question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
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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 $t$.</... | 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 k... | 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 ... | 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.<... | 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 ... | 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 ve... | 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 th... | 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 cor... | g11675 | [
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<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... | 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 o... | g11677 | [
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<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 b... | 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 ... | 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... | 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... | 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... | 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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<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 so... | g11686 | [
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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 equatio... | g11687 | [
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<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 | [
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<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 physicall... | g11689 | [
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<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 constru... | g11690 | [
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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 o... | g11691 | [
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<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 | [
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<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 ... | g11693 | [
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<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 $d-n(2-d)/2$.... | g11694 | [
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<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 ... | g11695 | [
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<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 | [
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<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 co... | g11697 | [
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<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 ... | g11698 | [
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0.029597684741020203,
0.04455699771642685,
0.06686731427907944,
-0.046384382992982864,
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0.04113141819834709,
-0.08008215576410294,
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 y... | g11699 | [
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0.028718311339616776,
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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="schem... | g11700 | [
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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 e... | g11701 | [
0.010699625127017498,
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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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<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, e... | g234 | [
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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... | g11703 | [
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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, fro... | g11704 | [
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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 achiev... | g11705 | [
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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 &... | g11706 | [
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0.08762851357460022,
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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 | [
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<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 w... | g11708 | [
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<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... | g11709 | [
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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 ... | g11710 | [
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0.02747640758752823,
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-0.... |
<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.wikipedi... | g11711 | [
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-0.0... |
<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... | g11712 | [
0.014806486666202545,
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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 ... | g11713 | [
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0.028718583285808563,
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-0.004... |
<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-... | g11714 | [
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<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... | g11715 | [
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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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0.07868171483278275,
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... | g11718 | [
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0.05029427632689476,
0.04282936826348305,
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0.03... |
<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 | [
0.011036088690161705,
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0.017956597730517387,
0.03169296309351921,
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0.... |
<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>
<blo... | g11721 | [
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-0.0118... |
<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-Fo... | g11722 | [
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0.021734554320573807,
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 a... | 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 ... | 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 rotatio... | g11726 | [
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<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 = .002... | g11727 | [
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<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 t... | g11728 | [
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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 perio... | g11729 | [
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... |
<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/~minwal... | g371 | [
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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}... | g11730 | [
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<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 | [
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<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_lum... | g11732 | [
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<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>
</blockquot... | g11733 | [
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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>
</blockq... | g11734 | [
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<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... | g11735 | [
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<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... | g11736 | [
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<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 th... | g11737 | [
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<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}}$$</p>
<p>Is there a general formula to compute the luminosity distance $D_{L}$ from $D_{A}$ without assuming an homogeneous cosmology ?</p> | g11738 | [
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<p>Recently I've been puzzling over the definitions of first and second order phase transitions. The <a href="https://en.wikipedia.org/wiki/Phase_transition#Classifications" rel="nofollow">Wikipedia article</a> (at the time of writing) starts by explaining that Ehrenfest's original definition was that a first-order tra... | g11739 | [
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<p>I didn't have to take much physics for my advanced college degree, so I apologize if my question is painful.</p>
<p>From reading and experience it seems that water is a better thermal conductor than air. I wish to verify this as well as know how water compares against: alloys, pure metals, and oil.</p>
<p>If my qu... | g11740 | [
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0.... |
<p>How can I find the unit vector of a three dimensional vector? For example, I have a problem that I am working on that tells me that I have a vector $\hat{r}$ that is a unit vector, and I am told to prove this fact:</p>
<blockquote>
<p>$\hat{r} = \frac{2}{3}\hat{i} - \frac{1}{3}\hat{j} - \frac{2}{3}\hat{k}$</p>
</... | g11741 | [
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<p>When you compute the average potential energy of a horizontal spring mass system from the mean position to the positive amplitude A, the value comes out to be $\frac{1}{6}kA^2$. For the average kinetic energy over the same range and direction, it is $\frac{1}{3}kA^2$, which is double the average potential energy. Wh... | g11742 | [
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0.0015660... |
<p>According to <a href="http://en.wikipedia.org/wiki/Scale_invariance" rel="nofollow">this wikipedia article</a> in the $\phi^4$ section, the equation</p>
<p>$$\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... | g11743 | [
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0.029269222170114517,
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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... | g11744 | [
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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 r... | g11745 | [
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<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... | g11746 | [
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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 ... | g98 | [
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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 | [
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<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>$$ \sum\limits_{n=1}^\infty n e^{-\alpha n^2} $... | g11747 | [
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0.0030398168601095676,
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0.05118635669350624,
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... |
<p>We have known for some time now that when electric field is applied across any conducting shell, then electric field inside it would be zero. It also has some fantastic applications such as electrostatic shielding. </p>
<p>However, is it possible to know for sure that the field inside a conductor becomes zero? For... | g11748 | [
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<p>I read the defination of spin stiffness <a href="http://en.wikipedia.org/wiki/Spin_stiffness#Mathematically" rel="nofollow">here</a></p>
<p><img src="http://i.stack.imgur.com/Odf86.png" alt="enter image description here"></p>
<p>But I can't understand how to twist an angle. Any help will be appreciated!</p> | g11749 | [
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0.010431553237140179,
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<p>As far as I know things like rocks, walls, rubber balls, polished tables etc. exert a short range repulsive force on other everyday objects that is responsible for hardness, softness, collisions, friction etc.</p>
<p>Take a pair of electrically neutral solid materials. I am not interested in pairs of magnetic mater... | g11750 | [
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0.06331045925617218,
0.007937561720609665,
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<p>Suppose I have a two dimensional <em>classical</em> Dirac Hamiltonian with $\Psi=(\psi_1,\psi_2)^T$:
$$
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 relat... | g11751 | [
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0.00807299092411995,
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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 dimension... | g11752 | [
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<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... | g11753 | [
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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 escapin... | g11754 | [
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-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 ca... | g11755 | [
0.001169603900052607,
0.02667248249053955,
0.007675073575228453,
0.044378072023391724,
0.052203234285116196,
0.06824687123298645,
0.05445321276783943,
0.044937316328287125,
-0.022376399487257004,
-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 p... | g11756 | [
0.09058386832475662,
-0.03420504555106163,
0.019129391759634018,
0.008099470287561417,
0.04407339543104172,
0.017971446737647057,
0.0632825493812561,
0.008027431555092335,
-0.060577236115932465,
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>) show... | g11757 | [
0.01901215687394142,
0.011367080733180046,
0.03877164050936699,
-0.041761841624975204,
-0.005213318392634392,
-0.0435650497674942,
0.008828677237033844,
0.036940302699804306,
-0.02834094688296318,
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 distance... | g11758 | [
-0.0008735111332498491,
-0.022213609889149666,
0.016509167850017548,
-0.03608420491218567,
0.00948217324912548,
0.04102551192045212,
0.008153033442795277,
0.03102441132068634,
0.000014951632692827843,
-0.06895509362220764,
-0.037693314254283905,
-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,
-0.011358194053173065,
0.0022560397628694773,
0.05224916338920593,
0.0039037943352013826,
-0.024297967553138733,
0.07354605197906494,
-0.02020997367799282,
-0.03874657675623894,
-0.04737947881221771,
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,
0.058442968875169754,
0.026400629431009293,
0.024867108091711998,
-0.046528466045856476,
0.0046356855891644955,
-0.02499600686132908,
-0.0040687196888029575,
-0.028527120128273964,
-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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-0.07489971816539764,
0.004668809939175844,
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 wi... | 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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