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<p>Creating a beam of antiprotons allows to create antineutrons by charge exchange. How does this exchange work?
The question pops up after the question "<a href="http://physics.stackexchange.com/questions/134174/is-there-a-strong-evidence-of-antineutron-existance/134175?noredirect=1#comment274838_134175">Is there a strong evidence of antineutron existance?</a>"</p>
| 4,912 |
<p>I thought I knew how to use calculus of variations, but then I started thinking about the problem of a rotating liquid and it confused me a great deal. It would be nice to hear your thoughts on the problem.</p>
<p>Suppose we have a liquid in a spinning cylinder in an equilibrium (i.e. the liquid is still in the rotating frame). The name of the game is to find $h_{(r)}$, the height of the liquid as a function of the radial coordinate, under the constraint of a constant volume of the liquid.</p>
<p>My approach was to use the calculus of variation to find $h_{(r)}$ that makes the total energy of the system stationary. I got an answer in the form of:
$$ h_{(r)} = c_1 - c_2 r^2$$ where $c_1$ and $c_2$ are constants. If you use the Lagrangian, the answer you get is $$ h_{(r)} = c_1 + c_2 r^2$$ and the constants match the accepted solution (from the books).</p>
<p>My question is why does minimising the total energy fail? </p>
<p>EDIT: $c_2 = \frac{\omega^2}{2g}$</p>
| 4,913 |
<p>A chain of some mass, forming a circle, is slipped on a smooth cone.
If we consider an infinitesimally small section of the chain, a component of gravity will try to accelerate it along the surface of the cone. So there must be some tension in the string that prevents the acceleration. What will be the direction of the tension on this section of the chain?</p>
<p>Will it be towards the height of the cone, parallel to the ground?</p>
| 4,914 |
<p>How does the number of blades in a fan affect the flux of air? I read that 3 blades are the best option but some companies uses more blades because there's a misconception among people that more blades generates more air. </p>
| 4,915 |
<p>Supposing it's possible to see some distant galaxies with an earth telescope, then, at the tip of the telescope lens there are photons comming from the distant galaxy...</p>
<p>So, if I extend my hand in a dark night without visible moon, and far from city lights, photons from distant galaxies are in my hand skin... if it is true... is kind of amazing...</p>
<p>Then at that moment if photons of EVERY visible galaxy (from an earth telescope) are in my hand, then why my hand didn't bright? knowing (from photoelectric effect) that photons act as a whole or don't act, then why my hand didn't bright?</p>
| 4,916 |
<p>I'm given a wave propagation in an anisotropic medium with the following properties:</p>
<p>$\epsilon=\left[\begin{array}{ccc} \epsilon_{11} & 0 & 0 \\
\epsilon_{21} & \epsilon_{22} & \epsilon_{23} \\
0 & 0 & \epsilon_{33} \end{array}\right] $ </p>
<p>$\mu=\left[\begin{array}{ccc} \mu_{11} & 0 & 0 \\
\mu_{21} & \mu_{22} & \mu_{23} \\
0 & 0 & \mu_{33} \end{array}\right] $ </p>
<p>And we place a perfect conductor in the XY plane. Then I should compute the vanishing components of the electromagnetic field in the XY plane,and if given the current and charge superficial densities, the rest of the componentes of the electromagnetic field. </p>
<p>Any hints, please?</p>
<p>May I change the coordinates to a diagonal form for both $\epsilon $ and $\mu$ or something?</p>
<p>Thanks</p>
| 4,917 |
<p>Bear with me while I try to explain exactly what the question is. The question <a href="http://physics.stackexchange.com/questions/122392/can-a-curvature-in-time-and-not-space-cause-acceleration">Can a curvature in time (and not space) cause acceleration?</a> is imagining a coordinate system in which the curvature is only in the time coordinate. I want to be as precise as possible about what we mean by <em>curvature in the time coordinate</em>.</p>
<p>It seems to me that a good starting point is the geodesic equation:</p>
<p>$$ {d^2 x^\mu \over d\tau^2} + \Gamma^\mu_{\alpha\beta} {dx^\alpha \over d\tau} {dx^\beta \over d\tau} = 0 $$</p>
<p>because if we stick to Cartesian coordinates then in flat space all the Christoffel symbols vanish and we're left with:</p>
<p>$$ {d^2 x^\mu \over d\tau^2} = 0 $$</p>
<p>So a coordinate system in which spacetime is only curved in the time coordinate, $x^0$, would be one in which:</p>
<p>$$\begin{align}
{d^2 x^0 \over d\tau^2} &\ne 0 \\
{d^2 x^{\mu\ne 0} \over d\tau^2} &= 0
\end{align}$$</p>
<p>So my question is whether this is a sensible perspective.</p>
| 4,918 |
<p>I am just curious about the formalism of basic Quantum Mechanics. Lets take for instance the system of a spin-$\frac{1}{2}$ particle. The state of the particle is described by a vector in an abstract Hilbert space that is two dimensional (say $\mathcal{H}$). The set of Endomorphisms on $\mathcal{H}$ form a group (which i hope will be the $SU(2)$ group). Now I will just define an abstract Endomorphic map in $\mathcal H$, such that
$$ \hat\sigma_z : \left|+\right> \rightarrow \left|+\right> \qquad || \qquad \left|-\right> \rightarrow -\left|-\right>$$
where $\left|+\right>,\left|-\right> \in \mathcal H$</p>
<p>Clearly, the operator $\hat \sigma_z$ is Hermitian and the eigenvectors are orthonormal and hence can be chosen as a basis set.
Hence any arbitrary vector can be expanded about this.
$$ \left|\psi\right> = c_+\left|+\right> + c_-\left|-\right> \qquad ~~{where}~~\qquad \mathbf C \ni c_\pm = \left<\pm|\psi\right> $$
Now from what I have learnt so far, I sort of see that I can construct an a map called Representation $\mathcal R$ such all the elements for $\mathcal H$ gets mapped to $\mathbf C^2 $</p>
<p>$$ \mathcal R : \mathcal H \rightarrow \mathbf C^2 \qquad | \qquad \mathcal R\big(\left|\psi\right> \big) = \begin{pmatrix}
c_+\\
c_-\\
\end{pmatrix}
$$</p>
<p>This representation map preserves the inner product also I believe. For instance,</p>
<p>$$ \left<\phi|\psi\right> \rightarrow \begin{pmatrix}
d_+ & d_-\\
\end{pmatrix}
\begin{pmatrix}
c_+\\
c_-\\
\end{pmatrix} \in \textbf C
$$</p>
<p>Further the operators can also be mapped by this representation map, where the abstract operators get mapped to square matrices.</p>
<p>$$ \mathcal R : \text{End}(\mathcal H) \rightarrow \text{End}(\mathbf C^2) \quad|\quad \mathcal R(\hat A) = \begin{pmatrix}
\left<+\right|\hat A\left|+\right> & \left<+\right|\hat A\left|-\right>\\
\left<-\right|\hat A\left|+\right> & \left<-\right|\hat A\left|-\right>\\
\end{pmatrix}
$$</p>
<p>With this setup, the Pauli matrices and the vector's 2-D irrep all correspond this map $\mathcal R$ right ? So all those things correspond to a representation constructed using the eigen vectors of $\sigma_z$ ?</p>
<p>I also wish to know how would one make this kind of a connection in the cases of position basis, especially between $\left|x\right>$ and $L_2$ spaces.</p>
<p>PS: I know this question is of least use to any particular community of research or even people learning, but this is just out of my curiosity. Pardon me if this is a very ridiculous question.</p>
| 4,919 |
<p>In the one-dimensional spin-$\frac12$ XXZ Heisenberg model,
$$H=J\sum_i{S_i^x S_{i+1}^x + S_i^y S_{i+1}^y+\Delta S_i^z S_{i+1}^z},$$
with $J>0$. There are two transition points:</p>
<ul>
<li>$\Delta=1$</li>
<li>$\Delta=-1$</li>
</ul>
<p>The transition at $\Delta=1$ is of BKT type. What about the transition at $\Delta=-1$? Could anyone provide some reference? </p>
| 4,920 |
<p>At the back of my mind I know they should be equal, but mathematically, how are the two $\Delta \phi$ angles equal?
<img src="http://i.stack.imgur.com/qIxBs.png" alt="Angles Image"></p>
<p>The only explanation present in the text is that, "both velocities are perpendicular to the radii vectors," but I don't see how that makes them equal.</p>
<p>Also how will you make those two triangles in the 2 diagrams similar? Any images to support the explanation would be appreciated.</p>
| 4,921 |
<p>Under light from the sun, a red object will scatter the red component of light, and absorb all others. Hence, the human eye perceives it as "red". White objects scatter all wavelengths of light.</p>
<p>Yesterday I bought an orange light bulb. Under its light, orange/reddish carrots look white. Why is that? A "white" object would have to scatter all wavelengths of light, but there's only red light to begin with.</p>
<p>Here's a photo of a person's hand, in white then in red light. Notice the color of the red nails. Do they appear white in red light, or does the white skin appear red?</p>
<p><img src="http://i.stack.imgur.com/BRxDo.jpg" alt="Gorgeous red nails under red and white light"></p>
| 4,922 |
<p>One way of detecting exoplanets orbiting around a star is the <a href="http://en.wikipedia.org/wiki/Methods_of_detecting_exoplanets#Radial_velocity" rel="nofollow">Radial velocity method</a>.</p>
<p>Can this be used to detect multiple planets? Wouldn't the star orbit the center of mass of the whole system with a constant period? Or is there a separate oscillation of the star for each planet?</p>
| 4,923 |
<p>The following is an old question from an exam in a Physics $2$ course
I am taking, I have tried to solve the question and after I thought
I got the answer I looked at the solution and saw it isn't correct.</p>
<p>The solution explains what the answer is, but doesn't really explains
the facts used.</p>
<blockquote>
<p>In the lab frame there is an electric field $E=E_{y}$ and a magnetic
field $B_{z}=\beta E$.</p>
<p>We place a cube made of a conducting material, point $a$ is at the
center of the cube while point $b$ is far from it.</p>
<p>Calculate the following: $$ E_{y}(a),E_{y}(b),B_{z}(a),B_{z}(b) $$
and $$ E'_{y}(a),E'_{y}(b),B'_{z}(a),B'_{z}(b) $$ as they are seen in
a frame of reference moving at a speed $c\beta\hat{x}$.</p>
</blockquote>
<p><strong>My efforts:</strong></p>
<p>I wrote that
$$
E_{y}(a)=E_{y}(b)=E_{y}=E
$$</p>
<p>because the electric field is constant (in the lab frame).</p>
<p>Similarly, I wrote that
$$
B_{y}(a)=B_{y}(b)=B_{z}=B
$$</p>
<p>because the magnetic field is constant (in the lab frame).</p>
<p>Then I used field transformation
$$
E'_{\perp}=\gamma(E_{\perp}+\beta\times B)
$$
$$
B'_{\perp}=\gamma(B_{\perp}+-\beta\times E)
$$</p>
<p>to calculate the other four values requested.</p>
<p>I then looked at the solution, the solution claims that
$$
E_{y}(a)=0,\, E_{y}(b)=E
$$</p>
<p>$$
B_{z}(a)=\beta E,\, B_{z}(b)=\beta E
$$</p>
<p>and the other field were calculated using the above transformations.</p>
<p>I then remembered that in a conductor the electric field is $0$,
this explains why $E_{y}(a)=0$.</p>
<p>I don't understand this situation completely, Please help me understand it by answering the following questions (that goes a bit beyond the question, but I find interesting and am having difficulties answering myself):</p>
<blockquote>
<p>1) Why does $b$ have to be far from the conductor so we can say that
the electric is $E$ there ? what happens near the conductor ? (I
wonder if we can say something about the charge distribution on it
boundary, $\sigma$)</p>
<p>2) Why does the magnetic field does not change in space, inside or
outside the conductor ? (I know that the electric field does change,
at least inside the conductor, why shouldn't the magnetic field change
as well ?)</p>
<p>3) What can we say about the work done while moving the conductor in
the lab ?</p>
</blockquote>
| 4,924 |
<p>Say, I'm amplifying a signal using a device with gain bandwidth, ΔG Hz, which is unknown.</p>
<p>My source signal which is being amplified is known to have a bandwidth of X Hz, and the amplified output signal has a measured bandwidth of Y Hz.</p>
<p>Is it possible to process the input and output signal to find the gain bandwidth?</p>
<p>I was thinking that the output spectrum is likely to be the convolution of the gain profile and input spectrum, so maybe deconvolution would work? </p>
<p>In theory, could I measure input and output spectra and then try to numerically deconvolve, or would I need to first approximate the spectral shape (e.g. Lorentz, Gaussian etc.)?</p>
<p>Thanks for any tips!</p>
| 4,925 |
<p>Ok I am hoping to apply this answer to a piece of software, but it uses physics to work out the result so I require some help in that department. </p>
<p>I will attempt to explain this the best I can.</p>
<p>I need to work out the continual position of a scrolling list. If you were to flick the list it would continue to scroll (without the user touching it) for set amount of time decelerating as it does this.</p>
<p>The information I can gather.</p>
<ol>
<li>The start position of the users touch</li>
<li>The end position of the users touch </li>
<li>The distance between the touches</li>
<li>Believe I can then get the speed of this (speed = distance/time)</li>
<li>The continual time the scroll will last after the touch is 2400ms</li>
</ol>
<p>I have read that the deceleration of the scroller happens every 325ms at a factor of 0.95 targeting a fps of 60. Giving this 325 is -16.7 / ln(0.95). Though I do not know is this is correct. </p>
<p>I really need to know, the point that the scroller will stop after the 2400ms and ideally an update of the current position every 100ms. I just need to know the physics behind this as the programming will be simple from there. </p>
<hr>
<p><strong>Edit</strong></p>
<p>I think that the scroller velocity does reduce at a factor of 0.95 every 325ms. I have found this information from this useful <a href="http://ariya.ofilabs.com/2011/10/flick-list-with-its-momentum-scrolling-and-deceleration.html" rel="nofollow">article</a>. </p>
<blockquote>
<p>This observation led me to believe that the momentum scrolling is a sort of exponential decay. It is characterized by the speed of the decay. There are two different ways to express it: half-life (remember radioactive decay?) or time constant. For the latter, it is very much related to the step response of a first order system. In other words, the deceleration system is just an overdamped spring-mass system. Turns out, everything is still based on physics.</p>
</blockquote>
<pre><code>amplitude = initialVelocity * scaleFactor;
step = 0;
ticker = setInterval(function() {
var delta = amplitude / timeConstant;
position += delta;
amplitude -= delta;
step += 1;
if (step > 6 * timeConstant) {
clearInterval(ticker);
}
}, updateInterval);
</code></pre>
<blockquote>
<p>In fact, this is how the deceleration is implemented in Apple’s own PastryKit library (and now part of iAd). It reduces the scrolling speed by a factor of 0.95 for each animation tick (16.7 msec, targeting 60 fps). This corresponds to a time constant of 325 msec. If you are a math geek, then obviously you realize that the exponential nature of the scroll velocity will yield the exponential decay in the position. With a little bit of scriblling, eventually you find out that 325 is -16.7 / ln(0.95).</p>
</blockquote>
<p>This <a href="https://docs.google.com/spreadsheet/ccc?key=0AsWoSGXwvajGdDMzUE42VU12X3FDVUNheFFRd3M1aHc" rel="nofollow">Google Doc</a> should show the formulas and hopefully I am doing it correctly. On the left is the standard formula. On the right I have attempted to reduce the velocity by 0.95 (velocity*0.95). I have added real information from my testing to show the problem I am having. If all the equations are correct and it being done the correctly logically way, I must be the data going in.</p>
| 4,926 |
<p>I am slightly getting confused on the following issue:</p>
<p>When performing double-slit experiment of electrons, a screen allows the matter waves to be detected as particles. And as we all know that everything around us in fact consists of matter waves, the screen must also be formed of matter waves.</p>
<p>Then, what makes matter waves to collapse into particles? Does the screen allow detection as particles because it is a different type of particles? </p>
| 4,927 |
<p>Fastest baseball pitch ever recorded was in 1974 at a speed of 100.9 miles per hour.</p>
<p>Does this mean that the pitcher's hand was also traveling at that speed or just the ball?</p>
<p>Is it physically possible to move hand/leg at that speed?</p>
<p>I'm asking this because basically pitcher's hand was moving 17.7 inches per 10 millisecond which is really a super(unbelievable) speed for human.</p>
| 4,928 |
<p>I think this is supposed to be a simple problem but I am having a hang up converting it to a one-body problem. It's one-dimensional. +q and -q a distance d apart, held stationary then let go at t=0. The potential is V(x)=kq^2/x. If I turn it into a one body problem, then m-->m/2, but how do i interpret the new x? Both particles are moving toward each other, so they travel a distance d/2 before colliding. I am guessing the relevant equation will be $t = {\sqrt{\frac{m}{2}}} \int \frac{dr}{\sqrt{E - V(x)}}$</p>
<p>What concepts am I lacking? I think this is supposed to be really easy, but it's not for me.</p>
<p>edit, so x is now the relative distance between the two particles so it should be like one particle traveling the whole distance d ? I get a negative value, but is that acceptable? Something like</p>
<p>$t=\frac{\sqrt{m}}{2} \int_d^0 \sqrt{\frac{d}{kq^2}} \frac{dx}{\sqrt{1-d/x}}$ And that isn't giving me a very good answer when I calculate it.</p>
| 4,929 |
<p>So when two boxes are connected together, and force is applied, two boxes move with the same acceleration. (assuming force is constant.) My question is, how are forces between two boxes get cancelled out? When force is applied to the first box, it would exert force into the second box which pushes the first box with the same reaction force... And I am not sure afterawards. </p>
<p>"By connected together" I mean that two boxes are stick together literally. There's no string or something like that. It's basically glued together.</p>
| 4,930 |
<p>According to special relativity, time starts to slow down as we increase our speed and eventually stops once we get to the speed of light. By that logic, photons don't age in a vacuum state as, to us, the time stops for them. However, in a medium, their speed decreases, that means time is 'stationary'. Does that mean they start to age in a medium?</p>
| 4,931 |
<p>Whenever one needs to calculate correlation functions in QFT using perturbations one encounters the following expression:</p>
<p>$\langle 0| some\ operators \times \exp(iS_{(t)}) |0\rangle$</p>
<p>where, depending on the textbook S is either (up to a sign)</p>
<ol>
<li><p>$\int \mathcal{L}dt$ where $\mathcal{L}$ is the interaction Lagrangian</p>
<p>or </p></li>
<li><p>$\int \mathcal{H}dt$ where $\mathcal{H}$ is the interaction Hamiltonian.</p></li>
</ol>
<p>It is straightforward to prove that if you do not have time derivatives in the interaction terms these two expressions are equivalent. However these expressions are derived through different approaches and I can not explain from first principles why (and when) are they giving the same answer.</p>
<p>Result 1 comes from the path-integral approach where we start with a Lagrangian and do perturbation with respect to the action which is the integral of the Lagrangian. Roughly, <strong>the exponential is the probability amplitude of the trajectory</strong>.</p>
<p>Result 2 comes from the approach taught in QFT 101: Starting from the Schrödinger equation, we <strong>guess</strong> relativistic generalizations (Dirac and Klein-Gordon) and we <strong>guess</strong> the commutation relations to be used for second quantization. Then we proceed to the usual perturbation theory in the interaction picture. Roughly, <strong>the exponential is the time evolution operator</strong>.</p>
<p>Why and when are the results the same? Why and when the probability amplitude from the path integral approach is roughly the same thing as the time evolution operator?</p>
<p>Or restated one more time: Why the point of view where the exponential is a probability amplitude and the point of view where the exponential is the evolution operator give the same results?</p>
| 4,932 |
<p>The Randall-Sundrum extra dimension scenario had been one of the most extensively studied class of theories. This offered a solution to the hierarchy problem. However, if this picture is not supported by the LHC, will it become completely defunct? What about theories like little higgs, composite higgs, technicolor, higgsless models (perhaps already practically abandoned?)?</p>
| 4,933 |
<p>Imagine I have room that is very hot and it is colder outside. I want to cool it down using a fan.</p>
<h2>Scenario 1</h2>
<p>There is only one door. I have one fan.</p>
<p>Where should I put it and which way should it blow?</p>
<p><img src="http://i.stack.imgur.com/540TE.png" alt="Room with a door"></p>
<h2>Scenario 2</h2>
<p>I have two doors, one on each end. I still only have one fan.</p>
<p><img src="http://i.stack.imgur.com/MtOg9.png" alt="Room with two doors"></p>
<h2>Scenario 3</h2>
<p>Same as scenario 2, but I now have multiple fans.</p>
<p>For convenience, it is fine to assume that the room is a cuboid and that the fan emits no heat.</p>
| 4,934 |
<p>For a bipartite quantum system evolving under some master equation, is the time derivative of the reduced density matrix equal to the partial trace of the time derivative of the matrix? </p>
<p>In other words, is the following true:</p>
<p>$\dot{\rho}_{A} = Tr_B(\dot{\rho}_{AB})$</p>
<p>(Where $\rho_A = Tr_B(\rho_{AB})$)</p>
<p>If not, is there some other simple method to find $\dot{\rho}_{A}$ from $\dot{\rho}_{AB}$?</p>
| 4,935 |
<p>What is a good definition on Space, <a href="http://physics.stackexchange.com/q/17056/2451">Time</a> and the most specific topic "<a href="http://en.wikipedia.org/wiki/Spacetime" rel="nofollow">Spacetime</a>"? Because someone told me that spacetime is the foundation of the entire universe?</p>
<p>And also, Is it possible to create spacetime?</p>
| 4,936 |
<p>The <strong>ADM mass</strong> is expressed in terms of the initial data as a surface integral over a surface $S$ at spatial infinity:
$$M:=-\frac{1}{8\pi}\lim_{r\to \infty}\int_S(k-k_0)\sqrt{\sigma}dS$$
where $\sigma_{ij}$ is the induced metric on $S$, $k=\sigma^{ij}k_{ij}$ is the trace of the extrinsic curvature of $S$ embedded in $\Sigma$ ($\Sigma$ is a hypersurface in spacetime containing $S$). and $k_0$ is the trace of extrinsic curvature of $S$ embedded in flat space.</p>
<p>Can someone explain to me why ADM mass is defined so. Why is integral of difference of traces of extrinsic curvatures important?</p>
| 4,937 |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/10309/conservation-law-of-energy-and-big-bang">Conservation law of energy and Big Bang?</a> </p>
</blockquote>
<p>If energy can't be created or destroyed then how did the big bang create energy? and if energy can't be created then does that mean that there's a set amount of energy in our universe?</p>
| 166 |
<p>Is it possible that a false vacuum bubble to nucleate into our universe rather than a true vacuum one ? If yes,it will expand at speed of light within our spacetime or what ?</p>
| 4,938 |
<p>Let's consider a bubble nucleation phase transition between different vacua via quantum tunnelling .For my understanding a particle must penetrate the potential barrier and find herself in an another energy state over the barrier. But this doesn't mean that the parent vacuum loses the particle ?This doesn't violate the conservation of energy laws?</p>
| 4,939 |
<p>On a question from my book:</p>
<blockquote>
<p>A long straight wire with a circular cross section of radius $R$ carries a current $I$. Assume the current density is not constant over the cross section of the wire, but rather varies as $J=\alpha r$ where $\alpha$ is a constant. Given $I, R$ </p>
<p>Find $\alpha$ </p>
<p>Find the magnetic field as a function of r both inside and outside the wire</p>
</blockquote>
<p>I think it's just the calculus parts confuses me. My attempt:</p>
<p>$$J=\alpha r' = \frac{dI}{dA}$$
$$dI = 2 \pi r'^2 dr' \alpha$$</p>
<p>$$I = 2 \pi \alpha \int_0^R r'^2 dr'$$
$$I = 2 \pi R^3 \alpha /3$$
$$\alpha = \frac{3I}{2 \pi R^3}$$</p>
<p>from here you just use ampere's and I believe there's no variance issues?</p>
<p>$$\oint \vec{B} \cdot \vec{dl} = \mu_0 I_{in}$$</p>
<p>apply J=I/A</p>
<p>$$B 2 \pi r = \mu_0 \alpha r A$$</p>
<p>$$B = \frac{\mu_0 \alpha A}{2 \pi}$$]</p>
<p>$$B = \frac{3 \mu_0 I r^2}{2 R^3}$$</p>
<p>Is this right? The units seem to line up so I'm hopeful.</p>
<p>Outside the wire is treated as the general uniform wire case I assume and am not too worried about that.</p>
| 4,940 |
<p>It was a few days ago, and there was a very heavy storm(currents were flowing beside the sidewalks as normal). I became intrigued by a thin film of gasoline that got caught in one of the currents. The visible colors of course changed by my angle of incidence, yet because there was a current, the thickness of the film also changed, as it spread out and moved along with the water. I would like to make something of this. How did an unchanged angle of observation result in so many different changes in which colors were the most visible at a certain time? </p>
| 4,941 |
<p>I'm stuck on a problem of two satellites going towards each other. The mass of the first satellite is 400kg and the mass of the second satellite is 100kg. The altitude of the satellites is 1000km. I want to know if once the satellites collide, will they continue in orbit or will they crash and burn into the Earth? </p>
<p>I know that you can get the velocity of each satellite by using this equation:</p>
<p>$$v = \sqrt{GM/R}$$</p>
<p>Where $v$ is the velocity, $G$ is $6.67\cdot 10^{-11}$, $M$ is the mass of the planet, and $R$ is the radius.<br>
I can get the velocities, but i don't know where to go from here. Also when I get $R$, do I also have to add the radius of the planet as well? so it would be 1000km + radius of planet?</p>
<p>If you guys would help me with this, it would be amazing.</p>
| 4,942 |
<p>I'm trying to make a simple conceptual map regarding some of the things in the title as they pertain to quantum mechanics and or quantum field theory, and I'm finding that I'm a little perplexed about a couple of items. Let me summarize a few things I have as being true, and then state what I don't understand.</p>
<ol>
<li><p>Generally the propagator $K$ or often $D(x-y)$ is a Green's function of the quantum operator sometimes the Schroedinger operator, or the Klein-Gordon operator or analogous items. In the K-G case we would have something like $(\partial_u\partial^u +m^2)D\propto \delta^4(x)$</p></li>
<li><p>The "transition amplitude" I would tend to think should quantitate a probability of a system in state progressing to another state in time, ie $\left \langle x'',t'' \right |\left. x',t'\right\rangle$</p></li>
<li><p>The path integral $\int \mathcal{D}e^{iS}$ should be interchangeble with a transition amplitude, at least according to a few of my texts.</p></li>
</ol>
<p>What I am struggling on could be precisely what is meant by "transition amplitude" in some cases. Take for example the propagator for the Klein-Gordon equation.</p>
<p>$$D=\int d^4p{1\over 2\pi\hbar}^4{1\over E^2}e^{{i\over\hbar}p\cdot x}$$ </p>
<p>As far as I can tell from it's form, the propagator for the k-g equation is NOT from it's form a (Dirac )delta function $\delta^4 (x)$ or even $\delta^3(x)$ I don't actually think that it should be given point number 1. </p>
<p>However, I am failing to recognize its relation to "transition amplitude" in this case because I would usually equate a terminology such as "transition amplitude" with a probability. As the K-G propagator is NOT a normalized distribution, i.e. does not have the form of a delta function, what precisely is it supposed to quantify here?</p>
<p>P.S: Update since original post (above)--I've since noted that the term 'propagator' may be used somewhat differently in different contexts. Specifially, going back to J.J Sakurai Modern Quantum Mech. --chapter 2.5(ish--dont have the book in front of me now) he uses the K to represent what is termed the propogator of the Schrodinger system. He then discussed this in it's equivalent to the Feynman Path integral approach to determine $<x'',t''|x',t'>$
The use of $D(x-y)$ ,also referred to as the propagator, in Quantum Field Theory approaches by contrast seems to have a different meaning. I now realize $D(x-y)$ is not equivalent to $\int\mathcal{D}e^{iS}$ but rather something different as is apparent to me now. So I think that straightens some significant things out in my head. If anyone has anything to add or correct me on, please do.</p>
| 4,943 |
<p>I have a $2D$ fluid parcel with coordinates $(0.5,-0.5), (-0.5,-0.5), (0.5,0.5)$ and $(-0.5,0.5)$ and this parcel is deformed by a steady flow field of $u=ay$ and $v=0$, defined on the basis ${(1,0), (0,1)}$. I tried to calculate the velocity gradient tensor $\tau_{ij}$ given by the matrix
$ \left( \begin{array}{ccc}
0 & a \\
0 & 0 \end{array} \right) $. I now need to decompose this into the symmetric strain rate tensor and the antisymmetric rotation tensor. However, this matrix isn't diagonalizable. Am I missing something here? </p>
<hr>
<p>I need to use this part to "solve" the transformation equation of a point that is given by $$x_i(t+dt)=x_i+(u_i+du_i)dt$$where $du_i = \tau_{ij}dx_j$. Then, I must remove the rotation rate tensor from the velocity gradient tensor (which basically means I have the strain rate tensor left, if I am not mistaken) and use that to show that the transformation equation then becomes $$x_i(t+dt)=x_i+(u_i+\frac{1}{2}(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i})\partial x_j)dt$$ and finally determine the transformation equations for $x(t+dt), y(t+dt)$. </p>
| 4,944 |
<p>I've been directed to a few articles, and I am sure there is a related post, but can someone explain the procedure by which we can view classic electromagnetism through quantum mechanics? Indeed we need to be able to look at any field as an ensemble of particles (photons), but how can we develop classic field theory assuming quantum mechanics? </p>
| 167 |
<p>Below is an image showing transducer A transmitting a signal with an amplitude of 3000mV, I am trying to calculate the amplitude of the signal received by transducer B in mV,
I understand that there are dB losses at each of the acoustic interference (1 to 5), </p>
<ol>
<li><p>Which of the two formulae (given below) are relevant at each of the acoustic
interference (1 to 5) and why?</p></li>
<li><p>How are these three parameters related - transmitted signal in mV (transducer A), dB loss and received signal in mV (transducer B)?</p></li>
</ol>
<p>I have looked at many articles online, but they haven't helped me. Can someone please suggest me or guide me to help answer the above questions.</p>
<p><img src="http://i.stack.imgur.com/tUYzk.png" alt="enter image description here"></p>
<p><strong>Formula 1:</strong>
The dB loss of energy on transmitting a signal from medium 1 into medium 2 is given by</p>
<p><img src="http://i.stack.imgur.com/wQb0M.jpg" alt="enter image description here"></p>
<p><strong>Formula 2:</strong>
The dB loss of energy of the echo signal in medium 1 reflecting from an interface boundary with medium 2 is given by:</p>
<p><img src="http://i.stack.imgur.com/rXs9P.jpg" alt="enter image description here"></p>
<p> </p>
| 4,945 |
<p>Some background:</p>
<p>I'm majoring in Electronics and Instrumentation engineering, but I want to pursue theoretical physics. I'm currently In my second year of undergrad engineering. I attend some physics classes in the weekends and I've learnt classical mechanics (from John R. Taylor's book predominantly, with occasional references to Goldstein and David Tong's lecture notes). My math background includes differential equations, multivariable calculus and a bit of linear algebra (working on this now). In the second year, we've started off with Griffiths electrodynamics and Griffiths quantum mechanics.</p>
<p>Now my questions:</p>
<ol>
<li><p>To supplement my lack of formal mathematical training (engg math is not rigorous) I've taken to books such as Artin Algebra, Boyce and diprima differential equations(I've completed this book), linear algebra by Sheldon Axler etc. Due to the sheer amount of math there is, I'm quite confused as to what to study. Which are the essential math topics I, as an aspiring theoretical physicist must know? Please suggest a textbook for them. </p></li>
<li><p>In my weekend classes, neither thermodynamics nor optics is covered. Must I study these in depth? If so, from which textbook?</p></li>
<li><p>Any other suggestions? </p></li>
</ol>
| 4,946 |
<p>Lets say you have a cylinder of length L, radius R, and mass M. How fast will it accelerate a mass of mass M2 that is entering the "throat" of the cylinder, considering the effects of <a href="https://en.wikipedia.org/wiki/Gravitoelectromagnetism" rel="nofollow">gravitoelectromagnetism</a>?</p>
<p>By Gravitoelectromagnetism, I'm specifically talking about the effect where a spinning body will pull an object through the "throat" of its spin.</p>
<p>Also, I'm wondering what the practical limit of this is: considering the strongest known materials, how fast could a cylinder be spun? </p>
| 457 |
<p>Assume this question:</p>
<blockquote>
<p>Three events A, B, C are seen by observer O to occur in the order ABC. Another observer O$^\prime$ sees the events to occur in the order CBA. Is it possible that a third observer sees the events in the order ACB?</p>
</blockquote>
<p>I could draw spacetime diagram for three arbitrary-ordered events for O and O$^{\prime}$. But I couldn't draw spacetime diagram for third observer. Could someone help me figure this out?</p>
| 4,947 |
<p>For a project I'm working on I'm using an accelerometer which measures acceleration in 3 directions, x, y and z.</p>
<p>My question is: How can I calculate the total acceleration in a certain direction from these 3 values?</p>
<p>Considering this simple graph layout: <img src="http://i.stack.imgur.com/UX9S8.png" alt="enter image description here"></p>
<p>My initial idea is: </p>
<ul>
<li>Take the sqrt of (x^2 + z^2) to calculate the resulting value in the zx plane.</li>
<li>Take this value, square it and add y^2, take the square root of that</li>
<li>Final equation: Sqrt(y^2 + Sqrt(x^2 + z^2))</li>
</ul>
<p>Is this correct? On some sites I see x^2 + y^2 + z^2 being used, but I don't know if that's right and why it's right.</p>
<p><strong>EDIT:</strong> I just figured that taking the Sqrt of (x^2 + z^2) and squaring it just results back in x^2 + z^2, so that's why I can use x^2 + y^2 + z^2.</p>
<p>Another thing: Do I have to normalize for gravity? I think I do, but how would I go about this? Do I need to know the exact position and tilt of my device as it will be in the end?</p>
| 4,948 |
<p>A potential that depends on time is usually solved using the time dependent perturbation theory in standard undergraduate textbooks in quantum mechanics. The reason usually mentioned is that time dependent potentials cannot be solved using separation of variables. </p>
<p>Is this the only reason why it has to be solved using time dependent perturbation theory (Just because we cannot use methods of separation of variables)?</p>
| 4,949 |
<p>I have this continuum version $$ H_{R}=\int dx\psi^{\dagger}(x)(\frac{p^{2}}{2}+V)\psi(x) $$ with $V$ as constant potential.</p>
<p>Is it always justified to go from this to $$ \sum_{i}c_{i}^{ \dagger }\left[c_{i+1}+c_{i-1}-2c_{i}\right] +V \sum_{i}c_{i}^{ \dagger }c_{i} $$
using the finite difference form of the one-dimensional second derivative?
Ignore the factor $-1/2 $ and assume lattice constant $a= 1 $ and $\hbar =1 $. </p>
<p>Actually I am thinking whether it is justified to use this even when the derivative of eigenfunction is discontinuous at some of the points in real space like for the delta-function barrier. Will that affect the second derivative of the field operators ? </p>
| 4,950 |
<p>I report to you an interesting excerpt from my Physics book.
It is an Italian version, so I apologize in advance, as I'm sure I won't give proper justice to its beauty in the translation as the authors would have done.</p>
<p>Talking about </p>
<blockquote>
<p>There is a profound theoretical connection between quantities that are preserved and symmetries of nature. So the principle of conservation of the linear momentum is related to the <em>spatial</em> symmetry of nature, which implies that an experiment done in a place give identical results to an equal experiment performed in any other place. [...] The principle of conservation of energy is related to the <em>temporal</em> symmetry: the result of an experiment today will be equal to the result of the same experiment did yesterday.</p>
</blockquote>
<p>Physics I - Resnick, Halliday, Krane</p>
<p>After this words, the authors start talking about the conservations of the linear momentum in the canonical way.
However, I was captured by this fly away and I want to find out more. How can I do that?</p>
<p>In synthesis:</p>
<ol>
<li><p><em>Spatial</em> symmetry of nature $~\Rightarrow~\ldots?? \ldots~\Rightarrow~$ Conservation of the linear momentum </p></li>
<li><p><em>Temporal</em> symmetry of nature $~\Rightarrow~\ldots?? \ldots~\Rightarrow~$
Conservation of energy </p></li>
</ol>
<p>What do you think is in between?</p>
| 4,951 |
<p>Can one explain the relativistic energy transformation formula:</p>
<p>$$E = \gamma\ E',$$</p>
<p>where the primed frame has a velocity $v$ relative to the unprimed frame, in terms of relativistic time dilation and the quantum relation $E=h\nu$?</p>
<p>I imagine a pair of observers, A and B, initially at rest, each with an identical quantum system with oscillation period $T$.</p>
<p>Now A stays at rest whereas B is boosted to velocity $v$.</p>
<p>Just as in the "twin paradox" the two observers are no longer identical: B has experienced a boost whereas A has not. Both observers should agree on the fact that B has more energy than A.</p>
<p>From A's perspective B has extra kinetic energy by virtue of his velocity $v$. Relativistically A should use the energy transformation formula above.</p>
<p>But we should also be able to argue that B has more energy from B's perspective as well.</p>
<p>From B's perspective he is stationary and A has velocity $-v$. Therefore, due to relativistic time dilation, B sees A's oscillation period $T$ increased to $\gamma\ T$.</p>
<p>Thus B finds that his quantum oscillator will perform a factor of $\gamma\ T/T=\gamma$ more oscillations in the same period as A's quantum system. </p>
<p>Thus B sees that the frequency of his quantum system has increased by a factor of $\gamma$ over the frequency of A's system.</p>
<p>As we have the quantum relation, $E=h\nu$, this implies that B observes that the energy of his quantum system is a factor of $\gamma$ larger than the energy of A's stationary system.</p>
<p>Thus observer B too, using his frame of reference, can confirm that his system has more energy than observer A's system.</p>
<p>Is this reasoning correct?</p>
| 4,952 |
<p>I have calculated the dipole transition elements of electronic states $\langle a|D_1^m|b \rangle$ following the book of Cohen-Tannoudji (Complement $E_X$) and tried then to calculate from that the Rabi frequency $$\Omega_{a\to b}=\frac{1}{2\hbar}E_m \langle a|D_1^m|b \rangle.$$
But what is the direction of the E-field vector $E_m$ for the $\pi$, $\sigma^+$, $\sigma^-$ transitions?</p>
| 4,953 |
<p>Using the <a href="http://books.google.ie/books?id=ecS5DKstwREC&pg=PA196&dq=%22engineers%20and%20physicists%20who%20use%20the%20Laplacian%22&hl=en&sa=X&ei=7f96UqXOG8PQ7AbG7YG4Ag&ved=0CDEQ6AEwAA#v=onepage&q=%22engineers%20and%20physicists%20who%20use%20the%20Laplacian%22&f=false">intuitive interpretation</a> of the Laplacian $\vec{\nabla}^2$ as the difference between the average value of a field in the neighbourhood of a point & the value of the field at that point, one can pretty easily & quickly derive the form of the heat equation, Poisson's equation & the wave equation (as is done in that link if anyone's interested: Davis - Fourier Series & Orthogonal Functions P196). I quite honestly cannot remember those equations, I re-derive them using the intuition that the Laplacian affords me mixed with physical reasoning drawn from the situation (drawn from the field we're using whether it's temperature, concentration, electric potential or displacement). </p>
<p>I'm wondering if similar intuition can be used to derive the form of the Helmholtz equation, the Schrodinger equation, the Dirac equation, & really any other nice equation from mathematical physics that people have nice intuition for in their head & wouldn't mind sharing. It doesn't have to be in any way rigorous or even necessarily completely logical so long as you get the right result, though it should really be quick & to the point, thanks.</p>
| 4,954 |
<p>According to the <a href="http://en.wikipedia.org/wiki/Haag%E2%80%93Lopuszanski%E2%80%93Sohnius_theorem">Haag-Lopuszanski-Sohnius theorem</a> the most general symmetry that a consistent 4 dimensional field theory can enjoy is <a href="http://en.wikipedia.org/wiki/Supersymmetry">supersymmery</a>, seen as an extension of <a href="http://en.wikipedia.org/wiki/Poincar%C3%A9_group">Poincarè symmetry</a>, in direct product with the <a href="http://en.wikipedia.org/wiki/Gauge_symmetry">internal gauge symmetry</a>.</p>
<p>But we know that conformal theories, having as a symmetry group the conformal group (which is indeed an extension of the Poincarè group) in direct product with the internal gauge group exist.
Also there exist superconformal theories, which enjoy both conformal symmetry, supersymmetry and gauge internal symmetry.
All this theories are consistent, from a theoretical point of view, and well definite in $d=4$.</p>
<p>Therefore I ask, how does superconformal field theories avoid the Haag-Lopuszanski-Sohnius theorem?</p>
| 4,955 |
<p>A charged particle moving in a magnetic field experiences a Lorentz force $F=qv\times B$. A charged particle in a electric field experiences a force given by Coulomb's inverse square law. </p>
<p>But for a magnet we have what seems to be adhoc ways to calculate how the magnet will rotate.
In the above case we speak concretely of a charged particle being influenced by a magnetic field or an electric field. But what is the analogous "thing" or "particle" causing the magnet to rotate?</p>
<p>It feels like classical electromagnetism is Maxwell's equations plus laws for how a charged particle behaves in a magnetic field and electric field, but notably missing corresponding Coulomb and Lorentz force laws for "magnets".</p>
| 4,956 |
<p>I recently got confused (and slightly annoyed by the lack of technical details) when reading a popular <a href="http://www.scientificamerican.com/article.cfm?id=dark-worlds" rel="nofollow">article</a> (authored by Jonathan Feng and Mark Trodden) introducing the concept of super WIMPs.</p>
<p>The article characterized super WIMPs (without giving more detailed explanations) as follows: </p>
<ul>
<li><p>WIMPs could probably decay to so-called super WIMPs, which would only gravitationally interact with visible matter </p></li>
<li><p>different kinds of super WIMP particles could interact via additional newly postulated weak "dark forces" ( = gauge bosons ?) with each other</p></li>
<li><p>this kind of dark matter particles can probably interact with dark energy ( how? What is dark energy in this particular scenarios suposed to be? )</p></li>
<li><p>the authors vaguely stated the super WIMP models are some kind of extensions of supersymmetric models that lead to the "ordinary" WIMPs</p></li>
</ul>
<p>From this characterization I really dont get what super WIMPs are suposed to be so my question is:</p>
<p>What are the underlying theoretical ideas behind these phenomenological models? Are they derived in some "top down" approach from high energy theories or is some "buttom up" extension of something like the MSSM for example applied ?</p>
<p>And I would appreciate a technically more accurate description of the super WIMP particles and their interactions.</p>
| 4,957 |
<p>In the letter of introduction to Einstein's 1916 paper on General Relativity, he writes, "The mathematical tool sthat are necessary for general relativity were readily available in the 'absolute different calculus,' which is based upon the research on non-Euclidean manifolds by Gauss, Riemann, and Christoffel, and which has been systematized by Ricci and Levi-Civita and has already been applied to problems of theoretical physics."</p>
<p>In what way had it already been applied to problems of theoretical physics?</p>
<p>See <a href="http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf">http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf</a> for the quote.</p>
| 4,958 |
<p>Referencing this news article:
<a href="http://www.smh.com.au/technology/sci-tech/cosmic-burst-in-far-away-galaxy-puzzles-nasa-20110408-1d6kz.html" rel="nofollow">http://www.smh.com.au/technology/sci-tech/cosmic-burst-in-far-away-galaxy-puzzles-nasa-20110408-1d6kz.html</a></p>
<p>It also references an event id:<br>
(GRB) 110328A</p>
<p>The article seems to imply that the reason for the unusually long period of gamma bursts being visible is because the remnants of the exploding star is near the centre of that galaxies nucleaus, and hence probably near the supermassive black hole. It goes on to say that the observable event is a stream of this energy towards the sm-bh.<br>
Is this the most logical hypothesis for this event?<br>
What other possibilities could explain such a lengthy burst of gamma radiation being visible?</p>
<p>Edit:<br>
If it is even speculation that it is a star being ripped apart, then what other possibilites could explain the explosion that lead to the unusually long bursts?</p>
| 4,959 |
<p>Can someone explain why the rotation matrix is a unitary, specifically orthogonal, operator?</p>
| 4,960 |
<p>Who is the author of the term "Coulomb logarithm"? In fact, Coulomb logarithm was computed by Langmuir in his paper of 1928 where the term "plasma" was introduced into physics, but the term "Coulomb logarithm" seemed to appear later. The earliest reference I found is the paper <a href="http://www.fnti.kiae.ru/content/raboti/B_1956_DAN_r_ab.pdf" rel="nofollow">Relativistic kinetic equation </a> by Belyaev & Budker (1956). </p>
<p>UPDATE: Using Google Labs I found <a href="http://books.google.com/books?id=FQnyAAAAMAAJ&q=%22%D0%BA%D1%83%D0%BB%D0%BE%D0%BD%D0%BE%D0%B2%D1%81%D0%BA%D0%B8%D0%B9%20%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%22&dq=%22%D0%BA%D1%83%D0%BB%D0%BE%D0%BD%D0%BE%D0%B2%D1%81%D0%BA%D0%B8%D0%B9%20%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%22&hl=ru&ei=97-eTpLyDMGA-waYp9mDDQ&sa=X&oi=book_result&ct=book-thumbnail&resnum=5&ved=0CEMQ6wEwBA" rel="nofollow">a reference dated by 1937</a> in very rare Georgian journal in Russian. </p>
| 4,961 |
<p>I have read through the wikipedia page and several lecture notes/arxiv papers from my google search (and several related P.SE questions), but I'm still hopelessly confused.</p>
<ol>
<li><p>Consider a 'classical Schrodinger field in a box' problem. Since the field evolves just like a normal wavefunction, I could still extract the x-projection of any operators I want from it, in addition to the field momentum $\frac{\partial\mathcal{L}}{\partial\dot{\phi}}$ or any other field variables.</p></li>
<li><p>From my understanding, there are two ways to arrive at QFT:</p>
<ul>
<li>from QM/RQM: we change our basis into particle-number basis (fock space).</li>
<li>from CFT: we "2nd quantize" the field and field-momentum.</li>
</ul></li>
</ol>
<p>Looks like the "particle creation" interpretation of the field in QFT can be deduced only from the first approach. Which means, the interpretation of the latter approach can't be completely independent from the former.
But they don't give me any hint on how to interpret the classical field. Or am I missing something? Or should I just give it up because the quantum field is not an observable?</p>
<p>Random comment: I could still see $\hbar$ lurking inside CFT (some people might argue that it's there to keep the dimension consistent, but I could apply the same argument to Schrodinger equation, too).</p>
| 4,962 |
<p>For those spin liquids with <em>SU(2) spin-rotation symmetry</em> <strong>or</strong> <em>time-reversal(TR) symmetry</em> , the Spin Density Wave (SDW) order parameters are always zero, say $\left \langle \mathbf{S}_i \right \rangle=\mathbf{0}$, due to the spin-rotation symmetry or TR symmetry.</p>
<p>But if a spin-liquid state is <em>neither</em> spin-rotation symmetric <em>nor</em> TR symmetric, <em>e.g.</em> the exact <em>chiral spin liquid</em> ground state of the <a href="http://prl.aps.org/abstract/PRL/v99/i24/e247203" rel="nofollow">generalized Kitaev model on the <em>decorated</em> honeycomb lattice</a>, is there any possibility that the SDW order parameters $\left \langle \mathbf{S}_i \right \rangle\neq \mathbf{0}$ ? Therefore, if a spin-liquid state has <em>nonzero</em> order parameters $\left \langle \mathbf{S}_i \right \rangle$, why we still call it a "spin liquid" rather than a "SDW phase"?</p>
<p><strong>Remarks:</strong> The <em>spin-rotation</em> mentioned here should be understood as the <strong>continuous $SU(2)$ or $SO(3)$ one</strong>, say <strong>all</strong> the spin-rotation transformations. Although the <a href="http://prl.aps.org/abstract/PRL/v99/i24/e247203" rel="nofollow">Kitaev model(on the <em>decorated</em> honeycomb lattice)</a> and its ground state <strong>break</strong> this <em>continuous spin-rotation symmetry</em>, they still <strong>possess</strong> the <em>$\pi$ spin-rotation symmetry</em> about $S_x,S_y$ and $S_z$ spin-axes, and this is <em>enough</em> to ensure $\left \langle \mathbf{S}_i \right \rangle=\mathbf{0}$.</p>
<p>Thanks in advance.</p>
| 4,963 |
<p>Leslie Ballentine develops in QM: A Modern Development an interpretation based on the ensemble interpretation, and responds to most criticisms. </p>
<p>My question: what criticisms still exist against this interpretation such that it is not recognized as the standard interpretation within the physics community? </p>
<p>What problems still exist? </p>
<p><a href="http://en.wikipedia.org/wiki/Ensemble_interpretation" rel="nofollow">http://en.wikipedia.org/wiki/Ensemble_interpretation</a></p>
| 4,964 |
<p>I am trying to understand the balance of energy -law from continuum mechanics, fourth law <a href="http://en.wikipedia.org/wiki/Continuum_mechanics#Balance_laws" rel="nofollow">here</a>. Could someone break this a bit to help me understand it? From chemistry, I can recall $$dU = \partial Q + \partial W$$ where $U$ is the internal energy, $Q$ is heat and $W$ is the work. How is the fourth law of conservation in CM:</p>
<p>$$\rho_{0}\dot{e} - \bf{P}^{T} : \bf{\dot{F}}+\nabla_{0} \cdot \bf{q} -\rho_{0}S = 0$$</p>
<p>related to that?</p>
<p><strong>Terms</strong></p>
<ul>
<li>$e(\bar{x}, t) = \text{internal energy per mass}$</li>
<li>$q(\bar{x}, t) = \text{heat flux vector}$</li>
<li>$\rho(\bar{x}, t) = \text{mass density}$</li>
</ul>
<p><strong>Operations</strong></p>
<ul>
<li>$: \text{ -operation} = \text{Frobenius inner product?}$ (<a href="http://math.stackexchange.com/questions/65546/a-i-jb-i-j-is-matrix-dot-product-in-einstein-notation">related</a>)</li>
<li>$\dot{\text{v}} = \text{derivative of vector } v$</li>
<li>$\dot{\text{M}} = \text{transpose of matrix } M$</li>
</ul>
| 4,965 |
<p>Can any one suggest a good reference for studying renormalization of disjoint, nested and overlapping divergences in Feynman diagrams (for example, $\Phi^4$ theory)?</p>
| 168 |
<p>I have a problem with the transition from quantum relativistic wave equations (specifically Klein-Gordon equation) to QFT, since a lot of assumptions seem implicit. For example I have a problem with the time evolution operator, which is crucial on deriving the perturbative expansion $-$ the main tool in QFT I believe.
c
So here's what I have a problem with: when we make the leap from Schrödinger equation to a Klein-Gordon equation, we get a second order time derivative, and hence loose the simple concepts from nonrelativistic QM like: the Hamiltonian, time evolution operator etc.</p>
<p>But for a scalar quantum field we can make a Lagrangian density:</p>
<p>$$
\mathcal{L}(x) = \hbar^2 c^2 g^{\mu \nu} \partial_\mu \phi \partial_\nu \phi^* - m^2c^4 \phi \phi^*
$$</p>
<p>and perform the "second quantization", from which we get a Hamiltonian, canonical commutation relations and the ability to use pictures (Schrödinger's, Heisenberg's...).</p>
<p>So how does this work? Before there was no Hamiltonian in principle, and now there is. Is this the Hamiltonian we pluck into the perturbative expansions' formulas? What changed, when compared to the single solution wave equation in the beginning?</p>
| 4,966 |
<p>In Griffiths' electrodynamics book, he uses the equation,
$$\nabla^2\mathbf{A}=-\mu_0 \mathbf{J},$$
to state that
$$\mathbf{A}(\mathbf{r}) = \frac{\mu_0}{4\pi}\int\frac{\mathbf{J}(\mathbf{r}')}{|\mathbf{r}'-\mathbf{r}|}\mathrm{d}\tau'.$$
This is, of course, justified by the fact that each cartesian component of $\mathbf{A}$ obeys Poisson's equation, according to the first equation.</p>
<p>But then he went on to say that to evaluate the integral you are restricted to use cartesian coordinates because that was our assumption in deriving the second equation from the first. (4th edition, page 244, footnote 19).</p>
<p>This seems wrong to me. As far as I can imagine, the value of the integral is independent of the system of coordinates you use. </p>
| 4,967 |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/4669/what-are-the-most-important-discoveries-breakthroughs-in-physics-recently">What are the most important discoveries/breakthroughs in physics recently?</a> </p>
</blockquote>
<p>The last two decades have seen significant advances in mathematics, where long standing conjectures have been proved, leading to much further research.
Two great examples would be Wiles' proof of the Taniyama-Shimura conjecture (and hence, Fermat's Last Theorem) and Perelman's proof of the Poincare and Thurston conjectures.</p>
<p>Have there been any comparable advances in theoretical physics in the last 20 years ?</p>
<p>I know there have been very important experimental discoveries such as the accelerating universe and neutrino oscillations.</p>
<p>But I am asking specifically about theoretical discoveries in the last 20 years where, say, some long unexplained phenomenon has been understood and predictions have matched quantitatively with experiment to high accuracy.</p>
| 169 |
<p>If we would hypothetically be exactly on the event horizon, we should see our own back, because of the circular motion of photons on the event horizon, right?</p>
<p>But what would be the image size, or $-$ asking differently $-$ how far away, would our back seem to be? Would it be magnified or minified, when compared to the image of a person $2 \pi R_{Schwarzschild}$ away?</p>
| 4,968 |
<p>How would I go about showing:</p>
<p>$$\hat{A}^{\dagger} + \hat{B}^{\dagger} = \left( \hat{A} + \hat{B} \right) ^{\dagger}$$</p>
| 4,969 |
<p>In quantum physics we've defined:
$$ \psi (x) = \sqrt{ \dfrac{1}{2 \pi \hbar} } \int^{ \infty }_{-\infty } \phi (p) \exp \left( i \dfrac{px}{ \hbar} \right) dp $$
Now,
$$a(k) \equiv \sqrt{ \hbar } \phi (p)\quad {\rm and}\quad k = \dfrac{p}{ \hbar } $$
Where,
$$ a(k) = \left\{ \begin{array}{cccc} 0 & k < - \dfrac{ \epsilon }{2} \\ \sigma + \dfrac{2 \sigma }{ \epsilon } k & - \dfrac{ \epsilon }{2} < k < 0 \\ \sigma - \dfrac{2 \sigma }{ \epsilon } k & 0 < k < \dfrac{ \epsilon }{2} \\ 0 & k > \dfrac{ \epsilon }{2} \\ \end{array} \right.$$</p>
<p>Normalizing $a(k)$ I get $\sigma$ to be:</p>
<p>$$ \sigma = \sqrt{ \dfrac{3}{ \epsilon } } $$
But I can't get anything reasonable from the Fourier Integral.</p>
| 4,970 |
<p>I understand that a voltmeter is used for measuring potential electrical difference, but how exactly should said voltmeter be connected with the resistor in circuit? </p>
| 4,971 |
<p>During Hawking's radiation, a virtual particle with negative energy and mass (from pair of particle and antiparticle) fall into black hole and its real partner having positive energy escape from vicinity of black hole. And it <em>appears</em> to have been emitted from black hole. <em>Since these pair of particles were present outside the black hole</em>, flow of negative energy particles reduces its mass. As the black hole loses its mass the area of event horizon gets smaller. And so, it must decrease the entropy of the black hole.</p>
<p>So, how the entropy of the black hole always increase? What I am missing here. Please explain. </p>
| 4,972 |
<p>What is the direction is the magnetic force vectors pointing from a coil of wire that has current running through it?</p>
<p><a href="http://www.ndt-ed.org/EducationResources/CommunityCollege/MagParticle/Graphics/coil1.gif" rel="nofollow">http://www.ndt-ed.org/EducationResources/CommunityCollege/MagParticle/Graphics/coil1.gif</a></p>
<p>The above link is a picture of a wire with current running through it. I see the blue arrows indicating the magnetic field lines, but I am having trouble visualizing the magnetic force lines. Where are they pointing? Please help.</p>
| 368 |
<p>In the case of dispersion relation of silicon having crystal plane orientation 111; what is the <a href="http://en.wikipedia.org/wiki/Sellmeier_equation" rel="nofollow">Sellmeier's equation</a> for refractive index $n$ of silicon orientation 111 & what it's extinction coefficient $K$?</p>
| 4,973 |
<p>I am trying to teach myself about electricity and magnetism and I have a few questions about <a href="http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity" rel="nofollow">resistance</a>. How does resistance of say a long wire compare to that of a a short wire? what about thick and thin? </p>
| 4,974 |
<p>How do I calculate the <a href="http://en.wikipedia.org/wiki/Power_%28physics%29" rel="nofollow">power</a> of a lightbulb? I have values but I don't know the equation to use. </p>
| 4,975 |
<p><strong>Question</strong></p>
<p><img src="http://i.stack.imgur.com/9JcHo.png" alt="http://i.imgur.com/ALUdyoB.png"></p>
<p>Create a set-up, as shown in the Figure, consisting of two mirror tiles (A and B)
and a bird face, facing to the right . Make sure the two mirrors are perpendicular to the table and parallel to each other. The situation shown is a front view of the situation.</p>
<p>Question A: If look at a mirror from the same direction and angle as one of the two arrows that are drawn, you will see the bird in the mirror. Draw the two mirror images of the bird, making sure the bird mirror is facing to the correct side! </p>
<p><strong>My Try</strong></p>
<p>I tried to draw a mirror reflection.</p>
<p><img src="http://i.stack.imgur.com/32wfh.png" alt="[IMG]http://i.imgur.com/9U67i12.png[/IMG]"></p>
<p>But Can the light ray (in yellow) simply go through the bird?</p>
| 4,976 |
<p>The rear wheels of a car always face in the direction the car is moving. The front wheels are able to turn left or right and thus can point in the direction the car is moving towards. What I don't understand is how a car can turn with all four wheels rotating (not skidding). That is, how is it possible that the front two tires can face in one direction, the rear two tires in another direction, with the four tires all connected by rigid rods and with all four tires rotating without skidding? </p>
<p>I'm trying to visualize this assuming the car is moving very slowly, but even then the situation just seems impossible to me. Is it in fact that the rear tires are skidding in just very small micro-steps so that we don't actually observe it happening?</p>
| 4,977 |
<p>Why <a href="http://en.wikipedia.org/wiki/Fermion_field" rel="nofollow">fermion field</a> is treated as anti-commuting and <a href="http://en.wikipedia.org/wiki/Boson" rel="nofollow">boson</a> field as truly classical in standard model?</p>
| 4,978 |
<p>What is the total amount of energy in the universe? is there the same amount of energy as negative energy, cancelling each other out? Or is it something different?</p>
| 27 |
<p>The one-form
$$\theta=\sum_i p_i\, \text dq^i$$
is a central object in hamiltonian mechanics. It has a bunch of applications: $\omega=\text d\theta$ is the symplectic structure on phase space, $S=\int\theta$ is the classical action, and so on and so forth. It is associated with the names Liouville one-form, Poincaré one-form, canonical one-form, and symplectic potential, none of which surprises me, but its <a href="http://en.wikipedia.org/wiki/Tautological_one-form" rel="nofollow">Wikipedia entry</a> informs me that the preferred<sup>[by whom?]</sup> name for it is actually "tautological" one-form, on the grounds that 'canonical' (which would be my natural choice) is 'already heavily loaded', and because of the risk of confusion with <a href="http://en.wikipedia.org/wiki/Canonical_class" rel="nofollow">some algebraic thingammy</a>.</p>
<p>This name completely mystifies me. <strong>Why was the name "tautological" chosen for this object?</strong> When, where, and by whom? Or was this name chosen <a href="http://xkcd.com/703/" rel="nofollow">because that's its name</a>?</p>
| 4,979 |
<p>I always thought about symplectic forms as elements of areas in little subspaces because of the Darboux theorem, however I cannot get the physical intuition for it and for the hamiltonian vector field. </p>
<p>To simplify things, let's consider the configuration space $TQ$, we know that $T^{*}Q$ always have a symplectic structure by putting $\omega = d\theta$ where $\theta = \sum p_i dq_i$ is the Liouville one-form, then the hamiltonian vector field is defined by $\omega(X_H, Y) = dH(Y)$ and I can change from the Lagrangian $L : TQ \longrightarrow \mathbb{R}$ to the hamiltonian $H :T^{*}Q \longrightarrow \mathbb{R}$ by the mass (1, 1)-tensor $M=M_i^j$. So what's the physical intuition for $\omega$, $X_H$ and $\theta$? Why do people uses a symplectic structure in mechanics (if it's to define $X_H$, what's the utility of $X_H$?)? Furthermore is the unique utility in changing the lagrangian to the hamiltonian the existence of a symplectic form in $T^{*}Q$?</p>
| 4,980 |
<p>The following is the problem that I am working on.</p>
<blockquote>
<p>A bullet of $.01\: \mathrm{kg}$ is shot into a block of mass $.89\: \mathrm{kg}$ that is hanging from the ceiling. After the bullet has been caught in the block, it swings and rises $.40\: \mathrm{m}$ from its initial height. Find the initial velocity of the bullet.</p>
</blockquote>
<p>I though that $\frac{1}{2}m{v_0}^2 = (m+M)gh$ would give me the solution $25.6\: \mathrm{m/s}$, but the answer is supposedly $2.5 \times 10^2\: \mathrm{m/s}$. What am I missing ?</p>
| 4,981 |
<p>I read a book on the wave property of light where the author mentioned that the electric field, instead of magnetic field, dominates the light property. I don't understand why.</p>
<p>In Maxwell's theory, a light field has an electric and magnetic field at the same time and they are perpendicular. Also, in some books, where they consider the polarization, they only use the electric field as example. For example, if the vibration of the electric field is up and down, it cannot go through a polarizer which orients 90 degree to the vibration direction of the field, so no light goes through the polarizer. But what happened to the magnetic field? The magnetic field is perpendicular to the electric field, so in this case, the magnetic field should pass the polarizer, and we should have outgoing light -- but we don't. Why is this so? </p>
| 4,982 |
<p>Which properties are sufficient evidence for a material to be not superconducting?
I am looking for a set of statements like</p>
<blockquote>
<p>If the material is semiconducting, it is not superconducting</p>
</blockquote>
<p>Edit:
I am not looking for a definition of superconductivity, or for introductional literature like the famous W. Buckel. </p>
<p>I am looking for properties, that would forbid superconductivity. If you have a source for it i would be very glad. As far I remember magnetic atoms will forbid superconductivity too, but i could not find a source yet.</p>
| 4,983 |
<p>How can we charge a metal electrode with large charges ? When i saw a video about measuring a charge using a visiostat on a balloon , the charge was 0.6 nano-coulomb. Is the charge of 1 coulomb unachievable? </p>
| 4,984 |
<p>Let us say that I am sitting in a room with all the drapes open. Bright sunlight is coming through the window. The whole room is brilliantly lighted. I will not be able to see the dust particles suspended in air.</p>
<p>Now, if I draw the drapes close, keeping a small slit open, allowing only a beam of sunlight to come in, I will readily see the suspended dust particles in that beam. The same thing will happen in a dark night with the beam of light from a handheld battery torch.</p>
<p>What will be the scientific explanation for this? I can not see the dust particles
when I have more light. But when I actually reduce the light and there is only one narrow beam present, I can see those minuscule particles. </p>
<p>How does a narrow beam of light enable me to see those fine elements?</p>
| 4,985 |
<p>My question is simple. Green light is more similar to red light than violet, then why is violet reddish and green not? in the language of frequencies and wavelengths, red and violet should contrast each other. Then why do they don't? </p>
| 170 |
<p>Fundamental interactions, such as electromagnetism, the strong force, the weak force, and possibly gravitation, all have something in common: They can be described in terms of relativistic quantum fields, and are clearly the results of interactions between two different kinds of fields. For example, with an electron interacting via the electromagnetic force, one can describe the electromagnetic field using quantum electrodynamics, and an equation of motion can be obtained from the QED lagrangian:
$$\mathcal{L}_{QED} = \bar{\psi} (i \gamma^{\mu} D_{\mu} - m)\psi - \frac{1}{4} F_{\mu \nu} F^{\mu \nu}$$
And, the interaction picture here is clear: The electron field ($\psi$) interacts with the electromagnetic field, resulting in its change in motion.</p>
<p>However, with an entropic force (such as the elasticity of a polymer), can the same be done? Can one construct a Lagrangian for the elastic force of a polymer, and is there some sort of "entropy force field" that can act as the relativistic quantum field with which polymer molecules interact? Or is the entropic force not a force at all, just a consequence of the universe tending towards maximum entropy? Or, alternatively, is it possible that every entropic force that exists in this universe is actually a manifestation of one of the fundamental forces (electromagnetism, strong force, weak force, gravity), meaning that the elastic force in a polymer is really something like electromagnetic interaction?</p>
| 4,986 |
<p>Imagine I have a solenoid connected to a power supply. Solenoid produces an electromagnetic field. Now I take a permanent magnet and place it inside the solenoid. How will the magnet align itself (assuming there is no gravity) inside the solenoid and will it rotate itself around the central axis "aligning" itself?</p>
<p>From these two cases cases, which one is correct behaviour and where would the "north" pole point (up, down, left or right):</p>
<p>One:</p>
<p><img src="http://i.stack.imgur.com/8rI1t.png" alt="enter image description here"></p>
<p>Two:</p>
<p><img src="http://i.stack.imgur.com/uVdWC.png" alt="enter image description here"></p>
<p>P.S. What if the magnet is shaped differently, for example like a horseshoe, will it change its behaviour?</p>
| 4,987 |
<p>How does a universal battery charger, such as <a href="http://rads.stackoverflow.com/amzn/click/B002XY5F6A" rel="nofollow">this one</a> work, i.e. how does it know what voltage, current and polarity is appropriate for the battery inserted? Do batteries have some form of protocol to tell the charger these parameters?</p>
| 4,988 |
<p>First I want to consider an example of 1D motion. Lagrange equation:</p>
<p>$$ \frac{d}{dt} \frac{\partial L}{\partial \dot x} - \frac{\partial L}{\partial x} = 0 $$</p>
<p>If we transform $ L \rightarrow L+a $ with $a$ a is constant, the equation of motion remains unchanged. This is global symmetry.</p>
<p>To obtain local symmetry we want when transforming $L \rightarrow L+a(x) $ we still have the same equation. To obtain that we introduce the "total derivative":</p>
<p>$$\frac{Df}{dt} = \frac{df}{dt} + \frac{\partial a}{\partial x}$$</p>
<p>Then the equantion of motion would be unchanged under any local transformation:</p>
<p>$$\frac{D}{dt} \frac{\partial L}{\partial \dot x} - \frac{\partial L}{\partial x} = 0$$</p>
<p>$\frac{\partial a}{\partial x}$ is considered related to the geometry of 1D space.</p>
<p>I see $\frac{\partial a}{\partial x}$ is similar to the Christoffel symbols in general relativity.</p>
<p>Is there anyway to construct General Relativity by demanding local symmetry like this?</p>
| 4,989 |
<p>QFT is a nonlocal unitary transformation and so can generate entanglement in a system. It means a separable pure state can be converted into an entangled pure state. Now since the presence of entanglement can be witnessed via an increase in the entropy of the subsystems. Since all the subsystems witness a positive entropy change ,does the entropy of the complete system also increase (it seems to increase since entropy is additive) ? Now if it does increase , It seems to violate reversible nature of Quantum algorithms. I am very confused. </p>
| 4,990 |
<p>Let's say there is a dielectric ring of charge with radius $a$ and charge $q_1$. I could calculate the electrostatic force applied on a point charge with charge $q_2$ and which is collinear with the centre of the ring with these equations(the distance between ring and point charge is $r$ and the distance between the centre of the ring and point charge is $d$):
$$
dE= (k.dq)/r^2
$$
$$
dE_x=(k.dq)/r^2\cos(\theta)
$$
$$
dE_x=(k.d.dq)/(a^2+d^2)^{(3⁄2)}
$$
$$
E_x=∫(k.d.dq)/(a^2+d^2)^{(3⁄2)} =(k.d)/(a^2+d^2)^{(3⁄2)}∫dq=kdq/(a^2+d^2)^{(3⁄2)}
$$
$$
F=kdq_1q_2/(a^2+d^2)^{(3⁄2)}
$$
Here is the figure of the ring:
<img src="http://i.stack.imgur.com/0Ha0o.png" alt="enter image description here">
However, I couldn't find a proper answer to how to calculate the electrostatic force between two dielectric rings of charge with radius $a_1,a_2$ charge $q_1,q_2$ respectively. I would be grateful if someone could help me on this subject. Also please show me which formula did you use rather than just a solution. Feel free to ask me anything about this question.</p>
| 4,991 |
<p>I was given this worksheet from my teacher and well im finding it really tough so far ..
the question below is just crushing my skull .. so i would appreciate it if you guys would guide me through it</p>
<blockquote>
<p>A particle projected from ground takes time $t_1$ to reach $\frac{15}{16} H$ and time $t_2$ to cover the rest of distance to the ground. If $H$ is the maximum height attained. find the ratio $\frac{t_1}{t_2}$</p>
</blockquote>
<p>well my options were many ... they were $\frac{1}{3}$, $\frac{3}{1}$, $\frac{5}{3}$ and $\frac{3}{5}$</p>
<p>and well using my knowledge of atleast what i know is:</p>
<ol>
<li>the object has <strong>almost</strong> reached the max height so the ratio wont
be that big </li>
<li>i tried using the equations of motions and to no
avail i still didnt get anywhere</li>
<li>$u \sin(\theta) t_1-\frac{1}{2}g
(t_1)^2= \frac{15}{16} H$ </li>
<li>and $\frac{\left(u \sin\theta\right)^2} {2g} =H$</li>
</ol>
<p>keeping in mind that $t_2$ has to obviously be greater than $t_1$ ... the second and the third options are eliminated ... well it surely cant be $\frac{1}{3}$(maybe) .. because that is a really big ratio ...</p>
<p>is there some other extra formula or something other than the common formulae (like max height and range and splitting of vectors)i am supposed to know to solve this question
am i missing out anything?</p>
| 4,992 |
<p>Why is geometric optics the low wavelength limit of the wave theory of light? I can't seem to grasp why either a low or high wavelength limit would be necessary.</p>
| 171 |
<p>If we have a one-loop diagram in $\phi ^ 3$ scalar field theory with $n$ external lines, then what is its symmetry factor?</p>
<p><img src="http://i.stack.imgur.com/ssYJ7.jpg" alt="enter image description here"></p>
<p>I have drawn the diagram I am looking for, but instead of $6$ external lines, I want the diagram to have $n$ external lines. Please ignore the arrows in my diagram and assume that the external points are held fixed.</p>
| 172 |
<p>In the classical description of <a href="http://en.wikipedia.org/wiki/Raman_scattering" rel="nofollow">Raman effect</a> the object of study is the electric polarizability of the system.
Since I'm interested in learning the quantum description of the Raman effect and in Bernath's "Spectra of atoms and molecules" is said that we are interested in studying the transition dipole moment like:
\begin{equation}
M_{10}=\langle \Psi_1\mid\mu\mid\Psi_0\rangle
\end{equation}
Where $\mid\Psi_i\rangle$ are the $i-$level state of the system.</p>
<p>How this two description are related?</p>
| 4,993 |
<p>Taking this post: <a href="http://physics.stackexchange.com/a/71870/44176">"Is there a proof of existence of time?"</a>, as a starting point. Therein was mentioned that there is confusion between:</p>
<p>"<em>time</em>" and "<em>flow of time</em>".</p>
<p>There was a comment (of mine) that the confusion is not between <em>time</em> and <em>flow of time</em> (which are equivalent), but between <em>time</em> and <em>duration</em> of which one is a dimension (i.e <em>duration</em>).</p>
<p>Given the importance of the problem of <em>time</em> in General Relativity and Quantum Gravity.</p>
<p>Having made this disctinction is an important step, since duration can easily be considered as a dimension (with the proper $c$ factor) along with other space dimensions, than actual <em>time</em> (or <em>flow of time</em>).</p>
<blockquote>
<p>Can we say that <em>time</em> parameter/dimension in SR/GR actually
represents not <em>event time</em> but <em>duration</em> (i.e time-interval)?</p>
</blockquote>
<p><em>By the way this would elucidate the wick-rotation method, as transforming from "duration" to "frequency" representation.</em></p>
<p>(Not to mention that one can have as many duration dimensions in a manifold as one wants with <strong>no</strong> conceptual or definition problems like when one attempts that with extra <em>time</em> dimensions, per some theoretical proposals)</p>
| 4,994 |
<p>I have the following readings for length of a wire:</p>
<p>10.2 ± 0.1 cm</p>
<p>10.3 ± 0.1 cm</p>
<p>10.1 ± 0.1 cm</p>
<p>10.2 ± 0.1 cm</p>
<p>Now, when I find out the mean value, I get:</p>
<p>(10.2 ± 0.1 + 10.3 ± 0.1 + 10.1 ± 0.1 + 10.2 ± 0.1) cm / 4</p>
<p>So, will I get the answer as (10.2 ± 0.1) cm or (10.2 ± 0.4) cm? Why?</p>
| 4,995 |
<p>Let's say that you are doing some Monte-Carlo simulations of a statistical system on a lattice and you observe scale invariance, meaning that you are at a conformal point. Can you get a numerical appreciation of the central charge?</p>
<p>I know how the central charge is related on the free energy (on a cylinder for example) or to the stress-energy tensor but these are not direct observable in a Monte-Carlo.</p>
<p>Is there a systematic method for that? Has it already been done?</p>
| 4,996 |
<p>In an certain question my teacher asked to find the maximum force. She said that the maximum force in electrostatics means $\frac{dF}{dx}=0$. Why is it like that?</p>
| 4,997 |
<p>If we place two glass plates of refractive index n and each having thickness t,on the way of a light ray the increase in optical path becomes <img src="http://i.stack.imgur.com/7p0h5.jpg" alt="enter image description here"> (S2P-S1P)=2(n-1)t due to refraction through them,and the path difference(or extra path traversed by light) due to reflection at the second surface of one glass plate is <img src="http://i.stack.imgur.com/NNxzf.gif" alt="enter image description here"> 2ntcos(alpha).Without seeing the expression if we look at the phenomenon directly,aren't they basically same? as both are going through a glass media of same length!!</p>
| 4,998 |
<p>There is known to be a lower limit on space, which can be derived from the Planck units. It can describe the minimum distance resolvable between two points; but what then would the structure of space look like?</p>
<p>Would it be a lattice, where each point of space, planck length apart on each axis, forms the 3 dimensional space, and space is absolute? Or is it literally just the limiting distance between two arbitrary points? Thoughts? </p>
| 173 |
<p>Recently I learned about a technique in image processing, which has its roots in something called the 'heat equation' from physics. The original creators of this technique were inspired by the physics of how heat diffuses through an object. </p>
<p>The objective of course is to 'smooth out' the image, for general noise removal. This was done by taking a Gaussian kernel, and convolving it with the image. However, the professor says that the heat-equation is actually a generalization of this process, and in fact, we can get much better techniques using the heat-equation framework. </p>
<p>Essentially, if the original image we have is $I$, then the heat equation framework says that:</p>
<p>$$
I(t) = \nabla \cdot (\ D(x,y) \ \nabla I)
$$</p>
<p>where the $\nabla$ means spatial derivative, (I think). The $I(t)$ indicates the image new image at some point in time as it evolves - as heat flows - as this algorithm is run. Finally, the $D(x,y)$ is the "diffusion co-efficient", and if $D=1$, (or any constant), then the above simply collapses to a Gaussian kernel convolving the image $I$. </p>
<p>Now, what I am hoping for is the following: I am hoping someone here can add some intuitive insight into how/why this is working, vis-a-vis a physical analogy to 'heat flow' in the image. </p>
<p>The way I currently understand it, is that we have an image. The bigger the amplitude of certain pixels, the 'hotter' those pixels are. In fact every image pixel is as hot as its amplitude. Now, we also know from physics and entropy, that the heat will try to dissipate, so that eventually, the "temperature" across the image becomes equal. (This I take it, is what is happening when a gaussian convolves the image - this is the 'smearing' we are seeking for removal of noise...). </p>
<p>Now, with the diffusion co-efficient being a constant or 1, this 'heat flow' occurs everywhere. However, if the diffusion co-efficient is, say, a binary function of the spatial image, the the co-ordinates of where $D(x,y)$ equal 0, are where no heat can flow through, and so those are pixels that are spared from the heat flow... </p>
<p>Is my understanding of this physically inspired algorithmic technique correct? Are we really doing nothing but 'simulating' heat flow, except in the frame work of an image? Thank you so much.</p>
| 4,999 |
<p>I made a simple bulb-battery circuit and then I cut one of the wires and attached both ends to cemented floor, the bulb didn't glow, this means <strong><code>cemented floor</code></strong> is a poor conductor of electricity. Then how does <strong>earthing</strong> work ? This idea of activity came from when I got a shock being barefoot but got no shock from same source with slippers on.<br>
So, </p>
<p><code>How can electrons pass through insulator like cemented floor during earthing ?</code></p>
| 5,000 |
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