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|---|---|---|
<p>I have chosen to make my own solar filter using Baader as opposed to Mylar or anything else based on these: <a href="http://physics.stackexchange.com/a/25204/6805">http://physics.stackexchange.com/a/25204/6805</a> and <a href="http://irwincur.tripod.com/mylar_vs__baader.htm" rel="nofollow">http://irwincur.tripod.com/mylar_vs__baader.htm</a> and others.</p>
<p>My last solar filter was the product which is no longer available direct from Celestron (I'm not even sure what it was made with).</p>
<p><strong>My questions</strong>: </p>
<p>Does "flapping in the wind" baader effect image quality? See the images below to understand what I mean...</p>
<p>Is it possible to achieve a better taut fitting when making my own?</p>
<p>As seen here </p>
<p><img src="http://i.stack.imgur.com/BcsMd.jpg" alt="enter image description here"></p>
<p>it is not flat or tight like this glass one is</p>
<p><img src="http://i.stack.imgur.com/EHj3t.jpg" alt="enter image description here"></p> | g14072 | [
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<p>A Lightning rod is fixed to the building and it is not given earthing then what happens? How does the lightning reach the ground through the building?</p> | g14073 | [
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<p>I'm trying to understand the constraints on the disk CFT correlation function $\langle O_1(y_1)O_2(y_2)\rangle$, where the $O_i$'s are boundary operators that are not necessarily primary. It's a well-known fact that the corresponding sphere correlator is determined up to an overall constant, but I seem to be getting two independent constants in the case of the disk. </p>
<p>Let me just quickly give the argument that I've come up with. For $y_{1}>y_2$, we can make the $PSL(2,R)$ transformation $y'=(y_1-y_2)y+y_2$, under which $(\infty,1,0)\mapsto(\infty,y_1,y_2)$. This gives
\begin{align*}
\langle O_1(y_1)O_2(y_2)\rangle=(y_1-y_2)^{-2(h_1+h_2)}\langle O_1(1)O_2(0)\rangle.
\end{align*}
For $y_2>y_1$, we instead transform $y'=(y_2-y_1)y+y_1$, giving
\begin{align*}
\langle O_1(y_1)O_2(y_2)\rangle=(y_2-y_1)^{-2(h_1+h_2)}\langle O_1(0)O_2(1)\rangle.
\end{align*}
Putting them together,
\begin{align*}
\langle O_1(y_1)O_2(y_2)\rangle=|y_1-y_2|^{-2(h_1+h_2)}(\langle O_1(1)O_2(0)\rangle\theta(y_1-y_2)+\langle O_1(0)O_2(1)\rangle\theta(y_2-y_1)).
\end{align*}</p>
<p>Now, for primary operators it's straightforward to show that $\langle O_1(1)O_2(0)\rangle=\langle O_1(0)O_2(1)\rangle$, but I don't see why (or if) this is true for nonprimaries. Are there just two independent constants in this case?</p>
<p>Thanks for your help!</p> | g14074 | [
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<p>If I have a spring being compressed by two bodies, A and B, with different masses, how much energy would be transferred to each one when they are released and the spring expanded?</p> | g14075 | [
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<p>In my exam today I've been given this problem, yet even with the results at hand I simply can't warp my head around it; </p>
<p>Given the picture below, a bar is placed on two conducting rails with a resistor (in the form of a single thin wire) at the left. Now at t=0 the magnetic field changes which causes the bar to move. (and a current flows through the "circuit").</p>
<p>The current can easily be found by Lenz's law:</p>
<p>$$ \mathscr{E} = -\frac{\mathrm{d}\Phi_b}{\mathrm{d}t} = -\ell\frac{\mathrm{d}\left( Bx \right )}{\mathrm{d}t} = -\ell x\frac{\mathrm{d} B }{\mathrm{d}t} -\ell B v $$</p>
<p><img src="http://i.stack.imgur.com/TnAlF.png" alt="enter image description here"></p>
<p>Now this is follow up text for the problem</p>
<blockquote>
<p>It may be assumed that the conducting bar <strong>has a negligible mass and
friction</strong>, so it will immediately move to a position $x$ in which there
is no force exerted on it.</p>
<p>b) Explain why the relation between the actual position $x$ and the
actual value of the magnetic field $B$ is given by $Bx = B_0x_0$.</p>
</blockquote>
<p>What did the prof try to explain here? No force means constant speed, so not a "position" at all right?<br>
Well the result sheet shows:</p>
<blockquote>
<p>No force means $\frac{\mathrm{d}(Bx)}{\mathrm{d}t} = 0$ Hence $Bx$ is constant .....</p>
</blockquote>
<p>what???? Sorry but maybe it stems from the fact that I already didn't understand what "no force" meant in the text but I can't understand this.</p> | g14076 | [
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<p>Using differential forms <a href="http://em.groups.et.byu.net/pdfs/publications/formsj.pdf">and their picture interpretations</a>, I wonder if it's possible to give a nice geometric & physical motivation for the form of the Electromagnetic Lagrangian density?</p>
<p>The Lagrangian for the electromagnetic field without current sources <a href="http://en.wikipedia.org/wiki/Lagrangian#Electromagnetism_using_differential_forms">in terms of differential forms</a> is $F \wedge * F$, where $F$ is the exterior derivative of a 4-potential $A$. Another way to say this is that $F$ is the four-dimensional <a href="http://www.gauge-institute.org/Vector/MagneticMonopoles.pdf">curl</a> of a 4-potential $A$, i.e. the <a href="http://users.wfu.edu/parslerj/math733/lecture%20notes%201-4.pdf">anti-symmetric part of the flow of the determinant of the Jacobian of a vector field</a> $A$, and since we can physically interpret the curl of a vector field as the instantaneous rotation of the elements of volume that $A$ acts on, it seems as though we can interpret varying $F \wedge * F$ as saying that we are trying to minimize the instantaneous four-dimensional volume of rotation of the electromagnetic field (since the Hodge dual on 2-forms gives 2-forms 'perpendicular' to our original ones, wedging a form with it's dual <a href="http://em.groups.et.byu.net/pdfs/publications/formsj.pdf">gives us a 4-d volume</a>, so here we are getting the rotation of a volume element in spacetime).</p>
<p>Is that correct?</p>
<p>There is also the issue of defining the same action just in different spaces, using $F_{ij}F^{ij}$ and so a similar interpretation must exist... If I interpret $F_{ab}$ as I've interpreted $F$ above, i.e. a 4-d curl, and $F^{cd}$ similarly just in the dual space, then in order to get a scalar from these I have to take <a href="http://physicspages.com/2013/03/15/electromagnetic-field-tensor-contractions-with-metric-tensor/">the trace of the matrix product</a> $F_{ab}F^{cd}$, which seems to me as though it can be interpreted as the divergence of the volume of rotation, thus minimizing the action seems to be saying that we are minimizing the flow of rotation per unit volume.</p>
<p>Is this correct?</p>
<p>If these interpretations are in any way valid, can anyone suggest a similar interpretation for the $A_idx^i$ term in the Lagrangian, either when we're getting the Lorentz force law or the other Maxwell equations? Vaguely thinking about interpreting this term in terms of current and getting Maxwell's equations hints at what I've written above to have at least some validity!</p>
<p>Interestingly, if correct I would imagine all of this has a fantastic global interpretation in terms of fiber bundles, if anybody sees a relationship that would be interesting.</p>
<p>(Page 9 of <a href="http://users.wfu.edu/parslerj/math733/lecture%20notes%201-4.pdf">this</a> pdf are where I'm getting this interpretation of divergence and curl via the Jacobian, and I'm mixing it with the geometric interpretation of differential forms ala MTW's Gravitation)</p>
<p>I understand Landau's mathematical derivation of the $F_{ij}$ field tensor, Lorentz invariant scalar w.r.t. to the Minkowski inner product, linearity of the EOM, and eliminating direct dependence on the potentials, but physical motivation for it's form is lacking. Since one can loosely interpret minimizing $\mathcal{L} = T - V$ as minimizing the excess of kinetic over potential energy over the path of a particle, and for a free particle as simply minimizing the energy, I don't see why a loose interpretation of the EM Lagrangian can't be given. Any thoughts are welcome.</p>
<p>References: </p>
<ol>
<li>Math 733: Vector Fields, Differential Forms, and Cohomology, Lecture
notes, R. Jason Parsley</li>
<li>Warnick, Selfridge, Arnold - Teaching Electromagnetic Field Theory Using Differential Forms</li>
</ol> | g14077 | [
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<p>How do we know for certain that space is expanding?</p>
<p>Let's say that in the year 1950, we observe that galaxy 1 is 5 billion light years away from us and galaxy 2 is 10 billion light years away from us, putting both galaxies at a distance of 5 billion light years from each other. Then in 2013, we observe that they are now 7 billion light years away from each other so we conclude space is expanding.</p>
<p>We see that galaxies are move away from each other but how does that prove that space is expanding? Could this illusion of expanding space simply be due to something larger in mass pulling the farther galaxy 2 away from galaxy 1? This larger mass could be accelerating the velocity of galaxy 2 faster then it's accelerating the velocity of galaxy 1.</p> | g14078 | [
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<p>When I was riding a car (I was not the driver), my eardrum felt a little similar to the case when I was in a plane that was taking off, and little loss of hearing. Nothing was played inside. The feeling was gone, when I left the car. This don't happen often when I ride a car. So I wonder what might be the reason? Thanks!</p>
<p>That happened when the car was moving on a plain. at normal speed on a road in a city in NY. The weather was normal. I didn't sneeze. Perhaps swallowing helped a little. Windows were closed probably. </p>
<p>Is this not good to health?</p> | g14079 | [
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<p>I have seen case studies of the 3D Debye model where the vibrational modes of a solid is taken to be harmonic with dispersion relation $\omega = c_sk$. It is said that for temperatures much less than the Debye temperature, the heat capacity at constant volume $$C_V\sim T^3$$.</p>
<p>Now I want to show that for bosons with dispersion relation $\omega\sim A\sqrt k$ has heat capacity $$C_V\sim T^4$$ for $T\ll T_{Debye}$. </p>
<p>In the case studies I have read, I can't find where the dispersion relation comes into play. I have no idea how to see this. Please help!</p>
<hr>
<p>Perhaps I could get a response if I change the question to: How does the dispersion relation come into the calculations for the Debye model? Links to notes or an answer would be very much appreciated!!</p>
<hr>
<p>@MarkMitchison kindly pointed out that the density of state depends on the dispersion relation. What are the general definitions of $$E, p$$ in terms of $$\omega, k$$? E.g. for the first case $E=\hbar \omega$ and $p=\hbar k$. So the question is: what are the respective values for $E,p$ in general?</p> | g14080 | [
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<p>Schrodinger's Equation does not set a limit on the size of wave functions but to normalize a wave function a limit must be set. How is this consistent physically and mathematically with Schrodinger's Equation.</p> | g14081 | [
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<p>In AQFT one specifies the structure of the observables as a $C^*$-algebra. This seems to excludes algebras that don't have a norm, such as the Heisenberg algebra. Fortunately for this case one turns to Weyl algebra. </p>
<p>Is that trick always possible? </p>
<p><em>Additional material:</em></p>
<ul>
<li><p>Related to <a href="http://physics.stackexchange.com/q/27257/">this</a> Phys.SE post.</p></li>
<li><p>In Haag's book "Local quantum physics" p.5, he says that one can always come down to the study of bounded operators as discussed in I.E. Segal "Postulate for general quantum mechanics" 1947. However I don't see the answer to that question in this paper.</p></li>
<li><p>It seems that from an self adjoint operator in a Hilbert space one can always define a unitary operator, Reed & Simon Thm VIII.7.</p></li>
</ul> | g14082 | [
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<p>I am running an animation of a satellite in an elliptic orbit (defined by a parametric equation for $x$ and $y$ as a function of $t$) and want to make sure the spacecraft is traveling at the right speeds at different points in its orbit. That is, it should go slower at is apoapsis and much faster at its periapsis. I can easily calculate the <em>tangential</em> speed of the satellite using this equation:</p>
<p>$v=\sqrt{GM(\cfrac{2}{r}-\cfrac{1}{a})}$</p>
<p>How do I convert this to the <em>angular</em> speed of the satellite at this point?</p>
<p>I've done extensive research (hours and hours) but haven't found anything of value. The closest thing was this expression of Kepler's Third Law:</p>
<p>$\cfrac{dA}{dt}=\cfrac{1}{2}r^2\omega$</p>
<p>Since $\cfrac{dA}{dt}$ is a rate (area swept out per second) I rewrote this equation as</p>
<p>$\cfrac{A}{P}=\cfrac{1}{2}r^2\omega$</p>
<p>where $A$ is the area of the elliptic orbit (given by $A=\pi ab$ where $a$ and $b$ are the semi-major and semi-minor axes of the ellipse, respectively), and $P$ is the period of the elliptic orbit (given by $P=2 \pi \sqrt{\cfrac{a^3}{GM}}$). Solving this for $\omega$ yields:</p>
<p>$\omega=\cfrac{2A}{Pr^2}$</p>
<p>For each time step in my simulation I use the satellite's current position in this equation to compute $\omega$ and then use the result to update the current $\theta$. This updated $\theta$ is then plugged into the parametric equation mentioned above to get the satellite's $x$ and $y$ position. </p>
<p>I can't find my mistake anywhere and would really appreciate it if someone could point it out to me.</p> | g14083 | [
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<p>I have been told that the AdS/CFT correspondence proof does not rely on the validity of string theory. To be honest I don't know what to make of this. The idea of taking seriously the results of applying the techniques of this correspondence is appealing, but before I head in that direction, I need some help finding any references that actually make clear the fact that such a correspondence is independent of the validity of string theory. I am also curious as to the original explicit derivation of the correspondence. I just want to be able to really learn and truly believe the results myself before considering working applying its results.
I'm not contesting results of any kind, I just want to know this stuff well. </p> | g14084 | [
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<p>the quadrupole formula has some counterintuitive consequences, when analysing the power output averaged over a period</p>
<p>$$ P = \langle \frac{d^3 Q_{ij}}{dt^3} \frac{d^3 Q_{ij}}{dt^3} \rangle $$</p>
<p>Specifically, if two separated sources are considered inside the radiation zone, $\rho_1$ and $\rho_2$, and assume that each orbit around separate centers $C_1$ and $C_2$ by a length $R$, the quadrupole moment of the pair is going to be (around the common center $C_1 + \frac{R}{2} = C_2 - \frac{R}{2}$)</p>
<p>$$ \int ( \rho_1(x) + \rho_2(x) ) x^j x^k d^3x = \int \rho_1(x) (x_1 - \frac{R}{2})^j (x_1 - \frac{R}{2})^k d^3x + \int \rho_2(x) (x_2 + \frac{R}{2})^j (x_2 + \frac{R}{2})^k d^3x = \int \rho_1(x) x_1^j x_1^k d^3x - \frac{R^j}{2} \int \rho_1(x) x_1^k d^3x - \frac{R^k}{2} \int \rho_1(x) x_1^j d^3x
+ \int \rho_2(x) x_2^j x_2^k d^3x + \frac{R^j}{2} \int \rho_2(x) x_2^k d^3x + \frac{R^k}{2} \int \rho_2(x) x_2^j d^3x$$</p>
<p>$$ = \int \rho_1(x) x_1^j x_1^k d^3x + \int \rho_2(x) x_2^j x_2^k d^3x + \frac{R^j}{2}( \int \rho_2(x) x_2^k d^3x - \int \rho_1(x) x_1^k d^3x ) + \frac{R^k}{2}( \int \rho_2(x) x_2^j d^3x - \int \rho_1(x) x_1^j d^3x )$$</p>
<p>plus some other terms that are constant over time that are not needed</p>
<p>However, the terms $\frac{R^k}{2} \int \rho_c(x) x_c^j d^3x$ will have nonzero third time derivatives in general, so they will contribute to the overall power, even though they depend on an arbitrary choice of a center over which the quadrupole moments are calculated?</p>
<p>What is wrong with this expression, and how to obtain a power output from the quadrupolar moment that doesn't depend over what origin of coordinates is chosen for the calculation?</p> | g14085 | [
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<p><strong>A simple explanation for photon entanglement experiments</strong></p>
<p>Example: Quantum teleportation La Palma-Teneriffa in 2012 (distance 143 km) - Photons were entangled in such a way that when measuring polarization of one of the photons (obtaining a random result) the other photon will show a perfectly correlated polarization. Both measuring events may even happen at a timelike interval.</p>
<p>Today we know that there is nothing "spooky" about it, no information is transmitted at more than speed of light. But is there a realistic and local explanation how both events may happen at a timelike interval?</p>
<p>My proposal: Apply relativity of simultaneity to photons in the same way as to any other object moving in space. In order to determine simultaneity of events of any object moving in space, </p>
<ol>
<li>I make my observations about the movement of the object (speed, time, distance)</li>
<li>I enter my observations into my own (observer's) Minkowski diagram (Edit: in order to simplify this question I suppose that there is only one space dimension so that my Minkowski diagram is similar to a sheet of paper)</li>
<li>Than I apply the factor 1/γ (<em>reciprocal Lorentz factor</em>) to all values (speed, time, distance) in order to know about what is simultaneous for the object.</li>
</ol>
<p>But for entangled photons, scientists are doing exactly the contrary:
Distances and traveling time of photons are always measured on the basis of light speed c (300.000 km/sec.). Simultaneity of 2 events is determined accordingly. However, according to time dilation formulas of special relativity (T'=T/γ) these measured values are no <strong>real</strong> values, but only <strong>observed</strong> values, observed by any observer, which are not permitting so say something about simultaneity of events of a photon. An application of these formulas (and more precisely: of the factor <em>reciprocal gamma</em>) yields that the <strong>real</strong> speed of light is <strong>not defined</strong> (zero-by-zero division) and the distances and times are shrinking down to <strong>zero</strong>. As a result it seems clear that all events of photons are taking place simultaneously, and thus photons may be here and there simultaneously - thus no paradox at all!</p>
<p>I learned already that possibly relativity and time dilation do not apply to particles moving at light speed. But what is the sound reason for such an exception if on the other hand this is prohibiting a resolution of the EPR paradox?</p>
<p>It is also important that not only reference frames are subject to the factor reciprocal gamma: The factor is part of my (observer's) diagram, and even any fictive movements or any average of two movements is subject to the fact that their real movement is <strong>not</strong> the observed movement.</p>
<p><em>Edit: Further current errors to related issues:</em></p>
<p>1.The Lorentz factor does not derive from Lorentz transformation but directly from the two SR postulates - see light clock thought experiment introduced in 1909 by Gilbert Newton Lewis und Richard C. Tolman. By contrast, it is correct that Lorentz transformation uses the Lorentz factor.</p>
<p>2.Accordingly, not only reference frames may be observed and submitted to reciprocal Lorentz factor. </p>
<p><strong>Example:</strong> We observe an object which is moving over a distance of 100 light years (in our reference frame). We measure its speed (according to our reference frame). If its speed is respectively</p>
<p>0.6c/ 0.8c/ 0.9c/ 0.99c /0.9999c or 1.0c, </p>
<p>the reciprocal Lorentz factor yields for 100 light years a proper distance of respectively </p>
<p>80/ 60/ 44/ 17/ 1.4 and 0 light years. </p>
<p>My question refers to the fact that these 0 light years are currently replaced by the <strong>observed</strong> 100 light years. This would mean a leap in a curve which is tending towards zero</p>
<p>3.There is no "proper speed of light". When proper time and proper distance are reduced to zero by reciprocal gamma, the result is that speed is <strong>undefined</strong> (zero by zero division).</p> | g14086 | [
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0.006089286413043737,
-0.02234603650867939,
-0.002064585452899337,
0.049709778279066086,
-0.01... |
<p>I know that <a href="http://en.wikipedia.org/wiki/Superfluidity" rel="nofollow">superfluidity</a> is caused by the fluid having zero viscosity. This only happens at very low temperature, so the fluid (e.g. Helium-4) is a Bose-Einstein condensate.</p>
<p>I also know that in a <a href="http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensation" rel="nofollow">Bose-Einstein condensate</a> all the particles are in the ground state.</p>
<p>Now, that said:</p>
<p>How can this explain superfluidity? Many websites say that <em>the particles behave as a sigle giant matter wave,</em> but what is this due to and what does it mean physically?</p> | g14087 | [
0.046354781836271286,
0.038908254355192184,
-0.016092317178845406,
0.02437613345682621,
0.07241269201040268,
0.04902373626828194,
0.01428578794002533,
0.11735948175191879,
0.01403223816305399,
-0.07357284426689148,
-0.018152760341763496,
-0.023469237610697746,
0.016762474551796913,
0.03633... |
<p>Combining the first and second law of thermodynamics we can get the following equation</p>
<p>$$TdS=dU-P_{ext}dV$$</p>
<p>First question: Is this equation applicable for irreversible processes such that that $dS≠\dfrac{dQ}{T}$?</p>
<p>Second question:If the system temperature $T_{sys}$ is smaller than the surrounding temperature $T_{sur}$, which temperature should we put in the equation? </p>
<p>I have this question because sometimes people use $T_{sur}$ instead of $T_{sys}$ (e.g. <a href="http://www.youtube.com/watch?v=jsoD3oZAAXI&list=WL" rel="nofollow">http://www.youtube.com/watch?v=jsoD3oZAAXI&list=WL</a>, <a href="http://www.youtube.com/watch?v=jsoD3oZAAXI&list=WL&t=19m45s" rel="nofollow">19:45</a>) but the equation is supposed to describe changes in the system.</p> | g895 | [
0.05887715518474579,
0.00028834669501520693,
-0.01665945164859295,
0.0008092827047221363,
0.011975007131695747,
-0.026255887001752853,
-0.0252267736941576,
0.03472872078418732,
-0.0297975093126297,
-0.018150318413972855,
-0.026113316416740417,
0.08874648809432983,
0.06476089358329773,
0.01... |
<p>In my book's thermodynamics chapter, it says that an </p>
<blockquote>
<p>"object that radiates heat faster also absorbs heat faster. This means
that an object that is a more efficient radiator comes to equilibrium
with its environment more quickly. With this in mind, is it better to
paint your house black or white?"</p>
</blockquote>
<p>I am confused which it would be.
The book says white because </p>
<blockquote>
<p>"in summer, you house is cooler than the environment and white
reflects away the heat. In winter your house is warmer than the
environment and white radiates away the heat" </p>
</blockquote> | g508 | [
0.08745677769184113,
0.03753971680998802,
0.03354384005069733,
-0.009476195089519024,
0.05664608255028725,
-0.0022400885354727507,
0.039427850395441055,
0.0647912546992302,
-0.011065127328038216,
0.0029132624622434378,
0.030074818059802055,
0.08736023306846619,
0.0465325228869915,
0.022421... |
<p>In quantum optics (and hence also cv quantum information), given the annihilation and creation operators of the electromagnetic fields $a$ and $a^{\dagger}$, the "position" and "momentum" operators that we can construct in analogue with the harmonic oscillator, i.e.
$$ x:=\frac{1}{\sqrt2}(a^{\dagger}+a) \quad\text{and}\quad p:=\frac{1}{\sqrt2}(a^{\dagger}-a)$$
are called <a href="http://en.wikipedia.org/wiki/Quadrature" rel="nofollow"><em>quadratures</em></a>.</p>
<p>The name suggests a deeper meaning (or a mental picture - like the annihilation and creation operators suggest particle creation and annihilation), but I haven't found any. Can anyone give a suggestion?</p> | g14088 | [
0.026555964723229408,
-0.041507892310619354,
-0.03150853514671326,
-0.08743049204349518,
0.07599212229251862,
0.00460321269929409,
0.03736646845936775,
-0.005978405009955168,
0.0006197377224452794,
0.06553385406732559,
-0.016829919070005417,
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0.030136747285723686,
-0.0... |
<p>I'm trying to come up with a simple experiment that can demonstrate the properties of Gauss's Law for Magnetism. I am aware that it is a mathematical representation of the fact that magnetic monopoles don't exist (at least as far as we know), but are there any simple experiments that I could set up that a high schooler would be able to understand (without any higher level physics)?</p> | g14089 | [
-0.027415521442890167,
0.05436588451266289,
0.00447011599317193,
-0.06911015510559082,
0.04239869862794876,
0.026781955733895302,
-0.0263349749147892,
0.043929487466812134,
0.06683961302042007,
0.0037199489306658506,
-0.05096891522407532,
0.012130371294915676,
0.056683845818042755,
0.00390... |
<p>If, say, a particle with energy $E<V_0$, approaches a finite potential barrier with height $V_0$, and happens to tunnel through, where would the particle be during the time period when it is to the left of the potential barrier and to the right of the potential barrier? Surely there must be a finite amount of time for it to travel through to the other side, unless it simply teleports there? If it travels through with energy less than $V_0$, however, doesn't that mean it cannot enter in the region of the potential barrier?</p> | g14090 | [
0.02702796831727028,
0.11051326245069504,
0.0125898327678442,
-0.004715898539870977,
-0.003240701276808977,
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0.019515378400683403,
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0.022364037111401558,
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0.022467054426670074,
-0.007659577764570713,
0.0002... |
<p>What specific behaviour confirmed the existence of the W and Z bosons at the UA1 and UA2 experiments?</p>
<p>Thanks!</p> | g14091 | [
-0.014330930076539516,
-0.01732943393290043,
-0.002952713519334793,
-0.0006301263929344714,
0.037695109844207764,
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0.04778466373682022,
0.02387571707367897,
0.008217844180762768,
-0.020173614844679832,
0.009954212233424187,
0.058639731258153915,
0.015297045931220055,
0... |
<p>this is my first question on PhysicsSE (I'm already an user of MathSE). </p>
<p>I'm a mathematics students trying to understand Faraday's law, that is </p>
<p>$$\varepsilon= -\frac{d \Phi_B}{dt}$$</p>
<p>where $\varepsilon$ means electromotive force and </p>
<p>$$\Phi_B=\iint \mathbf{B}\cdot d\mathbf{S}$$ </p>
<p>means flux of magnetic field. As my textbook points out, there is an interpretation problem here: if the change in magnetic flux is due to movement of the conductor, then free charges in it are subject to Lorentz force, which then causes a current. On the contrary, if the conductor holds steady in a changing magnetic field, the induced current must be explained in terms of an electric field $\mathbf{E}$, described by the equations </p>
<p>$$\begin{cases} \nabla \cdot \mathbf{E}=\frac{\rho}{\varepsilon_0} \\ \nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}\end{cases}.$$</p>
<p><strong>Question</strong> Do those equations hold if we have a moving conductor in a stationary magnetic field? I guess not: this would mean $\mathbf{E}=\mathbf{0}$. How to solve this?</p> | g142 | [
0.04056326672434807,
0.023642713204026222,
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0.06898484379053116,
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-0.0201374813914299,
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0.046480219811201096,
-0.010077322833240032,
0.0... |
<p>Two point charges, -2.5 micro coulombs and 6 micro coulombs, are separated by a distance of 1m (with the -2.5 charge on the left and 6 on the right).</p>
<p>What is the point where the electric field is zero?</p>
<p>This seems exceptionally easy, but I can't figure it out. I can calculate the answer if both charges are negative/positive easily, but the fact that they're different is confusing me.</p>
<p>Thanks!</p> | g14092 | [
0.06290601193904877,
0.0009812240023165941,
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0.03890044614672661,
0.10454931855201721,
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0.02138676866889,
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<p><a href="http://en.wikipedia.org/wiki/Bessel_function" rel="nofollow">Hankel functions</a> are solutions to the scalar Helmholtz-equation $$\Delta\psi + k_e^2\psi = 0$$ in cylindrical and spherical geometry (with respect to a separated angular dependence). Thus, they are very important describing <strong>spherical</strong> and <strong>cylindrical</strong> waves. Here is an example of such a propagation in the spherical case taken from <a href="http://iem.at/Members/zotter/spherical_soundfield/gif_anims/RadialPropagationOutgoing.html" rel="nofollow">Franz Zotter</a>:</p>
<p><img src="http://i.stack.imgur.com/GSClW.gif" alt="animation"></p>
<p>I am searching for a reference that states the <strong>phase accumulation</strong> of <a href="http://en.wikipedia.org/wiki/Bessel_function#Hankel_functions%3a_H.CE.B1.281.29.2C_H.CE.B1.282.29" rel="nofollow">Hankel waves</a> of the form $$F_H^{\mathrm{out/in}}(\mathbf{r}) = H_m^{1/2}(k\rho)\ .$$
Assumed is stationarity with an $e^{-\mathrm{i}\omega t}$ time dependence fixing the meaning of the two different Hankel-waves as outgoing/incoming.</p>
<p>For <strong>plane waves</strong> one finds that the accumulated phase of a wave in $x$-direction, $$F_p=e^{\mathrm{i}kx}$$ is simply related to its argument, $$\phi_{\mathrm{acc}}(x_1,x_2)=\mathrm{Arg}(F_p(x_2))-\mathrm{Arg}(F_p(x_1)) = k(x_2 - x_1)$$ and it is <strong>natural</strong> to just use this formula in the Hankel-case, e.g. $$\phi_{\mathrm{acc}}(\rho_1,\rho_2)=\mathrm{Arg}(F_H^{\mathrm{out/in}}(\rho_2))-\mathrm{Arg}(F_H^{\mathrm{out/in}}(\rho_1))$$</p>
<p>However, I was not able to find a <strong>suitable reference</strong>. Hence my question:</p>
<blockquote>
<h3>Is there a reference defining the phase accumulation of Hankel waves?</h3>
</blockquote>
<p><strong>Thank you</strong> in advance.</p> | g14093 | [
0.019705740734934807,
-0.013137469068169594,
0.010279587469995022,
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0.01622994802892208,
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0.039933282881975174,
0.01089872233569622,
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0.006414870731532574,
-0.07292542606592178,
-0.008288200944662094,
0.060307227075099945,
0.04... |
<p>I suspect not, because moving forward (or backwards for that matter) is an important part, but I would like to confirm.</p>
<p><strong>UPDATE</strong>: Clearly it's possible
<div style="z-index:0;">
<object style="height: 385px; width: 640px">
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<param name="allowFullScreen" value="true">
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<param name="wmode" value="opaque">
<embed src="http://www.youtube.com/v/NuJvH1W7s1Y?version=3&start=0&feature=player_embedded" type="application/x-shockwave-flash" allowfullscreen="true" allowScriptAccess="always" width="640" height="385" wmode="transparent">
</object>
</div>
Can someone explain why?</p> | g14094 | [
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0.02813105657696724,
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0.014324294403195381,
0.023905528709292412,
0.... |
<p>The physical continuum is commonly assumed to have a mathematical continuum of points, that is, with a cardinality equinumerous with the Power Set of the set of natural numbers. However, since
[ZFC + "there exists an inaccessible cardinal"]
suffices to model analysis, and
[ZFC + "there exists an inaccessible cardinal"+ the negation of the continuum hypothesis]
is equiconsistent with the former,
but that the existence of aleph-one is a useful assumption (Borel sets, etc.),<br>
wouldn't it be more appropriate to assume only that space-time has (at least) a cardinality of aleph-one? </p> | g14095 | [
0.002943530445918441,
0.07325661927461624,
0.00005740839696954936,
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0.03381715714931488,
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-0.012715899385511875,
0.035858239978551865,
-0.014614377170801163,
0.03621743246912956,
... |
<p>How does one know the correct position of planets in relation to the sun when viewing the solar system from different angles makes the appearance of the planets different? I would think that it would require a satellite to orbit in a circular pattern above and below the entire solar system to get correct bearings.</p> | g14096 | [
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0.03646939992904663,
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0.04366915300488472,
-0.0264763031154871,
0.011688223108649254,
0.018548153340816498,
0.09713819622993469,
0.00120... |
<p>I was interested in making what I thought would be a simple simulation of an electron encountering a positron by numerically solving the Schrodinger equation over several time steps, but I've run into 1 problem: the potential used in most textbooks (to solve the hydrogen atom for example) are still of a classical point particle, rather than a wavefunction. How do I generate the potential field from two real, moving and interacting wavefunctions?</p> | g14097 | [
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0.06741213798522949,
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0.020130803808569908,
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0.03556106612086296,
-... |
<p>I have a set of samples that represents a waveform. This waveform resembles a frequency modulated sinusoidal wave (only it is not).</p>
<p>I would like to invert this waveform or <strike>shift it by $2\pi$</strike> shift it by $\pi$. of course taking the cosine of samples as they are without preprocessing is wrong.</p>
<p>What should I do to achieve this? </p>
<p>Thank you.</p> | g14098 | [
-0.012463461607694626,
-0.026704147458076477,
-0.004779789596796036,
-0.05729913339018822,
0.07308895885944366,
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0.01815907657146454,
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-0.041404660791158676,
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0.052818939089775085,
-0.013291308656334877,... |
<p>The ground state for a quantum Hall system on a torus with fractional filling factor can be classified by the Chern number, which is why the Hall conductance is quantized. Is there another method or classification one can use to distinguish states?</p> | g14099 | [
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0.03563999384641647,
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0.028685353696346283,
0.0509067103266716,
-0.019990695640444756,
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0.04480830579996109,
-0.0013585272245109081,
0... |
<p>I know that sound travels faster in water compared to air and say faster in steel than in what're so
What would the density have to be to cause sound to approach the speed of light</p> | g14100 | [
0.055559758096933365,
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0.006734142079949379,
0.014037080109119415,
0.027964720502495766,
0... |
<p>It's comparatively easy (cum grano salis) to grasp the following concepts:</p>
<ul>
<li>Euclidean space-time <em>(continous space and continuous time)</em></li>
<li>classical mechanics <em>(discretely distributed matter in continous space and continuous time)</em></li>
<li>Minkowskian space <em>(continously intermingled space and time)</em></li>
<li>special relativistic mechanics <em>(discretely distributed matter in continously intermingled space and time)</em></li>
<li>classical electrodynamics</li>
<li>classical quantum mechanics <em>(discrete energies, continuously distributed matter in continous space and continuous time)</em></li>
<li>quantum electrodynamics</li>
<li>general relativity <em>(continously intermingled space-time and matter)</em></li>
</ul>
<p>Accordingly, there are lots of introductory texts and text-books.</p>
<p>It's also easy to grasp</p>
<ul>
<li>numerical simulations <em>(on artificially - and mostly unphysically - discretized spaces, times, and space-times)</em></li>
<li>cellular automata <em>(on unphysical regular spatial grids)</em></li>
</ul>
<p>It's definitely hard to grasp (for somehow graspable reasons)</p>
<ul>
<li>quantum gravity</li>
</ul>
<p>I do not know whether there are empirical evidences for a discrete space-time or only theoretical desiderata, anyhow I cannot figure a discrete space and/or time out.</p>
<p>Why is it so hard to introduce and explain the concept of a physical discrete space-time?</p>
<p>Why are there no easy to understand
introductory texts or text-books on definitions,
concepts, models, pros and cons of
discrete space, time, and - finally -
space-time? </p>
<p>Respectively: <em>Where are they?</em></p>
<p>Are the reasons for this maybe related to the reasons why quantum gravity is so hard to grasp?</p> | g14101 | [
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0.021880803629755974,
0.021104... |
<p>I was reading the Wikipedia article on <a href="http://en.wikipedia.org/wiki/Lagrangian_point">Lagrangian points</a> and doing the requisite wiki walk through the various quasi-satellites of Earth when a question occurred to me:</p>
<blockquote>
<p>Could there be a stable or Lissajous orbit around the minor body perpendicular to the ecliptic that passes through or near L<sub>4</sub> and L<sub>5</sub>?</p>
</blockquote> | g14102 | [
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-0.043372537940740585,
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0.041084595024585724,
0.08137480169534683,
0.01063... |
<p>The formula for parrallel resistors is $\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$</p>
<p>But how can you use this formula when one of the branches is a superconductor, eg:
<img src="http://i.stack.imgur.com/ltS11.png" alt="image description"></p>
<p>Where the red resistor represents a wire with some resistance and the blue line represents a superconducting wire, how can the above equation be used to find the resistance between A and B, as it would mean dividing by zero?</p> | g14103 | [
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-0.02275707758963108,
-0.06203978508710861,
0.028988832607865334,
-0.031087404116988182,
0.... |
<blockquote>
<p>Generate two entangled photons, send one to a message sender and the other to the intended receiver. Both the sender and the receiver recover the same piece of quantum information from the photons, then the sender scrambles the message to be sent by some reversible function determined by the quantum information, and send this scrambled data to the receiver who is now capable of unscrambling it thanks to having the quantum information that was used for the scrambling procedure.</p>
</blockquote>
<p>This description as far as I can tell would be a valid simplified explanation of both <a href="http://en.wikipedia.org/wiki/Quantum_cryptography" rel="nofollow">quantum cryptography</a> and <a href="http://en.wikipedia.org/wiki/Quantum_teleportation" rel="nofollow">quantum teleportation</a>. What exactly is the difference between the two terms?</p> | g14104 | [
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-0.027042971923947334,
-0.029133161529898643,
0.03138177841901779,
0.025907445698976517,
-0.05... |
<p>Is there any physics theory that depicts our universe as $2+1$ dimensional?</p>
<p>I heard that black holes seem to suggest that the world might be $2+1$ dimensional, so I am curious whether such theory exists?</p>
<p>Just for curiosity.</p> | g14105 | [
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<p>I have read and heard in a number of places that <em>extra dimension might be as big as $x$ mm.</em> What I'm wondering is the following:
How is length assigned to these extra dimensions? </p>
<p>I mean you can probably not get your ruler out and compare with the extent of an extra-dimension directly, can you? So if not how can you compare one dimension with the other? Does one have some sort of <em>canonical</em> metric? Could one also assign a length (in meters) to time in this way?</p> | g706 | [
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<p>To me there seems to be quite a few different definitions of $f_{NL}$ in cosmology and I would like to know if or how they are equivalent. Let me cite at least 3 such,</p>
<ul>
<li><p>One can see the equation 6.71 on page 100 of the book "The Primordial Density Perturbation" by Liddle and Lyth. The closest one can make 6.71 look like the following two is through equations 25.21 and 25.22 - but it still doesn't really become equal to the following.</p></li>
<li><p>One can see equation 2 (page 3) of <a href="http://arxiv.org/abs/1111.6966" rel="nofollow">this paper.</a> In this equation I am hoping that the quantity $\Phi(x)$ called the "Bardeen's curvature perturbation" really what is called $\xi$ in the Liidle and Lyth book or in Dodelson's. </p></li>
<li><p>One can see the definition at the bottom of page 1 in <a href="http://arxiv.org/abs/0807.1770" rel="nofollow">this</a> very famous paper. Here curiously though the equation looks exactly the same as in the paper above, the quantity $\Phi(x)$ is called the "gravitational potential in the matter era"</p></li>
</ul>
<p>I wonder if one can hope to somewhat translate between the last two definitions by using the relation $\xi = \frac{2}{3}\Phi \vert_{post\text{ }inflation}$ - but even then the last two definitions are not really "equal". </p>
<p>Further this "discrepancy" between the definitions of $f_{NL}$ seem to be kind of related to the same problem with the definition of the ``transfer function" ($T(k)$),</p>
<ul>
<li><p>In the <a href="http://arxiv.org/abs/1111.6966" rel="nofollow">first paper</a> cited above, one sees a definition of $T(k)$ in equation 9 and 10.</p></li>
<li><p>But the closest one can get to the above is if one eliminates $\Phi(\vec{k},a)$ between equation 7.7 and 7.5 in Dodelson and then replaces $\Phi_p$ as $\Phi \vert_{post\text{ }inflation}$ and converts that into $\xi$ through $\xi = \frac{2}{3}\Phi \vert_{post\text{ }inflation}$ (..and hope that $\Phi$ in equation 2 and 9 of of the <a href="http://arxiv.org/abs/1111.6966" rel="nofollow">paper</a> is actually $\xi$..)</p>
<p>But still the two definitions of transfer function don't match!</p></li>
<li><p>And the above two definitions are anyway still very far from the definition of $T(k)$ as in equation 8.52 (page 125) of the above cited book by Liddle and Lyth.</p></li>
</ul>
<p>It would be very helpful if someone can help reconcile the above! </p> | g14106 | [
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<p>The fact that the bosons of the weak force have mass is something that I think technically poses many problems.</p>
<p>To avoid this and other problems with the masses of the particles devised a mechanism within the standart model $SM$ of particle physics $"smpf"$ called "the Higgs field." This field is transmitted by a boson and the passage of particles interacting with him for the generated field causes an inertia that is what we perceive as "mass". The Higgs mechanism is accepted as part of SMPF, but can not be verified until we find the corresponding Higgs boson in a particle accelerator.</p>
<p>Higgs boson we think we know that its mass is between $115 Gev$ and $200 Gev$, so it is expected to locate in the new collider at CERN: the LHC (Large Hadron Collider). As it is believed, has not been able to fit the force of gravity with quantum mechanics. A partial unification of the force would be the existence of a boson which would transmit the gravitational force, which we call graviton. If there was such a graviton. The graviton would be a hypothetical particle that many physicists believe.</p>
<p>The $smpf$ presents the problem that for the 20 core values to build a coherent theory need a very fine adjustment. String theory and other developments raise the possibility that this model is part of a collection
larger particles called supersymmetry. If supersymmetry were valid, this would require fine-tuning the values of the particles. Supersymmetry is the existence of a correspondence between fermions and bosons in the
that every fermion has a boson superpartner similar characteristics, and each one boson fermion superpartner.</p>
<p>The problem is that the fermions and bosons we know there is neither a single case of correspondence. That is, if supersymmetry is correct, we should
still find the superpartners of all particles in the model. The hypothetical fermions superpartners of bosons be called photino, winos, gluinos, etc.. And the superpartners of fermions bosons be called
Selectron, sneutrino, squark, etc.. Is it possible perhaps that the existence of these superpartners dramatically change the established concept of the standard model and open the door to a group of new models that do not understand, or hardly understand?</p> | g14107 | [
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0... |
<p>I understand that for low cross-section events a very high luminosity is necessary in order to obtain enough data to produce meaningful statistics. That is why the <a href="http://en.wikipedia.org/wiki/Large_Hadron_Collider" rel="nofollow">LHC</a> was built.</p>
<p>But which are these event which we are interested in? What are the events which would hint at new physics or would confirm theoretical models?</p> | g14108 | [
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<p>Since outer space is not quite a vacuum, and the distribution of various heavenly bodies is locally inhomogeneous, it seems reasonable to expect that the density and variety of particles 'contaminating' the vacuum varies with time and space. Are there any maps or data sets which detail this variation?</p> | g14109 | [
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<p>We believe that time is a dimension and that $x$,$ y$, $z$ are dimensions in space. Is quantity a dimension like these? And if not, how do we have dimensionless numbers (like $e$, $\pi$ etc.)? </p> | g14110 | [
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<p>In his lectures professor Hamber said that the metric tensor is not unique, just like the 4 vector potential is not unique for a unique field in electrodynamics. Since the metric tensor is symmetric, only ten components of the metric tensor are unique. </p>
<p>However, as the covariant divergence of the Einstein's tensor is zero, 4 more constraints are imposed and hence the number of independent components of metric tensor now has come down to 6. Finally he says that only two are unique.</p>
<p>How did he arrive at the final result of 2 unique components of metric tensor. Can you please explain tis me ? Also, what is the physical difference between Ricci tensor and Reimann tensor ?</p> | g14111 | [
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<p>"A bar magnet is moved towards a freely hanging coil. Determine if the coil stays stationary or not. If it moves, determine if it moves away or towards the magnet."</p>
<p>My hypothesis: From Lenz's law an e.m.f will be induced in the coil to oppose the change in magnetic flux due to the relative approach of the bar magnet. The resultant current in the coil produces a force on the coil equal to the Lorentz force due to the approach of the bar magnet, and in the opposite direction. As such, the forces should cancel out, causing the magnet to remain stationary.</p>
<p>I suspect that there are some flaws in my hypothesis. Are my deductions correct, and is there a better explanation? (note: I'm not sure if the coil will move or not)</p> | g14112 | [
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0.016599440947175026,
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0.02790... |
<p>Our universe has a finite size. It is often called the "radius of the universe", or "distance of the cosmic horizon".</p>
<p>If we would fly with relativistic speed at the position of our Earth, would this finite size Lorentz-contract? Or would it stay the same?</p>
<p>In simple words: Does the universe Lorentz-contract? </p>
<p>Would be observe the same size for the universe whatever our speed with respect to the reference frame defined by the average mass in the universe?</p> | g14113 | [
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0.009388179518282413,
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... |
<p>I have this childrens rubber ball which glows in the dark after it's exposed to light. I "charge" it with a flash light then play with my dogs at night. I thought to try a very intense green laser, and see how the ball reacted.</p>
<p>The laser light had no effect on the balls ability to glow. So I'm left wondering, why does laser light not allow luminescence (maybe not the right word) materials to glow?</p>
<p>EDIT In Response to Answer.</p>
<p>So I tried a little modification. I tried exciting the ball with three different light sources; a "super bright" Red LED, a very very "super bright" white LED and a blue LED of unknown specs (no package, bottom of my kit). I held the ball to each light source (driven with the same current) for the same approximate amount of time and compared the results. The red LED had no effect. The white had a bit of an effect, enough to see dimly in normal room lighting. The blue led had a significant effect, causing a bright glow. This was interesting as the blue LED was the least bright visually. Yay science!</p> | g14114 | [
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<p>So, how do we know $J_{+}|j,(m=j)\rangle =|0\rangle$?</p>
<p>I.e. that m is bounded by j.</p>
<p>We know that $J_{+}|j,(m=j)\rangle =C|j, j+1\rangle$, but how do I know that gives zero? Is it by looking at its norm-square?</p> | g14115 | [
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<p>This is a problem in a college physics textbook, and its bugging me that I can't get it. </p>
<p>The figure shows a circuit model for the transmission of an electrical signal, such as cable TV, to a large number of subscribers. Each subscriber connects a load resistance RL between the transmission line and the ground. The ground is assumed to be at zero potential and able to carry any current between any ground connections with negligible resistance. The resistance of the transmission line itself between the connection points of different subscribers is modeled as the constant resistance RT.</p>
<p><strong>Prove the the equivilent resistance as seen by the cable tv company is the equation at the top of the image.</strong></p>
<p>I found this suggestion: Because the number of subscribers is large, the equivalent resistance would not change noticably if the first subscriber cancelled his service. Consequently, the equivalent resistance of the section of the circuit to the right of the first load resistor is nearly equal to Req.</p>
<p><img src="http://i.stack.imgur.com/EGFya.gif" alt="enter image description here"></p> | g14116 | [
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... |
<p>The situation I am looking at is a magneto-static problem of a finite magnetic film with magnetization $\bf{M}$. I would like to find the the magnetic field far above the plate. My expectation is that far above the plate, the field should approach the dipolar field which scales as $1/r^3$. However my numerical calculations are yielding $1/r^4$.</p>
<p>I am using Jackson's book (3rd ed.) as a guide. I assume discontinuous magnetization at the surface so I can use Jackson's Eq. 5.100 which is
the magnetic scalar potential:</p>
<p>$\Phi_M (\bf{x}) = \frac{1}{4 \pi} \oint_S \frac{\bf{n}' \cdot \bf{M}(\bf{x}')}{|\bf{x}-\bf{x}'|}da'$ assuming that the magnetization $\bf{M}(\bf{x}')$ is uniform within the volume. The top and bottom surfaces of the film will contribute to the potential. If I focus just on the top surface and assume a normalized magnetization $\bf{M} = M \hat{z}$:</p>
<p>$\Phi_M (\bf{x}) = \frac{1}{4 \pi} \oint_{top} \frac{ M}{|\bf{x}-\bf{x}'|}da'$.</p>
<p>I do not see where to go from here or how the expected $1/r^2$ dependence will arise.</p> | g14117 | [
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<p>I have encountered the minimal coupling between a field and charges before $$H = \frac{1}{2m}(p-qA)^2,$$</p>
<p>whereby I am considering the classical case. </p>
<p>The description minimal leads me to ask if there exist <a href="http://www.google.com/#q=exotic+couplings" rel="nofollow">exotic couplings</a> (non-minimal)? Could some examples of such couplings be discussed? </p> | g14118 | [
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... |
<p>How did gunsmiths create revolver cylinders holes in 1850's without the use of electrical drill?</p>
<p>Which referces/ books specialize providing knowledge in similar molding method?</p> | g14119 | [
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0.00... |
<p>I have a question which asks me to determine what x is for the following nuclear transition</p>
<p>$$^{29}Si(\alpha, n)X$$</p>
<p>But I don't have any idea what this notation implies.</p>
<p>Another example:</p>
<p>$$^{111}Cd(n,x)^{112}Cd$$</p> | g14120 | [
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<p>(I don't have a direct reference so this is a little fishy and I'll delete it if nobody recognises what I'm talking about, but I though for starters I'll ask anyway)</p>
<p>I've heard at university that if you have a operator (linear Hilbert space operator?) which is bounded on a restricted (compact?) domain, then it's bounded on the whole space. Put differently, to prove that an operator is bounded, you don't actually need to show it in the whole space.</p>
<p>However, if you restrict the domain of the position operator it becomes unbouned right? That's a contradiction.</p>
<p>In a finite dimensional example I see that you just have to check eigenvalues and hence consider the action on the base. The domain of the position operator is the function space with deltas as its base right? does restricting the domain here mean cut of $\delta(x-a)$ after $a\in \mathbb{R}$ has reached a certain value? I.e. considering only functions of compact support?</p> | g14121 | [
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... |
<p>On Earth, UVB (280nm - 315nm or 320nm depending on the source) undergoes extensive attenuation through the atmosphere, when observed at the planet's surface, as illustrated below:</p>
<p><img src="http://i.stack.imgur.com/utbcZ.png" alt="enter image description here"></p>
<p><a href="http://en.wikipedia.org/wiki/Ultraviolet">Image source</a></p>
<p>This is primarily due to the ozone layer, a feature unique to Earth amongst the terrestrial planets (Venus, Earth and Mars).</p>
<p>Given the different atmospheric chemistries and differences in distances from the Sun of Venus and Mars, what UVB attenuation has been observed or simulated for Venus and Mars?</p>
<p>Additionally, what UVB attenuation has been observed (or simulated in this case) on Titan?</p>
<p>Any peer reviewed resources would be appreciated here.</p> | g14122 | [
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<p>Quantum levitation, flux pinning -- basically, when a superconductor floats above a permanent magnet, is really fascinating. But does the strength of the magnetic field influence the superconductor's height? And what relationship/formula suggests this?</p>
<p>For example, if I had a coil wrapped around a metal object and then ran a small current through it, a small magnetic field would be generated and a superconductor exposed to it would float about it at some height that I put it on.</p>
<p>But what if I increased the current, so that the magnetic field also increased? What happens to the superconductor? Does its height change? Or does it just get harder to "pull out" of its levitating state?</p> | g14123 | [
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<p>As a picture is worth a thousand words, here is my problem:</p>
<p><img src="http://s21.postimage.org/rv7a0t8br/problem_pressure.png" alt="Picture here"></p>
<p>It is a closed water column with a bit of air in the top section.
If I run the pump and make the water flow from IN to OUT,</p>
<ol>
<li>Will the level stay the same and the water circulate indefinitely? or</li>
<li>Will slowly start to go down in the column and and the left side rise until it overflow?</li>
</ol> | g14124 | [
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<p>I am getting into friction on an atomic scale. For instance, take two rigid layers of atoms of the kind A that are placed on top of each other, just like putting two boards of wood on top of each other. Then place some atoms or molecules of the kind B between those two rigid layers, i.e. put some pebbles between the two wooden boards. Now start pushing one of the rigid layers horizontally, i.e. start pushing the wooden board on top.</p>
<p>On the macroscopic scale, we will be able to treat this system with Newtonian Mechanics and (relatively) simple approximations, i.e. friction forces.</p>
<p>How about the microscopic scale? When I google "friction microscopic scale", I get lots of results about ongoing research that is a bit above my level.</p>
<p>Where would be a good place to start reading about this in general?</p>
<p>I plan to dive into this, bearing in mind to maybe go on and model such systems computationally. </p> | g14125 | [
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0.009811684489250183,
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0.00539771793410182,
-... |
<p>I got to read Feynman vol I and there was written that at absolute zero, molecular motion doesn't cease at all, because if so happens, we will be able to make precise determination of position and momentum of the atom. But we do know that Heisenberg uncertainty principle holds for microscopic particle IN MOTION....then what is wrong to consider that all molecular motion ceases at absolute zero...need some help! </p> | g14126 | [
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0.03972157835960388,
0.07452178746461868,
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0.01341511495411396,
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-0.03633667528629303,
-0.06013662740588188,
-0.0213... |
<p>Lets say i have density Matrix on the usual base</p>
<p>$$ \rho = \left(
\begin{array}{cccc}
\frac{3}{14} & \frac{3}{14} & 0 & 0 \\
\frac{3}{14} & \frac{3}{14} & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & \frac{4}{7} \\
\end{array}
\right) $$</p>
<p>from this two states</p>
<p>$$|v_1\rangle=\frac{1}{\sqrt{2}}\left(
\begin{array}{c}
1\\
1 \\
0 \\
0 \\
\end{array}
\right);|v_2\rangle=\left(
\begin{array}{c}
0\\
0 \\
0 \\
1 \\
\end{array}
\right)$$ with weights $\frac{3}{7}$ and $\frac{4}{7}$ respectively</p>
<p>And two observables A and B</p>
<p>$$A=\left(
\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 2 & 0 \\
0 & 0 & 0 & 2 \\
\end{array}
\right) $$</p>
<p>$$B=\left(
\begin{array}{cccc}
3 & 0 & 0 & 0 \\
0 & 4 & 0 & 0 \\
0 & 0 & 3 & 0 \\
0 & 0 & 0 & 4 \\
\end{array}
\right)
$$</p>
<p>If you measure $A$ and $B$ at the same time, what you are doing is measuring $A$ with some state and measuring $B$ with not necessarily the same state but it may be the same.</p>
<p>So if I am trying to measure probability of measuring 2 and 4, that is $p(2)\times p(4)$ ?</p>
<p>Thats $p(2) = \frac{4}{7} $ and $p(4) = \frac{11}{14}$ then obtaining the two at the same time is $ \frac{4}{7}\times\frac{11}{14} = \frac{22}{49}$</p>
<p>What confuses me is, why is lower than $\frac{4}{7}$, since $|v_2\rangle$ has that chance of being measured, the other state just adds chances of measuring 4 with B.</p>
<p>Whats really going on here?</p> | g14127 | [
0.06517963111400604,
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... |
<p>This is a simple question. Does the Energy create both Fermion and Boson particles ? or just only the Fermion particles?</p> | g14128 | [
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0.023163603618741035,
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0.016654103994369507,
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-0.... |
<p>I have what may be a dummy question. In NMR or in the study of liquid crystals for example, an order parameter $S$ is often used:
$$
S=\left\langle\frac{1}{2}\left(3\cos^2\theta−1\right)\right\rangle
$$
with $\theta$ the angle of the molecule with a "director" (the magnetic field in NMR, the normal to a membrane for lipids, the global direction in a nematic phase etc). $S$ corresponds to a second-order Legendre polynomial.
I have often read that in an isotropic environment, $S=0$ whereas when all the molecules are well aligned with the reference vector (director), $S=1$. I understand why $S=1$ as $\theta=0$° but I can't find why $S=0$ when all the orientations are random.
Can anyone help me?</p>
<p>Liam </p> | g14129 | [
-0.011855613440275192,
0.011931297369301319,
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0.007431353908032179,
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0.01967639848589897,
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0.025142919272184372,
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0.02000095322728157,
0.0009153487626463175,
0.0... |
<p>I am trying to understand pure and mixed states better. If I have N quantum particles in an isolated system. The many-particle state is a superposition of the product of single-particle states by the appropriate statistics (bosons, fermions, or distinguishable). Would this state be still considered pure since there is no interaction with the environment? </p>
<p>Does that mean isolated systems or microcanonical ensembles are always pure? </p> | g14130 | [
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0.022223472595214844,
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0.025306088849902153,
0.0... |
<p>I have an aluminium baking plate that I did put in a very hot oven and now it is soft, so I can bend it or almost roll it up. Why? </p> | g14131 | [
0.03735506907105446,
0.04982433095574379,
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0.037313349545001984,
0.016083355993032455,
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0.0016064484370872378,
0.060019999742507935,
-0.02416030690073967,
0.0... |
<p>I am having an hard time trying to understand why the radiated power per unit area $P$ of a black body is given by
$$P=\frac{c}{4} u$$
in terms of the energy density $u$ and the velocity of light.</p>
<p>I know there is a derivation in <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/radpow.html" rel="nofollow">HyperPhysics</a>, but I did not find it particularly convincing. I cannot understand the physical significance of the parameter $\theta$ and what is its relationship with the the total energy per unit time provided by a unit area. Could someone explain it better to me?</p> | g14132 | [
0.05139514431357384,
0.07192840427160263,
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0.05993044376373291,
0.008617728017270565,
0.040946006774902344,
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-0.013981730677187443,
0.015234467573463917,
0.01830214075744152,
0.002446805825456977,
0.017... |
<p>Quantum mechanics is non-local in that long distance correlations are present, though there is no signalling possible. But QFT is Lorentz invariant and contains quantum mechanics as a special case. I assume this is not a paradox as paradoxes do not exist but I do not understand the details. Can anyone supply a reference or satisfactory explanation?</p> | g14133 | [
0.04129553958773613,
0.023982133716344833,
-0.006251099985092878,
-0.04836999252438545,
0.04151461273431778,
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0.02945587784051895,
0.012270772829651833,
-0.0... |
<p>Almost every book and article I can think of represents states of QFT using the Heisenberg picture of Hilbert space vectors, but Visser in "Lorentzian wormholes" does mention that you can also represent them as a functional.</p>
<p>It is very briefly mentionned, and he does not mention any sources for it, just the result : </p>
<p>$\Psi_0[t, \Phi(\vec{x})] \propto e^{-\frac{1}{2\hbar c}\int d^3x\Phi(\vec{x}) \sqrt{-\nabla^2} \Phi(\vec{x})} e^{-\frac{i}{\hbar}E_0t}$</p>
<p>With $\sqrt{-\nabla^2}$ some pseudodifferential operator.</p>
<p>Is there any source, book or otherwise, that expands on this topic? </p> | g14134 | [
-0.0075330669060349464,
0.062392089515924454,
-0.024763736873865128,
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0.03857526555657387,
0.0019293419318273664,
0.02161235734820366,
0.017788918688893318,
-0.03669709339737892,
0.005907665006816387,
0.0348551981151104,
0.05... |
<p>Why is it that the bound charge is $Q_b = - \oint_S{\mathbf{P} \cdot d\mathbf{S}}$? In particular, why is there a negative sign? Hayt's book on electromagnetism describes this as the "net increase in bound charge within the closed surface". Compared to Gauss' law $Q_{f} = \oint_S{\mathbf{D} \cdot d\mathbf{S}}$, the free charge is just the electric flux, so I don't see why the bound charge has a negative sign.</p>
<p>Also, if the electric flux is independent of bound charge, how come the D-field changes across material boundaries? I thought the D-field was defined as $\mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P}$ to cancel out the effect of the bound charge (since the effect of polarization is already incorporated into the E-field). Is the D-field dependent on bound charge? </p>
<p>Just to add to the second part of my question. I know that for a dielectric-dielectric boundary the tangential components $\frac{D_{t1}}{\epsilon_1} = \frac{D_{t2}}{\epsilon_2}$ and if $Q_{free} = 0$ on the boundary, then the normal components $D_{n1} = D_{n2}$. The tangential component will not contribute to the flux integral so for any $\epsilon_1$ and $\epsilon_2$ across a boundary the electric flux integral will evaluate to 0. It's clear that the flux is independent of the bound charge, but the the tangential component changes so the D-field is not? </p> | g14135 | [
0.04168824106454849,
0.009791376069188118,
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0.00031423952896147966,
0.050482675433158875,
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0.04191518574953079,
0.00040039801388047636,
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0.05632123723626137,
0.05691416189074516,
-0... |
<p>What aspects of "conventional" quantum field theory (i.e. what's used by most practicing physicists) are considered to be lacking mathematical rigor? </p> | g14136 | [
-0.03125028312206268,
0.033979322761297226,
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0.002079879632219672,
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0.032969940453767776,
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0.017615992575883865,
-0.006238753907382488,
0.021612612530589104,
-0.022241516038775444,
-0.012242180295288563,
... |
<p>There's a question I've come across that I've got some confusion on. </p>
<blockquote>
<p>A drum of mass $M_A$ and radius $a$ rotates freely with initial angular speed $\omega _0$. A second drum of radius $b>a$ and mass $M_B$ is mounted on the same axis, although it is free to rotate. A thin layer of sand $M_s$ is evenly distributed on the inner surface of the smaller drum (drum $A$). At $t=0$ small perforations in the inner drum are opened, and sand starts to fly out at a rate $\dfrac{dM}{dt}=\lambda$ and sticks to the outer drum. Find subsequent angular velocities of the two drums. Ignore the transit time of the sand </p>
</blockquote>
<p>In this question, we start off with an initial angular momentum of $L_0 = I_A \omega = (M_A +M_s ) a^2 \omega _0 $ (where the moment of inertia for a drum is $I=mr^2$). If my understanding of conservation of angular momentum holds, this should mean that at all times, this system <em>must</em> maintain this initial value of $L$. </p>
<p>I understand that as long as there is no external torque, $\frac{dL}{dt}=0$, and hence be constant. </p>
<p>Here's where my confusion comes in. Say we only include drum $A$ to be in our system. It's starts off with $L_0$, and as it loses mass, it must continue to rotate faster in order to keep $L_0$ constant. But if we now consider both drum $A$ and $B$ to be in our system, this can't possibly be the case. If drum $A$ continues to "compensate" for this loss in mass by having an angular acceleration, drum $B$ would have to remain stationary so that our value of $L_0$ remains stationary. In both cases, we have zero external forces, and so that means $\tau = 0$, but in the second system, we have an internal torque being applied to drum $B$ by the sand. </p>
<p>Where's my error? </p> | g14137 | [
0.11383721232414246,
-0.013244432397186756,
0.018623111769557,
0.002385925967246294,
0.04063199833035469,
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0.10875997692346573,
-0.03067457489669323,
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-0.019847162067890167,
-0.05214649811387062,
0.032317645847797394,
-0.008930725045502186,
0.0144179... |
<p>I have to Taylor expand an effective potential $U_{eff}$, which is given by:</p>
<p>$$U_{eff}(r)=-\frac{Gm_{1}m_{2}}{r}+\frac{l^{2}}{2\mu r^{2}}$$</p>
<p>I then expand it and get:</p>
<p>$$U_{eff}(r)=U_{eff}(r_{min})+\frac{dU_{eff}}{dr}\bigg|_{r=r_{min}}(r-r_{min}) +\frac{1}{2}\frac{d^{2}U_{eff}}{dr^{2}}\bigg|_{r=r_{min}}(r-r_{min})^{2} + \dots$$</p>
<p>Now, according to my book, it says that the 2nd term equals zero, or at least the derivative term of the 2nd term is. But it doesn't say why, so I'm kinda confused as why this is ? Is it some basic stuff I have forgotten, or is it something else ?</p> | g14138 | [
0.016705958172678947,
0.004654869902879,
-0.0006967306253500283,
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0.019848693162202835,
0.038270145654678345,
0.018213557079434395,
0.019306911155581474,
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-0.0014747491804882884,
-0.021287022158503532,
0.08016598969697952,
0.048093393445014954,
-... |
<p>I want to show:$$ Tr\left (F\tilde{F} \right )=\partial_{\mu}K^{\mu }=\partial_{\mu}\left (\varepsilon _{\mu \nu \rho \sigma }Tr\left ( F_{\nu \varrho }A_{\sigma }-\frac{2}{3}A_{\nu }A_{\rho }A_{\sigma} \right )\right ).$$</p> | g14139 | [
0.021908055990934372,
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0.02513296529650688,
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0.051235102117061615,
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0.014924485236406326,
-0.0034278302919119596,
0.033875472843647,
0.03089568205177784,
-0.03029894270002842,
0.02... |
<p>I am reading Jackson, Classical Electrodynamics, and I have a question regarding the electrodynamic <a href="http://en.wikipedia.org/wiki/Multipole_expansion" rel="nofollow">multipole expansion</a> (with page numbers I refer to the 3rd edition). So on page 409, he gives in equation 9.9 the general formula for the expansion of the vector potential:</p>
<p>$$\lim_{kr \rightarrow \infty} \mathbf A (\mathbf x) = \frac{\mu_0}{4\pi} \frac{e^{ikr}}{r} \sum_n \frac{(-ik)^n}{n!} \int \mathbf j (\mathbf x' ) (\mathbf n \cdot \mathbf x')^n d^3 x'$$</p>
<p>In the following, he takes the orders $n=0$ and $n=1$ and constructs the vector potential with the "physical" multipole moments, i. e. in order $n=0$ the electric dipole moment and for $n=1$ the electric quadrupole tensor and the magnetic dipole moment. Then on p. 415 he says, that from order $n=2$ upwards, the labor becomes increasingly prohibitive to do this decomposition in physical moments again. Instead, he indicates, that a systematic expansion is much easier (what, of course, I understand). </p>
<p>So I'm wondering now, if this decomposition has ever been done for $n=2$ (to get the electric octupole and the magnetic quadrupole tensor) or even higher orders, and if so, if is there a paper where this sophisticated task has been written down?</p> | g14140 | [
0.026389071717858315,
0.030086899176239967,
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0.02115613967180252,
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0.020373599603772163,
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0.03175296634435654,
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0.03287486732006073,
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<p>A spherical capacitor with inner radius $r_1$ and outer radius $r_2$ is filled with dielectric material with permittivity $\epsilon=\epsilon_0+\epsilon_1\cos^2\theta $.<br>
$\theta$ is the polar angle. Furthermore there is a charge $Q$ on the inner surface at $r_1$ and a charge $-Q$ on the surface at $r_2$. </p>
<p>Give reasons why the potential $\Phi(r,\theta,\varphi)$ is for all $r$ independent of $\theta$ and $\varphi$. </p>
<p>The independence of $\varphi$ is clear as our problem is invariant under $\varphi$-rotations. I'm not able to find a valid argument why the potential is independent of $\theta$. </p>
<p>Thanks in advance for help !</p> | g14141 | [
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0.032591767609119415,
0.004751681350171566,
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0.0664958730340004,
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0.061715275049209595,
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-0... |
<p>We measure distances in universe by the units of light year/s or parsec. Which means distance traveled by light in one year equals one light year. Thus the lights we receive from the distant stars or galaxies are coming from many light years away.</p>
<p>So how do we know the age of the light so that we determine the distance it has traveled to reach earth ?</p> | g14142 | [
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-0.057471729815006256,
0.005817676894366741,
0.005610087886452675,
0.0962827056646347,
0.0... |
<p>I recently read an article on dark matter and I could understand this things given as follows
All the ordinary matter we can find accounts for only about 4 percent of the universe. We know this by calculating how much mass would be needed to hold galaxies together and cause them to move about the way they do when they gather in large clusters. Another way to weigh the unseen matter is to look at how gravity bends the light from distant objects. Every measure tells astronomers that most of the universe is invisible. </p>
<p>I want to say that the universe must be full of dark clouds of dust or dead stars and be done with it, but there are persuasive arguments that this is not the case. First, although there are ways to spot even the darkest forms of matter, almost every attempt to find missing clouds and stars has failed. Second, and more convincing, cosmologists can make very precise calculations of the nuclear reactions that occurred right after the Big Bang and compare the expected results with the actual composition of the universe. Those calculations show that the total amount of ordinary matter, composed of familiar protons and neutrons, is much less than the total mass of the universe. Whatever the rest is, it isn't like the stuff of which we're made.
But what actually is dark energy ? How should I connect dark energy with dark matter ?</p> | g438 | [
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<p>I've been learning about pressure and fluid dynamics, and I've stumbled onto a problem. Say you have a straw in a cup. The surface area of the water in the cup is much greater than that of the straw. </p>
<p>So, I would expect Atm. Pressure × Large Area (of the cup) gives a <em>much</em> greater force than Atm. Pressure × Small Area (of the straw). In fact, the force is so much larger I would expect a spectacular jet of water, which obviously does not happen.</p>
<p>What am I missing?</p>
<p>Thanks</p>
<p>EDIT: So I chose a <em>really</em> bad example. Consider any amount of fluid with two openings of different size (facing upwards). Shouldn't the force due to the atmosphere shoot the water out the smaller opening, since the force on the larger opening due to the atmosphere is greater?</p> | g14143 | [
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<p>In some specifications for telescopes, I saw a value marked as f/4.6. What does it mean exactly, and how important is when it comes to choosing a telescope?</p> | g14144 | [
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0.11240722984075546,
... |
<p>The $E$ string of a violin has a linear density of $0.5 g / m$ and is subjected to a
$80\text{N}$ of tension, tuned for a frequency $u = 660 \text{Hz}$:</p>
<ol>
<li>What is the length of the rope?</li>
</ol>
<p>I know that in order to answer the question I have manipulate the equation:</p>
<p>$$
\nu = \sqrt\frac{\tau}{\mu}
$$</p>
<p>Getting this equation:</p>
<p>$$
L = \frac{m v^2}{T}
$$</p>
<p>I have tried to find the mass but my attempts was unsucessufull. </p>
<p>I think that i could use the equation:</p>
<p>$$
f_1 = \frac{\sqrt\frac{T}{m/L}}{2L}
$$</p>
<p>In order to find the lenght, but I need help to find the mass of the rope.</p> | g14145 | [
0.044752202928066254,
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0.006437229923903942,
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0.029103726148605347,
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-0.... |
<p>Assuming two stars are 1 light year apart and a traveler is travelling at 0.75 of $c$, from the point of view of the traveler what would be the observed time en route? Also, if a vehicle is constantly accelerating, will it reach 0.75 of $c$ within a reasonable amount of time? What would the Lorenz transforms look like for these situations?</p>
<p>Be gentle, I'm not a physicist. I'm writing book, and I'm trying to devise a scenario whereby a vehicle with a practically unlimited amount of energy can travel between stars. I don't care about the actual travel time only that experienced by the travelers. </p> | g14146 | [
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0.011786977760493755,
0.01914518140256405,
... |
<p>I wanted to know how a radio frequency accelerating cavity actually works. I know that an electric field is used to accelerate the charged particles. However, is this done by using metal plates with opposite polarities or are there tubes (like in the linac) within the accelerating cavity which have fields in between the gaps?</p> | g439 | [
0.04862663149833679,
0.05660029500722885,
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<p>I know that when photons pass through matter, the law that describes the intensity in function of the thickness is:</p>
<p>$$I(x)=I_0 e^{-\mu x}$$ </p>
<p>where $\mu = \rho \frac{N_a}{A} \sigma$ and $\rho$=density of the matter, $N_a$= Avogadro constant, A= mass number of the matter and $\sigma$=cross section.</p>
<p>My question is about the units of measurement of $\mu$. I know that $[\mu]=[l^{-1}]$ but if I do the dimensional analysis, I obtain:</p>
<p>$$[\mu]=\frac{[m]}{[l^3]} \frac{atoms}{[mol]}\frac{[mol]}{[m]}[l^2]$$</p>
<p>and so I have: </p>
<p>$$[\mu]=[l^{-1}]\cdot atoms$$</p>
<p>Could you explain me why there is "atoms"? </p> | g14147 | [
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-0.... |
<p>Usually one finds this expression for the low energy action</p>
<p>$$S = \frac{1}{2\kappa_0^2}\int d^D X\; \sqrt{-G}\; \mathrm{e}^{-2\Phi}\,(R-\frac{1}{12}H_{\mu\nu\lambda}H^{\mu\nu\lambda}+4 \partial_{\mu}\Phi\partial^{\mu}\Phi).$$</p>
<p>On dimensional grounds one can deduce $\kappa_0^2$ near $\ell_s^{24}$ (for $D=26$) or $\ell_s^8$ (for $D=10$).</p>
<p>Some authors use (obvious for the superstring, not for $D=26$ string):</p>
<p>$$2\kappa_0^2=(2\pi)^7\alpha'^4$$
with $\ell_s=2\pi\sqrt{\alpha'}$. Btw. this also confuses me, is $\ell_s=\sqrt{\alpha'}$?</p>
<p>So my question is how is $2\kappa_0^2$ determined?</p> | g14148 | [
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0.021518608555197716,
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0.034607477486133575,
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<p>Questions first, then my rough estimations:</p>
<p>1) Is it possible to perform moon laser ranging with amateur motorized 114mm telescope? My calculations suggest that for 1mJ laser it should receive ~2 photons per source 1mJ laser pulse. </p>
<p>2) Given that we already talking about individual photons, how it was possible to perform moon laser ranging BEFORE retro-reflectors were deployed to the moon? Retroreflector sends back light in ~1arcsecond angle, while bare lunar sufrace - in ~6 archours, which means we supposed to receive signal ~(6*60*60)^2 = 4.5*10^8 weaker, i.e. even with 2.5 meter telescopes we are talking 1 photon per 250 1J pulses.</p>
<p><strong>My rough estimations:</strong>
Given that atmosphere turbulence limits telescope resolution to ~1 arcsecond (adaptive optics was not available when laser ranging experiments started, nor it is available now for amateurs), if we use telescope with diameter larger than ~150mm (so that we are limited by atmosphere, not diffraction) to expand the laser beam we will get ~1939x1939 meter illuminated area on the moon surface (tan(1arcsec)*400'000km). Which means only 1/(1939*1939) part of our energy will reach reflector. </p>
<p>Retroreflector is ~1x1 meter in size. It will reflect the light with same beam divergence - 1arcsecond. Too sad, as diffraction limit for retro-reflector of such size is ~0.2 arcsecond.</p>
<p>So, if our receiving telescope has area of ~1 meter^2, we will receive again 1/(1939*1939) part of what reached the moon, so total attenuation is ~ 1.4*10^13. </p>
<p>If we use 532nm pulse laser with 1mJ pulse energy, it will emit 2.67*10^15 photons, which means we are going to receive ~190 photons per pulse. Sounds realistic. </p>
<p>These calculations suggests that 114mm amateur telescope should be able to detect 2 photon per pulse - again should be detectable statistically.</p> | g14149 | [
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<p><img src="http://i.stack.imgur.com/nXoEe.jpg" alt="enter image description here"></p>
<p>I cannot understand how and why those two expressions are coming (the ones I have highlighted). Please explain.</p> | g14150 | [
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0.044... |
<p>$\int\frac{GMm}{x^2}dx$ where $x$ varies from $\infty$ to $r$.</p>
<p>Situation we are bringing a very small mass from infinity to a distance r in the gravitational field of Earth with constant velocity(distances are measured between earth and small mass).
now work done by gravity is $\int\frac{GMm}{x^2}dx$ (where $x$ varies from $\infty$ to $r$) as force and displacement are in same direction; so work done by gravity should come out to be $+ve$.
but after solving this integral it comes out to be $-ve$. how can work be $-ve$ when force and displacement are in same direction.</p>
<p>But the $-ve$ work satisfies the eq. that $W\text{(gravity)} = -\Delta u$ if we take the $-ve$ work to be potential energy at distance $r$.</p>
<p>BUT the point is work done should be $+ve$. please explain (mathematically). </p> | g14151 | [
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<p>In another StackExchange Physics question, @Rego had found the following equation to calculate the lift force generated by <strong>a simple rectangular blade</strong>.</p>
<blockquote>
<p>$$F = \omega^2 L^2 l\rho\sin^2\phi$$
in which $\omega$ is the angular velocity, $L$ is the lenght of the helix, $l$ is the width of the helix, $\rho$ is the air density at normal conditions, and $\phi$ is the angular deviation of the helix related to the rotating axis. So a 4-helix propeller would lead to $F=4\omega^2 L^2 l\rho\sin^2\phi$ and so on."* </p>
<p><em>(source: <a href="http://physics.stackexchange.com/questions/23109/calculation-for-force-generated-by-a-rotating-rectangular-blade">Calculation for force generated by a rotating rectangular blade</a>)</em></p>
</blockquote>
<p>So when substituting the variables with the real values, he obtains this.</p>
<p>$$F=4\times(2\pi\times13000/60)^2\times(5\times10^{-2})^2\times(10^{-2})\times1.293\times(\sin1^0)^2$$$$\therefore F=0.072995N$$</p>
<p>However, when calculating this, I get $239.631...$. What steps have been taken between the result of this calculus and the Newton value he ended up with, and why ?</p> | g14152 | [
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<p>I am having trouble understanding how the following statement (taken from some old notes) is true:</p>
<blockquote>
<p>For a 2 dimensional space such that $$ds^2=\frac{1}{u^2}(-du^2+dv^2)$$
the timelike geodesics are given by $$u^2=v^2+av+b$$ where $a,b$ are constants.</p>
</blockquote>
<p>When I see "geodesics" I jump to the Euler-Lagrange equations. They give me
$$\frac{d}{d\lambda}(-2\frac{\dot u}{u^2})=(-\dot u^2+\dot v^2)(-\frac{2}{u^3})\\
\implies \frac{\ddot u}{u^2}-2\frac{\dot u^2}{u^3}=\frac{1}{u^3}(-\dot u^2+\dot v^2)\\
\implies u\ddot u-\dot u^2-\dot v^2=0$$
and
$$\frac{d}{d\lambda}(2\frac{\dot v}{u^2})=0\\
\implies \dot v=cu^2$$
where $c$ is some constant.</p>
<p>Timelike implies $$\dot x^a\dot x_a=-1$$ where I have adopted the $(-+++)$ signature.</p>
<p>I can't for the life of me see how the statement results from these. Would someone mind explaining? Thanks.</p> | g14153 | [
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0.03... |
<p>I understand einstein's train paradox. Where one man on a platform is passed by a man in a traincar, at the moment they meet a flash of light is given off in the middle of the train car. To the man on the platform the light hits the ends of the car at opposite moments in time. To the man in the train car they hit at the same time. </p>
<p>The man on the train sees the ends of the car at a fixed distance from each other, thus the light hits each end at the same time (same distance to travel). The man on the platform however sees the rear of the car catching up to the light while the front is moving away from it (light going to the front of the train has longer distance to go). </p>
<p>So, the only reason the light ever reaches the front of the wall is because it is not moving at the speed of light. Light catches up to it. </p>
<p>How would this experiment be different if the train is moving at the speed of light?</p>
<p>To the man on the train nothing would change I would have to say, because he is in his same reference frame of the train still. The man on the platform though, what would he see?</p>
<p>Would he see light hit the back of the train at the exact same time the flash happens, and never see the flash hit the front of the train but always [length of train car]/2 meters away from the front of the train car?</p>
<p>Edit: Looks like I forgot to say this is a hypothetical question. Unless one of you all have a speed of light train, this question is purely a thought experiment. If that does not satisfy you, then yes I have a train that does 671 million mph and I am just trying to understand my results of the first test run.</p> | g14154 | [
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<p>I understand that the massless fields of the Type I string theory are the described by:
[\begin{array}{*{20}{c}}
{{\rm{Sector}}}&{{\rm{Massless fields}}}\\
{{\rm{R - R}}}&{{C_0}}\\
{{\rm{NS - NS}}}&{{g_{\mu \nu }},\Phi }\\
{{\rm{R - NS}}}&{{\Psi _\mu }}\\
{{\rm{NS - R}}}&{\lambda'}\\
{\rm{R}}&{}\\
{{\rm{NS}}}&{}
\end{array}]</p>
<p>I have 6 questions:</p>
<ol>
<li><p>Are there any (massless) fields in the R and NS sectors (open strings)?</p></li>
<li><p>What is the projection of state vectors from the Type IIB string theory to the Type I string theory?</p></li>
<li><p>Is putting the ' necessary in the NS - R sector massless field?</p></li>
<li><p>What exactly are the spectra of state vectors (in terms of $\mathbf{8}_s$, $\mathbf{8}_v$ etc.) in the Type I string theory?</p></li>
<li><p>If the Type I string theory is a projection of the Type IIB string theory, where do the open strings come from?</p></li>
<li><p>What is the mass spectrum of the Type I string theory?</p></li>
</ol>
<p>Thanks in advance!</p> | g14155 | [
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<p>How does the path of light become visible due to scaterring of light? According to me it will only tell the presence of colloidal particle but the book give the example of cinema hall projector and says that you could tell path of light due to scattering of light. Nevertheless, without scaterring of light also we can tell its path.</p> | g14156 | [
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<p>Suppose I wrap wire around a bar magnet, creating a solenoid such that the poles of a bar magnet and the poles of solenoid are opposite to each other. If I were to hold a compass near one side, which pole would the compass detect? That of the bar magnet or of the solenoid?</p> | g14157 | [
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<p>Take an shell or bubble.
The bubble is strong enough to maintain it's static sphere shape, except when a photon bounces off the inner surface.</p>
<p>A photon fires from inside the bubble.</p>
<p>The inner surface gets pelted by this photon, and the inner surface bounces it back similar to a trampoline bounce. The effect of the bounce on the inner surface pushes the photon back in the same velocity it arrived. The entire inside of the bubble is like this, but strong enough to stay it's static sphere shape. What happens? Does the photon ever escape?</p>
<p>Does the photon endlessly stay a photon in the bubble at this rate? CURIOUS!</p> | g14158 | [
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<p>Please forgive: I am a layman when it comes to physics and cosmology, and have tried finding an answer to this that I can understand, with no luck.</p>
<p>As I understand it, the solar system evolved from a massive molecular cloud. To me, this seems to break the second law of thermodynamics, as I think it suggests order from disorder.</p>
<p>I know there must be something wrong with my logic, but am really stuck.</p>
<p>Can anyone explain this one in layman's terms?</p>
<p>(Posting to both "Astronomy" and "Physics", as it seems to overlap these subjects)</p> | g779 | [
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<p>I have to use the Green's function for the 2D Helmholz equation
$$(-\nabla^2 - E) \psi(x, y) = 0$$ on the rectangular domain $[0, L_x] \times [0, L_y]$ with Dirichlet boundary conditions:
$$\psi(0, y) = \psi(L_x, y) = \psi(x, 0) = \psi(x, L_y) = 0$$ in my calculations. </p>
<p>To get the Green's function I used eigenfunction expansion, so after the separation of variables and simple calculations we get eigenfunctions and eigenenergies indexed by $n \ge 1, m \ge 1$:</p>
<p>$$k_n^x = \frac{\pi n}{L_x}$$</p>
<p>$$k_m^y = \frac{\pi m}{L_y}$$</p>
<p>$$\psi_{n,m}(x, y) = \sqrt{\frac{2}{L_x}} \sin(k_n^x x) \sqrt{\frac{2}{L_y}} \sin(k_m^y y)$$</p>
<p>$$\lambda_{n,m} = (k_n^x)^2 + (k_m^y)^2 - E,$$
so the expansion is:</p>
<p>$$G(x, y, x_s, y_s; E) = \sum\limits_{n = 1}^\infty \sum\limits_{m = 1}^\infty \frac{ \sqrt{\frac{2}{L_x}} \sin(k_n^x x) \sqrt{\frac{2}{L_y}} \sin(k_m^y y) \sqrt{\frac{2}{L_x}} \sin(k_n^x x) \sqrt{\frac{2}{L_y}} \sin(k_m^y y) }{(k_n^x)^2 + (k_m^y)^2 - E}.$$</p>
<p>The only simplification I was able to do is to get rid of one sum by using the <a href="http://www.greensfunction.unl.edu/glibcontent/node42.html" rel="nofollow">known</a> closed form expression for 1D Helmholtz Green's function:</p>
<p>$$G(x, y, x_s, y_s; E) = \sum\limits_{n = 1}^\infty \sqrt{\frac{2}{L_x}} \sqrt{\frac{2}{L_x}} \sin(k_n^x x) \sin(k_n^x x) \sum\limits_{m = 1}^\infty \frac{ \sqrt{\frac{2}{L_y}} \sin(k_m^y y) \sqrt{\frac{2}{L_y}} \sin(k_m^y y) }{(k_m^y)^2 - (E - (k_n^x)^2)} = \\
\sum\limits_{n = 1}^\infty \sqrt{\frac{2}{L_x}} \sqrt{\frac{2}{L_x}} \sin(k_n^x x) \sin(k_n^x x) G_{1D}(y, y_s; E - (k_n^x)^2),$$</p>
<p>which is much better now, but I wonder if it is possible to go further and throw off the remaining sum? If it is possible and the closed form expression does exist, is there some general method of evaluating sums of that form?</p> | g14159 | [
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0... |
<p>I read photons do not age because they move at the speed of light. So when a photon interacts with my eyes, aren't they apart in space-time by the difference of the time in the frame of reference of the eye and the time when the photon started traveling?</p>
<p>I guess I am imagining a 4D-space here. What is my error in doing so? Shouldn't particles only interact when they share the same place and time (or are close, obviously they can't be in the same place)?</p> | g14160 | [
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0.04747035726904869,
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<p>I recently followed courses on QFT and the subject of renormalization was discussed in some detail, largely following Peskin and Schroeder's book. However, the chapter on the renomalization group is giving me headaches and I think there are many conceptual issues which are explained in a way that is too abstract for me to understand. </p>
<p>A key point in the renormalization group flow discussion seems to be the fact that the relevant and marginal operators correspond precisely to superrenormalizable and renormalizable operators. I.e., the non-renormalizable couplings die out and the (super)renormalizble couplings remain. In my lectures the remark was that this explains why the theories studied ($\phi^4$, QED) seem (at least to low energies) to be renormalisable QFTs. This is rather vague to me, and I don't know how to interpret this correspondance between relevant/marginal and renormalizable/superrenomalizable theories.</p>
<p>If I understand well, flowing under the renormalization group corresponds to integrating out larger and larger portions of high momentum / small distance states. Is there a natural way to see why this procedure should in the end give renormalizable QFTs?</p>
<p>Also, it appears that the cut-off scale $\Lambda$ is a natural order of magnitude for the mass. Since the mass parameter grows under RG flow for $\phi^4$-theory, after a certain amount of iterations we will have $m^2 \sim \Lambda^2$. But what does it mean to say that $m^2 \sim \Lambda^2$ only after a large number of iterations? The remark is that effective field theory at momenta small compared to the cutoff should just be free field theory with negligible nonlinear interaction. </p>
<p>Also, there is a remark that a renormalized field theory with the cutoff taken arbitrarily large corresponds to a trajectory that takes an arbitrary long time to evolve to a large value of the mass parameter. It would be helpful to get some light shed on such remarks.</p> | g14161 | [
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<p>Is it possible for a massless particle to undergo zitterbewegung? In massive Dirac theory the Zitterbewegung frequency comes out to be $2mc^2/\hbar$. It looks like the effect will vanish for a massless particle. But the effect is due to the interference between particle and antiparticle state which is also there for a massless particle. So what would be the outcome?</p> | g14162 | [
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<blockquote>
<p><strong>Premises And the Conclusion of the Paradox</strong>: (1) When the arrow is in a place just its own size, it’s at rest. (2) At every moment of its flight, the arrow is in a place just its own size. (3) Therefore, at every moment of its flight, the arrow is at rest.</p>
</blockquote>
<p>If something is at rest, it certainly has $0$ or no velocity. So, in modern terms, what the paradox says is that the velocity of the arrow in "motion" at any instant $t$ (a duration-less duration) of time is '$0$'. </p>
<p>I read a solution to this logical paradox. I do not remember who proposed it, but the solution was something like this: </p>
<blockquote>
<p>Let the average velocity of the arrow be the ratio $$\frac{\Delta s}{\Delta t}.$$
Where $\Delta s$ is a 'finite' interval of distance, travelled over a finite duration $\Delta t$ of time. Because an instant is duration-less, and no distance is travelled during the instant, therefore $$\frac{\Delta s}{\Delta t}=\frac{0}{0}$$ or, $$0 \cdot \Delta s=0 \cdot \Delta t.$$
In other words, the velocity at an instant is indeterminate, because the equation above has no unique solution.</p>
</blockquote>
<p>This solution denies the concept of a 'definite' instantaneous velocity at some instant $t$ given by the limit of the ratio $\frac{\Delta s}{\Delta t}$ or $$v(t)= \lim_{\Delta t \to 0} \frac{\Delta s}{\Delta t}.$$</p>
<p>Whatever be the velocity at some instant $t$, how does the above "definition of the instantaneous velocity" or the calculus tell us that the arrow or any other object in motion is moving at an instant? How can something move in a duration-less instant, when it has no time to move? What is the standard modern science solution to understand this logical paradox?</p> | g14163 | [
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<p>I'm doing magnification and lens in class currently, and I really don't get why virtual and real images are called what they are.</p>
<p>A virtual image occurs the object is less than the focal length of the lens from the lens, and a real image occurs when an object is further than focal length.</p>
<p>By why virtual and real? What's the difference? You can't touch an image no matter what it's called, because it's just light.</p> | g209 | [
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