question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
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<p>The old saying goes, nature abhors a vacuum, but that isn't exactly true. The universe is <em>full</em> of vacuum; what nature abhors large energy differentials.</p>
<p>So for example, a vacuum chamber has to be strong enough to withstand the ~101kPa of pressure on the surface, and typically the materials required ... | g16665 | [
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<p>I have a stupid question about Eq. (1.3.22) in Polchinski's string theory volume 1.
In the equation of motion for an open string, Eq. (1.3.22), </p>
<p>$$X^i (\tau, \sigma) = x^i + \frac{ p^i}{p^+} \tau + i \bigl(2 \alpha'\bigr)^{1/2} \sum_{\substack{n= -\infty,\\n\neq0}}^{\infty} \frac{1}{n} \alpha_n^i \exp\bigg... | g16666 | [
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<p>When you stand on a bathroom scale, I know that the force displayed is the normal force. Since it is the normal force, then technically the force displayed would actually be Fg= (mass)(acceleration) right? If this is true, then why is it that your normal force changes in an elevator? (i.e. if you travel down an elev... | g16667 | [
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<p>No long explanation is needed,</p>
<p>What would happen if I were to allow one end of a rope to fall past the event horizon of a black hole while I held the other end?</p>
<p>Would I be able to pull it out? Would the rope feel extremely (infinitely?) heavy? </p> | g16668 | [
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<p>I have doubts with the solution of a certain problem. I will give the entire solution below and will lay out my doubts as well.<br><br>
A point mass $m_1$ is separated by a distance $r$ from a long rod of mass $m_2$ and length $L$.The objective is to find the total gravitational force exerted by the rod on the point... | g16669 | [
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<p>We have all learned that the earth is getting heat up because of the CO<sub>2</sub> and CO molecules absorbing heat. However, how is heat actually kept in those molecules. When photons heat them up, their electron gets excited and goes to a higher energy level; however, we know that atoms want to remain at a low ene... | g504 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/6646/physics-of-simple-collisions">Physics of simple collisions</a> </p>
</blockquote>
<p>I have looked around the internet and gradually built up a better understanding. However I'm still not 100% clear... | g287 | [
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<p>I came by some graphs showing the declination for sun and moon (between angles of -30° and +30°). The graphs look very much like sine waves. </p>
<p>I googled a bit and read about what the declination is, and I found tools to look up the declination for a certain date. However, what I really haven't understood yet ... | g16670 | [
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<p>I know that the field inside a dielectric is changed and is $\epsilon$
times less the original field (some books use $K$ for this constant).</p>
<p>This is because the induced field inside the dielectric is in opposite
direction to the original field.</p>
<p>But what happens to the field after it passes the dielec... | g16671 | [
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<p>I find plane waves are uncompatible with light cone.</p>
<p>Perhaps plane waves are "virtual" and can never be measured
in that case, shouldn't we call plane waves as "virtual plane waves"?
(other option could be that plane waves allows waves travel faster than c)</p>
<p>I would like to clarify this point through ... | g16672 | [
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<p>I have a question about the Lorentz force on a charge $q$:</p>
<p>$$\mathbf{F}=q(\mathbf{E}+\mathbf{v}\times\mathbf{B}).$$</p>
<p>I understand that if one performs a Lorentz boost then the electric field $\mathbf{E}$, magnetic field $\mathbf{B}$ and the velocity of the particle $\mathbf{v}$ will all change.</p>
<... | g16673 | [
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<p>Imagine we are plotting some date points $\left(x_i,f(x_i)\right)$ that we obtained experimentally, and that we want to know what $f(x)$ is.
The way to do this is to use some software and try to fit the data to some guessed function. For example, if the behavior of the data points looks like exponential decay we th... | g16674 | [
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<p>To focus this question let us consider first classical mechanics (which is time-symmetric). Given a final condition (and sufficient information) one can calculate the system conditions of an earlier time (retrodiction).</p>
<p>Given Quantum Mechanics (which is time-symmetric) and a final condition what is the statu... | g16675 | [
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<p>As I understand, the hydrogen is produced by water thermolysis, which need quite high temperature. This temperature is close to previously observed corium temperatures. So:</p>
<ol>
<li>Is the eutectic temperature of the corium of those type of reactors known and publicly accessible?</li>
<li>Isn't the hydrogen pre... | g16676 | [
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<p>Given an uncharged continuum the EM field produces no force on it. Yet in a discrete system we know that atoms are not uncharged locally and momentum can be exchanged due to the electric field(Which Maxwell's equations are suppose to govern).</p>
<p>viz., The transfer of momentum between atoms is due to the electri... | g16677 | [
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<p>I was told that "Snell's law of refraction implies that a light ray in an isotropic medium travels from point a to point b in stationary time." Why is this true?</p>
<p>Thanks.</p> | g16678 | [
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<p>For a molecule with spherical symmetry, the energy level of rotation for quantum number $J$ is:</p>
<p>$$E(J)=\frac{J(J+1)\hbar^2}{8\pi^{2}I}$$</p>
<p>"$I$" is the Moment of inertia for the molecule ($I_{x}=I_{y}=I_{z}$ for a molecule with spherical symmetry)</p>
<p>For an asymmetric molecule however, $I_x$, $I_y... | g16679 | [
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<p>In my syllabus about solid state physics they state that lattice vibration is quantized, analogous to the harmonic oscillator:
$$E = (n+\frac{1}{2})\hbar\omega$$
So the lattice vibration has zero-point energy $\frac{1}{2}\hbar\omega$.</p>
<p>I wonder what this actually means: are all possible vibration modes of the... | g16680 | [
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<p>Consider a body which can freely rotate with respect to the inertial frame, and a rotating disk whose axis is fixed in body frame. </p>
<p>When applying the lagrangian method (does that make a difference?), is the kinetic energy of the disk with respect to the body frame (for constant disk rotation rate, the kineti... | g16681 | [
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<p>In reading Goldstein's Classical Mechanics (2nd edition) I came across a confusing derivation. Goldstein (Eq. 1-71) derives the total kinetic energy of a system of (classical) particles as:</p>
<p>$$ T = \sum_i \frac{1}{2}m_iv_i^2 = \sum_i \frac{1}{2}m_i \left( \sum_j \frac{\partial \mathbf{r}_i}{\partial q_j} \dot... | g16682 | [
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<p>Suppose I cook a stew or soup and then take it off of the stove and leave it uncovered to cool. Of course, it will cool faster if I stir it (more surface area), but it will, eventually, cool to room temperature even if I leave it alone. As it cools, it loses liquid to evaporation — steam rises from it — ... | g16683 | [
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<p>Let us assume a cartesian space, where the directions are given by $\hat{i},\hat{j},\hat{k}$.
The degree of freedom of a rigid body is $6$. The first three correspond to the position coordinates $\left(x,y,z\right)$, and the next three correspond to the velocity coordinates $\left(\dot{x},\dot{y},\dot{z}\right)$. S... | g16684 | [
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<p>Suppose I have a function $f = xy$. A partial derivative of $f$ with respect to $x$ implies holding $y$ constant: </p>
<p>$$ \frac{\partial f}{\partial x} = y $$</p>
<p>Does this mean that in order to evaluate this derivative, $y$ cannot depend on $x$? For example, if $y = x$ then </p>
<p>$$ \frac{\partial f}{\pa... | g505 | [
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<p>This is a simple question. Please forgive me, as I am a lowly experimentalist.</p>
<p>Suppose we have two free spin 1/2 particles, i.e. a 4-fold degenerate system. What is the set of symmetry operations on this system? Is it $SU(2) \times SU(2)$, $SU(4)$, or something else? Or am I misunderstanding all of this ... | g16685 | [
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<p>The <a href="http://www.google.com/search?as_q=walecka+model" rel="nofollow">Walecka</a> or $\sigma$/$\omega$-model is an effective theory describing nucleon-nucleon interaction by an exchange of $\sigma$/$\omega$-mesons. Why does it not include interactions by pions?</p> | g16686 | [
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<p>I tried to mimic the mechanism of typical screens to produce white color out of red, green and blue.</p>
<p>What I did is displayed the attached image on the screen, and moved far away as to let the diffraction effects take place, so that the three colors appear as if they're coming from the same point.</p>
<p>Non... | g16687 | [
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<p>"The best understanding we have is that it [light] is a disturbance in the electromagnetic fields of charged bodies."
<a href="http://einstein.stanford.edu/content/relativity/q212.html" rel="nofollow">http://einstein.stanford.edu/content/relativity/q212.html</a></p>
<p>This is a link to the most recent report I cou... | g16688 | [
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<p>I've been thinking about batteries a whole lot, and I've uncovered why the battery symbol looks like a pair of cap-like things in circuit diagrams: it's modeled as two cap-like things using an equivalent circuit diagram:<img src="http://i.stack.imgur.com/3zCA9.png" alt="enter image description here"></p>
<p>We see ... | g16689 | [
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<p>I might be raising measurement problem in quantum physics in different words, but I will ask the question.</p>
<p>Quantum decoherence has been proposed by proponents as a theory that eliminates all weird issues involving quantum mechanics, such as Schrodinger's cats and measurement problem.</p>
<p>So in quantum de... | g16690 | [
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<p>People usually don't carry pure gold and silver coins in their wallets.</p>
<p>If I put some in my wallet, would it be likely that airport security would detect some anomaly with my wallet as compared to other wallets?</p>
<p>Can physics answer this?</p> | g16691 | [
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0.0044... |
<p><a href="http://en.wikipedia.org/wiki/X-ray_telescope" rel="nofollow">X-ray telescopes</a> are required to be above the atmosphere as the atmosphere blocks EM waves with wavelengths < UV . Does this mean that the Earth's atmosphere can be thought of as a Faraday cage only allowing low energy light to pass through... | g16692 | [
-0.021059058606624603,
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0.012229053303599358,
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0.0051984041929244995,
-0.037973545491695404,
0.08170261979103088,
0.05634832754731178,
0.0012922764290124178,
-0.... |
<p>First, we consider the time independent Schrodinger equation of the form:
$$\bigg(-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+u(x) \bigg)\phi_A(x)=E_A\phi_A(x)$$
Where $u(x)$ is a potential created by a single ion (of a one dimensional single ion crystal lattice). Then now we expand the case from a single ion case to a $M$... | g16693 | [
-0.01247546635568142,
0.06299521774053574,
-0.012176408432424068,
-0.01646832935512066,
0.005292093846946955,
-0.0037245876155793667,
0.0031428083311766386,
0.052923690527677536,
0.028647758066654205,
0.012909168377518654,
0.048756614327430725,
0.045979540795087814,
-0.008576193824410439,
... |
<p>Telescopes with adaptive optics (AO) have been in use for several decades. To my knowledge, the lowest wavelengths utilized are in the near-infrared. It's known that Fried parameters are smaller for visible versus infrared ranges.</p>
<blockquote>
<p>Are there any earth-based observatories utlizing AO in the visi... | g16694 | [
-0.00481317238882184,
-0.03068533167243004,
-0.017711615189909935,
0.019210081547498703,
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0.007442009169608355,
0.016071872785687447,
0.06436959654092789,
0.04463066905736923,
0.06384886056184769,
0.05707387626171112,
0.036109622567892075,
0.035... |
<p>Is there some book or paper that formalizes statistical mechanics, like some people have done with relativity, and proves <a href="http://en.wikipedia.org/wiki/Second_law_of_thermodynamics" rel="nofollow">the second law of thermodynamics</a> from more foundational axioms?</p> | g232 | [
0.08844773471355438,
0.040691182017326355,
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0.01325287576764822,
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0.015044057741761208,
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-0.008865142241120338,
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0.05666661635041237,
-0.... |
<p>Classically, we know from $\mathbf{F}=q\mathbf{v}\times \mathbf{B}$ that magnetic field does no work on a charged particle. In quantum mechanics, the Hamiltonian of a charged particle in a magnetic field is given by </p>
<p>$$\hat{H}~=~\frac{1}{2m} \left[\frac{\hbar}{i}\vec\nabla - \frac{q}{c}\vec A\right]^2.$$</p>... | g16695 | [
0.004362326115369797,
0.03467723727226257,
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0.10636522620916367,
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0.010436803102493286,
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0.03696228563785553,
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-0.007769... |
<p>It's almost impossible to balance on a single ice skate if you're standing still. But give yourself just a little forward motion—it doesn't take very much—and it suddenly becomes easy. You can stand there on one leg and glide effortlessly half way across the rink. Friction will cause you to gradually slow down, a... | g16696 | [
0.037816133350133896,
0.06967318803071976,
0.0195437204092741,
0.08013531565666199,
0.04921349138021469,
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0.06000596284866333,
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-0.04791327565908432,
-0.05821075290441513,
-0.04459318146109581,
-0.023051... |
<p>Why do we always classify states under covering group representations instead of the group itself? For example see the following picture I lifted from <a href="http://www.jptp.uni-bayreuth.de/vorlesungen/symmetry.pdf">'Symmetry in physics' by Gross</a></p>
<p><img src="http://i.stack.imgur.com/JLJMs.jpg" alt="enter... | g16697 | [
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0.00710874330252409,
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0.027417544275522232,
0.02... |
<p>The textbook(F.A.Jenkins and H.E.White <strong><em>Fundamentals of Optics</em></strong>) states that the <a href="http://en.wikipedia.org/wiki/Fermat%27s_principle" rel="nofollow">Fermat's principle</a> is that </p>
<blockquote>
<p><em>the path taken by a light ray in going from one point to another through any s... | g16698 | [
0.03278094157576561,
0.013766933232545853,
0.007359711453318596,
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0.03325415030121803,
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0.029349463060498238,
0.01757175661623478,
0.006... |
<p>I have seen that one can make an operator with
$$
L^i=\epsilon^{ijk}x_{j}\partial_{k}
$$
But what if I want to make instead items that are sums, instead of differences. For instance
$$\mathcal{L}^z=x\partial_y +y\partial_x$$
Is there an object like $|\epsilon_{ijk}|$ that has only 1s (no -1s)?</p>
<p>Thanks,</p> | g16699 | [
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0... |
<p>In my question "<a href="http://physics.stackexchange.com/q/47737/55">Resonance in a 1 ft granite box</a>", someone answered that my granite box (a one foot cube) would make a very poor resonator, which makes me ask what characteristics make a good resonator? Is there a difference between a cube or other rectangular... | g16700 | [
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0.00990876741707325,
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... |
<p><img src="http://i.stack.imgur.com/mjhTo.jpg" alt="enter image description here">
Looking at the above photo, you will soon find it is impossible to explain what actually happens (with today's physics),
in one word star is like a nuclear fusion bomb which its pressure is in balance against gravitational force.</p>... | g16701 | [
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0.029791690409183502,
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-0.0... |
<p>I'm currently struggling to understand the physics behind this question (purely because our lecture hasn't given us proper grounding in quantum mechanics). In a double slit experiment, you are given $\psi_1= A_1e^{-i(ky-wt)/\sqrt{1+y^2}}$ and $\psi_2 = A_2e^{-i(ky+\pi y-wt)/\sqrt{1+y^2}}$ where $A_1$ and $A_2$ are n... | g16702 | [
0.005869563668966293,
0.01174101885408163,
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0.07249127328395844,
0.059245459735393524,
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0.012861140072345734,
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0.017817024141550064,
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0.... |
<p>All of the force-particles in the standard model are bosons, now my question is pretty short, namely:</p>
<blockquote>
<p><em>Why are all force particles bosons?</em></p>
</blockquote>
<p>This can't be a coincidence.</p> | g670 | [
0.06477750837802887,
0.04102017730474472,
0.03753577917814255,
0.0018019411945715547,
0.09786581993103027,
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0.02180051989853382,
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<p>Why aren't all spinning galaxies shaped as discs as my young mind would expect? I understand how the innermost parts of a galaxy spin faster than the outer parts, and that could explain why some galaxies are more spiraled than others based on age. Though, this doesn't explain how the arms came into existence in the ... | g16703 | [
0.03313726559281349,
0.007908106781542301,
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0.003200580831617117,
0.0761866420507431,
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0.019635459408164024,
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0.0012269651051610708,
-0.04152238741517067,
0.015771061182022095,
0.03474502... |
<p>I have a question about derivation 11.2.10 in Wald (page 289). Here is a screenshot of the relevant passage: </p>
<p><img src="http://i.stack.imgur.com/UI69w.png" alt="Wald p289"></p>
<p>I don't get the step $$-\frac{1}{4\pi}\int _{\Sigma}R^{d}{}{}_{f}\xi^{f}\epsilon_{deab} = \frac{1}{4\pi}\int _{\Sigma}R_{ab}n^{a... | g16704 | [
-0.0027092364616692066,
0.015221310779452324,
-0.02246876247227192,
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0.058257751166820526,
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0.044619765132665634,
0.06429450213909149,
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-0.03291231393814087,
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0.02225351892411709,
0.0263605285435915,
0.013... |
<p>I was playing a table-top rpg with a friend. It was set... well it was pretty weird, so I won't get into it. Suffice it to say the bad guy had a stick of dynamite and we were on a volcano. I hit the dynamite with my slingshot, knocking it into the lava directly behind the villain. My DM said the dynamite melts away.... | g16705 | [
0.031626373529434204,
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0.023619046434760094,
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0.013014350086450577,
0.02146471105515957,
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0.014352922327816486,
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0.0019368109060451388,
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-0.00992107018828392,
0.003276937175542116,
... |
<p>The use of imaginary and complex values comes up in many physics and engineering derivations. I have a question about that: <strong>Is the use of complex numbers simply to make the process of derivation easier, or is it an essential ingredient, without which it would be impossible to derive some results?</strong> </... | g560 | [
0.010430609807372093,
0.002909861970692873,
0.012178357690572739,
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0.0011688466183841228,
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0.0006634046440012753,
0.04709431156516075,
0.013475772924721241,
-0.00953733455389738,
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0.05307689309120178,
... |
<p>Imagine an astronaut floating in free-space with no significant nearby gravitational influences. The astronaut takes an arbitrarily thin pole of uniform density with length $l$ and mass $m$, orients it vertically from his perspective, and then positions it some distance $h$ in front of him. </p>
<p>Finally, once ... | g16706 | [
0.038346003741025925,
0.08447857946157455,
-0.01152125559747219,
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0.05922471359372139,
0.025289926677942276,
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0.011236761696636677,
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0.027096422389149666,
-0.0... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/14255/experimental-evidence-for-parallel-universes">Experimental evidence for parallel universes</a> </p>
</blockquote>
<p>Is there an universe similar to ours somewhere else, I mean I had heard from Ein... | g255 | [
0.054130446165800095,
0.05552857369184494,
0.0341678149998188,
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0.00988201517611742,
0.010576550848782063,
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0.03644447401165962,
0.04415631666779518,
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0.025834744796156883,
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0.051190... |
<p>I believe it is only a technical question. However I cannot realize it. It is said in 2d spacetime the gauge fields $A_\mu$ can be rewritten in lightcone coordinates as $A_+=ig\partial_+g^{-1}$ and $A_-=ih\partial_-h^{-1}$, where $g$ and $h$ are the elements of the gauge group.</p>
<p>Anyone could give me a simple ... | g16707 | [
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0.0012770338216796517,
0.008679226040840149,
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0.002487616380676627,
-0.... |
<p>How Newton found Gravitational acceleration (g) of The Earth?</p>
<p>Can you describe the methods to find and prove it(g value)? </p>
<p>(may be describe both classical methods and modern methods)</p> | g16708 | [
0.09444853663444519,
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0.04202045500278473,
0.04... |
<p>Is all of the visible Universe exactly the same age everywhere? What about the Universe beyond what we can see?</p> | g16709 | [
0.014633743092417717,
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0.04766806960105896,
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0.045616425573825836,
... |
<ol>
<li>What is a quark condensate? is it a bound state between 2 quarks? can we have 3(or more)-quarks condensate?</li>
<li>What mediates the interaction between the constituents of the condensate?</li>
<li>Are the constituents of the condensate always fermions?</li>
</ol> | g16710 | [
0.01462537981569767,
0.01652468927204609,
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0.011200694367289543,
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0.007471758406609297,
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0.02... |
<p>It will probably depend on the size of the pieces... but at what point should I stop assuming a linear relationship?</p>
<p>I was prompted to ask in <a href="http://physics.stackexchange.com/questions/13595/where-does-the-excess-energy-emitted-by-a-microwave-go">a previous question</a>.</p> | g16711 | [
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0.034004513174295425,
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0.... |
<p>A motorcycle is known to accelerate from rest to 190km/h in 402m.</p>
<p>Considering the rate of acceleration is constant, how should I go about calculating the acceleration rate and the time it took the bike to complete the distance?</p> | g16712 | [
0.04171357676386833,
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0.00714494101703167,
0.04159804433584213,
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0.018465202301740646,
0.09027025103569031,
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0.005441819783300161,
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-0... |
<p>Well, the question has somewhat been answered before, but there's one part missing, which - I'd think - is in conflict with the physical laws.</p>
<p>The earlier reply says that the gravitational pull even at the event horizon is so big, that not even the other forces can overcome this. So far, so good...this part ... | g16713 | [
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0.04538561403751373,
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0.05736468359827995,
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0.006002083420753479,
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-0... |
<p>I'm toying with an infrared thermometer - one which you point onto an object, press the button and it instantly measures the temperature by estimating the infrared radiation from the object. It shows more or less the room temperature when I point it to things in the room.</p>
<p>Now I open the window. The temperatu... | g16714 | [
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0.022619109600782394,
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0.02874913066625595,
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0.026396499946713448,
0.036004893481731415,
0.00533584738150239,
0.052... |
<p>On electric circuits, with $120$ or $230$ AC mains, there are the wires Live and Neutral.
The wiring isn't symmetrical : following the circuit, you cannot switch $L$ and $N$.</p>
<p>However, in Italy, sockets and plugs don't have a specific orientation : it is a matter of how the user push the plug in the socket.
... | g16715 | [
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0.007060745730996132,
0.005087269935756922,
0.025577900931239128,
0.011801040731370449,
... |
<p>What do we really mean when we say that the neutron and proton wavefunctions together form an $SU(2)$ doublet? What is the significance of this? What does this transformation really doing to the wavefunctions (or fields)?</p> | g16716 | [
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0.02956356666982174,
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<p>I'm trying to solve for the motion of a particle, accounting for both viscous and drag forces. (There is no potential)</p>
<p>The total resistance by medium is modeled by:</p>
<p>$\vec{F}=-(\mu_1v + \mu_2v^2)\hat{v} $</p>
<p>Where $v$ is the velocity; There is no potential.</p>
<p>I need to set up the Lagrangian... | g16717 | [
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0.0... |
<p>If you turn on a fluorescent tube-lamp, it flickers before lighting up.<br>
If you then turn it off and turn it back on after 2 seconds, this time it doesn't flicker but lights up straight away.<br>
If you wait for some time (say 10 minutes) and switch on the light again, it flickers before lighting-up, again.</p>
... | g16718 | [
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0.06027644872665405,
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-0.04233633726835251,
-0.00679134763777256,
0.04051170498132706,
0.01107736211270094,
-0.0025... |
<p>While the gases are present in very different abundances, and the atmospheres have very different pressures, Earth, Mars and Venus all have a similar cast of gases: nitrogen, argon, CO2, others in trace amounts. </p>
<p>I've asked an earth scientist friend and his short answer was "volcanoes." I'm afraid I don't kn... | g16719 | [
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-0.0606168657541275,
0.0029368631076067686,
-0.01867409609258175,
0.06983964145183563,
0.022... |
<p>My Question goes like this:
If a mosquito inside the bus wants to move from back to front, will there be any difference if the bus is stationary or moving (ie extra effort in the latter case?)? Consider it as a closed bus & mosquito at a fixed point in bus, ie the air column will be constant throughout the proce... | g506 | [
0.01038165669888258,
-0.03782512992620468,
0.02860984206199646,
0.040377967059612274,
0.06389521807432175,
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0.052515946328639984,
0.016576198861002922,
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-0.07367639988660812,
0.012495866045355797,
0.03155510127544403,
-0.09951864928007126,
0.00123... |
<p>I found this formula (I dont know its name) and I'm trying to apply it in order to find the last position given a time and velocity.</p>
<p>$ s = s_0 + v_0 \cdot t + \frac{1}{2} \cdot a \cdot t² $</p>
<p>given</p>
<p>$ t = 3h $</p>
<p>$ v = 100km/h $</p>
<p>$ a= \frac{v}{t} $</p>
<p>results</p>
<p>$
s = 0 + 0... | g16720 | [
0.06907353550195694,
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0.016110839322209358,
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<blockquote>
<p><em>Any 3d TQFT (topological-quantum-field-theory) associates a number to a closed oriented 3-manifold, a vector space to a Riemann surface, a category to a circle, and a 2-category to a point.</em></p>
</blockquote>
<p>This is properly well-known in category theory. I learned it from <a href="http:/... | g16721 | [
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<p>I have a cylinder full of water with diameter $D$ with a round opening on the bottom with diameter $d$. The water is friction-free and incompressible. Now I need a relationship for the efflux speed $v$ with which water exits the cylinder and I shouldn't use the approximation $d \ll D$, but formulate a general relati... | g16722 | [
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0.051... |
<p>Suppose I have a <a href="http://en.wikipedia.org/wiki/Caliper" rel="nofollow">caliper</a> that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational.</p>
<p>If I were to use this caliper to measure any small object, would the cal... | g682 | [
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... |
<p>Hi my question is if a compound lens system if filled with gas or a liquid how does it affect the system when compared to the lens system being separated by air alone. Does this affect the focal power of the system or the effective power at all. </p> | g16723 | [
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<p>"What's the maximum acceleration you can achieve in a a water-slide at a 34 degree angle (If you can't use your arms and legs)"?</p>
<p>This is the free-body-diagram that I drew, assuming $g = 10m/s^2$:<img src="http://i.stack.imgur.com/XmXqF.png" alt="FBD"></p>
<p>The maximum acceleration is when there is no fric... | g16724 | [
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<p>I remember reading that X-Rays are generated by 'braking' electrons in a Coolidge tube.</p>
<p>Is it fundamentally a matter that the extreme gravity immediately before a star ignites is so strong that it affects the hydrogen atoms to the point the velocity of it's components must be let-off in the form of heat &... | g16725 | [
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<blockquote>
<p>In each one of the following figures there's a pole of length $1.2
\text{m}$ and there's a force $\vec F = 150 \text{N}$ acting on it.
Determine the torque that is created by the force relative to the axis
of rotation $O$.</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/qKq0L.png" alt="I... | g16726 | [
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<p>This might sound like a silly question. Is it possible for the earth's magnetic field to actually destroy or harm earth? (implosion, crushing etc.)</p> | g16727 | [
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<p>when electric charges are placed on the medium then force of interaction between them decreases. We say this factor permitivity of the medium. The force of interaction between the charges is max if the charges are at space or if there is absence of medium. We know the <a href="http://en.wikipedia.org/wiki/Vacuum_per... | g16728 | [
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... |
<p><a href="http://en.wikipedia.org/wiki/Quantum_superposition" rel="nofollow">Wikipedia</a> says:</p>
<blockquote>
<p><em>Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system—such as an electron—exists partly in all its particular, theoretically possible states (or... | g16729 | [
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<p>I'm looking for more articles/reactions/critiques/support for Philip Mannheim's recent conformal gravity theory. </p>
<p>See here: <a href="http://arxiv.org/abs/1101.2186v1">http://arxiv.org/abs/1101.2186v1</a></p>
<p>Any ideas on where to start? </p> | g16730 | [
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0.047... |
<p>I need some help understanding how much information I can pull out of this data. I have a sample made up of two materials. Materials A and material B. Then I took a picture of the sample.</p>
<p>The two materials mix quite well, but not perfectly, so on my image I can see that some areas are mostly material A, some... | g16731 | [
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... |
<p><a href="http://chemistry.stackexchange.com/questions/3972/how-do-the-molecules-know-the-future-how-do-they-proceed-to-form-most-stable/">This question is a cross post from chemistry</a>. I'm not very convinced with the answer there. So, I'm posting it here.</p>
<p>I'm tutoring few students for Chemistry. During th... | g16732 | [
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<p>I am curious to find the braking distance for a car on a road.</p>
<p>In attempting to find this out, I found that the braking distance for a car (on a flat road) is
$$
d = \frac{v^2}{2\mu g}
$$
where
$\mu$ is the coefficient of friction between the road and tires (CRF),
$g$ is gravity, and
$d$ is the distance tr... | g16733 | [
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<p><a href="http://mathoverflow.net/q/165038/14414">http://mathoverflow.net/q/165038/14414</a></p>
<p>Motivation : Here is a motivation as to why this problem is so important.</p>
<p>Let $f(t)$ be an audio signal. We can safely asume it to be bandlimited to 0-20kHz as we cannot hear anything above that. Capture this ... | g16734 | [
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<p>I'm trying to understand the connections between quantum models in d dimensions and classical models in (d+1) dimensions within two, possibly related, contexts:</p>
<p>(i) in path integral monte carlo, the Trotter-Suzuki decomposition gives an equivalence between a d-dimensional quantum spin model at a given temper... | g16735 | [
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<p>I was wondering who used the term 'mass' in physics and in what context? <a href="http://www.etymonline.com/index.php?allowed_in_frame=0&search=mass&searchmode=none" rel="nofollow">The Online Etymology Dictionary</a> says it is in use since 1704. According to the <a href="http://en.wikipedia.org/wiki/Writing... | g16736 | [
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0.0057723... |
<p>With Fourier-Series Expansion, we can write a function as sum of many non-repating different frequncied different amplituded sine and cosine functions.</p>
<p>Lets assume we know electric-field and magnetic-field representation function of Hydrogen atoms or Iron atoms as a periodic-lattice <strong>(If we cannot kno... | g16737 | [
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<p>It is common knowledge that the transition from the Spring to the Summer season occurs in the Summer Solstice when the "Sun reaches its highest excursion relative to the celestial equator on the celestial sphere" (as stated in <a href="http://en.wikipedia.org/wiki/Solstice" rel="nofollow">Wikipedia</a>).</p>
<p>It ... | g16738 | [
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<p>Given the standard Ising partition function:
$$Z(\theta ,h) = \sum\limits_{\bf{x}} {\exp \left\{ {\theta \sum\limits_{(i,j) \in E} {{x_i}{x_j}} + h\sum\limits_{i \in V} {{x_i}} } \right\}}, $$</p>
<p>is there a closed form expression for the lower bound of the free-energy (Pressure) per-site, defined as,</p>
<p>... | g16739 | [
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... |
<p>to be quite honest, I have no idea where to start on this problem mathematically. However, it struck my curiosity and would love to know how it works on a mathematical level.</p>
<h1>the problem</h1>
<p>You have a guitar. All of the strings start at a resting position. When you play a string, it is now oscillating... | g16740 | [
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<p>I am quoting Chaikin, Lubensky, <em>Principles of Condensed Matter Physics</em>, p. 4.</p>
<blockquote>
<p>Now suppose we have a closed container of water vapor at a density of 0.322 g/cc at room temperature. As the temperature is lowered...</p>
</blockquote>
<p>It then proceeds to describe condensation, and say... | g16741 | [
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<p>I hope this is the right place for this kind of post.</p>
<p>A friend is trying to derive the equation for the energy stored in a capacitor by analysing the change in potential on one plate when the capacitor is shorted, however I don't think this valid. Could anyone explain why this is right or wrong?</p>
<p>He s... | g16742 | [
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<p>The situation is as follows:</p>
<p><img src="http://i.stack.imgur.com/UXYod.png" alt="Hello, world!"></p>
<p>I am told that $F_{net} = mg - T$ in this case, but doesn't that not take into account that $T$ isn't applied to the center of mass? Newton's second law is defined for discrete particles, but this is a con... | g16743 | [
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<p>$\mathbf{Background:}$ Consider a free scalar field $\phi$ ($\mathcal{L}_0 = \frac{1}{2}\partial_\mu \phi \partial^\mu \phi + \frac{1}{2}m^2 \phi^2$).</p>
<p>In the Hamiltonian viewpoint, this system has a Hilbert space $\mathcal{H}_0$ (the Fock space). We can write down a resolution of the identity in $\mathcal{H... | g16744 | [
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<p>My bare bookshelves are crying out for the addition of a new family member, more specifically a book:</p>
<ol>
<li><p>Discussing the classical Klein-Gordon field, spinor fields, gauge fields and all other matter fields in a generally co-variant fashion.</p></li>
<li><p>Discussing of the Schrodinger (non-relativisti... | g16745 | [
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<p>Effective mass of a Bloch electron in a periodic potential is negative why ? </p> | g16746 | [
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<p>Water comes out of a horizontally stationed hose and creates an arc as it heads towards the ground. Can I determine the speed the water was traveling in when it exited the hose by the measuring the arc which is created? For example, let's say that I measure that the water has dropped 2 inches vertically when measuri... | g16747 | [
0.03460773453116417,
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0.007270882837474346,
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<p>Groups of particles can interfere with one another; In the double slit experiment when measuring single photons at the screen each one arrives at the screen in a random manner and they only show the interference pattern once several particles are detected.</p>
<p>Obviously two waves can obviously interfere with on... | g16748 | [
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0.029544299468398094,
0.02772163227200508,
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0.034250... |
<p>Is there any phase transition occur in paramagnetism to diamagnetism transitions state. What should be the order and how will I calculate the order? </p> | g16749 | [
0.0038358133751899004,
0.03257150575518608,
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<p>I have been reading research papers in mathematical physics for some months now, and I've seen the the term "anharmonic oscillator" quite frequently. At first I assumed that given a Schrodinger equation</p>
<p>$$\frac{d^2u}{dx^2}+(E-V(x))u=0$$</p>
<p>where $E$ is the energy, and $V(x)$ is the potential function. I... | g16750 | [
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<p>Systems have mutual inductance and self inductance-however won't the effects of these two effect each other as well?
Do systems undergo current and magnetic field behavior that are, in this way, dictated by differential equations?</p> | g16751 | [
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0.028959717601537704,
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... |
<p>Don't hit me if the question is too lame but here it goes</p>
<p>1) We all know that to see something light must get reflected from it's surface and then reach our eye's </p>
<p>2) Any thing which goes in black holes get incinerated and destroyed completely</p>
<p>3) For a observer outside the event horizon he wi... | g16752 | [
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<p>I recently got a correction to a paper that I am writing. The correction references a section in which I talk about nearest neighbors. The comment says:</p>
<blockquote>
<p>Do you mean NN, NNN, etc., or NN, 2NN, 3NN? It's different. </p>
</blockquote>
<p>To clarify: here is the (111) face of an FCC crystal with ... | g16753 | [
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<p>In Peskin & Schroeder's book page 524, the following diagram is calculated for the gauge boson self-energy in order $g^2$:</p>
<p><img src="http://i.stack.imgur.com/i7pTt.png" alt="enter image description here"> </p>
<p>In dimensional regularization, its contribution is given by</p>
<p>$$-g^2C_2(G)\delta^{ab}... | g16754 | [
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<p>If we just look at our local galactic cluster, if all of the galaxies that are a part of it are moving away from each other, and so the overall 'density' of the strength of gravity in the cluster is decreasing over time, does that mean that time itself is also speeding up?</p>
<p>If this is the case, would it be on... | g16755 | [
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... |
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