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<p>In one of tasks I met the concept of unitarily similar matrices: in particular, I need to prove that sets $\gamma_{\mu}, -\gamma_{\mu}$ (Dirac gamma matrices) are unitarily similar. I don't know what does it mean, so can someone tell me? Maybe, I need to find some unitary transformation that connects first and second sets?</p>
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<p>We consider that the force acting on a current carrying wire placed in a uniform magnetic field perpendicular to the length of the wire is given by $IBl$. If the wire moves by a distance $x$ in a direction perpendicular to its length the raise in its kinetic energy is $IBlx$</p>
<p>Now basically the magnetic forces are acting on the electrons moving inside the wire and is always perpendicular to the instantaneous velocity so it cannot perform any work on it and normals are also unable to provide any net work done on the system, so what provides the change in kinetic energy of the system?</p>
| 7,030 |
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<p>In a recent question <a href="http://physics.stackexchange.com/questions/31686/can-colliders-detect-b-violation">Can colliders detect B violation?</a> I asked about detecting B violation in collisions. Here I am interested in the theory aspect. (I asked both questions originally in the same question, but I got one answer which was more on the experimental side, and I don't think the two domains of expertise overlap enough to keep the questions merged. I am also interested in the purely theoretical question)</p>
<p>What is the rate of B violation expected in the standard model in high energy proton-proton or proton-anti-proton collisions? The rate is known to be vanishingly small at ordinary temperatures and energies, but this is because the instantons that cause the effect are suppressed by the Higgs. At high temperatures, the effect is believed to be significant, but this doesn't mean it is significant in 2 body collisions.</p>
<p>Is it also significant at high energy collisions? I have seen arguments that localized 2-body collision cannot produce an instanton-like configuration (I don't remember the exact paper), but I am not sure if this conclusion is trustworthy.</p>
<p>What is the rate of B violation for parton collisions in the standard model? Is it always negligible?</p>
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<p>I am learning how to install water pipes and I was told that to check if a pipe is leaking water I need to check the water pressure. But I don't understanding how water pressure works inside the pipe.</p>
<p>For example, a water pump is connected to a valve and to a tap like this:</p>
<p>pump ----> valve ---->tap </p>
<p>the water pressure is caused by the pump. Now if I close the valve and blocking the water from the pump to the tap, what will be the water pressue in the segment of pipe between the valve and the tap? i.e.</p>
<p>pump ----> X ----> tap</p>
<p>My understanding is that the pressure should drop to zero as this segment is disconnected from any "source of water pressure" (the pump). But If I connect a meter to the tap before closing the valve:</p>
<p>pump ----> X ----> meter</p>
<p>The reading on the meter doesn't drop to zero. Instead, if there is a water pressure drop, it indicates a leakage. But what causes the pressure when the valve is closed?</p>
<p>I know air pressure inside a sealed system is caused by the Brownian motion of the air molecule does the same thing applies to water?</p>
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<p>What is the time dilation formula by constant velocity?</p>
<p>Is the right formula
$$t'=t\times \sqrt{1-v^2/c^2}$$ or is it
$$t'=\frac{t}{\sqrt{1-v^2/c^2}}$$ ?</p>
<p>And can someone show me a computational example regarding the time dilation formula?</p>
<p>Thank you in advance.</p>
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<p>If it is true that particles are in different potential locations until an observer comes along and collapses the wave function, then how can a blind man throw a ball and hit a wall if the particles are spread out?</p>
| 7,034 |
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<p>In softly broken SUSY, the bare mass parameters may be specified at e.g. the GUT scale, and then we can run these down to another scale using RGEs, similar in form to the RGEs for gauge couplings, with a 1-loop and 2-loop differential beta function. Once these parameters have been run to the desired scale, tree-level physical masses are computed via diagonalization of the mass matrices depending on how the mixings were determined. Next, additional accuracy is gained by working out the loop corrections to the physical masses with self-energy graphs. </p>
<p>I am confused by why the physical masses that you determine from diagonalizing the soft parameters are considered tree-level masses if they are determined from 2-loop RGEs. Could you have determined the physical masses at the high scale and computed the self-energy loop corrections there, and then renormalized the physical mass down to the lower scale?</p>
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<p>Why isn't Newtonian mechanics valid in Quantum world? Suppose you isolate an alpha particle and accelerate it in absolute vacuum. Why it doesn't follow the equation $F=ma$? If Newtonian mechanics is invalid in quantum world, what is the guarantee that Quantum mechanics is valid in macroscopic world?</p>
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<p>I have a question related to the interference (thought)experiment with water waves given in the book Feynman Lectures on Physics Vol.3. When only one hole (hole 1) is open the measured wave intensity at the second wall varies with the distance from the center. It is shown in the figure as $I_1$ which has a peak right at the point exactly opposite to the hole 1. Now my question is : Why is the wave intensity has the variation as given by $I_1$. Shouldn't it be constant. The hole 1 acts as a source with wave propagating in all directions from it. </p>
<p>Let this wave be given as real part of $e^{j(kx-\omega t)}$ where $x$ is the distance travelled by the wave along the direction of propagation. Then by this equation the intensity of the wave at any point on the second wall should be the same equal to 1.</p>
<p>Feynman assumes the wave be given as $h_1 e^{j\omega t}$ where $h_1$ is some complex number but does not mention what it is. I wonder how he got the intensity as $I_1$ when only hole 1 is open. Kindly request you to explain me in detail (possibly with a reference) as evidently I seem to miss something in wave propagation.</p>
<p><img src="http://i.stack.imgur.com/jlXIP.jpg" alt="enter image description here"></p>
<p><strong>Image Source :</strong> The Feynman Lectures on Physics Vol. 3.</p>
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<p>From most graph, when the tire doesn't slip, then the friction is zero, for example see the below image</p>
<p>Why there is no friction when there is no slip? As the car stand still on slope, there is no slip but still there is friction holding the car against gravity</p>
<p><img src="http://i.stack.imgur.com/mbyPe.jpg" alt="wheel slip"></p>
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] |
<p>How will an electric fields affect the formation of plasma sheaths?</p>
| 7,039 |
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<p>When taking the EH action, $$S_{EH} = \frac{1}{16\pi G}\int_M d^4x \sqrt{-g}R$$ and making a small variation in the metric while ignoring boundary terms, we obtain</p>
<p>$$\delta S_{EH} = \frac{1}{16\pi G}\int_M d^4x \sqrt{-g}\left(\frac{1}{2} g^{\mu \nu}R -R^{\mu \nu}\right)\delta g_{\mu \nu} $$.</p>
<p>When looking for solutions we demand $\delta S = 0$, and so we get the vacuum Einstein field equations, $$\frac{1}{2} g^{\mu \nu}R -R^{\mu \nu}=0$$ which the Schwarzschild metric satisfies. So far so good.</p>
<p>Now we want to add the GHY term to the action, $$S_{GHY} = \frac{1}{8\pi G}\int_{\partial M} d^3x \sqrt{-h}K$$ which will cancel out any boundary terms we neglected arbitrarily in the former variation. When varying the metric we obtain</p>
<p>$$\delta S_{EH+GBY} = \frac{1}{16\pi G}\int_M d^4x \sqrt{-g}(\frac{1}{2} g^{\mu \nu}R -R^{\mu \nu})\delta g_{\mu \nu}\\ + \frac{1}{8\pi G}\int_{\partial M} d^3x \sqrt{-h}\frac{1}{2}( h^{\mu \nu}K -K^{\mu \nu})\delta g_{\mu \nu}$$</p>
<p>This gives a new set of field equations. My problem is that it seems to me the Schwarzschild metric is no longer a solution: we know the first term vanishes identically since it satisfies the original Einstein equations, so in order for it to be an extremal point of the metric, the second term also has to vanish identically. i.e., the coefficient of $\delta g_{\mu \nu}$ must vanish:</p>
<p>$$\sqrt{-h}\frac{1}{2}( h^{\mu \nu}K -K^{\mu \nu}) = 0.$$</p>
<p>Multiplying the equality by $g_{\mu \nu}$ and removing non-zero constants, we get</p>
<p>$$K=0,$$</p>
<p>which doesn't hold for a surface of constant radius embedded in the Schwarzschild metric. Even if we take Gibbons' and Hawking's normalization by subtracting a boundary term for the extrinsic curvature of the boundary embedded in flat space, we would get</p>
<p>$$K = K_0,$$</p>
<p>which still doesn't hold for a surface of constant radius. </p>
<p>Can anyone please tell me where I've gone wrong?</p>
| 7,040 |
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<p>The Hamiltonian of the spin $S$ quantum Heisenberg model is
$$H = J\sum_{<i,j>}\mathbf{S}_{i}\cdot\mathbf{S}_{j}$$
I have read that when the spin quantum number $S\to\infty$, quantum fluctuation vanishes, and then the model is identical to the classical Heisenberg model where the spins are treated classically, not quantum mechanically.</p>
<p>But I can't understand it clearly. Is there any relationship to <a href="http://en.wikipedia.org/wiki/Correspondence_principle" rel="nofollow">Bohr's correspondence principle</a> ?</p>
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<p>Consider two entangled photons with two mutally conjugate circular polarization. What happens when one photon which is, say, left hand polarized gets destroyed. Will the other photon retains its right hand polarization or will it assume some random state? There is another possibility that it looses its circular polarization altogether. Nothing in the literature tells what happens post death. </p>
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<p>I am developing a sensor calibration capability that compares a telescope lunar observation to a physics-based radiometric model. I'd like to find some high quality lunar images to test our solution against a wide range of data. To be useful, I need several key pieces of metadata:</p>
<ul>
<li>Raw camera data or close to it</li>
<li>Spectral band </li>
<li>Exposure time</li>
<li>Observer location</li>
<li>Date and time of the collection</li>
</ul>
<p>My searches of open-source astronomy sites suggest that the focus of most astronomical observatories is deep space. So the question is, "Where should I look or who should I contact for this sort of data?"</p>
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<p>Consider a system which is in an equilibrium state. Now, a small perturbation causes it to start oscillating about the equilibrium state, but over time, the momentum with which it overshoots the equilibrium state keeps on increasing. This can be considered as an exact opposite of what can be expected of reaching a normal stable equilibrium state (frictional forces reducing excess momentum until equilibrium is reached).</p>
<p>What is such kind of an equilibrium state called? Is it still referred to as a stable equilibrium since we keep oscillating about the state?</p>
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<p>In the book 'Modern Particle Physics' byM. thomson the Higgs doublet is written as </p>
<p>$$\phi = \left(\begin{matrix} \phi^+ \\ \phi^0 \end{matrix}\right)=\phi = \left(\begin{matrix} \phi_1 +i\phi_2 \\ \phi_3+i\phi_4 \end{matrix}\right) $$</p>
<p>With the comment</p>
<blockquote>
<p>Because the Higgs mechanism is required to generate the masses of the electroweak gauge bosons, one of the scalar fields must be neutral, written as $\phi^0$, and the other must be charged such that $\phi^+$ and $(\phi^+)^*$ = $\phi^-$ give the longitudinal degrees of freedom of the $W^+$ and $W^-$.</p>
</blockquote>
<p>I don't understand why can we interpret these component is being charged? Ok by assuming that the degrees of freedom are being 'eaten' by the weak-bosons corresponding to $\phi_i$, $i\in \lbrace 1,2,3\rbrace$. Which, from the argument above, the first two should be eaten by the charged $W$'s and the last one by the neutral $Z$. However this seems to be somewhat ad hoc... </p>
<p>I don't see why the fact that their degree of freedom is transferred to the bosons is a longitudinal polarization implies that these components must be charged...</p>
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<p>I'm a high school physics student, and part of our project requires us to make an electromagnet. We have an iron core, and it will go inside a solenoid. The problem is, we don't know what the relative permeability constant of iron is so we can calculate the magnetic field with the iron. How can we get this constant?</p>
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<p>$\frac{d}{dt}$$\hat{H}$ = $\frac{i}{\hbar}$$[\hat{H},\hat{H}]$ +$\frac{\partial{\hat{H}}}{\partial{t}}$</p>
<p>That's as far as I've got. I do not know much about the Heisenberg equation or even what it represents. Could someone give me a beginners intro to it ?</p>
<p>I do have one idea : $\hat{H}$ = $i\hbar$$\frac{d}{dt}$</p>
<p>I've been told that if there is no time dependence then $\frac{\partial{\hat{H}}}{\partial{t}}$ in the Heisenberg equation goes to 0.</p>
<p>I am not sure if the Hamiltonian has no time dependence because of that derivative wrt to time in the above equation.</p>
<p>Secondly, even if I could prove $\frac{\partial{\hat{H}}}{\partial{t}}$ = 0 I have absolutely no idea whatsoever what $\frac{i}{\hbar}$$[\hat{H},\hat{H}]$ means. I have no clue how to evaluate it or what its significance is.</p>
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<p>Why is the critical point for the phase diagram of pure water degrees of freedom equal to 0? Maybe, you know what is the mathematical explanation for the fact that the number of degrees of freedom at the critical point is 0? What else is affected by the lack of degrees of freedom in addition to the Gibbs phase rule? </p>
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<p>I am studying the time evolution of a density matrix using the <a href="http://en.wikipedia.org/wiki/Lindblad_equation" rel="nofollow">Lindblad equation</a>.
My initial density matrix is $\rho(0)=|\alpha\rangle\langle\alpha|$, where $|\alpha\rangle$ is a coherent state. Then I have to compute $\mbox{Tr}\rho^2$.
Due to the easy numerical computation, I can do the same with the Stochastic Schrodinger equation using the Jump method. From the literature I understand that, in order to find the time evolution I have to take many different initial conditions !!!!</p>
<p>My question is about choosing $|\psi(0)\rangle=|\alpha\rangle$ as a wavefunction which corresponds to the initial density matrix. To make the average over different trajectory how can I take a different initial condition. I think that my initial wavefunction always should be $|\psi(0)\rangle=|\alpha\rangle$ since I take $\rho(0)=|\alpha\rangle\langle\alpha|$ !! Can anybody clarify my doubt ??
Could you also tell me about the evaluation of the density matrix at any instant from the stochastic wavefunction in order to compute $\mbox{Tr}\rho^2$.</p>
| 7,049 |
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] |
<p>How do we decide whether a quantum circuit can be realized physically or not ? I was wondering for physical realization of Shor's factoring algorithm using NMR ( I mean can we do it? ). </p>
| 7,050 |
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<p><strong>SUPERFLUIDITY:</strong></p>
<p>Superfluidity is one of the most amazing quantum phenomena, which we can sit and watch them happening before our eyes! Watch this video, it is only a couple of minutes long, which will bring you face-to-face with quantum mechanics in all its beauty. Then take a look at the questions below.</p>
<p><a href="http://www.youtube.com/watch?v=9FudzqfpLLs" rel="nofollow">http://www.youtube.com/watch?v=9FudzqfpLLs</a></p>
<p><strong>QUESTIONS:</strong></p>
<p>A superfluid has the amazing ability to climb up the walls of the glass container that it is in: <strong>Does it defy gravity?</strong></p>
<p>A superfluid can get out through the walls of the glass container: <strong>Quantum tunnelling in action before our eyes?</strong></p>
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] |
<p>Sometimes it happens that when you pour a boiling water into a glass jar, it cracks. Since glass is very hard material and resilient to pressure, the tension must be very high. Is it possible to estimate what forces / pressure / tension occur in such a moment?</p>
<p>Some supplementary questions:</p>
<ul>
<li>Is it true that a thin glass is less likely to crack than a thick glass?</li>
<li>What other factors can influence cracking? (Like surface scratches etc.)</li>
</ul>
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<p>Displacing something against the gravitational field, gains it potential energy. Moving something against the nature requires work. If the electric field of a negative source charge 'Q' points inward, then by definition, it would require some work to displace a negative test charge 'q' against 'Q'. According to the Coulomb's law, like charges repel and unlike attract. Two negative charges are like, and they are supposed to be repelling each other and no work is required to keep them apart. I think the electric field of a negative charge pointing inward is nothing more than a surmise. What does a theoretical physicist think?</p>
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<p>If a linear polarized single photon strikes a linear polarizer such that its polarization is at 45 degrees to the polarization axis of the polarizer, what happens?
There is a nearly 50% chance that the photon is transmitted, and assuming it is transmitted, it somehow rotates its polarization to match that of the polarizer axis. But the photon has energy defined by E=hv before and after it encounters the polarizer. So it cannot lose energy by projecting its amplitude onto the polarization axis, as per the normal explanation.
Also assuming the linear polarizer is a dichroic type, then I understand that this means the long molecules in the film have their long axis aligned perpendicular to the polarization axis - so how does the photon encounter the molecules. Is it absorbed and then re-emitted orthogonal to the molecular axis somehow?</p>
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<p>I've noticed a general phenomenon in compactifying on a circle where if you start with, say, an NS field, then the KK fields with an index along the circle will be in the R sector, and those without will of course remain in the NS sector. </p>
<p>I am wondering how to understand this phenomenon. What is the story for fermions? Their behavior under compactification is quite different, with the spinor bundle tending to split as a tensor product rather than as a direct sum.</p>
| 7,055 |
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<p>I am an app developer and I am trying to build a physics app to calculate distance based on the quantities the user gives. for example if the user gives initial speed, time and acceleration, using Newton's 2nd equation, my program can calculate distance. So for example if I have six basic formulas which are:-</p>
<p>$$s = \frac{d}{t}$$<br>
$$d = ut + \frac{at^2}{2}$$<br>
$$v^2 - u^2 = 2ad$$
$$s = \frac{u+v}{2}$$
$$a = \frac{v-u}{t}$$<br>
$$v = u + at$$</p>
<p>where:</p>
<p>$s$ = average speed</p>
<p>$d$ = distance</p>
<p>$u$ and $v$ are initial and final speed</p>
<p>$t$ = time</p>
<p>$a$ = acceleration</p>
<p>Out of these, are there a definite number of equations I can derive to calculate distance if some combinations of quantities are given or will it be way too many as I might have some more equations.</p>
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<p>When a car is traveling round a banked track as fast as possible, it has a tendency to slip up the slope.</p>
<p>Opposite in the case when the car travels slowly and has a tendency to slip down.</p>
<p>Can someone please give me an intuitive reason as to why this "tendency to slip up or down" occurs.</p>
| 7,057 |
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<p>Suppose we have a pseudo-Riemannian manifold (modeled by $\mathbb R^{p,q}$) with signature</p>
<p>$$(\underbrace{+,+,\cdots,+}_p,\underbrace{-,-,\cdots,-}_q)$$</p>
<p>Meaning we have $q$ spacelike dimensions and $p$ timelike dimensions. For a given observer in this manifold, we can define the position vector $\mathbf S$ of an object by</p>
<p>$$ \mathbf S = (\vec T,\vec X) $$</p>
<p>Composed of vectors $\vec X = (X_1,X_2,\cdots,X_q)$ (the spatial position vector of the object) and $\vec T = (T_1,T_2,\cdots,T_p)$ (the "temporal position" vector. Note $T = c\cdot t$).</p>
<p>Given this, we can define the Jacobian of $\vec X$ with respect to $\vec T$, matrix $\mathbf B$</p>
<p>$$ \mathbf J (\vec X) = \mathbf B =
\begin{bmatrix}
\frac {\partial X_1}{\partial T_1} & \frac {\partial X_1}{\partial T_2} & \cdots & \frac {\partial X_1}{\partial T_p} \\
\frac {\partial X_2}{\partial T_1} & \frac {\partial X_2}{\partial T_2} & \cdots & \frac {\partial X_2}{\partial T_p} \\
\vdots & \vdots & \ddots & \vdots \\
\frac {\partial X_q}{\partial T_1} & \frac {\partial X_q}{\partial T_2} & \cdots & \frac {\partial X_q}{\partial T_p} \\
\end{bmatrix} =
\begin{bmatrix}
\beta_{11} & \beta_{12} & \cdots & \beta_{1p} \\
\beta_{21} & \beta_{22} & \cdots & \beta_{2p} \\
\vdots & \vdots & \ddots & \vdots \\
\beta_{q1} & \beta_{q2} & \cdots & \beta_{qp} \\
\end{bmatrix}
\;\therefore\;d\vec X = \mathbf B\cdot d\vec T$$</p>
<p>Where $\beta = \frac{d(\lVert\vec X\lVert)}{dT} = \frac{d(\lVert\vec X\lVert)}{c\cdot dt} = \frac vc$. This matrix should then give a representation of the velocity of the object in all spatial dimensions with respect to all temporal dimensions, which must somehow be related to the velocity measured by the observer.</p>
<p>Knowing that vector $\vec X$ defines a path through the spatial dimensions, and vector $\vec T$ defines a path through the temporal dimensions (which are related by the equation stated above), we can take the lengths of those paths to be $s$ and $w$ respectively. If we define their gradients over vector $\vec T$, namely</p>
<p>$$
\nabla s = \left(\frac{\partial s}{\partial T_1},\frac{\partial s}{\partial T_2},\cdots,\frac{\partial s}{\partial T_p}\right)\\
\nabla w = \left(\frac{\partial w}{\partial T_1},\frac{\partial w}{\partial T_2},\cdots,\frac{\partial w}{\partial T_p}\right)
$$</p>
<p>We can say</p>
<p>$$
ds = \nabla s\cdot d\vec T\\
dw = \nabla w\cdot d\vec T
$$</p>
<p>Knowing that the scalar velocity measured by the observer, $\beta^*$, is simply defined by the derivative of the spatial distance moved ($ds$) with respect to time as measured by the observer's clock (which would correspond to $dw$), we can derive</p>
<p>$$ \beta^* = \frac{ds}{dw} $$</p>
<p>And therefore we can conclude the following</p>
<p>$$ ds = \beta^*\cdot dw \;\therefore\; \nabla s\cdot d\vec T =\beta^*\cdot(\nabla w\cdot d\vec T) \;\therefore\; \nabla (s-\beta^* w)\cdot d\vec T = 0 $$</p>
<p>Is there any way to relate this last expression with the matrix $\mathbf B$?</p>
<p>Much appreciated.</p>
| 7,058 |
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<p>I want to show that $\delta q$ is not an exact differential.</p>
<p>Starting from $dE = \delta q - pdV$ and because $E := E(V, T)$ is a state function, which allows to express the exact differential as
$$
dE = \left.\frac{\partial E}{\partial V}\right|_T dV +\left.\frac{\partial E}{\partial T}\right|_V dT,
$$
the two expressions can be set equal giving after rearrangement
$$
\delta q = \left[ \left.\frac{\partial E}{\partial V}\right|_T + p \right]dV + \left.\frac{\partial E}{\partial T}\right|_V dT
$$
and therefore also
$$
\delta q = \left[ \left.\frac{\partial E}{\partial V}\right|_T + p \right]dV + C_V dT.
$$</p>
<p>Now, by definition $\partial E/\partial T|_V = C_V$, and so
$$
\left.\frac{\partial C_V}{\partial V}\right|_T =\left[\frac{\partial}{\partial V}\left.\frac{\partial E}{\partial T}\right|_V\right]_T
$$
and because $E$ is a state function, the sequence of partial derivatives can be exchanged (according to Schwarz' theorem, while I don't understand how it works), allowing to write
$$
\left.\frac{\partial C_V}{\partial V}\right|_T =\left[\frac{\partial}{\partial T}\left.\frac{\partial E}{\partial V}\right|_T\right]_V. (*)
$$</p>
<p>Also, multiplying the above expression for $\delta q$ by $1/\partial V$ at constant $T$, I obtain
$$
\left.\frac{\delta q}{\partial V}\right|_T = \left[ \left.\frac{\partial E}{\partial V}\right|_T + p \right]\left.\frac{\partial V}{\partial V}\right|_T + C_V \left.\frac{\partial T}{\partial V}\right|_T
$$
where $\partial V/\partial V = 1$ and the second term on the right hand side equals $0$ because $\partial T = 0$ at constant temperature. Multiplying the remaining equation by $\partial / \partial T$ at constant $V$ gives
$$
\left[\frac{\partial}{\partial T}\left.\frac{\delta q}{\partial V}\right|_T\right]_V = \left[ \frac{\partial}{\partial T} \left(\left.\frac{\partial E}{\partial V}\right|_T + p \right)\right]_V.
$$</p>
<p>Now <em>assuming</em> $\delta q$ were exact, again the sequence of partial derivatives would not matter and I could write
$$
\left[\frac{\partial}{\partial V}\left.\frac{\delta q}{\partial T}\right|_V\right]_T = \left[ \frac{\partial}{\partial T} \left(\left.\frac{\partial E}{\partial V}\right|_T + p \right)\right]_V
$$
and by using $q=E$ since the "inner" differential on the left side is evaluated at constant volume,
$$
\left[\frac{\partial}{\partial V}\left.\frac{\partial E}{\partial T}\right|_V\right]_T = \left.\frac{\partial}{\partial V} C_V\right|_T = \left[ \frac{\partial}{\partial T} \left(\left.\frac{\partial E}{\partial V}\right|_T + p \right)\right]_V. (**)
$$
From this we find that $(*)$ and $(**)$ are different and thus the assumption must be wrong and therefore $\delta q$ is not an exact differential.</p>
<p>Does this make any sense?</p>
<hr>
<p>Exact wording from book:</p>
<blockquote>
<p>Starting with $dE = \delta q - pV$, show that</p>
<p>a) $\delta q = C_V dT + [P+(\partial E/\partial V)_T] dV$</p>
<p>b) $\left(\frac{\partial C_V}{\partial V}\right)_T = \left[\frac{\partial}{\partial T} \left(\frac{\partial E}{\partial V}\right)_T\right]_V$</p>
<p>c) $\delta q$ is not an exact differential.</p>
</blockquote>
<p>For c), the book states</p>
<blockquote>
<p>If $\delta q$ were an exact differential, then by solution to a), $(\partial C_V/\partial V)_T$ would have to be equal to $[\partial /\partial T(P+(\partial E/\partial V)_T)]_V$ but it is not according to solution of b), hence $\delta q$ is not exact.</p>
</blockquote>
| 7,059 |
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<p>Let's say I'm in a space station, hurtling towards our galaxy nearly close to the speed of light. From my reference frame, I see the galaxy coming towards my ship at the same speed.</p>
<p>I pass the Sun, and am affected by its gravity.</p>
<p>From Earth's point of view, the gravity of the sun deflected my spaceship's trajectory. From my point of view in the spaceship, the trajectory of the entire galaxy changed very rapidly.</p>
<p>From my reference frame, how did my space station cause an entire galaxy to change course?</p>
<p><sup><em>Originally had multiple questions, removed all but one</em></sup></p>
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<p>The ISS and other objects in orbit still experience small acceleration outside from the perfect line of orbit (of the system CM). For instance, two objects in the ISS that are let to be at rest will pass by each other twice as the station makes one orbit because the two items are in separate orbits, and all orbits pass over the same point because they are <a href="http://en.wikipedia.org/wiki/Great_circle">great circles</a> over the Earth.</p>
<p>My question is how would you actually quantify this? Regarding the ISS, the entire craft could rotate just so it is effectively tidally locked with the Earth. If you assume it does that, then you have one axis along which it is totally acceleration-less relative to the craft. Looking forward along that line, moving to the left or right would create an acceleration back to the line. Moving up or down would also create an acceleration toward the line since they would assume more elliptical orbits. But I'm really curious as to whether there would also be a acceleration parallel to the line of orbit, and I'm also really curious if it would be unstable or stable.</p>
<p>So if the line of orbit is x, down toward the Earth is the negative z, and right of the line of motion is y, then my intuition is that the system is stable on the y-axis, it is stable up-and-down for the z-axis, but movement up the z-axis would create acceleration in the negative x-axis.</p>
<p>One major consequence would be if you left a hammer just outisde the airlock, the stability of these fields would dictate whether it sticks around or leaves. Could we find a simple $(x,y,z)$ equation for the acceleration? I can't find anything that quite answers this, and I my attempts result in more questions than answers.</p>
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<p>I have prepared a paper that relies on work of Joe Rosen on symmetry (e.g. "Symmetry Rules: How Science and Nature Are Founded on Symmetry"). I am wondering about his influence. For example, when I once asked on Math.SE about status of Curie symmetry principle, the question was closed, being also repelled by physics.SE. So the topic seems to be perceived as unscientific.</p>
<p>Then I found the Rosen book and papers, where he put much effort on giving Curie principle scientific rigor. Yet, the book seems to be unknown. Rosen proofs that dirrectly correlate symmetry and entropy seem to be ignored (the proof is given in <a href="http://www.mdpi.com/1099-4300/7/4/308/pdf" rel="nofollow">The Symmetry Principle</a>).</p>
<p>But, the fact that Rosen's book is in Springer's Frontiers Collection seem to support his reputation? I have used Rosen's work in my paper and I am wondering e.g. if receiveing review only from Rosen-related group will not be too hermetic. I myself am a big fan of Rosen's work and of his determination on bringing symmetry-level reasoning to mainstream science (e.g. his first book on the topic was published in 1995).</p>
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] |
<p>Since the fine structure constant (denoted alpha) is a pure real number, it just occured to me to ask if it is a rational number or not.</p>
| 7,063 |
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<p>As far as my knowledge is concerned, a vector quantity should possess magnitude and direction & more over it should also obey the laws of vector addition.</p>
<p>As we all know that the vector sum of 3 newtons in the x direction and 4 newtons in the y direction will acting at a point will produce a resultant of 5 newtons. Where did the remaining 2 newtons go?</p>
<p>I mean we have applied a total of 7 newtons of force on a point sized particle but the output is only 5 newtons, so it appears as if a 2 newton force is disappearing here. In which other form does it reappear rather than the resultant? Or is it something like the remaining 2 newtons of force just vanishes and it doesn't appears in any other form?</p>
<p>Please correct me if I am going wrong on this issue.</p>
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<p>Imagine you have a stone that is being hit by focused sunlight from a magnifying glass. Later you will place the stone into water to heat it. What type of stone will transfer the most energy into the water and why? </p>
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<p>This is an assignment question for online AP physics. As if it isn't already tough. This question is killing me. I even asked my physics teacher from last year and my calculus teacher. It stumped them, too. I would show some kind of attempt at solving the question, but I've got nothing. I don't even understand how to begin solving this.</p>
<p>The question is: </p>
<blockquote>
<p>The space shuttle tracking system predicts the position of the shuttle orbiter with an accuracy that varies between 30 m and 100 m. Its orbital radius is slightly larger than the radius of the Earth (average orbit altitude is 340 km). What, approximately, is the ratio of the position error to the size of the shuttle’s orbit? The orbiter is approximately 37 m long and 17 high. ($R_{Earth} = 6378$ km)`</p>
</blockquote>
<p>Any help with this would be greatly appreciated!</p>
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] |
<p>If you have $N$ 1ohm resistors, how many distinct equivalent resistances can you create?
Assume that only parallel and series and mixture of them is allowed and no bridging between two parallel connections is allowed.</p>
| 7,067 |
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<p>The free particle solution in stationary state (with definite energy) to the Schrödinger equation is </p>
<p>$$\psi(x,t) =Ae^{i(kx-\omega t)} + Be^{-i(kx+\omega t)}$$</p>
<p>Since the energy is definite, and hence the momentum is definite, the uncertainty in position must be infinite. How is this reflected by the probability distribution function:</p>
<p>$$\Psi = |\psi(x,t)\psi^*(x,t)| $$</p>
<p>The book that I am using just look at the first term of the solution, and derive that the probability distribution function is $A^2$. However, I do not understand why we can do that?</p>
<p>Does it imply that if wave function is made up of n terms such that each individual term has a constant probability distribution function, the whole wave function also has a constant probability distribution function? If so, how can I prove it?</p>
<p>I know my question might be very vague but that is precisely the problem I am facing now, I don't even know how to ask about the things that I don't understand.</p>
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<p>The <a href="http://en.wikipedia.org/wiki/Uncertainty_principle" rel="nofollow">Uncertainty principle</a> says that "△x△p>h/2"; we cannot precisely obtain both position $x$ and momentum $p$ simultaneously.</p>
<p>Is this because the uncertainty is the natural characteristic or it is because we do not know additional values? (ex. like additional 11 dimensions in superstring theory.)</p>
| 7,069 |
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<p>I am confused by a simple fact about the $\beta^{-}$ decay of ${}^{60}{\rm Co}$ nucleus. According to <a href="http://en.wikipedia.org/wiki/Cobalt-60" rel="nofollow">Wikipedia</a>, the most likely decay branch is to an excited state of ${}^{60}{\rm Ni}$, see the diagram:</p>
<p><img src="http://i.stack.imgur.com/cvidr.png" alt="Decay scheme of Co-60"></p>
<p>But the energy indicated on the diagram (0.31 MeV) is less than the electron rest mass (0.511 MeV)! How is that possible?</p>
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<p>Studying on own quantum mechanics I came across:</p>
<blockquote>
<p><strong>Preceeding text:</strong>
A basic postulate of quantum mechanics tells us how to set up the operator corresponding to a given observable. Observables, $\Omega$, are represented by operators, $\hat\Omega$, built
from the following position and momentum operators</p>
</blockquote>
<p>$$\hat x=x\times \;,\qquad \hat p_x=\frac {\hbar}i\frac d{dx}.$$</p>
<p>How are they given? I think they are been postulated, but how?
Also related question is why the eigenvalue of the operator corresponding to an observable is the value of the observable?</p>
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] |
<p>In Hawking's paper, <a href="http://books.google.com/books?id=aKcJO8CZ1kIC&pg=PA112&lpg=PA112&dq=Breakdown%20of%20predictability%20in%20gravitational%20collapse&source=bl&ots=uFiQcMfhDF&sig=_7fLRLAEeDnL0AbEgyzERRA70iI&hl=en&sa=X&ei=HBxmUPDLDpDm8QS5l4HADw&ved=0CDwQ6AEwAw#v=onepage&q=Breakdown%20of%20predictability%20in%20gravitational%20collapse&f=false" rel="nofollow">"Breakdown of predictability in gravitational collapse"</a>, the crux of Hawking's argument is as follows:</p>
<blockquote>
<p>...,one can extend the principle to treatments in which the gravitational field is also quantized by means of Feynman sum over histories. In this one performs an integration (with an as yet undetermined measure) over all configurations of both matter and gravitational fields. The classical example of black-hole event horizons shows that in this integral one has to include metrics in which the interaction region (i.e. the region over which the action is evaluated) is bounded, not only by the initial and final surfaces, but by a hidden surface as well. Indeed, in any quantum gravitational situation there is a possibility of "virtual" black holes which arise from vacuum fluctuations and which appear out of nothing and disappear again. One therefore has to include in the sum over histories metrics containing transient holes, leading either to singularities or to other space-time regions about which one has no knowledge. One therefore has to introduce a hidden surface around each of these holes and apply the principle of ignorance to say that all field configurations on these hidden surfaces are equally probable provided they are compatible with conservation of mass, angular momentum, etc...</p>
</blockquote>
<p>The setup for the argument he provides is to define three Hilbert spaces, $H_1$, $H_2$, $H_3$ for the initial, "hidden", and final space which contains all the data for each respective surface. He the defines a tensor $S_{ABC}$ with indices that refer to each space, with states in the each Hilbert space defined as:</p>
<p>$$\xi_C \in H_1$$ $$\zeta_B \in H_2 $$ $$\chi_A \in H_3$$</p>
<p>such that:</p>
<p>$$\sum \sum \sum S_{ABC} \chi_A \zeta_B \xi_C$$</p>
<p>defines the amplitude to have the initial state, final state and the hidden state on the hidden surface. The arguments is given the initial state, one is unable to determine the final state but, </p>
<blockquote>
<p>only the element $\sum S_{ABC}\xi_C$ of the tensor product $H_1 \otimes H_2$.</p>
</blockquote>
<p>This is the heart of the information loss problem discussed recently by <a href="http://blogs.discovermagazine.com/cosmicvariance/2012/09/27/guest-post-joe-polchinski-on-black-holes-complementarity-and-firewalls/" rel="nofollow">Polchinksi</a>.</p>
<p>Here is where I have an issue. I see the vacuum as a type of black hole. So if one adds another hidden surface into the mix, it is essentially the same as mapping back to some vacuum state. The classical black hole might be distorting the path of particles from initial to final surface, but if I think of the initial and final surfaces as black hole surfaces as well, then it doesn't seem to be too much of a problem. </p>
<p>In the most radical sense, the particles become free particles as far as the rest of the universe is concerned, so there simply isn't any way for them to interact inside the hole and decohere, so whatever information the particle is carrying is perfectly preserved to be spit out again when infalling Hawking radiation "liberates" the information during the evaporation process (e.g. perfectly preserved information of the past can now be passed back to the universe as it is once again allowed to interact with infalling particles, quantum mechanics ensures that state of the outgoing Hawking radiation will be completely consistent). Essentially, I think Hawking's insertion of a interim surface appears to be capricious fiction.</p>
<p>I am curious as to what is wrong with this argument. </p>
<p>UPDATE: I thought a <a href="http://arxiv.org/abs/1401.5761" rel="nofollow">link to Hawking's new paper</a> is a worthwhile addendum. </p>
| 7,072 |
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<p>I have to to write an 4000 word research paper for my IB diploma in high school. It is called the extended essay. I was thinking about writing on the physics of breaking eggs. I came up with the idea that their might be some experiments I could do and find the best way to crack an egg. I'm having trouble finding sources. I think I need help with some directions I could take this topic as I find it very interesting. </p>
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<p>Consider throwing a stone at an object from rest, it travels at Vms-1. Now throw that stone whilst running at Ums-1. It seems in the latter scenario the total speed of stone is V + U. Now imagine Running at Ums-1, throwing a stone at Vms-1 whilst on a moving train with speed Wms-1 - total stone speed would be V+U+W. </p>
<p>Let's extrapolate this to the case where you have a stack of moving platforms, the bottom platform begins to accelerate, once reaching top speed, the platform on top begins to accelerate, and so on and so forth. In a vacuum could it be theoretically possible to reach near infinite projectile velocities using these cumulative platform velocities? </p>
<p><img src="http://i.stack.imgur.com/G5wtQ.jpg" alt="enter image description here"></p>
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] |
<p>In section 4.3 of Griffths' "Introduction to Quantum Mechanics", just below Figure 4.6, the sentence begins </p>
<blockquote>
<p><em>Let $\hbar \ell$ be the eigenvalue of $L_z$ at this top rung...</em> </p>
</blockquote>
<p>Why is this valid? In the previous pages, there is no derivation of this fact. It's not surprising that this eigenvalue has $\hbar$ in it, but I don't see why I should expect it to be an integer multiple of $\hbar$.</p>
| 7,075 |
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<p>I'm a bit confused about the equivalence principle in GR.</p>
<p>I'm quoting from <a href="http://en.wikipedia.org/wiki/Introduction_to_general_relativity" rel="nofollow">Wikipedia</a>:</p>
<blockquote>
<p>An observer in an accelerated reference frame must introduce what
physicists call fictitious forces to account for the acceleration
experienced by himself and objects around him. One example, the force
pressing the driver of an accelerating car into his or her seat, has
already been mentioned; another is the force you can feel pulling your
arms up and out if you attempt to spin around like a top. Einstein's
master insight was that the constant, familiar pull of the Earth's
gravitational field is fundamentally the same as these fictitious
forces</p>
</blockquote>
<p>Later it is written: </p>
<blockquote>
<p>The equivalence between gravitational and inertial effects does not
constitute a complete theory of gravity. When it comes to explaining
gravity near our own location on the Earth's surface, noting that our
reference frame is not in free fall, so that fictitious forces are to
be expected, provides a suitable explanation. But a freely falling
reference frame on one side of the Earth cannot explain why the people
on the opposite side of the Earth experience a gravitational pull in
the opposite direction</p>
</blockquote>
<p>Here are some things I hope I understand correctly:</p>
<ul>
<li>A particle in free fall is in an inertial frame of reference</li>
<li>Curvature of spacetime in only required in order to explain tidal forces, as long as you ignore tidal forces, you can explain gravity without curvature.</li>
<li>Gravity is a fictious force experienced in a non-inertial reference frame</li>
</ul>
<p>My Questions (2 very related questions)</p>
<ul>
<li>1) The statement that curvature of spacetime in only required to explain tidal forces seems weird to me.
In the case that there is no curvature of spacetime, what explains gravity?
I mean, if gravity is a "fictitious-force", what is the "real cause" of it?
(Again this question stems from the statement that curvature is only needed to explain tidal forces, and not all of gravity).</li>
</ul>
<p>Last example from Wikipedia:</p>
<blockquote>
<p>For gravitational fields, the absence or presence of tidal forces
determines whether or not the influence of gravity can be eliminated
by choosing a freely falling reference frame</p>
</blockquote>
<ul>
<li>2) If I'm in outer space and I'm freely falling towards earth, let's say I'm very small and I don't experience tidal forces, both me and earth are freely falling and thus in inertial reference frames, and yet I see the earth accelerating towards me, in my frame is it said that "gravity is eliminated"? just because I feel no tidal forces?</li>
</ul>
| 7,076 |
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<p>(I know whether I understand this or not doesn't matter much to my work & study but am just curious.)</p>
<p>I still can't differentiate in my head <a href="http://en.wikipedia.org/wiki/Kinetics_%28physics%29" rel="nofollow">kinetics</a> and <a href="http://en.wikipedia.org/wiki/Kinematics" rel="nofollow">kinematics</a> (similar thread is found but doesn't explicitly answer to my question yet <a href="http://physics.stackexchange.com/questions/1135/what-is-the-difference-between-kinematics-and-dynamics">What is the difference between "kinematics" and "dynamics"?</a>).</p>
<p>Some websites out there say (<a href="http://www.wisegeek.com/what-is-kinetics.htm" rel="nofollow">ex.</a>) explain that force is only considered in kinematics. Does this mean for example Newton-Euler method is in kinetics and Lagrangian is in kinematics?</p>
<p>I also prefer concrete examples in both category.</p>
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<blockquote>
<p>If I consider equations of motion derived from the pinciple of least action for an <em>explicilty time dependend</em> Lagrangian</p>
<p>$$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$</p>
<p>under what circumstances (i.e. which explicit functional $t$-dependence) is the force conservative?</p>
</blockquote>
<p>By force I understand here the term on the right hand side of the equation, if I shove everything to the right except the expression $mq''(t)$.</p>
<hr>
<p>As a sidenote, besides the technical answer I'd be interested here in some words about the physical motivations involved. I'm somewhat unhappy with a formal $\text{curl}[F]=0$ condition, since it seems to be to easy to fulfill (namely we have to consider closed circles only at single points in time, respecively). The physical motivation behind conservative forces is the conservation of energy on closed paths, where any parametrization $q(s)$ of curves can be considered. But practically, only loops tracked in finite time are physically realizable, i.e. we would move in a circle while t changes. </p>
<p>I guess as soon as one computes the r.h.s. for the equations of motion, one would also be able to define a more physical alternaltive to the above stated idea of conservative forces in this case. I.e. a ask-if-the-forces-integrate-to-zero-on-a-closed-loop functional for a rout between two points in time $t_1$ and $t_2$. This would be an integral where the momentarily force along the point in the path I'm taking would be taken into account. It wouldn't be path independend of course. (We could then even construct another optimization problem on its own, by asking for path with the smallest energy difference, which really would be a sensible question if friction is involved.)</p>
| 7,078 |
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<p>In a philosophically rather interesting experiment, <a href="http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys2294.html" rel="nofollow">Ma et al.</a> show that backward causality exists in quantum physics. An <a href="http://arstechnica.com/science/2012/04/decision-to-entangle-effects-results-of-measurements-taken-beforehand/" rel="nofollow"> Ars Technnica-article</a> gives a less technical account.</p>
<p>From Ars Technica:</p>
<blockquote>
<p>Delayed-choice entanglement swapping consists of the following steps.
(I use the same names for the fictional experimenters as in the paper
for convenience, but note that they represent acts of measurement, not
literal people.)</p>
<ul>
<li><p>Two independent sources (labeled I and II) produce pairs photons such that their polarization states are entangled. One photon from I
goes to Alice, while one photon from II is sent to Bob. The second
photon from each source goes to Victor. (I'm not sure why the third
party is named "Victor".)</p></li>
<li><p>Alice and Bob independently perform polarization measurements; no communication passes between them during the experiment—they set the
orientation of their polarization filters without knowing what the
other is doing.</p></li>
<li><p>At some time after Alice and Bob perform their measurements, Victor makes a choice (the "delayed choice" in the name). He either allows
his two photons from I and II to travel on without doing anything, or
he combines them so that their polarization states are entangled. A
final measurement determines the polarization state of those two
photons.</p></li>
</ul>
<p>The results of all four measurements are then compared. If Victor did
not entangle his two photons, the photons received by Alice and Bob
are uncorrelated with each other: the outcome of their measurements
are consistent with random chance. (This is the "entanglement
swapping" portion of the name.) If Victor entangled the photons, then
Alice and Bob's photons have correlated polarizations—even though they
were not part of the same system and never interacted.</p>
</blockquote>
<p>Now, this is rather interesting in itself. My interpretation is that the universe already "knows" whether Victor will entangle or not at the time of Alice's and Bob's measurements (since it controls Victor's random generator). This kind of avoids the paradox. </p>
<p>The real interesting question, however, is why they haven't designed the experiment in the following way:</p>
<p>Instead of letting Victor randomize whether to entangle, he should base his decision on the measurements of Alice and Bob: if they measured correlated polarizations, he should not entangle; if they measured uncorrelated polarizations, he should entangle. </p>
<p>Seemingly, this would force the universe to produce correlated polarizations for Alice and Bob, despite there being no entanglement-chain connecting them. (Because, clearly, it would be contradictory if they were uncorrelated, despite there being a chain connecting them.)</p>
<p>To me, this seems like a more interesting experiment/result. Any idea why they didn't do it this way? </p>
<p>Update to answer @Nathaniel's comment:
I don't think several measurements is necessary. Let's say that both Alice and Bob check for horizontal polarization: then if Victor decides to entangle, both Alice and Bob must get the same outcome (either fire, or don't fire). Obviously, it is not contradictory that they both get the same outcome even if there's no chain, but the experiment I'm suggesting would imply that they would <i>always</i> get the same outcome, despite there <i>never</i> being any chain. </p>
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<p>Summary: when the Moon is x degrees below the horizon, it interferes
with stargazing the same as astronomical twilight would. What is x (as a
function of the Moon's phase)? </p>
<p>We define civil, nautical, and astronomical twilight as when the sun
is 0-6, 6-12, and 12-18 degrees below the horizon respectively. This
corresponds roughly to what most people call twilight, the ability to
distinguish a horizon at sea, and the ability to see 6th magnitude
stars at the zenith. </p>
<p>However, even when below the horizon, the Moon shines brightly enough
to interfere with stargazing. What are the equivalent twilight angles
for the Moon? I realize that even the full Moon overhead isn't bright
enough for civil twilight, so my real interest is in astronomical
twilight. Of course, this will vary greatly with the Moon's phase, and
slightly with Moon's distance. </p>
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<p>People talk about orbital angular momentum (OAM) of photons. Is there some physical example that cannot be explained without assuming that photons have non-zero OAM? Does different photons have different values of OAM? If yes, then what determines the value of the value orbital angular momentum carried by individual photons?</p>
| 7,081 |
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<p>According to maxwell-ampere equation, the curl of magnetic field at that point equals the current density at that point + change of electric field at that point w.r.t. time. Now, the second factor i.e. change of electric field is also caused by some moving charge at some other point.</p>
<p>$$
\nabla \times \vec B = \mu \vec J + \epsilon \mu \frac {\partial \vec E}{\partial t}
$$</p>
<p>So is it correct to say that magnetic field are ultimately caused by currents ? ( and when the current isn't at the point where you calculated the current, you take the changing electric field factor due to that current) or can electric field be changed without reference to any charges and produce a magnetic field on its own.</p>
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<p>I'm looking for an intuitive sketch of how one shows the correspondence of string theory to a certain QFT. My best guess is that one calculates the scattering amplitudes in the string theory as a series in some parameter (string length?) and shows that the leading order term is equal to the scattering amplitudes in the corresponding QFT.</p>
<p>If this is the case then my hope is that someone can elaborate and perhaps point me to some references. If I'm off base then my hope is that I can get a sketch and not be bogged down in heavy math (at this stage). </p>
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<p>Let be the unitary evolution operator of a quantum system be $U(t)=\exp(itH)$ for $t >0$.</p>
<p>Then what is the meaning of the equation</p>
<p>$$\det\bigl(I-U(t)e^{itE}\bigr)=0$$</p>
<p>where $E$ is a real variable?</p>
| 7,084 |
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<p>I know this is a rather basic question, but how do you charge an object? Not a battery, an object. I'm guessing it involves static electricity, but I'm not sure. Some resources I've been reading talk about charging two objects with opposing voltages, and I am trying to figure out how you do it. I think you do it with DC current, but past that, I'm not sure.</p>
<p>Here is the paper I am talking about: <a href="http://www.avonhistory.org/school/gravitor.htm" rel="nofollow">http://www.avonhistory.org/school/gravitor.htm</a></p>
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] |
<p>I'm looking for a filter that lets through as many wavelengths as possible (from 200 to 5000 nm).</p>
<p>Is that even possible?</p>
| 7,086 |
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<p>I am reading the book <a href="http://books.google.com/books/about/Computer_Simulation_of_Liquids.html?id=O32VXB9e5P4C" rel="nofollow"><em>Computer Simulation of Liquids</em> by Allen and Tildesley</a> (<a href="http://rads.stackoverflow.com/amzn/click/0198556454" rel="nofollow">here</a> is another link). On page 80, the authors describe the leap-frog algorithm, which is used extensively in molecular dynamics (MD) simulations. The leap-frog algorithm is a modification to the basic Verlet algorithm. The authors state: </p>
<blockquote>
<p>Modifications to the basic Verlet scheme have been proposed to tackle [the deficiencies of the basic Verlet scheme]. One of these is a so-called half-step 'leap-frog' scheme. The origin of the name becomes apparent when we write the algorithm down:</p>
<p>$$\textbf{r}(t + \delta t) = \textbf{r}(t) + \textbf{v}(t + \frac{1}{2} \delta t) \delta t \; \; \; \; \textbf{(3.17a)}$$</p>
<p>$$\textbf{v}(t + \frac{1}{2} \delta t) = \textbf{v}(t - \frac{1}{2} \delta t) + \textbf{a}(t) \delta t \; \; \; \; \textbf{(3.17b)}$$</p>
<p>The stored quantities are the current positions $\textbf{r}(t)$ and accelerations $\textbf{a}(t)$ together with the mid-step velocities $\textbf{v}(t - \frac{1}{2} \delta t)$. The velocity equation <strong>(3.17b)</strong> is implemented first, and the velocities leap over the coordinates to give the next mid-step values $\textbf{v}(t + \frac{1}{2} \delta t)$. During this step, the current velocities may be calculated: </p>
<p>$$\textbf{v}(t) = \frac{1}{2} \left[ \textbf{v}(t + \frac{1}{2} \delta t) + \textbf{v}(t - \frac{1}{2} \delta t) \right] \; \; \; \; \textbf{(3.18)}$$</p>
<p>This is necessary so that the energy ($\mathcal{H} = \mathcal{K} + \mathcal{V}$) at time $t$ can be calculated, as well as any other quantities that require positions and velocities at the same instant. Following this, equation <strong>(3.17a)</strong> is used to propel the positions once more ahead of the velocities. After this, the new accelerations may be evaluated ready for the next step. This is illustrated in Fig. 3.2.</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/QQysm.gif" alt="Leap-frog"></p>
<p>I have pasted Fig. 3.2 above; panel (b), framed in red, refers to the leap-frog algorithm.</p>
<p>My question is, how is the acceleration computed in this algorithm?</p>
<p>In Fig. 3.2(b), it appears that the first step (which I have personally highlighted in yellow) is to somehow compute $\textbf{a}(t)$ from $\textbf{r}(t)$. However, I do not see an equation for this. Do you know what equation the step highlighted in yellow would be? Thanks.</p>
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<p>I was thinking about it some time ago, and now that I've discovered this site I would like to ask it here because I couldn't work it out then.</p>
<p>I know that the higher temperature the air in my room has, the more energy the molecules have. But temperature isn't energy because otherwise we'd be measuring temperature in joules, and we don't. And then temperature would depend on the number of molecules in the room, and that doesn't make any sense. So what I thought temperature had to be was the total energy that the molecules in the room have divided by something, for example the number of molecules or the volume of the room. If it was the latter, then temperature would be exactly like density, only with energy instead of mass. But in any case, I went to Wikipedia and tried to see if I could understand what they said about temperature. I didn't understand too much, but I saw that they used something called entropy to define temperature. I couldn't understand the article on entropy at all, but I think it means my thinking must have been incorrect because otherwise they would mention something simple like this in the article. Could you please explain it to me?</p>
<p>EDIT: Here's why I thought it should be the total energy divided by the volume rather than by the number of particles: because if we divided energy by a number, it would still be energy, and we measure energy in joules, not kelvins.</p>
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<p>Many believe that nothing can travel faster than speed of light, not even information. Personally, i think theoretically information can. Consider this following imaginary experiment:</p>
<p>Imagine we are living on a planet that is big enough for a, let's say, 10-light-seconds-tall tower to erect. We hang a pendulum near the planet's surface using a long thin wire at the top of the tower. If someone at top of the tower cut the wire then the pendulum will instantly falling to the ground. In this case we can say that the information "someone cuts the wire" travels 10-light-seconds distance in no time. </p>
<p>Since someone on the surface can only see the act of cutting the wire 10 seconds later, can we infer that the information travels faster than light?</p>
| 4 |
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<p>I'm sorry if the answer is obvious for you guys, but why don't we all (including buildings, road, people, the ground) collapse to the center of the earth because of gravity? Is it because we have velocity, just like the earth not falling to the sun (or electrons not falling to the protons)? But that analogy doesn't sound right because those involve wide empty space.</p>
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] |
<p>I have three questions to ask:</p>
<ol>
<li><p>Why do electrons (in an atom) specifically move in orbits and not some other type of motion?</p></li>
<li><p>Where does the energy comes from, for the electron to move at much higher speed, enough to create centrifugal force?</p></li>
<li><p>And when electrons enter an orbit, at which angle will it specifically enter?</p></li>
</ol>
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] |
<p>I couldn't find on web how can I get the velocity dispersion and velocity maps of galaxies from the 3D data cube I get from integral field spectrograph. </p>
| 7,091 |
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<p>I came across a problem in Griffiths where the derivative of the wave function (with respect to position in one dimension) evaluated at $\pm\infty$ is zero. Why is this? Is it true for any function that evaluates to zero at $\pm\infty$ or is there a special constraint on the wave function that I am forgetting?</p>
| 7,092 |
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<p>These three questions are phrased as alternative-history questions, but my real intent is to understand better how well different modeling approaches fit the phenomena they are used to describe; see <sup>1</sup> below for more discussion of that point.</p>
<p>Short "informed opinion" answers are fine (better, actually).</p>
<ol>
<li><p>If <a href="http://en.wikipedia.org/wiki/Mendeleev">Dmitri Mendeleev</a> had had access to and a full understanding of modern <a href="http://en.wikipedia.org/wiki/Group_theory">group theory</a>, could have plausibly structured the <a href="http://en.wikipedia.org/wiki/Periodic_table">periodic table</a> of chemistry in terms of group theory, as opposed to the simpler data-driven tabular format that he actually used?</p></li>
<li><p>If Mendeleev really had created a group-theory-based Periodic Table, would it have provided any specific insights, e.g. perhaps early insights into quantum theory?</p></li>
<li><p>The inverse question: If <a href="http://en.wikipedia.org/wiki/Gell-Mann">Murray Gell-Mann</a> and others had not used group theory concepts such as <a href="http://en.wikipedia.org/wiki/Special_unitary_group">$SU(3)$</a> to organize particles into families, and had instead relied on simple grouping and graphical organization methods more akin to those of Mendeleev, is there any significant chance they could have succeeded? Or less speculatively, is it possible to create useful, concise, and accurate organizational structures (presumably quark based) that fully explain the particle data of the 1970s without making <em>any</em> reference to algebraic structures?</p></li>
</ol>
<hr>
<p><sup>1</sup> Background: My perspective on the above questions is to understand the interplay between expressive power and noise in real theory structures. One way to explain that is to note that mathematical modeling of data sets has certain strong (and deep) similarities to the concept of data compression.</p>
<p>On the positive side, a good theory and a good compression both manage to express all of the known data by using only a much smaller number of formula (characters). On the negative side, even very good compressions can go a astray by adding "artifacts," that is, details that are not in the original data, and which therefore constitute a form of noise. Similarly, theories can also add "artifacts" or details not in the original data set.</p>
<p>The table-style periodic table and $SU(3)$ represent two extremes of representation style. The table format of the periodic table would seem to have low expressive power and low precision, whereas $SU(3)$ has high representational power and precision. The asymmetric and ultimately misleading emphasis on strangeness in the original <a href="http://en.wikipedia.org/wiki/Eightfold_Way_%28physics%29">Eight-Fold Way</a> is an explicit example of an artifact introduced by that higher power. We now know that strangeness is just a fragment -- the first "down quark" parallel -- of the <a href="http://en.wikipedia.org/wiki/Generation_%28particle_physics%29">three-generations issue</a>, and that strangeness showed up first only because it was more easily accessible by the particle accelerators of that time.</p>
<hr>
<p><strong>2012-06-30 - Update on final answers</strong></p>
<p>I have selected <a href="http://physics.stackexchange.com/users/1236/lubos-motl">Luboš Motl</a>'s <a href="http://physics.stackexchange.com/a/30234/7670">answer</a> as the most persuasive with respect to the questions I asked. If you look at the link he includes, you will see that he has looked into this issue in minute detail with regards to what kind of representation works best, and why. Since that issue of "what is the most apt form of representation" was at the heart of my question, his answer is impressive.</p>
<p>With that said, I would also recommend that anyone interested in how and to what degree group theory can be applied to interesting and unexpected complexity problems, even if only approximately, should also look closely at <a href="http://physics.stackexchange.com/users/2190/david-bar-moshe">David Bar Moshe</a>'s fascinating <a href="http://physics.stackexchange.com/a/30247/7670">answer about an entire conference</a> that looked at whether group theory could be meaningfully applied to the chemical elements. This excellent answer points out a rich and unexpected set of historical explorations of the question. If I could, I would also flag this as an answer from a different perspective.</p>
<p>Finally, <a href="http://physics.stackexchange.com/users/7924/arnold-neumaier">Arnold Neumaier</a>'s <a href="http://physics.stackexchange.com/a/30259/7670">answer</a> shows how a carefully defined subset of the problem can be tractable to group theoretic methods in away that is predictive -- which to me is the single most fundamental criterion for when a model crosses over from being "just data" into becoming true theory. And again, I would flag this one as an answer if I could.</p>
<p>Impressive insights all, and my thanks to all three of you for providing such interesting, unexpected, and deeply insightful answers!</p>
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<p>I am traveling on a train running at a speed of 100mph. If from the train I shoot a ball at a speed of 100mph in opposite direction then what would be the speed of the ball with respect to a person standing outside the train, <strike> given that I shoot the ball as soon as the person standing out comes in parallel to my position in the train.</strike></p>
| 7,094 |
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<p>I'm confused with the latest home lightning bulbs.</p>
<p>Understanding filament bulbs was easy. For example take 220V, 100W filament bulb:</p>
<p>Power = $V^2/R$ Filament gets heated and emits energy in the form of light & heat. Whose sum is 100J per second. I'm getting a light energy of little less than 100J per sec. Its very clear!</p>
<p>Now lets take latest CFL :</p>
<p><img src="http://7fff.com/wp-content/uploads/2008/09/cfl.jpg" alt="enter image description here"></p>
<p>How can it be equivalent to 6 filament bulbs in light and yet consume same amount of energy as a single bulb (or even less in some cases).</p>
<p>Isn't conservation of energy getting violated here?
Isn't More light implies, more light energy implies more electrical energy consumption?</p>
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<p>If we take a light switch to embody an entire category, we could take the light switch to be a set with two elements and the morphisms are all endofunctions. Let's say, for fun, that we define the endofunctor for the monad as: </p>
<blockquote>
<p>flip switch up $\rightarrow$ light turns on</p>
<p>flip switch down $\rightarrow$ light turns off</p>
<p>flip switch $\rightarrow$ light toggles</p>
<p>do nothing to switch $\rightarrow$ light does nothing</p>
</blockquote>
<p>This looks like the identity endofunctor. Now, this endofunctor, in my mind, is deeply fundamental as it is used to test a causal relation between things like the light and the light-switch. The monad is nothing but the identity monad and so, I think, the algebra is nothing but an identity element. (I already asked at mathematics stack). One normally looks at this kind of thing as passing a signal from one system to another and this then goes up to information theory. If you have read my post correctly, though, you will see that I am trying to lift that whole idea up to where we talk only about morphisms and causal structure as opposed to systems of state and the information that encode them. It was a let down to find that the algebra was this trivial for such an important bit of behaviour, one that every physicist working in a lab will use every day.</p>
<p>Can anyone take this thinking and get the first non-trivial algebra (it should be TINY!!!) and keep the spirit of "behaviours in a laboratory"? The co-algebra is also interesting.</p>
<p>If anyone is wondering where this is coming from, consider the fact that one can construct a TQFT entirely within FDHilb by replacing the usual category of cobordisms with the internal category of comonoids. Thus, the background becomes the internal category of classical structures. The category of internal comonoids is defined with axioms that look like the copying and deleting of information. If you read this post carefully you will see that I am abstracting this idea to replace the category of internal comonoids with just comonads. To me, this then looks like an operationalist view of a topological quantum field theory.</p>
| 7,096 |
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<p>If the graph isomorphism problem can't be solved in polynomial time, do spin-networks in loop quantum gravity violate the Church-Turing thesis? To determine whether or not two graphs are isomorphic (labelled in the case of spin networks, but this doesn't change anything essential) is conjectured to be unsolvable in polynomial time in the worst case scenario. It may or may not be solvable in polynomial time using quantum computers. To compute using spin-networks, we have to determine whether or not two components describe the same network when summing up over quantum states and computing bra-ket norms.</p>
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<p>So, in the calculation of $ D(t,r) = \left[ \phi(x) , \phi(y) \right] $, where $ t= x^0 - y^0,~ \vec{r} = \vec{x} - \vec{y} $ you need to calculate the following integral
$$
D(t,r) = \frac{1}{2\pi^2 r} \int\limits_0^\infty dp \frac{ p \sin(p r) \sin \left[(p^2 + m^2)^{1/2} t \right]} { (p^2 + m^2 )^{1/2}}
$$
For $m=0$, the integral is simple. We get
$$
D(t,r) = \frac{1}{4\pi r} \left[ \delta(t - r) - \delta(t + r) \right]
$$
I even know what the answer for $ m \neq 0 $. I have no idea how to calculate it though. Any help?</p>
| 7,098 |
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<p>Does the transmission medium affect the speed of a signal? For instance does light traveling through a fiber cable get a bit from A => B faster than copper can transmit a bit the over the same distance?</p>
| 7,099 |
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<p>I was doing this question about the energy released in a fusion reaction: </p>
<p><img src="http://i.stack.imgur.com/Cogxc.jpg" alt="enter image description here"></p>
<p>In the mark scheme it included the mass of the electrons (for part cii) on the left and just used the mass of protons for the H. Do the H in this case not contain electrons and if so why do we not include them in the calculation but do the once on the left??</p>
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<p>At university, I was shown the Schrodinger Equation, and how to solve it, including in the $1/r$ potential, modelling the hydrogen atom.</p>
<p>And it was then asserted that the differences between the eigenvalues of the operator were the permitted frequencies of emitted and absorbed photons.</p>
<p>This calculation agrees with experimentally measured spectral lines, but why would we expect it to be true, even if we accept that the electron moves according to the Schrodinger equation?</p>
<p>After all, there's no particular reason for an electron to be in an eigenstate.</p>
<p>What would make people think it was anything more than a (very suggestive) coincidence?</p>
| 7,101 |
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] |
<p>According to quantum mechanics each state has a specific shape. So, how does the electron get into that shape of the orbital?</p>
| 7,102 |
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] |
<p>A uncharged capacitor $C$ is connected to a battery with potential $V$. It becomes fully charged and has a charge $Q=CV$ stored on it. </p>
<p>Now the polarity of the battery is reversed. The capacitor will have the charge $Q$ still but with polarity reversed too.</p>
<p>My question is: <em>What is the work done by the the battery?</em></p>
<p>According to me, during 1st charging it will do a work of $QV$. The energy of the capacitor is also not changing, then what is the work done to change its polarity? </p>
| 7,103 |
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<p>Even though dust particles are neutral, they tend to be attracted to a charged surface. I am guessing this is due to charge induction. </p>
<p>Is there a way I can compute the attraction? how will it vary based on: </p>
<ul>
<li><p><strong>separation distance.</strong>
I think the distance will affect as inverse square law (1/r^2) [Coulomb's law]. But to calculate the force, I need to know how much charge has been induced ( how do I find that?) and does that vary due to separation distance.</p></li>
<li><p><strong>type of dust.</strong>
Do all material act the same , or are some material gets more charge induced? ( metals, for example with more free electrons)</p></li>
<li><p><strong>the size of dust particles.</strong>
Intuition suggests that bigger particles will be induced less, but I am not sure. </p></li>
</ul>
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] |
<p>Take the state vector for a single photon as </p>
<p>$\psi = \int \gamma_{\omega} | \omega \rangle \otimes (\alpha |H \rangle + \beta | V \rangle )d \omega$</p>
<p>$H, V, \omega$ are the horizontal polarization, vertical polarization and frequency components of the photon. We have a nice, big tensor product space of states for this photon. In particular, we have entangled single photon states! The entanglement of the single photon comes from entangling the polarization with its own frequency. Is it possible to use this effect to create decoherence free subspaces that would be useful in transmitting information within the polarization state of single photons?</p>
| 7,105 |
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<p>Are non-associative operators (or other kind of elements) used in Physics?</p>
<p>For example, in QM I'm looking for something like this: $A(BC)|\psi\rangle \ne (AB)C|\psi\rangle$</p>
<p>NOTE: I think that this question does not make much sense, in that case I will close it.</p>
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] |
<p>I'm trying to understand how people actually measure decay constants that are discussed in meson decays. As a concrete example lets consider the pion decay constant. The amplitude for $\pi ^-$ decay is given by,
\begin{equation}
\big\langle 0 | T \exp \big[ i \int \,d^4x {\cal H} \big] | \pi ^- ( p _\pi ) \big\rangle
\end{equation}
To lowest order this is given by,
\begin{equation}
i \int \,d^4x \left\langle 0 | T W _\mu J ^\mu | \pi ^- ( p _\pi ) \right\rangle
\end{equation}
If we square this quantity and integrate over phase space then we will get the decay rate.</p>
<p>On the other hand, the pion decay constant is defined through,
\begin{equation}
\left\langle 0 | J ^\mu | \pi ^- \right\rangle = - i f _\pi p _\pi ^\mu
\end{equation}
This is clearly related to the above, but it seems to me there are a couple of subtleties. In particular,</p>
<ol>
<li>How do we get rid of the time-ordering symbol?</li>
<li>Since we don't have a value for $ W _\mu $ how can we go ahead and
extract $f _\pi $ ?</li>
</ol>
| 7,107 |
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<p><img src="http://i.stack.imgur.com/vlpOb.jpg" alt="enter image description here"><img src="http://i.stack.imgur.com/SOeju.jpg" alt="enter image description here"></p>
<p>i'm solved this question, I'm sure that solution is right, but my instructor says that V1=116V, and also he said that he will not show how he get this result.Please help to identify who is right.</p>
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] |
<p><img src="http://i.stack.imgur.com/qlOgY.png" alt="this equatio was just randomly given without any description "></p>
<p>i would greatly appreciate it if someone could provide me with the concept to learn about this equation</p>
| 7,109 |
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<p>There have been a number of intriguing ideas over the years hinting at the possibility that a black hole might not have an inside, that it might consist of nothing but a surface and an external gravitational field.</p>
<p>Here are some of the ideas that lead me to ask the question, in no particular order:</p>
<ul>
<li><p>Black hole firewalls---of which Raphael Bousso says: "In some sense, space and time actually end there." <a href="http://worldsciencefestival.com/videos/the_black_hole_mystery_that_keeps_physicist_raphael_bousso_up_at_night" rel="nofollow">http://worldsciencefestival.com/videos/the_black_hole_mystery_that_keeps_physicist_raphael_bousso_up_at_night</a>"</p></li>
<li><p>According to the Cambridge astrophysicist, Professor Donald Lynden-Bell and Professor Emeritus, Joseph Katz, Racah Institute of Physics, in their paper <em>Gravitational field energy density for spheres and black holes</em>, the total <strong>coordinate-independent</strong> field energy distributed in the gravitational field of a Schwarzschild black hole is mc^2. They conclude, explicitly, that <strong>all</strong> the mass of the black hole resides outside the event horizon. <a href="http://adsabs.harvard.edu/full/1985MNRAS.213P..21L" rel="nofollow">http://adsabs.harvard.edu/full/1985MNRAS.213P..21L</a> </p></li>
<li><p>The radial component of the Schwarzschild metric shows that, due to metric stretching, the energy density of space thins out and disappears at the event horizon.</p></li>
<li><p>There is no ironclad rule that requires the spacetime manifold to continue past the event horizon.</p></li>
<li><p>There is no way to verify (or falsify) what we think goes on inside the event horizon.</p></li>
</ul>
<p>These ideas, individually and collectively, point to the possibility that its surface and its external field might be all there is to a black hole. What's particularly interesting to me is that this "surface only" picture is entirely consistent with them being cutouts, or holes, in the spacetime manifold.</p>
<p>Any thoughts would, of course, be most welcome.</p>
<p>Update: Here's a quote from a recent, six minute NPR interview with Leonard Susskind and Joesph Polchinski. Polchinski, speaking for his research group, says :"Our hypothesis is that the inside of a black hole — it may not be there. Probably that's the end of space itself. There's no inside at all."</p>
<p>Here's the link to the interview: <a href="http://www.npr.org/player/v2/mediaPlayer.html" rel="nofollow">http://www.npr.org/player/v2/mediaPlayer.html</a>? action=1&t=1&islist=false&id=256897343&m=257674048</p>
<p>And a short article quoting from the interview: <a href="http://www.npr.org/2013/12/27/256897343/stretch-or-splat-how-a-black-hole-kills-you-matters-a-lot" rel="nofollow">http://www.npr.org/2013/12/27/256897343/stretch-or-splat-how-a-black-hole-kills-you-matters-a-lot</a></p>
| 7,110 |
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<p>I have recently been reading <em>Intro to Lie algebras and representation theory</em> by Humphreys, and when I am finished I am interested in reading about Lie groups and Lie algebras and their applications to particle physics.</p>
<blockquote>
<p>Is there a book that assumes basic knowledge of Lie algebras, and no knowledge of lie groups and particle physics/quantum mechanics?</p>
</blockquote>
<p>I have seen Howard Georgi's book, but it assumes good knowledge of particle physics. </p>
<p>In addition, I do not know differential geometry.</p>
| 177 |
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<p>I am able to explicitly verify to one-loop order that pole masses are independent of the choice of gauge paramter.</p>
<p>But how do I use the Ward-Identity/Taylor-Slavnov identity show that the position of the poles in Greens functions are gauge-independent to all orders?</p>
<p>The difficulty I'm running into is in using the identities to make statements about the analytic structure of Green's functions.</p>
| 7,111 |
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<p>This is a common assumption in the study of quantum computation to assume that the quantum systems involved are finite-dimensional, since qubits lives in the two-dimensional Hilbert space. </p>
<p>According to <a href="http://arxiv.org/abs/0710.5239" rel="nofollow">Roman Gielerak and Marek Sawerwain</a>, the quantum registers corresponding to a quantum computing machine with coherent pulses of light must have an infinite-dimensional character. </p>
<p>I am looking for arguments for and against the hypothesis that finite-dimensional structures are sufficient to study quantum computation.</p>
| 7,112 |
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<p>A 2500.0kg car is going at a constant velocity of 14.0 m/s and hits the breaks to stop. It skids 25m. What is the coefficient of friction of the tires to the ground? </p>
<p>So I have acceleration = -4.0 m/s^2
Normal force = 24525 N</p>
<p>I got Fnet = -100,000 N</p>
<p>And I don't know what to do now because normally I take the difference of Fnet between the amount of force applied and the amount of force that worked. But then what should have happened was that the brakes were hit and the car immediately stops but then distance = 0 and I can't divide by 0. So I'm probably forgetting something...</p>
<p>Thanks</p>
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<p>How would I show the acceleration vector</p>
<p>$
a^\mu = u^\nu \bigtriangledown_\nu u^\mu = \bigtriangledown^\mu lnV
$</p>
<p>for an observer instantaneously 'at rest,' where $u^\mu = dx^\mu/d\tau$ and $V^2 = -\xi_\mu \xi^\mu$ ($\xi^\mu$ is timelike killing vector field). I guess we're assuming that we have a stationary spacetime metric.</p>
<p>I'm looking at Sean Carroll's Spacetime and Geometry, page 274 equation 6.15. They leave out the derivation for this. So V is the redshift factor.</p>
| 7,114 |
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<p>Does one exist, or do you think it would be possible to design a tracking magnetic field distortion detector to detect fast moving magnetic anomalies in our air space. ie; track a stealth aircraft or unidentified flying object at some distance by detecting the disturbance of the ambient magnetic fields?</p>
| 7,115 |
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<p>I'm doing a mobile/wireless networking subject and the physics aspect is giving me some trouble. I'm mainly confused about the conversion of dB, dBm and dBW and how to calculate the gain/loss from an input. </p>
<p>The problem I'm trying to solve is what the resulting power (in milliwatts) is at certain points in a circuit (x and y). I've tried to describe the scenario as best I can (let me know if I need to clear anything or post a picture)</p>
<p>In a circuit a 100mW input receives a 10 dB Gain and continues to point 'x' where it receives a 2 dB Loss. Then it receives another 2 dB Loss on the way to point 'y', where it receives another 2 db Loss.</p>
<p>To simplify it I guess it would look something like </p>
<p>100mW --> +10 dB --> -2 dB --> Point 'x' --> -2 dB --> -2 dB --> Point 'y'</p>
<p>Any help would be much appreciated, thanks in advance</p>
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<p>If photons are emitted at intervals a, from the top of a tower of height $h$, down to earth, is this formula correct for the intervals b in which they are received at earth? $b=a(1-gh/c^2)$
If so, how does it not lead to a paradox, if say we wait a long time N, then at the top of the tower, N/a photons have been emitted. But a photon is received at earth every b seconds, so N/b>N/a, so eventually more photons have been received then emitted?</p>
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<p>So I am studying CP violation in SM. Experimentalists are trying to study B meson decays now a days. B meson systems involve quarks from the third generation and hence B physics gives more information than the Kaon system. Is there any other reason?</p>
| 7,118 |
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] |
<p>Is it possible to write down a Lagrangian for a string theory with a critical dimension different than the familiar 10 or 26? How could one find a string theory Lagrangian for a given dimension? Could you prove that no string theory exists for a given critical dimension?</p>
| 7,119 |
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<p>Assume a very simplified model without Corolis effect, the falloff of the local gravitational field and the like. My answer is <em>no</em>. It is sufficient to look at the vertical velocity of the projectile, because only that determines the time. The periods do not equal, because it is possible to vertically accelerate the projectile to a velocity which is greater than the terminal velocity $v_{term.}$ of the projectile in the medium. Therfore it may take longer for the projectile to come back down because it can only approach $v_{term.}$. I am not sure, though, how it behaves if the initial velocity is lower than $v_{term.}$. My guts say it behaves the same but a different explanation comes into effect. The projectile cannot reach the height which it would if there was no drag. Hence, the projectile cannot reach the initial velocity on the way back to the ground either and it takes longer.</p>
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<p>My apologies in advance if this question is poorly worded or doesn't make any sense, however I have just finished reading into this theory and it seems as though Hawkings No Boundary Universe is basically emergent from a Universal Wave Function that is timeless. So no time took place before the big bang.</p>
<p>However to the question-</p>
<p>If the universal wavefunction is static how does a universe(or multiverse if you prefer) emerge at all? </p>
<p>If it is static wouldn't nothing ever change?</p>
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<p>I've been playing around with some <a href="http://en.wikipedia.org/wiki/Contactless_payment" rel="nofollow">contactless bank cards</a> and an <a href="https://github.com/nadam/nfc-reader" rel="nofollow">RFID reader app</a> on my phone. As expected, if I wrap the card in foil, the reader no longer detects it. But I was surprised to find that if I place a layer of foil on a flat surface, put the card on top of it and the phone on top of that, it also fails to detect the card. Why does placing a barrier behind the card prevent communication? </p>
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<p>Suppose we have some very imprecise knowledge of classical particle's coordinates and momentum: what we can only tell is the probability density to find it in some point of phase space. This is (almost?) all what is usually known by quantum state function.</p>
<p>For quantum particle, there's an equation, which governs such initial state — it's Schrödinger equation.</p>
<p>Is there any known equation, which would similarly govern evolution of classical particle in some external potential, given initial probability density in phase space?</p>
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<p>Pardon my ignorance but I just can seem to find an Answer to my question and I hope that you can help me.</p>
<p>What is the equation for calculating how long a Lithium Battery can supply a device?</p>
<p>For instance a Lithium battery has a capacity of 5600mAh, and an Output of 5V 2A. The drawing device requires 350mA and 5Vdc. </p>
<p>Is it as simple as dividing 350 into 5600 which would give me 16 hours of charge with optimal conditions? (This seems too easy.) or am I missing something?</p>
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<p>Stephen Wolfram's <em>A New Kind of Science</em> (NKS) hit the bookstores in 2002 with maximum hype.
His thesis is that the laws of physics can be generated by various cellular automata--simple programs producing complexity. Occasionally (meaning rarely) I look at the NKS blog and look for any new applications. I see nothing I consider meaningful. Is anyone aware of any advances in any physics theory resulting from NKS?
While CA are both interesting and fun (John Conway, Game of Life), as a theory of everything, I see problems. The generator rules are deterministic, and they are local in that each cell state depends on its immediate neighbors. So NKS is a local deterministic model of reality. Bell has shown that this cannot be. Can anyone conversant with CA comment?</p>
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<p>I have read Sean Carrol's book. I have listened to Roger Penrose talk on "Before the Big Bang". Both are offering to explain the mystery of low entropy, highly ordered state, at the Big Bang.
Since the second law of thermodynamics is considered a fundamental law of nature, and since it states that in a closed system entropy either must stay the same or increase, the entropy at the time of the Big Bang must have been much lower than it is now. Also, the thermodynamic arrow was explained by Boltzmann in 1896 embodied in $S=k\ln W$ which was inscribed on his tombstone. $W$ is the number of distinct microstates of the system. It seems to me that trivially this number will be less in the past than in the future since entropy obeys the 2nd law. This determines the thermodynamic arrow of time. Why do we need more explanation of a "fundamental law"?</p>
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