radial symmetric) potential. And since forces that are gradient fields are per definition conservative forces, central forces must be conservative. As far as I understand, a central force can have a (radial symmetric) potential but this is not necessarily always the case. </p> | g11721 | [
0.02932543307542801,
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<p>Couder experiments ( <a href="https://www.youtube.com/watch?feature=player_embedded&v=W9yWv5dqSKk" rel="nofollow">https://www.youtube.com/watch?feature=player_embedded&v=W9yWv5dqSKk</a> and <a href="https://hekla.ipgp.fr/IMG/pdf/Couder-Fort_PRL_2006.pdf" rel="nofollow">https://hekla.ipgp.fr/IMG/pdf/Couder-Fort_PRL_2006.pdf</a>), published in 2006, state that by dropping silicon droplets into a vertically vibrated bath, we can observe the whole paths of these droplets and see how interference works out. </p>
<p>1) Wouldn't this violate the uncertainty principle that states that $\sigma_x$ or $\sigma_p$ can never be zero? The only way I could imagine is that $\sigma_p$ becomes infinite. Can any experiment produce the case where $\sigma_p$ is infintie quantum-theoretically? (and is this paper's conclusion - that $\sigma_p$ is infinite during the experiments?)</p>
<p>2) This experiment is macroscopic; but some people are saying that this in fact reveals much about quantum world, and I am curious how macroscopic observation be directly applicable to microscopic world.</p>
<p>3) We all know that photons behave differently; we cannot see photons until they hit the screen and we can only know their interference patterns. We have to try to measure them before they hit the screen, but then interference is destroyed both in reality and in theory. Does this experiment imply that there might be a way to see the whole path and the interference pattern of photons together?</p>
<p>4) The path taken by each droplet seems still probability issues - while we can see them, there is no way we can predict exactly where the droplet goes. Does this experiment in any way reopen the question like Einstein's dream of determinism?</p> | g11722 | [
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0.006520251743495464,
0.0131... |
<p>I know that if you held an infrared remote in front of a digital camera, it'll flash a blue/purplish light when you press the buttons. Why?</p> | g11723 | [
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0.06742526590824127,
0.05410713329911232,
0.0621... |
<p>In Wikipedia article about time dilation, it says: </p>
<p>"Hafele and Keating, in 1971, flew caesium atomic clocks east and west around the Earth in commercial airliners...the moving clocks were expected to age more slowly because of the speed of their travel." </p>
<p>Is it really true? My belief was that only acceleration/deceleration takes effect when comparing two clocks in the same frame after certain kinds of motions. According to my belief, I thought the time difference of two clocks in the aforementioned test is the same regardless of the length of the flight, if we ignore the difference of gravitational potential caused by different heights.</p> | g11724 | [
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0.04039628803730011,
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0.022165244445204735,
0.027719... |
<p>Is there any true <a href="https://en.wikipedia.org/wiki/Inertial_frame_of_reference" rel="nofollow">inertial reference frame</a> in the universe?</p>
<p>Newton's first law states that an object at rest remains at rest, and an object performing uniform motion performs uniform motion, until and unless acted upon by an external force, if viewed from an inertial frame. It is the definition of an inertial frame of reference. And Newton's second law states that the net external force acting on a particle equals its mass times its acceleration. Thus we need to have an inertial frame in order for Newton's 1st and 2nd laws to be applicable.</p>
<p>Scientists claim that Earth is an inertial frame, either the <a href="http://en.wikipedia.org/wiki/ECEF" rel="nofollow">ECEF</a> frame or the <a href="http://en.wikipedia.org/wiki/Earth-Centered_Inertial" rel="nofollow">ECI</a> frame. Why is that? Earth's different parts have different accelerations when it performs rotational motion about its axis. Now you may say that Earth's axis is inertial, but the Earth is also revolving around the Sun. Thus Earth's frame should be non-inertial.</p>
<p>Even supposing that earth's frame is inertial, then it means that rest of the universe is non-inertial, because only a frame that moves with constant velocity with respect to an inertial frame is also an inertial frame and according to various scientific experiments there is no other matter in this universe which satisfies that criterion. Now you may say that earth is an approximate inertial frame, but still, my question is: is there any perfect inertial frame in the universe where Newton's laws are exactly applicable? </p> | g11725 | [
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0.03038... |
<p>I was solving a practice test problem and it was just a conservation of energy problem
where a spherical ball is falls from a height h to the ground such that</p>
<p>$$mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$$</p>
<p>what I can't quite picture in my head is how there is an energy contribution from the rotation at a fixed point in time. obviously there is a instantaneous rate of change of the center of mass </p>
<p>$$v_{cm} = \frac {d \vec {x_{cm}} }{dt}$$
for any fixed point in time
in my head I can see this as contributing to energy</p>
<p>but the angular velocity can't be similarly treated like it is all at a point
$$ \vec{\omega} = \frac{d\ \vec{\theta} } {dt}$$ </p>
<p>here i understand this vector of angular rotation exists but I am confused as to why it adds to the energy of the system</p>
<p>I just somehow can't wrap my head about energy of rotation when there is already some energy due to the center of mass' translation... i'm not sure exactly why sorry if this is vague but I figured i'd ask if someone has some way to think about this. maybe in terms of DOF's?</p> | g11726 | [
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0.016818160191178322,
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-0... |
<p>suppose you have a pita pocket of radius 5cm or .05m. We will model the pita pocket as consisting of disk with a layer of air of volume V which is contained by the surface of the bread. We will assume that no cracks or perforations exist in the pita pocket.
supposing the thickness of the pocket is d = .5cm = .0025m. we can calculate the volume from the radius and thickness of the disk </p>
<p>$V_{pita}$ = $\pi r^2d$</p>
<p>suppose that the pita contains a volume of air inside </p>
<p>$V_{air} = \frac {V_{pita}}{5}$ </p>
<p>and that the rest of the volume of the pita is a solid. Model the forces and pressure that cause the pita to expand. at what temperature will the air pressure inside be able to break the bonds holding the top sides of the bread together and allow it to expand under your models assumptions? rough order of magnitude estimates are fine--- but all answers should agree with experimental values of pita expansion as a function of Temperature</p> | g11727 | [
0.04258260503411293,
0.01584634557366371,
0.006416032090783119,
-0.006758471950888634,
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-0.0185865368694067,
-0.03633446618914604,
-0.07512116432189941,
-0.0209... |
<p>I am wondering how one can quantize the free electro-magnetic field
in the two dimensional space-time. The standard method of fixing the
Coulomb gauge in 4d does not seem to generalize immediately to 2d.</p>
<p>If one tries to generalize it directly then, as in 4d, after a gauge
transformation one may assume that the scalar potential vanishes.
Thus $A_\mu=(0,A_1)$. Then the Maxwell equations imply easily that
$$\frac{\partial A_1}{\partial x^0}\equiv C=const$$
where $x^0$ is the time coordinate. Hence $A_1(x)=C x^0+h(x^1)$. Now
one can apply a gauge transformation such that $h$ will vanish:
$A_\mu(x)=(0,Cx^0)$. <strong>Thus there is no degrees of freedom to
quantize!!</strong></p>
<p><strong>Another problem is that the
expression $\frac{1}{q^2+i0}$ which appears in the free photon
propagator in 4d, is not well defined in 2d</strong> for purely mathematical reasons if I
understand correctly (there is no such generalized function:
the problem in at $q=0$).</p>
<p>Is there a treatment of this in literature?</p>
<p>Actually the above question was motivated by my attempt to read J.
Schwinger's paper "Gauge invariance and mass, II", Phys. Review,
128, number 5 (1962). There he studies QED in 2d (so called
Schwinger's model). Is there a more modern and/or detailed
exposition of this paper?</p> | g11728 | [
0.03095928020775318,
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-0.020710572600364685,
0.028723692521452904,
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0.06184634193778038,
0.03847208246588707,
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0.021801309660077095,
-0.009981016628444195,
-0.008107258006930351,
0.006853682454675436,
0.0... |
<p>given the differential operator Eigenvalue problem $ -D^{2}y(x)=E_{n}y(x) $ with boundary periodic conditions $ y(x)=y(x+1)$</p>
<p>my question is if there is a similar probelm for the Dilation operator $ T= xD $ with 'D' the derivative respect to 'x' i mean solve</p>
<p>$ T^{2}y(x)=E_{n}y(x)$ with dilation periodic condition</p>
<p>my question is how can i impose PERIODIC conditions but not for the traslation group (Yx+1) but for the Dilation group, i believe that some periodic conditions involving dilations would be $ y(x)=y(2x)$ but i am not sure</p>
<p>how can i impose PERIODIC conditions if the LIe group is just the Dilations in 1-D ??</p>
<p>thanks.</p> | g11729 | [
0.0055257296189665794,
-0.021062703803181648,
0.012143183499574661,
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0.0009056924609467387,
0.039591044187545776,
0.01937810331583023,
-0.013732089661061764,
... |
<p>I would like to know if there are any online collections of lecture videos on QCD or non-Abelian QFT at a graduate level (at the level of volume 2 of Weinberg's QFT books?)</p>
<p>For example:
In String Theory I think this one by Shiraz is a great (only?) online resource -
<a href="http://theory.tifr.res.in/~minwalla/" rel="nofollow">http://theory.tifr.res.in/~minwalla/</a></p> | g371 | [
0.016526395455002785,
0.010234885849058628,
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0.02619118243455887,
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0.020392056554555893,
0.014963367022573948,
0.01967274211347103,
-0.004230652470141649,
0.018696408718824387,
0.... |
<p>Zee's QFT book mentions the Lagrangian of a square 2D horizontal lattice of point masses, connected by springs, and considering only vertical displacements $q_{i}$, as</p>
<p>$ L = \frac{1}{2} \sum\limits_{a}(m \dot{q}_{a}^{2}) - \frac{1}{2} \sum\limits_{ab}(k_{ab}q_{a}q_{b}) - \frac{1}{2} \sum\limits_{abc}(g_{abc}q_{a}q_{b}q_{c}) - ...$</p>
<p>I have done elementary exercises in Lagrangian Mechanics, using $\frac{1}{2}k(l-l_{0})^{2}$ as the potential energy of the springs, but, after naively trying to derive (with which I mean "to build") that Lagrangian by myself, I suspect I must be missing some kind of additional cross-contributions to the potential energy (and I have no idea where did that triple products $q_{a}q_{b}q_{c}$ emerged from...).</p>
<p>I know this is the <em>abc</em> of solid state physics, that gives rise to the phonons and other interesting stuff, but I am almost completely ignorant in that area. Can anybody at least put me in the right track on how to derive (i.e. to build, departing from some given assumptions) that Lagrangian?</p>
<p>NOTE: In other words, say you want to <em>build</em> that Lagrangian, considering only vertical movements of the masses. The kinetic energy term is obvious, but for the potential energy, is it enough to naively sum $\frac{1}{2}k(l-l_{0})^{2}$ of all the springs? (of course written as a function of the $q_{i}$). Or, perhaps, is there any additional contribution to the potential energy that comes from the fact that the springs are somehow having some influence on each other?</p>
<hr>
<p>EDIT with some remarks:</p>
<p>Remark 1:
A somewhat similar approach to what I am looking for, can be found for a linear chain of atoms, <a href="http://www.tcm.phy.cam.ac.uk/~bds10/tp3/introduction.pdf" rel="nofollow">here</a> (Ben Simons, Notes on Quantum Condensed Matter Field Theory, chapter 1)</p>
<p>Remark 2:
Thanks very much for correcting my misuse of the english word "derive". Ok, a Lagrangian is not derived. When I say "to derive a Lagrangian" I want to mean "to build a Lagrangian departing from some assumptions" like is the usual approach. For example, I can build the Lagrangian from a double pendulum from the assumptions that the masses of the rods can be neglected and there is no friction, and so I simply add the kinetic energy of the two masses and subtract their gravitational potential energy. </p> | g11730 | [
0.07358159869909286,
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0.0027478488627821207,
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0.04930176958441734,
0.0000664709514239803,
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-0.02685561776161194,
-0.05756871774792671,
0.02696876972913742,
0.0738411545753479,
-0.0... |
<p>If energy is conserved in all quantum mechanical interactions, how are there classical interactions in which energy is <em>not</em> conserved, given that classical interactions are a macroscopic approximation to the quantum mechanical interactions?</p> | g11731 | [
0.06310569494962692,
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0.011306867934763432,
0.03350115939974785,
0.014954577200114727,
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-0.03521567955613136,
0.014936380088329315,
-0.022460831329226494,
-0.03960850462317467,
0.0050... |
<p>A stellar-mass black hole has recently been discovered in the Andromeda galaxy. One interesting part of <a href="http://arstechnica.com/science/2012/12/astronomers-locate-a-miniature-quasar-in-andromeda/">the release</a> is that this black hole shines close to its <a href="http://en.wikipedia.org/wiki/Eddington_luminosity">Eddington limit</a>.</p>
<blockquote>
<p>Quasars are supermassive black holes shining at or near the Eddington luminosity, and microquasars are likely stellar-mass black holes whose accretion is similarly close to the theoretical maximum.</p>
</blockquote>
<p>Wikipedia derives the equation for the Eddington limit (although I'm not sure about the applicability of its assumptions to small black holes) to be proportional to $M$. The Hawking radiation from a black hole goes as $1/M^2$. This implies that a cross-over point where both formulas calculate the same power. I can calculate this to be about $4 \times 10^{10} kg$.</p>
<p>What would be an accurate picture of a micro black hole, given sufficient matter around to feed it? I think that the Eddington limit is a balance between the gravitational pull and the radiation pressure, but in the case where Hawking radiation is present, would the picture be significantly different?</p> | g11732 | [
-0.03011258877813816,
0.028199151158332825,
0.0006800176342949271,
-0.04894360527396202,
-0.021495310589671135,
0.001525111380033195,
-0.01477453950792551,
0.0014659685548394918,
-0.025819193571805954,
0.004404367413371801,
0.06762002408504486,
0.05061016604304314,
0.023858996108174324,
0.... |
<p>The documentation for <a href="http://reference.wolfram.com/mathematica/ref/AstronomicalData.html" rel="nofollow">an API</a> I often use for quick astronomical modeling and figure drawing says </p>
<blockquote>
<p>Positions are given in FK5 heliocentric coordinates in the equinox of the date used.</p>
</blockquote>
<p>What does "equinox of the date used" mean. Does it simply mean that the epoch for a value at time $t$ is $t$, rather than some other time (e.g. J2000)?</p> | g11733 | [
0.044807519763708115,
0.02213140018284321,
-0.010260126553475857,
-0.08860094100236893,
0.03564140945672989,
-0.011137234047055244,
0.011463823728263378,
-0.028783872723579407,
-0.03698764368891716,
-0.014484480023384094,
0.004149796906858683,
-0.012271040119230747,
0.11674773693084717,
0.... |
<p>The problem description is as follows:</p>
<blockquote>
<p>Boron is used to dope 1 kg of germanium (Ge). How much boron (B) is required to establish a charge carrier density of 3.091 x 10^17 / cm^3. One mole of germanium has a volume of 13.57 cm^3 and weighs 72.61 gram. Give answer in grams of boron.</p>
</blockquote>
<p>I'd like some advice on how this problem should be solved. I've tried finding the conductivity first, but it seems that this practice exam did not have a graph for the Hole Mobility (I suppose a Hole Mobility vs. Impurity Concentration graph), so I assumed there must be another way of solving this.</p> | g11734 | [
-0.023716457188129425,
0.07207704335451126,
0.025290442630648613,
-0.024570997804403305,
0.025383152067661285,
0.014544219709932804,
0.03152541443705559,
0.04394692927598953,
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0.08522515743970871,
-0.03166825324296951,
0.05037454143166542,
-0.048018667846918106,
-0.00... |
<p>I'm confused about the difference between voltage and potential energy in a capacitor. Suppose you have a capacitor with a voltage V and capacitance C, and you release a particle with charge $+Q$ from the positive end of the capacitor. Is the potential energy of the particle that gets converted to kinetic energy $(1/2)CV^2$ or $QV$? What is the difference between these two quantities?</p> | g11735 | [
0.07089827209711075,
-0.005224849563091993,
-0.006811422295868397,
0.008627481758594513,
0.018266187980771065,
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0.006753271445631981,
-0.014694607816636562,
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0.015357021242380142,
-0.02271030656993389,
0.0615139864385128,
0.00481768324971199,
0.0... |
<p>I've looked in several books and they all show how to obtain electrical interactions by forcing local gauge invariance of any complex scalar field Lagrangian (like Klein-Gordon or Dirac). I manage to separate the new Lagrangian into the original one (the free Lagrangian) and the interaction part of it. But how I get Maxwell's Lagrangian from this? As the fields that are inserted to keep the Lagrangian gauge invariant should have it's dynamics described by Maxwell's. So, how to does the term $F^{\mu\nu}F_{\mu\nu}$ enter the new Lagrangian naturally?</p>
<p>Thanks</p> | g11736 | [
0.06588596105575562,
-0.0220250952988863,
-0.01743122935295105,
-0.04763249680399895,
0.0380190946161747,
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-0.036228347569704056,
0.005778931546956301,
0.008739970624446869,
0.01097151543945074,
0.0362837... |
<p>As can be seen on this page <a href="http://en.wikipedia.org/wiki/Multipole_expansion" rel="nofollow">http://en.wikipedia.org/wiki/Multipole_expansion</a> when we take a multipole expansion <em>without</em> assuming azimuthal symmetry we end up with $2l+1$ coefficients for the $l^{th}$ moment in the expansion. So the dipole moment has 3 terms, the quadrupole has 5 and so on. This is different to the case of azimuthal symmetry as each we need only one co-efficient for each term.</p>
<p>Interpreting 3 coefficients for the dipole moment isn't too bad. I'm guessing it represents the dipole moments along the 3 Cartesian axes? And how do we interpret having to have $2l+1$ coefficients for each term?</p> | g11737 | [
-0.02872701920568943,
0.06772897392511368,
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0.03155612573027611,
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0.03683501109480858,
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-0.03361715003848076,
0.021343203261494637,
-0.03... |
<p>Consider that I know the cosmological angular diameter distance at a given redshift :</p>
<p>$$D_{A}\left(z\right)=\frac{x_{object}}{\theta_{observer}}$$</p>
<p>Is there a general formula to compute the luminosity distance $D_{L}$ from $D_{A}$ without assuming an homogeneous cosmology ?</p> | g11738 | [
-0.02029612474143505,
-0.00019623544358182698,
-0.019429104402661324,
-0.07318811863660812,
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0.0019672331400215626,
-0.06719988584518433,
0.031143421307206154,
0.017370836809277534,
0.10462786257266998,
... |
<p>Recently I've been puzzling over the definitions of first and second order phase transitions. The <a href="https://en.wikipedia.org/wiki/Phase_transition#Classifications" rel="nofollow">Wikipedia article</a> (at the time of writing) starts by explaining that Ehrenfest's original definition was that a first-order transition exhibits a discontinuity in the first derivative of the free energy with respect to some thermodynamic parameter, whereas a second-order transition has a discontinuity in the second derivative.</p>
<p>However, it then says </p>
<blockquote>
<p>Though useful, Ehrenfest's classification has been found to be an inaccurate method of classifying phase transitions, for it does not take into account the case where a derivative of free energy diverges (which is only possible in the thermodynamic limit).</p>
</blockquote>
<p>After this it lists various characteristics of second-order transitions (in terms of correlation lengths etc.), but it doesn't say how or whether Ehrenfest's definition can be modified to properly characterise them. Other online resources seem to be similar, tending to list examples rather than starting with a definition.</p>
<p>Below is my guess about what the modern classification must look like in terms of derivatives of the free energy. Firstly I'd like to know if it's correct. If it is, I have a few questions about it. Finally, I'd like to know where I can read more about this, i.e. I'm looking for a text that focuses on the underlying theory, rather than specific examples.</p>
<p>The Boltzmann distribution is given by $p_i = \frac{1}{Z}e^{-
\beta E_i}$, where $p_i$ is the probability of the system being in state $i$, $E_i$ is the energy associated the $i^\text{th}$ state, $\beta=1/k_B T$ is the inverse temperature, and the normalising factor $Z$ is known as the partition function.</p>
<p>Some important parameters of this probability distribution are the expected energy, $\sum_i p_i E_i$, which I'll denote $E$, and the "dimensionless free energy" or "free entropy", $\log Z$, where $Z$ is the partition function. These may be considered functions of $\beta$. </p>
<p>It can be shown that $E = -\frac{d \log Z}{d \beta}$. The second derivative $\frac{d^2 \log Z}{d \beta^2}$ is equal to the variance of $E_i$, and may be thought of as a kind of dimensionless heat capacity. (The actual heat capacity is $\beta^2 \frac{d^2 \log Z}{d \beta^2}$.) We also have that the entropy $S=H(\{p_i\}) = \log Z + \beta E$, although I won't make use of this below.</p>
<p>A first-order phase transition has a discontinuity in the first derivative of $\log Z$ with respect to $\beta$: </p>
<p><img src="http://i.stack.imgur.com/n5nNt.png" alt="enter image description here"></p>
<p>Since the energy is related to the slope of this curve ($E = -d \log Z / d\beta$), this leads directly to the classic plot of energy against (inverse) temperature, showing a discontinuity where the vertical line segment is the latent heat:</p>
<p><img src="http://i.stack.imgur.com/gvTuX.png" alt="enter image description here"></p>
<p>If we tried to plot the second derivative $\frac{d^2 \log Z}{d\beta^2}$, we would find that it's infinite at the transition temperature but finite everywhere else. With the interpretation of the second derivative in terms of heat capacity, this is again familiar from classical thermodynamics.</p>
<p>So far so uncontroversial. The part I'm less sure about is how these plots change in a second-order transition. My <em>guess</em> is that the energy versus $\beta$ plot now looks like this, where the blue dot represents a single point at which the slope of the curve is infinite:</p>
<p><img src="http://i.stack.imgur.com/j3btZ.png" alt="enter image description here"></p>
<p>The negative slope of this curve must then look like this, which makes sense of the comment on Wikipedia about a [higher] derivative of the free energy "diverging".</p>
<p><img src="http://i.stack.imgur.com/xEbg0.png" alt="enter image description here"></p>
<p>If this is what second order transitions are like then it would make quite a bit of sense out of the things I've read. In particular it makes it intuitively clear why there would be critical opalescence (apparently a second-order phenomenon) around the critical point of a liquid-gas transition, but not at other points along the phase boundary. This is because second-order transitions seem to be "doubly critical", in that they seem to be in some sense the limit of a first-order transition as the latent heat goes to zero.</p>
<p>However, I've never seen it explained that way, and I have also never seen the third of the above plots presented anywhere, so I would like to know if this is correct.</p>
<p>If it is correct then my next question is <em>why</em> are critical phenomena (diverging correlation lengths etc.) associated only with this type of transition? I realise this is a pretty big question, but none of the resources I've found address it at all, so I'd be very grateful for any insight anyone has.</p>
<p>I'm also not quite sure how other concepts such as symmetry breaking and the order parameter fit into this picture. I do understand those terms, but I just don't have a clear idea of how they relate to the story outlined above.</p>
<p>I'd also like to know if these are the only types of phase transition that can exist. Are there second-order transitions of the type that Ehrenfest conceived, where the second derivative of $\log Z$ is discontinuous rather than divergent, for example? What about discontinuities and divergences in other thermodynamic quantities and their derivatives?</p>
<p>Finally, as I said, I'd really appreciate pointers toward a good resource on this stuff, where the focus is on the behaviour of thermodynamic variables and statistical quantities near phase transitions in general, rather than on working through specific examples.</p> | g11739 | [
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-0... |
<p>I didn't have to take much physics for my advanced college degree, so I apologize if my question is painful.</p>
<p>From reading and experience it seems that water is a better thermal conductor than air. I wish to verify this as well as know how water compares against: alloys, pure metals, and oil.</p>
<p>If my question is too general, please school me on what additional knowledge I should know to ask a better question. :)</p>
<p><strong>Edit:</strong></p>
<p>So doing some searching, I found <a href="http://www.coolmagnetman.com/magcondb.htm" rel="nofollow">http://www.coolmagnetman.com/magcondb.htm</a> which gives a good break down of resistance of different metals. This lead me to some googling, which lead me to wikipedia's <a href="http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity" rel="nofollow">http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity</a> </p>
<p>The wiki looks to mention the water's resistance depends on the amount of salt, which makes sense, as I believe salt is an electrolyte. The wiki also has a reference of "drinking water" which is compared to the other types. It clearly looks to be that metal conducts better. From <a href="https://van.physics.illinois.edu/qa/listing.php?id=1854" rel="nofollow">https://van.physics.illinois.edu/qa/listing.php?id=1854</a> it looks like pure metals conduct better than alloys. I'm still not sure how oils fit in the comparisons though.</p> | g11740 | [
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0.06825834512710571,
0.012080899439752102,
0.007771903183311224,
0.... |
<p>How can I find the unit vector of a three dimensional vector? For example, I have a problem that I am working on that tells me that I have a vector $\hat{r}$ that is a unit vector, and I am told to prove this fact:</p>
<blockquote>
<p>$\hat{r} = \frac{2}{3}\hat{i} - \frac{1}{3}\hat{j} - \frac{2}{3}\hat{k}$</p>
</blockquote>
<p>I know that with a two-dimension unit vector that you can split it up into components, treat it as a right-triangle, and find the hypotenuse. Following that idea, I tried something like this, where I found the magnitude of the vectors $\hat{i}$ and $\hat{j}$, then using that vector, found the magnitude between ${\hat{v}}_{ij}$ and $\hat{k}$:</p>
<blockquote>
<p>$\left|\hat{r}\right| = \sqrt{\sqrt{{\left(\frac{2}{3}\right)}^{2} + {\left(\frac{-1}{3}\right)}^{2}} + {\left(\frac{-2}{3}\right)}^{2}}$</p>
</blockquote>
<p>However, this does not prove that I was working with a unit vector, as the answer did not evaluate to one. How can I find the unit vector of a three-dimensional vector?</p>
<p>Thank you for your time.</p> | g11741 | [
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0.028992531821131706,
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-0.053... |
<p>When you compute the average potential energy of a horizontal spring mass system from the mean position to the positive amplitude A, the value comes out to be $\frac{1}{6}kA^2$. For the average kinetic energy over the same range and direction, it is $\frac{1}{3}kA^2$, which is double the average potential energy. What the physical explanation of the different average values of PE and KE?</p>
<p>P.S. No mathematical explanations please, i.e. area under the graph, etc, only explanations in terms physics of the event are appreciated. The question does not involve time averages of PE and KE. Snapshots of derivations can be uploaded if requested.</p> | g11742 | [
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0.03001534193754196,
0.05141918733716011,
-0.06510801613330841,
0.02072470635175705,
-0.01427445001900196,
-0.042938731610774994,
0.071492500603199,
0.0015660... |
<p>According to <a href="http://en.wikipedia.org/wiki/Scale_invariance" rel="nofollow">this wikipedia article</a> in the $\phi^4$ section, the equation</p>
<p>$$\frac{1}{c^2}\frac{∂^2}{∂t^2}\phi(x,t)-\sum_i\frac{∂^2}{∂x_i^2}\phi(x,t)+g\ \phi(x,t)^3=0,$$</p>
<p>in 4 dimensions is invariant under</p>
<p>$$x\rightarrow \lambda\ x,$$
$$t\rightarrow \lambda\ t,$$
$$\phi\rightarrow \lambda^{-1}\ \phi.$$</p>
<p>I have a problem seeing this, which might be because I don't really know what to do with the derivatives. If I just replace $\phi(x,t)$ by $\lambda^{-1}\ \phi(\lambda x,\lambda t)$, then I get </p>
<p>$$\frac{1}{c^2}\lambda^2\lambda^{-1}\frac{∂^2}{∂(\lambda\ t)^2}\phi(\lambda x,\lambda t)-\lambda^2\lambda^{-1}\sum_i\frac{∂^2}{∂(\lambda\ x_i)^2}\phi(\lambda x,\lambda t)+\lambda^{-3} g\ \phi(\lambda x,\lambda t)^3=0,$$</p>
<p>which doesn't work out. </p>
<p>If I compare with <a href="http://en.wikipedia.org/wiki/Scale_invariance#Other_examples_of_scale_invariance" rel="nofollow">the last section</a> then this seems to be what one should do. Because In that case</p>
<p>$$x\rightarrow \lambda\ x,$$
$$t\rightarrow \lambda\ t,$$
$$\rho\rightarrow \lambda\ \rho,$$
$$u\rightarrow u,$$
and therefore the naviar stokes equation with
$$...+\rho\ u\ \nabla u+\mu\ \nabla^2 u+...$$
is such, that its invariant if the derivative produces an additional $\lambda$, the way I did above.</p>
<p>Sidenote: is <em>scale invariance</em> $\phi(x)=\phi^{-\Delta}(\lambda x)$ of fields something that should more acurately be called self similarity?</p>
<p>Also, I don't understand the last sentence in the $\phi^4$ paragraph, which says that the dimensionlessness of the coupling $g$ is "the main point". Why is it a problem to also scale the coupling? However, I never understood why dimensionless couplings are prefered anyway. If the coupling is somehow unique, then why does it make sense to search for a process dependend coupling in renormalization theory?</p> | g11743 | [
0.06722459197044373,
0.0018664207309484482,
-0.012833372689783573,
-0.055608030408620834,
-0.02134232223033905,
0.06878774613142014,
0.026582416146993637,
0.015700481832027435,
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0.029269222170114517,
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0.021983005106449127,
-0.028104977682232857,
0... |
<p>I would like to set up the equations of motion for a simple spring oscillator. </p>
<p>Let's have a spring lying horizontally; we attach a small mass $m$ to the (massless) spring. </p>
<p>The force of the spring on the mass is</p>
<p>$$F_\text{spring} = - k x$$</p>
<p>where $k$ is the spring constant, and $x$ is the displacement from the position of rest.</p>
<p>Since I am considering the system in motion, I only need to account for the kinetic friction.
I know that the magnitude for the kinetic friction is:</p>
<p>$$F_\text{fric} = F_g \mu$$</p>
<p>where $\mu$ is the coefficient of kinetic friction, $F_g$ equals the Normal Force on the surface and is also equal to the gravitational force.</p>
<p>But the direction of the force is always antilinear to the direction of motion. </p>
<p>How do I set this up correctly in my approach for the equations of motion?
My approach is</p>
<p>$$m a = -k x - \operatorname{sign}(x) F_\text{fric}$$</p>
<p>where $a$ is the acceleration of the mass point, and $\operatorname{sign}$ is the sign function.</p>
<p>Is this correct?</p> | g11744 | [
0.08606486767530441,
-0.004135896917432547,
-0.02552620880305767,
0.02381604164838791,
0.0384424664080143,
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0.06668839603662491,
0.0007537261699326336,
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-0.04526246339082718,
-0.009101004339754581,
0.010977024212479591,
0.03277665004134178,
0.0017... |
<p>In an x-ray tube, the atoms in the anode are ionized by incident electrons "knocking" their K-shell electrons out of orbit. Following this, an outer-shell electron decays to fill the vacancy. Now:</p>
<blockquote>
<p>An atom remains ionized for a very short time (about $10^{-14}$ second) and thus an atom can be repeatedly ionized by the incident electrons which arrive about every $10^{-12}$ second. (<a href="http://www.ndt-ed.org/EducationResources/CommunityCollege/Radiography/Physics/xrays.htm" rel="nofollow">NDT</a>)</p>
</blockquote>
<p>What causes the un-ionization, if there's another $10^{-12}$ second until the next incident electron arrives?</p> | g11745 | [
0.010046344250440598,
0.0946851596236229,
-0.00031210988527163863,
-0.02333301678299904,
0.04463347792625427,
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-0.03602519631385803,
0.033415742218494415,
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-0.016701726242899895,
0.00029853664455004036,
0.08948103338479996,
0.005516034550964832,
... |
<p>There are many classical systems with different potential functions. My problem is that I do not understand how one can construct a certain potential function for a certain system. Are there any references I can look up in order to understand how the potential functions must look for a system that I am interested in building?</p> | g11746 | [
-0.03819902241230011,
0.0593678243458271,
0.014132292941212654,
-0.010338949039578438,
0.0024117142893373966,
0.0024269912391901016,
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0.015027670189738274,
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-0.04127144813537598,
-0.03559594601392746,
0.022114016115665436,
0.060706425458192825,
0... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/6068/list-of-good-classical-physics-books">List of good classical physics books</a> </p>
</blockquote>
<p>my name is Bruno Alano. As stated in the title, <strong>I'm 15 years old</strong> (I'll do 16 on 7 of Feb) and much love <strong>Computer Science</strong> (C, C++), <strong>Mathematics</strong> and <strong>Physics</strong>.</p>
<p>Some information may have been unnecessary, but my question is: <strong>What is the suggestion of a good physics book for a teenager of my age?</strong> I know basic things (speed, shoveller these issues and basic primary and secondary).</p>
<p>A good reason for this is my Awe in mathematics and physics. Besides that maybe one day be useful in what I really want a career (science or computer engineering).</p>
<p><strong>And another question: It is interesting physics in the area I want to go? I'm at an age that would be good to learn beyond what is taught in common schools?</strong></p> | g98 | [
0.0056739263236522675,
0.0425448901951313,
0.01241138856858015,
-0.02069176733493805,
0.014893203042447567,
0.07381240278482437,
0.023201800882816315,
-0.018161145970225334,
0.013694294728338718,
-0.026414059102535248,
0.01626577600836754,
0.015272136777639389,
0.058915261179208755,
-0.021... |
<p>What is it that makes an electron maintain a distance from the positively charged nucleus? Why aren't electrons merely pulled into and absorbed by the nucleus ?</p> | g132 | [
0.008909366093575954,
0.03765905648469925,
-0.00640862574800849,
-0.017947925254702568,
0.050380829721689224,
0.03098057024180889,
-0.025145161896944046,
0.01590733230113983,
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-0.04854562506079674,
-0.017864620313048363,
-0.013676038943231106,
0.01753012277185917,
0.0... |
<p>I am trying to evaluate the <a href="http://en.wikipedia.org/wiki/Casimir_effect" rel="nofollow">Casimir force</a> using a Gaussian regulator (I know there are other much easier ways to do this, but I want to try this!) We then are reduced to evaluating the sum</p>
<p>$$ \sum\limits_{n=1}^\infty n e^{-\alpha n^2} $$ </p>
<p>Moreover, I am interested in the series expansion of the above sum around $\alpha = 0$. Any ideas how I would go about obtaining this sum?</p>
<p>PS - I don't want to use the Euler-Mclaurin formula.That was used to show that a general regulator would always give one the same answer, so this would just be a special case of the that proof and not a very novel way. Any other ideas?</p> | g11747 | [
-0.013820196501910686,
0.04118705913424492,
-0.020122624933719635,
-0.12221385538578033,
0.002690037479624152,
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0.031136060133576393,
0.03077133744955063,
0.007888969033956528,
0.0030398168601095676,
-0.03923426568508148,
0.05118635669350624,
-0.00010863979696296155,
... |
<p>We have known for some time now that when electric field is applied across any conducting shell, then electric field inside it would be zero. It also has some fantastic applications such as electrostatic shielding. </p>
<p>However, is it possible to know for sure that the field inside a conductor becomes zero? For example, if we place a transmitter inside a conducting shell to resolve whether the field inside shell is non-zero or otherwise, won't it disturb the field setup while transmitting the message?</p>
<p>In other words, is it possible to be sure about this effect for a uniform conducting shell, and similar closed-body structures? </p> | g11748 | [
-0.020970897749066353,
0.0189496036618948,
0.010880367830395699,
-0.05127616599202156,
0.10955102741718292,
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0.015456845052540302,
0.02538233995437622,
-0.024937769398093224,
-0.08748240768909454,
0.027617208659648895,
-0.013872714713215828,
-0... |
<p>I read the defination of spin stiffness <a href="http://en.wikipedia.org/wiki/Spin_stiffness#Mathematically" rel="nofollow">here</a></p>
<p><img src="http://i.stack.imgur.com/Odf86.png" alt="enter image description here"></p>
<p>But I can't understand how to twist an angle. Any help will be appreciated!</p> | g11749 | [
-0.00798994954675436,
-0.014517505653202534,
-0.02561705745756626,
-0.006629927549511194,
0.05744033679366112,
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0.0541529506444931,
0.04790796339511871,
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0.02235434018075466,
-0.02628178335726261,
0.010431553237140179,
-0.003324659774079919,
-0.0... |
<p>As far as I know things like rocks, walls, rubber balls, polished tables etc. exert a short range repulsive force on other everyday objects that is responsible for hardness, softness, collisions, friction etc.</p>
<p>Take a pair of electrically neutral solid materials. I am not interested in pairs of magnetic materials or astral bodies. Related to this I have a question:</p>
<p>Are there any such pairs with significantly longer range repulsions? So significant, in fact, that we can observe them repelling each other at large macroscopic scales. Could such materials have applications like anti-gravity?</p> | g11750 | [
0.06013651564717293,
0.09307755529880524,
0.006332483608275652,
-0.011262236163020134,
0.03831350430846214,
0.044323910027742386,
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-0.045356836169958115,
0.06331045925617218,
0.007937561720609665,
-0.007003823295235634,
-... |
<p>Suppose I have a two dimensional <em>classical</em> Dirac Hamiltonian with $\Psi=(\psi_1,\psi_2)^T$:
$$
H=\int \mathrm{d}x \mathrm{d}y \Psi^\dagger(\sigma^x i\partial_x+\sigma^y i\partial_y+m\sigma^z)\Psi.
$$
The partition function is given by
$$
Z=\int[\mathrm d\psi^\dagger][\mathrm d\psi]e^{-H}.
$$
How can I relate it to a (1+1)-dim <em>quantum</em> system? </p>
<p>A simple replacement $x\rightarrow t$ seems to be wrong. Because in the standard (1+1)-dim Dirac action, the time derivative term must be $\Psi^\dagger\partial_\tau\Psi$, i.e. with identity matrix in front of the time derivative, to ensure the conjugate momenta of $\Psi$ is just $i\Psi^\dagger$.</p> | g11751 | [
0.0193913746625185,
-0.0727924033999443,
-0.018030516803264618,
-0.01645941101014614,
0.012947400100529194,
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0.0615987665951252,
0.006158576346933842,
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-0.021825693547725677,
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0.00807299092411995,
-0.004065196495503187,
0.03483... |
<p>String Theory is formulated in 10 or 11 (or 26?) dimensions where it is assumed that all of the space dimensions except for 3 (large) space dimensions and 1 time dimension are a compact manifold with very small dimensions. The question is what is assumed about the curvature of the large 3 space and 1 time dimensions? If these dimensions are assumed to be flat, then how is String Theory ever able to reproduce the equations of General Relativity which require curved space time in the presence of mass-energy (of course, the actual source term for General Relativity is the stress energy tensor).</p>
<p>On the other hand if String Theory is formulated on a general curved space-time with an unknown metric (usually signified by $g_{\mu\nu}$) how do the equations of General Relativity that puts constraints on $g_{\mu\nu}$ arise from string theory?</p>
<p>It is well known that General Relativity requires a spin-2 massless particle as the "force mediation" particle (similar to the photon as the spin-1 massless force mediation particle of electromagnetism). It is also well know that String Theory can accommodate the purported spin-2 massless particle as the oscillation of a closed string. But how does this graviton particle relate to the curvature of the large dimensions of space-time?</p>
<p>I am aware that " <a href="http://physics.stackexchange.com/questions/30005/how-does-string-theory-predict-gravity">How does String Theory predict Gravity?</a> " is somewhat similar to this question, but I do not think it actually contains an answers to this question so please don't mark it as a duplicate question. I would especially appreciate an answer that could be understood by a non-theoretical ("String Theory") physicist - hopefully the answer would be at a level higher than a popular non-mathematical explanation. In other words, assume the reader of the answer understands General Relativity and particle physics, but not String Theory.</p>
<p><em>Update from Comment to Clarify: If you start with flat space then $g_{\mu\nu}$ isn't the metric tensor since you assumed flat space. If you start with arbitrarily curved space why would and how could you prove that the components of the graviton give you the metric tensor? I am interested in the strongly curved space case since that is where GR differs the most from Newtonian gravity. In flat space you could sort of consider weak Newtonian gravity to be the result of the exchange of massless spin-2 particles. But strong gravity needs actual space curvature to be equivalent to GR.</em></p> | g11752 | [
0.028379129245877266,
0.0016094776801764965,
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-0.022910598665475845,
0.008189531043171883,
0.059970561414957047,
0.03817074000835419,
0.002763439202681184,
-0.010012827813625336,
-0.01841207593679428,
-0.003548437962308526,
-0.01712249591946602,
0.08039668202400208,
-... |
<p><a href="http://io9.com/5744143/particles-can-be-quantum-entangled-through-time-as-well-as-space" rel="nofollow">http://io9.com/5744143/particles-can-be-quantum-entangled-through-time-as-well-as-space</a></p>
<p><a href="http://arxiv.org/abs/1101.2565" rel="nofollow">http://arxiv.org/abs/1101.2565</a></p>
<ol>
<li><p>How to make timelike entanglement in the laboratory?</p></li>
<li><p>How to test whether mixed state exist in time series or control system in math?</p></li>
</ol> | g11753 | [
-0.005648006685078144,
-0.013993495143949986,
0.011946863494813442,
-0.06433609127998352,
0.04620906338095665,
0.020679492503404617,
0.04923001304268837,
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0.012423387728631496,
0.009976614266633987,
0.01217646524310112,
-0.008513388223946095,
0.025921935215592384,
0.... |
<p>Normal-density materials have internal energy, which is the sum of the average energies associated to each of the degrees of freedom. Degrees of freedom can be described as vibrational, translational, and rotational. If you compress this material in such a way that matter cannot escape, you can detect energy escaping in the form of heat.</p>
<p>Now imagine an extremely high-density material such as a neutron star or black hole. I suspect it's not possible to describe the internal energy of (or anything about) an individual atom inside a black hole, since it's impossible to inspect beyond the event horizon, and since I assume that atoms don't exist in an distinguishable form there. But presumably the atoms <em>had</em> energy when they became part of the thing. How is that energy accounted for?</p> | g11754 | [
0.01482242438942194,
0.04687961935997009,
0.014360382221639156,
-0.025659197941422462,
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0.06503761559724808,
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-0.00580850662663579,
-0.008076655678451061,
-0.0024010397028177977,
-0.000661092868540436,... |
<p><em>Very unintuitive observation:</em></p>
<p>I pour myself a Guinness and the bubbles in my glass seem to move down toward the bottom of the glass instead of rising directly to the top of the glass as foam.</p>
<p>How can this be explained? Why is it that I observe this behavior drinking Guinness and not other carbonated drinks? What system properties (ie, temperature, nature of the solute and solvent) would affect this behavior?</p> | g11755 | [
0.001169603900052607,
0.02667248249053955,
0.007675073575228453,
0.044378072023391724,
0.052203234285116196,
0.06824687123298645,
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-0.02202201448380947,
0.027059318497776985,
0.010911171324551105,
0.04974282905459404,
0.03210... |
<blockquote>
<p>A small ball of mass $m$ is connected to one side of a string with
length $L$ (see illustration). The other side of the string is fixed
in the point $O$. The ball is being released from its horizontal
straight position. When the string reaches vertical position, it wraps
around a rod in the point $C$ (this system is called "Euler's pendulum").
Prove that the maximal angle $\alpha$, when the trajectory of the ball is still circular, satisfies the equality: $\cos \alpha = \frac{2}{3}$.</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/2HcJU.png" alt="Illustration"></p>
<p>In the previous part of the question, they asked to find the velocity at any given angle $\alpha$, and I solved it right using the law of conservation of energy:</p>
<p>$V_{\alpha}=\sqrt{gL(1-\cos\alpha)}$</p>
<p>Now, they ask to find the maximal angle at which the ball will still be in circular motion. The ball is in circular motion as long as the tension of the string is not zero. Therefore, we should see when the tension force becomes zero. So I did the following:</p>
<p>In the radial axis we have the tension force and the weight component (it might be negative - depends on the angle). So the net force in that direction equals to the centripetal force:
$T_{\alpha}+mg\cos\alpha=m \frac{V_{\alpha}^2}{L}$</p>
<p>If we substitute the velocity, we get:</p>
<p>$T_{\alpha}=m \left(\frac{V_{\alpha}^2}{L}-g\cos\alpha \right)=m \left[\frac{gL(1-\cos \alpha)}{L}-g\cos\alpha \right]=mg(1-2\cos\alpha)$</p>
<p>When the tension force becomes zero:</p>
<p>$0=1-2\cos\alpha\\
\cos\alpha=\frac{1}{2}
$</p>
<p>And that's not the right angle. So my question is - why? Where's my mistake? I was thinking that maybe I've got some problem with the centripetal force equation, but I can't figure out what's the problem. Or maybe the book is wrong? Thanks in advance.</p> | g11756 | [
0.09058386832475662,
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0.019129391759634018,
0.008099470287561417,
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0.008027431555092335,
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0.013289593160152435,
-0.04253228008747101,
-0.005255494266748428,
-0.013225940056145191,
-0.03... |
<p>I know many collaborations are attempting to detect the interaction of WIMPs with nucleons or with themselves, with the recent result from Ice Cube (<a href="http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.131302" rel="nofollow">http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.131302</a>) showing no evidence for WIMP self-interaction. I am wondering if WIMPs might actually have zero non-gravitational interaction with SM particles and zero self-interaction. Is such a thing possible or likely? If so, what sorts of theories predict such WIMP candidates, and could they be detected indirectly by other means (e.g., cosmological ratio of WIMP mass-energy to ordinary matter mass-energy, or something like that)? </p> | g11757 | [
0.01901215687394142,
0.011367080733180046,
0.03877164050936699,
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0.008828677237033844,
0.036940302699804306,
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0.004596109502017498,
-0.012915872037410736,
0.013445173390209675,
-0.05025992542505264,
0.03... |
<p>What are the ways to modify the form of magnetic field from the permanent magnet? For example I have a permanent neodymium magnet. Its magnetic field is distributed at large volume around the magnet, with decreasing strength at larger distances from the magnet. I'd like to make it concentrated in very small distances around this magnet, and to have no field or largely less strong field beyond some given distance from the magnet.
Is it possible at all, and if yes, how?</p> | g11758 | [
-0.0008735111332498491,
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0.016509167850017548,
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0.00948217324912548,
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0.03102441132068634,
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-0.06895509362220764,
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-0.039636000990867615,
0.05450912564992905,
... |
<p>In high energy physics there are different channels of particle production: t-channel, s-channel. What do they mean? And are there any other channels besides "t" and "s"?</p> | g11759 | [
0.019422467797994614,
0.08151135593652725,
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0.0022560397628694773,
0.05224916338920593,
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0.011238460429012775,
0.05096479505300522,
-0.0... |
<p>Is it possible, for the sake of argument, to launch a payload into an orbit around the earth by putting almost all the energy going at a 90 degree angle? What velocity would it take, and what horizontal orbital burns would you need?</p> | g11760 | [
0.012440708465874195,
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-0.011285532265901566,
-0.007710638456046581,
0.01652750000357628,
0.008500219322741032,
... |
<p>Is it possible to have a plasma made of polyatomic ions instead of monoatomic ions? </p>
<p>I want to know all the details why such a thing may be attainable or not and, if possible, what methods we can use to create such a substance.</p> | g11761 | [
0.042181942611932755,
0.041719283908605576,
-0.004435899667441845,
0.006937568541616201,
0.04936010017991066,
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0.00130533950868994,
-0.009798589162528515,
0.014264260418713093,
0.04029116407036781,
0.024444159120321274,
-0.0... |
<p>When some materials are chafed one to another, they obtain opposite electric charges. Does it mean that if these materials will then be connected to the ground, the direct currents of opposite direction will occur? And if we put some dc device like a lamp in the open of wire connecting statically charged material with the ground, should it light until the static charge is gone?</p> | g11762 | [
0.06984061747789383,
0.028181683272123337,
-0.010072646662592888,
-0.03533904254436493,
0.08722075819969177,
0.06639428436756134,
0.006423315964639187,
0.011077170260250568,
-0.03884370997548103,
0.01872383989393711,
-0.044139765202999115,
0.00405047507956624,
0.014665222726762295,
0.02435... |
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