question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>Suppose that you want to launch an object that travels the longest distance, given the starting speed (or the force applied). You have to determine the angle that al you to reach the longest distance, before it touches the ground.</p>
<p>For simplicity, the launch happens at the ground level, so no change in altitude happens (same gravitational potential energy at the start and at the end).</p>
<p>In the case of a flat surface and with no air resistance, I would say that the optimal angle is 45° (and it should be easy to determine). But how the earth curvature plays in the calculation?</p>
<p><strong>Optional:</strong> how can you introduce the effect of air resistance, without making the problem too complex? Is it possible to model it in a simple way, such as an arbitrary force depending only on the speed, mantaining the problem solvable? It would be also sufficient to say if the angle is unaffected or goes up/down, with some justification.</p>
<p>For simplicity, assume that the object has to remain in the atmosphere, so putting it in the orbit is not an option :)</p> | g11022 | [
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<p>So I've had this question bugging me ever since I saw sound at physics class:</p>
<p>How is it possible to match the resonance frequency of a column of air in an organ pipe and form a standing sound wave by simply blowing air into the column? </p>
<p>The main reason I see this problematic is because I can't figure out how a continuous stream of air (what I blew in) would make it possible for there to be parts of the air column which are not moving at all (namely, the nodes in the standing wave).</p>
<p>In a simple way, how does this work? (Blowing air and creating a standing wave pattern)</p> | g11023 | [
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<p>How can i check and calculate if a certain vacuum pump can hold an object that weights X kg? By "hold" I mean not let that object fall to the floor due to gravity</p> | g11024 | [
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<p>Is there a good reference for the distinction between projection operators in QFT, with an eigenvalue spectrum of $\{1,0\}$, representing yes/no measurements, the prototype of which is the Vacuum Projection Operator $\left|0\right>\left<0\right|$, which allows the elementary construction of a panoply of projection operators such as $$\frac{\hat\phi_f\left|0\right>\left<0\right|\hat\phi_f^\dagger}{\left<0\right|\hat\phi_f^\dagger\hat\phi_f\left|0\right>},\qquad \frac{\hat\phi_f\hat\phi_g\left|0\right>\left<0\right|\hat\phi_g^\dagger\hat\phi_f^\dagger}{\left<0\right|\hat\phi_g^\dagger\hat\phi_f^\dagger\hat\phi_f\hat\phi_g\left|0\right>},$$ or of higher degree; in contrast to (smeared) field operators such as $\hat\phi_f$, which have a continuous spectrum of eigenvalues? I see this as effectively the distinction between, respectively, the S-matrix and the Wightman field as observables.</p>
<p>I'm particularly interested in anything that considers the operational difference between these different classes of QFT observables in detail. It's obvious that the projection operators are nonlocal, insofar as they clearly don't satisfy microcausality, in contrast to the requirement of microcausality for the field operators. It also seems that the field operators cannot be used on their own to construct models for the detection of a particle, which is a yes/no event, without introducing the vacuum projection operator (<s>but <em>is there</em> a way of constructing projection operators without introducing the vacuum projection operator?</s> EDIT: yes, obviously enough, "is the observed value in the range $[a..b]$" is a yes/no observable, <em>etc., etc., ...</em>.)</p> | g11025 | [
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<p>I am a beginner in QFT, and my question is probably very basic. </p>
<p>As far as I understand, usually in QFT, in particular in QED, one postulates existence of IN and OUT states. Unitarity of the S-matrix is also essentially postulated. On the other hand, in more classical and better understood non-relativistic scattering theory unitarity of S-matrix is a non-trivial theorem which is proved under some assumptions on the
scattering potential, which are not satisfied automatically in general.
For example, unitarity of the S-matrix may be violated if the potential is too strongly attractive at small distances:
in that case a particle (or two interacting with each other particles) may approach each other from infinity and form a bound state.
(However the Coulomb potential is not enough attractive for this phenomenon.)</p>
<p><strong>The first question is why this cannot happen in the relativistic situation, say in QED.
Why electron and positron (or better anti-muon) cannot approach each other from infinity and form a bound state?</strong></p>
<p>As far as I understand, this would contradict the unitarity of S-matrix.
On the other hand, in principle S-matrix can be computed, using Feynmann rules, to any order of approximation in the coupling constants. Thus in principle unitarity of S-matrix could be probably checked in this sense to any order.</p>
<p><strong>The second question is whether such a proof, for QED or any other theory, was done anywhere? Is it written somewhere?</strong></p> | g11026 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/45105/does-fire-conduct-electricity-why">Does Fire Conduct Electricity? Why?</a><br>
<a href="http://physics.stackexchange.com/q/23469/520">Is fire plasma?</a></p>
</blockquote>
<p>Does a flame produce free electrons ? Or is the answer sometimes depending on the chemicals ? Does the answer depend on the exact heat ?
Does a (strong) magnet influence a flame ? Can that be seen ?</p> | g354 | [
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<p>To make it simple, take the spin foam formalism of ($SU(2)$) 3D gravity. My question is about the choice of the data that will replace the (smoothly defined) fields $e$ (the triad) and $\omega$ (the connection) on the disretized version of space-time $\mathcal{M}$: the 2-complex $\Delta$: why choose to replace $e$ by the assignment of elemnts $e\in su(2)$ to each 1-cell of $\Delta$, and elements $g_{e}\in SU(2)$ to each edge in the dual 2-complex $\mathcal{J}_{\Delta}$? I mean, these are both $su(2)$-valued 1-forms, thus, roughly speaking, assigning elements of $su(2)$ to vectors of the tangent bundle $\mathcal{TM}$, in other terms assigning elements of $su(2)$ to infinitesimal displacements represented by the 1-cells of $\Delta$. I can understand the choise for $e$, but not for $\omega$, why this is so? Why it is not the inverse choice?</p> | g11027 | [
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<p>I understand the idea of swapping from unit systems, say from ms$^{-1}$ to kms$^{-1}$, but why can we just delete the units altogether?</p>
<p>My question is: what exactly are we doing when we say that $c=1$?</p> | g11028 | [
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<p><img src="http://i.stack.imgur.com/zs2Uz.png" alt="enter image description here"></p>
<p>Suppose we have a setup like this. Here $a_1,a_2,b_1,b_2$ are acceleration magnitudes($b_1,b_2$ being relative) and $P,Q,R,S$ are not pulley/blocks but are points on the rope. If I use a geometrical constraint then ($k$ is constant)
$$PQ+QR+RS=k$$
$$\ddot {PQ}+\ddot{QR}+\ddot{RS}=0$$
And here since $\ddot {PQ}=b_1,\ddot {RS}=b_2, \ddot{QR}=-(a_1+a_2)$ we have
$$b_1+b_2=a_1+a_2$$
This is fine, but how do I get a relation between $\vec{a_1},\vec{a_2},\vec{b_1},\vec{b_2}$? Can it be obtained in any geometrical way without listing out forces (assuming those triangular blocks are isosceles and have base angle $\theta$, base moving on ground)?</p>
<p>Thanks in advance.</p> | g11029 | [
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<p><a href="http://en.wikipedia.org/wiki/Orders_of_magnitude_%28magnetic_field%29" rel="nofollow">This Wikipedia article</a> provides a wonderful way to fathom the scale of the tesla. I cannot seem to find a similar set of examples about magnetic flux. I know that the milli-, micro- and nanoweber are the most widely used. Just how strong (weak) is one weber?</p> | g11030 | [
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<p>Why a day is divided by 12/24 hours? Why the number 12? Why not using 10 or 6 or 14, 16? Who invented this? Any physical reasons behind this?</p> | g11031 | [
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<p>As a foreigner, United States has a very complex time system for me. <code>Central Time Zone</code>, <code>North American Eastern Time Zone</code>, <code>Mountain Time Zone</code>, <code>Alaska Time Zone</code>, <code>Pacific Time Zone</code>, <code>Samoa Time Zone</code>, <code>Atlantic Time Zone</code>, <code>Hawaii–Aleutian Time Zone</code>. And also plus <code>DST</code> (<code>Daylight saving time</code>).</p>
<p>I heard people saying this can save a lot of energy. I want to know if there is any <strong>scientific report</strong> to support this. Or it's just people they like this system. Thanks</p> | g11032 | [
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<p>I have derived geometric optics for gravitational waves and I am trying to interpret one of the results. I have </p>
<p>\begin{equation}
k_{\rho}k^{\rho}=0
\end{equation}</p>
<p>for the wavevector. For the case of electromagnetic waves, Misner, Thorne and Wheeler say that this means the wavevector is "null". What does this mean?</p>
<p>At the moment, I can see two things. First and most obviously, it's the 'dot' product of a four-vector with itself, which equals zero. I'm not exactly sure what this means.</p>
<p>Secondly, if we take $p=\hbar k$ then we find that</p>
<p>\begin{equation}
p_{\mu}p^{\mu}=0
\end{equation}</p>
<p>or </p>
<p>\begin{equation}
m=0.
\end{equation}</p>
<p>With $m=0$ we would presumably say that the particle associated with the wave (photon, or graviton in this case) is massless, and thus they travel along null geodesics. Am I missing something or do we <em>need</em> to talk about particles? After all, our original equation involved $k$, which is a *wave*vector. Is there an interpretation from GR itself?</p> | g11033 | [
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<p>Suppose a particle is moving on a surface of a sphere,then it contains a holonomic constraint and so the three Cartesian co-ordinates are available with a constraint equation(equation of surface in Cartesian co-ordinate system). Then there must exist two generalized co-ordinates in form of which Lagrange equation can be constructed.Then is it true to say that the generalized co-ordinate system in this particular case represent <a href="http://en.wikipedia.org/wiki/Riemannian_manifold" rel="nofollow">Riemannian manifold</a> and so Lagrange equation is equation of motion on this Riemannian manifold?I should made one more important specification that work done by forces of constraints are zero.</p> | g11034 | [
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<p>Is my derivation of the action of the parity operator $\mathbb{P}$ on the $|p\rangle$ representation correct?</p>
<p>$$\left( \mathbb{P}\tilde\psi \right)(p)= - \tilde\psi (p).$$</p>
<p>Obtained from</p>
<p>$$\left( \mathbb{P}\tilde\psi \right)(p) = \frac{1}{\sqrt{2\pi\hbar}}\int_{-\infty}^{\infty} dx \, e^{-\frac{i}{\hbar}px}(\mathbb{P}\psi)(x)= $$</p>
<p>$$ = \frac{1}{\sqrt{2\pi\hbar}}\int_{-\infty}^{\infty} dx \, e^{-\frac{i}{\hbar}px}\psi(-x)=$$</p>
<p>$$= -\frac{1}{\sqrt{2\pi\hbar}}\int_{\infty}^{-\infty} dx \, e^{-\frac{i}{\hbar}(-p)x}\psi(x)=-\tilde\psi(p).$$</p>
<p>$$= \frac{1}{\sqrt{2\pi\hbar}}\int_{-\infty}^{\infty} dx \, e^{-\frac{i}{\hbar}(-p)x}\psi(x)=\tilde\psi(-p).$$</p> | g11035 | [
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<p>This piece of argument has been repeated again and again by experts, that is</p>
<blockquote>
<p>Since the fermions are gapped, then I can integrate it out.</p>
</blockquote>
<p>but I have no idea of what will happen if the fermions are not gapped. </p>
<p>Can I still integrate it out safely?</p>
<p>For an ordinary insulator which is gapped, then after integrating out the fermions, we have an low energy (frequency) effective action</p>
<p>$$S=\int d^4x\, \frac{1}{16\pi} (F^{\mu\nu})^2 + \frac{1}{2} F^{\mu\nu}\mathcal{P}^{\mu\nu}-j^\mu A_\mu $$
where $\mathcal{P}_{\mu\nu}$ is the response to $\bf B$ and $\bf E$, i.e. $\bf M$ and $\bf P$. If we vary vector potential we have the good old Maxwell equations inside a medium. </p>
<p>It can be understood easily: if the external gauge field has frequency lower than the band gap, the medium can be viewed as a collections of dipoles; otherwise high energy photons will tear off electrons from atoms.</p>
<p>In the case of metal, it is not gapped (I think it is improper to call it gapless), photon of any frequency will excite a electron. We know that there is an additional Ohm's law added to describe a metal. </p>
<blockquote>
<p>Can we obtain effective theory (Ohm+Maxwell) of metal by integrating out "ungapped" electrons?</p>
</blockquote>
<p>In addition,</p>
<blockquote>
<p>for a gapless conductor, say graphene, what happens if I integrate out Dirac electrons?</p>
</blockquote> | g11036 | [
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<p>Does anyone have images of the electric field created by a <strong>real</strong> plate of charge? I'm not looking for an image of a theoretical infinite sheet of charge, I'm looking for an image of a real large one.</p>
<p>By a real plate, I mean a finite one.</p>
<p>Thanks a lot.</p> | g11037 | [
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<p>What speed should have an alone planet to have a habitable zone due to relic radiation, without any star involvement?</p>
<p>How much time the planet will be able to remain in the habitable zone before the speed drops, given the planet has no engines?</p>
<p>Are such speeds achievable using gravity assist of the galactic center or similar objects?</p>
<p>What would be effect of non-CMB sources like particles and stellar radiation at such speed?</p> | g11038 | [
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<p>A few sequential questions:</p>
<ul>
<li>Is it possible for a nuclear explosion to be small enough to produce a 250-ml (one cup) mushroom cloud?</li>
<li>If so, how much uranium would that take?</li>
<li>How close to the explosion could one be (in normal clothing) not to suffer from burns or excessive radiation exposure?</li>
</ul> | g11039 | [
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<p>If water is cycled through a thin pipe by a pump, and a certain spot on that pump is made of thin copper that is being heated by a 1000 C source, will the water, as a whole, attain a heat of 1000 C (or close to it) and keep cycling, making the entire pipe incredibly hot? Oh, and this would be a closed loop cycle.</p> | g11040 | [
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<p>Wikipedia <a href="https://en.wikipedia.org/wiki/Nordstr%C3%B6m%27s_theory_of_gravitation#Development_of_the_theories" rel="nofollow">says</a> that Nordstrom theory with equations of motion of the test particle
$$\tag{1}
\frac{d (\varphi u_{\alpha})}{d \tau} = \partial_{\alpha} \varphi
$$
and field equation
$$\tag{2}
\varphi \square \varphi = 4 \pi \rho
$$
is equal to the conditions
$$\tag{3}
C_{\alpha \beta \gamma \delta} = 0, \quad R = 24 \pi T, \quad T = g^{\mu \nu} T_{\mu \nu},
$$
so the metrics
$$
g_{\alpha \beta} = e^{2\psi}\eta_{\alpha \beta}, \quad \varphi = e^{\psi}
$$
with condition $R = 24 \pi T$ represents Nordstrom theory.</p>
<p>I have some questions about it.</p>
<p>If the statement about the equivalence of Nordstrom theory and $(3)$ is correct, I will get from it geodesic and field equations which are equal to $(1), (2)$ respectively.</p>
<p>First, let's get <strong>the geodesic equation</strong>. By using expression
$$
\Gamma_{\alpha \beta \gamma} = (g_{\alpha \beta}\partial_{\gamma}\psi + g_{\alpha \gamma}\partial_{\beta}\psi - g_{\beta \gamma}\partial_{\alpha}\psi )
$$
I got
$$
\frac{d u_{\alpha}}{d \tau} + \Gamma_{\alpha \beta \gamma}u^{\beta} u^{\gamma} = \frac{d u^{\alpha}}{d \tau} + \left(g_{\alpha \beta}\partial_{\gamma}\psi + g_{\alpha \gamma}\partial_{\beta}\psi - g_{\beta \gamma}\partial_{\alpha}\psi \right) u^{\beta}u^{\gamma}
$$
using
$\left|g_{\beta \gamma} u^{\beta} u^{\gamma} = 1\right|$
$$\tag{4}
\frac{d u_{\alpha}}{d \tau} + 2 u_{\alpha}u^{\beta}\partial_{\beta} \psi - \partial_{\alpha}\psi = 0 \quad\Longrightarrow\quad \frac{d}{d \tau}(\varphi^{2} u_{\alpha}) = \frac{1}{2}\partial_{\alpha} \varphi^{2}
$$
which isn't equal to $(1)$.</p>
<p>Second, let's get <strong>the field equation</strong>. </p>
<p>By using $R = 24 \pi T$ I got (in terms of $\psi$)
\begin{align}
e^{-2\psi}\left(-6\square \psi - 6 \partial_{\lambda} \psi \partial^{\lambda} \psi \right)
&= -6\frac{ \square \varphi}{\varphi^{3}} \\
&= 24 \pi T
\end{align}
then using $T\approx\rho$ we get
$$\tag{5}
24\pi T = 24 \pi \rho,
$$
which also isn't equal to $(2)$ (I used the non-relativistic limit of stress-energy tensor of macroscopic body $T_{\mu \nu} = (p + \rho)u_{\mu} u_{\nu} - pg_{\mu \nu}$). </p>
<p>Where is the problem?</p> | g11041 | [
0.053649332374334335,
-0.0019122589146718383,
-0.01676243729889393,
-0.0389847494661808,
0.04055716469883919,
0.017771072685718536,
0.0348670594394207,
-0.042264606803655624,
-0.02100982703268528,
-0.021161559969186783,
0.03891991823911667,
0.0012033747043460608,
-0.01715119555592537,
-0.0... |
<p>Suppose two rings are kept facing each other and that one ring have some current which increases constantly. Will the other ring be attracted or repelled? Does this also depend on <em>how they are kept</em>?</p> | g11042 | [
0.011707106605172157,
-0.01470203697681427,
0.017105959355831146,
-0.026683365926146507,
0.0686379075050354,
0.03501339629292488,
0.005143375601619482,
0.004008978605270386,
-0.023734301328659058,
0.01892191544175148,
-0.03253992646932602,
0.06470273435115814,
-0.03682984784245491,
-0.0345... |
<p>I've recently restored my interest on theoretical physics (I have a master degree in Electrical Engineering) and began my study with first volume of the Physics Course by Landau and Lifshitz. This is a very good and interesting book, and it just blows my mind (both in a positive and negative ways) - you spend really a lot of time trying to understand everything out of this textbook. Maybe someone can suggest somewhat sort of helping sidenotes for this book?</p>
<p>Thank you for your help.</p> | g98 | [
0.0036227423697710037,
0.04500984773039818,
0.015266758389770985,
-0.011612487956881523,
0.0060248346999287605,
0.034270867705345154,
0.005055591464042664,
0.07309771329164505,
0.008177586831152439,
0.028535272926092148,
0.021199319511651993,
0.0020046504214406013,
0.004433868918567896,
0.... |
<p>The NY Times article on Firewalls today has the following paragraph:</p>
<blockquote>
<p><em>Quantum field theory is how the world works [quoting a physicist]. It had a major triumph just a year ago, when the Higgs boson, a subatomic particle responsible for the mass of other subatomic particles, was discovered after a 40-year search, at the Large Hadron Collider at CERN.</em></p>
</blockquote>
<p>Is it correct that </p>
<ol>
<li><p>the Higgs (boson, mechanism, field, etc) is needed for <a href="http://en.wikipedia.org/wiki/Quantum_field_theory" rel="nofollow">QFT</a> <em>per se</em>, or </p></li>
<li><p>is it "just" needed for the particular <em>application</em> of QFT known as the standard model, electroweak theory etc? </p></li>
</ol>
<p>Couldn't QFT still be the correct framework for "how the world works" if the Higgs model turned out to be wrong?</p> | g11043 | [
0.021501410752534866,
0.08537833392620087,
0.000033159562008222565,
0.0040168859995901585,
0.05188887566328049,
-0.006323790177702904,
0.010545841418206692,
0.00016637220687698573,
0.0064488067291677,
-0.03287467733025551,
-0.013337897136807442,
-0.04732910543680191,
0.0034129193518310785,
... |
<p>From Surely you must be joking, Mr Feynman.</p>
<blockquote>
<p>You blast off in a rocket which has a
clock on board, and there's a clock on
the ground. The idea is that you have
to be back when the clock on the
ground says one hour has passed. Now
you want it so that when you come
back, your clock is as far ahead as
possible. According to Einstein, if
you go very high, your clock will go
faster, because the higher something
is in a gravitational field, the
faster its clock goes. But if you try
to go too high, since you've only got
an hour, you have to go so fast to get
there that the speed slows your clock
down. So you can't go too high. The
question is, exactly what program of
speed and height should you make so
that you get the maximum time on your
clock?</p>
<p>This assistant of Einstein worked on
it for quite a bit before he realized
that the answer is the real motion of
matter. If you shoot something up in a
normal way, so that the time it takes
the shell to go up and come down is an
hour, that's the correct motion. It's
the fundamental principle of
Einstein's gravity--that is, what's
called the "proper time" is at a
maximum for the actual curve.</p>
</blockquote>
<p>How is this result proven?</p> | g11044 | [
0.0629572793841362,
0.059807583689689636,
0.022096775472164154,
0.024149077013134956,
0.04296509176492691,
0.003931460436433554,
0.02339276298880577,
-0.008735580369830132,
-0.042232487350702286,
-0.007346962578594685,
-0.025067757815122604,
0.0185275636613369,
0.004662095569074154,
0.0063... |
<p>In Newton's ring experiment, it is said that the Newton's ring experiment is used to explain this phenomena as depicted in the image.
<img src="http://i.stack.imgur.com/F1Njj.jpg" alt="enter image description here"></p>
<p>Now, the interference pattern here is forming on the surface of the lens itself.
<img src="http://i.stack.imgur.com/lbnYD.jpg" alt="enter image description here"></p>
<p>But here in this case the reflected rays will meet and interfere on a screen finally instead of interfering on the lens itself or the region between the lens and the flat glass slab. So how are the rings seen on the lens explained by this phenomena?</p>
<p><img src="http://i.stack.imgur.com/slpma.jpg" alt="enter image description here"></p>
<p>or where are the rings formed ? </p> | g11045 | [
0.0029241875745356083,
0.009338103234767914,
0.013980378396809101,
-0.031981226056814194,
0.06664937734603882,
0.03662543743848801,
0.043925691395998,
0.022344138473272324,
0.016688819974660873,
-0.022257838398218155,
-0.003942023031413555,
0.027854114770889282,
0.02911771833896637,
-0.015... |
<p>What is the difference between <a href="http://en.wikipedia.org/wiki/Fraunhofer_diffraction" rel="nofollow">Fraunhofer diffraction</a> and <a href="http://en.wikipedia.org/wiki/Fresnel_diffraction" rel="nofollow">Fresnel diffraction</a>? I mean diffraction is just bending of light waves or waves in general around a point. So how can there be two types of diffractions?</p>
<p>If Diffraction means something else in this context, then please explain the difference between these two types of diffraction.</p> | g11046 | [
0.040610961616039276,
-0.029518162831664085,
-0.010934233665466309,
-0.0013936550822108984,
0.05503549799323082,
0.017429322004318237,
0.05015822499990463,
0.035859882831573486,
-0.03361723572015762,
-0.10236947238445282,
-0.02566811628639698,
0.04153656214475632,
0.03569396957755089,
0.03... |
<p>I believe I understand how tuning a radio with an analog tuner works: turning the dial physically changes the length of the antenna, which determines which broadcast wavelength will resonate in the antenna and get picked up. In contrast, what is the mechanism that makes a digital tuner work? My guess is it'll be some clever little circuit that somehow selects a resonant frequency by changing the amount of current going through it (or something like that). </p> | g11047 | [
-0.003595801768824458,
0.012650064192712307,
0.002571457764133811,
-0.013942081481218338,
-0.0014672428369522095,
0.006236738990992308,
0.0033959513530135155,
-0.03285914286971092,
-0.00727095315232873,
-0.06297449767589569,
-0.025069519877433777,
0.003706376999616623,
0.03318535536527634,
... |
<p>Imagine there is a string, not a massless one but a heavy one, which is attached to the ceiling where the angle between the ceiling and the tangent at the end of the string is $\theta$. (First visualize it, or draw it somewhere). Let at any point the tension in the string be T. Now obviously there are components of forces acting, as T$\sin\theta$ is balancing its weight. But if I nudge the string from that point with a very lightly, I actually do not experience a resistive force (I've tried it several times). But I know T$\cos\theta$ is acting towards me.</p>
<p>So my question is, why do not I experience a resistive force?</p>
<p>Also, when we derive the expression for centripetal force, we do not take components of Tension but of its weight, because it "sounds" meaningless.</p>
<p>Is it logical to take components of T?</p> | g11048 | [
0.05110453441739082,
-0.011234838515520096,
0.005780789535492659,
-0.041476570069789886,
0.0558750256896019,
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0.04475877434015274,
0.02941499650478363,
-0.016407186165452003,
-0.01844032295048237,
-0.014870289713144302,
-0.013536623679101467,
-0.05292448773980141,
-0.0... |
<p>Instead of using tokomak/torus shaped tubing to confine plasma and slow it down to "useable" speeds. Is it practical to slow down plasma (with a magnetic field) over a long path using a spiral shaped confinement to increase direct plasma converter efficiency ?</p> | g11049 | [
0.03145706281065941,
0.03020169399678707,
0.0025359562132507563,
-0.014802750200033188,
0.02604222483932972,
-0.0460866279900074,
0.06453794240951538,
0.023700065910816193,
-0.07012241333723068,
-0.010980361141264439,
0.05944285914301872,
0.00270387576892972,
0.04341982305049896,
-0.013028... |
<p>Let's imagine this in an situation where a person jumps down from a smaller building, a garage for example. The exact numbers aren't really important here, since I'm not aiming for an exact answer, but we can call it 2 metres in height.</p>
<p>To have both situations as similar to each other as possible, let's define them like this:</p>
<ol>
<li><p>In first "try", the person runs on the building, the jumps down. He is not jumping up to increase his jumping distance, he simply 'drops down', but considering that he's running with a certain speed forward, he will be falling in about 45 degrees angle. He drops at the distance <strong>X</strong> from the building.</p></li>
<li><p>In second "try", the person runs on the building, but does a forward somersault during the flight. As before, he doesn't necessarily jumps up, as the building height is already enough for him to complete the sault and as with the previous situation, he drops at the same distanes <strong>X</strong> from the building.</p></li>
</ol>
<p>In which scenario does this person hits the ground at the lower fall speed?</p> | g11050 | [
0.07782157510519028,
0.015755200758576393,
-0.005438604857772589,
0.03997579589486122,
-0.028604451566934586,
0.05809258669614792,
0.04588562622666359,
-0.04958514869213104,
-0.05931710824370384,
-0.041813187301158905,
-0.0439850278198719,
-0.01754607819020748,
-0.015343667939305305,
-0.00... |
<p>Is it possible to ionized a liquid and use magnetic field lines to guide the free electrons like a gas in a tokamak ?</p> | g11051 | [
-0.029266048222780228,
0.04289966821670532,
-0.011326568201184273,
-0.03049943596124649,
0.06218335032463074,
-0.008720270358026028,
-0.06576652824878693,
0.010312211699783802,
-0.046521950513124466,
-0.044807810336351395,
0.02967924252152443,
0.009405901655554771,
-0.020868372172117233,
0... |
<p>A friend of mine fell while he was snowboarding which led to a discussion. He mentioned that, in general, if your center of mass is traveling at a certain velocity, and you fall forward, your head would contact the ground at twice the velocity that your center of mass was traveling. Is this true? And if so can you explain the physics behind it to me?</p> | g11052 | [
0.07137839496135712,
0.035246822983026505,
0.022248737514019012,
0.017518363893032074,
0.029023805633187294,
0.01843840815126896,
0.04800419136881828,
-0.01191671285778284,
-0.008214415051043034,
-0.015613703057169914,
-0.052412249147892,
-0.09056651592254639,
0.005858832038938999,
-0.0059... |
<p>What is the the cosmological footprint of humanity? By this I mean, how might a cosmological observer detect humanity or its products on earth?</p>
<ul>
<li>How far away can humanity or it's products (not mere landscape changes that might have happened naturally) be detected by humanly visible Light? (The story of the Great Wall of China visible from moon is a legend, but the shadows of the Great Pyramids and other huge buildings can be seen from outer orbits.)</li>
<li>When was humanity first detectable in space by something else than visible light? (EM-Emission, other waves?)</li>
<li>What products of humanity other than EM-Waves are there in outer space and how far are they away? (Voyager, Lunar and Mars Rovers)</li>
<li>In what parts of the EM-spectrum is humanity clearly detectable against the Sun's background emission and how far away is that possible? (How far away can a cosmological observer watch human television or listen to human radio?)</li>
</ul> | g11053 | [
-0.010898892767727375,
0.022126521915197372,
0.02482515200972557,
-0.012209223583340645,
-0.019355375319719315,
0.07630500942468643,
0.05268093943595886,
-0.0004479520721361041,
0.008890057913959026,
-0.0323265977203846,
0.03460126742720604,
0.011782362125813961,
0.03932846710085869,
0.045... |
<p>It is often said that faster than light travel would violate causality.</p>
<p>However, because the universe is expanding, there are actually distant stars that move away from us at a speed greater than the speed of light.</p>
<p>Why is this allowed, even though it could violate causality?</p> | g11054 | [
0.06172754615545273,
0.04244351014494896,
0.01738549955189228,
0.009524738416075706,
-0.027289120480418205,
0.012214790098369122,
0.014902478083968163,
0.03634209930896759,
-0.04784006252884865,
-0.062380775809288025,
0.062104929238557816,
-0.002440782729536295,
0.04026375338435173,
0.0143... |
<p>A common justification for prohibiting many unusual phenomena such as faster than light travel is that if they were possible, causality would be violated.</p>
<p>Let's define causality as:</p>
<blockquote>
<p>You cannot change the past.</p>
</blockquote>
<p>Meaning that at any given moment $t_1$, it is impossible to influence any event which took place at $t_0<t_1$.</p>
<p>Obviously, no one has ever heard of this being violated. Is there a reason why? Is it just because nobody has managed to build a time machine yet, or does something in physics expressly forbid causality from being violated? In other words, is causality a law of physics, and how much of physics would have to be rolled back and re-written if I built a time machine (it's probably easier to say what physics there would be left)?</p>
<p>There are some (in)famous paradoxes that arise if you are able to influence the past. There is probably no need to restate these for this question, unless these paradoxes <em>per se</em> are the justification for expecting causality to not be violated.</p>
<hr>
<p>Question motivated by <a href="http://physics.stackexchange.com/questions/95200/doesnt-warp-theory-violate-causality/95203?noredirect=1#comment244265_95203">John Rennie's comment</a>.</p>
<p>Some examples of how causality can be violated:</p>
<ul>
<li>A device which can travel faster than light</li>
<li>A device which can travel into the past</li>
<li><a href="https://en.wikipedia.org/wiki/Newcomb%27s_paradox" rel="nofollow">Newcomb's paradox</a></li>
</ul> | g11055 | [
0.03922712802886963,
0.03292366489768028,
0.030937716364860535,
-0.012376547791063786,
0.01193479634821415,
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0.07279737293720245,
0.061399929225444794,
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-0.030459437519311905,
0.05484022945165634,
-0.020508795976638794,
0.02959050051867962,
0.019... |
<p>Why is the alpha, beta or gamma decay of an unstable nucleus unaffected by the chemical situation of an atom, such as the nature of the molecule or solid in which it is bound? The chemical situation of the atom can, however, have an effect on the half life in <a href="http://en.wikipedia.org/wiki/Electron_capture" rel="nofollow">electron capture</a>. Why is this so?</p> | g11056 | [
0.006825028453022242,
-0.021647434681653976,
-0.008721206337213516,
-0.038840021938085556,
0.08475478738546371,
0.022821122780442238,
-0.027051374316215515,
0.02633705548942089,
-0.01486259326338768,
-0.02743656188249588,
-0.0114207174628973,
0.00568433990702033,
-0.010797028429806232,
0.0... |
<p>We can use Gauss's law to find out the electric field $\vec{E}(\vec{r})$ due to an infinite cylinder of charge.</p>
<p><img src="http://i.stack.imgur.com/SNR2j.jpg" alt="enter image description here"></p>
<p>But if the cylinder is of finite length then it is said that $|\vec{E}(\vec{r})|$ is valid at $\vec{r}$ when $r<< R$.</p>
<p>Why this is so? And how can I prove this condition mathematically?</p> | g11057 | [
0.05407094582915306,
0.0037245971616357565,
-0.010804432444274426,
-0.011271878145635128,
0.07797613739967346,
0.010086789727210999,
-0.0029045704286545515,
0.011016953736543655,
-0.02691112644970417,
0.024019310250878334,
-0.0494907945394516,
0.011667812243103981,
-0.0313875675201416,
-0.... |
<p>Suppose a charge $q = +Z e$ is moving along positive $+x$ direction with electron below $x-$axis and the charge is moving fast enough to consider electron at rest, then what is the maximum value of energy that is transferred to electron? </p>
<p>According to my note, </p>
<blockquote>
<p>"it can be showed that $E_{max} = 2m\gamma^2 v^2$ "</p>
</blockquote>
<p>where $\gamma$ is Lorentz factor and $v, m$ are velocity and mass of the charge. My note is probably based on J.D. Jackson's Classical Electrodynamics. I haven't read that whole book. But as far as I know, such results are not derived on that book. How do I arrive at above result.</p>
<p>So far, I know, energy transfer can be calculated as
$$\Delta E = \frac{2 Z^2 e^4}{mb^2v^2}$$
where $b$ is impact parameter. As $b \to 0, \Delta E \to \infty$, the original problem is to find the bounds for $b$.</p> | g11058 | [
0.03155193105340004,
-0.018854999914765358,
0.020610012114048004,
0.05486030876636505,
0.04327012225985527,
0.022250670939683914,
0.01855645142495632,
0.000693368841893971,
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0.04062655568122864,
-0.02321183681488037,
0.07665397226810455,
0.05141275003552437,
0.00355204... |
<p>I have a single 1 meter array of 5 fiber bragg gratings that has FC/APC connectors on both ends. I will be embedding the array in a material and want to be able to do a quick check that the array is ok and can transmit light before I ship it off somewhere. </p>
<p>I have a fiber meter to recieve the light, but I need some kind of light source to send light through the array and test. I am hoping for a cheap option.</p>
<p>Any thoughts would be much appreciated!</p>
<p>-Mike</p> | g11059 | [
0.019395897164940834,
-0.0050716944970190525,
0.007757185027003288,
-0.06270593404769897,
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0.015453715808689594,
-0.05199240520596504,
0.04922609403729439,
0.03514402359724045,
-0.020513802766799927,
... |
<p>I've always heard fusion depends on incredible temperatures and pressures, but I'm curious what the temperature dependence of fission is.</p>
<p>For instance, if I had uranium and heated it to a sufficiently hot temperature wouldn't it decay at a faster rate at some point? I'm not talking about 300 K, but instead say we had 5800 K or 11600 K or 17400 K. At some point I would expect the decay rate to increase, so does anybody have more information on this?</p> | g11060 | [
0.04436636343598366,
0.04536982625722885,
0.01601557992398739,
0.08270426839590073,
-0.01630665734410286,
-0.025120476260781288,
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0.09418980032205582,
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-0.05506310611963272,
-0.006339001469314098,
0.00903321709483862,
-0.006569611839950085,
0.000... |
<p><a href="http://electronics.stackexchange.com/questions/111582/capacitance-between-earth-and-moon">This question (What is the capacitance between the Earth and Moon?)</a> on EESE makes me wonder: How can a vacuum have a breakdown voltage? </p>
<p>If electrons can find the shortest path through a vacuum, how is that possible? With nothing to carry the charge, I can't understand how the charge can traverse a vacuum.</p>
<p>The value for dielectric strength of a vacuum comes from <a href="https://en.wikipedia.org/wiki/Dielectric_strength" rel="nofollow">Wikipedia</a></p> | g11061 | [
-0.001352267456240952,
0.05333312973380089,
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0.025467699393630028,
0.007184161338955164,
0.054082658141851425,
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0.012657689861953259,
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-0.03247295320034027,
-0.01759784296154976,
-0.00799667276442051,
0.03811580315232277,
0.... |
<p>so I'm working on length contraction in relativity theory. I feel pretty confident time dilation and have not really gone over Lorentz Transformations that much.</p>
<p>The question itself lies at the bottom if you want to skip to there. The following just shows my process and conclusion</p>
<p>So, I'm working on a thought experiment where a snake is moving relative to Observer 2. I'm trying to determine the relation between the lengths of each reference frame: snake and Observer 2. Here is a (very messy) illustration:
<img src="http://i.stack.imgur.com/01qxi.png" alt="illustration of length contraction"></p>
<p>Okay so the variables for each reference frame would be:
$$ S_1(snake): \Delta t_1 , L_1 $$
$$ S_2: \Delta t_2 , L_2 $$</p>
<p>And</p>
<blockquote>
<blockquote>
<p>Event 1 = the measure at the point at the rear side of the snake.
Event 2 = the measure at the point at the front side of the snake. </p>
</blockquote>
</blockquote>
<p>I am just going to assume that the following equation is true for now after having previously proved it in a time dilation experiment:</p>
<p>$$ \Delta t = \gamma \Delta t_o $$</p>
<p>Since in both reference frames, $S_1 , S_2$, Event 1 and Event 2 do not occur at the same point, we can say the proper time $\Delta t_o$ cannot be found in either of the frames. Likewise, it will be found in some other frame. Therefore, from the equation found in the time dilation experiment, we can reasonably say:
$$\Delta t_1 = \gamma \Delta t_o$$
$$\Delta t_2 = \gamma \Delta t_o $$
Where the values of $\gamma$ in each equation are equal because V would be equal in each equation. Then we conclude:
$$\Delta t_1 = \Delta t_2 $$
From there, since $L = V \Delta t$, we can say:</p>
<p>$$L_2 = V \Delta t_2 $$</p>
<p>Since both times values are equivalent:
$$L_2 = V \Delta t_1 $$
Then, we can replace $\Delta t_1$ with $L_1 \over V$.
Plugging that back into the equation:
$$L_2 = V {L_1 \over V} $$ and
$$L_2 = L_1 $$
This seems to be rather uneventful, and I'm assuming I did something wrong. It would make sense that if time can be different in different frames then length would be too. I'm pretty sure the reason this lame result occurred was because I assumed that the $\Delta t$ in each frame of reference was the same. The text I'm reading states that the following equation: $$L_2 = {L_1 \over \gamma}$$
I know I'm forgetting something, but I can't figure out what it is. Can anyone see what I'm doing wrong?</p>
<p>Thanks!</p> | g11062 | [
0.01691305823624134,
-0.006615127436816692,
0.01600736379623413,
-0.0676005631685257,
0.03356876224279404,
-0.035833559930324554,
0.01732935942709446,
0.019645201042294502,
-0.007443659007549286,
0.02797696553170681,
-0.01725785620510578,
0.03680264577269554,
0.012117442674934864,
0.011103... |
<p>MRI expert Pierre-Marie Robitaille on the design flaws of COBE, WMAP, & Planck and the violation Kirchhoff's Law:</p>
<p>Here are his talks:</p>
<p><strong><a href="https://www.youtube.com/watch?v=i8ijbu3bSqI" rel="nofollow">Pierre-Marie Robitaille: The Cosmic Microwave Background</a></strong></p>
<p><strong><a href="https://www.youtube.com/watch?v=3Hstum3U2zw" rel="nofollow">Pierre-Marie Robitaille: On the Validity of Kirchhoff's Law</a></strong></p>
<p>Robitaille holds the world record for highest resolution MRI imaging.</p>
<p>An interesting point he makes is that cosmological sources would not vary over time, yet the COBE, WMAP, and Plank data are highly variable.</p>
<p>Here are his papers detailing the design flaws of COBE, WMAP, and Planck:</p>
<p>Robitaille P.-M.
WMAP: A Radiological Analysis
<a href="http://www.ptep-online.com/index_files/2007/PP-08-01.PDF" rel="nofollow">http://www.ptep-online.com/index_files/2007/PP-08-01.PDF</a></p>
<p>Robitaille P.-M.
COBE: A Radiological Analysis
<a href="http://www.ptep-online.com/index_files/2009/PP-19-03.PDF" rel="nofollow">http://www.ptep-online.com/index_files/2009/PP-19-03.PDF</a></p>
<p>Robitaille P.-M.
The Planck Satellite LFI and the Microwave Background: Importance of the 4K Reference Targets
<a href="http://www.ptep-online.com/index_files/2010/PP-22-02.PDF" rel="nofollow">http://www.ptep-online.com/index_files/2010/PP-22-02.PDF</a></p> | g355 | [
-0.006918401923030615,
0.004002491012215614,
0.0014713406562805176,
-0.020135954022407532,
0.033073458820581436,
0.044824182987213135,
0.011883807368576527,
0.019183609634637833,
-0.06912010163068771,
0.024939052760601044,
0.0718938484787941,
-0.026388244703412056,
0.059720393270254135,
0.... |
<p>I have a rather broad question and a specific problem. Let's take a orthonormal single-particle basis $\{ \vert i \rangle \}$, a simple single-particle Hamiltonian
$$\tilde{H} = \sum_{i, j} h_{i j} \vert i \rangle \langle j \vert$$
and its second-quantized form
$$ H = \sum_{i, j} h_{ij} a^\dagger_i a_j ~.$$
Now I add a constant $C$, i.e. $H_C = \sum_{i, j} h_{ij} a^\dagger_i a_j + C ~.$
The broad question is, if this constant is relevant. Does it have any effect? How does one deal with a constant operator in Fock space? What is the single-particle version of $\tilde{H}_C$? I was unable to find literature about this. Such constants sometimes appear when one wants to define a Hamiltonian with a particular symmetry, e.g. particle-hole symmetry, and as far as I can tell, these constants are ignored or considered unimportant.</p>
<p>The specific problem, why I want to know about the consequences of these constants, is the following. (Don't worry about the details, just concentrate on the Hamiltonian.) The single-particle imaginary-time Green's function is defined as
$$ G_{k l}(\tau) = - \frac{1}{Z} \mathrm{Tr}(e^{-\beta H} \mathcal{T} a_k[\tau] a^\dagger_k) ~,$$
with $Z = \mathrm{Tr}\left( e^{-\beta H} \right)$, $\beta = 1/T$ and $a_k[\tau] = e^{\tau H} a_k e^{-\tau H}$. It's Fourier transformation is defined as
$$ G_{k l}(i \omega) = \int_0^\beta d\tau e^{i \omega \tau} G_{k l}(\tau) ~.$$
They fulfill the relations
$$\begin{align}
\partial_\tau G_{k l}(\tau) &= -\delta(\tau) \delta_{k l} - \sum_{m} h_{k m} G_{m l}(\tau) \\
\delta_{k l} &= \sum_{m} (i\omega \cdot \delta_{k m} - h_{k m}) G_{m l}(i\omega) ~. \tag{1} \end{align}$$
We see that $G(i\omega)$ -- understood as a matrix -- is inverse to $Q$ with $Q_{k l} := (i\omega \cdot \delta_{k l} - h_{k l})$. Another approach is given by the resolvent $\mathcal{G}(z) = (z - \tilde{H})^{-1}$. Then $\mathcal{G}_{k l}(i \omega) = \langle k \vert (i \omega - \tilde{H})^{-1} \vert l \rangle$ which apparently satisfies Eq. <a href="http://physics.stackexchange.com/questions/133009/are-constant-terms-in-second-quantization-relevant#mjx-eq-1">(1)</a> and therefore $\mathcal{G}_{k l}(i \omega) = G_{k l}(i\omega)$. This is a useful relation and used at several occasions in the previous research from students and my research.</p>
<p>Now what happens if we use $H_C$ instead of $H$ in the definitions of $G(\tau)$ and $\mathcal{G}$? Naively I would expect the constant to drop out from $G(\tau)$ as it appears in the enumerator and denominator and can be factored out. But I can't see something similar happen for $\mathcal{G}$. Does the equality not hold anymore?</p> | g11063 | [
0.004568100906908512,
-0.010658361949026585,
-0.004843631759285927,
-0.09145258367061615,
0.06895707547664642,
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0.04420536756515503,
0.012297602370381355,
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0.03747822716832161,
-0.06176368519663811,
0.04614558815956116,
0.017355244606733322,
0.011... |
<p>I am unable to figure out how we get two peaks in the <a href="http://en.wikipedia.org/wiki/Electron_paramagnetic_resonance" rel="nofollow">Electron Spin Resonance</a> (ESR) experiment, in which we use Helmholtz coils as B source with modulation, and a basic unit as a source of radio waves.</p> | g11064 | [
-0.007442149333655834,
0.01623084954917431,
-0.036608949303627014,
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0.06305452436208725,
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-0.029624056071043015,
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0.05432940274477005,
-0.014411171898245811,
-0.0441049262881279,
0.04867587983608246,
0.039399661123752594,
0.... |
<p>When the current in 2 parallel wires flows in same direction they attract each other.Shouldn't the electrons travelling in opposite direction should also repel ?</p> | g11065 | [
0.04204205796122551,
0.022070065140724182,
0.0020982776768505573,
-0.03323537856340408,
0.07060196250677109,
0.05057680234313011,
0.020865274593234062,
0.040085725486278534,
-0.040179766714572906,
-0.002088394947350025,
0.015727438032627106,
0.0895954966545105,
-0.06892129778862,
0.0131858... |
<p>I've heard that light can form a curve if they travel near high-mass stars or even a black hole with strong gravity. Which is according to this <a href="http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation" rel="nofollow">Newtonian formula</a></p>
<p>$$\large F_{g}=\dfrac{Gm_1m_2}{r^2}.$$</p>
<p>But I've also heard that photons do not have (rest) mass! So it doesn't fit that equation anymore! But why can photons be pulled by gravities without (rest) mass? Could someone explain that?</p> | g143 | [
-0.04408017918467522,
-0.0020479150116443634,
-0.026728982105851173,
0.020437108352780342,
0.0008534922963008285,
0.050219643861055374,
-0.0022304735612124205,
0.023825017735362053,
-0.022094080224633217,
-0.04743990674614906,
-0.0026120427064597607,
0.0046983566135168076,
0.0241584349423646... |
<p>Voyager I, as an example, taking account gravity<br>
and setting aside effects of speed as cause of time dilation.</p>
<p>If it is very far away from earth and sun,
so then there must be a difference in the spacetime curvature there
in the ship compared with here in earth,
It means a detectable difference between our local clocks and its onboard clocks.</p>
<p>Imagine a signal transmision was designed to be at 1 byte for second
at local Voyager clock</p>
<p>Should we receive it at higher and higher rates ?</p>
<p>( because of solar system gravity decrease as it(Voyager) moves away and it will keep decreasing while it doesn't reach a middle point between another massive object)</p>
<p>Or the middle Voyager-Earth light path would compensate the effect, making the high rates generation from low curvature zones being delayed enough for us to receive it at same rate that it was generated? </p> | g11066 | [
0.011420326307415962,
0.058813758194446564,
0.01638571359217167,
-0.007790922652930021,
0.019766664132475853,
0.024425046518445015,
0.06852342933416367,
0.011578721925616264,
-0.01700100675225258,
-0.038828294724226,
0.03742966428399086,
0.03280354291200638,
0.04876008629798889,
0.04496769... |
<p>I am trying to get the distance a projectile travels, so I can display it in my program.</p>
<p>I'm sort of new to physics, but I've tried looking this up.</p>
<p>I'm not getting the right results however, and me being new to physics, I'm not sure if I'm just using the wrong formula or what.</p>
<p>This is the formula I have tried using:</p>
<p><img src="http://upload.wikimedia.org/math/c/1/d/c1da5860501561519415962ddda5e85e.png" alt=""></p>
<p>As far as I've read, a projectile launched at 15 degrees would travel the same distance as one launched at 75 degrees, however when I run the calculation I get two different distances for those two instances.</p>
<p>Is this not the correct formula, or maybe I'm using it wrong?</p>
<p>These are the values I get for 15 degrees and 75:</p>
<p>15:
velocity vector = (5,-19)
magnitude = 20
vCos = -15.2
vSin = 13
gravity = 9.8
output = 41</p>
<p>75:
velocity vector = (19,-5)
magnitude = 20
vCos = 18.4
vSin = -7.8
gravity = 9.8
output = 2</p>
<p>The projectile starts on the ground and gets launched at the specified angle over a flat surface.</p>
<p>Not sure where I'm going wrong.</p>
<p>All help is greatly appreciated.</p> | g11067 | [
0.05514221638441086,
-0.007265448570251465,
-0.011008424684405327,
-0.02435828000307083,
0.012515350244939327,
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-0.02655782178044319,
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0.06889494508504868,
0.08994805812835693,
-0.032... |
<p>Given a Quantum field theory, for a scalar field $\phi$ with generic Action $S[\phi]$, we have the generating functional $$Z[J] = e^{iW[J]} =
\frac{\int \mathcal{D}\phi e^{i(S[\phi]+\int d^4x J(x)\phi(x))}}
{\int \mathcal{D}\phi e^{iS[\phi]}}.$$ </p>
<p>The one-point function in the presence of a source $J$ is.</p>
<p>$$\phi_{cl}(x) = \langle \Omega | \phi(x) | \Omega \rangle_J =
{\delta\over\delta J}W[J]
= \frac{\int \mathcal{D}\phi \ \phi(x)e^{i(S[\phi]+\int d^4x J(x)\phi(x))}}
{\int \mathcal{D}\phi \ e^{i(S[\phi]+\int d^4x J(x)\phi(x))}}.$$</p>
<p>The effective Action is defined as the Legendre transform of $W$</p>
<p>$$\Gamma[\phi_{cl}]=
W[J] -\int d^4y J(y)\phi_{cl}(y),$$
where $J$ is understood as a function of $\phi_{cl}$.</p>
<p>That means we have to invert the relation $$\phi_{cl}(x) = {\delta\over\delta J}W[J]$$ to $J = J(\phi_{cl})$.</p>
<p>How do we know that the inverse $J = J(\phi_{cl})$ exists?
And does the inverse exist for every $\phi_{cl}$? Why?</p> | g11068 | [
-0.011303184553980827,
-0.025971055030822754,
-0.026971114799380302,
-0.05209185555577278,
0.05359720066189766,
-0.011755669489502907,
0.02521730400621891,
0.01840469054877758,
-0.04096877947449684,
0.01847437024116516,
-0.08318448811769485,
0.055758967995643616,
-0.05079120770096779,
0.01... |
<p>I am trying to calculate the Hawking temperature of a Schwarzschild black hole in a spacetime which is asymptotically dS. Ignoring the 2-sphere, the metric is given by
$ds^2=\left(1-\frac{2M}{r}-\frac{r^2}{L^2}\right)d\tau^2+\left(1-\frac{2M}{r}-\frac{r^2}{L^2}\right)^{-1}dr^2$ </p>
<p>where $\tau=it$ the Euclidean time and $L^2=\frac{3}{\Lambda}$.</p>
<p>In asymptotically flat space ($\Lambda=0$), one has to require that $\tau$ be periodic in the inverse temperature $\beta$ in order to prevent a conical singularity at the event horizon, from which the temperature follows.</p>
<p>In asymptotically de Sitter spacetime however, there are 2 positive roots of $g_{\tau\tau}$: the event horizon of the black hole $r_h$, but also the cosmological horizon $r_c>r_h$. As in the flat case, we can deduce the period of $\tau$ that is needed to prevent a conical singularity at $r_h$, but then we're still left with a conical singularity at $r_c$. Similarly we could make $\tau$ periodic in a way such that the conical singularity at $r_c$ disappears. </p>
<p>However, we cannot make both conical singularities disappear! Then how can we derive the black hole's Hawking temperature in this case? Should I just ignore the singularity at the cosmological horizon? Or should I use different coordinate patches?</p> | g11069 | [
0.05979764088988304,
-0.043152958154678345,
0.004545073490589857,
-0.01947086490690708,
0.0015421152347698808,
0.023117944598197937,
-0.011703389696776867,
0.025535691529512405,
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0.02215787023305893,
0.04409416392445564,
0.050763726234436035,
0.01840810850262642,
0.0692... |
<p>When throwing a ball straight up, most experts say that it momentarily comes to a stop at its apex before its return fall. If it stops, wouldn't we know its velocity and position and wouldn't this violate the uncertainty principle?</p> | g11070 | [
0.06455006450414658,
-0.011603026650846004,
0.0036112857051193714,
0.013708372600376606,
0.022586267441511154,
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0.029016291722655296,
0.014557188376784325,
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-0.01796249859035015,
-0.039813362061977386,
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0.0024299609940499067,
-... |
<p>For a presentation in physics I am going to talk about black body radiation since our book just mentions <a href="http://en.wikipedia.org/wiki/Planck%27s_law" rel="nofollow">Planck's law</a>, Wien's displacement law and Stefan-Boltzmann's law. I want to derive Wien's law and Stefan-Boltzmann's law from Planck's law. I have managed to derive Stefan-Boltzmann's law from: $$u(\nu)=\frac{2\pi h \nu^3}{c^2}\frac{1}{e^\frac{h\nu}{kT}-1}$$ by integrating over all $\nu$ from $0$ to $\infty$. However, my textbook says: $$u(\lambda,T)=\frac{2\pi hc^2 }{\lambda^5}\frac{1}{e^\frac{hc}{\lambda kT}-1}$$ If I can get from the second formula to the first, I will be happy alltough, a simple and informal derivation of Plack's law would be very satisfying.
I also managed to derive Wien's law by derivation and setting equal to zero by using: $$u_\lambda=\frac{8\pi hc }{\lambda^5}\frac{1}{e^\frac{hc}{\lambda kT}-1}$$
What are the differences? And please, since I am Norwegian and do not know very advanced physics, do not use any advanced expression without explaining them.
Thanks!</p> | g144 | [
-0.021384846419095993,
-0.012501503340899944,
0.00291204615496099,
0.013300914317369461,
0.035695306956768036,
0.0037504397332668304,
0.0353795662522316,
0.04287591576576233,
-0.03582869842648506,
-0.02119501493871212,
-0.04485832899808884,
0.03452792391180992,
0.015117377042770386,
0.0033... |
<p>Let's say you had 2 nano-engineered surfaces of diamond which were as 'flat' as possible (of course considering the radii of each carbon atom in the lattice)... would there be any friction between these 2 flat diamond surfaces when rubbed together? </p>
<p>My thinking is that there would be very little to no friction due to the electron repulsion and there being no imperfections in the surfaces.</p> | g11071 | [
0.061060354113578796,
0.029729513451457024,
0.009843073785305023,
-0.01271311566233635,
0.009888618253171444,
0.0715528279542923,
-0.004472753033041954,
-0.012160646729171276,
0.0006220508948899806,
-0.029750360175967216,
0.02269831672310829,
0.012078282423317432,
-0.040834251791238785,
-0... |
<p>Pretty simple question (I think), probably stemming from my lack of formal background in physics.</p>
<p>I've been reading questions like <a href="http://physics.stackexchange.com/questions/11542/why-is-gravitation-force-always-attractive">this one</a> related to attraction with respect to spin (a term I'm not familiar with but have a basic understanding of thanks to this reading), and have become curious about something. Are anti-particles still spin-2? I would think that the reversal of their physical state would reverse pretty much all of their other properties as well, like giving them negative mass, yet they still appear to "seek out" normal matter through some form of attraction, or at the very least their net force doesn't <em>repel</em> normal matter. Is that because of gravity (in which case they must be spin-2 and not have negative mass)? Or is there another explanation for this? Or does my physics noob-ish-ness have me completely turned around and barking up the wrong tree entirely?</p>
<p><strong>Edit:</strong> The linked question explains that mediators governed by an even-spin field will attract when their charges are similar, and repel when they are dissimilar, while mediators governed by an odd-spin field will do the opposite (as in electromagnetism).</p> | g11072 | [
0.01650656759738922,
0.010303834453225136,
-0.0017719154711812735,
0.0030093041714280844,
0.03856712207198143,
0.0727381780743599,
0.020396502688527107,
-0.0038674536626785994,
-0.024480484426021576,
-0.041044026613235474,
0.02163608931005001,
0.05109858140349388,
0.03969387337565422,
-0.0... |
<p>To calculate the angular momentum of a body we need to specify a point (or an axis?) from which to define the displacement vector $\vec{r}$, so that $\vec{L} = \vec{r} \times \vec{p}$.</p>
<p>For a rigid body, the formula becomes $\vec{L}=I\vec{\omega}$, assuming the moment of inertia is not a tensor. So in this case we need to specify an axis.</p>
<p>NOW: what if I wanted to calculate the <em>total</em> angular momentum of the Earth-Moon system?
What is the most sensible point/axis to choose? </p>
<p>I would say, intuitively, the centre of mass of the system.</p>
<p>So about the CoM,</p>
<p>$$\begin{align}\vec{L}_\text{tot}
&= \vec{L}\text{ of the Earth due to its orbit about centre of mass} \\
&+ \vec{L}\text{ of Moon due to its orbit about centre of mass} \\
&+ \text{angular momenta due to rotations of Earth and Moon around their own axes}?\end{align}$$</p>
<p>I am not sure if and how to include the rotations of Moon and Earth around their axes: I know they have to enter somehow because of the tidal friction effect on the orbit of the Moon, but I don't know how to reconcile this with the fact that I chose the centre of mass as the point of reference here, and none of the rotation axes have anything to do with the centre of mass of the Earth-Moon system.</p> | g11073 | [
0.03489226847887039,
-0.025976624339818954,
0.0031063775531947613,
-0.012911932542920113,
0.05813756212592125,
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0.033602453768253326,
0.0021738118957728148,
0.022196628153324127,
0.04069162905216217,
0.012424955144524574,
-0.008561721071600914,
0.008229491300880909,
-... |
<p>I need to produce custom star charts for my website. I want to be able to do the following:</p>
<ol>
<li>Specify a region, maybe a constellation or just an arbitrary region</li>
<li>Specify what appears on the chart (e.g. the Messier objects or the objects in some other AL observing list)</li>
<li>Specify which markings appear (e.g. constellation boundaries, ecliptic, asterisms, etc.)</li>
</ol>
<p>Does such software exist?</p> | g11074 | [
-0.01881641149520874,
-0.01475355215370655,
-0.0037475908175110817,
-0.11256840825080872,
-0.005641263909637928,
-0.030761417001485825,
-0.020899806171655655,
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0.024220159277319908,
-0.07465273141860962,
0.04482804983854294,
0.0029835645109415054,
0.13525789976119995,
... |
<p>I have a set of data on all the stars (well, to a magnitude of 9 or so) with the values of the following properties:</p>
<ul>
<li>magnitude, </li>
<li>right ascension and,</li>
<li>declination.</li>
</ul>
<p>Now I'd like to create a planar (rectangle in shape) map of the entire sky (both hemispheres), without stretching anything (keeping all constellations etc., as seen in the sky.)</p>
<p>I know this is more of a math question, but I guess there's some fairly known function (or ratio? I haven't found it on Google, though) to achieve this; if so, how?</p> | g11075 | [
-0.021258236840367317,
-0.012683981098234653,
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-0.05655403435230255,
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0.004031718242913485,
-0.029911434277892113,
-0.022751249372959137,
0.029317695647478104,
-0.0385795459151268,
0.023371178656816483,
0.01149534061551094,
0.07459127902984619,
0.... |
<p>How to derive <a href="http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law" rel="nofollow">Stefan</a> constant from <a href="http://en.wikipedia.org/wiki/Planck%27s_law" rel="nofollow">Planck</a>'s <a href="http://en.wikipedia.org/wiki/Black-body_radiation" rel="nofollow">Blackbody radiation</a>?
Consider the following expression relating to blackbody radiation:
$$\phi(\lambda) d\lambda= E({\lambda}) \, f({E(\lambda}))\,D({\lambda})d{\lambda}$$
$$\phi(\lambda) d\lambda=\left( \frac{hc}{\lambda}\right) \left(\frac{1}{e^g-1}\right) \left( \frac{8\pi}{\lambda^4} \right) d\lambda \, \, ,$$ where $g = \frac{hc}{k_BT\lambda}$.</p>
<p>I know that $D({\lambda})d{\lambda}$ is the density of states within $d{\lambda}$. </p>
<p>What is $\phi(\lambda) d\lambda$? The book says radiation energy density.</p>
<p>What does it mean that $\phi(\lambda)$ = (energy of state) * (probability distribution) * (density of states) = energy of state distributed among the density of the states?
And then $\int\phi(\lambda) d\lambda$ is the density of energy distributed within the interval $d\lambda$?</p>
<p>What can I do to relate $\phi(\lambda) d\lambda$ to intensity, and then get $I=\sigma T^4$?</p> | g11076 | [
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<p>I've always wondered, that since the Earth is moving at a very fast velocity around the Sun, why is it that when astronauts leave the Earth, the Earth doesn't immediately move away from them at extremely large speeds? </p> | g11077 | [
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<p>Could someone provide me with a mathematical proof of why, a system with an absolute <a href="http://en.wikipedia.org/wiki/Negative_temperature">negative Kelvin temperature</a> (such that of a spin system) is <a href="http://en.wikipedia.org/wiki/Negative_temperature#Heat_and_molecular_energy_distribution">hotter</a> than any system with a positive temperature (in the sense that if a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system).</p> | g278 | [
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<p>I am considering purchasing an EMF reader, to collect data about what is being thrown off of power lines and various other sources in the house to reach some conclusions.</p>
<p>An issue is, the meter can only read in Teslas or gauss. This is fine, however a Tesla is equal to $\frac{Wb}{m^2}$ and one Weber being one volt-second or joule/ampere and I get confused.</p>
<p>My intention is just to derive the total power at that specific point that the source is radiating.</p>
<p>Is there a direct conversion from µT to $\frac{W}{m^2}$ I am missing?</p>
<p>Since Teslas are measuring the magnetic flux density of the low frequency radiation coming off of power lines, does that skew my result if it is not also measuring the electric field? Would I be better off creating an antenna/inductor and measure µW (or similar) induced directly in different areas?</p>
<p><strong>Update:</strong> Seems I cannot get reasonable numbers with the following formulas (from "in plane waves, poynting vector, see [2]):</p>
<p>$B = 0.000004$ (4μT)<br>
$B_0 = \frac{1}{c}E_0$, so, $E_0 = \frac{B_0}{\frac{1}{c}} = 1199.169832\frac{V}{m}$ </p>
<p>so..
$S = \frac{1}{\mu_0} E\times B = 3817.07613$ which = $\frac{3.8kW}{m^2}$)</p>
<p>or..
$S = \frac{cB_0^2}{2\mu_{0}} = 1908.538065$ which = $\frac{1.9kW}{m^2}$</p>
<p>I am probably doing something grossly wrong, I need to realise my mistakes so I can calm my mind and learn how to apply these formulas. I assume the $B_0$ means at time 0, which I can consider the peak field amplitude in my purposes, no?</p>
<p>Tesla unit resource: <a href="http://en.wikipedia.org/wiki/Tesla_%28unit%29" rel="nofollow">http://en.wikipedia.org/wiki/Tesla_%28unit%29</a><br>
Poynting vector: <a href="http://en.wikipedia.org/wiki/Poynting_vector" rel="nofollow">http://en.wikipedia.org/wiki/Poynting_vector</a></p> | g11078 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/16781/how-long-does-it-take-for-expanding-space-to-double-in-size">How long does it take for expanding space to double in size</a> </p>
</blockquote>
<p>According to the standard concordence model, I heard that it's likely that space is doubled after 11.4 billion years. Am I right? Then, how fast (<-acceleration) is this happening? (By speed, I mean distance/time)</p>
<p>Also, is space being doubled based on observation data?
Thanks. </p> | g356 | [
0.049727607518434525,
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0.030109260231256485,
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0.011857131496071815,
0.0371350422501564,
-0.00... |
<p>For a <a href="http://en.wikipedia.org/wiki/Ising_model#Two_dimensions" rel="nofollow">2D Ising model</a> with zero applied field, it seems logical to me that the phases above and below T_c will have different <a href="http://en.wikipedia.org/wiki/Percolation_theory" rel="nofollow">percolation</a> behaviour. I would expect that percolation occurs (and hence there is a spanning cluster) below T_c and that it does not occur (no spanning clusters) above T_c. I'm looking for conformation that this is true, but haven't found anything so far. Is my conjecture correct?</p> | g11079 | [
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0.035210151225328445,
0.018894366919994354,
-0.0390... |
<p>Why is the ground state assignment $0^{+}$ whenever the number of neutrons and protons are both even? </p> | g11080 | [
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0.0317... |
<p>Many hall sensors on the market have a datasheet that explain the proportional relationship between the analog voltage that is outputted and the relative gauss/tesla reading (for example: 2.5mV = 1Gauss). How would one go about selectively measuring AC fields in the same manner with for example this Hall effect sensor: <a href="https://www.sparkfun.com/products/9312" rel="nofollow">https://www.sparkfun.com/products/9312</a> . Is it even possible? Am I missing something?</p> | g11081 | [
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<p>I'm working on a physics engine for a game and I need something clarified.</p>
<p>Let's say I have a stationary sphere, sitting atop a platform. The sphere's mass is 10kg, and gravity is $10m/s^2$, for the sake of simplicity. That means that, due to $W = mg = F$, it is exerting a force of 100N on the platform.</p>
<p>Now, imagine the sphere being 100m above the platform, with starting velocity of 0m/s. For simplicity's sake, I'm ignoring drag. Using $v^2 = u^2 + 2as$, the final velocity when it reaches the platform is 63m/s. Now let's say that the time of impact between the sphere and platform is 0.2s, would I be correct if I use $F = m (v-u)/t$ to prove that more force is being exerted on the platform than in the first case?</p>
<p>Thanks in advance :)</p> | g11082 | [
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<p>I work on the Kitaev toy model for Majorana fermions. He writes that in Majorana basis the Hamiltonian becomes in general</p>
<p>$$
H = \frac{i}{4} \sum_{l,m} A_{l,m}\gamma_{l}\gamma_{m}
$$</p>
<p>where $\gamma$ is the creation operator for Majorana fermions and $A$ is a skew-symmetrix matrix. Now he say that the ground state of this Hamiltonian has an even fermionic parity for the case without Majorana fermions at the end of the wire.</p>
<p>To calculate the eigenvalues of the Hamiltonian we can bring the Hamiltonian in block diagonal form with a Transformation $WAW^{T}$ where W is a real orthogonal matrix whose rows are eigenvectors of A. If $W$ has the form $W = e^{D}$ for some skew-symmetrix matrix $D$ or if $\rm{det}(W) = +1$ the parity doesn't change. Otherwise the Transformation $WAW^{T}$ changes the parity of the ground state (here now $\rm{det}(W) = -1$).</p>
<p>My question is now: Why changes the parity of the ground state when $\rm{det}(W) = -1$? Further, what is the reason for the even parity of the ground state (he writes that the ground state is superposition of states with even number of electrons but what happens when when the number of electrons is odd)?</p> | g11083 | [
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0.0375... |
<p>Can someone give a simple expose on <a href="http://en.wikipedia.org/wiki/Coleman%E2%80%93Mandula_theorem" rel="nofollow">Coleman Mandula theorem</a> and what <a href="http://en.wikipedia.org/wiki/Mandelstam_variables" rel="nofollow">Mandelstam variables</a> are?</p>
<p>Coleman-Mandula is often cited as being the key theorem that leads us to consider Supersymmetry for unification. An overview discussion with sufficient detail is missing in many popular texts. So how does Coleman Mandula theorem actually meet its no-go claim? </p> | g11084 | [
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0.018655071035027504,
0... |
<p>Meaning, why is it the exact number that it is? Why not 2x10^8 /mps instead of 3? Does it have something to do with the mass, size or behavior of a photon? To be clear, I'm not asking "how we determined the speed of light". I know there isn't a clear answer, I'm really looking for the prevailing theories.</p> | g283 | [
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<p>My book says: </p>
<blockquote>
<ul>
<li><p>A pure semiconductor at room temperature possesses free electrons and holes but their number is so small that conductivity offered by the pure semiconductor cannot be made of any practical use. By addition of impurities to the pure semiconductor in a very small ratio ($1:10^6$), the conductivity of a $Si$-crystal (or $Ge$ crystal) can be remarkably improved. </p></li>
<li><p>The process of adding impurity to a pure semiconductor crystal so as to improve its conductivity is called <em>doping</em>. During doping, the impurity atoms are added to the silicon crystal in a small ratio, its atoms replace the silicon atoms here and there.<br>
<img src="http://i.stack.imgur.com/uw9kZ.gif" alt="enter image description here">
<img src="http://i.stack.imgur.com/9mKNS.gif" alt="enter image description here"></p></li>
</ul>
<p><em>Fig (left): Substituting a phosphorus atom (with five valence electrons) for a silicon atom in a silicon crystal leaves an extra, unbonded electron that is relatively free to move around the crystal</em></p>
<p><em>Fig (right): Substituting a boron atom (with three valence electrons) for a silicon atom in a silicon crystal leaves a hole (a bond missing an electron) that is relatively free to move around the crystal</em></p>
</blockquote>
<p>I got few questions here, how are silicon atoms replaced, did impurity atoms exerted force to make position? </p>
<p>In chemistry we are taught about defects i.e some of the atoms might be missing from the crystal. So, I assumed some of silicon atoms to be missing, thus impurity atoms can be thought to go and fit into those vacancies. But, considering this to be true I got few troubles, </p>
<ul>
<li>Leaving those vacancies (without adding impurity atom) will be far better because, we will have $4$ unpaired bonding electrons and thus $4$ holes (considering coordination no. to be $4$), this is greater than having impurity atom in that vacancy which produces single hole from trivalent impurity. Absolutely there might be some thing wrong going here, because in reality adding impurity increases conductivity than staying quite without adding. Then is it that impurity atoms didn't go into vacancies, did they actually exerted force on silicon atoms to make position? </li>
</ul>
<p>Adding pentavalent impurity i.e, adding single pentavalent impurity atom to $10^6$ silicon atoms would fetch only one free electron. How could this increase conductivity remarkably? We already have free electrons at room temperature, with out the one pentavalent impurity atom also conductivity should have remained same. But it is not the case. Then how could this single impurity atom make such a difference in conductivity (in a crystal of $10^6$ silicon atoms)? </p>
<p>I don't know whether I have misunderstood anywhere, if so pardon me and explain. </p>
<p>Sometimes I might not be communicating with you better, if so please comment on the part where explanation on the problem is to be extended.</p> | g11085 | [
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<p>I've heard that one of the reasons that we don't have commercial supersonic flight is because of the sonic boom produced. Is this really a deal-breaker and if not, how do you get around/minimize the nuisance?</p> | g11086 | [
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<p>Today, the obliquity of the earth is about 23.4°.
6500 years ago, it was about 24.1°</p>
<p><img src="http://i.stack.imgur.com/i8p2T.png" alt="enter image description here"></p>
<p>Imagine the blue square is the constellation of Orion, and the yellow star is the sun. Viewpoint B is you, on earth, today, when the obliquity is 23.4°. When you look at Orion, you see it as below the ecliptic. But with a change in obliquity, your viewpoint moves to Viewpoint A. Now when you you look at Orion, it appears to be on the ecliptic.</p>
<p>Am I correct, or have I got it wholly wrong?</p>
<p>I realise the diagram greatly exaggerates the angles, as well as condenses the distances, but the principle is there. The question is, does the principle apply in the case of Orion?</p>
<p>I'm exploring a hypothesis that at some time in the past (I chose the date of 6500 years ago, because the Vernal Equinox was closest to Orion at that time), Orion seemed to be closer to the sun's path than it does today. However, it has been suggested to me that it may actually have been further away.</p>
<p>So, would the change in obliquity have any effect on the view of Orion, or not?</p>
<p><strong>EDIT after first 2 answers</strong></p>
<p>Here's an image that better expresses what I mean:</p>
<p><img src="http://i.stack.imgur.com/45ckE.jpg" alt="parallax"></p>
<p>Your viewpoint A is where you are on earth today, when the earth is at 23° axial tilt. Looking at the sun, you see no stars on the celestial sphere behind it. But when the earth was tilted 24°, when you look at the sun you see Orion behind it. (Obviously, this is imaginary, as you don't see the sun and stars in the sky at the same time, but it illustrates the principle of where the ecliptic is.) </p>
<p>Because the celestial sphere is much further away from the earth than the sun the distance C-D seems much greater than the distance A-B, even though the angles are the same. So the optical effect is that Orion appears on the ecliptic, or not, depending on what angle the earth is tilted at. Yes or no?</p>
<p><strong>2nd edit</strong></p>
<p>Without wishing to sidetrack, it might help if I explained why I'm so interested in this. I'm studying Egyptology. Among the few certainties we have are that a) their religion/myth was astronomically based, and b) their god Osiris was the constellation of Orion. Now, Osiris' name is written with the hieroglyphs of an eye and a throne. Because the eye is a common symbol for the sun, Egyptologists such as Lefebure and Brugsch, and others, have suggested that the name simply means "the seat, or throne, of the sun (god)". This is disputed by others, of course. </p>
<p>Now I'm re-examining the problem, without having a vested interest, one way or the other, in the outcome. My reasoning goes like this; a phrase such as "the seat of the sun" or sometimes "house of the sun" is well-documented in many ancient cultures as referring to a stage in the sun's path; that most often seems to refer to the equinoxes or solstices, but can also refer to the zodiacal constellations. The implication is that Orion was given this name because of some sort of relationship between him and the sun. 6500 years ago, the Vernal Equinox was directly above Orion: <em>above</em>, but not <em>in</em>, because Orion is not on the ecliptic.</p>
<p>However, Egyptian myth tells us that Osiris was murdered by being struck down (or in a variant text, drowned). This implies a downward movement. The name "the seat of the sun" makes absolutely no sense whatsoever, unless the Vernal Equinox was actually <em>in</em> Orion, and not several degrees above it. And so, I'm wondering if the myth of Orion/Osiris being struck down or drowned is somehow an attempt to describe the visual effect of an axial shift; I'm hypothesising that perhaps 6500 years ago, from the viewpoint of an observer on earth, the sun <em>did</em> appear to be closer to Orion than it currently is, close enough to be described as in rather than above. </p>
<p>We cannot be absolutely sure precisely which stars of Orion represented Osiris for the Egyptians; we only have a general idea. But it's a fairly safe bet that the principal 7 or 8 stars of the 'hourglass' shape were included. Also, as Orion was frequently depicted in astronomical texts with one arm raised, much like the constellation is today, it's very probable that Chi 1 and Chi 2 Orionis were also included. </p>
<p>So, in order to demonstrate that, at the time of the Vernal Equinox, the sun was in Orion, I would need to somehow show that the sun appeared slightly lower in the sky, not necessarily low enough to cross Orion's Belt (which would be more than I could possibly hope for!), but low enough to even cross his raised arm. That would probably be enough. Look at the map: it's only a few degrees from the ecliptic to the arm... is there no way this could be possible?</p>
<p>It's not exactly a world-shattering event, but it would settle a long-running debate between Egyptologists once and for all.</p> | g11087 | [
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<p>Given an astrophoto with a resolution between 0.5 and 5 arcseconds per pixel, which ways exist to identify the direction of view, field of view, and objects in the picture?</p>
<p>I believe most amateur astrophotographers are in this resolution range, and I believe most of us would like to confirm the captured images. I have read about the <a href="http://astrometry.net" rel="nofollow">http://astrometry.net</a> project and I'm wondering if there are any similar services available.</p> | g11088 | [
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<p>I've already posted <a href="http://www.quora.com/What-is-the-average-distance-between-stars-throughout-the-galaxy-and-does-the-mean-distance-decrease-towards-the-centre-of-the-galaxy" rel="nofollow">here on quora</a>. But, I'm not totally sure if it's the most reasonable method. </p>
<p>Would anyone care to elaborate on how to find the average distance between stars in a given galaxy (For instance, let's take Milky way), somewhat efficiently and accurately - or at least clarify that my method is sufficiently efficient and accurate?</p> | g11089 | [
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0.0... |
<p>We've all seen the telescope photographs of andromeda galaxy:
<img src="http://i.stack.imgur.com/l4EOK.jpg" alt="enter image description here"></p>
<p>I'm wondering if it were possible to travel close enough to the andromeda galaxy could you achieve a same perspective with the naked eye? What distance away from andromeda would give you the same vantage point as the photograph to the point that you could take the same photograph with a regular point and shoot camera?</p>
<p>I assume you would be in intergalactic space between andromeda and the milky way. </p>
<p>On that note, if you were halfway between the two, would you be able to clearly make out both galaxies in their entirety or would you simply see 2 points of light that more resemble stars than galaxies?</p> | g11090 | [
-0.0287153460085392,
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0.02520507574081421,
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0.0796031802892685,
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0.001... |
<p><a href="http://lightyears.blogs.cnn.com/2011/11/03/asteroid-to-pass-closer-to-earth-than-the-moon/?hpt=hp_t2" rel="nofollow">In the news</a>, it has been stated that there will be a fairly large asteroid passing fairly close to Earth soon. I've been trying to find a good observation guide, including determining how bright it will be, with bad luck. Specifically, I want to find out if this is a naked eye visible object, and if so, how to find it. Thanks!</p> | g11091 | [
-0.001274876412935555,
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<p>I always see pictures of the solar system where our sun is in the middle and the planets surround the sun. All these planets move on orbits on the same layer. Why?</p> | g231 | [
0.022835643962025642,
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0.023978382349014282,
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<p>Well there is a problem in my book which lists this problem:</p>
<blockquote>
<p>Calculate the probability that a particle will be found at $0.49L$ and $0.51L$ in a box of length $L$ when it has (a) $n = 1$. Take the wave function to be constant in this range.</p>
</blockquote>
<p>The answer in the solutions manual for this specific problem is given as:</p>
<p><img src="http://i.stack.imgur.com/LW8Kt.png" alt="Solution"></p>
<p>However when I workout the equation myself I get this:</p>
<p><img src="http://i.stack.imgur.com/MJieW.jpg" alt="What I got"></p>
<p>So i don't understand why the solutions book says that:
$$\frac{2}{L}\int \sin^2 \left(\frac{n \pi x}{L} \right) \; \mathrm{d} x \approx \frac{2 \Delta x}{L} \sin^2 \left(\frac{n \pi x}{L} \right)$$</p>
<p>What am I doing wrong here??</p> | g11092 | [
0.029556695371866226,
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-0.02962307073175907,
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0.07555905729532242,
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0.0231269... |
<p>A superconducting wire($SC$) is moved rapidly in a magnetic field( $1$ $Tesla$), what would happen to the wire? Are there any forces induced of attraction or repulsion? </p>
<p>In a typical conductor, we know that if it is moved around a magnetic field $-V$ is induced within the wire based on Faraday's law, however, with the condition of the $SC$ what could happen if $R = 0$ $ohms$? </p>
<p>Will Faraday's law still be applied to that wire with no resistance?
moving a $SC$ in a magnetic field will not induced $EMF$?</p> | g11093 | [
0.011527257040143013,
0.04979250952601433,
0.003833064576610923,
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0.04543331637978554,
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-0.03295036032795906,
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0.029740560799837112,
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-0.014... |
<p>If you were staring to the sky in a big city and electricity is turned off in a big area around you, would you be seeing the sky with little light pollution instantly?</p> | g11094 | [
0.012593992054462433,
0.009422116912901402,
0.006298856809735298,
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-0.018843084573745728,
0.022519323974847794,
0.025632616132497787,
0.0019056641031056643,
0.0... |
<p>I think in quantum mechanics we assign to each system a specific Hilbert space i.e. if systems are different then their Hilbert spaces are different.
Is this true? If not why?
For differernt system I mean their hamiltonians are different.</p> | g11095 | [
-0.004974319599568844,
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0.00881271343678236,
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0.014070024713873863,
-0.012115346267819405,
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0.02218550629913807,
0.021563943475484848... |
<p>Related: <a href="http://physics.stackexchange.com/questions/116452/why-did-high-quality-mirrors-use-aluminum-coatings-instead-of-silver/116547#116547">Why did high quality mirrors use aluminum coatings instead of silver?</a></p>
<p>After reading Chris White’s and LDC3’s comments in the above related link, it got me wondering about silver’s atomic structure. When looking at the reflectance vs. wavelength plot below,</p>
<p><img src="http://i.stack.imgur.com/vqJJw.gif" alt="enter image description here"></p>
<p>silver has a particularly strong resonance slightly around 315 nm when compared to the other metals. I believe that I have good understanding what silver is doing at optical frequencies (see this previous <a href="http://physics.stackexchange.com/questions/74760/why-do-most-metals-appear-silver-in-color-with-gold-being-an-exception-from-a-sc/74761#74761">post</a>) but I have no idea why there is such a strong UV absorption around 315 nm in silver. Can someone explain what is going on?</p> | g11096 | [
0.0620599165558815,
0.012866890989243984,
0.005193961318582296,
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0.03064185008406639,
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0.007206200622022152,
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0.030414892360568047,
0.05867263302206993,
0.04409017041325569,
0.011872587725520134,
-0.003466... |
<p>Here at the company we've been working on a new product, and it will more than a few times a day and with a considerable force, slide on a plastic surface, being itself, another plastic body, roughly the same material, on will be injected to a mould and the other extruded, thats the main difference. </p>
<p>As we design, we thought of a friction problem due to the drag forces and the parts being in constant physical contact and one sliding on top of the other.</p>
<p>We thought we could reduce this problem by adding tiny spheric fixed protuberances that would reduce the contact area, this was 3D printed and tested and actually works, but we are worried that it will wear out soon due to extensive use. What other "mechanical tricks" are there to reduce friction between two surfaces?</p>
<p>Thank you for your answers :)</p> | g11097 | [
0.07945643365383148,
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0.009323660284280777,
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0.023488277569413185,
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0.03108... |
<p>The total mass is 2300kg (weight = 5072lbs). Find the size of the force due to wind and rolling friction when the van speed is 44.86mph (1mph= 0.447m/s).</p>
<p><img src="http://i.stack.imgur.com/oXku9.gif" alt="image"></p>
<p>I am really at a loss of what to do here.</p>
<p>Part 2:</p>
<p>How much net power, in hp (1 hp=746W) must the engine deliver to maintain a speed of 44.86mph (20.05m/s) (Neglect losses involved in delivering the power).</p> | g11098 | [
-0.00423636008054018,
0.013272593729197979,
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0.030559342354536057,
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0.017431916669011116,
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... |
<p>I have looked at <a href="http://physics.stackexchange.com/questions/54556/how-to-calculate-the-intensity-of-the-interference-of-two-waves-in-a-given-point">this</a>, but it did not help with <em>locations</em>. Really this just comes down to mathematical manipulation, which for some reason I fail to see. Here is my paraphrased setup:</p>
<blockquote>
<p>Consider two sources of light separated by some distance $a$, and suppose they are emitting uniformly in all directions, at the same angular frequency, and same wave number. Determine the locations on a plane, which is parallel to the line joining the two light sources, at which the intensity is a minimum. </p>
</blockquote>
<p>This is what I have. Let $r_1$ denote the distance from the first source to a point on the screen, $r_2$ for the second source to the point, and $L$ be the distance from the midpoint of the charges to the screen. Consider some point $p = (y,z)$ on the screen. Letting the x-axis be orthogonal to the screen and its origin at the midpoint, and the y and z axes to be parallel to the screen, we can write $$r_1 = \sqrt{L^2+y^2+(z-a/2)^2} \space\space\space \text{&} \space\space\space r_2 = \sqrt{L^2+y^2+(z+a/2)^2}$$ From this, we know that we can write the total wave at a point $p$ as $$E(t) = e^{iwt}(E_1e^{ikr_1}+E_2e^{ikr_2})$$ I am not substituting in yet for clarity, and note that $E_1$ and $E_2$ are the amplitudes of the respective waves. Now we also know that the intensity at this point has the following relationship: $I \propto |E|^2$, and we know from above that</p>
<p>$$|E|^2 = E_1^2+E_2^2+2E_1E_2cos\biggl[k\Bigl(\sqrt{L^2+y^2+(z-\frac{a}{2})^2}-\sqrt{L^2+y^2+(z+\frac{a}{2})^2}\Bigr)\biggr]$$ </p>
<p>If things are correct up to this point, then it is clear that the minimum intensity locations occur when this cosine is a minimum. Namely, when </p>
<p>$$\sqrt{L^2+y^2+(z-\frac{a}{2})^2}-\sqrt{L^2+y^2+(z+\frac{a}{2})^2} = \frac{(2n+1)\pi}{k} \space\space n \in \mathbb{Z}$$ </p>
<p>However, I cannot seem to put this into a nice simplified form for z as a function of y. I suspect that it is a hyperbolic relationship, but is there a nice way to reduce this to a compact form?</p> | g11099 | [
0.023712199181318283,
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0.008020787499845028,
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0.023724040016531944,
0.006795189809054136,
0.014219806529581547,
... |
<p>I have heard about <a href="http://en.wikipedia.org/wiki/Dark_matter" rel="nofollow">dark matter</a> that's called the Master Of The Universe. What's this and is the dark matter the reason galaxies exist?</p> | g11100 | [
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0.003430164884775877,
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0.03384621813893318,
-0... |
<p>What is exactly a <a href="http://en.wikipedia.org/wiki/Dobsonian_telescope" rel="nofollow">Dobsonian telescope</a>, and what are the differences between this technical choice over a <a href="http://en.wikipedia.org/wiki/Schmidt%E2%80%93Cassegrain_telescope" rel="nofollow">Schmidt-Cassegrain</a> or a <a href="http://en.wikipedia.org/wiki/Newtonian_telescope" rel="nofollow">Newtonian</a> configurations?</p> | g11101 | [
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0.047700099647045135,
-0.00760619854554534,
0.08126009255647659,
-0.... |
<p>Can any telescope, such as a 8" reflector, that is normally used at night to look at planets be used or adapted for solar observing?</p>
<p>What kind of adapters or filters are required or is it better to get a dedicated solar telescope?</p>
<p>I'd like to look at sunspots, flares, prominences, eclipses, etc.</p> | g11102 | [
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0.01658935844898224,
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0.053523752838373184,
-0.04634920880198479,
0.03763166815042496,
0.0971488282084465,
0.03254833444952965,
-0.025222... |
<p>Sorry for posting what may be an obvious question but we just learning about friction at school and my teacher couldn't explain well enough to me and I would appreciate your inputs.</p>
<p>Consider the following 3 cases:</p>
<p>1) A load of mass $m_2$ lies on a surface. The coefficient of friction between the load and the ground is $\mu$. You need to exert a force $F=\mu\cdot m_2\cdot g$ to pull the load, right?</p>
<p>2) A driver, e.g. locomotive of mass $m_1$ sits on the same surface and has the same coefficient of friction $\mu$ to it. The maximum force that this can exert is $\mu\cdot m_1\cdot g$, right?</p>
<p>3) Now, how can the locomotive pull the load at all? After all, it can just about pull itself? Now, I know that locomotives are able to pull their loads without issues. I mean, I am not getting some important concept here. Does the maximum traction that a locomotive can achieve increase if we hang a large load at it's back? That seems counterintuitive to me.</p>
<p>I would appreciate your help in understanding this. And thanks for your patience with a physics newbie.</p>
<p>Regards,
Victor</p> | g11103 | [
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0.03253858536481857,
-0.0337... |
<p>Is there any (interesting) HEP process whose study would take advantage from $e^-e^-$ or $e^+e^+$ collisions with respect to $e^+e^-$ collisions?</p> | g11104 | [
0.013053075410425663,
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0.02464... |
<p><a href="http://en.wikipedia.org/wiki/Deformation_%28mechanics%29" rel="nofollow">Strain</a> is defined as
$$\epsilon=\frac{1}{2}\left( \nabla u + \nabla u^T\right).$$</p>
<p>I found a formula for the strain tensor in 3D decomposed into volumetric and deviatoric components:</p>
<p>$$\epsilon= v + d,$$<br>
where $v=\frac{1}{3}\epsilon_v I$ is the volumetric strain with $\epsilon_v=trace(\epsilon)$ and $d$ is the deviatoric strain.</p>
<p>Does this formula apply in 2D as well? Or is $v=\epsilon_v=\frac{1}{2}\epsilon_v I$ in 2D?</p> | g11105 | [
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0.01574668660759926,
... |
<p>$$\nabla_{j} v^{i}~=~g^{ik}\nabla_{j}v_{k}.$$</p>
<ol>
<li><p>Does this equality involve an intermediate step, where I take the metric inside the derivative, and then use the fact that covariant derivative of the metric is zero? </p></li>
<li><p>Or is this true just because the covariant derivative transforms as a tensor (independent of the fact that the covariant derivative of the metric is zero)? </p></li>
</ol> | g11106 | [
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0.01789018325507641,
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0.016346167773008347,
0.03037945367395878,
-0.053... |
<p>I'm a physics major so bear with me here on the math. This is related to a problem from the textbook General Relativity - Wald. In classical electromagnetism if we have a vector field say $V$ defined on all of $\mathbb{R}^{3}$ such that $V\rightarrow 0$ , dropping off as $O(1/r^{3})$, in the limit as $r\rightarrow \infty $ then when calculating $\int_{\mathbb{R}^{3}}\partial _{i}V^{i}d^{3}x$ one usually takes a closed ball $\bar{B_{r}}(x)\subset \mathbb{R}^{3}$ and, using the fact that $\bigcup _{r}\bar{B_{r}}(x) = \mathbb{R}^{3}$ gives us, with an appropriate limit theorem, that $\int_{\mathbb{R}^{3}}\partial _{i}V^{i}d^{3}x = lim_{r\rightarrow \infty }\int_{\bar{B_{r}}(x)}\partial _{i}V^{i}d^{3}x$ to which we can then apply the divergence theorem to state that $lim_{r\rightarrow \infty }\int_{\bar{B_{r}}(x)}\partial _{i}V^{i}d^{3}x = lim_{r\rightarrow \infty }\int_{\partial \bar{B_{r}}(x)}V^{i}n_{i}d^{2}x = 0$ where the zero comes from the fact that the integral will drop off as $O(1/r^{2})$ as $r\rightarrow \infty $ so the sequence of surface integrals will eventually converge to zero. </p>
<p>This is all fine and dandy but my problem deals with a background flat space - time with metric perturbation $(M,\eta _{ab} + \gamma _{ab})$ where $\eta _{ab}$ is the minkowski metric and $|\gamma _{ab}| << 1$ as usual. We have a space - like hypersurface $\Sigma $ of this manifold, the Landau Lifshitz pseudo tensor $t_{ab}$, which is divergence free, and the total energy $E = \int_{\Sigma } t_{00}d^{3}x$. We must show that $E$ is time translation invariant. Using the facts that $\partial ^{a}t_{ab} = 0, \partial _{0}E = -\partial ^{0}E$ we proceed: $\partial _{0}E = -\partial ^{0}E = -\partial ^{0}\int_{\Sigma }t_{00}d^{3}x = -\int_{\Sigma }\partial ^{0}t_{00}d^{3}x = \int_{\Sigma }\partial ^{i}t_{i0}d^{3}x$. We are also given that $t_{\mu \nu }\rightarrow 0$ identically, dropping off as $O(1/r^{3})$, in the limit $r\rightarrow \infty $. </p>
<p>This is, of course, very similar in situation to the electromagnetic case and one would ideally like to use the divergence theorem to get the desired result that $\partial _{0}E = 0$ however here we do not have a prescribed metric $d$ on $\Sigma$ to make sense of closed balls as far as I can tell and even if there is some natural choice of metric $d$ for $\Sigma$ how will we know if the closed balls with respect to $d$ will be orientable? Thanks for any and all help and sorry if this was a bit long winded; it is my first post here so I'm not sure how it is meant to work :[; I just wanted to be thorough in explaining my issue. Thanks again. </p> | g11107 | [
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0.03319845721125603,
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-0.0... |
<p>In non-abelian gauge theories self interaction of gauge fields is permitted, allowing coupling such as $WWZ$ (i.e. $Z$-boson decaying to $W^+W^-$) or ggg (i.e. gluon splitting into two new gluons). </p>
<p>The aforementioned particles are spin-1 particles, thus I'd assume that the above processes are prohibited from spin considerations. Consider for example a spin +1 gluon splitting in two new gluons, their total spin can either add to +2 or 0. </p>
<p>I am well aware that spin itself is not conserved in these interactions but only the <em>total angular momentum</em> $J=S+L$, thus I'd assume that the two gluons have a nonzero relative angular momentum $L$. </p>
<p>My question is whether that is the correct explanation for the phenomenon. My QM skills are a little bit rusty, so any help is appreciated!</p> | g11108 | [
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<p><img src="http://i.stack.imgur.com/tGcgA.png" alt=""> </p>
<p><strong>In the equation (1.18) they omitted the translation vector $a^\mu$, but why?</strong></p> | g11109 | [
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0.003065... |
<p>As I understand it, the explanation of the windchill factor goes like this:</p>
<blockquote>
<p>Your body is warmer than the air around it, therefore it loses a
certain amount of heat to the air. This warms up the air immediately
around you first. The heat will then gradually be transferred to the
air further away through convection, but there's so much more of the
air than there is of you that the air essentially acts as a perfect
heat sink, and your body heat isn't likely to raise the overall
temperature of the air in even a moderately-sized room by any
measurable degree.</p>
<p>However, you're still warming the air immediately around your body
first. When the air is moving, it blows away the air immediately
around your body, which is slightly warmer than the rest of the air,
and replaces it with the slightly cooler air that hasn't been warmed
up yet. Since the speed of convective heat transfer is based on the
difference between the temperatures of the bodies involved, this means
that you lose heat faster, and feel chilled more than you would at the
same temperature if there was no wind.</p>
</blockquote>
<p>However, I have memories of days when the temperature was well over 100 degrees, and breezes were still a relief. By the explanation above, wind should have made the heat <em>even more oppressive</em> because the convective heat transfer is flowing in the opposite direction, into my body rather than out of it. What's the principle here that makes this possible?</p> | g11110 | [
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0.0... |
<p>I think this problem is much more difficult than what I've learned so far.</p>
<blockquote>
<p><img src="http://i.stack.imgur.com/OCh1Z.jpg" alt="Problem"></p>
</blockquote>
<p>B) is the problem I'm having a hard time with. I think it is much more difficult to consider because as the red object begins compressing the spring the blue object will begin to move as well. </p>
<p>It also seems apparent that there must be some kind of relationship of how much force is instantaneously transferred to the blue object as it is compressed by the red object. </p>
<p>I'm really not sure how to do this to be honest. I haven't learned how to make work with springs besides energy equations. I've tried the spring constant (N/m) x the incoming speed (m/s) to determine how many newton's per second are being exerted during the collision, but I haven't figured out where to go from there. </p> | g11111 | [
0.04685403034090996,
0.03808115795254707,
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0.016949402168393135,
0.06815934181213379,
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0.0... |
<p>I have seen two form of <a href="http://en.wikipedia.org/wiki/Hubbard_model" rel="nofollow">Hubbard model</a>, one is:
$$H=-t\sum_{<ij>s}c_{is}^\dagger c_{js}+h.c.+U\sum_i(n_{i\uparrow}-1/2)(n_{i\downarrow}-1/2)-\mu\sum_{is}n_{is}$$</p>
<p>The other is a more familiar one, which writes:</p>
<p>$$H=-t\sum_{<ij>s}c_{is}^\dagger c_{js}+h.c.+U\sum_i n_{i\uparrow}n_{i\downarrow}-\mu\sum_{is}n_{is}$$</p>
<p>I want to know if these two forms are equivalent. If not, on what conditions they are equivalent?(lattice type, filling,type of ground-state,attractive U of repulsive U etc.)</p> | g11112 | [
-0.005898724310100079,
0.026672352105379105,
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0.0256... |
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